Subgroups — #4464

Order 192.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#875	C₂	1	1	yes	maximal, characteristic
2	C₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
3	#803	C₂	1	1	yes	maximal, characteristic, complemented
4	#329	—	3	1	no	maximal, Sylow
5	C₂×D₁₂	C₄	1	1	yes	characteristic
6	C₂×Dic₆	C₄	1	1	yes	characteristic
7	C₂×C₃×C₈	—	2	1	no	—
8	C₃×C₄²	C₂²	1	1	yes	characteristic
9	(C₂×D₃)⋊C₄	—	2	1	no	—
10	(C₂×D₃)⋊C₄	—	2	1	no	—
11	C₂×C₃⋊C₈	—	2	1	no	—
12	#124	—	3	1	no	—
13	#97	—	3	1	no	—
14	#97	D₃	1	1	yes	characteristic, complemented
15	C₂²×D₃	—	2	1	no	—
16	C₂×C₃×C₄	C₂×C₄	1	1	yes	characteristic
17	C₂×C₃×C₄	D₄	1	1	yes	characteristic
18	C₂×C₃×C₄	D₄	1	1	yes	characteristic
19	C₂×Dic₃	—	2	1	no	—
20	D₁₂	—	4	1	no	—
21	Dic₆	—	4	1	no	—
22	C₃×C₈	—	2	2	no	—
23	C₃⋊C₈	—	2	2	no	—
24	C₂×Q₈	—	3	1	no	—
25	C₂×D₄	—	3	1	no	—
26	C₂×C₈	—	2	1	no	—
27	C₂×C₈	—	6	1	no	—
28	C₂²⋊C₄	—	6	1	no	—
29	C₂²⋊C₄	—	6	1	no	—
30	C₄²	C₂×D₃	1	1	yes	characteristic
31	C₂²×C₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×D₃	—	4	1	no	—
33	C₂×D₃	—	4	1	no	—
34	C₂×D₃	—	4	1	no	—
35	C₃×C₄	—	2	1	no	—
36	C₃×C₄	—	2	1	no	—
37	C₃×C₄	—	2	1	no	—
38	Dic₃	—	4	1	no	—
39	C₂³	—	6	1	no	—
40	Q₈	—	12	1	no	—
41	D₄	—	12	1	no	—
42	C₂×C₄	—	6	1	no	—
43	C₂×C₄	C₄×D₃	1	1	yes	characteristic
44	C₂×C₄	D₁₂	1	1	yes	characteristic
45	C₂×C₄	#67	1	1	yes	characteristic
46	C₈	—	2	2	no	—
47	C₈	—	6	2	no	—
48	C₂×C₃	#100	1	1	yes	characteristic
49	C₂×C₃	#104	1	1	yes	characteristic
50	C₂×C₃	#104	1	1	yes	characteristic
51	D₃	—	8	1	no	—
52	C₂²	—	12	1	no	—
53	C₂²	—	12	1	no	—
54	C₂²	—	12	1	no	—
55	C₂²	(C₂×D₃)⋊C₄	1	1	yes	characteristic
56	C₄	—	2	1	no	—
57	C₄	—	2	1	no	—
58	C₄	—	2	1	no	—
59	C₄	—	12	1	no	—
60	C₃	#329	1	1	yes	characteristic, complemented, Sylow
61	C₂	—	24	1	no	—
62	C₂	#805	1	1	yes	characteristic
63	C₂	#823	1	1	yes	characteristic
64	C₂	#825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	(C₂×D₃)⋊C₄
commutator	C₂×C₃×C₄	C₂×C₄
Frattini	C₄²	C₂×D₃
Fitting	C₃×#97	C₂
socle	C₂²×C₃	C₂²⋊C₄
prime radical	C₂×D₁₂	C₄
cosocle	C₃×C₄²	C₂²
hypercenter	#97	D₃
hypocenter	C₃	#329
LCS	G ▷ C₂×C₃×C₄ ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

Complements

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

N	H ≅ G/N	type
2. C₃×#97	C₂	semidirect
3. #803	C₂	semidirect
14. #97	D₃	semidirect
60. C₃	#329	semidirect

Maximal subgroups

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

subgroup	index
#875	2
C₃×#97	2
#803	2
#329	3