Subgroups — #14643192

Order 2816.

666 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622538	C₂	1	2	yes	maximal
2	#13066447	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₁₁×M₁₆	C₄	1	2	yes	—
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₄×C₁₁×M₁₆	—	2	2	no	—
7	C₄×C₁₁×M₁₆	—	2	2	no	—
8	C₂×C₁₁×#97	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₄	1	2	yes	—
10	C₂×C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
11	#10622538	—	2	2	no	—
12	#10622538	—	2	2	no	—
13	#10622538	C₄	1	4	yes	—
14	#10622538	C₂²	1	4	yes	—
15	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
16	C₂×C₄×C₁₁⋊C₈	C₄	1	4	yes	—
17	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
19	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
20	C₂×C₁₁×M₁₆	—	2	4	no	—
21	C₂×C₁₁×M₁₆	—	2	4	no	—
22	C₂×C₁₁×M₁₆	C₈	1	8	yes	complemented
23	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
25	C₂×C₄²×C₁₁	C₂×C₄	1	2	yes	—
26	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
28	C₂×C₄²×C₁₁	D₄	1	2	yes	—
29	C₂×C₄²×C₁₁	D₄	1	2	yes	—
30	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
32	C₂²×C₁₁⋊C₈	—	2	4	no	—
33	C₁₁×#97	—	2	4	no	—
34	C₄×C₈×C₁₁	—	2	2	no	—
35	C₄×C₈×C₁₁	—	2	2	no	—
36	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
37	C₂²⋊(C₁₁⋊C₈)	—	2	4	no	—
38	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
39	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
40	C₄×C₁₁⋊C₈	—	2	4	no	—
41	C₄×C₁₁⋊C₈	C₂×C₄	1	8	yes	—
42	#7860	—	11	1	no	maximal, Sylow
43	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₁	—	4	2	no	—
45	C₂²×C₄×C₁₁	—	4	2	no	—
46	C₂²×C₄×C₁₁	C₄²	1	2	yes	—
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
50	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
53	C₂²×C₄×C₁₁	C₄⋊C₄	1	2	yes	—
54	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₁	C₂×C₈	1	4	yes	—
56	C₂²×C₄×C₁₁	M₁₆	1	4	yes	—
57	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
60	C₁₁×M₁₆	—	2	16	no	—
61	C₂×C₈×C₁₁	—	2	4	no	—
62	C₂×C₈×C₁₁	—	2	4	no	—
63	C₂×C₈×C₁₁	C₂×C₈	1	8	yes	complemented
64	C₄²×C₁₁	C₄²	1	1	yes	characteristic
65	C₄²×C₁₁	C₄²	1	1	yes	characteristic
66	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
67	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
68	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
69	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
70	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
71	C₄²×C₁₁	C₄⋊C₄	1	2	yes	—
72	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
73	C₄²×C₁₁	C₂×D₄	1	2	yes	—
74	C₂×C₁₁⋊C₈	—	2	8	no	—
75	C₂×C₁₁⋊C₈	—	4	8	no	—
76	C₂×#431	—	11	2	no	—
77	C₂×C₄×M₁₆	D₁₁	1	1	yes	characteristic
78	#1275	—	11	4	no	—
79	C₂³×C₁₁	—	4	1	no	—
80	C₂³×C₁₁	—	4	1	no	—
81	C₂³×C₁₁	#95	1	2	yes	—
82	C₂³×C₁₁	C₄⋊C₈	1	4	yes	—
83	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×C₁₁	—	2	4	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	4	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	4	2	no	—
89	C₂×C₄×C₁₁	—	4	2	no	—
90	C₂×C₄×C₁₁	—	4	1	no	—
91	C₂×C₄×C₁₁	—	4	1	no	—
92	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
93	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
94	C₂×C₄×C₁₁	#95	1	2	yes	—
95	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
96	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
97	C₂×C₄×C₁₁	C₄×C₈	1	4	yes	—
98	C₂×C₄×C₁₁	#97	1	4	yes	—
99	C₂×C₄×C₁₁	C₂²⋊C₈	1	8	yes	—
100	C₂×C₄×C₁₁	C₄⋊C₈	1	4	yes	—
101	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
102	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	2	yes	—
103	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
105	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
106	C₂×C₄×C₁₁	C₂×M₁₆	1	2	yes	—
107	C₈×C₁₁	—	2	8	no	—
108	C₁₁⋊C₈	—	4	8	no	—
109	C₂²×M₁₆	Dic₁₁	1	2	yes	—
110	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
111	#431	—	11	4	no	—
112	#431	—	11	4	no	—
113	#431	—	22	2	no	—
114	#431	—	22	2	no	—
115	C₂×C₄⋊C₈	—	22	2	no	—
116	C₂×C₂²⋊C₈	—	22	2	no	—
117	C₄×M₁₆	—	2	2	no	—
118	C₄×M₁₆	—	2	2	no	—
119	C₂×#97	C₂×D₁₁	1	2	yes	—
120	C₂×C₄×C₈	—	11	4	no	—
121	C₂×C₄×C₈	Dic₁₁	1	2	yes	—
122	C₂²×C₁₁	—	2	2	no	—
123	C₂²×C₁₁	—	2	1	no	—
124	C₂²×C₁₁	—	2	2	no	—
125	C₂²×C₁₁	—	2	1	no	—
126	C₂²×C₁₁	—	4	4	no	—
127	C₂²×C₁₁	#336	1	4	yes	—
128	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
129	C₂²×C₁₁	C₂×C₄⋊C₈	1	2	yes	—
130	C₄×C₁₁	—	2	1	no	—
131	C₄×C₁₁	—	2	2	no	—
132	C₄×C₁₁	—	2	1	no	—
133	C₄×C₁₁	—	2	2	no	—
134	C₄×C₁₁	#336	1	4	yes	—
135	C₄×C₁₁	H(3,ℤ/4)	1	2	yes	—
136	C₄×C₁₁	#338	1	2	yes	—
137	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
138	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
139	C₄×C₁₁	C₂×C₂²⋊C₈	1	2	yes	—
140	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
141	C₂³×C₄	D₄₄	1	1	yes	characteristic
142	C₂³×C₄	C₂×Dic₁₁	1	1	yes	characteristic
143	C₂×M₁₆	—	2	4	no	—
144	C₂×M₁₆	—	2	4	no	—
145	C₂×M₁₆	C₁₁⋊C₈	1	8	yes	complemented
146	C₂²×C₈	—	22	4	no	—
147	C₂²×C₈	C₂×Dic₁₁	1	4	yes	—
148	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
149	C₂×C₄²	C₄×D₁₁	1	2	yes	—
150	C₂×C₄²	C₄×D₁₁	1	2	yes	—
151	C₂×C₄²	D₄₄	1	1	yes	characteristic
152	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
153	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
154	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
155	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
156	C₄⋊C₈	—	22	4	no	—
157	C₄⋊C₈	—	22	4	no	—
158	C₂²⋊C₈	—	22	4	no	—
159	C₂²⋊C₈	—	22	4	no	—
160	#97	—	2	4	no	—
161	C₄×C₈	—	2	2	no	—
162	C₄×C₈	—	2	2	no	—
163	C₄×C₈	—	11	8	no	—
164	C₄×C₈	—	22	4	no	—
165	C₂×C₁₁	—	2	4	no	—
166	C₂×C₁₁	—	2	2	no	—
167	C₂×C₁₁	C₂×#336	1	1	yes	characteristic
168	C₂×C₁₁	C₂×H(3,ℤ/4)	1	1	yes	characteristic
169	C₂×C₁₁	C₂×#338	1	1	yes	characteristic
170	C₂⁴	C₄⋊Dic₁₁	1	1	yes	characteristic
171	C₂²×C₄	—	4	2	no	—
172	C₂²×C₄	—	4	2	no	—
173	C₂²×C₄	C₂×C₁₁⋊C₈	1	4	yes	—
174	C₂²×C₄	#4318	1	4	yes	—
175	C₂²×C₄	C₄×Dic₁₁	1	2	yes	—
176	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
177	C₂²×C₄	Dic₁₁⋊C₄	1	2	yes	—
178	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
179	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
180	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
181	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
182	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
183	C₂²×C₄	C₂²⋊Dic₁₁	1	2	yes	—
184	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
186	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
187	M₁₆	—	2	16	no	—
188	C₂×C₈	—	2	4	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	22	8	no	—
191	C₂×C₈	—	44	8	no	—
192	C₂×C₈	C₂×C₁₁⋊C₈	1	8	yes	complemented
193	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
194	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
195	C₄²	Dic₁₁⋊C₄	1	2	yes	—
196	C₄²	Dic₁₁⋊C₄	1	2	yes	—
197	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
198	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
199	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
200	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
201	C₄²	C₂×C₄×D₁₁	1	2	yes	—
202	C₄²	C₂×C₂²⋊D₁₁	1	2	yes	—
203	C₁₁	#7860	1	1	yes	characteristic, complemented, Sylow
204	C₂³	—	4	1	no	—
205	C₂³	—	4	1	no	—
206	C₂³	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
207	C₂³	C₁₁⋊#95	1	2	yes	—
208	C₂³	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	4	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	4	2	no	—
214	C₂×C₄	—	4	2	no	—
215	C₂×C₄	—	4	1	no	—
216	C₂×C₄	—	4	1	no	—
217	C₂×C₄	C₄×C₁₁⋊C₈	1	4	yes	—
218	C₂×C₄	#66867	1	4	yes	—
219	C₂×C₄	C₄⋊(C₁₁⋊C₈)	1	4	yes	—
220	C₂×C₄	C₂²⋊(C₁₁⋊C₈)	1	8	yes	—
221	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
222	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
223	C₂×C₄	C₁₁⋊#95	1	2	yes	—
224	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
225	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
226	C₂×C₄	C₂²×C₁₁⋊C₈	1	2	yes	—
227	C₂×C₄	C₂×#4318	1	2	yes	—
228	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
229	C₂×C₄	C₂×Dic₁₁⋊C₄	1	2	yes	—
230	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	2	yes	—
231	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
232	C₈	—	2	8	no	—
233	C₈	—	44	8	no	—
234	C₂²	—	2	2	no	—
235	C₂²	—	2	1	no	—
236	C₂²	—	2	2	no	—
237	C₂²	—	2	1	no	—
238	C₂²	—	4	4	no	—
239	C₂²	#10622162	1	4	yes	—
240	C₂²	C₂×C₄⋊(C₁₁⋊C₈)	1	2	yes	—
241	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
242	C₄	—	2	2	no	—
243	C₄	—	2	1	no	—
244	C₄	—	2	1	no	—
245	C₄	—	2	2	no	—
246	C₄	#10622162	1	4	yes	—
247	C₄	#10622195	1	2	yes	—
248	C₄	C₁₁⋊#338	1	2	yes	—
249	C₄	C₂×C₄×C₁₁⋊C₈	1	1	yes	characteristic
250	C₄	C₂×#66867	1	1	yes	characteristic
251	C₄	C₂×C₂²⋊(C₁₁⋊C₈)	1	2	yes	—
252	C₂	—	2	2	no	—
253	C₂	—	2	4	no	—
254	C₂	C₂×#10622162	1	1	yes	characteristic
255	C₂	C₂×#10622195	1	1	yes	characteristic
256	C₂	C₂×C₁₁⋊#338	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₄×Dic₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₄×C₁₁×M₁₆	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×C₄×M₁₆	D₁₁
hypocenter	C₁₁	#7860
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
2. #13066447	C₂	semidirect
22. C₂×C₁₁×M₁₆	C₈	semidirect
63. C₂×C₈×C₁₁	C₂×C₈	semidirect
145. C₂×M₁₆	C₁₁⋊C₈	semidirect
192. C₂×C₈	C₂×C₁₁⋊C₈	semidirect
203. C₁₁	#7860	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622538	2
#13066447	2
C₂×C₄×C₁₁×M₁₆	2
#7860	11