Subgroups — #14909152

Order 2816.

590 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622296	C₂	1	1	yes	maximal, characteristic, complemented
2	#13079044	C₂	1	1	yes	maximal, characteristic
3	#13070862	C₂	1	2	yes	maximal, complemented
4	#13070858	C₂	1	2	yes	maximal, complemented
5	#13070848	C₂	1	4	yes	maximal, complemented
6	#13070329	C₂	1	4	yes	maximal, complemented
7	C₄×C₁₁×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#66957	—	2	1	no	—
9	C₂×#66957	C₂²	1	2	yes	—
10	#10623008	—	2	1	no	—
11	C₂×#66923	—	2	1	no	—
12	C₂×C₁₁×M₃₂	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
14	C₂×#66882	C₂²	1	2	yes	—
15	C₂×#66881	—	2	1	no	—
16	#10622312	C₂²	1	1	yes	characteristic
17	#10622309	—	2	1	no	—
18	#10622309	C₂²	1	2	yes	—
19	#10622308	C₂²	1	1	yes	characteristic
20	#10622306	—	2	1	no	—
21	#10622296	—	2	1	no	—
22	#10622296	—	2	1	no	—
23	#10622296	C₂²	1	2	yes	—
24	#10622296	C₂²	1	2	yes	—
25	C₁₁×#346	C₂²	1	2	yes	—
26	C₄×C₁₁×C₁₆	C₂²	1	2	yes	—
27	#10622147	C₂²	1	8	yes	—
28	#10622141	C₂²	1	8	yes	—
29	C₂×#4339	—	2	2	no	—
30	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
33	#66983	—	4	2	no	—
34	C₂×C₄⋊Dic₁₁	—	2	2	no	—
35	C₂×Dic₁₁⋊C₄	—	4	2	no	—
36	C₂×Dic₄₄	—	2	1	no	—
37	C₂×Dic₄₄	C₂³	1	2	yes	—
38	#66957	—	2	8	no	—
39	#66957	—	4	4	no	—
40	C₂×D₈₈	—	2	1	no	—
41	C₂×D₈₈	C₂³	1	2	yes	—
42	C₂×#4314	—	2	2	no	—
43	C₂×#4314	—	2	2	no	—
44	#66928	—	2	2	no	—
45	#66927	—	2	1	no	—
46	C₄×D₄₄	—	4	2	no	—
47	#66923	—	2	2	no	—
48	#66923	—	2	2	no	—
49	#66923	—	4	2	no	—
50	#66922	—	2	1	no	—
51	C₁₁×M₃₂	—	2	4	no	—
52	C₂×C₁₁×C₁₆	C₂³	1	4	yes	—
53	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
54	C₄×C₈×C₁₁	D₄	1	1	yes	characteristic
55	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
56	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
57	#66882	—	2	2	no	—
58	#66882	C₂³	1	4	yes	—
59	#66881	—	2	2	no	—
60	#66881	—	2	2	no	—
61	#33708	—	11	1	no	maximal, Sylow
62	C₂²×C₄×C₁₁	D₈	1	2	yes	—
63	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
64	C₂×C₂²⋊D₁₁	—	4	2	no	—
65	C₂²×Dic₁₁	—	4	2	no	—
66	#4339	—	4	4	no	—
67	#4339	—	4	4	no	—
68	C₂×D₄₄	—	2	2	no	—
69	C₂×D₄₄	—	4	2	no	—
70	C₂×C₄×D₁₁	—	4	2	no	—
71	C₂×Dic₂₂	—	2	2	no	—
72	C₂×C₈×C₁₁	SD₁₆	1	4	yes	—
73	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
74	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
75	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
76	C₂×C₈×C₁₁	#41	1	4	yes	—
77	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
78	C₄²×C₁₁	D₈	1	2	yes	—
79	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
80	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
81	(C₂×D₁₁)⋊C₄	—	4	4	no	—
82	C₄⋊Dic₁₁	—	2	4	no	—
83	C₄⋊Dic₁₁	—	4	2	no	—
84	C₄⋊Dic₁₁	—	4	2	no	—
85	Dic₁₁⋊C₄	—	4	4	no	—
86	Dic₁₁⋊C₄	—	4	4	no	—
87	Dic₄₄	—	2	4	no	—
88	Dic₄₄	—	4	2	no	—
89	D₈₈	—	2	4	no	—
90	D₈₈	—	4	2	no	—
91	#4314	—	4	4	no	—
92	#4314	—	4	4	no	—
93	C₁₁×C₁₆	—	2	4	no	—
94	C₂×#499	—	11	1	no	—
95	#3147	—	11	1	no	—
96	#2245	—	11	2	no	—
97	#2244	—	11	2	no	—
98	#2242	—	11	4	no	—
99	#2139	—	11	4	no	—
100	C₄×M₃₂	D₁₁	1	1	yes	characteristic, complemented
101	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
102	C₂²×D₁₁	—	4	2	no	—
103	C₂×C₄×C₁₁	—	4	2	no	—
104	C₂×C₄×C₁₁	#124	1	2	yes	—
105	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
106	C₂×C₄×C₁₁	C₂×D₈	1	2	yes	—
107	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
108	C₂×C₄×C₁₁	C₂×SD₁₆	1	2	yes	—
109	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
110	C₂²⋊D₁₁	—	8	4	no	—
111	C₂×Dic₁₁	—	4	4	no	—
112	C₂×Dic₁₁	—	4	2	no	—
113	C₂×Dic₁₁	—	8	4	no	—
114	D₄₄	—	4	2	no	—
115	D₄₄	—	4	2	no	—
116	D₄₄	—	8	4	no	—
117	C₄×D₁₁	—	8	4	no	—
118	Dic₂₂	—	4	2	no	—
119	Dic₂₂	—	4	2	no	—
120	C₈×C₁₁	#124	1	2	yes	—
121	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
122	C₈×C₁₁	C₂×SD₁₆	1	2	yes	—
123	C₈×C₁₁	C₂×#41	1	2	yes	—
124	C₂×#135	—	11	2	no	—
125	C₂×#135	—	22	1	no	—
126	#532	—	22	1	no	—
127	C₂×#125	—	22	1	no	—
128	C₂×M₃₂	C₂×D₁₁	1	2	yes	—
129	#499	—	11	2	no	—
130	#499	—	11	2	no	—
131	#499	—	22	1	no	—
132	#499	—	22	1	no	—
133	#495	—	11	2	no	—
134	#495	—	22	1	no	—
135	#494	—	11	1	no	—
136	#493	—	11	1	no	—
137	#492	—	22	1	no	—
138	C₂×#107	—	11	2	no	—
139	C₂×#106	—	22	1	no	—
140	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
141	#358	—	11	8	no	—
142	#357	—	11	8	no	—
143	#346	C₂×D₁₁	1	2	yes	—
144	C₄×C₁₆	C₂×D₁₁	1	2	yes	—
145	C₂²×C₁₁	—	2	2	no	—
146	C₂²×C₁₁	#486	1	2	yes	—
147	C₂²×C₁₁	C₂²×D₈	1	1	yes	characteristic
148	C₂×D₁₁	—	8	2	no	—
149	C₂×D₁₁	—	8	4	no	—
150	C₄×C₁₁	—	2	2	no	—
151	C₄×C₁₁	—	2	2	no	—
152	C₄×C₁₁	#486	1	2	yes	—
153	C₄×C₁₁	C₂×#124	1	1	yes	characteristic
154	C₄×C₁₁	C₂²×SD₁₆	1	1	yes	characteristic
155	Dic₁₁	—	8	2	no	—
156	Dic₁₁	—	8	4	no	—
157	C₂×#41	—	22	2	no	—
158	#135	—	22	8	no	—
159	#135	—	44	4	no	—
160	C₂×Q₁₆	—	11	2	no	—
161	C₂×Q₁₆	—	22	1	no	—
162	C₂×SD₁₆	—	22	2	no	—
163	C₂×SD₁₆	—	22	2	no	—
164	C₂×D₈	—	11	2	no	—
165	C₂×D₈	—	22	1	no	—
166	C₂²×C₈	D₄₄	1	1	yes	characteristic
167	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
168	C₄⋊Q₈	—	22	1	no	—
169	#127	—	22	1	no	—
170	#125	—	22	2	no	—
171	#125	—	22	2	no	—
172	#125	—	44	2	no	—
173	#124	—	22	2	no	—
174	#121	—	44	2	no	—
175	C₄×D₄	—	44	2	no	—
176	C₂×C₄⋊C₄	—	22	2	no	—
177	C₂×C₄⋊C₄	—	44	2	no	—
178	C₂×C₄²	D₄₄	1	1	yes	characteristic
179	M₃₂	—	2	4	no	—
180	C₂×C₁₆	C₂²×D₁₁	1	4	yes	—
181	#107	—	11	4	no	—
182	#107	—	22	2	no	—
183	#106	—	22	2	no	—
184	#106	—	22	2	no	—
185	C₄×C₈	D₄₄	1	1	yes	characteristic
186	C₄×C₈	D₄₄	1	1	yes	characteristic
187	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
188	C₄×C₈	C₂²×D₁₁	1	1	yes	characteristic
189	C₂×C₁₁	—	2	2	no	—
190	C₂×C₁₁	C₂×#486	1	1	yes	characteristic
191	C₂×C₁₁	#3414	1	2	yes	—
192	D₁₁	—	16	2	no	—
193	#41	—	44	4	no	—
194	#41	—	44	4	no	—
195	C₂×Q₈	—	22	2	no	—
196	C₂×D₄	—	22	2	no	—
197	C₂×D₄	—	44	2	no	—
198	C₂×D₄	—	44	2	no	—
199	C₂²×C₄	—	44	2	no	—
200	C₂²×C₄	—	44	2	no	—
201	C₂²×C₄	D₈₈	1	2	yes	—
202	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
203	Q₁₆	—	22	4	no	—
204	Q₁₆	—	44	2	no	—
205	SD₁₆	—	44	4	no	—
206	SD₁₆	—	44	4	no	—
207	D₈	—	22	4	no	—
208	D₈	—	44	2	no	—
209	C₂×C₈	#4314	1	4	yes	—
210	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
211	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
212	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
213	C₂×C₈	#4339	1	4	yes	—
214	C₂×C₈	C₂³×D₁₁	1	1	yes	characteristic
215	C₄⋊C₄	—	22	4	no	—
216	C₄⋊C₄	—	44	2	no	—
217	C₄⋊C₄	—	44	4	no	—
218	C₄⋊C₄	—	44	4	no	—
219	C₄⋊C₄	—	44	2	no	—
220	C₂²⋊C₄	—	44	4	no	—
221	C₄²	D₈₈	1	2	yes	—
222	C₄²	C₂×D₄₄	1	1	yes	characteristic
223	C₄²	C₂×D₄₄	1	1	yes	characteristic
224	C₁₆	—	2	4	no	—
225	C₁₁	#33708	1	1	yes	characteristic, complemented, Sylow
226	C₂³	—	44	2	no	—
227	C₂³	C₂×D₈₈	1	1	yes	characteristic
228	Q₈	—	44	2	no	—
229	Q₈	—	44	2	no	—
230	D₄	—	44	2	no	—
231	D₄	—	44	2	no	—
232	D₄	—	88	4	no	—
233	D₄	—	88	4	no	—
234	C₂×C₄	—	4	2	no	—
235	C₂×C₄	—	44	2	no	—
236	C₂×C₄	—	44	4	no	—
237	C₂×C₄	—	88	4	no	—
238	C₂×C₄	—	88	4	no	—
239	C₂×C₄	#66928	1	2	yes	—
240	C₂×C₄	C₂×#4314	1	2	yes	—
241	C₂×C₄	C₂×D₈₈	1	2	yes	—
242	C₂×C₄	C₂×D₈₈	1	2	yes	—
243	C₂×C₄	C₂×D₈₈	1	1	yes	characteristic
244	C₂×C₄	C₂²×D₄₄	1	1	yes	characteristic
245	C₈	#66928	1	2	yes	—
246	C₈	C₂×#4314	1	2	yes	—
247	C₈	C₂×#4314	1	2	yes	—
248	C₈	C₂×#4339	1	2	yes	—
249	C₂²	—	2	2	no	—
250	C₂²	—	88	2	no	—
251	C₂²	—	88	4	no	—
252	C₂²	#10622307	1	2	yes	—
253	C₂²	C₂²×D₈₈	1	1	yes	characteristic
254	C₄	—	2	2	no	—
255	C₄	—	2	2	no	—
256	C₄	—	88	2	no	—
257	C₄	—	88	4	no	—
258	C₄	#10622307	1	2	yes	—
259	C₄	C₂×#66928	1	1	yes	characteristic
260	C₄	C₂²×#4314	1	1	yes	characteristic
261	C₂	—	2	2	no	—
262	C₂	—	176	2	no	—
263	C₂	C₂×#10622307	1	1	yes	characteristic
264	C₂	#13081752	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₈₈
commutator, cosocle	C₂×C₈×C₁₁	C₂⁴
Frattini	C₂×C₈	C₂³×D₁₁
Fitting	C₄×C₁₁×M₃₂	C₂
socle	C₂²×C₁₁	C₂²×D₈
prime radical	#13079044	C₂
hypercenter	C₄×M₃₂	D₁₁
hypocenter	C₁₁	#33708
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
1. C₂×#10622296	C₂	semidirect
3. #13070862	C₂	semidirect
4. #13070858	C₂	semidirect
5. #13070848	C₂	semidirect
6. #13070329	C₂	semidirect
7. C₄×C₁₁×M₃₂	C₂	semidirect
100. C₄×M₃₂	D₁₁	semidirect
225. C₁₁	#33708	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622296	2
#13079044	2
#13070862	2
#13070858	2
#13070848	2
#13070329	2
C₄×C₁₁×M₃₂	2
#33708	11