Subgroups — #13073135

Order 1408.

436 conjugacy classes of subgroups.

The subgroup lattice has 246 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#66943	C₂	1	2	yes	maximal
2	C₁₁×#389	C₂	1	1	yes	maximal, characteristic
3	#10622598	C₂	1	1	yes	maximal, characteristic
4	#10622598	C₂	1	1	yes	maximal, characteristic
5	#10622597	C₂	1	2	yes	maximal
6	#10622589	C₂	1	1	yes	maximal, characteristic
7	C₄⋊C₄×Dic₁₁	C₂	1	1	yes	maximal, characteristic
8	C₄×C₄⋊Dic₁₁	C₂	1	1	yes	maximal, characteristic
9	#10622541	C₂	1	1	yes	maximal, characteristic
10	#10622273	C₂	1	2	yes	maximal
11	#10622268	C₂	1	2	yes	maximal
12	C₂×C₁₁×C₄⋊C₄	C₂²	1	2	yes	—
13	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₁₁×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₄²×C₁₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₁₁	C₂²	1	2	yes	—
18	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊Dic₁₁	C₂²	1	1	yes	characteristic
22	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	—
23	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	—
24	C₂×Dic₁₁⋊C₄	C₂²	1	2	yes	—
25	C₂×C₄×Dic₁₁	C₂²	1	2	yes	—
26	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₁₁	C₂²	1	1	yes	characteristic
28	#66943	—	2	8	no	—
29	C₁₁×#95	C₂²	1	2	yes	—
30	C₁₁⋊#95	C₂²	1	1	yes	characteristic
31	C₁₁⋊#95	C₂²	1	2	yes	—
32	C₁₁⋊#95	C₂²	1	2	yes	—
33	C₁₁⋊#95	C₂²	1	1	yes	characteristic
34	C₁₁⋊#95	C₂²	1	2	yes	—
35	C₁₁⋊#95	C₂²	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
38	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₁₁	C₂³	1	2	yes	—
40	C₂²×C₄×C₁₁	C₂³	1	1	yes	characteristic
41	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
42	C₂²×Dic₁₁	C₂³	1	2	yes	—
43	C₂²×Dic₁₁	C₂³	1	2	yes	—
44	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
45	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
46	C₂²×Dic₁₁	C₂³	1	1	yes	characteristic
47	C₁₁×C₄⋊C₄	—	2	4	no	—
48	C₁₁×C₄⋊C₄	—	2	2	no	—
49	C₁₁×C₄⋊C₄	Q₈	1	4	yes	—
50	C₄²×C₁₁	—	2	2	no	—
51	C₄⋊Dic₁₁	—	2	4	no	—
52	C₄⋊Dic₁₁	—	2	4	no	—
53	C₄⋊Dic₁₁	—	2	2	no	—
54	C₄⋊Dic₁₁	—	2	2	no	—
55	C₄⋊Dic₁₁	—	2	2	no	—
56	C₄⋊Dic₁₁	D₄	1	4	yes	—
57	Dic₁₁⋊C₄	—	2	4	no	—
58	Dic₁₁⋊C₄	—	2	4	no	—
59	Dic₁₁⋊C₄	—	2	4	no	—
60	C₄×Dic₁₁	—	2	4	no	—
61	C₄×Dic₁₁	—	2	2	no	—
62	C₄×Dic₁₁	—	2	2	no	—
63	#2506	—	11	1	no	maximal, Sylow
64	C₂³×C₁₁	C₂⁴	1	1	yes	characteristic
65	C₂×C₄×C₁₁	—	2	2	no	—
66	C₂×C₄×C₁₁	—	2	1	no	—
67	C₂×C₄×C₁₁	—	2	1	no	—
68	C₂×C₄×C₁₁	—	2	2	no	—
69	C₂×C₄×C₁₁	—	2	2	no	—
70	C₂×C₄×C₁₁	—	2	2	no	—
71	C₂×C₄×C₁₁	—	2	1	no	—
72	C₂×C₄×C₁₁	—	2	2	no	—
73	C₂×C₄×C₁₁	—	2	1	no	—
74	C₂×C₄×C₁₁	—	2	1	no	—
75	C₂×C₄×C₁₁	C₂×D₄	1	2	yes	—
76	C₂×C₄×C₁₁	C₂×Q₈	1	4	yes	—
77	C₂×C₄×C₁₁	C₂×Q₈	1	2	yes	—
78	C₂×C₄×C₁₁	#41	1	2	yes	—
79	C₂×C₄×C₁₁	#41	1	2	yes	—
80	C₂×Dic₁₁	—	2	1	no	—
81	C₂×Dic₁₁	—	2	1	no	—
82	C₂×Dic₁₁	—	2	1	no	—
83	C₂×Dic₁₁	—	2	1	no	—
84	C₂×Dic₁₁	—	2	1	no	—
85	C₂×Dic₁₁	—	2	1	no	—
86	C₂×Dic₁₁	—	2	2	no	—
87	C₂×Dic₁₁	—	2	2	no	—
88	C₂×Dic₁₁	—	2	1	no	—
89	C₂×Dic₁₁	—	2	2	no	—
90	C₂×Dic₁₁	—	2	2	no	—
91	C₂×Dic₁₁	—	2	2	no	—
92	C₂×Dic₁₁	—	2	1	no	—
93	C₂×Dic₁₁	—	2	2	no	—
94	C₂×Dic₁₁	—	2	1	no	—
95	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
96	C₂×Dic₁₁	C₂×D₄	1	2	yes	—
97	C₂×Dic₁₁	#41	1	2	yes	—
98	C₂×#125	—	11	2	no	—
99	#400	—	11	2	no	—
100	#398	—	11	2	no	—
101	#389	—	11	1	no	—
102	#389	—	11	1	no	—
103	#389	—	11	1	no	—
104	#389	D₁₁	1	1	yes	characteristic
105	#387	—	11	2	no	—
106	#384	—	11	1	no	—
107	C₄×C₄⋊C₄	—	11	1	no	—
108	C₄×C₄⋊C₄	—	11	1	no	—
109	C₂²×C₁₁	C₂²×D₄	1	1	yes	characteristic
110	C₂²×C₁₁	C₂²×Q₈	1	1	yes	characteristic
111	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
112	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
113	C₂²×C₁₁	C₂×#41	1	1	yes	characteristic
114	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
115	C₂²×C₁₁	2₋¹⁺⁴	1	1	yes	characteristic
116	C₄×C₁₁	—	2	2	no	—
117	C₄×C₁₁	—	2	4	no	—
118	C₄×C₁₁	—	4	2	no	—
119	C₄×C₁₁	—	4	1	no	—
120	C₄×C₁₁	#125	1	4	yes	complemented
121	Dic₁₁	—	2	2	no	—
122	Dic₁₁	—	2	2	no	—
123	Dic₁₁	—	2	2	no	—
124	Dic₁₁	—	4	2	no	—
125	Dic₁₁	—	4	2	no	—
126	Dic₁₁	—	4	1	no	—
127	#125	—	22	8	no	—
128	C₂×C₄⋊C₄	—	11	1	no	—
129	C₂×C₄⋊C₄	—	11	2	no	—
130	C₂×C₄⋊C₄	—	11	2	no	—
131	C₂×C₄⋊C₄	—	11	2	no	—
132	C₂×C₄⋊C₄	—	11	2	no	—
133	C₂×C₄⋊C₄	—	11	1	no	—
134	C₂×C₄⋊C₄	—	11	1	no	—
135	C₂×C₄⋊C₄	—	11	2	no	—
136	C₂×C₄⋊C₄	—	11	1	no	—
137	C₂×C₄⋊C₄	C₂×D₁₁	1	2	yes	—
138	C₂×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
139	C₂×C₄⋊C₄	C₂×D₁₁	1	1	yes	characteristic
140	C₂×C₄²	—	11	2	no	—
141	C₂×C₄²	—	11	1	no	—
142	C₂×C₄²	—	11	1	no	—
143	C₂×C₄²	C₂×D₁₁	1	1	yes	characteristic
144	#95	—	11	1	no	—
145	#95	—	11	2	no	—
146	#95	—	11	1	no	—
147	#95	—	11	2	no	—
148	#95	—	11	2	no	—
149	#95	—	11	2	no	—
150	#95	C₂×D₁₁	1	2	yes	—
151	C₂×C₁₁	C₂×#125	1	1	yes	characteristic
152	C₂×C₁₁	#532	1	1	yes	characteristic
153	C₂×C₁₁	#541	1	1	yes	characteristic
154	C₂×C₁₁	#547	1	1	yes	characteristic
155	C₂×C₁₁	D₄×Q₈	1	1	yes	characteristic
156	C₂×C₁₁	#552	1	1	yes	characteristic
157	C₂×C₁₁	#557	1	1	yes	characteristic
158	C₂²×C₄	—	11	1	no	—
159	C₂²×C₄	—	11	1	no	—
160	C₂²×C₄	—	11	1	no	—
161	C₂²×C₄	—	11	1	no	—
162	C₂²×C₄	—	11	2	no	—
163	C₂²×C₄	—	11	2	no	—
164	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
165	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
166	C₂²×C₄	C₂²×D₁₁	1	2	yes	—
167	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
168	C₂²×C₄	C₂²×D₁₁	1	1	yes	characteristic
169	C₄⋊C₄	—	2	4	no	—
170	C₄⋊C₄	—	2	2	no	—
171	C₄⋊C₄	—	11	4	no	—
172	C₄⋊C₄	—	22	4	no	—
173	C₄⋊C₄	—	22	4	no	—
174	C₄⋊C₄	—	22	4	no	—
175	C₄⋊C₄	—	22	4	no	—
176	C₄⋊C₄	—	22	2	no	—
177	C₄⋊C₄	—	22	4	no	—
178	C₄⋊C₄	—	22	2	no	—
179	C₄⋊C₄	—	22	2	no	—
180	C₄⋊C₄	Dic₂₂	1	4	yes	—
181	C₄²	—	2	2	no	—
182	C₄²	—	22	4	no	—
183	C₄²	—	22	2	no	—
184	C₄²	—	22	2	no	—
185	C₁₁	#2506	1	1	yes	characteristic, complemented, Sylow
186	C₂³	C₂³×D₁₁	1	1	yes	characteristic
187	C₂×C₄	—	2	2	no	—
188	C₂×C₄	—	2	1	no	—
189	C₂×C₄	—	2	1	no	—
190	C₂×C₄	—	2	2	no	—
191	C₂×C₄	—	2	2	no	—
192	C₂×C₄	—	2	1	no	—
193	C₂×C₄	—	2	2	no	—
194	C₂×C₄	—	2	1	no	—
195	C₂×C₄	—	2	2	no	—
196	C₂×C₄	—	2	1	no	—
197	C₂×C₄	—	11	2	no	—
198	C₂×C₄	—	11	2	no	—
199	C₂×C₄	—	11	2	no	—
200	C₂×C₄	—	22	1	no	—
201	C₂×C₄	—	22	1	no	—
202	C₂×C₄	—	22	1	no	—
203	C₂×C₄	—	22	1	no	—
204	C₂×C₄	—	22	1	no	—
205	C₂×C₄	—	22	1	no	—
206	C₂×C₄	—	22	2	no	—
207	C₂×C₄	—	22	2	no	—
208	C₂×C₄	—	22	2	no	—
209	C₂×C₄	—	22	1	no	—
210	C₂×C₄	—	22	2	no	—
211	C₂×C₄	—	22	2	no	—
212	C₂×C₄	—	22	2	no	—
213	C₂×C₄	—	22	1	no	—
214	C₂×C₄	—	22	1	no	—
215	C₂×C₄	C₂×Dic₂₂	1	4	yes	—
216	C₂×C₄	C₂×Dic₂₂	1	2	yes	—
217	C₂×C₄	D₄×D₁₁	1	2	yes	—
218	C₂×C₄	#4341	1	2	yes	—
219	C₂×C₄	#4343	1	2	yes	—
220	C₂²	C₂²×Dic₂₂	1	1	yes	characteristic
221	C₂²	C₂×D₄×D₁₁	1	1	yes	characteristic
222	C₂²	C₂×#4341	1	1	yes	characteristic
223	C₂²	C₂×#4343	1	1	yes	characteristic
224	C₂²	#67040	1	1	yes	characteristic
225	C₂²	#41×D₁₁	1	1	yes	characteristic
226	C₂²	#67043	1	1	yes	characteristic
227	C₄	—	2	4	no	—
228	C₄	—	2	2	no	—
229	C₄	—	4	2	no	—
230	C₄	—	4	1	no	—
231	C₄	—	22	2	no	—
232	C₄	—	22	2	no	—
233	C₄	—	22	2	no	—
234	C₄	—	44	2	no	—
235	C₄	—	44	2	no	—
236	C₄	—	44	1	no	—
237	C₄	#66943	1	4	yes	complemented
238	C₂	C₂×#66943	1	1	yes	characteristic
239	C₂	D₄×Dic₂₂	1	1	yes	characteristic
240	C₂	#10623100	1	1	yes	characteristic
241	C₂	#10623127	1	1	yes	characteristic
242	C₂	#10623156	1	1	yes	characteristic
243	C₂	#10623225	1	1	yes	characteristic
244	C₂	#10623257	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₁
commutator, socle, prime radical, cosocle	C₂³×C₁₁	C₂⁴
Fitting	C₁₁×#389	C₂
hypercenter	#389	D₁₁
hypocenter	C₁₁	#2506
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ #389

Complements

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

N	H ≅ G/N	type
120. C₄×C₁₁	#125	semidirect
185. C₁₁	#2506	semidirect
237. C₄	#66943	semidirect

Maximal subgroups

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

subgroup	index
C₂×#66943	2
C₁₁×#389	2
#10622598	2
#10622597	2
#10622589	2
C₄⋊C₄×Dic₁₁	2
C₄×C₄⋊Dic₁₁	2
#10622541	2
#10622273	2
#10622268	2
#2506	11