Subgroups — #14907418

Order 2816.

486 conjugacy classes of subgroups.

The subgroup lattice has 178 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	#13070419	C₂	1	4	yes	maximal
3	#13070415	C₂	1	2	yes	maximal
4	C₂×C₈×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×Q₈×C₁₁	C₄	1	1	yes	characteristic
6	C₈×Q₈×C₁₁	C₄	1	4	yes	—
7	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
8	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
9	C₂×C₁₁×C₄⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
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	8	yes	—
16	C₄×C₁₁⋊C₁₆	C₂²	1	4	yes	—
17	C₂²×Q₈×C₁₁	C₈	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂×C₄	1	2	yes	—
20	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₄×Q₈×C₁₁	C₈	1	4	yes	—
22	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
23	C₂×C₁₁×C₄⋊C₄	C₈	1	2	yes	—
24	C₂×C₁₁×C₄⋊C₄	C₈	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
28	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
29	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
31	C₄×C₈×C₁₁	C₂³	1	2	yes	—
32	C₄×C₈×C₁₁	C₂³	1	4	yes	—
33	C₂×C₁₁⋊C₁₆	C₂³	1	8	yes	—
34	#33497	—	11	1	no	maximal, Sylow
35	C₂×Q₈×C₁₁	—	2	4	no	—
36	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	—
37	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
38	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
39	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
40	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	—	2	2	no	—
43	C₂×C₈×C₁₁	—	4	1	no	—
44	C₂×C₈×C₁₁	—	4	2	no	—
45	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
47	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
48	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
49	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
50	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
51	C₄²×C₁₁	C₂×C₈	1	4	yes	—
52	C₄²×C₁₁	C₂×C₈	1	2	yes	—
53	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
54	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
55	C₁₁⋊C₁₆	—	2	8	no	—
56	C₂×C₈×Q₈	D₁₁	1	1	yes	characteristic
57	#2183	—	11	8	no	—
58	#2163	—	11	4	no	—
59	#2162	—	11	2	no	—
60	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
61	Q₈×C₁₁	—	2	8	no	—
62	C₂×C₄×C₁₁	—	2	4	no	—
63	C₂×C₄×C₁₁	—	2	1	no	—
64	C₂×C₄×C₁₁	—	2	1	no	—
65	C₂×C₄×C₁₁	—	4	2	no	—
66	C₂×C₄×C₁₁	—	4	1	no	—
67	C₂×C₄×C₁₁	M₃₂	1	4	yes	—
68	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
70	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
71	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
72	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
73	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
74	C₈×C₁₁	—	2	1	no	—
75	C₈×C₁₁	—	2	2	no	—
76	C₈×C₁₁	—	2	4	no	—
77	C₈×C₁₁	2₋¹⁺⁴	1	2	yes	—
78	C₂×C₄×Q₈	Dic₁₁	1	1	yes	characteristic
79	C₈×Q₈	Dic₁₁	1	4	yes	—
80	C₈×Q₈	C₂×D₁₁	1	4	yes	—
81	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
82	C₂×C₄⋊C₈	Dic₁₁	1	1	yes	characteristic
83	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
84	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
85	C₄⋊C₁₆	—	11	4	no	—
86	C₄⋊C₁₆	—	11	8	no	—
87	C₂²⋊C₁₆	—	11	4	no	—
88	#346	—	11	8	no	—
89	C₄×C₁₆	—	11	4	no	—
90	C₂²×C₁₁	—	2	1	no	—
91	C₂²×C₁₁	—	2	1	no	—
92	C₂²×C₁₁	C₂×M₃₂	1	2	yes	—
93	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
94	C₄×C₁₁	—	2	4	no	—
95	C₄×C₁₁	—	2	4	no	—
96	C₄×C₁₁	—	2	2	no	—
97	C₄×C₁₁	—	2	1	no	—
98	C₄×C₁₁	C₂×M₃₂	1	4	yes	—
99	C₄×C₁₁	#519	1	1	yes	characteristic
100	C₄×C₁₁	#568	1	1	yes	characteristic
101	C₂²×Q₈	C₁₁⋊C₈	1	1	yes	characteristic
102	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
103	C₂²×C₈	C₂×Dic₁₁	1	2	yes	—
104	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
105	C₄×Q₈	C₁₁⋊C₈	1	4	yes	—
106	C₄×Q₈	C₂×Dic₁₁	1	4	yes	—
107	C₂×C₄⋊C₄	C₁₁⋊C₈	1	2	yes	—
108	C₂×C₄⋊C₄	C₁₁⋊C₈	1	1	yes	characteristic
109	C₂×C₄²	C₂×Dic₁₁	1	2	yes	—
110	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
111	C₂×C₁₆	—	11	8	no	—
112	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
113	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
114	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
115	C₄×C₈	C₂×Dic₁₁	1	4	yes	—
116	C₄×C₈	C₂²×D₁₁	1	2	yes	—
117	C₄×C₈	C₂²×D₁₁	1	4	yes	—
118	C₂×C₁₁	—	2	2	no	—
119	C₂×C₁₁	#2982	1	1	yes	characteristic
120	C₂×C₁₁	C₂²×M₃₂	1	1	yes	characteristic
121	C₂×C₁₁	#3407	1	1	yes	characteristic
122	C₂×Q₈	—	2	4	no	—
123	C₂×Q₈	C₂×C₁₁⋊C₈	1	4	yes	—
124	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
125	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
126	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
127	C₂²×C₄	C₂×C₁₁⋊C₈	1	1	yes	characteristic
128	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
129	C₂×C₈	—	2	2	no	—
130	C₂×C₈	—	4	1	no	—
131	C₂×C₈	—	4	2	no	—
132	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
133	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
134	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
135	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
136	C₄⋊C₄	C₂×C₁₁⋊C₈	1	8	yes	—
137	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
138	C₄²	C₂×C₁₁⋊C₈	1	4	yes	—
139	C₄²	C₂×C₁₁⋊C₈	1	2	yes	—
140	C₄²	C₂²×Dic₁₁	1	4	yes	—
141	C₄²	C₂²×Dic₁₁	1	2	yes	—
142	C₁₆	—	22	8	no	—
143	C₁₁	#33497	1	1	yes	characteristic, complemented, Sylow
144	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
145	Q₈	—	2	8	no	—
146	C₂×C₄	—	2	4	no	—
147	C₂×C₄	—	2	1	no	—
148	C₂×C₄	—	2	1	no	—
149	C₂×C₄	—	4	2	no	—
150	C₂×C₄	—	4	1	no	—
151	C₂×C₄	#66876	1	4	yes	—
152	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
153	C₂×C₄	C₂²×C₁₁⋊C₈	1	4	yes	—
154	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
155	C₂×C₄	C₂²×C₁₁⋊C₈	1	4	yes	—
156	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
157	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
158	C₈	—	2	1	no	—
159	C₈	—	2	2	no	—
160	C₈	—	2	4	no	—
161	C₈	#67040	1	2	yes	—
162	C₂²	—	2	1	no	—
163	C₂²	—	2	1	no	—
164	C₂²	C₂×#66876	1	2	yes	—
165	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
166	C₄	—	2	4	no	—
167	C₄	—	2	4	no	—
168	C₄	—	2	2	no	—
169	C₄	—	2	1	no	—
170	C₄	C₂×#66876	1	4	yes	—
171	C₄	#10623343	1	1	yes	characteristic
172	C₄	#10623350	1	1	yes	characteristic
173	C₂	—	2	2	no	—
174	C₂	#13077697	1	1	yes	characteristic
175	C₂	C₂²×#66876	1	1	yes	characteristic
176	C₂	#13081719	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₂×C₈×Q₈×C₁₁	C₂
prime radical	C₂³×C₁₁	C₂²×C₈
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	C₂×C₈×Q₈	D₁₁
hypocenter	C₁₁	#33497
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₈×Q₈

Complements

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

N	H ≅ G/N	type
1. #13070525	C₂	semidirect
143. C₁₁	#33497	semidirect

Maximal subgroups

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

subgroup	index
#13070525	2
#13070419	2
#13070415	2
C₂×C₈×Q₈×C₁₁	2
#33497	11