Subgroups — C₁₁×#12017 #14589210

Order 2816.

232 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2163	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2150	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₁×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1370	C₂	1	2	yes	maximal, complemented
5	C₁₁×#1367	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₁×M₃₂	—	2	1	no	—
7	C₁₁×#431	C₄	1	1	yes	characteristic
8	C₄×C₁₁×M₁₆	C₄	1	1	yes	characteristic
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₁₁×C₄⋊C₁₆	—	2	1	no	—
11	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
12	C₁₁×C₄⋊C₁₆	C₂²	1	2	yes	—
13	C₁₁×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
14	C₁₁×C₂²⋊C₁₆	—	2	1	no	—
15	C₁₁×#346	—	2	1	no	—
16	C₁₁×#322	C₄	1	2	yes	—
17	C₈²×C₁₁	C₂²	1	2	yes	—
18	C₂×C₁₁×M₁₆	C₈	1	2	yes	—
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
21	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₁₁×M₃₂	—	4	2	no	—
23	C₂×C₁₁×C₁₆	—	2	2	no	—
24	C₂×C₁₁×C₁₆	—	2	1	no	—
25	C₂×C₁₁×C₁₆	—	2	1	no	—
26	C₁₁×C₄⋊C₈	—	2	1	no	—
27	C₁₁×C₂²⋊C₈	—	2	1	no	—
28	C₁₁×#97	C₈	1	1	yes	characteristic
29	C₁₁×#97	C₈	1	1	yes	characteristic
30	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
31	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	Q₈	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
36	#12017	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₁	C₂×C₈	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	M₁₆	1	1	yes	characteristic
40	C₁₁×M₁₆	—	2	4	no	—
41	C₂×C₈×C₁₁	—	2	1	no	—
42	C₂×C₈×C₁₁	—	2	1	no	—
43	C₂×C₈×C₁₁	—	2	2	no	—
44	C₂×C₈×C₁₁	—	4	1	no	—
45	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
48	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
49	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
51	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
52	C₄²×C₁₁	C₂×C₈	1	1	yes	characteristic
53	C₄²×C₁₁	M₁₆	1	1	yes	characteristic
54	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₁₁×C₁₆	—	4	1	no	—
56	C₁₁×C₁₆	—	4	2	no	—
57	C₁₁×C₁₆	—	4	1	no	—
58	#2163	C₂×C₁₁	1	1	yes	characteristic
59	#2150	C₂×C₁₁	1	1	yes	characteristic
60	C₈×M₁₆	C₂×C₁₁	1	1	yes	characteristic
61	#1370	C₂×C₁₁	1	2	yes	complemented
62	#1367	C₂×C₁₁	1	2	yes	complemented
63	C₂³×C₁₁	C₄⋊C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₁	—	2	1	no	—
65	C₂×C₄×C₁₁	—	2	1	no	—
66	C₂×C₄×C₁₁	—	2	2	no	—
67	C₂×C₄×C₁₁	—	4	1	no	—
68	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₄⋊C₈	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
74	C₈×C₁₁	—	2	1	no	—
75	C₈×C₁₁	—	2	1	no	—
76	C₈×C₁₁	—	2	1	no	—
77	C₈×C₁₁	—	2	2	no	—
78	C₈×C₁₁	—	4	2	no	—
79	C₈×C₁₁	M₃₂	1	4	yes	complemented
80	C₈×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
81	C₈×C₁₁	#137	1	1	yes	characteristic
82	C₂×M₃₂	—	2	1	no	—
83	#431	C₄×C₁₁	1	1	yes	characteristic
84	C₄×M₁₆	C₄×C₁₁	1	1	yes	characteristic
85	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
86	C₄⋊C₁₆	—	2	1	no	—
87	C₄⋊C₁₆	C₂²×C₁₁	1	1	yes	characteristic
88	C₄⋊C₁₆	C₂²×C₁₁	1	2	yes	—
89	C₄⋊C₁₆	C₂²×C₁₁	1	1	yes	characteristic
90	C₂²⋊C₁₆	—	2	1	no	—
91	#346	—	2	1	no	—
92	#322	C₄×C₁₁	1	2	yes	—
93	C₈²	C₂²×C₁₁	1	2	yes	—
94	C₂²×C₁₁	—	2	1	no	—
95	C₂²×C₁₁	—	2	1	no	—
96	C₂²×C₁₁	—	2	1	no	—
97	C₂²×C₁₁	C₂×C₄⋊C₈	1	1	yes	characteristic
98	C₄×C₁₁	—	2	1	no	—
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	—	2	1	no	—
102	C₄×C₁₁	#428	1	1	yes	characteristic
103	C₄×C₁₁	#430	1	1	yes	characteristic
104	C₄×C₁₁	C₂×M₃₂	1	2	yes	—
105	C₂×M₁₆	C₈×C₁₁	1	2	yes	—
106	C₂²×C₈	D₄×C₁₁	1	1	yes	characteristic
107	C₂²×C₈	Q₈×C₁₁	1	1	yes	characteristic
108	C₂×C₄²	C₂×C₄×C₁₁	1	1	yes	characteristic
109	M₃₂	—	4	2	no	—
110	C₂×C₁₆	—	2	1	no	—
111	C₂×C₁₆	—	2	1	no	—
112	C₂×C₁₆	—	2	2	no	—
113	C₄⋊C₈	—	2	1	no	—
114	C₂²⋊C₈	—	2	1	no	—
115	#97	C₈×C₁₁	1	1	yes	characteristic
116	#97	C₈×C₁₁	1	1	yes	characteristic
117	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
118	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
119	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
120	C₄×C₈	D₄×C₁₁	1	1	yes	characteristic
121	C₄×C₈	Q₈×C₁₁	1	1	yes	characteristic
122	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
123	C₂×C₁₁	—	4	1	no	—
124	C₂×C₁₁	#1565	1	1	yes	characteristic
125	C₂×C₁₁	#2150	1	1	yes	characteristic
126	C₂×C₁₁	#2153	1	1	yes	characteristic
127	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
128	C₂²×C₄	C₂×C₈×C₁₁	1	1	yes	characteristic
129	C₂²×C₄	C₁₁×M₁₆	1	1	yes	characteristic
130	M₁₆	—	2	4	no	—
131	C₂×C₈	—	2	1	no	—
132	C₂×C₈	—	2	1	no	—
133	C₂×C₈	—	2	2	no	—
134	C₂×C₈	—	4	1	no	—
135	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₈	C₁₁×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
138	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
139	C₂×C₈	C₂×D₄×C₁₁	1	1	yes	characteristic
140	C₂×C₈	C₂×Q₈×C₁₁	1	1	yes	characteristic
141	C₄²	C₁₁×C₄⋊C₄	1	1	yes	characteristic
142	C₄²	C₂×C₈×C₁₁	1	1	yes	characteristic
143	C₄²	C₁₁×M₁₆	1	1	yes	characteristic
144	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
145	C₁₆	—	4	2	no	—
146	C₁₆	—	4	1	no	—
147	C₁₆	—	4	1	no	—
148	C₁₁	#12017	1	1	yes	characteristic, direct product factor, Sylow
149	C₂³	C₁₁×C₄⋊C₈	1	1	yes	characteristic
150	C₂×C₄	—	2	2	no	—
151	C₂×C₄	—	2	1	no	—
152	C₂×C₄	—	2	1	no	—
153	C₂×C₄	—	4	1	no	—
154	C₂×C₄	C₁₁×C₄⋊C₈	1	1	yes	characteristic
155	C₂×C₄	C₁₁×C₄⋊C₈	1	1	yes	characteristic
156	C₂×C₄	C₁₁×C₄⋊C₈	1	1	yes	characteristic
157	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄	C₂²×C₈×C₁₁	1	1	yes	characteristic
159	C₂×C₄	C₂×C₁₁×M₁₆	1	1	yes	characteristic
160	C₈	—	2	2	no	—
161	C₈	—	2	1	no	—
162	C₈	—	2	1	no	—
163	C₈	—	2	1	no	—
164	C₈	—	4	2	no	—
165	C₈	C₁₁×M₃₂	1	4	yes	complemented
166	C₈	C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic
167	C₈	C₁₁×#137	1	1	yes	characteristic
168	C₂²	—	2	1	no	—
169	C₂²	—	2	1	no	—
170	C₂²	—	2	1	no	—
171	C₂²	C₂×C₁₁×C₄⋊C₈	1	1	yes	characteristic
172	C₄	—	2	1	no	—
173	C₄	—	2	1	no	—
174	C₄	—	2	1	no	—
175	C₄	—	2	1	no	—
176	C₄	C₁₁×#428	1	1	yes	characteristic
177	C₄	C₁₁×#430	1	1	yes	characteristic
178	C₄	C₂×C₁₁×M₃₂	1	2	yes	—
179	C₂	—	4	1	no	—
180	C₂	C₁₁×#1565	1	1	yes	characteristic
181	C₂	C₁₁×#2150	1	1	yes	characteristic
182	C₂	C₁₁×#2153	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈×C₁₁	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₁
Frattini, cosocle	C₄×C₈	C₂³×C₁₁
socle	C₂²×C₁₁	C₂×C₄⋊C₈
prime radical	C₂³×C₁₁	C₄⋊C₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₁₁×#1370	C₂	semidirect
5. C₁₁×#1367	C₂	semidirect
36. #12017	C₁₁	direct (N × H)
61. #1370	C₂×C₁₁	semidirect
62. #1367	C₂×C₁₁	semidirect
79. C₈×C₁₁	M₃₂	semidirect
148. C₁₁	#12017	direct (N × H)
165. C₈	C₁₁×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#2163	2
C₁₁×#2150	2
C₈×C₁₁×M₁₆	2
C₁₁×#1370	2
C₁₁×#1367	2
#12017	11

Subgroups — C11×#12017 #14589210

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#12017 #14589210