Subgroups — C₄×#217 #5209

Order 192.

258 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	C₂×#217	C₂	1	2	yes	maximal
3	C₂×C₄×Dic₃	C₂	1	2	yes	maximal, complemented
4	C₃⋊#95	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊C₄	—	3	1	no	maximal, Sylow
6	C₂⁴×C₃	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	—	2	4	no	—
8	C₂²×C₃×C₄	C₄	1	4	yes	complemented
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×Dic₃	C₂²	1	4	yes	—
12	#217	C₄	1	8	yes	direct product factor
13	C₄×Dic₃	—	2	4	no	—
14	C₂³×C₄	D₃	1	1	yes	characteristic
15	C₂×C₂²⋊C₄	—	3	2	no	—
16	C₂×C₄²	—	3	2	no	—
17	#95	—	3	2	no	—
18	C₂³×C₃	—	2	2	no	—
19	C₂³×C₃	—	2	2	no	—
20	C₂³×C₃	C₂×C₄	1	4	yes	—
21	C₂³×C₃	C₂×C₄	1	2	yes	—
22	C₂³×C₃	C₂³	1	1	yes	characteristic
23	C₂×C₃×C₄	—	2	2	no	—
24	C₂×C₃×C₄	—	2	8	no	—
25	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
26	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
27	C₂×C₃×C₄	D₄	1	4	yes	—
28	C₂×Dic₃	—	2	4	no	—
29	C₂×Dic₃	—	2	4	no	—
30	C₂×Dic₃	C₂×C₄	1	8	yes	complemented
31	C₂⁴	C₂×D₃	1	1	yes	characteristic
32	C₂²×C₄	—	2	4	no	—
33	C₂²×C₄	—	3	4	no	—
34	C₂²×C₄	Dic₃	1	4	yes	complemented
35	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
36	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
37	C₂²⋊C₄	—	3	8	no	—
38	C₄²	—	6	4	no	—
39	C₂²×C₃	—	2	2	no	—
40	C₂²×C₃	—	2	2	no	—
41	C₂²×C₃	—	2	8	no	—
42	C₂²×C₃	C₄²	1	4	yes	complemented
43	C₂²×C₃	C₂²×C₄	1	2	yes	—
44	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₃	C₂×D₄	1	2	yes	—
46	C₂²×C₃	#41	1	2	yes	—
47	C₃×C₄	—	2	2	no	—
48	C₃×C₄	C₂²⋊C₄	1	4	yes	complemented
49	Dic₃	—	2	8	no	—
50	C₂³	—	2	2	no	—
51	C₂³	—	2	2	no	—
52	C₂³	C₄×D₃	1	4	yes	—
53	C₂³	C₂×Dic₃	1	2	yes	—
54	C₂³	C₂²×D₃	1	1	yes	characteristic
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	8	no	—
57	C₂×C₄	—	3	8	no	—
58	C₂×C₄	—	6	4	no	—
59	C₂×C₄	—	6	4	no	—
60	C₂×C₄	C₂×Dic₃	1	2	yes	—
61	C₂×C₄	C₂×Dic₃	1	2	yes	—
62	C₂×C₄	#67	1	4	yes	—
63	C₂×C₃	—	2	4	no	—
64	C₂×C₃	C₂×C₄²	1	1	yes	characteristic
65	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
66	C₂×C₃	#117	1	1	yes	characteristic
67	C₂×C₃	C₄×D₄	1	4	yes	—
68	C₂²	—	2	2	no	—
69	C₂²	—	2	8	no	—
70	C₂²	—	2	2	no	—
71	C₂²	C₄×Dic₃	1	4	yes	complemented
72	C₂²	C₂×C₄×D₃	1	2	yes	—
73	C₂²	#235	1	2	yes	—
74	C₂²	C₂²×Dic₃	1	1	yes	characteristic
75	C₂²	C₂×#67	1	2	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	6	8	no	—
78	C₄	#217	1	4	yes	direct product factor
79	C₃	C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
80	C₂	—	2	4	no	—
81	C₂	C₂×C₄×Dic₃	1	1	yes	characteristic
82	C₂	#926	1	1	yes	characteristic
83	C₂	C₄×#67	1	4	yes	—
84	C₂	C₂×#217	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×Dic₃	C₂	semidirect
4. C₃⋊#95	C₂	semidirect
8. C₂²×C₃×C₄	C₄	semidirect
12. #217	C₄	direct (N × H)
30. C₂×Dic₃	C₂×C₄	semidirect
34. C₂²×C₄	Dic₃	semidirect
42. C₂²×C₃	C₄²	semidirect
48. C₃×C₄	C₂²⋊C₄	semidirect
71. C₂²	C₄×Dic₃	semidirect
78. C₄	#217	direct (N × H)
79. C₃	C₄×C₂²⋊C₄	semidirect

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
C₂×#217	2
C₂×C₄×Dic₃	2
C₃⋊#95	2
C₄×C₂²⋊C₄	3

Subgroups — C4×#217 #5209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#217 #5209