Finite Group Databasebeta

← C73×#36746 #32946150

Subgroups — C73×#36746 #32946150

Order 18688.

2152 conjugacy classes of subgroups.

The subgroup lattice has 1626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C73C211yesmaximal, characteristic, complemented
2C2×#539×C73C211yesmaximal, characteristic, complemented
3C73×#2854C211yesmaximal, characteristic, complemented
4C73×#2850C211yesmaximal, characteristic, complemented
5C73×#2719C211yesmaximal, characteristic, complemented
6C73×#2711C211yesmaximal, characteristic, complemented
7C73×#2709C211yesmaximal, characteristic, complemented
8C73×#2708C211yesmaximal, characteristic, complemented
9C73×#2706C211yesmaximal, characteristic, complemented
10C73×#2703C211yesmaximal, characteristic, complemented
11C73×#2695C211yesmaximal, characteristic, complemented
12C73×#2693C211yesmaximal, characteristic, complemented
13C73×#2691C211yesmaximal, characteristic, complemented
14C73×#2690C211yesmaximal, characteristic, complemented
15C73×#2688C211yesmaximal, characteristic, complemented
16C73×#2687C211yesmaximal, characteristic, complemented
17C73×#2676C211yesmaximal, characteristic, complemented
18C73×#2673C211yesmaximal, characteristic, complemented
19C73×#2672C211yesmaximal, characteristic, complemented
20C73×#2671C211yesmaximal, characteristic, complemented
21C73×#2663C211yesmaximal, characteristic, complemented
22C73×#2661C211yesmaximal, characteristic, complemented
23C73×#2611C211yesmaximal, characteristic, complemented
24C73×#2603C211yesmaximal, characteristic, complemented
25C73×#2602C211yesmaximal, characteristic, complemented
26C73×#2601C211yesmaximal, characteristic, complemented
27C73×#2591C211yesmaximal, characteristic, complemented
28C73×#2562C211yesmaximal, characteristic, complemented
29C73×#2414C211yesmaximal, characteristic, complemented
30C73×#2413C211yesmaximal, characteristic, complemented
31C73×#2290C211yesmaximal, characteristic, complemented
32#540×C73—28no—
33#539×C73—28no—
34C2×#127×C73C2211yescharacteristic
35C2×#126×C73C2211yescharacteristic
36C2×#126×C73C2211yescharacteristic
37C2×#125×C73C2211yescharacteristic
38C2×#125×C73C2211yescharacteristic
39C2×#125×C73C2211yescharacteristic
40C2×#124×C73C2211yescharacteristic
41C2×#123×C73C2211yescharacteristic
42C2×#123×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×C22⋊Q8×C73C2211yescharacteristic
52C2×C22⋊Q8×C73C2211yescharacteristic
53C2×#121×C73C2211yescharacteristic
54C2×#121×C73C2211yescharacteristic
55C2×#121×C73C2211yescharacteristic
56C2×#121×C73C2211yescharacteristic
57C2×#121×C73C2211yescharacteristic
58C2×#121×C73C2211yescharacteristic
59C2×#121×C73C2211yescharacteristic
60C2×#121×C73C2211yescharacteristic
61C2×#121×C73C2211yescharacteristic
62C2×C4×D4×C73C2211yescharacteristic
63C2×C4×D4×C73C2211yescharacteristic
64C2×C4×D4×C73C2211yescharacteristic
65C2×#117×C73C2211yescharacteristic
66C2×#117×C73C2211yescharacteristic
67C22×C4⋊C4×C73C2211yescharacteristic
68C22×C42×C73C2211yescharacteristic
69#400×C73C2211yescharacteristic
70#400×C73C2211yescharacteristic
71#400×C73C2211yescharacteristic
72#400×C73C2211yescharacteristic
73#400×C73C2211yescharacteristic
74#400×C73C2211yescharacteristic
75#399×C73C2211yescharacteristic
76#399×C73C2211yescharacteristic
77#398×C73C2211yescharacteristic
78#398×C73C2211yescharacteristic
79#398×C73C2211yescharacteristic
80#398×C73C2211yescharacteristic
81#398×C73C2211yescharacteristic
82#398×C73C2211yescharacteristic
83#397×C73C2211yescharacteristic
84#397×C73C2211yescharacteristic
85#397×C73C2211yescharacteristic
86#397×C73C2211yescharacteristic
87#397×C73C2211yescharacteristic
88#397×C73C2211yescharacteristic
89#396×C73C2211yescharacteristic
90#396×C73C2211yescharacteristic
91#396×C73C2211yescharacteristic
92#396×C73C2211yescharacteristic
93#395×C73C2211yescharacteristic
94#394×C73C2211yescharacteristic
95#394×C73C2211yescharacteristic
96#394×C73C2211yescharacteristic
97#394×C73C2211yescharacteristic
98#394×C73C2211yescharacteristic
99#394×C73C2211yescharacteristic
100#394×C73C2211yescharacteristic
101#394×C73C2211yescharacteristic
102#394×C73C2211yescharacteristic
103#394×C73C2211yescharacteristic
104#394×C73C2211yescharacteristic
105#394×C73C2211yescharacteristic
106#394×C73C2211yescharacteristic
107#394×C73C2211yescharacteristic
108#394×C73C2211yescharacteristic
109#393×C73C2211yescharacteristic
110#392×C73C2211yescharacteristic
111#392×C73C2211yescharacteristic
112#392×C73C2211yescharacteristic
113#392×C73C2211yescharacteristic
114#392×C73C2211yescharacteristic
115#392×C73C2211yescharacteristic
116#392×C73C2211yescharacteristic
117#391×C73C2211yescharacteristic
118#390×C73C2211yescharacteristic
119#390×C73C2211yescharacteristic
120#390×C73C2211yescharacteristic
121#390×C73C2211yescharacteristic
122#390×C73C2211yescharacteristic
123#390×C73C2211yescharacteristic
124#389×C73C2211yescharacteristic
125#389×C73C2211yescharacteristic
126#389×C73C2211yescharacteristic
127#389×C73C2211yescharacteristic
128#389×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#388×C73C2211yescharacteristic
138#388×C73C2211yescharacteristic
139#388×C73C2211yescharacteristic
140#388×C73C2211yescharacteristic
141#388×C73C2211yescharacteristic
142#388×C73C2211yescharacteristic
143#388×C73C2211yescharacteristic
144#388×C73C2211yescharacteristic
145#387×C73C2211yescharacteristic
146#387×C73C2211yescharacteristic
147#387×C73C2211yescharacteristic
148#387×C73C2211yescharacteristic
149#387×C73C2211yescharacteristic
150#387×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#386×C73C2211yescharacteristic
163#386×C73C2211yescharacteristic
164#386×C73C2211yescharacteristic
165#386×C73C2211yescharacteristic
166#386×C73C2211yescharacteristic
167#386×C73C2211yescharacteristic
168#385×C73C2211yescharacteristic
169#385×C73C2211yescharacteristic
170#385×C73C2211yescharacteristic
171#385×C73C2211yescharacteristic
172#385×C73C2211yescharacteristic
173#385×C73C2211yescharacteristic
174#385×C73C2211yescharacteristic
175#385×C73C2211yescharacteristic
176#385×C73C2211yescharacteristic
177#382×C73C2211yescharacteristic
178#381×C73C2211yescharacteristic
179#380×C73C2211yescharacteristic
180#380×C73C2211yescharacteristic
181#380×C73C2211yescharacteristic
182#380×C73C2211yescharacteristic
183#380×C73C2211yescharacteristic
184#380×C73C2211yescharacteristic
185C4×C4⋊C4×C73C2211yescharacteristic
186C4×C22⋊C4×C73C2211yescharacteristic
187C4×C22⋊C4×C73C2211yescharacteristic
188#376×C73C2211yescharacteristic
189C22×Q8×C73C2311yescharacteristic
190C22×D4×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
205C23×C4×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
215#127×C73—24no—
216#126×C73—24no—
217#126×C73—24no—
218#125×C73—24no—
219#125×C73—24no—
220#125×C73—24no—
221#124×C73—42no—
222#123×C73—24no—
223#123×C73—24no—
224#123×C73—24no—
225#123×C73—24no—
226#123×C73—24no—
227#123×C73—24no—
228#123×C73—24no—
229#123×C73—24no—
230#123×C73—42no—
231C22⋊Q8×C73—24no—
232C22⋊Q8×C73—24no—
233C22⋊Q8×C73—24no—
234#121×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—42no—
242#121×C73—42no—
243C4×D4×C73—24no—
244C4×D4×C73—24no—
245C4×D4×C73D418yescomplemented
246#117×C73—24no—
247#117×C73—42no—
248C2×C4⋊C4×C73—24no—
249C2×C4⋊C4×C73C2311yescharacteristic
250C2×C4⋊C4×C73C2311yescharacteristic
251C2×C4⋊C4×C73C2311yescharacteristic
252C2×C4⋊C4×C73C2311yescharacteristic
253C2×C4⋊C4×C73C2311yescharacteristic
254C2×C4⋊C4×C73C2311yescharacteristic
255C2×C4⋊C4×C73C2311yescharacteristic
256C2×C4⋊C4×C73C2311yescharacteristic
257C2×C4⋊C4×C73C2311yescharacteristic
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×C22⋊C4×C73C2311yescharacteristic
284C2×C22⋊C4×C73C2311yescharacteristic
285C2×C22⋊C4×C73C2311yescharacteristic
286C2×C22⋊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×C42×C73—42no—
334C2×C42×C73C2311yescharacteristic
335C2×C42×C73C2311yescharacteristic
336C2×C42×C73C2311yescharacteristic
337C2×C42×C73C2311yescharacteristic
338C2×C42×C73C2311yescharacteristic
339C2×C42×C73C2311yescharacteristic
340C2×C42×C73C2311yescharacteristic
341C2×C42×C73C2311yescharacteristic
342C2×C42×C73C2311yescharacteristic
343#95×C73C2311yescharacteristic
344#95×C73C2311yescharacteristic
345#95×C73C2311yescharacteristic
346#95×C73C2311yescharacteristic
347#95×C73C2311yescharacteristic
348#95×C73C2311yescharacteristic
349#95×C73C2311yescharacteristic
350#95×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
379C24×C73C2411yescharacteristic
380C24×C73C2411yescharacteristic
381C24×C73C2411yescharacteristic
382C24×C73C2411yescharacteristic
383C24×C73C2411yescharacteristic
384C24×C73C2411yescharacteristic
385C2×Q8×C73—22no—
386C2×Q8×C73—41no—
387C2×Q8×C73—41no—
388C2×D4×C73—22no—
389C2×D4×C73—22no—
390C2×D4×C73—22no—
391C2×D4×C73—22no—
392C2×D4×C73—22no—
393C2×D4×C73—22no—
394C2×D4×C73—22no—
395C2×D4×C73—22no—
396C2×D4×C73—22no—
397C2×D4×C73—22no—
398C2×D4×C73—22no—
399C2×D4×C73—22no—
400C2×D4×C73—41no—
401C2×D4×C73—41no—
402C2×D4×C73—41no—
403C2×D4×C73—41no—
404C2×D4×C73—41no—
405C2×D4×C73—41no—
406C2×D4×C73—41no—
407C2×D4×C73—41no—
408C2×D4×C73—41no—
409C2×D4×C73—41no—
410C2×D4×C73—41no—
411C2×D4×C73—41no—
412C2×D4×C73—41no—
413C2×D4×C73—41no—
414C2×D4×C73—41no—
415C2×D4×C73—41no—
416C2×D4×C73—41no—
417C2×D4×C73—41no—
418C2×D4×C73—41no—
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×C73C2×D414yes—
433C22×C4×C73—22no—
434C22×C4×C73—22no—
435C22×C4×C73—22no—
436C22×C4×C73—22no—
437C22×C4×C73—22no—
438C22×C4×C73—22no—
439C22×C4×C73—22no—
440C22×C4×C73—41no—
441C22×C4×C73—41no—
442C22×C4×C73—41no—
443C22×C4×C73—41no—
444C22×C4×C73—41no—
445C22×C4×C73—41no—
446C22×C4×C73—41no—
447C22×C4×C73—41no—
448C22×C4×C73—41no—
449C22×C4×C73—41no—
450C22×C4×C73—41no—
451C22×C4×C73—41no—
452C22×C4×C73—41no—
453C22×C4×C73—41no—
454C22×C4×C73—41no—
455C22×C4×C73—41no—
456C22×C4×C73—41no—
457C22×C4×C73—41no—
458C22×C4×C73—41no—
459C22×C4×C73—41no—
460C22×C4×C73—41no—
461C22×C4×C73C2×D414yes—
462C22×C4×C73C2×D414yes—
463C22×C4×C73C2411yescharacteristic
464C22×C4×C73C2411yescharacteristic
465C22×C4×C73C2411yescharacteristic
466C22×C4×C73C2411yescharacteristic
467C22×C4×C73C2411yescharacteristic
468C22×C4×C73C2411yescharacteristic
469C22×C4×C73C2411yescharacteristic
470C22×C4×C73C2411yescharacteristic
471C22×C4×C73C2411yescharacteristic
472C22×C4×C73C2411yescharacteristic
473C22×C4×C73C2411yescharacteristic
474C22×C4×C73C2411yescharacteristic
475C22×C4×C73C2411yescharacteristic
476C22×C4×C73C2411yescharacteristic
477C22×C4×C73C2411yescharacteristic
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
488C4⋊C4×C73—22no—
489C4⋊C4×C73—22no—
490C4⋊C4×C73—22no—
491C4⋊C4×C73—22no—
492C4⋊C4×C73—22no—
493C4⋊C4×C73—22no—
494C4⋊C4×C73—22no—
495C4⋊C4×C73—22no—
496C4⋊C4×C73—22no—
497C4⋊C4×C73—22no—
498C4⋊C4×C73—22no—
499C4⋊C4×C73—22no—
500C4⋊C4×C73—22no—
501C4⋊C4×C73—22no—
502C4⋊C4×C73—22no—
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—41no—
511C4⋊C4×C73—41no—
512C4⋊C4×C73—41no—
513C4⋊C4×C73—41no—
514C4⋊C4×C73—41no—
515C4⋊C4×C73—41no—
516C4⋊C4×C73—41no—
517C4⋊C4×C73—41no—
518C4⋊C4×C73—41no—
519C4⋊C4×C73—41no—
520C4⋊C4×C73—41no—
521C4⋊C4×C73C2×D414yes—
522C22⋊C4×C73—22no—
523C22⋊C4×C73—22no—
524C22⋊C4×C73—22no—
525C22⋊C4×C73—22no—
526C22⋊C4×C73—22no—
527C22⋊C4×C73—22no—
528C22⋊C4×C73—22no—
529C22⋊C4×C73—22no—
530C22⋊C4×C73—22no—
531C22⋊C4×C73—22no—
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—41no—
542C22⋊C4×C73—41no—
543C22⋊C4×C73—41no—
544C22⋊C4×C73—41no—
545C22⋊C4×C73—41no—
546C22⋊C4×C73—41no—
547C22⋊C4×C73—41no—
548C22⋊C4×C73—41no—
549C22⋊C4×C73—41no—
550C22⋊C4×C73—41no—
551C22⋊C4×C73—41no—
552C22⋊C4×C73—41no—
553C22⋊C4×C73—41no—
554C22⋊C4×C73—41no—
555C22⋊C4×C73—41no—
556C22⋊C4×C73—41no—
557C22⋊C4×C73—41no—
558C22⋊C4×C73—41no—
559C22⋊C4×C73—41no—
560C22⋊C4×C73—41no—
561C22⋊C4×C73—41no—
562C22⋊C4×C73—41no—
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×C73C2×D414yes—
571C22⋊C4×C73C2×D414yes—
572C42×C73—22no—
573C42×C73—22no—
574C42×C73—22no—
575C42×C73—22no—
576C42×C73—41no—
577C42×C73—41no—
578C42×C73—41no—
579C42×C73—41no—
580C42×C73C2×D414yes—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73—21no—
588C23×C73—21no—
589C23×C73—21no—
590C23×C73—21no—
591C23×C73—21no—
592C23×C73—21no—
593C23×C73—21no—
594C23×C73—21no—
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×C73C22×D412yes—
622C23×C73C22×D412yes—
623C23×C73C2511yescharacteristic
624Q8×C73—82no—
625D4×C73—44no—
626D4×C73—44no—
627D4×C73—44no—
628D4×C73—82no—
629D4×C73—82no—
630D4×C73—82no—
631D4×C73—82no—
632D4×C73—82no—
633D4×C73—82no—
634D4×C73—82no—
635D4×C73—82no—
636D4×C73—82no—
637D4×C73—82no—
638D4×C73—82no—
639D4×C73—82no—
640C2×C4×C73—21no—
641C2×C4×C73—21no—
642C2×C4×C73—21no—
643C2×C4×C73—21no—
644C2×C4×C73—21no—
645C2×C4×C73—21no—
646C2×C4×C73—21no—
647C2×C4×C73—21no—
648C2×C4×C73—21no—
649C2×C4×C73—21no—
650C2×C4×C73—21no—
651C2×C4×C73—21no—
652C2×C4×C73—21no—
653C2×C4×C73—21no—
654C2×C4×C73—21no—
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—44no—
710C2×C4×C73—44no—
711C2×C4×C73—44no—
712C2×C4×C73—44no—
713C2×C4×C73—44no—
714C2×C4×C73—44no—
715C2×C4×C73—82no—
716C2×C4×C73—82no—
717C2×C4×C73—82no—
718C2×C4×C73—82no—
719C2×C4×C73C22×D412yes—
720C2×C4×C73C22×D412yes—
721C2×C4×C73C22×D412yes—
722C2×C4×C73C22×D412yes—
723C2×C4×C73C22×D412yes—
724C2×C4×C73H(5,𝔽2)12yes—
725C22×C73—22no—
726C22×C73—22no—
727C22×C73—22no—
728C22×C73—22no—
729C22×C73—22no—
730C22×C73—22no—
731C22×C73—41no—
732C22×C73—41no—
733C22×C73—41no—
734C22×C73—41no—
735C22×C73—41no—
736C22×C73—41no—
737C22×C73—41no—
738C22×C73—41no—
739C22×C73—41no—
740C22×C73—41no—
741C22×C73—41no—
742C22×C73—41no—
743C22×C73—41no—
744C22×C73—41no—
745C22×C73—41no—
746C22×C73—41no—
747C22×C73—41no—
748C22×C73—41no—
749C22×C73—41no—
750C22×C73—41no—
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×C73C23×D411yescharacteristic
768C22×C73C2×H(5,𝔽2)11yescharacteristic
769C22×C73#58511yescharacteristic
770C22×C73#58511yescharacteristic
771C22×C73#58511yescharacteristic
772C22×C73#58511yescharacteristic
773C22×C73#58511yescharacteristic
774C4×C73—22no—
775C4×C73—22no—
776C4×C73—22no—
777C4×C73—22no—
778C4×C73—22no—
779C4×C73—22no—
780C4×C73—41no—
781C4×C73—41no—
782C4×C73—41no—
783C4×C73—41no—
784C4×C73—41no—
785C4×C73—41no—
786C4×C73—41no—
787C4×C73—41no—
788C4×C73—41no—
789C4×C73—41no—
790C4×C73—41no—
791C4×C73—41no—
792C4×C73—41no—
793C4×C73—41no—
794C4×C73—41no—
795C4×C73—41no—
796C4×C73—41no—
797C4×C73—41no—
798C4×C73—41no—
799#36746C7311yesmaximal, characteristic, direct product factor, Sylow
800C2×C73—42no—
801C2×C73—42no—
802C2×C73—81no—
803C2×C73—81no—
804C2×C73—81no—
805C2×C73—81no—
806C2×C73#344911yescharacteristic
807C2×C73#349611yescharacteristic
808C2×C73#350011yescharacteristic
809C2×C73#353311yescharacteristic
810C2×C73#353911yescharacteristic
811C2×C73#356611yescharacteristic
812C2×C73#356711yescharacteristic
813C2×#540C2×C7311yescharacteristic, complemented
814C2×#539C2×C7311yescharacteristic, complemented
815#2854C2×C7311yescharacteristic, complemented
816#2850C2×C7311yescharacteristic, complemented
817#2719C2×C7311yescharacteristic, complemented
818#2711C2×C7311yescharacteristic, complemented
819#2709C2×C7311yescharacteristic, complemented
820#2708C2×C7311yescharacteristic, complemented
821#2706C2×C7311yescharacteristic, complemented
822#2703C2×C7311yescharacteristic, complemented
823#2695C2×C7311yescharacteristic, complemented
824#2693C2×C7311yescharacteristic, complemented
825#2691C2×C7311yescharacteristic, complemented
826#2690C2×C7311yescharacteristic, complemented
827#2688C2×C7311yescharacteristic, complemented
828#2687C2×C7311yescharacteristic, complemented
829#2676C2×C7311yescharacteristic, complemented
830#2673C2×C7311yescharacteristic, complemented
831#2672C2×C7311yescharacteristic, complemented
832#2671C2×C7311yescharacteristic, complemented
833#2663C2×C7311yescharacteristic, complemented
834#2661C2×C7311yescharacteristic, complemented
835#2611C2×C7311yescharacteristic, complemented
836#2603C2×C7311yescharacteristic, complemented
837#2602C2×C7311yescharacteristic, complemented
838#2601C2×C7311yescharacteristic, complemented
839#2591C2×C7311yescharacteristic, complemented
840#2562C2×C7311yescharacteristic, complemented
841#2414C2×C7311yescharacteristic, complemented
842#2413C2×C7311yescharacteristic, complemented
843#2290C2×C7311yescharacteristic, complemented
844C73#3674611yescharacteristic, direct product factor, Sylow
845#540—28no—
846#539—28no—
847C2×#127C22×C7311yescharacteristic
848C2×#126C22×C7311yescharacteristic
849C2×#126C22×C7311yescharacteristic
850C2×#125C22×C7311yescharacteristic
851C2×#125C22×C7311yescharacteristic
852C2×#125C22×C7311yescharacteristic
853C2×#124C22×C7311yescharacteristic
854C2×#123C22×C7311yescharacteristic
855C2×#123C22×C7311yescharacteristic
856C2×#123C22×C7311yescharacteristic
857C2×#123C22×C7311yescharacteristic
858C2×#123C22×C7311yescharacteristic
859C2×#123C22×C7311yescharacteristic
860C2×#123C22×C7311yescharacteristic
861C2×#123C22×C7311yescharacteristic
862C2×#123C22×C7311yescharacteristic
863C2×C22⋊Q8C22×C7311yescharacteristic
864C2×C22⋊Q8C22×C7311yescharacteristic
865C2×C22⋊Q8C22×C7311yescharacteristic
866C2×#121C22×C7311yescharacteristic
867C2×#121C22×C7311yescharacteristic
868C2×#121C22×C7311yescharacteristic
869C2×#121C22×C7311yescharacteristic
870C2×#121C22×C7311yescharacteristic
871C2×#121C22×C7311yescharacteristic
872C2×#121C22×C7311yescharacteristic
873C2×#121C22×C7311yescharacteristic
874C2×#121C22×C7311yescharacteristic
875C2×C4×D4C22×C7311yescharacteristic
876C2×C4×D4C22×C7311yescharacteristic
877C2×C4×D4C22×C7311yescharacteristic
878C2×#117C22×C7311yescharacteristic
879C2×#117C22×C7311yescharacteristic
880C22×C4⋊C4C22×C7311yescharacteristic
881C22×C42C22×C7311yescharacteristic
882#400C22×C7311yescharacteristic
883#400C22×C7311yescharacteristic
884#400C22×C7311yescharacteristic
885#400C22×C7311yescharacteristic
886#400C22×C7311yescharacteristic
887#400C22×C7311yescharacteristic
888#399C22×C7311yescharacteristic
889#399C22×C7311yescharacteristic
890#398C22×C7311yescharacteristic
891#398C22×C7311yescharacteristic
892#398C22×C7311yescharacteristic
893#398C22×C7311yescharacteristic
894#398C22×C7311yescharacteristic
895#398C22×C7311yescharacteristic
896#397C22×C7311yescharacteristic
897#397C22×C7311yescharacteristic
898#397C22×C7311yescharacteristic
899#397C22×C7311yescharacteristic
900#397C22×C7311yescharacteristic
901#397C22×C7311yescharacteristic
902#396C22×C7311yescharacteristic
903#396C22×C7311yescharacteristic
904#396C22×C7311yescharacteristic
905#396C22×C7311yescharacteristic
906#395C22×C7311yescharacteristic
907#394C22×C7311yescharacteristic
908#394C22×C7311yescharacteristic
909#394C22×C7311yescharacteristic
910#394C22×C7311yescharacteristic
911#394C22×C7311yescharacteristic
912#394C22×C7311yescharacteristic
913#394C22×C7311yescharacteristic
914#394C22×C7311yescharacteristic
915#394C22×C7311yescharacteristic
916#394C22×C7311yescharacteristic
917#394C22×C7311yescharacteristic
918#394C22×C7311yescharacteristic
919#394C22×C7311yescharacteristic
920#394C22×C7311yescharacteristic
921#394C22×C7311yescharacteristic
922#393C22×C7311yescharacteristic
923#392C22×C7311yescharacteristic
924#392C22×C7311yescharacteristic
925#392C22×C7311yescharacteristic
926#392C22×C7311yescharacteristic
927#392C22×C7311yescharacteristic
928#392C22×C7311yescharacteristic
929#392C22×C7311yescharacteristic
930#391C22×C7311yescharacteristic
931#390C22×C7311yescharacteristic
932#390C22×C7311yescharacteristic
933#390C22×C7311yescharacteristic
934#390C22×C7311yescharacteristic
935#390C22×C7311yescharacteristic
936#390C22×C7311yescharacteristic
937#389C22×C7311yescharacteristic
938#389C22×C7311yescharacteristic
939#389C22×C7311yescharacteristic
940#389C22×C7311yescharacteristic
941#389C22×C7311yescharacteristic
942#388C22×C7311yescharacteristic
943#388C22×C7311yescharacteristic
944#388C22×C7311yescharacteristic
945#388C22×C7311yescharacteristic
946#388C22×C7311yescharacteristic
947#388C22×C7311yescharacteristic
948#388C22×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#387C22×C7311yescharacteristic
959#387C22×C7311yescharacteristic
960#387C22×C7311yescharacteristic
961#387C22×C7311yescharacteristic
962#387C22×C7311yescharacteristic
963#387C22×C7311yescharacteristic
964#386C22×C7311yescharacteristic
965#386C22×C7311yescharacteristic
966#386C22×C7311yescharacteristic
967#386C22×C7311yescharacteristic
968#386C22×C7311yescharacteristic
969#386C22×C7311yescharacteristic
970#386C22×C7311yescharacteristic
971#386C22×C7311yescharacteristic
972#386C22×C7311yescharacteristic
973#386C22×C7311yescharacteristic
974#386C22×C7311yescharacteristic
975#386C22×C7311yescharacteristic
976#386C22×C7311yescharacteristic
977#386C22×C7311yescharacteristic
978#386C22×C7311yescharacteristic
979#386C22×C7311yescharacteristic
980#386C22×C7311yescharacteristic
981#385C22×C7311yescharacteristic
982#385C22×C7311yescharacteristic
983#385C22×C7311yescharacteristic
984#385C22×C7311yescharacteristic
985#385C22×C7311yescharacteristic
986#385C22×C7311yescharacteristic
987#385C22×C7311yescharacteristic
988#385C22×C7311yescharacteristic
989#385C22×C7311yescharacteristic
990#382C22×C7311yescharacteristic
991#381C22×C7311yescharacteristic
992#380C22×C7311yescharacteristic
993#380C22×C7311yescharacteristic
994#380C22×C7311yescharacteristic
995#380C22×C7311yescharacteristic
996#380C22×C7311yescharacteristic
997#380C22×C7311yescharacteristic
998C4×C4⋊C4C22×C7311yescharacteristic
999C4×C22⋊C4C22×C7311yescharacteristic
1000C4×C22⋊C4C22×C7311yescharacteristic
1001#376C22×C7311yescharacteristic
1002C22×Q8C23×C7311yescharacteristic
1003C22×D4C23×C7311yescharacteristic
1004C22×D4C23×C7311yescharacteristic
1005C22×D4C23×C7311yescharacteristic
1006C22×D4C23×C7311yescharacteristic
1007C22×D4C23×C7311yescharacteristic
1008C22×D4C23×C7311yescharacteristic
1009C22×D4C23×C7311yescharacteristic
1010C22×D4C23×C7311yescharacteristic
1011C22×D4C23×C7311yescharacteristic
1012C22×D4C23×C7311yescharacteristic
1013C22×D4C23×C7311yescharacteristic
1014C22×D4C23×C7311yescharacteristic
1015C22×D4C23×C7311yescharacteristic
1016C22×D4C23×C7311yescharacteristic
1017C22×D4C23×C7311yescharacteristic
1018C23×C4C23×C7311yescharacteristic
1019C23×C4C23×C7311yescharacteristic
1020C23×C4C23×C7311yescharacteristic
1021C23×C4C23×C7311yescharacteristic
1022C23×C4C23×C7311yescharacteristic
1023C23×C4C23×C7311yescharacteristic
1024C23×C4C23×C7311yescharacteristic
1025C23×C4C23×C7311yescharacteristic
1026C23×C4C23×C7311yescharacteristic
1027C23×C4C23×C7311yescharacteristic
1028#127—24no—
1029#126—24no—
1030#126—24no—
1031#125—24no—
1032#125—24no—
1033#125—24no—
1034#124—42no—
1035#123—24no—
1036#123—24no—
1037#123—24no—
1038#123—24no—
1039#123—24no—
1040#123—24no—
1041#123—24no—
1042#123—24no—
1043#123—42no—
1044C22⋊Q8—24no—
1045C22⋊Q8—24no—
1046C22⋊Q8—24no—
1047#121—24no—
1048#121—24no—
1049#121—24no—
1050#121—24no—
1051#121—24no—
1052#121—24no—
1053#121—24no—
1054#121—42no—
1055#121—42no—
1056C4×D4—24no—
1057C4×D4—24no—
1058C4×D4D4×C7318yescomplemented
1059#117—24no—
1060#117—42no—
1061C2×C4⋊C4—24no—
1062C2×C4⋊C4C23×C7311yescharacteristic
1063C2×C4⋊C4C23×C7311yescharacteristic
1064C2×C4⋊C4C23×C7311yescharacteristic
1065C2×C4⋊C4C23×C7311yescharacteristic
1066C2×C4⋊C4C23×C7311yescharacteristic
1067C2×C4⋊C4C23×C7311yescharacteristic
1068C2×C4⋊C4C23×C7311yescharacteristic
1069C2×C4⋊C4C23×C7311yescharacteristic
1070C2×C4⋊C4C23×C7311yescharacteristic
1071C2×C4⋊C4C23×C7311yescharacteristic
1072C2×C4⋊C4C23×C7311yescharacteristic
1073C2×C4⋊C4C23×C7311yescharacteristic
1074C2×C4⋊C4C23×C7311yescharacteristic
1075C2×C4⋊C4C23×C7311yescharacteristic
1076C2×C4⋊C4C23×C7311yescharacteristic
1077C2×C4⋊C4C23×C7311yescharacteristic
1078C2×C4⋊C4C23×C7311yescharacteristic
1079C2×C4⋊C4C23×C7311yescharacteristic
1080C2×C4⋊C4C23×C7311yescharacteristic
1081C2×C4⋊C4C23×C7311yescharacteristic
1082C2×C4⋊C4C23×C7311yescharacteristic
1083C2×C4⋊C4C23×C7311yescharacteristic
1084C2×C4⋊C4C23×C7311yescharacteristic
1085C2×C4⋊C4C23×C7311yescharacteristic
1086C2×C4⋊C4C23×C7311yescharacteristic
1087C2×C4⋊C4C23×C7311yescharacteristic
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×C22⋊C4C23×C7311yescharacteristic
1097C2×C22⋊C4C23×C7311yescharacteristic
1098C2×C22⋊C4C23×C7311yescharacteristic
1099C2×C22⋊C4C23×C7311yescharacteristic
1100C2×C22⋊C4C23×C7311yescharacteristic
1101C2×C22⋊C4C23×C7311yescharacteristic
1102C2×C22⋊C4C23×C7311yescharacteristic
1103C2×C22⋊C4C23×C7311yescharacteristic
1104C2×C22⋊C4C23×C7311yescharacteristic
1105C2×C22⋊C4C23×C7311yescharacteristic
1106C2×C22⋊C4C23×C7311yescharacteristic
1107C2×C22⋊C4C23×C7311yescharacteristic
1108C2×C22⋊C4C23×C7311yescharacteristic
1109C2×C22⋊C4C23×C7311yescharacteristic
1110C2×C22⋊C4C23×C7311yescharacteristic
1111C2×C22⋊C4C23×C7311yescharacteristic
1112C2×C22⋊C4C23×C7311yescharacteristic
1113C2×C22⋊C4C23×C7311yescharacteristic
1114C2×C22⋊C4C23×C7311yescharacteristic
1115C2×C22⋊C4C23×C7311yescharacteristic
1116C2×C22⋊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×C42—42no—
1147C2×C42C23×C7311yescharacteristic
1148C2×C42C23×C7311yescharacteristic
1149C2×C42C23×C7311yescharacteristic
1150C2×C42C23×C7311yescharacteristic
1151C2×C42C23×C7311yescharacteristic
1152C2×C42C23×C7311yescharacteristic
1153C2×C42C23×C7311yescharacteristic
1154C2×C42C23×C7311yescharacteristic
1155C2×C42C23×C7311yescharacteristic
1156#95C23×C7311yescharacteristic
1157#95C23×C7311yescharacteristic
1158#95C23×C7311yescharacteristic
1159#95C23×C7311yescharacteristic
1160#95C23×C7311yescharacteristic
1161#95C23×C7311yescharacteristic
1162#95C23×C7311yescharacteristic
1163#95C23×C7311yescharacteristic
1164#95C23×C7311yescharacteristic
1165#95C23×C7311yescharacteristic
1166#95C23×C7311yescharacteristic
1167#95C23×C7311yescharacteristic
1168#95C23×C7311yescharacteristic
1169#95C23×C7311yescharacteristic
1170#95C23×C7311yescharacteristic
1171#95C23×C7311yescharacteristic
1172#95C23×C7311yescharacteristic
1173#95C23×C7311yescharacteristic
1174#95C23×C7311yescharacteristic
1175#95C23×C7311yescharacteristic
1176#95C23×C7311yescharacteristic
1177#95C23×C7311yescharacteristic
1178#95C23×C7311yescharacteristic
1179#95C23×C7311yescharacteristic
1180#95C23×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
1192C24C24×C7311yescharacteristic
1193C24C24×C7311yescharacteristic
1194C24C24×C7311yescharacteristic
1195C24C24×C7311yescharacteristic
1196C24C24×C7311yescharacteristic
1197C24C24×C7311yescharacteristic
1198C2×Q8—22no—
1199C2×Q8—41no—
1200C2×Q8—41no—
1201C2×D4—22no—
1202C2×D4—22no—
1203C2×D4—22no—
1204C2×D4—22no—
1205C2×D4—22no—
1206C2×D4—22no—
1207C2×D4—22no—
1208C2×D4—22no—
1209C2×D4—22no—
1210C2×D4—22no—
1211C2×D4—22no—
1212C2×D4—22no—
1213C2×D4—41no—
1214C2×D4—41no—
1215C2×D4—41no—
1216C2×D4—41no—
1217C2×D4—41no—
1218C2×D4—41no—
1219C2×D4—41no—
1220C2×D4—41no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—41no—
1224C2×D4—41no—
1225C2×D4—41no—
1226C2×D4—41no—
1227C2×D4—41no—
1228C2×D4—41no—
1229C2×D4—41no—
1230C2×D4—41no—
1231C2×D4—41no—
1232C2×D4—41no—
1233C2×D4—41no—
1234C2×D4—41no—
1235C2×D4—41no—
1236C2×D4—41no—
1237C2×D4—41no—
1238C2×D4—41no—
1239C2×D4—41no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—41no—
1245C2×D4C2×D4×C7314yes—
1246C22×C4—22no—
1247C22×C4—22no—
1248C22×C4—22no—
1249C22×C4—22no—
1250C22×C4—22no—
1251C22×C4—22no—
1252C22×C4—22no—
1253C22×C4—41no—
1254C22×C4—41no—
1255C22×C4—41no—
1256C22×C4—41no—
1257C22×C4—41no—
1258C22×C4—41no—
1259C22×C4—41no—
1260C22×C4—41no—
1261C22×C4—41no—
1262C22×C4—41no—
1263C22×C4—41no—
1264C22×C4—41no—
1265C22×C4—41no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—41no—
1273C22×C4—41no—
1274C22×C4C2×D4×C7314yes—
1275C22×C4C2×D4×C7314yes—
1276C22×C4C24×C7311yescharacteristic
1277C22×C4C24×C7311yescharacteristic
1278C22×C4C24×C7311yescharacteristic
1279C22×C4C24×C7311yescharacteristic
1280C22×C4C24×C7311yescharacteristic
1281C22×C4C24×C7311yescharacteristic
1282C22×C4C24×C7311yescharacteristic
1283C22×C4C24×C7311yescharacteristic
1284C22×C4C24×C7311yescharacteristic
1285C22×C4C24×C7311yescharacteristic
1286C22×C4C24×C7311yescharacteristic
1287C22×C4C24×C7311yescharacteristic
1288C22×C4C24×C7311yescharacteristic
1289C22×C4C24×C7311yescharacteristic
1290C22×C4C24×C7311yescharacteristic
1291C22×C4C24×C7311yescharacteristic
1292C22×C4C24×C7311yescharacteristic
1293C22×C4C24×C7311yescharacteristic
1294C22×C4C24×C7311yescharacteristic
1295C22×C4C24×C7311yescharacteristic
1296C22×C4C24×C7311yescharacteristic
1297C22×C4C24×C7311yescharacteristic
1298C22×C4C24×C7311yescharacteristic
1299C22×C4C24×C7311yescharacteristic
1300C22×C4C24×C7311yescharacteristic
1301C4⋊C4—22no—
1302C4⋊C4—22no—
1303C4⋊C4—22no—
1304C4⋊C4—22no—
1305C4⋊C4—22no—
1306C4⋊C4—22no—
1307C4⋊C4—22no—
1308C4⋊C4—22no—
1309C4⋊C4—22no—
1310C4⋊C4—22no—
1311C4⋊C4—22no—
1312C4⋊C4—22no—
1313C4⋊C4—22no—
1314C4⋊C4—22no—
1315C4⋊C4—22no—
1316C4⋊C4—22no—
1317C4⋊C4—22no—
1318C4⋊C4—22no—
1319C4⋊C4—22no—
1320C4⋊C4—22no—
1321C4⋊C4—22no—
1322C4⋊C4—22no—
1323C4⋊C4—41no—
1324C4⋊C4—41no—
1325C4⋊C4—41no—
1326C4⋊C4—41no—
1327C4⋊C4—41no—
1328C4⋊C4—41no—
1329C4⋊C4—41no—
1330C4⋊C4—41no—
1331C4⋊C4—41no—
1332C4⋊C4—41no—
1333C4⋊C4—41no—
1334C4⋊C4C2×D4×C7314yes—
1335C22⋊C4—22no—
1336C22⋊C4—22no—
1337C22⋊C4—22no—
1338C22⋊C4—22no—
1339C22⋊C4—22no—
1340C22⋊C4—22no—
1341C22⋊C4—22no—
1342C22⋊C4—22no—
1343C22⋊C4—22no—
1344C22⋊C4—22no—
1345C22⋊C4—22no—
1346C22⋊C4—22no—
1347C22⋊C4—22no—
1348C22⋊C4—22no—
1349C22⋊C4—22no—
1350C22⋊C4—22no—
1351C22⋊C4—22no—
1352C22⋊C4—22no—
1353C22⋊C4—22no—
1354C22⋊C4—41no—
1355C22⋊C4—41no—
1356C22⋊C4—41no—
1357C22⋊C4—41no—
1358C22⋊C4—41no—
1359C22⋊C4—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
1373C22⋊C4—41no—
1374C22⋊C4—41no—
1375C22⋊C4—41no—
1376C22⋊C4—41no—
1377C22⋊C4—41no—
1378C22⋊C4—41no—
1379C22⋊C4—41no—
1380C22⋊C4—41no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4C2×D4×C7314yes—
1384C22⋊C4C2×D4×C7314yes—
1385C42—22no—
1386C42—22no—
1387C42—22no—
1388C42—22no—
1389C42—41no—
1390C42—41no—
1391C42—41no—
1392C42—41no—
1393C42C2×D4×C7314yes—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—21no—
1401C23—21no—
1402C23—21no—
1403C23—21no—
1404C23—21no—
1405C23—21no—
1406C23—21no—
1407C23—21no—
1408C23—21no—
1409C23—21no—
1410C23—21no—
1411C23—21no—
1412C23—21no—
1413C23—21no—
1414C23—21no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23C22×D4×C7312yes—
1435C23C22×D4×C7312yes—
1436C23C25×C7311yescharacteristic
1437Q8—82no—
1438D4—44no—
1439D4—44no—
1440D4—44no—
1441D4—82no—
1442D4—82no—
1443D4—82no—
1444D4—82no—
1445D4—82no—
1446D4—82no—
1447D4—82no—
1448D4—82no—
1449D4—82no—
1450D4—82no—
1451D4—82no—
1452D4—82no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—21no—
1463C2×C4—21no—
1464C2×C4—21no—
1465C2×C4—21no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
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—44no—
1523C2×C4—44no—
1524C2×C4—44no—
1525C2×C4—44no—
1526C2×C4—44no—
1527C2×C4—44no—
1528C2×C4—82no—
1529C2×C4—82no—
1530C2×C4—82no—
1531C2×C4—82no—
1532C2×C4C22×D4×C7312yes—
1533C2×C4C22×D4×C7312yes—
1534C2×C4C22×D4×C7312yes—
1535C2×C4C22×D4×C7312yes—
1536C2×C4C22×D4×C7312yes—
1537C2×C4H(5,𝔽2)×C7312yes—
1538C22—22no—
1539C22—22no—
1540C22—22no—
1541C22—22no—
1542C22—22no—
1543C22—22no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—41no—
1549C22—41no—
1550C22—41no—
1551C22—41no—
1552C22—41no—
1553C22—41no—
1554C22—41no—
1555C22—41no—
1556C22—41no—
1557C22—41no—
1558C22—41no—
1559C22—41no—
1560C22—41no—
1561C22—41no—
1562C22—41no—
1563C22—41no—
1564C22—41no—
1565C22—41no—
1566C22—41no—
1567C22—41no—
1568C22—41no—
1569C22—41no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—41no—
1579C22—41no—
1580C22C23×D4×C7311yescharacteristic
1581C22C2×H(5,𝔽2)×C7311yescharacteristic
1582C22#585×C7311yescharacteristic
1583C22#585×C7311yescharacteristic
1584C22#585×C7311yescharacteristic
1585C22#585×C7311yescharacteristic
1586C22#585×C7311yescharacteristic
1587C4—22no—
1588C4—22no—
1589C4—22no—
1590C4—22no—
1591C4—22no—
1592C4—22no—
1593C4—41no—
1594C4—41no—
1595C4—41no—
1596C4—41no—
1597C4—41no—
1598C4—41no—
1599C4—41no—
1600C4—41no—
1601C4—41no—
1602C4—41no—
1603C4—41no—
1604C4—41no—
1605C4—41no—
1606C4—41no—
1607C4—41no—
1608C4—41no—
1609C4—41no—
1610C4—41no—
1611C4—41no—
1612C2—42no—
1613C2—42no—
1614C2—81no—
1615C2—81no—
1616C2—81no—
1617C2—81no—
1618C2C73×#344911yescharacteristic
1619C2C73×#349611yescharacteristic
1620C2C73×#350011yescharacteristic
1621C2C73×#353311yescharacteristic
1622C2C73×#353911yescharacteristic
1623C2C73×#356611yescharacteristic
1624C2C73×#356711yescharacteristic
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×#540×C73C2semidirect
2. C2×#539×C73C2semidirect
3. C73×#2854C2semidirect
4. C73×#2850C2semidirect
5. C73×#2719C2semidirect
6. C73×#2711C2semidirect
7. C73×#2709C2semidirect
8. C73×#2708C2semidirect
9. C73×#2706C2semidirect
10. C73×#2703C2semidirect
11. C73×#2695C2semidirect
12. C73×#2693C2semidirect
13. C73×#2691C2semidirect
14. C73×#2690C2semidirect
15. C73×#2688C2semidirect
16. C73×#2687C2semidirect
17. C73×#2676C2semidirect
18. C73×#2673C2semidirect
19. C73×#2672C2semidirect
20. C73×#2671C2semidirect
21. C73×#2663C2semidirect
22. C73×#2661C2semidirect
23. C73×#2611C2semidirect
24. C73×#2603C2semidirect
25. C73×#2602C2semidirect
26. C73×#2601C2semidirect
27. C73×#2591C2semidirect
28. C73×#2562C2semidirect
29. C73×#2414C2semidirect
30. C73×#2413C2semidirect
31. C73×#2290C2semidirect
245. C4×D4×C73D4semidirect
799. #36746C73direct (N × H)
813. C2×#540C2×C73semidirect
814. C2×#539C2×C73semidirect
815. #2854C2×C73semidirect
816. #2850C2×C73semidirect
817. #2719C2×C73semidirect
818. #2711C2×C73semidirect
819. #2709C2×C73semidirect
820. #2708C2×C73semidirect
821. #2706C2×C73semidirect
822. #2703C2×C73semidirect
823. #2695C2×C73semidirect
824. #2693C2×C73semidirect
825. #2691C2×C73semidirect
826. #2690C2×C73semidirect
827. #2688C2×C73semidirect
828. #2687C2×C73semidirect
829. #2676C2×C73semidirect
830. #2673C2×C73semidirect
831. #2672C2×C73semidirect
832. #2671C2×C73semidirect
833. #2663C2×C73semidirect
834. #2661C2×C73semidirect
835. #2611C2×C73semidirect
836. #2603C2×C73semidirect
837. #2602C2×C73semidirect
838. #2601C2×C73semidirect
839. #2591C2×C73semidirect
840. #2562C2×C73semidirect
841. #2414C2×C73semidirect
842. #2413C2×C73semidirect
843. #2290C2×C73semidirect
844. C73#36746direct (N × H)
1058. C4×D4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C732
C2×#539×C732
C73×#28542
C73×#28502
C73×#27192
C73×#27112
C73×#27092
C73×#27082
C73×#27062
C73×#27032
C73×#26952
C73×#26932
C73×#26912
C73×#26902
C73×#26882
C73×#26872
C73×#26762
C73×#26732
C73×#26722
C73×#26712
C73×#26632
C73×#26612
C73×#26112
C73×#26032
C73×#26022
C73×#26012
C73×#25912
C73×#25622
C73×#24142
C73×#24132
C73×#22902
#3674673