Subgroups — #14907439

Order 2816.

444 conjugacy classes of subgroups.

The subgroup lattice has 160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13070525	C₂	1	8	yes	maximal, complemented
2	#13070423	C₂	1	4	yes	maximal
3	#13070419	C₂	1	2	yes	maximal
4	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#533	C₄	1	1	yes	characteristic
6	C₁₁×#446	C₄	1	4	yes	—
7	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
8	C₁₁×#424	C₄	1	2	yes	—
9	C₁₁×#423	C₄	1	1	yes	characteristic
10	C₁₁×#405	C₂²	1	2	yes	—
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	—
13	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	—
14	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	8	yes	—
15	#10622099	C₂²	1	4	yes	—
16	#10622099	C₂²	1	4	yes	—
17	C₄×C₁₁⋊C₁₆	C₂²	1	4	yes	—
18	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
19	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₁₁×C₄⋊Q₈	C₈	1	2	yes	—
22	C₁₁×#125	C₈	1	2	yes	—
23	C₁₁×C₂²⋊Q₈	C₈	1	4	yes	—
24	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
25	C₁₁×#117	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
28	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
29	C₁₁×#97	C₂×C₄	1	4	yes	—
30	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₁₁	C₂³	1	4	yes	—
32	C₄×C₈×C₁₁	C₂³	1	2	yes	—
33	C₂×C₁₁⋊C₁₆	C₂³	1	8	yes	—
34	#33501	—	11	1	no	maximal, Sylow
35	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	—
36	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
38	C₁₁×M₁₆	—	4	2	no	—
39	C₂×C₈×C₁₁	—	2	2	no	—
40	C₂×C₈×C₁₁	—	4	1	no	—
41	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
43	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
44	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
45	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
46	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
47	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
48	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
49	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
50	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
51	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
52	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
53	C₁₁⋊C₁₆	—	2	8	no	—
54	#2960	D₁₁	1	1	yes	characteristic
55	#2183	—	11	8	no	—
56	#2164	—	11	4	no	—
57	#2163	—	11	2	no	—
58	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
59	Q₈×C₁₁	—	4	4	no	—
60	C₂×C₄×C₁₁	—	2	1	no	—
61	C₂×C₄×C₁₁	—	2	1	no	—
62	C₂×C₄×C₁₁	—	4	2	no	—
63	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
65	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
66	C₂×C₄×C₁₁	C₂²×C₈	1	8	yes	—
67	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
68	C₈×C₁₁	—	2	1	no	—
69	C₈×C₁₁	—	2	2	no	—
70	C₈×C₁₁	—	2	4	no	—
71	C₈×C₁₁	2₋¹⁺⁴	1	2	yes	—
72	#533	Dic₁₁	1	1	yes	characteristic
73	#446	Dic₁₁	1	4	yes	—
74	C₈×Q₈	C₂×D₁₁	1	4	yes	—
75	#424	Dic₁₁	1	2	yes	—
76	#423	Dic₁₁	1	1	yes	characteristic
77	#405	C₂×D₁₁	1	2	yes	—
78	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
79	C₄⋊C₁₆	—	11	4	no	—
80	C₄⋊C₁₆	—	11	8	no	—
81	C₂²⋊C₁₆	—	11	4	no	—
82	#346	—	11	4	no	—
83	#346	—	11	4	no	—
84	C₄×C₁₆	—	11	4	no	—
85	C₂²×C₁₁	—	2	2	no	—
86	C₂²×C₁₁	—	2	1	no	—
87	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
88	C₄×C₁₁	—	2	2	no	—
89	C₄×C₁₁	—	2	2	no	—
90	C₄×C₁₁	—	2	8	no	—
91	C₄×C₁₁	—	2	1	no	—
92	C₄×C₁₁	#519	1	1	yes	characteristic
93	C₄×C₁₁	#568	1	1	yes	characteristic
94	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
95	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
96	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
97	C₄⋊Q₈	C₁₁⋊C₈	1	2	yes	—
98	#125	C₁₁⋊C₈	1	2	yes	—
99	C₂²⋊Q₈	C₁₁⋊C₈	1	4	yes	—
100	C₄×Q₈	C₂×Dic₁₁	1	4	yes	—
101	#117	C₂×Dic₁₁	1	2	yes	—
102	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
103	C₂×C₁₆	—	11	8	no	—
104	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
105	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
106	#97	C₂×Dic₁₁	1	4	yes	—
107	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
108	C₄×C₈	C₂²×D₁₁	1	4	yes	—
109	C₄×C₈	C₂²×D₁₁	1	2	yes	—
110	C₂×C₁₁	—	4	1	no	—
111	C₂×C₁₁	#2982	1	1	yes	characteristic
112	C₂×C₁₁	#3407	1	2	yes	—
113	C₂×Q₈	C₂×C₁₁⋊C₈	1	4	yes	—
114	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
115	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
116	M₁₆	—	4	2	no	—
117	C₂×C₈	—	2	2	no	—
118	C₂×C₈	—	4	1	no	—
119	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
120	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
121	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
122	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
123	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
124	C₄⋊C₄	C₂×C₁₁⋊C₈	1	8	yes	—
125	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
126	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
127	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
128	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
129	C₄²	C₂²×Dic₁₁	1	2	yes	—
130	C₄²	C₂²×Dic₁₁	1	4	yes	—
131	C₁₆	—	22	8	no	—
132	C₁₁	#33501	1	1	yes	characteristic, complemented, Sylow
133	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
134	Q₈	—	4	4	no	—
135	C₂×C₄	—	2	1	no	—
136	C₂×C₄	—	2	1	no	—
137	C₂×C₄	—	4	2	no	—
138	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
139	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
140	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
141	C₂×C₄	C₂²×C₁₁⋊C₈	1	8	yes	—
142	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
143	C₈	—	2	1	no	—
144	C₈	—	2	2	no	—
145	C₈	—	2	4	no	—
146	C₈	#67040	1	2	yes	—
147	C₂²	—	2	2	no	—
148	C₂²	—	2	1	no	—
149	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
150	C₄	—	2	2	no	—
151	C₄	—	2	2	no	—
152	C₄	—	2	8	no	—
153	C₄	—	2	1	no	—
154	C₄	#10623343	1	1	yes	characteristic
155	C₄	#10623350	1	1	yes	characteristic
156	C₂	—	4	1	no	—
157	C₂	#13077697	1	1	yes	characteristic
158	C₂	#13081719	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2960	C₂
prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2960	D₁₁
hypocenter	C₁₁	#33501
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
1. #13070525	C₂	semidirect
132. C₁₁	#33501	semidirect

Maximal subgroups

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

subgroup	index
#13070525	2
#13070423	2
#13070419	2
C₁₁×#2960	2
#33501	11