Subgroups — #21444122

Order 7808.

214 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11758194	C₂	1	2	yes	maximal
2	#16839484	C₂	1	2	yes	maximal, complemented
3	#16839483	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#92418	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×M₁₆×C₆₁	C₂	1	1	yes	maximal, characteristic
6	C₂×#11758194	C₄	1	4	yes	—
7	#14519688	C₄	1	4	yes	—
8	C₄×#92418	C₂²	1	2	yes	—
9	C₄×#92418	C₂²	1	2	yes	—
10	C₂×M₁₆×C₆₁	C₄	1	2	yes	—
11	C₂×C₄²×C₆₁	C₂²	1	1	yes	characteristic
12	#97×C₆₁	C₄	1	2	yes	—
13	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
14	C₄×C₈×C₆₁	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₆₁	C₂×C₄	1	2	yes	—
16	C₂²×C₄×C₆₁	C₂×C₄	1	1	yes	characteristic
17	M₁₆×C₆₁	—	2	4	no	—
18	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
19	C₂×C₈×C₆₁	C₂×C₄	1	2	yes	—
20	C₄²×C₆₁	C₂×C₄	1	2	yes	—
21	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
22	C₄²×C₆₁	C₂³	1	1	yes	characteristic
23	#11758194	—	2	8	no	—
24	C₂×#92418	C₂×C₄	1	4	yes	—
25	C₂×#92418	C₂×C₄	1	4	yes	—
26	C₂³×C₆₁	C₄²	1	1	yes	characteristic
27	C₂×C₄×C₆₁	—	2	4	no	—
28	C₂×C₄×C₆₁	—	2	2	no	—
29	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₆₁	C₄²	1	2	yes	—
31	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₆₁	—	2	2	no	—
34	C₈×C₆₁	M₁₆	1	4	yes	complemented
35	#92418	—	2	4	no	—
36	#92418	M₁₆	1	8	yes	complemented
37	C₂²×C₆₁	—	2	2	no	—
38	C₂²×C₆₁	—	2	1	no	—
39	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
40	C₄×C₆₁	—	2	2	no	—
41	C₄×C₆₁	—	2	1	no	—
42	C₄×C₆₁	C₂×M₁₆	1	4	yes	—
43	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
44	#1455	—	61	1	no	maximal, Sylow
45	C₂×C₆₁	—	4	1	no	—
46	C₂×C₆₁	C₄×M₁₆	1	2	yes	—
47	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
48	C₄×M₁₆	—	61	2	no	—
49	C₄×M₁₆	D₆₁	1	1	yes	characteristic
50	#322	—	61	1	no	—
51	#322	—	61	2	no	—
52	C₈²	—	61	1	no	—
53	C₆₁	#1455	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	61	4	no	—
55	C₂×M₁₆	Dic₆₁	1	2	yes	—
56	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
57	#97	—	61	4	no	—
58	#97	Dic₆₁	1	2	yes	—
59	C₄×C₈	—	61	2	no	—
60	C₄×C₈	—	61	2	no	—
61	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
63	C₂²×C₄	C₄×D₆₁	1	2	yes	—
64	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
65	M₁₆	—	2	4	no	—
66	M₁₆	—	122	8	no	—
67	C₂×C₈	—	61	4	no	—
68	C₂×C₈	—	61	4	no	—
69	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
70	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
71	C₄²	C₄×D₆₁	1	2	yes	—
72	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
73	C₄²	C₂²×D₆₁	1	1	yes	characteristic
74	C₂³	C₄×Dic₆₁	1	1	yes	characteristic
75	C₂×C₄	—	2	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
78	C₂×C₄	C₄×Dic₆₁	1	2	yes	—
79	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
80	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	61	8	no	—
83	C₈	—	122	4	no	—
84	C₈	#11758194	1	4	yes	complemented
85	C₂²	—	2	2	no	—
86	C₂²	—	2	1	no	—
87	C₂²	C₂×C₄×Dic₆₁	1	1	yes	characteristic
88	C₄	—	2	2	no	—
89	C₄	—	2	1	no	—
90	C₄	M₁₆×D₆₁	1	4	yes	—
91	C₄	C₂×#11758194	1	2	yes	—
92	C₂	—	4	1	no	—
93	C₂	M₁₆×Dic₆₁	1	2	yes	—
94	C₂	C₄×#11758194	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂²×D₆₁
commutator, socle	C₂²×C₆₁	C₂×C₄²
Fitting	C₄×M₁₆×C₆₁	C₂
hypercenter	C₄×M₁₆	D₆₁
hypocenter	C₆₁	#1455
LCS	G ▷ C₂²×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄² ◁ C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #16839484	C₂	semidirect
3. #16839483	C₂	semidirect
4. C₈×#92418	C₂	semidirect
34. C₈×C₆₁	M₁₆	semidirect
36. #92418	M₁₆	semidirect
53. C₆₁	#1455	semidirect
84. C₈	#11758194	semidirect