Subgroups — #30595286

Order 15616.

146 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21460957	C₂	1	2	yes	maximal, complemented
2	#21445425	C₂	1	1	yes	maximal, characteristic
3	#16840673	—	2	2	no	—
4	#16840142	C₂²	1	1	yes	characteristic
5	#16840139	C₄	1	1	yes	characteristic
6	#16840109	—	2	2	no	—
7	C₈²×C₆₁	C₄	1	1	yes	characteristic
8	#14519838	—	4	2	no	—
9	C₂×Dic₂₄₄	—	4	1	no	—
10	C₂×D₄₈₈	—	4	1	no	—
11	#14519777	D₄	1	2	yes	—
12	#14519774	—	2	1	no	—
13	#14519699	—	4	4	no	—
14	C₄×C₈×C₆₁	—	2	1	no	—
15	C₄×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×D₂₄₄	—	4	2	no	—
17	C₂×D₂₄₄	—	4	1	no	—
18	C₂×Dic₁₂₂	—	2	2	no	—
19	#11758217	—	8	2	no	—
20	C₂×C₈×C₆₁	—	2	1	no	—
21	C₂×C₈×C₆₁	—	2	2	no	—
22	C₄²×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₄⋊Dic₆₁	—	4	2	no	—
24	Dic₂₄₄	—	8	2	no	—
25	D₄₈₈	—	8	2	no	—
26	C₂²×D₆₁	—	8	1	no	—
27	C₂×C₄×C₆₁	—	2	1	no	—
28	C₂×C₄×C₆₁	#99	1	1	yes	characteristic
29	C₂×Dic₆₁	—	4	2	no	—
30	D₂₄₄	—	8	2	no	—
31	D₂₄₄	—	8	4	no	—
32	Dic₁₂₂	—	8	2	no	—
33	#92420	—	16	2	no	—
34	C₈×C₆₁	—	2	2	no	—
35	C₈×C₆₁	—	4	2	no	—
36	#7531	—	61	1	no	maximal, Sylow
37	C₂²×C₆₁	#353	1	1	yes	characteristic
38	C₂×D₆₁	—	16	2	no	—
39	C₂×D₆₁	—	16	1	no	—
40	C₄×C₆₁	—	2	2	no	—
41	C₄×C₆₁	—	2	1	no	—
42	Dic₆₁	—	8	2	no	—
43	#1709	—	61	1	no	—
44	#1411	—	61	2	no	—
45	C₂×C₆₁	—	2	1	no	—
46	C₂×C₆₁	#1408	1	1	yes	characteristic
47	D₆₁	—	32	1	no	—
48	#494	—	61	1	no	—
49	#493	—	61	1	no	—
50	#486	—	122	2	no	—
51	#356	—	122	2	no	—
52	C₈²	#6923	1	1	yes	characteristic
53	C₆₁	#7531	1	1	yes	characteristic, complemented, Sylow
54	C₂×Q₁₆	—	244	1	no	—
55	C₂×D₈	—	244	1	no	—
56	C₄⋊Q₈	—	61	2	no	—
57	#127	—	122	1	no	—
58	#102	—	244	4	no	—
59	#101	—	244	2	no	—
60	C₄×C₈	—	2	1	no	—
61	C₄×C₈	C₂×#6923	1	1	yes	characteristic
62	C₂×Q₈	—	122	2	no	—
63	C₂×D₄	—	244	2	no	—
64	C₂×D₄	—	244	1	no	—
65	Q₁₆	—	488	2	no	—
66	D₈	—	488	2	no	—
67	M₁₆	—	488	2	no	—
68	C₂×C₈	—	2	1	no	—
69	C₂×C₈	—	2	2	no	—
70	C₄⋊C₄	—	244	2	no	—
71	C₄²	C₂²⋊#6923	1	1	yes	characteristic
72	C₂³	—	488	1	no	—
73	Q₈	—	488	2	no	—
74	D₄	—	488	2	no	—
75	D₄	—	488	4	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	244	2	no	—
78	C₂×C₄	#14519836	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	4	2	no	—
81	C₈	—	976	2	no	—
82	C₂²	—	976	2	no	—
83	C₂²	—	976	1	no	—
84	C₂²	#16840667	1	1	yes	characteristic
85	C₄	—	2	2	no	—
86	C₄	—	2	1	no	—
87	C₄	—	488	2	no	—
88	C₂	—	2	1	no	—
89	C₂	—	1952	1	no	—
90	C₂	#21460951	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#21460951
commutator	C₄×C₈×C₆₁	C₂×C₄
Frattini	C₄×C₈	C₂×#6923
Fitting	C₈²×C₆₁	C₄
socle	C₂×C₆₁	#1408
prime radical	#16840139	C₄
cosocle	#16840142	C₂²
hypercenter	C₈²	#6923
hypocenter	C₆₁	#7531
LCS	G ▷ C₄×C₈×C₆₁ ▷ C₄²×C₆₁ ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₈²

Complements

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

N	H ≅ G/N	type
1. #21460957	C₂	semidirect
53. C₆₁	#7531	semidirect

Maximal subgroups

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

subgroup	index
#21460957	2
#21445425	2
#7531	61