Subgroups — C₂×#20259996 #27136379

Order 12352.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259996	C₂	1	4	yes	maximal, direct product factor
2	C₂×#15690567	C₂	1	2	yes	maximal, complemented
3	C₂×#15690563	C₂	1	1	yes	maximal, characteristic
4	#15690567	C₂²	1	4	yes	complemented
5	#15690563	C₄	1	2	yes	—
6	#15690563	C₂²	1	2	yes	—
7	C₂×#13095400	C₄	1	1	yes	characteristic
8	C₂×#13095400	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₉₃	C₄	1	1	yes	characteristic
10	#13095400	C₂×C₄	1	2	yes	—
11	#13095400	C₂×C₄	1	1	yes	characteristic
12	#13095400	C₂³	1	1	yes	characteristic
13	C₂²×D₁₉₃	C₈	1	1	yes	characteristic
14	C₂×Dic₁₉₃	C₂×C₄	1	1	yes	characteristic
15	C₄×D₁₉₃	C₈	1	2	yes	—
16	C₄×D₁₉₃	C₂×C₄	1	2	yes	—
17	C₂×C₄×C₁₉₃	C₈	1	1	yes	characteristic
18	C₂²×C₁₉₃	C₂×C₈	1	1	yes	characteristic
19	C₂×D₁₉₃	—	2	2	no	—
20	C₂×D₁₉₃	C₂×C₈	1	2	yes	—
21	C₄×C₁₉₃	C₂×C₈	1	2	yes	—
22	Dic₁₉₃	C₂×C₈	1	1	yes	characteristic
23	Dic₁₉₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×C₁₉₃	M₃₂	1	2	yes	complemented
25	C₂×C₁₉₃	C₂²×C₈	1	1	yes	characteristic
26	D₁₉₃	—	2	2	no	—
27	C₁₉₃	C₂×M₃₂	1	1	yes	characteristic, complemented, Sylow
28	C₂×M₃₂	—	193	1	no	maximal, Sylow
29	C₂²×C₈	—	193	1	no	—
30	M₃₂	—	193	4	no	—
31	C₂×C₁₆	—	193	2	no	—
32	C₂²×C₄	—	193	1	no	—
33	C₂×C₈	—	193	1	no	—
34	C₂×C₈	—	193	1	no	—
35	C₂×C₈	—	193	2	no	—
36	C₂×C₈	—	193	2	no	—
37	C₁₆	—	193	4	no	—
38	C₂³	—	193	1	no	—
39	C₂×C₄	—	193	1	no	—
40	C₂×C₄	—	193	2	no	—
41	C₂×C₄	—	193	2	no	—
42	C₂×C₄	#13095402	1	1	yes	characteristic
43	C₈	—	193	1	no	—
44	C₈	—	193	2	no	—
45	C₈	—	193	1	no	—
46	C₂²	—	386	2	no	—
47	C₂²	—	193	2	no	—
48	C₂²	C₂×#13095402	1	1	yes	characteristic
49	C₄	—	193	1	no	—
50	C₄	—	193	1	no	—
51	C₄	C₂×#13095402	1	2	yes	—
52	C₂	—	386	2	no	—
53	C₂	#20259996	1	2	yes	direct product factor
54	C₂	C₂²×#13095402	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13095402
commutator	C₂×C₁₉₃	C₂²×C₈
Frattini	C₂	C₂²×#13095402
Fitting	C₂×C₄×C₁₉₃	C₈
socle	C₂²×C₁₉₃	C₂×C₈
prime radical	C₂²×D₁₉₃	C₈
cosocle	#13095400	C₂³
hypercenter	C₂×C₄	#13095402
hypocenter	C₁₉₃	C₂×M₃₂
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #20259996	C₂	direct (N × H)
2. C₂×#15690567	C₂	semidirect
4. #15690567	C₂²	semidirect
24. C₂×C₁₉₃	M₃₂	semidirect
27. C₁₉₃	C₂×M₃₂	semidirect
53. C₂	#20259996	direct (N × H)

Maximal subgroups

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

subgroup	index
#20259996	2
C₂×#15690567	2
C₂×#15690563	2
C₂×M₃₂	193

Subgroups — C2×#20259996 #27136379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20259996 #27136379