Subgroups — C₁₁×#22277 #14599470

Order 2816.

826 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×#494	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2327	C₂	1	2	yes	maximal
3	C₁₁×#1960	C₂	1	2	yes	maximal
4	C₁₁×#1878	C₂	1	8	yes	maximal
5	C₁₁×#1835	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1746	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₁₁×Q₁₆	C₂²	1	4	yes	—
8	C₂×C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
9	C₂×C₄×Q₈×C₁₁	C₂²	1	4	yes	—
10	C₁₁×#494	C₄	1	8	yes	complemented
11	C₂×C₁₁×#103	C₂²	1	8	yes	—
12	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₁₁×#391	C₂²	1	4	yes	—
15	C₁₁×#387	—	2	8	no	—
16	C₁₁×#382	C₂²	1	2	yes	—
17	C₁₁×#376	C₂²	1	1	yes	characteristic
18	C₁₁×#340	C₂²	1	4	yes	—
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
21	C₂×C₁₁×Q₁₆	—	4	8	no	—
22	C₂×C₁₁×Q₁₆	C₂×C₄	1	16	yes	—
23	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
24	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
25	C₁₁×C₄⋊Q₈	—	2	4	no	—
26	C₁₁×C₄⋊Q₈	C₂×C₄	1	8	yes	—
27	C₄×Q₈×C₁₁	—	4	8	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
29	C₂×C₁₁×C₄⋊C₄	—	2	4	no	—
30	C₂×C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
31	C₂×C₄²×C₁₁	—	2	4	no	—
32	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
33	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
34	C₁₁×#103	—	4	8	no	—
35	C₁₁×#97	—	2	2	no	—
36	C₄×C₈×C₁₁	C₂×C₄	1	4	yes	—
37	C₁₁×#95	—	2	4	no	—
38	C₁₁×#95	—	2	8	no	—
39	C₁₁×#95	D₄	1	4	yes	—
40	#22277	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×Q₈×C₁₁	—	2	4	no	—
42	C₂×Q₈×C₁₁	—	2	8	no	—
43	C₂×Q₈×C₁₁	—	2	8	no	—
44	C₂×Q₈×C₁₁	C₂²×C₄	1	8	yes	—
45	C₂²×C₄×C₁₁	—	2	4	no	—
46	C₂²×C₄×C₁₁	—	2	4	no	—
47	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
48	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
49	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
50	C₁₁×Q₁₆	—	4	16	no	—
51	C₂×C₈×C₁₁	—	2	2	no	—
52	C₂×C₈×C₁₁	—	2	4	no	—
53	C₂×C₈×C₁₁	—	2	4	no	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
55	C₁₁×C₄⋊C₄	—	2	16	no	—
56	C₁₁×C₄⋊C₄	—	2	8	no	—
57	C₁₁×C₄⋊C₄	—	4	8	no	—
58	C₄²×C₁₁	—	2	4	no	—
59	C₄²×C₁₁	—	4	8	no	—
60	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
61	C₄²×C₁₁	#41	1	2	yes	—
62	C₂×#494	C₂×C₁₁	1	1	yes	characteristic
63	#2327	C₂×C₁₁	1	2	yes	—
64	#1960	C₂×C₁₁	1	2	yes	—
65	#1878	C₂×C₁₁	1	8	yes	—
66	#1835	C₂×C₁₁	1	1	yes	characteristic
67	#1746	C₂×C₁₁	1	1	yes	characteristic
68	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
69	Q₈×C₁₁	—	2	16	no	—
70	Q₈×C₁₁	—	4	8	no	—
71	C₂×C₄×C₁₁	—	2	4	no	—
72	C₂×C₄×C₁₁	—	2	8	no	—
73	C₂×C₄×C₁₁	—	2	4	no	—
74	C₂×C₄×C₁₁	—	2	8	no	—
75	C₂×C₄×C₁₁	—	4	4	no	—
76	C₂×C₄×C₁₁	—	4	4	no	—
77	C₂×C₄×C₁₁	—	4	4	no	—
78	C₂×C₄×C₁₁	—	4	8	no	—
79	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
80	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×#41	1	1	yes	characteristic
82	C₂×C₄×C₁₁	H(5,𝔽₂)	1	4	yes	—
83	C₈×C₁₁	—	2	4	no	—
84	C₈×C₁₁	—	4	2	no	—
85	C₂²×Q₁₆	C₂²×C₁₁	1	4	yes	—
86	C₂×C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
87	C₂×C₄×Q₈	C₂²×C₁₁	1	4	yes	—
88	#494	C₄×C₁₁	1	8	yes	complemented
89	C₂×#103	C₂²×C₁₁	1	8	yes	—
90	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
91	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
92	#391	C₂²×C₁₁	1	4	yes	—
93	#387	—	2	8	no	—
94	#382	C₂²×C₁₁	1	2	yes	—
95	#376	C₂²×C₁₁	1	1	yes	characteristic
96	#340	C₂²×C₁₁	1	4	yes	—
97	#336	C₂²×C₁₁	1	4	yes	—
98	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
99	C₂²×C₁₁	#535	1	2	yes	—
100	C₂²×C₁₁	#578	1	4	yes	—
101	C₄×C₁₁	—	2	4	no	—
102	C₄×C₁₁	—	4	8	no	—
103	C₄×C₁₁	—	4	4	no	—
104	C₄×C₁₁	—	8	4	no	—
105	C₄×C₁₁	#518	1	2	yes	—
106	C₄×C₁₁	#540	1	2	yes	—
107	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
108	C₂×Q₁₆	—	4	8	no	—
109	C₂×Q₁₆	C₂×C₄×C₁₁	1	16	yes	—
110	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
111	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
112	C₄⋊Q₈	—	2	4	no	—
113	C₄⋊Q₈	C₂×C₄×C₁₁	1	8	yes	—
114	C₄×Q₈	—	4	8	no	—
115	C₂×C₄⋊C₄	—	2	4	no	—
116	C₂×C₄⋊C₄	—	2	4	no	—
117	C₂×C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
118	C₂×C₄²	—	2	4	no	—
119	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
120	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
121	#103	—	4	8	no	—
122	#97	—	2	2	no	—
123	C₄×C₈	C₂×C₄×C₁₁	1	4	yes	—
124	#95	—	2	4	no	—
125	#95	—	2	8	no	—
126	#95	D₄×C₁₁	1	4	yes	—
127	C₂×C₁₁	#2328	1	1	yes	characteristic
128	C₂×C₁₁	#2950	1	2	yes	—
129	C₂×C₁₁	#3223	1	4	yes	—
130	C₂×Q₈	—	2	4	no	—
131	C₂×Q₈	—	2	8	no	—
132	C₂×Q₈	—	2	8	no	—
133	C₂×Q₈	C₂²×C₄×C₁₁	1	8	yes	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	—	2	4	no	—
136	C₂²×C₄	C₂×D₄×C₁₁	1	4	yes	—
137	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
138	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
139	Q₁₆	—	4	16	no	—
140	C₂×C₈	—	2	4	no	—
141	C₂×C₈	—	2	2	no	—
142	C₂×C₈	—	2	4	no	—
143	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
144	C₄⋊C₄	—	2	16	no	—
145	C₄⋊C₄	—	2	8	no	—
146	C₄⋊C₄	—	4	8	no	—
147	C₄²	—	2	4	no	—
148	C₄²	—	4	8	no	—
149	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
150	C₄²	C₁₁×#41	1	2	yes	—
151	C₁₁	#22277	1	1	yes	characteristic, direct product factor, Sylow
152	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
153	Q₈	—	2	16	no	—
154	Q₈	—	4	8	no	—
155	C₂×C₄	—	2	4	no	—
156	C₂×C₄	—	2	8	no	—
157	C₂×C₄	—	2	4	no	—
158	C₂×C₄	—	2	8	no	—
159	C₂×C₄	—	4	4	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	4	4	no	—
162	C₂×C₄	—	4	8	no	—
163	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
164	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
165	C₂×C₄	C₂×C₁₁×#41	1	1	yes	characteristic
166	C₂×C₄	C₁₁×H(5,𝔽₂)	1	4	yes	—
167	C₈	—	2	4	no	—
168	C₈	—	4	2	no	—
169	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
170	C₂²	C₁₁×#535	1	2	yes	—
171	C₂²	C₁₁×#578	1	4	yes	—
172	C₄	—	2	4	no	—
173	C₄	—	4	4	no	—
174	C₄	—	4	8	no	—
175	C₄	—	8	4	no	—
176	C₄	C₁₁×#518	1	2	yes	—
177	C₄	C₁₁×#540	1	2	yes	—
178	C₂	C₁₁×#2328	1	1	yes	characteristic
179	C₂	C₁₁×#2950	1	2	yes	—
180	C₂	C₁₁×#3223	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ C₁₁×#376 ◁ G

Complements

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

N	H ≅ G/N	type
10. C₁₁×#494	C₄	semidirect
40. #22277	C₁₁	direct (N × H)
88. #494	C₄×C₁₁	semidirect
151. C₁₁	#22277	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×#494	2
C₁₁×#2327	2
C₁₁×#1960	2
C₁₁×#1878	2
C₁₁×#1835	2
C₁₁×#1746	2
#22277	11

Subgroups — C11×#22277 #14599470

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22277 #14599470