Subgroups — C₂²⋊#15690569 #27136385

Order 12352.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690569	C₂	1	2	yes	maximal, complemented
2	C₂²×#13095402	C₂	1	1	yes	maximal, characteristic
3	#15690569	—	2	2	no	—
4	C₂×#13095402	—	2	2	no	—
5	C₂×#13095402	C₄	1	1	yes	characteristic
6	C₂×#13095402	C₂²	1	1	yes	characteristic
7	C₂²×#11715871	C₄	1	1	yes	characteristic
8	#13095402	—	2	1	no	—
9	#13095402	D₄	1	2	yes	—
10	C₂×#11715871	—	2	1	no	—
11	C₂×#11715871	—	2	1	no	—
12	C₂×#11715871	C₈	1	1	yes	characteristic
13	C₂×#11715871	C₂×C₄	1	1	yes	characteristic
14	C₂²×D₁₉₃	C₈	1	1	yes	characteristic
15	C₂²×C₁₉₃	C₁₆	1	1	yes	characteristic, complemented
16	C₂×D₁₉₃	—	2	1	no	—
17	C₂×D₁₉₃	—	2	1	no	—
18	C₂×D₁₉₃	C₁₆	1	1	yes	characteristic, complemented
19	C₂×D₁₉₃	C₂×C₈	1	1	yes	characteristic
20	#11715871	—	2	1	no	—
21	#11715871	C₂²⋊C₄	1	1	yes	characteristic
22	#11715871	M₁₆	1	1	yes	characteristic
23	C₂×C₁₉₃	—	2	1	no	—
24	C₂×C₁₉₃	C₂×C₁₆	1	1	yes	characteristic
25	D₁₉₃	—	2	1	no	—
26	D₁₉₃	C₂²⋊C₈	1	1	yes	characteristic
27	D₁₉₃	M₃₂	1	1	yes	characteristic
28	C₁₉₃	C₂²⋊C₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂²⋊C₁₆	—	193	1	no	maximal, Sylow
30	C₂²×C₈	—	193	1	no	—
31	C₂×C₁₆	—	193	2	no	—
32	C₂²×C₄	—	193	1	no	—
33	C₂×C₈	—	386	2	no	—
34	C₂×C₈	—	193	1	no	—
35	C₂×C₈	—	193	1	no	—
36	C₁₆	—	386	2	no	—
37	C₂³	—	193	1	no	—
38	C₂×C₄	—	386	1	no	—
39	C₂×C₄	—	386	1	no	—
40	C₂×C₄	—	193	1	no	—
41	C₂×C₄	—	193	1	no	—
42	C₈	—	386	1	no	—
43	C₈	—	193	2	no	—
44	C₂²	—	386	1	no	—
45	C₂²	—	386	1	no	—
46	C₂²	—	193	1	no	—
47	C₂²	—	193	1	no	—
48	C₂²	#15690569	1	1	yes	characteristic, complemented
49	C₄	—	386	1	no	—
50	C₄	—	193	1	no	—
51	C₄	—	193	1	no	—
52	C₂	—	2	1	no	—
53	C₂	—	386	1	no	—
54	C₂	—	193	1	no	—
55	C₂	—	193	1	no	—
56	C₂	C₂×#15690569	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂×#15690569
commutator, socle	C₂×C₁₉₃	C₂×C₁₆
Fitting	C₂²×C₁₉₃	C₁₆
prime radical	C₂²×D₁₉₃	C₈
cosocle	C₂×#13095402	C₂²
hypercenter	C₂²	#15690569
hypocenter	C₁₉₃	C₂²⋊C₁₆
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂ ◁ C₂²

Complements

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

N	H ≅ G/N	type
1. C₂×#15690569	C₂	semidirect
15. C₂²×C₁₉₃	C₁₆	semidirect
18. C₂×D₁₉₃	C₁₆	semidirect
28. C₁₉₃	C₂²⋊C₁₆	semidirect
48. C₂²	#15690569	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15690569	2
C₂²×#13095402	2
C₂²⋊C₁₆	193

Subgroups — C22⋊#15690569 #27136385

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²⋊#15690569 #27136385