Finite Group Databasebeta

← #29779446

Subgroups — #29779446

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#21449691C211yesmaximal, characteristic
2#21447321C211yesmaximal, characteristic, complemented
3#21447233C211yesmaximal, characteristic
4#21447134C211yesmaximal, characteristic
5#21446970C211yesmaximal, characteristic, complemented
6#21446783C211yesmaximal, characteristic, complemented
7#21446676C211yesmaximal, characteristic
8#21446515C211yesmaximal, characteristic
9#21446512C211yesmaximal, characteristic, complemented
10#21446512C211yesmaximal, characteristic, complemented
11#21446397C211yesmaximal, characteristic, complemented
12#21446156C211yesmaximal, characteristic
13#21445694C211yesmaximal, characteristic, complemented
14#21445647C211yesmaximal, characteristic
15C61×#2514C211yesmaximal, characteristic, complemented
16C22×#11758201C2211yescharacteristic
17C2×#14519769C2211yescharacteristic
18C2×C4×D244C2211yescharacteristic
19C2×#14519708C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×#14519701C2211yescharacteristic
22C2×#14519701C2211yescharacteristic
23C2×#14519701C2211yescharacteristic
24C2×#14519697C2211yescharacteristic
25C2×#14519697C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519688C2211yescharacteristic
28C2×#14519688C2211yescharacteristic
29C2×C4×#92418C2211yescharacteristic
30#16839697—21no—
31#16839686—21no—
32#16839664C2211yescharacteristic
33#16839664C2211yescharacteristic
34#16839660C2211yescharacteristic
35#16839660C2211yescharacteristic
36#16839633—21no—
37#16839621—21no—
38#16839524C2211yescharacteristic
39#16839524C2211yescharacteristic
40#16839524C2211yescharacteristic
41#16839524C2211yescharacteristic
42#16839524C2211yescharacteristic
43#16839524C2211yescharacteristic
44#16839524C2211yescharacteristic
45#16839524C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C61×#401—21no—
49C61×#400—21no—
50C61×#391C2211yescharacteristic
51C61×#391C2211yescharacteristic
52C61×#391C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C61×#387—21no—
55C61×#383—21no—
56C61×#382C2211yescharacteristic
57C4×C4⋊C4×C61C2211yescharacteristic
58C4×C4⋊C4×C61C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C2×#11758201—22no—
62C2×#11758201—22no—
63C2×#11758201—41no—
64C22×#92418C2311yescharacteristic
65C22×#92418C2311yescharacteristic
66C22×#92418C2311yescharacteristic
67C22×#92418C2311yescharacteristic
68#14519769—22no—
69#14519769—41no—
70C4×D244—22no—
71C4×D244—41no—
72C2×C4⋊Dic61C2311yescharacteristic
73C2×C4⋊Dic61C2311yescharacteristic
74C2×C4⋊Dic61C2311yescharacteristic
75C2×#11758196—21no—
76C2×#11758196—21no—
77C2×#11758196—21no—
78C2×#11758196—21no—
79C2×#11758198—21no—
80C2×#11758198—21no—
81C2×#11758198—21no—
82C2×#11758198—21no—
83C2×#11758198—21no—
84#14519708—22no—
85C4⋊#92418—22no—
86#14519701—22no—
87#14519701—22no—
88#14519701—41no—
89#14519697—22no—
90#14519697—22no—
91#14519697—22no—
92#14519688—22no—
93#14519688—41no—
94C4×#92418—41no—
95#14519684—21no—
96#14519684—21no—
97C22×Q8×C61C2311yescharacteristic
98C2×C4⋊C4×C61—21no—
99C2×C4⋊C4×C61D411yescharacteristic
100C2×C4⋊C4×C61D411yescharacteristic
101C2×C4⋊C4×C61C2311yescharacteristic
102C2×C4⋊C4×C61C2311yescharacteristic
103C2×C4⋊C4×C61C2311yescharacteristic
104C2×C42×C61—21no—
105C2×C42×C61C2311yescharacteristic
106C2×C42×C61C2311yescharacteristic
107C2×C42×C61C2311yescharacteristic
108#95×C61—21no—
109#95×C61—21no—
110#95×C61—21no—
111#95×C61—21no—
112#95×C61—21no—
113#95×C61—21no—
114#95×C61—21no—
115#95×C61—21no—
116#95×C61—21no—
117#95×C61—21no—
118#95×C61D411yescharacteristic
119#95×C61D411yescharacteristic
120C23×D61—21no—
121C2×Q8×C61—21no—
122C2×Q8×C61—21no—
123C2×Q8×C61—21no—
124C2×Q8×C61—21no—
125C2×Q8×C61—21no—
126C2×Q8×C61—21no—
127C22×C4×C61—21no—
128C22×C4×C61—21no—
129C22×C4×C61—21no—
130C22×C4×C61—21no—
131C22×C4×C61C2×D411yescharacteristic
132C22×C4×C61C2×D411yescharacteristic
133C22×C4×C61C2×D411yescharacteristic
134C22×C4×C61C2×D411yescharacteristic
135C22×C4×C61C2×D411yescharacteristic
136C22×C4×C61C2×D411yescharacteristic
137C22×C4×C61C2411yescharacteristic
138C22×Dic61—21no—
139C22×Dic61—21no—
140C22×Dic61—21no—
141C2×D244—21no—
142C2×D244—21no—
143C2×D244—21no—
144C2×D244—21no—
145C2×D244—21no—
146C2×D244#4112yes—
147C2×C4×D61—42no—
148C2×C4×D61—42no—
149C2×C4×D61—81no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—21no—
156C4⋊C4×C61—41no—
157C4⋊C4×C61—41no—
158C4⋊C4×C61—42no—
159C42×C61—21no—
160C42×C61—21no—
161C42×C61—21no—
162C42×C61—21no—
163C42×C61—21no—
164C42×C61—21no—
165C42×C61—42no—
166#11758201—44no—
167#11758198—42no—
168#11758198—42no—
169#11758198—81no—
170#11758198—81no—
171#11758198—81no—
172C4⋊Dic61—21no—
173C4⋊Dic61—21no—
174C4⋊Dic61—21no—
175C4⋊Dic61—21no—
176C4⋊Dic61—21no—
177C4⋊Dic61#4112yes—
178#11758196—42no—
179#11758196—42no—
180#11758196—81no—
181#11758196—81no—
182C2×#92418—21no—
183C2×#92418—21no—
184C2×#92418—21no—
185C2×#92418—21no—
186C2×#92418—21no—
187C2×#92418—21no—
188C2×#92418—21no—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418#4112yes—
193C2×#92418#4112yes—
194C23×C61C22×D411yescharacteristic
195C22×D61—22no—
196C22×D61—41no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202Q8×C61—41no—
203Q8×C61—41no—
204Q8×C61—41no—
205Q8×C61—41no—
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×C61—21no—
221C2×C4×C61—21no—
222C2×C4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—41no—
225C2×C4×C61—41no—
226C2×C4×C61—41no—
227C2×C4×C61—41no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—41no—
233C2×C4×C61—41no—
234C2×C4×C61—41no—
235C2×C4×C61—41no—
236C2×C4×C61C2×#4111yescharacteristic
237C2×C4×C61C2×#4111yescharacteristic
238C2×C4×C61C2×#4111yescharacteristic
239C2×C4×C61C2×#4111yescharacteristic
240C2×C4×C61H(5,𝔽2)11yescharacteristic
241C2×C4×C612−1+411yescharacteristic
242C2×Dic61—22no—
243C2×Dic61—41no—
244C2×Dic61—41no—
245C2×Dic61—41no—
246C2×Dic61—41no—
247C2×Dic61—41no—
248C2×Dic61—41no—
249C2×Dic61—41no—
250C2×Dic61—41no—
251D244—22no—
252D244—22no—
253D244—41no—
254D244—41no—
255C4×D61—84no—
256#92418—22no—
257#92418—22no—
258#92418—41no—
259#92418—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—81no—
282C4×C61—81no—
283C4×C61—81no—
284C4×C61—81no—
285C4×C61#52911yescharacteristic
286C4×C61#53911yescharacteristic
287C4×C61#55111yescharacteristic
288C4×C61#55611yescharacteristic
289Dic61—42no—
290Dic61—81no—
291Dic61—81no—
292#2514D6111yescharacteristic, complemented
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#1771—611no—
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⋊C8—611no—
320C2×#103—611no—
321C2×#103—611no—
322C2×#103—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×#102—611no—
326C2×#97—611no—
327C2×#97—611no—
328C2×C4×C8—611no—
329#401—21no—
330#400—21no—
331#399—1221no—
332#396—1221no—
333#391C2×D6111yescharacteristic
334#391C2×D6111yescharacteristic
335#391C2×D6111yescharacteristic
336#390—611no—
337#390—611no—
338#389—611no—
339#389—611no—
340#389C2×D6111yescharacteristic
341#387—21no—
342#385—1221no—
343#383—21no—
344#382C2×D6111yescharacteristic
345#380—1221no—
346C4×C4⋊C4C2×D6111yescharacteristic
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#336—611no—
357#336—611no—
358C61#2910011yescharacteristic, complemented, Sylow
359C22×Q8C22×D6111yescharacteristic
360C22×D4—611no—
361C23×C4—1221no—
362C2×SD16—1222no—
363C2×SD16—1222no—
364C2×SD16—2441no—
365C22×C8—611no—
366C22×C8—611no—
367C22×C8—611no—
368C22×C8—611no—
369#125—1222no—
370#125—2441no—
371C4×D4—1222no—
372C4×D4—2441no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—611no—
376C2×C4⋊C4—611no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4C22⋊D6111yescharacteristic
382C2×C4⋊C4C22⋊D6111yescharacteristic
383C2×C4⋊C4C22×D6111yescharacteristic
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C22⋊C4—1221no—
387C2×C22⋊C4—1221no—
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C42—21no—
392C2×C42C22×D6111yescharacteristic
393C2×C42C22×D6111yescharacteristic
394C2×C42C22×D6111yescharacteristic
395#106—1222no—
396C4⋊C8—1222no—
397#103—1222no—
398#103—1222no—
399#103—2441no—
400#102—1222no—
401#102—1222no—
402#102—1222no—
403#97—1222no—
404#97—2441no—
405C4×C8—2441no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—1221no—
417#95—1221no—
418#95C22⋊D6111yescharacteristic
419#95C22⋊D6111yescharacteristic
420C24—1221no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×D4—612no—
428C2×D4—1221no—
429C2×D4—1221no—
430C2×D4—1221no—
431C2×D4—1221no—
432C2×D4—1221no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—1221no—
438C22×C4—1221no—
439C22×C4—1221no—
440C22×C4—4881no—
441C22×C4—2442no—
442C22×C4—2442no—
443C22×C4C2×C22⋊D6111yescharacteristic
444C22×C4C2×C22⋊D6111yescharacteristic
445C22×C4C2×C22⋊D6111yescharacteristic
446C22×C4C2×C22⋊D6111yescharacteristic
447C22×C4C2×C22⋊D6111yescharacteristic
448C22×C4C2×C22⋊D6111yescharacteristic
449C22×C4C23×D6111yescharacteristic
450SD16—2444no—
451C2×C8—612no—
452C2×C8—612no—
453C2×C8—1221no—
454C2×C8—1221no—
455C2×C8—1221no—
456C2×C8—1221no—
457C2×C8—1221no—
458C2×C8—1221no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—42no—
472C4⋊C4—612no—
473C4⋊C4—1221no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—4881no—
479C4⋊C4—4881no—
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—42no—
494C23—1222no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23—2441no—
500C23—2441no—
501C23C22×C22⋊D6111yescharacteristic
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
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—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—1222no—
541C2×C4—4884no—
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×C4#41×D6111yescharacteristic
553C2×C4#41×D6111yescharacteristic
554C2×C4#1451982311yescharacteristic
555C2×C4#1451982411yescharacteristic
556C8—1222no—
557C8—1222no—
558C8—2441no—
559C8—2441no—
560C22—4881no—
561C22—4881no—
562C22—4881no—
563C22—4881no—
564C22—2442no—
565C22—2442no—
566C22—2442no—
567C22#1684030811yescharacteristic
568C22#1684040011yescharacteristic
569C22#1684041911yescharacteristic
570C22#1684056011yescharacteristic
571C22#1684056011yescharacteristic
572C22#1684057011yescharacteristic
573C22#1684057011yescharacteristic
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4—81no—
584C4—4881no—
585C4—4881no—
586C4—2442no—
587C4#1684029511yescharacteristic
588C4#1684035311yescharacteristic
589C4#1684043711yescharacteristic
590C4#1684047911yescharacteristic
591C2—4882no—
592C2#2145096111yescharacteristic
593C2#2145644811yescharacteristic
594C2#2145654211yescharacteristic
595C2#2145784911yescharacteristic
596C2#2145793911yescharacteristic
597C2#2145864011yescharacteristic
598C2#2145864011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2514C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#2514D61
hypocenterC61#29100
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #2514

Complements

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

NH ≅ G/Ntype
2. #21447321C2semidirect
5. #21446970C2semidirect
6. #21446783C2semidirect
9. #21446512C2semidirect
10. #21446512C2semidirect
11. #21446397C2semidirect
13. #21445694C2semidirect
15. C61×#2514C2semidirect
292. #2514D61semidirect
358. C61#29100semidirect

Maximal subgroups

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

subgroupindex
#214496912
#214473212
#214472332
#214471342
#214469702
#214467832
#214466762
#214465152
#214465122
#214463972
#214461562
#214456942
#214456472
C61×#25142
#2910061