Subgroups — #14653788

Order 2816.

458 conjugacy classes of subgroups.

The subgroup lattice has 218 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#66923	C₂	1	1	yes	maximal, characteristic
2	#13068768	C₂	1	1	yes	maximal, characteristic
3	#13066456	C₂	1	4	yes	maximal
4	C₁₁×#1744	C₂	1	1	yes	maximal, characteristic
5	C₂×#66923	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₁	C₂²	1	2	yes	—
7	C₄³×C₁₁	C₂²	1	1	yes	characteristic
8	#10622549	C₄	1	1	yes	characteristic
9	C₄×C₄⋊Dic₁₁	C₂²	1	2	yes	—
10	#10622546	—	2	2	no	—
11	C₄×Dic₁₁⋊C₄	—	2	2	no	—
12	#10622541	C₄	1	2	yes	—
13	C₂×C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₁₁×#336	—	2	2	no	—
16	C₂²×C₈×C₁₁	—	2	2	no	—
17	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄²×C₁₁	D₄	1	2	yes	—
20	C₂×C₄²×C₁₁	D₄	1	2	yes	—
21	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
22	C₂×C₄⋊Dic₁₁	C₂×C₄	1	2	yes	—
23	C₂×C₄⋊Dic₁₁	C₂×C₄	1	2	yes	—
24	C₂×Dic₁₁⋊C₄	—	2	2	no	—
25	C₂×Dic₁₁⋊C₄	—	2	2	no	—
26	C₂×C₄×Dic₁₁	—	2	2	no	—
27	C₂²×C₁₁⋊C₈	—	2	2	no	—
28	#66923	—	2	2	no	—
29	#66923	C₈	1	4	yes	complemented
30	C₄×C₈×C₁₁	—	2	2	no	—
31	C₄×C₈×C₁₁	Q₈	1	4	yes	—
32	C₁₁⋊#95	—	2	2	no	—
33	C₁₁⋊#95	—	2	2	no	—
34	C₁₁⋊#95	—	2	2	no	—
35	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
36	C₄⋊(C₁₁⋊C₈)	—	4	4	no	—
37	#9872	—	11	1	no	maximal, Sylow
38	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
39	C₂²×C₄×C₁₁	C₂²⋊C₄	1	2	yes	—
40	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₂²×Dic₁₁	—	2	2	no	—
44	C₂²×Dic₁₁	—	2	2	no	—
45	C₂×C₈×C₁₁	—	2	4	no	—
46	C₂×C₈×C₁₁	—	4	4	no	—
47	C₄²×C₁₁	—	2	2	no	—
48	C₄²×C₁₁	—	2	2	no	—
49	C₄²×C₁₁	—	2	2	no	—
50	C₄²×C₁₁	—	4	2	no	—
51	C₄²×C₁₁	C₂×C₈	1	2	yes	—
52	C₄²×C₁₁	M₁₆	1	2	yes	—
53	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
54	C₄²×C₁₁	#41	1	2	yes	—
55	C₄⋊Dic₁₁	—	2	2	no	—
56	C₄⋊Dic₁₁	—	2	4	no	—
57	C₄⋊Dic₁₁	C₂×C₈	1	4	yes	—
58	Dic₁₁⋊C₄	—	2	8	no	—
59	Dic₁₁⋊C₄	—	4	4	no	—
60	C₄×Dic₁₁	—	4	2	no	—
61	C₄×Dic₁₁	—	4	2	no	—
62	C₂×C₁₁⋊C₈	—	4	2	no	—
63	C₂×C₁₁⋊C₈	—	4	4	no	—
64	C₄×#125	—	11	1	no	—
65	#1842	—	11	1	no	—
66	#1744	D₁₁	1	1	yes	characteristic
67	#1279	—	11	4	no	—
68	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
69	C₂×C₄×C₁₁	—	2	2	no	—
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	—	2	2	no	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	2	no	—
74	C₂×C₄×C₁₁	—	2	2	no	—
75	C₂×C₄×C₁₁	C₂²⋊C₈	1	4	yes	—
76	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
77	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
78	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
79	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
80	C₂×C₄×C₁₁	C₂²×C₈	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×M₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₁	#131	1	2	yes	—
83	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
84	C₂×C₄×C₁₁	#137	1	2	yes	—
85	C₂×Dic₁₁	—	2	4	no	—
86	C₂×Dic₁₁	—	4	2	no	—
87	C₂×Dic₁₁	—	4	2	no	—
88	C₂×Dic₁₁	—	4	2	no	—
89	C₂×Dic₁₁	—	4	2	no	—
90	C₂×Dic₁₁	—	4	2	no	—
91	C₈×C₁₁	—	4	4	no	—
92	C₁₁⋊C₈	—	8	2	no	—
93	C₂×#125	—	11	1	no	—
94	C₂×C₄⋊C₈	—	11	2	no	—
95	C₂×C₄⋊C₈	—	22	2	no	—
96	C₂×C₄×C₈	C₂×D₁₁	1	2	yes	—
97	#389	—	11	2	no	—
98	#387	—	22	2	no	—
99	#382	—	11	1	no	—
100	C₄×C₄⋊C₄	—	11	2	no	—
101	C₄×C₄⋊C₄	—	22	2	no	—
102	C₄³	C₂×D₁₁	1	1	yes	characteristic
103	#336	—	2	2	no	—
104	C₂²×C₁₁	#391	1	1	yes	characteristic
105	C₂²×C₁₁	C₂×C₂²⋊C₈	1	1	yes	characteristic
106	C₂²×C₁₁	#408	1	1	yes	characteristic
107	C₂²×C₁₁	#417	1	2	yes	—
108	C₂²×C₁₁	#421	1	2	yes	—
109	C₄×C₁₁	—	2	4	no	—
110	C₄×C₁₁	—	2	2	no	—
111	C₄×C₁₁	—	4	2	no	—
112	C₄×C₁₁	C₈×Q₈	1	2	yes	—
113	C₄×C₁₁	#446	1	2	yes	—
114	C₄×C₁₁	#490	1	1	yes	characteristic
115	C₄×C₁₁	#491	1	1	yes	characteristic
116	C₄×C₁₁	#501	1	2	yes	—
117	Dic₁₁	—	4	4	no	—
118	Dic₁₁	—	8	2	no	—
119	C₂²×C₈	—	2	2	no	—
120	C₂²×C₈	—	22	2	no	—
121	#125	—	11	4	no	—
122	#125	—	22	2	no	—
123	C₂×C₄⋊C₄	—	11	2	no	—
124	C₂×C₄⋊C₄	—	11	2	no	—
125	C₂×C₄⋊C₄	—	22	2	no	—
126	C₂×C₄⋊C₄	—	22	2	no	—
127	C₂×C₄²	—	22	2	no	—
128	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
129	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
130	C₂×C₄²	D₄₄	1	2	yes	—
131	C₂×C₄²	C₂²⋊D₁₁	1	2	yes	—
132	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
133	C₄⋊C₈	—	22	4	no	—
134	C₄⋊C₈	—	44	4	no	—
135	C₄×C₈	—	2	2	no	—
136	C₄×C₈	Dic₂₂	1	4	yes	—
137	#95	—	22	2	no	—
138	#95	—	22	2	no	—
139	#95	—	22	2	no	—
140	C₂×C₁₁	#1477	1	2	yes	—
141	C₂×C₁₁	#1495	1	2	yes	—
142	C₂×C₁₁	#1984	1	1	yes	characteristic
143	C₂×C₁₁	#1992	1	1	yes	characteristic
144	C₂×C₁₁	#1995	1	1	yes	characteristic
145	C₂²×C₄	—	22	2	no	—
146	C₂²×C₄	—	22	2	no	—
147	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
148	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	2	yes	—
149	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
150	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
151	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
152	C₂×C₈	—	2	4	no	—
153	C₂×C₈	—	4	4	no	—
154	C₂×C₈	—	44	2	no	—
155	C₂×C₈	—	44	4	no	—
156	C₄⋊C₄	—	11	4	no	—
157	C₄⋊C₄	—	22	8	no	—
158	C₄⋊C₄	—	22	2	no	—
159	C₄⋊C₄	—	22	4	no	—
160	C₄⋊C₄	—	44	4	no	—
161	C₄²	—	2	2	no	—
162	C₄²	—	2	2	no	—
163	C₄²	—	2	2	no	—
164	C₄²	—	4	2	no	—
165	C₄²	—	44	2	no	—
166	C₄²	—	44	2	no	—
167	C₄²	C₈×D₁₁	1	2	yes	—
168	C₄²	#4313	1	2	yes	—
169	C₄²	C₂×Dic₂₂	1	2	yes	—
170	C₄²	#4339	1	2	yes	—
171	C₁₁	#9872	1	1	yes	characteristic, complemented, Sylow
172	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
173	C₂×C₄	—	2	2	no	—
174	C₂×C₄	—	2	2	no	—
175	C₂×C₄	—	2	2	no	—
176	C₂×C₄	—	2	2	no	—
177	C₂×C₄	—	2	2	no	—
178	C₂×C₄	—	2	2	no	—
179	C₂×C₄	—	22	4	no	—
180	C₂×C₄	—	44	2	no	—
181	C₂×C₄	—	44	2	no	—
182	C₂×C₄	—	44	2	no	—
183	C₂×C₄	—	44	2	no	—
184	C₂×C₄	—	44	2	no	—
185	C₂×C₄	(C₂×D₁₁)⋊C₈	1	4	yes	—
186	C₂×C₄	C₄×Dic₂₂	1	2	yes	—
187	C₂×C₄	#66922	1	1	yes	characteristic
188	C₂×C₄	#66928	1	1	yes	characteristic
189	C₂×C₄	C₂×C₈×D₁₁	1	1	yes	characteristic
190	C₂×C₄	C₂×#4313	1	1	yes	characteristic
191	C₂×C₄	#66954	1	2	yes	—
192	C₂×C₄	#66961	1	2	yes	—
193	C₂×C₄	#66962	1	2	yes	—
194	C₂×C₄	#66977	1	2	yes	—
195	C₈	—	4	4	no	—
196	C₈	—	88	2	no	—
197	C₂²	#10622542	1	1	yes	characteristic
198	C₂²	#10622618	1	2	yes	—
199	C₂²	C₂×(C₂×D₁₁)⋊C₈	1	1	yes	characteristic
200	C₂²	#10622723	1	1	yes	characteristic
201	C₂²	#10622746	1	2	yes	—
202	C₄	—	2	2	no	—
203	C₄	—	2	4	no	—
204	C₄	—	4	2	no	—
205	C₄	—	44	4	no	—
206	C₄	—	88	2	no	—
207	C₄	C₈×Dic₂₂	1	2	yes	—
208	C₄	#10622292	1	2	yes	—
209	C₄	#10622315	1	2	yes	—
210	C₄	#10622316	1	1	yes	characteristic
211	C₄	#10622326	1	1	yes	characteristic
212	C₂	#13067004	1	2	yes	—
213	C₂	#13067082	1	2	yes	—
214	C₂	#13069552	1	1	yes	characteristic
215	C₂	#13069585	1	1	yes	characteristic
216	C₂	#13069597	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₄₄
commutator	C₂×C₄×C₁₁	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1744	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1744	D₁₁
hypocenter	C₁₁	#9872
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₄³ ◁ #1744

Complements

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

N	H ≅ G/N	type
29. #66923	C₈	semidirect
171. C₁₁	#9872	semidirect

Maximal subgroups

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

subgroup	index
C₄×#66923	2
#13068768	2
#13066456	2
C₁₁×#1744	2
#9872	11