Subgroups — #14653146

Order 2816.

394 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	#13079130	C₂	1	1	yes	maximal, characteristic
2	#13067179	C₂	1	4	yes	maximal
3	#13066899	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1846	C₂	1	1	yes	maximal, characteristic
5	#10623001	C₂²	1	2	yes	—
6	C₂×C₁₁×#107	—	2	1	no	—
7	C₂×C₁₁×#106	—	2	1	no	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₁₁×#382	C₂²	1	2	yes	—
10	#10622719	—	2	1	no	—
11	#10622719	—	2	1	no	—
12	#10622538	C₂²	1	2	yes	—
13	#10622296	—	2	1	no	—
14	#10622296	—	2	1	no	—
15	#10622295	C₄	1	2	yes	complemented
16	#10622293	C₄	1	2	yes	complemented
17	#10622093	—	2	1	no	—
18	C₈×C₁₁⋊C₈	—	2	1	no	—
19	#10622090	—	2	8	no	—
20	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
22	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	#66979	—	2	2	no	—
25	#66977	—	2	4	no	—
26	#66923	—	2	2	no	—
27	#66922	C₂×C₄	1	4	yes	—
28	C₄×Dic₂₂	—	2	4	no	—
29	C₁₁×#107	—	4	2	no	—
30	C₁₁×#106	—	4	2	no	—
31	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₄×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
34	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
35	C₁₁×#95	—	2	4	no	—
36	C₂²⋊(C₁₁⋊C₈)	D₄	1	4	yes	—
37	#66882	—	2	2	no	—
38	#66882	—	2	2	no	—
39	#66881	—	2	2	no	—
40	#66881	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
42	C₄×C₁₁⋊C₈	—	2	2	no	—
43	#9755	—	11	1	no	maximal, Sylow
44	C₂²×C₄×C₁₁	—	4	2	no	—
45	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
46	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
47	C₂×Dic₂₂	—	2	4	no	—
48	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
53	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
54	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
55	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
56	C₁₁×C₄⋊C₄	—	4	2	no	—
57	C₁₁×C₄⋊C₄	—	4	2	no	—
58	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
60	C₄²×C₁₁	#41	1	2	yes	—
61	C₂²⋊Dic₁₁	—	4	2	no	—
62	C₄⋊Dic₁₁	—	2	4	no	—
63	C₄⋊Dic₁₁	—	2	4	no	—
64	Dic₁₁⋊C₄	—	4	4	no	—
65	C₄×Dic₁₁	—	4	2	no	—
66	C₂×C₁₁⋊C₈	—	2	4	no	—
67	#3160	—	11	1	no	—
68	#1846	D₁₁	1	1	yes	characteristic
69	#1518	—	11	4	no	—
70	#1450	—	11	1	no	—
71	C₂³×C₁₁	#127	1	1	yes	characteristic
72	C₂×C₄×C₁₁	—	4	2	no	—
73	C₂×C₄×C₁₁	—	8	4	no	—
74	C₂×C₄×C₁₁	—	8	2	no	—
75	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
76	C₂×C₄×C₁₁	C₄×D₄	1	2	yes	—
77	C₂×C₄×C₁₁	#121	1	2	yes	—
78	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
83	C₂×Dic₁₁	—	4	4	no	—
84	Dic₂₂	—	8	4	no	—
85	C₈×C₁₁	#103	1	2	yes	—
86	C₈×C₁₁	#103	1	2	yes	—
87	C₈×C₁₁	#103	1	2	yes	—
88	C₈×C₁₁	#103	1	2	yes	—
89	C₁₁⋊C₈	—	4	4	no	—
90	#533	—	11	2	no	—
91	#500	—	11	2	no	—
92	#499	—	22	1	no	—
93	#499	—	22	1	no	—
94	#498	—	11	2	no	—
95	#431	—	11	2	no	—
96	#427	—	22	1	no	—
97	#427	—	22	1	no	—
98	C₂×#107	—	2	1	no	—
99	C₂×#106	—	2	1	no	—
100	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
101	#382	C₂×D₁₁	1	2	yes	—
102	#328	—	22	8	no	—
103	#322	—	22	1	no	—
104	C₈²	—	22	1	no	—
105	C₂²×C₁₁	—	2	2	no	—
106	C₂²×C₁₁	#390	1	1	yes	characteristic
107	C₂²×C₁₁	#492	1	1	yes	characteristic
108	C₂²×C₁₁	#494	1	1	yes	characteristic
109	C₄×C₁₁	—	2	2	no	—
110	C₄×C₁₁	—	2	2	no	—
111	C₄×C₁₁	—	16	2	no	—
112	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
113	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
114	C₄×C₁₁	#487	1	1	yes	characteristic
115	C₄×C₁₁	#487	1	1	yes	characteristic
116	Dic₁₁	—	8	4	no	—
117	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
118	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
119	C₄⋊Q₈	—	11	4	no	—
120	#125	—	22	2	no	—
121	C₂²⋊Q₈	—	22	4	no	—
122	C₄×Q₈	—	22	4	no	—
123	#117	—	22	2	no	—
124	C₂×C₄⋊C₄	—	2	2	no	—
125	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
126	#107	—	4	2	no	—
127	#107	—	22	2	no	—
128	#107	—	22	2	no	—
129	#106	—	4	2	no	—
130	#106	—	22	2	no	—
131	#106	—	22	2	no	—
132	C₄⋊C₈	—	22	2	no	—
133	C₂²⋊C₈	—	11	4	no	—
134	C₄×C₈	—	22	2	no	—
135	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
136	C₄×C₈	C₄×D₁₁	1	1	yes	characteristic
137	C₄×C₈	D₄₄	1	1	yes	characteristic
138	C₄×C₈	D₄₄	1	1	yes	characteristic
139	#95	—	2	4	no	—
140	C₂×C₁₁	—	2	1	no	—
141	C₂×C₁₁	—	2	1	no	—
142	C₂×C₁₁	#1956	1	1	yes	characteristic
143	C₂×C₁₁	#1976	1	2	yes	—
144	C₂×Q₈	—	22	4	no	—
145	C₂²×C₄	—	4	2	no	—
146	C₂²×C₄	D₄×D₁₁	1	2	yes	—
147	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
148	C₂×C₈	—	22	4	no	—
149	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
150	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
151	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
152	C₂×C₈	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
153	C₂×C₈	#4324	1	2	yes	—
154	C₂×C₈	#4324	1	2	yes	—
155	C₂×C₈	#4326	1	2	yes	—
156	C₂×C₈	#4326	1	2	yes	—
157	C₄⋊C₄	—	4	2	no	—
158	C₄⋊C₄	—	4	2	no	—
159	C₄⋊C₄	—	22	4	no	—
160	C₄⋊C₄	—	22	4	no	—
161	C₄⋊C₄	—	44	4	no	—
162	C₂²⋊C₄	—	44	2	no	—
163	C₄²	—	44	2	no	—
164	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
165	C₄²	C₂×D₄₄	1	1	yes	characteristic
166	C₄²	#4343	1	2	yes	—
167	C₁₁	#9755	1	1	yes	characteristic, complemented, Sylow
168	C₂³	#66993	1	1	yes	characteristic
169	Q₈	—	88	4	no	—
170	C₂×C₄	—	4	2	no	—
171	C₂×C₄	—	8	4	no	—
172	C₂×C₄	—	8	2	no	—
173	C₂×C₄	—	44	4	no	—
174	C₂×C₄	#66946	1	2	yes	—
175	C₂×C₄	#66948	1	2	yes	—
176	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
177	C₂×C₄	C₂×#4324	1	1	yes	characteristic
178	C₂×C₄	C₂×#4324	1	1	yes	characteristic
179	C₂×C₄	C₂×#4326	1	1	yes	characteristic
180	C₂×C₄	C₂×#4326	1	1	yes	characteristic
181	C₂×C₄	#67000	1	1	yes	characteristic
182	C₈	—	44	4	no	—
183	C₈	#66874	1	2	yes	—
184	C₈	#66874	1	2	yes	—
185	C₈	#66874	1	2	yes	—
186	C₈	#66874	1	2	yes	—
187	C₂²	—	2	2	no	—
188	C₂²	#10622601	1	1	yes	characteristic
189	C₂²	#10622689	1	1	yes	characteristic
190	C₂²	#10622705	1	1	yes	characteristic
191	C₄	—	2	2	no	—
192	C₄	—	2	2	no	—
193	C₄	—	16	2	no	—
194	C₄	—	88	4	no	—
195	C₄	C₂×#66874	1	1	yes	characteristic
196	C₄	C₂×#66874	1	1	yes	characteristic
197	C₄	#10622706	1	1	yes	characteristic
198	C₄	#10622706	1	1	yes	characteristic
199	C₂	—	2	1	no	—
200	C₂	—	2	1	no	—
201	C₂	#13069417	1	1	yes	characteristic
202	C₂	#13069512	1	2	yes	—

	subgroup	G/H
center	C₂²	#10622601
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1846	C₂
socle	C₂²×C₁₁	#390
prime radical	C₂³×C₁₁	#127
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1846	D₁₁
hypocenter	C₁₁	#9755
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1846

Complements

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

N	H ≅ G/N	type
15. #10622295	C₄	semidirect
16. #10622293	C₄	semidirect
167. C₁₁	#9755	semidirect

Maximal subgroups

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

subgroup	index
#13079130	2
#13067179	2
#13066899	2
C₁₁×#1846	2
#9755	11