Subgroups — #37574407

Order 24448.

144 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27133095	C₂	1	1	yes	maximal, characteristic
2	#27132781	C₂	1	2	yes	maximal, complemented
3	#27132493	C₂	1	1	yes	maximal, characteristic, complemented
4	#27132471	C₂	1	2	yes	maximal, complemented
5	#346×C₁₉₁	C₂	1	1	yes	maximal, characteristic, complemented
6	#20259344	C₂²	1	2	yes	—
7	#20259328	—	2	2	no	—
8	Dic₁₅₂₈	C₄	1	1	yes	characteristic, complemented
9	#20259267	C₄	1	2	yes	complemented
10	D₃₀₅₆	C₄	1	1	yes	characteristic, complemented
11	#20259258	C₂²	1	2	yes	—
12	#20259250	—	2	2	no	—
13	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
15	C₄×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
16	#15690287	—	2	2	no	—
17	Dic₇₆₄	C₂×C₄	1	2	yes	—
18	#15690276	—	2	2	no	—
19	D₁₅₂₈	C₂×C₄	1	2	yes	—
20	#15690271	—	2	2	no	—
21	#15690270	—	4	2	no	—
22	C₈×D₁₉₁	—	4	2	no	—
23	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
24	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
25	C₄²×C₁₉₁	D₄	1	1	yes	characteristic
26	C₁₆×C₁₉₁	—	2	1	no	—
27	C₁₆×C₁₉₁	C₂×C₄	1	1	yes	characteristic
28	C₁₆×C₁₉₁	C₂×C₄	1	1	yes	characteristic
29	Dic₃₈₂	—	2	2	no	—
30	D₇₆₄	—	2	2	no	—
31	C₂²⋊D₁₉₁	—	4	2	no	—
32	C₄×D₁₉₁	—	4	2	no	—
33	C₁₉₁⋊C₈	—	4	2	no	—
34	C₂×C₄×C₁₉₁	—	2	1	no	—
35	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
36	C₈×C₁₉₁	D₈	1	2	yes	—
37	C₈×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
38	C₈×C₁₉₁	#41	1	1	yes	characteristic
39	C₂²×C₁₉₁	#135	1	1	yes	characteristic
40	C₂×D₁₉₁	—	4	2	no	—
41	C₄×C₁₉₁	—	4	1	no	—
42	C₄×C₁₉₁	C₄×D₄	1	1	yes	characteristic
43	C₄×C₁₉₁	C₂×D₈	1	1	yes	characteristic
44	Dic₁₉₁	—	4	2	no	—
45	C₂×C₁₉₁	—	2	1	no	—
46	C₂×C₁₉₁	C₄×D₈	1	1	yes	characteristic
47	D₁₉₁	—	8	2	no	—
48	C₁₉₁	#2179	1	1	yes	characteristic, complemented, Sylow
49	#2179	—	191	1	no	maximal, Sylow
50	#508	—	191	1	no	—
51	#443	—	191	2	no	—
52	#368	—	191	1	no	—
53	#359	—	191	2	no	—
54	#346	D₁₉₁	1	1	yes	characteristic, complemented
55	#135	—	191	2	no	—
56	#131	—	382	2	no	—
57	Q₃₂	—	191	1	no	—
58	SD₃₂	—	191	2	no	—
59	D₁₆	—	191	1	no	—
60	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
61	C₂×C₁₆	C₂×D₁₉₁	1	1	yes	characteristic
62	#108	—	191	2	no	—
63	#104	—	382	2	no	—
64	C₄×C₈	C₂×D₁₉₁	1	1	yes	characteristic
65	#41	—	382	2	no	—
66	Q₁₆	—	191	2	no	—
67	SD₁₆	—	382	2	no	—
68	D₈	—	191	2	no	—
69	M₁₆	—	382	2	no	—
70	M₁₆	—	764	2	no	—
71	C₂×C₈	—	764	2	no	—
72	C₂×C₈	D₇₆₄	1	1	yes	characteristic
73	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
74	C₄²	D₇₆₄	1	1	yes	characteristic
75	C₁₆	—	2	1	no	—
76	C₁₆	C₄×D₁₉₁	1	1	yes	characteristic
77	C₁₆	C₄×D₁₉₁	1	1	yes	characteristic
78	Q₈	—	382	2	no	—
79	D₄	—	382	2	no	—
80	D₄	—	764	2	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	764	2	no	—
83	C₂×C₄	C₂×D₇₆₄	1	1	yes	characteristic
84	C₈	—	764	2	no	—
85	C₈	D₁₅₂₈	1	2	yes	—
86	C₈	C₂×C₄×D₁₉₁	1	1	yes	characteristic
87	C₈	#15690287	1	1	yes	characteristic
88	C₂²	—	764	2	no	—
89	C₂²	#20259344	1	1	yes	characteristic
90	C₄	—	4	1	no	—
91	C₄	—	764	2	no	—
92	C₄	C₄×D₇₆₄	1	1	yes	characteristic
93	C₄	C₂×D₁₅₂₈	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	1528	2	no	—
96	C₂	C₄×D₁₅₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₅₂₈
commutator	C₈×C₁₉₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉₁
Fitting	#346×C₁₉₁	C₂
socle	C₂×C₁₉₁	C₄×D₈
prime radical	#27133095	C₂
cosocle	C₂×C₈×C₁₉₁	C₂³
hypercenter	#346	D₁₉₁
hypocenter	C₁₉₁	#2179
LCS	G ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈ ◁ #346

Complements

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

N	H ≅ G/N	type
2. #27132781	C₂	semidirect
3. #27132493	C₂	semidirect
4. #27132471	C₂	semidirect
5. #346×C₁₉₁	C₂	semidirect
8. Dic₁₅₂₈	C₄	semidirect
9. #20259267	C₄	semidirect
10. D₃₀₅₆	C₄	semidirect
48. C₁₉₁	#2179	semidirect
54. #346	D₁₉₁	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#27133095	2
#27132781	2
#27132493	2
#27132471	2
#346×C₁₉₁	2
#2179	191