Finite Group Databasebeta

← C73×#59735 #32969139

Subgroups — C73×#59735 #32969139

Order 18688.

2378 conjugacy classes of subgroups.

The subgroup lattice has 1660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#559×C73C211yesmaximal, characteristic, complemented
2C2×#553×C73C211yesmaximal, characteristic, complemented
3C73×#2715C211yesmaximal, characteristic, complemented
4C73×#2708C211yesmaximal, characteristic, complemented
5C73×#2676C211yesmaximal, characteristic, complemented
6C73×#2673C211yesmaximal, characteristic, complemented
7C73×#2600C211yesmaximal, characteristic, complemented
8C73×#2600C211yesmaximal, characteristic, complemented
9C73×#2558C211yesmaximal, characteristic, complemented
10C73×#2557C211yesmaximal, characteristic, complemented
11C73×#2555C211yesmaximal, characteristic, complemented
12C73×#2555C211yesmaximal, characteristic, complemented
13C73×#2554C211yesmaximal, characteristic, complemented
14C73×#2521C211yesmaximal, characteristic, complemented
15C73×#2474C211yesmaximal, characteristic, complemented
16C73×#2469C211yesmaximal, characteristic, complemented
17C73×#2462C211yesmaximal, characteristic, complemented
18C73×#2461C211yesmaximal, characteristic, complemented
19C73×#2456C211yesmaximal, characteristic, complemented
20C73×#2456C211yesmaximal, characteristic, complemented
21C73×#2455C211yesmaximal, characteristic, complemented
22C73×#2443C211yesmaximal, characteristic, complemented
23C73×#2428C211yesmaximal, characteristic, complemented
24C73×#2425C211yesmaximal, characteristic, complemented
25C73×#2367C211yesmaximal, characteristic, complemented
26C73×#2364C211yesmaximal, characteristic, complemented
27C73×#2360C211yesmaximal, characteristic, complemented
28C73×#2359C211yesmaximal, characteristic, complemented
29C4×#123×C73C211yesmaximal, characteristic, complemented
30C4×#121×C73C211yesmaximal, characteristic, complemented
31C4×#121×C73C211yesmaximal, characteristic, complemented
32#559×C73—28no—
33#553×C73—28no—
34C2×#127×C73C2211yescharacteristic
35C2×#126×C73C2211yescharacteristic
36C2×#126×C73C2211yescharacteristic
37C2×#125×C73C2211yescharacteristic
38C2×#124×C73C2211yescharacteristic
39C2×#124×C73C2211yescharacteristic
40C2×#124×C73C2211yescharacteristic
41C2×#124×C73C2211yescharacteristic
42C2×#124×C73C2211yescharacteristic
43C2×#123×C73C2211yescharacteristic
44C2×#123×C73C2211yescharacteristic
45C2×#123×C73C2211yescharacteristic
46C2×#123×C73C2211yescharacteristic
47C2×#123×C73C2211yescharacteristic
48C2×#123×C73C2211yescharacteristic
49C2×#123×C73C2211yescharacteristic
50C2×C22⋊Q8×C73C2211yescharacteristic
51C2×#121×C73C2211yescharacteristic
52C2×#121×C73C2211yescharacteristic
53C2×#121×C73C2211yescharacteristic
54C2×#121×C73C2211yescharacteristic
55C2×#121×C73C2211yescharacteristic
56C2×#121×C73C2211yescharacteristic
57C2×#121×C73C2211yescharacteristic
58C2×#121×C73C2211yescharacteristic
59C2×C4×Q8×C73C2211yescharacteristic
60C2×C4×Q8×C73C2211yescharacteristic
61C2×C4×D4×C73C2211yescharacteristic
62C2×C4×D4×C73C2211yescharacteristic
63C2×C4×D4×C73C2211yescharacteristic
64C2×C4×D4×C73C2211yescharacteristic
65C2×C4×D4×C73C2211yescharacteristic
66C2×C4×D4×C73C2211yescharacteristic
67C2×C4×D4×C73C2211yescharacteristic
68C2×C4×D4×C73C2211yescharacteristic
69C2×C4×D4×C73C2211yescharacteristic
70C2×C4×D4×C73C2211yescharacteristic
71C2×C4×D4×C73C2211yescharacteristic
72C2×#117×C73C2211yescharacteristic
73C22×C4⋊C4×C73C2211yescharacteristic
74C22×C42×C73C2211yescharacteristic
75#400×C73C2211yescharacteristic
76#399×C73C2211yescharacteristic
77#398×C73C2211yescharacteristic
78#398×C73C2211yescharacteristic
79#397×C73C2211yescharacteristic
80#397×C73C2211yescharacteristic
81#397×C73C2211yescharacteristic
82#397×C73C2211yescharacteristic
83#396×C73C2211yescharacteristic
84#396×C73C2211yescharacteristic
85#396×C73C2211yescharacteristic
86#396×C73C2211yescharacteristic
87#395×C73C2211yescharacteristic
88#395×C73C2211yescharacteristic
89#395×C73C2211yescharacteristic
90#394×C73C2211yescharacteristic
91#394×C73C2211yescharacteristic
92#394×C73C2211yescharacteristic
93#394×C73C2211yescharacteristic
94#394×C73C2211yescharacteristic
95#394×C73C2211yescharacteristic
96#394×C73C2211yescharacteristic
97#394×C73C2211yescharacteristic
98#393×C73C2211yescharacteristic
99#392×C73C2211yescharacteristic
100#392×C73C2211yescharacteristic
101#392×C73C2211yescharacteristic
102#392×C73C2211yescharacteristic
103#392×C73C2211yescharacteristic
104#392×C73C2211yescharacteristic
105#392×C73C2211yescharacteristic
106#392×C73C2211yescharacteristic
107#391×C73C2211yescharacteristic
108#391×C73C2211yescharacteristic
109#390×C73C2211yescharacteristic
110#390×C73C2211yescharacteristic
111#390×C73C2211yescharacteristic
112#390×C73C2211yescharacteristic
113#390×C73C2211yescharacteristic
114#389×C73C2211yescharacteristic
115#389×C73C2211yescharacteristic
116#389×C73C2211yescharacteristic
117#389×C73C2211yescharacteristic
118#389×C73C2211yescharacteristic
119#388×C73C2211yescharacteristic
120#388×C73C2211yescharacteristic
121#388×C73C2211yescharacteristic
122#388×C73C2211yescharacteristic
123#388×C73C2211yescharacteristic
124#388×C73C2211yescharacteristic
125#388×C73C2211yescharacteristic
126#388×C73C2211yescharacteristic
127#388×C73C2211yescharacteristic
128#388×C73C2211yescharacteristic
129#388×C73C2211yescharacteristic
130#388×C73C2211yescharacteristic
131#388×C73C2211yescharacteristic
132#388×C73C2211yescharacteristic
133#388×C73C2211yescharacteristic
134#388×C73C2211yescharacteristic
135#388×C73C2211yescharacteristic
136#388×C73C2211yescharacteristic
137#387×C73C2211yescharacteristic
138#387×C73C2211yescharacteristic
139#387×C73C2211yescharacteristic
140#387×C73C2211yescharacteristic
141#387×C73C2211yescharacteristic
142#387×C73C2211yescharacteristic
143#387×C73C2211yescharacteristic
144#387×C73C2211yescharacteristic
145#387×C73C2211yescharacteristic
146#387×C73C2211yescharacteristic
147#386×C73C2211yescharacteristic
148#386×C73C2211yescharacteristic
149#386×C73C2211yescharacteristic
150#386×C73C2211yescharacteristic
151#386×C73C2211yescharacteristic
152#386×C73C2211yescharacteristic
153#386×C73C2211yescharacteristic
154#386×C73C2211yescharacteristic
155#386×C73C2211yescharacteristic
156#386×C73C2211yescharacteristic
157#386×C73C2211yescharacteristic
158#386×C73C2211yescharacteristic
159#386×C73C2211yescharacteristic
160#386×C73C2211yescharacteristic
161#386×C73C2211yescharacteristic
162#385×C73C2211yescharacteristic
163#385×C73C2211yescharacteristic
164#385×C73C2211yescharacteristic
165#385×C73C2211yescharacteristic
166#385×C73C2211yescharacteristic
167#385×C73C2211yescharacteristic
168#385×C73C2211yescharacteristic
169#385×C73C2211yescharacteristic
170#385×C73C2211yescharacteristic
171#381×C73C2211yescharacteristic
172#380×C73C2211yescharacteristic
173#380×C73C2211yescharacteristic
174C4×C4⋊C4×C73C2211yescharacteristic
175C4×C4⋊C4×C73C2211yescharacteristic
176C4×C4⋊C4×C73C2211yescharacteristic
177C4×C4⋊C4×C73C2211yescharacteristic
178C4×C4⋊C4×C73C2211yescharacteristic
179C4×C22⋊C4×C73C2211yescharacteristic
180C4×C22⋊C4×C73C2211yescharacteristic
181C4×C22⋊C4×C73C2211yescharacteristic
182C4×C22⋊C4×C73C2211yescharacteristic
183C4×C22⋊C4×C73C2211yescharacteristic
184C4×C22⋊C4×C73C2211yescharacteristic
185C4×C22⋊C4×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188C2×#95×C73C2211yescharacteristic
189C22×Q8×C73C2311yescharacteristic
190C22×Q8×C73C2311yescharacteristic
191C22×D4×C73C2311yescharacteristic
192C22×D4×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C22×D4×C73C2311yescharacteristic
196C22×D4×C73C2311yescharacteristic
197C22×D4×C73C2311yescharacteristic
198C22×D4×C73C2311yescharacteristic
199C22×D4×C73C2311yescharacteristic
200C22×D4×C73C2311yescharacteristic
201C22×D4×C73C2311yescharacteristic
202C22×D4×C73C2311yescharacteristic
203C22×D4×C73C2311yescharacteristic
204C22×D4×C73C2311yescharacteristic
205C22×D4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C23×C4×C73C2311yescharacteristic
208C23×C4×C73C2311yescharacteristic
209C23×C4×C73C2311yescharacteristic
210C23×C4×C73C2311yescharacteristic
211C23×C4×C73C2311yescharacteristic
212C23×C4×C73C2311yescharacteristic
213C23×C4×C73C2311yescharacteristic
214C23×C4×C73C2311yescharacteristic
215C23×C4×C73C2311yescharacteristic
216C23×C4×C73C2311yescharacteristic
217C23×C4×C73C2311yescharacteristic
218#127×C73—24no—
219#126×C73—24no—
220#126×C73—24no—
221#125×C73—24no—
222#124×C73—24no—
223#124×C73—24no—
224#124×C73—24no—
225#124×C73—24no—
226#124×C73—24no—
227#123×C73—24no—
228#123×C73—24no—
229#123×C73—24no—
230#123×C73—24no—
231#123×C73—24no—
232#123×C73—42no—
233#123×C73D418yescomplemented
234C22⋊Q8×C73—24no—
235#121×C73—24no—
236#121×C73—24no—
237#121×C73—24no—
238#121×C73—24no—
239#121×C73—24no—
240#121×C73—24no—
241#121×C73—24no—
242#121×C73—42no—
243C4×Q8×C73—24no—
244C4×Q8×C73—24no—
245C4×D4×C73—24no—
246C4×D4×C73—24no—
247C4×D4×C73—24no—
248C4×D4×C73—24no—
249C4×D4×C73—24no—
250C4×D4×C73—24no—
251C4×D4×C73—24no—
252C4×D4×C73—24no—
253C4×D4×C73—42no—
254C4×D4×C73—42no—
255C4×D4×C73—42no—
256#117×C73—24no—
257C2×C4⋊C4×C73—24no—
258C2×C4⋊C4×C73C2311yescharacteristic
259C2×C4⋊C4×C73C2311yescharacteristic
260C2×C4⋊C4×C73C2311yescharacteristic
261C2×C4⋊C4×C73C2311yescharacteristic
262C2×C4⋊C4×C73C2311yescharacteristic
263C2×C4⋊C4×C73C2311yescharacteristic
264C2×C4⋊C4×C73C2311yescharacteristic
265C2×C4⋊C4×C73C2311yescharacteristic
266C2×C4⋊C4×C73C2311yescharacteristic
267C2×C4⋊C4×C73C2311yescharacteristic
268C2×C4⋊C4×C73C2311yescharacteristic
269C2×C4⋊C4×C73C2311yescharacteristic
270C2×C4⋊C4×C73C2311yescharacteristic
271C2×C4⋊C4×C73C2311yescharacteristic
272C2×C4⋊C4×C73C2311yescharacteristic
273C2×C4⋊C4×C73C2311yescharacteristic
274C2×C4⋊C4×C73C2311yescharacteristic
275C2×C4⋊C4×C73C2311yescharacteristic
276C2×C4⋊C4×C73C2311yescharacteristic
277C2×C4⋊C4×C73C2311yescharacteristic
278C2×C4⋊C4×C73C2311yescharacteristic
279C2×C4⋊C4×C73C2311yescharacteristic
280C2×C4⋊C4×C73C2311yescharacteristic
281C2×C4⋊C4×C73C2311yescharacteristic
282C2×C4⋊C4×C73C2311yescharacteristic
283C2×C4⋊C4×C73C2311yescharacteristic
284C2×C4⋊C4×C73C2311yescharacteristic
285C2×C4⋊C4×C73C2311yescharacteristic
286C2×C4⋊C4×C73C2311yescharacteristic
287C2×C22⋊C4×C73C2311yescharacteristic
288C2×C22⋊C4×C73C2311yescharacteristic
289C2×C22⋊C4×C73C2311yescharacteristic
290C2×C22⋊C4×C73C2311yescharacteristic
291C2×C22⋊C4×C73C2311yescharacteristic
292C2×C22⋊C4×C73C2311yescharacteristic
293C2×C22⋊C4×C73C2311yescharacteristic
294C2×C22⋊C4×C73C2311yescharacteristic
295C2×C22⋊C4×C73C2311yescharacteristic
296C2×C22⋊C4×C73C2311yescharacteristic
297C2×C22⋊C4×C73C2311yescharacteristic
298C2×C22⋊C4×C73C2311yescharacteristic
299C2×C22⋊C4×C73C2311yescharacteristic
300C2×C22⋊C4×C73C2311yescharacteristic
301C2×C22⋊C4×C73C2311yescharacteristic
302C2×C22⋊C4×C73C2311yescharacteristic
303C2×C22⋊C4×C73C2311yescharacteristic
304C2×C22⋊C4×C73C2311yescharacteristic
305C2×C22⋊C4×C73C2311yescharacteristic
306C2×C22⋊C4×C73C2311yescharacteristic
307C2×C22⋊C4×C73C2311yescharacteristic
308C2×C22⋊C4×C73C2311yescharacteristic
309C2×C22⋊C4×C73C2311yescharacteristic
310C2×C22⋊C4×C73C2311yescharacteristic
311C2×C22⋊C4×C73C2311yescharacteristic
312C2×C22⋊C4×C73C2311yescharacteristic
313C2×C22⋊C4×C73C2311yescharacteristic
314C2×C22⋊C4×C73C2311yescharacteristic
315C2×C22⋊C4×C73C2311yescharacteristic
316C2×C22⋊C4×C73C2311yescharacteristic
317C2×C22⋊C4×C73C2311yescharacteristic
318C2×C22⋊C4×C73C2311yescharacteristic
319C2×C22⋊C4×C73C2311yescharacteristic
320C2×C22⋊C4×C73C2311yescharacteristic
321C2×C22⋊C4×C73C2311yescharacteristic
322C2×C22⋊C4×C73C2311yescharacteristic
323C2×C22⋊C4×C73C2311yescharacteristic
324C2×C22⋊C4×C73C2311yescharacteristic
325C2×C22⋊C4×C73C2311yescharacteristic
326C2×C22⋊C4×C73C2311yescharacteristic
327C2×C22⋊C4×C73C2311yescharacteristic
328C2×C22⋊C4×C73C2311yescharacteristic
329C2×C22⋊C4×C73C2311yescharacteristic
330C2×C22⋊C4×C73C2311yescharacteristic
331C2×C22⋊C4×C73C2311yescharacteristic
332C2×C22⋊C4×C73C2311yescharacteristic
333C2×C22⋊C4×C73C2311yescharacteristic
334C2×C22⋊C4×C73C2311yescharacteristic
335C2×C42×C73—42no—
336C2×C42×C73C2311yescharacteristic
337C2×C42×C73C2311yescharacteristic
338C2×C42×C73C2311yescharacteristic
339C2×C42×C73C2311yescharacteristic
340C2×C42×C73C2311yescharacteristic
341C2×C42×C73C2311yescharacteristic
342C2×C42×C73C2311yescharacteristic
343C2×C42×C73C2311yescharacteristic
344C2×C42×C73C2311yescharacteristic
345C2×C42×C73C2311yescharacteristic
346C2×C42×C73C2311yescharacteristic
347C2×C42×C73C2311yescharacteristic
348C2×C42×C73C2311yescharacteristic
349C2×C42×C73C2311yescharacteristic
350C2×C42×C73C2311yescharacteristic
351#95×C73C2311yescharacteristic
352#95×C73C2311yescharacteristic
353#95×C73C2311yescharacteristic
354#95×C73C2311yescharacteristic
355#95×C73C2311yescharacteristic
356#95×C73C2311yescharacteristic
357#95×C73C2311yescharacteristic
358#95×C73C2311yescharacteristic
359#95×C73C2311yescharacteristic
360#95×C73C2311yescharacteristic
361#95×C73C2311yescharacteristic
362#95×C73C2311yescharacteristic
363#95×C73C2311yescharacteristic
364#95×C73C2311yescharacteristic
365#95×C73C2311yescharacteristic
366#95×C73C2311yescharacteristic
367#95×C73C2311yescharacteristic
368#95×C73C2311yescharacteristic
369#95×C73C2311yescharacteristic
370#95×C73C2311yescharacteristic
371#95×C73C2311yescharacteristic
372#95×C73C2311yescharacteristic
373#95×C73C2311yescharacteristic
374#95×C73C2311yescharacteristic
375#95×C73C2311yescharacteristic
376#95×C73C2311yescharacteristic
377#95×C73C2311yescharacteristic
378#95×C73C2311yescharacteristic
379#95×C73C2311yescharacteristic
380#95×C73C2311yescharacteristic
381#95×C73C2311yescharacteristic
382#95×C73C2311yescharacteristic
383#95×C73C2311yescharacteristic
384#95×C73C2311yescharacteristic
385C24×C73C2411yescharacteristic
386C24×C73C2411yescharacteristic
387C24×C73C2411yescharacteristic
388C24×C73C2411yescharacteristic
389C24×C73C2411yescharacteristic
390C24×C73C2411yescharacteristic
391C2×Q8×C73—22no—
392C2×Q8×C73—22no—
393C2×Q8×C73—22no—
394C2×Q8×C73—22no—
395C2×Q8×C73—41no—
396C2×Q8×C73—41no—
397C2×D4×C73—22no—
398C2×D4×C73—22no—
399C2×D4×C73—22no—
400C2×D4×C73—22no—
401C2×D4×C73—22no—
402C2×D4×C73—22no—
403C2×D4×C73—22no—
404C2×D4×C73—22no—
405C2×D4×C73—22no—
406C2×D4×C73—22no—
407C2×D4×C73—22no—
408C2×D4×C73—22no—
409C2×D4×C73—22no—
410C2×D4×C73—22no—
411C2×D4×C73—22no—
412C2×D4×C73—22no—
413C2×D4×C73—22no—
414C2×D4×C73—22no—
415C2×D4×C73—22no—
416C2×D4×C73—22no—
417C2×D4×C73—22no—
418C2×D4×C73—22no—
419C2×D4×C73—41no—
420C2×D4×C73—41no—
421C2×D4×C73—41no—
422C2×D4×C73—41no—
423C2×D4×C73—41no—
424C2×D4×C73—41no—
425C2×D4×C73—41no—
426C2×D4×C73—41no—
427C2×D4×C73—41no—
428C2×D4×C73—41no—
429C2×D4×C73—41no—
430C2×D4×C73—41no—
431C2×D4×C73—41no—
432C2×D4×C73—41no—
433C2×D4×C73—41no—
434C2×D4×C73—41no—
435C2×D4×C73—41no—
436C2×D4×C73—41no—
437C2×D4×C73—41no—
438C2×D4×C73—41no—
439C2×D4×C73—41no—
440C2×D4×C73—41no—
441C2×D4×C73C2×D414yes—
442C22×C4×C73—22no—
443C22×C4×C73—22no—
444C22×C4×C73—22no—
445C22×C4×C73—22no—
446C22×C4×C73—22no—
447C22×C4×C73—22no—
448C22×C4×C73—22no—
449C22×C4×C73—22no—
450C22×C4×C73—22no—
451C22×C4×C73—22no—
452C22×C4×C73—22no—
453C22×C4×C73—22no—
454C22×C4×C73—22no—
455C22×C4×C73—22no—
456C22×C4×C73—41no—
457C22×C4×C73—41no—
458C22×C4×C73—41no—
459C22×C4×C73—41no—
460C22×C4×C73—41no—
461C22×C4×C73—41no—
462C22×C4×C73—41no—
463C22×C4×C73—41no—
464C22×C4×C73—41no—
465C22×C4×C73—41no—
466C22×C4×C73—41no—
467C22×C4×C73—41no—
468C22×C4×C73—41no—
469C22×C4×C73—41no—
470C22×C4×C73—41no—
471C22×C4×C73—41no—
472C22×C4×C73—41no—
473C22×C4×C73—41no—
474C22×C4×C73—41no—
475C22×C4×C73—41no—
476C22×C4×C73—41no—
477C22×C4×C73C2×D414yes—
478C22×C4×C73C2411yescharacteristic
479C22×C4×C73C2411yescharacteristic
480C22×C4×C73C2411yescharacteristic
481C22×C4×C73C2411yescharacteristic
482C22×C4×C73C2411yescharacteristic
483C22×C4×C73C2411yescharacteristic
484C22×C4×C73C2411yescharacteristic
485C22×C4×C73C2411yescharacteristic
486C22×C4×C73C2411yescharacteristic
487C22×C4×C73C2411yescharacteristic
488C22×C4×C73C2411yescharacteristic
489C22×C4×C73C2411yescharacteristic
490C22×C4×C73C2411yescharacteristic
491C22×C4×C73C2411yescharacteristic
492C22×C4×C73C2411yescharacteristic
493C22×C4×C73C2411yescharacteristic
494C22×C4×C73C2411yescharacteristic
495C22×C4×C73C2411yescharacteristic
496C22×C4×C73C2411yescharacteristic
497C22×C4×C73C2411yescharacteristic
498C22×C4×C73C2411yescharacteristic
499C22×C4×C73C2411yescharacteristic
500C22×C4×C73C2411yescharacteristic
501C22×C4×C73C2411yescharacteristic
502C22×C4×C73C2411yescharacteristic
503C4⋊C4×C73—22no—
504C4⋊C4×C73—22no—
505C4⋊C4×C73—22no—
506C4⋊C4×C73—22no—
507C4⋊C4×C73—22no—
508C4⋊C4×C73—22no—
509C4⋊C4×C73—22no—
510C4⋊C4×C73—22no—
511C4⋊C4×C73—22no—
512C4⋊C4×C73—22no—
513C4⋊C4×C73—22no—
514C4⋊C4×C73—22no—
515C4⋊C4×C73—22no—
516C4⋊C4×C73—22no—
517C4⋊C4×C73—22no—
518C4⋊C4×C73—22no—
519C4⋊C4×C73—22no—
520C4⋊C4×C73—22no—
521C4⋊C4×C73—22no—
522C4⋊C4×C73—41no—
523C4⋊C4×C73—41no—
524C4⋊C4×C73—41no—
525C4⋊C4×C73—41no—
526C4⋊C4×C73—41no—
527C4⋊C4×C73—41no—
528C4⋊C4×C73—41no—
529C4⋊C4×C73C2×D414yes—
530C4⋊C4×C73C2×D414yes—
531C4⋊C4×C73#4114yes—
532C22⋊C4×C73—22no—
533C22⋊C4×C73—22no—
534C22⋊C4×C73—22no—
535C22⋊C4×C73—22no—
536C22⋊C4×C73—22no—
537C22⋊C4×C73—22no—
538C22⋊C4×C73—22no—
539C22⋊C4×C73—22no—
540C22⋊C4×C73—22no—
541C22⋊C4×C73—22no—
542C22⋊C4×C73—22no—
543C22⋊C4×C73—22no—
544C22⋊C4×C73—22no—
545C22⋊C4×C73—22no—
546C22⋊C4×C73—22no—
547C22⋊C4×C73—22no—
548C22⋊C4×C73—22no—
549C22⋊C4×C73—22no—
550C22⋊C4×C73—22no—
551C22⋊C4×C73—22no—
552C22⋊C4×C73—22no—
553C22⋊C4×C73—22no—
554C22⋊C4×C73—22no—
555C22⋊C4×C73—22no—
556C22⋊C4×C73—22no—
557C22⋊C4×C73—22no—
558C22⋊C4×C73—22no—
559C22⋊C4×C73—22no—
560C22⋊C4×C73—22no—
561C22⋊C4×C73—22no—
562C22⋊C4×C73—22no—
563C22⋊C4×C73—41no—
564C22⋊C4×C73—41no—
565C22⋊C4×C73—41no—
566C22⋊C4×C73—41no—
567C22⋊C4×C73—41no—
568C22⋊C4×C73—41no—
569C22⋊C4×C73—41no—
570C22⋊C4×C73—41no—
571C22⋊C4×C73—41no—
572C22⋊C4×C73—41no—
573C22⋊C4×C73—41no—
574C22⋊C4×C73—41no—
575C22⋊C4×C73—41no—
576C22⋊C4×C73C2×D414yes—
577C22⋊C4×C73C2×D414yes—
578C22⋊C4×C73C2×D414yes—
579C22⋊C4×C73#4114yes—
580C42×C73—22no—
581C42×C73—22no—
582C42×C73—22no—
583C42×C73—22no—
584C42×C73—22no—
585C42×C73—22no—
586C42×C73—22no—
587C42×C73—22no—
588C42×C73—22no—
589C42×C73—22no—
590C42×C73—22no—
591C42×C73—41no—
592C42×C73—41no—
593C42×C73—41no—
594C42×C73—41no—
595C23×C73—21no—
596C23×C73—21no—
597C23×C73—21no—
598C23×C73—21no—
599C23×C73—21no—
600C23×C73—21no—
601C23×C73—21no—
602C23×C73—21no—
603C23×C73—21no—
604C23×C73—21no—
605C23×C73—21no—
606C23×C73—21no—
607C23×C73—21no—
608C23×C73—21no—
609C23×C73—21no—
610C23×C73—21no—
611C23×C73—21no—
612C23×C73—21no—
613C23×C73—21no—
614C23×C73—21no—
615C23×C73—21no—
616C23×C73—21no—
617C23×C73—21no—
618C23×C73—21no—
619C23×C73—21no—
620C23×C73—21no—
621C23×C73—21no—
622C23×C73—21no—
623C23×C73—21no—
624C23×C73—21no—
625C23×C73—21no—
626C23×C73—21no—
627C23×C73—21no—
628C23×C73—21no—
629C23×C73—21no—
630C23×C73—21no—
631C23×C73—21no—
632C23×C73—21no—
633C23×C73—21no—
634C23×C73C22×D412yes—
635C23×C73C22×D412yes—
636C23×C73C2×#4112yes—
637C23×C73C2511yescharacteristic
638Q8×C73—44no—
639Q8×C73—44no—
640D4×C73—44no—
641D4×C73—44no—
642D4×C73—44no—
643D4×C73—44no—
644D4×C73—44no—
645D4×C73—44no—
646D4×C73—44no—
647D4×C73—44no—
648D4×C73—44no—
649D4×C73—44no—
650D4×C73—44no—
651D4×C73—82no—
652D4×C73—82no—
653D4×C73—82no—
654D4×C73—82no—
655C2×C4×C73—21no—
656C2×C4×C73—21no—
657C2×C4×C73—21no—
658C2×C4×C73—21no—
659C2×C4×C73—21no—
660C2×C4×C73—21no—
661C2×C4×C73—21no—
662C2×C4×C73—21no—
663C2×C4×C73—21no—
664C2×C4×C73—21no—
665C2×C4×C73—21no—
666C2×C4×C73—21no—
667C2×C4×C73—21no—
668C2×C4×C73—21no—
669C2×C4×C73—21no—
670C2×C4×C73—21no—
671C2×C4×C73—21no—
672C2×C4×C73—21no—
673C2×C4×C73—21no—
674C2×C4×C73—21no—
675C2×C4×C73—21no—
676C2×C4×C73—21no—
677C2×C4×C73—21no—
678C2×C4×C73—21no—
679C2×C4×C73—21no—
680C2×C4×C73—21no—
681C2×C4×C73—21no—
682C2×C4×C73—21no—
683C2×C4×C73—21no—
684C2×C4×C73—21no—
685C2×C4×C73—21no—
686C2×C4×C73—21no—
687C2×C4×C73—21no—
688C2×C4×C73—21no—
689C2×C4×C73—21no—
690C2×C4×C73—21no—
691C2×C4×C73—21no—
692C2×C4×C73—21no—
693C2×C4×C73—21no—
694C2×C4×C73—21no—
695C2×C4×C73—21no—
696C2×C4×C73—21no—
697C2×C4×C73—21no—
698C2×C4×C73—21no—
699C2×C4×C73—21no—
700C2×C4×C73—21no—
701C2×C4×C73—21no—
702C2×C4×C73—21no—
703C2×C4×C73—21no—
704C2×C4×C73—21no—
705C2×C4×C73—21no—
706C2×C4×C73—21no—
707C2×C4×C73—21no—
708C2×C4×C73—21no—
709C2×C4×C73—21no—
710C2×C4×C73—21no—
711C2×C4×C73—21no—
712C2×C4×C73—21no—
713C2×C4×C73—21no—
714C2×C4×C73—21no—
715C2×C4×C73—21no—
716C2×C4×C73—21no—
717C2×C4×C73—21no—
718C2×C4×C73—21no—
719C2×C4×C73—44no—
720C2×C4×C73—44no—
721C2×C4×C73—44no—
722C2×C4×C73—44no—
723C2×C4×C73—44no—
724C2×C4×C73—82no—
725C2×C4×C73—82no—
726C2×C4×C73—82no—
727C2×C4×C73—82no—
728C2×C4×C73—82no—
729C2×C4×C73—82no—
730C2×C4×C73—82no—
731C2×C4×C73C22×D412yes—
732C2×C4×C73C22×D412yes—
733C2×C4×C73C22×D412yes—
734C2×C4×C73C22×D412yes—
735C2×C4×C73C22×D412yes—
736C2×C4×C73C2×#4112yes—
737C2×C4×C73C2×#4112yes—
738C2×C4×C73C2×#4112yes—
739C2×C4×C73C2×#4112yes—
740C2×C4×C73C2×#4112yes—
741C2×C4×C73H(5,𝔽2)12yes—
742C22×C73—22no—
743C22×C73—22no—
744C22×C73—22no—
745C22×C73—22no—
746C22×C73—22no—
747C22×C73—22no—
748C22×C73—22no—
749C22×C73—22no—
750C22×C73—22no—
751C22×C73—41no—
752C22×C73—41no—
753C22×C73—41no—
754C22×C73—41no—
755C22×C73—41no—
756C22×C73—41no—
757C22×C73—41no—
758C22×C73—41no—
759C22×C73—41no—
760C22×C73—41no—
761C22×C73—41no—
762C22×C73—41no—
763C22×C73—41no—
764C22×C73—41no—
765C22×C73—41no—
766C22×C73—41no—
767C22×C73—41no—
768C22×C73—41no—
769C22×C73—41no—
770C22×C73—41no—
771C22×C73—41no—
772C22×C73—41no—
773C22×C73—41no—
774C22×C73—41no—
775C22×C73—41no—
776C22×C73—41no—
777C22×C73—41no—
778C22×C73—41no—
779C22×C73—41no—
780C22×C73—41no—
781C22×C73—41no—
782C22×C73—41no—
783C22×C73—41no—
784C22×C73C23×D411yescharacteristic
785C22×C73C22×#4111yescharacteristic
786C22×C73C22×#4111yescharacteristic
787C22×C73C2×H(5,𝔽2)11yescharacteristic
788C22×C73#58511yescharacteristic
789C22×C73#58511yescharacteristic
790C22×C73#58511yescharacteristic
791C4×C73—22no—
792C4×C73—22no—
793C4×C73—22no—
794C4×C73—22no—
795C4×C73—22no—
796C4×C73—22no—
797C4×C73—22no—
798C4×C73—22no—
799C4×C73—22no—
800C4×C73—22no—
801C4×C73—22no—
802C4×C73—41no—
803C4×C73—41no—
804C4×C73—41no—
805C4×C73—41no—
806C4×C73—41no—
807C4×C73—41no—
808C4×C73—41no—
809C4×C73—41no—
810C4×C73—41no—
811C4×C73—41no—
812C4×C73—41no—
813C4×C73—41no—
814C4×C73—41no—
815C4×C73—41no—
816#59735C7311yesmaximal, characteristic, direct product factor, Sylow
817C2×C73—42no—
818C2×C73—42no—
819C2×C73—42no—
820C2×C73—81no—
821C2×C73—81no—
822C2×C73—81no—
823C2×C73D4×#4111yescharacteristic
824C2×C73D4×#4111yescharacteristic
825C2×C73#348011yescharacteristic
826C2×C73#349611yescharacteristic
827C2×C73#350611yescharacteristic
828C2×C73#351311yescharacteristic
829C2×C73#356611yescharacteristic
830C2×#559C2×C7311yescharacteristic, complemented
831C2×#553C2×C7311yescharacteristic, complemented
832#2715C2×C7311yescharacteristic, complemented
833#2708C2×C7311yescharacteristic, complemented
834#2676C2×C7311yescharacteristic, complemented
835#2673C2×C7311yescharacteristic, complemented
836#2600C2×C7311yescharacteristic, complemented
837#2600C2×C7311yescharacteristic, complemented
838#2558C2×C7311yescharacteristic, complemented
839#2557C2×C7311yescharacteristic, complemented
840#2555C2×C7311yescharacteristic, complemented
841#2555C2×C7311yescharacteristic, complemented
842#2554C2×C7311yescharacteristic, complemented
843#2521C2×C7311yescharacteristic, complemented
844#2474C2×C7311yescharacteristic, complemented
845#2469C2×C7311yescharacteristic, complemented
846#2462C2×C7311yescharacteristic, complemented
847#2461C2×C7311yescharacteristic, complemented
848#2456C2×C7311yescharacteristic, complemented
849#2456C2×C7311yescharacteristic, complemented
850#2455C2×C7311yescharacteristic, complemented
851#2443C2×C7311yescharacteristic, complemented
852#2428C2×C7311yescharacteristic, complemented
853#2425C2×C7311yescharacteristic, complemented
854#2367C2×C7311yescharacteristic, complemented
855#2364C2×C7311yescharacteristic, complemented
856#2360C2×C7311yescharacteristic, complemented
857#2359C2×C7311yescharacteristic, complemented
858C4×#123C2×C7311yescharacteristic, complemented
859C4×#121C2×C7311yescharacteristic, complemented
860C4×#121C2×C7311yescharacteristic, complemented
861C73#5973511yescharacteristic, direct product factor, Sylow
862#559—28no—
863#553—28no—
864C2×#127C22×C7311yescharacteristic
865C2×#126C22×C7311yescharacteristic
866C2×#126C22×C7311yescharacteristic
867C2×#125C22×C7311yescharacteristic
868C2×#124C22×C7311yescharacteristic
869C2×#124C22×C7311yescharacteristic
870C2×#124C22×C7311yescharacteristic
871C2×#124C22×C7311yescharacteristic
872C2×#124C22×C7311yescharacteristic
873C2×#123C22×C7311yescharacteristic
874C2×#123C22×C7311yescharacteristic
875C2×#123C22×C7311yescharacteristic
876C2×#123C22×C7311yescharacteristic
877C2×#123C22×C7311yescharacteristic
878C2×#123C22×C7311yescharacteristic
879C2×#123C22×C7311yescharacteristic
880C2×C22⋊Q8C22×C7311yescharacteristic
881C2×#121C22×C7311yescharacteristic
882C2×#121C22×C7311yescharacteristic
883C2×#121C22×C7311yescharacteristic
884C2×#121C22×C7311yescharacteristic
885C2×#121C22×C7311yescharacteristic
886C2×#121C22×C7311yescharacteristic
887C2×#121C22×C7311yescharacteristic
888C2×#121C22×C7311yescharacteristic
889C2×C4×Q8C22×C7311yescharacteristic
890C2×C4×Q8C22×C7311yescharacteristic
891C2×C4×D4C22×C7311yescharacteristic
892C2×C4×D4C22×C7311yescharacteristic
893C2×C4×D4C22×C7311yescharacteristic
894C2×C4×D4C22×C7311yescharacteristic
895C2×C4×D4C22×C7311yescharacteristic
896C2×C4×D4C22×C7311yescharacteristic
897C2×C4×D4C22×C7311yescharacteristic
898C2×C4×D4C22×C7311yescharacteristic
899C2×C4×D4C22×C7311yescharacteristic
900C2×C4×D4C22×C7311yescharacteristic
901C2×C4×D4C22×C7311yescharacteristic
902C2×#117C22×C7311yescharacteristic
903C22×C4⋊C4C22×C7311yescharacteristic
904C22×C42C22×C7311yescharacteristic
905#400C22×C7311yescharacteristic
906#399C22×C7311yescharacteristic
907#398C22×C7311yescharacteristic
908#398C22×C7311yescharacteristic
909#397C22×C7311yescharacteristic
910#397C22×C7311yescharacteristic
911#397C22×C7311yescharacteristic
912#397C22×C7311yescharacteristic
913#396C22×C7311yescharacteristic
914#396C22×C7311yescharacteristic
915#396C22×C7311yescharacteristic
916#396C22×C7311yescharacteristic
917#395C22×C7311yescharacteristic
918#395C22×C7311yescharacteristic
919#395C22×C7311yescharacteristic
920#394C22×C7311yescharacteristic
921#394C22×C7311yescharacteristic
922#394C22×C7311yescharacteristic
923#394C22×C7311yescharacteristic
924#394C22×C7311yescharacteristic
925#394C22×C7311yescharacteristic
926#394C22×C7311yescharacteristic
927#394C22×C7311yescharacteristic
928#393C22×C7311yescharacteristic
929#392C22×C7311yescharacteristic
930#392C22×C7311yescharacteristic
931#392C22×C7311yescharacteristic
932#392C22×C7311yescharacteristic
933#392C22×C7311yescharacteristic
934#392C22×C7311yescharacteristic
935#392C22×C7311yescharacteristic
936#392C22×C7311yescharacteristic
937#391C22×C7311yescharacteristic
938#391C22×C7311yescharacteristic
939#390C22×C7311yescharacteristic
940#390C22×C7311yescharacteristic
941#390C22×C7311yescharacteristic
942#390C22×C7311yescharacteristic
943#390C22×C7311yescharacteristic
944#389C22×C7311yescharacteristic
945#389C22×C7311yescharacteristic
946#389C22×C7311yescharacteristic
947#389C22×C7311yescharacteristic
948#389C22×C7311yescharacteristic
949#388C22×C7311yescharacteristic
950#388C22×C7311yescharacteristic
951#388C22×C7311yescharacteristic
952#388C22×C7311yescharacteristic
953#388C22×C7311yescharacteristic
954#388C22×C7311yescharacteristic
955#388C22×C7311yescharacteristic
956#388C22×C7311yescharacteristic
957#388C22×C7311yescharacteristic
958#388C22×C7311yescharacteristic
959#388C22×C7311yescharacteristic
960#388C22×C7311yescharacteristic
961#388C22×C7311yescharacteristic
962#388C22×C7311yescharacteristic
963#388C22×C7311yescharacteristic
964#388C22×C7311yescharacteristic
965#388C22×C7311yescharacteristic
966#388C22×C7311yescharacteristic
967#387C22×C7311yescharacteristic
968#387C22×C7311yescharacteristic
969#387C22×C7311yescharacteristic
970#387C22×C7311yescharacteristic
971#387C22×C7311yescharacteristic
972#387C22×C7311yescharacteristic
973#387C22×C7311yescharacteristic
974#387C22×C7311yescharacteristic
975#387C22×C7311yescharacteristic
976#387C22×C7311yescharacteristic
977#386C22×C7311yescharacteristic
978#386C22×C7311yescharacteristic
979#386C22×C7311yescharacteristic
980#386C22×C7311yescharacteristic
981#386C22×C7311yescharacteristic
982#386C22×C7311yescharacteristic
983#386C22×C7311yescharacteristic
984#386C22×C7311yescharacteristic
985#386C22×C7311yescharacteristic
986#386C22×C7311yescharacteristic
987#386C22×C7311yescharacteristic
988#386C22×C7311yescharacteristic
989#386C22×C7311yescharacteristic
990#386C22×C7311yescharacteristic
991#386C22×C7311yescharacteristic
992#385C22×C7311yescharacteristic
993#385C22×C7311yescharacteristic
994#385C22×C7311yescharacteristic
995#385C22×C7311yescharacteristic
996#385C22×C7311yescharacteristic
997#385C22×C7311yescharacteristic
998#385C22×C7311yescharacteristic
999#385C22×C7311yescharacteristic
1000#385C22×C7311yescharacteristic
1001#381C22×C7311yescharacteristic
1002#380C22×C7311yescharacteristic
1003#380C22×C7311yescharacteristic
1004C4×C4⋊C4C22×C7311yescharacteristic
1005C4×C4⋊C4C22×C7311yescharacteristic
1006C4×C4⋊C4C22×C7311yescharacteristic
1007C4×C4⋊C4C22×C7311yescharacteristic
1008C4×C4⋊C4C22×C7311yescharacteristic
1009C4×C22⋊C4C22×C7311yescharacteristic
1010C4×C22⋊C4C22×C7311yescharacteristic
1011C4×C22⋊C4C22×C7311yescharacteristic
1012C4×C22⋊C4C22×C7311yescharacteristic
1013C4×C22⋊C4C22×C7311yescharacteristic
1014C4×C22⋊C4C22×C7311yescharacteristic
1015C4×C22⋊C4C22×C7311yescharacteristic
1016C4×C22⋊C4C22×C7311yescharacteristic
1017C4×C22⋊C4C22×C7311yescharacteristic
1018C2×#95C22×C7311yescharacteristic
1019C22×Q8C23×C7311yescharacteristic
1020C22×Q8C23×C7311yescharacteristic
1021C22×D4C23×C7311yescharacteristic
1022C22×D4C23×C7311yescharacteristic
1023C22×D4C23×C7311yescharacteristic
1024C22×D4C23×C7311yescharacteristic
1025C22×D4C23×C7311yescharacteristic
1026C22×D4C23×C7311yescharacteristic
1027C22×D4C23×C7311yescharacteristic
1028C22×D4C23×C7311yescharacteristic
1029C22×D4C23×C7311yescharacteristic
1030C22×D4C23×C7311yescharacteristic
1031C22×D4C23×C7311yescharacteristic
1032C22×D4C23×C7311yescharacteristic
1033C22×D4C23×C7311yescharacteristic
1034C22×D4C23×C7311yescharacteristic
1035C22×D4C23×C7311yescharacteristic
1036C23×C4C23×C7311yescharacteristic
1037C23×C4C23×C7311yescharacteristic
1038C23×C4C23×C7311yescharacteristic
1039C23×C4C23×C7311yescharacteristic
1040C23×C4C23×C7311yescharacteristic
1041C23×C4C23×C7311yescharacteristic
1042C23×C4C23×C7311yescharacteristic
1043C23×C4C23×C7311yescharacteristic
1044C23×C4C23×C7311yescharacteristic
1045C23×C4C23×C7311yescharacteristic
1046C23×C4C23×C7311yescharacteristic
1047C23×C4C23×C7311yescharacteristic
1048#127—24no—
1049#126—24no—
1050#126—24no—
1051#125—24no—
1052#124—24no—
1053#124—24no—
1054#124—24no—
1055#124—24no—
1056#124—24no—
1057#123—24no—
1058#123—24no—
1059#123—24no—
1060#123—24no—
1061#123—24no—
1062#123—42no—
1063#123D4×C7318yescomplemented
1064C22⋊Q8—24no—
1065#121—24no—
1066#121—24no—
1067#121—24no—
1068#121—24no—
1069#121—24no—
1070#121—24no—
1071#121—24no—
1072#121—42no—
1073C4×Q8—24no—
1074C4×Q8—24no—
1075C4×D4—24no—
1076C4×D4—24no—
1077C4×D4—24no—
1078C4×D4—24no—
1079C4×D4—24no—
1080C4×D4—24no—
1081C4×D4—24no—
1082C4×D4—24no—
1083C4×D4—42no—
1084C4×D4—42no—
1085C4×D4—42no—
1086#117—24no—
1087C2×C4⋊C4—24no—
1088C2×C4⋊C4C23×C7311yescharacteristic
1089C2×C4⋊C4C23×C7311yescharacteristic
1090C2×C4⋊C4C23×C7311yescharacteristic
1091C2×C4⋊C4C23×C7311yescharacteristic
1092C2×C4⋊C4C23×C7311yescharacteristic
1093C2×C4⋊C4C23×C7311yescharacteristic
1094C2×C4⋊C4C23×C7311yescharacteristic
1095C2×C4⋊C4C23×C7311yescharacteristic
1096C2×C4⋊C4C23×C7311yescharacteristic
1097C2×C4⋊C4C23×C7311yescharacteristic
1098C2×C4⋊C4C23×C7311yescharacteristic
1099C2×C4⋊C4C23×C7311yescharacteristic
1100C2×C4⋊C4C23×C7311yescharacteristic
1101C2×C4⋊C4C23×C7311yescharacteristic
1102C2×C4⋊C4C23×C7311yescharacteristic
1103C2×C4⋊C4C23×C7311yescharacteristic
1104C2×C4⋊C4C23×C7311yescharacteristic
1105C2×C4⋊C4C23×C7311yescharacteristic
1106C2×C4⋊C4C23×C7311yescharacteristic
1107C2×C4⋊C4C23×C7311yescharacteristic
1108C2×C4⋊C4C23×C7311yescharacteristic
1109C2×C4⋊C4C23×C7311yescharacteristic
1110C2×C4⋊C4C23×C7311yescharacteristic
1111C2×C4⋊C4C23×C7311yescharacteristic
1112C2×C4⋊C4C23×C7311yescharacteristic
1113C2×C4⋊C4C23×C7311yescharacteristic
1114C2×C4⋊C4C23×C7311yescharacteristic
1115C2×C4⋊C4C23×C7311yescharacteristic
1116C2×C4⋊C4C23×C7311yescharacteristic
1117C2×C22⋊C4C23×C7311yescharacteristic
1118C2×C22⋊C4C23×C7311yescharacteristic
1119C2×C22⋊C4C23×C7311yescharacteristic
1120C2×C22⋊C4C23×C7311yescharacteristic
1121C2×C22⋊C4C23×C7311yescharacteristic
1122C2×C22⋊C4C23×C7311yescharacteristic
1123C2×C22⋊C4C23×C7311yescharacteristic
1124C2×C22⋊C4C23×C7311yescharacteristic
1125C2×C22⋊C4C23×C7311yescharacteristic
1126C2×C22⋊C4C23×C7311yescharacteristic
1127C2×C22⋊C4C23×C7311yescharacteristic
1128C2×C22⋊C4C23×C7311yescharacteristic
1129C2×C22⋊C4C23×C7311yescharacteristic
1130C2×C22⋊C4C23×C7311yescharacteristic
1131C2×C22⋊C4C23×C7311yescharacteristic
1132C2×C22⋊C4C23×C7311yescharacteristic
1133C2×C22⋊C4C23×C7311yescharacteristic
1134C2×C22⋊C4C23×C7311yescharacteristic
1135C2×C22⋊C4C23×C7311yescharacteristic
1136C2×C22⋊C4C23×C7311yescharacteristic
1137C2×C22⋊C4C23×C7311yescharacteristic
1138C2×C22⋊C4C23×C7311yescharacteristic
1139C2×C22⋊C4C23×C7311yescharacteristic
1140C2×C22⋊C4C23×C7311yescharacteristic
1141C2×C22⋊C4C23×C7311yescharacteristic
1142C2×C22⋊C4C23×C7311yescharacteristic
1143C2×C22⋊C4C23×C7311yescharacteristic
1144C2×C22⋊C4C23×C7311yescharacteristic
1145C2×C22⋊C4C23×C7311yescharacteristic
1146C2×C22⋊C4C23×C7311yescharacteristic
1147C2×C22⋊C4C23×C7311yescharacteristic
1148C2×C22⋊C4C23×C7311yescharacteristic
1149C2×C22⋊C4C23×C7311yescharacteristic
1150C2×C22⋊C4C23×C7311yescharacteristic
1151C2×C22⋊C4C23×C7311yescharacteristic
1152C2×C22⋊C4C23×C7311yescharacteristic
1153C2×C22⋊C4C23×C7311yescharacteristic
1154C2×C22⋊C4C23×C7311yescharacteristic
1155C2×C22⋊C4C23×C7311yescharacteristic
1156C2×C22⋊C4C23×C7311yescharacteristic
1157C2×C22⋊C4C23×C7311yescharacteristic
1158C2×C22⋊C4C23×C7311yescharacteristic
1159C2×C22⋊C4C23×C7311yescharacteristic
1160C2×C22⋊C4C23×C7311yescharacteristic
1161C2×C22⋊C4C23×C7311yescharacteristic
1162C2×C22⋊C4C23×C7311yescharacteristic
1163C2×C22⋊C4C23×C7311yescharacteristic
1164C2×C22⋊C4C23×C7311yescharacteristic
1165C2×C42—42no—
1166C2×C42C23×C7311yescharacteristic
1167C2×C42C23×C7311yescharacteristic
1168C2×C42C23×C7311yescharacteristic
1169C2×C42C23×C7311yescharacteristic
1170C2×C42C23×C7311yescharacteristic
1171C2×C42C23×C7311yescharacteristic
1172C2×C42C23×C7311yescharacteristic
1173C2×C42C23×C7311yescharacteristic
1174C2×C42C23×C7311yescharacteristic
1175C2×C42C23×C7311yescharacteristic
1176C2×C42C23×C7311yescharacteristic
1177C2×C42C23×C7311yescharacteristic
1178C2×C42C23×C7311yescharacteristic
1179C2×C42C23×C7311yescharacteristic
1180C2×C42C23×C7311yescharacteristic
1181#95C23×C7311yescharacteristic
1182#95C23×C7311yescharacteristic
1183#95C23×C7311yescharacteristic
1184#95C23×C7311yescharacteristic
1185#95C23×C7311yescharacteristic
1186#95C23×C7311yescharacteristic
1187#95C23×C7311yescharacteristic
1188#95C23×C7311yescharacteristic
1189#95C23×C7311yescharacteristic
1190#95C23×C7311yescharacteristic
1191#95C23×C7311yescharacteristic
1192#95C23×C7311yescharacteristic
1193#95C23×C7311yescharacteristic
1194#95C23×C7311yescharacteristic
1195#95C23×C7311yescharacteristic
1196#95C23×C7311yescharacteristic
1197#95C23×C7311yescharacteristic
1198#95C23×C7311yescharacteristic
1199#95C23×C7311yescharacteristic
1200#95C23×C7311yescharacteristic
1201#95C23×C7311yescharacteristic
1202#95C23×C7311yescharacteristic
1203#95C23×C7311yescharacteristic
1204#95C23×C7311yescharacteristic
1205#95C23×C7311yescharacteristic
1206#95C23×C7311yescharacteristic
1207#95C23×C7311yescharacteristic
1208#95C23×C7311yescharacteristic
1209#95C23×C7311yescharacteristic
1210#95C23×C7311yescharacteristic
1211#95C23×C7311yescharacteristic
1212#95C23×C7311yescharacteristic
1213#95C23×C7311yescharacteristic
1214#95C23×C7311yescharacteristic
1215C24C24×C7311yescharacteristic
1216C24C24×C7311yescharacteristic
1217C24C24×C7311yescharacteristic
1218C24C24×C7311yescharacteristic
1219C24C24×C7311yescharacteristic
1220C24C24×C7311yescharacteristic
1221C2×Q8—22no—
1222C2×Q8—22no—
1223C2×Q8—22no—
1224C2×Q8—22no—
1225C2×Q8—41no—
1226C2×Q8—41no—
1227C2×D4—22no—
1228C2×D4—22no—
1229C2×D4—22no—
1230C2×D4—22no—
1231C2×D4—22no—
1232C2×D4—22no—
1233C2×D4—22no—
1234C2×D4—22no—
1235C2×D4—22no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—22no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—22no—
1245C2×D4—22no—
1246C2×D4—22no—
1247C2×D4—22no—
1248C2×D4—22no—
1249C2×D4—41no—
1250C2×D4—41no—
1251C2×D4—41no—
1252C2×D4—41no—
1253C2×D4—41no—
1254C2×D4—41no—
1255C2×D4—41no—
1256C2×D4—41no—
1257C2×D4—41no—
1258C2×D4—41no—
1259C2×D4—41no—
1260C2×D4—41no—
1261C2×D4—41no—
1262C2×D4—41no—
1263C2×D4—41no—
1264C2×D4—41no—
1265C2×D4—41no—
1266C2×D4—41no—
1267C2×D4—41no—
1268C2×D4—41no—
1269C2×D4—41no—
1270C2×D4—41no—
1271C2×D4C2×D4×C7314yes—
1272C22×C4—22no—
1273C22×C4—22no—
1274C22×C4—22no—
1275C22×C4—22no—
1276C22×C4—22no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—22no—
1281C22×C4—22no—
1282C22×C4—22no—
1283C22×C4—22no—
1284C22×C4—22no—
1285C22×C4—22no—
1286C22×C4—41no—
1287C22×C4—41no—
1288C22×C4—41no—
1289C22×C4—41no—
1290C22×C4—41no—
1291C22×C4—41no—
1292C22×C4—41no—
1293C22×C4—41no—
1294C22×C4—41no—
1295C22×C4—41no—
1296C22×C4—41no—
1297C22×C4—41no—
1298C22×C4—41no—
1299C22×C4—41no—
1300C22×C4—41no—
1301C22×C4—41no—
1302C22×C4—41no—
1303C22×C4—41no—
1304C22×C4—41no—
1305C22×C4—41no—
1306C22×C4—41no—
1307C22×C4C2×D4×C7314yes—
1308C22×C4C24×C7311yescharacteristic
1309C22×C4C24×C7311yescharacteristic
1310C22×C4C24×C7311yescharacteristic
1311C22×C4C24×C7311yescharacteristic
1312C22×C4C24×C7311yescharacteristic
1313C22×C4C24×C7311yescharacteristic
1314C22×C4C24×C7311yescharacteristic
1315C22×C4C24×C7311yescharacteristic
1316C22×C4C24×C7311yescharacteristic
1317C22×C4C24×C7311yescharacteristic
1318C22×C4C24×C7311yescharacteristic
1319C22×C4C24×C7311yescharacteristic
1320C22×C4C24×C7311yescharacteristic
1321C22×C4C24×C7311yescharacteristic
1322C22×C4C24×C7311yescharacteristic
1323C22×C4C24×C7311yescharacteristic
1324C22×C4C24×C7311yescharacteristic
1325C22×C4C24×C7311yescharacteristic
1326C22×C4C24×C7311yescharacteristic
1327C22×C4C24×C7311yescharacteristic
1328C22×C4C24×C7311yescharacteristic
1329C22×C4C24×C7311yescharacteristic
1330C22×C4C24×C7311yescharacteristic
1331C22×C4C24×C7311yescharacteristic
1332C22×C4C24×C7311yescharacteristic
1333C4⋊C4—22no—
1334C4⋊C4—22no—
1335C4⋊C4—22no—
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—22no—
1343C4⋊C4—22no—
1344C4⋊C4—22no—
1345C4⋊C4—22no—
1346C4⋊C4—22no—
1347C4⋊C4—22no—
1348C4⋊C4—22no—
1349C4⋊C4—22no—
1350C4⋊C4—22no—
1351C4⋊C4—22no—
1352C4⋊C4—41no—
1353C4⋊C4—41no—
1354C4⋊C4—41no—
1355C4⋊C4—41no—
1356C4⋊C4—41no—
1357C4⋊C4—41no—
1358C4⋊C4—41no—
1359C4⋊C4C2×D4×C7314yes—
1360C4⋊C4C2×D4×C7314yes—
1361C4⋊C4#41×C7314yes—
1362C22⋊C4—22no—
1363C22⋊C4—22no—
1364C22⋊C4—22no—
1365C22⋊C4—22no—
1366C22⋊C4—22no—
1367C22⋊C4—22no—
1368C22⋊C4—22no—
1369C22⋊C4—22no—
1370C22⋊C4—22no—
1371C22⋊C4—22no—
1372C22⋊C4—22no—
1373C22⋊C4—22no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—22no—
1382C22⋊C4—22no—
1383C22⋊C4—22no—
1384C22⋊C4—22no—
1385C22⋊C4—22no—
1386C22⋊C4—22no—
1387C22⋊C4—22no—
1388C22⋊C4—22no—
1389C22⋊C4—22no—
1390C22⋊C4—22no—
1391C22⋊C4—22no—
1392C22⋊C4—22no—
1393C22⋊C4—41no—
1394C22⋊C4—41no—
1395C22⋊C4—41no—
1396C22⋊C4—41no—
1397C22⋊C4—41no—
1398C22⋊C4—41no—
1399C22⋊C4—41no—
1400C22⋊C4—41no—
1401C22⋊C4—41no—
1402C22⋊C4—41no—
1403C22⋊C4—41no—
1404C22⋊C4—41no—
1405C22⋊C4—41no—
1406C22⋊C4C2×D4×C7314yes—
1407C22⋊C4C2×D4×C7314yes—
1408C22⋊C4C2×D4×C7314yes—
1409C22⋊C4#41×C7314yes—
1410C42—22no—
1411C42—22no—
1412C42—22no—
1413C42—22no—
1414C42—22no—
1415C42—22no—
1416C42—22no—
1417C42—22no—
1418C42—22no—
1419C42—22no—
1420C42—22no—
1421C42—41no—
1422C42—41no—
1423C42—41no—
1424C42—41no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—21no—
1454C23—21no—
1455C23—21no—
1456C23—21no—
1457C23—21no—
1458C23—21no—
1459C23—21no—
1460C23—21no—
1461C23—21no—
1462C23—21no—
1463C23—21no—
1464C23C22×D4×C7312yes—
1465C23C22×D4×C7312yes—
1466C23C2×#41×C7312yes—
1467C23C25×C7311yescharacteristic
1468Q8—44no—
1469Q8—44no—
1470D4—44no—
1471D4—44no—
1472D4—44no—
1473D4—44no—
1474D4—44no—
1475D4—44no—
1476D4—44no—
1477D4—44no—
1478D4—44no—
1479D4—44no—
1480D4—44no—
1481D4—82no—
1482D4—82no—
1483D4—82no—
1484D4—82no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—21no—
1534C2×C4—21no—
1535C2×C4—21no—
1536C2×C4—21no—
1537C2×C4—21no—
1538C2×C4—21no—
1539C2×C4—21no—
1540C2×C4—21no—
1541C2×C4—21no—
1542C2×C4—21no—
1543C2×C4—21no—
1544C2×C4—21no—
1545C2×C4—21no—
1546C2×C4—21no—
1547C2×C4—21no—
1548C2×C4—21no—
1549C2×C4—44no—
1550C2×C4—44no—
1551C2×C4—44no—
1552C2×C4—44no—
1553C2×C4—44no—
1554C2×C4—82no—
1555C2×C4—82no—
1556C2×C4—82no—
1557C2×C4—82no—
1558C2×C4—82no—
1559C2×C4—82no—
1560C2×C4—82no—
1561C2×C4C22×D4×C7312yes—
1562C2×C4C22×D4×C7312yes—
1563C2×C4C22×D4×C7312yes—
1564C2×C4C22×D4×C7312yes—
1565C2×C4C22×D4×C7312yes—
1566C2×C4C2×#41×C7312yes—
1567C2×C4C2×#41×C7312yes—
1568C2×C4C2×#41×C7312yes—
1569C2×C4C2×#41×C7312yes—
1570C2×C4C2×#41×C7312yes—
1571C2×C4H(5,𝔽2)×C7312yes—
1572C22—22no—
1573C22—22no—
1574C22—22no—
1575C22—22no—
1576C22—22no—
1577C22—22no—
1578C22—22no—
1579C22—22no—
1580C22—22no—
1581C22—41no—
1582C22—41no—
1583C22—41no—
1584C22—41no—
1585C22—41no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22C23×D4×C7311yescharacteristic
1615C22C22×#41×C7311yescharacteristic
1616C22C22×#41×C7311yescharacteristic
1617C22C2×H(5,𝔽2)×C7311yescharacteristic
1618C22#585×C7311yescharacteristic
1619C22#585×C7311yescharacteristic
1620C22#585×C7311yescharacteristic
1621C4—22no—
1622C4—22no—
1623C4—22no—
1624C4—22no—
1625C4—22no—
1626C4—22no—
1627C4—22no—
1628C4—22no—
1629C4—22no—
1630C4—22no—
1631C4—22no—
1632C4—41no—
1633C4—41no—
1634C4—41no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C2—42no—
1647C2—42no—
1648C2—42no—
1649C2—81no—
1650C2—81no—
1651C2—81no—
1652C2D4×#41×C7311yescharacteristic
1653C2D4×#41×C7311yescharacteristic
1654C2C73×#348011yescharacteristic
1655C2C73×#349611yescharacteristic
1656C2C73×#350611yescharacteristic
1657C2C73×#351311yescharacteristic
1658C2C73×#356611yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#559×C73C2semidirect
2. C2×#553×C73C2semidirect
3. C73×#2715C2semidirect
4. C73×#2708C2semidirect
5. C73×#2676C2semidirect
6. C73×#2673C2semidirect
7. C73×#2600C2semidirect
8. C73×#2600C2semidirect
9. C73×#2558C2semidirect
10. C73×#2557C2semidirect
11. C73×#2555C2semidirect
12. C73×#2555C2semidirect
13. C73×#2554C2semidirect
14. C73×#2521C2semidirect
15. C73×#2474C2semidirect
16. C73×#2469C2semidirect
17. C73×#2462C2semidirect
18. C73×#2461C2semidirect
19. C73×#2456C2semidirect
20. C73×#2456C2semidirect
21. C73×#2455C2semidirect
22. C73×#2443C2semidirect
23. C73×#2428C2semidirect
24. C73×#2425C2semidirect
25. C73×#2367C2semidirect
26. C73×#2364C2semidirect
27. C73×#2360C2semidirect
28. C73×#2359C2semidirect
29. C4×#123×C73C2semidirect
30. C4×#121×C73C2semidirect
31. C4×#121×C73C2semidirect
233. #123×C73D4semidirect
816. #59735C73direct (N × H)
830. C2×#559C2×C73semidirect
831. C2×#553C2×C73semidirect
832. #2715C2×C73semidirect
833. #2708C2×C73semidirect
834. #2676C2×C73semidirect
835. #2673C2×C73semidirect
836. #2600C2×C73semidirect
837. #2600C2×C73semidirect
838. #2558C2×C73semidirect
839. #2557C2×C73semidirect
840. #2555C2×C73semidirect
841. #2555C2×C73semidirect
842. #2554C2×C73semidirect
843. #2521C2×C73semidirect
844. #2474C2×C73semidirect
845. #2469C2×C73semidirect
846. #2462C2×C73semidirect
847. #2461C2×C73semidirect
848. #2456C2×C73semidirect
849. #2456C2×C73semidirect
850. #2455C2×C73semidirect
851. #2443C2×C73semidirect
852. #2428C2×C73semidirect
853. #2425C2×C73semidirect
854. #2367C2×C73semidirect
855. #2364C2×C73semidirect
856. #2360C2×C73semidirect
857. #2359C2×C73semidirect
858. C4×#123C2×C73semidirect
859. C4×#121C2×C73semidirect
860. C4×#121C2×C73semidirect
861. C73#59735direct (N × H)
1063. #123D4×C73semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#559×C732
C2×#553×C732
C73×#27152
C73×#27082
C73×#26762
C73×#26732
C73×#26002
C73×#25582
C73×#25572
C73×#25552
C73×#25542
C73×#25212
C73×#24742
C73×#24692
C73×#24622
C73×#24612
C73×#24562
C73×#24552
C73×#24432
C73×#24282
C73×#24252
C73×#23672
C73×#23642
C73×#23602
C73×#23592
C4×#123×C732
C4×#121×C732
#5973573