Finite Group Databasebeta

← #29650652

Subgroups — #29650652

Order 15616.

582 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456419C211yesmaximal, characteristic
2#21454964C211yesmaximal, characteristic
3#21454914C211yesmaximal, characteristic, complemented
4#21444725C211yesmaximal, characteristic, complemented
5#21444724C211yesmaximal, characteristic, complemented
6#21444713C211yesmaximal, characteristic, complemented
7#21444706C211yesmaximal, characteristic, complemented
8#21444635C211yesmaximal, characteristic, complemented
9#21444634C211yesmaximal, characteristic, complemented
10#21444623C211yesmaximal, characteristic, complemented
11#21444616C211yesmaximal, characteristic, complemented
12#21444584C211yesmaximal, characteristic, complemented
13#21444280C211yesmaximal, characteristic
14C8×#11758194C211yesmaximal, characteristic, complemented
15C61×#1493C211yesmaximal, characteristic, complemented
16#16840296C2211yescharacteristic
17#16840168C411yescharacteristic
18#16840154C411yescharacteristic
19#16840130C411yescharacteristic
20#16840124C411yescharacteristic
21#16840018C411yescharacteristic
22#16840018C411yescharacteristic
23#16840010C411yescharacteristic
24#16840010C411yescharacteristic
25#16839893—21no—
26#16839893—21no—
27#16839893C2211yescharacteristic
28#16839893C2211yescharacteristic
29#16839889C2211yescharacteristic
30Q8×#92418C2211yescharacteristic
31Q8×#92418C2211yescharacteristic
32#16839886C2211yescharacteristic
33C4×#11758202C2211yescharacteristic
34C4×#11758202C2211yescharacteristic
35C4×#11758201C2211yescharacteristic
36C4×#11758201C2211yescharacteristic
37#16839839C2211yescharacteristic
38#16839838—21no—
39#16839831—21no—
40#16839827C2211yescharacteristic
41#16839823—21no—
42#16839823—21no—
43#16839822—21no—
44#16839819C2211yescharacteristic
45#16839815C2211yescharacteristic
46#16839787—21no—
47C4×#11758194C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839491C2211yescharacteristic
55#16839491C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58C8×#92418C2211yescharacteristic
59C8×#92418C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×Q8⋊C8C2211yescharacteristic
66C61×Q8⋊C8C2211yescharacteristic
67C2×#11758202C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758201C2×C411yescharacteristic
70C2×#11758201C2×C411yescharacteristic
71C2×#11758194C2×C411yescharacteristic
72C2×#11758194C2×C411yescharacteristic
73C2×#11758189—21no—
74C2×C8×D61—21no—
75#14519771—21no—
76#14519769C2×C411yescharacteristic
77#14519765C2×C411yescharacteristic
78#14519760—21no—
79#14519756C2×C411yescharacteristic
80#14519751C2×C411yescharacteristic
81C4×Dic122C2311yescharacteristic
82C4×D244C2311yescharacteristic
83C4×C22⋊D61—21no—
84#14519734—21no—
85#14519710C2×C411yescharacteristic
86#14519710C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88#14519708C2×C411yescharacteristic
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418D411yescharacteristic
94C4⋊#92418D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519701C2×C411yescharacteristic
100#14519701C2×C411yescharacteristic
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519700C2×C411yescharacteristic
105#14519697C2×C411yescharacteristic
106#14519697C2×C411yescharacteristic
107C22⋊#92418—21no—
108C22⋊#92418D411yescharacteristic
109C22⋊#92418D411yescharacteristic
110#14519689—21no—
111#14519689—21no—
112#14519688—21no—
113#14519688—21no—
114#14519688—21no—
115#14519688C2×C411yescharacteristic
116#14519688C2×C411yescharacteristic
117#14519687—21no—
118C4×#92418—21no—
119C4×#92418—21no—
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C4×#92418C2311yescharacteristic
124C8×Dic61—21no—
125C2×M16×C61—21no—
126C22×C8×C61—21no—
127C4⋊Q8×C61C2×C411yescharacteristic
128C4⋊Q8×C61C2×C411yescharacteristic
129#125×C61—21no—
130C22⋊Q8×C61—21no—
131C22⋊Q8×C61C2×C411yescharacteristic
132C22⋊Q8×C61C2×C411yescharacteristic
133C4×Q8×C61—21no—
134C4×Q8×C61C2311yescharacteristic
135C4×Q8×C61C2311yescharacteristic
136#117×C61—21no—
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—21no—
139C4⋊C8×C61C2311yescharacteristic
140C4⋊C8×C61C2311yescharacteristic
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61C22×C411yescharacteristic
146C2×Q8×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C2×D411yescharacteristic
149C22×C4×C61#4111yescharacteristic
150C2×C22⋊D61—21no—
151C2×D244C22×C411yescharacteristic
152C2×C4×D61—21no—
153C2×Dic122C22×C411yescharacteristic
154M16×C61—81no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—42no—
160C4⋊C4×C61—21no—
161C4⋊C4×C61—21no—
162C4⋊C4×C61—21no—
163C4⋊C4×C61—21no—
164C4⋊C4×C61—21no—
165C4⋊C4×C61—21no—
166C4⋊C4×C61—21no—
167C4⋊C4×C61C22×C411yescharacteristic
168C4⋊C4×C61C22×C411yescharacteristic
169C22⋊C4×C61—21no—
170C22⋊C4×C61—21no—
171C42×C61—21no—
172C42×C61—21no—
173C42×C61C22×C411yescharacteristic
174C42×C61C2×D411yescharacteristic
175C42×C61#4111yescharacteristic
176C42×C61C2411yescharacteristic
177C22⋊Dic61—21no—
178#11758202—22no—
179#11758202—22no—
180#11758201—22no—
181#11758201—22no—
182#11758198—21no—
183#11758198—21no—
184#11758198—21no—
185#11758198—21no—
186C4⋊Dic61C22×C411yescharacteristic
187C4⋊Dic61C22×C411yescharacteristic
188#11758196—21no—
189#11758196—21no—
190#11758196—21no—
191#11758196—21no—
192C4×Dic61—21no—
193#11758194—22no—
194#11758194—22no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418C22×C411yescharacteristic
198C2×#92418C22×C411yescharacteristic
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C2×D411yescharacteristic
202C2×#92418C2×D411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205#11758189—81no—
206C8×D61—81no—
207C23×C61C4×D411yescharacteristic
208C22×D61—21no—
209Q8×C61—21no—
210Q8×C61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
213Q8×C61—81no—
214C2×C4×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—21no—
221C2×C4×C61—21no—
222C2×C4×C61—41no—
223C2×C4×C61C4×D411yescharacteristic
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C23×C411yescharacteristic
227C2×C4×C61C22×D411yescharacteristic
228C2×C4×C61C2×#4111yescharacteristic
229C22⋊D61—81no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233D244—21no—
234D244—21no—
235C4×D61—41no—
236C4×D61—41no—
237Dic122—21no—
238Dic122—21no—
239C8×C61—22no—
240C8×C61—41no—
241C8×C61—41no—
242C8×C61—41no—
243#92418—21no—
244#92418—21no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—41no—
250#92418—41no—
251#92418#13112yes—
252#92418#13112yes—
253#17969—611nomaximal, Sylow
254C22×C61—21no—
255C22×C61—21no—
256C22×C61—21no—
257C22×C61C2×C4×D411yescharacteristic
258C2×D61—41no—
259C2×D61—41no—
260C2×D61—41no—
261C4×C61—21no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—41no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61C2×#13111yescharacteristic
270C4×C61C2×#13111yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276#3172—611no—
277#2993—611no—
278#2985—611no—
279#1593—611no—
280#1592—611no—
281#1591—611no—
282#1590—611no—
283#1579—611no—
284SD16⋊C8—611no—
285C8×Q16—611no—
286C8×SD16—611no—
287#1569—611no—
288#1494—611no—
289#1493D6111yescharacteristic, complemented
290C8×M16—611no—
291C2×C61—41no—
292C2×C61#293111yescharacteristic
293C2×C61#294711yescharacteristic
294C2×C61#295611yescharacteristic
295D61—81no—
296#533C2×D6111yescharacteristic
297#529—611no—
298#501—611no—
299#497—611no—
300#491—611no—
301#489—611no—
302#470—611no—
303#470—611no—
304#468—611no—
305#468—611no—
306#446—611no—
307#446—611no—
308#446—611no—
309#446—1221no—
310#446—1221no—
311C8×Q8—611no—
312C8×Q8—611no—
313C8×Q8—611no—
314C4×Q16—611no—
315C4×Q16—611no—
316C4×SD16—611no—
317C4×SD16—611no—
318#436—611no—
319#436—1221no—
320#435—1221no—
321C8×D4—611no—
322#433—1221no—
323#433—1221no—
324#433—1221no—
325#432—611no—
326#431—611no—
327#424—1221no—
328#423C2×D6111yescharacteristic
329C4×M16—611no—
330C2×C4×C8C2×D6111yescharacteristic
331#335—611no—
332#335—611no—
333#334—611no—
334#334—611no—
335Q8⋊C8—611no—
336Q8⋊C8—611no—
337Q8⋊C8C2×D6111yescharacteristic
338Q8⋊C8C2×D6111yescharacteristic
339Q8⋊C8C2×D6111yescharacteristic
340Q8⋊C8C2×D6111yescharacteristic
341D4⋊C8—611no—
342D4⋊C8—611no—
343#322—611no—
344#322—611no—
345C82—611no—
346C82—611no—
347C61#1796911yescharacteristic, complemented, Sylow
348C2×Q16—611no—
349C2×Q16—611no—
350C2×SD16—611no—
351C2×SD16—611no—
352C2×M16—21no—
353C2×M16—611no—
354C2×M16—611no—
355C2×M16—1221no—
356C22×C8—21no—
357C22×C8—1221no—
358C4⋊Q8C4×D6111yescharacteristic
359C4⋊Q8C4×D6111yescharacteristic
360#126—1221no—
361#125—21no—
362#125—611no—
363#124—611no—
364#123—1221no—
365C22⋊Q8—21no—
366C22⋊Q8—611no—
367C22⋊Q8C4×D6111yescharacteristic
368C22⋊Q8C4×D6111yescharacteristic
369#121—611no—
370C4×Q8—21no—
371C4×Q8—611no—
372C4×Q8C22×D6111yescharacteristic
373C4×Q8C22×D6111yescharacteristic
374C4×D4—611no—
375C4×D4—1221no—
376#117—21no—
377#117—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—21no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—611no—
387C4⋊C8—611no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8—1221no—
394C4⋊C8C22×D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396#103—611no—
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#102—611no—
403#102—611no—
404C22⋊C8—611no—
405C22⋊C8—611no—
406C22⋊C8—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409#97—611no—
410#97—611no—
411#97—1221no—
412#97—1221no—
413#97—1221no—
414#97—1221no—
415C4×C8—21no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C2×Q8—21no—
426C2×Q8—611no—
427C2×Q8C2×C4×D6111yescharacteristic
428C2×Q8C2×C4×D6111yescharacteristic
429C2×D4—611no—
430C2×D4—1221no—
431C22×C4—1221no—
432C22×C4C2×C4×D6111yescharacteristic
433C22×C4D4×D6111yescharacteristic
434C22×C4#1175822411yescharacteristic
435Q16—1222no—
436Q16—1222no—
437SD16—1222no—
438SD16—1222no—
439M16—81no—
440M16—1222no—
441M16—1222no—
442M16—4881no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—42no—
448C2×C8—611no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—4881no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—611no—
467C4⋊C4—611no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4C2×C4×D6111yescharacteristic
473C4⋊C4C2×C4×D6111yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C22⋊C4—1221no—
480C22⋊C4—1221no—
481C42—21no—
482C42—21no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42D4×D6111yescharacteristic
486C42#1175822411yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23#1451973711yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—81no—
495Q8—1221no—
496Q8—1221no—
497D4—1221no—
498D4—1221no—
499D4—4881no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—41no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—2441no—
513C2×C4—2441no—
514C2×C4#1451973711yescharacteristic
515C2×C4#1451973711yescharacteristic
516C2×C4#1451973711yescharacteristic
517C2×C4C22×C4×D6111yescharacteristic
518C2×C4C2×D4×D6111yescharacteristic
519C2×C4C2×#1175822411yescharacteristic
520C8—22no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—612no—
525C8—612no—
526C8—1221no—
527C8—1221no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—2441no—
533C8—2441no—
534C22—21no—
535C22—21no—
536C22—21no—
537C22—2441no—
538C22—2441no—
539C22—2441no—
540C22C2×#1451973711yescharacteristic
541C4—21no—
542C4—21no—
543C4—21no—
544C4—21no—
545C4—41no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4#131×D6111yescharacteristic
553C4#131×D6111yescharacteristic
554C4#1684056811yescharacteristic
555C4#1684057511yescharacteristic
556C2—41no—
557C2—4881no—
558C2#2145452711yescharacteristic
559C2#2145465611yescharacteristic
560C2#2145472511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1493C2
socleC22×C61C2×C4×D4
prime radical#14519751C2×C4
cosocleC42×C61C24
hypercenter#1493D61
hypocenterC61#17969
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1493

Complements

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

NH ≅ G/Ntype
3. #21454914C2semidirect
4. #21444725C2semidirect
5. #21444724C2semidirect
6. #21444713C2semidirect
7. #21444706C2semidirect
8. #21444635C2semidirect
9. #21444634C2semidirect
10. #21444623C2semidirect
11. #21444616C2semidirect
12. #21444584C2semidirect
14. C8×#11758194C2semidirect
15. C61×#1493C2semidirect
289. #1493D61semidirect
347. C61#17969semidirect

Maximal subgroups

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

subgroupindex
#214564192
#214549642
#214549142
#214447252
#214447242
#214447132
#214447062
#214446352
#214446342
#214446232
#214446162
#214445842
#214442802
C8×#117581942
C61×#14932
#1796961