Subgroups — C₁₁×#3155 #13065993

Order 1408.

596 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₁×#535	C₂	1	2	yes	maximal, complemented
5	C₁₁×#496	C₂	1	4	yes	maximal, complemented
6	C₁₁×#495	C₂	1	2	yes	maximal, complemented
7	C₁₁×#493	C₂	1	2	yes	maximal, complemented
8	C₁₁×#405	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₁₁×#41	C₂²	1	2	yes	—
10	C₂²×D₄×C₁₁	C₂²	1	2	yes	—
11	C₁₁×AGL(1,ℤ/8)	—	2	8	no	—
12	C₁₁×#135	—	2	4	no	—
13	C₂×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
14	C₂×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
15	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
16	C₂×C₁₁×D₈	—	2	4	no	—
17	C₂×C₁₁×D₈	C₂²	1	2	yes	—
18	C₂×C₁₁×D₈	C₂²	1	2	yes	—
19	C₂×C₁₁×D₈	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₁₁×D₈	C₂²	1	4	yes	complemented
21	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₈×C₁₁	C₂²	1	1	yes	characteristic
23	C₁₁×#127	C₂²	1	4	yes	complemented
24	C₁₁×#124	C₂²	1	4	yes	complemented
25	C₁₁×#121	—	2	4	no	—
26	C₁₁×#120	—	2	4	no	—
27	C₁₁×#117	C₂²	1	1	yes	characteristic
28	C₁₁×#97	C₂²	1	2	yes	complemented
29	C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
30	C₂⁴×C₁₁	—	2	2	no	—
31	C₁₁×#41	—	2	4	no	—
32	C₁₁×#41	—	2	4	no	—
33	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
34	C₂×D₄×C₁₁	—	2	2	no	—
35	C₂×D₄×C₁₁	—	2	4	no	—
36	C₂×D₄×C₁₁	—	2	4	no	—
37	C₂×D₄×C₁₁	—	2	2	no	—
38	C₂×D₄×C₁₁	—	2	8	no	—
39	C₂×D₄×C₁₁	C₂³	1	4	yes	—
40	C₂×D₄×C₁₁	C₂³	1	2	yes	—
41	C₂²×C₄×C₁₁	—	2	2	no	—
42	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
43	C₁₁×Q₁₆	—	2	2	no	—
44	C₁₁×SD₁₆	—	2	4	no	—
45	C₁₁×SD₁₆	—	2	8	no	—
46	C₁₁×D₈	—	2	4	no	—
47	C₁₁×D₈	—	2	4	no	—
48	C₁₁×D₈	—	2	2	no	—
49	C₁₁×D₈	—	2	8	no	—
50	C₁₁×M₁₆	D₄	1	4	yes	complemented
51	C₂×C₈×C₁₁	D₄	1	4	yes	complemented
52	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
53	C₂×C₈×C₁₁	C₂³	1	2	yes	—
54	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
55	C₁₁×C₄⋊C₄	D₄	1	2	yes	—
56	C₁₁×C₂²⋊C₄	—	2	8	no	—
57	C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
58	C₄²×C₁₁	C₂³	1	2	yes	—
59	#3155	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
60	C₂³×C₁₁	—	2	4	no	—
61	C₂³×C₁₁	—	2	2	no	—
62	C₂³×C₁₁	—	4	4	no	—
63	C₂³×C₁₁	—	8	4	no	—
64	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
65	Q₈×C₁₁	—	2	2	no	—
66	Q₈×C₁₁	—	2	2	no	—
67	D₄×C₁₁	—	2	4	no	—
68	D₄×C₁₁	—	2	2	no	—
69	D₄×C₁₁	—	2	4	no	—
70	D₄×C₁₁	—	2	2	no	—
71	D₄×C₁₁	—	4	4	no	—
72	D₄×C₁₁	—	4	4	no	—
73	D₄×C₁₁	—	8	8	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	4	4	no	—
76	C₂×C₄×C₁₁	C₂×D₄	1	4	yes	—
77	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
79	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
81	C₈×C₁₁	C₂×D₄	1	2	yes	—
82	C₈×C₁₁	C₂×D₄	1	2	yes	—
83	C₈×C₁₁	C₂×D₄	1	4	yes	—
84	C₂×AGL(1,ℤ/8)	C₂×C₁₁	1	2	yes	complemented
85	C₂×#135	C₂×C₁₁	1	1	yes	characteristic, complemented
86	C₂²×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
87	#535	C₂×C₁₁	1	2	yes	complemented
88	#496	C₂×C₁₁	1	4	yes	complemented
89	#495	C₂×C₁₁	1	2	yes	complemented
90	#493	C₂×C₁₁	1	2	yes	complemented
91	#405	C₂×C₁₁	1	1	yes	characteristic, complemented
92	C₂²×C₁₁	—	2	2	no	—
93	C₂²×C₁₁	—	4	2	no	—
94	C₂²×C₁₁	—	4	4	no	—
95	C₂²×C₁₁	—	4	4	no	—
96	C₂²×C₁₁	—	4	8	no	—
97	C₂²×C₁₁	—	8	8	no	—
98	C₂²×C₁₁	#127	1	2	yes	—
99	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₁₁	—	2	4	no	—
101	C₄×C₁₁	—	4	2	no	—
102	C₄×C₁₁	#127	1	2	yes	—
103	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
104	C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
105	C₂×#41	C₂²×C₁₁	1	2	yes	—
106	C₂²×D₄	C₂²×C₁₁	1	2	yes	—
107	AGL(1,ℤ/8)	—	2	8	no	—
108	#135	—	2	4	no	—
109	C₂×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
110	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
111	C₂×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
112	C₂×D₈	—	2	4	no	—
113	C₂×D₈	C₂²×C₁₁	1	2	yes	—
114	C₂×D₈	C₂²×C₁₁	1	2	yes	—
115	C₂×D₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
116	C₂×D₈	C₂²×C₁₁	1	4	yes	complemented
117	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
118	C₂²×C₈	C₂²×C₁₁	1	1	yes	characteristic
119	#127	C₂²×C₁₁	1	4	yes	complemented
120	#124	C₂²×C₁₁	1	4	yes	complemented
121	#121	—	2	4	no	—
122	#120	—	2	4	no	—
123	#117	C₂²×C₁₁	1	1	yes	characteristic
124	#97	C₂²×C₁₁	1	2	yes	complemented
125	C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
126	C₂×C₁₁	—	2	2	no	—
127	C₂×C₁₁	—	8	2	no	—
128	C₂×C₁₁	—	8	4	no	—
129	C₂×C₁₁	C₂×#127	1	1	yes	characteristic
130	C₂×C₁₁	#576	1	2	yes	—
131	C₂⁴	—	2	2	no	—
132	#41	—	2	4	no	—
133	#41	—	2	4	no	—
134	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
135	C₂×D₄	—	2	2	no	—
136	C₂×D₄	—	2	4	no	—
137	C₂×D₄	—	2	4	no	—
138	C₂×D₄	—	2	2	no	—
139	C₂×D₄	—	2	8	no	—
140	C₂×D₄	C₂³×C₁₁	1	4	yes	—
141	C₂×D₄	C₂³×C₁₁	1	2	yes	—
142	C₂²×C₄	—	2	2	no	—
143	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
144	Q₁₆	—	2	2	no	—
145	SD₁₆	—	2	4	no	—
146	SD₁₆	—	2	8	no	—
147	D₈	—	2	4	no	—
148	D₈	—	2	4	no	—
149	D₈	—	2	2	no	—
150	D₈	—	2	8	no	—
151	M₁₆	D₄×C₁₁	1	4	yes	complemented
152	C₂×C₈	D₄×C₁₁	1	4	yes	complemented
153	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
154	C₂×C₈	C₂³×C₁₁	1	2	yes	—
155	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
156	C₄⋊C₄	D₄×C₁₁	1	2	yes	—
157	C₂²⋊C₄	—	2	8	no	—
158	C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
159	C₄²	C₂³×C₁₁	1	2	yes	—
160	C₁₁	#3155	1	1	yes	characteristic, direct product factor, Sylow
161	C₂³	—	2	4	no	—
162	C₂³	—	2	2	no	—
163	C₂³	—	4	4	no	—
164	C₂³	—	8	4	no	—
165	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
166	Q₈	—	2	2	no	—
167	Q₈	—	2	2	no	—
168	D₄	—	2	4	no	—
169	D₄	—	2	2	no	—
170	D₄	—	2	4	no	—
171	D₄	—	2	2	no	—
172	D₄	—	4	4	no	—
173	D₄	—	4	4	no	—
174	D₄	—	8	8	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	4	4	no	—
177	C₂×C₄	C₂×D₄×C₁₁	1	4	yes	—
178	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
179	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
180	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
181	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
182	C₈	C₂×D₄×C₁₁	1	2	yes	—
183	C₈	C₂×D₄×C₁₁	1	2	yes	—
184	C₈	C₂×D₄×C₁₁	1	4	yes	—
185	C₂²	—	2	2	no	—
186	C₂²	—	4	2	no	—
187	C₂²	—	4	4	no	—
188	C₂²	—	4	4	no	—
189	C₂²	—	4	8	no	—
190	C₂²	—	8	8	no	—
191	C₂²	C₁₁×#127	1	2	yes	—
192	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
193	C₄	—	2	4	no	—
194	C₄	—	4	2	no	—
195	C₄	C₁₁×#127	1	2	yes	—
196	C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
197	C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
198	C₂	—	2	2	no	—
199	C₂	—	8	4	no	—
200	C₂	—	8	2	no	—
201	C₂	C₂×C₁₁×#127	1	1	yes	characteristic
202	C₂	C₁₁×#576	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₁×AGL(1,ℤ/8)	C₂	semidirect
2. C₂×C₁₁×#135	C₂	semidirect
3. C₂²×C₁₁×D₈	C₂	semidirect
4. C₁₁×#535	C₂	semidirect
5. C₁₁×#496	C₂	semidirect
6. C₁₁×#495	C₂	semidirect
7. C₁₁×#493	C₂	semidirect
8. C₁₁×#405	C₂	semidirect
13. C₂×C₁₁×Q₁₆	C₂²	semidirect
14. C₂×C₁₁×SD₁₆	C₂²	semidirect
15. C₂×C₁₁×SD₁₆	C₂²	semidirect
19. C₂×C₁₁×D₈	C₂²	semidirect
20. C₂×C₁₁×D₈	C₂²	semidirect
23. C₁₁×#127	C₂²	semidirect
24. C₁₁×#124	C₂²	semidirect
28. C₁₁×#97	C₂²	semidirect
29. C₄×C₈×C₁₁	C₂²	semidirect
50. C₁₁×M₁₆	D₄	semidirect
51. C₂×C₈×C₁₁	D₄	semidirect
59. #3155	C₁₁	direct (N × H)
84. C₂×AGL(1,ℤ/8)	C₂×C₁₁	semidirect
85. C₂×#135	C₂×C₁₁	semidirect
86. C₂²×D₈	C₂×C₁₁	semidirect
87. #535	C₂×C₁₁	semidirect
88. #496	C₂×C₁₁	semidirect
89. #495	C₂×C₁₁	semidirect
90. #493	C₂×C₁₁	semidirect
91. #405	C₂×C₁₁	semidirect
109. C₂×Q₁₆	C₂²×C₁₁	semidirect
110. C₂×SD₁₆	C₂²×C₁₁	semidirect
111. C₂×SD₁₆	C₂²×C₁₁	semidirect
115. C₂×D₈	C₂²×C₁₁	semidirect
116. C₂×D₈	C₂²×C₁₁	semidirect
119. #127	C₂²×C₁₁	semidirect
120. #124	C₂²×C₁₁	semidirect
124. #97	C₂²×C₁₁	semidirect
125. C₄×C₈	C₂²×C₁₁	semidirect
151. M₁₆	D₄×C₁₁	semidirect
152. C₂×C₈	D₄×C₁₁	semidirect
160. C₁₁	#3155	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×AGL(1,ℤ/8)	2
C₂×C₁₁×#135	2
C₂²×C₁₁×D₈	2
C₁₁×#535	2
C₁₁×#496	2
C₁₁×#495	2
C₁₁×#493	2
C₁₁×#405	2
#3155	11

Subgroups — C11×#3155 #13065993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3155 #13065993