Subgroups — C₁₁×#3208 #13066046

Order 1408.

488 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₁×#127	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#492	C₂	1	2	yes	maximal, complemented
4	C₁₁×#486	C₂	1	2	yes	maximal, complemented
5	C₁₁×#460	C₂	1	4	yes	maximal, complemented
6	C₁₁×#450	C₂	1	4	yes	maximal, complemented
7	C₁₁×#431	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×D₄×C₁₁	—	2	1	no	—
9	C₂²×D₄×C₁₁	—	2	1	no	—
10	C₂²×D₄×C₁₁	C₂²	1	2	yes	—
11	C₂×C₁₁×SD₁₆	C₂²	1	8	yes	complemented
12	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
13	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
14	C₁₁×#127	—	2	1	no	—
15	C₁₁×#127	—	2	1	no	—
16	C₁₁×#127	C₂²	1	2	yes	—
17	C₁₁×#127	C₂²	1	2	yes	—
18	C₁₁×#125	—	2	1	no	—
19	C₁₁×C₂²⋊Q₈	—	2	1	no	—
20	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
21	C₄×Q₈×C₁₁	—	2	1	no	—
22	C₄×Q₈×C₁₁	C₂²	1	2	yes	complemented
23	C₁₁×#117	—	2	1	no	—
24	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
25	C₁₁×C₄⋊C₈	C₂²	1	2	yes	complemented
26	C₁₁×#102	C₂²	1	8	yes	complemented
27	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₄×C₈×C₁₁	C₂²	1	2	yes	complemented
29	C₂⁴×C₁₁	—	2	2	no	—
30	C₂×Q₈×C₁₁	—	2	1	no	—
31	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
32	C₂×D₄×C₁₁	—	2	2	no	—
33	C₂×D₄×C₁₁	—	2	2	no	—
34	C₂×D₄×C₁₁	—	2	2	no	—
35	C₂×D₄×C₁₁	—	2	2	no	—
36	C₂×D₄×C₁₁	—	2	2	no	—
37	C₂×D₄×C₁₁	—	4	4	no	—
38	C₂×D₄×C₁₁	—	4	4	no	—
39	C₂×D₄×C₁₁	—	4	4	no	—
40	C₂×D₄×C₁₁	C₂³	1	4	yes	—
41	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
44	C₁₁×SD₁₆	—	4	8	no	—
45	C₂×C₈×C₁₁	C₂³	1	4	yes	—
46	C₁₁×C₄⋊C₄	—	2	1	no	—
47	C₁₁×C₄⋊C₄	—	2	1	no	—
48	C₁₁×C₄⋊C₄	—	2	1	no	—
49	C₁₁×C₄⋊C₄	—	2	2	no	—
50	C₁₁×C₄⋊C₄	—	2	2	no	—
51	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
52	C₁₁×C₂²⋊C₄	—	2	2	no	—
53	C₄²×C₁₁	—	2	2	no	—
54	C₄²×C₁₁	D₄	1	1	yes	characteristic
55	C₄²×C₁₁	D₄	1	1	yes	characteristic
56	C₄²×C₁₁	C₂³	1	1	yes	characteristic
57	C₄²×C₁₁	C₂³	1	1	yes	characteristic
58	#3208	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
59	C₂³×C₁₁	—	2	4	no	—
60	C₂³×C₁₁	—	4	4	no	—
61	C₂³×C₁₁	—	4	4	no	—
62	C₂³×C₁₁	—	4	4	no	—
63	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
64	Q₈×C₁₁	—	2	4	no	—
65	Q₈×C₁₁	—	4	2	no	—
66	D₄×C₁₁	—	2	8	no	—
67	D₄×C₁₁	—	4	4	no	—
68	D₄×C₁₁	—	4	4	no	—
69	D₄×C₁₁	—	4	4	no	—
70	D₄×C₁₁	—	4	4	no	—
71	D₄×C₁₁	—	4	4	no	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	—	2	2	no	—
76	C₂×C₄×C₁₁	SD₁₆	1	4	yes	complemented
77	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
83	C₈×C₁₁	—	2	4	no	—
84	#533	C₂×C₁₁	1	1	yes	characteristic, complemented
85	C₂×#127	C₂×C₁₁	1	1	yes	characteristic
86	#492	C₂×C₁₁	1	2	yes	complemented
87	#486	C₂×C₁₁	1	2	yes	complemented
88	#460	C₂×C₁₁	1	4	yes	complemented
89	#450	C₂×C₁₁	1	4	yes	complemented
90	#431	C₂×C₁₁	1	1	yes	characteristic, complemented
91	C₂²×C₁₁	—	2	1	no	—
92	C₂²×C₁₁	—	2	1	no	—
93	C₂²×C₁₁	—	4	4	no	—
94	C₂²×C₁₁	—	4	4	no	—
95	C₂²×C₁₁	—	4	4	no	—
96	C₂²×C₁₁	—	8	8	no	—
97	C₂²×C₁₁	C₂×SD₁₆	1	2	yes	—
98	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
99	C₄×C₁₁	—	2	1	no	—
100	C₄×C₁₁	—	2	1	no	—
101	C₄×C₁₁	—	4	2	no	—
102	C₄×C₁₁	—	4	2	no	—
103	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
104	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
105	C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
106	C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
107	C₂²×D₄	—	2	1	no	—
108	C₂²×D₄	—	2	1	no	—
109	C₂²×D₄	C₂²×C₁₁	1	2	yes	—
110	C₂×SD₁₆	C₂²×C₁₁	1	8	yes	complemented
111	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
112	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
113	#127	—	2	1	no	—
114	#127	—	2	1	no	—
115	#127	C₂²×C₁₁	1	2	yes	—
116	#127	C₂²×C₁₁	1	2	yes	—
117	#125	—	2	1	no	—
118	C₂²⋊Q₈	—	2	1	no	—
119	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
120	C₄×Q₈	—	2	1	no	—
121	C₄×Q₈	C₂²×C₁₁	1	2	yes	complemented
122	#117	—	2	1	no	—
123	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
124	C₄⋊C₈	C₂²×C₁₁	1	2	yes	complemented
125	#102	C₂²×C₁₁	1	8	yes	complemented
126	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
127	C₄×C₈	C₂²×C₁₁	1	2	yes	complemented
128	C₂×C₁₁	—	2	2	no	—
129	C₂×C₁₁	—	8	4	no	—
130	C₂×C₁₁	#535	1	1	yes	characteristic
131	C₂×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
132	C₂×C₁₁	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
133	C₂⁴	—	2	2	no	—
134	C₂×Q₈	—	2	1	no	—
135	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
136	C₂×D₄	—	2	2	no	—
137	C₂×D₄	—	2	2	no	—
138	C₂×D₄	—	2	2	no	—
139	C₂×D₄	—	2	2	no	—
140	C₂×D₄	—	2	2	no	—
141	C₂×D₄	—	4	4	no	—
142	C₂×D₄	—	4	4	no	—
143	C₂×D₄	—	4	4	no	—
144	C₂×D₄	C₂³×C₁₁	1	4	yes	—
145	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
146	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
147	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
148	SD₁₆	—	4	8	no	—
149	C₂×C₈	C₂³×C₁₁	1	4	yes	—
150	C₄⋊C₄	—	2	1	no	—
151	C₄⋊C₄	—	2	1	no	—
152	C₄⋊C₄	—	2	1	no	—
153	C₄⋊C₄	—	2	2	no	—
154	C₄⋊C₄	—	2	2	no	—
155	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
156	C₂²⋊C₄	—	2	2	no	—
157	C₄²	—	2	2	no	—
158	C₄²	D₄×C₁₁	1	1	yes	characteristic
159	C₄²	D₄×C₁₁	1	1	yes	characteristic
160	C₄²	C₂³×C₁₁	1	1	yes	characteristic
161	C₄²	C₂³×C₁₁	1	1	yes	characteristic
162	C₁₁	#3208	1	1	yes	characteristic, direct product factor, Sylow
163	C₂³	—	2	4	no	—
164	C₂³	—	4	4	no	—
165	C₂³	—	4	4	no	—
166	C₂³	—	4	4	no	—
167	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
168	Q₈	—	2	4	no	—
169	Q₈	—	4	2	no	—
170	D₄	—	2	8	no	—
171	D₄	—	4	4	no	—
172	D₄	—	4	4	no	—
173	D₄	—	4	4	no	—
174	D₄	—	4	4	no	—
175	D₄	—	4	4	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	C₁₁×SD₁₆	1	4	yes	complemented
181	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
182	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
183	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
184	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
185	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
186	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
187	C₈	—	2	4	no	—
188	C₂²	—	2	1	no	—
189	C₂²	—	2	1	no	—
190	C₂²	—	4	4	no	—
191	C₂²	—	4	4	no	—
192	C₂²	—	4	4	no	—
193	C₂²	—	8	8	no	—
194	C₂²	C₂×C₁₁×SD₁₆	1	2	yes	—
195	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
196	C₄	—	2	1	no	—
197	C₄	—	2	1	no	—
198	C₄	—	4	2	no	—
199	C₄	—	4	2	no	—
200	C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
201	C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
202	C₄	C₁₁×AGL(1,ℤ/8)	1	2	yes	—
203	C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
204	C₂	—	2	2	no	—
205	C₂	—	8	4	no	—
206	C₂	C₁₁×#535	1	1	yes	characteristic
207	C₂	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
208	C₂	C₂×C₁₁×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₂×C₁₁×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#533	C₂	semidirect
3. C₁₁×#492	C₂	semidirect
4. C₁₁×#486	C₂	semidirect
5. C₁₁×#460	C₂	semidirect
6. C₁₁×#450	C₂	semidirect
7. C₁₁×#431	C₂	semidirect
11. C₂×C₁₁×SD₁₆	C₂²	semidirect
12. C₁₁×C₄⋊Q₈	C₂²	semidirect
13. C₁₁×C₄⋊Q₈	C₂²	semidirect
22. C₄×Q₈×C₁₁	C₂²	semidirect
25. C₁₁×C₄⋊C₈	C₂²	semidirect
26. C₁₁×#102	C₂²	semidirect
28. C₄×C₈×C₁₁	C₂²	semidirect
58. #3208	C₁₁	direct (N × H)
76. C₂×C₄×C₁₁	SD₁₆	semidirect
84. #533	C₂×C₁₁	semidirect
86. #492	C₂×C₁₁	semidirect
87. #486	C₂×C₁₁	semidirect
88. #460	C₂×C₁₁	semidirect
89. #450	C₂×C₁₁	semidirect
90. #431	C₂×C₁₁	semidirect
110. C₂×SD₁₆	C₂²×C₁₁	semidirect
111. C₄⋊Q₈	C₂²×C₁₁	semidirect
112. C₄⋊Q₈	C₂²×C₁₁	semidirect
121. C₄×Q₈	C₂²×C₁₁	semidirect
124. C₄⋊C₈	C₂²×C₁₁	semidirect
125. #102	C₂²×C₁₁	semidirect
127. C₄×C₈	C₂²×C₁₁	semidirect
162. C₁₁	#3208	direct (N × H)
180. C₂×C₄	C₁₁×SD₁₆	semidirect

Maximal subgroups

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

subgroup	index
C₁₁×#533	2
C₂×C₁₁×#127	2
C₁₁×#492	2
C₁₁×#486	2
C₁₁×#460	2
C₁₁×#450	2
C₁₁×#431	2
#3208	11

Subgroups — C11×#3208 #13066046

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3208 #13066046