Finite Group Databasebeta

← #29671004

Subgroups — #29671004

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#21458682C211yesmaximal, characteristic
2#21458464C211yesmaximal, characteristic
3#21458213C211yesmaximal, characteristic, complemented
4#21445493C211yesmaximal, characteristic, complemented
5#21445342C211yesmaximal, characteristic, complemented
6#21445275C211yesmaximal, characteristic, complemented
7#21445221C211yesmaximal, characteristic, complemented
8#21445191C211yesmaximal, characteristic, complemented
9#21445025C211yesmaximal, characteristic, complemented
10#21444991C211yesmaximal, characteristic, complemented
11#21444953C211yesmaximal, characteristic, complemented
12#21444952C211yesmaximal, characteristic, complemented
13#21444646C211yesmaximal, characteristic
14#21444638C211yesmaximal, characteristic, complemented
15C61×#3356C211yesmaximal, characteristic, complemented
16#16840472C2211yescharacteristic
17#16840472C2211yescharacteristic
18#16840167C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840161—21no—
21#16840141C2211yescharacteristic
22#16840116—21no—
23#16840114C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840096—21no—
26#16840096—21no—
27#16840069—21no—
28#16840062—21no—
29#16840059—21no—
30#16840057C2211yescharacteristic
31#16840057C2211yescharacteristic
32#16840052C2211yescharacteristic
33#16840052C2211yescharacteristic
34#16840049C2211yescharacteristic
35#16840000—21no—
36#16839974—21no—
37#16839964C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39Q8×#92418C2211yescharacteristic
40C4×#11758201—21no—
41C4×#11758199—21no—
42C4×#11758199C2211yescharacteristic
43C8×D244C2211yescharacteristic
44#107×D61—21no—
45#16839514C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839511C2211yescharacteristic
48#16839510C2211yescharacteristic
49#16839510C2211yescharacteristic
50#16839508C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55#16839483C2211yescharacteristic
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—41no—
68C2×#11758201—21no—
69C2×#11758199D411yescharacteristic
70C2×C8×D61—21no—
71#14519777C2311yescharacteristic
72#14519777C2311yescharacteristic
73#14519769—21no—
74#14519769—21no—
75#14519755—41no—
76#14519755—41no—
77#14519753—21no—
78#14519753—21no—
79C4×D244—21no—
80C4×D244—21no—
81C4×D244C2311yescharacteristic
82C4⋊C4×D61—21no—
83C4⋊C4×D61—21no—
84#14519711—21no—
85#14519711—21no—
86#14519710—21no—
87#14519710—21no—
88#14519710—21no—
89#14519710—21no—
90#14519710D411yescharacteristic
91#14519708—21no—
92#14519708—21no—
93#14519708—21no—
94C4⋊#92418—21no—
95C4⋊#92418—21no—
96C4⋊#92418C2311yescharacteristic
97C4⋊#92418C2311yescharacteristic
98C4⋊#92418C2311yescharacteristic
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519701—21no—
103#14519701—21no—
104#14519700—41no—
105#14519698—21no—
106#14519698—21no—
107#14519698D411yescharacteristic
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111C4×#92418—21no—
112C4×#92418—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×D244C2×D411yescharacteristic
152C2×C4×D61—21no—
153C2×C4×D61—41no—
154C2×C4×D61—41no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157Q16×C61—22no—
158M16×C61—42no—
159C2×C8×C61—21no—
160C2×C8×C61C2×D411yescharacteristic
161C2×C8×C61C2×D411yescharacteristic
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61—41no—
169C4⋊C4×C61—41no—
170C4⋊C4×C61—41no—
171C4⋊C4×C61C2×D411yescharacteristic
172C4⋊C4×C61C2×D411yescharacteristic
173C4⋊C4×C61C2×D411yescharacteristic
174C22⋊C4×C61—21no—
175C22⋊C4×C61—41no—
176C22⋊C4×C61—41no—
177C22⋊C4×C61—41no—
178C42×C61—21no—
179C42×C61—21no—
180C42×C61—41no—
181C42×C61C2411yescharacteristic
182#11758202—82no—
183#11758201—42no—
184#11758199—22no—
185#11758198—21no—
186#11758198—41no—
187#11758198—41no—
188C4⋊Dic61—21no—
189C4⋊Dic61—21no—
190C4⋊Dic61—21no—
191C4⋊Dic61—21no—
192C4⋊Dic61C2×D411yescharacteristic
193#11758196—41no—
194#11758196—41no—
195#11758196—41no—
196#11758196—41no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C8×D61—42no—
204C23×C61—21no—
205C22×D61—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—41no—
230C2×Dic61—41no—
231D244—21no—
232D244#13712yes—
233C4×D61—41no—
234C4×D61—41no—
235C4×D61—161no—
236C4×D61—161no—
237Dic122—81no—
238Dic122—81no—
239C8×C61—21no—
240C8×C61—41no—
241C8×C61#13512yes—
242#92418—21no—
243#92418—21no—
244#92418—41no—
245#92418—41no—
246#92418—41no—
247#92418—41no—
248#19865—611nomaximal, Sylow
249C22×C61—41no—
250C22×C61—41no—
251C22×C61—41no—
252C22×C61D4211yescharacteristic
253C2×D61—22no—
254C2×D61—41no—
255C2×D61—41no—
256C4×C61—21no—
257C4×C61—41no—
258C4×C61—41no—
259C4×C61—41no—
260C4×C61—41no—
261C4×C61—41no—
262C4×C61—81no—
263C4×C61—81no—
264C4×C61C2×#13511yescharacteristic
265C4×C61C2×#13711yescharacteristic
266C4×C61#57811yescharacteristic
267C4×C61#57811yescharacteristic
268Dic61—41no—
269Dic61—81no—
270Dic61—81no—
271#3380—611no—
272#3360—611no—
273#3356D6111yescharacteristic, complemented
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—81no—
287C2×C61#327011yescharacteristic
288C2×C61#328311yescharacteristic
289C2×C61#328811yescharacteristic
290D61—42no—
291#556C2×D6111yescharacteristic
292#554—611no—
293#554—611no—
294#554C2×D6111yescharacteristic
295#500—611no—
296#500—611no—
297#499—1221no—
298#498C2×D6111yescharacteristic
299#494—611no—
300#488—1221no—
301#487—611no—
302#487—611no—
303#485—21no—
304#484—1221no—
305#484—1221no—
306#483—21no—
307#479—1221no—
308#478—1221no—
309#478—1221no—
310#477—611no—
311#477—611no—
312#477C2×D6111yescharacteristic
313#476—611no—
314#476—611no—
315#476—611no—
316#475C2×D6111yescharacteristic
317#470—21no—
318#467—1221no—
319#463—1221no—
320#461—611no—
321C8×Q8—611no—
322C8×Q8—611no—
323C4×Q16C2×D6111yescharacteristic
324C4×SD16—1221no—
325C4×D8—611no—
326C4×D8—1221no—
327#436C2×D6111yescharacteristic
328C8×D4—611no—
329#428—21no—
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—2441no—
344C2×Q16C22⋊D6111yescharacteristic
345C2×SD16—1221no—
346C2×D8—611no—
347C2×M16—21no—
348C22×C8—1221no—
349C4⋊Q8—611no—
350C4⋊Q8—611no—
351C4⋊Q8C22×D6111yescharacteristic
352C4⋊Q8C22×D6111yescharacteristic
353#126—41no—
354#125—21no—
355#125—1221no—
356#125—1221no—
357#124—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—1221no—
362C22⋊Q8—1221no—
363C22⋊Q8—2441no—
364C22⋊Q8—2441no—
365C4×Q8—21no—
366C4×Q8C22×D6111yescharacteristic
367C4×Q8C22×D6111yescharacteristic
368C4×D4—21no—
369C4×D4—611no—
370C4×D4—1221no—
371C4×D4—1221no—
372C4×D4C22×D6111yescharacteristic
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377#107—21no—
378#107—611no—
379#107—1221no—
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—21no—
389#106—1221no—
390#106—1221no—
391#106—1221no—
392C4⋊C8—611no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8C22×D6111yescharacteristic
398#103—21no—
399#103—21no—
400#103—1221no—
401#103—1221no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—2441no—
406#103C22⋊D6111yescharacteristic
407#103C22⋊D6111yescharacteristic
408#102—611no—
409#102—611no—
410#102—1221no—
411#102—1221no—
412#102—1221no—
413C22⋊C8—21no—
414C22⋊C8—1221no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—1221no—
418C4×C8—1221no—
419C4×C8C22×D6111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8C2×C22⋊D6111yescharacteristic
425C2×Q8C2×C22⋊D6111yescharacteristic
426C2×D4—611no—
427C2×D4D4×D6111yescharacteristic
428C22×C4—21no—
429C22×C4—41no—
430C22×C4—1221no—
431C22×C4—2441no—
432C22×C4—2441no—
433Q16—22no—
434Q16—4882no—
435SD16—2442no—
436D8—1222no—
437M16—42no—
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—21no—
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—2441no—
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—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—1221no—
474C22⋊C4—2441no—
475C22⋊C4—2441no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42C23×D6111yescharacteristic
480C23—21no—
481C23—1221no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—4881no—
490Q8—4881no—
491D4—21no—
492D4—21no—
493D4—612no—
494D4—1221no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—161no—
505C2×C4—1221no—
506C2×C4—9761no—
507C2×C4—9761no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4C2×D4×D6111yescharacteristic
513C2×C4C22×C22⋊D6111yescharacteristic
514C2×C4#1451982211yescharacteristic
515C8—21no—
516C8—41no—
517C8—1221no—
518C8—1221no—
519C8—2441no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C8#1451979712yes—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—1222no—
528C22—2441no—
529C22—2441no—
530C22D4×C22⋊D6111yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—4881no—
540C4—4881no—
541C4—2441no—
542C4C2×#1451979711yescharacteristic
543C4#137×D6111yescharacteristic
544C4#1684057711yescharacteristic
545C4#1684057811yescharacteristic
546C2—81no—
547C2—2442no—
548C2#2145738311yescharacteristic
549C2#2145753711yescharacteristic
550C2#2145758111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3356C2
socleC22×C61D42
prime radicalC2×#11758199D4
hypercenter#3356D61
hypocenterC61#19865
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3356

Complements

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

NH ≅ G/Ntype
3. #21458213C2semidirect
4. #21445493C2semidirect
5. #21445342C2semidirect
6. #21445275C2semidirect
7. #21445221C2semidirect
8. #21445191C2semidirect
9. #21445025C2semidirect
10. #21444991C2semidirect
11. #21444953C2semidirect
12. #21444952C2semidirect
14. #21444638C2semidirect
15. C61×#3356C2semidirect
273. #3356D61semidirect
342. C61#19865semidirect

Maximal subgroups

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

subgroupindex
#214586822
#214584642
#214582132
#214454932
#214453422
#214452752
#214452212
#214451912
#214450252
#214449912
#214449532
#214449522
#214446462
#214446382
C61×#33562
#1986561