Subgroups — #14668783

Order 2816.

354 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₃₂×Dic₁₁	C₂	1	2	yes	maximal
2	#97×Dic₁₁	C₂	1	1	yes	maximal, characteristic
3	#13066696	C₂	1	1	yes	maximal, characteristic
4	#13066695	C₂	1	2	yes	maximal
5	C₁₁×#1375	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	#10622140	C₄	1	4	yes	complemented
16	C₁₆×Dic₁₁	C₄	1	4	yes	complemented
17	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₁	—	2	2	no	—
21	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄×Dic₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₁₁⋊C₈	C₂×C₄	1	1	yes	characteristic
25	C₁₁×M₃₂	—	2	2	no	—
26	C₁₁×M₃₂	—	2	2	no	—
27	C₂×C₁₁×C₁₆	C₂×C₄	1	4	yes	—
28	C₁₁×#97	—	2	2	no	—
29	#66879	—	2	1	no	—
30	#66879	—	2	1	no	—
31	#66879	C₈	1	4	yes	—
32	C₈×Dic₁₁	—	2	2	no	—
33	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
34	C₈×Dic₁₁	C₂×C₄	1	2	yes	—
35	#66876	—	2	2	no	—
36	#66876	—	2	2	no	—
37	C₂×C₁₁⋊C₁₆	C₂×C₄	1	4	yes	—
38	#66867	C₈	1	4	yes	—
39	#12594	—	11	1	no	maximal, Sylow
40	C₂²×C₄×C₁₁	—	2	1	no	—
41	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
42	C₂²×Dic₁₁	—	2	1	no	—
43	C₂²×Dic₁₁	M₁₆	1	2	yes	—
44	C₂×C₈×C₁₁	—	2	1	no	—
45	C₂×C₈×C₁₁	—	2	1	no	—
46	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
47	C₂×C₈×C₁₁	C₂²×C₄	1	2	yes	—
48	C₂×C₈×C₁₁	#41	1	2	yes	—
49	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
50	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
51	C₄²×C₁₁	—	2	1	no	—
52	C₄²×C₁₁	C₂×C₈	1	2	yes	—
53	C₄×Dic₁₁	—	2	1	no	—
54	C₄×Dic₁₁	—	4	4	no	—
55	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
56	C₄×Dic₁₁	C₄²	1	1	yes	characteristic
57	C₄×Dic₁₁	C₂×C₈	1	2	yes	—
58	C₄×Dic₁₁	M₁₆	1	2	yes	—
59	C₂×C₁₁⋊C₈	—	2	1	no	—
60	C₂×C₁₁⋊C₈	—	2	1	no	—
61	C₂×C₁₁⋊C₈	C₄²	1	2	yes	—
62	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	—
63	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	—
64	C₂×C₁₁⋊C₈	C₂×C₈	1	2	yes	—
65	C₁₁×C₁₆	—	2	4	no	—
66	C₁₁⋊C₁₆	—	2	4	no	—
67	C₄×M₃₂	—	11	2	no	—
68	C₄×#97	—	11	1	no	—
69	#1375	—	11	2	no	—
70	#1375	—	11	1	no	—
71	#1375	D₁₁	1	1	yes	characteristic
72	C₂³×C₁₁	C₂×M₁₆	1	1	yes	characteristic
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	4	2	no	—
75	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
76	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
77	C₂×C₄×C₁₁	#117	1	1	yes	characteristic
78	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
81	C₂×Dic₁₁	—	2	4	no	—
82	C₂×Dic₁₁	—	2	2	no	—
83	C₂×Dic₁₁	—	4	2	no	—
84	C₂×Dic₁₁	#97	1	2	yes	—
85	C₂×Dic₁₁	#97	1	2	yes	—
86	C₈×C₁₁	—	2	2	no	—
87	C₈×C₁₁	#117	1	2	yes	—
88	C₈×C₁₁	#117	1	2	yes	—
89	C₁₁⋊C₈	—	2	2	no	—
90	C₁₁⋊C₈	C₄×C₈	1	4	yes	—
91	C₂×M₃₂	—	11	2	no	—
92	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
93	C₂×#97	—	11	1	no	—
94	C₂×#97	—	11	1	no	—
95	C₂×#97	—	11	1	no	—
96	C₂×#97	C₂×D₁₁	1	1	yes	characteristic
97	C₂×C₄×C₈	—	11	1	no	—
98	C₂×C₄×C₈	—	11	1	no	—
99	C₄³	—	11	1	no	—
100	#346	—	11	4	no	—
101	C₄×C₁₆	—	11	4	no	—
102	C₂²×C₁₁	—	2	2	no	—
103	C₂²×C₁₁	C₂×#97	1	1	yes	characteristic
104	C₂²×C₁₁	#431	1	1	yes	characteristic
105	C₂²×C₁₁	#431	1	1	yes	characteristic
106	C₄×C₁₁	—	4	2	no	—
107	C₄×C₁₁	#376	1	1	yes	characteristic
108	C₄×C₁₁	C₂×C₄×C₈	1	1	yes	characteristic
109	C₄×C₁₁	#431	1	1	yes	characteristic
110	C₄×C₁₁	#431	1	1	yes	characteristic
111	Dic₁₁	—	2	2	no	—
112	Dic₁₁	—	4	2	no	—
113	Dic₁₁	#347	1	4	yes	—
114	C₂²×C₈	—	11	1	no	—
115	C₂²×C₈	—	11	1	no	—
116	C₂²×C₈	C₄×D₁₁	1	1	yes	characteristic
117	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
118	C₂×C₄²	—	11	1	no	—
119	C₂×C₄²	—	11	1	no	—
120	C₂×C₄²	—	22	2	no	—
121	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
122	M₃₂	—	2	2	no	—
123	M₃₂	—	2	2	no	—
124	M₃₂	—	22	2	no	—
125	M₃₂	—	22	2	no	—
126	C₂×C₁₆	—	11	4	no	—
127	C₂×C₁₆	C₄×D₁₁	1	4	yes	—
128	#97	—	2	2	no	—
129	#97	—	11	4	no	—
130	#97	—	11	4	no	—
131	#97	—	22	1	no	—
132	#97	—	22	1	no	—
133	C₄×C₈	—	11	2	no	—
134	C₄×C₈	—	11	2	no	—
135	C₄×C₈	—	22	2	no	—
136	C₂×C₁₁	—	2	1	no	—
137	C₂×C₁₁	—	2	1	no	—
138	C₂×C₁₁	#1744	1	1	yes	characteristic
139	C₂×C₁₁	C₂×#347	1	2	yes	—
140	C₂²×C₄	—	2	1	no	—
141	C₂²×C₄	—	11	2	no	—
142	C₂²×C₄	—	22	1	no	—
143	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	—	2	1	no	—
146	C₂×C₈	—	11	2	no	—
147	C₂×C₈	—	11	2	no	—
148	C₂×C₈	—	11	2	no	—
149	C₂×C₈	—	11	2	no	—
150	C₂×C₈	—	22	1	no	—
151	C₂×C₈	—	22	1	no	—
152	C₂×C₈	C₈×D₁₁	1	2	yes	—
153	C₂×C₈	C₂×C₄×D₁₁	1	2	yes	—
154	C₂×C₈	#4341	1	1	yes	characteristic
155	C₂×C₈	#4341	1	2	yes	—
156	C₂×C₈	#4343	1	1	yes	characteristic
157	C₄²	—	2	1	no	—
158	C₄²	—	11	1	no	—
159	C₄²	—	11	1	no	—
160	C₄²	—	11	2	no	—
161	C₄²	—	11	2	no	—
162	C₄²	—	22	1	no	—
163	C₄²	—	44	4	no	—
164	C₄²	C₈×D₁₁	1	2	yes	—
165	C₁₆	—	2	4	no	—
166	C₁₆	—	22	4	no	—
167	C₁₁	#12594	1	1	yes	characteristic, complemented, Sylow
168	C₂³	M₁₆×D₁₁	1	1	yes	characteristic
169	C₂×C₄	—	2	2	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	11	2	no	—
172	C₂×C₄	—	11	2	no	—
173	C₂×C₄	—	22	4	no	—
174	C₂×C₄	—	22	2	no	—
175	C₂×C₄	—	44	2	no	—
176	C₂×C₄	C₄²×D₁₁	1	1	yes	characteristic
177	C₂×C₄	#66930	1	1	yes	characteristic
178	C₂×C₄	#66945	1	1	yes	characteristic
179	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
180	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
181	C₂×C₄	M₁₆×D₁₁	1	1	yes	characteristic
182	C₈	—	2	2	no	—
183	C₈	—	11	4	no	—
184	C₈	—	22	2	no	—
185	C₈	#66930	1	2	yes	—
186	C₈	#66945	1	2	yes	—
187	C₂²	—	2	2	no	—
188	C₂²	D₁₁×#97	1	1	yes	characteristic
189	C₂²	#10622331	1	1	yes	characteristic
190	C₂²	#10622446	1	1	yes	characteristic
191	C₄	—	4	2	no	—
192	C₄	—	11	4	no	—
193	C₄	—	22	2	no	—
194	C₄	—	44	2	no	—
195	C₄	#10622261	1	1	yes	characteristic
196	C₄	C₄×C₈×D₁₁	1	1	yes	characteristic
197	C₄	#10622331	1	1	yes	characteristic
198	C₄	#10622446	1	1	yes	characteristic
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	#13068360	1	1	yes	characteristic
202	C₂	D₁₁×#347	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₁
commutator	C₄×C₁₁	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1375	C₂
socle	C₂²×C₁₁	C₂×#97
prime radical	C₂³×C₁₁	C₂×M₁₆
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1375	D₁₁
hypocenter	C₁₁	#12594
LCS	G ▷ C₄×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂×C₄ ◁ #1375

Complements

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

N	H ≅ G/N	type
15. #10622140	C₄	semidirect
16. C₁₆×Dic₁₁	C₄	semidirect
167. C₁₁	#12594	semidirect

Maximal subgroups

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

subgroup	index
M₃₂×Dic₁₁	2
#97×Dic₁₁	2
#13066696	2
#13066695	2
C₁₁×#1375	2
#12594	11