Subgroups — C₂²⋊#19129188 #36342199

Order 21568.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19129188	C₂	1	2	yes	maximal, complemented
2	C₂²×#14582106	C₂	1	1	yes	maximal, characteristic
3	#19129188	—	2	2	no	—
4	C₂×#14582106	—	2	2	no	—
5	C₂×#14582106	C₄	1	1	yes	characteristic
6	C₂×#14582106	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₃₃₇	C₄	1	1	yes	characteristic
8	#14582106	—	2	1	no	—
9	#14582106	D₄	1	2	yes	—
10	C₂³×C₃₃₇	C₈	1	1	yes	characteristic
11	C₂×C₄×C₃₃₇	—	2	1	no	—
12	C₂×C₄×C₃₃₇	—	2	1	no	—
13	C₂×C₄×C₃₃₇	C₈	1	1	yes	characteristic
14	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃₃₇	—	2	1	no	—
16	C₂²×C₃₃₇	—	2	1	no	—
17	C₂²×C₃₃₇	C₁₆	1	2	yes	complemented
18	C₂²×C₃₃₇	C₂×C₈	1	1	yes	characteristic
19	C₄×C₃₃₇	—	2	1	no	—
20	C₄×C₃₃₇	C₂²⋊C₄	1	1	yes	characteristic
21	C₄×C₃₃₇	M₁₆	1	1	yes	characteristic
22	C₂×C₃₃₇	—	2	2	no	—
23	C₂×C₃₃₇	C₂²⋊C₈	1	1	yes	characteristic
24	C₂×C₃₃₇	C₂×C₁₆	1	1	yes	characteristic
25	C₂×C₃₃₇	M₃₂	1	1	yes	characteristic
26	C₃₃₇	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
27	C₂²⋊C₁₆	—	337	1	no	maximal, Sylow
28	C₂²×C₈	—	337	1	no	—
29	C₂×C₁₆	—	337	2	no	—
30	C₂²×C₄	#13062438	1	1	yes	characteristic
31	C₂×C₈	—	337	1	no	—
32	C₂×C₈	—	337	1	no	—
33	C₂×C₈	—	674	2	no	—
34	C₁₆	—	674	2	no	—
35	C₂³	#14582113	1	1	yes	characteristic
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	#14582113	1	1	yes	characteristic
39	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
40	C₈	—	337	2	no	—
41	C₈	—	674	1	no	—
42	C₂²	—	2	1	no	—
43	C₂²	—	2	1	no	—
44	C₂²	#19129188	1	2	yes	complemented
45	C₂²	C₂×#14582113	1	1	yes	characteristic
46	C₄	—	2	1	no	—
47	C₄	C₂²⋊#13062438	1	1	yes	characteristic
48	C₄	#19129194	1	1	yes	characteristic
49	C₂	—	2	2	no	—
50	C₂	C₂²⋊#14582113	1	1	yes	characteristic
51	C₂	C₂×#19129188	1	1	yes	characteristic
52	C₂	#24925033	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×#19129188	C₂	semidirect
17. C₂²×C₃₃₇	C₁₆	semidirect
26. C₃₃₇	C₂²⋊C₁₆	semidirect
44. C₂²	#19129188	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19129188	2
C₂²×#14582106	2
C₂²⋊C₁₆	337

Subgroups — C22⋊#19129188 #36342199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#19129188 #36342199