Subgroups — C₁₁×#33474 #14610667

Order 2816.

506 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2960	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2183	C₂	1	4	yes	maximal, complemented
3	Q₈×C₁₁×C₁₆	C₂	1	4	yes	maximal, complemented
4	C₁₁×#2151	C₂	1	2	yes	maximal
5	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#2108	C₂	1	2	yes	maximal
7	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
8	C₁₁×#533	C₄	1	1	yes	characteristic
9	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
10	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
12	C₁₁×#446	C₄	1	4	yes	—
13	C₈×Q₈×C₁₁	C₂²	1	4	yes	—
14	C₁₁×#424	C₄	1	2	yes	—
15	C₁₁×#423	C₄	1	1	yes	characteristic
16	C₁₁×#405	C₂²	1	2	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×C₄⋊C₁₆	C₂²	1	4	yes	—
19	C₁₁×C₄⋊C₁₆	C₂²	1	8	yes	—
20	C₁₁×#346	C₂²	1	4	yes	—
21	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
22	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
23	C₄×C₁₁×C₁₆	C₂²	1	4	yes	—
24	C₂×C₁₁×M₁₆	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
27	C₁₁×C₄⋊Q₈	C₈	1	2	yes	—
28	C₁₁×#125	C₈	1	2	yes	—
29	C₁₁×C₂²⋊Q₈	C₈	1	4	yes	—
30	C₄×Q₈×C₁₁	C₂×C₄	1	4	yes	—
31	C₁₁×#117	C₂×C₄	1	2	yes	—
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₁₁×M₃₂	—	2	4	no	—
34	C₂×C₁₁×C₁₆	—	2	2	no	—
35	C₂×C₁₁×C₁₆	Q₈	1	4	yes	complemented
36	C₂×C₁₁×C₁₆	C₂³	1	2	yes	—
37	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
38	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
39	C₂×C₁₁×C₁₆	C₂³	1	1	yes	characteristic
40	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
41	C₁₁×C₄⋊C₈	C₂×C₄	1	8	yes	—
42	C₁₁×#97	C₂×C₄	1	4	yes	—
43	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
44	C₄×C₈×C₁₁	C₂³	1	2	yes	—
45	C₄×C₈×C₁₁	C₂³	1	4	yes	—
46	#33474	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	C₂×Q₈×C₁₁	C₂×C₈	1	4	yes	—
48	C₂²×C₄×C₁₁	C₂×C₈	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
50	C₁₁×M₁₆	—	2	4	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
56	C₂×C₈×C₁₁	#41	1	2	yes	—
57	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
59	C₁₁×C₄⋊C₄	C₂×C₈	1	8	yes	—
60	C₁₁×C₄⋊C₄	C₂×C₈	1	4	yes	—
61	C₁₁×C₂²⋊C₄	C₂×C₈	1	4	yes	—
62	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
63	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
64	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
65	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
66	C₁₁×C₁₆	—	2	2	no	—
67	C₁₁×C₁₆	—	2	4	no	—
68	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
69	C₁₁×C₁₆	C₂×Q₈	1	2	yes	—
70	#2960	C₂×C₁₁	1	1	yes	characteristic
71	#2183	C₂×C₁₁	1	4	yes	complemented
72	Q₈×C₁₆	C₂×C₁₁	1	4	yes	complemented
73	#2151	C₂×C₁₁	1	2	yes	—
74	#2150	C₂×C₁₁	1	1	yes	characteristic
75	#2108	C₂×C₁₁	1	2	yes	—
76	C₂×C₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic
77	C₂³×C₁₁	C₂²×C₈	1	1	yes	characteristic
78	Q₈×C₁₁	—	2	8	no	—
79	C₂×C₄×C₁₁	—	2	4	no	—
80	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
81	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
82	C₂×C₄×C₁₁	C₂²×C₈	1	8	yes	—
83	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
84	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
85	C₂×C₄×C₁₁	#131	1	2	yes	—
86	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
87	C₈×C₁₁	—	2	2	no	—
88	C₈×C₁₁	—	2	4	no	—
89	C₈×C₁₁	C₄×Q₈	1	2	yes	—
90	C₈×C₁₁	C₂²×Q₈	1	1	yes	characteristic
91	C₈×C₁₁	C₂×#41	1	1	yes	characteristic
92	#533	C₄×C₁₁	1	1	yes	characteristic
93	C₂×M₃₂	C₂²×C₁₁	1	2	yes	—
94	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
95	C₂²×C₁₆	C₂²×C₁₁	1	1	yes	characteristic
96	#446	C₄×C₁₁	1	4	yes	—
97	C₈×Q₈	C₂²×C₁₁	1	4	yes	—
98	#424	C₄×C₁₁	1	2	yes	—
99	#423	C₄×C₁₁	1	1	yes	characteristic
100	#405	C₂²×C₁₁	1	2	yes	—
101	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
102	C₄⋊C₁₆	C₂²×C₁₁	1	4	yes	—
103	C₄⋊C₁₆	C₂²×C₁₁	1	8	yes	—
104	#346	C₂²×C₁₁	1	4	yes	—
105	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
106	C₄×C₁₆	C₂²×C₁₁	1	2	yes	—
107	C₄×C₁₆	C₂²×C₁₁	1	4	yes	—
108	C₂²×C₁₁	—	2	2	no	—
109	C₂²×C₁₁	C₈×Q₈	1	2	yes	—
110	C₂²×C₁₁	C₂³×C₈	1	1	yes	characteristic
111	C₄×C₁₁	—	2	2	no	—
112	C₄×C₁₁	—	2	8	no	—
113	C₄×C₁₁	C₈×Q₈	1	2	yes	—
114	C₄×C₁₁	#504	1	4	yes	—
115	C₄×C₁₁	C₂×C₄×Q₈	1	1	yes	characteristic
116	C₄×C₁₁	C₂×#131	1	1	yes	characteristic
117	C₂×M₁₆	C₂×C₄×C₁₁	1	2	yes	—
118	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
119	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
120	C₄⋊Q₈	C₈×C₁₁	1	2	yes	—
121	#125	C₈×C₁₁	1	2	yes	—
122	C₂²⋊Q₈	C₈×C₁₁	1	4	yes	—
123	C₄×Q₈	C₂×C₄×C₁₁	1	4	yes	—
124	#117	C₂×C₄×C₁₁	1	2	yes	—
125	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
126	M₃₂	—	2	4	no	—
127	C₂×C₁₆	—	2	2	no	—
128	C₂×C₁₆	Q₈×C₁₁	1	4	yes	complemented
129	C₂×C₁₆	C₂³×C₁₁	1	2	yes	—
130	C₂×C₁₆	C₂³×C₁₁	1	4	yes	—
131	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
132	C₂×C₁₆	C₂³×C₁₁	1	1	yes	characteristic
133	C₄⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
134	C₄⋊C₈	C₂×C₄×C₁₁	1	8	yes	—
135	#97	C₂×C₄×C₁₁	1	4	yes	—
136	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
137	C₄×C₈	C₂³×C₁₁	1	2	yes	—
138	C₄×C₈	C₂³×C₁₁	1	4	yes	—
139	C₂×C₁₁	—	2	2	no	—
140	C₂×C₁₁	C₂×C₈×Q₈	1	1	yes	characteristic
141	C₂×C₁₁	C₂×#504	1	2	yes	—
142	C₂×Q₈	C₂×C₈×C₁₁	1	4	yes	—
143	C₂²×C₄	C₂×C₈×C₁₁	1	2	yes	—
144	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
145	M₁₆	—	2	4	no	—
146	C₂×C₈	—	2	2	no	—
147	C₂×C₈	C₂²×C₄×C₁₁	1	2	yes	—
148	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
149	C₂×C₈	C₂²×C₄×C₁₁	1	1	yes	characteristic
150	C₂×C₈	C₂×Q₈×C₁₁	1	2	yes	—
151	C₂×C₈	C₁₁×#41	1	2	yes	—
152	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
153	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
154	C₄⋊C₄	C₂×C₈×C₁₁	1	8	yes	—
155	C₄⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
156	C₂²⋊C₄	C₂×C₈×C₁₁	1	4	yes	—
157	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
158	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
159	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
160	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
161	C₁₆	—	2	2	no	—
162	C₁₆	—	2	4	no	—
163	C₁₆	C₂×Q₈×C₁₁	1	2	yes	—
164	C₁₆	C₂×Q₈×C₁₁	1	2	yes	—
165	C₁₁	#33474	1	1	yes	characteristic, direct product factor, Sylow
166	C₂³	C₂²×C₈×C₁₁	1	1	yes	characteristic
167	Q₈	—	2	8	no	—
168	C₂×C₄	—	2	4	no	—
169	C₂×C₄	C₄×Q₈×C₁₁	1	2	yes	—
170	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
171	C₂×C₄	C₂²×C₈×C₁₁	1	8	yes	—
172	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
173	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
174	C₂×C₄	C₁₁×#131	1	2	yes	—
175	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
176	C₈	—	2	2	no	—
177	C₈	—	2	4	no	—
178	C₈	C₄×Q₈×C₁₁	1	2	yes	—
179	C₈	C₂²×Q₈×C₁₁	1	1	yes	characteristic
180	C₈	C₂×C₁₁×#41	1	1	yes	characteristic
181	C₂²	—	2	2	no	—
182	C₂²	C₈×Q₈×C₁₁	1	2	yes	—
183	C₂²	C₂³×C₈×C₁₁	1	1	yes	characteristic
184	C₄	—	2	2	no	—
185	C₄	—	2	8	no	—
186	C₄	C₈×Q₈×C₁₁	1	2	yes	—
187	C₄	C₁₁×#504	1	4	yes	—
188	C₄	C₂×C₄×Q₈×C₁₁	1	1	yes	characteristic
189	C₄	C₂×C₁₁×#131	1	1	yes	characteristic
190	C₂	—	2	2	no	—
191	C₂	C₂×C₈×Q₈×C₁₁	1	1	yes	characteristic
192	C₂	C₂×C₁₁×#504	1	2	yes	—

	subgroup	G/H
center	C₂×C₁₁×C₁₆	C₂³
commutator	C₂²	C₂³×C₈×C₁₁
Frattini, cosocle	C₂×C₈	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂³×C₈
prime radical	C₂³×C₁₁	C₂²×C₈
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₁₁×C₁₆ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₁×#2183	C₂	semidirect
3. Q₈×C₁₁×C₁₆	C₂	semidirect
35. C₂×C₁₁×C₁₆	Q₈	semidirect
46. #33474	C₁₁	direct (N × H)
71. #2183	C₂×C₁₁	semidirect
72. Q₈×C₁₆	C₂×C₁₁	semidirect
128. C₂×C₁₆	Q₈×C₁₁	semidirect
165. C₁₁	#33474	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₁×#2960	2
C₁₁×#2183	2
Q₈×C₁₁×C₁₆	2
C₁₁×#2151	2
C₁₁×#2150	2
C₁₁×#2108	2
C₂×C₄×C₁₁×C₁₆	2
#33474	11

Subgroups — C11×#33474 #14610667

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#33474 #14610667