Subgroups — C₃²×#2247 #11769296

Order 1152.

528 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×Q₃₂	C₂	1	4	yes	maximal
2	C₃²×#494	C₂	1	2	yes	maximal
3	C₃²×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₃×#2247	C₃	1	4	yes	maximal, direct product factor
5	C₂×C₃²×Q₁₆	—	2	2	no	—
6	C₂×C₃²×Q₁₆	C₂²	1	4	yes	—
7	C₃²×C₄⋊Q₈	—	2	2	no	—
8	C₃²×Q₃₂	—	2	8	no	—
9	C₂×C₃²×C₁₆	C₂²	1	2	yes	—
10	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₃×Q₃₂	C₂×C₃	1	16	yes	—
12	C₃×#494	C₂×C₃	1	8	yes	—
13	C₃×C₄×C₁₆	C₂×C₃	1	4	yes	—
14	C₂×C₃²×Q₈	—	2	4	no	—
15	C₃²×Q₁₆	—	2	8	no	—
16	C₃²×Q₁₆	—	4	4	no	—
17	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
18	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
19	C₃²×C₄⋊C₄	—	4	4	no	—
20	C₃²×C₄²	D₄	1	1	yes	characteristic
21	C₃²×C₁₆	D₄	1	4	yes	—
22	#2247	C₃²	1	1	yes	characteristic, direct product factor, Sylow
23	C₂×C₃×Q₁₆	—	2	8	no	—
24	C₂×C₃×Q₁₆	C₂²×C₃	1	16	yes	—
25	C₃×C₄⋊Q₈	—	2	8	no	—
26	C₃×Q₃₂	—	2	32	no	—
27	C₂×C₃×C₁₆	C₂²×C₃	1	8	yes	—
28	C₃×C₄×C₈	C₂²×C₃	1	4	yes	—
29	C₃²×Q₈	—	4	4	no	—
30	C₃²×Q₈	—	4	4	no	—
31	C₂×C₃²×C₄	—	4	4	no	—
32	C₂×C₃²×C₄	D₈	1	2	yes	—
33	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
34	C₃²×C₈	D₈	1	2	yes	—
35	C₃²×C₈	C₂×D₄	1	2	yes	—
36	C₂×Q₃₂	C₂×C₃²	1	4	yes	—
37	#494	C₂×C₃²	1	2	yes	—
38	C₄×C₁₆	C₂×C₃²	1	1	yes	characteristic
39	C₂×C₃×Q₈	—	2	16	no	—
40	C₃×Q₁₆	—	2	32	no	—
41	C₃×Q₁₆	—	4	16	no	—
42	C₂×C₃×C₈	C₃×D₄	1	4	yes	—
43	C₂×C₃×C₈	C₂³×C₃	1	4	yes	—
44	C₃×C₄⋊C₄	—	4	16	no	—
45	C₃×C₄²	C₃×D₄	1	4	yes	—
46	C₃×C₁₆	C₃×D₄	1	16	yes	—
47	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
48	C₃²×C₄	—	8	4	no	—
49	C₃²×C₄	Q₃₂	1	4	yes	complemented
50	C₃²×C₄	#127	1	1	yes	characteristic
51	C₃²×C₄	C₂×D₈	1	1	yes	characteristic
52	C₂×Q₁₆	—	2	2	no	—
53	C₂×Q₁₆	C₂²×C₃²	1	4	yes	—
54	C₄⋊Q₈	—	2	2	no	—
55	Q₃₂	—	2	8	no	—
56	C₂×C₁₆	C₂²×C₃²	1	2	yes	—
57	C₄×C₈	C₂²×C₃²	1	1	yes	characteristic
58	C₃×Q₈	—	4	16	no	—
59	C₃×Q₈	—	4	16	no	—
60	C₂×C₃×C₄	—	4	16	no	—
61	C₂×C₃×C₄	C₃×D₈	1	8	yes	—
62	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
63	C₃×C₈	C₃×D₈	1	8	yes	—
64	C₃×C₈	C₂×C₃×D₄	1	8	yes	—
65	C₂×C₃²	#493	1	1	yes	characteristic
66	C₂×C₃²	C₂×Q₃₂	1	2	yes	—
67	C₂×Q₈	—	2	4	no	—
68	Q₁₆	—	2	8	no	—
69	Q₁₆	—	4	4	no	—
70	C₂×C₈	C₃²×D₄	1	1	yes	characteristic
71	C₂×C₈	C₂³×C₃²	1	1	yes	characteristic
72	C₄⋊C₄	—	4	4	no	—
73	C₄²	C₃²×D₄	1	1	yes	characteristic
74	C₁₆	C₃²×D₄	1	4	yes	—
75	C₂²×C₃	C₂×C₃×D₈	1	4	yes	—
76	C₃×C₄	—	8	16	no	—
77	C₃×C₄	C₃×Q₃₂	1	16	yes	complemented
78	C₃×C₄	C₃×#127	1	4	yes	—
79	C₃×C₄	C₂×C₃×D₈	1	4	yes	—
80	C₃²	#2247	1	1	yes	characteristic, direct product factor, Sylow
81	Q₈	—	4	4	no	—
82	Q₈	—	4	4	no	—
83	C₂×C₄	—	4	4	no	—
84	C₂×C₄	C₃²×D₈	1	2	yes	—
85	C₂×C₄	C₂×C₃²×D₄	1	1	yes	characteristic
86	C₈	C₃²×D₈	1	2	yes	—
87	C₈	C₂×C₃²×D₄	1	2	yes	—
88	C₂×C₃	C₃×#493	1	4	yes	—
89	C₂×C₃	C₂×C₃×Q₃₂	1	8	yes	—
90	C₂²	C₂×C₃²×D₈	1	1	yes	characteristic
91	C₄	—	8	4	no	—
92	C₄	C₃²×Q₃₂	1	4	yes	complemented
93	C₄	C₃²×#127	1	1	yes	characteristic
94	C₄	C₂×C₃²×D₈	1	1	yes	characteristic
95	C₃	C₃×#2247	1	4	yes	direct product factor
96	C₂	C₃²×#493	1	1	yes	characteristic
97	C₂	C₂×C₃²×Q₃₂	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂²×C₃²	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₃²
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ C₃²×C₄² ◁ C₃²×C₄×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₃×#2247	C₃	direct (N × H)
22. #2247	C₃²	direct (N × H)
49. C₃²×C₄	Q₃₂	semidirect
77. C₃×C₄	C₃×Q₃₂	semidirect
80. C₃²	#2247	direct (N × H)
92. C₄	C₃²×Q₃₂	semidirect
95. C₃	C₃×#2247	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×C₃²×Q₃₂	2
C₃²×#494	2
C₃²×C₄×C₁₆	2
C₃×#2247	3

Subgroups — C32×#2247 #11769296

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃²×#2247 #11769296