Subgroups — Dic₁₁×#347 #14668599

Order 2816.

418 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622104	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622150	C₂	1	2	yes	maximal
3	M₃₂×Dic₁₁	C₂	1	2	yes	maximal
4	#97×Dic₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×#347	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
7	C₂×C₁₁×#97	C₂²	1	1	yes	characteristic
8	C₂×#66879	C₄	1	1	yes	characteristic
9	C₂×#66879	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₁	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₁	C₂²	1	1	yes	characteristic
12	C₂×#66876	C₂²	1	2	yes	—
13	C₄²×Dic₁₁	C₄	1	1	yes	characteristic
14	C₂×#66867	C₄	1	1	yes	characteristic
15	C₁₁×#347	C₄	1	4	yes	complemented
16	#10622150	C₄	1	8	yes	complemented
17	#10622140	C₄	1	4	yes	complemented
18	C₁₆×Dic₁₁	C₄	1	4	yes	complemented
19	#10622104	C₄	1	4	yes	complemented
20	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₁	—	2	2	no	—
24	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
28	C₁₁×M₃₂	C₂×C₄	1	4	yes	—
29	C₁₁×M₃₂	C₂×C₄	1	4	yes	—
30	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
31	C₁₁×#97	C₂×C₄	1	2	yes	—
32	C₁₁×#97	C₂×C₄	1	2	yes	—
33	#66879	—	2	2	no	—
34	#66879	C₂×C₄	1	4	yes	—
35	C₈×Dic₁₁	—	2	2	no	—
36	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
37	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
38	#66876	C₂×C₄	1	4	yes	—
39	#66876	C₂×C₄	1	4	yes	—
40	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
41	#66867	—	2	2	no	—
42	C₄×#347	—	11	1	no	maximal, Sylow
43	C₂²×C₄×C₁₁	—	2	1	no	—
44	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₁₁	—	2	1	no	—
46	C₂²×Dic₁₁	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₁	—	2	1	no	—
48	C₂×C₈×C₁₁	—	2	1	no	—
49	C₂×C₈×C₁₁	C₄²	1	2	yes	—
50	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
51	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
53	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₁	—	2	1	no	—
55	C₄²×C₁₁	C₄²	1	2	yes	—
56	C₄×Dic₁₁	—	2	1	no	—
57	C₄×Dic₁₁	—	4	4	no	—
58	C₄×Dic₁₁	C₄²	1	2	yes	—
59	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
60	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
61	C₄×Dic₁₁	M₁₆	1	2	yes	—
62	C₂×C₁₁⋊C₈	—	2	1	no	—
63	C₂×C₁₁⋊C₈	—	2	1	no	—
64	C₂×C₁₁⋊C₈	C₄²	1	2	yes	—
65	C₂×C₁₁⋊C₈	C₄²	1	2	yes	—
66	C₂×C₁₁⋊C₈	M₁₆	1	2	yes	—
67	C₂×C₁₁⋊C₈	M₁₆	1	2	yes	—
68	C₁₁×C₁₆	C₄²	1	8	yes	complemented
69	C₁₁⋊C₁₆	C₄²	1	8	yes	complemented
70	C₂×#347	—	11	2	no	—
71	C₂×#347	—	11	1	no	—
72	C₂×#347	D₁₁	1	1	yes	characteristic
73	C₄×M₃₂	—	11	2	no	—
74	C₄×#97	—	11	1	no	—
75	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
76	C₂×C₄×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	—	4	2	no	—
78	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
84	C₂×Dic₁₁	—	2	4	no	—
85	C₂×Dic₁₁	—	2	2	no	—
86	C₂×Dic₁₁	—	4	2	no	—
87	C₂×Dic₁₁	#97	1	2	yes	—
88	C₂×Dic₁₁	#97	1	2	yes	—
89	C₈×C₁₁	—	2	2	no	—
90	C₈×C₁₁	C₂×C₄²	1	2	yes	—
91	C₈×C₁₁	C₂×C₄²	1	2	yes	—
92	C₁₁⋊C₈	—	2	2	no	—
93	C₁₁⋊C₈	#97	1	4	yes	—
94	C₂×M₃₂	—	11	2	no	—
95	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
96	C₂×#97	—	11	1	no	—
97	C₂×#97	—	11	1	no	—
98	C₂×#97	—	11	1	no	—
99	C₂×#97	C₂×D₁₁	1	1	yes	characteristic
100	C₂×C₄×C₈	—	11	1	no	—
101	C₂×C₄×C₈	—	11	1	no	—
102	C₄³	—	11	1	no	—
103	#347	—	11	8	no	—
104	#347	—	11	4	no	—
105	#347	Dic₁₁	1	4	yes	direct product factor
106	#346	—	11	4	no	—
107	C₄×C₁₆	—	11	4	no	—
108	C₂²×C₁₁	—	2	2	no	—
109	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
110	C₂²×C₁₁	C₄×M₁₆	1	1	yes	characteristic
111	C₂²×C₁₁	C₄×M₁₆	1	1	yes	characteristic
112	C₄×C₁₁	—	4	2	no	—
113	C₄×C₁₁	C₄³	1	1	yes	characteristic
114	C₄×C₁₁	C₂×#97	1	1	yes	characteristic
115	C₄×C₁₁	C₄×M₁₆	1	1	yes	characteristic
116	C₄×C₁₁	C₄×M₁₆	1	1	yes	characteristic
117	Dic₁₁	—	2	2	no	—
118	Dic₁₁	—	4	2	no	—
119	Dic₁₁	#347	1	4	yes	direct product factor
120	C₂²×C₈	—	11	1	no	—
121	C₂²×C₈	—	11	1	no	—
122	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
123	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
124	C₂×C₄²	—	11	1	no	—
125	C₂×C₄²	—	11	1	no	—
126	C₂×C₄²	—	22	2	no	—
127	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
128	M₃₂	—	11	4	no	—
129	M₃₂	—	11	4	no	—
130	M₃₂	C₄×D₁₁	1	4	yes	—
131	M₃₂	C₂×Dic₁₁	1	4	yes	—
132	C₂×C₁₆	—	11	4	no	—
133	C₂×C₁₆	C₄×D₁₁	1	4	yes	—
134	#97	—	11	4	no	—
135	#97	—	22	2	no	—
136	#97	—	22	2	no	—
137	#97	C₄×D₁₁	1	2	yes	—
138	#97	C₂×Dic₁₁	1	2	yes	—
139	C₄×C₈	—	11	2	no	—
140	C₄×C₈	—	11	2	no	—
141	C₄×C₈	—	22	2	no	—
142	C₂×C₁₁	—	2	1	no	—
143	C₂×C₁₁	—	2	1	no	—
144	C₂×C₁₁	C₄×#97	1	1	yes	characteristic
145	C₂×C₁₁	C₂×#347	1	2	yes	—
146	C₂²×C₄	—	2	1	no	—
147	C₂²×C₄	—	11	2	no	—
148	C₂²×C₄	—	22	1	no	—
149	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
150	C₂×C₈	—	2	1	no	—
151	C₂×C₈	—	2	1	no	—
152	C₂×C₈	—	11	2	no	—
153	C₂×C₈	—	11	2	no	—
154	C₂×C₈	—	11	2	no	—
155	C₂×C₈	—	11	2	no	—
156	C₂×C₈	—	22	1	no	—
157	C₂×C₈	—	22	1	no	—
158	C₂×C₈	C₄×Dic₁₁	1	2	yes	—
159	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
160	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
161	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
162	C₂×C₈	C₂²×Dic₁₁	1	1	yes	characteristic
163	C₄²	—	2	1	no	—
164	C₄²	—	11	1	no	—
165	C₄²	—	11	1	no	—
166	C₄²	—	11	2	no	—
167	C₄²	—	11	2	no	—
168	C₄²	—	22	1	no	—
169	C₄²	—	44	4	no	—
170	C₄²	C₄×Dic₁₁	1	2	yes	—
171	C₁₆	—	11	8	no	—
172	C₁₆	C₄×Dic₁₁	1	8	yes	complemented
173	C₁₁	C₄×#347	1	1	yes	characteristic, complemented, Sylow
174	C₂³	M₁₆×D₁₁	1	1	yes	characteristic
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	4	2	no	—
177	C₂×C₄	—	11	2	no	—
178	C₂×C₄	—	11	2	no	—
179	C₂×C₄	—	22	4	no	—
180	C₂×C₄	—	22	2	no	—
181	C₂×C₄	—	44	2	no	—
182	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
183	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
184	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
185	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
186	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
187	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
188	C₈	—	2	2	no	—
189	C₈	—	11	4	no	—
190	C₈	—	22	2	no	—
191	C₈	C₄²×D₁₁	1	2	yes	—
192	C₈	C₂×C₄×Dic₁₁	1	2	yes	—
193	C₂²	—	2	2	no	—
194	C₂²	D₁₁×#97	1	1	yes	characteristic
195	C₂²	#10622320	1	1	yes	characteristic
196	C₂²	M₁₆×Dic₁₁	1	1	yes	characteristic
197	C₄	—	4	2	no	—
198	C₄	—	11	4	no	—
199	C₄	—	22	2	no	—
200	C₄	—	44	2	no	—
201	C₄	D₁₁×#97	1	1	yes	characteristic
202	C₄	#10622320	1	1	yes	characteristic
203	C₄	C₄²×Dic₁₁	1	1	yes	characteristic
204	C₄	M₁₆×Dic₁₁	1	1	yes	characteristic
205	C₂	—	2	1	no	—
206	C₂	—	2	1	no	—
207	C₂	#97×Dic₁₁	1	1	yes	characteristic
208	C₂	D₁₁×#347	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₁
commutator	C₄×C₁₁	C₄³
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#347	C₂
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#347	D₁₁
hypocenter	C₁₁	C₄×#347
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#347

Complements

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

N	H ≅ G/N	type
15. C₁₁×#347	C₄	semidirect
16. #10622150	C₄	semidirect
17. #10622140	C₄	semidirect
18. C₁₆×Dic₁₁	C₄	semidirect
19. #10622104	C₄	semidirect
68. C₁₁×C₁₆	C₄²	semidirect
69. C₁₁⋊C₁₆	C₄²	semidirect
105. #347	Dic₁₁	direct (N × H)
119. Dic₁₁	#347	direct (N × H)
172. C₁₆	C₄×Dic₁₁	semidirect
173. C₁₁	C₄×#347	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#10622104	2
C₂×#10622150	2
M₃₂×Dic₁₁	2
#97×Dic₁₁	2
C₂×C₁₁×#347	2
C₄×#347	11

Subgroups — Dic11×#347 #14668599

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₁₁×#347 #14668599