Finite Group Databasebeta

← #30611969

Subgroups — #30611969

Order 15616.

904 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462746C211yesmaximal, characteristic
2#21462746C211yesmaximal, characteristic
3#21461358C211yesmaximal, characteristic, complemented
4#21461349C212yesmaximal, complemented
5#21461341C212yesmaximal, complemented
6#21461341C212yesmaximal, complemented
7#21461334C211yesmaximal, characteristic, complemented
8#21461328C211yesmaximal, characteristic, complemented
9#21461324C211yesmaximal, characteristic, complemented
10D61⋊#332C212yesmaximal, complemented
11#21459634C211yesmaximal, characteristic
12#16840812—21no—
13#16840812—21no—
14#16840794—22no—
15#16840794—22no—
16#16840790—21no—
17#16840790—21no—
18#16840785C2212yes—
19#16840785C2212yes—
20#16840779C2211yescharacteristic
21#16840779C2211yescharacteristic
22#16840765C2211yescharacteristic
23#16840765C2211yescharacteristic
24D61⋊(C4⋊C8)C2212yes—
25D61⋊(C4⋊C8)C2212yes—
26#16840621C2211yescharacteristic
27#16840621C2212yes—
28#16840621C2212yes—
29#16840621C2212yes—
30#16840621C2211yescharacteristic
31#16840621C2211yescharacteristic
32#16840621C2211yescharacteristic
33#16840621C2212yes—
34#16840621C2212yes—
35#16840621C2212yes—
36#16840492—21no—
37#16840489—21no—
38#16840468—21no—
39#16840466—22no—
40#16840427—21no—
41#16840425—22no—
42#16840392C412yes—
43#16840390C411yescharacteristic
44#16840389C412yes—
45#16840318C2212yes—
46#16840315C2211yescharacteristic
47C2×#14519776C2211yescharacteristic
48C4⋊Q8×D61C2212yes—
49#16840243C411yescharacteristic
50#16840242C411yescharacteristic
51#16840230C2211yescharacteristic
52C61×#544C411yescharacteristic
53C2×#11758217—21no—
54C2×#11758217—21no—
55C2×D61⋊C8—22no—
56C2×D61⋊C8—22no—
57#14519844C2311yescharacteristic
58#14519844C2311yescharacteristic
59#14519844C2312yes—
60#14519844C2312yes—
61#14519844C2311yescharacteristic
62#14519844C2311yescharacteristic
63C4⋊#92420—22no—
64C4⋊#92420—22no—
65C4⋊#92420—21no—
66C4⋊#92420—21no—
67#14519834—22no—
68#14519834—22no—
69C22⋊#92420—21no—
70C22⋊#92420—21no—
71#14519832—22no—
72#14519832—22no—
73C4×#92420—21no—
74C4×#92420—21no—
75C2×#11758222C2×C411yescharacteristic
76C22×Dic122—21no—
77C2×Q8×D61—22no—
78#14519777C2×C412yes—
79#14519776—21no—
80#14519776—22no—
81#14519776—21no—
82#14519776—22no—
83#14519776—21no—
84#14519776C2×C412yes—
85#14519776C2311yescharacteristic
86#14519776C2312yes—
87#14519776C2311yescharacteristic
88#14519775—22no—
89#14519775—22no—
90#14519769C2×C412yes—
91#14519768—21no—
92#14519768C2×C411yescharacteristic
93#14519768C2×C411yescharacteristic
94#14519767—22no—
95#14519767—22no—
96#14519757—22no—
97#14519755—22no—
98#14519755—22no—
99#14519755—22no—
100#14519755—22no—
101#14519754—21no—
102#14519754—21no—
103#14519754—22no—
104#14519753—22no—
105C4×Dic122—21no—
106C4×Dic122—21no—
107C4×Dic122—21no—
108#14519742—21no—
109#14519742—22no—
110#14519742—22no—
111#14519742D411yescharacteristic
112#14519742D411yescharacteristic
113C4×D244—21no—
114#14519739—21no—
115#14519739D411yescharacteristic
116#14519739D411yescharacteristic
117C4×C22⋊D61—22no—
118#14519737—22no—
119#14519737D412yes—
120#14519737D412yes—
121#14519736C2×C411yescharacteristic
122#14519735C2×C412yes—
123#14519735C2×C412yes—
124#14519734C2×C412yes—
125C2×C4⋊Dic61C2×C411yescharacteristic
126C2×#11758196—21no—
127C4⋊C4×D61—22no—
128C4⋊C4×D61C2×C412yes—
129C4⋊C4×D61C2×C412yes—
130C2×C4×Dic61C2311yescharacteristic
131C42×D61C2312yes—
132C4⋊Q8×C61—21no—
133C4⋊Q8×C61C2×C412yes—
134#125×C61—21no—
135#125×C61C2×C412yes—
136C22⋊Q8×C61—22no—
137#117×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139C2×C4⋊C4×C61C2×C411yescharacteristic
140C2×Q8×C61—22no—
141C22×C4×C61—21no—
142C22×C4×C61C22×C411yescharacteristic
143C2×C22⋊D61C22⋊C412yes—
144C22×Dic61—21no—
145C22×Dic61C2×D411yescharacteristic
146C22×Dic61C2×D411yescharacteristic
147Q8×D61—82no—
148Q8×D61—82no—
149#11758222—24no—
150C2×D244C22⋊C411yescharacteristic
151C2×C4×D61—22no—
152C2×C4×D61—22no—
153C2×C4×D61C22×C412yes—
154C2×C4×D61C2×D412yes—
155C2×C4×D61C2×D412yes—
156C2×Dic122—21no—
157C2×Dic122—22no—
158C2×Dic122—21no—
159C2×Dic122—22no—
160C2×Dic122—22no—
161C2×Dic122—81no—
162C2×Dic122—81no—
163C2×Dic122C22⋊C411yescharacteristic
164#11758217—81no—
165#11758217—81no—
166C2×#92420—21no—
167C2×#92420—21no—
168C2×#92420—21no—
169C2×#92420—21no—
170C2×#92420—22no—
171C2×#92420—22no—
172D61⋊C8—82no—
173D61⋊C8—82no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—22no—
176C4⋊C4×C61—22no—
177C4⋊C4×C61—22no—
178C4⋊C4×C61C22⋊C411yescharacteristic
179C4⋊C4×C61C22⋊C411yescharacteristic
180C4⋊C4×C61C22×C412yes—
181C4⋊C4×C61C22×C411yescharacteristic
182C4⋊C4×C61C22×C411yescharacteristic
183C22⋊C4×C61—21no—
184C22⋊C4×C61C22⋊C412yes—
185C42×C61—21no—
186C42×C61C22×C412yes—
187C22⋊Dic61—21no—
188#11758198—22no—
189#11758198—22no—
190#11758198C22⋊C412yes—
191#11758198C22⋊C412yes—
192C4⋊Dic61—22no—
193C4⋊Dic61—21no—
194C4⋊Dic61—21no—
195C4⋊Dic61—21no—
196C4⋊Dic61C22×C411yescharacteristic
197C4⋊Dic61C22×C412yes—
198C4⋊Dic61C22×C411yescharacteristic
199#11758196—22no—
200#11758196—22no—
201#11758196—22no—
202#11758196—22no—
203#11758196—22no—
204#11758196—21no—
205#11758196—21no—
206#11758196—21no—
207#11758196—22no—
208#11758196—21no—
209#11758196C22⋊C412yes—
210#11758196C22⋊C412yes—
211C4×Dic61—21no—
212C4×Dic61—22no—
213C4×Dic61—22no—
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217C4×Dic61C2×D412yes—
218C4×Dic61C2×D412yes—
219C4×Dic61C2411yescharacteristic
220C23×C61C2×C22⋊C411yescharacteristic
221C22×D61C2×C22⋊C412yes—
222Q8×C61—82no—
223C2×C4×C61—22no—
224C2×C4×C61—21no—
225C2×C4×C61—22no—
226C2×C4×C61—21no—
227C2×C4×C61—81no—
228C2×C4×C61C2×C22⋊C412yes—
229C2×C4×C61C2×C22⋊C412yes—
230C2×C4×C61C2×C22⋊C411yescharacteristic
231C2×C4×C61C23×C411yescharacteristic
232C22⋊D61—24no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236C2×Dic61—21no—
237C2×Dic61—21no—
238C2×Dic61—22no—
239C2×Dic61—21no—
240C2×Dic61—81no—
241C2×Dic61C2×C22⋊C412yes—
242C2×Dic61C2×C22⋊C411yescharacteristic
243C2×Dic61C2×C22⋊C411yescharacteristic
244C2×Dic61C22×D411yescharacteristic
245C2×Dic61C22×D411yescharacteristic
246D244#10114yes—
247C4×D61—24no—
248C4×D61—22no—
249C4×D61—22no—
250C4×D61—22no—
251C4×D61—22no—
252C4×D61—82no—
253C4×D61—82no—
254Dic122—22no—
255Dic122—42no—
256Dic122—41no—
257Dic122—41no—
258Dic122—42no—
259Dic122—41no—
260Dic122—41no—
261Dic122—82no—
262Dic122—82no—
263#92420—41no—
264#92420—42no—
265#92420—41no—
266#92420—42no—
267#92420—41no—
268#92420—41no—
269#17774—611nomaximal, Sylow
270C22×C61—21no—
271C22×C61—21no—
272C22×C61—21no—
273C22×C61C22×C22⋊C411yescharacteristic
274C2×D61—22no—
275C2×D61—22no—
276C2×D61C2×#10114yes—
277C4×C61—21no—
278C4×C61—22no—
279C4×C61—22no—
280C4×C61—42no—
281C4×C61—41no—
282C4×C61—41no—
283C4×C61C2×#10112yes—
284Dic61—22no—
285Dic61—21no—
286Dic61—21no—
287Dic61—41no—
288Dic61—42no—
289Dic61—41no—
290Dic61#57611yescharacteristic
291Dic61#57711yescharacteristic
292Dic61#57711yescharacteristic
293Dic61#57811yescharacteristic
294#3503—611no—
295#2990—611no—
296#2990—611no—
297#1561—611no—
298#1556—612no—
299#1552—612no—
300#1552—612no—
301#1549—611no—
302#1546—611no—
303#1544—611no—
304C2×#332—612no—
305C2×C61—41no—
306C2×C61C22×#10111yescharacteristic
307C2×C61#289711yescharacteristic
308C2×C61#289811yescharacteristic
309D61—24no—
310Q82—1221no—
311#557—1221no—
312#554—1222no—
313#554—1221no—
314D4×Q8—1222no—
315D4×Q8—1221no—
316#544—612no—
317#544—612no—
318#544—611no—
319#544#692311yescharacteristic
320#533—612no—
321#533—611no—
322C2×C4⋊Q8—612no—
323C2×C4⋊Q8—611no—
324#520—611no—
325#520—611no—
326C4×#41—611no—
327#446—1221no—
328#446—1221no—
329#435—1222no—
330#435—1222no—
331C8×D4—1221no—
332C8×D4—1221no—
333#432—612no—
334#432—612no—
335#431—611no—
336#431—611no—
337#423—611no—
338#423—611no—
339C2×C4⋊C8—612no—
340C2×C4⋊C8—612no—
341#332—611no—
342#332—612no—
343#332—612no—
344#332—612no—
345#332—611no—
346#332—611no—
347#332—611no—
348#332—612no—
349#332—612no—
350#332—612no—
351C61#1777411yescharacteristic, complemented, Sylow
352C2×#41—611no—
353C22×Q8—1221no—
354C22×Q8—1222no—
355C2×M16—1221no—
356C2×M16—1221no—
357C22×C8—1222no—
358C22×C8—1222no—
359C4⋊Q8—21no—
360C4⋊Q8—611no—
361C4⋊Q8—612no—
362C4⋊Q8—612no—
363C4⋊Q8—611no—
364C4⋊Q8—612no—
365C4⋊Q8—1221no—
366C4⋊Q8—1222no—
367C4⋊Q8—1221no—
368C4⋊Q8—1222no—
369C4⋊Q8—1222no—
370C4⋊Q8—1222no—
371C4⋊Q8—1221no—
372C4⋊Q8C2×#692312yes—
373#125—21no—
374#125—611no—
375#125—611no—
376#125—612no—
377#125—1222no—
378#125—1222no—
379#125—1221no—
380#125C2×#692312yes—
381C22⋊Q8—22no—
382C22⋊Q8—1221no—
383C22⋊Q8—1221no—
384C22⋊Q8—1222no—
385C22⋊Q8—1222no—
386C22⋊Q8—1222no—
387C22⋊Q8—1222no—
388C22⋊Q8—1222no—
389C22⋊Q8—1222no—
390C22⋊Q8—1222no—
391C4×Q8—611no—
392C4×Q8—611no—
393C4×Q8—1221no—
394C4×Q8—1221no—
395C4×Q8—1221no—
396C4×Q8—1222no—
397C4×Q8—1222no—
398C4×Q8—1221no—
399C4×D4—611no—
400C4×D4—611no—
401C4×D4—612no—
402C4×D4—612no—
403C4×D4—1221no—
404C4×D4—1222no—
405C4×D4—1221no—
406C4×D4—1222no—
407#117—612no—
408#117—611no—
409#117—612no—
410#117—612no—
411#117C2×#692311yescharacteristic
412#117C2×#692311yescharacteristic
413C2×C4⋊C4—611no—
414C2×C4⋊C4—612no—
415C2×C4⋊C4—612no—
416C2×C4⋊C4—1222no—
417C2×C4⋊C4—1221no—
418C2×C4⋊C4C2×#692311yescharacteristic
419C2×C42—611no—
420C2×C42—612no—
421C4⋊C8—611no—
422C4⋊C8—611no—
423C4⋊C8—612no—
424C4⋊C8—612no—
425C4⋊C8—611no—
426C4⋊C8—611no—
427C4⋊C8—1222no—
428C4⋊C8—1222no—
429C4⋊C8—1221no—
430C4⋊C8—1221no—
431C22⋊C8—1221no—
432C22⋊C8—1221no—
433C22⋊C8—1222no—
434C22⋊C8—1222no—
435#97—1222no—
436#97—1222no—
437C4×C8—1221no—
438C4×C8—1221no—
439#41—1224no—
440C2×Q8—22no—
441C2×Q8—611no—
442C2×Q8—1222no—
443C2×Q8—1221no—
444C2×Q8—1221no—
445C2×Q8—1222no—
446C2×Q8—1222no—
447C2×Q8—4881no—
448C2×Q8—4881no—
449C2×Q8—4882no—
450C2×Q8—4882no—
451C2×D4—612no—
452C2×D4—611no—
453C22×C4—21no—
454C22×C4—611no—
455C22×C4—611no—
456C22×C4—612no—
457C22×C4—612no—
458C22×C4—612no—
459C22×C4—1222no—
460C22×C4—1222no—
461C22×C4—1221no—
462C22×C4C22×#692311yescharacteristic
463M16—4881no—
464M16—4881no—
465C2×C8—1221no—
466C2×C8—1221no—
467C2×C8—1221no—
468C2×C8—1221no—
469C2×C8—1222no—
470C2×C8—1222no—
471C2×C8—4882no—
472C2×C8—4882no—
473C4⋊C4—22no—
474C4⋊C4—21no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—612no—
478C4⋊C4—612no—
479C4⋊C4—612no—
480C4⋊C4—611no—
481C4⋊C4—611no—
482C4⋊C4—1222no—
483C4⋊C4—1222no—
484C4⋊C4—1221no—
485C4⋊C4—1222no—
486C4⋊C4—1222no—
487C4⋊C4—1221no—
488C4⋊C4—1221no—
489C4⋊C4—1221no—
490C4⋊C4—1221no—
491C4⋊C4—1221no—
492C4⋊C4—1221no—
493C4⋊C4—1222no—
494C4⋊C4—1222no—
495C4⋊C4—1222no—
496C4⋊C4C22⋊#692311yescharacteristic
497C4⋊C4C22⋊#692311yescharacteristic
498C4⋊C4C22×#692311yescharacteristic
499C4⋊C4C22×#692312yes—
500C4⋊C4C22×#692311yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—612no—
503C22⋊C4—612no—
504C22⋊C4—1222no—
505C22⋊C4—1222no—
506C22⋊C4—1221no—
507C22⋊C4C22⋊#692312yes—
508C42—21no—
509C42—611no—
510C42—611no—
511C42—612no—
512C42—612no—
513C42—611no—
514C42—611no—
515C42—1222no—
516C42—1222no—
517C42—1221no—
518C42C22×#692312yes—
519C23—612no—
520C23C2×C22⋊#692311yescharacteristic
521Q8—82no—
522Q8—1222no—
523Q8—4882no—
524Q8—4882no—
525Q8—2441no—
526Q8—2441no—
527Q8—2442no—
528Q8—2442no—
529Q8—2441no—
530Q8—2441no—
531D4—614no—
532D4—1224no—
533C2×C4—22no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—22no—
537C2×C4—81no—
538C2×C4—611no—
539C2×C4—611no—
540C2×C4—612no—
541C2×C4—611no—
542C2×C4—611no—
543C2×C4—1222no—
544C2×C4—1222no—
545C2×C4—1222no—
546C2×C4—1222no—
547C2×C4—1224no—
548C2×C4—1221no—
549C2×C4—1221no—
550C2×C4—1221no—
551C2×C4—1221no—
552C2×C4—1221no—
553C2×C4—1222no—
554C2×C4—1221no—
555C2×C4—4882no—
556C2×C4—4882no—
557C2×C4—4881no—
558C2×C4C2×C22⋊#692312yes—
559C2×C4C2×C22⋊#692312yes—
560C2×C4C2×C22⋊#692311yescharacteristic
561C2×C4C23×#692311yescharacteristic
562C8—2441no—
563C8—2441no—
564C8—2441no—
565C8—2441no—
566C8—2442no—
567C8—2442no—
568C22—21no—
569C22—21no—
570C22—21no—
571C22—614no—
572C22—1222no—
573C22—1222no—
574C22C22×C22⋊#692311yescharacteristic
575C4—21no—
576C4—22no—
577C4—22no—
578C4—42no—
579C4—41no—
580C4—41no—
581C4—611no—
582C4—611no—
583C4—611no—
584C4—611no—
585C4—1222no—
586C4—1221no—
587C4—1221no—
588C4—2441no—
589C4—2442no—
590C4—2441no—
591C4D61⋊#10112yes—
592C2—41no—
593C2—1224no—
594C2C2×D61⋊#10111yescharacteristic
595C2#2146244011yescharacteristic
596C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#544C4
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC4×Dic61C24
hypercenter#544#6923
hypocenterC61#17774
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ #117 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #21461358C2semidirect
4. #21461349C2semidirect
5. #21461341C2semidirect
6. #21461341C2semidirect
7. #21461334C2semidirect
8. #21461328C2semidirect
9. #21461324C2semidirect
10. D61⋊#332C2semidirect
351. C61#17774semidirect

Maximal subgroups

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

subgroupindex
#214627462
#214613582
#214613492
#214613412
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