Subgroups — C₁₁×#33398 #14610591

Order 2816.

706 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#504	C₂	1	2	yes	maximal
2	C₄×C₁₁×#131	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#2151	C₂	1	6	yes	maximal, complemented
4	C₁₁×#2150	C₂	1	3	yes	maximal, complemented
5	C₂×C₁₁×C₄⋊C₁₆	C₂	1	3	yes	maximal, complemented
6	C₂×C₁₁×#131	C₄	1	1	yes	characteristic
7	C₂×C₁₁×#131	C₂²	1	1	yes	characteristic
8	C₄×C₁₁×#41	C₄	1	1	yes	characteristic
9	C₁₁×#504	—	2	8	no	—
10	C₂×C₁₁×M₃₂	C₂²	1	6	yes	—
11	C₂²×C₁₁×C₁₆	C₂²	1	6	yes	—
12	C₁₁×#405	C₄	1	3	yes	—
13	C₁₁×#405	C₂²	1	3	yes	—
14	C₄×C₁₁×M₁₆	C₄	1	3	yes	—
15	C₂×C₄×C₈×C₁₁	C₂²	1	3	yes	—
16	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
17	C₁₁×C₄⋊C₁₆	C₂²	1	3	yes	—
18	C₁₁×C₄⋊C₁₆	C₂²	1	6	yes	—
19	C₁₁×C₄⋊C₁₆	C₂²	1	6	yes	—
20	C₂×C₁₁×#41	C₂×C₄	1	1	yes	characteristic
21	C₁₁×#131	—	2	4	no	—
22	C₁₁×#131	D₄	1	4	yes	—
23	C₁₁×#131	Q₈	1	4	yes	—
24	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
25	C₂×C₁₁×M₁₆	C₂×C₄	1	3	yes	—
26	C₂²×C₈×C₁₁	C₂×C₄	1	3	yes	—
27	C₂²×C₈×C₁₁	C₂³	1	3	yes	—
28	C₄×Q₈×C₁₁	C₈	1	1	yes	characteristic
29	C₄×Q₈×C₁₁	C₈	1	1	yes	characteristic
30	C₄×D₄×C₁₁	C₈	1	3	yes	—
31	C₄×D₄×C₁₁	C₈	1	3	yes	—
32	C₁₁×#117	C₂×C₄	1	3	yes	—
33	C₂×C₄²×C₁₁	C₂×C₄	1	3	yes	—
34	C₁₁×M₃₂	—	2	12	no	—
35	C₂×C₁₁×C₁₆	—	2	12	no	—
36	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
37	C₂×C₁₁×C₁₆	C₂³	1	6	yes	—
38	C₁₁×#97	C₂×C₄	1	6	yes	—
39	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
40	C₄×C₈×C₁₁	C₂×C₄	1	3	yes	—
41	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
42	C₄×C₈×C₁₁	C₂³	1	3	yes	—
43	#33398	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₁₁×#41	C₄⋊C₄	1	4	yes	—
45	C₁₁×#41	M₁₆	1	4	yes	—
46	C₂×Q₈×C₁₁	C₂×C₈	1	1	yes	characteristic
47	C₂×D₄×C₁₁	C₂×C₈	1	3	yes	—
48	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
49	C₂²×C₄×C₁₁	C₂×C₈	1	3	yes	—
50	C₂²×C₄×C₁₁	C₂²×C₄	1	3	yes	—
51	C₁₁×M₁₆	—	2	6	no	—
52	C₁₁×M₁₆	C₄⋊C₄	1	12	yes	—
53	C₂×C₈×C₁₁	—	2	6	no	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	3	yes	—
57	C₂×C₈×C₁₁	C₂×D₄	1	6	yes	—
58	C₂×C₈×C₁₁	C₂×Q₈	1	6	yes	—
59	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
60	C₁₁×C₄⋊C₄	C₂×C₈	1	3	yes	—
61	C₁₁×C₄⋊C₄	C₂×C₈	1	3	yes	—
62	C₁₁×C₂²⋊C₄	C₂×C₈	1	6	yes	—
63	C₄²×C₁₁	C₂×C₈	1	3	yes	—
64	C₄²×C₁₁	C₂×C₈	1	3	yes	—
65	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
66	C₄²×C₁₁	C₂²×C₄	1	3	yes	—
67	C₁₁×C₁₆	—	2	2	no	—
68	C₁₁×C₁₆	—	2	6	no	—
69	C₂×#504	C₂×C₁₁	1	2	yes	—
70	C₄×#131	C₂×C₁₁	1	1	yes	characteristic
71	#2151	C₂×C₁₁	1	6	yes	complemented
72	#2150	C₂×C₁₁	1	3	yes	complemented
73	C₂×C₄⋊C₁₆	C₂×C₁₁	1	3	yes	complemented
74	C₂³×C₁₁	C₂²×C₈	1	3	yes	—
75	Q₈×C₁₁	C₄⋊C₈	1	4	yes	—
76	D₄×C₁₁	C₄⋊C₈	1	12	yes	—
77	C₂×C₄×C₁₁	—	2	6	no	—
78	C₂×C₄×C₁₁	—	4	3	no	—
79	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
80	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
82	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
83	C₂×C₄×C₁₁	C₂²×C₈	1	3	yes	—
84	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₂×M₁₆	1	6	yes	—
86	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
87	C₈×C₁₁	—	2	1	no	—
88	C₈×C₁₁	—	2	3	no	—
89	C₈×C₁₁	C₂×C₄⋊C₄	1	6	yes	—
90	C₈×C₁₁	C₂²×D₄	1	1	yes	characteristic
91	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
92	C₂×#131	C₄×C₁₁	1	1	yes	characteristic
93	C₂×#131	C₂²×C₁₁	1	1	yes	characteristic
94	C₄×#41	C₄×C₁₁	1	1	yes	characteristic
95	#504	—	2	8	no	—
96	C₂×M₃₂	C₂²×C₁₁	1	6	yes	—
97	C₂²×C₁₆	C₂²×C₁₁	1	6	yes	—
98	#405	C₄×C₁₁	1	3	yes	—
99	#405	C₂²×C₁₁	1	3	yes	—
100	C₄×M₁₆	C₄×C₁₁	1	3	yes	—
101	C₂×C₄×C₈	C₂²×C₁₁	1	3	yes	—
102	C₄⋊C₁₆	C₂²×C₁₁	1	1	yes	characteristic
103	C₄⋊C₁₆	C₂²×C₁₁	1	3	yes	—
104	C₄⋊C₁₆	C₂²×C₁₁	1	6	yes	—
105	C₄⋊C₁₆	C₂²×C₁₁	1	6	yes	—
106	C₂²×C₁₁	—	2	3	no	—
107	C₂²×C₁₁	—	2	3	no	—
108	C₂²×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
109	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
110	C₄×C₁₁	—	2	3	no	—
111	C₄×C₁₁	—	2	1	no	—
112	C₄×C₁₁	—	2	3	no	—
113	C₄×C₁₁	C₂×C₄⋊C₈	1	6	yes	—
114	C₄×C₁₁	#504	1	2	yes	complemented
115	C₄×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
116	C₄×C₁₁	C₂²×M₁₆	1	1	yes	characteristic
117	C₂×#41	C₂×C₄×C₁₁	1	1	yes	characteristic
118	#131	—	2	4	no	—
119	#131	D₄×C₁₁	1	4	yes	—
120	#131	Q₈×C₁₁	1	4	yes	—
121	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
122	C₂×M₁₆	C₂×C₄×C₁₁	1	3	yes	—
123	C₂²×C₈	C₂×C₄×C₁₁	1	3	yes	—
124	C₂²×C₈	C₂³×C₁₁	1	3	yes	—
125	C₄×Q₈	C₈×C₁₁	1	1	yes	characteristic
126	C₄×Q₈	C₈×C₁₁	1	1	yes	characteristic
127	C₄×D₄	C₈×C₁₁	1	3	yes	—
128	C₄×D₄	C₈×C₁₁	1	3	yes	—
129	#117	C₂×C₄×C₁₁	1	3	yes	—
130	C₂×C₄²	C₂×C₄×C₁₁	1	3	yes	—
131	M₃₂	—	2	12	no	—
132	C₂×C₁₆	—	2	12	no	—
133	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
134	C₂×C₁₆	C₂³×C₁₁	1	6	yes	—
135	#97	C₂×C₄×C₁₁	1	6	yes	—
136	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
137	C₄×C₈	C₂×C₄×C₁₁	1	3	yes	—
138	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
139	C₄×C₈	C₂³×C₁₁	1	3	yes	—
140	C₂×C₁₁	—	2	6	no	—
141	C₂×C₁₁	C₂²×C₄⋊C₈	1	1	yes	characteristic
142	C₂×C₁₁	C₂×#504	1	1	yes	characteristic
143	C₂×C₁₁	#3407	1	1	yes	characteristic
144	#41	C₁₁×C₄⋊C₄	1	4	yes	—
145	#41	C₁₁×M₁₆	1	4	yes	—
146	C₂×Q₈	C₂×C₈×C₁₁	1	1	yes	characteristic
147	C₂×D₄	C₂×C₈×C₁₁	1	3	yes	—
148	C₂²×C₄	C₂×C₈×C₁₁	1	3	yes	—
149	C₂²×C₄	C₂×C₈×C₁₁	1	3	yes	—
150	C₂²×C₄	C₂²×C₄×C₁₁	1	3	yes	—
151	M₁₆	—	2	6	no	—
152	M₁₆	C₁₁×C₄⋊C₄	1	12	yes	—
153	C₂×C₈	—	2	6	no	—
154	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
155	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
156	C₂×C₈	C₂²×C₄×C₁₁	1	3	yes	—
157	C₂×C₈	C₂×D₄×C₁₁	1	6	yes	—
158	C₂×C₈	C₂×Q₈×C₁₁	1	6	yes	—
159	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
160	C₄⋊C₄	C₂×C₈×C₁₁	1	3	yes	—
161	C₄⋊C₄	C₂×C₈×C₁₁	1	3	yes	—
162	C₂²⋊C₄	C₂×C₈×C₁₁	1	6	yes	—
163	C₄²	C₂×C₈×C₁₁	1	3	yes	—
164	C₄²	C₂×C₈×C₁₁	1	3	yes	—
165	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
166	C₄²	C₂²×C₄×C₁₁	1	3	yes	—
167	C₁₆	—	2	2	no	—
168	C₁₆	—	2	6	no	—
169	C₁₁	#33398	1	1	yes	characteristic, direct product factor, Sylow
170	C₂³	C₂²×C₈×C₁₁	1	3	yes	—
171	Q₈	C₁₁×C₄⋊C₈	1	4	yes	—
172	D₄	C₁₁×C₄⋊C₈	1	12	yes	—
173	C₂×C₄	—	2	6	no	—
174	C₂×C₄	—	4	3	no	—
175	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	6	yes	—
176	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
177	C₂×C₄	C₂²×C₈×C₁₁	1	3	yes	—
178	C₂×C₄	C₂²×C₈×C₁₁	1	3	yes	—
179	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
180	C₂×C₄	C₂²×C₈×C₁₁	1	3	yes	—
181	C₂×C₄	C₂×C₁₁×M₁₆	1	6	yes	—
182	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
183	C₈	—	2	1	no	—
184	C₈	—	2	3	no	—
185	C₈	C₂×C₁₁×C₄⋊C₄	1	6	yes	—
186	C₈	C₂²×D₄×C₁₁	1	1	yes	characteristic
187	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
188	C₂²	—	2	3	no	—
189	C₂²	—	2	3	no	—
190	C₂²	C₂×C₁₁×C₄⋊C₈	1	6	yes	—
191	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
192	C₄	—	2	3	no	—
193	C₄	—	2	1	no	—
194	C₄	—	2	3	no	—
195	C₄	C₂×C₁₁×C₄⋊C₈	1	6	yes	—
196	C₄	C₁₁×#504	1	2	yes	complemented
197	C₄	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
198	C₄	C₂²×C₁₁×M₁₆	1	1	yes	characteristic
199	C₂	—	2	6	no	—
200	C₂	C₂²×C₁₁×C₄⋊C₈	1	1	yes	characteristic
201	C₂	C₂×C₁₁×#504	1	1	yes	characteristic
202	C₂	C₁₁×#3407	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂⁴
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂³×C₈
prime radical	C₂×C₁₁×#41	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#2151	C₂	semidirect
4. C₁₁×#2150	C₂	semidirect
5. C₂×C₁₁×C₄⋊C₁₆	C₂	semidirect
43. #33398	C₁₁	direct (N × H)
71. #2151	C₂×C₁₁	semidirect
72. #2150	C₂×C₁₁	semidirect
73. C₂×C₄⋊C₁₆	C₂×C₁₁	semidirect
114. C₄×C₁₁	#504	semidirect
169. C₁₁	#33398	direct (N × H)
196. C₄	C₁₁×#504	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#504	2
C₄×C₁₁×#131	2
C₁₁×#2151	2
C₁₁×#2150	2
C₂×C₁₁×C₄⋊C₁₆	2
#33398	11

Subgroups — C11×#33398 #14610591

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33398 #14610591