Finite Group Databasebeta

← #29663056

Subgroups — #29663056

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455884C211yesmaximal, characteristic
2#21455601C211yesmaximal, characteristic
3#21454837C211yesmaximal, characteristic
4#21445391C211yesmaximal, characteristic, complemented
5#21445363C211yesmaximal, characteristic, complemented
6#21445315C211yesmaximal, characteristic, complemented
7#21445305C211yesmaximal, characteristic, complemented
8#21445274C211yesmaximal, characteristic, complemented
9#21445246C211yesmaximal, characteristic, complemented
10#21445198C211yesmaximal, characteristic, complemented
11#21445186C211yesmaximal, characteristic, complemented
12#21444571C211yesmaximal, characteristic, complemented
13#21444529C211yesmaximal, characteristic, complemented
14#21444519C211yesmaximal, characteristic, complemented
15C61×#3185C211yesmaximal, characteristic, complemented
16C4×#11758222C2211yescharacteristic
17#16840100—21no—
18#16840066—21no—
19#16840059—21no—
20#16840054C2211yescharacteristic
21#16840049C2211yescharacteristic
22#16840044C2211yescharacteristic
23#16840044C2211yescharacteristic
24#16840039C2211yescharacteristic
25#16840039C2211yescharacteristic
26#16839969C2211yescharacteristic
27#16839964C2211yescharacteristic
28#16839922—21no—
29C8×Dic122C2211yescharacteristic
30C8×Dic122C2211yescharacteristic
31C4×#11758202—21no—
32C4×#11758201—21no—
33#16839841C2211yescharacteristic
34#16839841C2211yescharacteristic
35#16839838—21no—
36#16839838—21no—
37#16839819C2211yescharacteristic
38#16839817—21no—
39#16839815C2211yescharacteristic
40#16839798—21no—
41C2×C4⋊#92418C2211yescharacteristic
42#16839756—21no—
43#16839714—21no—
44#16839515C2211yescharacteristic
45#16839515C2211yescharacteristic
46#16839513C2211yescharacteristic
47#16839513C2211yescharacteristic
48#16839511C2211yescharacteristic
49#16839511C2211yescharacteristic
50#16839508C2211yescharacteristic
51#16839508C2211yescharacteristic
52#16839508C2211yescharacteristic
53#16839508C2211yescharacteristic
54#16839508C2211yescharacteristic
55#16839508C2211yescharacteristic
56C61×#533C2211yescharacteristic
57C61×#533C2211yescharacteristic
58C61×#498C2211yescharacteristic
59C61×#494C2211yescharacteristic
60C61×#487C2211yescharacteristic
61C61×#487C2211yescharacteristic
62C61×#470—21no—
63C61×#470—21no—
64C61×#441—21no—
65C61×#441—21no—
66C4×M16×C61C2211yescharacteristic
67C2×#11758222D411yescharacteristic
68C2×#11758202—21no—
69C2×#11758201—21no—
70C2×#11758189—21no—
71C2×#11758189—21no—
72C22×#92418—21no—
73C4×Dic122D411yescharacteristic
74C4×Dic122C2311yescharacteristic
75C4×D244D411yescharacteristic
76C4×D244C2311yescharacteristic
77C4×C22⋊D61—21no—
78C4×C22⋊D61—21no—
79#14519736D411yescharacteristic
80#14519734—21no—
81C42×D61—21no—
82#14519710—21no—
83#14519710—21no—
84#14519710—21no—
85#14519708—21no—
86#14519708—21no—
87#14519708—21no—
88C4⋊#92418—21no—
89C4⋊#92418C2311yescharacteristic
90C4⋊#92418C2311yescharacteristic
91C4⋊#92418C2311yescharacteristic
92C4⋊#92418C2311yescharacteristic
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95#14519706—21no—
96#14519706—21no—
97#14519701—21no—
98#14519701—21no—
99#14519700—21no—
100#14519700—21no—
101#14519700—21no—
102#14519697—21no—
103#14519697—21no—
104#14519697—21no—
105C22⋊#92418—21no—
106C22⋊#92418—21no—
107#14519689—21no—
108#14519689—21no—
109#14519688—21no—
110C4×#92418—21no—
111C8×Dic61—21no—
112C8×Dic61—21no—
113C2×Q16×C61—21no—
114C2×Q16×C61—21no—
115C2×M16×C61D411yescharacteristic
116C2×M16×C61D411yescharacteristic
117C4⋊Q8×C61C2311yescharacteristic
118C4⋊Q8×C61C2311yescharacteristic
119C4⋊Q8×C61C2311yescharacteristic
120C4⋊Q8×C61C2311yescharacteristic
121#125×C61—21no—
122#125×C61—21no—
123C22⋊Q8×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—21no—
127C4×Q8×C61—21no—
128C4×Q8×C61—21no—
129C4×Q8×C61—21no—
130C4×Q8×C61—21no—
131#117×C61—21no—
132#117×C61—21no—
133C2×C42×C61C2311yescharacteristic
134#106×C61—21no—
135#106×C61—21no—
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#97×C61D411yescharacteristic
141#97×C61D411yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C2×C22⋊D61—21no—
152#11758222—22no—
153#11758222—41no—
154C2×D244C2×D411yescharacteristic
155C2×C4×D61—21no—
156C2×C4×D61—21no—
157C2×C4×D61—21no—
158C2×Dic122C2×D411yescharacteristic
159Q16×C61—42no—
160Q16×C61—42no—
161M16×C61—22no—
162M16×C61—41no—
163C2×C8×C61C2×D411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
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×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—21no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61—41no—
177C4⋊C4×C61—41no—
178C4⋊C4×C61—41no—
179C22⋊C4×C61—41no—
180C22⋊C4×C61—41no—
181C42×C61—41no—
182C42×C61—41no—
183C42×C61C2×D411yescharacteristic
184C42×C61C2×D411yescharacteristic
185C42×C61#4111yescharacteristic
186C42×C61C2411yescharacteristic
187C22⋊Dic61—21no—
188#11758202—42no—
189#11758201—42no—
190#11758198—21no—
191#11758198—21no—
192C4⋊Dic61C2×D411yescharacteristic
193C4⋊Dic61C2×D411yescharacteristic
194#11758196—21no—
195#11758196—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418—21no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—42no—
206#11758189—42no—
207#11758189—42no—
208C23×C61#12111yescharacteristic
209C22×D61—21no—
210Q8×C61—41no—
211Q8×C61—41no—
212Q8×C61—41no—
213Q8×C61—41no—
214Q8×C61—41no—
215Q8×C61—41no—
216Q8×C61—81no—
217C2×C4×C61—21no—
218C2×C4×C61—21no—
219C2×C4×C61—21no—
220C2×C4×C61—21no—
221C2×C4×C61—41no—
222C2×C4×C61—41no—
223C2×C4×C61—41no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61#12111yescharacteristic
227C2×C4×C61#12111yescharacteristic
228C2×C4×C61#12111yescharacteristic
229C2×C4×C61C22×D411yescharacteristic
230C2×C4×C61C22×D411yescharacteristic
231C2×C4×C61C2×#4111yescharacteristic
232C22⋊D61—42no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
236D244—21no—
237D244—21no—
238C4×D61—42no—
239C4×D61—41no—
240C4×D61—41no—
241C4×D61—81no—
242Dic122—21no—
243Dic122#13712yes—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61#13512yes—
248#92418—41no—
249#92418—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#19185—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×#12111yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—81no—
267C4×C61—81no—
268C4×C61—81no—
269C4×C61—81no—
270C4×C61C2×#13511yescharacteristic
271C4×C61C2×#13711yescharacteristic
272C4×C61#57511yescharacteristic
273C4×C61#57511yescharacteristic
274Dic61—22no—
275Dic61—41no—
276Dic61—41no—
277#3185D6111yescharacteristic, complemented
278#3107—611no—
279#3076—611no—
280#2971—611no—
281#1703—611no—
282#1699—611no—
283#1691—611no—
284#1689—611no—
285#1684—611no—
286#1680—611no—
287#1672—611no—
288#1670—611no—
289#1565—611no—
290#1554—611no—
291#1552—611no—
292C2×C61—41no—
293C2×C61#303511yescharacteristic
294C2×C61#305611yescharacteristic
295C2×C61#306911yescharacteristic
296D61—81no—
297#533C2×D6111yescharacteristic
298#533C2×D6111yescharacteristic
299C4×#41—611no—
300#498C2×D6111yescharacteristic
301#494C2×D6111yescharacteristic
302#487C2×D6111yescharacteristic
303#487C2×D6111yescharacteristic
304#485—1221no—
305#479—1221no—
306#478—1221no—
307#477—611no—
308#476—611no—
309#475—611no—
310#475—611no—
311#474—611no—
312#474—611no—
313#470—21no—
314#470—21no—
315#462—611no—
316#461—611no—
317#452—1221no—
318C8×Q8—611no—
319C8×Q8—611no—
320#441—21no—
321#441—21no—
322C4×Q16—1221no—
323C4×SD16—1221no—
324#436—611no—
325#436—611no—
326#436—1221no—
327#436—1221no—
328#432—611no—
329#432—1221no—
330#431—611no—
331#427—1221no—
332C2×C4⋊C8—611no—
333#416—1221no—
334C4×M16—1221no—
335C4×M16C2×D6111yescharacteristic
336#335—611no—
337#335—611no—
338#334—611no—
339#334—611no—
340#333—611no—
341#333—611no—
342#332—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347#332—611no—
348C61#1918511yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—21no—
351C2×Q16—21no—
352C2×Q16—1221no—
353C2×SD16—1221no—
354C2×M16—1221no—
355C2×M16—1221no—
356C2×M16C22⋊D6111yescharacteristic
357C2×M16C22⋊D6111yescharacteristic
358C22×C8—1221no—
359C4⋊Q8C22×D6111yescharacteristic
360C4⋊Q8C22×D6111yescharacteristic
361C4⋊Q8C22×D6111yescharacteristic
362C4⋊Q8C22×D6111yescharacteristic
363#125—21no—
364#125—21no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8—21no—
368C22⋊Q8—21no—
369C4×Q8—21no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8—611no—
374C4×Q8—611no—
375C4×D4—611no—
376C4×D4—611no—
377C4×D4—1221no—
378C4×D4—1221no—
379#117—21no—
380#117—21no—
381#117—611no—
382#117—1221no—
383C2×C42—1221no—
384C2×C42C22×D6111yescharacteristic
385#107—1221no—
386#107—1221no—
387#107—1221no—
388#106—21no—
389#106—21no—
390#106—1221no—
391#106—1221no—
392#106—1221no—
393C4⋊C8—611no—
394C4⋊C8—611no—
395C4⋊C8—611no—
396C4⋊C8—611no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—1221no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—1221no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#102—1221no—
412#102—1221no—
413#102—1221no—
414C22⋊C8—1221no—
415C22⋊C8—1221no—
416C22⋊C8—1221no—
417C22⋊C8—1221no—
418#97—1221no—
419#97C22⋊D6111yescharacteristic
420#97C22⋊D6111yescharacteristic
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—1222no—
427#41—2441no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—611no—
433C2×D4—611no—
434C2×D4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4D4×D6111yescharacteristic
439C22×C4#1175822411yescharacteristic
440C22×C4C2×C22⋊D6111yescharacteristic
441Q16—42no—
442Q16—42no—
443Q16—2442no—
444SD16—2442no—
445M16—22no—
446M16—41no—
447M16—2442no—
448M16—2442no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—1221no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—2442no—
456C2×C8C2×C22⋊D6111yescharacteristic
457C2×C8C2×C22⋊D6111yescharacteristic
458C2×C8C2×C22⋊D6111yescharacteristic
459C2×C8C2×C22⋊D6111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—611no—
473C4⋊C4—611no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—41no—
482C42—41no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42D4×D6111yescharacteristic
487C42#1175822411yescharacteristic
488C42C2×C22⋊D6111yescharacteristic
489C42C23×D6111yescharacteristic
490C23—1221no—
491C23#1451974811yescharacteristic
492Q8—41no—
493Q8—41no—
494Q8—41no—
495Q8—41no—
496Q8—41no—
497Q8—41no—
498Q8—81no—
499Q8—612no—
500Q8—1221no—
501D4—1221no—
502D4—1221no—
503D4—2442no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—4881no—
517C2×C4—2442no—
518C2×C4—2441no—
519C2×C4—2441no—
520C2×C4#1451974811yescharacteristic
521C2×C4#1451974811yescharacteristic
522C2×C4#1451974811yescharacteristic
523C2×C4C2×D4×D6111yescharacteristic
524C2×C4C22×C22⋊D6111yescharacteristic
525C2×C4C2×#1175822411yescharacteristic
526C8—21no—
527C8—21no—
528C8—21no—
529C8—2441no—
530C8—2441no—
531C8—2441no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8#1451979712yes—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2441no—
540C22—2441no—
541C22—2441no—
542C22C2×#1451974811yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—1222no—
552C4—2441no—
553C4—2441no—
554C4C2×#1451979711yescharacteristic
555C4#137×D6111yescharacteristic
556C4#1684056011yescharacteristic
557C4#1684056111yescharacteristic
558C2—41no—
559C2—4881no—
560C2#2145526811yescharacteristic
561C2#2145544311yescharacteristic
562C2#2145555211yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3185C2
socleC22×C61C2×#121
prime radicalC2×#11758222D4
hypercenter#3185D61
hypocenterC61#19185
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3185

Complements

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

NH ≅ G/Ntype
4. #21445391C2semidirect
5. #21445363C2semidirect
6. #21445315C2semidirect
7. #21445305C2semidirect
8. #21445274C2semidirect
9. #21445246C2semidirect
10. #21445198C2semidirect
11. #21445186C2semidirect
12. #21444571C2semidirect
13. #21444529C2semidirect
14. #21444519C2semidirect
15. C61×#3185C2semidirect
277. #3185D61semidirect
348. C61#19185semidirect

Maximal subgroups

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

subgroupindex
#214558842
#214556012
#214548372
#214453912
#214453632
#214453152
#214453052
#214452742
#214452462
#214451982
#214451862
#214445712
#214445292
#214445192
C61×#31852
#1918561