Finite Group Databasebeta

← #33096060

Subgroups — #33096060

Order 18688.

874 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22612417C211yesmaximal, characteristic
2#22610546C211yesmaximal, characteristic, complemented
3#22610543C211yesmaximal, characteristic, complemented
4#22610542C211yesmaximal, characteristic, complemented
5#22610541C211yesmaximal, characteristic, complemented
6#22610540C211yesmaximal, characteristic, complemented
7#22610538C211yesmaximal, characteristic, complemented
8#22610537C211yesmaximal, characteristic, complemented
9#22609910C211yesmaximal, characteristic, complemented
10#22609908C211yesmaximal, characteristic, complemented
11#22609842C211yesmaximal, characteristic
12#22609842C211yesmaximal, characteristic
13#22609698C211yesmaximal, characteristic, complemented
14#22609696C211yesmaximal, characteristic, complemented
15C73×#1923C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×#14556548C2211yescharacteristic
18C2×C42×D73C2211yescharacteristic
19C2×C4⋊#10596831C2211yescharacteristic
20C2×#14556520C2211yescharacteristic
21C2×#14556520C2211yescharacteristic
22C2×C22⋊#10596831C2211yescharacteristic
23C2×C22⋊#10596831C2211yescharacteristic
24C2×#14556503C2211yescharacteristic
25C2×#14556503C2211yescharacteristic
26C2×#14556503C2211yescharacteristic
27C2×#14556503C2211yescharacteristic
28C2×#14556503C2211yescharacteristic
29C2×#14556503C2211yescharacteristic
30C2×#14556503C2211yescharacteristic
31C2×#14556503C2211yescharacteristic
32C2×#14556502C2211yescharacteristic
33C2×#14556501C2211yescharacteristic
34C2×C8×Dic73C2211yescharacteristic
35#17988491C411yescharacteristic
36#17988491C411yescharacteristic
37#17988487C411yescharacteristic
38#17988487C411yescharacteristic
39#17988465C411yescharacteristic
40#17988465C411yescharacteristic
41#17988463C411yescharacteristic
42#17988463C411yescharacteristic
43C4×#11924005C2211yescharacteristic
44C4×#11924005C2211yescharacteristic
45C4×C22⋊Dic73C2211yescharacteristic
46#17988342C2211yescharacteristic
47#17988342C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52C2×C4⋊C8×C73C2211yescharacteristic
53C2×C22⋊C8×C73C2211yescharacteristic
54C2×C22⋊C8×C73C2211yescharacteristic
55C2×C4×C8×C73C2211yescharacteristic
56C4×C22⋊C4×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C2×#11924028—22no—
60C2×#11924028—22no—
61C2×#11924028—41no—
62C2×#11924028—41no—
63C2×#11924028—41no—
64C2×#11924028—41no—
65C22×Dic146C2×C411yescharacteristic
66C22×D292C2×C411yescharacteristic
67C22×C22⋊D73C2×C411yescharacteristic
68C22×C22⋊D73C2×C411yescharacteristic
69C22×C4×D73C2×C411yescharacteristic
70C22×C4×D73C2×C411yescharacteristic
71C22×C4×D73C2311yescharacteristic
72C22×C4×D73C2311yescharacteristic
73C22×#10596831C2311yescharacteristic
74C22×#10596831C2311yescharacteristic
75C22×#10596831C2311yescharacteristic
76C22×#10596831C2311yescharacteristic
77#14556548—41no—
78#14556548—41no—
79C2×#11924007C2×C411yescharacteristic
80C2×#11924007C2×C411yescharacteristic
81C2×C22⋊Dic73C2×C411yescharacteristic
82C2×C22⋊Dic73C2×C411yescharacteristic
83C2×#11924005C2×C411yescharacteristic
84C2×#11924005C2×C411yescharacteristic
85C2×#11924005C2×C411yescharacteristic
86C2×#11924005C2×C411yescharacteristic
87C2×#11924005C2×C411yescharacteristic
88C2×#11924005C2×C411yescharacteristic
89C2×C4×Dic73C2×C411yescharacteristic
90C2×C4×Dic73C2×C411yescharacteristic
91C2×C4×Dic73C2311yescharacteristic
92C2×C4×Dic73C2311yescharacteristic
93C42×D73—41no—
94C42×D73—41no—
95C4⋊#10596831—41no—
96#14556520—41no—
97#14556520—41no—
98C22⋊#10596831—41no—
99C22⋊#10596831—41no—
100#14556503—22no—
101#14556503—22no—
102#14556503—22no—
103#14556503—22no—
104#14556503—41no—
105#14556503—41no—
106#14556503—41no—
107#14556503—41no—
108#14556502—41no—
109#14556501—41no—
110C8×Dic73—41no—
111#14556498C2×C411yescharacteristic
112#14556498C2×C411yescharacteristic
113#14556498C2×C411yescharacteristic
114#14556498C2×C411yescharacteristic
115#14556498C2×C411yescharacteristic
116#14556498C2×C411yescharacteristic
117C23×C4×C73C2311yescharacteristic
118C22×C8×C73C2311yescharacteristic
119C22×C8×C73C2311yescharacteristic
120C22×C8×C73C2311yescharacteristic
121C22×C8×C73C2311yescharacteristic
122C2×C22⋊C4×C73C2×C411yescharacteristic
123C2×C22⋊C4×C73C2×C411yescharacteristic
124C2×C42×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126C4⋊C8×C73—41no—
127C22⋊C8×C73—41no—
128C22⋊C8×C73—41no—
129C4×C8×C73—41no—
130#95×C73C2×C411yescharacteristic
131#95×C73C2×C411yescharacteristic
132C23×D73C22×C411yescharacteristic
133C23×D73C22×C411yescharacteristic
134#11924028—44no—
135#11924028—44no—
136#11924028—44no—
137#11924028—44no—
138C2×Dic146—22no—
139C2×Dic146—41no—
140C2×Dic146—41no—
141C2×D292—22no—
142C2×D292—41no—
143C2×D292—41no—
144C2×C22⋊D73—22no—
145C2×C22⋊D73—22no—
146C2×C22⋊D73—41no—
147C2×C22⋊D73—41no—
148C2×C22⋊D73—41no—
149C2×C22⋊D73—41no—
150C22×Dic73C22×C411yescharacteristic
151C22×Dic73C22×C411yescharacteristic
152C22×Dic73C22×C411yescharacteristic
153C22×Dic73C22×C411yescharacteristic
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C2×C4×D73—21no—
157C2×C4×D73—21no—
158C2×C4×D73—21no—
159C2×C4×D73—21no—
160C2×C4×D73—22no—
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—21no—
166C2×C4×D73—21no—
167C2×C4×D73—22no—
168C2×C4×D73—41no—
169C2×C4×D73—41no—
170C2×C4×D73—41no—
171C2×C4×D73—41no—
172C2×C4×D73#4112yes—
173C2×C4×D73#4112yes—
174C2×#10596831—21no—
175C2×#10596831—21no—
176C2×#10596831—21no—
177C2×#10596831—21no—
178C2×#10596831—21no—
179C2×#10596831—21no—
180C2×#10596831—21no—
181C2×#10596831—21no—
182C2×#10596831—21no—
183C2×#10596831—21no—
184C2×#10596831—21no—
185C2×#10596831—21no—
186#11924007—41no—
187#11924007—41no—
188C22⋊Dic73—22no—
189C22⋊Dic73—41no—
190#11924005—22no—
191#11924005—22no—
192#11924005—41no—
193#11924005—41no—
194#11924005—41no—
195#11924005—41no—
196C4×Dic73—21no—
197C4×Dic73—21no—
198C4×Dic73—21no—
199C4×Dic73—21no—
200C4×Dic73—41no—
201C4×Dic73—41no—
202C24×C73C22×C411yescharacteristic
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73C22×C411yescharacteristic
210C22×C4×C73C22×C411yescharacteristic
211C22×C4×C73C22×C411yescharacteristic
212C22×C4×C73C22×C411yescharacteristic
213C22×C4×C73C22×C411yescharacteristic
214C22×C4×C73C2411yescharacteristic
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C22⋊C4×C73—22no—
228C22⋊C4×C73—41no—
229C42×C73—21no—
230C42×C73—21no—
231C42×C73—21no—
232C42×C73—21no—
233C23×C73—21no—
234C23×C73—21no—
235C23×C73—21no—
236C23×C73—21no—
237C23×C73—21no—
238C23×C73—21no—
239C23×C73—21no—
240C23×C73C23×C411yescharacteristic
241C22×D73—21no—
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73—21no—
249C22×D73—21no—
250C22×D73—21no—
251C22×D73—21no—
252C22×D73—21no—
253C22×D73—21no—
254C22×D73#11712yes—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—21no—
262C2×C4×C73—21no—
263C2×C4×C73—21no—
264C2×C4×C73—21no—
265C2×C4×C73—21no—
266C2×C4×C73—21no—
267C2×C4×C73—21no—
268C2×C4×C73—21no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73#13112yes—
274C2×C4×C73C2×#4111yescharacteristic
275C2×C4×C73C2×#4111yescharacteristic
276C2×C4×C73H(5,𝔽2)11yescharacteristic
277C2×C4×C73H(5,𝔽2)11yescharacteristic
278C2×C4×C73H(5,𝔽2)11yescharacteristic
279C2×C4×C73H(5,𝔽2)11yescharacteristic
280C22⋊D73—44no—
281C22⋊D73—44no—
282C2×Dic73—21no—
283C2×Dic73—21no—
284C2×Dic73—21no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—21no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—21no—
292C2×Dic73—21no—
293C2×Dic73—21no—
294C2×Dic73—21no—
295C2×Dic73—21no—
296C2×Dic73—21no—
297C2×Dic73—21no—
298C2×Dic73#11712yes—
299C2×Dic73#13112yes—
300D292—44no—
301C4×D73—22no—
302C4×D73—22no—
303C4×D73—22no—
304C4×D73—22no—
305C4×D73—44no—
306C4×D73—44no—
307C4×D73—41no—
308C4×D73—41no—
309C4×D73—41no—
310C4×D73—41no—
311Dic146—44no—
312C8×C73—41no—
313C8×C73—41no—
314C8×C73—41no—
315C8×C73—41no—
316#10596831—41no—
317#10596831—41no—
318#10596831—41no—
319#10596831—41no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73—41no—
323C22×C73—41no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73C2×#11711yescharacteristic
328C22×C73#51811yescharacteristic
329C22×C73#51811yescharacteristic
330C22×C73C2×#13111yescharacteristic
331C22×C73C2×#13111yescharacteristic
332C22×C73#56811yescharacteristic
333C22×C73#56811yescharacteristic
334C2×D73—22no—
335C2×D73—22no—
336C2×D73—22no—
337C2×D73—41no—
338C2×D73—41no—
339C2×D73—41no—
340C2×D73—41no—
341C2×D73—41no—
342C2×D73—41no—
343C2×D73—41no—
344C2×D73—41no—
345C2×D73—41no—
346C2×D73—41no—
347C2×D73—41no—
348C4×C73—22no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—41no—
352C4×C73—41no—
353C4×C73#53811yescharacteristic
354C4×C73#53811yescharacteristic
355C4×C73#53811yescharacteristic
356C4×C73#53811yescharacteristic
357Dic73—22no—
358Dic73—22no—
359Dic73—41no—
360Dic73—41no—
361Dic73—41no—
362Dic73—41no—
363#21911—731nomaximal, Sylow
364C2×C73—81no—
365C2×C73#231211yescharacteristic
366C2×C73#292511yescharacteristic
367C2×C73#292511yescharacteristic
368C2×C73#297711yescharacteristic
369C2×C73#297811yescharacteristic
370C2×C73#298111yescharacteristic
371C2×C73#298111yescharacteristic
372D73—42no—
373D73—81no—
374#2297—731no—
375#1924—731no—
376#1924—731no—
377#1924—731no—
378#1924—731no—
379#1923—731no—
380#1923—731no—
381#1923—731no—
382#1923D7311yescharacteristic, complemented
383#1797—731no—
384#1797—731no—
385#1780—731no—
386#1780—731no—
387#1750—731no—
388#1750—731no—
389C73#2191111yescharacteristic, complemented, Sylow
390C22×#41—731no—
391C2×#117—731no—
392C22×C42—731no—
393C2×C4⋊C8—731no—
394C2×C4⋊C8—731no—
395C2×C4⋊C8—731no—
396C2×C4⋊C8C2×D7311yescharacteristic
397C2×C22⋊C8—731no—
398C2×C22⋊C8—731no—
399C2×C22⋊C8—731no—
400C2×C22⋊C8—731no—
401C2×C22⋊C8—731no—
402C2×C22⋊C8—731no—
403C2×C22⋊C8—731no—
404C2×C22⋊C8—731no—
405C2×C22⋊C8—731no—
406C2×C22⋊C8—731no—
407C2×C22⋊C8C2×D7311yescharacteristic
408C2×C22⋊C8C2×D7311yescharacteristic
409C2×#97—731no—
410C2×#97—731no—
411C2×C4×C8—731no—
412C2×C4×C8C2×D7311yescharacteristic
413#391—731no—
414#391—731no—
415#390—731no—
416#390—731no—
417#386—731no—
418#386—731no—
419#386—731no—
420#386—731no—
421C4×C22⋊C4—731no—
422C4×C22⋊C4—731no—
423C4×C22⋊C4—731no—
424C4×C22⋊C4C2×D7311yescharacteristic
425#336—731no—
426#336—731no—
427#336—731no—
428#336—731no—
429#336—731no—
430#336—731no—
431#336C2×D7311yescharacteristic
432#336C2×D7311yescharacteristic
433C2×#41—2921no—
434C2×#41—2921no—
435C2×#41—2921no—
436C2×#41—2921no—
437C2×#41—1462no—
438C2×#41—1462no—
439C22×Q8—731no—
440C22×D4—731no—
441C22×D4—731no—
442C22×D4—731no—
443C23×C4—731no—
444C23×C4—731no—
445C23×C4—731no—
446C23×C4—731no—
447C23×C4C22×D7311yescharacteristic
448C22×C8—731no—
449C22×C8—731no—
450C22×C8—731no—
451C22×C8—731no—
452C22×C8C22×D7311yescharacteristic
453C22×C8C22×D7311yescharacteristic
454C22×C8C22×D7311yescharacteristic
455C22×C8C22×D7311yescharacteristic
456#117—2921no—
457#117—2921no—
458C2×C4⋊C4—731no—
459C2×C4⋊C4—731no—
460C2×C22⋊C4—731no—
461C2×C22⋊C4—731no—
462C2×C22⋊C4—731no—
463C2×C22⋊C4—731no—
464C2×C22⋊C4—731no—
465C2×C22⋊C4—731no—
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4C4×D7311yescharacteristic
469C2×C22⋊C4C4×D7311yescharacteristic
470C2×C42—2921no—
471C2×C42—2921no—
472C2×C42—731no—
473C2×C42—731no—
474C2×C42—731no—
475C2×C42—731no—
476C2×C42C22×D7311yescharacteristic
477C2×C42C22×D7311yescharacteristic
478C4⋊C8—41no—
479C4⋊C8—2921no—
480C4⋊C8—2921no—
481C4⋊C8—2921no—
482C22⋊C8—41no—
483C22⋊C8—41no—
484C22⋊C8—2921no—
485C22⋊C8—2921no—
486C22⋊C8—2921no—
487C22⋊C8—2921no—
488C22⋊C8—2921no—
489C22⋊C8—2921no—
490C22⋊C8—1462no—
491C22⋊C8—1462no—
492C22⋊C8—1462no—
493C22⋊C8—1462no—
494#97—2921no—
495#97—2921no—
496C4×C8—41no—
497C4×C8—2921no—
498#95—731no—
499#95—731no—
500#95—731no—
501#95—731no—
502#95—731no—
503#95—731no—
504#95C4×D7311yescharacteristic
505#95C4×D7311yescharacteristic
506C24—731no—
507C24—731no—
508C24C2×C4×D7311yescharacteristic
509#41—2924no—
510#41—2924no—
511#41—2924no—
512#41—2924no—
513C2×Q8—2921no—
514C2×Q8—2921no—
515C2×Q8—1462no—
516C2×D4—2921no—
517C2×D4—2921no—
518C2×D4—2921no—
519C2×D4—2921no—
520C2×D4—2921no—
521C2×D4—2921no—
522C2×D4—1462no—
523C2×D4—1462no—
524C2×D4—1462no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—2921no—
532C22×C4—2921no—
533C22×C4—2921no—
534C22×C4—2921no—
535C22×C4—731no—
536C22×C4—731no—
537C22×C4—732no—
538C22×C4—732no—
539C22×C4—731no—
540C22×C4—731no—
541C22×C4—731no—
542C22×C4—731no—
543C22×C4—1462no—
544C22×C4—1462no—
545C22×C4—1461no—
546C22×C4—1461no—
547C22×C4—1461no—
548C22×C4—1461no—
549C22×C4—1461no—
550C22×C4—1461no—
551C22×C4—1461no—
552C22×C4—1461no—
553C22×C4—1461no—
554C22×C4—1461no—
555C22×C4C2×C4×D7311yescharacteristic
556C22×C4C2×C4×D7311yescharacteristic
557C22×C4C2×C4×D7311yescharacteristic
558C22×C4C2×C4×D7311yescharacteristic
559C22×C4C2×C4×D7311yescharacteristic
560C22×C4C23×D7311yescharacteristic
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—1461no—
574C2×C8—1461no—
575C2×C8—1461no—
576C2×C8—1461no—
577C2×C8—1461no—
578C2×C8—1461no—
579C2×C8—1461no—
580C2×C8—1461no—
581C2×C8—1461no—
582C2×C8—1461no—
583C2×C8—1461no—
584C2×C8—1461no—
585C4⋊C4—2921no—
586C4⋊C4—2921no—
587C22⋊C4—22no—
588C22⋊C4—41no—
589C22⋊C4—2921no—
590C22⋊C4—2921no—
591C22⋊C4—2921no—
592C22⋊C4—2921no—
593C22⋊C4—2921no—
594C22⋊C4—1462no—
595C22⋊C4—1462no—
596C22⋊C4—1462no—
597C42—21no—
598C42—21no—
599C42—21no—
600C42—21no—
601C42—2921no—
602C42—2921no—
603C42—1461no—
604C42—1461no—
605C42—1461no—
606C42—1461no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—21no—
612C23—21no—
613C23—21no—
614C23—732no—
615C23—1461no—
616C23—1461no—
617C23—1461no—
618C23—1461no—
619C23—1461no—
620C23—1461no—
621C23—1461no—
622C23—1461no—
623C23—1461no—
624C23—1461no—
625C23—1461no—
626C23—1461no—
627C23—1461no—
628C23C22×C4×D7311yescharacteristic
629Q8—2924no—
630D4—2924no—
631D4—2924no—
632D4—2924no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—2924no—
652C2×C4—2924no—
653C2×C4—2921no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—2921no—
657C2×C4—732no—
658C2×C4—732no—
659C2×C4—1461no—
660C2×C4—1461no—
661C2×C4—1461no—
662C2×C4—1461no—
663C2×C4—1461no—
664C2×C4—1461no—
665C2×C4—1461no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1461no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4—1461no—
673C2×C4—1461no—
674C2×C4—1461no—
675C2×C4—1462no—
676C2×C4—1462no—
677C2×C4—1462no—
678C2×C4—1462no—
679C2×C4#1455659712yes—
680C2×C4#41×D7311yescharacteristic
681C2×C4#41×D7311yescharacteristic
682C2×C4#1455663611yescharacteristic
683C2×C4#1455663611yescharacteristic
684C2×C4#1455663711yescharacteristic
685C2×C4#1455663711yescharacteristic
686C8—41no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—2921no—
691C8—2921no—
692C8—2921no—
693C8—2921no—
694C22—41no—
695C22—41no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—2921no—
702C22—2921no—
703C22—2921no—
704C22—2921no—
705C22—2921no—
706C22—2921no—
707C22—2921no—
708C22—2921no—
709C22—2921no—
710C22—2921no—
711C22—2921no—
712C22—1462no—
713C22—1462no—
714C22—1462no—
715C22#117×D7311yescharacteristic
716C22#1798905911yescharacteristic
717C22#1798905911yescharacteristic
718C22#131×D7311yescharacteristic
719C22C2×#1455659711yescharacteristic
720C22#1798935211yescharacteristic
721C22#1798935311yescharacteristic
722C4—22no—
723C4—41no—
724C4—41no—
725C4—41no—
726C4—41no—
727C4—2921no—
728C4—2921no—
729C4—2921no—
730C4—2921no—
731C4—1462no—
732C4—1462no—
733C4#1798916911yescharacteristic
734C4#1798917111yescharacteristic
735C4#1798917311yescharacteristic
736C4#1798917611yescharacteristic
737C2—81no—
738C2—2922no—
739C2—5841no—
740C2#2261252511yescharacteristic
741C2#2261859211yescharacteristic
742C2#2261859411yescharacteristic
743C2#2261898411yescharacteristic
744C2#2261898811yescharacteristic
745C2#2261900311yescharacteristic
746C2#2261900511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC73×#1923C2
prime radicalC22×#11924028C22
cosocleC22×C4×C73C24
hypercenter#1923D73
hypocenterC73#21911
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #22610546C2semidirect
3. #22610543C2semidirect
4. #22610542C2semidirect
5. #22610541C2semidirect
6. #22610540C2semidirect
7. #22610538C2semidirect
8. #22610537C2semidirect
9. #22609910C2semidirect
10. #22609908C2semidirect
13. #22609698C2semidirect
14. #22609696C2semidirect
15. C73×#1923C2semidirect
382. #1923D73semidirect
389. C73#21911semidirect

Maximal subgroups

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

subgroupindex
#226124172
#226105462
#226105432
#226105422
#226105412
#226105402
#226105382
#226105372
#226099102
#226099082
#226098422
#226096982
#226096962
C73×#19232
#2191173