Subgroups — #14653929

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	#13068733	C₂	1	1	yes	maximal, characteristic
2	#13068469	C₂	1	1	yes	maximal, characteristic
3	#13066499	C₂	1	4	yes	maximal
4	C₁₁×#2868	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
6	C₂×C₁₁×C₄⋊Q₈	—	2	1	no	—
7	C₂×C₁₁×C₄⋊Q₈	C₄	1	2	yes	—
8	C₁₁×#384	—	2	1	no	—
9	C₁₁×#384	—	2	1	no	—
10	C₁₁×#384	C₄	1	2	yes	—
11	C₁₁×#384	C₂²	1	2	yes	—
12	C₄³×C₁₁	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₁₁⋊C₈)	C₂²	1	2	yes	—
15	C₂×#66867	—	2	1	no	—
16	#10622162	—	2	1	no	—
17	#10622162	—	2	1	no	—
18	#10622162	—	2	1	no	—
19	C₂²×Q₈×C₁₁	—	2	2	no	—
20	C₁₁×C₄⋊Q₈	—	4	4	no	—
21	C₁₁×C₄⋊Q₈	—	4	4	no	—
22	C₁₁×C₄⋊Q₈	—	4	2	no	—
23	C₁₁×C₄⋊Q₈	—	4	2	no	—
24	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
25	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
26	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
27	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
28	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₁×C₄⋊C₄	C₂×C₄	1	4	yes	—
30	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
37	C₂²×C₁₁⋊C₈	—	2	2	no	—
38	C₂²×C₁₁⋊C₈	—	2	2	no	—
39	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
40	C₄⋊(C₁₁⋊C₈)	—	2	4	no	—
41	C₄⋊(C₁₁⋊C₈)	Q₈	1	4	yes	complemented
42	#66867	—	4	2	no	—
43	#9905	—	11	1	no	maximal, Sylow
44	C₂×Q₈×C₁₁	—	4	4	no	—
45	C₂×Q₈×C₁₁	—	4	4	no	—
46	C₂×Q₈×C₁₁	—	4	4	no	—
47	C₂²×C₄×C₁₁	—	2	4	no	—
48	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
49	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
50	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
51	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
52	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
53	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
55	C₁₁×C₄⋊C₄	—	4	4	no	—
56	C₁₁×C₄⋊C₄	—	4	4	no	—
57	C₁₁×C₄⋊C₄	—	4	4	no	—
58	C₁₁×C₄⋊C₄	—	4	4	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	4	2	no	—
61	C₁₁×C₄⋊C₄	—	4	4	no	—
62	C₄²×C₁₁	—	2	2	no	—
63	C₄²×C₁₁	—	2	2	no	—
64	C₄²×C₁₁	—	2	2	no	—
65	C₄²×C₁₁	—	2	2	no	—
66	C₄²×C₁₁	—	2	2	no	—
67	C₄²×C₁₁	D₈	1	2	yes	—
68	C₄²×C₁₁	SD₁₆	1	2	yes	—
69	C₄²×C₁₁	C₂×Q₈	1	2	yes	—
70	C₄²×C₁₁	#41	1	2	yes	—
71	C₂×C₁₁⋊C₈	—	2	4	no	—
72	C₂×C₁₁⋊C₈	—	4	2	no	—
73	C₂×C₁₁⋊C₈	—	4	2	no	—
74	C₂×C₁₁⋊C₈	—	4	2	no	—
75	C₂×C₁₁⋊C₈	—	4	2	no	—
76	C₂×C₁₁⋊C₈	—	4	2	no	—
77	#2868	D₁₁	1	1	yes	characteristic
78	#1831	—	11	1	no	—
79	#1767	—	11	1	no	—
80	#1296	—	11	4	no	—
81	C₂³×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
82	Q₈×C₁₁	—	8	8	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	—	2	1	no	—
93	C₂×C₄×C₁₁	—	4	4	no	—
94	C₂×C₄×C₁₁	—	4	4	no	—
95	C₂×C₄×C₁₁	—	4	4	no	—
96	C₂×C₄×C₁₁	#100	1	2	yes	—
97	C₂×C₄×C₁₁	#101	1	2	yes	—
98	C₂×C₄×C₁₁	#102	1	2	yes	—
99	C₂×C₄×C₁₁	#102	1	2	yes	—
100	C₂×C₄×C₁₁	C₄×Q₈	1	2	yes	—
101	C₂×C₄×C₁₁	C₂²⋊Q₈	1	2	yes	—
102	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
103	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
104	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
105	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₁	AGL(1,ℤ/8)	1	2	yes	—
107	C₂×C₄×C₁₁	#137	1	2	yes	—
108	C₂×C₄×C₁₁	#137	1	2	yes	—
109	C₁₁⋊C₈	—	4	4	no	—
110	C₁₁⋊C₈	—	8	2	no	—
111	C₂×C₄⋊Q₈	—	2	1	no	—
112	C₂×C₄⋊Q₈	—	2	1	no	—
113	C₂×C₄⋊Q₈	Dic₁₁	1	2	yes	—
114	C₂×C₄⋊C₈	—	11	2	no	—
115	C₂×C₄⋊C₈	—	11	2	no	—
116	C₂×#97	—	22	1	no	—
117	#384	—	2	1	no	—
118	#384	—	2	1	no	—
119	#384	Dic₁₁	1	2	yes	—
120	#384	C₂×D₁₁	1	2	yes	—
121	C₄³	C₂×D₁₁	1	1	yes	characteristic
122	#336	—	22	1	no	—
123	#336	—	22	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	—	8	4	no	—
138	C₄×C₁₁	#474	1	2	yes	—
139	C₄×C₁₁	#475	1	2	yes	—
140	C₄×C₁₁	#489	1	2	yes	—
141	C₄×C₁₁	#501	1	2	yes	—
142	C₂²×Q₈	—	2	2	no	—
143	C₂²×C₈	—	22	2	no	—
144	C₂²×C₈	—	22	2	no	—
145	C₄⋊Q₈	—	4	4	no	—
146	C₄⋊Q₈	—	4	4	no	—
147	C₄⋊Q₈	—	4	2	no	—
148	C₄⋊Q₈	—	4	2	no	—
149	C₂×C₄⋊C₄	—	2	2	no	—
150	C₂×C₄⋊C₄	—	2	2	no	—
151	C₂×C₄⋊C₄	—	2	2	no	—
152	C₂×C₄⋊C₄	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	2	no	—
154	C₂×C₄⋊C₄	C₂×Dic₁₁	1	4	yes	—
155	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
156	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
157	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
158	C₂×C₄²	C₂²⋊D₁₁	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	—	11	4	no	—
163	C₄⋊C₈	—	22	2	no	—
164	C₄⋊C₈	—	22	4	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	—	4	4	no	—
174	C₂×Q₈	—	4	4	no	—
175	C₂×Q₈	—	4	4	no	—
176	C₂²×C₄	—	2	4	no	—
177	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
178	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
179	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
180	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
181	C₂²×C₄	C₂²×Dic₁₁	1	1	yes	characteristic
182	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
183	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
184	C₂×C₈	—	22	4	no	—
185	C₂×C₈	—	44	2	no	—
186	C₂×C₈	—	44	2	no	—
187	C₂×C₈	—	44	2	no	—
188	C₂×C₈	—	44	2	no	—
189	C₂×C₈	—	44	2	no	—
190	C₄⋊C₄	—	4	4	no	—
191	C₄⋊C₄	—	4	4	no	—
192	C₄⋊C₄	—	4	4	no	—
193	C₄⋊C₄	—	4	4	no	—
194	C₄⋊C₄	—	4	2	no	—
195	C₄⋊C₄	—	4	4	no	—
196	C₄⋊C₄	—	4	2	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	#4323	1	2	yes	—
203	C₄²	#4324	1	2	yes	—
204	C₄²	Q₈×D₁₁	1	2	yes	—
205	C₄²	#4343	1	2	yes	—
206	C₁₁	#9905	1	1	yes	characteristic, complemented, Sylow
207	C₂³	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
208	Q₈	—	8	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	—	4	4	no	—
220	C₂×C₄	—	4	4	no	—
221	C₂×C₄	—	4	4	no	—
222	C₂×C₄	#66896	1	2	yes	—
223	C₂×C₄	#66896	1	2	yes	—
224	C₂×C₄	#66897	1	2	yes	—
225	C₂×C₄	#66900	1	2	yes	—
226	C₂×C₄	C₂×#4323	1	1	yes	characteristic
227	C₂×C₄	#66985	1	2	yes	—
228	C₂×C₄	C₂×#4324	1	1	yes	characteristic
229	C₂×C₄	#66995	1	2	yes	—
230	C₂×C₄	#66995	1	2	yes	—
231	C₂×C₄	#66997	1	1	yes	characteristic
232	C₂×C₄	Q₈×Dic₁₁	1	2	yes	—
233	C₂×C₄	#66999	1	2	yes	—
234	C₂×C₄	#67000	1	1	yes	characteristic
235	C₈	—	44	4	no	—
236	C₈	—	88	2	no	—
237	C₂²	C₂×#66896	1	1	yes	characteristic
238	C₂²	#10622828	1	1	yes	characteristic
239	C₂²	C₂×#66897	1	1	yes	characteristic
240	C₂²	#10622838	1	1	yes	characteristic
241	C₂²	#10622838	1	1	yes	characteristic
242	C₂²	C₂×#66900	1	1	yes	characteristic
243	C₂²	#10622843	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	—	8	4	no	—
250	C₄	#10622693	1	2	yes	—
251	C₄	#10622700	1	2	yes	—
252	C₄	#10622702	1	2	yes	—
253	C₄	#10622707	1	2	yes	—
254	C₂	#13067284	1	1	yes	characteristic
255	C₂	#13067288	1	1	yes	characteristic
256	C₂	#13067333	1	1	yes	characteristic
257	C₂	#13067342	1	1	yes	characteristic
258	C₂	#13069569	1	1	yes	characteristic
259	C₂	#13069590	1	1	yes	characteristic
260	C₂	#13069606	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₁
commutator	C₂²×C₄×C₁₁	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₁₁×#2868	C₂
socle, prime radical	C₂³×C₁₁	C₂×C₂²⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	#2868	D₁₁
hypocenter	C₁₁	#9905
LCS	G ▷ C₂²×C₄×C₁₁ ▷ C₂²×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2868

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
#13068733	2
#13068469	2
#13066499	2
C₁₁×#2868	2
#9905	11