Subgroups — #14674287

Order 2816.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622144	C₂	1	2	yes	maximal
2	#13066820	C₂	1	4	yes	maximal, complemented
3	C₂×C₁₁×M₆₄	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
5	C₂×#66883	—	2	2	no	—
6	C₁₁×M₆₄	C₄	1	4	yes	—
7	C₂×C₁₁×C₃₂	C₂²	1	2	yes	—
8	#10622144	—	2	2	no	—
9	#10622144	C₂²	1	4	yes	—
10	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
11	C₂×#4318	—	4	2	no	—
12	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
13	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
14	C₂×C₁₁×C₁₆	Q₈	1	2	yes	—
15	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
16	#66883	—	2	4	no	—
17	#66883	—	4	2	no	—
18	C₁₁×C₃₂	C₂×C₄	1	4	yes	—
19	#13636	—	11	1	no	maximal, Sylow
20	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
21	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
22	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
23	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
24	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
25	#4318	—	4	4	no	—
26	#4318	—	8	2	no	—
27	C₂×C₁₁⋊C₈	—	8	2	no	—
28	C₁₁×C₁₆	C₄⋊C₄	1	2	yes	—
29	C₁₁×C₁₆	C₂²×C₄	1	1	yes	characteristic
30	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
31	C₂×M₆₄	D₁₁	1	1	yes	characteristic
32	C₂×#368	—	11	2	no	—
33	#1425	—	11	4	no	—
34	C₂³×C₁₁	Q₃₂	1	1	yes	characteristic
35	C₂×C₄×C₁₁	#107	1	2	yes	—
36	C₂×C₄×C₁₁	D₁₆	1	2	yes	—
37	C₂×C₄×C₁₁	Q₃₂	1	1	yes	characteristic
38	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
39	C₈×C₁₁	#107	1	2	yes	—
40	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
41	C₈×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
42	C₁₁⋊C₈	—	8	4	no	—
43	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
44	C₂×#108	—	22	2	no	—
45	M₆₄	Dic₁₁	1	4	yes	—
46	C₂×C₃₂	C₂×D₁₁	1	2	yes	—
47	#368	—	11	4	no	—
48	#368	—	22	2	no	—
49	C₂²×C₁₁	—	4	1	no	—
50	C₂²×C₁₁	#366	1	2	yes	—
51	C₂²×C₁₁	C₂×Q₃₂	1	1	yes	characteristic
52	C₄×C₁₁	#366	1	2	yes	—
53	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
54	C₄×C₁₁	C₂×D₁₆	1	1	yes	characteristic
55	C₂×M₁₆	—	44	2	no	—
56	C₂²×C₈	D₄₄	1	1	yes	characteristic
57	C₂×C₁₆	Dic₂₂	1	2	yes	—
58	C₂×C₁₆	D₄₄	1	1	yes	characteristic
59	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
60	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
61	#108	—	22	4	no	—
62	#108	—	44	2	no	—
63	C₃₂	C₂×Dic₁₁	1	4	yes	—
64	C₂×C₁₁	—	2	2	no	—
65	C₂×C₁₁	—	2	1	no	—
66	C₂×C₁₁	C₂×#366	1	1	yes	characteristic
67	C₂²×C₄	D₈₈	1	1	yes	characteristic
68	M₁₆	—	44	4	no	—
69	M₁₆	—	88	2	no	—
70	C₂×C₈	—	88	2	no	—
71	C₂×C₈	D₈₈	1	1	yes	characteristic
72	C₂×C₈	Dic₄₄	1	2	yes	—
73	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
74	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
75	C₁₆	C₄⋊Dic₁₁	1	2	yes	—
76	C₁₆	C₂×Dic₂₂	1	1	yes	characteristic
77	C₁₆	C₂²×Dic₁₁	1	1	yes	characteristic
78	C₁₁	#13636	1	1	yes	characteristic, complemented, Sylow
79	C₂³	Dic₈₈	1	1	yes	characteristic
80	C₂×C₄	D₁₇₆	1	2	yes	—
81	C₂×C₄	Dic₈₈	1	1	yes	characteristic
82	C₂×C₄	#66882	1	2	yes	—
83	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
84	C₈	—	88	4	no	—
85	C₈	#66882	1	2	yes	—
86	C₈	C₂×Dic₄₄	1	1	yes	characteristic
87	C₈	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
88	C₂²	—	4	1	no	—
89	C₂²	#10622142	1	2	yes	—
90	C₂²	C₂×Dic₈₈	1	1	yes	characteristic
91	C₄	#10622142	1	2	yes	—
92	C₄	C₂×D₁₇₆	1	1	yes	characteristic
93	C₄	C₂×#66882	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	2	2	no	—
96	C₂	C₂×#10622142	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₁₇₆
commutator	C₁₁×C₁₆	C₂²×C₄
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₂×C₁₁×M₆₄	C₂
socle	C₂×C₁₁	C₂×#366
prime radical	C₂³×C₁₁	Q₃₂
cosocle	C₂×C₁₁×C₁₆	C₂³
hypercenter	C₂×M₆₄	D₁₁
hypocenter	C₁₁	#13636
LCS	G ▷ C₁₁×C₁₆ ▷ C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ C₂×M₆₄

Complements

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

N	H ≅ G/N	type
2. #13066820	C₂	semidirect
78. C₁₁	#13636	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622144	2
#13066820	2
C₂×C₁₁×M₆₄	2
#13636	11