Subgroups — #21443782

Order 7808.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×Dic₂₄₄	C₂	1	1	yes	maximal, characteristic
2	C₄×#11758185	C₂	1	1	yes	maximal, characteristic
3	C₆₁×#335	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₂₄₄	C₄	1	1	yes	characteristic
5	C₄×Dic₁₂₂	—	2	1	no	—
6	C₂×#11758185	—	2	1	no	—
7	#14519711	C₄	1	1	yes	characteristic
8	#14519702	—	2	1	no	—
9	C₄⋊C₈×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₂₂	—	2	1	no	—
12	C₂×C₈×C₆₁	—	4	1	no	—
13	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₄²×C₆₁	D₄	1	1	yes	characteristic
16	C₄⋊Dic₆₁	—	2	1	no	—
17	#11758196	—	4	1	no	—
18	C₄×Dic₆₁	—	4	1	no	—
19	Dic₂₄₄	—	2	1	no	—
20	Dic₂₄₄	C₈	1	2	yes	complemented
21	#11758185	—	2	2	no	—
22	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×C₄×C₆₁	D₈	1	1	yes	characteristic
24	C₂×C₄×C₆₁	SD₁₆	1	1	yes	characteristic
25	C₂×Dic₆₁	—	4	1	no	—
26	C₂×Dic₆₁	—	4	1	no	—
27	Dic₁₂₂	—	2	2	no	—
28	Dic₁₂₂	—	4	1	no	—
29	C₈×C₆₁	—	2	1	no	—
30	C₈×C₆₁	—	8	1	no	—
31	C₈×C₆₁	C₂×C₈	1	1	yes	characteristic
32	C₈×C₆₁	M₁₆	1	1	yes	characteristic
33	C₂²×C₆₁	#102	1	1	yes	characteristic
34	C₄×C₆₁	—	2	1	no	—
35	C₄×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₆₁	#104	1	1	yes	characteristic
37	C₄×C₆₁	SD₃₂	1	1	yes	characteristic
38	C₄×C₆₁	Q₃₂	1	1	yes	characteristic
39	Dic₆₁	—	4	2	no	—
40	Dic₆₁	—	8	1	no	—
41	#1332	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
43	C₂×C₆₁	#358	1	1	yes	characteristic
44	C₂×C₆₁	#359	1	1	yes	characteristic
45	C₄×Q₁₆	—	61	1	no	—
46	C₄×C₁₆	—	61	1	no	—
47	#335	D₆₁	1	1	yes	characteristic
48	C₆₁	#1332	1	1	yes	characteristic, complemented, Sylow
49	C₂×Q₁₆	—	61	1	no	—
50	C₄×Q₈	—	122	1	no	—
51	C₂×C₁₆	—	122	1	no	—
52	#107	—	61	1	no	—
53	C₄⋊C₈	—	2	1	no	—
54	#103	—	122	1	no	—
55	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
56	C₂×Q₈	—	122	1	no	—
57	Q₁₆	—	61	2	no	—
58	Q₁₆	—	122	1	no	—
59	C₂×C₈	—	4	1	no	—
60	C₂×C₈	C₄×D₆₁	1	1	yes	characteristic
61	C₂×C₈	D₂₄₄	1	1	yes	characteristic
62	C₄⋊C₄	—	122	1	no	—
63	C₄⋊C₄	—	244	1	no	—
64	C₄²	—	244	1	no	—
65	C₄²	C₂²⋊D₆₁	1	1	yes	characteristic
66	C₁₆	—	122	2	no	—
67	Q₈	—	122	2	no	—
68	Q₈	—	244	1	no	—
69	C₂×C₄	—	244	1	no	—
70	C₂×C₄	—	244	1	no	—
71	C₂×C₄	#11758198	1	1	yes	characteristic
72	C₂×C₄	#11758199	1	1	yes	characteristic
73	C₂×C₄	#11758201	1	1	yes	characteristic
74	C₈	—	2	1	no	—
75	C₈	—	8	1	no	—
76	C₈	C₈×D₆₁	1	1	yes	characteristic
77	C₈	#11758189	1	1	yes	characteristic
78	C₂²	#14519697	1	1	yes	characteristic
79	C₄	—	2	1	no	—
80	C₄	—	488	1	no	—
81	C₄	—	244	2	no	—
82	C₄	#14519689	1	1	yes	characteristic
83	C₄	#14519703	1	1	yes	characteristic
84	C₄	#14519721	1	1	yes	characteristic
85	C₄	#14519723	1	1	yes	characteristic
86	C₂	#16839489	1	1	yes	characteristic
87	C₂	#16839565	1	1	yes	characteristic
88	C₂	#16839568	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11758199
commutator	C₈×C₆₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×#335	C₂
socle	C₂²×C₆₁	#102
hypercenter	#335	D₆₁
hypocenter	C₆₁	#1332
LCS	G ▷ C₈×C₆₁ ▷ C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
20. Dic₂₄₄	C₈	semidirect
48. C₆₁	#1332	semidirect