Subgroups — C₂×#20259987 #27136336

Order 12352.

266 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20259987	C₂	1	8	yes	maximal, direct product factor
2	C₂×#15690565	C₂	1	3	yes	maximal, complemented
3	C₂×#15690563	C₂	1	3	yes	maximal, complemented
4	C₂×#15690556	C₂	1	1	yes	maximal, characteristic
5	#15690565	C₂²	1	12	yes	complemented
6	#15690563	C₂²	1	12	yes	complemented
7	C₂×#13095400	C₂²	1	1	yes	characteristic
8	C₂×#13095400	C₂²	1	3	yes	—
9	#15690556	C₄	1	4	yes	—
10	#15690556	C₂²	1	4	yes	—
11	C₂×D₇₇₂	C₄	1	3	yes	—
12	C₂×C₄×D₁₉₃	C₂²	1	3	yes	—
13	C₂×Q₈×C₁₉₃	C₄	1	1	yes	characteristic
14	#13095400	C₂³	1	2	yes	—
15	#13095400	C₂³	1	6	yes	—
16	C₂²×D₁₉₃	C₂×C₄	1	3	yes	—
17	D₇₇₂	C₂×C₄	1	12	yes	—
18	C₂×Dic₁₉₃	C₂³	1	1	yes	characteristic
19	C₄×D₁₉₃	C₂×C₄	1	6	yes	—
20	C₄×D₁₉₃	C₂³	1	6	yes	—
21	Q₈×C₁₉₃	C₂×C₄	1	4	yes	—
22	C₂×C₄×C₁₉₃	C₂×C₄	1	3	yes	—
23	C₂²×C₁₉₃	C₂²×C₄	1	1	yes	characteristic
24	C₂×D₁₉₃	—	2	6	no	—
25	C₂×D₁₉₃	C₂²×C₄	1	6	yes	—
26	C₄×C₁₉₃	C₂²×C₄	1	6	yes	—
27	Dic₁₉₃	C₂²×C₄	1	1	yes	characteristic
28	Dic₁₉₃	C₂⁴	1	1	yes	characteristic
29	C₂×C₁₉₃	#131	1	2	yes	complemented
30	C₂×C₁₉₃	C₂³×C₄	1	1	yes	characteristic
31	D₁₉₃	—	2	6	no	—
32	C₁₉₃	C₂×#131	1	1	yes	characteristic, complemented, Sylow
33	C₂×#131	—	193	1	no	maximal, Sylow
34	C₂×#41	—	193	1	no	—
35	#131	—	193	8	no	—
36	C₂×M₁₆	—	193	3	no	—
37	C₂²×C₈	—	193	3	no	—
38	#41	—	193	4	no	—
39	#41	—	193	4	no	—
40	C₂×Q₈	#11715871	1	1	yes	characteristic
41	C₂×D₄	—	193	3	no	—
42	C₂²×C₄	—	193	3	no	—
43	M₁₆	—	193	12	no	—
44	C₂×C₈	—	193	1	no	—
45	C₂×C₈	—	193	3	no	—
46	C₂×C₈	—	193	12	no	—
47	C₂³	—	193	3	no	—
48	Q₈	C₂×#11715871	1	4	yes	—
49	D₄	—	193	12	no	—
50	C₂×C₄	—	193	1	no	—
51	C₂×C₄	—	193	6	no	—
52	C₂×C₄	—	193	6	no	—
53	C₂×C₄	C₂×#11715871	1	3	yes	—
54	C₈	—	193	2	no	—
55	C₈	—	193	6	no	—
56	C₂²	—	386	6	no	—
57	C₂²	—	193	6	no	—
58	C₂²	C₂²×#11715871	1	1	yes	characteristic
59	C₄	—	193	1	no	—
60	C₄	—	193	1	no	—
61	C₄	C₂²×#11715871	1	6	yes	—
62	C₂	—	386	6	no	—
63	C₂	#20259987	1	2	yes	direct product factor
64	C₂	C₂³×#11715871	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#11715871
commutator	C₂×C₁₉₃	C₂³×C₄
Frattini	C₂	C₂³×#11715871
Fitting	C₂×Q₈×C₁₉₃	C₄
socle	C₂²×C₁₉₃	C₂²×C₄
prime radical	C₂×#15690556	C₂
cosocle	Dic₁₉₃	C₂⁴
hypercenter	C₂×Q₈	#11715871
hypocenter	C₁₉₃	C₂×#131
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. #20259987	C₂	direct (N × H)
2. C₂×#15690565	C₂	semidirect
3. C₂×#15690563	C₂	semidirect
5. #15690565	C₂²	semidirect
6. #15690563	C₂²	semidirect
29. C₂×C₁₉₃	#131	semidirect
32. C₁₉₃	C₂×#131	semidirect
63. C₂	#20259987	direct (N × H)

Maximal subgroups

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

subgroup	index
#20259987	2
C₂×#15690565	2
C₂×#15690563	2
C₂×#15690556	2
C₂×#131	193

Subgroups — C2×#20259987 #27136336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20259987 #27136336