Subgroups — C₂×#26044186 #37554178

Order 23488.

162 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₇₃₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃₆₇	C₂	1	1	yes	maximal, characteristic
3	#26044186	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₇₃₄	—	2	2	no	—
6	C₂×Dic₇₃₄	—	2	1	no	—
7	C₂×Dic₇₃₄	C₄	1	4	yes	complemented
8	C₂×Dic₇₃₄	C₂²	1	2	yes	—
9	C₂²×Dic₃₆₇	—	2	1	no	—
10	C₂²×Dic₃₆₇	—	2	1	no	—
11	C₄⋊Dic₃₆₇	—	2	1	no	—
12	C₄⋊Dic₃₆₇	C₂²	1	2	yes	—
13	C₂²×C₄×C₃₆₇	C₂²	1	1	yes	characteristic
14	C₂×C₈×C₃₆₇	—	2	2	no	—
15	C₂×C₈×C₃₆₇	C₂²	1	2	yes	—
16	Dic₇₃₄	—	2	4	no	—
17	Dic₇₃₄	—	2	2	no	—
18	Dic₇₃₄	C₂×C₄	1	4	yes	complemented
19	C₂×Dic₃₆₇	—	2	4	no	—
20	C₂×Dic₃₆₇	—	2	2	no	—
21	C₂×Dic₃₆₇	—	2	2	no	—
22	C₂×Dic₃₆₇	—	4	2	no	—
23	C₂³×C₃₆₇	D₄	1	1	yes	characteristic
24	C₂×C₄×C₃₆₇	C₂×C₄	1	2	yes	—
25	C₂×C₄×C₃₆₇	D₄	1	2	yes	—
26	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
27	C₂×C₄×C₃₆₇	C₂³	1	1	yes	characteristic
28	C₈×C₃₆₇	—	2	2	no	—
29	C₂²×C₃₆₇	C₂²⋊C₄	1	2	yes	—
30	C₂²×C₃₆₇	SD₁₆	1	2	yes	—
31	C₂²×C₃₆₇	Q₁₆	1	2	yes	—
32	C₂²×C₃₆₇	C₂×D₄	1	1	yes	characteristic
33	C₄×C₃₆₇	C₂²⋊C₄	1	2	yes	—
34	C₄×C₃₆₇	C₂²×C₄	1	1	yes	characteristic
35	C₄×C₃₆₇	C₂×D₄	1	1	yes	characteristic
36	Dic₃₆₇	—	2	4	no	—
37	Dic₃₆₇	—	4	2	no	—
38	C₂×C₃₆₇	#103	1	4	yes	complemented
39	C₂×C₃₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
40	C₂×C₃₆₇	C₂×SD₁₆	1	1	yes	characteristic
41	C₂×C₃₆₇	C₂×Q₁₆	1	1	yes	characteristic
42	C₃₆₇	C₂×#103	1	1	yes	characteristic, complemented, Sylow
43	C₂×#103	—	367	1	no	maximal, Sylow
44	C₂²×Q₈	—	367	1	no	—
45	C₂²×C₈	D₃₆₇	1	1	yes	characteristic
46	C₂×C₄⋊C₄	—	367	1	no	—
47	#103	—	367	4	no	—
48	C₂×Q₈	—	367	4	no	—
49	C₂×Q₈	—	367	2	no	—
50	C₂×Q₈	—	734	2	no	—
51	C₂×Q₈	—	734	1	no	—
52	C₂²×C₄	—	734	1	no	—
53	C₂²×C₄	—	734	1	no	—
54	C₂²×C₄	C₂×D₃₆₇	1	1	yes	characteristic
55	C₂×C₈	—	2	2	no	—
56	C₂×C₈	C₂×D₃₆₇	1	2	yes	—
57	C₄⋊C₄	—	367	2	no	—
58	C₄⋊C₄	—	734	1	no	—
59	C₂³	D₁₄₆₈	1	1	yes	characteristic
60	Q₈	—	367	4	no	—
61	Q₈	—	734	4	no	—
62	Q₈	—	734	2	no	—
63	C₂×C₄	—	1468	2	no	—
64	C₂×C₄	—	734	2	no	—
65	C₂×C₄	—	734	4	no	—
66	C₂×C₄	—	734	2	no	—
67	C₂×C₄	C₄×D₃₆₇	1	2	yes	—
68	C₂×C₄	C₂²⋊D₃₆₇	1	2	yes	—
69	C₂×C₄	D₁₄₆₈	1	1	yes	characteristic
70	C₂×C₄	C₂²×D₃₆₇	1	1	yes	characteristic
71	C₈	—	2	2	no	—
72	C₂²	(C₂×D₃₆₇)⋊C₄	1	2	yes	—
73	C₂²	#19154566	1	2	yes	—
74	C₂²	Dic₁₄₆₈	1	2	yes	—
75	C₂²	C₂×D₁₄₆₈	1	1	yes	characteristic
76	C₄	—	1468	2	no	—
77	C₄	—	734	4	no	—
78	C₄	(C₂×D₃₆₇)⋊C₄	1	2	yes	—
79	C₄	C₂×C₄×D₃₆₇	1	1	yes	characteristic
80	C₄	C₂×C₂²⋊D₃₆₇	1	1	yes	characteristic
81	C₂	#26044186	1	4	yes	direct product factor
82	C₂	C₂×(C₂×D₃₆₇)⋊C₄	1	1	yes	characteristic
83	C₂	C₂×#19154566	1	1	yes	characteristic
84	C₂	C₂×Dic₁₄₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₁₄₆₈
commutator	C₄×C₃₆₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₆₇
Fitting	C₂²×C₈×C₃₆₇	C₂
socle, prime radical	C₂³×C₃₆₇	D₄
cosocle	C₂×C₄×C₃₆₇	C₂³
hypercenter	C₂²×C₈	D₃₆₇
hypocenter	C₃₆₇	C₂×#103
LCS	G ▷ C₄×C₃₆₇ ▷ C₂×C₃₆₇ ▷ C₃₆₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
3. #26044186	C₂	direct (N × H)
7. C₂×Dic₇₃₄	C₄	semidirect
18. Dic₇₃₄	C₂×C₄	semidirect
38. C₂×C₃₆₇	#103	semidirect
42. C₃₆₇	C₂×#103	semidirect
81. C₂	#26044186	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×Dic₇₃₄	2
C₂×C₄⋊Dic₃₆₇	2
#26044186	2
C₂²×C₈×C₃₆₇	2
C₂×#103	367

Subgroups — C2×#26044186 #37554178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26044186 #37554178