Finite Group Databasebeta

← #34019236

Subgroups — #34019236

Order 18688.

650 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626878C211yesmaximal, characteristic, complemented
2#22626787C211yesmaximal, characteristic, complemented
3#22625568C211yesmaximal, characteristic, complemented
4#22625564C211yesmaximal, characteristic, complemented
5#22625561C211yesmaximal, characteristic, complemented
6#22625552C211yesmaximal, characteristic, complemented
7#22625552C211yesmaximal, characteristic, complemented
8#22625546C211yesmaximal, characteristic, complemented
9#22625514C211yesmaximal, characteristic, complemented
10D8×#10596833C211yesmaximal, characteristic, complemented
11#22625506C211yesmaximal, characteristic, complemented
12#22625282C211yesmaximal, characteristic, complemented
13C2×D4⋊#10596833C211yesmaximal, characteristic, complemented
14#22625136C211yesmaximal, characteristic, complemented
15#22619973C211yesmaximal, characteristic
16#17989637C2211yescharacteristic, complemented
17#17989636C2211yescharacteristic, complemented
18#17989622C2211yescharacteristic
19#17989622C2211yescharacteristic
20#17989622C2211yescharacteristic, complemented
21#17989618—21no—
22#17989618—21no—
23#17989618—21no—
24D4×#10596833—21no—
25D4×#10596833C2211yescharacteristic
26D4×#10596833C2211yescharacteristic
27D4×#10596833C2211yescharacteristic, complemented
28#17989611—21no—
29#17989608C2211yescharacteristic
30#17989604C2211yescharacteristic
31#17989593—21no—
32C2×C4⋊#10596833C2211yescharacteristic
33#17989557—21no—
34C2×C22⋊#10596833—21no—
35C2×C4×#10596833C2211yescharacteristic
36#17989450C2211yescharacteristic, complemented
37#17989450C2211yescharacteristic, complemented
38#17989449C2211yescharacteristic, complemented
39#17989449C2211yescharacteristic, complemented
40#17989437C2211yescharacteristic, complemented
41#17989437C2211yescharacteristic, complemented
42D4⋊#10596833C2211yescharacteristic
43D4⋊#10596833C2211yescharacteristic
44D4⋊#10596833C2211yescharacteristic
45D4⋊#10596833C2211yescharacteristic
46D4⋊#10596833C2211yescharacteristic, complemented
47D4⋊#10596833C2211yescharacteristic, complemented
48#17989429C2211yescharacteristic, complemented
49#17989429C2211yescharacteristic, complemented
50C8×#10596833C2211yescharacteristic, complemented
51C8×#10596833C2211yescharacteristic, complemented
52#17989118C2211yescharacteristic
53C2×D4×Dic73C2211yescharacteristic
54#17988923C411yescharacteristic
55#17988903C411yescharacteristic
56#17988885C411yescharacteristic
57#17988885C411yescharacteristic
58#17988800C411yescharacteristic
59#17988800C411yescharacteristic
60#17988738C411yescharacteristic
61#17988678C2211yescharacteristic
62#17988678C2211yescharacteristic
63D8×Dic73C2211yescharacteristic
64D8×Dic73C2211yescharacteristic
65#17988637C2211yescharacteristic
66#447×C73C411yescharacteristic
67C2×#11924037—21no—
68C2×#11924037—21no—
69C2×#11924037—21no—
70C22×#10596833—21no—
71C22×#10596833—21no—
72C22×#10596833—21no—
73C22×#10596833—21no—
74C22×#10596833—21no—
75#14556658—21no—
76#14556658D411yescharacteristic
77#14556658D411yescharacteristic
78C4⋊#10596833—21no—
79C4⋊#10596833—21no—
80C4⋊#10596833C2311yescharacteristic
81C4⋊#10596833C2311yescharacteristic
82C4⋊#10596833C2311yescharacteristic
83C4⋊#10596833C2311yescharacteristic
84C22⋊#10596833—21no—
85C22⋊#10596833—21no—
86C22⋊#10596833—21no—
87C22⋊#10596833—21no—
88C22⋊#10596833—21no—
89C22⋊#10596833—21no—
90C22⋊#10596833—21no—
91C22⋊#10596833D411yescharacteristic
92C22⋊#10596833D411yescharacteristic
93#14556646—21no—
94#14556646—21no—
95C4×#10596833—21no—
96C4×#10596833—21no—
97C4×#10596833C2311yescharacteristic
98C4×#10596833C2311yescharacteristic
99C4×#10596833C2311yescharacteristic
100C4×#10596833C2311yescharacteristic
101C23×Dic73—21no—
102C2×#11924016C2×C411yescharacteristic
103C2×#11924016C2×C411yescharacteristic
104#14556584—21no—
105#14556582C2×C411yescharacteristic
106#14556578C2×C411yescharacteristic
107#14556572—21no—
108#14556570C2×C411yescharacteristic
109#14556556C2311yescharacteristic
110D4×Dic73—21no—
111D4×Dic73—21no—
112D4×Dic73—21no—
113D4×Dic73C2×C411yescharacteristic
114D4×Dic73C2×C411yescharacteristic
115D4×Dic73C2311yescharacteristic
116D4×Dic73C2311yescharacteristic
117D4×Dic73C2311yescharacteristic
118#14556547—21no—
119C2×C4⋊Dic73C2×C411yescharacteristic
120C2×C22⋊Dic73—21no—
121C2×C4×Dic73C2311yescharacteristic
122#14556525C2×C411yescharacteristic
123#14556525C2×C411yescharacteristic
124#14556522C2×C411yescharacteristic
125#14556522C2×C411yescharacteristic
126#14556520C2×C411yescharacteristic
127#14556520C2×C411yescharacteristic
128#14556516C2×C411yescharacteristic
129#14556516C2×C411yescharacteristic
130#14556512C2×C411yescharacteristic
131#14556512C2×C411yescharacteristic
132#14556512C2×C411yescharacteristic
133#14556512C2×C411yescharacteristic
134C22⋊#10596831C2×C411yescharacteristic
135C8×Dic73C2311yescharacteristic
136C8×Dic73C2311yescharacteristic
137C22×D4×C73C2×C411yescharacteristic
138C2×D8×C73C2×C411yescharacteristic
139C2×D8×C73C2×C411yescharacteristic
140#121×C73C2×C411yescharacteristic
141#102×C73C2×C411yescharacteristic
142#102×C73C2×C411yescharacteristic
143C22⋊C8×C73C2×C411yescharacteristic
144#11924037—81no—
145#11924037—81no—
146#11924037—81no—
147C2×#10596833—24no—
148C2×#10596833—21no—
149C2×#10596833—21no—
150C2×#10596833—21no—
151C2×#10596833—21no—
152C2×#10596833—21no—
153C2×#10596833—21no—
154C2×#10596833—81no—
155C2×#10596833—81no—
156C2×#10596833—81no—
157C2×#10596833—81no—
158C2×#10596833C2×D411yescharacteristic
159C2×#10596833C2×D411yescharacteristic
160C2×#10596833C2×D411yescharacteristic
161C2×#10596833C2×D411yescharacteristic
162C2×Dic146C22×C411yescharacteristic
163C22×Dic73—21no—
164C22×Dic73—21no—
165C22×Dic73—21no—
166C22×Dic73—21no—
167C22×Dic73—21no—
168C22×Dic73—21no—
169C22×Dic73—81no—
170C22×Dic73—81no—
171C22×Dic73C2×D411yescharacteristic
172C22×Dic73#4111yescharacteristic
173#11924016—22no—
174#11924016—41no—
175C2×#10596831C22×C411yescharacteristic
176C2×#10596831C22×C411yescharacteristic
177C4⋊Dic73—21no—
178C4⋊Dic73—21no—
179C4⋊Dic73C22×C411yescharacteristic
180C4⋊Dic73C22×C411yescharacteristic
181C4⋊Dic73C22×C411yescharacteristic
182#11924007—21no—
183#11924007—21no—
184#11924007—21no—
185C22⋊Dic73—21no—
186C22⋊Dic73—21no—
187C22⋊Dic73—21no—
188C22⋊Dic73—21no—
189C22⋊Dic73—21no—
190C22⋊Dic73—21no—
191C22⋊Dic73—21no—
192C22⋊Dic73—21no—
193C4×Dic73—21no—
194C4×Dic73C22×C411yescharacteristic
195C4×Dic73C2×D411yescharacteristic
196C4×Dic73#4111yescharacteristic
197C4×Dic73C2411yescharacteristic
198C24×C73—21no—
199C2×D4×C73—22no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—41no—
203C2×D4×C73C22×C411yescharacteristic
204C2×D4×C73C22×C411yescharacteristic
205C2×D4×C73C22×C411yescharacteristic
206C22×C4×C73C22×C411yescharacteristic
207D8×C73—22no—
208D8×C73—41no—
209C2×C8×C73C22×C411yescharacteristic
210C2×C8×C73C22×C411yescharacteristic
211C4⋊C4×C73C22×C411yescharacteristic
212C22⋊C4×C73—21no—
213C23×C73—21no—
214C23×C73—21no—
215C23×C73—21no—
216C23×C73—42no—
217C23×C73—42no—
218C23×C73—81no—
219C23×C73C4×D411yescharacteristic
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224D4×C73—21no—
225D4×C73—42no—
226D4×C73—42no—
227D4×C73#13112yes—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73C4×D411yescharacteristic
232C2×C4×C73C23×C411yescharacteristic
233C2×Dic73—22no—
234C2×Dic73—21no—
235C2×Dic73—21no—
236C2×Dic73—21no—
237C2×Dic73—21no—
238C2×Dic73—21no—
239C2×Dic73—21no—
240C2×Dic73—41no—
241C2×Dic73—41no—
242C2×Dic73—41no—
243C2×Dic73—41no—
244C2×Dic73—41no—
245C2×Dic73—41no—
246C2×Dic73—81no—
247C2×Dic73—81no—
248C2×Dic73—81no—
249C2×Dic73C4×D411yescharacteristic
250C2×Dic73C4×D411yescharacteristic
251C2×Dic73C22×D411yescharacteristic
252C2×Dic73C2×#4111yescharacteristic
253Dic146—21no—
254Dic146—21no—
255#10596833—22no—
256#10596833—22no—
257#10596833—21no—
258#10596833—21no—
259#10596833—21no—
260#10596833—21no—
261#10596833—41no—
262#10596833—41no—
263#10596833—41no—
264#10596833—41no—
265C8×C73—21no—
266C8×C73—21no—
267#10596831—21no—
268#10596831—21no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—22no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—41no—
276C22×C73—41no—
277C22×C73—41no—
278C22×C73—41no—
279C22×C73—41no—
280C22×C73—84no—
281C22×C73#44312yes—
282C22×C73C2×C4×D411yescharacteristic
283C4×C73—21no—
284C4×C73—41no—
285C4×C73C2×#13111yescharacteristic
286C4×C73#56811yescharacteristic
287Dic73—21no—
288Dic73—21no—
289Dic73—21no—
290Dic73—41no—
291Dic73—41no—
292Dic73—41no—
293Dic73—41no—
294Dic73#57611yescharacteristic
295Dic73#57711yescharacteristic
296#18014—731nomaximal, Sylow
297C2×C73—22no—
298C2×C73—42no—
299C2×C73—81no—
300C2×C73—81no—
301C2×C73#293311yescharacteristic
302C2×C73#294611yescharacteristic
303C2×C73C2×#44311yescharacteristic
304#3105—731no—
305#2994—731no—
306#2974—731no—
307#1590—731no—
308#1589—731no—
309#1588—731no—
310#1586—731no—
311#1586—731no—
312#1585—731no—
313C8×SD16—731no—
314C8×D8—731no—
315#1573—731no—
316#1494—731no—
317C2×D4⋊C8—731no—
318#1450—731no—
319C73#1801411yescharacteristic, complemented, Sylow
320#529—731no—
321C2×C4×D4—731no—
322#484—731no—
323#481—731no—
324#478—731no—
325#478—731no—
326#463—731no—
327#463—731no—
328#450—731no—
329#447#6440811yescharacteristic
330#446—731no—
331C8×Q8—731no—
332C4×SD16—731no—
333C4×SD16—731no—
334C4×D8—731no—
335C4×D8—731no—
336#436—731no—
337#436—731no—
338#436—731no—
339#435—1461no—
340#435—1461no—
341#435—1461no—
342C8×D4—731no—
343C8×D4—731no—
344C8×D4—731no—
345C8×D4—1461no—
346#433—1461no—
347#432—731no—
348#431—731no—
349#431—731no—
350#424—1461no—
351C2×C4⋊C8—731no—
352#407—1461no—
353C2×C22⋊C8—1461no—
354C2×C4×C8—731no—
355#335—731no—
356#335—731no—
357#334—731no—
358#334—731no—
359Q8⋊C8—731no—
360Q8⋊C8—731no—
361D4⋊C8—731no—
362D4⋊C8—731no—
363D4⋊C8—731no—
364D4⋊C8—731no—
365D4⋊C8—731no—
366D4⋊C8—731no—
367#322—731no—
368#322—731no—
369C82—731no—
370C82—731no—
371C22×D4C2×#6440811yescharacteristic
372C23×C4—1461no—
373C2×SD16—731no—
374C2×SD16—731no—
375C2×D8C2×#6440811yescharacteristic
376C2×D8C2×#6440811yescharacteristic
377C2×M16—1461no—
378C2×M16—1461no—
379C2×M16—1461no—
380C22×C8—1461no—
381C22×C8—1461no—
382C22×C8—1461no—
383C22×C8—1461no—
384C22×C8—1461no—
385#126—1461no—
386#125—731no—
387#124—731no—
388#123—1461no—
389C22⋊Q8—731no—
390#121C2×#6440811yescharacteristic
391C4×Q8—731no—
392C4×D4—731no—
393C4×D4—731no—
394C4×D4—731no—
395C4×D4—731no—
396C4×D4—731no—
397C4×D4—1461no—
398C4×D4—1461no—
399C4×D4—1461no—
400#117—1461no—
401C2×C4⋊C4—731no—
402C2×C22⋊C4—1461no—
403C2×C42—731no—
404#107—731no—
405#107—731no—
406#106—731no—
407#106—731no—
408C4⋊C8—731no—
409C4⋊C8—731no—
410C4⋊C8—731no—
411C4⋊C8—731no—
412C4⋊C8—731no—
413C4⋊C8—731no—
414C4⋊C8—731no—
415C4⋊C8—731no—
416C4⋊C8—1461no—
417C4⋊C8—1461no—
418C4⋊C8—1461no—
419#103—731no—
420#103—731no—
421#102—731no—
422#102—731no—
423#102—731no—
424#102—731no—
425#102C2×#6440811yescharacteristic
426#102C2×#6440811yescharacteristic
427C22⋊C8—731no—
428C22⋊C8—731no—
429C22⋊C8—731no—
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—
439#97—1461no—
440C4×C8—731no—
441C4×C8—731no—
442C4×C8—731no—
443C4×C8—731no—
444C4×C8—731no—
445C4×C8—731no—
446C4×C8—1461no—
447C4×C8—1461no—
448C24—21no—
449C2×Q8—731no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4C22×#6440811yescharacteristic
455C2×D4C22×#6440811yescharacteristic
456C2×D4C22×#6440811yescharacteristic
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×C4—1461no—
467C22×C4C22×#6440811yescharacteristic
468SD16—2921no—
469SD16—1462no—
470D8—22no—
471D8—41no—
472M16—5841no—
473M16—5841no—
474M16—5841no—
475C2×C8—5841no—
476C2×C8—5841no—
477C2×C8—5841no—
478C2×C8—5841no—
479C2×C8—731no—
480C2×C8—731no—
481C2×C8—731no—
482C2×C8—731no—
483C2×C8—731no—
484C2×C8—731no—
485C2×C8—1461no—
486C2×C8—1461no—
487C2×C8—1461no—
488C2×C8—1461no—
489C2×C8—1461no—
490C2×C8—1461no—
491C2×C8—1464no—
492C2×C8C22×#6440811yescharacteristic
493C2×C8C22×#6440811yescharacteristic
494C4⋊C4—731no—
495C4⋊C4—731no—
496C4⋊C4—731no—
497C4⋊C4—1461no—
498C4⋊C4—1461no—
499C4⋊C4—1461no—
500C4⋊C4—1461no—
501C4⋊C4—1461no—
502C4⋊C4C22×#6440811yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—1461no—
505C22⋊C4—1461no—
506C22⋊C4—1461no—
507C22⋊C4—1461no—
508C22⋊C4—1461no—
509C22⋊C4—1461no—
510C22⋊C4—1461no—
511C22⋊C4—1461no—
512C42—731no—
513C42—731no—
514C42—731no—
515C42—731no—
516C42—1461no—
517C23—21no—
518C23—21no—
519C23—21no—
520C23—42no—
521C23—42no—
522C23—81no—
523C23D4×#6440811yescharacteristic
524Q8—1461no—
525Q8—1461no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—42no—
532D4—42no—
533D4#1455667812yes—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—2921no—
538C2×C4—2921no—
539C2×C4—2921no—
540C2×C4—2921no—
541C2×C4—2921no—
542C2×C4—2921no—
543C2×C4—5841no—
544C2×C4—5841no—
545C2×C4—5841no—
546C2×C4—731no—
547C2×C4—731no—
548C2×C4—731no—
549C2×C4—731no—
550C2×C4—1461no—
551C2×C4—1461no—
552C2×C4—1461no—
553C2×C4—1461no—
554C2×C4—1461no—
555C2×C4—1461no—
556C2×C4—1462no—
557C2×C4D4×#6440811yescharacteristic
558C2×C4C23×#6440811yescharacteristic
559C8—21no—
560C8—21no—
561C8—2921no—
562C8—2921no—
563C8—2921no—
564C8—2921no—
565C8—1461no—
566C8—1461no—
567C8—1461no—
568C8—1461no—
569C8—1462no—
570C8—1462no—
571C8—1461no—
572C8—1461no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—84no—
585C22#1798962912yes—
586C22C2×D4×#6440811yescharacteristic
587C4—21no—
588C4—41no—
589C4—2921no—
590C4—2921no—
591C4—2921no—
592C4—2921no—
593C4—731no—
594C4—731no—
595C4—1461no—
596C4—1461no—
597C4—1461no—
598C4C2×#1455667811yescharacteristic
599C4#1798966511yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—81no—
604C2#2262666311yescharacteristic
605C2#2262668811yescharacteristic
606C2C2×#1798962911yescharacteristic
subgroupG/H
centerC22C2×D4×#64408
commutatorC2×C4×C73C23×C4
FrattiniC2×C4C23×#64408
Fitting, prime radical#447×C73C4
socleC22×C73C2×C4×D4
cosocleC4×Dic73C24
hypercenter#447#64408
hypocenterC73#18014
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. #22626878C2semidirect
2. #22626787C2semidirect
3. #22625568C2semidirect
4. #22625564C2semidirect
5. #22625561C2semidirect
6. #22625552C2semidirect
7. #22625552C2semidirect
8. #22625546C2semidirect
9. #22625514C2semidirect
10. D8×#10596833C2semidirect
11. #22625506C2semidirect
12. #22625282C2semidirect
13. C2×D4⋊#10596833C2semidirect
14. #22625136C2semidirect
16. #17989637C22semidirect
17. #17989636C22semidirect
20. #17989622C22semidirect
27. D4×#10596833C22semidirect
36. #17989450C22semidirect
37. #17989450C22semidirect
38. #17989449C22semidirect
39. #17989449C22semidirect
40. #17989437C22semidirect
41. #17989437C22semidirect
46. D4⋊#10596833C22semidirect
47. D4⋊#10596833C22semidirect
48. #17989429C22semidirect
49. #17989429C22semidirect
50. C8×#10596833C22semidirect
51. C8×#10596833C22semidirect
319. C73#18014semidirect

Maximal subgroups

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

subgroupindex
#226268782
#226267872
#226255682
#226255642
#226255612
#226255522
#226255462
#226255142
D8×#105968332
#226255062
#226252822
C2×D4⋊#105968332
#226251362
#226199732
#1801473