Subgroups — #4977

Order 192.

154 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₃	C₂	1	1	yes	maximal, characteristic
4	C₃⋊#95	C₂	1	4	yes	maximal
5	#382	—	3	1	no	maximal, Sylow
6	C₂²×C₃×C₄	C₂²	1	2	yes	—
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂²×Dic₃	C₂²	1	2	yes	—
9	C₂²×Dic₃	C₂²	1	2	yes	—
10	C₃×C₄⋊C₄	—	2	2	no	—
11	C₄⋊Dic₃	—	2	2	no	—
12	C₄×Dic₃	C₄	1	4	yes	complemented
13	C₂×C₄⋊C₄	—	3	1	no	—
14	C₂×C₄⋊C₄	D₃	1	1	yes	characteristic
15	C₂×C₄²	—	3	1	no	—
16	#95	—	3	4	no	—
17	C₂³×C₃	C₂³	1	1	yes	characteristic
18	C₂×C₃×C₄	—	2	2	no	—
19	C₂×C₃×C₄	—	2	4	no	—
20	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
21	C₂×C₃×C₄	D₄	1	2	yes	—
22	C₂×C₃×C₄	Q₈	1	2	yes	—
23	C₂×Dic₃	—	2	2	no	—
24	C₂×Dic₃	—	2	2	no	—
25	C₂×Dic₃	—	2	2	no	—
26	C₂×Dic₃	—	2	4	no	—
27	C₂×Dic₃	C₂×C₄	1	4	yes	—
28	C₂²×C₄	—	3	2	no	—
29	C₂²×C₄	—	3	2	no	—
30	C₂²×C₄	C₂×D₃	1	2	yes	—
31	C₂²×C₄	C₂×D₃	1	1	yes	characteristic
32	C₄⋊C₄	—	2	2	no	—
33	C₄⋊C₄	—	6	2	no	—
34	C₄²	—	3	4	no	—
35	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
37	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
38	C₂²×C₃	#41	1	2	yes	—
39	C₂²×C₃	#41	1	2	yes	—
40	C₃×C₄	—	4	2	no	—
41	C₃×C₄	C₄⋊C₄	1	4	yes	—
42	Dic₃	—	2	4	no	—
43	Dic₃	—	4	2	no	—
44	C₂³	C₂²×D₃	1	1	yes	characteristic
45	C₂×C₄	—	2	4	no	—
46	C₂×C₄	—	2	2	no	—
47	C₂×C₄	—	3	4	no	—
48	C₂×C₄	—	6	2	no	—
49	C₂×C₄	—	6	2	no	—
50	C₂×C₄	—	6	4	no	—
51	C₂×C₄	—	6	2	no	—
52	C₂×C₄	Dic₆	1	2	yes	—
53	C₂×C₄	C₄×D₃	1	2	yes	—
54	C₂×C₄	#67	1	2	yes	—
55	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₃	#117	1	2	yes	—
57	C₂×C₃	#124	1	1	yes	characteristic
58	C₂×C₃	#124	1	1	yes	characteristic
59	C₂×C₃	#125	1	2	yes	—
60	C₂²	C₂×Dic₆	1	1	yes	characteristic
61	C₂²	C₂×C₄×D₃	1	1	yes	characteristic
62	C₂²	#237	1	2	yes	—
63	C₂²	#239	1	2	yes	—
64	C₂²	C₂×#67	1	1	yes	characteristic
65	C₄	—	4	2	no	—
66	C₄	—	6	4	no	—
67	C₄	—	12	2	no	—
68	C₄	Dic₃⋊C₄	1	4	yes	—
69	C₃	#382	1	1	yes	characteristic, complemented, Sylow
70	C₂	#890	1	2	yes	—
71	C₂	#892	1	2	yes	—
72	C₂	C₂×Dic₃⋊C₄	1	1	yes	characteristic
73	C₂	#936	1	1	yes	characteristic
74	C₂	#947	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₃
commutator	C₂²×C₃	C₂²×C₄
Fitting	C₂×C₃×C₄⋊C₄	C₂
socle, prime radical, cosocle	C₂³×C₃	C₂³
hypercenter	C₂×C₄⋊C₄	D₃
hypocenter	C₃	#382
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
12. C₄×Dic₃	C₄	semidirect
69. C₃	#382	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄⋊C₄	2
C₂×C₄⋊Dic₃	2
C₂×C₄×Dic₃	2
C₃⋊#95	2
#382	3