Subgroups — #37570509

Order 24448.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27132921	C₂	1	1	yes	maximal, characteristic
2	#27132420	C₂	1	1	yes	maximal, characteristic
3	#349×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₆₄	C₄	1	1	yes	characteristic, complemented
5	#20259301	—	2	1	no	—
6	#20259281	—	2	1	no	—
7	#20259254	C₄	1	1	yes	characteristic, complemented
8	#20259247	—	2	1	no	—
9	C₂×M₁₆×C₁₉₁	C₂²	1	1	yes	characteristic
10	M₃₂×C₁₉₁	—	2	1	no	—
11	C₂×Dic₃₈₂	—	2	1	no	—
12	Dic₇₆₄	—	4	1	no	—
13	C₄⋊Dic₁₉₁	—	2	1	no	—
14	C₄⋊Dic₁₉₁	—	4	1	no	—
15	Dic₁₉₁⋊C₄	—	4	1	no	—
16	C₂²⋊Dic₁₉₁	—	4	1	no	—
17	C₂²⋊Dic₁₉₁	—	4	1	no	—
18	C₄×Dic₁₉₁	—	2	2	no	—
19	C₂²×C₄×C₁₉₁	D₄	1	1	yes	characteristic
20	M₁₆×C₁₉₁	—	4	1	no	—
21	C₂×C₈×C₁₉₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
23	C₁₆×C₁₉₁	—	4	1	no	—
24	Dic₃₈₂	—	4	1	no	—
25	Dic₃₈₂	—	4	1	no	—
26	C₂×Dic₁₉₁	—	4	2	no	—
27	C₂×Dic₁₉₁	—	4	1	no	—
28	C₂×Dic₁₉₁	—	4	1	no	—
29	C₂³×C₁₉₁	D₈	1	1	yes	characteristic
30	C₂×C₄×C₁₉₁	—	2	1	no	—
31	C₂×C₄×C₁₉₁	—	2	1	no	—
32	C₂×C₄×C₁₉₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₁₉₁	SD₁₆	1	1	yes	characteristic
34	C₈×C₁₉₁	—	2	1	no	—
35	C₈×C₁₉₁	—	2	1	no	—
36	C₂²×C₁₉₁	—	2	1	no	—
37	C₂²×C₁₉₁	—	4	1	no	—
38	C₂²×C₁₉₁	#102	1	1	yes	characteristic
39	C₄×C₁₉₁	—	2	1	no	—
40	C₄×C₁₉₁	#99	1	1	yes	characteristic
41	C₄×C₁₉₁	#104	1	1	yes	characteristic
42	Dic₁₉₁	—	8	1	no	—
43	Dic₁₉₁	—	8	2	no	—
44	Dic₁₉₁	—	8	1	no	—
45	C₂×C₁₉₁	—	2	1	no	—
46	C₂×C₁₉₁	—	4	1	no	—
47	C₂×C₁₉₁	#327	1	1	yes	characteristic
48	C₁₉₁	#1340	1	1	yes	characteristic, complemented, Sylow
49	#1340	—	191	1	no	maximal, Sylow
50	#470	—	191	1	no	—
51	#349	D₁₉₁	1	1	yes	characteristic
52	H(3,ℤ/4)	—	191	1	no	—
53	C₂×Q₁₆	—	191	1	no	—
54	C₂×M₁₆	C₂×D₁₉₁	1	1	yes	characteristic
55	C₂²⋊Q₈	—	382	1	no	—
56	#117	—	382	1	no	—
57	M₃₂	—	2	1	no	—
58	#106	—	191	1	no	—
59	#103	—	382	1	no	—
60	C₂×Q₈	—	382	1	no	—
61	C₂²×C₄	D₇₆₄	1	1	yes	characteristic
62	Q₁₆	—	764	1	no	—
63	M₁₆	—	4	1	no	—
64	C₂×C₈	C₄×D₁₉₁	1	1	yes	characteristic
65	C₂×C₈	C₂²⋊D₁₉₁	1	1	yes	characteristic
66	C₄⋊C₄	—	382	1	no	—
67	C₄⋊C₄	—	764	1	no	—
68	C₄⋊C₄	—	764	1	no	—
69	C₂²⋊C₄	—	764	1	no	—
70	C₂²⋊C₄	—	764	1	no	—
71	C₄²	—	382	2	no	—
72	C₁₆	—	4	1	no	—
73	C₂³	D₁₅₂₈	1	1	yes	characteristic
74	Q₈	—	764	1	no	—
75	Q₈	—	764	1	no	—
76	C₂×C₄	—	2	1	no	—
77	C₂×C₄	—	2	1	no	—
78	C₂×C₄	—	764	2	no	—
79	C₂×C₄	—	764	1	no	—
80	C₂×C₄	—	764	1	no	—
81	C₂×C₄	(C₂×D₁₉₁)⋊C₄	1	1	yes	characteristic
82	C₂×C₄	#15690276	1	1	yes	characteristic
83	C₈	—	2	1	no	—
84	C₈	—	2	1	no	—
85	C₂²	—	2	1	no	—
86	C₂²	—	4	1	no	—
87	C₂²	#20259244	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	1528	1	no	—
90	C₄	—	1528	2	no	—
91	C₄	—	1528	1	no	—
92	C₄	#20259236	1	1	yes	characteristic
93	C₄	#20259248	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	4	1	no	—
96	C₂	#27132398	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#27132398
commutator	C₂×C₈×C₁₉₁	C₂×C₄
Frattini	C₂×M₁₆	C₂×D₁₉₁
Fitting	#349×C₁₉₁	C₂
socle	C₂×C₁₉₁	#327
prime radical	C₂³×C₁₉₁	D₈
cosocle	C₂×M₁₆×C₁₉₁	C₂²
hypercenter	#349	D₁₉₁
hypocenter	C₁₉₁	#1340
LCS	G ▷ C₂×C₈×C₁₉₁ ▷ C₂×C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×M₁₆ ◁ #349

Complements

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

N	H ≅ G/N	type
4. C₂×Dic₇₆₄	C₄	semidirect
7. #20259254	C₄	semidirect
48. C₁₉₁	#1340	semidirect

Maximal subgroups

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

subgroup	index
#27132921	2
#27132420	2
#349×C₁₉₁	2
#1340	191