Finite Group Databasebeta

← #29671011

Subgroups — #29671011

Order 15616.

572 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458466C211yesmaximal, characteristic
2#21458434C211yesmaximal, characteristic, complemented
3#21458207C211yesmaximal, characteristic, complemented
4#21445495C211yesmaximal, characteristic, complemented
5#21445340C211yesmaximal, characteristic, complemented
6#21445277C211yesmaximal, characteristic, complemented
7#21445220C211yesmaximal, characteristic, complemented
8#21445196C211yesmaximal, characteristic, complemented
9#21445026C211yesmaximal, characteristic, complemented
10#21444989C211yesmaximal, characteristic, complemented
11#21444953C211yesmaximal, characteristic, complemented
12#21444951C211yesmaximal, characteristic, complemented
13#21444649C211yesmaximal, characteristic
14#21444636C211yesmaximal, characteristic, complemented
15C61×#3380C211yesmaximal, characteristic
16#16840482C2211yescharacteristic
17#16840469C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840158C2211yescharacteristic
20#16840141C2211yescharacteristic
21#16840115—21no—
22#16840113C2211yescharacteristic
23#16840112C2211yescharacteristic
24#16840100—21no—
25#16840097—21no—
26#16840095—21no—
27#16840092—21no—
28#16840068—21no—
29#16840057C2211yescharacteristic
30#16840054C2211yescharacteristic
31#16840054C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840047C2211yescharacteristic
34#16840018—21no—
35#16840001—21no—
36#16839975—21no—
37#16839967C2211yescharacteristic
38C8×Dic122C2211yescharacteristic
39C4×#11758202C2211yescharacteristic
40#16839853—21no—
41#16839840C2211yescharacteristic
42D4×#92418C2211yescharacteristic
43#16839802—21no—
44C2×#14519710—21no—
45#16839515C2211yescharacteristic
46#16839512C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839509C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52#16839492C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54D4⋊#92418C2211yescharacteristic
55#16839484C2211yescharacteristic
56C61×#554C2211yescharacteristic
57C61×#554C2211yescharacteristic
58C61×#500C2211yescharacteristic
59C61×#499—21no—
60C61×#478—21no—
61C61×#478—21no—
62C61×#476C2211yescharacteristic
63C61×#476C2211yescharacteristic
64C8×Q8×C61C2211yescharacteristic
65C4×D8×C61—21no—
66C4×D8×C61C2211yescharacteristic
67C2×#11758202—41no—
68C2×#11758202D411yescharacteristic
69C2×#11758200—21no—
70C2×#11758194—21no—
71C22×#92418—21no—
72#14519777C2311yescharacteristic
73#14519777C2311yescharacteristic
74#14519770—41no—
75#14519768—21no—
76#14519764—21no—
77#14519756—21no—
78#14519756—21no—
79#14519754—41no—
80C4×Dic122C2311yescharacteristic
81#14519742—21no—
82D4×Dic61—21no—
83#14519736—21no—
84C2×C4⋊Dic61—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94#14519708—21no—
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98#14519706—21no—
99#14519702—21no—
100#14519702—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—41no—
104#14519701D411yescharacteristic
105#14519700—21no—
106#14519700—21no—
107#14519700—21no—
108#14519700D411yescharacteristic
109#14519698—21no—
110C22⋊#92418—21no—
111C22⋊#92418—21no—
112C4×#92418C2311yescharacteristic
113C4×#92418C2311yescharacteristic
114C8×Dic61—21no—
115C2×D8×C61D411yescharacteristic
116C4⋊Q8×C61C2311yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118#125×C61—21no—
119#125×C61—21no—
120C22⋊Q8×C61—21no—
121C22⋊Q8×C61—21no—
122C22⋊Q8×C61—41no—
123C22⋊Q8×C61—41no—
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61—21no—
127C4×D4×C61C2311yescharacteristic
128C4×D4×C61C2311yescharacteristic
129C2×C4⋊C4×C61—21no—
130C2×C4⋊C4×C61—21no—
131#107×C61—21no—
132#107×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138#102×C61—21no—
139#102×C61—21no—
140#102×C61D411yescharacteristic
141#102×C61D411yescharacteristic
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147C2×D4×C61C2×D411yescharacteristic
148C2×D4×C61C2×D411yescharacteristic
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—41no—
152C22×C4×C61—41no—
153C22×Dic61—41no—
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122C2×D411yescharacteristic
157D8×C61—22no—
158C2×C8×C61—21no—
159C2×C8×C61C2×D411yescharacteristic
160C2×C8×C61C2×D411yescharacteristic
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×C61—41no—
170C4⋊C4×C61C2×D411yescharacteristic
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C42×C61—21no—
178C42×C61C2411yescharacteristic
179C22⋊Dic61—41no—
180C22⋊Dic61—41no—
181C22⋊Dic61—41no—
182#11758202—22no—
183#11758202—82no—
184#11758200—42no—
185C4⋊Dic61—21no—
186C4⋊Dic61—21no—
187C4⋊Dic61—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61—41no—
190C4⋊Dic61C2×D411yescharacteristic
191#11758196—21no—
192#11758196—41no—
193#11758196—41no—
194C4×Dic61—21no—
195C4×Dic61—41no—
196#11758194—42no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—42no—
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C23×C61—21no—
205C23×C61—21no—
206Q8×C61—21no—
207Q8×C61—21no—
208Q8×C61—81no—
209Q8×C61—81no—
210D4×C61—21no—
211D4×C61—21no—
212D4×C61—21no—
213D4×C61#13712yes—
214C2×C4×C61—21no—
215C2×C4×C61—21no—
216C2×C4×C61—21no—
217C2×C4×C61—21no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—161no—
225C2×C4×C61—161no—
226C2×C4×C61C22×D411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61H(5,𝔽2)11yescharacteristic
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—161no—
234Dic122—21no—
235Dic122—21no—
236Dic122—41no—
237Dic122—41no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—41no—
242#92418—21no—
243#92418—41no—
244#92418—41no—
245#92418—41no—
246#92418—41no—
247#92418#13512yes—
248#19865—611nomaximal, Sylow
249C22×C61—22no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61—41no—
253C22×C61—41no—
254C22×C61—41no—
255C22×C61D4211yescharacteristic
256C4×C61—21no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—81no—
262C4×C61—81no—
263C4×C61C2×#13511yescharacteristic
264C4×C61C2×#13711yescharacteristic
265C4×C61#57811yescharacteristic
266C4×C61#57811yescharacteristic
267Dic61—41no—
268Dic61—41no—
269Dic61—81no—
270Dic61—81no—
271#3380D6111yescharacteristic
272#3360—611no—
273#3356—611no—
274#3338—611no—
275#1723—611no—
276#1695—611no—
277#1684—611no—
278#1676—611no—
279#1671—611no—
280#1643—611no—
281#1638—611no—
282#1632—611no—
283#1632—611no—
284#1581—611no—
285#1579—611no—
286C2×C61—42no—
287C2×C61—81no—
288C2×C61#327011yescharacteristic
289C2×C61#328311yescharacteristic
290C2×C61#328811yescharacteristic
291#556—611no—
292#554—611no—
293#554C2×D6111yescharacteristic
294#554C2×D6111yescharacteristic
295#500—611no—
296#500C2×D6111yescharacteristic
297#499—21no—
298#498—611no—
299#494—611no—
300#488—1221no—
301#487—611no—
302#487—611no—
303#485—1221no—
304#484—1221no—
305#484—1221no—
306#483—1221no—
307#479—1221no—
308#478—21no—
309#478—21no—
310#477—611no—
311#477—611no—
312#477—611no—
313#476—611no—
314#476C2×D6111yescharacteristic
315#476C2×D6111yescharacteristic
316#475—611no—
317#470—1221no—
318#467—1221no—
319#463—1221no—
320#461—611no—
321C8×Q8—611no—
322C8×Q8C2×D6111yescharacteristic
323C4×Q16—611no—
324C4×SD16—1221no—
325C4×D8—21no—
326C4×D8C2×D6111yescharacteristic
327#436—611no—
328C8×D4—611no—
329#428—1221no—
330C2×#107—1221no—
331#335—611no—
332#334—611no—
333#333—611no—
334#333—611no—
335#333—611no—
336#332—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339D4⋊C8—611no—
340D4⋊C8—611no—
341#322—611no—
342C61#1986511yescharacteristic, complemented, Sylow
343C2×Q16—611no—
344C2×Q16—2441no—
345C2×SD16—1221no—
346C2×D8C22⋊D6111yescharacteristic
347C2×M16—1221no—
348C22×C8—1221no—
349C4⋊Q8—611no—
350C4⋊Q8—611no—
351C4⋊Q8C22×D6111yescharacteristic
352C4⋊Q8C22×D6111yescharacteristic
353#126—2441no—
354#125—21no—
355#125—21no—
356#125—1221no—
357#124—1221no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362C22⋊Q8—1221no—
363C22⋊Q8—1221no—
364C22⋊Q8—2441no—
365C4×Q8—611no—
366C4×Q8—1221no—
367C4×Q8C22×D6111yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—1221no—
371C4×D4C22×D6111yescharacteristic
372C4×D4C22×D6111yescharacteristic
373#117—1221no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—1221no—
377#107—21no—
378#107—21no—
379#107—611no—
380#107—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#107C22⋊D6111yescharacteristic
386#106—21no—
387#106—21no—
388#106—1221no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392C4⋊C8—21no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—1221no—
397C4⋊C8C22×D6111yescharacteristic
398#103—611no—
399#103—611no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—2441no—
408#102—21no—
409#102—21no—
410#102—1221no—
411#102C22⋊D6111yescharacteristic
412#102C22⋊D6111yescharacteristic
413C22⋊C8—1221no—
414C22⋊C8—1221no—
415C4×C8—21no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—1221no—
419C4×C8C22×D6111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—611no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8D4×D6111yescharacteristic
426C2×D4C2×C22⋊D6111yescharacteristic
427C2×D4C2×C22⋊D6111yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—2441no—
433Q16—1222no—
434Q16—4882no—
435SD16—2442no—
436D8—22no—
437M16—2442no—
438C2×C8—21no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—1221no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—2442no—
446C2×C8C2×C22⋊D6111yescharacteristic
447C2×C8C2×C22⋊D6111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—611no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—2441no—
464C4⋊C4—2441no—
465C4⋊C4—2441no—
466C4⋊C4D4×D6111yescharacteristic
467C4⋊C4C2×C22⋊D6111yescharacteristic
468C4⋊C4C2×C22⋊D6111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—2441no—
474C22⋊C4—2441no—
475C22⋊C4—2441no—
476C42—21no—
477C42—1221no—
478C42—2441no—
479C42C23×D6111yescharacteristic
480C23—21no—
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—81no—
485Q8—81no—
486Q8—1221no—
487Q8—1221no—
488Q8—4881no—
489Q8—2441no—
490Q8—2441no—
491D4—21no—
492D4—21no—
493D4—21no—
494D4#1451980812yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—161no—
506C2×C4—161no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—9761no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4C2×D4×D6111yescharacteristic
513C2×C4C22×C22⋊D6111yescharacteristic
514C2×C4#1451982211yescharacteristic
515C8—21no—
516C8—21no—
517C8—41no—
518C8—612no—
519C8—1221no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C8—2441no—
524C22—22no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D4×C22⋊D6111yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—81no—
537C4—81no—
538C4—4881no—
539C4—4881no—
540C4—2441no—
541C4—2441no—
542C4#135×D6111yescharacteristic
543C4C2×#1451980811yescharacteristic
544C4#1684057611yescharacteristic
545C4#1684057711yescharacteristic
546C2—42no—
547C2—81no—
548C2#2145739011yescharacteristic
549C2#2145753511yescharacteristic
550C2#2145758311yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3380C2
socleC22×C61D42
prime radicalC2×D8×C61D4
hypercenter#3380D61
hypocenterC61#19865
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3380

Complements

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

NH ≅ G/Ntype
2. #21458434C2semidirect
3. #21458207C2semidirect
4. #21445495C2semidirect
5. #21445340C2semidirect
6. #21445277C2semidirect
7. #21445220C2semidirect
8. #21445196C2semidirect
9. #21445026C2semidirect
10. #21444989C2semidirect
11. #21444953C2semidirect
12. #21444951C2semidirect
14. #21444636C2semidirect
342. C61#19865semidirect

Maximal subgroups

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

subgroupindex
#214584662
#214584342
#214582072
#214454952
#214453402
#214452772
#214452202
#214451962
#214450262
#214449892
#214449532
#214449512
#214446492
#214446362
C61×#33802
#1986561