Subgroups — #14906968

Order 2816.

674 conjugacy classes of subgroups.

The subgroup lattice has 228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622753	C₂	1	2	yes	maximal, complemented
2	#13070442	C₂	1	8	yes	maximal, complemented
3	#13070372	C₂	1	1	yes	maximal, characteristic, complemented
4	#13070230	C₂	1	2	yes	maximal, complemented
5	C₂×#10622099	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#2931	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×#131	C₂²	1	2	yes	—
8	C₁₁×#532	C₄	1	1	yes	characteristic
9	C₁₁×#436	C₄	1	4	yes	—
10	C₈×D₄×C₁₁	C₂²	1	4	yes	—
11	C₁₁×#423	C₄	1	1	yes	characteristic
12	C₁₁×#408	C₄	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	#10622753	—	2	8	no	—
15	C₂×#66876	C₂²	1	2	yes	—
16	C₂×#66876	C₂²	1	4	yes	—
17	C₂²×C₁₁⋊C₁₆	C₂²	1	4	yes	—
18	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₁₁⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂²⋊(C₁₁⋊C₁₆)	C₂²	1	8	yes	—
21	C₄⋊(C₁₁⋊C₁₆)	C₂²	1	4	yes	—
22	#10622099	C₂²	1	4	yes	—
23	C₂×C₁₁×#41	C₂×C₄	1	2	yes	—
24	C₁₁×#131	—	2	4	no	—
25	C₁₁×#131	—	2	4	no	—
26	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
28	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₈×C₁₁	C₂³	1	4	yes	—
30	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
31	C₁₁×C₄⋊Q₈	C₈	1	1	yes	characteristic
32	C₁₁×#127	C₈	1	1	yes	characteristic
33	C₁₁×#124	C₈	1	2	yes	—
34	C₁₁×#121	C₈	1	4	yes	—
35	C₄×D₄×C₁₁	C₂×C₄	1	4	yes	—
36	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
38	C₁₁×C₂²⋊C₈	C₂×C₄	1	8	yes	—
39	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
40	C₄×C₈×C₁₁	C₂³	1	2	yes	—
41	#66876	—	2	4	no	—
42	#66876	—	2	8	no	—
43	C₂×C₁₁⋊C₁₆	—	2	2	no	—
44	C₂×C₁₁⋊C₁₆	—	2	8	no	—
45	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	complemented
46	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
47	C₂×C₁₁⋊C₁₆	C₂³	1	4	yes	—
48	C₂×C₁₁⋊C₁₆	C₂³	1	2	yes	—
49	#33435	—	11	1	no	maximal, Sylow
50	C₁₁×#41	—	2	4	no	—
51	C₁₁×#41	—	2	4	no	—
52	C₂×Q₈×C₁₁	C₂×C₈	1	2	yes	—
53	C₂×D₄×C₁₁	C₂×C₈	1	4	yes	—
54	C₂×D₄×C₁₁	C₂×C₈	1	2	yes	—
55	C₂×D₄×C₁₁	C₂×C₈	1	4	yes	—
56	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
58	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₁₁×M₁₆	—	2	8	no	—
60	C₁₁×M₁₆	—	2	4	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₂×C₈×C₁₁	—	2	2	no	—
64	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
65	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
66	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
67	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
68	C₂×C₈×C₁₁	#41	1	2	yes	—
69	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
70	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
71	C₁₁×C₂²⋊C₄	C₂×C₈	1	8	yes	—
72	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
73	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
74	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
75	C₁₁⋊C₁₆	—	2	4	no	—
76	C₁₁⋊C₁₆	—	2	2	no	—
77	C₁₁⋊C₁₆	C₂×D₄	1	4	yes	—
78	C₂×#504	—	11	2	no	—
79	#2931	D₁₁	1	1	yes	characteristic
80	#2168	—	11	8	no	—
81	#2150	—	11	1	no	—
82	#2113	—	11	2	no	—
83	C₂×#346	—	11	1	no	—
84	C₂³×C₁₁	C₂²×C₈	1	4	yes	—
85	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
86	Q₈×C₁₁	—	2	4	no	—
87	D₄×C₁₁	—	2	8	no	—
88	D₄×C₁₁	—	2	4	no	—
89	D₄×C₁₁	—	4	4	no	—
90	C₂×C₄×C₁₁	—	2	4	no	—
91	C₂×C₄×C₁₁	—	2	4	no	—
92	C₂×C₄×C₁₁	—	4	2	no	—
93	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
94	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
95	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
96	C₂×C₄×C₁₁	C₂²×C₈	1	4	yes	—
97	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
98	C₂×C₄×C₁₁	#131	1	2	yes	—
99	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
100	C₈×C₁₁	—	2	4	no	—
101	C₈×C₁₁	—	2	2	no	—
102	C₈×C₁₁	C₄×D₄	1	2	yes	—
103	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
104	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
105	C₂×#131	C₂×D₁₁	1	2	yes	—
106	#532	Dic₁₁	1	1	yes	characteristic
107	#504	—	22	8	no	—
108	C₂×M₃₂	—	11	2	no	—
109	C₂×M₃₂	—	11	4	no	—
110	C₂²×C₁₆	—	11	1	no	—
111	C₂²×C₁₆	—	11	1	no	—
112	C₂²×C₁₆	—	11	4	no	—
113	#436	Dic₁₁	1	4	yes	—
114	C₈×D₄	C₂×D₁₁	1	4	yes	—
115	#423	Dic₁₁	1	1	yes	characteristic
116	#408	Dic₁₁	1	2	yes	—
117	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
118	C₄⋊C₁₆	—	11	4	no	—
119	C₂²⋊C₁₆	—	11	8	no	—
120	#346	—	11	4	no	—
121	C₂²×C₁₁	—	2	2	no	—
122	C₂²×C₁₁	—	2	8	no	—
123	C₂²×C₁₁	—	2	4	no	—
124	C₂²×C₁₁	C₈×D₄	1	2	yes	—
125	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
126	C₄×C₁₁	—	2	2	no	—
127	C₄×C₁₁	—	2	2	no	—
128	C₄×C₁₁	—	2	4	no	—
129	C₄×C₁₁	C₈×D₄	1	2	yes	—
130	C₄×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
131	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
132	C₂×#41	C₂×Dic₁₁	1	2	yes	—
133	#131	—	2	4	no	—
134	#131	—	2	4	no	—
135	C₂×M₁₆	C₂×Dic₁₁	1	2	yes	—
136	C₂×M₁₆	C₂×Dic₁₁	1	4	yes	—
137	C₂²×C₈	C₂×Dic₁₁	1	1	yes	characteristic
138	C₂²×C₈	C₂²×D₁₁	1	4	yes	—
139	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
140	C₄⋊Q₈	C₁₁⋊C₈	1	1	yes	characteristic
141	#127	C₁₁⋊C₈	1	1	yes	characteristic
142	#124	C₁₁⋊C₈	1	2	yes	—
143	#121	C₁₁⋊C₈	1	4	yes	—
144	C₄×D₄	C₂×Dic₁₁	1	4	yes	—
145	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
146	M₃₂	—	22	8	no	—
147	M₃₂	—	22	4	no	—
148	C₂×C₁₆	—	11	4	no	—
149	C₂×C₁₆	—	11	2	no	—
150	C₂×C₁₆	—	11	2	no	—
151	C₂×C₁₆	—	11	4	no	—
152	C₂×C₁₆	—	22	8	no	—
153	C₂×C₁₆	—	22	2	no	—
154	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
155	C₂²⋊C₈	C₂×Dic₁₁	1	8	yes	—
156	C₄×C₈	C₂×Dic₁₁	1	2	yes	—
157	C₄×C₈	C₂²×D₁₁	1	2	yes	—
158	C₂×C₁₁	—	2	2	no	—
159	C₂×C₁₁	—	4	4	no	—
160	C₂×C₁₁	C₂×C₈×D₄	1	1	yes	characteristic
161	C₂×C₁₁	#3407	1	2	yes	—
162	#41	—	2	4	no	—
163	#41	—	2	4	no	—
164	C₂×Q₈	C₂×C₁₁⋊C₈	1	2	yes	—
165	C₂×D₄	C₂×C₁₁⋊C₈	1	4	yes	—
166	C₂×D₄	C₂×C₁₁⋊C₈	1	2	yes	—
167	C₂×D₄	C₂×C₁₁⋊C₈	1	4	yes	—
168	C₂²×C₄	C₂×C₁₁⋊C₈	1	2	yes	—
169	C₂²×C₄	C₂²×Dic₁₁	1	4	yes	—
170	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
171	M₁₆	—	2	4	no	—
172	M₁₆	—	2	8	no	—
173	C₂×C₈	—	2	2	no	—
174	C₂×C₈	—	2	4	no	—
175	C₂×C₈	—	2	4	no	—
176	C₂×C₈	D₄×D₁₁	1	2	yes	—
177	C₂×C₈	#4341	1	2	yes	—
178	C₂×C₈	C₂²×Dic₁₁	1	2	yes	—
179	C₂×C₈	C₂²×Dic₁₁	1	4	yes	—
180	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
181	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
182	C₄⋊C₄	C₂×C₁₁⋊C₈	1	4	yes	—
183	C₂²⋊C₄	C₂×C₁₁⋊C₈	1	8	yes	—
184	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
185	C₄²	C₂×C₁₁⋊C₈	1	1	yes	characteristic
186	C₄²	C₂²×Dic₁₁	1	2	yes	—
187	C₁₆	—	11	4	no	—
188	C₁₆	—	22	4	no	—
189	C₁₆	—	22	2	no	—
190	C₁₁	#33435	1	1	yes	characteristic, complemented, Sylow
191	C₂³	C₂²×C₁₁⋊C₈	1	4	yes	—
192	C₂³	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
193	Q₈	—	2	4	no	—
194	D₄	—	2	8	no	—
195	D₄	—	2	4	no	—
196	D₄	—	4	4	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	4	no	—
199	C₂×C₄	—	4	2	no	—
200	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
201	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
202	C₂×C₄	C₂²×C₁₁⋊C₈	1	4	yes	—
203	C₂×C₄	C₂²×C₁₁⋊C₈	1	1	yes	characteristic
204	C₂×C₄	D₄×Dic₁₁	1	2	yes	—
205	C₂×C₄	#67001	1	2	yes	—
206	C₂×C₄	C₂³×Dic₁₁	1	1	yes	characteristic
207	C₈	—	2	4	no	—
208	C₈	—	2	2	no	—
209	C₈	D₄×Dic₁₁	1	2	yes	—
210	C₈	C₂×D₄×D₁₁	1	1	yes	characteristic
211	C₈	C₂×#4341	1	1	yes	characteristic
212	C₂²	—	2	2	no	—
213	C₂²	—	2	4	no	—
214	C₂²	—	2	8	no	—
215	C₂²	D₄×C₁₁⋊C₈	1	2	yes	—
216	C₂²	C₂³×C₁₁⋊C₈	1	1	yes	characteristic
217	C₄	—	2	4	no	—
218	C₄	—	2	2	no	—
219	C₄	—	2	2	no	—
220	C₄	D₄×C₁₁⋊C₈	1	2	yes	—
221	C₄	C₂×D₄×Dic₁₁	1	1	yes	characteristic
222	C₄	C₂×#67001	1	1	yes	characteristic
223	C₂	—	2	2	no	—
224	C₂	—	4	4	no	—
225	C₂	C₂×D₄×C₁₁⋊C₈	1	1	yes	characteristic
226	C₂	#13081719	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₁₁
commutator, socle	C₂²×C₁₁	C₂³×C₈
Fitting	C₁₁×#2931	C₂
prime radical	C₁₁×#532	C₄
cosocle	C₂×C₈×C₁₁	C₂⁴
hypercenter	#2931	D₁₁
hypocenter	C₁₁	#33435
LCS	G ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
1. C₂×#10622753	C₂	semidirect
2. #13070442	C₂	semidirect
3. #13070372	C₂	semidirect
4. #13070230	C₂	semidirect
5. C₂×#10622099	C₂	semidirect
45. C₂×C₁₁⋊C₁₆	D₄	semidirect
190. C₁₁	#33435	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622753	2
#13070442	2
#13070372	2
#13070230	2
C₂×#10622099	2
C₁₁×#2931	2
#33435	11