Subgroups — C₁₁×#3229 #13066067

Order 1408.

360 conjugacy classes of subgroups.

The subgroup lattice has 184 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
2	C₂×C₁₁×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₁₁×#498	C₂	1	2	yes	maximal, complemented
4	C₁₁×#487	C₂	1	2	yes	maximal, complemented
5	C₁₁×#483	C₂	1	4	yes	maximal
6	C₁₁×#475	C₂	1	4	yes	maximal, complemented
7	C₁₁×#431	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈×C₁₁	—	2	1	no	—
9	C₁₁×C₄⋊Q₈	—	2	1	no	—
10	C₁₁×C₄⋊Q₈	—	2	1	no	—
11	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₁₁×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
14	C₁₁×C₄⋊Q₈	C₂²	1	2	yes	—
15	C₁₁×#125	—	2	1	no	—
16	C₁₁×C₂²⋊Q₈	—	2	1	no	—
17	C₁₁×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₄×Q₈×C₁₁	—	2	1	no	—
19	C₄×Q₈×C₁₁	C₂²	1	2	yes	—
20	C₁₁×#117	—	2	1	no	—
21	C₂×C₁₁×C₄⋊C₄	—	2	1	no	—
22	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
24	C₁₁×#106	C₂²	1	8	yes	—
25	C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
26	C₁₁×#103	C₂²	1	8	yes	—
27	C₁₁×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₄×C₈×C₁₁	C₂²	1	2	yes	—
29	C₂×Q₈×C₁₁	—	2	1	no	—
30	C₂×Q₈×C₁₁	—	2	2	no	—
31	C₂×Q₈×C₁₁	—	2	2	no	—
32	C₂×Q₈×C₁₁	—	4	4	no	—
33	C₂×Q₈×C₁₁	C₂³	1	2	yes	—
34	C₂²×C₄×C₁₁	—	2	2	no	—
35	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
36	C₂²×C₄×C₁₁	D₄	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
38	C₂×C₈×C₁₁	C₂³	1	4	yes	—
39	C₁₁×C₄⋊C₄	—	2	2	no	—
40	C₁₁×C₄⋊C₄	—	2	2	no	—
41	C₁₁×C₄⋊C₄	—	2	2	no	—
42	C₁₁×C₄⋊C₄	—	2	1	no	—
43	C₁₁×C₄⋊C₄	—	2	1	no	—
44	C₁₁×C₄⋊C₄	—	2	1	no	—
45	C₁₁×C₄⋊C₄	—	2	2	no	—
46	C₁₁×C₄⋊C₄	—	2	2	no	—
47	C₁₁×C₄⋊C₄	C₂³	1	4	yes	—
48	C₁₁×C₄⋊C₄	C₂³	1	2	yes	—
49	C₁₁×C₂²⋊C₄	—	2	2	no	—
50	C₄²×C₁₁	—	2	2	no	—
51	C₄²×C₁₁	D₄	1	1	yes	characteristic
52	C₄²×C₁₁	D₄	1	1	yes	characteristic
53	C₄²×C₁₁	C₂³	1	1	yes	characteristic
54	C₄²×C₁₁	C₂³	1	1	yes	characteristic
55	#3229	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂³×C₁₁	C₂×D₄	1	1	yes	characteristic
57	Q₈×C₁₁	—	2	4	no	—
58	Q₈×C₁₁	—	4	4	no	—
59	Q₈×C₁₁	—	4	4	no	—
60	Q₈×C₁₁	—	4	2	no	—
61	C₂×C₄×C₁₁	—	2	2	no	—
62	C₂×C₄×C₁₁	—	2	2	no	—
63	C₂×C₄×C₁₁	—	2	2	no	—
64	C₂×C₄×C₁₁	—	2	2	no	—
65	C₂×C₄×C₁₁	—	2	4	no	—
66	C₂×C₄×C₁₁	—	4	4	no	—
67	C₂×C₄×C₁₁	SD₁₆	1	4	yes	—
68	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
70	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
74	C₈×C₁₁	—	2	4	no	—
75	#533	C₂×C₁₁	1	1	yes	characteristic
76	C₂×C₄⋊Q₈	C₂×C₁₁	1	1	yes	characteristic
77	#498	C₂×C₁₁	1	2	yes	complemented
78	#487	C₂×C₁₁	1	2	yes	complemented
79	#483	C₂×C₁₁	1	4	yes	—
80	#475	C₂×C₁₁	1	4	yes	complemented
81	#431	C₂×C₁₁	1	1	yes	characteristic
82	C₂²×C₁₁	—	2	1	no	—
83	C₂²×C₁₁	—	2	1	no	—
84	C₂²×C₁₁	C₂×SD₁₆	1	2	yes	—
85	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
86	C₄×C₁₁	—	2	1	no	—
87	C₄×C₁₁	—	2	1	no	—
88	C₄×C₁₁	—	4	2	no	—
89	C₄×C₁₁	—	4	4	no	—
90	C₄×C₁₁	—	4	2	no	—
91	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
92	C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
93	C₄×C₁₁	#137	1	2	yes	—
94	C₄×C₁₁	2₋¹⁺⁴	1	2	yes	—
95	C₂²×Q₈	—	2	1	no	—
96	C₄⋊Q₈	—	2	1	no	—
97	C₄⋊Q₈	—	2	1	no	—
98	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
99	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
100	C₄⋊Q₈	C₂²×C₁₁	1	2	yes	—
101	C₄⋊Q₈	C₂²×C₁₁	1	1	yes	characteristic
102	#125	—	2	1	no	—
103	C₂²⋊Q₈	—	2	1	no	—
104	C₂²⋊Q₈	C₂²×C₁₁	1	2	yes	—
105	C₄×Q₈	—	2	1	no	—
106	C₄×Q₈	C₂²×C₁₁	1	2	yes	—
107	#117	—	2	1	no	—
108	C₂×C₄⋊C₄	—	2	1	no	—
109	C₂×C₄⋊C₄	C₂²×C₁₁	1	2	yes	—
110	C₂×C₄²	C₂²×C₁₁	1	1	yes	characteristic
111	#106	C₂²×C₁₁	1	8	yes	—
112	C₄⋊C₈	C₂²×C₁₁	1	2	yes	—
113	#103	C₂²×C₁₁	1	8	yes	—
114	C₂²⋊C₈	C₂²×C₁₁	1	2	yes	—
115	C₄×C₈	C₂²×C₁₁	1	2	yes	—
116	C₂×C₁₁	—	2	2	no	—
117	C₂×C₁₁	#536	1	1	yes	characteristic
118	C₂×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
119	C₂×C₁₁	C₂×#137	1	1	yes	characteristic
120	C₂×Q₈	—	2	1	no	—
121	C₂×Q₈	—	2	2	no	—
122	C₂×Q₈	—	2	2	no	—
123	C₂×Q₈	—	4	4	no	—
124	C₂×Q₈	C₂³×C₁₁	1	2	yes	—
125	C₂²×C₄	—	2	2	no	—
126	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
127	C₂²×C₄	D₄×C₁₁	1	1	yes	characteristic
128	C₂²×C₄	C₂³×C₁₁	1	1	yes	characteristic
129	C₂×C₈	C₂³×C₁₁	1	4	yes	—
130	C₄⋊C₄	—	2	2	no	—
131	C₄⋊C₄	—	2	2	no	—
132	C₄⋊C₄	—	2	2	no	—
133	C₄⋊C₄	—	2	1	no	—
134	C₄⋊C₄	—	2	1	no	—
135	C₄⋊C₄	—	2	1	no	—
136	C₄⋊C₄	—	2	2	no	—
137	C₄⋊C₄	—	2	2	no	—
138	C₄⋊C₄	C₂³×C₁₁	1	4	yes	—
139	C₄⋊C₄	C₂³×C₁₁	1	2	yes	—
140	C₂²⋊C₄	—	2	2	no	—
141	C₄²	—	2	2	no	—
142	C₄²	D₄×C₁₁	1	1	yes	characteristic
143	C₄²	D₄×C₁₁	1	1	yes	characteristic
144	C₄²	C₂³×C₁₁	1	1	yes	characteristic
145	C₄²	C₂³×C₁₁	1	1	yes	characteristic
146	C₁₁	#3229	1	1	yes	characteristic, direct product factor, Sylow
147	C₂³	C₂×D₄×C₁₁	1	1	yes	characteristic
148	Q₈	—	2	4	no	—
149	Q₈	—	4	4	no	—
150	Q₈	—	4	4	no	—
151	Q₈	—	4	2	no	—
152	C₂×C₄	—	2	2	no	—
153	C₂×C₄	—	2	2	no	—
154	C₂×C₄	—	2	2	no	—
155	C₂×C₄	—	2	2	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	4	4	no	—
158	C₂×C₄	C₁₁×SD₁₆	1	4	yes	—
159	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
160	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
161	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
162	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
163	C₂×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
164	C₂×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
165	C₈	—	2	4	no	—
166	C₂²	—	2	1	no	—
167	C₂²	—	2	1	no	—
168	C₂²	C₂×C₁₁×SD₁₆	1	2	yes	—
169	C₂²	C₂²×D₄×C₁₁	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	1	no	—
172	C₄	—	4	2	no	—
173	C₄	—	4	4	no	—
174	C₄	—	4	2	no	—
175	C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
176	C₄	C₂×C₁₁×SD₁₆	1	2	yes	—
177	C₄	C₁₁×#137	1	2	yes	—
178	C₄	C₁₁×2₋¹⁺⁴	1	2	yes	—
179	C₂	—	2	2	no	—
180	C₂	C₁₁×#536	1	1	yes	characteristic
181	C₂	C₂²×C₁₁×SD₁₆	1	1	yes	characteristic
182	C₂	C₂×C₁₁×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₁
prime radical	C₂³×C₁₁	C₂×D₄
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
3. C₁₁×#498	C₂	semidirect
4. C₁₁×#487	C₂	semidirect
6. C₁₁×#475	C₂	semidirect
55. #3229	C₁₁	direct (N × H)
77. #498	C₂×C₁₁	semidirect
78. #487	C₂×C₁₁	semidirect
80. #475	C₂×C₁₁	semidirect
146. C₁₁	#3229	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×#533	2
C₂×C₁₁×C₄⋊Q₈	2
C₁₁×#498	2
C₁₁×#487	2
C₁₁×#483	2
C₁₁×#475	2
C₁₁×#431	2
#3229	11

Subgroups — C11×#3229 #13066067

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#3229 #13066067