Subgroups — C₂×C₄⋊(C₁₁⋊C₃₂) #14674253

Order 2816.

230 conjugacy classes of subgroups.

The subgroup lattice has 130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁⋊C₃₂	C₂	1	2	yes	maximal
2	C₄⋊(C₁₁⋊C₃₂)	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	C₄	1	1	yes	characteristic
5	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₄	1	1	yes	characteristic
7	C₄×C₁₁×C₁₆	C₄	1	2	yes	—
8	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
9	C₂×C₁₁⋊C₃₂	—	2	4	no	—
10	C₂×C₁₁⋊C₃₂	C₂²	1	4	yes	—
11	C₂²×C₈×C₁₁	C₈	1	1	yes	characteristic
12	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
13	C₂×C₄²×C₁₁	C₈	1	1	yes	characteristic
14	C₂×C₁₁×C₁₆	—	2	2	no	—
15	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
16	C₂×C₁₁×C₁₆	C₂×C₄	1	1	yes	characteristic
17	C₂×C₁₁×C₁₆	D₄	1	2	yes	—
18	C₂×C₁₁×C₁₆	Q₈	1	2	yes	—
19	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
20	C₄×C₈×C₁₁	C₈	1	2	yes	—
21	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
22	C₁₁⋊C₃₂	—	2	4	no	—
23	C₂×C₄⋊C₃₂	—	11	1	no	maximal, Sylow
24	C₂²×C₄×C₁₁	C₁₆	1	1	yes	characteristic
25	C₂²×C₄×C₁₁	C₁₆	1	1	yes	characteristic
26	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
27	C₂×C₈×C₁₁	—	2	2	no	—
28	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
29	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
30	C₂×C₈×C₁₁	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
32	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
33	C₄²×C₁₁	C₁₆	1	2	yes	—
34	C₄²×C₁₁	C₂×C₈	1	2	yes	—
35	C₁₁×C₁₆	—	2	2	no	—
36	C₁₁×C₁₆	C₄⋊C₄	1	2	yes	—
37	C₁₁×C₁₆	C₂×D₄	1	1	yes	characteristic
38	C₁₁×C₁₆	C₂×Q₈	1	1	yes	characteristic
39	C₂²×C₃₂	—	11	2	no	—
40	C₂×C₄×C₁₆	D₁₁	1	1	yes	characteristic
41	C₄⋊C₃₂	—	11	4	no	—
42	C₂³×C₁₁	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₁	—	2	2	no	—
44	C₂×C₄×C₁₁	C₃₂	1	4	yes	complemented
45	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
46	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
47	C₂×C₄×C₁₁	C₂×C₁₆	1	1	yes	characteristic
48	C₂×C₄×C₁₁	C₂×C₁₆	1	2	yes	—
49	C₂×C₄×C₁₁	M₃₂	1	2	yes	—
50	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
51	C₈×C₁₁	—	2	2	no	—
52	C₈×C₁₁	C₄⋊C₈	1	2	yes	—
53	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
54	C₈×C₁₁	C₂×M₁₆	1	1	yes	characteristic
55	C₂²×C₁₆	Dic₁₁	1	1	yes	characteristic
56	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
57	C₂×C₄×C₈	Dic₁₁	1	1	yes	characteristic
58	C₂×C₃₂	—	11	4	no	—
59	C₂×C₃₂	—	22	4	no	—
60	C₄×C₁₆	Dic₁₁	1	2	yes	—
61	C₄×C₁₆	C₂×D₁₁	1	2	yes	—
62	C₂²×C₁₁	C₄⋊C₁₆	1	2	yes	—
63	C₂²×C₁₁	C₂×C₃₂	1	2	yes	—
64	C₂²×C₁₁	M₆₄	1	2	yes	—
65	C₂²×C₁₁	C₂²×C₁₆	1	1	yes	characteristic
66	C₄×C₁₁	—	2	2	no	—
67	C₄×C₁₁	C₄⋊C₁₆	1	2	yes	—
68	C₄×C₁₁	C₂×C₃₂	1	4	yes	complemented
69	C₄×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
70	C₄×C₁₁	C₂×M₃₂	1	1	yes	characteristic
71	C₂²×C₈	C₁₁⋊C₈	1	1	yes	characteristic
72	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
73	C₂×C₄²	C₁₁⋊C₈	1	1	yes	characteristic
74	C₂×C₁₆	—	2	2	no	—
75	C₂×C₁₆	Dic₂₂	1	2	yes	—
76	C₂×C₁₆	D₄₄	1	2	yes	—
77	C₂×C₁₆	C₂×Dic₁₁	1	2	yes	—
78	C₂×C₁₆	C₂×Dic₁₁	1	1	yes	characteristic
79	C₂×C₁₆	C₂²×D₁₁	1	1	yes	characteristic
80	C₄×C₈	C₁₁⋊C₈	1	2	yes	—
81	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
82	C₃₂	—	22	4	no	—
83	C₂×C₁₁	C₄⋊C₃₂	1	4	yes	complemented
84	C₂×C₁₁	C₂×C₄⋊C₁₆	1	1	yes	characteristic
85	C₂×C₁₁	C₂²×C₃₂	1	1	yes	characteristic
86	C₂×C₁₁	C₂×M₆₄	1	1	yes	characteristic
87	C₂²×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
88	C₂²×C₄	C₁₁⋊C₁₆	1	1	yes	characteristic
89	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	C₂×C₁₁⋊C₈	1	2	yes	—
92	C₂×C₈	C₂×C₁₁⋊C₈	1	1	yes	characteristic
93	C₂×C₈	#4318	1	2	yes	—
94	C₂×C₈	C₄⋊Dic₁₁	1	2	yes	—
95	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
96	C₄²	C₁₁⋊C₁₆	1	2	yes	—
97	C₄²	C₂×C₁₁⋊C₈	1	2	yes	—
98	C₁₆	—	2	2	no	—
99	C₁₆	C₄⋊Dic₁₁	1	2	yes	—
100	C₁₆	C₂×Dic₂₂	1	1	yes	characteristic
101	C₁₆	C₂×D₄₄	1	1	yes	characteristic
102	C₁₁	C₂×C₄⋊C₃₂	1	1	yes	characteristic, complemented, Sylow
103	C₂³	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₁₁⋊C₃₂	1	4	yes	complemented
106	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
107	C₂×C₄	C₂×C₁₁⋊C₁₆	1	2	yes	—
108	C₂×C₄	C₂×C₁₁⋊C₁₆	1	1	yes	characteristic
109	C₂×C₄	C₂×C₁₁⋊C₁₆	1	2	yes	—
110	C₂×C₄	#66876	1	2	yes	—
111	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
112	C₈	—	2	2	no	—
113	C₈	C₄⋊(C₁₁⋊C₈)	1	2	yes	—
114	C₈	C₂×#4318	1	1	yes	characteristic
115	C₈	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
116	C₂²	C₄⋊(C₁₁⋊C₁₆)	1	2	yes	—
117	C₂²	C₂×C₁₁⋊C₃₂	1	2	yes	—
118	C₂²	#10622137	1	2	yes	—
119	C₂²	C₂²×C₁₁⋊C₁₆	1	1	yes	characteristic
120	C₄	—	2	2	no	—
121	C₄	C₄⋊(C₁₁⋊C₁₆)	1	2	yes	—
122	C₄	C₂×C₁₁⋊C₃₂	1	4	yes	complemented
123	C₄	C₂×C₄⋊(C₁₁⋊C₈)	1	1	yes	characteristic
124	C₄	C₂×#66876	1	1	yes	characteristic
125	C₂	C₄⋊(C₁₁⋊C₃₂)	1	4	yes	direct product factor
126	C₂	C₂×C₄⋊(C₁₁⋊C₁₆)	1	1	yes	characteristic
127	C₂	C₂²×C₁₁⋊C₃₂	1	1	yes	characteristic
128	C₂	C₂×#10622137	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₁₆	C₂×D₁₁
commutator	C₂×C₁₁	C₂²×C₃₂
Frattini	C₂×C₁₆	C₂²×D₁₁
Fitting	C₂×C₄×C₁₁×C₁₆	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₁₆
cosocle	C₂×C₁₁×C₁₆	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₁
hypocenter	C₁₁	C₂×C₄⋊C₃₂
LCS	G ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₁₆ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₄⋊(C₁₁⋊C₃₂)	C₂	direct (N × H)
44. C₂×C₄×C₁₁	C₃₂	semidirect
68. C₄×C₁₁	C₂×C₃₂	semidirect
83. C₂×C₁₁	C₄⋊C₃₂	semidirect
102. C₁₁	C₂×C₄⋊C₃₂	semidirect
105. C₂×C₄	C₁₁⋊C₃₂	semidirect
122. C₄	C₂×C₁₁⋊C₃₂	semidirect
125. C₂	C₄⋊(C₁₁⋊C₃₂)	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×C₁₁⋊C₃₂	2
C₄⋊(C₁₁⋊C₃₂)	2
C₂×C₄×C₁₁×C₁₆	2
C₂×C₄⋊C₃₂	11

Subgroups — C2×C4⋊(C11⋊C32) #14674253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄⋊(C₁₁⋊C₃₂) #14674253