Subgroups — #11772977

Order 1152.

234 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×D₁₆	C₂	1	1	yes	maximal, characteristic
2	#10589372	C₂	1	1	yes	maximal, characteristic, complemented
3	#10589365	C₂	1	1	yes	maximal, characteristic, complemented
4	#67825	—	3	4	no	maximal
5	C₂×C₃²×D₈	—	2	1	no	—
6	C₃²×D₁₆	—	2	1	no	—
7	C₃²×D₁₆	C₄	1	2	yes	—
8	C₂×C₃²×C₁₆	C₂²	1	1	yes	characteristic
9	#63646	—	2	1	no	—
10	C₃⋊(C₃⋊C₃₂)	—	2	1	no	—
11	C₂×C₃×D₁₆	D₃	1	4	yes	—
12	#4506	—	3	4	no	—
13	#4499	—	3	4	no	—
14	C₂×C₃²×D₄	—	4	1	no	—
15	C₃²×D₈	—	2	2	no	—
16	C₃²×D₈	—	4	1	no	—
17	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
18	#3748	—	4	1	no	—
19	C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
20	C₃²×C₁₆	D₄	1	1	yes	characteristic
21	#1419	—	9	1	no	Sylow
22	C₂×C₃×D₈	—	2	4	no	—
23	C₃×D₁₆	—	2	4	no	—
24	C₃×D₁₆	Dic₃	1	8	yes	—
25	C₂×C₃×C₁₆	C₂×D₃	1	4	yes	—
26	#819	—	6	4	no	—
27	C₃⋊C₃₂	—	6	4	no	—
28	C₂³×C₃²	—	8	1	no	—
29	C₃²×D₄	—	4	2	no	—
30	C₃²×D₄	—	8	1	no	—
31	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
32	C₃²×C₈	C₂²⋊C₄	1	1	yes	characteristic
33	C₃²×C₈	SD₁₆	1	1	yes	characteristic
34	C₃⋊(C₃⋊C₈)	—	8	1	no	—
35	C₂×D₁₆	C₃⋊D₃	1	1	yes	characteristic
36	M₆₄	—	9	1	no	—
37	#368	—	9	1	no	—
38	C₂×C₃×D₄	—	4	4	no	—
39	C₃×D₈	—	2	8	no	—
40	C₃×D₈	—	4	4	no	—
41	C₂×C₃×C₈	#67	1	4	yes	—
42	#208	—	12	4	no	—
43	C₃×C₁₆	C₂×Dic₃	1	4	yes	—
44	C₃×C₁₆	#67	1	4	yes	—
45	C₂²×C₃²	—	8	2	no	—
46	C₂²×C₃²	—	16	2	no	—
47	C₂²×C₃²	SD₃₂	1	1	yes	characteristic
48	C₃²×C₄	#102	1	1	yes	characteristic
49	C₃²×C₄	D₁₆	1	1	yes	characteristic
50	C₂×D₈	—	2	1	no	—
51	D₁₆	—	2	1	no	—
52	D₁₆	C₃⋊Dic₃	1	2	yes	—
53	C₂×C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
54	#108	—	18	1	no	—
55	C₃₂	—	18	1	no	—
56	C₂³×C₃	—	8	4	no	—
57	C₃×D₄	—	4	8	no	—
58	C₃×D₄	—	8	4	no	—
59	C₂×C₃×C₄	#213	1	4	yes	—
60	C₃×C₈	#214	1	4	yes	—
61	C₃×C₈	#217	1	4	yes	—
62	C₃⋊C₈	—	24	4	no	—
63	C₂×C₃²	—	2	1	no	—
64	C₂×C₃²	—	16	2	no	—
65	C₂×C₃²	#357	1	1	yes	characteristic
66	C₂×D₄	—	4	1	no	—
67	D₈	—	2	2	no	—
68	D₈	—	4	1	no	—
69	M₁₆	—	36	1	no	—
70	C₂×C₈	#638	1	1	yes	characteristic
71	C₁₆	C₂×C₃⋊Dic₃	1	1	yes	characteristic
72	C₁₆	#638	1	1	yes	characteristic
73	C₂²×C₃	—	8	8	no	—
74	C₂²×C₃	—	16	8	no	—
75	C₂²×C₃	#827	1	4	yes	—
76	C₃×C₄	#826	1	4	yes	—
77	C₃×C₄	#832	1	4	yes	—
78	C₃²	#1419	1	1	yes	characteristic, complemented, Sylow
79	C₂³	—	8	1	no	—
80	D₄	—	4	2	no	—
81	D₄	—	8	1	no	—
82	C₂×C₄	#3753	1	1	yes	characteristic
83	C₈	—	72	1	no	—
84	C₈	#3754	1	1	yes	characteristic
85	C₈	#3757	1	1	yes	characteristic
86	C₂×C₃	—	2	4	no	—
87	C₂×C₃	—	16	8	no	—
88	C₂×C₃	#4562	1	4	yes	—
89	C₂²	—	8	2	no	—
90	C₂²	—	16	2	no	—
91	C₂²	#63654	1	1	yes	characteristic
92	C₄	#63653	1	1	yes	characteristic
93	C₄	#63659	1	1	yes	characteristic
94	C₃	#67825	1	4	yes	complemented
95	C₂	—	2	1	no	—
96	C₂	—	16	2	no	—
97	C₂	#10589428	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#10589428
commutator	C₃²×C₁₆	C₂×C₄
Frattini	C₂×C₁₆	C₂×C₃⋊D₃
Fitting, prime radical	C₂×C₃²×D₁₆	C₂
socle	C₂×C₃²	#357
cosocle	C₂×C₃²×C₁₆	C₂²
hypercenter	C₂×D₁₆	C₃⋊D₃
hypocenter	C₃²	#1419
LCS	G ▷ C₃²×C₁₆ ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×D₁₆

Complements

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

N	H ≅ G/N	type
2. #10589372	C₂	semidirect
3. #10589365	C₂	semidirect
78. C₃²	#1419	semidirect
94. C₃	#67825	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃²×D₁₆	2
#10589372	2
#10589365	2
#67825	3