Finite Group Databasebeta

← #29662895

Subgroups — #29662895

Order 15616.

596 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456360C211yesmaximal, characteristic
2#21455857C211yesmaximal, characteristic
3#477×D61C211yesmaximal, characteristic
4Q8×#11758189C211yesmaximal, characteristic
5#21445348C211yesmaximal, characteristic, complemented
6#21445346C211yesmaximal, characteristic, complemented
7#21445324C211yesmaximal, characteristic, complemented
8#21445322C211yesmaximal, characteristic, complemented
9#21445223C211yesmaximal, characteristic, complemented
10#21445221C211yesmaximal, characteristic, complemented
11#21445199C211yesmaximal, characteristic, complemented
12#21444568C211yesmaximal, characteristic
13#21444508C211yesmaximal, characteristic
14#21444498C211yesmaximal, characteristic
15C61×#1672C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17C4⋊Q8×D61C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16840169—21no—
20#16840169—21no—
21#16840167C2211yescharacteristic
22#16840165C2211yescharacteristic
23#16840158C2211yescharacteristic
24#16840096—21no—
25#16840058C2211yescharacteristic
26#16840058C2211yescharacteristic
27#16840057C2211yescharacteristic
28#16840057C2211yescharacteristic
29#16840056—21no—
30#16840055—21no—
31#16840054C2211yescharacteristic
32#16839969C2211yescharacteristic
33#16839916—21no—
34#16839892—21no—
35#16839892C2211yescharacteristic
36#16839889—21no—
37#16839889C2211yescharacteristic
38Q8×#92418C2211yescharacteristic
39Q16×Dic61—21no—
40#16839854—21no—
41#16839814C2211yescharacteristic
42#16839801—21no—
43#16839801—21no—
44#107×D61—21no—
45#16839784—21no—
46#16839784C2211yescharacteristic
47C4⋊C8×D61C2211yescharacteristic
48#103×D61—21no—
49C4×#11758189—21no—
50C4×#11758189C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839512C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839510C2211yescharacteristic
58#16839510C2211yescharacteristic
59#16839508C2211yescharacteristic
60C61×#498C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#462C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#334C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61—21no—
68C2×Q8×D61D411yescharacteristic
69C2×#11758202—21no—
70C2×#11758189—21no—
71C2×#11758189D411yescharacteristic
72C2×#11758189D411yescharacteristic
73C2×C8×D61—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519776—21no—
77#14519776—21no—
78#14519775—21no—
79#14519768—21no—
80#14519757—21no—
81#14519753—21no—
82Q8×Dic61—21no—
83Q8×Dic61D411yescharacteristic
84C4×Dic122—21no—
85C4×Dic122C2311yescharacteristic
86#14519742—21no—
87#14519742—21no—
88#14519742D411yescharacteristic
89#14519735—21no—
90C4⋊C4×D61—21no—
91C4⋊C4×D61—21no—
92C4⋊C4×D61—21no—
93C4⋊C4×D61D411yescharacteristic
94C42×D61—21no—
95C42×D61C2311yescharacteristic
96#14519711—21no—
97#14519711—21no—
98#14519711—21no—
99#14519711—21no—
100#14519710—21no—
101#14519710—21no—
102#14519710—21no—
103#14519710—21no—
104#14519710—21no—
105#14519708—21no—
106#14519708—21no—
107C4⋊#92418—21no—
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110C4⋊#92418C2311yescharacteristic
111#14519706—21no—
112#14519706—21no—
113#14519706—21no—
114#14519706—21no—
115#14519702—21no—
116#14519702—21no—
117#14519701—21no—
118#14519701—21no—
119#14519701—21no—
120#14519700—21no—
121#14519689—21no—
122#14519687—21no—
123#14519687—21no—
124#14519687D411yescharacteristic
125#14519687D411yescharacteristic
126C4×#92418—21no—
127C4×#92418C2311yescharacteristic
128C8×Dic61—21no—
129C2×Q16×C61—21no—
130C4⋊Q8×C61C2311yescharacteristic
131C4⋊Q8×C61C2311yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133#107×C61—21no—
134#106×C61—21no—
135#106×C61—21no—
136C4⋊C8×C61—21no—
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C4⋊C8×C61C2311yescharacteristic
140#103×C61—21no—
141#103×C61—21no—
142C4×C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61C2×D411yescharacteristic
147Q8×D61—22no—
148Q8×D61—41no—
149Q8×D61—82no—
150C2×C4×D61—21no—
151C2×C4×D61—21no—
152C2×C4×D61—41no—
153C2×C4×D61C2×D411yescharacteristic
154C2×C4×D61C2×D411yescharacteristic
155C2×C4×D61#4111yescharacteristic
156C2×Dic122—21no—
157C2×Dic122—21no—
158C2×Dic122—21no—
159C2×Dic122—41no—
160C2×Dic122C2×D411yescharacteristic
161Q16×C61—42no—
162C2×C8×C61—21no—
163C2×C8×C61—21no—
164C2×C8×C61—21no—
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C4⋊C4×C61—21no—
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61C2×D411yescharacteristic
173C42×C61—21no—
174C42×C61C2411yescharacteristic
175#11758202—42no—
176#11758198—41no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—41no—
183C4⋊Dic61C2×D411yescharacteristic
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—41no—
188#11758196—41no—
189#11758196—41no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—41no—
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61C2×D411yescharacteristic
196C4×Dic61#4111yescharacteristic
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418C2×D411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202#11758189—22no—
203#11758189—42no—
204#11758189Q1614yescomplemented
205C8×D61—42no—
206C22×D61#12111yescharacteristic
207Q8×C61—21no—
208Q8×C61—41no—
209Q8×C61—41no—
210Q8×C61—81no—
211Q8×C61#13712yes—
212C2×C4×C61—21no—
213C2×C4×C61—21no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61C22×D411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C2×Dic61—21no—
220C2×Dic61—21no—
221C2×Dic61—41no—
222C2×Dic61—41no—
223C2×Dic61#12111yescharacteristic
224C2×Dic61#12111yescharacteristic
225C2×Dic61#12111yescharacteristic
226C4×D61—21no—
227C4×D61—21no—
228C4×D61—41no—
229C4×D61—42no—
230C4×D61—81no—
231C4×D61—82no—
232C4×D61C2×Q1612yes—
233C4×D61#13712yes—
234Dic122—21no—
235Dic122—21no—
236Dic122—42no—
237Dic122—82no—
238Dic122—81no—
239Dic122—81no—
240C8×C61—21no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61C2×Q1612yes—
245#92418—21no—
246#92418—41no—
247#92418—41no—
248#92418—41no—
249#92418C2×Q1612yes—
250#19173—611nomaximal, Sylow
251C22×C61C2×#12111yescharacteristic
252C2×D61—21no—
253C2×D61—21no—
254C2×D61#46212yes—
255C4×C61—22no—
256C4×C61—21no—
257C4×C61—41no—
258C4×C61—81no—
259C4×C61—81no—
260C4×C61C22×Q1611yescharacteristic
261C4×C61C2×#13711yescharacteristic
262C4×C61C2×#13711yescharacteristic
263C4×C61#57511yescharacteristic
264Dic61—21no—
265Dic61—21no—
266Dic61—41no—
267Dic61—41no—
268Dic61—81no—
269Dic61—81no—
270Dic61#46212yes—
271#3165—611no—
272#3104—611no—
273C2×#477—611no—
274Q8×M16—611no—
275#1696—611no—
276#1696—611no—
277#1692—611no—
278#1692—611no—
279#1676—611no—
280#1676—611no—
281#1672—611no—
282#1672D6111yescharacteristic, complemented
283#1565—611no—
284#1550—611no—
285#1548—611no—
286C2×C61C2×#46211yescharacteristic
287C2×C61#305611yescharacteristic
288C2×C61#306811yescharacteristic
289D61—22no—
290#533—611no—
291C2×C4⋊Q8—611no—
292C2×C4×Q8—611no—
293#501—1221no—
294#501—1221no—
295#500—611no—
296#500—611no—
297#498—611no—
298#498C2×D6111yescharacteristic
299#484—1221no—
300#477—611no—
301#477—611no—
302#477—611no—
303#477—611no—
304#477—611no—
305#477—1221no—
306#477—1221no—
307#477C2×D6111yescharacteristic
308#462—611no—
309#462C2×D6111yescharacteristic
310#451—1221no—
311#446—611no—
312#446—611no—
313#446—1221no—
314#446—1221no—
315C8×Q8—611no—
316C8×Q8C2×D6111yescharacteristic
317C4×Q16—1221no—
318C4×Q16—1221no—
319#431—611no—
320#428—1221no—
321#428—1221no—
322C2×#107—1221no—
323#423—611no—
324#423—1221no—
325C2×C4⋊C8—611no—
326C2×#103—1221no—
327C4×M16—611no—
328C4×M16—1221no—
329#335—611no—
330#335—611no—
331#334—611no—
332#334C2×D6111yescharacteristic
333#333—611no—
334#333—611no—
335#333—611no—
336#333—611no—
337#333—611no—
338#333C2×D6111yescharacteristic
339#332—611no—
340#332C2×D6111yescharacteristic
341C61#1917311yescharacteristic, complemented, Sylow
342C22×Q8—611no—
343C22×Q8—1221no—
344C2×Q16—21no—
345C2×Q16—1221no—
346C2×M16—611no—
347C2×M16—611no—
348C2×M16—1221no—
349C22×C8—1221no—
350C4⋊Q8—611no—
351C4⋊Q8—611no—
352C4⋊Q8—1221no—
353C4⋊Q8—1221no—
354C4⋊Q8—1221no—
355C4⋊Q8C22×D6111yescharacteristic
356C4⋊Q8C22×D6111yescharacteristic
357#125—1221no—
358C22⋊Q8—1221no—
359C22⋊Q8—1221no—
360C4×Q8—611no—
361C4×Q8—611no—
362C4×Q8—611no—
363C4×Q8—1221no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8C22×D6111yescharacteristic
368#117—1221no—
369C2×C4⋊C4—611no—
370C2×C4⋊C4—1221no—
371C2×C4⋊C4—1221no—
372C2×C4⋊C4—1221no—
373C2×C42—611no—
374C2×C42—1221no—
375#107—21no—
376#107—1221no—
377#107—1221no—
378#107—1221no—
379#107—1221no—
380#107—1221no—
381#107—1221no—
382#107—1221no—
383#107—1221no—
384#107—1221no—
385#106—21no—
386#106—21no—
387#106—1221no—
388#106—1221no—
389C4⋊C8—21no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8C22×D6111yescharacteristic
399C4⋊C8C22×D6111yescharacteristic
400C4⋊C8C22×D6111yescharacteristic
401#103—21no—
402#103—21no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409C22⋊C8—1221no—
410#97—611no—
411#97—611no—
412#97—1221no—
413#97—1221no—
414C4×C8—21no—
415C4×C8—611no—
416C4×C8—1221no—
417C4×C8—1221no—
418C4×C8C22×D6111yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—611no—
422C2×Q8—1221no—
423C2×Q8—1222no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—4882no—
427C2×Q8—2441no—
428C2×Q8—2441no—
429C2×Q8D4×D6111yescharacteristic
430C22×C4—611no—
431C22×C4—611no—
432C22×C4—611no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—2441no—
436Q16—42no—
437Q16—2442no—
438M16—614no—
439M16—1222no—
440M16—2442no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—611no—
445C2×C8—611no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—2442no—
450C2×C8D4×D6111yescharacteristic
451C2×C8D4×D6111yescharacteristic
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—611no—
458C4⋊C4—1221no—
459C4⋊C4—1221no—
460C4⋊C4—1221no—
461C4⋊C4—1221no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—2441no—
467C4⋊C4—2441no—
468C4⋊C4—2441no—
469C4⋊C4—2441no—
470C4⋊C4D4×D6111yescharacteristic
471C22⋊C4—2441no—
472C42—21no—
473C42—611no—
474C42—611no—
475C42—611no—
476C42—1221no—
477C42—1221no—
478C42—1221no—
479C42—2441no—
480C42C23×D6111yescharacteristic
481C23—611no—
482Q8—21no—
483Q8—41no—
484Q8—41no—
485Q8—81no—
486Q8—1221no—
487Q8—1221no—
488Q8—4881no—
489Q8—4881no—
490Q8—4882no—
491Q8—2442no—
492Q8#1451980612yes—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—611no—
498C2×C4—612no—
499C2×C4—612no—
500C2×C4—611no—
501C2×C4—611no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—4881no—
507C2×C4—4882no—
508C2×C4—2441no—
509C2×C4—2442no—
510C2×C4—2441no—
511C2×C4—2441no—
512C2×C4C2×D4×D6111yescharacteristic
513C2×C4C2×D4×D6111yescharacteristic
514C2×C4#41×D6111yescharacteristic
515C8—21no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—612no—
520C8—1221no—
521C8—2441no—
522C8—2441no—
523C8—2441no—
524C8Q16×D6112yes—
525C22—612no—
526C22—1221no—
527C22—1221no—
528C22#121×D6111yescharacteristic
529C4—22no—
530C4—21no—
531C4—41no—
532C4—81no—
533C4—81no—
534C4—612no—
535C4—1221no—
536C4—1221no—
537C4—4881no—
538C4—4881no—
539C4—2441no—
540C4—2441no—
541C4C2×Q16×D6111yescharacteristic
542C4#137×D6111yescharacteristic
543C4C2×#1451980611yescharacteristic
544C4#1684055911yescharacteristic
545C2—1222no—
546C2#462×D6111yescharacteristic
547C2#2145544211yescharacteristic
548C2#2145554211yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1672C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1672D61
hypocenterC61#19173
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1672

Complements

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

NH ≅ G/Ntype
5. #21445348C2semidirect
6. #21445346C2semidirect
7. #21445324C2semidirect
8. #21445322C2semidirect
9. #21445223C2semidirect
10. #21445221C2semidirect
11. #21445199C2semidirect
15. C61×#1672C2semidirect
204. #11758189Q16semidirect
282. #1672D61semidirect
341. C61#19173semidirect

Maximal subgroups

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

subgroupindex
#214563602
#214558572
#477×D612
Q8×#117581892
#214453482
#214453462
#214453242
#214453222
#214452232
#214452212
#214451992
#214445682
#214445082
#214444982
C61×#16722
#1917361