Subgroups — #14652438

Order 2816.

370 conjugacy classes of subgroups.

The subgroup lattice has 230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13069374	C₂	1	2	yes	maximal
2	#13068773	C₂	1	1	yes	maximal, characteristic
3	C₂×#10622096	C₂	1	1	yes	maximal, characteristic
4	#13066500	C₂	1	2	yes	maximal
5	C₁₁×#1770	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₁×#97	—	2	1	no	—
8	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
9	C₄×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
10	C₂×#66881	—	2	1	no	—
11	C₂×#66881	—	2	1	no	—
12	C₂×#66871	—	2	2	no	—
13	#10622548	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₁₁×#336	—	2	1	no	—
16	#10622167	—	2	2	no	—
17	#10622096	C₄	1	4	yes	complemented
18	C₂²×C₈×C₁₁	—	2	1	no	—
19	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
20	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
21	C₂×C₁₁×C₄⋊C₄	D₄	1	2	yes	—
22	C₂×C₄²×C₁₁	—	2	1	no	—
23	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
24	C₂×C₄⋊Dic₁₁	—	2	2	no	—
25	C₂×C₄⋊Dic₁₁	—	2	2	no	—
26	C₂×C₄⋊Dic₁₁	—	2	2	no	—
27	C₂²×C₁₁⋊C₈	—	2	2	no	—
28	C₁₁×C₄⋊C₈	—	2	1	no	—
29	C₁₁×C₄⋊C₈	Q₈	1	2	yes	—
30	C₁₁×#97	—	4	2	no	—
31	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
32	C₄×C₈×C₁₁	Q₈	1	2	yes	—
33	C₁₁×#95	—	2	1	no	—
34	#66881	—	4	2	no	—
35	#66881	—	4	2	no	—
36	#66871	—	4	4	no	—
37	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
38	C₄⋊(C₁₁⋊C₈)	C₂×C₄	1	4	yes	—
39	#9617	—	11	1	no	maximal, Sylow
40	C₂²×C₄×C₁₁	—	2	2	no	—
41	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
43	C₂²×C₄×C₁₁	#41	1	1	yes	characteristic
44	C₂²×Dic₁₁	—	4	2	no	—
45	C₂×C₈×C₁₁	—	2	2	no	—
46	C₂×C₈×C₁₁	—	2	1	no	—
47	C₂×C₈×C₁₁	—	2	1	no	—
48	C₂×C₈×C₁₁	—	4	1	no	—
49	C₂×C₈×C₁₁	—	4	1	no	—
50	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
51	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₁	D₈	1	2	yes	—
53	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
54	C₁₁×C₄⋊C₄	—	2	2	no	—
55	C₁₁×C₄⋊C₄	—	2	2	no	—
56	C₄²×C₁₁	—	4	1	no	—
57	C₄²×C₁₁	—	4	1	no	—
58	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
59	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
60	C₄²×C₁₁	C₂×Q₈	1	1	yes	characteristic
61	C₄²×C₁₁	#41	1	1	yes	characteristic
62	C₄⋊Dic₁₁	—	4	2	no	—
63	C₄⋊Dic₁₁	—	4	2	no	—
64	C₄⋊Dic₁₁	—	4	2	no	—
65	C₄⋊Dic₁₁	—	4	2	no	—
66	C₄⋊Dic₁₁	—	8	2	no	—
67	C₂×C₁₁⋊C₈	—	2	4	no	—
68	C₂×C₁₁⋊C₈	—	4	2	no	—
69	C₂×C₁₁⋊C₈	—	4	2	no	—
70	#1947	—	11	2	no	—
71	#1844	—	11	1	no	—
72	#1770	D₁₁	1	1	yes	characteristic
73	C₂×#335	—	11	1	no	—
74	#1296	—	11	2	no	—
75	C₂³×C₁₁	#121	1	1	yes	characteristic
76	C₂×C₄×C₁₁	—	2	2	no	—
77	C₂×C₄×C₁₁	—	4	2	no	—
78	C₂×C₄×C₁₁	—	4	2	no	—
79	C₂×C₄×C₁₁	—	4	2	no	—
80	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₄×D₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₄×Q₈	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂²⋊Q₈	1	1	yes	characteristic
84	C₂×C₄×C₁₁	#125	1	1	yes	characteristic
85	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
86	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
87	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
88	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
89	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	1	yes	characteristic
90	C₂×C₄×C₁₁	#137	1	2	yes	—
91	C₂×C₄×C₁₁	#137	1	1	yes	characteristic
92	C₂×Dic₁₁	—	8	2	no	—
93	C₂×Dic₁₁	—	8	2	no	—
94	C₂×Dic₁₁	—	8	2	no	—
95	C₈×C₁₁	—	2	2	no	—
96	C₈×C₁₁	—	4	2	no	—
97	C₈×C₁₁	#107	1	4	yes	complemented
98	C₁₁⋊C₈	—	4	4	no	—
99	C₂×#107	—	22	2	no	—
100	C₂×#106	—	22	1	no	—
101	C₂×#106	—	22	1	no	—
102	C₂×C₄⋊C₈	—	11	2	no	—
103	C₂×C₄⋊C₈	C₂×D₁₁	1	1	yes	characteristic
104	C₂×#97	—	2	1	no	—
105	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
106	#384	—	11	2	no	—
107	C₄×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
108	#340	—	22	2	no	—
109	#336	—	2	1	no	—
110	#335	—	11	4	no	—
111	C₂²×C₁₁	#389	1	1	yes	characteristic
112	C₂²×C₁₁	#459	1	1	yes	characteristic
113	C₂²×C₁₁	#462	1	1	yes	characteristic
114	C₂²×C₁₁	#468	1	2	yes	—
115	C₂²×C₁₁	#471	1	2	yes	—
116	C₄×C₁₁	—	2	1	no	—
117	C₄×C₁₁	—	2	1	no	—
118	C₄×C₁₁	—	8	2	no	—
119	C₄×C₁₁	C₂×#107	1	1	yes	characteristic
120	C₄×C₁₁	#428	1	1	yes	characteristic
121	C₄×C₁₁	#441	1	1	yes	characteristic
122	C₄×C₁₁	#442	1	1	yes	characteristic
123	C₄×C₁₁	#474	1	1	yes	characteristic
124	C₄×C₁₁	#477	1	1	yes	characteristic
125	C₄×C₁₁	#501	1	2	yes	—
126	Dic₁₁	—	16	2	no	—
127	C₂²×C₈	—	2	1	no	—
128	C₂²×C₈	—	22	2	no	—
129	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
130	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
131	C₂×C₄⋊C₄	—	22	2	no	—
132	C₂×C₄⋊C₄	—	22	2	no	—
133	C₂×C₄⋊C₄	—	22	2	no	—
134	C₂×C₄⋊C₄	D₄₄	1	2	yes	—
135	C₂×C₄²	—	2	1	no	—
136	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
137	#107	—	44	4	no	—
138	#106	—	44	2	no	—
139	#106	—	44	2	no	—
140	C₄⋊C₈	—	2	1	no	—
141	C₄⋊C₈	—	11	4	no	—
142	C₄⋊C₈	—	22	2	no	—
143	C₄⋊C₈	Dic₂₂	1	2	yes	—
144	#97	—	4	2	no	—
145	C₄×C₈	Dic₂₂	1	2	yes	—
146	C₄×C₈	C₄×D₁₁	1	2	yes	—
147	#95	—	2	1	no	—
148	C₂×C₁₁	#1685	1	2	yes	—
149	C₂×C₁₁	#1692	1	2	yes	—
150	C₂×C₁₁	#1943	1	1	yes	characteristic
151	C₂×C₁₁	#1947	1	1	yes	characteristic
152	C₂×C₁₁	#1951	1	1	yes	characteristic
153	C₂²×C₄	—	2	2	no	—
154	C₂²×C₄	—	44	2	no	—
155	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
156	C₂²×C₄	#4339	1	1	yes	characteristic
157	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
158	C₂×C₈	—	2	1	no	—
159	C₂×C₈	—	2	1	no	—
160	C₂×C₈	—	2	2	no	—
161	C₂×C₈	—	4	1	no	—
162	C₂×C₈	—	4	1	no	—
163	C₂×C₈	—	22	4	no	—
164	C₂×C₈	—	44	2	no	—
165	C₂×C₈	—	44	2	no	—
166	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
167	C₂×C₈	Dic₁₁⋊C₄	1	2	yes	—
168	C₂×C₈	#4323	1	2	yes	—
169	C₂×C₈	#4326	1	2	yes	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	2	2	no	—
172	C₄⋊C₄	—	44	2	no	—
173	C₄⋊C₄	—	44	2	no	—
174	C₄⋊C₄	—	44	2	no	—
175	C₄⋊C₄	—	44	2	no	—
176	C₄⋊C₄	—	88	2	no	—
177	C₄²	—	4	1	no	—
178	C₄²	—	4	1	no	—
179	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
180	C₄²	C₂×Dic₂₂	1	1	yes	characteristic
181	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
182	C₄²	#4339	1	1	yes	characteristic
183	C₁₁	#9617	1	1	yes	characteristic, complemented, Sylow
184	C₂³	#66983	1	1	yes	characteristic
185	C₂×C₄	—	2	2	no	—
186	C₂×C₄	—	4	2	no	—
187	C₂×C₄	—	4	2	no	—
188	C₂×C₄	—	4	2	no	—
189	C₂×C₄	—	88	2	no	—
190	C₂×C₄	—	88	2	no	—
191	C₂×C₄	—	88	2	no	—
192	C₂×C₄	C₄×Dic₂₂	1	1	yes	characteristic
193	C₂×C₄	#66922	1	1	yes	characteristic
194	C₂×C₄	#66923	1	1	yes	characteristic
195	C₂×C₄	C₄×D₄₄	1	1	yes	characteristic
196	C₂×C₄	#66961	1	2	yes	—
197	C₂×C₄	#66962	1	2	yes	—
198	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
199	C₂×C₄	#66977	1	1	yes	characteristic
200	C₂×C₄	C₂×#4323	1	1	yes	characteristic
201	C₂×C₄	C₂×#4326	1	1	yes	characteristic
202	C₂×C₄	#67002	1	1	yes	characteristic
203	C₂×C₄	#67004	1	1	yes	characteristic
204	C₈	—	2	2	no	—
205	C₈	—	4	2	no	—
206	C₈	—	44	4	no	—
207	C₈	#66871	1	4	yes	complemented
208	C₂²	#10622541	1	1	yes	characteristic
209	C₂²	#10622628	1	1	yes	characteristic
210	C₂²	#10622644	1	1	yes	characteristic
211	C₂²	#10622747	1	2	yes	—
212	C₂²	#10622754	1	2	yes	—
213	C₄	—	2	1	no	—
214	C₄	—	2	1	no	—
215	C₄	—	8	2	no	—
216	C₄	—	176	2	no	—
217	C₄	#10622315	1	2	yes	—
218	C₄	#10622324	1	1	yes	characteristic
219	C₄	#10622329	1	1	yes	characteristic
220	C₄	C₂×#66871	1	1	yes	characteristic
221	C₄	#10622608	1	1	yes	characteristic
222	C₄	#10622620	1	1	yes	characteristic
223	C₄	#10622634	1	1	yes	characteristic
224	C₂	#13068081	1	2	yes	—
225	C₂	#13068122	1	2	yes	—
226	C₂	#13069354	1	1	yes	characteristic
227	C₂	#13069374	1	1	yes	characteristic
228	C₂	#13069396	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#66983
commutator	C₄²×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1770	C₂
socle, prime radical	C₂³×C₁₁	#121
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1770	D₁₁
hypocenter	C₁₁	#9617
LCS	G ▷ C₄²×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1770

Complements

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

N	H ≅ G/N	type
17. #10622096	C₄	semidirect
97. C₈×C₁₁	#107	semidirect
183. C₁₁	#9617	semidirect
207. C₈	#66871	semidirect

Maximal subgroups

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

subgroup	index
#13069374	2
#13068773	2
C₂×#10622096	2
#13066500	2
C₁₁×#1770	2
#9617	11