Finite Group Databasebeta

← #29650084

Subgroups — #29650084

Order 15616.

596 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#21455895C211yesmaximal, characteristic
2#21454899C211yesmaximal, characteristic, complemented
3#21444695C211yesmaximal, characteristic, complemented
4#21444688C211yesmaximal, characteristic, complemented
5#21444667C211yesmaximal, characteristic, complemented
6#21444660C211yesmaximal, characteristic, complemented
7#21444636C211yesmaximal, characteristic, complemented
8#21444631C211yesmaximal, characteristic, complemented
9C8×#11758202C211yesmaximal, characteristic, complemented
10C8×#11758200C211yesmaximal, characteristic, complemented
11#21444610C211yesmaximal, characteristic, complemented
12#21444247C211yesmaximal, characteristic, complemented
13#21444227C211yesmaximal, characteristic
14#21444119C211yesmaximal, characteristic, complemented
15C61×#2993C211yesmaximal, characteristic
16C2×C4×Dic122C2211yescharacteristic
17#16840090C411yescharacteristic
18#16840073C411yescharacteristic
19#16840066C411yescharacteristic
20#16840066C411yescharacteristic
21#16839981C411yescharacteristic
22#16839981C411yescharacteristic
23#16839917C411yescharacteristic
24#16839900C411yescharacteristic
25C8×Dic122C2211yescharacteristic
26C8×Dic122C2211yescharacteristic
27C8×Dic122C2211yescharacteristic
28C8×Dic122C2211yescharacteristic
29#16839886—21no—
30#16839886—21no—
31C4×#11758202C2211yescharacteristic
32C4×#11758202C2211yescharacteristic
33C4×#11758200C2211yescharacteristic
34C4×#11758200C2211yescharacteristic
35#16839815C2211yescharacteristic
36#16839815C2211yescharacteristic
37#16839815C2211yescharacteristic
38#16839812—21no—
39#16839812—21no—
40#16839514C2211yescharacteristic
41#16839514C2211yescharacteristic
42#16839512C2211yescharacteristic
43#16839512C2211yescharacteristic
44Q8⋊#92418C2211yescharacteristic
45Q8⋊#92418C2211yescharacteristic
46#16839492C2211yescharacteristic
47#16839492C2211yescharacteristic
48#16839492C2211yescharacteristic
49#16839492C2211yescharacteristic
50D4⋊#92418C2211yescharacteristic
51D4⋊#92418C2211yescharacteristic
52#16839484C2211yescharacteristic
53#16839484C2211yescharacteristic
54#16839483C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#529C2211yescharacteristic
57C61×#446C2211yescharacteristic
58C8×Q8×C61C2211yescharacteristic
59C61×#436—21no—
60C61×#436C2211yescharacteristic
61C61×#435—21no—
62C8×D4×C61C2211yescharacteristic
63C61×#433—21no—
64C61×#431C2211yescharacteristic
65C61×#424—21no—
66C61×#423C2211yescharacteristic
67C22×Dic122C2×C411yescharacteristic
68C2×#11758202C2×C411yescharacteristic
69C2×#11758202C2×C411yescharacteristic
70C2×#11758200C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C4×Dic122—21no—
73C4×Dic122—21no—
74C4×Dic122C2×C411yescharacteristic
75C4×Dic122C2×C411yescharacteristic
76C4×Dic122C2311yescharacteristic
77C4×Dic122C2311yescharacteristic
78C2×C4⋊Dic61C2×C411yescharacteristic
79C2×#11758196—21no—
80C2×C4×Dic61—21no—
81#14519710C2×C411yescharacteristic
82#14519710C2×C411yescharacteristic
83#14519708C2×C411yescharacteristic
84#14519708C2×C411yescharacteristic
85C4⋊#92418—21no—
86C4⋊#92418C2×C411yescharacteristic
87C4⋊#92418C2×C411yescharacteristic
88C4⋊#92418C2311yescharacteristic
89C4⋊#92418C2311yescharacteristic
90#14519706—21no—
91#14519706—21no—
92#14519706—21no—
93#14519706—21no—
94#14519701C2×C411yescharacteristic
95#14519701C2×C411yescharacteristic
96#14519700C2×C411yescharacteristic
97#14519700C2×C411yescharacteristic
98#14519700C2×C411yescharacteristic
99#14519700C2×C411yescharacteristic
100#14519698C2×C411yescharacteristic
101#14519698C2×C411yescharacteristic
102C22⋊#92418—21no—
103C22⋊#92418—21no—
104C22⋊#92418C2×C411yescharacteristic
105C22⋊#92418C2×C411yescharacteristic
106C4×#92418—21no—
107C4×#92418C2311yescharacteristic
108C4×#92418C2311yescharacteristic
109C4×#92418C2311yescharacteristic
110C4×#92418C2311yescharacteristic
111C8×Dic61—21no—
112C8×Dic61—21no—
113C8×Dic61—21no—
114C8×Dic61—21no—
115C2×M16×C61—21no—
116C2×M16×C61—21no—
117C22×C8×C61—21no—
118#126×C61—21no—
119#125×C61C2×C411yescharacteristic
120#124×C61C2×C411yescharacteristic
121#123×C61—21no—
122C22⋊Q8×C61C2×C411yescharacteristic
123#121×C61C2×C411yescharacteristic
124C4×Q8×C61C2311yescharacteristic
125C4×D4×C61—21no—
126C4×D4×C61C2311yescharacteristic
127#117×C61—21no—
128C2×C42×C61C2311yescharacteristic
129C4⋊C8×C61—21no—
130C4⋊C8×C61—21no—
131C4⋊C8×C61—21no—
132C4⋊C8×C61D411yescharacteristic
133C4⋊C8×C61D411yescharacteristic
134C4⋊C8×C61C2311yescharacteristic
135C4⋊C8×C61C2311yescharacteristic
136C22⋊C8×C61—21no—
137C22⋊C8×C61—21no—
138C22⋊C8×C61D411yescharacteristic
139C22⋊C8×C61D411yescharacteristic
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—21no—
154C2×Dic122—22no—
155C2×Dic122—22no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158M16×C61—81no—
159M16×C61—81no—
160C2×C8×C61—21no—
161C2×C8×C61—21no—
162C2×C8×C61—81no—
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×C61C22×C411yescharacteristic
172C4⋊C4×C61C22×C411yescharacteristic
173C22⋊C4×C61—21no—
174C22⋊C4×C61—21no—
175C22⋊C4×C61—21no—
176C22⋊C4×C61—21no—
177C22⋊C4×C61—21no—
178C42×C61—21no—
179C42×C61C22×C411yescharacteristic
180C42×C61C2×D411yescharacteristic
181C42×C61#4111yescharacteristic
182C42×C61C2411yescharacteristic
183#11758202—22no—
184#11758202—22no—
185#11758200—22no—
186#11758200—22no—
187C4⋊Dic61—21no—
188C4⋊Dic61C22×C411yescharacteristic
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194C4×Dic61—21no—
195C4×Dic61—21no—
196C4×Dic61—21no—
197C4×Dic61—21no—
198C2×#92418—21no—
199C2×#92418—21no—
200C2×#92418—21no—
201C2×#92418—21no—
202C2×#92418C22×C411yescharacteristic
203C2×#92418C22×C411yescharacteristic
204C2×#92418C22×C411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C23×C61—21no—
207C23×C61C4×D411yescharacteristic
208Q8×C61—21no—
209Q8×C61—21no—
210D4×C61—21no—
211D4×C61—21no—
212D4×C61—81no—
213C2×C4×C61—21no—
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—41no—
221C2×C4×C61—41no—
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
229C2×Dic61—24no—
230C2×Dic61—21no—
231C2×Dic61—21no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—81no—
235Dic122—24no—
236Dic122—21no—
237Dic122—21no—
238Dic122#13112yes—
239Dic122#13112yes—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—41no—
245C8×C61—41no—
246#92418—21no—
247#92418—21no—
248#92418—21no—
249#92418—21no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#17919—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61—41no—
259C22×C61—41no—
260C22×C61—41no—
261C22×C61C2×C4×D411yescharacteristic
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61C2×#13111yescharacteristic
270C4×C61C2×#13111yescharacteristic
271C4×C61#57711yescharacteristic
272C4×C61#57811yescharacteristic
273Dic61—22no—
274Dic61—22no—
275Dic61—41no—
276Dic61—41no—
277#3108—611no—
278#2993D6111yescharacteristic
279#2982—611no—
280#1588—611no—
281#1587—611no—
282#1584—611no—
283#1583—611no—
284#1579—611no—
285SD16⋊C8—611no—
286C8×Q16—611no—
287C8×SD16—611no—
288#1574—611no—
289#1487—611no—
290#1482—611no—
291#1454—611no—
292C2×C61—41no—
293C2×C61—81no—
294C2×C61#292911yescharacteristic
295C2×C61#294711yescharacteristic
296C2×C61#295711yescharacteristic
297#529C2×D6111yescharacteristic
298C2×C4×Q8—611no—
299#483—611no—
300#480—611no—
301#479—611no—
302#479—611no—
303#464—611no—
304#464—611no—
305#451—611no—
306#448—611no—
307#446C2×D6111yescharacteristic
308C8×Q8—611no—
309C8×Q8—611no—
310C8×Q8—611no—
311C8×Q8—611no—
312C8×Q8—1221no—
313C8×Q8—1221no—
314C8×Q8C2×D6111yescharacteristic
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319#436—21no—
320#436C2×D6111yescharacteristic
321#435—21no—
322C8×D4C2×D6111yescharacteristic
323#433—21no—
324#431—611no—
325#431—611no—
326#431—611no—
327#431—1221no—
328#431—1221no—
329#431C2×D6111yescharacteristic
330#424—21no—
331#423C2×D6111yescharacteristic
332#335—611no—
333#335—611no—
334#334—611no—
335#334—611no—
336Q8⋊C8—611no—
337Q8⋊C8—611no—
338Q8⋊C8—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342D4⋊C8—611no—
343D4⋊C8—611no—
344#322—611no—
345#322—611no—
346#322—611no—
347C82—611no—
348C61#1791911yescharacteristic, complemented, Sylow
349C22×Q8—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16—611no—
354C2×M16—21no—
355C2×M16—21no—
356C22×C8—21no—
357#126—21no—
358#125C4×D6111yescharacteristic
359#124C4×D6111yescharacteristic
360#123—21no—
361C22⋊Q8C4×D6111yescharacteristic
362#121C4×D6111yescharacteristic
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—1221no—
368C4×Q8—1221no—
369C4×Q8C22×D6111yescharacteristic
370C4×D4—21no—
371C4×D4C22×D6111yescharacteristic
372#117—21no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—611no—
378#107—611no—
379#106—611no—
380#106—611no—
381C4⋊C8—21no—
382C4⋊C8—21no—
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⋊C8C22⋊D6111yescharacteristic
394C4⋊C8C22⋊D6111yescharacteristic
395C4⋊C8C22×D6111yescharacteristic
396C4⋊C8C22×D6111yescharacteristic
397#103—611no—
398#103—611no—
399#103—611no—
400#103—611no—
401#103—611no—
402#103—611no—
403#102—611no—
404#102—611no—
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—611no—
408C22⋊C8—611no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8C22⋊D6111yescharacteristic
412C22⋊C8C22⋊D6111yescharacteristic
413#97—21no—
414C4×C8—21no—
415C4×C8—611no—
416C4×C8—611no—
417C4×C8—611no—
418C4×C8—611no—
419C4×C8—1221no—
420C4×C8—1221no—
421C4×C8—1221no—
422C4×C8—1221no—
423C4×C8—1221no—
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426C2×Q8—611no—
427C2×Q8—611no—
428C2×Q8—1222no—
429C2×Q8—1222no—
430C2×Q8—1221no—
431C2×Q8C2×C4×D6111yescharacteristic
432C2×D4—21no—
433C2×D4C2×C4×D6111yescharacteristic
434C22×C4—21no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4#1175822211yescharacteristic
439C22×C4C2×C22⋊D6111yescharacteristic
440Q16—1222no—
441Q16—1222no—
442SD16—1222no—
443SD16—1222no—
444M16—81no—
445M16—81no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—81no—
449C2×C8—611no—
450C2×C8—611no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8C2×C22⋊D6111yescharacteristic
458C2×C8C2×C22⋊D6111yescharacteristic
459C2×C8C2×C22⋊D6111yescharacteristic
460C2×C8C2×C22⋊D6111yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—611no—
466C4⋊C4—611no—
467C4⋊C4—1221no—
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—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42#1175822211yescharacteristic
486C42C2×C22⋊D6111yescharacteristic
487C42C23×D6111yescharacteristic
488C23—21no—
489C23C4×C22⋊D6111yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—612no—
493Q8—612no—
494Q8—1224no—
495Q8—1221no—
496Q8—1221no—
497D4—21no—
498D4—21no—
499D4—81no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—1224no—
511C2×C4—1221no—
512C2×C4—1221no—
513C2×C4—1221no—
514C2×C4—1221no—
515C2×C4—4881no—
516C2×C4C4×C22⋊D6111yescharacteristic
517C2×C4C4×C22⋊D6111yescharacteristic
518C2×C4C4×C22⋊D6111yescharacteristic
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C22×C22⋊D6111yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—41no—
527C8—41no—
528C8—1221no—
529C8—1221no—
530C8—1221no—
531C8—1221no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22C2×C4×C22⋊D6111yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—1222no—
551C4—1222no—
552C4—2441no—
553C4—2441no—
554C4#131×D6111yescharacteristic
555C4#131×D6111yescharacteristic
556C4#1684057311yescharacteristic
557C4#1684057711yescharacteristic
558C2—41no—
559C2—81no—
560C2#2145451111yescharacteristic
561C2#2145465811yescharacteristic
562C2#2145473411yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2993C2
socleC22×C61C2×C4×D4
prime radical#121×C61C2×C4
cosocleC42×C61C24
hypercenter#2993D61
hypocenterC61#17919
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2993

Complements

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

NH ≅ G/Ntype
2. #21454899C2semidirect
3. #21444695C2semidirect
4. #21444688C2semidirect
5. #21444667C2semidirect
6. #21444660C2semidirect
7. #21444636C2semidirect
8. #21444631C2semidirect
9. C8×#11758202C2semidirect
10. C8×#11758200C2semidirect
11. #21444610C2semidirect
12. #21444247C2semidirect
14. #21444119C2semidirect
348. C61#17919semidirect

Maximal subgroups

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

subgroupindex
#214558952
#214548992
#214446952
#214446882
#214446672
#214446602
#214446362
#214446312
C8×#117582022
C8×#117582002
#214446102
#214442472
#214442272
#214441192
C61×#29932
#1791961