Subgroups — #16840796

Order 3904.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11758213	C₂	1	2	yes	maximal, complemented
2	C₄⋊#92420	C₂	1	1	yes	maximal, characteristic, complemented
3	#14519834	C₂	1	2	yes	maximal, complemented
4	C₄×#92420	C₂	1	1	yes	maximal, characteristic, complemented
5	#14519739	C₂	1	1	yes	maximal, characteristic
6	C₂×D₂₄₄	C₄	1	1	yes	characteristic
7	C₂×C₄×D₆₁	C₂²	1	2	yes	—
8	C₂×#92420	C₂²	1	1	yes	characteristic
9	C₂×#92420	C₂²	1	2	yes	—
10	C₂×#92420	C₂²	1	1	yes	characteristic
11	#11758213	—	2	4	no	—
12	C₄⋊C₄×C₆₁	C₄	1	1	yes	characteristic
13	#11758198	C₄	1	2	yes	—
14	C₄×Dic₆₁	C₂²	1	1	yes	characteristic
15	C₂²×D₆₁	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₆₁	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₆₁	C₂×C₄	1	1	yes	characteristic
19	C₂×Dic₆₁	C₂³	1	1	yes	characteristic
20	D₂₄₄	—	2	2	no	—
21	C₄×D₆₁	—	2	2	no	—
22	C₄×D₆₁	—	2	2	no	—
23	#92420	—	2	2	no	—
24	#92420	—	2	1	no	—
25	#92420	D₄	1	2	yes	complemented
26	C₂²×C₆₁	C₂²×C₄	1	1	yes	characteristic
27	C₂×D₆₁	—	2	2	no	—
28	C₂×D₆₁	—	2	2	no	—
29	C₂×D₆₁	—	2	2	no	—
30	C₄×C₆₁	—	2	2	no	—
31	C₄×C₆₁	M₁₆	1	2	yes	complemented
32	Dic₆₁	—	2	1	no	—
33	Dic₆₁	C₂×D₄	1	1	yes	characteristic
34	Dic₆₁	#41	1	1	yes	characteristic
35	C₂×C₆₁	C₄×D₄	1	1	yes	characteristic
36	C₂×C₆₁	C₂×M₁₆	1	1	yes	characteristic
37	C₂×C₆₁	#131	1	1	yes	characteristic
38	D₆₁	—	4	2	no	—
39	#436	—	61	1	no	maximal, Sylow
40	C₆₁	#436	1	1	yes	characteristic, complemented, Sylow
41	C₂×M₁₆	—	61	2	no	—
42	C₄×D₄	—	61	1	no	—
43	C₄⋊C₈	—	61	1	no	—
44	C₂²⋊C₈	—	61	2	no	—
45	C₄×C₈	—	61	1	no	—
46	C₂×D₄	—	61	1	no	—
47	C₂²×C₄	—	61	2	no	—
48	M₁₆	—	122	4	no	—
49	C₂×C₈	—	61	1	no	—
50	C₂×C₈	—	61	1	no	—
51	C₂×C₈	—	61	2	no	—
52	C₄⋊C₄	#6923	1	1	yes	characteristic
53	C₂²⋊C₄	—	61	2	no	—
54	C₄²	—	61	1	no	—
55	C₂³	—	61	2	no	—
56	D₄	—	122	2	no	—
57	C₂×C₄	—	61	1	no	—
58	C₂×C₄	—	61	1	no	—
59	C₂×C₄	—	122	2	no	—
60	C₂×C₄	—	122	2	no	—
61	C₂×C₄	C₂×#6923	1	2	yes	—
62	C₂×C₄	C₂×#6923	1	1	yes	characteristic
63	C₈	—	61	2	no	—
64	C₈	—	122	1	no	—
65	C₈	—	122	2	no	—
66	C₂²	—	122	2	no	—
67	C₂²	—	122	2	no	—
68	C₂²	—	122	2	no	—
69	C₂²	C₂²×#6923	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	61	1	no	—
72	C₄	—	61	1	no	—
73	C₄	—	122	1	no	—
74	C₄	#11758213	1	2	yes	complemented
75	C₂	—	244	2	no	—
76	C₂	D₄×#6923	1	1	yes	characteristic
77	C₂	C₂×#11758213	1	1	yes	characteristic
78	C₂	#14519865	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#6923
commutator, socle	C₂²×C₆₁	C₂²×C₄
Fitting	C₄⋊C₄×C₆₁	C₄
prime radical	C₂×D₂₄₄	C₄
cosocle	C₂×Dic₆₁	C₂³
hypercenter	C₄⋊C₄	#6923
hypocenter	C₆₁	#436
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#11758213	C₂	semidirect
2. C₄⋊#92420	C₂	semidirect
3. #14519834	C₂	semidirect
4. C₄×#92420	C₂	semidirect
25. #92420	D₄	semidirect
31. C₄×C₆₁	M₁₆	semidirect
40. C₆₁	#436	semidirect
74. C₄	#11758213	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11758213	2
C₄⋊#92420	2
#14519834	2
C₄×#92420	2
#14519739	2
#436	61