Subgroups — #14653927

Order 2816.

506 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077014	C₂	1	1	yes	maximal, characteristic
2	#13068469	C₂	1	1	yes	maximal, characteristic
3	#13066500	C₂	1	4	yes	maximal
4	C₁₁×#1831	C₂	1	1	yes	maximal, characteristic
5	C₂×#66922	—	2	1	no	—
6	C₂×#66922	—	2	1	no	—
7	C₂×#66922	C₄	1	2	yes	—
8	C₂×C₁₁×C₄⋊C₈	C₂²	1	2	yes	—
9	C₄³×C₁₁	C₂²	1	1	yes	characteristic
10	#10622548	—	2	1	no	—
11	#10622548	—	2	1	no	—
12	#10622548	C₄	1	2	yes	—
13	#10622548	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₂×#66867	—	2	1	no	—
16	C₁₁×#336	—	2	1	no	—
17	C₁₁×#336	—	2	1	no	—
18	#10622162	—	2	1	no	—
19	C₂²×Dic₂₂	—	2	2	no	—
20	C₂²×C₈×C₁₁	—	2	2	no	—
21	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
22	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
24	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
25	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
26	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
27	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
28	C₂×C₄⋊Dic₁₁	—	2	2	no	—
29	C₂×C₄⋊Dic₁₁	—	2	2	no	—
30	C₂×C₄⋊Dic₁₁	—	2	2	no	—
31	C₂×C₄⋊Dic₁₁	—	2	2	no	—
32	C₂×C₄⋊Dic₁₁	—	2	2	no	—
33	C₂×C₄⋊Dic₁₁	C₂×C₄	1	4	yes	—
34	C₂²×C₁₁⋊C₈	—	2	2	no	—
35	#66922	—	4	4	no	—
36	#66922	—	4	2	no	—
37	#66922	—	4	2	no	—
38	#66922	—	4	4	no	—
39	C₁₁×C₄⋊C₈	—	2	4	no	—
40	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
41	C₄⋊(C₁₁⋊C₈)	Q₈	1	4	yes	complemented
42	#66867	—	4	2	no	—
43	#9905	—	11	1	no	maximal, Sylow
44	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
51	C₂²×Dic₁₁	—	2	4	no	—
52	C₂×Dic₂₂	—	4	4	no	—
53	C₂×Dic₂₂	—	4	4	no	—
54	C₂×Dic₂₂	—	4	4	no	—
55	C₂×C₈×C₁₁	—	4	2	no	—
56	C₂×C₈×C₁₁	—	4	2	no	—
57	C₂×C₈×C₁₁	—	4	2	no	—
58	C₄²×C₁₁	—	2	2	no	—
59	C₄²×C₁₁	—	2	2	no	—
60	C₄²×C₁₁	—	2	2	no	—
61	C₄²×C₁₁	—	2	2	no	—
62	C₄²×C₁₁	—	2	2	no	—
63	C₄²×C₁₁	D₈	1	2	yes	—
64	C₄²×C₁₁	SD₁₆	1	2	yes	—
65	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
66	C₄²×C₁₁	#41	1	2	yes	—
67	C₄⋊Dic₁₁	—	4	4	no	—
68	C₄⋊Dic₁₁	—	4	4	no	—
69	C₄⋊Dic₁₁	—	4	4	no	—
70	C₄⋊Dic₁₁	—	4	4	no	—
71	C₄⋊Dic₁₁	—	4	2	no	—
72	C₄⋊Dic₁₁	—	4	2	no	—
73	C₄⋊Dic₁₁	—	4	4	no	—
74	C₂×C₁₁⋊C₈	—	2	4	no	—
75	C₂×C₁₁⋊C₈	—	4	2	no	—
76	C₂×C₁₁⋊C₈	—	4	2	no	—
77	#2868	—	11	1	no	—
78	#1831	D₁₁	1	1	yes	characteristic
79	#1767	—	11	1	no	—
80	#1296	—	11	4	no	—
81	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×C₁₁	—	2	1	no	—
83	C₂×C₄×C₁₁	—	2	1	no	—
84	C₂×C₄×C₁₁	—	2	1	no	—
85	C₂×C₄×C₁₁	—	2	1	no	—
86	C₂×C₄×C₁₁	—	2	1	no	—
87	C₂×C₄×C₁₁	—	2	1	no	—
88	C₂×C₄×C₁₁	—	2	1	no	—
89	C₂×C₄×C₁₁	—	2	1	no	—
90	C₂×C₄×C₁₁	—	2	1	no	—
91	C₂×C₄×C₁₁	—	2	1	no	—
92	C₂×C₄×C₁₁	#100	1	2	yes	—
93	C₂×C₄×C₁₁	#101	1	2	yes	—
94	C₂×C₄×C₁₁	#102	1	2	yes	—
95	C₂×C₄×C₁₁	#102	1	2	yes	—
96	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
97	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
98	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
100	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
101	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
102	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
103	C₂×C₄×C₁₁	#137	1	2	yes	—
104	C₂×C₄×C₁₁	#137	1	2	yes	—
105	C₂×Dic₁₁	—	4	4	no	—
106	C₂×Dic₁₁	—	4	4	no	—
107	C₂×Dic₁₁	—	4	4	no	—
108	Dic₂₂	—	8	8	no	—
109	C₈×C₁₁	—	8	2	no	—
110	C₁₁⋊C₈	—	4	4	no	—
111	C₂×C₄⋊Q₈	—	11	2	no	—
112	C₂×C₄⋊Q₈	—	22	1	no	—
113	C₂×C₄⋊Q₈	—	22	1	no	—
114	C₂×C₄⋊C₈	—	11	2	no	—
115	C₂×C₄⋊C₈	C₂×D₁₁	1	2	yes	—
116	C₂×#97	—	22	1	no	—
117	#384	—	11	2	no	—
118	#384	—	11	2	no	—
119	#384	—	22	1	no	—
120	#384	—	22	1	no	—
121	C₄³	C₂×D₁₁	1	1	yes	characteristic
122	#336	—	2	1	no	—
123	#336	—	2	1	no	—
124	#336	—	22	1	no	—
125	C₂²×C₁₁	#391	1	1	yes	characteristic
126	C₂²×C₁₁	C₂×#100	1	1	yes	characteristic
127	C₂²×C₁₁	C₂×#101	1	1	yes	characteristic
128	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
129	C₂²×C₁₁	#418	1	1	yes	characteristic
130	C₂²×C₁₁	#419	1	1	yes	characteristic
131	C₂²×C₁₁	#419	1	1	yes	characteristic
132	C₄×C₁₁	—	2	2	no	—
133	C₄×C₁₁	—	2	2	no	—
134	C₄×C₁₁	—	2	2	no	—
135	C₄×C₁₁	—	2	2	no	—
136	C₄×C₁₁	—	2	2	no	—
137	C₄×C₁₁	#474	1	2	yes	—
138	C₄×C₁₁	#475	1	2	yes	—
139	C₄×C₁₁	#489	1	2	yes	—
140	C₄×C₁₁	#501	1	2	yes	—
141	Dic₁₁	—	8	4	no	—
142	C₂²×Q₈	—	22	2	no	—
143	C₂²×C₈	—	2	2	no	—
144	C₂²×C₈	—	22	2	no	—
145	C₄⋊Q₈	—	44	4	no	—
146	C₄⋊Q₈	—	44	4	no	—
147	C₄⋊Q₈	—	44	2	no	—
148	C₄⋊Q₈	—	44	2	no	—
149	C₂×C₄⋊C₄	—	11	4	no	—
150	C₂×C₄⋊C₄	—	22	2	no	—
151	C₂×C₄⋊C₄	—	22	2	no	—
152	C₂×C₄⋊C₄	—	22	2	no	—
153	C₂×C₄⋊C₄	—	22	2	no	—
154	C₂×C₄⋊C₄	—	22	2	no	—
155	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
156	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
157	C₂×C₄²	D₄₄	1	1	yes	characteristic
158	C₂×C₄²	D₄₄	1	1	yes	characteristic
159	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
160	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
161	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
162	C₄⋊C₈	—	2	4	no	—
163	C₄⋊C₈	—	11	4	no	—
164	C₄⋊C₈	—	22	2	no	—
165	#97	—	44	2	no	—
166	C₂×C₁₁	#1545	1	1	yes	characteristic
167	C₂×C₁₁	#1546	1	1	yes	characteristic
168	C₂×C₁₁	#1556	1	1	yes	characteristic
169	C₂×C₁₁	#1558	1	1	yes	characteristic
170	C₂×C₁₁	#1988	1	1	yes	characteristic
171	C₂×C₁₁	#1993	1	1	yes	characteristic
172	C₂×C₁₁	#1997	1	1	yes	characteristic
173	C₂×Q₈	—	44	4	no	—
174	C₂×Q₈	—	44	4	no	—
175	C₂×Q₈	—	44	4	no	—
176	C₂²×C₄	—	22	4	no	—
177	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
178	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
179	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
180	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
181	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
182	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
184	C₂×C₈	—	4	2	no	—
185	C₂×C₈	—	4	2	no	—
186	C₂×C₈	—	4	2	no	—
187	C₂×C₈	—	22	4	no	—
188	C₂×C₈	—	44	2	no	—
189	C₂×C₈	—	44	2	no	—
190	C₄⋊C₄	—	44	4	no	—
191	C₄⋊C₄	—	44	4	no	—
192	C₄⋊C₄	—	44	4	no	—
193	C₄⋊C₄	—	44	4	no	—
194	C₄⋊C₄	—	44	2	no	—
195	C₄⋊C₄	—	44	2	no	—
196	C₄⋊C₄	—	44	4	no	—
197	C₄²	—	2	2	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	2	2	no	—
201	C₄²	—	2	2	no	—
202	C₄²	#4314	1	2	yes	—
203	C₄²	D₈₈	1	2	yes	—
204	C₄²	#4341	1	2	yes	—
205	C₄²	Q₈×D₁₁	1	2	yes	—
206	C₁₁	#9905	1	1	yes	characteristic, complemented, Sylow
207	C₂³	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
208	Q₈	—	88	8	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	1	no	—
212	C₂×C₄	—	2	1	no	—
213	C₂×C₄	—	2	1	no	—
214	C₂×C₄	—	2	1	no	—
215	C₂×C₄	—	2	1	no	—
216	C₂×C₄	—	2	1	no	—
217	C₂×C₄	—	2	1	no	—
218	C₂×C₄	—	2	1	no	—
219	C₂×C₄	—	44	4	no	—
220	C₂×C₄	—	44	4	no	—
221	C₂×C₄	—	44	4	no	—
222	C₂×C₄	#66885	1	2	yes	—
223	C₂×C₄	#66885	1	2	yes	—
224	C₂×C₄	#66887	1	2	yes	—
225	C₂×C₄	#66888	1	2	yes	—
226	C₂×C₄	#66940	1	2	yes	—
227	C₂×C₄	#66950	1	2	yes	—
228	C₂×C₄	C₂×#4314	1	1	yes	characteristic
229	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
230	C₂×C₄	#66962	1	2	yes	—
231	C₂×C₄	#66989	1	1	yes	characteristic
232	C₂×C₄	#66997	1	1	yes	characteristic
233	C₂×C₄	#67002	1	2	yes	—
234	C₂×C₄	#67004	1	2	yes	—
235	C₈	—	8	2	no	—
236	C₈	—	44	4	no	—
237	C₂²	#10622587	1	1	yes	characteristic
238	C₂²	#10622614	1	1	yes	characteristic
239	C₂²	#10622617	1	1	yes	characteristic
240	C₂²	C₂×#66885	1	1	yes	characteristic
241	C₂²	#10622733	1	1	yes	characteristic
242	C₂²	C₂×#66887	1	1	yes	characteristic
243	C₂²	C₂×#66888	1	1	yes	characteristic
244	C₄	—	2	2	no	—
245	C₄	—	2	2	no	—
246	C₄	—	2	2	no	—
247	C₄	—	2	2	no	—
248	C₄	—	2	2	no	—
249	C₄	—	88	4	no	—
250	C₄	#10622459	1	2	yes	—
251	C₄	#10622464	1	2	yes	—
252	C₄	#10622668	1	2	yes	—
253	C₄	#10622678	1	2	yes	—
254	C₂	#13067283	1	1	yes	characteristic
255	C₂	#13067287	1	1	yes	characteristic
256	C₂	#13067334	1	1	yes	characteristic
257	C₂	#13067341	1	1	yes	characteristic
258	C₂	#13069567	1	1	yes	characteristic
259	C₂	#13069588	1	1	yes	characteristic
260	C₂	#13069604	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₁)⋊C₄
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#1831	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#1831	D₁₁
hypocenter	C₁₁	#9905
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1831

Complements

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

N	H ≅ G/N	type
41. C₄⋊(C₁₁⋊C₈)	Q₈	semidirect
206. C₁₁	#9905	semidirect

Maximal subgroups

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

subgroup	index
#13077014	2
#13068469	2
#13066500	2
C₁₁×#1831	2
#9905	11