Finite Group Databasebeta

← #33102521

Subgroups — #33102521

Order 18688.

1036 conjugacy classes of subgroups.

The subgroup lattice has 704 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989141C211yesmaximal, characteristic
2C2×#17988718C211yesmaximal, characteristic, complemented
3#22610871C211yesmaximal, characteristic, complemented
4#22610871C211yesmaximal, characteristic, complemented
5#22610870C211yesmaximal, characteristic, complemented
6#22610870C211yesmaximal, characteristic, complemented
7#22610867C211yesmaximal, characteristic, complemented
8#22610866C211yesmaximal, characteristic, complemented
9#22609912C211yesmaximal, characteristic
10#22609912C211yesmaximal, characteristic
11#22609908C211yesmaximal, characteristic
12#22609700C211yesmaximal, characteristic
13#22609698C211yesmaximal, characteristic
14#22609694C211yesmaximal, characteristic
15C2×#446×C73C211yesmaximal, characteristic, complemented
16#17989141—24no—
17#17989141—24no—
18C2×#14556590C411yescharacteristic
19C2×#14556589C411yescharacteristic
20C2×#14556581C411yescharacteristic
21C2×#14556581C411yescharacteristic
22C2×#14556571C411yescharacteristic
23C2×#14556569C411yescharacteristic
24C2×#14556569C411yescharacteristic
25C2×#14556567C411yescharacteristic
26C2×C4×Dic146C2211yescharacteristic
27C2×C4×Dic146C2211yescharacteristic
28C2×C4×Dic146C2211yescharacteristic
29C2×#14556548C2211yescharacteristic
30C2×#14556548C2211yescharacteristic
31C2×C42×D73C2211yescharacteristic
32#17988718—24no—
33C2×C4⋊#10596831C2211yescharacteristic
34C2×C4⋊#10596831C2211yescharacteristic
35C2×C4⋊#10596831C2211yescharacteristic
36C2×#14556503C2211yescharacteristic
37C2×#14556503C2211yescharacteristic
38C2×#14556503C2211yescharacteristic
39C2×#14556503C2211yescharacteristic
40C2×#14556502C2211yescharacteristic
41C2×#14556502C2211yescharacteristic
42C2×C4×#10596831C2211yescharacteristic
43#17988341C2211yescharacteristic
44#17988341C2211yescharacteristic
45#17988341C2211yescharacteristic
46#17988341C2211yescharacteristic
47#17988341C2211yescharacteristic
48#17988341C2211yescharacteristic
49#17988341C2211yescharacteristic
50#17988341C2211yescharacteristic
51#17988341C2211yescharacteristic
52#17988341C2211yescharacteristic
53#17988341C2211yescharacteristic
54#17988341C2211yescharacteristic
55C2×C4×Q8×C73C2211yescharacteristic
56#446×C73—24no—
57C2×C4⋊C8×C73C2211yescharacteristic
58C2×C4⋊C8×C73C2211yescharacteristic
59C2×C4⋊C8×C73C2211yescharacteristic
60C2×#97×C73C2211yescharacteristic
61C2×#97×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63C22×Dic146C2×C411yescharacteristic
64C22×Dic146C2×C411yescharacteristic
65C22×Dic146C2×C411yescharacteristic
66C22×C4×D73C2×C411yescharacteristic
67C22×C4×D73C2×C411yescharacteristic
68C22×C4×D73C2311yescharacteristic
69C22×#10596831C2311yescharacteristic
70C22×#10596831C2311yescharacteristic
71C22×#10596831C2311yescharacteristic
72C22×#10596831C2311yescharacteristic
73#14556590—24no—
74#14556589—24no—
75#14556581—24no—
76#14556581—24no—
77#14556571—24no—
78#14556569—24no—
79#14556569—24no—
80#14556567—24no—
81C4×Dic146—22no—
82C4×Dic146—22no—
83C4×Dic146—22no—
84C4×Dic146—22no—
85C4×Dic146—22no—
86C4×Dic146—22no—
87#14556548—22no—
88#14556548—22no—
89#14556548—22no—
90#14556548—22no—
91C2×C4⋊Dic73C2×C411yescharacteristic
92C2×C4⋊Dic73C2×C411yescharacteristic
93C2×C4⋊Dic73C2×C411yescharacteristic
94C2×#11924007C2×C411yescharacteristic
95C2×#11924007C2×C411yescharacteristic
96C2×#11924007C2×C411yescharacteristic
97C2×#11924007C2×C411yescharacteristic
98C2×#11924007C2×C411yescharacteristic
99C2×#11924007C2×C411yescharacteristic
100C2×#11924007C2×C411yescharacteristic
101C2×#11924007C2×C411yescharacteristic
102C2×#11924007C2×C411yescharacteristic
103C2×#11924007C2×C411yescharacteristic
104C2×#11924005C2×C411yescharacteristic
105C2×#11924005C2×C411yescharacteristic
106C2×#11924005C2×C411yescharacteristic
107C2×#11924005C2×C411yescharacteristic
108C2×C4×Dic73C2×C411yescharacteristic
109C2×C4×Dic73C2×C411yescharacteristic
110C2×C4×Dic73C2311yescharacteristic
111C2×C4×Dic73C2311yescharacteristic
112C2×C4×Dic73C2311yescharacteristic
113C42×D73—22no—
114C42×D73—22no—
115C4⋊#10596831—22no—
116C4⋊#10596831—22no—
117C4⋊#10596831—22no—
118#14556503—22no—
119#14556503—22no—
120#14556503—22no—
121#14556503Q814yescomplemented
122#14556502—22no—
123#14556502—22no—
124C4×#10596831—22no—
125C22×Q8×C73C2×C411yescharacteristic
126C22×C8×C73C2311yescharacteristic
127C22×C8×C73C2311yescharacteristic
128C22×C8×C73C2311yescharacteristic
129C22×C8×C73C2311yescharacteristic
130C4×Q8×C73D414yes—
131C4×Q8×C73D414yes—
132C2×C4⋊C4×C73C2×C411yescharacteristic
133C2×C4⋊C4×C73C2×C411yescharacteristic
134C2×C4⋊C4×C73C2×C411yescharacteristic
135C2×C42×C73C2311yescharacteristic
136C2×C42×C73C2311yescharacteristic
137C2×C42×C73C2311yescharacteristic
138C4⋊C8×C73—22no—
139C4⋊C8×C73—22no—
140C4⋊C8×C73—22no—
141#97×C73—22no—
142#97×C73—22no—
143C4×C8×C73—22no—
144C23×D73C22×C411yescharacteristic
145C2×Dic146—22no—
146C2×Dic146—22no—
147C2×Dic146—22no—
148C2×Dic146—22no—
149C2×Dic146—22no—
150C2×Dic146—41no—
151C2×Dic146—41no—
152C2×Dic146—41no—
153C2×Dic146—41no—
154C22×Dic73C22×C411yescharacteristic
155C22×Dic73C22×C411yescharacteristic
156C22×Dic73C22×C411yescharacteristic
157C22×Dic73C22×C411yescharacteristic
158C22×Dic73C22×C411yescharacteristic
159C22×Dic73C22×C411yescharacteristic
160C22×Dic73C22×C411yescharacteristic
161C2×C4×D73—21no—
162C2×C4×D73—21no—
163C2×C4×D73—21no—
164C2×C4×D73—21no—
165C2×C4×D73—22no—
166C2×C4×D73—22no—
167C2×C4×D73—22no—
168C2×C4×D73—41no—
169C2×C4×D73—41no—
170C2×C4×D73—41no—
171C2×C4×D73C2×Q812yes—
172C2×C4×D73#4112yes—
173C2×#10596831—21no—
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×#10596831C2×Q812yes—
185C4⋊Dic73—22no—
186C4⋊Dic73—22no—
187C4⋊Dic73—22no—
188#11924007—22no—
189#11924007—22no—
190#11924007—22no—
191#11924007—22no—
192#11924007—22no—
193#11924007—22no—
194#11924007—22no—
195#11924007—22no—
196#11924007—22no—
197#11924007—22no—
198#11924005—22no—
199#11924005—22no—
200#11924005—22no—
201#11924005—22no—
202C4×Dic73—22no—
203C4×Dic73—22no—
204C4×Dic73—21no—
205C4×Dic73—21no—
206C4×Dic73—21no—
207C4×Dic73—21no—
208C4×Dic73—21no—
209C4×Dic73—21no—
210C2×Q8×C73—41no—
211C2×Q8×C73—41no—
212C2×Q8×C73C22⋊C414yes—
213C22×C4×C73C22×C411yescharacteristic
214C22×C4×C73C22×C411yescharacteristic
215C22×C4×C73C22×C411yescharacteristic
216C22×C4×C73C22×C411yescharacteristic
217C22×C4×C73C22×C411yescharacteristic
218C22×C4×C73C22×C411yescharacteristic
219C22×C4×C73C2411yescharacteristic
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—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73C2×Q812yes—
232C4⋊C4×C73C22⋊C414yes—
233C4⋊C4×C73C22⋊C414yes—
234C4⋊C4×C73C22⋊C414yes—
235C42×C73C2×D412yes—
236C42×C73C2×D412yes—
237C42×C73C2×D412yes—
238C42×C73C2×D412yes—
239C42×C73C2×D412yes—
240C42×C73C2×D412yes—
241C23×C73C23×C411yescharacteristic
242C22×D73—21no—
243C22×D73—21no—
244C22×D73—21no—
245C22×D73—21no—
246C22×D73—21no—
247C22×D73—21no—
248C22×D73C4×Q812yes—
249Q8×C73—44no—
250C2×C4×C73—21no—
251C2×C4×C73—21no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
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×C73C2×C22⋊C412yes—
263C2×C4×C73C2×C22⋊C412yes—
264C2×C4×C73C2×C22⋊C412yes—
265C2×C4×C73C2×C22⋊C412yes—
266C2×C4×C73C2×C22⋊C412yes—
267C2×C4×C73C2×C22⋊C412yes—
268C2×C4×C73C22×D411yescharacteristic
269C2×C4×C73C22×D411yescharacteristic
270C2×C4×C73C22×Q811yescharacteristic
271C2×C4×C73C2×#4111yescharacteristic
272C2×C4×C732−1+411yescharacteristic
273C2×C4×C732−1+411yescharacteristic
274C2×Dic73—21no—
275C2×Dic73—21no—
276C2×Dic73—21no—
277C2×Dic73—21no—
278C2×Dic73—21no—
279C2×Dic73—21no—
280C2×Dic73—21no—
281C2×Dic73—21no—
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×Dic73C4×Q812yes—
294C2×Dic73#13112yes—
295C4×D73—22no—
296C4×D73—22no—
297C4×D73—22no—
298C4×D73—22no—
299C4×D73—44no—
300C4×D73—44no—
301Dic146—44no—
302Dic146—44no—
303Dic146—44no—
304C8×C73—22no—
305C8×C73—41no—
306C8×C73—41no—
307C8×C73—41no—
308#10596831—22no—
309#10596831—41no—
310#10596831—41no—
311#10596831—41no—
312C22×C73C22×C22⋊C411yescharacteristic
313C22×C73C2×C4×Q811yescharacteristic
314C22×C73#51911yescharacteristic
315C22×C73C2×#13111yescharacteristic
316C22×C73#56811yescharacteristic
317C22×C73#56811yescharacteristic
318C22×C73#56811yescharacteristic
319C2×D73—22no—
320C2×D73—22no—
321C2×D73—22no—
322C2×D73—41no—
323C2×D73—41no—
324C2×D73—41no—
325C2×D73—41no—
326C4×C73—22no—
327C4×C73—22no—
328C4×C73—22no—
329C4×C73—22no—
330C4×C73—22no—
331C4×C73—22no—
332C4×C73#54811yescharacteristic
333C4×C73#54811yescharacteristic
334C4×C73D4×Q811yescharacteristic
335C4×C73D4×Q811yescharacteristic
336Dic73—22no—
337Dic73—22no—
338Dic73—41no—
339Dic73—41no—
340Dic73—41no—
341Dic73—41no—
342Dic73—41no—
343#22511—731nomaximal, Sylow
344C2×C73Q8×C22⋊C411yescharacteristic
345C2×C73#287911yescharacteristic
346C2×C73#288011yescharacteristic
347C2×C73#296111yescharacteristic
348C2×C73#296211yescharacteristic
349C2×C73#298511yescharacteristic
350C2×C73#298711yescharacteristic
351D73—42no—
352C2×#533—731no—
353C2×#446—731no—
354C2×#446D7311yescharacteristic, complemented
355#1985—731no—
356#1985—731no—
357#1985—731no—
358#1985—731no—
359#1984—731no—
360#1984—731no—
361#1798—731no—
362#1798—731no—
363#1797—731no—
364#1750—731no—
365#1750—731no—
366#1749—731no—
367C73#2251111yescharacteristic, complemented, Sylow
368#533—1464no—
369#533—1464no—
370C2×C4⋊Q8—731no—
371C2×C4⋊Q8—731no—
372C2×#125—731no—
373C2×#125—731no—
374C2×C22⋊Q8—731no—
375C2×C22⋊Q8—731no—
376C2×C22⋊Q8—731no—
377C2×C22⋊Q8—731no—
378C2×C4×Q8—731no—
379C2×C4×Q8—731no—
380C2×C4×Q8—731no—
381C2×C4×Q8C2×D7311yescharacteristic
382C2×#117—731no—
383C2×#117—731no—
384C22×C42—731no—
385#446—24no—
386#446—1464no—
387C2×C4⋊C8—731no—
388C2×C4⋊C8—731no—
389C2×C4⋊C8—731no—
390C2×C4⋊C8C2×D7311yescharacteristic
391C2×C4⋊C8C2×D7311yescharacteristic
392C2×C4⋊C8C2×D7311yescharacteristic
393C2×C22⋊C8—731no—
394C2×C22⋊C8—731no—
395C2×C22⋊C8—731no—
396C2×C22⋊C8—731no—
397C2×#97—731no—
398C2×#97—731no—
399C2×#97C2×D7311yescharacteristic
400C2×#97C2×D7311yescharacteristic
401C2×C4×C8—731no—
402C2×C4×C8C2×D7311yescharacteristic
403#336—731no—
404#336—731no—
405#336—731no—
406#336—731no—
407#336—731no—
408#336—731no—
409#336—731no—
410#336—731no—
411#336—731no—
412#336—731no—
413#336—731no—
414#336—731no—
415C22×Q8—731no—
416C22×Q8—731no—
417C22×Q8—731no—
418C22×Q8C4×D7311yescharacteristic
419C23×C4—731no—
420C23×C4—731no—
421C23×C4—731no—
422C22×C8—731no—
423C22×C8—731no—
424C22×C8—731no—
425C22×C8—731no—
426C22×C8C22×D7311yescharacteristic
427C22×C8C22×D7311yescharacteristic
428C22×C8C22×D7311yescharacteristic
429C22×C8C22×D7311yescharacteristic
430C4⋊Q8—1464no—
431C4⋊Q8—1464no—
432#125—1464no—
433#125—1464no—
434C22⋊Q8—1464no—
435C22⋊Q8—1464no—
436C22⋊Q8—1464no—
437C22⋊Q8—1464no—
438C4×Q8—1462no—
439C4×Q8—1462no—
440C4×Q8—1462no—
441C4×Q8—1462no—
442C4×Q8—1462no—
443C4×Q8—1462no—
444C4×Q8D29214yes—
445C4×Q8C22⋊D7314yes—
446#117—1462no—
447#117—1462no—
448#117—1462no—
449#117—1462no—
450C2×C4⋊C4—731no—
451C2×C4⋊C4—731no—
452C2×C4⋊C4—731no—
453C2×C4⋊C4—731no—
454C2×C4⋊C4—731no—
455C2×C4⋊C4—731no—
456C2×C4⋊C4—731no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4—731no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4C4×D7311yescharacteristic
464C2×C4⋊C4C4×D7311yescharacteristic
465C2×C4⋊C4C4×D7311yescharacteristic
466C2×C22⋊C4—731no—
467C2×C22⋊C4—731no—
468C2×C22⋊C4—731no—
469C2×C22⋊C4—731no—
470C2×C42—731no—
471C2×C42—731no—
472C2×C42—731no—
473C2×C42—731no—
474C2×C42—731no—
475C2×C42—1462no—
476C2×C42—1462no—
477C2×C42C22×D7311yescharacteristic
478C2×C42C22×D7311yescharacteristic
479C2×C42C22×D7311yescharacteristic
480C4⋊C8—22no—
481C4⋊C8—22no—
482C4⋊C8—22no—
483C4⋊C8—1462no—
484C4⋊C8—1462no—
485C4⋊C8—1462no—
486C22⋊C8—734no—
487C22⋊C8—1462no—
488C22⋊C8—1462no—
489C22⋊C8—1462no—
490#97—22no—
491#97—22no—
492#97—1462no—
493#97—1462no—
494C4×C8—22no—
495C4×C8—1462no—
496C24—731no—
497C2×Q8—41no—
498C2×Q8—41no—
499C2×Q8—2921no—
500C2×Q8—2921no—
501C2×Q8—2921no—
502C2×Q8—2921no—
503C2×Q8—1462no—
504C2×Q8—1462no—
505C2×Q8—1462no—
506C2×Q8—1462no—
507C2×Q8—1462no—
508C2×Q8#1192400514yes—
509C22×C4—2921no—
510C22×C4—2921no—
511C22×C4—2921no—
512C22×C4—731no—
513C22×C4—731no—
514C22×C4—732no—
515C22×C4—732no—
516C22×C4—731no—
517C22×C4—731no—
518C22×C4—731no—
519C22×C4—731no—
520C22×C4—731no—
521C22×C4—1462no—
522C22×C4—1462no—
523C22×C4—1462no—
524C22×C4—1461no—
525C22×C4—1461no—
526C22×C4—1461no—
527C22×C4—1461no—
528C22×C4C2×C4×D7311yescharacteristic
529C22×C4C2×C4×D7311yescharacteristic
530C22×C4C2×C4×D7311yescharacteristic
531C22×C4C2×C4×D7311yescharacteristic
532C22×C4C2×C4×D7311yescharacteristic
533C22×C4C2×C4×D7311yescharacteristic
534C22×C4C23×D7311yescharacteristic
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—732no—
547C2×C8—1461no—
548C2×C8—1461no—
549C2×C8—1461no—
550C2×C8—1461no—
551C2×C8—1461no—
552C2×C8—1461no—
553C2×C8—1461no—
554C2×C8—1461no—
555C2×C8—1461no—
556C2×C8—1461no—
557C2×C8—1461no—
558C2×C8Q8×D7312yes—
559C4⋊C4—1462no—
560C4⋊C4—1462no—
561C4⋊C4—1462no—
562C4⋊C4—1462no—
563C4⋊C4—1462no—
564C4⋊C4—1462no—
565C4⋊C4—1462no—
566C4⋊C4—1462no—
567C4⋊C4—1462no—
568C4⋊C4—1462no—
569C4⋊C4—1462no—
570C4⋊C4—1462no—
571C4⋊C4—1462no—
572C4⋊C4#1192400514yes—
573C4⋊C4#1192400514yes—
574C4⋊C4#1192400514yes—
575C22⋊C4—1462no—
576C22⋊C4—1462no—
577C22⋊C4—1462no—
578C22⋊C4—1462no—
579C42—1462no—
580C42—1462no—
581C42—1461no—
582C42—1461no—
583C42—1461no—
584C42—1461no—
585C42—1461no—
586C42—1461no—
587C42C2×C22⋊D7312yes—
588C42C2×C22⋊D7312yes—
589C42C2×C22⋊D7312yes—
590C42C2×D29212yes—
591C42C2×D29212yes—
592C42C2×D29212yes—
593C23—732no—
594C23—1461no—
595C23—1461no—
596C23—1461no—
597C23—1461no—
598C23—1461no—
599C23—1461no—
600C23C22×C4×D7311yescharacteristic
601Q8—44no—
602Q8—2924no—
603Q8—2924no—
604Q8—2924no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—2924no—
618C2×C4—2924no—
619C2×C4—732no—
620C2×C4—732no—
621C2×C4—1461no—
622C2×C4—1461no—
623C2×C4—1461no—
624C2×C4—1461no—
625C2×C4—1461no—
626C2×C4—1461no—
627C2×C4—1461no—
628C2×C4—1461no—
629C2×C4—1461no—
630C2×C4—1461no—
631C2×C4—1461no—
632C2×C4—1461no—
633C2×C4—1461no—
634C2×C4—1461no—
635C2×C4—1461no—
636C2×C4—1461no—
637C2×C4—1461no—
638C2×C4—1461no—
639C2×C4—1461no—
640C2×C4—1462no—
641C2×C4—1462no—
642C2×C4—1462no—
643C2×C4—1462no—
644C2×C4C2×#1192400512yes—
645C2×C4C2×#1192400512yes—
646C2×C4C2×#1192400512yes—
647C2×C4C2×#1192400512yes—
648C2×C4C2×#1192400512yes—
649C2×C4C2×#1192400512yes—
650C2×C4C22×C22⋊D7311yescharacteristic
651C2×C4C22×D29211yescharacteristic
652C2×C4C2×Q8×D7311yescharacteristic
653C2×C4#41×D7311yescharacteristic
654C2×C4#1455663811yescharacteristic
655C2×C4#1455663911yescharacteristic
656C8—22no—
657C8—41no—
658C8—41no—
659C8—41no—
660C8—2921no—
661C8—2921no—
662C8—2921no—
663C8—1462no—
664C22—2921no—
665C22—2921no—
666C22—2921no—
667C22—2921no—
668C22—1462no—
669C22—1462no—
670C22—1462no—
671C22C22×#1192400511yescharacteristic
672C22C4×Q8×D7311yescharacteristic
673C22#1798906311yescharacteristic
674C22#131×D7311yescharacteristic
675C22#1798935211yescharacteristic
676C22#1798935311yescharacteristic
677C22#1798935311yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—2921no—
685C4—2921no—
686C4—2921no—
687C4—2921no—
688C4—2921no—
689C4—1462no—
690C4—1462no—
691C4#1798924411yescharacteristic
692C4#1798924911yescharacteristic
693C4Q8×C22⋊D7311yescharacteristic
694C4Q8×D29211yescharacteristic
695C2—2922no—
696C2Q8×#1192400511yescharacteristic
697C2#2261837511yescharacteristic
698C2#2261837811yescharacteristic
699C2#2261886711yescharacteristic
700C2#2261887611yescharacteristic
701C2#2261902411yescharacteristic
702C2#2261903411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D73
commutator, socleC23×C73C23×C4
FittingC2×#446×C73C2
prime radicalC23×D73C22×C4
cosocleC22×C4×C73C24
hypercenterC2×#446D73
hypocenterC73#22511
LCSG ▷ C23×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
2. C2×#17988718C2semidirect
3. #22610871C2semidirect
4. #22610871C2semidirect
5. #22610870C2semidirect
6. #22610870C2semidirect
7. #22610867C2semidirect
8. #22610866C2semidirect
15. C2×#446×C73C2semidirect
121. #14556503Q8semidirect
354. C2×#446D73semidirect
367. C73#22511semidirect

Maximal subgroups

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

subgroupindex
C2×#179891412
C2×#179887182
#226108712
#226108702
#226108672
#226108662
#226099122
#226099082
#226097002
#226096982
#226096942
C2×#446×C732
#2251173