Subgroups — #21443776

Order 7808.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839841	C₂	1	1	yes	maximal, characteristic
2	#16839538	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11758189	—	2	1	no	—
5	C₄×D₂₄₄	C₄	1	1	yes	characteristic
6	C₂×#11758185	—	2	1	no	—
7	C₄⋊#92418	C₄	1	1	yes	characteristic
8	#14519689	—	2	1	no	—
9	C₂×C₁₆×C₆₁	—	2	1	no	—
10	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
11	C₂×D₂₄₄	C₈	1	1	yes	characteristic
12	C₂×C₄×D₆₁	—	2	1	no	—
13	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₆₁	D₄	1	1	yes	characteristic
15	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
16	#11758198	—	2	1	no	—
17	C₄⋊Dic₆₁	C₈	1	1	yes	characteristic
18	C₂×#92418	—	2	1	no	—
19	#11758189	—	4	1	no	—
20	#11758189	—	4	1	no	—
21	C₁₆×C₆₁	—	4	1	no	—
22	#11758185	—	2	2	no	—
23	C₂²×D₆₁	—	2	1	no	—
24	C₂×C₄×C₆₁	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₆₁	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₆₁	M₁₆	1	1	yes	characteristic
27	C₂×Dic₆₁	—	2	1	no	—
28	D₂₄₄	—	4	1	no	—
29	C₄×D₆₁	—	4	1	no	—
30	C₄×D₆₁	—	4	1	no	—
31	C₈×C₆₁	—	2	1	no	—
32	C₈×C₆₁	D₈	1	1	yes	characteristic
33	C₈×C₆₁	SD₁₆	1	1	yes	characteristic
34	#92418	—	4	1	no	—
35	C₂²×C₆₁	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₆₁	—	4	1	no	—
37	C₂×D₆₁	—	4	1	no	—
38	C₂×D₆₁	—	4	1	no	—
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	—	2	1	no	—
41	C₄×C₆₁	#102	1	1	yes	characteristic
42	C₄×C₆₁	#104	1	1	yes	characteristic
43	Dic₆₁	—	4	1	no	—
44	#1330	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	D₄⋊C₈	1	1	yes	characteristic
46	C₂×C₆₁	#349	1	1	yes	characteristic
47	C₂×C₆₁	#350	1	1	yes	characteristic
48	D₆₁	—	8	1	no	—
49	#436	—	61	1	no	—
50	C₄⋊C₁₆	D₆₁	1	1	yes	characteristic, complemented
51	#346	—	61	1	no	—
52	C₆₁	#1330	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	—	122	1	no	—
54	C₄×D₄	—	61	1	no	—
55	C₂×C₁₆	—	2	1	no	—
56	C₂×C₁₆	—	122	1	no	—
57	C₄⋊C₈	—	61	1	no	—
58	C₂²⋊C₈	—	122	1	no	—
59	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
60	C₂×D₄	—	61	1	no	—
61	C₂²×C₄	—	122	1	no	—
62	M₁₆	—	244	1	no	—
63	M₁₆	—	244	1	no	—
64	C₂×C₈	—	122	1	no	—
65	C₂×C₈	D₂₄₄	1	1	yes	characteristic
66	C₂×C₈	C₂²⋊D₆₁	1	1	yes	characteristic
67	C₄⋊C₄	—	61	1	no	—
68	C₂²⋊C₄	—	122	1	no	—
69	C₄²	C₄×D₆₁	1	1	yes	characteristic
70	C₁₆	—	4	1	no	—
71	C₁₆	—	122	2	no	—
72	C₂³	—	122	1	no	—
73	D₄	—	244	1	no	—
74	C₂×C₄	—	122	1	no	—
75	C₂×C₄	—	244	1	no	—
76	C₂×C₄	—	244	1	no	—
77	C₂×C₄	C₈×D₆₁	1	1	yes	characteristic
78	C₂×C₄	#11758189	1	1	yes	characteristic
79	C₂×C₄	#11758198	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	244	1	no	—
82	C₈	#11758199	1	1	yes	characteristic
83	C₈	#11758201	1	1	yes	characteristic
84	C₂²	—	244	1	no	—
85	C₂²	—	244	1	no	—
86	C₂²	—	244	1	no	—
87	C₂²	#14519689	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	244	1	no	—
91	C₄	#14519697	1	1	yes	characteristic
92	C₄	#14519703	1	1	yes	characteristic
93	C₂	—	488	1	no	—
94	C₂	#16839489	1	1	yes	characteristic
95	C₂	#16839543	1	1	yes	characteristic
96	C₂	#16839545	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#11758198
commutator	C₂×C₄×C₆₁	C₂×C₈
Frattini	C₄×C₈	C₂×D₆₁
Fitting	C₆₁×C₄⋊C₁₆	C₂
socle	C₂²×C₆₁	C₂²⋊C₈
hypercenter	C₄⋊C₁₆	D₆₁
hypocenter	C₆₁	#1330
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #16839538	C₂	semidirect
3. C₆₁×C₄⋊C₁₆	C₂	semidirect
50. C₄⋊C₁₆	D₆₁	semidirect
52. C₆₁	#1330	semidirect