Finite Group Databasebeta

← #29779442

Subgroups — #29779442

Order 15616.

682 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450427C211yesmaximal, characteristic, complemented
2#21449691C211yesmaximal, characteristic
3#21447317C211yesmaximal, characteristic, complemented
4#21447234C211yesmaximal, characteristic
5#21447137C211yesmaximal, characteristic
6#21446971C211yesmaximal, characteristic, complemented
7#21446784C211yesmaximal, characteristic, complemented
8#21446673C211yesmaximal, characteristic
9#21446516C211yesmaximal, characteristic
10#21446509C211yesmaximal, characteristic, complemented
11#21446509C211yesmaximal, characteristic, complemented
12#21446398C211yesmaximal, characteristic, complemented
13#21446152C211yesmaximal, characteristic
14#21445645C211yesmaximal, characteristic
15C61×#1771C211yesmaximal, characteristic, complemented
16C22×#11758190C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519709C2211yescharacteristic
20C2×#14519702C2211yescharacteristic
21C2×#14519702C2211yescharacteristic
22C2×#14519702C2211yescharacteristic
23C2×#14519699C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C61⋊#401—21no—
27#16839700—21no—
28#16839697—21no—
29#16839686—21no—
30#16839668C2211yescharacteristic
31#16839668C2211yescharacteristic
32#16839668C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839664C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839660C2211yescharacteristic
37#16839660C2211yescharacteristic
38#16839643—21no—
39#16839633—21no—
40#16839629—21no—
41#16839628C2211yescharacteristic
42#16839621—21no—
43C4×C4⋊Dic61C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839525C2211yescharacteristic
47#16839525C2211yescharacteristic
48#16839525C2211yescharacteristic
49#16839525C2211yescharacteristic
50#16839525C2211yescharacteristic
51#16839525C2211yescharacteristic
52C2×C4⋊C8×C61C2211yescharacteristic
53C2×#97×C61C2211yescharacteristic
54C2×#97×C61C2211yescharacteristic
55C2×C4×C8×C61C2211yescharacteristic
56C4×C4⋊C4×C61C2211yescharacteristic
57C61×#336C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×Dic122C2311yescharacteristic
60C22×D244C2311yescharacteristic
61C22×C4×D61—21no—
62C2×#11758190—22no—
63C2×#11758190—22no—
64C2×#11758190—41no—
65#14519769—22no—
66#14519769—41no—
67C4×D244—22no—
68C4×D244—41no—
69C2×C4⋊Dic61C2311yescharacteristic
70C2×C4⋊Dic61C2311yescharacteristic
71C2×C4⋊Dic61C2311yescharacteristic
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758196—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84C2×#11758198—21no—
85C2×C4×Dic61—21no—
86#14519709—22no—
87#14519702—22no—
88#14519702—22no—
89#14519702—41no—
90#14519699—22no—
91#14519699—22no—
92#14519699—22no—
93#14519684—21no—
94#14519684—21no—
95#14519684—21no—
96#14519684—21no—
97#14519684—21no—
98#14519684—21no—
99#14519684—21no—
100#14519684—21no—
101#14519684—21no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105C22×C8×C61C2311yescharacteristic
106C22×C8×C61C2311yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61D411yescharacteristic
110C2×C4⋊C4×C61D411yescharacteristic
111C2×C42×C61C2311yescharacteristic
112C2×C42×C61C2311yescharacteristic
113C2×C42×C61C2311yescharacteristic
114C4⋊C8×C61—22no—
115#97×C61—22no—
116#97×C61—41no—
117C4×C8×C61—41no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C23×D61—21no—
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61C2×D411yescharacteristic
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2×D411yescharacteristic
127C22×C4×C61C2411yescharacteristic
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61—21no—
131C22×Dic61—21no—
132C22×Dic61—21no—
133C22×Dic61—21no—
134C22×Dic61—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244—21no—
140C2×D244#4112yes—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×C4×D61—81no—
144C2×Dic122—21no—
145C2×Dic122—21no—
146C2×Dic122—21no—
147C2×Dic122—21no—
148C2×Dic122—21no—
149C2×Dic122—21no—
150C2×C8×C61—21no—
151C2×C8×C61—21no—
152C2×C8×C61—21no—
153C2×C8×C61—21no—
154C2×C8×C61—21no—
155C2×C8×C61—21no—
156C2×C8×C61—21no—
157C2×C8×C61—21no—
158C2×C8×C61—21no—
159C2×C8×C61—21no—
160C2×C8×C61#4112yes—
161C2×C8×C61#4112yes—
162C4⋊C4×C61—41no—
163C4⋊C4×C61—41no—
164C42×C61—21no—
165C42×C61—21no—
166C42×C61—21no—
167C42×C61—21no—
168C42×C61—21no—
169C42×C61—21no—
170#11758198—42no—
171#11758198—42no—
172#11758198—81no—
173#11758198—81no—
174#11758198—81no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61—21no—
178C4⋊Dic61—21no—
179C4⋊Dic61—21no—
180C4⋊Dic61—21no—
181C4⋊Dic61—21no—
182C4⋊Dic61—21no—
183C4⋊Dic61—21no—
184C4⋊Dic61—21no—
185C4⋊Dic61—21no—
186C4⋊Dic61#4112yes—
187#11758196—42no—
188#11758196—42no—
189#11758196—42no—
190#11758196—81no—
191#11758196—81no—
192C4×Dic61—42no—
193#11758190—44no—
194C23×C61C22×D411yescharacteristic
195C22×D61—22no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C2×C4×C61—21no—
203C2×C4×C61—21no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—21no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—21no—
212C2×C4×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×C61—21no—
220C2×C4×C61C2×#4111yescharacteristic
221C2×C4×C61C2×#4111yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61H(5,𝔽2)11yescharacteristic
225C2×C4×C612−1+411yescharacteristic
226C2×Dic61—22no—
227C2×Dic61—41no—
228C2×Dic61—41no—
229C2×Dic61—41no—
230C2×Dic61—41no—
231C2×Dic61—41no—
232C2×Dic61—41no—
233C2×Dic61—41no—
234C2×Dic61—41no—
235C2×Dic61—41no—
236C2×Dic61—41no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239C2×Dic61—41no—
240C2×Dic61—41no—
241C2×Dic61—41no—
242C2×Dic61—41no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247D244—22no—
248D244—22no—
249D244—41no—
250D244—41no—
251C4×D61—84no—
252Dic122—41no—
253Dic122—41no—
254Dic122—41no—
255Dic122—41no—
256C8×C61—22no—
257C8×C61—22no—
258C8×C61—41no—
259C8×C61—41no—
260#29100—611nomaximal, Sylow
261C22×C61#53211yescharacteristic
262C22×C61#54611yescharacteristic
263C22×C61#54811yescharacteristic
264C22×C61#57511yescharacteristic
265C22×C61#57511yescharacteristic
266C22×C61#57711yescharacteristic
267C22×C61#57711yescharacteristic
268C2×D61—42no—
269C2×D61—42no—
270C2×D61—42no—
271C2×D61—81no—
272C2×D61—81no—
273C2×D61—81no—
274C2×D61—81no—
275C4×C61—41no—
276C4×C61—41no—
277C4×C61—41no—
278C4×C61—41no—
279C4×C61—41no—
280C4×C61—41no—
281C4×C61#52911yescharacteristic
282C4×C61#53911yescharacteristic
283C4×C61#55111yescharacteristic
284C4×C61#55611yescharacteristic
285Dic61—42no—
286Dic61—81no—
287Dic61—81no—
288Dic61—81no—
289Dic61—81no—
290Dic61—81no—
291Dic61—81no—
292#2514—611no—
293#2454—611no—
294#2088—611no—
295#2073—611no—
296#2055—611no—
297#2026—611no—
298#1991—611no—
299#1968—611no—
300#1936—611no—
301#1935—611no—
302#1935—611no—
303#1919—611no—
304#1877—611no—
305#1771D6111yescharacteristic, complemented
306#1762—611no—
307C2×C61#256011yescharacteristic
308C2×C61#317411yescharacteristic
309C2×C61#318311yescharacteristic
310C2×C61#331111yescharacteristic
311C2×C61#331711yescharacteristic
312C2×C61#337611yescharacteristic
313C2×C61#337611yescharacteristic
314D61—82no—
315C22×SD16—611no—
316C2×#125—611no—
317C2×C4×D4—611no—
318C2×#106—611no—
319C2×C4⋊C8C2×D6111yescharacteristic
320C2×#103—611no—
321C2×#103—611no—
322C2×#103—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#102—611no—
326C2×#97C2×D6111yescharacteristic
327C2×#97C2×D6111yescharacteristic
328C2×C4×C8C2×D6111yescharacteristic
329#401—1221no—
330#400—1221no—
331#399—1221no—
332#396—1221no—
333#391—611no—
334#391—611no—
335#391—611no—
336#390—611no—
337#390—611no—
338#389—611no—
339#389—611no—
340#389—611no—
341#387—1221no—
342#385—1221no—
343#383—1221no—
344#382—611no—
345#380—1221no—
346C4×C4⋊C4—611no—
347C4×C4⋊C4C2×D6111yescharacteristic
348#340—611no—
349#340—611no—
350#340—611no—
351#340—611no—
352#340—611no—
353#340—611no—
354#340—611no—
355#340—611no—
356#336C2×D6111yescharacteristic
357#336C2×D6111yescharacteristic
358C61#2910011yescharacteristic, complemented, Sylow
359C22×Q8—611no—
360C22×D4—611no—
361C23×C4—1221no—
362C2×SD16—1222no—
363C2×SD16—1222no—
364C2×SD16—2441no—
365C22×C8C22×D6111yescharacteristic
366C22×C8C22×D6111yescharacteristic
367C22×C8C22×D6111yescharacteristic
368C22×C8C22×D6111yescharacteristic
369#125—1222no—
370#125—2441no—
371C4×D4—1222no—
372C4×D4—2441no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—611no—
378C2×C4⋊C4—611no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4D24411yescharacteristic
385C2×C4⋊C4D24411yescharacteristic
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—1221no—
392C2×C42C22×D6111yescharacteristic
393C2×C42C22×D6111yescharacteristic
394C2×C42C22×D6111yescharacteristic
395#106—1222no—
396C4⋊C8—22no—
397#103—1222no—
398#103—1222no—
399#103—2441no—
400#102—1222no—
401#102—1222no—
402#102—1222no—
403#97—22no—
404#97—41no—
405C4×C8—41no—
406#95—1221no—
407#95—1221no—
408#95—1221no—
409#95—1221no—
410#95—1221no—
411#95—1221no—
412#95—1221no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416#95—1221no—
417#95—1221no—
418#95D24411yescharacteristic
419#95D24411yescharacteristic
420C24—1221no—
421C2×Q8—1221no—
422C2×Q8—1221no—
423C2×Q8—1221no—
424C2×Q8—1221no—
425C2×Q8—1221no—
426C2×Q8—1221no—
427C2×D4—612no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—1221no—
436C22×C4—1221no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—4881no—
441C22×C4—2442no—
442C22×C4—2442no—
443C22×C4C2×D24411yescharacteristic
444C22×C4C2×D24411yescharacteristic
445C22×C4C2×D24411yescharacteristic
446C22×C4C2×D24411yescharacteristic
447C22×C4C2×D24411yescharacteristic
448C22×C4C2×D24411yescharacteristic
449C22×C4C23×D6111yescharacteristic
450SD16—2444no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8#1175822212yes—
462C2×C8#1175822212yes—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—612no—
466C4⋊C4—1221no—
467C4⋊C4—1221no—
468C4⋊C4—1221no—
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⋊C4—4881no—
478C4⋊C4—4881no—
479C4⋊C4—2442no—
480C4⋊C4—2442no—
481C4⋊C4—2442no—
482C22⋊C4—4881no—
483C22⋊C4—4881no—
484C22⋊C4—4881no—
485C22⋊C4—2442no—
486C22⋊C4—2442no—
487C42—21no—
488C42—21no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—21no—
493C42—2442no—
494C23—1222no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23—2441no—
500C23—2441no—
501C23C22×D24411yescharacteristic
502Q8—2441no—
503Q8—2441no—
504Q8—2441no—
505Q8—2441no—
506D4—1222no—
507D4—1222no—
508D4—2441no—
509D4—2441no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—1222no—
529C2×C4—4884no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4—2441no—
533C2×C4—2441no—
534C2×C4—2441no—
535C2×C4—2441no—
536C2×C4—2441no—
537C2×C4—2441no—
538C2×C4—2441no—
539C2×C4—2441no—
540C2×C4—2441no—
541C2×C4—2441no—
542C2×C4—2441no—
543C2×C4—2441no—
544C2×C4—2441no—
545C2×C4—2441no—
546C2×C4—2441no—
547C2×C4—2441no—
548C2×C4—2441no—
549C2×C4—2441no—
550C2×C4#41×D6111yescharacteristic
551C2×C4#41×D6111yescharacteristic
552C2×C4C2×#1175822211yescharacteristic
553C2×C4C2×#1175822211yescharacteristic
554C2×C4#1451982211yescharacteristic
555C2×C4#1451982511yescharacteristic
556C8—22no—
557C8—22no—
558C8—41no—
559C8—41no—
560C22—4881no—
561C22—4881no—
562C22—4881no—
563C22—4881no—
564C22—2442no—
565C22—2442no—
566C22—2442no—
567C22#1684031211yescharacteristic
568C22#1684040711yescharacteristic
569C22#1684042411yescharacteristic
570C22#1684056211yescharacteristic
571C22#1684056211yescharacteristic
572C22#1684057411yescharacteristic
573C22#1684057411yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—4881no—
581C4—4881no—
582C4—4881no—
583C4—4881no—
584C4—4881no—
585C4—4881no—
586C4—2442no—
587C4#1684029011yescharacteristic
588C4#1684035911yescharacteristic
589C4#1684044111yescharacteristic
590C4#1684048411yescharacteristic
591C2—4882no—
592C2#2145095711yescharacteristic
593C2#2145644711yescharacteristic
594C2#2145654811yescharacteristic
595C2#2145785711yescharacteristic
596C2#2145794711yescharacteristic
597C2#2145864811yescharacteristic
598C2#2145864811yescharacteristic
subgroupG/H
centerC23C22×D244
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1771C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1771D61
hypocenterC61#29100
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1771

Complements

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

NH ≅ G/Ntype
1. #21450427C2semidirect
3. #21447317C2semidirect
6. #21446971C2semidirect
7. #21446784C2semidirect
10. #21446509C2semidirect
11. #21446509C2semidirect
12. #21446398C2semidirect
15. C61×#1771C2semidirect
305. #1771D61semidirect
358. C61#29100semidirect

Maximal subgroups

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

subgroupindex
#214504272
#214496912
#214473172
#214472342
#214471372
#214469712
#214467842
#214466732
#214465162
#214465092
#214463982
#214461522
#214456452
C61×#17712
#2910061