Subgroups — C₁₁×#36584 #14613777

Order 2816.

1590 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	C₁₁×#2859	C₂	1	3	yes	maximal
2	C₁₁×#2571	C₂	1	6	yes	maximal
3	C₁₁×#2509	C₂	1	12	yes	maximal
4	C₁₁×#2351	C₂	1	4	yes	maximal
5	Q₈×C₁₁×C₄⋊C₄	C₂	1	2	yes	maximal
6	C₄×C₁₁×#125	C₂	1	3	yes	maximal
7	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₁×#125	C₂²	1	3	yes	—
9	C₂×C₄×Q₈×C₁₁	C₂²	1	2	yes	—
10	C₂×C₄×Q₈×C₁₁	C₂²	1	4	yes	—
11	C₂×C₄×Q₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#400	C₂²	1	24	yes	—
13	C₁₁×#389	C₂²	1	12	yes	—
14	C₁₁×#389	C₂²	1	12	yes	—
15	C₁₁×#389	C₂²	1	12	yes	—
16	C₁₁×#389	C₂²	1	12	yes	—
17	C₁₁×#389	C₂²	1	6	yes	—
18	C₁₁×#387	C₂²	1	12	yes	—
19	C₁₁×#384	C₂²	1	6	yes	—
20	C₁₁×#382	C₂²	1	12	yes	—
21	C₁₁×#382	C₂²	1	1	yes	characteristic
22	C₁₁×#382	C₂²	1	6	yes	—
23	C₄×C₁₁×C₄⋊C₄	C₂²	1	6	yes	—
24	C₄×C₁₁×C₄⋊C₄	C₂²	1	12	yes	—
25	C₄×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
26	C₄×C₁₁×C₄⋊C₄	C₂²	1	6	yes	—
27	C₄³×C₁₁	C₂²	1	3	yes	—
28	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
29	C₁₁×#125	—	2	12	no	—
30	C₄×Q₈×C₁₁	—	2	8	no	—
31	C₄×Q₈×C₁₁	—	2	16	no	—
32	C₄×Q₈×C₁₁	Q₈	1	8	yes	—
33	C₂×C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
34	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
35	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
36	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
37	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
38	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
39	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
40	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
41	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
42	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
43	C₂×C₄²×C₁₁	C₂³	1	12	yes	—
44	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
45	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
46	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×#95	C₂³	1	4	yes	—
48	C₁₁×#95	C₂³	1	6	yes	—
49	C₁₁×#95	C₂³	1	12	yes	—
50	C₁₁×#95	C₂³	1	12	yes	—
51	C₁₁×#95	C₂³	1	24	yes	—
52	#36584	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
53	C₂×Q₈×C₁₁	C₂×Q₈	1	4	yes	—
54	C₂×Q₈×C₁₁	#41	1	8	yes	—
55	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
56	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
57	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
58	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
59	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
60	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
61	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
62	C₁₁×C₄⋊C₄	—	2	12	no	—
63	C₁₁×C₄⋊C₄	—	2	24	no	—
64	C₁₁×C₄⋊C₄	—	2	24	no	—
65	C₁₁×C₄⋊C₄	—	2	12	no	—
66	C₁₁×C₄⋊C₄	—	2	4	no	—
67	C₁₁×C₄⋊C₄	—	4	12	no	—
68	C₁₁×C₄⋊C₄	—	4	12	no	—
69	C₁₁×C₄⋊C₄	C₂×Q₈	1	12	yes	—
70	C₄²×C₁₁	—	2	12	no	—
71	C₄²×C₁₁	—	2	24	no	—
72	C₄²×C₁₁	—	2	6	no	—
73	C₄²×C₁₁	—	4	6	no	—
74	C₄²×C₁₁	C₂×Q₈	1	12	yes	—
75	C₄²×C₁₁	#41	1	4	yes	—
76	#2859	C₂×C₁₁	1	3	yes	—
77	#2571	C₂×C₁₁	1	6	yes	—
78	#2509	C₂×C₁₁	1	12	yes	—
79	#2351	C₂×C₁₁	1	4	yes	—
80	Q₈×C₄⋊C₄	C₂×C₁₁	1	2	yes	—
81	C₄×#125	C₂×C₁₁	1	3	yes	—
82	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic
83	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
84	Q₈×C₁₁	#125	1	16	yes	complemented
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	6	no	—
88	C₂×C₄×C₁₁	—	2	4	no	—
89	C₂×C₄×C₁₁	—	2	12	no	—
90	C₂×C₄×C₁₁	—	2	6	no	—
91	C₂×C₄×C₁₁	—	2	12	no	—
92	C₂×C₄×C₁₁	—	2	6	no	—
93	C₂×C₄×C₁₁	—	2	4	no	—
94	C₂×C₄×C₁₁	—	2	6	no	—
95	C₂×C₄×C₁₁	—	2	12	no	—
96	C₂×C₄×C₁₁	—	2	4	no	—
97	C₂×C₄×C₁₁	C₂²×Q₈	1	6	yes	—
98	C₂×C₄×C₁₁	C₂²×Q₈	1	6	yes	—
99	C₂×C₄×C₁₁	C₂²×Q₈	1	2	yes	—
100	C₂×C₄×C₁₁	C₂×#41	1	4	yes	—
101	C₂×C₄×C₁₁	C₂×#41	1	12	yes	—
102	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
103	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
104	C₂×#125	C₂²×C₁₁	1	3	yes	—
105	C₂×C₄×Q₈	C₂²×C₁₁	1	4	yes	—
106	C₂×C₄×Q₈	C₂²×C₁₁	1	2	yes	—
107	C₂×C₄×Q₈	C₂²×C₁₁	1	1	yes	characteristic
108	#400	C₂²×C₁₁	1	24	yes	—
109	#389	C₂²×C₁₁	1	6	yes	—
110	#389	C₂²×C₁₁	1	12	yes	—
111	#389	C₂²×C₁₁	1	12	yes	—
112	#389	C₂²×C₁₁	1	12	yes	—
113	#389	C₂²×C₁₁	1	12	yes	—
114	#387	C₂²×C₁₁	1	12	yes	—
115	#384	C₂²×C₁₁	1	6	yes	—
116	#382	C₂²×C₁₁	1	1	yes	characteristic
117	#382	C₂²×C₁₁	1	6	yes	—
118	#382	C₂²×C₁₁	1	12	yes	—
119	C₄×C₄⋊C₄	C₂²×C₁₁	1	6	yes	—
120	C₄×C₄⋊C₄	C₂²×C₁₁	1	12	yes	—
121	C₄×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
122	C₄×C₄⋊C₄	C₂²×C₁₁	1	6	yes	—
123	C₄³	C₂²×C₁₁	1	3	yes	—
124	C₂²×C₁₁	C₂³×Q₈	1	1	yes	characteristic
125	C₂²×C₁₁	C₂²×#41	1	2	yes	—
126	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
127	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
128	C₂²×C₁₁	#585	1	2	yes	—
129	C₄×C₁₁	—	2	4	no	—
130	C₄×C₁₁	—	2	6	no	—
131	C₄×C₁₁	—	4	12	no	—
132	C₄×C₁₁	—	4	4	no	—
133	C₄×C₁₁	—	4	6	no	—
134	C₄×C₁₁	C₂×#125	1	12	yes	—
135	C₄×C₁₁	#557	1	4	yes	—
136	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
137	#125	—	2	12	no	—
138	C₄×Q₈	—	2	16	no	—
139	C₄×Q₈	—	2	8	no	—
140	C₄×Q₈	Q₈×C₁₁	1	8	yes	—
141	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
142	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
143	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
144	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
145	C₂×C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
146	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
147	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
148	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
149	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
150	C₂×C₄²	C₂³×C₁₁	1	12	yes	—
151	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
152	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
153	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
154	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
155	#95	C₂³×C₁₁	1	4	yes	—
156	#95	C₂³×C₁₁	1	6	yes	—
157	#95	C₂³×C₁₁	1	12	yes	—
158	#95	C₂³×C₁₁	1	12	yes	—
159	#95	C₂³×C₁₁	1	24	yes	—
160	C₂×C₁₁	C₂²×#125	1	1	yes	characteristic
161	C₂×C₁₁	C₂×#557	1	1	yes	characteristic
162	C₂×C₁₁	#3480	1	2	yes	—
163	C₂×C₁₁	#3504	1	1	yes	characteristic
164	C₂×C₁₁	#3518	1	2	yes	—
165	C₂×Q₈	C₂×Q₈×C₁₁	1	4	yes	—
166	C₂×Q₈	C₁₁×#41	1	8	yes	—
167	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
168	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
169	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
170	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
171	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
172	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
173	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
174	C₄⋊C₄	—	2	12	no	—
175	C₄⋊C₄	—	2	24	no	—
176	C₄⋊C₄	—	2	24	no	—
177	C₄⋊C₄	—	2	12	no	—
178	C₄⋊C₄	—	2	4	no	—
179	C₄⋊C₄	—	4	12	no	—
180	C₄⋊C₄	—	4	12	no	—
181	C₄⋊C₄	C₂×Q₈×C₁₁	1	12	yes	—
182	C₄²	—	2	12	no	—
183	C₄²	—	2	24	no	—
184	C₄²	—	2	6	no	—
185	C₄²	—	4	6	no	—
186	C₄²	C₂×Q₈×C₁₁	1	12	yes	—
187	C₄²	C₁₁×#41	1	4	yes	—
188	C₁₁	#36584	1	1	yes	characteristic, direct product factor, Sylow
189	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
190	Q₈	C₁₁×#125	1	16	yes	complemented
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	2	no	—
193	C₂×C₄	—	2	6	no	—
194	C₂×C₄	—	2	4	no	—
195	C₂×C₄	—	2	12	no	—
196	C₂×C₄	—	2	6	no	—
197	C₂×C₄	—	2	12	no	—
198	C₂×C₄	—	2	6	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	6	no	—
201	C₂×C₄	—	2	12	no	—
202	C₂×C₄	—	2	4	no	—
203	C₂×C₄	C₂²×Q₈×C₁₁	1	6	yes	—
204	C₂×C₄	C₂²×Q₈×C₁₁	1	6	yes	—
205	C₂×C₄	C₂²×Q₈×C₁₁	1	2	yes	—
206	C₂×C₄	C₂×C₁₁×#41	1	4	yes	—
207	C₂×C₄	C₂×C₁₁×#41	1	12	yes	—
208	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
209	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
210	C₂²	C₂³×Q₈×C₁₁	1	1	yes	characteristic
211	C₂²	C₂²×C₁₁×#41	1	2	yes	—
212	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
213	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	1	yes	characteristic
214	C₂²	C₁₁×#585	1	2	yes	—
215	C₄	—	2	4	no	—
216	C₄	—	2	6	no	—
217	C₄	—	4	12	no	—
218	C₄	—	4	4	no	—
219	C₄	—	4	6	no	—
220	C₄	C₂×C₁₁×#125	1	12	yes	—
221	C₄	C₁₁×#557	1	4	yes	—
222	C₂	C₂²×C₁₁×#125	1	1	yes	characteristic
223	C₂	C₂×C₁₁×#557	1	1	yes	characteristic
224	C₂	C₁₁×#3480	1	2	yes	—
225	C₂	C₁₁×#3504	1	1	yes	characteristic
226	C₂	C₁₁×#3518	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
52. #36584	C₁₁	direct (N × H)
84. Q₈×C₁₁	#125	semidirect
188. C₁₁	#36584	direct (N × H)
190. Q₈	C₁₁×#125	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#2859	2
C₁₁×#2571	2
C₁₁×#2509	2
C₁₁×#2351	2
Q₈×C₁₁×C₄⋊C₄	2
C₄×C₁₁×#125	2
C₄²×Q₈×C₁₁	2
#36584	11

Subgroups — C11×#36584 #14613777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36584 #14613777