Subgroups — #21445993

Order 7808.

212 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14519712	C₂	1	4	yes	maximal
2	#16839786	C₂	1	1	yes	maximal, characteristic
3	C₂×#14519688	C₂	1	1	yes	maximal, characteristic
4	C₆₁×#423	C₂	1	1	yes	maximal, characteristic
5	C₂×#11758194	C₂²	1	2	yes	—
6	C₂²×#92418	C₂²	1	2	yes	—
7	#14519712	—	2	8	no	—
8	C₄⋊#92418	—	2	2	no	—
9	#14519688	C₄	1	4	yes	—
10	C₂×M₁₆×C₆₁	C₂²	1	2	yes	—
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	C₄⋊C₈×C₆₁	—	2	2	no	—
13	C₂²×C₄×C₆₁	Q₈	1	2	yes	—
14	C₂²×C₄×C₆₁	C₂³	1	1	yes	characteristic
15	M₁₆×C₆₁	—	2	4	no	—
16	C₂×C₈×C₆₁	—	2	2	no	—
17	C₄²×C₆₁	C₂×C₄	1	2	yes	—
18	C₄²×C₆₁	D₄	1	2	yes	—
19	#11758194	—	2	4	no	—
20	C₂×#92418	—	2	2	no	—
21	C₂×#92418	C₂×C₄	1	4	yes	—
22	C₂×#92418	D₄	1	4	yes	—
23	C₂×#92418	Q₈	1	4	yes	—
24	C₂³×C₆₁	C₂×Q₈	1	1	yes	characteristic
25	C₂×C₄×C₆₁	—	4	2	no	—
26	C₂×C₄×C₆₁	C₄⋊C₄	1	4	yes	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×C₄×C₆₁	C₂×D₄	1	2	yes	—
29	C₂×C₄×C₆₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₂×Q₈	1	2	yes	—
31	C₈×C₆₁	—	4	2	no	—
32	#92418	—	4	2	no	—
33	#92418	C₄⋊C₄	1	8	yes	—
34	C₂²×C₆₁	—	2	2	no	—
35	C₂²×C₆₁	C₂×C₄⋊C₄	1	1	yes	characteristic
36	C₂²×C₆₁	C₄⋊Q₈	1	2	yes	—
37	C₄×C₆₁	—	2	4	no	—
38	C₄×C₆₁	C₂×C₄⋊C₄	1	2	yes	—
39	C₄×C₆₁	#127	1	1	yes	characteristic
40	C₄×C₆₁	C₄⋊Q₈	1	1	yes	characteristic
41	#1849	—	61	1	no	maximal, Sylow
42	C₂×C₆₁	—	2	2	no	—
43	C₂×C₆₁	#384	1	1	yes	characteristic
44	C₂×C₆₁	#430	1	2	yes	—
45	C₂×#108	—	61	4	no	—
46	#423	—	61	1	no	—
47	#423	D₆₁	1	1	yes	characteristic
48	C₂×#97	—	61	1	no	—
49	C₆₁	#1849	1	1	yes	characteristic, complemented, Sylow
50	C₂×M₁₆	—	61	2	no	—
51	C₂×M₁₆	C₂×D₆₁	1	2	yes	—
52	C₂²×C₈	—	61	2	no	—
53	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
54	#108	—	122	8	no	—
55	C₄⋊C₈	—	2	2	no	—
56	C₄⋊C₈	—	122	2	no	—
57	#97	—	61	4	no	—
58	C₂²×C₄	Dic₁₂₂	1	2	yes	—
59	C₂²×C₄	C₂²×D₆₁	1	1	yes	characteristic
60	M₁₆	—	2	4	no	—
61	M₁₆	—	122	4	no	—
62	C₂×C₈	—	2	2	no	—
63	C₂×C₈	—	61	4	no	—
64	C₂×C₈	—	61	4	no	—
65	C₂×C₈	—	61	4	no	—
66	C₂×C₈	—	122	2	no	—
67	C₄²	C₄×D₆₁	1	2	yes	—
68	C₄²	C₂²⋊D₆₁	1	2	yes	—
69	C₂³	C₂×Dic₁₂₂	1	1	yes	characteristic
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	#11758196	1	4	yes	—
72	C₂×C₄	C₂×C₄×D₆₁	1	1	yes	characteristic
73	C₂×C₄	D₄×D₆₁	1	2	yes	—
74	C₂×C₄	Q₈×D₆₁	1	2	yes	—
75	C₂×C₄	C₂×C₂²⋊D₆₁	1	1	yes	characteristic
76	C₈	—	4	2	no	—
77	C₈	—	61	8	no	—
78	C₈	—	244	2	no	—
79	C₂²	—	2	2	no	—
80	C₂²	C₂×#11758196	1	1	yes	characteristic
81	C₂²	#14519776	1	2	yes	—
82	C₄	—	2	4	no	—
83	C₄	C₄⋊C₄×D₆₁	1	2	yes	—
84	C₄	#14519773	1	1	yes	characteristic
85	C₄	#14519775	1	1	yes	characteristic
86	C₂	—	2	2	no	—
87	C₂	#16839631	1	1	yes	characteristic
88	C₂	#16839810	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₆₁
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₆₁
Fitting	C₆₁×#423	C₂
socle	C₂²×C₆₁	C₂×C₄⋊C₄
hypercenter	#423	D₆₁
hypocenter	C₆₁	#1849
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #423

Complements

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

N	H ≅ G/N	type
49. C₆₁	#1849	semidirect