Subgroups — C₁₁×#36608 #14613801

Order 2816.

1626 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#2862	C₂	1	3	yes	maximal
2	C₁₁×#2581	C₂	1	6	yes	maximal
3	C₁₁×#2514	C₂	1	12	yes	maximal
4	C₁₁×#2356	C₂	1	6	yes	maximal
5	C₄×C₁₁×C₄⋊Q₈	C₂	1	3	yes	maximal
6	C₄²×Q₈×C₁₁	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₁×C₄⋊Q₈	C₂²	1	3	yes	—
8	C₂×C₄×Q₈×C₁₁	C₂²	1	3	yes	—
9	C₂×C₄×Q₈×C₁₁	C₂²	1	6	yes	—
10	C₁₁×#401	C₂²	1	8	yes	—
11	C₁₁×#400	C₂²	1	12	yes	—
12	C₁₁×#395	C₂²	1	4	yes	—
13	C₁₁×#391	C₂²	1	6	yes	—
14	C₁₁×#391	C₂²	1	12	yes	—
15	C₁₁×#391	C₂²	1	12	yes	—
16	C₁₁×#389	C₂²	1	12	yes	—
17	C₁₁×#387	C₂²	1	24	yes	—
18	C₁₁×#384	C₂²	1	1	yes	characteristic
19	C₁₁×#383	C₂²	1	12	yes	—
20	C₁₁×#382	C₂²	1	6	yes	—
21	C₁₁×#382	C₂²	1	6	yes	—
22	C₄×C₁₁×C₄⋊C₄	C₂²	1	6	yes	—
23	C₄×C₁₁×C₄⋊C₄	C₂²	1	12	yes	—
24	C₄×C₁₁×C₄⋊C₄	C₂²	1	3	yes	—
25	C₁₁×#376	C₂²	1	4	yes	—
26	C₄³×C₁₁	C₂²	1	3	yes	—
27	C₂²×Q₈×C₁₁	C₂³	1	1	yes	characteristic
28	C₂²×Q₈×C₁₁	C₂³	1	6	yes	—
29	C₁₁×C₄⋊Q₈	—	2	12	no	—
30	C₄×Q₈×C₁₁	—	2	12	no	—
31	C₄×Q₈×C₁₁	—	2	24	no	—
32	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
33	C₂×C₁₁×C₄⋊C₄	C₂³	1	6	yes	—
34	C₂×C₁₁×C₄⋊C₄	C₂³	1	3	yes	—
35	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
36	C₂×C₁₁×C₄⋊C₄	C₂³	1	12	yes	—
37	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
38	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
39	C₂×C₄²×C₁₁	C₂³	1	6	yes	—
40	C₂×C₄²×C₁₁	C₂³	1	12	yes	—
41	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	3	yes	—
43	C₁₁×#95	C₂³	1	1	yes	characteristic
44	C₁₁×#95	C₂³	1	12	yes	—
45	C₁₁×#95	C₂³	1	3	yes	—
46	C₁₁×#95	C₂³	1	2	yes	—
47	C₁₁×#95	C₂³	1	24	yes	—
48	C₁₁×#95	C₂³	1	24	yes	—
49	C₁₁×#95	C₂³	1	12	yes	—
50	#36608	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂×Q₈×C₁₁	—	2	6	no	—
52	C₂×Q₈×C₁₁	—	2	12	no	—
53	C₂×Q₈×C₁₁	—	2	12	no	—
54	C₂×Q₈×C₁₁	—	2	12	no	—
55	C₂²×C₄×C₁₁	C₂⁴	1	6	yes	—
56	C₂²×C₄×C₁₁	C₂⁴	1	12	yes	—
57	C₂²×C₄×C₁₁	C₂⁴	1	4	yes	—
58	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
59	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
60	C₂²×C₄×C₁₁	C₂⁴	1	3	yes	—
61	C₁₁×C₄⋊C₄	—	2	12	no	—
62	C₁₁×C₄⋊C₄	—	2	6	no	—
63	C₁₁×C₄⋊C₄	—	2	12	no	—
64	C₁₁×C₄⋊C₄	—	2	24	no	—
65	C₁₁×C₄⋊C₄	—	2	24	no	—
66	C₄²×C₁₁	—	2	12	no	—
67	C₄²×C₁₁	—	2	24	no	—
68	C₄²×C₁₁	—	2	12	no	—
69	C₄²×C₁₁	—	2	6	no	—
70	C₄²×C₁₁	#41	1	12	yes	—
71	C₄²×C₁₁	#41	1	4	yes	—
72	#2862	C₂×C₁₁	1	3	yes	—
73	#2581	C₂×C₁₁	1	6	yes	—
74	#2514	C₂×C₁₁	1	12	yes	—
75	#2356	C₂×C₁₁	1	6	yes	—
76	C₄×C₄⋊Q₈	C₂×C₁₁	1	3	yes	—
77	C₄²×Q₈	C₂×C₁₁	1	1	yes	characteristic
78	C₂³×C₁₁	C₂⁵	1	1	yes	characteristic
79	Q₈×C₁₁	—	2	8	no	—
80	Q₈×C₁₁	—	4	24	no	—
81	C₂×C₄×C₁₁	—	2	6	no	—
82	C₂×C₄×C₁₁	—	2	6	no	—
83	C₂×C₄×C₁₁	—	2	12	no	—
84	C₂×C₄×C₁₁	—	2	6	no	—
85	C₂×C₄×C₁₁	—	2	12	no	—
86	C₂×C₄×C₁₁	—	2	12	no	—
87	C₂×C₄×C₁₁	—	2	6	no	—
88	C₂×C₄×C₁₁	—	2	6	no	—
89	C₂×C₄×C₁₁	—	2	12	no	—
90	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
91	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
92	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
93	C₂×C₄×C₁₁	C₂×#41	1	6	yes	—
94	C₂×C₄×C₁₁	2₋¹⁺⁴	1	6	yes	—
95	C₂×C₄⋊Q₈	C₂²×C₁₁	1	3	yes	—
96	C₂×C₄×Q₈	C₂²×C₁₁	1	6	yes	—
97	C₂×C₄×Q₈	C₂²×C₁₁	1	3	yes	—
98	#401	C₂²×C₁₁	1	8	yes	—
99	#400	C₂²×C₁₁	1	12	yes	—
100	#395	C₂²×C₁₁	1	4	yes	—
101	#391	C₂²×C₁₁	1	6	yes	—
102	#391	C₂²×C₁₁	1	12	yes	—
103	#391	C₂²×C₁₁	1	12	yes	—
104	#389	C₂²×C₁₁	1	12	yes	—
105	#387	C₂²×C₁₁	1	24	yes	—
106	#384	C₂²×C₁₁	1	1	yes	characteristic
107	#383	C₂²×C₁₁	1	12	yes	—
108	#382	C₂²×C₁₁	1	6	yes	—
109	#382	C₂²×C₁₁	1	6	yes	—
110	C₄×C₄⋊C₄	C₂²×C₁₁	1	12	yes	—
111	C₄×C₄⋊C₄	C₂²×C₁₁	1	3	yes	—
112	C₄×C₄⋊C₄	C₂²×C₁₁	1	6	yes	—
113	#376	C₂²×C₁₁	1	4	yes	—
114	C₄³	C₂²×C₁₁	1	3	yes	—
115	C₂²×C₁₁	C₂²×#41	1	3	yes	—
116	C₂²×C₁₁	C₂²×#41	1	1	yes	characteristic
117	C₂²×C₁₁	C₂×2₋¹⁺⁴	1	3	yes	—
118	C₄×C₁₁	—	2	6	no	—
119	C₄×C₁₁	—	2	6	no	—
120	C₄×C₁₁	—	4	4	no	—
121	C₄×C₁₁	—	4	12	no	—
122	C₄×C₁₁	—	4	6	no	—
123	C₄×C₁₁	#556	1	12	yes	—
124	C₂²×Q₈	C₂³×C₁₁	1	1	yes	characteristic
125	C₂²×Q₈	C₂³×C₁₁	1	6	yes	—
126	C₄⋊Q₈	—	2	12	no	—
127	C₄×Q₈	—	2	12	no	—
128	C₄×Q₈	—	2	24	no	—
129	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
130	C₂×C₄⋊C₄	C₂³×C₁₁	1	6	yes	—
131	C₂×C₄⋊C₄	C₂³×C₁₁	1	3	yes	—
132	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
133	C₂×C₄⋊C₄	C₂³×C₁₁	1	12	yes	—
134	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
135	C₂×C₄²	C₂³×C₁₁	1	12	yes	—
136	C₂×C₄²	C₂³×C₁₁	1	6	yes	—
137	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
138	C₂×C₄²	C₂³×C₁₁	1	3	yes	—
139	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
140	#95	C₂³×C₁₁	1	1	yes	characteristic
141	#95	C₂³×C₁₁	1	12	yes	—
142	#95	C₂³×C₁₁	1	3	yes	—
143	#95	C₂³×C₁₁	1	2	yes	—
144	#95	C₂³×C₁₁	1	24	yes	—
145	#95	C₂³×C₁₁	1	24	yes	—
146	#95	C₂³×C₁₁	1	12	yes	—
147	C₂×C₁₁	#3444	1	1	yes	characteristic
148	C₂×C₁₁	C₂×#556	1	3	yes	—
149	C₂×C₁₁	#3509	1	3	yes	—
150	C₂×Q₈	—	2	6	no	—
151	C₂×Q₈	—	2	12	no	—
152	C₂×Q₈	—	2	12	no	—
153	C₂×Q₈	—	2	12	no	—
154	C₂²×C₄	C₂⁴×C₁₁	1	6	yes	—
155	C₂²×C₄	C₂⁴×C₁₁	1	12	yes	—
156	C₂²×C₄	C₂⁴×C₁₁	1	4	yes	—
157	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
158	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
159	C₂²×C₄	C₂⁴×C₁₁	1	3	yes	—
160	C₄⋊C₄	—	2	12	no	—
161	C₄⋊C₄	—	2	6	no	—
162	C₄⋊C₄	—	2	12	no	—
163	C₄⋊C₄	—	2	24	no	—
164	C₄⋊C₄	—	2	24	no	—
165	C₄²	—	2	12	no	—
166	C₄²	—	2	24	no	—
167	C₄²	—	2	12	no	—
168	C₄²	—	2	6	no	—
169	C₄²	C₁₁×#41	1	12	yes	—
170	C₄²	C₁₁×#41	1	4	yes	—
171	C₁₁	#36608	1	1	yes	characteristic, direct product factor, Sylow
172	C₂³	C₂⁵×C₁₁	1	1	yes	characteristic
173	Q₈	—	2	8	no	—
174	Q₈	—	4	24	no	—
175	C₂×C₄	—	2	6	no	—
176	C₂×C₄	—	2	6	no	—
177	C₂×C₄	—	2	12	no	—
178	C₂×C₄	—	2	6	no	—
179	C₂×C₄	—	2	12	no	—
180	C₂×C₄	—	2	12	no	—
181	C₂×C₄	—	2	6	no	—
182	C₂×C₄	—	2	6	no	—
183	C₂×C₄	—	2	12	no	—
184	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
185	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
186	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
187	C₂×C₄	C₂×C₁₁×#41	1	6	yes	—
188	C₂×C₄	C₁₁×2₋¹⁺⁴	1	6	yes	—
189	C₂²	C₂²×C₁₁×#41	1	3	yes	—
190	C₂²	C₂²×C₁₁×#41	1	1	yes	characteristic
191	C₂²	C₂×C₁₁×2₋¹⁺⁴	1	3	yes	—
192	C₄	—	2	6	no	—
193	C₄	—	2	6	no	—
194	C₄	—	4	4	no	—
195	C₄	—	4	12	no	—
196	C₄	—	4	6	no	—
197	C₄	C₁₁×#556	1	12	yes	—
198	C₂	C₁₁×#3444	1	1	yes	characteristic
199	C₂	C₂×C₁₁×#556	1	3	yes	—
200	C₂	C₁₁×#3509	1	3	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₁
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
50. #36608	C₁₁	direct (N × H)
171. C₁₁	#36608	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×#2862	2
C₁₁×#2581	2
C₁₁×#2514	2
C₁₁×#2356	2
C₄×C₁₁×C₄⋊Q₈	2
C₄²×Q₈×C₁₁	2
#36608	11

Subgroups — C11×#36608 #14613801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#36608 #14613801