Finite Group Databasebeta

← #29677301

Subgroups — #29677301

Order 15616.

556 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458850C211yesmaximal, characteristic
2#21458749C211yesmaximal, characteristic, complemented
3#21458729C211yesmaximal, characteristic
4#21445414C211yesmaximal, characteristic, complemented
5#21445345C211yesmaximal, characteristic, complemented
6#21445322C211yesmaximal, characteristic, complemented
7#21445318C211yesmaximal, characteristic
8#21445311C211yesmaximal, characteristic, complemented
9#21445039C211yesmaximal, characteristic, complemented
10#21445026C211yesmaximal, characteristic
11#21444991C211yesmaximal, characteristic
12#21444976C211yesmaximal, characteristic, complemented
13#21444716C211yesmaximal, characteristic, complemented
14#21444707C211yesmaximal, characteristic
15C61×#3356C211yesmaximal, characteristic
16Q8×Dic122C2211yescharacteristic
17#16840491C2211yescharacteristic
18#16840172—21no—
19#16840170—21no—
20#16840165C2211yescharacteristic
21#16840160C2211yescharacteristic
22#16840157—21no—
23#16840141C2211yescharacteristic
24#16840114C2211yescharacteristic
25#16840112C2211yescharacteristic
26#16840067—21no—
27#16840066—21no—
28#16840057C2211yescharacteristic
29#16840054C2211yescharacteristic
30#16840052C2211yescharacteristic
31#16840047C2211yescharacteristic
32#16840045—21no—
33#16840042—21no—
34#16839981—21no—
35#16839972—21no—
36#16839969C2211yescharacteristic
37#16839967C2211yescharacteristic
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839892C2211yescharacteristic
41#16839869—21no—
42#16839867—21no—
43#16839862—21no—
44C4×#11758200C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53#16839492C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#556C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#485—21no—
60C61×#483—21no—
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C61×#470—21no—
64C4×Q16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#428—21no—
67C2×#11758202—21no—
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758200—21no—
71C2×#11758200D411yescharacteristic
72#14519777—21no—
73#14519777—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519776—21no—
77#14519776—41no—
78#14519768—21no—
79#14519768—41no—
80Q8×Dic61—21no—
81Q8×Dic61—21no—
82C4×Dic122—21no—
83C4×Dic122—21no—
84C4×Dic122C2311yescharacteristic
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519709—21no—
90#14519709—21no—
91#14519708—21no—
92#14519708—21no—
93#14519708D411yescharacteristic
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519706—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—41no—
104#14519700—21no—
105#14519700—21no—
106#14519700—41no—
107#14519700D411yescharacteristic
108#14519698—21no—
109#14519698D411yescharacteristic
110#14519688—21no—
111#14519688—21no—
112#14519687—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C2×Q16×C61D411yescharacteristic
116C2×M16×C61—21no—
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119#126×C61—41no—
120#125×C61—21no—
121#124×C61—21no—
122C22⋊Q8×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—41no—
125C4×Q8×C61—21no—
126C4×Q8×C61C2311yescharacteristic
127C4×Q8×C61C2311yescharacteristic
128C4×D4×C61—21no—
129C4×D4×C61C2311yescharacteristic
130#117×C61—21no—
131C2×C4⋊C4×C61—21no—
132#107×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135#106×C61—21no—
136#106×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×Q8×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—41no—
151C2×Dic122—21no—
152C2×Dic122—21no—
153C2×Dic122—41no—
154C2×Dic122C2×D411yescharacteristic
155Q16×C61—22no—
156M16×C61—42no—
157C2×C8×C61—21no—
158C2×C8×C61C2×D411yescharacteristic
159C2×C8×C61C2×D411yescharacteristic
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—41no—
167C4⋊C4×C61—41no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61C2×D411yescharacteristic
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C22⋊C4×C61—21no—
173C22⋊C4×C61—41no—
174C22⋊C4×C61—41no—
175C22⋊C4×C61—41no—
176C42×C61—21no—
177C42×C61—21no—
178C42×C61—41no—
179C42×C61C2411yescharacteristic
180#11758202—42no—
181#11758202—81no—
182#11758202—81no—
183#11758200—22no—
184#11758200—81no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—41no—
190C4⋊Dic61—41no—
191C4⋊Dic61—41no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—21no—
194#11758196—41no—
195#11758196—41no—
196C4×Dic61—21no—
197C4×Dic61—41no—
198C4×Dic61—41no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C23×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208Q8×C61—21no—
209Q8×C61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—81no—
213D4×C61—21no—
214D4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—161no—
225C2×C4×C61C22×D411yescharacteristic
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61H(5,𝔽2)11yescharacteristic
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232Dic122—21no—
233Dic122—21no—
234Dic122—41no—
235Dic122—41no—
236Dic122—81no—
237Dic122—161no—
238C8×C61—21no—
239C8×C61—41no—
240C8×C61#13712yes—
241#92418—21no—
242#92418—41no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#92418#13712yes—
247#20322—611nomaximal, Sylow
248C22×C61—41no—
249C22×C61—41no—
250C22×C61—41no—
251C22×C61D4211yescharacteristic
252C4×C61—21no—
253C4×C61—41no—
254C4×C61—41no—
255C4×C61—41no—
256C4×C61—41no—
257C4×C61—41no—
258C4×C61—81no—
259C4×C61—81no—
260C4×C61C2×#13711yescharacteristic
261C4×C61C2×#13711yescharacteristic
262C4×C61#57711yescharacteristic
263C4×C61#57811yescharacteristic
264Dic61—41no—
265Dic61—41no—
266Dic61—81no—
267Dic61—81no—
268#3398—611no—
269#3387—611no—
270#3385—611no—
271#3356D6111yescharacteristic
272#1707—611no—
273#1696—611no—
274#1692—611no—
275#1691—611no—
276#1690—611no—
277#1645—611no—
278#1643—611no—
279#1638—611no—
280#1636—611no—
281#1591—611no—
282#1590—611no—
283C2×C61—81no—
284C2×C61#327611yescharacteristic
285C2×C61#327811yescharacteristic
286C2×C61#329011yescharacteristic
287Q82—611no—
288#557—611no—
289#556C2×D6111yescharacteristic
290#554C2×D6111yescharacteristic
291#501—1221no—
292#501—1221no—
293#500—611no—
294#498—611no—
295#498C2×D6111yescharacteristic
296#497—1221no—
297#494—611no—
298#487—611no—
299#487—611no—
300#485—21no—
301#483—21no—
302#479—1221no—
303#479—1221no—
304#477—611no—
305#477—611no—
306#477C2×D6111yescharacteristic
307#476—611no—
308#475—611no—
309#475—1221no—
310#475C2×D6111yescharacteristic
311#474—1221no—
312#470—21no—
313#464—1221no—
314#462—611no—
315#462—1221no—
316#461—611no—
317#446—611no—
318#446—611no—
319#446—611no—
320#441—1221no—
321#441—1221no—
322#440—1221no—
323C4×Q16C2×D6111yescharacteristic
324C4×SD16—611no—
325#436C2×D6111yescharacteristic
326#428—21no—
327#335—611no—
328#334—611no—
329#333—611no—
330#333—611no—
331#332—611no—
332#332—611no—
333Q8⋊C8—611no—
334Q8⋊C8—611no—
335Q8⋊C8—611no—
336D4⋊C8—611no—
337C82—611no—
338C61#2032211yescharacteristic, complemented, Sylow
339C2×Q16—1221no—
340C2×Q16—1221no—
341C2×Q16—1221no—
342C2×Q16C22⋊D6111yescharacteristic
343C2×SD16—611no—
344C2×SD16—1221no—
345C2×M16—21no—
346C4⋊Q8—611no—
347C4⋊Q8—611no—
348C4⋊Q8—1221no—
349C4⋊Q8—1221no—
350C4⋊Q8—1221no—
351C4⋊Q8—2441no—
352C4⋊Q8C22×D6111yescharacteristic
353C4⋊Q8C22×D6111yescharacteristic
354#126—41no—
355#125—21no—
356#125—1221no—
357#125—2441no—
358#124—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—41no—
362C4×Q8—21no—
363C4×Q8—611no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8C22×D6111yescharacteristic
369C4×Q8C22×D6111yescharacteristic
370C4×D4—21no—
371C4×D4C22×D6111yescharacteristic
372#117—21no—
373C2×C4⋊C4—21no—
374#107—21no—
375#107—1221no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#107C22⋊D6111yescharacteristic
380#106—21no—
381#106—21no—
382#106—21no—
383#106—611no—
384#106—1221no—
385#106—1221no—
386#106—1221no—
387#106—1221no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395#103—21no—
396#103—21no—
397#103—611no—
398#103—1221no—
399#103—1221no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—2441no—
404#103—2441no—
405#103C22⋊D6111yescharacteristic
406#103C22⋊D6111yescharacteristic
407#102—611no—
408#102—1221no—
409C22⋊C8—21no—
410#97—1221no—
411#97—1221no—
412#97—1221no—
413C4×C8—611no—
414C4×C8—611no—
415C4×C8C22×D6111yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—611no—
419C2×Q8—1221no—
420C2×Q8—1221no—
421C2×Q8—2441no—
422C2×Q8C2×C22⋊D6111yescharacteristic
423C2×Q8C2×C22⋊D6111yescharacteristic
424C2×D4D4×D6111yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—22no—
428Q16—4881no—
429Q16—4881no—
430Q16—2442no—
431SD16—1222no—
432SD16—4881no—
433M16—42no—
434C2×C8—21no—
435C2×C8—611no—
436C2×C8—611no—
437C2×C8—1221no—
438C2×C8—1221no—
439C2×C8—1221no—
440C2×C8—1221no—
441C2×C8C2×C22⋊D6111yescharacteristic
442C2×C8C2×C22⋊D6111yescharacteristic
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—41no—
450C4⋊C4—41no—
451C4⋊C4—41no—
452C4⋊C4—611no—
453C4⋊C4—1221no—
454C4⋊C4—1221no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
458C4⋊C4—2441no—
459C4⋊C4—2441no—
460C4⋊C4—2441no—
461C4⋊C4—2441no—
462C4⋊C4—2441no—
463C4⋊C4D4×D6111yescharacteristic
464C4⋊C4C2×C22⋊D6111yescharacteristic
465C4⋊C4C2×C22⋊D6111yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—21no—
471C42—21no—
472C42—41no—
473C42—1221no—
474C42—2441no—
475C42—2441no—
476C42C23×D6111yescharacteristic
477C23—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—81no—
485Q8—1221no—
486Q8—1221no—
487Q8—9761no—
488Q8—4881no—
489Q8—2441no—
490Q8—2441no—
491D4—21no—
492D4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—161no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—2441no—
506C2×C4—2441no—
507C2×C4C2×D4×D6111yescharacteristic
508C2×C4C22×C22⋊D6111yescharacteristic
509C2×C4#1451982211yescharacteristic
510C8—21no—
511C8—41no—
512C8—612no—
513C8—1221no—
514C8—2441no—
515C8—2441no—
516C8—2441no—
517C8—2441no—
518C8#1451980712yes—
519C22—41no—
520C22—41no—
521C22—41no—
522C22D4×C22⋊D6111yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—4881no—
532C4—4881no—
533C4—2441no—
534C4—2441no—
535C4#137×D6111yescharacteristic
536C4C2×#1451980711yescharacteristic
537C4#1684057111yescharacteristic
538C4#1684057711yescharacteristic
539C2—81no—
540C2#2145746111yescharacteristic
541C2#2145747911yescharacteristic
542C2#2145759911yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3356C2
socleC22×C61D42
prime radicalC2×D4×C61C2×D4
hypercenter#3356D61
hypocenterC61#20322
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3356

Complements

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

NH ≅ G/Ntype
2. #21458749C2semidirect
4. #21445414C2semidirect
5. #21445345C2semidirect
6. #21445322C2semidirect
8. #21445311C2semidirect
9. #21445039C2semidirect
12. #21444976C2semidirect
13. #21444716C2semidirect
338. C61#20322semidirect

Maximal subgroups

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

subgroupindex
#214588502
#214587492
#214587292
#214454142
#214453452
#214453222
#214453182
#214453112
#214450392
#214450262
#214449912
#214449762
#214447162
#214447072
C61×#33562
#2032261