Subgroups — C₁₁×#21971 #14599164

Order 2816.

662 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2921	C₂	1	2	yes	maximal
2	C₂×C₁₁×#424	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#1950	C₂	1	8	yes	maximal, complemented
4	C₁₁×#1811	C₂	1	2	yes	maximal
5	C₁₁×#1810	C₂	1	2	yes	maximal
6	C₂²×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×C₁₁×#117	C₂²	1	1	yes	characteristic
9	C₁₁×#433	—	2	8	no	—
10	C₂×C₁₁×#108	C₂²	1	4	yes	—
11	C₂×C₁₁×#108	C₂²	1	4	yes	—
12	C₁₁×#424	C₄	1	8	yes	—
13	C₁₁×#423	C₂²	1	4	yes	—
14	C₂×C₁₁×C₄⋊C₈	C₂²	1	4	yes	—
15	C₁₁×#407	C₂²	1	4	yes	—
16	C₄×C₁₁×M₁₆	C₂²	1	4	yes	—
17	C₁₁×#341	C₂²	1	4	yes	—
18	C₁₁×#341	C₂²	1	4	yes	—
19	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₁₁×M₁₆	—	4	2	no	—
21	C₂×C₁₁×M₁₆	C₂×C₄	1	4	yes	—
22	C₂×C₁₁×M₁₆	C₂³	1	8	yes	—
23	C₂²×C₈×C₁₁	—	4	2	no	—
24	C₂²×C₈×C₁₁	C₂×C₄	1	4	yes	—
25	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
26	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
27	C₁₁×#117	C₂×C₄	1	4	yes	—
28	C₁₁×#117	D₄	1	4	yes	—
29	C₂×C₁₁×C₄⋊C₄	Q₈	1	2	yes	—
30	C₂×C₁₁×C₂²⋊C₄	Q₈	1	2	yes	—
31	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
32	C₁₁×#108	—	4	4	no	—
33	C₁₁×#108	—	4	4	no	—
34	C₁₁×C₄⋊C₈	—	2	8	no	—
35	C₁₁×C₄⋊C₈	C₂×C₄	1	16	yes	—
36	C₁₁×C₂²⋊C₈	—	2	8	no	—
37	C₁₁×#97	—	2	4	no	—
38	C₄×C₈×C₁₁	—	2	4	no	—
39	#21971	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂⁴×C₁₁	C₂×Q₈	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	—	2	2	no	—
42	C₂²×C₄×C₁₁	—	2	2	no	—
43	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
44	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
45	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂×Q₈	1	4	yes	—
47	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
48	C₁₁×M₁₆	—	2	8	no	—
49	C₁₁×M₁₆	—	2	8	no	—
50	C₁₁×M₁₆	—	4	4	no	—
51	C₂×C₈×C₁₁	—	2	8	no	—
52	C₂×C₈×C₁₁	—	2	4	no	—
53	C₂×C₈×C₁₁	—	2	4	no	—
54	C₂×C₈×C₁₁	—	4	4	no	—
55	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
56	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
57	C₁₁×C₄⋊C₄	C₄⋊C₄	1	8	yes	—
58	C₁₁×C₂²⋊C₄	C₄⋊C₄	1	8	yes	—
59	C₄²×C₁₁	C₂²×C₄	1	4	yes	—
60	C₄²×C₁₁	C₂×D₄	1	4	yes	—
61	#2921	C₂×C₁₁	1	2	yes	—
62	C₂×#424	C₂×C₁₁	1	1	yes	characteristic
63	#1950	C₂×C₁₁	1	8	yes	complemented
64	#1811	C₂×C₁₁	1	2	yes	—
65	#1810	C₂×C₁₁	1	2	yes	—
66	C₂³×C₁₁	—	2	2	no	—
67	C₂³×C₁₁	—	4	2	no	—
68	C₂³×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
69	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	4	no	—
74	C₂×C₄×C₁₁	—	4	4	no	—
75	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	8	yes	—
76	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	2	yes	—
77	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
80	C₂×C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
81	C₈×C₁₁	—	2	4	no	—
82	C₈×C₁₁	—	2	4	no	—
83	C₈×C₁₁	—	4	8	no	—
84	C₂²×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
85	C₂³×C₈	C₂²×C₁₁	1	1	yes	characteristic
86	C₂×#117	C₂²×C₁₁	1	1	yes	characteristic
87	#433	—	2	8	no	—
88	C₂×#108	C₂²×C₁₁	1	4	yes	—
89	C₂×#108	C₂²×C₁₁	1	4	yes	—
90	#424	C₄×C₁₁	1	8	yes	—
91	#423	C₂²×C₁₁	1	4	yes	—
92	C₂×C₄⋊C₈	C₂²×C₁₁	1	4	yes	—
93	#407	C₂²×C₁₁	1	4	yes	—
94	C₄×M₁₆	C₂²×C₁₁	1	4	yes	—
95	#341	C₂²×C₁₁	1	4	yes	—
96	#341	C₂²×C₁₁	1	4	yes	—
97	C₂²×C₁₁	—	2	2	no	—
98	C₂²×C₁₁	—	2	2	no	—
99	C₂²×C₁₁	—	2	4	no	—
100	C₂²×C₁₁	—	4	4	no	—
101	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₁₁	#544	1	2	yes	—
103	C₄×C₁₁	—	2	2	no	—
104	C₄×C₁₁	—	2	8	no	—
105	C₄×C₁₁	#518	1	1	yes	characteristic
106	C₄×C₁₁	#519	1	1	yes	characteristic
107	C₄×C₁₁	#537	1	2	yes	—
108	C₂³×C₄	C₂³×C₁₁	1	1	yes	characteristic
109	C₂×M₁₆	—	4	2	no	—
110	C₂×M₁₆	C₂×C₄×C₁₁	1	4	yes	—
111	C₂×M₁₆	C₂³×C₁₁	1	8	yes	—
112	C₂²×C₈	—	4	2	no	—
113	C₂²×C₈	C₂×C₄×C₁₁	1	4	yes	—
114	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
115	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
116	#117	C₂×C₄×C₁₁	1	4	yes	—
117	#117	D₄×C₁₁	1	4	yes	—
118	C₂×C₄⋊C₄	Q₈×C₁₁	1	2	yes	—
119	C₂×C₂²⋊C₄	Q₈×C₁₁	1	2	yes	—
120	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
121	#108	—	4	4	no	—
122	#108	—	4	4	no	—
123	C₄⋊C₈	—	2	8	no	—
124	C₄⋊C₈	C₂×C₄×C₁₁	1	16	yes	—
125	C₂²⋊C₈	—	2	8	no	—
126	#97	—	2	4	no	—
127	C₄×C₈	—	2	4	no	—
128	C₂×C₁₁	—	2	2	no	—
129	C₂×C₁₁	—	4	2	no	—
130	C₂×C₁₁	#2316	1	1	yes	characteristic
131	C₂×C₁₁	#2916	1	2	yes	—
132	C₂⁴	C₂×Q₈×C₁₁	1	1	yes	characteristic
133	C₂²×C₄	—	2	2	no	—
134	C₂²×C₄	—	2	2	no	—
135	C₂²×C₄	C₂²×C₄×C₁₁	1	2	yes	—
136	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
137	C₂²×C₄	C₂×Q₈×C₁₁	1	1	yes	characteristic
138	C₂²×C₄	C₂×Q₈×C₁₁	1	4	yes	—
139	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
140	M₁₆	—	2	8	no	—
141	M₁₆	—	2	8	no	—
142	M₁₆	—	4	4	no	—
143	C₂×C₈	—	2	4	no	—
144	C₂×C₈	—	2	4	no	—
145	C₂×C₈	—	2	8	no	—
146	C₂×C₈	—	4	4	no	—
147	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
148	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
149	C₄⋊C₄	C₁₁×C₄⋊C₄	1	8	yes	—
150	C₂²⋊C₄	C₁₁×C₄⋊C₄	1	8	yes	—
151	C₄²	C₂²×C₄×C₁₁	1	4	yes	—
152	C₄²	C₂×D₄×C₁₁	1	4	yes	—
153	C₁₁	#21971	1	1	yes	characteristic, direct product factor, Sylow
154	C₂³	—	2	2	no	—
155	C₂³	—	4	2	no	—
156	C₂³	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
157	C₂³	C₂²×Q₈×C₁₁	1	1	yes	characteristic
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	4	no	—
162	C₂×C₄	—	4	4	no	—
163	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	8	yes	—
164	C₂×C₄	C₂×C₁₁×C₄⋊C₄	1	2	yes	—
165	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
166	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
167	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
168	C₂×C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
169	C₈	—	2	4	no	—
170	C₈	—	2	4	no	—
171	C₈	—	4	8	no	—
172	C₂²	—	2	2	no	—
173	C₂²	—	2	4	no	—
174	C₂²	—	2	2	no	—
175	C₂²	—	4	4	no	—
176	C₂²	C₂²×C₁₁×C₄⋊C₄	1	1	yes	characteristic
177	C₂²	C₁₁×#544	1	2	yes	—
178	C₄	—	2	8	no	—
179	C₄	—	2	2	no	—
180	C₄	C₁₁×#518	1	1	yes	characteristic
181	C₄	C₁₁×#519	1	1	yes	characteristic
182	C₄	C₁₁×#537	1	2	yes	—
183	C₂	—	2	2	no	—
184	C₂	—	4	2	no	—
185	C₂	C₁₁×#2316	1	1	yes	characteristic
186	C₂	C₁₁×#2916	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₁	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#117 ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₁×#1950	C₂	semidirect
39. #21971	C₁₁	direct (N × H)
63. #1950	C₂×C₁₁	semidirect
153. C₁₁	#21971	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×#2921	2
C₂×C₁₁×#424	2
C₁₁×#1950	2
C₁₁×#1811	2
C₁₁×#1810	2
#21971	11

Subgroups — C11×#21971 #14599164

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#21971 #14599164