Subgroups — #21444116

Order 7808.

190 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16839815	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	C₄⋊#92418	C₄	1	4	yes	—
7	C₂²⋊#92418	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	C₂×#92418	C₂×C₄	1	4	yes	—
24	C₂×#92418	C₂×C₄	1	4	yes	—
25	C₂³×C₆₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	2	2	no	—
27	C₂×C₄×C₆₁	—	2	4	no	—
28	C₂×C₄×C₆₁	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₆₁	C₄²	1	2	yes	—
30	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₄×C₆₁	C₂²×C₄	1	2	yes	—
32	C₈×C₆₁	—	2	2	no	—
33	C₈×C₆₁	M₁₆	1	4	yes	—
34	#92418	—	2	4	no	—
35	#92418	—	2	4	no	—
36	C₂²×C₆₁	—	2	1	no	—
37	C₂²×C₆₁	—	2	2	no	—
38	C₂²×C₆₁	C₂×C₄²	1	1	yes	characteristic
39	C₄×C₆₁	—	2	1	no	—
40	C₄×C₆₁	—	2	2	no	—
41	C₄×C₆₁	C₂×M₁₆	1	2	yes	—
42	C₄×C₆₁	#131	1	4	yes	—
43	#1453	—	61	1	no	maximal, Sylow
44	C₂×C₆₁	—	4	1	no	—
45	C₂×C₆₁	C₄×M₁₆	1	1	yes	characteristic
46	C₂×C₆₁	#405	1	2	yes	—
47	#431	—	61	2	no	—
48	C₄×M₁₆	D₆₁	1	1	yes	characteristic
49	#322	—	61	1	no	—
50	#322	—	61	2	no	—
51	C₈²	—	61	1	no	—
52	C₆₁	#1453	1	1	yes	characteristic, complemented, Sylow
53	C₂×M₁₆	Dic₆₁	1	2	yes	—
54	C₂×C₄²	C₂×D₆₁	1	1	yes	characteristic
55	C₄⋊C₈	—	61	4	no	—
56	C₂²⋊C₈	—	61	4	no	—
57	#97	Dic₆₁	1	2	yes	—
58	C₄×C₈	—	61	2	no	—
59	C₄×C₈	—	61	2	no	—
60	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
61	C₄×C₈	C₂×D₆₁	1	1	yes	characteristic
62	C₂²×C₄	C₄×D₆₁	1	2	yes	—
63	C₂²×C₄	C₂×Dic₆₁	1	1	yes	characteristic
64	M₁₆	—	2	4	no	—
65	C₂×C₈	—	61	4	no	—
66	C₂×C₈	—	61	4	no	—
67	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
68	C₂×C₈	C₂×Dic₆₁	1	2	yes	—
69	C₄²	C₄×D₆₁	1	2	yes	—
70	C₄²	C₂×Dic₆₁	1	1	yes	characteristic
71	C₄²	C₂²×D₆₁	1	1	yes	characteristic
72	C₂³	C₄×Dic₆₁	1	1	yes	characteristic
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	4	no	—
75	C₂×C₄	C₄×Dic₆₁	1	1	yes	characteristic
76	C₂×C₄	C₄×Dic₆₁	1	2	yes	—
77	C₂×C₄	C₂×C₄×D₆₁	1	2	yes	—
78	C₂×C₄	C₂²×Dic₆₁	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	—	122	4	no	—
81	C₈	—	122	4	no	—
82	C₈	#11758194	1	4	yes	—
83	C₂²	—	2	1	no	—
84	C₂²	—	2	2	no	—
85	C₂²	C₂×C₄×Dic₆₁	1	1	yes	characteristic
86	C₄	—	2	1	no	—
87	C₄	—	2	2	no	—
88	C₄	C₂×#11758194	1	2	yes	—
89	C₄	#14519785	1	4	yes	—
90	C₂	—	4	1	no	—
91	C₂	C₄×#11758194	1	1	yes	characteristic
92	C₂	#16839720	1	2	yes	—

	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	#1453
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
52. C₆₁	#1453	semidirect