Finite Group Databasebeta

← C73×#36743 #32946147

Subgroups — C73×#36743 #32946147

Order 18688.

2064 conjugacy classes of subgroups.

The subgroup lattice has 1526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#542×C73C211yesmaximal, characteristic, complemented
2C2×#539×C73C211yesmaximal, characteristic, complemented
3C73×#2857C211yesmaximal, characteristic, complemented
4C73×#2854C211yesmaximal, characteristic, complemented
5C73×#2722C211yesmaximal, characteristic, complemented
6C73×#2720C211yesmaximal, characteristic, complemented
7C73×#2718C211yesmaximal, characteristic, complemented
8C73×#2717C211yesmaximal, characteristic, complemented
9C73×#2715C211yesmaximal, characteristic, complemented
10C73×#2713C211yesmaximal, characteristic, complemented
11C73×#2710C211yesmaximal, characteristic, complemented
12C73×#2708C211yesmaximal, characteristic, complemented
13C73×#2695C211yesmaximal, characteristic, complemented
14C73×#2692C211yesmaximal, characteristic, complemented
15C73×#2689C211yesmaximal, characteristic, complemented
16C73×#2686C211yesmaximal, characteristic, complemented
17C73×#2677C211yesmaximal, characteristic, complemented
18C73×#2674C211yesmaximal, characteristic, complemented
19C73×#2672C211yesmaximal, characteristic, complemented
20C73×#2671C211yesmaximal, characteristic
21C73×#2663C211yesmaximal, characteristic, complemented
22C73×#2663C211yesmaximal, characteristic, complemented
23C73×#2611C211yesmaximal, characteristic, complemented
24C73×#2604C211yesmaximal, characteristic, complemented
25C73×#2602C211yesmaximal, characteristic, complemented
26C73×#2601C211yesmaximal, characteristic, complemented
27C73×#2584C211yesmaximal, characteristic, complemented
28C73×#2583C211yesmaximal, characteristic, complemented
29C73×#2415C211yesmaximal, characteristic, complemented
30C73×#2413C211yesmaximal, characteristic, complemented
31C73×#2290C211yesmaximal, characteristic, complemented
32#542×C73—28no—
33#539×C73—28no—
34C2×C4⋊Q8×C73C2211yescharacteristic
35C2×C4⋊Q8×C73C2211yescharacteristic
36C2×#126×C73C2211yescharacteristic
37C2×#126×C73C2211yescharacteristic
38C2×#126×C73C2211yescharacteristic
39C2×#126×C73C2211yescharacteristic
40C2×#125×C73C2211yescharacteristic
41C2×#125×C73C2211yescharacteristic
42C2×#124×C73C2211yescharacteristic
43C2×#124×C73C2211yescharacteristic
44C2×#124×C73C2211yescharacteristic
45C2×#123×C73C2211yescharacteristic
46C2×#123×C73C2211yescharacteristic
47C2×#123×C73C2211yescharacteristic
48C2×#123×C73C2211yescharacteristic
49C2×#123×C73C2211yescharacteristic
50C2×#123×C73C2211yescharacteristic
51C2×#123×C73C2211yescharacteristic
52C2×C22⋊Q8×C73C2211yescharacteristic
53C2×C22⋊Q8×C73C2211yescharacteristic
54C2×C22⋊Q8×C73C2211yescharacteristic
55C2×C22⋊Q8×C73C2211yescharacteristic
56C2×C22⋊Q8×C73C2211yescharacteristic
57C2×C22⋊Q8×C73C2211yescharacteristic
58C2×C22⋊Q8×C73C2211yescharacteristic
59C2×#121×C73C2211yescharacteristic
60C2×#121×C73C2211yescharacteristic
61C2×#121×C73C2211yescharacteristic
62C2×C4×Q8×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#399×C73C2211yescharacteristic
74#399×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#398×C73C2211yescharacteristic
84#398×C73C2211yescharacteristic
85#397×C73C2211yescharacteristic
86#397×C73C2211yescharacteristic
87#397×C73C2211yescharacteristic
88#397×C73C2211yescharacteristic
89#397×C73C2211yescharacteristic
90#397×C73C2211yescharacteristic
91#397×C73C2211yescharacteristic
92#397×C73C2211yescharacteristic
93#396×C73C2211yescharacteristic
94#396×C73C2211yescharacteristic
95#396×C73C2211yescharacteristic
96#396×C73C2211yescharacteristic
97#395×C73C2211yescharacteristic
98#395×C73C2211yescharacteristic
99#395×C73C2211yescharacteristic
100#395×C73C2211yescharacteristic
101#395×C73C2211yescharacteristic
102#395×C73C2211yescharacteristic
103#395×C73C2211yescharacteristic
104#394×C73C2211yescharacteristic
105#394×C73C2211yescharacteristic
106#394×C73C2211yescharacteristic
107#394×C73C2211yescharacteristic
108#394×C73C2211yescharacteristic
109#394×C73C2211yescharacteristic
110#394×C73C2211yescharacteristic
111#394×C73C2211yescharacteristic
112#394×C73C2211yescharacteristic
113#393×C73C2211yescharacteristic
114#393×C73C2211yescharacteristic
115#393×C73C2211yescharacteristic
116#392×C73C2211yescharacteristic
117#391×C73C2211yescharacteristic
118#391×C73C2211yescharacteristic
119#391×C73C2211yescharacteristic
120#390×C73C2211yescharacteristic
121#390×C73C2211yescharacteristic
122#389×C73C2211yescharacteristic
123#389×C73C2211yescharacteristic
124#389×C73C2211yescharacteristic
125#389×C73C2211yescharacteristic
126#389×C73C2211yescharacteristic
127#389×C73C2211yescharacteristic
128#389×C73C2211yescharacteristic
129#389×C73C2211yescharacteristic
130#389×C73C2211yescharacteristic
131#389×C73C2211yescharacteristic
132#389×C73C2211yescharacteristic
133#389×C73C2211yescharacteristic
134#389×C73C2211yescharacteristic
135#389×C73C2211yescharacteristic
136#389×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#388×C73C2211yescharacteristic
146#388×C73C2211yescharacteristic
147#388×C73C2211yescharacteristic
148#388×C73C2211yescharacteristic
149#388×C73C2211yescharacteristic
150#388×C73C2211yescharacteristic
151#387×C73C2211yescharacteristic
152#387×C73C2211yescharacteristic
153#387×C73C2211yescharacteristic
154#387×C73C2211yescharacteristic
155#387×C73C2211yescharacteristic
156#387×C73C2211yescharacteristic
157#387×C73C2211yescharacteristic
158#387×C73C2211yescharacteristic
159#386×C73C2211yescharacteristic
160#386×C73C2211yescharacteristic
161#386×C73C2211yescharacteristic
162#386×C73C2211yescharacteristic
163#386×C73C2211yescharacteristic
164#386×C73C2211yescharacteristic
165#386×C73C2211yescharacteristic
166#385×C73C2211yescharacteristic
167#385×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#384×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×Q8×C73C2311yescharacteristic
191C22×Q8×C73C2311yescharacteristic
192C22×Q8×C73C2311yescharacteristic
193C22×D4×C73C2311yescharacteristic
194C22×D4×C73C2311yescharacteristic
195C22×D4×C73C2311yescharacteristic
196C22×D4×C73C2311yescharacteristic
197C22×D4×C73C2311yescharacteristic
198C22×D4×C73C2311yescharacteristic
199C23×C4×C73C2311yescharacteristic
200C23×C4×C73C2311yescharacteristic
201C23×C4×C73C2311yescharacteristic
202C23×C4×C73C2311yescharacteristic
203C23×C4×C73C2311yescharacteristic
204C23×C4×C73C2311yescharacteristic
205C23×C4×C73C2311yescharacteristic
206C23×C4×C73C2311yescharacteristic
207C4⋊Q8×C73—24no—
208C4⋊Q8×C73—42no—
209#126×C73—24no—
210#126×C73—24no—
211#126×C73—24no—
212#126×C73—24no—
213#125×C73—24no—
214#125×C73—24no—
215#124×C73—24no—
216#124×C73—24no—
217#124×C73—24no—
218#123×C73—24no—
219#123×C73—24no—
220#123×C73—24no—
221#123×C73—24no—
222#123×C73—24no—
223#123×C73—24no—
224#123×C73—42no—
225C22⋊Q8×C73—24no—
226C22⋊Q8×C73—24no—
227C22⋊Q8×C73—24no—
228C22⋊Q8×C73—24no—
229C22⋊Q8×C73—24no—
230C22⋊Q8×C73—24no—
231C22⋊Q8×C73—42no—
232#121×C73—24no—
233#121×C73—24no—
234#121×C73—42no—
235C4×Q8×C73—24no—
236C4×D4×C73—24no—
237C4×D4×C73D418yescomplemented
238#117×C73—24no—
239#117×C73—42no—
240C2×C4⋊C4×C73—24no—
241C2×C4⋊C4×C73C2311yescharacteristic
242C2×C4⋊C4×C73C2311yescharacteristic
243C2×C4⋊C4×C73C2311yescharacteristic
244C2×C4⋊C4×C73C2311yescharacteristic
245C2×C4⋊C4×C73C2311yescharacteristic
246C2×C4⋊C4×C73C2311yescharacteristic
247C2×C4⋊C4×C73C2311yescharacteristic
248C2×C4⋊C4×C73C2311yescharacteristic
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×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×C42×C73—42no—
328C2×C42×C73C2311yescharacteristic
329C2×C42×C73C2311yescharacteristic
330C2×C42×C73C2311yescharacteristic
331C2×C42×C73C2311yescharacteristic
332C2×C42×C73C2311yescharacteristic
333C2×C42×C73C2311yescharacteristic
334C2×C42×C73C2311yescharacteristic
335C2×C42×C73C2311yescharacteristic
336C2×C42×C73C2311yescharacteristic
337C2×C42×C73C2311yescharacteristic
338C2×C42×C73C2311yescharacteristic
339#95×C73C2311yescharacteristic
340#95×C73C2311yescharacteristic
341#95×C73C2311yescharacteristic
342#95×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
383C2×Q8×C73—22no—
384C2×Q8×C73—22no—
385C2×Q8×C73—22no—
386C2×Q8×C73—22no—
387C2×Q8×C73—41no—
388C2×Q8×C73—41no—
389C2×Q8×C73—41no—
390C2×Q8×C73—41no—
391C2×Q8×C73—41no—
392C2×Q8×C73—41no—
393C2×Q8×C73—41no—
394C2×Q8×C73—41no—
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×C73C2×D414yes—
413C22×C4×C73—22no—
414C22×C4×C73—22no—
415C22×C4×C73—22no—
416C22×C4×C73—22no—
417C22×C4×C73—22no—
418C22×C4×C73—22no—
419C22×C4×C73—22no—
420C22×C4×C73—41no—
421C22×C4×C73—41no—
422C22×C4×C73—41no—
423C22×C4×C73—41no—
424C22×C4×C73—41no—
425C22×C4×C73—41no—
426C22×C4×C73—41no—
427C22×C4×C73—41no—
428C22×C4×C73—41no—
429C22×C4×C73—41no—
430C22×C4×C73—41no—
431C22×C4×C73—41no—
432C22×C4×C73—41no—
433C22×C4×C73—41no—
434C22×C4×C73—41no—
435C22×C4×C73C2×D414yes—
436C22×C4×C73C2×D414yes—
437C22×C4×C73C2411yescharacteristic
438C22×C4×C73C2411yescharacteristic
439C22×C4×C73C2411yescharacteristic
440C22×C4×C73C2411yescharacteristic
441C22×C4×C73C2411yescharacteristic
442C22×C4×C73C2411yescharacteristic
443C22×C4×C73C2411yescharacteristic
444C22×C4×C73C2411yescharacteristic
445C22×C4×C73C2411yescharacteristic
446C22×C4×C73C2411yescharacteristic
447C22×C4×C73C2411yescharacteristic
448C22×C4×C73C2411yescharacteristic
449C22×C4×C73C2411yescharacteristic
450C22×C4×C73C2411yescharacteristic
451C22×C4×C73C2411yescharacteristic
452C22×C4×C73C2411yescharacteristic
453C22×C4×C73C2411yescharacteristic
454C22×C4×C73C2411yescharacteristic
455C22×C4×C73C2411yescharacteristic
456C22×C4×C73C2411yescharacteristic
457C22×C4×C73C2411yescharacteristic
458C22×C4×C73C2411yescharacteristic
459C22×C4×C73C2411yescharacteristic
460C22×C4×C73C2411yescharacteristic
461C22×C4×C73C2411yescharacteristic
462C22×C4×C73C2411yescharacteristic
463C22×C4×C73C2411yescharacteristic
464C4⋊C4×C73—22no—
465C4⋊C4×C73—22no—
466C4⋊C4×C73—22no—
467C4⋊C4×C73—22no—
468C4⋊C4×C73—22no—
469C4⋊C4×C73—22no—
470C4⋊C4×C73—22no—
471C4⋊C4×C73—22no—
472C4⋊C4×C73—22no—
473C4⋊C4×C73—22no—
474C4⋊C4×C73—22no—
475C4⋊C4×C73—22no—
476C4⋊C4×C73—22no—
477C4⋊C4×C73—22no—
478C4⋊C4×C73—22no—
479C4⋊C4×C73—22no—
480C4⋊C4×C73—22no—
481C4⋊C4×C73—22no—
482C4⋊C4×C73—22no—
483C4⋊C4×C73—22no—
484C4⋊C4×C73—22no—
485C4⋊C4×C73—22no—
486C4⋊C4×C73—22no—
487C4⋊C4×C73—22no—
488C4⋊C4×C73—22no—
489C4⋊C4×C73—22no—
490C4⋊C4×C73—22no—
491C4⋊C4×C73—22no—
492C4⋊C4×C73—41no—
493C4⋊C4×C73—41no—
494C4⋊C4×C73—41no—
495C4⋊C4×C73—41no—
496C4⋊C4×C73—41no—
497C4⋊C4×C73—41no—
498C4⋊C4×C73—41no—
499C4⋊C4×C73—41no—
500C4⋊C4×C73—41no—
501C4⋊C4×C73—41no—
502C4⋊C4×C73—41no—
503C4⋊C4×C73—41no—
504C4⋊C4×C73—41no—
505C4⋊C4×C73—41no—
506C4⋊C4×C73—41no—
507C4⋊C4×C73—41no—
508C4⋊C4×C73—41no—
509C4⋊C4×C73C2×D414yes—
510C22⋊C4×C73—22no—
511C22⋊C4×C73—22no—
512C22⋊C4×C73—22no—
513C22⋊C4×C73—22no—
514C22⋊C4×C73—22no—
515C22⋊C4×C73—22no—
516C22⋊C4×C73—22no—
517C22⋊C4×C73—22no—
518C22⋊C4×C73—22no—
519C22⋊C4×C73—22no—
520C22⋊C4×C73—22no—
521C22⋊C4×C73—22no—
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—41no—
536C22⋊C4×C73—41no—
537C22⋊C4×C73—41no—
538C22⋊C4×C73—41no—
539C22⋊C4×C73—41no—
540C22⋊C4×C73—41no—
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×C73C2×D414yes—
549C22⋊C4×C73C2×D414yes—
550C42×C73—22no—
551C42×C73—22no—
552C42×C73—22no—
553C42×C73—22no—
554C42×C73—22no—
555C42×C73—22no—
556C42×C73—41no—
557C42×C73—41no—
558C42×C73—41no—
559C42×C73—41no—
560C42×C73C2×D414yes—
561C23×C73—21no—
562C23×C73—21no—
563C23×C73—21no—
564C23×C73—21no—
565C23×C73—21no—
566C23×C73—21no—
567C23×C73—21no—
568C23×C73—21no—
569C23×C73—21no—
570C23×C73—21no—
571C23×C73—21no—
572C23×C73—21no—
573C23×C73—21no—
574C23×C73—21no—
575C23×C73—21no—
576C23×C73—21no—
577C23×C73—21no—
578C23×C73—21no—
579C23×C73—21no—
580C23×C73—21no—
581C23×C73—21no—
582C23×C73—21no—
583C23×C73—21no—
584C23×C73—21no—
585C23×C73—21no—
586C23×C73—21no—
587C23×C73C22×D412yes—
588C23×C73C22×D412yes—
589C23×C73C2511yescharacteristic
590Q8×C73—44no—
591Q8×C73—82no—
592Q8×C73—82no—
593Q8×C73—82no—
594D4×C73—44no—
595D4×C73—44no—
596D4×C73—82no—
597D4×C73—82no—
598D4×C73—82no—
599D4×C73—82no—
600C2×C4×C73—21no—
601C2×C4×C73—21no—
602C2×C4×C73—21no—
603C2×C4×C73—21no—
604C2×C4×C73—21no—
605C2×C4×C73—21no—
606C2×C4×C73—21no—
607C2×C4×C73—21no—
608C2×C4×C73—21no—
609C2×C4×C73—21no—
610C2×C4×C73—21no—
611C2×C4×C73—21no—
612C2×C4×C73—21no—
613C2×C4×C73—21no—
614C2×C4×C73—21no—
615C2×C4×C73—21no—
616C2×C4×C73—21no—
617C2×C4×C73—21no—
618C2×C4×C73—21no—
619C2×C4×C73—21no—
620C2×C4×C73—21no—
621C2×C4×C73—21no—
622C2×C4×C73—21no—
623C2×C4×C73—21no—
624C2×C4×C73—21no—
625C2×C4×C73—21no—
626C2×C4×C73—21no—
627C2×C4×C73—21no—
628C2×C4×C73—21no—
629C2×C4×C73—21no—
630C2×C4×C73—21no—
631C2×C4×C73—21no—
632C2×C4×C73—21no—
633C2×C4×C73—21no—
634C2×C4×C73—21no—
635C2×C4×C73—21no—
636C2×C4×C73—21no—
637C2×C4×C73—21no—
638C2×C4×C73—21no—
639C2×C4×C73—21no—
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—44no—
674C2×C4×C73—44no—
675C2×C4×C73—44no—
676C2×C4×C73—44no—
677C2×C4×C73—44no—
678C2×C4×C73—44no—
679C2×C4×C73—82no—
680C2×C4×C73—82no—
681C2×C4×C73C22×D412yes—
682C2×C4×C73C22×D412yes—
683C2×C4×C73C22×D412yes—
684C2×C4×C73C22×D412yes—
685C2×C4×C73C22×D412yes—
686C2×C4×C73H(5,𝔽2)12yes—
687C2×C4×C732−1+412yes—
688C2×C4×C732−1+412yes—
689C22×C73—22no—
690C22×C73—22no—
691C22×C73—22no—
692C22×C73—22no—
693C22×C73—22no—
694C22×C73—22no—
695C22×C73—41no—
696C22×C73—41no—
697C22×C73—41no—
698C22×C73—41no—
699C22×C73—41no—
700C22×C73—41no—
701C22×C73—41no—
702C22×C73—41no—
703C22×C73—41no—
704C22×C73—41no—
705C22×C73—41no—
706C22×C73—41no—
707C22×C73—41no—
708C22×C73—41no—
709C22×C73—41no—
710C22×C73—41no—
711C22×C73—41no—
712C22×C73—41no—
713C22×C73—41no—
714C22×C73—41no—
715C22×C73—41no—
716C22×C73—41no—
717C22×C73C23×D411yescharacteristic
718C22×C73C2×H(5,𝔽2)11yescharacteristic
719C22×C73C2×2−1+411yescharacteristic
720C22×C73C2×2−1+411yescharacteristic
721C22×C73#58511yescharacteristic
722C22×C73#58511yescharacteristic
723C22×C73#58511yescharacteristic
724C4×C73—22no—
725C4×C73—22no—
726C4×C73—22no—
727C4×C73—22no—
728C4×C73—22no—
729C4×C73—22no—
730C4×C73—22no—
731C4×C73—22no—
732C4×C73—41no—
733C4×C73—41no—
734C4×C73—41no—
735C4×C73—41no—
736C4×C73—41no—
737C4×C73—41no—
738C4×C73—41no—
739C4×C73—41no—
740C4×C73—41no—
741C4×C73—41no—
742C4×C73—41no—
743C4×C73—41no—
744C4×C73—41no—
745C4×C73—41no—
746C4×C73—41no—
747C4×C73—41no—
748C4×C73—41no—
749C4×C73—41no—
750C4×C73—41no—
751#36743C7311yesmaximal, characteristic, direct product factor, Sylow
752C2×C73—42no—
753C2×C73—42no—
754C2×C73—81no—
755C2×C73—81no—
756C2×C73#344911yescharacteristic
757C2×C73#349611yescharacteristic
758C2×C73#349911yescharacteristic
759C2×C73#353511yescharacteristic
760C2×C73#354111yescharacteristic
761C2×C73#355711yescharacteristic
762C2×C73#356511yescharacteristic
763C2×#542C2×C7311yescharacteristic, complemented
764C2×#539C2×C7311yescharacteristic, complemented
765#2857C2×C7311yescharacteristic, complemented
766#2854C2×C7311yescharacteristic, complemented
767#2722C2×C7311yescharacteristic, complemented
768#2720C2×C7311yescharacteristic, complemented
769#2718C2×C7311yescharacteristic, complemented
770#2717C2×C7311yescharacteristic, complemented
771#2715C2×C7311yescharacteristic, complemented
772#2713C2×C7311yescharacteristic, complemented
773#2710C2×C7311yescharacteristic, complemented
774#2708C2×C7311yescharacteristic, complemented
775#2695C2×C7311yescharacteristic, complemented
776#2692C2×C7311yescharacteristic, complemented
777#2689C2×C7311yescharacteristic, complemented
778#2686C2×C7311yescharacteristic, complemented
779#2677C2×C7311yescharacteristic, complemented
780#2674C2×C7311yescharacteristic, complemented
781#2672C2×C7311yescharacteristic, complemented
782#2671C2×C7311yescharacteristic
783#2663C2×C7311yescharacteristic, complemented
784#2663C2×C7311yescharacteristic, complemented
785#2611C2×C7311yescharacteristic, complemented
786#2604C2×C7311yescharacteristic, complemented
787#2602C2×C7311yescharacteristic, complemented
788#2601C2×C7311yescharacteristic, complemented
789#2584C2×C7311yescharacteristic, complemented
790#2583C2×C7311yescharacteristic, complemented
791#2415C2×C7311yescharacteristic, complemented
792#2413C2×C7311yescharacteristic, complemented
793#2290C2×C7311yescharacteristic, complemented
794C73#3674311yescharacteristic, direct product factor, Sylow
795#542—28no—
796#539—28no—
797C2×C4⋊Q8C22×C7311yescharacteristic
798C2×C4⋊Q8C22×C7311yescharacteristic
799C2×#126C22×C7311yescharacteristic
800C2×#126C22×C7311yescharacteristic
801C2×#126C22×C7311yescharacteristic
802C2×#126C22×C7311yescharacteristic
803C2×#125C22×C7311yescharacteristic
804C2×#125C22×C7311yescharacteristic
805C2×#124C22×C7311yescharacteristic
806C2×#124C22×C7311yescharacteristic
807C2×#124C22×C7311yescharacteristic
808C2×#123C22×C7311yescharacteristic
809C2×#123C22×C7311yescharacteristic
810C2×#123C22×C7311yescharacteristic
811C2×#123C22×C7311yescharacteristic
812C2×#123C22×C7311yescharacteristic
813C2×#123C22×C7311yescharacteristic
814C2×#123C22×C7311yescharacteristic
815C2×C22⋊Q8C22×C7311yescharacteristic
816C2×C22⋊Q8C22×C7311yescharacteristic
817C2×C22⋊Q8C22×C7311yescharacteristic
818C2×C22⋊Q8C22×C7311yescharacteristic
819C2×C22⋊Q8C22×C7311yescharacteristic
820C2×C22⋊Q8C22×C7311yescharacteristic
821C2×C22⋊Q8C22×C7311yescharacteristic
822C2×#121C22×C7311yescharacteristic
823C2×#121C22×C7311yescharacteristic
824C2×#121C22×C7311yescharacteristic
825C2×C4×Q8C22×C7311yescharacteristic
826C2×C4×D4C22×C7311yescharacteristic
827C2×C4×D4C22×C7311yescharacteristic
828C2×#117C22×C7311yescharacteristic
829C2×#117C22×C7311yescharacteristic
830C22×C4⋊C4C22×C7311yescharacteristic
831C22×C42C22×C7311yescharacteristic
832#400C22×C7311yescharacteristic
833#400C22×C7311yescharacteristic
834#400C22×C7311yescharacteristic
835#400C22×C7311yescharacteristic
836#399C22×C7311yescharacteristic
837#399C22×C7311yescharacteristic
838#399C22×C7311yescharacteristic
839#399C22×C7311yescharacteristic
840#398C22×C7311yescharacteristic
841#398C22×C7311yescharacteristic
842#398C22×C7311yescharacteristic
843#398C22×C7311yescharacteristic
844#398C22×C7311yescharacteristic
845#398C22×C7311yescharacteristic
846#398C22×C7311yescharacteristic
847#398C22×C7311yescharacteristic
848#397C22×C7311yescharacteristic
849#397C22×C7311yescharacteristic
850#397C22×C7311yescharacteristic
851#397C22×C7311yescharacteristic
852#397C22×C7311yescharacteristic
853#397C22×C7311yescharacteristic
854#397C22×C7311yescharacteristic
855#397C22×C7311yescharacteristic
856#396C22×C7311yescharacteristic
857#396C22×C7311yescharacteristic
858#396C22×C7311yescharacteristic
859#396C22×C7311yescharacteristic
860#395C22×C7311yescharacteristic
861#395C22×C7311yescharacteristic
862#395C22×C7311yescharacteristic
863#395C22×C7311yescharacteristic
864#395C22×C7311yescharacteristic
865#395C22×C7311yescharacteristic
866#395C22×C7311yescharacteristic
867#394C22×C7311yescharacteristic
868#394C22×C7311yescharacteristic
869#394C22×C7311yescharacteristic
870#394C22×C7311yescharacteristic
871#394C22×C7311yescharacteristic
872#394C22×C7311yescharacteristic
873#394C22×C7311yescharacteristic
874#394C22×C7311yescharacteristic
875#394C22×C7311yescharacteristic
876#393C22×C7311yescharacteristic
877#393C22×C7311yescharacteristic
878#393C22×C7311yescharacteristic
879#392C22×C7311yescharacteristic
880#391C22×C7311yescharacteristic
881#391C22×C7311yescharacteristic
882#391C22×C7311yescharacteristic
883#390C22×C7311yescharacteristic
884#390C22×C7311yescharacteristic
885#389C22×C7311yescharacteristic
886#389C22×C7311yescharacteristic
887#389C22×C7311yescharacteristic
888#389C22×C7311yescharacteristic
889#389C22×C7311yescharacteristic
890#389C22×C7311yescharacteristic
891#389C22×C7311yescharacteristic
892#389C22×C7311yescharacteristic
893#389C22×C7311yescharacteristic
894#389C22×C7311yescharacteristic
895#389C22×C7311yescharacteristic
896#389C22×C7311yescharacteristic
897#389C22×C7311yescharacteristic
898#389C22×C7311yescharacteristic
899#389C22×C7311yescharacteristic
900#388C22×C7311yescharacteristic
901#388C22×C7311yescharacteristic
902#388C22×C7311yescharacteristic
903#388C22×C7311yescharacteristic
904#388C22×C7311yescharacteristic
905#388C22×C7311yescharacteristic
906#388C22×C7311yescharacteristic
907#388C22×C7311yescharacteristic
908#388C22×C7311yescharacteristic
909#388C22×C7311yescharacteristic
910#388C22×C7311yescharacteristic
911#388C22×C7311yescharacteristic
912#388C22×C7311yescharacteristic
913#388C22×C7311yescharacteristic
914#387C22×C7311yescharacteristic
915#387C22×C7311yescharacteristic
916#387C22×C7311yescharacteristic
917#387C22×C7311yescharacteristic
918#387C22×C7311yescharacteristic
919#387C22×C7311yescharacteristic
920#387C22×C7311yescharacteristic
921#387C22×C7311yescharacteristic
922#386C22×C7311yescharacteristic
923#386C22×C7311yescharacteristic
924#386C22×C7311yescharacteristic
925#386C22×C7311yescharacteristic
926#386C22×C7311yescharacteristic
927#386C22×C7311yescharacteristic
928#386C22×C7311yescharacteristic
929#385C22×C7311yescharacteristic
930#385C22×C7311yescharacteristic
931#385C22×C7311yescharacteristic
932#385C22×C7311yescharacteristic
933#385C22×C7311yescharacteristic
934#385C22×C7311yescharacteristic
935#385C22×C7311yescharacteristic
936#385C22×C7311yescharacteristic
937#385C22×C7311yescharacteristic
938#385C22×C7311yescharacteristic
939#385C22×C7311yescharacteristic
940#384C22×C7311yescharacteristic
941#381C22×C7311yescharacteristic
942#380C22×C7311yescharacteristic
943#380C22×C7311yescharacteristic
944#380C22×C7311yescharacteristic
945#380C22×C7311yescharacteristic
946#380C22×C7311yescharacteristic
947#380C22×C7311yescharacteristic
948C4×C4⋊C4C22×C7311yescharacteristic
949C4×C22⋊C4C22×C7311yescharacteristic
950C4×C22⋊C4C22×C7311yescharacteristic
951#376C22×C7311yescharacteristic
952C22×Q8C23×C7311yescharacteristic
953C22×Q8C23×C7311yescharacteristic
954C22×Q8C23×C7311yescharacteristic
955C22×Q8C23×C7311yescharacteristic
956C22×D4C23×C7311yescharacteristic
957C22×D4C23×C7311yescharacteristic
958C22×D4C23×C7311yescharacteristic
959C22×D4C23×C7311yescharacteristic
960C22×D4C23×C7311yescharacteristic
961C22×D4C23×C7311yescharacteristic
962C23×C4C23×C7311yescharacteristic
963C23×C4C23×C7311yescharacteristic
964C23×C4C23×C7311yescharacteristic
965C23×C4C23×C7311yescharacteristic
966C23×C4C23×C7311yescharacteristic
967C23×C4C23×C7311yescharacteristic
968C23×C4C23×C7311yescharacteristic
969C23×C4C23×C7311yescharacteristic
970C4⋊Q8—24no—
971C4⋊Q8—42no—
972#126—24no—
973#126—24no—
974#126—24no—
975#126—24no—
976#125—24no—
977#125—24no—
978#124—24no—
979#124—24no—
980#124—24no—
981#123—24no—
982#123—24no—
983#123—24no—
984#123—24no—
985#123—24no—
986#123—24no—
987#123—42no—
988C22⋊Q8—24no—
989C22⋊Q8—24no—
990C22⋊Q8—24no—
991C22⋊Q8—24no—
992C22⋊Q8—24no—
993C22⋊Q8—24no—
994C22⋊Q8—42no—
995#121—24no—
996#121—24no—
997#121—42no—
998C4×Q8—24no—
999C4×D4—24no—
1000C4×D4D4×C7318yescomplemented
1001#117—24no—
1002#117—42no—
1003C2×C4⋊C4—24no—
1004C2×C4⋊C4C23×C7311yescharacteristic
1005C2×C4⋊C4C23×C7311yescharacteristic
1006C2×C4⋊C4C23×C7311yescharacteristic
1007C2×C4⋊C4C23×C7311yescharacteristic
1008C2×C4⋊C4C23×C7311yescharacteristic
1009C2×C4⋊C4C23×C7311yescharacteristic
1010C2×C4⋊C4C23×C7311yescharacteristic
1011C2×C4⋊C4C23×C7311yescharacteristic
1012C2×C4⋊C4C23×C7311yescharacteristic
1013C2×C4⋊C4C23×C7311yescharacteristic
1014C2×C4⋊C4C23×C7311yescharacteristic
1015C2×C4⋊C4C23×C7311yescharacteristic
1016C2×C4⋊C4C23×C7311yescharacteristic
1017C2×C4⋊C4C23×C7311yescharacteristic
1018C2×C4⋊C4C23×C7311yescharacteristic
1019C2×C4⋊C4C23×C7311yescharacteristic
1020C2×C4⋊C4C23×C7311yescharacteristic
1021C2×C4⋊C4C23×C7311yescharacteristic
1022C2×C4⋊C4C23×C7311yescharacteristic
1023C2×C4⋊C4C23×C7311yescharacteristic
1024C2×C4⋊C4C23×C7311yescharacteristic
1025C2×C4⋊C4C23×C7311yescharacteristic
1026C2×C4⋊C4C23×C7311yescharacteristic
1027C2×C4⋊C4C23×C7311yescharacteristic
1028C2×C4⋊C4C23×C7311yescharacteristic
1029C2×C4⋊C4C23×C7311yescharacteristic
1030C2×C4⋊C4C23×C7311yescharacteristic
1031C2×C4⋊C4C23×C7311yescharacteristic
1032C2×C4⋊C4C23×C7311yescharacteristic
1033C2×C4⋊C4C23×C7311yescharacteristic
1034C2×C4⋊C4C23×C7311yescharacteristic
1035C2×C4⋊C4C23×C7311yescharacteristic
1036C2×C4⋊C4C23×C7311yescharacteristic
1037C2×C4⋊C4C23×C7311yescharacteristic
1038C2×C4⋊C4C23×C7311yescharacteristic
1039C2×C4⋊C4C23×C7311yescharacteristic
1040C2×C4⋊C4C23×C7311yescharacteristic
1041C2×C4⋊C4C23×C7311yescharacteristic
1042C2×C4⋊C4C23×C7311yescharacteristic
1043C2×C4⋊C4C23×C7311yescharacteristic
1044C2×C4⋊C4C23×C7311yescharacteristic
1045C2×C4⋊C4C23×C7311yescharacteristic
1046C2×C4⋊C4C23×C7311yescharacteristic
1047C2×C4⋊C4C23×C7311yescharacteristic
1048C2×C4⋊C4C23×C7311yescharacteristic
1049C2×C4⋊C4C23×C7311yescharacteristic
1050C2×C22⋊C4C23×C7311yescharacteristic
1051C2×C22⋊C4C23×C7311yescharacteristic
1052C2×C22⋊C4C23×C7311yescharacteristic
1053C2×C22⋊C4C23×C7311yescharacteristic
1054C2×C22⋊C4C23×C7311yescharacteristic
1055C2×C22⋊C4C23×C7311yescharacteristic
1056C2×C22⋊C4C23×C7311yescharacteristic
1057C2×C22⋊C4C23×C7311yescharacteristic
1058C2×C22⋊C4C23×C7311yescharacteristic
1059C2×C22⋊C4C23×C7311yescharacteristic
1060C2×C22⋊C4C23×C7311yescharacteristic
1061C2×C22⋊C4C23×C7311yescharacteristic
1062C2×C22⋊C4C23×C7311yescharacteristic
1063C2×C22⋊C4C23×C7311yescharacteristic
1064C2×C22⋊C4C23×C7311yescharacteristic
1065C2×C22⋊C4C23×C7311yescharacteristic
1066C2×C22⋊C4C23×C7311yescharacteristic
1067C2×C22⋊C4C23×C7311yescharacteristic
1068C2×C22⋊C4C23×C7311yescharacteristic
1069C2×C22⋊C4C23×C7311yescharacteristic
1070C2×C22⋊C4C23×C7311yescharacteristic
1071C2×C22⋊C4C23×C7311yescharacteristic
1072C2×C22⋊C4C23×C7311yescharacteristic
1073C2×C22⋊C4C23×C7311yescharacteristic
1074C2×C22⋊C4C23×C7311yescharacteristic
1075C2×C22⋊C4C23×C7311yescharacteristic
1076C2×C22⋊C4C23×C7311yescharacteristic
1077C2×C22⋊C4C23×C7311yescharacteristic
1078C2×C22⋊C4C23×C7311yescharacteristic
1079C2×C22⋊C4C23×C7311yescharacteristic
1080C2×C22⋊C4C23×C7311yescharacteristic
1081C2×C22⋊C4C23×C7311yescharacteristic
1082C2×C22⋊C4C23×C7311yescharacteristic
1083C2×C22⋊C4C23×C7311yescharacteristic
1084C2×C22⋊C4C23×C7311yescharacteristic
1085C2×C22⋊C4C23×C7311yescharacteristic
1086C2×C22⋊C4C23×C7311yescharacteristic
1087C2×C22⋊C4C23×C7311yescharacteristic
1088C2×C22⋊C4C23×C7311yescharacteristic
1089C2×C22⋊C4C23×C7311yescharacteristic
1090C2×C42—42no—
1091C2×C42C23×C7311yescharacteristic
1092C2×C42C23×C7311yescharacteristic
1093C2×C42C23×C7311yescharacteristic
1094C2×C42C23×C7311yescharacteristic
1095C2×C42C23×C7311yescharacteristic
1096C2×C42C23×C7311yescharacteristic
1097C2×C42C23×C7311yescharacteristic
1098C2×C42C23×C7311yescharacteristic
1099C2×C42C23×C7311yescharacteristic
1100C2×C42C23×C7311yescharacteristic
1101C2×C42C23×C7311yescharacteristic
1102#95C23×C7311yescharacteristic
1103#95C23×C7311yescharacteristic
1104#95C23×C7311yescharacteristic
1105#95C23×C7311yescharacteristic
1106#95C23×C7311yescharacteristic
1107#95C23×C7311yescharacteristic
1108#95C23×C7311yescharacteristic
1109#95C23×C7311yescharacteristic
1110#95C23×C7311yescharacteristic
1111#95C23×C7311yescharacteristic
1112#95C23×C7311yescharacteristic
1113#95C23×C7311yescharacteristic
1114#95C23×C7311yescharacteristic
1115#95C23×C7311yescharacteristic
1116#95C23×C7311yescharacteristic
1117#95C23×C7311yescharacteristic
1118#95C23×C7311yescharacteristic
1119#95C23×C7311yescharacteristic
1120#95C23×C7311yescharacteristic
1121#95C23×C7311yescharacteristic
1122#95C23×C7311yescharacteristic
1123#95C23×C7311yescharacteristic
1124#95C23×C7311yescharacteristic
1125#95C23×C7311yescharacteristic
1126#95C23×C7311yescharacteristic
1127#95C23×C7311yescharacteristic
1128#95C23×C7311yescharacteristic
1129#95C23×C7311yescharacteristic
1130#95C23×C7311yescharacteristic
1131#95C23×C7311yescharacteristic
1132#95C23×C7311yescharacteristic
1133#95C23×C7311yescharacteristic
1134#95C23×C7311yescharacteristic
1135#95C23×C7311yescharacteristic
1136#95C23×C7311yescharacteristic
1137#95C23×C7311yescharacteristic
1138#95C23×C7311yescharacteristic
1139#95C23×C7311yescharacteristic
1140#95C23×C7311yescharacteristic
1141#95C23×C7311yescharacteristic
1142C24C24×C7311yescharacteristic
1143C24C24×C7311yescharacteristic
1144C24C24×C7311yescharacteristic
1145C24C24×C7311yescharacteristic
1146C2×Q8—22no—
1147C2×Q8—22no—
1148C2×Q8—22no—
1149C2×Q8—22no—
1150C2×Q8—41no—
1151C2×Q8—41no—
1152C2×Q8—41no—
1153C2×Q8—41no—
1154C2×Q8—41no—
1155C2×Q8—41no—
1156C2×Q8—41no—
1157C2×Q8—41no—
1158C2×D4—22no—
1159C2×D4—22no—
1160C2×D4—22no—
1161C2×D4—22no—
1162C2×D4—22no—
1163C2×D4—41no—
1164C2×D4—41no—
1165C2×D4—41no—
1166C2×D4—41no—
1167C2×D4—41no—
1168C2×D4—41no—
1169C2×D4—41no—
1170C2×D4—41no—
1171C2×D4—41no—
1172C2×D4—41no—
1173C2×D4—41no—
1174C2×D4—41no—
1175C2×D4C2×D4×C7314yes—
1176C22×C4—22no—
1177C22×C4—22no—
1178C22×C4—22no—
1179C22×C4—22no—
1180C22×C4—22no—
1181C22×C4—22no—
1182C22×C4—22no—
1183C22×C4—41no—
1184C22×C4—41no—
1185C22×C4—41no—
1186C22×C4—41no—
1187C22×C4—41no—
1188C22×C4—41no—
1189C22×C4—41no—
1190C22×C4—41no—
1191C22×C4—41no—
1192C22×C4—41no—
1193C22×C4—41no—
1194C22×C4—41no—
1195C22×C4—41no—
1196C22×C4—41no—
1197C22×C4—41no—
1198C22×C4C2×D4×C7314yes—
1199C22×C4C2×D4×C7314yes—
1200C22×C4C24×C7311yescharacteristic
1201C22×C4C24×C7311yescharacteristic
1202C22×C4C24×C7311yescharacteristic
1203C22×C4C24×C7311yescharacteristic
1204C22×C4C24×C7311yescharacteristic
1205C22×C4C24×C7311yescharacteristic
1206C22×C4C24×C7311yescharacteristic
1207C22×C4C24×C7311yescharacteristic
1208C22×C4C24×C7311yescharacteristic
1209C22×C4C24×C7311yescharacteristic
1210C22×C4C24×C7311yescharacteristic
1211C22×C4C24×C7311yescharacteristic
1212C22×C4C24×C7311yescharacteristic
1213C22×C4C24×C7311yescharacteristic
1214C22×C4C24×C7311yescharacteristic
1215C22×C4C24×C7311yescharacteristic
1216C22×C4C24×C7311yescharacteristic
1217C22×C4C24×C7311yescharacteristic
1218C22×C4C24×C7311yescharacteristic
1219C22×C4C24×C7311yescharacteristic
1220C22×C4C24×C7311yescharacteristic
1221C22×C4C24×C7311yescharacteristic
1222C22×C4C24×C7311yescharacteristic
1223C22×C4C24×C7311yescharacteristic
1224C22×C4C24×C7311yescharacteristic
1225C22×C4C24×C7311yescharacteristic
1226C22×C4C24×C7311yescharacteristic
1227C4⋊C4—22no—
1228C4⋊C4—22no—
1229C4⋊C4—22no—
1230C4⋊C4—22no—
1231C4⋊C4—22no—
1232C4⋊C4—22no—
1233C4⋊C4—22no—
1234C4⋊C4—22no—
1235C4⋊C4—22no—
1236C4⋊C4—22no—
1237C4⋊C4—22no—
1238C4⋊C4—22no—
1239C4⋊C4—22no—
1240C4⋊C4—22no—
1241C4⋊C4—22no—
1242C4⋊C4—22no—
1243C4⋊C4—22no—
1244C4⋊C4—22no—
1245C4⋊C4—22no—
1246C4⋊C4—22no—
1247C4⋊C4—22no—
1248C4⋊C4—22no—
1249C4⋊C4—22no—
1250C4⋊C4—22no—
1251C4⋊C4—22no—
1252C4⋊C4—22no—
1253C4⋊C4—22no—
1254C4⋊C4—22no—
1255C4⋊C4—41no—
1256C4⋊C4—41no—
1257C4⋊C4—41no—
1258C4⋊C4—41no—
1259C4⋊C4—41no—
1260C4⋊C4—41no—
1261C4⋊C4—41no—
1262C4⋊C4—41no—
1263C4⋊C4—41no—
1264C4⋊C4—41no—
1265C4⋊C4—41no—
1266C4⋊C4—41no—
1267C4⋊C4—41no—
1268C4⋊C4—41no—
1269C4⋊C4—41no—
1270C4⋊C4—41no—
1271C4⋊C4—41no—
1272C4⋊C4C2×D4×C7314yes—
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—22no—
1287C22⋊C4—22no—
1288C22⋊C4—22no—
1289C22⋊C4—22no—
1290C22⋊C4—22no—
1291C22⋊C4—22no—
1292C22⋊C4—22no—
1293C22⋊C4—22no—
1294C22⋊C4—22no—
1295C22⋊C4—22no—
1296C22⋊C4—22no—
1297C22⋊C4—22no—
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⋊C4—41no—
1308C22⋊C4—41no—
1309C22⋊C4—41no—
1310C22⋊C4—41no—
1311C22⋊C4C2×D4×C7314yes—
1312C22⋊C4C2×D4×C7314yes—
1313C42—22no—
1314C42—22no—
1315C42—22no—
1316C42—22no—
1317C42—22no—
1318C42—22no—
1319C42—41no—
1320C42—41no—
1321C42—41no—
1322C42—41no—
1323C42C2×D4×C7314yes—
1324C23—21no—
1325C23—21no—
1326C23—21no—
1327C23—21no—
1328C23—21no—
1329C23—21no—
1330C23—21no—
1331C23—21no—
1332C23—21no—
1333C23—21no—
1334C23—21no—
1335C23—21no—
1336C23—21no—
1337C23—21no—
1338C23—21no—
1339C23—21no—
1340C23—21no—
1341C23—21no—
1342C23—21no—
1343C23—21no—
1344C23—21no—
1345C23—21no—
1346C23—21no—
1347C23—21no—
1348C23—21no—
1349C23—21no—
1350C23C22×D4×C7312yes—
1351C23C22×D4×C7312yes—
1352C23C25×C7311yescharacteristic
1353Q8—44no—
1354Q8—82no—
1355Q8—82no—
1356Q8—82no—
1357D4—44no—
1358D4—44no—
1359D4—82no—
1360D4—82no—
1361D4—82no—
1362D4—82no—
1363C2×C4—21no—
1364C2×C4—21no—
1365C2×C4—21no—
1366C2×C4—21no—
1367C2×C4—21no—
1368C2×C4—21no—
1369C2×C4—21no—
1370C2×C4—21no—
1371C2×C4—21no—
1372C2×C4—21no—
1373C2×C4—21no—
1374C2×C4—21no—
1375C2×C4—21no—
1376C2×C4—21no—
1377C2×C4—21no—
1378C2×C4—21no—
1379C2×C4—21no—
1380C2×C4—21no—
1381C2×C4—21no—
1382C2×C4—21no—
1383C2×C4—21no—
1384C2×C4—21no—
1385C2×C4—21no—
1386C2×C4—21no—
1387C2×C4—21no—
1388C2×C4—21no—
1389C2×C4—21no—
1390C2×C4—21no—
1391C2×C4—21no—
1392C2×C4—21no—
1393C2×C4—21no—
1394C2×C4—21no—
1395C2×C4—21no—
1396C2×C4—21no—
1397C2×C4—21no—
1398C2×C4—21no—
1399C2×C4—21no—
1400C2×C4—21no—
1401C2×C4—21no—
1402C2×C4—21no—
1403C2×C4—21no—
1404C2×C4—21no—
1405C2×C4—21no—
1406C2×C4—21no—
1407C2×C4—21no—
1408C2×C4—21no—
1409C2×C4—21no—
1410C2×C4—21no—
1411C2×C4—21no—
1412C2×C4—21no—
1413C2×C4—21no—
1414C2×C4—21no—
1415C2×C4—21no—
1416C2×C4—21no—
1417C2×C4—21no—
1418C2×C4—21no—
1419C2×C4—21no—
1420C2×C4—21no—
1421C2×C4—21no—
1422C2×C4—21no—
1423C2×C4—21no—
1424C2×C4—21no—
1425C2×C4—21no—
1426C2×C4—21no—
1427C2×C4—21no—
1428C2×C4—21no—
1429C2×C4—21no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—44no—
1437C2×C4—44no—
1438C2×C4—44no—
1439C2×C4—44no—
1440C2×C4—44no—
1441C2×C4—44no—
1442C2×C4—82no—
1443C2×C4—82no—
1444C2×C4C22×D4×C7312yes—
1445C2×C4C22×D4×C7312yes—
1446C2×C4C22×D4×C7312yes—
1447C2×C4C22×D4×C7312yes—
1448C2×C4C22×D4×C7312yes—
1449C2×C4H(5,𝔽2)×C7312yes—
1450C2×C42−1+4×C7312yes—
1451C2×C42−1+4×C7312yes—
1452C22—22no—
1453C22—22no—
1454C22—22no—
1455C22—22no—
1456C22—22no—
1457C22—22no—
1458C22—41no—
1459C22—41no—
1460C22—41no—
1461C22—41no—
1462C22—41no—
1463C22—41no—
1464C22—41no—
1465C22—41no—
1466C22—41no—
1467C22—41no—
1468C22—41no—
1469C22—41no—
1470C22—41no—
1471C22—41no—
1472C22—41no—
1473C22—41no—
1474C22—41no—
1475C22—41no—
1476C22—41no—
1477C22—41no—
1478C22—41no—
1479C22—41no—
1480C22C23×D4×C7311yescharacteristic
1481C22C2×H(5,𝔽2)×C7311yescharacteristic
1482C22C2×2−1+4×C7311yescharacteristic
1483C22C2×2−1+4×C7311yescharacteristic
1484C22#585×C7311yescharacteristic
1485C22#585×C7311yescharacteristic
1486C22#585×C7311yescharacteristic
1487C4—22no—
1488C4—22no—
1489C4—22no—
1490C4—22no—
1491C4—22no—
1492C4—22no—
1493C4—22no—
1494C4—22no—
1495C4—41no—
1496C4—41no—
1497C4—41no—
1498C4—41no—
1499C4—41no—
1500C4—41no—
1501C4—41no—
1502C4—41no—
1503C4—41no—
1504C4—41no—
1505C4—41no—
1506C4—41no—
1507C4—41no—
1508C4—41no—
1509C4—41no—
1510C4—41no—
1511C4—41no—
1512C4—41no—
1513C4—41no—
1514C2—42no—
1515C2—42no—
1516C2—81no—
1517C2—81no—
1518C2C73×#344911yescharacteristic
1519C2C73×#349611yescharacteristic
1520C2C73×#349911yescharacteristic
1521C2C73×#353511yescharacteristic
1522C2C73×#354111yescharacteristic
1523C2C73×#355711yescharacteristic
1524C2C73×#356511yescharacteristic
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC73×#2671C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#542×C73C2semidirect
2. C2×#539×C73C2semidirect
3. C73×#2857C2semidirect
4. C73×#2854C2semidirect
5. C73×#2722C2semidirect
6. C73×#2720C2semidirect
7. C73×#2718C2semidirect
8. C73×#2717C2semidirect
9. C73×#2715C2semidirect
10. C73×#2713C2semidirect
11. C73×#2710C2semidirect
12. C73×#2708C2semidirect
13. C73×#2695C2semidirect
14. C73×#2692C2semidirect
15. C73×#2689C2semidirect
16. C73×#2686C2semidirect
17. C73×#2677C2semidirect
18. C73×#2674C2semidirect
19. C73×#2672C2semidirect
21. C73×#2663C2semidirect
22. C73×#2663C2semidirect
23. C73×#2611C2semidirect
24. C73×#2604C2semidirect
25. C73×#2602C2semidirect
26. C73×#2601C2semidirect
27. C73×#2584C2semidirect
28. C73×#2583C2semidirect
29. C73×#2415C2semidirect
30. C73×#2413C2semidirect
31. C73×#2290C2semidirect
237. C4×D4×C73D4semidirect
751. #36743C73direct (N × H)
763. C2×#542C2×C73semidirect
764. C2×#539C2×C73semidirect
765. #2857C2×C73semidirect
766. #2854C2×C73semidirect
767. #2722C2×C73semidirect
768. #2720C2×C73semidirect
769. #2718C2×C73semidirect
770. #2717C2×C73semidirect
771. #2715C2×C73semidirect
772. #2713C2×C73semidirect
773. #2710C2×C73semidirect
774. #2708C2×C73semidirect
775. #2695C2×C73semidirect
776. #2692C2×C73semidirect
777. #2689C2×C73semidirect
778. #2686C2×C73semidirect
779. #2677C2×C73semidirect
780. #2674C2×C73semidirect
781. #2672C2×C73semidirect
783. #2663C2×C73semidirect
784. #2663C2×C73semidirect
785. #2611C2×C73semidirect
786. #2604C2×C73semidirect
787. #2602C2×C73semidirect
788. #2601C2×C73semidirect
789. #2584C2×C73semidirect
790. #2583C2×C73semidirect
791. #2415C2×C73semidirect
792. #2413C2×C73semidirect
793. #2290C2×C73semidirect
794. C73#36743direct (N × H)
1000. C4×D4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#542×C732
C2×#539×C732
C73×#28572
C73×#28542
C73×#27222
C73×#27202
C73×#27182
C73×#27172
C73×#27152
C73×#27132
C73×#27102
C73×#27082
C73×#26952
C73×#26922
C73×#26892
C73×#26862
C73×#26772
C73×#26742
C73×#26722
C73×#26712
C73×#26632
C73×#26112
C73×#26042
C73×#26022
C73×#26012
C73×#25842
C73×#25832
C73×#24152
C73×#24132
C73×#22902
#3674373