Subgroups — #14671990

Order 2816.

510 conjugacy classes of subgroups.

The subgroup lattice has 214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622312	C₂	1	1	yes	maximal, characteristic
2	C₂×#10622130	C₂	1	4	yes	maximal
3	C₂×C₄×C₁₁⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	C₁₁×#1845	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₄₄	—	2	1	no	—
6	C₂²×Dic₄₄	C₂²	1	2	yes	—
7	C₂×#66922	—	2	1	no	—
8	C₂×C₁₁×#107	—	2	1	no	—
9	C₂×C₁₁×#107	C₂²	1	2	yes	—
10	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
11	C₁₁×#384	—	2	1	no	—
12	C₂²×C₁₁⋊C₁₆	C₂²	1	2	yes	—
13	#10622312	—	2	2	no	—
14	#10622312	C₄	1	4	yes	complemented
15	#10622130	—	2	8	no	—
16	C₄×C₁₁⋊C₁₆	—	2	2	no	—
17	C₂²×Dic₂₂	—	2	2	no	—
18	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
19	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
20	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
21	C₂×C₁₁×C₄⋊C₄	—	4	2	no	—
22	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
23	C₂×C₄⋊Dic₁₁	—	4	2	no	—
24	C₂×Dic₄₄	—	2	4	no	—
25	C₂×Dic₄₄	—	2	4	no	—
26	C₂×Dic₄₄	—	2	4	no	—
27	C₂×Dic₄₄	—	2	2	no	—
28	C₂×Dic₄₄	—	4	2	no	—
29	C₂×Dic₄₄	—	4	2	no	—
30	C₂×Dic₄₄	C₂×C₄	1	4	yes	—
31	#66922	—	2	4	no	—
32	#66922	—	4	2	no	—
33	C₁₁×#107	—	2	4	no	—
34	C₁₁×#107	—	4	2	no	—
35	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
36	C₄×C₈×C₁₁	D₄	1	2	yes	—
37	C₂×C₁₁⋊C₁₆	—	2	2	no	—
38	C₂×C₁₁⋊C₁₆	—	2	2	no	—
39	C₂×C₁₁⋊C₁₆	D₄	1	4	yes	—
40	#13203	—	11	1	no	maximal, Sylow
41	C₂²×C₄×C₁₁	—	4	2	no	—
42	C₂²×C₄×C₁₁	D₈	1	2	yes	—
43	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
44	C₂²×Dic₁₁	—	4	2	no	—
45	C₂×Dic₂₂	—	2	4	no	—
46	C₂×Dic₂₂	—	4	2	no	—
47	C₂×Dic₂₂	—	4	2	no	—
48	C₂×Dic₂₂	—	4	2	no	—
49	C₂×Dic₂₂	—	4	2	no	—
50	C₂×Dic₂₂	—	4	2	no	—
51	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
52	C₂×C₈×C₁₁	D₈	1	2	yes	—
53	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
54	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
55	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
56	C₂×C₈×C₁₁	C₂×D₄	1	2	yes	—
57	C₂×C₈×C₁₁	#41	1	2	yes	—
58	C₁₁×C₄⋊C₄	—	4	2	no	—
59	C₁₁×C₄⋊C₄	—	4	2	no	—
60	C₁₁×C₄⋊C₄	—	8	4	no	—
61	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
62	C₄²×C₁₁	SD₁₆	1	2	yes	—
63	C₄⋊Dic₁₁	—	4	8	no	—
64	Dic₄₄	—	2	8	no	—
65	Dic₄₄	—	4	8	no	—
66	Dic₄₄	—	4	4	no	—
67	C₁₁⋊C₁₆	—	2	4	no	—
68	C₂×#494	—	11	1	no	—
69	C₂×#358	—	11	4	no	—
70	C₂×C₄×C₁₆	—	11	1	no	—
71	#1845	D₁₁	1	1	yes	characteristic
72	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
73	C₂×C₄×C₁₁	—	8	2	no	—
74	C₂×C₄×C₁₁	—	8	4	no	—
75	C₂×C₄×C₁₁	#102	1	4	yes	—
76	C₂×C₄×C₁₁	SD₃₂	1	4	yes	—
77	C₂×C₄×C₁₁	Q₃₂	1	4	yes	—
78	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
80	C₂×C₄×C₁₁	#127	1	1	yes	characteristic
81	C₂×C₄×C₁₁	C₂×D₈	1	1	yes	characteristic
82	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
83	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
84	C₂×Dic₁₁	—	4	4	no	—
85	C₂×Dic₁₁	—	8	2	no	—
86	C₂×Dic₁₁	—	8	2	no	—
87	Dic₂₂	—	4	4	no	—
88	Dic₂₂	—	4	4	no	—
89	Dic₂₂	—	8	2	no	—
90	Dic₂₂	—	8	2	no	—
91	C₈×C₁₁	#102	1	4	yes	—
92	C₈×C₁₁	C₄×D₄	1	2	yes	—
93	C₈×C₁₁	#121	1	2	yes	—
94	C₂²×Q₁₆	—	11	2	no	—
95	C₂²×Q₁₆	—	22	1	no	—
96	C₂×C₄⋊Q₈	—	22	1	no	—
97	C₂²×C₁₆	—	11	2	no	—
98	#494	—	11	4	no	—
99	#494	—	22	2	no	—
100	C₂×#107	—	2	1	no	—
101	C₂×#107	C₂×D₁₁	1	2	yes	—
102	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
103	#384	—	2	1	no	—
104	#358	—	22	8	no	—
105	C₄×C₁₆	—	22	2	no	—
106	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
107	C₂²×C₁₁	#486	1	1	yes	characteristic
108	C₂²×C₁₁	#493	1	1	yes	characteristic
109	C₂²×C₁₁	C₂×SD₃₂	1	2	yes	—
110	C₂²×C₁₁	C₂×Q₃₂	1	2	yes	—
111	C₄×C₁₁	—	16	2	no	—
112	C₄×C₁₁	#358	1	8	yes	complemented
113	C₄×C₁₁	#390	1	1	yes	characteristic
114	C₄×C₁₁	C₂×#102	1	1	yes	characteristic
115	C₄×C₁₁	#486	1	1	yes	characteristic
116	C₄×C₁₁	#492	1	1	yes	characteristic
117	Dic₁₁	—	8	4	no	—
118	C₂²×Q₈	—	22	2	no	—
119	C₂×Q₁₆	—	11	4	no	—
120	C₂×Q₁₆	—	22	4	no	—
121	C₂×Q₁₆	—	22	2	no	—
122	C₂×Q₁₆	—	22	4	no	—
123	C₂×Q₁₆	—	22	4	no	—
124	C₂×Q₁₆	—	44	2	no	—
125	C₂×Q₁₆	—	44	2	no	—
126	C₂²×C₈	C₂²⋊D₁₁	1	1	yes	characteristic
127	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
128	C₄⋊Q₈	—	22	4	no	—
129	C₄⋊Q₈	—	44	2	no	—
130	C₂×C₄⋊C₄	—	2	2	no	—
131	C₂×C₄⋊C₄	—	4	2	no	—
132	C₂×C₄⋊C₄	—	44	2	no	—
133	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
134	C₂×C₁₆	—	11	4	no	—
135	C₂×C₁₆	—	22	2	no	—
136	C₂×C₁₆	—	22	2	no	—
137	#107	—	2	4	no	—
138	#107	—	4	2	no	—
139	C₄×C₈	C₄×D₁₁	1	2	yes	—
140	C₄×C₈	D₄₄	1	2	yes	—
141	C₂×C₁₁	#1957	1	1	yes	characteristic
142	C₂×C₁₁	C₂×#358	1	2	yes	—
143	C₂×C₁₁	#2241	1	2	yes	—
144	C₂×C₁₁	#2247	1	1	yes	characteristic
145	C₂×C₁₁	#2248	1	1	yes	characteristic
146	C₂×Q₈	—	22	4	no	—
147	C₂×Q₈	—	44	2	no	—
148	C₂×Q₈	—	44	2	no	—
149	C₂×Q₈	—	44	2	no	—
150	C₂×Q₈	—	44	2	no	—
151	C₂×Q₈	—	44	2	no	—
152	C₂²×C₄	—	4	2	no	—
153	C₂²×C₄	—	44	2	no	—
154	C₂²×C₄	#4323	1	2	yes	—
155	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
156	Q₁₆	—	22	8	no	—
157	Q₁₆	—	44	8	no	—
158	Q₁₆	—	44	4	no	—
159	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
160	C₂×C₈	#4323	1	2	yes	—
161	C₂×C₈	#4325	1	2	yes	—
162	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
163	C₂×C₈	C₂×D₄₄	1	1	yes	characteristic
164	C₂×C₈	D₄×D₁₁	1	2	yes	—
165	C₂×C₈	#4343	1	2	yes	—
166	C₄⋊C₄	—	4	2	no	—
167	C₄⋊C₄	—	4	2	no	—
168	C₄⋊C₄	—	8	4	no	—
169	C₄⋊C₄	—	44	8	no	—
170	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
171	C₄²	#4325	1	2	yes	—
172	C₁₆	—	22	4	no	—
173	C₁₁	#13203	1	1	yes	characteristic, complemented, Sylow
174	C₂³	C₂×#4323	1	1	yes	characteristic
175	Q₈	—	44	4	no	—
176	Q₈	—	44	4	no	—
177	Q₈	—	88	2	no	—
178	Q₈	—	88	2	no	—
179	C₂×C₄	—	8	4	no	—
180	C₂×C₄	—	8	2	no	—
181	C₂×C₄	—	44	4	no	—
182	C₂×C₄	—	88	2	no	—
183	C₂×C₄	—	88	2	no	—
184	C₂×C₄	#66873	1	4	yes	—
185	C₂×C₄	#66891	1	4	yes	—
186	C₂×C₄	#66893	1	4	yes	—
187	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
188	C₂×C₄	C₂×#4323	1	1	yes	characteristic
189	C₂×C₄	#66993	1	1	yes	characteristic
190	C₂×C₄	C₂×#4325	1	1	yes	characteristic
191	C₂×C₄	C₂×#4325	1	1	yes	characteristic
192	C₂×C₄	#67000	1	1	yes	characteristic
193	C₈	#66873	1	4	yes	—
194	C₈	#66946	1	2	yes	—
195	C₈	#66948	1	2	yes	—
196	C₂²	C₂×#66873	1	1	yes	characteristic
197	C₂²	#10622686	1	1	yes	characteristic
198	C₂²	#10622701	1	1	yes	characteristic
199	C₂²	C₂×#66891	1	2	yes	—
200	C₂²	C₂×#66893	1	2	yes	—
201	C₄	—	16	2	no	—
202	C₄	—	88	4	no	—
203	C₄	#10622130	1	8	yes	complemented
204	C₄	C₂×#66873	1	1	yes	characteristic
205	C₄	#10622601	1	1	yes	characteristic
206	C₄	#10622698	1	1	yes	characteristic
207	C₄	#10622701	1	1	yes	characteristic
208	C₂	#13069421	1	1	yes	characteristic
209	C₂	C₂×#10622130	1	2	yes	—
210	C₂	#13070845	1	2	yes	—
211	C₂	#13070868	1	1	yes	characteristic
212	C₂	#13070871	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#4323
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₁₁×#1845	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	#1845	D₁₁
hypocenter	C₁₁	#13203
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1845

Complements

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

N	H ≅ G/N	type
14. #10622312	C₄	semidirect
112. C₄×C₁₁	#358	semidirect
173. C₁₁	#13203	semidirect
203. C₄	#10622130	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622312	2
C₂×#10622130	2
C₂×C₄×C₁₁⋊C₁₆	2
C₁₁×#1845	2
#13203	11