Subgroups — #14671793

Order 2816.

318 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	C₂×#10622149	C₂	1	2	yes	maximal
2	#13070372	C₂	1	1	yes	maximal, characteristic
3	C₈×C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
4	#13066697	C₂	1	2	yes	maximal
5	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×C₈×Dic₁₁	C₂²	1	2	yes	—
10	C₂×#66876	C₂²	1	2	yes	—
11	C₄×C₄⋊Dic₁₁	C₄	1	1	yes	characteristic
12	C₂×C₄⋊(C₁₁⋊C₈)	C₄	1	1	yes	characteristic
13	C₁₁×#346	—	2	1	no	—
14	C₄×C₁₁×C₁₆	—	2	1	no	—
15	#10622188	C₄	1	2	yes	—
16	#10622149	—	2	4	no	—
17	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
18	C₄⋊(C₁₁⋊C₁₆)	—	2	1	no	—
19	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₁	—	2	1	no	—
23	C₂×C₄×Dic₁₁	C₂×C₄	1	2	yes	—
24	C₂²×C₁₁⋊C₈	C₂×C₄	1	2	yes	—
25	C₁₁×M₃₂	—	2	1	no	—
26	C₁₁×M₃₂	—	2	1	no	—
27	C₁₁×M₃₂	D₄	1	2	yes	—
28	C₁₁×M₃₂	Q₈	1	2	yes	—
29	C₂×C₁₁×C₁₆	—	2	1	no	—
30	C₂×C₁₁×C₁₆	—	2	1	no	—
31	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
32	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
33	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
34	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
35	C₁₁⋊#95	—	2	1	no	—
36	C₈×Dic₁₁	—	2	2	no	—
37	C₈×Dic₁₁	—	2	2	no	—
38	#66876	—	2	2	no	—
39	#66876	—	2	2	no	—
40	C₂×C₁₁⋊C₁₆	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	C₈	1	2	yes	—
42	C₄⋊(C₁₁⋊C₈)	C₈	1	2	yes	—
43	#13163	—	11	1	no	maximal, Sylow
44	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
47	C₂²×Dic₁₁	—	2	2	no	—
48	C₂×C₈×C₁₁	—	2	1	no	—
49	C₂×C₈×C₁₁	—	2	1	no	—
50	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
56	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
57	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
58	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
60	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
61	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
62	C₄⋊Dic₁₁	—	2	4	no	—
63	C₄×Dic₁₁	—	2	2	no	—
64	C₄×Dic₁₁	—	2	2	no	—
65	C₂×C₁₁⋊C₈	—	2	2	no	—
66	C₂×C₁₁⋊C₈	—	2	2	no	—
67	C₂×C₁₁⋊C₈	C₂×C₈	1	4	yes	—
68	C₁₁×C₁₆	—	2	2	no	—
69	C₁₁×C₁₆	—	2	2	no	—
70	C₁₁⋊C₁₆	—	4	2	no	—
71	C₂×#364	—	11	2	no	—
72	#2150	—	11	1	no	—
73	C₄×M₃₂	D₁₁	1	1	yes	characteristic
74	C₈×C₄⋊C₄	—	11	1	no	—
75	#1376	—	11	2	no	—
76	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
77	C₂×C₄×C₁₁	—	2	2	no	—
78	C₂×C₄×C₁₁	—	4	1	no	—
79	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
88	C₂×C₄×C₁₁	#131	1	1	yes	characteristic
89	C₂×Dic₁₁	—	2	4	no	—
90	C₂×Dic₁₁	—	4	2	no	—
91	C₂×Dic₁₁	—	4	2	no	—
92	C₈×C₁₁	—	2	1	no	—
93	C₈×C₁₁	—	2	1	no	—
94	C₈×C₁₁	#121	1	1	yes	characteristic
95	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
96	C₈×C₁₁	#125	1	1	yes	characteristic
97	C₈×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
98	C₁₁⋊C₈	—	2	4	no	—
99	C₂×M₃₂	—	11	2	no	—
100	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
101	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
102	C₂×C₄⋊C₈	—	11	1	no	—
103	C₂×C₄×C₈	—	11	2	no	—
104	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
105	C₄×C₄⋊C₄	—	11	1	no	—
106	#364	—	22	4	no	—
107	C₄⋊C₁₆	—	22	1	no	—
108	C₄⋊C₁₆	—	22	1	no	—
109	#346	—	2	1	no	—
110	C₄×C₁₆	—	2	1	no	—
111	#336	—	11	2	no	—
112	C₂²×C₁₁	—	2	1	no	—
113	C₂²×C₁₁	—	2	1	no	—
114	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
115	C₂²×C₁₁	#436	1	1	yes	characteristic
116	C₂²×C₁₁	#446	1	1	yes	characteristic
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	2	1	no	—
119	C₄×C₁₁	—	2	1	no	—
120	C₄×C₁₁	#364	1	2	yes	complemented
121	C₄×C₁₁	#389	1	1	yes	characteristic
122	C₄×C₁₁	#424	1	1	yes	characteristic
123	C₄×C₁₁	C₈×D₄	1	1	yes	characteristic
124	C₄×C₁₁	C₈×Q₈	1	1	yes	characteristic
125	Dic₁₁	—	4	4	no	—
126	C₂²×C₈	—	11	2	no	—
127	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
128	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
129	C₂×C₄⋊C₄	—	22	1	no	—
130	C₂×C₄²	—	11	2	no	—
131	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
132	M₃₂	—	2	1	no	—
133	M₃₂	—	2	1	no	—
134	M₃₂	—	22	2	no	—
135	M₃₂	—	22	2	no	—
136	M₃₂	Dic₂₂	1	2	yes	—
137	M₃₂	D₄₄	1	2	yes	—
138	C₂×C₁₆	—	2	1	no	—
139	C₂×C₁₆	—	2	1	no	—
140	C₂×C₁₆	—	22	2	no	—
141	C₄⋊C₈	—	11	2	no	—
142	C₄⋊C₈	—	11	2	no	—
143	C₄×C₈	—	22	2	no	—
144	C₄×C₈	—	22	2	no	—
145	C₄×C₈	Dic₂₂	1	1	yes	characteristic
146	C₄×C₈	Dic₂₂	1	1	yes	characteristic
147	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
148	C₄×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
149	#95	—	22	1	no	—
150	C₂×C₁₁	—	2	1	no	—
151	C₂×C₁₁	—	2	1	no	—
152	C₂×C₁₁	#1939	1	1	yes	characteristic
153	C₂×C₁₁	C₂×#364	1	1	yes	characteristic
154	C₂×C₁₁	#2153	1	1	yes	characteristic
155	C₂²×C₄	—	22	2	no	—
156	C₂²×C₄	#4313	1	1	yes	characteristic
157	C₂²×C₄	#4313	1	1	yes	characteristic
158	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	2	1	no	—
161	C₂×C₈	—	11	4	no	—
162	C₂×C₈	—	22	2	no	—
163	C₂×C₈	—	22	2	no	—
164	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
165	C₂×C₈	Dic₁₁⋊C₄	1	1	yes	characteristic
166	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
167	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
168	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
169	C₂×C₈	#4339	1	1	yes	characteristic
170	C₂×C₈	#4339	1	1	yes	characteristic
171	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
172	C₄⋊C₄	—	22	4	no	—
173	C₄²	—	22	2	no	—
174	C₄²	—	22	2	no	—
175	C₄²	C₈×D₁₁	1	1	yes	characteristic
176	C₄²	C₈×D₁₁	1	1	yes	characteristic
177	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
178	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
179	C₁₆	—	2	2	no	—
180	C₁₆	—	2	2	no	—
181	C₁₆	—	44	2	no	—
182	C₁₁	#13163	1	1	yes	characteristic, complemented, Sylow
183	C₂³	C₂×#4313	1	1	yes	characteristic
184	C₂×C₄	—	2	2	no	—
185	C₂×C₄	—	4	1	no	—
186	C₂×C₄	—	22	4	no	—
187	C₂×C₄	—	44	2	no	—
188	C₂×C₄	—	44	2	no	—
189	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
190	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
191	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
192	C₂×C₄	Dic₁₁⋊C₈	1	1	yes	characteristic
193	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
194	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
195	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
196	C₂×C₄	#66954	1	1	yes	characteristic
197	C₂×C₄	#66954	1	1	yes	characteristic
198	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
199	C₈	—	2	1	no	—
200	C₈	—	2	1	no	—
201	C₈	—	22	4	no	—
202	C₈	#66922	1	1	yes	characteristic
203	C₈	#66923	1	1	yes	characteristic
204	C₈	#66977	1	1	yes	characteristic
205	C₈	#66983	1	1	yes	characteristic
206	C₂²	—	2	1	no	—
207	C₂²	—	2	1	no	—
208	C₂²	#10622292	1	1	yes	characteristic
209	C₂²	#10622301	1	1	yes	characteristic
210	C₂²	C₂×Dic₁₁⋊C₈	1	1	yes	characteristic
211	C₄	—	2	1	no	—
212	C₄	—	2	1	no	—
213	C₄	—	2	1	no	—
214	C₄	—	44	4	no	—
215	C₄	#10622149	1	2	yes	complemented
216	C₄	C₈×Dic₂₂	1	1	yes	characteristic
217	C₄	C₈×D₄₄	1	1	yes	characteristic
218	C₄	#10622541	1	1	yes	characteristic
219	C₄	#10622715	1	1	yes	characteristic
220	C₂	—	2	1	no	—
221	C₂	—	2	1	no	—
222	C₂	#13069334	1	1	yes	characteristic
223	C₂	C₂×#10622149	1	1	yes	characteristic
224	C₂	#13070381	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₄×C₁₁×M₃₂	C₂
socle	C₂²×C₁₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	#13163
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
120. C₄×C₁₁	#364	semidirect
182. C₁₁	#13163	semidirect
215. C₄	#10622149	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622149	2
#13070372	2
C₈×C₄⋊Dic₁₁	2
#13066697	2
C₄×C₁₁×M₃₂	2
#13163	11