Finite Group Databasebeta

← #29738106

Subgroups — #29738106

Order 15616.

734 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21450856C211yesmaximal, characteristic, complemented
2#21448764C211yesmaximal, characteristic
3#21447190C211yesmaximal, characteristic
4#21447188C211yesmaximal, characteristic
5#21446966C211yesmaximal, characteristic
6#21446964C211yesmaximal, characteristic
7#21446776C211yesmaximal, characteristic, complemented
8#21446773C211yesmaximal, characteristic, complemented
9#21446579C211yesmaximal, characteristic, complemented
10#21446536C211yesmaximal, characteristic, complemented
11#21446400C211yesmaximal, characteristic, complemented
12#21445945C211yesmaximal, characteristic, complemented
13#21445818C211yesmaximal, characteristic
14#21445633C211yesmaximal, characteristic
15C61×#1919C211yesmaximal, characteristic, complemented
16C2×#14519769C2211yescharacteristic
17C2×#14519768C2211yescharacteristic
18C2×#14519739C2211yescharacteristic
19C2×#14519734—21no—
20C2×#14519708C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×#14519706C2211yescharacteristic
23C2×#14519706C2211yescharacteristic
24C2×#14519699C2211yescharacteristic
25C2×#14519699C2211yescharacteristic
26C2×#14519697C2211yescharacteristic
27C2×#14519697C2211yescharacteristic
28C2×C8×Dic61C2211yescharacteristic
29#16839696—21no—
30#16839695—21no—
31#16839664C2211yescharacteristic
32#16839663C2211yescharacteristic
33#16839661C2211yescharacteristic
34#16839659—21no—
35#16839653—21no—
36#16839651—21no—
37#16839631—21no—
38#16839631C2211yescharacteristic
39#16839631C2211yescharacteristic
40#16839621—21no—
41C4⋊C4×Dic61C2211yescharacteristic
42C4⋊C4×Dic61C2211yescharacteristic
43C4×#11758196C2211yescharacteristic
44#16839525C2211yescharacteristic
45#16839525C2211yescharacteristic
46#16839524C2211yescharacteristic
47#16839524C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839516C2211yescharacteristic
52C2×#106×C61C2211yescharacteristic
53C61×#389C2211yescharacteristic
54C4×C4⋊C4×C61C2211yescharacteristic
55C61×#340C2211yescharacteristic
56C61×#340C2211yescharacteristic
57C61×#340C2211yescharacteristic
58C61×#336C2211yescharacteristic
59C22×D244C2311yescharacteristic
60C22×C4×D61—21no—
61C22×#92418C2311yescharacteristic
62C22×#92418C2311yescharacteristic
63#14519769—22no—
64#14519769—41no—
65#14519768—22no—
66#14519768—41no—
67#14519739—22no—
68#14519739Q814yes—
69#14519734—44no—
70C2×C4⋊Dic61—21no—
71C2×C4⋊Dic61—21no—
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×#11758196—21no—
81C2×#11758196—21no—
82C2×#11758196D411yescharacteristic
83C2×#11758196D411yescharacteristic
84C2×#11758198—21no—
85C2×#11758198—21no—
86C2×#11758198—21no—
87C2×#11758198—21no—
88C2×#11758198—21no—
89C2×C4×Dic61—21no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519708—22no—
94C4⋊#92418—41no—
95#14519706—22no—
96#14519706—41no—
97#14519699—22no—
98#14519699—41no—
99#14519697—22no—
100#14519697—41no—
101C8×Dic61—22no—
102#14519684—21no—
103#14519684—21no—
104#14519684—21no—
105#14519684D411yescharacteristic
106#14519684D411yescharacteristic
107C22×C8×C61C2311yescharacteristic
108C22×C8×C61C2311yescharacteristic
109C2×C4⋊C4×C61—21no—
110C2×C4⋊C4×C61C2311yescharacteristic
111C2×C4⋊C4×C61C2311yescharacteristic
112C2×C4⋊C4×C61C2311yescharacteristic
113C2×C4⋊C4×C61C2311yescharacteristic
114C2×C42×C61—21no—
115C2×C42×C61C2311yescharacteristic
116#106×C61—22no—
117#95×C61—21no—
118#95×C61—21no—
119C23×D61—21no—
120C22×C4×C61—21no—
121C22×C4×C61—21no—
122C22×C4×C61—21no—
123C22×C4×C61—21no—
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61C2×D411yescharacteristic
126C22×C4×C61C2411yescharacteristic
127C22×Dic61—21no—
128C22×Dic61—21no—
129C22×Dic61—21no—
130C22×Dic61C2×D411yescharacteristic
131C22×Dic61C2×D411yescharacteristic
132C22×Dic61C2×D411yescharacteristic
133C22×Dic61C2×D411yescharacteristic
134C2×D244—21no—
135C2×D244—21no—
136C2×D244—21no—
137C2×D244—21no—
138C2×D244—21no—
139C2×D244C2×Q812yes—
140C2×C4×D61—24no—
141C2×C4×D61—42no—
142C2×C4×D61—42no—
143C2×C8×C61—21no—
144C2×C8×C61—21no—
145C2×C8×C61—21no—
146C2×C8×C61—21no—
147C2×C8×C61—21no—
148C2×C8×C61—21no—
149C4⋊C4×C61—21no—
150C4⋊C4×C61—21no—
151C4⋊C4×C61—21no—
152C4⋊C4×C61—21no—
153C4⋊C4×C61—21no—
154C4⋊C4×C61—21no—
155C4⋊C4×C61—81no—
156C4⋊C4×C61C2×Q812yes—
157C4⋊C4×C61#4112yes—
158C42×C61—21no—
159C42×C61—21no—
160C42×C61—42no—
161#11758198—24no—
162#11758198—42no—
163#11758198—42no—
164#11758198—81no—
165#11758198—81no—
166C4⋊Dic61—21no—
167C4⋊Dic61—21no—
168C4⋊Dic61—21no—
169C4⋊Dic61—21no—
170C4⋊Dic61—21no—
171C4⋊Dic61—42no—
172C4⋊Dic61—81no—
173C4⋊Dic61#4112yes—
174#11758196—22no—
175#11758196—22no—
176#11758196—42no—
177#11758196—42no—
178#11758196—42no—
179#11758196—42no—
180#11758196—42no—
181#11758196—81no—
182#11758196—81no—
183C4×Dic61—21no—
184C4×Dic61—21no—
185C4×Dic61—42no—
186C4×Dic61—42no—
187C4×Dic61C2×Q812yes—
188C4×Dic61#4112yes—
189C2×#92418—21no—
190C2×#92418—21no—
191C2×#92418—21no—
192C2×#92418—21no—
193C2×#92418—21no—
194C2×#92418—21no—
195C23×C61C22×D411yescharacteristic
196C22×D61—22no—
197C22×D61—41no—
198C22×D61—41no—
199C22×D61—41no—
200C22×D61—41no—
201C22×D61—41no—
202C22×D61—41no—
203C2×C4×C61—22no—
204C2×C4×C61—21no—
205C2×C4×C61—21no—
206C2×C4×C61—22no—
207C2×C4×C61—21no—
208C2×C4×C61—21no—
209C2×C4×C61—21no—
210C2×C4×C61—21no—
211C2×C4×C61—41no—
212C2×C4×C61—41no—
213C2×C4×C61—41no—
214C2×C4×C61—41no—
215C2×C4×C61—41no—
216C2×C4×C61—41no—
217C2×C4×C61—41no—
218C2×C4×C61—41no—
219C2×C4×C61—41no—
220C2×C4×C61—41no—
221C2×C4×C61C22×Q811yescharacteristic
222C2×C4×C61C2×#4111yescharacteristic
223C2×C4×C61C2×#4111yescharacteristic
224C2×C4×C61C2×#4111yescharacteristic
225C2×C4×C61H(5,𝔽2)11yescharacteristic
226C2×C4×C612−1+411yescharacteristic
227C2×Dic61—21no—
228C2×Dic61—21no—
229C2×Dic61—21no—
230C2×Dic61—21no—
231C2×Dic61—22no—
232C2×Dic61—21no—
233C2×Dic61—21no—
234C2×Dic61—21no—
235C2×Dic61—21no—
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×Dic61C22⋊Q812yes—
245C2×Dic61C22⋊Q812yes—
246C2×Dic61#13512yes—
247C2×Dic61AGL(1,ℤ/8)12yes—
248D244—22no—
249D244—22no—
250D244—41no—
251D244—41no—
252C4×D61—48no—
253C8×C61—41no—
254C8×C61—41no—
255#92418—41no—
256#92418—41no—
257#26021—611nomaximal, Sylow
258C22×C61C2×C22⋊Q811yescharacteristic
259C22×C61#54611yescharacteristic
260C22×C61#54811yescharacteristic
261C22×C61C2×#13511yescharacteristic
262C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C61#57711yescharacteristic
264C22×C61#57711yescharacteristic
265C2×D61—42no—
266C2×D61—42no—
267C2×D61—42no—
268C2×D61—81no—
269C2×D61—81no—
270C2×D61—81no—
271C2×D61—81no—
272C4×C61—42no—
273C4×C61—41no—
274C4×C61—42no—
275C4×C61—41no—
276C4×C61—81no—
277C4×C61—81no—
278C4×C61#53311yescharacteristic
279C4×C61#54411yescharacteristic
280C4×C61#55511yescharacteristic
281C4×C61#55611yescharacteristic
282Dic61—22no—
283Dic61—41no—
284Dic61—41no—
285Dic61—42no—
286Dic61—81no—
287Dic61—81no—
288Dic61#47814yes—
289#2552—611no—
290#2354—611no—
291#2065—611no—
292#2065—611no—
293#2025—611no—
294#2025—611no—
295#1989—611no—
296#1989—611no—
297#1948—611no—
298#1939—611no—
299#1919—611no—
300#1919D6111yescharacteristic, complemented
301#1834—611no—
302#1802—611no—
303C4×#102—611no—
304C2×C61#243911yescharacteristic
305C2×C61C2×#47811yescharacteristic
306C2×C61#308411yescharacteristic
307C2×C61#330311yescharacteristic
308C2×C61#333211yescharacteristic
309C2×C61#336011yescharacteristic
310C2×C61#336811yescharacteristic
311D61—82no—
312C2×#125—611no—
313C2×#125—611no—
314C2×C4×D4—611no—
315C2×#117—1221no—
316C2×#106—611no—
317C2×#106C2×D6111yescharacteristic
318C2×C4⋊C8—611no—
319C2×C4⋊C8—611no—
320C2×C4⋊C8—611no—
321C2×#102—611no—
322C2×#102—611no—
323C2×#102—611no—
324C2×#102—611no—
325C2×C4×C8—611no—
326#398—1221no—
327#398—1221no—
328#390—611no—
329#390—611no—
330#389—611no—
331#389—1221no—
332#389C2×D6111yescharacteristic
333#388—1221no—
334#388—1221no—
335#384—611no—
336#384—611no—
337#384—1221no—
338#380—1221no—
339C4×C4⋊C4—611no—
340C4×C4⋊C4—611no—
341C4×C4⋊C4—611no—
342C4×C4⋊C4C2×D6111yescharacteristic
343#340—611no—
344#340—611no—
345#340—611no—
346#340—611no—
347#340—611no—
348#340—611no—
349#340—611no—
350#340C2×D6111yescharacteristic
351#340C2×D6111yescharacteristic
352#340C2×D6111yescharacteristic
353#336—611no—
354#336C2×D6111yescharacteristic
355C61#2602111yescharacteristic, complemented, Sylow
356C22×D4—611no—
357C23×C4—1221no—
358C22×C8—611no—
359C22×C8—611no—
360C22×C8C22×D6111yescharacteristic
361C22×C8C22×D6111yescharacteristic
362#125—1222no—
363#125—1222no—
364#125—2441no—
365#125—2441no—
366C4×D4—614no—
367C4×D4—1222no—
368#117—2444no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—611no—
371C2×C4⋊C4—611no—
372C2×C4⋊C4—611no—
373C2×C4⋊C4—611no—
374C2×C4⋊C4—611no—
375C2×C4⋊C4—1221no—
376C2×C4⋊C4—1221no—
377C2×C4⋊C4—1221no—
378C2×C4⋊C4—1221no—
379C2×C4⋊C4—1221no—
380C2×C4⋊C4—1221no—
381C2×C4⋊C4—1221no—
382C2×C4⋊C4—1221no—
383C2×C4⋊C4—1221no—
384C2×C4⋊C4C22×D6111yescharacteristic
385C2×C4⋊C4C22×D6111yescharacteristic
386C2×C4⋊C4C22×D6111yescharacteristic
387C2×C4⋊C4C22×D6111yescharacteristic
388C2×C22⋊C4—1221no—
389C2×C22⋊C4—1221no—
390C2×C22⋊C4—1221no—
391C2×C22⋊C4—1221no—
392C2×C22⋊C4—1221no—
393C2×C42—21no—
394C2×C42—611no—
395C2×C42—611no—
396C2×C42—1221no—
397C2×C42—1221no—
398C2×C42C22×D6111yescharacteristic
399#106—22no—
400#106—1222no—
401C4⋊C8—1222no—
402C4⋊C8—2441no—
403C4⋊C8—2441no—
404#102—1222no—
405#102—1222no—
406#102—2441no—
407#102—2441no—
408C4×C8—1222no—
409#95—21no—
410#95—21no—
411#95—611no—
412#95—611no—
413#95—1221no—
414#95—1221no—
415#95—1221no—
416C24—1221no—
417C2×D4—612no—
418C2×D4—1221no—
419C2×D4—1221no—
420C2×D4—1221no—
421C2×D4—1221no—
422C2×D4—1221no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—611no—
428C22×C4—611no—
429C22×C4—611no—
430C22×C4—611no—
431C22×C4—1224no—
432C22×C4—1221no—
433C22×C4—1221no—
434C22×C4—1221no—
435C22×C4—2442no—
436C22×C4—2442no—
437C22×C4D4×D6111yescharacteristic
438C22×C4D4×D6111yescharacteristic
439C22×C4C23×D6111yescharacteristic
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—1221no—
447C2×C8—1221no—
448C2×C8—1221no—
449C2×C8—1221no—
450C2×C8—1221no—
451C2×C8—1221no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—81no—
459C4⋊C4—612no—
460C4⋊C4—1222no—
461C4⋊C4—1222no—
462C4⋊C4—1221no—
463C4⋊C4—1221no—
464C4⋊C4—1221no—
465C4⋊C4—1221no—
466C4⋊C4—1221no—
467C4⋊C4—4881no—
468C4⋊C4—4881no—
469C4⋊C4—4881no—
470C4⋊C4—2442no—
471C4⋊C4—2442no—
472C4⋊C4—2442no—
473C4⋊C4—2442no—
474C4⋊C4—2442no—
475C4⋊C4—2442no—
476C4⋊C4#1175822212yes—
477C4⋊C4Q8×D6112yes—
478C22⋊C4—1224no—
479C22⋊C4—4881no—
480C22⋊C4—4881no—
481C22⋊C4—2442no—
482C22⋊C4—2442no—
483C42—21no—
484C42—21no—
485C42—42no—
486C42—612no—
487C42—612no—
488C42—1221no—
489C42—1221no—
490C42—2442no—
491C42—2442no—
492C23—1222no—
493C23—2441no—
494C23—2441no—
495C23—2441no—
496C23—2441no—
497C23—2441no—
498C23—2441no—
499C23C2×D4×D6111yescharacteristic
500D4—1222no—
501D4—1222no—
502D4—2441no—
503D4—2441no—
504C2×C4—22no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—22no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—612no—
523C2×C4—612no—
524C2×C4—612no—
525C2×C4—612no—
526C2×C4—1221no—
527C2×C4—1221no—
528C2×C4—1221no—
529C2×C4—1221no—
530C2×C4—1221no—
531C2×C4—1221no—
532C2×C4—1221no—
533C2×C4—1221no—
534C2×C4—1222no—
535C2×C4—2448no—
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×C4C2×Q8×D6111yescharacteristic
545C2×C4#41×D6111yescharacteristic
546C2×C4#41×D6111yescharacteristic
547C2×C4C2×#1175822211yescharacteristic
548C2×C4#1451982311yescharacteristic
549C2×C4#1451982411yescharacteristic
550C8—41no—
551C8—41no—
552C8—2441no—
553C8—2441no—
554C22—4881no—
555C22—4881no—
556C22—4881no—
557C22—4881no—
558C22—2442no—
559C22—2442no—
560C22—2442no—
561C22C22⋊Q8×D6111yescharacteristic
562C22#1684040411yescharacteristic
563C22#1684042111yescharacteristic
564C22#135×D6111yescharacteristic
565C22AGL(1,ℤ/8)×D6111yescharacteristic
566C22#1684056811yescharacteristic
567C22#1684057111yescharacteristic
568C4—42no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—81no—
573C4—81no—
574C4—614no—
575C4—1222no—
576C4—4881no—
577C4—4881no—
578C4—2441no—
579C4—2442no—
580C4—2441no—
581C4#1684031611yescharacteristic
582C4#1684039211yescharacteristic
583C4#1684047511yescharacteristic
584C4#1684047911yescharacteristic
585C2—4882no—
586C2#2144950911yescharacteristic
587C2#478×D6111yescharacteristic
588C2#2145567811yescharacteristic
589C2#2145774511yescharacteristic
590C2#2145814411yescharacteristic
591C2#2145846911yescharacteristic
592C2#2145854911yescharacteristic
subgroupG/H
centerC23C2×D4×D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#1919C2
socleC23×C61C22×D4
prime radicalC22×D244C23
hypercenter#1919D61
hypocenterC61#26021
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1919

Complements

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

NH ≅ G/Ntype
1. #21450856C2semidirect
7. #21446776C2semidirect
8. #21446773C2semidirect
9. #21446579C2semidirect
10. #21446536C2semidirect
11. #21446400C2semidirect
12. #21445945C2semidirect
15. C61×#1919C2semidirect
300. #1919D61semidirect
355. C61#26021semidirect

Maximal subgroups

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

subgroupindex
#214508562
#214487642
#214471902
#214471882
#214469662
#214469642
#214467762
#214467732
#214465792
#214465362
#214464002
#214459452
#214458182
#214456332
C61×#19192
#2602161