Finite Group Databasebeta

← #29651286

Subgroups — #29651286

Order 15616.

592 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455895C211yesmaximal, characteristic
2#21454979C211yesmaximal, characteristic
3#21454909C211yesmaximal, characteristic, complemented
4#21444725C211yesmaximal, characteristic, complemented
5#21444718C211yesmaximal, characteristic, complemented
6#21444672C211yesmaximal, characteristic, complemented
7#21444666C211yesmaximal, characteristic, complemented
8#21444665C211yesmaximal, characteristic, complemented
9#21444652C211yesmaximal, characteristic, complemented
10#21444635C211yesmaximal, characteristic, complemented
11#21444628C211yesmaximal, characteristic, complemented
12#21444605C211yesmaximal, characteristic, complemented
13C2×#16839494C211yesmaximal, characteristic, complemented
14#21444111C211yesmaximal, characteristic, complemented
15C61×#1494C211yesmaximal, characteristic
16C2×C4×Dic122C2211yescharacteristic
17#16840090C411yescharacteristic
18#16840073C411yescharacteristic
19#16840066C411yescharacteristic
20#16840066C411yescharacteristic
21#16839981C411yescharacteristic
22#16839981C411yescharacteristic
23#16839917C411yescharacteristic
24#16839900C411yescharacteristic
25#16839893C2211yescharacteristic
26#16839890—21no—
27#16839890—21no—
28#16839889C2211yescharacteristic
29#16839889C2211yescharacteristic
30Q8×#92418C2211yescharacteristic
31#16839886C2211yescharacteristic
32#16839886C2211yescharacteristic
33C4×#11758202C2211yescharacteristic
34C4×#11758202C2211yescharacteristic
35C4×#11758200C2211yescharacteristic
36C4×#11758200C2211yescharacteristic
37#16839840C2211yescharacteristic
38#16839834—21no—
39D4×#92418—21no—
40D4×#92418C2211yescharacteristic
41#16839823—21no—
42#16839816—21no—
43#16839815C2211yescharacteristic
44#16839815C2211yescharacteristic
45#16839812—21no—
46#16839789—21no—
47C2×C4⋊#92418C2211yescharacteristic
48#16839514C2211yescharacteristic
49#16839514C2211yescharacteristic
50#16839512C2211yescharacteristic
51#16839512C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839484C2211yescharacteristic
57#16839484C2211yescharacteristic
58#16839484C2211yescharacteristic
59#16839484C2211yescharacteristic
60C61×#529C2211yescharacteristic
61C61×#432C2211yescharacteristic
62C2×C4×C8×C61C2211yescharacteristic
63C61×Q8⋊C8C2211yescharacteristic
64C61×Q8⋊C8C2211yescharacteristic
65C61×D4⋊C8C2211yescharacteristic
66C61×D4⋊C8C2211yescharacteristic
67C22×Dic122C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758194—21no—
73C22×#92418—21no—
74C22×#92418—21no—
75C4×Dic122—21no—
76C4×Dic122—21no—
77C4×Dic122C2×C411yescharacteristic
78C4×Dic122C2×C411yescharacteristic
79C4×Dic122C2311yescharacteristic
80C4×Dic122C2311yescharacteristic
81C2×C4⋊Dic61C2×C411yescharacteristic
82C2×#11758196—21no—
83C2×C4×Dic61—21no—
84#14519710C2×C411yescharacteristic
85#14519710C2×C411yescharacteristic
86#14519708C2×C411yescharacteristic
87#14519708C2×C411yescharacteristic
88C4⋊#92418—21no—
89C4⋊#92418—21no—
90C4⋊#92418—21no—
91C4⋊#92418C2×C411yescharacteristic
92C4⋊#92418C2×C411yescharacteristic
93C4⋊#92418D411yescharacteristic
94C4⋊#92418D411yescharacteristic
95C4⋊#92418C2311yescharacteristic
96C4⋊#92418C2311yescharacteristic
97#14519706—21no—
98#14519706—21no—
99#14519706—21no—
100#14519706—21no—
101#14519701C2×C411yescharacteristic
102#14519701C2×C411yescharacteristic
103#14519700C2×C411yescharacteristic
104#14519700C2×C411yescharacteristic
105#14519700C2×C411yescharacteristic
106#14519700C2×C411yescharacteristic
107#14519698C2×C411yescharacteristic
108#14519698C2×C411yescharacteristic
109C22⋊#92418—21no—
110C22⋊#92418—21no—
111C22⋊#92418C2×C411yescharacteristic
112C22⋊#92418C2×C411yescharacteristic
113C22⋊#92418D411yescharacteristic
114C22⋊#92418D411yescharacteristic
115#14519688—21no—
116#14519687—21no—
117#14519687—21no—
118C4×#92418—21no—
119C4×#92418C2311yescharacteristic
120C4×#92418C2311yescharacteristic
121C4×#92418C2311yescharacteristic
122C4×#92418C2311yescharacteristic
123C8×Dic61—21no—
124C8×Dic61—21no—
125C22×C8×C61—21no—
126#126×C61—21no—
127#125×C61C2×C411yescharacteristic
128#124×C61C2×C411yescharacteristic
129#123×C61—21no—
130C22⋊Q8×C61C2×C411yescharacteristic
131#121×C61C2×C411yescharacteristic
132C4×Q8×C61C2311yescharacteristic
133C4×D4×C61—21no—
134C4×D4×C61C2311yescharacteristic
135#117×C61—21no—
136C2×C42×C61C2311yescharacteristic
137C4⋊C8×C61C2311yescharacteristic
138C4⋊C8×C61C2311yescharacteristic
139C22⋊C8×C61—21no—
140#97×C61—21no—
141C4×C8×C61—21no—
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C2×D4×C61—21no—
146C2×D4×C61C22×C411yescharacteristic
147C22×C4×C61—21no—
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C2×D411yescharacteristic
150C22×C4×C61#4111yescharacteristic
151C22×Dic61—21no—
152C22×Dic61—21no—
153C2×Dic122—22no—
154C2×Dic122—21no—
155C2×Dic122—41no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—42no—
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—
171C22⋊C4×C61—21no—
172C22⋊C4×C61—21no—
173C22⋊C4×C61—21no—
174C42×C61—21no—
175C42×C61C22×C411yescharacteristic
176C42×C61C2×D411yescharacteristic
177C42×C61#4111yescharacteristic
178C42×C61C2411yescharacteristic
179#11758202—22no—
180#11758202—41no—
181#11758200—22no—
182#11758200—41no—
183C4⋊Dic61—21no—
184C4⋊Dic61C22×C411yescharacteristic
185C4⋊Dic61C22×C411yescharacteristic
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194#11758194—81no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—81no—
198C2×#92418—81no—
199C2×#92418C22×C411yescharacteristic
200C2×#92418C22×C411yescharacteristic
201C2×#92418C22×C411yescharacteristic
202C2×#92418C22×C411yescharacteristic
203C2×#92418C2×D411yescharacteristic
204C2×#92418C2×D411yescharacteristic
205C2×#92418C2×D411yescharacteristic
206C2×#92418C2×D411yescharacteristic
207C23×C61—21no—
208C23×C61C4×D411yescharacteristic
209Q8×C61—21no—
210Q8×C61—21no—
211D4×C61—21no—
212D4×C61—21no—
213D4×C61—42no—
214C2×C4×C61—22no—
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×C61—41no—
224C2×C4×C61C4×D411yescharacteristic
225C2×C4×C61C4×D411yescharacteristic
226C2×C4×C61C4×D411yescharacteristic
227C2×C4×C61C23×C411yescharacteristic
228C2×C4×C61C22×D411yescharacteristic
229C2×C4×C61C2×#4111yescharacteristic
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—42no—
235C2×Dic61—42no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—42no—
240Dic122#13112yes—
241C8×C61—41no—
242C8×C61—41no—
243C8×C61—41no—
244C8×C61—41no—
245#92418—21no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—21no—
251#92418—21no—
252#92418—21no—
253#92418—41no—
254#92418—41no—
255#18023—611nomaximal, Sylow
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61#44412yes—
262C22×C61C2×C4×D411yescharacteristic
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61C2×#13111yescharacteristic
271C4×C61#56811yescharacteristic
272C4×C61#57711yescharacteristic
273C4×C61#57811yescharacteristic
274Dic61—22no—
275Dic61—41no—
276Dic61—41no—
277Dic61—41no—
278#3108—611no—
279#2994—611no—
280#2984—611no—
281#1593—611no—
282#1592—611no—
283#1584—611no—
284#1584—611no—
285#1583—611no—
286#1582—611no—
287#1579—611no—
288SD16⋊C8—611no—
289#1573—611no—
290#1494D6111yescharacteristic
291C2×Q8⋊C8—611no—
292#1452—611no—
293C2×C61—22no—
294C2×C61—81no—
295C2×C61#293311yescharacteristic
296C2×C61#294711yescharacteristic
297C2×C61C2×#44411yescharacteristic
298#529C2×D6111yescharacteristic
299C2×C4×Q8—611no—
300#483—611no—
301#480—611no—
302#479—611no—
303#479—611no—
304#464—611no—
305#464—611no—
306#451—611no—
307#448—611no—
308#446—611no—
309#446—611no—
310#446—611no—
311#446—1221no—
312#446—1221no—
313C8×Q8—611no—
314C8×Q8—611no—
315C8×Q8—611no—
316C4×Q16—611no—
317C4×Q16—611no—
318C4×SD16—611no—
319C4×SD16—611no—
320#436—611no—
321#435—1221no—
322C8×D4—611no—
323C8×D4—1221no—
324#433—1221no—
325#432—1221no—
326#432C2×D6111yescharacteristic
327#431—611no—
328#431—611no—
329#431—1221no—
330#424—1221no—
331C2×C4⋊C8—611no—
332C2×C4×C8C2×D6111yescharacteristic
333#335—611no—
334#335—611no—
335#334—611no—
336#334—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8C2×D6111yescharacteristic
342Q8⋊C8C2×D6111yescharacteristic
343D4⋊C8C2×D6111yescharacteristic
344D4⋊C8C2×D6111yescharacteristic
345#322—611no—
346#322—611no—
347#322—611no—
348#322—611no—
349C61#1802311yescharacteristic, complemented, Sylow
350C22×Q8—611no—
351C2×Q16—611no—
352C2×Q16—611no—
353C2×SD16—611no—
354C2×SD16—611no—
355C2×M16—1221no—
356C22×C8—21no—
357C22×C8—1221no—
358C22×C8—1221no—
359#126—21no—
360#125C4×D6111yescharacteristic
361#124C4×D6111yescharacteristic
362#123—21no—
363C22⋊Q8C4×D6111yescharacteristic
364#121C4×D6111yescharacteristic
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—611no—
368C4×Q8—611no—
369C4×Q8—1221no—
370C4×Q8—1221no—
371C4×Q8C22×D6111yescharacteristic
372C4×D4—21no—
373C4×D4C22×D6111yescharacteristic
374#117—21no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—1221no—
377C2×C42—1221no—
378C2×C42C22×D6111yescharacteristic
379#107—611no—
380#107—611no—
381#106—611no—
382#106—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
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⋊C8—1221no—
396C4⋊C8C22×D6111yescharacteristic
397C4⋊C8C22×D6111yescharacteristic
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#102—611no—
405#102—611no—
406C22⋊C8—21no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—611no—
410C22⋊C8—611no—
411C22⋊C8—1221no—
412C22⋊C8—1221no—
413#97—21no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417C4×C8—21no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8—1221no—
425C4×C8C22×D6111yescharacteristic
426C4×C8C22×D6111yescharacteristic
427C2×Q8—611no—
428C2×Q8—611no—
429C2×Q8—1222no—
430C2×Q8—1221no—
431C2×Q8—2441no—
432C2×Q8C2×C4×D6111yescharacteristic
433C2×D4—21no—
434C2×D4C2×C4×D6111yescharacteristic
435C22×C4—21no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4C2×C4×D6111yescharacteristic
439C22×C4D4×D6111yescharacteristic
440C22×C4#1175822411yescharacteristic
441Q16—1222no—
442Q16—2441no—
443SD16—1222no—
444SD16—2441no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—42no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—4881no—
462C2×C8—4881no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—611no—
468C4⋊C4—611no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4C2×C4×D6111yescharacteristic
475C4⋊C4C2×C4×D6111yescharacteristic
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C22⋊C4—21no—
480C22⋊C4—21no—
481C42—21no—
482C42—1221no—
483C42—1221no—
484C42—1221no—
485C42—1221no—
486C42C2×C4×D6111yescharacteristic
487C42D4×D6111yescharacteristic
488C42#1175822411yescharacteristic
489C42C23×D6111yescharacteristic
490C23—21no—
491C23#1451973711yescharacteristic
492Q8—21no—
493Q8—21no—
494Q8—612no—
495Q8—1221no—
496Q8—1221no—
497Q8—1221no—
498Q8—2442no—
499D4—21no—
500D4—21no—
501D4—42no—
502C2×C4—22no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—1221no—
516C2×C4—2442no—
517C2×C4—2442no—
518C2×C4#1451973711yescharacteristic
519C2×C4#1451973711yescharacteristic
520C2×C4#1451973711yescharacteristic
521C2×C4C22×C4×D6111yescharacteristic
522C2×C4C2×D4×D6111yescharacteristic
523C2×C4C2×#1175822411yescharacteristic
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C22—21no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22#1683988112yes—
544C22C2×#1451973711yescharacteristic
545C4—21no—
546C4—21no—
547C4—21no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—1222no—
553C4—2441no—
554C4—2441no—
555C4—2441no—
556C4#131×D6111yescharacteristic
557C4#1684052711yescharacteristic
558C4#1684056911yescharacteristic
559C4#1684057611yescharacteristic
560C2—22no—
561C2—81no—
562C2#2145454911yescharacteristic
563C2#2145466511yescharacteristic
564C2C2×#1683988111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1494C2
socleC22×C61C2×C4×D4
prime radical#121×C61C2×C4
cosocleC42×C61C24
hypercenter#1494D61
hypocenterC61#18023
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1494

Complements

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

NH ≅ G/Ntype
3. #21454909C2semidirect
4. #21444725C2semidirect
5. #21444718C2semidirect
6. #21444672C2semidirect
7. #21444666C2semidirect
8. #21444665C2semidirect
9. #21444652C2semidirect
10. #21444635C2semidirect
11. #21444628C2semidirect
12. #21444605C2semidirect
13. C2×#16839494C2semidirect
14. #21444111C2semidirect
349. C61#18023semidirect

Maximal subgroups

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

subgroupindex
#214558952
#214549792
#214549092
#214447252
#214447182
#214446722
#214446662
#214446652
#214446522
#214446352
#214446282
#214446052
C2×#168394942
#214441112
C61×#14942
#1802361