Subgroups — #14907274

Order 2816.

490 conjugacy classes of subgroups.

The subgroup lattice has 186 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	#13070375	C₂	1	2	yes	maximal
3	#13070372	C₂	1	1	yes	maximal, characteristic
4	#13070213	C₂	1	2	yes	maximal
5	C₂×#10622099	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#533	C₄	1	1	yes	characteristic
8	C₁₁×#446	C₄	1	4	yes	—
9	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
10	C₁₁×#424	C₄	1	2	yes	—
11	C₁₁×#423	C₄	1	1	yes	characteristic
12	C₁₁×#405	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×#66876	C₂²	1	2	yes	—
15	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	—
18	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	8	yes	—
19	#10622099	C₂²	1	4	yes	—
20	#10622099	C₂²	1	4	yes	—
21	C₄×C₁₁⋊C₁₆	C₂²	1	4	yes	—
22	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
23	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
25	C₁₁×C₄⋊Q₈	C₈	1	2	yes	—
26	C₁₁×#125	C₈	1	2	yes	—
27	C₁₁×C₂²⋊Q₈	C₈	1	4	yes	—
28	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
29	C₁₁×#117	C₂×C₄	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
32	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
33	C₁₁×#97	C₂×C₄	1	4	yes	—
34	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
35	C₄×C₈×C₁₁	C₂³	1	4	yes	—
36	C₄×C₈×C₁₁	C₂³	1	2	yes	—
37	#66876	—	2	4	no	—
38	C₂×C₁₁⋊C₁₆	—	2	2	no	—
39	C₂×C₁₁⋊C₁₆	Q₈	1	4	yes	complemented
40	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
41	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
42	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
43	#33475	—	11	1	no	maximal, Sylow
44	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	—
45	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₁₁×M₁₆	—	2	4	no	—
48	C₂×C₈×C₁₁	—	2	2	no	—
49	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
50	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
51	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
53	C₂×C₈×C₁₁	#41	1	2	yes	—
54	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
55	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
56	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
57	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
58	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
59	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
60	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
61	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
62	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
63	C₁₁⋊C₁₆	—	2	2	no	—
64	C₁₁⋊C₁₆	—	2	4	no	—
65	C₁₁⋊C₁₆	C₂×Q₈	1	4	yes	—
66	#2960	D₁₁	1	1	yes	characteristic
67	#2183	—	11	8	no	—
68	#2151	—	11	2	no	—
69	#2150	—	11	1	no	—
70	#2108	—	11	2	no	—
71	C₂×#346	—	11	1	no	—
72	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
73	Q₈×C₁₁	—	4	4	no	—
74	C₂×C₄×C₁₁	—	4	2	no	—
75	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
76	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
77	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
78	C₂×C₄×C₁₁	C₂²×C₈	1	8	yes	—
79	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	#131	1	2	yes	—
81	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
82	C₈×C₁₁	—	2	2	no	—
83	C₈×C₁₁	—	2	4	no	—
84	C₈×C₁₁	C₄×Q₈	1	2	yes	—
85	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
86	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
87	#533	Dic₁₁	1	1	yes	characteristic
88	C₂×M₃₂	—	11	2	no	—
89	C₂²×C₁₆	—	11	1	no	—
90	C₂²×C₁₆	—	11	1	no	—
91	#446	Dic₁₁	1	4	yes	—
92	C₈×Q₈	C₂×D₁₁	1	4	yes	—
93	#424	Dic₁₁	1	2	yes	—
94	#423	Dic₁₁	1	1	yes	characteristic
95	#405	C₂×D₁₁	1	2	yes	—
96	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
97	C₄⋊C₁₆	—	11	4	no	—
98	C₄⋊C₁₆	—	11	8	no	—
99	#346	—	11	4	no	—
100	#346	—	11	4	no	—
101	C₄×C₁₆	—	11	4	no	—
102	C₂²×C₁₁	—	2	2	no	—
103	C₂²×C₁₁	C₈×Q₈	1	2	yes	—
104	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
105	C₄×C₁₁	—	2	2	no	—
106	C₄×C₁₁	—	2	2	no	—
107	C₄×C₁₁	—	2	8	no	—
108	C₄×C₁₁	C₈×Q₈	1	2	yes	—
109	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
110	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
111	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
112	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
113	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
114	C₄⋊Q₈	C₁₁⋊C₈	1	2	yes	—
115	#125	C₁₁⋊C₈	1	2	yes	—
116	C₂²⋊Q₈	C₁₁⋊C₈	1	4	yes	—
117	C₄×Q₈	C₂×Dic₁₁	1	4	yes	—
118	#117	C₂×Dic₁₁	1	2	yes	—
119	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
120	M₃₂	—	22	4	no	—
121	C₂×C₁₆	—	11	4	no	—
122	C₂×C₁₆	—	11	2	no	—
123	C₂×C₁₆	—	11	4	no	—
124	C₂×C₁₆	—	11	2	no	—
125	C₂×C₁₆	—	22	2	no	—
126	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
127	C₄⋊C₈	C₂×Dic₁₁	1	8	yes	—
128	#97	C₂×Dic₁₁	1	4	yes	—
129	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
130	C₄×C₈	C₂²×D₁₁	1	4	yes	—
131	C₄×C₈	C₂²×D₁₁	1	2	yes	—
132	C₂×C₁₁	—	2	2	no	—
133	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
134	C₂×C₁₁	#3407	1	2	yes	—
135	C₂×Q₈	C₂×C₁₁⋊C₈	1	4	yes	—
136	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
137	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
138	M₁₆	—	2	4	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	Q₈×D₁₁	1	2	yes	—
141	C₂×C₈	#4343	1	2	yes	—
142	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
143	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
144	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
145	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
146	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
147	C₄⋊C₄	C₂×C₁₁⋊C₈	1	8	yes	—
148	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
149	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
150	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
151	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
152	C₄²	C₂²×Dic₁₁	1	2	yes	—
153	C₄²	C₂²×Dic₁₁	1	4	yes	—
154	C₁₆	—	11	4	no	—
155	C₁₆	—	22	2	no	—
156	C₁₆	—	22	4	no	—
157	C₁₁	#33475	1	1	yes	characteristic, complemented, Sylow
158	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
159	Q₈	—	4	4	no	—
160	C₂×C₄	—	4	2	no	—
161	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
162	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
163	C₂×C₄	C₂²×C₁₁⋊C₈	1	8	yes	—
164	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
165	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
166	C₂×C₄	#67001	1	2	yes	—
167	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	2	4	no	—
170	C₈	Q₈×Dic₁₁	1	2	yes	—
171	C₈	C₂×Q₈×D₁₁	1	1	yes	characteristic
172	C₈	C₂×#4343	1	1	yes	characteristic
173	C₂²	—	2	2	no	—
174	C₂²	Q₈×C₁₁⋊C₈	1	2	yes	—
175	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
176	C₄	—	2	2	no	—
177	C₄	—	2	2	no	—
178	C₄	—	2	8	no	—
179	C₄	Q₈×C₁₁⋊C₈	1	2	yes	—
180	C₄	C₂×Q₈×Dic₁₁	1	1	yes	characteristic
181	C₄	C₂×#67001	1	1	yes	characteristic
182	C₂	—	2	2	no	—
183	C₂	C₂×Q₈×C₁₁⋊C₈	1	1	yes	characteristic
184	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	#33475
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
39. C₂×C₁₁⋊C₁₆	Q₈	semidirect
157. C₁₁	#33475	semidirect

Maximal subgroups

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

subgroup	index
#13070525	2
#13070375	2
#13070372	2
#13070213	2
C₂×#10622099	2
C₁₁×#2960	2
#33475	11