Subgroups — C₁₁×#3197 #13066035

Order 1408.

418 conjugacy classes of subgroups.

The subgroup lattice has 238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#525	C₂	1	2	yes	maximal, complemented
2	C₁₁×#485	C₂	1	2	yes	maximal, complemented
3	C₁₁×#482	C₂	1	2	yes	maximal, complemented
4	C₁₁×#470	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#469	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₁×#468	C₂	1	2	yes	maximal, complemented
7	C₁₁×#452	C₂	1	2	yes	maximal, complemented
8	C₁₁×#449	C₂	1	2	yes	maximal, complemented
9	C₁₁×#407	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₁₁×#41	C₂²	1	2	yes	—
11	C₂³×C₄×C₁₁	C₂²	1	1	yes	characteristic
12	C₂×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
13	C₂×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
14	C₂×C₁₁×D₈	C₂²	1	1	yes	characteristic, complemented
15	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₁₁×M₁₆	C₂²	1	1	yes	characteristic
17	C₁₁×#123	—	2	2	no	—
18	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
19	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
20	C₁₁×#121	C₂²	1	2	yes	—
21	C₁₁×#121	C₂²	1	2	yes	—
22	C₁₁×#120	—	2	2	no	—
23	C₄×D₄×C₁₁	—	2	2	no	—
24	C₄×D₄×C₁₁	—	2	2	no	—
25	C₁₁×#117	C₂²	1	2	yes	—
26	C₁₁×#107	C₂²	1	2	yes	complemented
27	C₁₁×#106	C₂²	1	1	yes	characteristic, complemented
28	C₁₁×#106	C₂²	1	1	yes	characteristic, complemented
29	C₁₁×#103	C₂²	1	2	yes	complemented
30	C₁₁×#103	C₂²	1	2	yes	complemented
31	C₁₁×#102	C₂²	1	2	yes	complemented
32	C₁₁×#102	C₂²	1	2	yes	complemented
33	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
35	C₂⁴×C₁₁	D₄	1	1	yes	characteristic
36	C₁₁×#41	—	4	2	no	—
37	C₁₁×#41	—	4	2	no	—
38	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
39	C₂×D₄×C₁₁	—	2	2	no	—
40	C₂×D₄×C₁₁	—	2	2	no	—
41	C₂×D₄×C₁₁	—	2	2	no	—
42	C₂×D₄×C₁₁	C₂³	1	2	yes	—
43	C₂²×C₄×C₁₁	—	2	2	no	—
44	C₂²×C₄×C₁₁	—	4	1	no	—
45	C₂²×C₄×C₁₁	—	4	1	no	—
46	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	D₄	1	2	yes	—
48	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
50	C₁₁×Q₁₆	—	4	1	no	—
51	C₁₁×SD₁₆	—	4	2	no	—
52	C₁₁×D₈	—	4	1	no	—
53	C₁₁×M₁₆	—	4	1	no	—
54	C₁₁×M₁₆	—	4	1	no	—
55	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂³	1	2	yes	—
57	C₂×C₈×C₁₁	C₂³	1	1	yes	characteristic
58	C₁₁×C₄⋊C₄	—	2	2	no	—
59	C₁₁×C₄⋊C₄	—	2	2	no	—
60	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
61	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
62	C₁₁×C₂²⋊C₄	—	2	2	no	—
63	C₁₁×C₂²⋊C₄	—	2	2	no	—
64	C₁₁×C₂²⋊C₄	—	2	2	no	—
65	C₁₁×C₂²⋊C₄	—	2	2	no	—
66	C₁₁×C₂²⋊C₄	—	2	2	no	—
67	C₄²×C₁₁	—	2	2	no	—
68	#3197	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₁	—	2	2	no	—
70	C₂³×C₁₁	—	4	1	no	—
71	C₂³×C₁₁	—	4	2	no	—
72	C₂³×C₁₁	C₂×D₄	1	2	yes	—
73	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
74	Q₈×C₁₁	—	2	2	no	—
75	Q₈×C₁₁	—	2	2	no	—
76	D₄×C₁₁	—	2	2	no	—
77	D₄×C₁₁	—	2	2	no	—
78	D₄×C₁₁	—	4	4	no	—
79	D₄×C₁₁	—	4	4	no	—
80	D₄×C₁₁	—	4	4	no	—
81	C₂×C₄×C₁₁	—	2	1	no	—
82	C₂×C₄×C₁₁	—	2	1	no	—
83	C₂×C₄×C₁₁	—	2	2	no	—
84	C₂×C₄×C₁₁	—	2	2	no	—
85	C₂×C₄×C₁₁	—	2	2	no	—
86	C₂×C₄×C₁₁	—	2	2	no	—
87	C₂×C₄×C₁₁	—	2	2	no	—
88	C₂×C₄×C₁₁	—	4	1	no	—
89	C₂×C₄×C₁₁	—	4	2	no	—
90	C₂×C₄×C₁₁	—	4	4	no	—
91	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
92	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
93	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
94	C₈×C₁₁	—	2	1	no	—
95	C₈×C₁₁	—	2	2	no	—
96	C₈×C₁₁	—	2	1	no	—
97	#525	C₂×C₁₁	1	2	yes	complemented
98	#485	C₂×C₁₁	1	2	yes	complemented
99	#482	C₂×C₁₁	1	2	yes	complemented
100	#470	C₂×C₁₁	1	1	yes	characteristic, complemented
101	#469	C₂×C₁₁	1	1	yes	characteristic, complemented
102	#468	C₂×C₁₁	1	2	yes	complemented
103	#452	C₂×C₁₁	1	2	yes	complemented
104	#449	C₂×C₁₁	1	2	yes	complemented
105	#407	C₂×C₁₁	1	1	yes	characteristic, complemented
106	C₂²×C₁₁	—	2	2	no	—
107	C₂²×C₁₁	—	2	1	no	—
108	C₂²×C₁₁	—	2	2	no	—
109	C₂²×C₁₁	—	2	2	no	—
110	C₂²×C₁₁	—	2	2	no	—
111	C₂²×C₁₁	—	4	4	no	—
112	C₂²×C₁₁	—	4	2	no	—
113	C₂²×C₁₁	—	4	2	no	—
114	C₂²×C₁₁	—	4	2	no	—
115	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
116	C₄×C₁₁	—	2	2	no	—
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	4	2	no	—
119	C₄×C₁₁	—	4	2	no	—
120	C₄×C₁₁	—	4	2	no	—
121	C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
122	C₄×C₁₁	H(5,𝔽₂)	1	1	yes	characteristic
123	C₂×#41	C₂²×C₁₁	1	2	yes	—
124	C₂³×C₄	C₂²×C₁₁	1	1	yes	characteristic
125	C₂×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
126	C₂×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
127	C₂×D₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
128	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
129	C₂×M₁₆	C₂²×C₁₁	1	1	yes	characteristic
130	#123	—	2	2	no	—
131	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
132	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
133	#121	C₂²×C₁₁	1	2	yes	—
134	#121	C₂²×C₁₁	1	2	yes	—
135	#120	—	2	2	no	—
136	C₄×D₄	—	2	2	no	—
137	C₄×D₄	—	2	2	no	—
138	#117	C₂²×C₁₁	1	2	yes	—
139	#107	C₂²×C₁₁	1	2	yes	complemented
140	#106	C₂²×C₁₁	1	1	yes	characteristic, complemented
141	#106	C₂²×C₁₁	1	1	yes	characteristic, complemented
142	#103	C₂²×C₁₁	1	2	yes	complemented
143	#103	C₂²×C₁₁	1	2	yes	complemented
144	#102	C₂²×C₁₁	1	2	yes	complemented
145	#102	C₂²×C₁₁	1	2	yes	complemented
146	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
147	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
148	C₂×C₁₁	—	4	2	no	—
149	C₂×C₁₁	—	4	1	no	—
150	C₂×C₁₁	—	8	2	no	—
151	C₂×C₁₁	#534	1	1	yes	characteristic
152	C₂×C₁₁	#575	1	2	yes	—
153	C₂⁴	D₄×C₁₁	1	1	yes	characteristic
154	#41	—	4	2	no	—
155	#41	—	4	2	no	—
156	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
157	C₂×D₄	—	2	2	no	—
158	C₂×D₄	—	2	2	no	—
159	C₂×D₄	—	2	2	no	—
160	C₂×D₄	C₂³×C₁₁	1	2	yes	—
161	C₂²×C₄	—	2	2	no	—
162	C₂²×C₄	—	4	1	no	—
163	C₂²×C₄	—	4	1	no	—
164	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
165	C₂²×C₄	D₄×C₁₁	1	2	yes	—
166	C₂²×C₄	C₂³×C₁₁	1	2	yes	—
167	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
168	Q₁₆	—	4	1	no	—
169	SD₁₆	—	4	2	no	—
170	D₈	—	4	1	no	—
171	M₁₆	—	4	1	no	—
172	M₁₆	—	4	1	no	—
173	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
174	C₂×C₈	C₂³×C₁₁	1	2	yes	—
175	C₂×C₈	C₂³×C₁₁	1	1	yes	characteristic
176	C₄⋊C₄	—	2	2	no	—
177	C₄⋊C₄	—	2	2	no	—
178	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
179	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
180	C₂²⋊C₄	—	2	2	no	—
181	C₂²⋊C₄	—	2	2	no	—
182	C₂²⋊C₄	—	2	2	no	—
183	C₂²⋊C₄	—	2	2	no	—
184	C₂²⋊C₄	—	2	2	no	—
185	C₄²	—	2	2	no	—
186	C₁₁	#3197	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³	—	2	2	no	—
188	C₂³	—	4	1	no	—
189	C₂³	—	4	2	no	—
190	C₂³	C₂×D₄×C₁₁	1	2	yes	—
191	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
192	Q₈	—	2	2	no	—
193	Q₈	—	2	2	no	—
194	D₄	—	2	2	no	—
195	D₄	—	2	2	no	—
196	D₄	—	4	4	no	—
197	D₄	—	4	4	no	—
198	D₄	—	4	4	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	1	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	2	no	—
203	C₂×C₄	—	2	2	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	4	2	no	—
208	C₂×C₄	—	4	4	no	—
209	C₂×C₄	C₂×D₄×C₁₁	1	2	yes	—
210	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
211	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
212	C₈	—	2	1	no	—
213	C₈	—	2	2	no	—
214	C₈	—	2	1	no	—
215	C₂²	—	2	2	no	—
216	C₂²	—	2	1	no	—
217	C₂²	—	2	2	no	—
218	C₂²	—	2	2	no	—
219	C₂²	—	2	2	no	—
220	C₂²	—	4	4	no	—
221	C₂²	—	4	2	no	—
222	C₂²	—	4	2	no	—
223	C₂²	—	4	2	no	—
224	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
225	C₄	—	2	2	no	—
226	C₄	—	2	1	no	—
227	C₄	—	4	2	no	—
228	C₄	—	4	2	no	—
229	C₄	—	4	2	no	—
230	C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
231	C₄	C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
232	C₂	—	4	2	no	—
233	C₂	—	4	1	no	—
234	C₂	—	8	2	no	—
235	C₂	C₁₁×#534	1	1	yes	characteristic
236	C₂	C₁₁×#575	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 ◁ C₂³×C₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₁×#525	C₂	semidirect
2. C₁₁×#485	C₂	semidirect
3. C₁₁×#482	C₂	semidirect
4. C₁₁×#470	C₂	semidirect
5. C₁₁×#469	C₂	semidirect
6. C₁₁×#468	C₂	semidirect
7. C₁₁×#452	C₂	semidirect
8. C₁₁×#449	C₂	semidirect
9. C₁₁×#407	C₂	semidirect
12. C₂×C₁₁×Q₁₆	C₂²	semidirect
13. C₂×C₁₁×SD₁₆	C₂²	semidirect
14. C₂×C₁₁×D₈	C₂²	semidirect
26. C₁₁×#107	C₂²	semidirect
27. C₁₁×#106	C₂²	semidirect
28. C₁₁×#106	C₂²	semidirect
29. C₁₁×#103	C₂²	semidirect
30. C₁₁×#103	C₂²	semidirect
31. C₁₁×#102	C₂²	semidirect
32. C₁₁×#102	C₂²	semidirect
68. #3197	C₁₁	direct (N × H)
97. #525	C₂×C₁₁	semidirect
98. #485	C₂×C₁₁	semidirect
99. #482	C₂×C₁₁	semidirect
100. #470	C₂×C₁₁	semidirect
101. #469	C₂×C₁₁	semidirect
102. #468	C₂×C₁₁	semidirect
103. #452	C₂×C₁₁	semidirect
104. #449	C₂×C₁₁	semidirect
105. #407	C₂×C₁₁	semidirect
125. C₂×Q₁₆	C₂²×C₁₁	semidirect
126. C₂×SD₁₆	C₂²×C₁₁	semidirect
127. C₂×D₈	C₂²×C₁₁	semidirect
139. #107	C₂²×C₁₁	semidirect
140. #106	C₂²×C₁₁	semidirect
141. #106	C₂²×C₁₁	semidirect
142. #103	C₂²×C₁₁	semidirect
143. #103	C₂²×C₁₁	semidirect
144. #102	C₂²×C₁₁	semidirect
145. #102	C₂²×C₁₁	semidirect
186. C₁₁	#3197	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×#525	2
C₁₁×#485	2
C₁₁×#482	2
C₁₁×#470	2
C₁₁×#469	2
C₁₁×#468	2
C₁₁×#452	2
C₁₁×#449	2
C₁₁×#407	2
#3197	11

Subgroups — C11×#3197 #13066035

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3197 #13066035