Subgroups — C₃×#398 #5272

Order 192.

150 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×C₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄⋊C₄	C₂	1	2	yes	maximal
4	C₃×#95	C₂	1	2	yes	maximal
5	C₃×#95	C₂	1	1	yes	maximal, characteristic
6	#398	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₄	C₂²	1	2	yes	—
9	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄	C₂²	1	2	yes	—
12	C₃×C₄⋊C₄	—	2	2	no	—
13	C₃×C₄⋊C₄	—	2	4	no	—
14	C₃×C₄⋊C₄	—	2	2	no	—
15	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
16	C₂×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂×C₃	1	2	yes	—
18	#95	C₂×C₃	1	2	yes	—
19	#95	C₂×C₃	1	1	yes	characteristic
20	C₂³×C₃	C₂³	1	1	yes	characteristic
21	C₂×C₃×C₄	—	2	1	no	—
22	C₂×C₃×C₄	—	2	2	no	—
23	C₂×C₃×C₄	—	2	1	no	—
24	C₂×C₃×C₄	—	2	2	no	—
25	C₂×C₃×C₄	—	2	2	no	—
26	C₂×C₃×C₄	—	2	2	no	—
27	C₂×C₃×C₄	—	2	2	no	—
28	C₂×C₃×C₄	—	2	1	no	—
29	C₂×C₃×C₄	—	2	2	no	—
30	C₂×C₃×C₄	—	2	2	no	—
31	C₂×C₃×C₄	D₄	1	2	yes	—
32	C₂×C₃×C₄	D₄	1	2	yes	—
33	C₂×C₃×C₄	Q₈	1	4	yes	—
34	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
35	C₂²×C₄	C₂²×C₃	1	2	yes	—
36	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
38	C₂²×C₄	C₂²×C₃	1	2	yes	—
39	C₄⋊C₄	—	2	2	no	—
40	C₄⋊C₄	—	2	4	no	—
41	C₄⋊C₄	—	2	2	no	—
42	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₃	C₂×Q₈	1	2	yes	—
45	C₂²×C₃	#41	1	1	yes	characteristic
46	C₂²×C₃	#41	1	2	yes	—
47	C₃×C₄	—	2	2	no	—
48	C₃×C₄	—	2	4	no	—
49	C₃×C₄	—	2	2	no	—
50	C₃×C₄	—	4	2	no	—
51	C₃×C₄	—	4	1	no	—
52	C₂³	C₂³×C₃	1	1	yes	characteristic
53	C₂×C₄	—	2	1	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	2	2	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	2	2	no	—
62	C₂×C₄	—	2	2	no	—
63	C₂×C₄	C₃×D₄	1	2	yes	—
64	C₂×C₄	C₃×D₄	1	2	yes	—
65	C₂×C₄	C₃×Q₈	1	4	yes	—
66	C₂×C₃	#121	1	1	yes	characteristic
67	C₂×C₃	C₂²⋊Q₈	1	2	yes	—
68	C₂×C₃	#123	1	1	yes	characteristic
69	C₂×C₃	#125	1	2	yes	—
70	C₂×C₃	C₄⋊Q₈	1	1	yes	characteristic
71	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
72	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
73	C₂²	C₂×C₃×Q₈	1	2	yes	—
74	C₂²	C₃×#41	1	1	yes	characteristic
75	C₂²	C₃×#41	1	2	yes	—
76	C₄	—	2	2	no	—
77	C₄	—	2	4	no	—
78	C₄	—	2	2	no	—
79	C₄	—	4	2	no	—
80	C₄	—	4	1	no	—
81	C₃	#398	1	1	yes	characteristic, direct product factor, Sylow
82	C₂	C₃×#121	1	1	yes	characteristic
83	C₂	C₃×C₂²⋊Q₈	1	2	yes	—
84	C₂	C₃×#123	1	1	yes	characteristic
85	C₂	C₃×#125	1	2	yes	—
86	C₂	C₃×C₄⋊Q₈	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
6. #398	C₃	direct (N × H)
81. C₃	#398	direct (N × H)

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
C₃×#95	2
#398	3

Subgroups — C3×#398 #5272

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#398 #5272