Subgroups — #37570353

Order 24448.

208 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27132716	C₂	1	2	yes	maximal
2	C₄³×C₁₉₁	C₂	1	1	yes	maximal, characteristic
3	C₄⋊(C₁₉₁⋊C₈)	C₄	1	4	yes	complemented
4	C₂²⋊(C₁₉₁⋊C₈)	—	2	2	no	—
5	C₄×C₁₉₁⋊C₈	—	2	2	no	—
6	C₂×C₄²×C₁₉₁	—	2	2	no	—
7	C₂×C₄²×C₁₉₁	C₄	1	2	yes	—
8	C₂×C₄²×C₁₉₁	C₂²	1	1	yes	characteristic
9	C₂×C₁₉₁⋊C₈	—	2	4	no	—
10	C₂²×C₄×C₁₉₁	—	2	2	no	—
11	C₂²×C₄×C₁₉₁	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₁₉₁	D₄	1	2	yes	—
13	C₄²×C₁₉₁	—	2	8	no	—
14	C₄²×C₁₉₁	—	2	2	no	—
15	C₄²×C₁₉₁	C₈	1	4	yes	complemented
16	C₄²×C₁₉₁	C₂×C₄	1	2	yes	—
17	C₄²×C₁₉₁	D₄	1	1	yes	characteristic
18	C₄²×C₁₉₁	Q₈	1	1	yes	characteristic
19	C₁₉₁⋊C₈	—	4	4	no	—
20	C₂³×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₁₉₁	—	2	8	no	—
22	C₂×C₄×C₁₉₁	—	2	4	no	—
23	C₂×C₄×C₁₉₁	—	2	4	no	—
24	C₂×C₄×C₁₉₁	C₄²	1	1	yes	characteristic
25	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	2	yes	—
26	C₂×C₄×C₁₉₁	C₄⋊C₄	1	2	yes	—
27	C₂×C₄×C₁₉₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₉₁	C₂×C₈	1	2	yes	—
29	C₂×C₄×C₁₉₁	M₁₆	1	2	yes	—
30	C₂²×C₁₉₁	—	2	2	no	—
31	C₂²×C₁₉₁	#95	1	1	yes	characteristic
32	C₂²×C₁₉₁	C₂²⋊C₈	1	2	yes	—
33	C₄×C₁₉₁	—	2	8	no	—
34	C₄×C₁₉₁	—	2	2	no	—
35	C₄×C₁₉₁	C₄×C₈	1	1	yes	characteristic
36	C₄×C₁₉₁	#97	1	1	yes	characteristic
37	C₄×C₁₉₁	#104	1	4	yes	—
38	C₄×C₁₉₁	C₄⋊C₈	1	2	yes	—
39	C₂×C₁₉₁	—	2	2	no	—
40	C₂×C₁₉₁	#336	1	1	yes	characteristic
41	C₂×C₁₉₁	#339	1	2	yes	—
42	C₁₉₁	#1276	1	1	yes	characteristic, complemented, Sylow
43	#1276	—	191	1	no	maximal, Sylow
44	#431	—	191	2	no	—
45	C₄³	D₁₉₁	1	1	yes	characteristic
46	C₂×C₄²	—	2	2	no	—
47	C₂×C₄²	Dic₁₉₁	1	2	yes	—
48	C₂×C₄²	C₂×D₁₉₁	1	1	yes	characteristic
49	C₄⋊C₈	—	191	4	no	—
50	C₂²⋊C₈	—	382	2	no	—
51	C₄×C₈	—	382	2	no	—
52	C₂²×C₄	—	2	2	no	—
53	C₂²×C₄	C₂×Dic₁₉₁	1	1	yes	characteristic
54	C₂²×C₄	C₂²⋊D₁₉₁	1	2	yes	—
55	C₂×C₈	—	382	4	no	—
56	C₄²	—	2	8	no	—
57	C₄²	—	2	2	no	—
58	C₄²	C₁₉₁⋊C₈	1	4	yes	complemented
59	C₄²	C₄×D₁₉₁	1	2	yes	—
60	C₄²	D₇₆₄	1	1	yes	characteristic
61	C₄²	Dic₃₈₂	1	1	yes	characteristic
62	C₂³	C₂²⋊Dic₁₉₁	1	1	yes	characteristic
63	C₂×C₄	—	2	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	4	no	—
66	C₂×C₄	C₄×Dic₁₉₁	1	1	yes	characteristic
67	C₂×C₄	(C₂×D₁₉₁)⋊C₄	1	2	yes	—
68	C₂×C₄	Dic₁₉₁⋊C₄	1	2	yes	—
69	C₂×C₄	C₄⋊Dic₁₉₁	1	1	yes	characteristic
70	C₂×C₄	C₂×C₁₉₁⋊C₈	1	2	yes	—
71	C₂×C₄	#15690271	1	2	yes	—
72	C₈	—	764	4	no	—
73	C₂²	—	2	2	no	—
74	C₂²	C₁₉₁⋊#95	1	1	yes	characteristic
75	C₂²	C₂²⋊(C₁₉₁⋊C₈)	1	2	yes	—
76	C₄	—	2	8	no	—
77	C₄	—	2	2	no	—
78	C₄	C₄×C₁₉₁⋊C₈	1	1	yes	characteristic
79	C₄	#20259233	1	1	yes	characteristic
80	C₄	#20259250	1	4	yes	—
81	C₄	C₄⋊(C₁₉₁⋊C₈)	1	2	yes	—
82	C₂	—	2	2	no	—
83	C₂	#27132418	1	1	yes	characteristic
84	C₂	#27132423	1	2	yes	—

	subgroup	G/H
center	C₄²	D₇₆₄
commutator	C₄×C₁₉₁	C₄×C₈
Frattini	C₂×C₄²	C₂×D₁₉₁
Fitting	C₄³×C₁₉₁	C₂
socle	C₂²×C₁₉₁	#95
prime radical	C₂³×C₁₉₁	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉₁	C₂²
hypercenter	C₄³	D₁₉₁
hypocenter	C₁₉₁	#1276
LCS	G ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄³

Complements

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

N	H ≅ G/N	type
3. C₄⋊(C₁₉₁⋊C₈)	C₄	semidirect
15. C₄²×C₁₉₁	C₈	semidirect
42. C₁₉₁	#1276	semidirect
58. C₄²	C₁₉₁⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#27132716	2
C₄³×C₁₉₁	2
#1276	191