Subgroups — C₁₁×#23200 #14600393

Order 2816.

878 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	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2950	C₂	1	4	yes	maximal
3	C₁₁×#1979	C₂	1	4	yes	maximal
4	C₁₁×#1886	C₂	1	4	yes	maximal
5	C₁₁×#1772	C₂	1	2	yes	maximal
6	C₂²×C₁₁×Q₁₆	C₂²	1	4	yes	—
7	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
8	C₁₁×#519	C₂²	1	4	yes	—
9	C₁₁×#494	C₄	1	8	yes	complemented
10	C₁₁×#441	—	2	8	no	—
11	C₄×C₁₁×Q₁₆	—	2	8	no	—
12	C₂×C₁₁×#108	C₂²	1	2	yes	—
13	C₁₁×#427	C₂²	1	2	yes	—
14	C₁₁×#419	C₂²	1	8	yes	—
15	C₂×C₁₁×#101	C₂²	1	4	yes	—
16	C₁₁×#405	C₂²	1	4	yes	—
17	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
18	C₁₁×#339	C₂²	1	4	yes	—
19	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
20	C₂×C₁₁×Q₁₆	—	2	4	no	—
21	C₂×C₁₁×Q₁₆	—	2	4	no	—
22	C₂×C₁₁×Q₁₆	—	2	8	no	—
23	C₂×C₁₁×Q₁₆	C₂×C₄	1	16	yes	—
24	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₁₁×C₄⋊Q₈	—	4	2	no	—
27	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
28	C₄×Q₈×C₁₁	—	2	16	no	—
29	C₁₁×#117	—	4	4	no	—
30	C₁₁×#117	C₂³	1	4	yes	—
31	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
32	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
33	C₁₁×#108	—	2	4	no	—
34	C₁₁×#107	D₄	1	4	yes	—
35	C₁₁×#106	D₄	1	4	yes	—
36	C₁₁×#103	—	2	16	no	—
37	C₁₁×#101	—	4	4	no	—
38	C₁₁×#97	—	2	4	no	—
39	C₄×C₈×C₁₁	—	2	4	no	—
40	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
41	#23200	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×Q₈×C₁₁	—	2	4	no	—
43	C₂×Q₈×C₁₁	—	2	8	no	—
44	C₂×Q₈×C₁₁	—	2	8	no	—
45	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
46	C₂²×C₄×C₁₁	—	2	1	no	—
47	C₂²×C₄×C₁₁	—	2	4	no	—
48	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
49	C₁₁×Q₁₆	—	2	16	no	—
50	C₁₁×Q₁₆	—	2	16	no	—
51	C₁₁×M₁₆	—	2	4	no	—
52	C₁₁×M₁₆	—	2	4	no	—
53	C₂×C₈×C₁₁	—	2	4	no	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
55	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
56	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₁	#41	1	4	yes	—
58	C₁₁×C₄⋊C₄	—	4	8	no	—
59	C₁₁×C₄⋊C₄	—	4	8	no	—
60	C₁₁×C₄⋊C₄	C₂×D₄	1	8	yes	—
61	C₁₁×C₂²⋊C₄	—	2	4	no	—
62	C₄²×C₁₁	—	2	4	no	—
63	C₄²×C₁₁	—	2	1	no	—
64	C₄²×C₁₁	—	4	8	no	—
65	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
66	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
67	#2950	C₂×C₁₁	1	4	yes	—
68	#1979	C₂×C₁₁	1	4	yes	—
69	#1886	C₂×C₁₁	1	4	yes	—
70	#1772	C₂×C₁₁	1	2	yes	—
71	C₂³×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
72	Q₈×C₁₁	—	2	16	no	—
73	Q₈×C₁₁	—	4	8	no	—
74	C₂×C₄×C₁₁	—	2	4	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	—	2	8	no	—
77	C₂×C₄×C₁₁	—	2	8	no	—
78	C₂×C₄×C₁₁	—	4	4	no	—
79	C₂×C₄×C₁₁	—	4	4	no	—
80	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
82	C₂×C₄×C₁₁	C₂×#41	1	2	yes	—
83	C₂×C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
84	C₈×C₁₁	—	4	4	no	—
85	C₈×C₁₁	C₄×D₄	1	4	yes	—
86	C₈×C₁₁	C₄×D₄	1	4	yes	—
87	C₂²×Q₁₆	C₂²×C₁₁	1	4	yes	—
88	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
89	#519	C₂²×C₁₁	1	4	yes	—
90	#494	C₄×C₁₁	1	8	yes	complemented
91	#441	—	2	8	no	—
92	C₄×Q₁₆	—	2	8	no	—
93	C₂×#108	C₂²×C₁₁	1	2	yes	—
94	#427	C₂²×C₁₁	1	2	yes	—
95	#419	C₂²×C₁₁	1	8	yes	—
96	C₂×#101	C₂²×C₁₁	1	4	yes	—
97	#405	C₂²×C₁₁	1	4	yes	—
98	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
99	#339	C₂²×C₁₁	1	4	yes	—
100	C₂²×C₁₁	—	2	2	no	—
101	C₂²×C₁₁	#518	1	1	yes	characteristic
102	C₂²×C₁₁	D₄²	1	1	yes	characteristic
103	C₂²×C₁₁	#559	1	1	yes	characteristic
104	C₄×C₁₁	—	2	4	no	—
105	C₄×C₁₁	—	4	8	no	—
106	C₄×C₁₁	—	4	8	no	—
107	C₄×C₁₁	C₂×C₄×D₄	1	2	yes	—
108	C₄×C₁₁	#550	1	2	yes	—
109	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
110	C₂×Q₁₆	—	2	4	no	—
111	C₂×Q₁₆	—	2	4	no	—
112	C₂×Q₁₆	—	2	8	no	—
113	C₂×Q₁₆	C₂×C₄×C₁₁	1	16	yes	—
114	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
115	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
116	C₄⋊Q₈	—	4	2	no	—
117	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
118	C₄×Q₈	—	2	16	no	—
119	#117	—	4	4	no	—
120	#117	C₂³×C₁₁	1	4	yes	—
121	C₂×C₄⋊C₄	—	4	2	no	—
122	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
123	#108	—	2	4	no	—
124	#107	D₄×C₁₁	1	4	yes	—
125	#106	D₄×C₁₁	1	4	yes	—
126	#103	—	2	16	no	—
127	#101	—	4	4	no	—
128	#97	—	2	4	no	—
129	C₄×C₈	—	2	4	no	—
130	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
131	C₂×C₁₁	—	2	1	no	—
132	C₂×C₁₁	—	2	1	no	—
133	C₂×C₁₁	#2366	1	1	yes	characteristic
134	C₂×C₁₁	#3293	1	2	yes	—
135	C₂×Q₈	—	2	4	no	—
136	C₂×Q₈	—	2	8	no	—
137	C₂×Q₈	—	2	8	no	—
138	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
139	C₂²×C₄	—	2	1	no	—
140	C₂²×C₄	—	2	4	no	—
141	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
142	Q₁₆	—	2	16	no	—
143	Q₁₆	—	2	16	no	—
144	M₁₆	—	2	4	no	—
145	M₁₆	—	2	4	no	—
146	C₂×C₈	—	2	4	no	—
147	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
148	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
149	C₂×C₈	C₂×D₄×C₁₁	1	2	yes	—
150	C₂×C₈	C₁₁×#41	1	4	yes	—
151	C₄⋊C₄	—	4	8	no	—
152	C₄⋊C₄	—	4	8	no	—
153	C₄⋊C₄	C₂×D₄×C₁₁	1	8	yes	—
154	C₂²⋊C₄	—	2	4	no	—
155	C₄²	—	2	4	no	—
156	C₄²	—	2	1	no	—
157	C₄²	—	4	8	no	—
158	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
159	C₁₁	#23200	1	1	yes	characteristic, direct product factor, Sylow
160	C₂³	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
161	Q₈	—	2	16	no	—
162	Q₈	—	4	8	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	2	no	—
165	C₂×C₄	—	2	8	no	—
166	C₂×C₄	—	2	8	no	—
167	C₂×C₄	—	4	4	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
170	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
171	C₂×C₄	C₂×C₁₁×#41	1	2	yes	—
172	C₂×C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
173	C₈	—	4	4	no	—
174	C₈	C₄×D₄×C₁₁	1	4	yes	—
175	C₈	C₄×D₄×C₁₁	1	4	yes	—
176	C₂²	—	2	2	no	—
177	C₂²	C₁₁×#518	1	1	yes	characteristic
178	C₂²	D₄²×C₁₁	1	1	yes	characteristic
179	C₂²	C₁₁×#559	1	1	yes	characteristic
180	C₄	—	2	4	no	—
181	C₄	—	4	8	no	—
182	C₄	—	4	8	no	—
183	C₄	C₂×C₄×D₄×C₁₁	1	2	yes	—
184	C₄	C₁₁×#550	1	2	yes	—
185	C₂	—	2	1	no	—
186	C₂	—	2	1	no	—
187	C₂	C₁₁×#2366	1	1	yes	characteristic
188	C₂	C₁₁×#3293	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₁₁	D₄²
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	H(5,𝔽₂)
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂²×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
9. C₁₁×#494	C₄	semidirect
41. #23200	C₁₁	direct (N × H)
90. #494	C₄×C₁₁	semidirect
159. C₁₁	#23200	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₁₁×#494	2
C₁₁×#2950	2
C₁₁×#1979	2
C₁₁×#1886	2
C₁₁×#1772	2
#23200	11

Subgroups — C11×#23200 #14600393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#23200 #14600393