Subgroups — C₃×#380 #5254

Order 192.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄⋊C₄	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×C₂²⋊C₄	C₂	1	2	yes	maximal
4	C₃×#95	C₂	1	2	yes	maximal, complemented
5	#380	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
6	C₂⁴×C₃	C₂²	1	1	yes	characteristic
7	C₂²×C₃×C₄	—	2	4	no	—
8	C₂²×C₃×C₄	C₄	1	4	yes	complemented
9	C₂²×C₃×C₄	C₂²	1	4	yes	—
10	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₄	C₂²	1	1	yes	characteristic
12	C₃×C₄⋊C₄	—	2	4	no	—
13	C₃×C₂²⋊C₄	—	2	4	no	—
14	C₂³×C₄	C₂×C₃	1	1	yes	characteristic
15	C₂×C₄⋊C₄	C₂×C₃	1	2	yes	complemented
16	C₂×C₂²⋊C₄	C₂×C₃	1	2	yes	—
17	#95	C₂×C₃	1	2	yes	complemented
18	C₂³×C₃	—	2	2	no	—
19	C₂³×C₃	—	2	2	no	—
20	C₂³×C₃	C₂×C₄	1	2	yes	—
21	C₂³×C₃	D₄	1	2	yes	—
22	C₂³×C₃	Q₈	1	2	yes	—
23	C₂³×C₃	C₂³	1	1	yes	characteristic
24	C₂×C₃×C₄	—	2	2	no	—
25	C₂×C₃×C₄	—	2	8	no	—
26	C₂×C₃×C₄	—	2	4	no	—
27	C₂×C₃×C₄	—	2	4	no	—
28	C₂×C₃×C₄	—	2	4	no	—
29	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
30	C₂×C₃×C₄	C₂×C₄	1	2	yes	—
31	C₂×C₃×C₄	D₄	1	4	yes	—
32	C₂⁴	C₂²×C₃	1	1	yes	characteristic
33	C₂²×C₄	—	2	4	no	—
34	C₂²×C₄	C₃×C₄	1	4	yes	complemented
35	C₂²×C₄	C₂²×C₃	1	4	yes	—
36	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
37	C₂²×C₄	C₂²×C₃	1	1	yes	characteristic
38	C₄⋊C₄	—	2	4	no	—
39	C₂²⋊C₄	—	2	4	no	—
40	C₂²×C₃	—	2	2	no	—
41	C₂²×C₃	—	2	2	no	—
42	C₂²×C₃	—	2	4	no	—
43	C₂²×C₃	—	2	4	no	—
44	C₂²×C₃	C₄⋊C₄	1	4	yes	complemented
45	C₂²×C₃	C₂²×C₄	1	1	yes	characteristic
46	C₂²×C₃	C₂×D₄	1	2	yes	—
47	C₂²×C₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₃	C₂×Q₈	1	1	yes	characteristic
49	C₂²×C₃	#41	1	2	yes	—
50	C₃×C₄	—	2	2	no	—
51	C₃×C₄	—	4	4	no	—
52	C₃×C₄	C₂²⋊C₄	1	4	yes	complemented
53	C₂³	—	2	2	no	—
54	C₂³	—	2	2	no	—
55	C₂³	C₂×C₃×C₄	1	2	yes	—
56	C₂³	C₃×D₄	1	2	yes	—
57	C₂³	C₃×Q₈	1	2	yes	—
58	C₂³	C₂³×C₃	1	1	yes	characteristic
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	8	no	—
61	C₂×C₄	—	2	4	no	—
62	C₂×C₄	—	2	4	no	—
63	C₂×C₄	—	2	4	no	—
64	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
65	C₂×C₄	C₂×C₃×C₄	1	2	yes	—
66	C₂×C₄	C₃×D₄	1	4	yes	—
67	C₂×C₃	—	2	4	no	—
68	C₂×C₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₃	C₂×C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₃	#117	1	1	yes	characteristic
71	C₂×C₃	#121	1	2	yes	—
72	C₂×C₃	C₂²⋊Q₈	1	2	yes	—
73	C₂²	—	2	2	no	—
74	C₂²	—	2	2	no	—
75	C₂²	—	2	4	no	—
76	C₂²	—	2	4	no	—
77	C₂²	C₃×C₄⋊C₄	1	4	yes	complemented
78	C₂²	C₂²×C₃×C₄	1	1	yes	characteristic
79	C₂²	C₂×C₃×D₄	1	2	yes	—
80	C₂²	C₂×C₃×D₄	1	1	yes	characteristic
81	C₂²	C₂×C₃×Q₈	1	1	yes	characteristic
82	C₂²	C₃×#41	1	2	yes	—
83	C₄	—	2	2	no	—
84	C₄	—	4	4	no	—
85	C₄	C₃×C₂²⋊C₄	1	4	yes	complemented
86	C₃	#380	1	1	yes	characteristic, direct product factor, Sylow
87	C₂	—	2	4	no	—
88	C₂	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
89	C₂	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
90	C₂	C₃×#117	1	1	yes	characteristic
91	C₂	C₃×#121	1	2	yes	—
92	C₂	C₃×C₂²⋊Q₈	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃	C₂³
commutator	C₂²	C₂²×C₃×C₄
Frattini, cosocle	C₂³	C₂³×C₃
prime radical	C₂⁴×C₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄⋊C₄	C₂	semidirect
4. C₃×#95	C₂	semidirect
5. #380	C₃	direct (N × H)
8. C₂²×C₃×C₄	C₄	semidirect
15. C₂×C₄⋊C₄	C₂×C₃	semidirect
17. #95	C₂×C₃	semidirect
34. C₂²×C₄	C₃×C₄	semidirect
44. C₂²×C₃	C₄⋊C₄	semidirect
52. C₃×C₄	C₂²⋊C₄	semidirect
77. C₂²	C₃×C₄⋊C₄	semidirect
85. C₄	C₃×C₂²⋊C₄	semidirect
86. C₃	#380	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄	2
C₂×C₃×C₄⋊C₄	2
C₂×C₃×C₂²⋊C₄	2
C₃×#95	2
#380	3

Subgroups — C3×#380 #5254

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#380 #5254