Subgroups — C₂×#26044197 #37554232

Order 23488.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19154561	C₂	1	2	yes	maximal
2	#26044197	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₈×C₃₆₇	C₂	1	1	yes	maximal, characteristic
4	#19154561	—	2	2	no	—
5	#19154561	C₂²	1	4	yes	—
6	C₂×C₃₆₇⋊C₈	—	2	2	no	—
7	C₂²×C₄×C₃₆₇	C₂²	1	1	yes	characteristic
8	C₂×C₈×C₃₆₇	C₄	1	2	yes	—
9	C₂×C₈×C₃₆₇	C₄	1	2	yes	—
10	C₂×C₈×C₃₆₇	C₂²	1	2	yes	—
11	C₃₆₇⋊C₈	—	2	4	no	—
12	C₂³×C₃₆₇	Q₈	1	1	yes	characteristic
13	C₂×C₄×C₃₆₇	C₂×C₄	1	1	yes	characteristic
14	C₂×C₄×C₃₆₇	C₂×C₄	1	1	yes	characteristic
15	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
16	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
17	C₂×C₄×C₃₆₇	Q₈	1	1	yes	characteristic
18	C₂×C₄×C₃₆₇	C₂³	1	1	yes	characteristic
19	C₈×C₃₆₇	C₂×C₄	1	4	yes	—
20	C₂²×C₃₆₇	—	2	2	no	—
21	C₂²×C₃₆₇	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₃₆₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂²×C₃₆₇	C₂×Q₈	1	1	yes	characteristic
24	C₄×C₃₆₇	C₄⋊C₄	1	1	yes	characteristic
25	C₄×C₃₆₇	C₄⋊C₄	1	1	yes	characteristic
26	C₄×C₃₆₇	C₂²×C₄	1	1	yes	characteristic
27	C₄×C₃₆₇	C₂×D₄	1	1	yes	characteristic
28	C₂×C₃₆₇	—	2	1	no	—
29	C₂×C₃₆₇	—	2	1	no	—
30	C₂×C₃₆₇	#108	1	2	yes	complemented
31	C₂×C₃₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	C₃₆₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
33	C₂×#108	—	367	1	no	maximal, Sylow
34	C₂×M₁₆	—	367	2	no	—
35	C₂²×C₈	D₃₆₇	1	1	yes	characteristic
36	#108	—	367	4	no	—
37	C₂²×C₄	C₂×D₃₆₇	1	1	yes	characteristic
38	M₁₆	—	367	4	no	—
39	M₁₆	—	734	2	no	—
40	C₂×C₈	—	734	2	no	—
41	C₂×C₈	Dic₃₆₇	1	2	yes	—
42	C₂×C₈	Dic₃₆₇	1	2	yes	—
43	C₂×C₈	C₂×D₃₆₇	1	2	yes	—
44	C₂³	Dic₇₃₄	1	1	yes	characteristic
45	C₂×C₄	C₂×Dic₃₆₇	1	1	yes	characteristic
46	C₂×C₄	C₂×Dic₃₆₇	1	1	yes	characteristic
47	C₂×C₄	D₁₄₆₈	1	1	yes	characteristic
48	C₂×C₄	D₁₄₆₈	1	1	yes	characteristic
49	C₂×C₄	Dic₇₃₄	1	1	yes	characteristic
50	C₂×C₄	C₂²×D₃₆₇	1	1	yes	characteristic
51	C₈	—	734	4	no	—
52	C₈	C₂×Dic₃₆₇	1	4	yes	—
53	C₂²	—	2	2	no	—
54	C₂²	C₄⋊Dic₃₆₇	1	1	yes	characteristic
55	C₂²	C₄⋊Dic₃₆₇	1	1	yes	characteristic
56	C₂²	C₂×Dic₇₃₄	1	1	yes	characteristic
57	C₄	C₄⋊Dic₃₆₇	1	1	yes	characteristic
58	C₄	C₄⋊Dic₃₆₇	1	1	yes	characteristic
59	C₄	C₂²×Dic₃₆₇	1	1	yes	characteristic
60	C₄	C₂×D₁₄₆₈	1	1	yes	characteristic
61	C₂	—	2	1	no	—
62	C₂	—	2	1	no	—
63	C₂	#26044197	1	2	yes	direct product factor
64	C₂	C₂×C₄⋊Dic₃₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₄₆₈
commutator	C₄×C₃₆₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₃₆₇
Fitting	C₂²×C₈×C₃₆₇	C₂
socle	C₂²×C₃₆₇	C₄⋊C₄
prime radical	C₂³×C₃₆₇	Q₈
cosocle	C₂×C₄×C₃₆₇	C₂³
hypercenter	C₂²×C₈	D₃₆₇
hypocenter	C₃₆₇	C₂×#108
LCS	G ▷ C₄×C₃₆₇ ▷ C₂×C₃₆₇ ▷ C₃₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #26044197	C₂	direct (N × H)
30. C₂×C₃₆₇	#108	semidirect
32. C₃₆₇	C₂×#108	semidirect
63. C₂	#26044197	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×#19154561	2
#26044197	2
C₂²×C₈×C₃₆₇	2
C₂×#108	367

Subgroups — C2×#26044197 #37554232

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26044197 #37554232