Subgroups — C₂×#27132489 #37574297

Order 24448.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#20259256	C₂	1	2	yes	maximal
2	#27132489	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₁₉₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₁₉₁	—	2	2	no	—
5	#20259256	—	2	2	no	—
6	#20259256	C₂²	1	4	yes	—
7	C₂²×C₈×C₁₉₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₁₉₁	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₁₉₁	C₂²	1	2	yes	—
10	C₂²×Dic₁₉₁	—	4	2	no	—
11	C₄⋊Dic₁₉₁	—	2	4	no	—
12	C₄⋊Dic₁₉₁	—	4	2	no	—
13	C₂²×C₄×C₁₉₁	D₄	1	1	yes	characteristic
14	C₂×C₈×C₁₉₁	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₉₁	D₄	1	1	yes	characteristic
16	C₂×C₈×C₁₉₁	Q₈	1	2	yes	—
17	C₂×C₈×C₁₉₁	C₂³	1	1	yes	characteristic
18	C₁₆×C₁₉₁	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₁₉₁	—	4	4	no	—
20	C₂×Dic₁₉₁	—	8	4	no	—
21	C₂³×C₁₉₁	D₈	1	1	yes	characteristic
22	C₂×C₄×C₁₉₁	C₄⋊C₄	1	2	yes	—
23	C₂×C₄×C₁₉₁	D₈	1	1	yes	characteristic
24	C₂×C₄×C₁₉₁	Q₁₆	1	2	yes	—
25	C₂×C₄×C₁₉₁	C₂×D₄	1	1	yes	characteristic
26	C₈×C₁₉₁	C₄⋊C₄	1	2	yes	—
27	C₈×C₁₉₁	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₁₉₁	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₁₉₁	#107	1	2	yes	—
30	C₂²×C₁₉₁	D₁₆	1	2	yes	—
31	C₂²×C₁₉₁	Q₃₂	1	2	yes	—
32	C₂²×C₁₉₁	C₂×D₈	1	1	yes	characteristic
33	C₄×C₁₉₁	#107	1	2	yes	—
34	C₄×C₁₉₁	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₁₉₁	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₁₉₁	—	8	4	no	—
37	C₂×C₁₉₁	#366	1	4	yes	complemented
38	C₂×C₁₉₁	C₂×#107	1	1	yes	characteristic
39	C₂×C₁₉₁	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₁₉₁	C₂×Q₃₂	1	1	yes	characteristic
41	C₁₉₁	C₂×#366	1	1	yes	characteristic, complemented, Sylow
42	C₂×#366	—	191	1	no	maximal, Sylow
43	C₂²×C₁₆	D₁₉₁	1	1	yes	characteristic
44	C₂×#107	—	191	2	no	—
45	#366	—	191	4	no	—
46	C₂²×C₈	C₂×D₁₉₁	1	1	yes	characteristic
47	C₂×C₄⋊C₄	—	382	2	no	—
48	C₂×C₁₆	Dic₁₉₁	1	4	yes	complemented
49	C₂×C₁₆	C₂×D₁₉₁	1	2	yes	—
50	#107	—	382	2	no	—
51	#107	—	191	4	no	—
52	C₂²×C₄	—	764	2	no	—
53	C₂²×C₄	D₇₆₄	1	1	yes	characteristic
54	C₂×C₈	C₂×Dic₁₉₁	1	2	yes	—
55	C₂×C₈	D₇₆₄	1	1	yes	characteristic
56	C₂×C₈	Dic₃₈₂	1	2	yes	—
57	C₂×C₈	C₂²×D₁₉₁	1	1	yes	characteristic
58	C₄⋊C₄	—	382	4	no	—
59	C₄⋊C₄	—	764	2	no	—
60	C₁₆	C₂×Dic₁₉₁	1	4	yes	complemented
61	C₂³	D₁₅₂₈	1	1	yes	characteristic
62	C₂×C₄	—	1528	4	no	—
63	C₂×C₄	—	764	4	no	—
64	C₂×C₄	C₄⋊Dic₁₉₁	1	2	yes	—
65	C₂×C₄	D₁₅₂₈	1	1	yes	characteristic
66	C₂×C₄	Dic₇₆₄	1	2	yes	—
67	C₂×C₄	C₂×D₇₆₄	1	1	yes	characteristic
68	C₈	C₄⋊Dic₁₉₁	1	2	yes	—
69	C₈	C₂²×Dic₁₉₁	1	1	yes	characteristic
70	C₈	C₂×Dic₃₈₂	1	1	yes	characteristic
71	C₂²	#20259256	1	2	yes	—
72	C₂²	D₃₀₅₆	1	2	yes	—
73	C₂²	Dic₁₅₂₈	1	2	yes	—
74	C₂²	C₂×D₁₅₂₈	1	1	yes	characteristic
75	C₄	—	1528	4	no	—
76	C₄	#20259256	1	2	yes	—
77	C₄	C₂×C₄⋊Dic₁₉₁	1	1	yes	characteristic
78	C₄	C₂×Dic₇₆₄	1	1	yes	characteristic
79	C₂	#27132489	1	4	yes	direct product factor
80	C₂	C₂×#20259256	1	1	yes	characteristic
81	C₂	C₂×D₃₀₅₆	1	1	yes	characteristic
82	C₂	C₂×Dic₁₅₂₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₅₂₈
commutator	C₈×C₁₉₁	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₁₉₁
Fitting	C₂²×C₁₆×C₁₉₁	C₂
socle, prime radical	C₂³×C₁₉₁	D₈
cosocle	C₂×C₈×C₁₉₁	C₂³
hypercenter	C₂²×C₁₆	D₁₉₁
hypocenter	C₁₉₁	C₂×#366
LCS	G ▷ C₈×C₁₉₁ ▷ C₄×C₁₉₁ ▷ C₂×C₁₉₁ ▷ C₁₉₁
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #27132489	C₂	direct (N × H)
8. C₂×C₁₆×C₁₉₁	C₄	semidirect
18. C₁₆×C₁₉₁	C₂×C₄	semidirect
37. C₂×C₁₉₁	#366	semidirect
41. C₁₉₁	C₂×#366	semidirect
48. C₂×C₁₆	Dic₁₉₁	semidirect
60. C₁₆	C₂×Dic₁₉₁	semidirect
79. C₂	#27132489	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#20259256	2
#27132489	2
C₂²×C₁₆×C₁₉₁	2
C₂×#366	191

Subgroups — C2×#27132489 #37574297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#27132489 #37574297