Subgroups — C₃×#448 #5322

Order 192.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₃×#121	C₂	1	1	yes	maximal, characteristic
4	C₃×#103	C₂	1	2	yes	maximal, complemented
5	C₃×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#448	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
7	C₂×C₃×Q₈	—	2	4	no	—
8	C₂×C₃×Q₈	—	2	1	no	—
9	C₂×C₃×Q₈	C₂²	1	2	yes	—
10	C₂×C₃×D₄	—	2	1	no	—
11	C₂×C₃×D₄	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄	—	2	1	no	—
13	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
14	C₃×SD₁₆	—	2	4	no	—
15	C₂×C₃×C₈	C₂²	1	2	yes	—
16	C₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×C₂²⋊C₄	—	2	1	no	—
18	C₂²×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
19	C₂×SD₁₆	C₂×C₃	1	2	yes	complemented
20	#121	C₂×C₃	1	1	yes	characteristic
21	#103	C₂×C₃	1	2	yes	complemented
22	C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic, complemented
23	C₂³×C₃	—	2	1	no	—
24	C₂³×C₃	D₄	1	1	yes	characteristic
25	C₃×Q₈	—	2	4	no	—
26	C₃×Q₈	—	2	2	no	—
27	C₃×Q₈	D₄	1	4	yes	complemented
28	C₃×D₄	—	2	2	no	—
29	C₃×D₄	—	4	2	no	—
30	C₂×C₃×C₄	—	2	4	no	—
31	C₂×C₃×C₄	—	2	2	no	—
32	C₂×C₃×C₄	—	2	2	no	—
33	C₂×C₃×C₄	—	2	1	no	—
34	C₂×C₃×C₄	D₄	1	1	yes	characteristic
35	C₂×C₃×C₄	C₂³	1	1	yes	characteristic
36	C₃×C₈	—	2	2	no	—
37	C₂×Q₈	—	2	4	no	—
38	C₂×Q₈	—	2	1	no	—
39	C₂×Q₈	C₂²×C₃	1	2	yes	—
40	C₂×D₄	—	2	1	no	—
41	C₂×D₄	C₂²×C₃	1	1	yes	characteristic
42	C₂²×C₄	—	2	1	no	—
43	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
44	SD₁₆	—	2	4	no	—
45	C₂×C₈	C₂²×C₃	1	2	yes	—
46	C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
47	C₂²⋊C₄	—	2	1	no	—
48	C₂²×C₃	—	2	1	no	—
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	4	1	no	—
51	C₂²×C₃	—	4	1	no	—
52	C₂²×C₃	—	4	1	no	—
53	C₂²×C₃	SD₁₆	1	2	yes	complemented
54	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
55	C₃×C₄	—	2	4	no	—
56	C₃×C₄	—	2	1	no	—
57	C₃×C₄	—	4	1	no	—
58	C₃×C₄	C₂×D₄	1	2	yes	—
59	C₂³	—	2	1	no	—
60	C₂³	C₃×D₄	1	1	yes	characteristic
61	Q₈	—	2	4	no	—
62	Q₈	—	2	2	no	—
63	Q₈	C₃×D₄	1	4	yes	complemented
64	D₄	—	2	2	no	—
65	D₄	—	4	2	no	—
66	C₂×C₄	—	2	4	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	2	2	no	—
69	C₂×C₄	—	2	1	no	—
70	C₂×C₄	C₃×D₄	1	1	yes	characteristic
71	C₂×C₄	C₂³×C₃	1	1	yes	characteristic
72	C₈	—	2	2	no	—
73	C₂×C₃	—	2	2	no	—
74	C₂×C₃	—	8	1	no	—
75	C₂×C₃	#120	1	1	yes	characteristic
76	C₂×C₃	C₂×SD₁₆	1	1	yes	characteristic
77	C₂×C₃	#137	1	1	yes	characteristic
78	C₂²	—	2	1	no	—
79	C₂²	—	2	1	no	—
80	C₂²	—	4	1	no	—
81	C₂²	—	4	1	no	—
82	C₂²	—	4	1	no	—
83	C₂²	C₃×SD₁₆	1	2	yes	complemented
84	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	2	1	no	—
87	C₄	—	4	1	no	—
88	C₄	C₂×C₃×D₄	1	2	yes	—
89	C₃	#448	1	1	yes	characteristic, direct product factor, Sylow
90	C₂	—	2	2	no	—
91	C₂	—	8	1	no	—
92	C₂	C₃×#120	1	1	yes	characteristic
93	C₂	C₂×C₃×SD₁₆	1	1	yes	characteristic
94	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	C₃×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×Q₈	C₂	semidirect
2. C₂×C₃×SD₁₆	C₂	semidirect
4. C₃×#103	C₂	semidirect
5. C₃×C₂²⋊C₈	C₂	semidirect
6. #448	C₃	direct (N × H)
18. C₂²×Q₈	C₂×C₃	semidirect
19. C₂×SD₁₆	C₂×C₃	semidirect
21. #103	C₂×C₃	semidirect
22. C₂²⋊C₈	C₂×C₃	semidirect
27. C₃×Q₈	D₄	semidirect
53. C₂²×C₃	SD₁₆	semidirect
63. Q₈	C₃×D₄	semidirect
83. C₂²	C₃×SD₁₆	semidirect
89. C₃	#448	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×Q₈	2
C₂×C₃×SD₁₆	2
C₃×#121	2
C₃×#103	2
C₃×C₂²⋊C₈	2
#448	3

Subgroups — C3×#448 #5322

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#448 #5322