Subgroups — #21462190

Order 7808.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16840684	C₂	1	2	yes	maximal, complemented
2	#16840659	C₂	1	2	yes	maximal
3	#16840654	C₂	1	2	yes	maximal, complemented
4	#16839714	C₂	1	1	yes	maximal, characteristic
5	#14519851	C₂²	1	4	yes	—
6	C₂×#11758189	C₄	1	1	yes	characteristic
7	C₂×#11758189	C₂²	1	1	yes	characteristic
8	C₄²×D₆₁	C₄	1	1	yes	characteristic
9	#14519688	C₂²	1	1	yes	characteristic
10	C₈×Dic₆₁	C₄	1	1	yes	characteristic
11	C₈×Dic₆₁	C₂²	1	1	yes	characteristic
12	#97×C₆₁	C₄	1	1	yes	characteristic
13	C₂×C₄×D₆₁	—	2	1	no	—
14	C₂×C₄×D₆₁	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
16	C₂×C₈×C₆₁	C₂×C₄	1	1	yes	characteristic
17	C₄²×C₆₁	C₂×C₄	1	1	yes	characteristic
18	C₄×Dic₆₁	—	2	1	no	—
19	C₄×Dic₆₁	C₂×C₄	1	1	yes	characteristic
20	C₂×#92418	C₂×C₄	1	1	yes	characteristic
21	C₂×#92418	C₂³	1	1	yes	characteristic
22	#11758189	—	2	2	no	—
23	#11758189	—	2	2	no	—
24	#11758187	—	2	4	no	—
25	C₂²×D₆₁	M₁₆	1	1	yes	characteristic
26	C₂×C₄×C₆₁	—	2	1	no	—
27	C₂×C₄×C₆₁	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₆₁	—	2	1	no	—
29	C₂×Dic₆₁	M₁₆	1	1	yes	characteristic
30	C₄×D₆₁	—	2	1	no	—
31	C₄×D₆₁	—	2	1	no	—
32	C₄×D₆₁	—	4	2	no	—
33	C₈×C₆₁	—	2	1	no	—
34	C₈×C₆₁	M₁₆	1	2	yes	—
35	#92418	—	2	1	no	—
36	#92418	#41	1	2	yes	—
37	C₂²×C₆₁	C₂×M₁₆	1	1	yes	characteristic
38	C₂×D₆₁	—	2	1	no	—
39	C₂×D₆₁	—	4	1	no	—
40	C₄×C₆₁	—	4	1	no	—
41	C₄×C₆₁	#117	1	1	yes	characteristic
42	C₄×C₆₁	C₂×M₁₆	1	1	yes	characteristic
43	Dic₆₁	—	2	2	no	—
44	Dic₆₁	—	2	1	no	—
45	#2165	—	61	1	no	maximal, Sylow
46	C₂×C₆₁	—	2	1	no	—
47	C₂×C₆₁	#432	1	1	yes	characteristic
48	D₆₁	—	4	1	no	—
49	C₄×M₁₆	—	61	1	no	—
50	#364	—	61	2	no	—
51	#349	—	61	2	no	—
52	#347	—	61	2	no	—
53	C₆₁	#2165	1	1	yes	characteristic, complemented, Sylow
54	C₂×M₁₆	—	61	1	no	—
55	C₂×M₁₆	—	61	1	no	—
56	C₂×C₄²	—	61	1	no	—
57	M₃₂	—	61	4	no	—
58	#97	—	61	1	no	—
59	#97	#6923	1	1	yes	characteristic
60	C₄×C₈	—	61	1	no	—
61	C₄×C₈	—	61	1	no	—
62	C₂²×C₄	—	61	1	no	—
63	C₂²×C₄	—	122	1	no	—
64	M₁₆	—	122	2	no	—
65	M₁₆	—	122	2	no	—
66	C₂×C₈	—	61	1	no	—
67	C₂×C₈	—	61	1	no	—
68	C₂×C₈	C₂×#6923	1	1	yes	characteristic
69	C₂×C₈	C₂×#6923	1	1	yes	characteristic
70	C₄²	—	61	1	no	—
71	C₄²	—	122	1	no	—
72	C₄²	C₂×#6923	1	1	yes	characteristic
73	C₁₆	—	122	4	no	—
74	C₂³	—	61	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	61	1	no	—
77	C₂×C₄	—	122	1	no	—
78	C₂×C₄	—	122	1	no	—
79	C₂×C₄	—	122	1	no	—
80	C₂×C₄	—	244	2	no	—
81	C₂×C₄	C₂²×#6923	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	61	2	no	—
84	C₈	—	122	1	no	—
85	C₈	#11758213	1	2	yes	—
86	C₂²	—	122	1	no	—
87	C₂²	—	244	1	no	—
88	C₂²	D₆₁⋊M₁₆	1	1	yes	characteristic
89	C₄	—	4	1	no	—
90	C₄	—	122	2	no	—
91	C₄	—	122	1	no	—
92	C₄	#14519856	1	1	yes	characteristic
93	C₄	C₂×#11758213	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	244	1	no	—
96	C₂	#16840784	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14519856
commutator	C₂×C₄×C₆₁	C₂²×C₄
Frattini	C₂×C₄	C₂²×#6923
Fitting	#97×C₆₁	C₄
socle	C₂×C₆₁	#432
hypercenter	#97	#6923
hypocenter	C₆₁	#2165
LCS	G ▷ C₂×C₄×C₆₁ ▷ C₂×C₆₁ ▷ C₆₁
UCS	C₁ ◁ C₄ ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
1. #16840684	C₂	semidirect
3. #16840654	C₂	semidirect
53. C₆₁	#2165	semidirect