Subgroups — C₂×#20259956 #27136228

Order 12352.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13095400	C₂	1	2	yes	maximal, complemented
2	#20259956	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₄×D₁₉₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#13095400	—	2	4	no	—
5	C₂×#13095400	C₂²	1	4	yes	complemented
6	C₂³×D₁₉₃	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₉₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×D₁₉₃	—	2	4	no	—
9	C₂×C₄×D₁₉₃	C₄	1	2	yes	—
10	C₂×C₄×D₁₉₃	C₂²	1	2	yes	—
11	C₂²×C₄×C₁₉₃	C₄	1	1	yes	characteristic
12	#13095400	—	2	4	no	—
13	C₂²×D₁₉₃	—	2	2	no	—
14	C₂²×D₁₉₃	—	2	2	no	—
15	C₂²×D₁₉₃	C₈	1	4	yes	complemented
16	C₂²×D₁₉₃	C₂×C₄	1	2	yes	—
17	C₂×Dic₁₉₃	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₉₃	D₄	1	4	yes	—
19	C₂×Dic₁₉₃	C₂³	1	1	yes	characteristic
20	C₄×D₁₉₃	—	2	4	no	—
21	C₄×D₁₉₃	—	2	4	no	—
22	C₂³×C₁₉₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₁₉₃	—	2	2	no	—
24	C₂×C₄×C₁₉₃	C₂×C₄	1	2	yes	—
25	C₂²×C₁₉₃	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₁₉₃	C₂×C₈	1	2	yes	—
27	C₂²×C₁₉₃	M₁₆	1	2	yes	—
28	C₂²×C₁₉₃	C₂²×C₄	1	1	yes	characteristic
29	C₂×D₁₉₃	—	2	8	no	—
30	C₂×D₁₉₃	—	2	2	no	—
31	C₂×D₁₉₃	—	2	2	no	—
32	C₂×D₁₉₃	C₂×C₈	1	4	yes	complemented
33	C₄×C₁₉₃	—	2	2	no	—
34	Dic₁₉₃	C₂²⋊C₄	1	2	yes	—
35	Dic₁₉₃	C₂×D₄	1	2	yes	—
36	C₂×C₁₉₃	C₂²⋊C₈	1	4	yes	complemented
37	C₂×C₁₉₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
38	C₂×C₁₉₃	C₂²×C₈	1	1	yes	characteristic
39	C₂×C₁₉₃	C₂×M₁₆	1	1	yes	characteristic
40	D₁₉₃	—	2	4	no	—
41	C₁₉₃	C₂×C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
42	C₂×C₂²⋊C₈	—	193	1	no	maximal, Sylow
43	C₂³×C₄	—	193	1	no	—
44	C₂²×C₈	—	193	2	no	—
45	C₂²⋊C₈	—	193	4	no	—
46	C₂⁴	—	193	1	no	—
47	C₂²×C₄	—	386	4	no	—
48	C₂²×C₄	—	193	2	no	—
49	C₂²×C₄	—	193	2	no	—
50	C₂²×C₄	—	193	1	no	—
51	C₂²×C₄	#11715871	1	1	yes	characteristic
52	C₂×C₈	—	386	4	no	—
53	C₂×C₈	—	193	4	no	—
54	C₂³	—	386	2	no	—
55	C₂³	—	386	2	no	—
56	C₂³	—	193	4	no	—
57	C₂³	—	193	2	no	—
58	C₂³	C₂×#11715871	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	386	4	no	—
61	C₂×C₄	—	386	4	no	—
62	C₂×C₄	—	193	4	no	—
63	C₂×C₄	—	193	1	no	—
64	C₂×C₄	—	193	1	no	—
65	C₂×C₄	C₂×#11715871	1	2	yes	—
66	C₈	—	386	4	no	—
67	C₂²	—	386	8	no	—
68	C₂²	—	386	2	no	—
69	C₂²	—	386	2	no	—
70	C₂²	—	193	4	no	—
71	C₂²	C₂²⋊#11715871	1	2	yes	—
72	C₂²	#15690563	1	2	yes	—
73	C₂²	#15690565	1	2	yes	—
74	C₂²	C₂²×#11715871	1	1	yes	characteristic
75	C₄	—	2	2	no	—
76	C₄	—	193	2	no	—
77	C₄	—	193	2	no	—
78	C₂	—	386	4	no	—
79	C₂	#20259956	1	4	yes	direct product factor
80	C₂	C₂×C₂²⋊#11715871	1	1	yes	characteristic
81	C₂	C₂×#15690563	1	1	yes	characteristic
82	C₂	C₂×#15690565	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#11715871
commutator	C₂×C₁₉₃	C₂²×C₈
Frattini	C₂²	C₂²×#11715871
Fitting	C₂²×C₄×C₁₉₃	C₄
socle	C₂³×C₁₉₃	C₂×C₄
prime radical	C₂³×D₁₉₃	C₄
cosocle	C₂×Dic₁₉₃	C₂³
hypercenter	C₂²×C₄	#11715871
hypocenter	C₁₉₃	C₂×C₂²⋊C₈
LCS	G ▷ C₂×C₁₉₃ ▷ C₁₉₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×#13095400	C₂	semidirect
2. #20259956	C₂	direct (N × H)
5. C₂×#13095400	C₂²	semidirect
15. C₂²×D₁₉₃	C₈	semidirect
32. C₂×D₁₉₃	C₂×C₈	semidirect
36. C₂×C₁₉₃	C₂²⋊C₈	semidirect
41. C₁₉₃	C₂×C₂²⋊C₈	semidirect
79. C₂	#20259956	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13095400	2
#20259956	2
C₂²×C₄×D₁₉₃	2
C₂×C₂²⋊C₈	193

Subgroups — C2×#20259956 #27136228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20259956 #27136228