Finite Group Databasebeta

← #29663862

Subgroups — #29663862

Order 15616.

602 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456404C211yesmaximal, characteristic
2#21455625C211yesmaximal, characteristic
3#21455619C211yesmaximal, characteristic
4C8×Q8×D61C211yesmaximal, characteristic
5#21445278C211yesmaximal, characteristic, complemented
6#21445277C211yesmaximal, characteristic, complemented
7#21445274C211yesmaximal, characteristic, complemented
8#21445222C211yesmaximal, characteristic, complemented
9#21445221C211yesmaximal, characteristic, complemented
10#21445188C211yesmaximal, characteristic, complemented
11#21445187C211yesmaximal, characteristic, complemented
12#21444576C211yesmaximal, characteristic
13#21444508C211yesmaximal, characteristic
14#21444506C211yesmaximal, characteristic
15C61×#1684C211yesmaximal, characteristic, complemented
16#16840317C2211yescharacteristic
17#16840317C2211yescharacteristic
18C4×Q8×D61C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840141C2211yescharacteristic
21#16840113C2211yescharacteristic
22#16840072—21no—
23#16840071—21no—
24#16840068—21no—
25#16840067—21no—
26#16840058C2211yescharacteristic
27#16840057C2211yescharacteristic
28#16840054C2211yescharacteristic
29#16840048C2211yescharacteristic
30#16840047C2211yescharacteristic
31#16840044C2211yescharacteristic
32#16840002—21no—
33#16840002—21no—
34Q8×#92418C2211yescharacteristic
35C8×Dic122—21no—
36C8×Dic122C2211yescharacteristic
37#16839886—21no—
38#16839886C2211yescharacteristic
39#16839854—21no—
40#16839854—21no—
41#16839803—21no—
42#16839801—21no—
43#16839784C2211yescharacteristic
44#16839784C2211yescharacteristic
45C4⋊C8×D61—21no—
46C4⋊C8×D61C2211yescharacteristic
47#16839769—21no—
48#16839769—21no—
49C4×C8×D61—21no—
50C4×C8×D61C2211yescharacteristic
51#16839515C2211yescharacteristic
52#16839514C2211yescharacteristic
53#16839514C2211yescharacteristic
54#16839511C2211yescharacteristic
55#16839510C2211yescharacteristic
56#16839510C2211yescharacteristic
57#16839509C2211yescharacteristic
58#16839508C2211yescharacteristic
59#16839507C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#477C2211yescharacteristic
62C61×#475C2211yescharacteristic
63C8×Q8×C61C2211yescharacteristic
64C61×#335C2211yescharacteristic
65C61×#333C2211yescharacteristic
66C61×#332C2211yescharacteristic
67C2×Q8×D61D411yescharacteristic
68C2×#11758202—21no—
69C2×#11758202—21no—
70C2×#11758189—21no—
71C2×#11758189—21no—
72C2×C8×D61—21no—
73C2×C8×D61D411yescharacteristic
74C2×C8×D61D411yescharacteristic
75#14519777C2311yescharacteristic
76#14519777C2311yescharacteristic
77#14519768—21no—
78#14519768—21no—
79#14519757—21no—
80#14519757—21no—
81#14519753—21no—
82#14519753—21no—
83Q8×Dic61—21no—
84Q8×Dic61—21no—
85Q8×Dic61D411yescharacteristic
86C4×Dic122—21no—
87C4×Dic122C2311yescharacteristic
88#14519742—21no—
89#14519742—21no—
90#14519742—21no—
91#14519742D411yescharacteristic
92#14519735—21no—
93#14519735—21no—
94C4⋊C4×D61—21no—
95C4⋊C4×D61D411yescharacteristic
96C42×D61—21no—
97C42×D61C2311yescharacteristic
98#14519711—21no—
99#14519710—21no—
100#14519710—21no—
101#14519710—21no—
102#14519710—21no—
103#14519709—21no—
104#14519708—21no—
105#14519708—21no—
106C4⋊#92418—21no—
107C4⋊#92418C2311yescharacteristic
108C4⋊#92418C2311yescharacteristic
109C4⋊#92418C2311yescharacteristic
110#14519706—21no—
111#14519706—21no—
112#14519706—21no—
113#14519706—21no—
114#14519706—21no—
115#14519702—21no—
116#14519702—21no—
117#14519702—21no—
118#14519702—21no—
119#14519701—21no—
120#14519701—21no—
121#14519700—21no—
122#14519700—21no—
123C4×#92418—21no—
124C4×#92418C2311yescharacteristic
125C8×Dic61—21no—
126C8×Dic61—21no—
127C8×Dic61D411yescharacteristic
128C8×Dic61D411yescharacteristic
129C4⋊Q8×C61C2311yescharacteristic
130C4⋊Q8×C61C2311yescharacteristic
131C4×Q8×C61C2311yescharacteristic
132#107×C61—21no—
133#106×C61—21no—
134C4⋊C8×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136C4⋊C8×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138#103×C61—21no—
139#103×C61—21no—
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×D61Q1614yescomplemented
149C2×C4×D61—21no—
150C2×C4×D61—21no—
151C2×C4×D61C2×D411yescharacteristic
152C2×C4×D61C2×D411yescharacteristic
153C2×C4×D61#4111yescharacteristic
154C2×Dic122—21no—
155C2×Dic122—21no—
156C2×Dic122—21no—
157C2×Dic122C2×D411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61C2×D411yescharacteristic
162C2×C8×C61C2×D411yescharacteristic
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61—21no—
168C4⋊C4×C61C2×D411yescharacteristic
169C42×C61—21no—
170C42×C61C2411yescharacteristic
171#11758202—42no—
172#11758202—42no—
173#11758198—41no—
174#11758198—41no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—41no—
181C4⋊Dic61—41no—
182C4⋊Dic61C2×D411yescharacteristic
183#11758196—21no—
184#11758196—21no—
185#11758196—21no—
186#11758196—41no—
187#11758196—41no—
188C4×Dic61—21no—
189C4×Dic61—21no—
190C4×Dic61—21no—
191C4×Dic61—41no—
192C4×Dic61—41no—
193C4×Dic61C2×D411yescharacteristic
194C4×Dic61C2×D411yescharacteristic
195C4×Dic61#4111yescharacteristic
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418C2×D411yescharacteristic
200C2×#92418C2×D411yescharacteristic
201#11758189—42no—
202#11758189—42no—
203C8×D61—22no—
204C8×D61—41no—
205C8×D61—42no—
206C22×D61#12111yescharacteristic
207Q8×C61—21no—
208Q8×C61—41no—
209Q8×C61—41no—
210Q8×C61—81no—
211Q8×C61C2×Q1612yes—
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—24no—
227C4×D61—21no—
228C4×D61—21no—
229C4×D61—41no—
230C4×D61—42no—
231C4×D61C2×Q1612yes—
232C4×D61#13512yes—
233Dic122—21no—
234Dic122—24no—
235Dic122—41no—
236Dic122—41no—
237Dic122—81no—
238Dic122C2×Q1612yes—
239C8×C61—21no—
240C8×C61—21no—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244#92418—21no—
245#92418—41no—
246#92418—41no—
247#92418—41no—
248#92418#13712yes—
249#19262—611nomaximal, Sylow
250C22×C61C2×#12111yescharacteristic
251C2×D61—21no—
252C2×D61—21no—
253C2×D61#46712yes—
254C4×C61—22no—
255C4×C61—21no—
256C4×C61—41no—
257C4×C61—81no—
258C4×C61—81no—
259C4×C61C22×Q1611yescharacteristic
260C4×C61C2×#13511yescharacteristic
261C4×C61C2×#13711yescharacteristic
262C4×C61#57511yescharacteristic
263Dic61—21no—
264Dic61—22no—
265Dic61—21no—
266Dic61—41no—
267Dic61—81no—
268Dic61—81no—
269Dic61#46712yes—
270#3170—611no—
271#3078—611no—
272#3078—611no—
273C2×C8×Q8—611no—
274#1684—611no—
275#1684—611no—
276#1684—611no—
277#1684D6111yescharacteristic, complemented
278#1676—611no—
279#1676—611no—
280#1670—611no—
281#1670—611no—
282#1567—611no—
283#1550—611no—
284#1550—611no—
285C2×C61#303711yescharacteristic
286C2×C61C2×#46711yescharacteristic
287C2×C61#306711yescharacteristic
288D61—22no—
289#533—611no—
290#533—611no—
291C2×C4×Q8—611no—
292#500—611no—
293#494—611no—
294#487—611no—
295#487C2×D6111yescharacteristic
296#479—1221no—
297#479—1221no—
298#479—1221no—
299#479—1221no—
300#477—611no—
301#477—611no—
302#477—611no—
303#477C2×D6111yescharacteristic
304#475—611no—
305#475—611no—
306#475—611no—
307#475C2×D6111yescharacteristic
308#467—1221no—
309#467—1221no—
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—1221no—
314C8×Q8—1221no—
315C8×Q8C2×D6111yescharacteristic
316C4×Q16—1221no—
317C4×Q16—1221no—
318#428—1221no—
319#428—1221no—
320#423—611no—
321#423—611no—
322C2×C4⋊C8—611no—
323C2×C4⋊C8—1221no—
324#419—1221no—
325#419—1221no—
326C2×C4×C8—611no—
327C2×C4×C8—1221no—
328#335—611no—
329#335—611no—
330#335—611no—
331#335C2×D6111yescharacteristic
332#333—611no—
333#333—611no—
334#333—611no—
335#333C2×D6111yescharacteristic
336#332—611no—
337#332—611no—
338#332—611no—
339#332C2×D6111yescharacteristic
340C61#1926211yescharacteristic, complemented, Sylow
341C22×Q8—611no—
342C2×Q16—1221no—
343C2×Q16—1221no—
344C2×M16—1221no—
345C2×M16—1221no—
346C22×C8—611no—
347C22×C8—611no—
348C22×C8—1221no—
349C4⋊Q8—611no—
350C4⋊Q8—611no—
351C4⋊Q8C22×D6111yescharacteristic
352C4⋊Q8C22×D6111yescharacteristic
353#125—1221no—
354#125—1221no—
355C22⋊Q8—1221no—
356C22⋊Q8—1221no—
357C22⋊Q8—1221no—
358C22⋊Q8—1221no—
359C4×Q8—611no—
360C4×Q8—611no—
361C4×Q8—611no—
362C4×Q8—1221no—
363C4×Q8—1221no—
364C4×Q8—1221no—
365C4×Q8—1221no—
366C4×Q8—1221no—
367C4×Q8—1221no—
368C4×Q8C22×D6111yescharacteristic
369#117—1221no—
370#117—1221no—
371C2×C4⋊C4—611no—
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#106—21no—
382#106—1221no—
383#106—1221no—
384#106—1221no—
385C4⋊C8—21no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—1221no—
403#103—1221no—
404#103—1221no—
405#103—1221no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410C4×C8—21no—
411C4×C8—611no—
412C4×C8—611no—
413C4×C8—611no—
414C4×C8—1221no—
415C4×C8—1221no—
416C4×C8—1221no—
417C4×C8C22×D6111yescharacteristic
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—614no—
421C2×Q8—611no—
422C2×Q8—1221no—
423C2×Q8—1222no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8D4×D6111yescharacteristic
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—1221no—
431C22×C4—1221no—
432Q16—2442no—
433Q16—2442no—
434M16—2442no—
435M16—2442no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—611no—
440C2×C8—611no—
441C2×C8—1222no—
442C2×C8—1221no—
443C2×C8—1221no—
444C2×C8—1221no—
445C2×C8—2441no—
446C2×C8—2442no—
447C2×C8D4×D6111yescharacteristic
448C2×C8D4×D6111yescharacteristic
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—611no—
455C4⋊C4—1221no—
456C4⋊C4—1221no—
457C4⋊C4—1221no—
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⋊C4—2441no—
467C4⋊C4D4×D6111yescharacteristic
468C22⋊C4—2441no—
469C22⋊C4—2441no—
470C42—21no—
471C42—611no—
472C42—611no—
473C42—611no—
474C42—1221no—
475C42—1221no—
476C42—1221no—
477C42—2441no—
478C42—2441no—
479C42C23×D6111yescharacteristic
480C23—611no—
481Q8—21no—
482Q8—41no—
483Q8—41no—
484Q8—81no—
485Q8—612no—
486Q8—1224no—
487Q8—1221no—
488Q8—4881no—
489Q8—2441no—
490Q8—2441no—
491Q8Q16×D6112yes—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—611no—
497C2×C4—612no—
498C2×C4—612no—
499C2×C4—611no—
500C2×C4—611no—
501C2×C4—1224no—
502C2×C4—1221no—
503C2×C4—1221no—
504C2×C4—1221no—
505C2×C4—1221no—
506C2×C4—2441no—
507C2×C4—2442no—
508C2×C4—2441no—
509C2×C4—2441no—
510C2×C4C2×D4×D6111yescharacteristic
511C2×C4C2×D4×D6111yescharacteristic
512C2×C4#41×D6111yescharacteristic
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—612no—
519C8—1221no—
520C8—2441no—
521C8—2441no—
522C8—2441no—
523C22—612no—
524C22—1221no—
525C22—1221no—
526C22#121×D6111yescharacteristic
527C4—22no—
528C4—21no—
529C4—41no—
530C4—81no—
531C4—81no—
532C4—612no—
533C4—1222no—
534C4—1221no—
535C4—1221no—
536C4—4881no—
537C4—4881no—
538C4—2441no—
539C4C2×Q16×D6111yescharacteristic
540C4#135×D6111yescharacteristic
541C4#137×D6111yescharacteristic
542C4#1684055911yescharacteristic
543C2—1222no—
544C2#2145528911yescharacteristic
545C2#467×D6111yescharacteristic
546C2#2145553411yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1684C2
socleC22×C61C2×#121
prime radicalC22×D61#121
hypercenter#1684D61
hypocenterC61#19262
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1684

Complements

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

NH ≅ G/Ntype
5. #21445278C2semidirect
6. #21445277C2semidirect
7. #21445274C2semidirect
8. #21445222C2semidirect
9. #21445221C2semidirect
10. #21445188C2semidirect
11. #21445187C2semidirect
15. C61×#1684C2semidirect
148. Q8×D61Q16semidirect
277. #1684D61semidirect
340. C61#19262semidirect

Maximal subgroups

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

subgroupindex
#214564042
#214556252
#214556192
C8×Q8×D612
#214452782
#214452772
#214452742
#214452222
#214452212
#214451882
#214451872
#214445762
#214445082
#214445062
C61×#16842
#1926261