Subgroups — C₂×#24925032 #36342359

Order 21568.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925032	C₂	1	4	yes	maximal, direct product factor
2	C₂×#19129188	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×D₃₃₇	C₂	1	1	yes	maximal, characteristic
4	#19129188	C₂²	1	4	yes	complemented
5	C₂×C₄×D₃₃₇	C₄	1	1	yes	characteristic
6	C₂×#14582106	C₂²	1	1	yes	characteristic
7	C₈×D₃₃₇	C₄	1	2	yes	—
8	C₈×D₃₃₇	C₂²	1	2	yes	—
9	C₂×C₈×C₃₃₇	C₄	1	1	yes	characteristic
10	C₂²×D₃₃₇	C₈	1	1	yes	characteristic
11	C₂×Dic₃₃₇	C₈	1	1	yes	characteristic
12	C₄×D₃₃₇	C₈	1	2	yes	—
13	C₄×D₃₃₇	C₂×C₄	1	2	yes	—
14	#14582106	C₂×C₄	1	1	yes	characteristic
15	#14582106	C₂³	1	1	yes	characteristic
16	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
17	C₈×C₃₃₇	C₂×C₄	1	2	yes	—
18	C₂²×C₃₃₇	C₂×C₈	1	1	yes	characteristic
19	C₂×D₃₃₇	C₁₆	1	4	yes	complemented
20	C₂×D₃₃₇	C₂×C₈	1	2	yes	—
21	C₄×C₃₃₇	C₂×C₈	1	1	yes	characteristic
22	C₄×C₃₃₇	C₂²×C₄	1	1	yes	characteristic
23	Dic₃₃₇	C₂×C₈	1	2	yes	—
24	C₂×C₃₃₇	C₂×C₁₆	1	2	yes	complemented
25	C₂×C₃₃₇	C₂²×C₈	1	1	yes	characteristic
26	D₃₃₇	C₂×C₁₆	1	4	yes	complemented
27	C₃₃₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
28	C₂²×C₁₆	—	337	1	no	maximal, Sylow
29	C₂²×C₈	—	337	1	no	—
30	C₂×C₁₆	—	337	2	no	—
31	C₂×C₁₆	—	337	4	no	—
32	C₂²×C₄	—	337	1	no	—
33	C₂×C₈	—	337	1	no	—
34	C₂×C₈	—	337	2	no	—
35	C₂×C₈	—	337	2	no	—
36	C₂×C₈	#13062438	1	1	yes	characteristic
37	C₁₆	—	337	4	no	—
38	C₂³	—	337	1	no	—
39	C₂×C₄	—	337	1	no	—
40	C₂×C₄	—	337	2	no	—
41	C₂×C₄	—	337	2	no	—
42	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
43	C₈	—	337	1	no	—
44	C₈	—	337	1	no	—
45	C₈	C₂×#13062438	1	2	yes	—
46	C₂²	—	337	4	no	—
47	C₂²	—	337	2	no	—
48	C₂²	#19129193	1	1	yes	characteristic
49	C₄	—	337	2	no	—
50	C₄	#19129193	1	1	yes	characteristic
51	C₄	C₂²×#13062438	1	1	yes	characteristic
52	C₂	—	337	4	no	—
53	C₂	#24925032	1	2	yes	direct product factor
54	C₂	C₂×#19129193	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₈	#13062438
commutator, hypocenter	C₃₃₇	C₂²×C₁₆
Frattini	C₄	C₂²×#13062438
Fitting	C₂×C₈×C₃₃₇	C₄
socle	C₂²×C₃₃₇	C₂×C₈
prime radical	C₂²×D₃₃₇	C₈
cosocle	#14582106	C₂³
LCS	G ▷ C₃₃₇
UCS	C₁ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
1. #24925032	C₂	direct (N × H)
2. C₂×#19129188	C₂	semidirect
4. #19129188	C₂²	semidirect
19. C₂×D₃₃₇	C₁₆	semidirect
24. C₂×C₃₃₇	C₂×C₁₆	semidirect
26. D₃₃₇	C₂×C₁₆	semidirect
27. C₃₃₇	C₂²×C₁₆	semidirect
53. C₂	#24925032	direct (N × H)

Maximal subgroups

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

subgroup	index
#24925032	2
C₂×#19129188	2
C₂×C₈×D₃₃₇	2
C₂²×C₁₆	337

Subgroups — C2×#24925032 #36342359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#24925032 #36342359