Subgroups — C₂²⋊#19129199 #36342431

Order 21568.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19129199	C₂	1	2	yes	maximal, complemented
2	C₂²×#14582115	C₂	1	1	yes	maximal, characteristic
3	#19129199	—	2	2	no	—
4	C₂×#14582115	—	2	2	no	—
5	C₂×#14582115	C₄	1	1	yes	characteristic
6	C₂×#14582115	C₂²	1	1	yes	characteristic
7	C₂²×#13062438	C₄	1	1	yes	characteristic
8	#14582115	—	2	1	no	—
9	#14582115	D₄	1	2	yes	—
10	C₂×#13062438	—	2	1	no	—
11	C₂×#13062438	—	2	1	no	—
12	C₂×#13062438	C₈	1	1	yes	characteristic
13	C₂×#13062438	C₂×C₄	1	1	yes	characteristic
14	C₂²×D₃₃₇	C₈	1	1	yes	characteristic
15	C₂²×C₃₃₇	C₁₆	1	1	yes	characteristic, complemented
16	C₂×D₃₃₇	—	2	1	no	—
17	C₂×D₃₃₇	—	2	1	no	—
18	C₂×D₃₃₇	C₁₆	1	1	yes	characteristic, complemented
19	C₂×D₃₃₇	C₂×C₈	1	1	yes	characteristic
20	#13062438	—	2	1	no	—
21	#13062438	C₂²⋊C₄	1	1	yes	characteristic
22	#13062438	M₁₆	1	1	yes	characteristic
23	C₂×C₃₃₇	—	2	1	no	—
24	C₂×C₃₃₇	C₂×C₁₆	1	1	yes	characteristic
25	D₃₃₇	—	2	1	no	—
26	D₃₃₇	C₂²⋊C₈	1	1	yes	characteristic
27	D₃₃₇	M₃₂	1	1	yes	characteristic
28	C₃₃₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²⋊C₁₆	—	337	1	no	maximal, Sylow
30	C₂²×C₈	—	337	1	no	—
31	C₂×C₁₆	—	337	2	no	—
32	C₂²×C₄	—	337	1	no	—
33	C₂×C₈	—	337	1	no	—
34	C₂×C₈	—	337	1	no	—
35	C₂×C₈	—	674	2	no	—
36	C₁₆	—	674	2	no	—
37	C₂³	—	337	1	no	—
38	C₂×C₄	—	337	1	no	—
39	C₂×C₄	—	337	1	no	—
40	C₂×C₄	—	674	1	no	—
41	C₂×C₄	—	674	1	no	—
42	C₈	—	337	2	no	—
43	C₈	—	674	1	no	—
44	C₂²	—	337	1	no	—
45	C₂²	—	337	1	no	—
46	C₂²	—	674	1	no	—
47	C₂²	—	674	1	no	—
48	C₂²	#19129199	1	1	yes	characteristic, complemented
49	C₄	—	337	1	no	—
50	C₄	—	337	1	no	—
51	C₄	—	674	1	no	—
52	C₂	—	2	1	no	—
53	C₂	—	337	1	no	—
54	C₂	—	337	1	no	—
55	C₂	—	674	1	no	—
56	C₂	C₂×#19129199	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#19129199
commutator, socle	C₂×C₃₃₇	C₂×C₁₆
Fitting	C₂²×C₃₃₇	C₁₆
prime radical	C₂²×D₃₃₇	C₈
cosocle	C₂×#14582115	C₂²
hypercenter	C₂²	#19129199
hypocenter	C₃₃₇	C₂²⋊C₁₆
LCS	G ▷ C₂×C₃₃₇ ▷ C₃₃₇
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#19129199	C₂	semidirect
15. C₂²×C₃₃₇	C₁₆	semidirect
18. C₂×D₃₃₇	C₁₆	semidirect
28. C₃₃₇	C₂²⋊C₁₆	semidirect
48. C₂²	#19129199	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19129199	2
C₂²×#14582115	2
C₂²⋊C₁₆	337

Subgroups — C22⋊#19129199 #36342431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#19129199 #36342431