Subgroups — #14671833

Order 2816.

274 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622144	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622142	C₂	1	1	yes	maximal, characteristic
3	#13069401	C₂	1	2	yes	maximal
4	#13066725	C₂	1	2	yes	maximal
5	C₁₁×#2108	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×M₃₂	C₂²	1	1	yes	characteristic
7	C₂²×C₁₁×C₁₆	C₂²	1	1	yes	characteristic
8	C₁₁×#405	C₂²	1	1	yes	characteristic
9	C₂×#66883	C₂²	1	2	yes	—
10	C₂×#66882	C₂²	1	2	yes	—
11	#10622608	—	2	2	no	—
12	C₁₁×#346	—	2	1	no	—
13	C₄×C₁₁×C₁₆	—	2	1	no	—
14	#10622192	—	2	2	no	—
15	#10622144	C₄	1	4	yes	complemented
16	#10622142	—	2	1	no	—
17	#10622142	—	2	1	no	—
18	C₂×C₁₁×M₁₆	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
20	C₁₁×#117	D₄	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₁	—	2	2	no	—
22	C₂×#4318	—	2	2	no	—
23	C₁₁×M₃₂	—	2	1	no	—
24	C₁₁×M₃₂	Q₈	1	2	yes	—
25	C₂×C₁₁×C₁₆	—	2	1	no	—
26	C₂×C₁₁×C₁₆	C₂×C₄	1	2	yes	—
27	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
28	C₂×C₁₁×C₁₆	D₄	1	1	yes	characteristic
29	C₂×C₁₁×C₁₆	Q₈	1	2	yes	—
30	C₁₁×#97	—	2	1	no	—
31	C₄×C₈×C₁₁	—	2	1	no	—
32	#66883	—	2	2	no	—
33	#66883	C₂×C₄	1	4	yes	—
34	#66882	—	2	2	no	—
35	#66882	—	2	2	no	—
36	#66872	—	4	2	no	—
37	#66871	—	4	2	no	—
38	#13171	—	11	1	no	maximal, Sylow
39	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
40	C₂²×Dic₁₁	—	4	2	no	—
41	C₁₁×M₁₆	—	2	1	no	—
42	C₁₁×M₁₆	Q₁₆	1	2	yes	—
43	C₂×C₈×C₁₁	—	2	1	no	—
44	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
46	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
47	C₂×C₈×C₁₁	C₂×Q₈	1	1	yes	characteristic
48	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
49	C₂×C₈×C₁₁	#41	1	1	yes	characteristic
50	C₁₁×C₄⋊C₄	D₈	1	1	yes	characteristic
51	C₁₁×C₄⋊C₄	D₈	1	1	yes	characteristic
52	C₁₁×C₂²⋊C₄	—	2	1	no	—
53	C₄²×C₁₁	—	2	1	no	—
54	C₄⋊Dic₁₁	—	4	2	no	—
55	C₄⋊Dic₁₁	—	4	2	no	—
56	#4318	—	2	4	no	—
57	#4318	—	4	2	no	—
58	C₂×C₁₁⋊C₈	—	4	2	no	—
59	C₁₁×C₁₆	—	2	2	no	—
60	C₁₁×C₁₆	C₄⋊C₄	1	2	yes	—
61	C₁₁×C₁₆	C₄⋊C₄	1	2	yes	—
62	C₂×#368	—	11	1	no	—
63	C₂×#366	—	11	1	no	—
64	#2108	D₁₁	1	1	yes	characteristic
65	#1952	—	11	2	no	—
66	#1387	—	11	2	no	—
67	C₂³×C₁₁	#135	1	1	yes	characteristic
68	C₂×C₄×C₁₁	—	2	1	no	—
69	C₂×C₄×C₁₁	—	2	1	no	—
70	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
71	C₂×C₄×C₁₁	#121	1	1	yes	characteristic
72	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
73	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
74	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₁	#135	1	1	yes	characteristic
76	C₂×Dic₁₁	—	8	2	no	—
77	C₂×Dic₁₁	—	16	2	no	—
78	C₈×C₁₁	—	2	2	no	—
79	C₈×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
80	C₈×C₁₁	C₄×Q₈	1	1	yes	characteristic
81	C₈×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
82	C₈×C₁₁	#125	1	1	yes	characteristic
83	C₁₁⋊C₈	—	4	4	no	—
84	C₂×M₃₂	C₂×D₁₁	1	1	yes	characteristic
85	C₂²×C₁₆	C₂×D₁₁	1	1	yes	characteristic
86	C₂×#108	—	11	2	no	—
87	#428	—	22	2	no	—
88	C₂×#107	—	11	2	no	—
89	#405	C₂×D₁₁	1	1	yes	characteristic
90	#368	—	11	4	no	—
91	#366	—	22	1	no	—
92	#366	—	22	1	no	—
93	#346	—	2	1	no	—
94	C₄×C₁₆	—	2	1	no	—
95	#343	—	22	2	no	—
96	C₂²×C₁₁	—	2	1	no	—
97	C₂²×C₁₁	—	2	1	no	—
98	C₂²×C₁₁	C₄×Q₁₆	1	1	yes	characteristic
99	C₂²×C₁₁	#466	1	1	yes	characteristic
100	C₂²×C₁₁	#499	1	1	yes	characteristic
101	C₄×C₁₁	—	4	1	no	—
102	C₄×C₁₁	—	4	1	no	—
103	C₄×C₁₁	#389	1	1	yes	characteristic
104	C₄×C₁₁	C₄×D₈	1	1	yes	characteristic
105	C₄×C₁₁	#467	1	1	yes	characteristic
106	C₄×C₁₁	#500	1	1	yes	characteristic
107	Dic₁₁	—	16	2	no	—
108	C₂×M₁₆	—	22	2	no	—
109	C₂×M₁₆	D₄₄	1	1	yes	characteristic
110	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
111	#117	D₄₄	1	1	yes	characteristic
112	C₂×C₄⋊C₄	—	22	2	no	—
113	M₃₂	—	2	1	no	—
114	M₃₂	Dic₂₂	1	2	yes	—
115	C₂×C₁₆	—	2	1	no	—
116	C₂×C₁₆	Dic₂₂	1	2	yes	—
117	C₂×C₁₆	C₄×D₁₁	1	2	yes	—
118	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
119	C₂×C₁₆	C₂²⋊D₁₁	1	1	yes	characteristic
120	#108	—	11	4	no	—
121	#108	—	22	2	no	—
122	#107	—	22	2	no	—
123	#107	—	22	2	no	—
124	#107	—	44	2	no	—
125	#106	—	44	2	no	—
126	#97	—	2	1	no	—
127	C₄×C₈	—	2	1	no	—
128	C₂×C₁₁	—	2	1	no	—
129	C₂×C₁₁	—	2	1	no	—
130	C₂×C₁₁	#1942	1	1	yes	characteristic
131	C₂×C₁₁	#2221	1	1	yes	characteristic
132	C₂×C₁₁	#2222	1	1	yes	characteristic
133	C₂²×C₄	—	44	2	no	—
134	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
135	M₁₆	—	2	1	no	—
136	M₁₆	—	22	4	no	—
137	M₁₆	—	44	2	no	—
138	M₁₆	Dic₄₄	1	2	yes	—
139	C₂×C₈	—	2	1	no	—
140	C₂×C₈	—	44	2	no	—
141	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
142	C₂×C₈	C₂×Dic₂₂	1	1	yes	characteristic
143	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
144	C₂×C₈	#4339	1	1	yes	characteristic
145	C₂×C₈	#4339	1	1	yes	characteristic
146	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
147	C₄⋊C₄	—	44	2	no	—
148	C₄⋊C₄	—	44	2	no	—
149	C₄⋊C₄	D₈₈	1	1	yes	characteristic
150	C₄⋊C₄	D₈₈	1	1	yes	characteristic
151	C₂²⋊C₄	—	2	1	no	—
152	C₄²	—	2	1	no	—
153	C₁₆	—	2	2	no	—
154	C₁₆	Dic₁₁⋊C₄	1	2	yes	—
155	C₁₆	Dic₁₁⋊C₄	1	2	yes	—
156	C₁₁	#13171	1	1	yes	characteristic, complemented, Sylow
157	C₂³	#66957	1	1	yes	characteristic
158	C₂×C₄	—	2	1	no	—
159	C₂×C₄	—	2	1	no	—
160	C₂×C₄	—	88	2	no	—
161	C₂×C₄	—	176	2	no	—
162	C₂×C₄	#66922	1	1	yes	characteristic
163	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
164	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
165	C₂×C₄	#66957	1	1	yes	characteristic
166	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
167	C₂×C₄	#66983	1	1	yes	characteristic
168	C₈	—	2	2	no	—
169	C₈	—	44	4	no	—
170	C₈	C₄×Dic₂₂	1	1	yes	characteristic
171	C₈	#66923	1	1	yes	characteristic
172	C₈	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
173	C₈	#66977	1	1	yes	characteristic
174	C₂²	—	2	1	no	—
175	C₂²	—	2	1	no	—
176	C₂²	#10622296	1	1	yes	characteristic
177	C₂²	C₄×Dic₄₄	1	1	yes	characteristic
178	C₂²	#10622728	1	1	yes	characteristic
179	C₄	—	4	1	no	—
180	C₄	—	4	1	no	—
181	C₄	—	176	2	no	—
182	C₄	#10622295	1	1	yes	characteristic
183	C₄	C₄×D₈₈	1	1	yes	characteristic
184	C₄	#10622541	1	1	yes	characteristic
185	C₄	#10622729	1	1	yes	characteristic
186	C₂	—	2	1	no	—
187	C₂	—	2	1	no	—
188	C₂	#13069349	1	1	yes	characteristic
189	C₂	#13070736	1	1	yes	characteristic
190	C₂	#13070741	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#10622728
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#2108	C₂
socle	C₂²×C₁₁	#466
prime radical	C₂³×C₁₁	#135
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#2108	D₁₁
hypocenter	C₁₁	#13171
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #405 ◁ #2108

Complements

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

N	H ≅ G/N	type
15. #10622144	C₄	semidirect
156. C₁₁	#13171	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622144	2
C₂×#10622142	2
#13069401	2
#13066725	2
C₁₁×#2108	2
#13171	11