Subgroups — C₂×C₃⋊#95 #5208

Order 192.

330 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂³×Dic₃	C₂	1	2	yes	maximal
3	C₃⋊#95	C₂	1	4	yes	maximal, direct product factor
4	C₂×#95	—	3	1	no	maximal, Sylow
5	C₂⁴×C₃	C₂²	1	1	yes	characteristic
6	C₂²×C₃×C₄	—	2	4	no	—
7	C₂²×C₃×C₄	C₄	1	4	yes	complemented
8	C₂²×C₃×C₄	C₂²	1	2	yes	—
9	C₂²×Dic₃	—	2	4	no	—
10	C₂²×Dic₃	—	2	4	no	—
11	C₂²×Dic₃	C₄	1	8	yes	complemented
12	C₂²×Dic₃	C₂²	1	4	yes	—
13	C₂³×C₄	—	3	2	no	—
14	C₂³×C₄	D₃	1	1	yes	characteristic
15	#95	—	3	4	no	—
16	C₂³×C₃	C₂×C₄	1	4	yes	—
17	C₂³×C₃	C₂×C₄	1	2	yes	—
18	C₂³×C₃	D₄	1	2	yes	—
19	C₂³×C₃	D₄	1	4	yes	—
20	C₂³×C₃	Q₈	1	2	yes	—
21	C₂³×C₃	C₂³	1	1	yes	characteristic
22	C₂×C₃×C₄	—	2	8	no	—
23	C₂×C₃×C₄	—	2	4	no	—
24	C₂×C₃×C₄	C₂×C₄	1	4	yes	complemented
25	C₂×Dic₃	—	2	16	no	—
26	C₂×Dic₃	—	2	4	no	—
27	C₂×Dic₃	—	2	4	no	—
28	C₂×Dic₃	C₂×C₄	1	8	yes	complemented
29	C₂⁴	C₂×D₃	1	1	yes	characteristic
30	C₂²×C₄	—	2	4	no	—
31	C₂²×C₄	—	3	8	no	—
32	C₂²×C₄	—	3	4	no	—
33	C₂²×C₄	—	6	4	no	—
34	C₂²×C₄	—	6	4	no	—
35	C₂²×C₄	Dic₃	1	4	yes	complemented
36	C₂²×C₄	C₂×D₃	1	2	yes	—
37	C₂²×C₃	C₄²	1	4	yes	—
38	C₂²×C₃	C₂²⋊C₄	1	8	yes	—
39	C₂²×C₃	C₂²⋊C₄	1	4	yes	—
40	C₂²×C₃	C₄⋊C₄	1	8	yes	—
41	C₂²×C₃	C₄⋊C₄	1	4	yes	—
42	C₂²×C₃	C₂²×C₄	1	2	yes	—
43	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
44	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
45	C₂²×C₃	C₂×D₄	1	2	yes	—
46	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
47	C₃×C₄	—	2	4	no	—
48	Dic₃	—	2	8	no	—
49	C₂³	Dic₆	1	2	yes	—
50	C₂³	C₄×D₃	1	4	yes	—
51	C₂³	D₁₂	1	2	yes	—
52	C₂³	C₂×Dic₃	1	2	yes	—
53	C₂³	#67	1	4	yes	—
54	C₂³	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₄	—	2	8	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	3	8	no	—
58	C₂×C₄	—	6	16	no	—
59	C₂×C₄	—	6	4	no	—
60	C₂×C₄	—	6	4	no	—
61	C₂×C₄	C₂×Dic₃	1	4	yes	complemented
62	C₂×C₃	#95	1	8	yes	complemented
63	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₃	C₂×C₂²⋊C₄	1	2	yes	—
65	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₃	C₂×C₄⋊C₄	1	2	yes	—
67	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
68	C₂²	C₄×Dic₃	1	4	yes	—
69	C₂²	Dic₃⋊C₄	1	8	yes	—
70	C₂²	C₄⋊Dic₃	1	4	yes	—
71	C₂²	(C₂×D₃)⋊C₄	1	8	yes	—
72	C₂²	#217	1	4	yes	—
73	C₂²	C₂×Dic₆	1	1	yes	characteristic
74	C₂²	C₂×C₄×D₃	1	2	yes	—
75	C₂²	C₂×D₁₂	1	1	yes	characteristic
76	C₂²	C₂²×Dic₃	1	1	yes	characteristic
77	C₂²	C₂×#67	1	2	yes	—
78	C₄	—	2	4	no	—
79	C₄	—	6	8	no	—
80	C₃	C₂×#95	1	1	yes	characteristic, complemented, Sylow
81	C₂	C₃⋊#95	1	8	yes	direct product factor
82	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic
83	C₂	C₂×Dic₃⋊C₄	1	2	yes	—
84	C₂	C₂×C₄⋊Dic₃	1	1	yes	characteristic
85	C₂	C₂×(C₂×D₃)⋊C₄	1	2	yes	—
86	C₂	C₂×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×D₃
commutator	C₂×C₃	C₂×C₄²
Frattini	C₂³	C₂²×D₃
Fitting	C₂³×C₃×C₄	C₂
socle, prime radical	C₂⁴×C₃	C₂²
cosocle	C₂³×C₃	C₂³
hypercenter	C₂³×C₄	D₃
hypocenter	C₃	C₂×#95
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄

Complements

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

N	H ≅ G/N	type
3. C₃⋊#95	C₂	direct (N × H)
7. C₂²×C₃×C₄	C₄	semidirect
11. C₂²×Dic₃	C₄	semidirect
24. C₂×C₃×C₄	C₂×C₄	semidirect
28. C₂×Dic₃	C₂×C₄	semidirect
35. C₂²×C₄	Dic₃	semidirect
61. C₂×C₄	C₂×Dic₃	semidirect
62. C₂×C₃	#95	semidirect
80. C₃	C₂×#95	semidirect
81. C₂	C₃⋊#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂³×Dic₃	2
C₃⋊#95	2
C₂×#95	3

Subgroups — C2×C3⋊#95 #5208

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃⋊#95 #5208