Subgroups — C₁₁×#22259 #14599452

Order 2816.

594 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁×#3162	C₂	1	1	yes	maximal, characteristic
2	C₁₁×#2961	C₂	1	2	yes	maximal
3	C₁₁×#1994	C₂	1	2	yes	maximal
4	C₁₁×#1922	C₂	1	8	yes	maximal
5	C₁₁×#1838	C₂	1	1	yes	maximal, characteristic
6	C₁₁×#1745	C₂	1	1	yes	maximal, characteristic
7	C₁₁×#533	C₂²	1	2	yes	—
8	C₁₁×#501	C₄	1	8	yes	complemented
9	C₁₁×#446	—	2	8	no	—
10	C₁₁×#427	C₂²	1	4	yes	—
11	C₁₁×#424	C₂²	1	4	yes	—
12	C₁₁×#423	C₂²	1	2	yes	—
13	C₁₁×#405	C₂²	1	4	yes	—
14	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
15	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
16	C₄³×C₁₁	C₂²	1	1	yes	characteristic
17	C₁₁×#341	C₂²	1	4	yes	—
18	C₁₁×#339	C₂²	1	8	yes	—
19	C₁₁×#336	C₂²	1	4	yes	—
20	C₂×C₁₁×M₁₆	C₂³	1	4	yes	—
21	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
22	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
23	C₁₁×C₄⋊Q₈	C₂×C₄	1	4	yes	—
24	C₁₁×#125	C₂×C₄	1	4	yes	—
25	C₁₁×C₂²⋊Q₈	—	2	4	no	—
26	C₄×Q₈×C₁₁	—	2	4	no	—
27	C₁₁×#117	C₂³	1	4	yes	—
28	C₂×C₄²×C₁₁	—	2	2	no	—
29	C₂×C₄²×C₁₁	C₂³	1	2	yes	—
30	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
31	C₁₁×#107	C₂×C₄	1	8	yes	—
32	C₁₁×#106	C₂×C₄	1	8	yes	—
33	C₁₁×C₄⋊C₈	—	2	8	no	—
34	C₁₁×C₄⋊C₈	—	2	4	no	—
35	C₁₁×#97	—	2	4	no	—
36	C₁₁×#97	C₂×C₄	1	4	yes	—
37	C₁₁×#97	D₄	1	4	yes	—
38	C₄×C₈×C₁₁	—	2	4	no	—
39	#22259	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂×Q₈×C₁₁	—	2	4	no	—
41	C₂²×C₄×C₁₁	—	2	2	no	—
42	C₂²×C₄×C₁₁	#41	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
44	C₁₁×M₁₆	—	2	8	no	—
45	C₂×C₈×C₁₁	—	2	4	no	—
46	C₂×C₈×C₁₁	—	2	4	no	—
47	C₂×C₈×C₁₁	—	2	4	no	—
48	C₂×C₈×C₁₁	C₂²×C₄	1	4	yes	—
49	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	—
50	C₁₁×C₄⋊C₄	—	2	8	no	—
51	C₁₁×C₄⋊C₄	—	2	4	no	—
52	C₁₁×C₄⋊C₄	C₂²×C₄	1	8	yes	—
53	C₁₁×C₂²⋊C₄	—	2	4	no	—
54	C₄²×C₁₁	—	2	4	no	—
55	C₄²×C₁₁	—	2	4	no	—
56	C₄²×C₁₁	—	4	4	no	—
57	C₄²×C₁₁	C₂²×C₄	1	2	yes	—
58	C₄²×C₁₁	C₂×D₄	1	2	yes	—
59	#3162	C₂×C₁₁	1	1	yes	characteristic
60	#2961	C₂×C₁₁	1	2	yes	—
61	#1994	C₂×C₁₁	1	2	yes	—
62	#1922	C₂×C₁₁	1	8	yes	—
63	#1838	C₂×C₁₁	1	1	yes	characteristic
64	#1745	C₂×C₁₁	1	1	yes	characteristic
65	C₂³×C₁₁	C₂×#41	1	1	yes	characteristic
66	Q₈×C₁₁	—	8	4	no	—
67	C₂×C₄×C₁₁	—	2	4	no	—
68	C₂×C₄×C₁₁	—	2	8	no	—
69	C₂×C₄×C₁₁	—	4	2	no	—
70	C₂×C₄×C₁₁	—	4	2	no	—
71	C₂×C₄×C₁₁	—	4	2	no	—
72	C₂×C₄×C₁₁	C₄×D₄	1	4	yes	—
73	C₂×C₄×C₁₁	C₂³×C₄	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
75	C₂×C₄×C₁₁	2₋¹⁺⁴	1	4	yes	—
76	C₈×C₁₁	—	2	4	no	—
77	C₈×C₁₁	—	2	4	no	—
78	C₈×C₁₁	—	4	4	no	—
79	#533	C₂²×C₁₁	1	2	yes	—
80	#501	C₄×C₁₁	1	8	yes	complemented
81	#446	—	2	8	no	—
82	#427	C₂²×C₁₁	1	4	yes	—
83	#424	C₂²×C₁₁	1	4	yes	—
84	#423	C₂²×C₁₁	1	2	yes	—
85	#405	C₂²×C₁₁	1	4	yes	—
86	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
87	C₂×#97	C₂²×C₁₁	1	1	yes	characteristic
88	C₄³	C₂²×C₁₁	1	1	yes	characteristic
89	#341	C₂²×C₁₁	1	4	yes	—
90	#339	C₂²×C₁₁	1	8	yes	—
91	#336	C₂²×C₁₁	1	4	yes	—
92	C₂²×C₁₁	—	2	2	no	—
93	C₂²×C₁₁	C₂×C₄×D₄	1	1	yes	characteristic
94	C₂²×C₁₁	#541	1	2	yes	—
95	C₄×C₁₁	—	2	4	no	—
96	C₄×C₁₁	—	4	4	no	—
97	C₄×C₁₁	—	4	8	no	—
98	C₄×C₁₁	#519	1	2	yes	—
99	C₄×C₁₁	#536	1	2	yes	—
100	C₂×M₁₆	C₂³×C₁₁	1	4	yes	—
101	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
102	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
103	C₄⋊Q₈	C₂×C₄×C₁₁	1	4	yes	—
104	#125	C₂×C₄×C₁₁	1	4	yes	—
105	C₂²⋊Q₈	—	2	4	no	—
106	C₄×Q₈	—	2	4	no	—
107	#117	C₂³×C₁₁	1	4	yes	—
108	C₂×C₄²	—	2	2	no	—
109	C₂×C₄²	C₂³×C₁₁	1	2	yes	—
110	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
111	#107	C₂×C₄×C₁₁	1	8	yes	—
112	#106	C₂×C₄×C₁₁	1	8	yes	—
113	C₄⋊C₈	—	2	8	no	—
114	C₄⋊C₈	—	2	4	no	—
115	#97	—	2	4	no	—
116	#97	C₂×C₄×C₁₁	1	4	yes	—
117	#97	D₄×C₁₁	1	4	yes	—
118	C₄×C₈	—	2	4	no	—
119	C₂×C₁₁	—	2	2	no	—
120	C₂×C₁₁	#2327	1	1	yes	characteristic
121	C₂×C₁₁	#2956	1	2	yes	—
122	C₂×Q₈	—	2	4	no	—
123	C₂²×C₄	—	2	2	no	—
124	C₂²×C₄	C₁₁×#41	1	2	yes	—
125	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
126	M₁₆	—	2	8	no	—
127	C₂×C₈	—	2	4	no	—
128	C₂×C₈	—	2	4	no	—
129	C₂×C₈	—	2	4	no	—
130	C₂×C₈	C₂²×C₄×C₁₁	1	4	yes	—
131	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	—
132	C₄⋊C₄	—	2	8	no	—
133	C₄⋊C₄	—	2	4	no	—
134	C₄⋊C₄	C₂²×C₄×C₁₁	1	8	yes	—
135	C₂²⋊C₄	—	2	4	no	—
136	C₄²	—	2	4	no	—
137	C₄²	—	2	4	no	—
138	C₄²	—	4	4	no	—
139	C₄²	C₂²×C₄×C₁₁	1	2	yes	—
140	C₄²	C₂×D₄×C₁₁	1	2	yes	—
141	C₁₁	#22259	1	1	yes	characteristic, direct product factor, Sylow
142	C₂³	C₂×C₁₁×#41	1	1	yes	characteristic
143	Q₈	—	8	4	no	—
144	C₂×C₄	—	2	4	no	—
145	C₂×C₄	—	2	8	no	—
146	C₂×C₄	—	4	2	no	—
147	C₂×C₄	—	4	2	no	—
148	C₂×C₄	—	4	2	no	—
149	C₂×C₄	C₄×D₄×C₁₁	1	4	yes	—
150	C₂×C₄	C₂³×C₄×C₁₁	1	1	yes	characteristic
151	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
152	C₂×C₄	C₁₁×2₋¹⁺⁴	1	4	yes	—
153	C₈	—	2	4	no	—
154	C₈	—	2	4	no	—
155	C₈	—	4	4	no	—
156	C₂²	—	2	2	no	—
157	C₂²	C₂×C₄×D₄×C₁₁	1	1	yes	characteristic
158	C₂²	C₁₁×#541	1	2	yes	—
159	C₄	—	2	4	no	—
160	C₄	—	4	4	no	—
161	C₄	—	4	8	no	—
162	C₄	C₁₁×#519	1	2	yes	—
163	C₄	C₁₁×#536	1	2	yes	—
164	C₂	—	2	2	no	—
165	C₂	C₁₁×#2327	1	1	yes	characteristic
166	C₂	C₁₁×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₁
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₁
socle	C₂²×C₁₁	C₂×C₄×D₄
prime radical	C₂³×C₁₁	C₂×#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₁₁×#97 ◁ G

Complements

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

N	H ≅ G/N	type
8. C₁₁×#501	C₄	semidirect
39. #22259	C₁₁	direct (N × H)
80. #501	C₄×C₁₁	semidirect
141. C₁₁	#22259	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×#3162	2
C₁₁×#2961	2
C₁₁×#1994	2
C₁₁×#1922	2
C₁₁×#1838	2
C₁₁×#1745	2
#22259	11

Subgroups — C11×#22259 #14599452

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#22259 #14599452