Finite Group Databasebeta

← #30612819

Subgroups — #30612819

Order 15616.

594 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462626C211yesmaximal, characteristic
2#21462607C211yesmaximal, characteristic, complemented
3#21461465C211yesmaximal, characteristic, complemented
4#21461464C211yesmaximal, characteristic, complemented
5#21461463C211yesmaximal, characteristic, complemented
6#21461461C211yesmaximal, characteristic, complemented
7#21461431C211yesmaximal, characteristic, complemented
8#21461430C211yesmaximal, characteristic, complemented
9#21461427C211yesmaximal, characteristic, complemented
10#21461426C211yesmaximal, characteristic, complemented
11#21461395C211yesmaximal, characteristic, complemented
12#21461156C211yesmaximal, characteristic
13#21461141C211yesmaximal, characteristic, complemented
14#21461030C211yesmaximal, characteristic, complemented
15#21455885C211yesmaximal, characteristic
16#16840814—21no—
17#16840813C2211yescharacteristic
18#16840812C2211yescharacteristic
19#16840812C2211yescharacteristic
20#16840812C2211yescharacteristic
21#16840811—21no—
22#16840811C2211yescharacteristic
23Q8×#92420C2211yescharacteristic
24#16840796C2211yescharacteristic
25#16840796C2211yescharacteristic
26#16840791—21no—
27#16840791—21no—
28#16840781—21no—
29#16840778C2211yescharacteristic
30#16840768—21no—
31#16840765C2211yescharacteristic
32#16840726—21no—
33C4×#11758213—21no—
34C4×#11758217C2211yescharacteristic
35C2×C4×#92420C2211yescharacteristic
36#16840626C2211yescharacteristic
37#16840625C2211yescharacteristic
38#16840624C2211yescharacteristic
39#16840623C2211yescharacteristic
40#16840612C2211yescharacteristic
41#16840612C2211yescharacteristic
42#16840612C2211yescharacteristic
43#16840612C2211yescharacteristic
44Q8⋊#92420C2211yescharacteristic
45Q8⋊#92420C2211yescharacteristic
46#16840610C2211yescharacteristic
47#16840610C2211yescharacteristic
48#92420⋊C8C2211yescharacteristic
49#92420⋊C8C2211yescharacteristic
50#16840603C2211yescharacteristic
51#16840603C2211yescharacteristic
52#16840314C2211yescharacteristic
53#16840230C2211yescharacteristic
54#16840103C411yescharacteristic
55#16840046C411yescharacteristic
56#16840041C411yescharacteristic
57#16839971C411yescharacteristic
58#16839966C411yescharacteristic
59#16839926C411yescharacteristic
60#16839922C411yescharacteristic
61#16839856C2211yescharacteristic
62#16839854C2211yescharacteristic
63#16839849C2211yescharacteristic
64#16839847C2211yescharacteristic
65#16839812C2211yescharacteristic
66C61×#485C411yescharacteristic
67C2×#11758213—21no—
68C2×#11758213—21no—
69C2×#11758217—21no—
70C2×#11758217—21no—
71C22×#92420D411yescharacteristic
72C22×#92420D411yescharacteristic
73#14519844—21no—
74#14519844—21no—
75#14519844—21no—
76C4⋊#92420—21no—
77C4⋊#92420—21no—
78C4⋊#92420—21no—
79C4⋊#92420—21no—
80C4⋊#92420C2311yescharacteristic
81C4⋊#92420C2311yescharacteristic
82C4⋊#92420C2311yescharacteristic
83C4⋊#92420C2311yescharacteristic
84#14519834—21no—
85#14519834—21no—
86C22⋊#92420—21no—
87#14519832—21no—
88#14519832—21no—
89#14519832—21no—
90#14519832—21no—
91#14519832—21no—
92C4×#92420—21no—
93C4×#92420—21no—
94C4×#92420—21no—
95C4×#92420D411yescharacteristic
96C4×#92420D411yescharacteristic
97C4×#92420C2311yescharacteristic
98C4×#92420C2311yescharacteristic
99C4×#92420C2311yescharacteristic
100C4×#92420C2311yescharacteristic
101C2×#11758222C2×C411yescharacteristic
102C2×Dic244C2×C411yescharacteristic
103C2×#11758202C2×C411yescharacteristic
104C2×#11758190C2×C411yescharacteristic
105C2×#11758201C2×C411yescharacteristic
106#14519776C2×C411yescharacteristic
107#14519775C2×C411yescharacteristic
108#14519767—21no—
109#14519756C2×C411yescharacteristic
110#14519754—21no—
111Q8×Dic61C2311yescharacteristic
112#14519742—21no—
113#14519742C2×C411yescharacteristic
114#14519742C2311yescharacteristic
115#14519742C2311yescharacteristic
116#14519739C2×C411yescharacteristic
117#14519739C2311yescharacteristic
118#14519737—21no—
119#14519737—21no—
120#14519734—21no—
121#14519733—21no—
122C2×C4×Dic61C2311yescharacteristic
123C42×D61—21no—
124#14519710C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519706C2×C411yescharacteristic
127#14519706C2×C411yescharacteristic
128#14519702C2×C411yescharacteristic
129#14519700C2×C411yescharacteristic
130#14519700C2×C411yescharacteristic
131#14519700C2×C411yescharacteristic
132#14519699C2×C411yescharacteristic
133#14519697C2×C411yescharacteristic
134C22⋊#92418C2×C411yescharacteristic
135C8×Dic61C2311yescharacteristic
136C8×Dic61C2311yescharacteristic
137C22⋊Q8×C61C2×C411yescharacteristic
138#117×C61C2×C411yescharacteristic
139#107×C61C2×C411yescharacteristic
140#106×C61C2×C411yescharacteristic
141#103×C61C2×C411yescharacteristic
142#103×C61C2×C411yescharacteristic
143C22⋊C8×C61C2×C411yescharacteristic
144C2×Q8×C61C22×C411yescharacteristic
145C22×C4×C61C22×C411yescharacteristic
146C2×C22⋊D61—21no—
147C22×Dic61C2×D411yescharacteristic
148C22×Dic61#4111yescharacteristic
149#11758222—41no—
150#11758222—41no—
151C2×D244C22×C411yescharacteristic
152C2×C4×D61—21no—
153C2×C4×D61—21no—
154C2×C4×D61—21no—
155C2×Dic122—21no—
156C2×Dic122C22×C411yescharacteristic
157C2×Dic122C22×C411yescharacteristic
158#11758217—42no—
159#11758217—42no—
160C2×#92420—22no—
161C2×#92420—21no—
162C2×#92420—21no—
163C2×#92420—21no—
164C2×#92420—21no—
165C2×#92420—21no—
166C2×#92420—21no—
167C2×#92420—41no—
168C2×#92420C2×D411yescharacteristic
169C2×#92420C2×D411yescharacteristic
170C2×#92420C2×D411yescharacteristic
171C2×#92420C2×D411yescharacteristic
172#11758213—42no—
173#11758213—42no—
174C2×C8×C61C22×C411yescharacteristic
175C2×C8×C61C22×C411yescharacteristic
176C4⋊C4×C61—21no—
177C4⋊C4×C61C22×C411yescharacteristic
178C4⋊C4×C61C22×C411yescharacteristic
179C4⋊C4×C61C22×C411yescharacteristic
180C22⋊C4×C61—21no—
181C22⋊C4×C61—21no—
182C42×C61—21no—
183C22⋊Dic61—21no—
184#11758202—41no—
185#11758201—41no—
186#11758198—21no—
187#11758198—21no—
188C4⋊Dic61—21no—
189C4⋊Dic61C22×C411yescharacteristic
190#11758196—21no—
191#11758196—21no—
192#11758196—21no—
193#11758196—21no—
194#11758196—21no—
195#11758196—21no—
196#11758196—21no—
197C4×Dic61—21no—
198C4×Dic61—21no—
199C4×Dic61—21no—
200C4×Dic61—21no—
201C4×Dic61C22×C411yescharacteristic
202C4×Dic61C2×D411yescharacteristic
203C4×Dic61#4111yescharacteristic
204C4×Dic61C2411yescharacteristic
205C2×#92418C22×C411yescharacteristic
206C2×#92418C22×C411yescharacteristic
207Dic244—41no—
208#11758190—41no—
209C23×C61C4×D411yescharacteristic
210C22×D61—21no—
211Q8×C61—21no—
212Q8×C61—21no—
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×C61C4×D411yescharacteristic
220C2×C4×C61C23×C411yescharacteristic
221C22⋊D61—42no—
222C2×Dic61—21no—
223C2×Dic61—21no—
224C2×Dic61—22no—
225C2×Dic61—21no—
226C2×Dic61—21no—
227C2×Dic61—21no—
228C2×Dic61C4×D411yescharacteristic
229C2×Dic61C4×D411yescharacteristic
230C2×Dic61C22×D411yescharacteristic
231C2×Dic61C2×#4111yescharacteristic
232D244—21no—
233D244—21no—
234C4×D61—42no—
235C4×D61—41no—
236C4×D61—41no—
237C4×D61—42no—
238Dic122—21no—
239Dic122—21no—
240Dic122—21no—
241Dic122—21no—
242Dic122—42no—
243#92420—21no—
244#92420—21no—
245#92420—21no—
246#92420—41no—
247#92420—41no—
248#92420—41no—
249#92420—41no—
250#92420—41no—
251#92420—41no—
252#92420#13712yes—
253C8×C61—21no—
254C8×C61—21no—
255#92418—21no—
256#92418—21no—
257#17941—611nomaximal, Sylow
258C22×C61—21no—
259C22×C61—21no—
260C22×C61—21no—
261C22×C61C2×C4×D411yescharacteristic
262C2×D61—41no—
263C2×D61—41no—
264C2×D61—41no—
265C4×C61—21no—
266C4×C61—41no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61#56811yescharacteristic
271C4×C61#56811yescharacteristic
272Dic61—21no—
273Dic61—21no—
274Dic61—41no—
275Dic61—41no—
276Dic61—41no—
277Dic61#44412yes—
278Dic61C2×#13711yescharacteristic
279Dic61#57511yescharacteristic
280#3107—611no—
281#2965—611no—
282#2960—611no—
283#1593—611no—
284#1593—611no—
285#1592—611no—
286#1592—611no—
287#1584—611no—
288#1584—611no—
289#1583—611no—
290#1583—611no—
291#1574—611no—
292#1489—611no—
293#1485—611no—
294#1451—611no—
295C2×C61—41no—
296C2×C61#293011yescharacteristic
297C2×C61C4×#13711yescharacteristic
298C2×C61C2×#44411yescharacteristic
299D61—81no—
300#533—611no—
301C4×#41—611no—
302#485—611no—
303#485#692311yescharacteristic
304#475—611no—
305#474—611no—
306#462—611no—
307#461—611no—
308#452—611no—
309#452—611no—
310#446—611no—
311#446—611no—
312#446—611no—
313#446—611no—
314#446—1221no—
315C8×Q8—611no—
316C8×Q8—611no—
317C8×Q8—1221no—
318C4×Q16—611no—
319C4×Q16—611no—
320C4×SD16—611no—
321C4×SD16—611no—
322#436—611no—
323#436—611no—
324#435—1221no—
325#435—1221no—
326#431—611no—
327#431—611no—
328#431—1221no—
329#424—1221no—
330#423—611no—
331#405—1221no—
332C4×M16—611no—
333C4×M16—1221no—
334C2×C4×C8—611no—
335#335—611no—
336#335—611no—
337#334—611no—
338#334—611no—
339Q8⋊C8—611no—
340Q8⋊C8—611no—
341Q8⋊C8—611no—
342Q8⋊C8—611no—
343Q8⋊C8—611no—
344Q8⋊C8—611no—
345D4⋊C8—611no—
346D4⋊C8—611no—
347#322—611no—
348#322—611no—
349#322—611no—
350#322—611no—
351C61#1794111yescharacteristic, complemented, Sylow
352C2×#41—611no—
353C2×Q16—611no—
354C2×Q16—611no—
355C2×SD16—611no—
356C2×SD16—611no—
357C2×M16—1221no—
358C2×M16—1221no—
359C2×M16—1221no—
360C2×M16—1221no—
361C22×C8—611no—
362C22×C8—611no—
363C4⋊Q8—611no—
364C4⋊Q8—611no—
365#125—1221no—
366C22⋊Q8—611no—
367C22⋊Q8—1221no—
368C22⋊Q8C2×#692311yescharacteristic
369C4×Q8—611no—
370C4×Q8—611no—
371C4×Q8—611no—
372C4×Q8—611no—
373C4×Q8—1221no—
374C4×D4—611no—
375C4×D4—611no—
376C4×D4—1221no—
377C4×D4—1221no—
378#117—1221no—
379#117—1221no—
380#117C2×#692311yescharacteristic
381C2×C42—611no—
382C2×C42—1221no—
383#107—611no—
384#107C2×#692311yescharacteristic
385#106—611no—
386#106C2×#692311yescharacteristic
387C4⋊C8—611no—
388C4⋊C8—611no—
389C4⋊C8—611no—
390C4⋊C8—611no—
391C4⋊C8—611no—
392C4⋊C8—611no—
393C4⋊C8—1221no—
394C4⋊C8—1221no—
395C4⋊C8—1221no—
396C4⋊C8—1221no—
397C4⋊C8—1221no—
398C4⋊C8—1221no—
399C4⋊C8—1221no—
400#103—611no—
401#103—611no—
402#103—611no—
403#103—611no—
404#103C2×#692311yescharacteristic
405#103C2×#692311yescharacteristic
406#102—611no—
407#102—611no—
408C22⋊C8—611no—
409C22⋊C8—1221no—
410C22⋊C8—1221no—
411C22⋊C8—1221no—
412C22⋊C8C2×#692311yescharacteristic
413#97—1221no—
414#97—1221no—
415#97—1221no—
416#97—1221no—
417#97—1221no—
418C4×C8—611no—
419C4×C8—611no—
420C4×C8—611no—
421C4×C8—611no—
422C4×C8—611no—
423C4×C8—611no—
424C4×C8—611no—
425C4×C8—611no—
426C4×C8—1221no—
427C4×C8—1221no—
428C4×C8—1221no—
429#41—2441no—
430#41—2441no—
431C2×Q8—611no—
432C2×Q8—611no—
433C2×Q8—1221no—
434C2×Q8C22×#692311yescharacteristic
435C2×D4—611no—
436C2×D4—1221no—
437C22×C4—611no—
438C22×C4—611no—
439C22×C4—1221no—
440C22×C4—1221no—
441C22×C4—1221no—
442C22×C4C22×#692311yescharacteristic
443Q16—2441no—
444Q16—2441no—
445SD16—2441no—
446SD16—2441no—
447M16—2442no—
448M16—2442no—
449M16—2442no—
450M16—2442no—
451C2×C8—611no—
452C2×C8—611no—
453C2×C8—611no—
454C2×C8—611no—
455C2×C8—611no—
456C2×C8—611no—
457C2×C8—1222no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8—1221no—
464C2×C8—2441no—
465C2×C8C22×#692311yescharacteristic
466C2×C8C22×#692311yescharacteristic
467C4⋊C4—21no—
468C4⋊C4—611no—
469C4⋊C4—1221no—
470C4⋊C4—1221no—
471C4⋊C4—1221no—
472C4⋊C4—1221no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4C22×#692311yescharacteristic
478C4⋊C4C22×#692311yescharacteristic
479C4⋊C4C22×#692311yescharacteristic
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—1221no—
483C22⋊C4—1221no—
484C22⋊C4—1221no—
485C42—21no—
486C42—611no—
487C42—611no—
488C42—611no—
489C42—611no—
490C42—1221no—
491C42—1221no—
492C42—1221no—
493C42—1221no—
494C23—1221no—
495C23D4×#692311yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—1221no—
499Q8—1221no—
500Q8—1221no—
501Q8—1221no—
502Q8—2442no—
503D4—1221no—
504D4—1221no—
505D4—2442no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—611no—
513C2×C4—611no—
514C2×C4—611no—
515C2×C4—611no—
516C2×C4—1221no—
517C2×C4—1221no—
518C2×C4—1222no—
519C2×C4—1221no—
520C2×C4—1221no—
521C2×C4—1221no—
522C2×C4—2442no—
523C2×C4—2441no—
524C2×C4—2441no—
525C2×C4—2442no—
526C2×C4D4×#692311yescharacteristic
527C2×C4C23×#692311yescharacteristic
528C8—21no—
529C8—21no—
530C8—612no—
531C8—1221no—
532C8—1221no—
533C8—1221no—
534C8—1221no—
535C8—1221no—
536C8—2441no—
537C8—2441no—
538C8—2441no—
539C8—2441no—
540C8—2441no—
541C8—2441no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—2441no—
546C22—2441no—
547C22—2441no—
548C22C2×D4×#692311yescharacteristic
549C4—21no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—611no—
555C4—611no—
556C4—612no—
557C4—1221no—
558C4—1221no—
559C4—2441no—
560C4—2441no—
561C4—2441no—
562C4#1684084111yescharacteristic
563C4#1684084111yescharacteristic
564C2—41no—
565C2—4881no—
566C2#2146254011yescharacteristic
567C2#137×#692311yescharacteristic
568C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#485C4
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C2×C4
cosocleC4×Dic61C24
hypercenter#485#6923
hypocenterC61#17941
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
2. #21462607C2semidirect
3. #21461465C2semidirect
4. #21461464C2semidirect
5. #21461463C2semidirect
6. #21461461C2semidirect
7. #21461431C2semidirect
8. #21461430C2semidirect
9. #21461427C2semidirect
10. #21461426C2semidirect
11. #21461395C2semidirect
13. #21461141C2semidirect
14. #21461030C2semidirect
351. C61#17941semidirect

Maximal subgroups

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

subgroupindex
#214626262
#214626072
#214614652
#214614642
#214614632
#214614612
#214614312
#214614302
#214614272
#214614262
#214613952
#214611562
#214611412
#214610302
#214558852
#1794161