Subgroups — C₂×#24925030 #36342319

Order 21568.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19129195	C₂	1	2	yes	maximal
2	#24925030	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×D₃₃₇	C₂	1	1	yes	maximal, characteristic
4	#19129195	—	2	2	no	—
5	#19129195	C₂²	1	4	yes	—
6	C₂×#14582113	—	2	2	no	—
7	C₂×C₄×D₃₃₇	C₂²	1	1	yes	characteristic
8	C₂×#14582106	C₄	1	1	yes	characteristic
9	C₈×D₃₃₇	C₄	1	2	yes	—
10	C₈×D₃₃₇	C₂²	1	2	yes	—
11	C₂×C₈×C₃₃₇	C₄	1	1	yes	characteristic
12	#14582113	—	2	4	no	—
13	C₂²×D₃₃₇	Q₈	1	1	yes	characteristic
14	C₂×Dic₃₃₇	D₄	1	1	yes	characteristic
15	C₄×D₃₃₇	C₂×C₄	1	1	yes	characteristic
16	C₄×D₃₃₇	D₄	1	1	yes	characteristic
17	C₄×D₃₃₇	Q₈	1	1	yes	characteristic
18	C₄×D₃₃₇	C₂³	1	1	yes	characteristic
19	#14582106	C₂×C₄	1	2	yes	—
20	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
21	C₈×C₃₃₇	C₂×C₄	1	2	yes	—
22	C₂²×C₃₃₇	C₄⋊C₄	1	1	yes	characteristic
23	C₂×D₃₃₇	—	2	2	no	—
24	C₂×D₃₃₇	C₄⋊C₄	1	1	yes	characteristic
25	C₂×D₃₃₇	C₂×Q₈	1	1	yes	characteristic
26	C₄×C₃₃₇	C₄⋊C₄	1	1	yes	characteristic
27	C₄×C₃₃₇	C₂²×C₄	1	1	yes	characteristic
28	Dic₃₃₇	C₄⋊C₄	1	1	yes	characteristic
29	Dic₃₃₇	C₂×D₄	1	1	yes	characteristic
30	C₂×C₃₃₇	#108	1	2	yes	complemented
31	C₂×C₃₃₇	C₂×C₄⋊C₄	1	1	yes	characteristic
32	D₃₃₇	—	2	1	no	—
33	D₃₃₇	—	2	1	no	—
34	C₃₃₇	C₂×#108	1	1	yes	characteristic, complemented, Sylow
35	C₂×#108	—	337	1	no	maximal, Sylow
36	C₂×M₁₆	—	337	2	no	—
37	C₂²×C₈	—	337	1	no	—
38	#108	—	337	4	no	—
39	C₂²×C₄	—	337	1	no	—
40	M₁₆	—	337	4	no	—
41	M₁₆	—	674	2	no	—
42	C₂×C₈	—	337	1	no	—
43	C₂×C₈	—	337	2	no	—
44	C₂×C₈	—	337	2	no	—
45	C₂×C₈	—	674	2	no	—
46	C₂×C₈	#13062438	1	1	yes	characteristic
47	C₂³	—	337	1	no	—
48	C₂×C₄	—	337	1	no	—
49	C₂×C₄	—	337	1	no	—
50	C₂×C₄	—	337	1	no	—
51	C₂×C₄	—	337	1	no	—
52	C₂×C₄	—	337	1	no	—
53	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
54	C₈	—	337	2	no	—
55	C₈	—	674	4	no	—
56	C₈	C₂×#13062438	1	2	yes	—
57	C₂²	—	337	1	no	—
58	C₂²	—	337	1	no	—
59	C₂²	—	674	2	no	—
60	C₂²	C₄⋊#13062438	1	1	yes	characteristic
61	C₄	—	337	1	no	—
62	C₄	—	337	1	no	—
63	C₄	C₄⋊#13062438	1	1	yes	characteristic
64	C₄	C₂²×#13062438	1	1	yes	characteristic
65	C₂	—	674	1	no	—
66	C₂	—	674	1	no	—
67	C₂	#24925030	1	2	yes	direct product factor
68	C₂	C₂×C₄⋊#13062438	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₄⋊#13062438
commutator	C₄×C₃₃₇	C₂²×C₄
Frattini	C₄	C₂²×#13062438
Fitting	C₂×C₈×C₃₃₇	C₄
socle	C₂²×C₃₃₇	C₄⋊C₄
prime radical	C₂²×D₃₃₇	Q₈
cosocle	C₄×D₃₃₇	C₂³
hypercenter	C₂×C₈	#13062438
hypocenter	C₃₃₇	C₂×#108
LCS	G ▷ C₄×C₃₃₇ ▷ C₂×C₃₃₇ ▷ C₃₃₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
2. #24925030	C₂	direct (N × H)
30. C₂×C₃₃₇	#108	semidirect
34. C₃₃₇	C₂×#108	semidirect
67. C₂	#24925030	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×#19129195	2
#24925030	2
C₂×C₈×D₃₃₇	2
C₂×#108	337

Subgroups — C2×#24925030 #36342319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#24925030 #36342319