Subgroups — #14640959

Order 2816.

262 conjugacy classes of subgroups.

The subgroup lattice has 226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13068776	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622096	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₁×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×C₁₆	—	2	1	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₂×#66882	—	2	1	no	—
7	C₂×#66882	C₄	1	2	yes	—
8	#10622548	—	2	1	no	—
9	C₂×C₄⋊(C₁₁⋊C₈)	—	2	1	no	—
10	C₁₁×C₄⋊C₁₆	—	2	1	no	—
11	C₁₁×C₄⋊C₁₆	C₄	1	2	yes	complemented
12	#10622096	—	2	1	no	—
13	#10622096	C₄	1	2	yes	complemented
14	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
17	C₂×C₄⋊Dic₁₁	—	2	2	no	—
18	C₂×C₄⋊Dic₁₁	—	4	1	no	—
19	C₂×C₄⋊Dic₁₁	—	4	1	no	—
20	C₂²×C₁₁⋊C₈	—	4	1	no	—
21	C₂×C₁₁×C₁₆	—	2	2	no	—
22	C₂×C₁₁×C₁₆	—	4	1	no	—
23	C₂×C₁₁×C₁₆	—	4	1	no	—
24	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
27	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
28	#66882	—	4	1	no	—
29	#66882	—	4	1	no	—
30	#66882	—	4	2	no	—
31	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
32	C₄⋊(C₁₁⋊C₈)	—	4	1	no	—
33	#7274	—	11	1	no	maximal, Sylow
34	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	SD₁₆	1	1	yes	characteristic
37	C₂²×Dic₁₁	—	4	2	no	—
38	C₂×C₈×C₁₁	—	2	1	no	—
39	C₂×C₈×C₁₁	—	2	1	no	—
40	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
41	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₁	D₈	1	1	yes	characteristic
45	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
46	C₂×C₈×C₁₁	SD₁₆	1	1	yes	characteristic
47	C₂×C₈×C₁₁	Q₁₆	1	1	yes	characteristic
48	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
50	C₄²×C₁₁	SD₁₆	1	1	yes	characteristic
51	C₄²×C₁₁	Q₁₆	1	1	yes	characteristic
52	C₄⋊Dic₁₁	—	4	2	no	—
53	C₄⋊Dic₁₁	—	4	2	no	—
54	C₄⋊Dic₁₁	—	8	2	no	—
55	C₄⋊Dic₁₁	—	8	1	no	—
56	C₄⋊Dic₁₁	—	8	1	no	—
57	C₂×C₁₁⋊C₈	—	4	2	no	—
58	C₂×C₁₁⋊C₈	—	8	1	no	—
59	C₂×C₁₁⋊C₈	—	8	1	no	—
60	C₁₁×C₁₆	—	4	2	no	—
61	C₂×C₄⋊C₁₆	D₁₁	1	1	yes	characteristic
62	#1845	—	11	1	no	—
63	C₂×#335	—	11	1	no	—
64	C₂³×C₁₁	#102	1	1	yes	characteristic
65	C₂×C₄×C₁₁	—	2	1	no	—
66	C₂×C₄×C₁₁	—	2	1	no	—
67	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
68	C₂×C₄×C₁₁	#100	1	1	yes	characteristic
69	C₂×C₄×C₁₁	#101	1	1	yes	characteristic
70	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
71	C₂×C₄×C₁₁	#102	1	1	yes	characteristic
72	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
73	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
74	C₂×C₄×C₁₁	#103	1	1	yes	characteristic
75	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
76	C₂×C₄×C₁₁	#107	1	1	yes	characteristic
77	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
78	C₂×C₄×C₁₁	SD₃₂	1	1	yes	characteristic
79	C₂×C₄×C₁₁	SD₃₂	1	1	yes	characteristic
80	C₂×C₄×C₁₁	Q₃₂	1	1	yes	characteristic
81	C₂×Dic₁₁	—	8	2	no	—
82	C₂×Dic₁₁	—	8	2	no	—
83	C₂×Dic₁₁	—	8	2	no	—
84	C₈×C₁₁	—	2	1	no	—
85	C₈×C₁₁	—	2	1	no	—
86	C₈×C₁₁	#102	1	1	yes	characteristic
87	C₈×C₁₁	#103	1	1	yes	characteristic
88	C₈×C₁₁	#106	1	1	yes	characteristic
89	C₈×C₁₁	#107	1	1	yes	characteristic
90	C₁₁⋊C₈	—	8	2	no	—
91	C₂²×C₁₆	—	2	1	no	—
92	C₂×#107	—	11	2	no	—
93	C₂×#107	—	22	1	no	—
94	C₂×C₄⋊C₈	—	22	1	no	—
95	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
96	#384	—	22	1	no	—
97	C₄⋊C₁₆	—	2	1	no	—
98	C₄⋊C₁₆	Dic₁₁	1	2	yes	complemented
99	#335	—	11	2	no	—
100	#335	—	22	1	no	—
101	C₂²×C₁₁	#331	1	1	yes	characteristic
102	C₂²×C₁₁	#332	1	1	yes	characteristic
103	C₂²×C₁₁	#340	1	1	yes	characteristic
104	C₂²×C₁₁	#357	1	1	yes	characteristic
105	C₂²×C₁₁	#358	1	1	yes	characteristic
106	C₂²×C₁₁	#361	1	1	yes	characteristic
107	C₂²×C₁₁	#362	1	1	yes	characteristic
108	C₄×C₁₁	—	2	1	no	—
109	C₄×C₁₁	—	2	1	no	—
110	C₄×C₁₁	#332	1	1	yes	characteristic
111	C₄×C₁₁	#333	1	1	yes	characteristic
112	C₄×C₁₁	#340	1	1	yes	characteristic
113	C₄×C₁₁	#343	1	1	yes	characteristic
114	C₄×C₁₁	#357	1	1	yes	characteristic
115	C₄×C₁₁	#358	1	1	yes	characteristic
116	C₄×C₁₁	#366	1	1	yes	characteristic
117	C₄×C₁₁	#367	1	1	yes	characteristic
118	Dic₁₁	—	16	2	no	—
119	C₂²×C₈	—	44	1	no	—
120	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
121	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
122	C₂×C₄⋊C₄	—	22	2	no	—
123	C₂×C₄⋊C₄	—	44	1	no	—
124	C₂×C₄⋊C₄	—	44	1	no	—
125	C₂×C₄²	D₄₄	1	1	yes	characteristic
126	C₂×C₁₆	—	2	2	no	—
127	C₂×C₁₆	—	4	1	no	—
128	C₂×C₁₆	—	4	1	no	—
129	#107	—	44	1	no	—
130	#107	—	44	1	no	—
131	#107	—	44	2	no	—
132	C₄⋊C₈	—	22	2	no	—
133	C₄⋊C₈	—	44	1	no	—
134	C₄×C₈	Dic₂₂	1	1	yes	characteristic
135	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
136	C₄×C₈	C₂×Dic₁₁	1	1	yes	characteristic
137	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
138	C₂×C₁₁	#1296	1	1	yes	characteristic
139	C₂×C₁₁	#1361	1	1	yes	characteristic
140	C₂×C₁₁	#1362	1	1	yes	characteristic
141	C₂×C₁₁	#1364	1	1	yes	characteristic
142	C₂×C₁₁	#1365	1	1	yes	characteristic
143	C₂×C₁₁	#1380	1	1	yes	characteristic
144	C₂×C₁₁	#1387	1	1	yes	characteristic
145	C₂²×C₄	—	44	2	no	—
146	C₂²×C₄	#4314	1	1	yes	characteristic
147	C₂²×C₄	D₈₈	1	1	yes	characteristic
148	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	—	2	1	no	—
151	C₂×C₈	—	44	2	no	—
152	C₂×C₈	—	88	1	no	—
153	C₂×C₈	—	88	1	no	—
154	C₂×C₈	C₄×Dic₁₁	1	1	yes	characteristic
155	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
156	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
157	C₂×C₈	#4323	1	1	yes	characteristic
158	C₂×C₈	#4324	1	1	yes	characteristic
159	C₂×C₈	#4325	1	1	yes	characteristic
160	C₂×C₈	#4326	1	1	yes	characteristic
161	C₂×C₈	C₂²⋊Dic₁₁	1	1	yes	characteristic
162	C₄⋊C₄	—	44	2	no	—
163	C₄⋊C₄	—	44	2	no	—
164	C₄⋊C₄	—	88	2	no	—
165	C₄⋊C₄	—	88	1	no	—
166	C₄⋊C₄	—	88	1	no	—
167	C₄²	#4314	1	1	yes	characteristic
168	C₄²	Dic₄₄	1	1	yes	characteristic
169	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
170	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
171	C₁₆	—	4	2	no	—
172	C₁₁	#7274	1	1	yes	characteristic, complemented, Sylow
173	C₂³	#66885	1	1	yes	characteristic
174	C₂×C₄	—	2	1	no	—
175	C₂×C₄	—	2	1	no	—
176	C₂×C₄	—	88	2	no	—
177	C₂×C₄	—	88	2	no	—
178	C₂×C₄	—	88	2	no	—
179	C₂×C₄	D₁₇₆	1	1	yes	characteristic
180	C₂×C₄	#66864	1	1	yes	characteristic
181	C₂×C₄	#66864	1	1	yes	characteristic
182	C₂×C₄	Dic₈₈	1	1	yes	characteristic
183	C₂×C₄	#66873	1	1	yes	characteristic
184	C₂×C₄	#66874	1	1	yes	characteristic
185	C₂×C₄	#66880	1	1	yes	characteristic
186	C₂×C₄	#66880	1	1	yes	characteristic
187	C₂×C₄	#66881	1	1	yes	characteristic
188	C₂×C₄	#66882	1	1	yes	characteristic
189	C₂×C₄	#66885	1	1	yes	characteristic
190	C₂×C₄	#66887	1	1	yes	characteristic
191	C₂×C₄	#66888	1	1	yes	characteristic
192	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
193	C₈	—	2	1	no	—
194	C₈	—	2	1	no	—
195	C₈	—	88	2	no	—
196	C₈	#66871	1	1	yes	characteristic
197	C₈	#66872	1	1	yes	characteristic
198	C₈	#66896	1	1	yes	characteristic
199	C₈	#66899	1	1	yes	characteristic
200	C₂²	#10622123	1	1	yes	characteristic
201	C₂²	#10622124	1	1	yes	characteristic
202	C₂²	#10622141	1	1	yes	characteristic
203	C₂²	#10622147	1	1	yes	characteristic
204	C₂²	#10622154	1	1	yes	characteristic
205	C₂²	#10622155	1	1	yes	characteristic
206	C₂²	#10622189	1	1	yes	characteristic
207	C₄	—	2	1	no	—
208	C₄	—	2	1	no	—
209	C₄	—	176	2	no	—
210	C₄	#10622119	1	1	yes	characteristic
211	C₄	#10622120	1	1	yes	characteristic
212	C₄	#10622141	1	1	yes	characteristic
213	C₄	#10622142	1	1	yes	characteristic
214	C₄	#10622143	1	1	yes	characteristic
215	C₄	#10622147	1	1	yes	characteristic
216	C₄	#10622167	1	1	yes	characteristic
217	C₄	#10622192	1	1	yes	characteristic
218	C₂	#13066500	1	1	yes	characteristic
219	C₂	#13066663	1	1	yes	characteristic
220	C₂	#13066666	1	1	yes	characteristic
221	C₂	#13066670	1	1	yes	characteristic
222	C₂	#13066673	1	1	yes	characteristic
223	C₂	#13066708	1	1	yes	characteristic
224	C₂	#13066725	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66885
commutator	C₂×C₈×C₁₁	C₄²
Frattini	C₂×C₄×C₈	C₂×D₁₁
Fitting	C₂×C₁₁×C₄⋊C₁₆	C₂
socle, prime radical	C₂³×C₁₁	#102
cosocle	C₂×C₄×C₈×C₁₁	C₂²
hypercenter	C₂×C₄⋊C₁₆	D₁₁
hypocenter	C₁₁	#7274
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄⋊C₁₆

Complements

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

N	H ≅ G/N	type
11. C₁₁×C₄⋊C₁₆	C₄	semidirect
13. #10622096	C₄	semidirect
98. C₄⋊C₁₆	Dic₁₁	semidirect
172. C₁₁	#7274	semidirect

Maximal subgroups

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

subgroup	index
#13068776	2
C₂×#10622096	2
C₂×C₁₁×C₄⋊C₁₆	2
#7274	11