Finite Group Databasebeta

← #34018658

Subgroups — #34018658

Order 18688.

648 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626873C211yesmaximal, characteristic, complemented
2#22626781C211yesmaximal, characteristic, complemented
3#22625553C211yesmaximal, characteristic, complemented
4#22625547C211yesmaximal, characteristic, complemented
5#22625535C211yesmaximal, characteristic, complemented
6#22625533C211yesmaximal, characteristic, complemented
7#22625528C211yesmaximal, characteristic, complemented
8#22625523C211yesmaximal, characteristic, complemented
9#22625516C211yesmaximal, characteristic, complemented
10#22625511C211yesmaximal, characteristic, complemented
11#22625507C211yesmaximal, characteristic, complemented
12#22625258C211yesmaximal, characteristic, complemented
13#22625242C211yesmaximal, characteristic, complemented
14#22625152C211yesmaximal, characteristic, complemented
15#22619975C211yesmaximal, characteristic
16#17989637C2211yescharacteristic, complemented
17#17989636C2211yescharacteristic, complemented
18#17989622—21no—
19#17989622C2211yescharacteristic, complemented
20#17989618—21no—
21#17989615—21no—
22#17989615—21no—
23#17989615C2211yescharacteristic
24#17989615C2211yescharacteristic
25#17989615C2211yescharacteristic
26#17989615C2211yescharacteristic
27D4×#10596833C2211yescharacteristic, complemented
28#17989611—21no—
29#17989604C2211yescharacteristic
30#17989603C2211yescharacteristic
31#17989603C2211yescharacteristic
32#17989593—21no—
33#17989590C2211yescharacteristic
34#17989555—21no—
35#17989555—21no—
36#17989451C2211yescharacteristic, complemented
37#17989450C2211yescharacteristic, complemented
38#17989449C2211yescharacteristic, complemented
39#17989448C2211yescharacteristic, complemented
40#17989437C2211yescharacteristic, complemented
41#17989437C2211yescharacteristic, complemented
42#17989435C2211yescharacteristic
43#17989435C2211yescharacteristic
44#17989435C2211yescharacteristic
45#17989435C2211yescharacteristic
46D4⋊#10596833C2211yescharacteristic, complemented
47D4⋊#10596833C2211yescharacteristic, complemented
48#17989429C2211yescharacteristic, complemented
49#17989429C2211yescharacteristic, complemented
50#17989428C2211yescharacteristic, complemented
51C8×#10596833C2211yescharacteristic, complemented
52#17989118C2211yescharacteristic
53C2×#14556553C2211yescharacteristic
54#17988922C411yescharacteristic
55#17988886C411yescharacteristic
56#17988886C411yescharacteristic
57#17988801C411yescharacteristic
58#17988801C411yescharacteristic
59#17988740C411yescharacteristic
60#17988720C411yescharacteristic
61#17988674C2211yescharacteristic
62#17988674C2211yescharacteristic
63#17988667C2211yescharacteristic
64#17988667C2211yescharacteristic
65#17988637C2211yescharacteristic
66#481×C73C411yescharacteristic
67C2×#11924037—21no—
68C2×#11924037—21no—
69C2×#11924036—21no—
70C2×#11924036—21no—
71C2×#11924036—21no—
72C2×#11924036—21no—
73C22×#10596833—21no—
74#14556658—21no—
75#14556658—21no—
76#14556658—21no—
77C4⋊#10596833—21no—
78C4⋊#10596833D411yescharacteristic
79C4⋊#10596833D411yescharacteristic
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82C4⋊#10596833C2311yescharacteristic
83C4⋊#10596833C2311yescharacteristic
84#14556648—21no—
85#14556648—21no—
86#14556648—21no—
87#14556648—21no—
88C22⋊#10596833—21no—
89C22⋊#10596833—21no—
90C22⋊#10596833—21no—
91C22⋊#10596833—21no—
92C22⋊#10596833D411yescharacteristic
93C22⋊#10596833D411yescharacteristic
94#14556646—21no—
95C4×#10596833—21no—
96C4×#10596833—21no—
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101C22×D292C2×C411yescharacteristic
102C22×C4×D73—21no—
103C2×#11924017C2×C411yescharacteristic
104C2×#11924017C2×C411yescharacteristic
105C2×#11924013C2×C411yescharacteristic
106C2×#11924013C2×C411yescharacteristic
107#14556584—21no—
108#14556582C2×C411yescharacteristic
109#14556578C2×C411yescharacteristic
110#14556572—21no—
111#14556570C2×C411yescharacteristic
112#14556556C2311yescharacteristic
113D4×Dic73—21no—
114D4×Dic73C2311yescharacteristic
115#14556553—21no—
116#14556553—21no—
117#14556553C2×C411yescharacteristic
118#14556553C2×C411yescharacteristic
119#14556553C2311yescharacteristic
120#14556553C2311yescharacteristic
121#14556547—21no—
122C2×#11924005—21no—
123C2×C4×Dic73C2311yescharacteristic
124#14556524C2×C411yescharacteristic
125#14556524C2×C411yescharacteristic
126#14556520C2×C411yescharacteristic
127#14556520C2×C411yescharacteristic
128#14556514C2×C411yescharacteristic
129#14556514C2×C411yescharacteristic
130#14556513C2×C411yescharacteristic
131#14556513C2×C411yescharacteristic
132#14556511C2×C411yescharacteristic
133#14556511C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135C8×Dic73C2311yescharacteristic
136C8×Dic73C2311yescharacteristic
137#121×C73C2×C411yescharacteristic
138C2×C4⋊C4×C73C2×C411yescharacteristic
139#106×C73C2×C411yescharacteristic
140#106×C73C2×C411yescharacteristic
141#102×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143C22⋊C8×C73C2×C411yescharacteristic
144#11924037—81no—
145#11924037—81no—
146#11924036—81no—
147#11924036—81no—
148#11924036—81no—
149#11924036—81no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—21no—
155C2×#10596833—21no—
156C2×#10596833—81no—
157C2×#10596833C2×D411yescharacteristic
158C2×#10596833C2×D411yescharacteristic
159C2×#10596833C2×D411yescharacteristic
160C2×#10596833C2×D411yescharacteristic
161C23×D73—21no—
162C2×Dic146C22×C411yescharacteristic
163C2×D292—21no—
164C2×D292—22no—
165C2×D292—22no—
166C2×D292C22×C411yescharacteristic
167C2×D292C22×C411yescharacteristic
168C22×Dic73—21no—
169C22×Dic73C2×D411yescharacteristic
170C22×Dic73#4111yescharacteristic
171C2×C4×D73—21no—
172C2×C4×D73—21no—
173C2×C4×D73—21no—
174C2×C4×D73—21no—
175C2×C4×D73—81no—
176C2×C4×D73—81no—
177#11924017—22no—
178#11924017—22no—
179#11924013—22no—
180#11924013—22no—
181C2×#10596831C22×C411yescharacteristic
182C2×#10596831C22×C411yescharacteristic
183C4⋊Dic73—21no—
184C4⋊Dic73C22×C411yescharacteristic
185#11924007—21no—
186#11924007—21no—
187#11924007—21no—
188C22⋊Dic73—21no—
189C22⋊Dic73—21no—
190C22⋊Dic73—21no—
191C22⋊Dic73—21no—
192#11924005—21no—
193#11924005—21no—
194#11924005—21no—
195#11924005—21no—
196C4×Dic73—21no—
197C4×Dic73C22×C411yescharacteristic
198C4×Dic73C2×D411yescharacteristic
199C4×Dic73#4111yescharacteristic
200C4×Dic73C2411yescharacteristic
201C2×D4×C73—21no—
202C2×D4×C73C22×C411yescharacteristic
203C22×C4×C73—21no—
204C22×C4×C73C22×C411yescharacteristic
205C2×C8×C73C22×C411yescharacteristic
206C2×C8×C73C22×C411yescharacteristic
207C4⋊C4×C73—21no—
208C4⋊C4×C73C22×C411yescharacteristic
209C4⋊C4×C73C22×C411yescharacteristic
210C4⋊C4×C73C22×C411yescharacteristic
211C22⋊C4×C73—21no—
212C23×C73—21no—
213C23×C73C4×D411yescharacteristic
214C22×D73—21no—
215C22×D73—21no—
216C22×D73—24no—
217C22×D73—81no—
218C22×D73—81no—
219D4×C73—21no—
220D4×C73—21no—
221D4×C73—81no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—81no—
228C2×C4×C73C4×D411yescharacteristic
229C2×C4×C73C23×C411yescharacteristic
230C2×Dic73—21no—
231C2×Dic73—21no—
232C2×Dic73—21no—
233C2×Dic73—21no—
234C2×Dic73—41no—
235C2×Dic73—41no—
236C2×Dic73—41no—
237C2×Dic73C4×D411yescharacteristic
238C2×Dic73C4×D411yescharacteristic
239C2×Dic73C22×D411yescharacteristic
240C2×Dic73C2×#4111yescharacteristic
241D292—24no—
242D292—21no—
243D292—21no—
244D292#13112yes—
245D292#13112yes—
246C4×D73—41no—
247C4×D73—41no—
248C4×D73—41no—
249C4×D73—41no—
250C4×D73—81no—
251C4×D73—81no—
252Dic146—21no—
253Dic146—21no—
254#10596833—21no—
255#10596833—21no—
256#10596833—21no—
257#10596833—21no—
258#10596833—41no—
259#10596833—41no—
260#10596833—41no—
261#10596833—41no—
262#10596833—41no—
263#10596833—41no—
264C8×C73—21no—
265C8×C73—21no—
266#10596831—21no—
267#10596831—21no—
268C22×C73—21no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—41no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73C2×C4×D411yescharacteristic
275C2×D73—22no—
276C2×D73—22no—
277C2×D73—41no—
278C2×D73—41no—
279C2×D73—41no—
280C2×D73—41no—
281C2×D73—84no—
282C4×C73—21no—
283C4×C73—41no—
284C4×C73—41no—
285C4×C73—41no—
286C4×C73C2×#13111yescharacteristic
287C4×C73C2×#13111yescharacteristic
288Dic73—21no—
289Dic73—21no—
290Dic73—21no—
291Dic73—41no—
292Dic73—41no—
293Dic73#57611yescharacteristic
294Dic73#57711yescharacteristic
295#17918—731nomaximal, Sylow
296C2×C73—41no—
297C2×C73—81no—
298C2×C73#292911yescharacteristic
299C2×C73#294611yescharacteristic
300C2×C73#295711yescharacteristic
301D73—42no—
302D73—42no—
303#3105—731no—
304#2993—731no—
305#2972—731no—
306#1586—731no—
307#1585—731no—
308#1582—731no—
309#1581—731no—
310#1580—731no—
311SD16⋊C8—731no—
312C8×SD16—731no—
313C8×D8—731no—
314#1574—731no—
315#1486—731no—
316#1482—731no—
317#1454—731no—
318C73#1791811yescharacteristic, complemented, Sylow
319#529—731no—
320C2×C4×D4—731no—
321#484—731no—
322#481#6440811yescharacteristic
323#478—731no—
324#478—731no—
325#463—731no—
326#463—731no—
327#450—731no—
328#447—731no—
329#446—731no—
330C8×Q8—731no—
331C4×SD16—731no—
332C4×SD16—731no—
333C4×D8—731no—
334C4×D8—731no—
335#436—731no—
336#436—1461no—
337#435—1461no—
338C8×D4—731no—
339C8×D4—731no—
340C8×D4—731no—
341C8×D4—731no—
342C8×D4—731no—
343C8×D4—1461no—
344C8×D4—1461no—
345#433—1461no—
346#431—731no—
347#431—731no—
348#431—731no—
349#431—731no—
350#424—1461no—
351#423—731no—
352C2×C22⋊C8—1461no—
353C2×C22⋊C8—1461no—
354#335—731no—
355#335—731no—
356#334—731no—
357#334—731no—
358Q8⋊C8—731no—
359Q8⋊C8—731no—
360D4⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366#322—731no—
367#322—731no—
368#322—731no—
369C82—731no—
370C22×D4—731no—
371C23×C4—1461no—
372C2×SD16—731no—
373C2×SD16—731no—
374C2×D8—731no—
375C2×D8—731no—
376C2×M16—1461no—
377C2×M16—1461no—
378C22×C8—1461no—
379C22×C8—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383#126—1461no—
384#125—731no—
385#124—731no—
386#123—1461no—
387C22⋊Q8—731no—
388#121C2×#6440811yescharacteristic
389C4×Q8—731no—
390C4×D4—731no—
391C4×D4—731no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—731no—
395C4×D4—1461no—
396C4×D4—1461no—
397C4×D4—1461no—
398#117—1461no—
399C2×C4⋊C4C2×#6440811yescharacteristic
400C2×C22⋊C4—1461no—
401C2×C42—731no—
402#107—731no—
403#107—731no—
404#106C2×#6440811yescharacteristic
405#106C2×#6440811yescharacteristic
406C4⋊C8—731no—
407C4⋊C8—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—731no—
414C4⋊C8—1461no—
415C4⋊C8—1461no—
416C4⋊C8—1461no—
417C4⋊C8—1461no—
418#103—731no—
419#103—731no—
420#102—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102C2×#6440811yescharacteristic
425#102C2×#6440811yescharacteristic
426C22⋊C8—731no—
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—1461no—
430C22⋊C8—1461no—
431C22⋊C8—1461no—
432C22⋊C8—1461no—
433C22⋊C8—1461no—
434C22⋊C8—1461no—
435C22⋊C8—1461no—
436C22⋊C8—1461no—
437C22⋊C8C2×#6440811yescharacteristic
438#97—1461no—
439C4×C8—731no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—731no—
445C4×C8—1461no—
446C4×C8—1461no—
447C24—1461no—
448C2×Q8—731no—
449C2×D4—21no—
450C2×D4—731no—
451C2×D4—731no—
452C2×D4—1462no—
453C2×D4—1462no—
454C2×D4—1461no—
455C2×D4C22×#6440811yescharacteristic
456C22×C4—21no—
457C22×C4—5841no—
458C22×C4—5841no—
459C22×C4—731no—
460C22×C4—731no—
461C22×C4—1461no—
462C22×C4—1461no—
463C22×C4—1461no—
464C22×C4—1461no—
465C22×C4—1461no—
466C22×C4C22×#6440811yescharacteristic
467SD16—1462no—
468SD16—1462no—
469D8—1462no—
470D8—1462no—
471M16—5841no—
472M16—5841no—
473C2×C8—5841no—
474C2×C8—5841no—
475C2×C8—5841no—
476C2×C8—5841no—
477C2×C8—5841no—
478C2×C8—731no—
479C2×C8—731no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—1461no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8C22×#6440811yescharacteristic
491C2×C8C22×#6440811yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—731no—
494C4⋊C4—1461no—
495C4⋊C4—1461no—
496C4⋊C4—1461no—
497C4⋊C4—1461no—
498C4⋊C4C22×#6440811yescharacteristic
499C4⋊C4C22×#6440811yescharacteristic
500C4⋊C4C22×#6440811yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—1461no—
503C22⋊C4—1461no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C42—731no—
511C42—731no—
512C42—731no—
513C42—731no—
514C42—1461no—
515C23—21no—
516C23—5841no—
517C23—5841no—
518C23—1464no—
519C23—1461no—
520C23—1461no—
521C23D4×#6440811yescharacteristic
522Q8—1461no—
523Q8—1461no—
524D4—21no—
525D4—21no—
526D4—81no—
527D4—732no—
528D4—732no—
529D4—1464no—
530D4—1461no—
531D4—1461no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—81no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—2921no—
544C2×C4—2921no—
545C2×C4—5841no—
546C2×C4—5841no—
547C2×C4—731no—
548C2×C4—731no—
549C2×C4—731no—
550C2×C4—731no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4D4×#6440811yescharacteristic
556C2×C4C23×#6440811yescharacteristic
557C8—21no—
558C8—21no—
559C8—2921no—
560C8—2921no—
561C8—2921no—
562C8—2921no—
563C8—2921no—
564C8—2921no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1461no—
570C8—1461no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—2921no—
578C22—2921no—
579C22—2921no—
580C22—2921no—
581C22—5844no—
582C22—1462no—
583C22—1462no—
584C22C2×D4×#6440811yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—2921no—
590C4—2921no—
591C4—731no—
592C4—731no—
593C4—1461no—
594C4—1461no—
595C4—1461no—
596C4D73⋊#13111yescharacteristic
597C4D73⋊#13111yescharacteristic
598C2—41no—
599C2—81no—
600C2—2922no—
601C2—2922no—
602C2#2262664811yescharacteristic
603C2#2262668811yescharacteristic
604C2#2262670911yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting#481×C73C4
socleC22×C73C2×C4×D4
prime radical#17988720C4
cosocleC4×Dic73C24
hypercenter#481#64408
hypocenterC73#17918
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
1. #22626873C2semidirect
2. #22626781C2semidirect
3. #22625553C2semidirect
4. #22625547C2semidirect
5. #22625535C2semidirect
6. #22625533C2semidirect
7. #22625528C2semidirect
8. #22625523C2semidirect
9. #22625516C2semidirect
10. #22625511C2semidirect
11. #22625507C2semidirect
12. #22625258C2semidirect
13. #22625242C2semidirect
14. #22625152C2semidirect
16. #17989637C22semidirect
17. #17989636C22semidirect
19. #17989622C22semidirect
27. D4×#10596833C22semidirect
36. #17989451C22semidirect
37. #17989450C22semidirect
38. #17989449C22semidirect
39. #17989448C22semidirect
40. #17989437C22semidirect
41. #17989437C22semidirect
46. D4⋊#10596833C22semidirect
47. D4⋊#10596833C22semidirect
48. #17989429C22semidirect
49. #17989429C22semidirect
50. #17989428C22semidirect
51. C8×#10596833C22semidirect
318. C73#17918semidirect

Maximal subgroups

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

subgroupindex
#226268732
#226267812
#226255532
#226255472
#226255352
#226255332
#226255282
#226255232
#226255162
#226255112
#226255072
#226252582
#226252422
#226251522
#226199752
#1791873