Subgroups — C₃×#474 #5348

Order 192.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₄×D₄	C₂	1	1	yes	maximal, characteristic
3	C₃×#107	C₂	1	2	yes	maximal, complemented
4	C₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#102	C₂	1	2	yes	maximal
6	#474	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	—	2	1	no	—
8	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₄	—	2	1	no	—
10	C₂×C₃×C₈	C₂²	1	2	yes	—
11	C₃×C₄⋊C₄	—	2	1	no	—
12	C₃×C₄⋊C₄	C₂²	1	2	yes	—
13	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₃×C₂²⋊C₄	—	2	1	no	—
15	C₃×C₄²	C₂²	1	1	yes	characteristic
16	C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
17	C₄×D₄	C₂×C₃	1	1	yes	characteristic
18	#107	C₂×C₃	1	2	yes	complemented
19	C₄⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
20	#102	C₂×C₃	1	2	yes	—
21	C₂³×C₃	—	2	1	no	—
22	C₃×Q₈	—	4	2	no	—
23	C₃×D₄	—	2	1	no	—
24	C₃×D₄	Q₈	1	2	yes	complemented
25	C₂×C₃×C₄	—	2	1	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	—	4	2	no	—
28	C₂×C₃×C₄	D₄	1	1	yes	characteristic
29	C₂×C₃×C₄	D₄	1	1	yes	characteristic
30	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
31	C₃×C₈	—	2	2	no	—
32	C₂×Q₈	—	2	1	no	—
33	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
34	C₂²×C₄	—	2	1	no	—
35	C₂×C₈	C₂²×C₃	1	2	yes	—
36	C₄⋊C₄	—	2	1	no	—
37	C₄⋊C₄	C₂²×C₃	1	2	yes	—
38	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
39	C₂²⋊C₄	—	2	1	no	—
40	C₄²	C₂²×C₃	1	1	yes	characteristic
41	C₂²×C₃	—	2	2	no	—
42	C₂²×C₃	—	4	1	no	—
43	C₂²×C₃	—	4	1	no	—
44	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
45	C₃×C₄	—	2	1	no	—
46	C₃×C₄	—	4	1	no	—
47	C₃×C₄	—	4	2	no	—
48	C₃×C₄	D₈	1	2	yes	—
49	C₃×C₄	C₂×Q₈	1	1	yes	characteristic
50	C₃×C₄	#41	1	1	yes	characteristic
51	C₂³	—	2	1	no	—
52	Q₈	—	4	2	no	—
53	D₄	—	2	1	no	—
54	D₄	C₃×Q₈	1	2	yes	complemented
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	4	2	no	—
58	C₂×C₄	C₃×D₄	1	1	yes	characteristic
59	C₂×C₄	C₃×D₄	1	1	yes	characteristic
60	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₂×C₃	—	4	2	no	—
63	C₂×C₃	C₂²⋊Q₈	1	1	yes	characteristic
64	C₂×C₃	C₂×D₈	1	1	yes	characteristic
65	C₂×C₃	#137	1	1	yes	characteristic
66	C₂²	—	2	2	no	—
67	C₂²	—	4	1	no	—
68	C₂²	—	4	1	no	—
69	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	4	1	no	—
72	C₄	—	4	2	no	—
73	C₄	C₃×D₈	1	2	yes	—
74	C₄	C₂×C₃×Q₈	1	1	yes	characteristic
75	C₄	C₃×#41	1	1	yes	characteristic
76	C₃	#474	1	1	yes	characteristic, direct product factor, Sylow
77	C₂	—	4	2	no	—
78	C₂	C₃×C₂²⋊Q₈	1	1	yes	characteristic
79	C₂	C₂×C₃×D₈	1	1	yes	characteristic
80	C₂	C₃×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₃
prime radical	C₂×C₃×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₄⋊Q₈	C₂	semidirect
3. C₃×#107	C₂	semidirect
4. C₃×C₄⋊C₈	C₂	semidirect
6. #474	C₃	direct (N × H)
16. C₄⋊Q₈	C₂×C₃	semidirect
18. #107	C₂×C₃	semidirect
19. C₄⋊C₈	C₂×C₃	semidirect
24. C₃×D₄	Q₈	semidirect
54. D₄	C₃×Q₈	semidirect
76. C₃	#474	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄⋊Q₈	2
C₃×C₄×D₄	2
C₃×#107	2
C₃×C₄⋊C₈	2
C₃×#102	2
#474	3

Subgroups — C3×#474 #5348

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#474 #5348