Subgroups — C₁₁×#8294 #14585487

Order 2816.

358 conjugacy classes of subgroups.

The subgroup lattice has 190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₁₁×#108	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#1564	C₂	1	1	yes	maximal, characteristic
3	C₈×C₁₁×M₁₆	C₂	1	2	yes	maximal
4	C₂×C₁₁×#322	C₂	1	1	yes	maximal, characteristic
5	C₁₁×#1278	C₂	1	2	yes	maximal
6	C₁₁×#431	C₂²	1	2	yes	—
7	C₂×C₁₁×#108	C₄	1	2	yes	—
8	C₄×C₁₁×M₁₆	C₂²	1	2	yes	—
9	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
12	C₁₁×#341	C₄	1	2	yes	—
13	C₁₁×#335	C₄	1	2	yes	—
14	C₁₁×#334	C₄	1	2	yes	—
15	C₁₁×#322	—	2	2	no	—
16	C₁₁×#322	C₄	1	2	yes	—
17	C₁₁×#322	C₄	1	2	yes	—
18	C₈²×C₁₁	—	2	2	no	—
19	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
20	C₂²×C₈×C₁₁	—	2	1	no	—
21	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₈×C₁₁	Q₈	1	2	yes	—
24	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
25	C₁₁×#108	C₈	1	8	yes	complemented
26	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
27	C₁₁×C₂²⋊C₈	—	2	2	no	—
28	C₁₁×#97	—	2	2	no	—
29	C₄×C₈×C₁₁	—	2	2	no	—
30	C₄×C₈×C₁₁	—	2	2	no	—
31	C₄×C₈×C₁₁	—	2	1	no	—
32	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
33	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
37	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
38	C₄×C₈×C₁₁	D₄	1	2	yes	—
39	#8294	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
43	C₁₁×M₁₆	—	2	4	no	—
44	C₁₁×M₁₆	C₂×C₈	1	8	yes	—
45	C₂×C₈×C₁₁	—	2	2	no	—
46	C₂×C₈×C₁₁	—	2	4	no	—
47	C₂×C₈×C₁₁	—	2	4	no	—
48	C₂×C₈×C₁₁	—	2	2	no	—
49	C₂×C₈×C₁₁	—	4	2	no	—
50	C₂×C₈×C₁₁	—	4	2	no	—
51	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
52	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
53	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
54	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₄⋊C₄	1	4	yes	—
56	C₂×C₈×C₁₁	C₂×C₈	1	4	yes	—
57	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
58	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₁	#41	1	1	yes	characteristic
61	C₄×#108	C₂×C₁₁	1	1	yes	characteristic
62	#1564	C₂×C₁₁	1	1	yes	characteristic
63	C₈×M₁₆	C₂×C₁₁	1	2	yes	—
64	C₂×#322	C₂×C₁₁	1	1	yes	characteristic
65	#1278	C₂×C₁₁	1	2	yes	—
66	C₂³×C₁₁	C₄×Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₁	—	2	2	no	—
68	C₂×C₄×C₁₁	—	2	2	no	—
69	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
75	C₂×C₄×C₁₁	C₂²×C₈	1	2	yes	—
76	C₂×C₄×C₁₁	#131	1	2	yes	—
77	C₈×C₁₁	—	2	1	no	—
78	C₈×C₁₁	—	2	1	no	—
79	C₈×C₁₁	—	2	4	no	—
80	C₈×C₁₁	—	2	8	no	—
81	C₈×C₁₁	—	4	2	no	—
82	C₈×C₁₁	—	4	4	no	—
83	C₈×C₁₁	C₄×C₈	1	2	yes	—
84	C₈×C₁₁	C₄×C₈	1	2	yes	—
85	#431	C₂²×C₁₁	1	2	yes	—
86	C₂×#108	C₄×C₁₁	1	2	yes	—
87	C₄×M₁₆	C₂²×C₁₁	1	2	yes	—
88	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
89	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
90	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
91	#341	C₄×C₁₁	1	2	yes	—
92	#335	C₄×C₁₁	1	2	yes	—
93	#334	C₄×C₁₁	1	2	yes	—
94	#322	—	2	2	no	—
95	#322	C₄×C₁₁	1	2	yes	—
96	#322	C₄×C₁₁	1	2	yes	—
97	C₈²	—	2	2	no	—
98	C₂²×C₁₁	—	2	1	no	—
99	C₂²×C₁₁	—	2	1	no	—
100	C₂²×C₁₁	C₄×C₄⋊C₄	1	1	yes	characteristic
101	C₂²×C₁₁	C₈×Q₈	1	2	yes	—
102	C₄×C₁₁	—	2	1	no	—
103	C₄×C₁₁	—	2	1	no	—
104	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
105	C₄×C₁₁	#405	1	1	yes	characteristic
106	C₄×C₁₁	#430	1	2	yes	—
107	C₄×C₁₁	C₈×D₄	1	2	yes	—
108	C₄×C₁₁	#444	1	2	yes	—
109	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
110	C₂²×C₈	—	2	1	no	—
111	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
112	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
113	C₂²×C₈	Q₈×C₁₁	1	2	yes	—
114	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
115	#108	C₈×C₁₁	1	8	yes	complemented
116	C₄⋊C₈	C₂×C₄×C₁₁	1	4	yes	—
117	C₂²⋊C₈	—	2	2	no	—
118	#97	—	2	2	no	—
119	C₄×C₈	—	2	2	no	—
120	C₄×C₈	—	2	2	no	—
121	C₄×C₈	—	2	1	no	—
122	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
123	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
124	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
125	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
126	C₄×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
127	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
128	C₄×C₈	D₄×C₁₁	1	2	yes	—
129	C₂×C₁₁	—	2	2	no	—
130	C₂×C₁₁	C₈×C₄⋊C₄	1	1	yes	characteristic
131	C₂×C₁₁	#1773	1	1	yes	characteristic
132	C₂×C₁₁	#1778	1	1	yes	characteristic
133	C₂²×C₄	C₂²×C₄×C₁₁	1	1	yes	characteristic
134	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
135	C₂²×C₄	C₁₁×#41	1	1	yes	characteristic
136	M₁₆	—	2	4	no	—
137	M₁₆	C₂×C₈×C₁₁	1	8	yes	—
138	C₂×C₈	—	2	4	no	—
139	C₂×C₈	—	2	2	no	—
140	C₂×C₈	—	2	2	no	—
141	C₂×C₈	—	2	4	no	—
142	C₂×C₈	—	4	2	no	—
143	C₂×C₈	—	4	2	no	—
144	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
145	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
146	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
147	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
148	C₂×C₈	C₁₁×C₄⋊C₄	1	4	yes	—
149	C₂×C₈	C₂×C₈×C₁₁	1	4	yes	—
150	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
151	C₄²	C₂²×C₄×C₁₁	1	1	yes	characteristic
152	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
153	C₄²	C₁₁×#41	1	1	yes	characteristic
154	C₁₁	#8294	1	1	yes	characteristic, direct product factor, Sylow
155	C₂³	C₄×Q₈×C₁₁	1	1	yes	characteristic
156	C₂×C₄	—	2	2	no	—
157	C₂×C₄	—	2	2	no	—
158	C₂×C₄	C₂×C₄²×C₁₁	1	1	yes	characteristic
159	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	1	yes	characteristic
160	C₂×C₄	C₁₁×#117	1	1	yes	characteristic
161	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
162	C₂×C₄	C₄×D₄×C₁₁	1	1	yes	characteristic
163	C₂×C₄	C₄×Q₈×C₁₁	1	1	yes	characteristic
164	C₂×C₄	C₂²×C₈×C₁₁	1	2	yes	—
165	C₂×C₄	C₁₁×#131	1	2	yes	—
166	C₈	—	2	1	no	—
167	C₈	—	2	1	no	—
168	C₈	—	2	4	no	—
169	C₈	—	2	8	no	—
170	C₈	—	4	2	no	—
171	C₈	—	4	4	no	—
172	C₈	C₄×C₈×C₁₁	1	2	yes	—
173	C₈	C₄×C₈×C₁₁	1	2	yes	—
174	C₂²	—	2	1	no	—
175	C₂²	—	2	1	no	—
176	C₂²	C₄×C₁₁×C₄⋊C₄	1	1	yes	characteristic
177	C₂²	C₈×Q₈×C₁₁	1	2	yes	—
178	C₄	—	2	1	no	—
179	C₄	—	2	1	no	—
180	C₄	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
181	C₄	C₁₁×#405	1	1	yes	characteristic
182	C₄	C₁₁×#430	1	2	yes	—
183	C₄	C₈×D₄×C₁₁	1	2	yes	—
184	C₄	C₁₁×#444	1	2	yes	—
185	C₂	—	2	2	no	—
186	C₂	C₈×C₁₁×C₄⋊C₄	1	1	yes	characteristic
187	C₂	C₁₁×#1773	1	1	yes	characteristic
188	C₂	C₁₁×#1778	1	1	yes	characteristic

	subgroup	G/H
center	C₄²×C₁₁	C₂×D₄
commutator	C₄	C₂×C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄²	C₂³×C₁₁
socle	C₂²×C₁₁	C₄×C₄⋊C₄
prime radical	C₂³×C₁₁	C₄×Q₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
25. C₁₁×#108	C₈	semidirect
39. #8294	C₁₁	direct (N × H)
115. #108	C₈×C₁₁	semidirect
154. C₁₁	#8294	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₁₁×#108	2
C₁₁×#1564	2
C₈×C₁₁×M₁₆	2
C₂×C₁₁×#322	2
C₁₁×#1278	2
#8294	11

Subgroups — C11×#8294 #14585487

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#8294 #14585487