Finite Group Databasebeta

← #29650446

Subgroups — #29650446

Order 15616.

568 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#21455891C211yesmaximal, characteristic
2#21454932C211yesmaximal, characteristic
3#21454913C211yesmaximal, characteristic, complemented
4#21444729C211yesmaximal, characteristic, complemented
5#21444723C211yesmaximal, characteristic, complemented
6#21444717C211yesmaximal, characteristic, complemented
7#21444711C211yesmaximal, characteristic, complemented
8#21444699C211yesmaximal, characteristic, complemented
9#21444692C211yesmaximal, characteristic, complemented
10#21444671C211yesmaximal, characteristic, complemented
11#21444664C211yesmaximal, characteristic, complemented
12#21444604C211yesmaximal, characteristic, complemented
13#21444254C211yesmaximal, characteristic
14#21444223C211yesmaximal, characteristic, complemented
15C61×#1454C211yesmaximal, characteristic, complemented
16#16840319C2211yescharacteristic
17C4×#11758222C2211yescharacteristic
18#16840104C411yescharacteristic
19#16840104C411yescharacteristic
20#16840048C411yescharacteristic
21#16840043C411yescharacteristic
22#16839973C411yescharacteristic
23#16839968C411yescharacteristic
24#16839926C411yescharacteristic
25#16839926C411yescharacteristic
26#16839892C2211yescharacteristic
27#16839892C2211yescharacteristic
28#16839892C2211yescharacteristic
29#16839892C2211yescharacteristic
30#16839891—21no—
31#16839891—21no—
32C8×Dic122C2211yescharacteristic
33C8×Dic122C2211yescharacteristic
34C4×Dic244C2211yescharacteristic
35C4×Dic244C2211yescharacteristic
36C4×#11758190C2211yescharacteristic
37C4×#11758190C2211yescharacteristic
38#16839841C2211yescharacteristic
39#16839841C2211yescharacteristic
40#16839830—21no—
41#16839830—21no—
42#16839820—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic
45#16839818—21no—
46#16839784—21no—
47C2×C4⋊#92418C2211yescharacteristic
48#16839515C2211yescharacteristic
49#16839515C2211yescharacteristic
50#16839513C2211yescharacteristic
51#16839513C2211yescharacteristic
52#16839494C2211yescharacteristic
53#16839494C2211yescharacteristic
54#16839494C2211yescharacteristic
55#16839494C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58#16839491C2211yescharacteristic
59#16839491C2211yescharacteristic
60C61×#431C2211yescharacteristic
61C61×#431C2211yescharacteristic
62C61×#431C2211yescharacteristic
63C61×#322C2211yescharacteristic
64C61×#322C2211yescharacteristic
65C61×#322C2211yescharacteristic
66C82×C61C2211yescharacteristic
67C2×#11758222C2×C411yescharacteristic
68C2×Dic244C2×C411yescharacteristic
69C2×Dic244C2×C411yescharacteristic
70C2×#11758190C2×C411yescharacteristic
71C2×#11758190C2×C411yescharacteristic
72C2×#11758189—21no—
73C2×#11758189—21no—
74C22×#92418—21no—
75#14519777C2×C411yescharacteristic
76#14519777C2×C411yescharacteristic
77#14519769—21no—
78#14519756—21no—
79#14519756C2×C411yescharacteristic
80#14519756C2×C411yescharacteristic
81C4×Dic122—21no—
82C4×Dic122C2×C411yescharacteristic
83C4×Dic122C2311yescharacteristic
84C4×Dic122C2311yescharacteristic
85C4×Dic122C2311yescharacteristic
86C4×D244C2×C411yescharacteristic
87C4×D244C2311yescharacteristic
88C4×C22⋊D61—21no—
89C4×C22⋊D61—21no—
90#14519736—21no—
91#14519736C2×C411yescharacteristic
92#14519734—21no—
93C42×D61—21no—
94#14519711C2×C411yescharacteristic
95#14519711C2×C411yescharacteristic
96#14519709C2×C411yescharacteristic
97#14519709C2×C411yescharacteristic
98C4⋊#92418—21no—
99C4⋊#92418C2311yescharacteristic
100C4⋊#92418C2311yescharacteristic
101C4⋊#92418C2311yescharacteristic
102C4⋊#92418C2311yescharacteristic
103#14519706—21no—
104#14519706—21no—
105#14519706—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519702C2×C411yescharacteristic
110#14519702C2×C411yescharacteristic
111#14519702C2×C411yescharacteristic
112#14519702C2×C411yescharacteristic
113#14519702C2×C411yescharacteristic
114#14519702C2×C411yescharacteristic
115#14519699C2×C411yescharacteristic
116#14519699C2×C411yescharacteristic
117C22⋊#92418—21no—
118#14519689—21no—
119#14519689—21no—
120#14519688—21no—
121#14519687—21no—
122#14519687—21no—
123#14519687—21no—
124#14519687—21no—
125C8×Dic61—21no—
126C8×Dic61—21no—
127C2×C42×C61C2311yescharacteristic
128C4⋊C8×C61—21no—
129C4⋊C8×C61C2×C411yescharacteristic
130C4⋊C8×C61C2×C411yescharacteristic
131C4⋊C8×C61D411yescharacteristic
132C4⋊C8×C61D411yescharacteristic
133C22⋊C8×C61—21no—
134C22⋊C8×C61C2×C411yescharacteristic
135C22⋊C8×C61C2×C411yescharacteristic
136C22⋊C8×C61D411yescharacteristic
137C22⋊C8×C61D411yescharacteristic
138C4×C8×C61C2311yescharacteristic
139C4×C8×C61C2311yescharacteristic
140C4×C8×C61C2311yescharacteristic
141C4×C8×C61C2311yescharacteristic
142C4×C8×C61C2311yescharacteristic
143C4×C8×C61C2311yescharacteristic
144C22×C4×C61C22×C411yescharacteristic
145C22×C4×C61C2×D411yescharacteristic
146C22×C4×C61#4111yescharacteristic
147C2×C22⋊D61—21no—
148#11758222—41no—
149#11758222—41no—
150C2×D244C22×C411yescharacteristic
151C2×C4×D61—21no—
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×Dic122—21no—
155C2×Dic122C22×C411yescharacteristic
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61C22×C411yescharacteristic
161C2×C8×C61C22×C411yescharacteristic
162C2×C8×C61C22×C411yescharacteristic
163C2×C8×C61C22×C411yescharacteristic
164C2×C8×C61C2×D411yescharacteristic
165C2×C8×C61C2×D411yescharacteristic
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C42×C61C22×C411yescharacteristic
169C42×C61C2×D411yescharacteristic
170C42×C61#4111yescharacteristic
171C42×C61C2411yescharacteristic
172C22⋊Dic61—21no—
173C22⋊Dic61—21no—
174C22⋊Dic61—21no—
175#11758198—21no—
176#11758198—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61C22×C411yescharacteristic
181C4⋊Dic61C22×C411yescharacteristic
182C4⋊Dic61C22×C411yescharacteristic
183C4⋊Dic61C22×C411yescharacteristic
184#11758196—21no—
185#11758196—21no—
186#11758196—21no—
187#11758196—21no—
188#11758196—21no—
189#11758196—21no—
190C4×Dic61—21no—
191C4×Dic61—21no—
192C4×Dic61—21no—
193C4×Dic61—21no—
194C4×Dic61—21no—
195C2×#92418—21no—
196C2×#92418—21no—
197C2×#92418—21no—
198C2×#92418—21no—
199C2×#92418—81no—
200Dic244—41no—
201Dic244—41no—
202#11758190—41no—
203#11758190—41no—
204#11758189—81no—
205#11758189—81no—
206C23×C61C4×D411yescharacteristic
207C22×D61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×C61—41no—
213C2×C4×C61C4×D411yescharacteristic
214C2×C4×C61C4×D411yescharacteristic
215C2×C4×C61C4×D411yescharacteristic
216C2×C4×C61C23×C411yescharacteristic
217C2×C4×C61C22×D411yescharacteristic
218C2×C4×C61C2×#4111yescharacteristic
219C22⋊D61—42no—
220C2×Dic61—21no—
221C2×Dic61—21no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—21no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227D244—21no—
228D244—21no—
229C4×D61—42no—
230C4×D61—41no—
231C4×D61—41no—
232C4×D61—81no—
233Dic122—21no—
234Dic122—21no—
235Dic122—21no—
236Dic122—21no—
237Dic122—21no—
238Dic122—21no—
239Dic122—81no—
240C8×C61—21no—
241C8×C61—21no—
242C8×C61—21no—
243C8×C61—21no—
244C8×C61—21no—
245C8×C61—21no—
246C8×C61—21no—
247C8×C61—21no—
248C8×C61—41no—
249C8×C61—41no—
250#92418—41no—
251#92418—41no—
252#92418—41no—
253#92418—41no—
254#17949—611nomaximal, Sylow
255C22×C61—21no—
256C22×C61—21no—
257C22×C61—21no—
258C22×C61C2×C4×D411yescharacteristic
259C2×D61—41no—
260C2×D61—41no—
261C2×D61—41no—
262C4×C61—21no—
263C4×C61—21no—
264C4×C61—21no—
265C4×C61—21no—
266C4×C61#56811yescharacteristic
267C4×C61#56811yescharacteristic
268C4×C61#57711yescharacteristic
269C4×C61#57811yescharacteristic
270Dic61—41no—
271Dic61—41no—
272Dic61—41no—
273Dic61—41no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277#3107—611no—
278#2989—611no—
279#2985—611no—
280#1593—611no—
281#1592—611no—
282#1591—611no—
283#1590—611no—
284#1588—611no—
285#1587—611no—
286#1584—611no—
287#1583—611no—
288#1573—611no—
289#1488—611no—
290#1481—611no—
291#1454D6111yescharacteristic, complemented
292C2×C61—41no—
293C2×C61#293011yescharacteristic
294C2×C61#294711yescharacteristic
295C2×C61#295711yescharacteristic
296D61—81no—
297#533—611no—
298C4×#41—611no—
299#485—611no—
300#485—611no—
301#475—611no—
302#474—611no—
303#462—611no—
304#461—611no—
305#452—611no—
306#452—611no—
307#446—611no—
308#446—611no—
309#446—611no—
310#446—611no—
311#446—1221no—
312#446—1221no—
313C8×Q8—611no—
314C8×Q8—611no—
315C4×Q16—611no—
316C4×Q16—611no—
317C4×SD16—611no—
318C4×SD16—611no—
319#436—611no—
320#436—611no—
321#435—1221no—
322#435—1221no—
323#433—1221no—
324#433—1221no—
325#432—611no—
326#432—1221no—
327#431C2×D6111yescharacteristic
328#431C2×D6111yescharacteristic
329#431C2×D6111yescharacteristic
330#423—1221no—
331C2×C4⋊C8—611no—
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#322C2×D6111yescharacteristic
345#322C2×D6111yescharacteristic
346#322C2×D6111yescharacteristic
347C82C2×D6111yescharacteristic
348C61#1794911yescharacteristic, complemented, Sylow
349C2×#41—611no—
350C2×Q16—611no—
351C2×Q16—611no—
352C2×SD16—611no—
353C2×SD16—611no—
354C2×M16—1221no—
355C2×M16—1221no—
356C22×C8—1221no—
357C4⋊Q8—611no—
358C4⋊Q8—611no—
359#125—1221no—
360C22⋊Q8—611no—
361C22⋊Q8—611no—
362C22⋊Q8—1221no—
363C4×Q8—611no—
364C4×Q8—611no—
365C4×Q8—611no—
366C4×Q8—611no—
367C4×Q8—1221no—
368C4×D4—611no—
369C4×D4—611no—
370C4×D4—1221no—
371C4×D4—1221no—
372#117—611no—
373#117—1221no—
374#117—1221no—
375C2×C42—1221no—
376C2×C42C22×D6111yescharacteristic
377#107—611no—
378#107—611no—
379#106—611no—
380#106—611no—
381C4⋊C8—21no—
382C4⋊C8—611no—
383C4⋊C8—611no—
384C4⋊C8—611no—
385C4⋊C8—611no—
386C4⋊C8—1221no—
387C4⋊C8—1221no—
388C4⋊C8—1221no—
389C4⋊C8—1221no—
390C4⋊C8—1221no—
391C4⋊C8—1221no—
392C4⋊C8—1221no—
393C4⋊C8C4×D6111yescharacteristic
394C4⋊C8C4×D6111yescharacteristic
395C4⋊C8D24411yescharacteristic
396C4⋊C8D24411yescharacteristic
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—1221no—
407C22⋊C8—1221no—
408C22⋊C8—1221no—
409C22⋊C8C4×D6111yescharacteristic
410C22⋊C8C4×D6111yescharacteristic
411C22⋊C8D24411yescharacteristic
412C22⋊C8D24411yescharacteristic
413#97—1221no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417#97—1221no—
418C4×C8—1221no—
419C4×C8—1221no—
420C4×C8C22×D6111yescharacteristic
421C4×C8C22×D6111yescharacteristic
422C4×C8C22×D6111yescharacteristic
423C4×C8C22×D6111yescharacteristic
424C4×C8C22×D6111yescharacteristic
425C4×C8C22×D6111yescharacteristic
426#41—2441no—
427#41—2441no—
428C2×Q8—611no—
429C2×Q8—611no—
430C2×Q8—611no—
431C2×Q8—1221no—
432C2×D4—611no—
433C2×D4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4C2×C4×D6111yescharacteristic
438C22×C4C2×D24411yescharacteristic
439C22×C4#1175822211yescharacteristic
440Q16—2441no—
441Q16—2441no—
442SD16—2441no—
443SD16—2441no—
444M16—4881no—
445M16—4881no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C2×C8—4881no—
453C2×C8C2×C4×D6111yescharacteristic
454C2×C8C2×C4×D6111yescharacteristic
455C2×C8C2×C4×D6111yescharacteristic
456C2×C8C2×C4×D6111yescharacteristic
457C2×C8C2×D24411yescharacteristic
458C2×C8C2×D24411yescharacteristic
459C2×C8C2×D24411yescharacteristic
460C2×C8C2×D24411yescharacteristic
461C4⋊C4—611no—
462C4⋊C4—611no—
463C4⋊C4—611no—
464C4⋊C4—611no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C22⋊C4—1221no—
475C22⋊C4—1221no—
476C22⋊C4—1221no—
477C22⋊C4—1221no—
478C22⋊C4—1221no—
479C42—1221no—
480C42—1221no—
481C42—1221no—
482C42—1221no—
483C42—1221no—
484C42C2×C4×D6111yescharacteristic
485C42C2×D24411yescharacteristic
486C42#1175822211yescharacteristic
487C42C23×D6111yescharacteristic
488C23—1221no—
489C23C4×D24411yescharacteristic
490Q8—1221no—
491Q8—1221no—
492Q8—1221no—
493Q8—1221no—
494Q8—1221no—
495Q8—1221no—
496Q8—4881no—
497D4—1221no—
498D4—1221no—
499D4—2442no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—41no—
505C2×C4—1221no—
506C2×C4—1221no—
507C2×C4—1221no—
508C2×C4—1221no—
509C2×C4—1221no—
510C2×C4—1221no—
511C2×C4—1221no—
512C2×C4—4881no—
513C2×C4—2442no—
514C2×C4—2441no—
515C2×C4—2441no—
516C2×C4C4×D24411yescharacteristic
517C2×C4C4×D24411yescharacteristic
518C2×C4C4×D24411yescharacteristic
519C2×C4C22×C4×D6111yescharacteristic
520C2×C4C22×D24411yescharacteristic
521C2×C4C2×#1175822211yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—2441no—
533C8—2441no—
534C8—2441no—
535C8—2441no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—2441no—
540C22—2441no—
541C22—2441no—
542C22C2×C4×D24411yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—21no—
547C4—2441no—
548C4—2441no—
549C4—2441no—
550C4—2441no—
551C4—2441no—
552C4—2441no—
553C4—2441no—
554C4#1684052711yescharacteristic
555C4#1684052711yescharacteristic
556C4#1684057411yescharacteristic
557C4#1684057911yescharacteristic
558C2—41no—
559C2—4881no—
560C2#2145452411yescharacteristic
561C2#2145466411yescharacteristic
562C2#2145473711yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1454C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1454D61
hypocenterC61#17949
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ #431 ◁ #1454

Complements

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

NH ≅ G/Ntype
3. #21454913C2semidirect
4. #21444729C2semidirect
5. #21444723C2semidirect
6. #21444717C2semidirect
7. #21444711C2semidirect
8. #21444699C2semidirect
9. #21444692C2semidirect
10. #21444671C2semidirect
11. #21444664C2semidirect
12. #21444604C2semidirect
14. #21444223C2semidirect
15. C61×#1454C2semidirect
291. #1454D61semidirect
348. C61#17949semidirect

Maximal subgroups

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

subgroupindex
#214558912
#214549322
#214549132
#214447292
#214447232
#214447172
#214447112
#214446992
#214446922
#214446712
#214446642
#214446042
#214442542
#214442232
C61×#14542
#1794961