Subgroups — #14684965

Order 2816.

1710 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10622548	C₂	1	2	yes	maximal
2	C₂×#10622549	C₂	1	4	yes	maximal
3	#13066846	C₂	1	8	yes	maximal
4	C₂×C₄³×C₁₁	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	4	yes	—
6	C₂²×C₄²×C₁₁	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊Dic₁₁	C₂²	1	8	yes	—
9	C₂²×C₄⋊Dic₁₁	C₂²	1	4	yes	—
10	C₄³×C₁₁	C₄	1	8	yes	complemented
11	C₂×C₁₁⋊#95	C₂²	1	16	yes	—
12	#10622549	—	2	16	no	—
13	#10622548	—	2	8	no	—
14	C₂³×C₄×C₁₁	C₂³	1	4	yes	—
15	C₂³×C₄×C₁₁	C₂³	1	1	yes	characteristic
16	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
17	C₂³×Dic₁₁	C₂³	1	8	yes	—
18	C₂×C₄²×C₁₁	—	2	16	no	—
19	C₂×C₄²×C₁₁	C₂×C₄	1	16	yes	—
20	C₂×C₄²×C₁₁	C₂×C₄	1	4	yes	—
21	C₂×C₄²×C₁₁	C₂×C₄	1	8	yes	—
22	C₂×C₄²×C₁₁	D₄	1	4	yes	—
23	C₂×C₄²×C₁₁	D₄	1	8	yes	—
24	C₂×C₄²×C₁₁	Q₈	1	4	yes	—
25	C₂×C₄²×C₁₁	Q₈	1	8	yes	—
26	C₂×C₄⋊Dic₁₁	—	2	16	no	—
27	C₂×C₄⋊Dic₁₁	—	2	8	no	—
28	C₂×C₄⋊Dic₁₁	—	2	16	no	—
29	C₂×C₄⋊Dic₁₁	—	2	32	no	—
30	C₁₁⋊#95	—	2	32	no	—
31	#14687	—	11	1	no	maximal, Sylow
32	C₂⁴×C₁₁	C₂⁴	1	1	yes	characteristic
33	C₂²×C₄×C₁₁	—	2	16	no	—
34	C₂²×C₄×C₁₁	C₂²×C₄	1	8	yes	—
35	C₂²×C₄×C₁₁	C₂²×C₄	1	2	yes	—
36	C₂²×C₄×C₁₁	C₂²×C₄	1	4	yes	—
37	C₂²×C₄×C₁₁	C₂×D₄	1	8	yes	—
38	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
39	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
40	C₂²×C₄×C₁₁	C₂×D₄	1	4	yes	—
41	C₂²×C₄×C₁₁	C₂×Q₈	1	8	yes	—
42	C₂²×C₄×C₁₁	C₂×Q₈	1	4	yes	—
43	C₂²×C₄×C₁₁	C₂×Q₈	1	2	yes	—
44	C₂²×C₄×C₁₁	C₂×Q₈	1	4	yes	—
45	C₂²×C₄×C₁₁	#41	1	16	yes	—
46	C₂²×Dic₁₁	—	2	16	no	—
47	C₂²×Dic₁₁	—	2	8	no	—
48	C₂²×Dic₁₁	—	2	32	no	—
49	C₄²×C₁₁	—	2	32	no	—
50	C₄²×C₁₁	C₄⋊C₄	1	16	yes	—
51	C₄²×C₁₁	C₄⋊C₄	1	32	yes	complemented
52	C₄⋊Dic₁₁	—	4	32	no	—
53	C₄⋊Dic₁₁	—	4	16	no	—
54	C₂×#384	—	11	2	no	—
55	C₂×#382	—	11	4	no	—
56	C₂×C₄³	D₁₁	1	1	yes	characteristic
57	C₄⋊#95	—	11	8	no	—
58	C₂³×C₁₁	C₂³×C₄	1	1	yes	characteristic
59	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
60	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
61	C₂³×C₁₁	C₂²×Q₈	1	1	yes	characteristic
62	C₂³×C₁₁	C₂²×Q₈	1	2	yes	—
63	C₂³×C₁₁	C₂×#41	1	8	yes	—
64	C₂×C₄×C₁₁	—	2	16	no	—
65	C₂×C₄×C₁₁	—	2	16	no	—
66	C₂×C₄×C₁₁	—	2	16	no	—
67	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	16	yes	—
68	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	8	yes	—
69	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	4	yes	—
70	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	8	yes	—
71	C₂×C₄×C₁₁	#117	1	16	yes	—
72	C₂×C₄×C₁₁	#124	1	16	yes	—
73	C₂×C₄×C₁₁	#125	1	16	yes	—
74	C₂×C₄×C₁₁	#127	1	4	yes	—
75	C₂×C₄×C₁₁	C₄⋊Q₈	1	8	yes	—
76	C₂×C₄×C₁₁	C₄⋊Q₈	1	4	yes	—
77	C₂×Dic₁₁	—	4	16	no	—
78	C₂×Dic₁₁	—	4	8	no	—
79	C₂×Dic₁₁	—	4	32	no	—
80	C₂²×C₄⋊C₄	—	11	8	no	—
81	C₂²×C₄⋊C₄	—	11	4	no	—
82	C₂²×C₄²	C₂×D₁₁	1	4	yes	—
83	C₂²×C₄²	C₂×D₁₁	1	2	yes	—
84	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
85	#384	—	22	8	no	—
86	#382	—	22	16	no	—
87	C₂×#95	—	11	16	no	—
88	C₄³	Dic₁₁	1	8	yes	complemented
89	C₂²×C₁₁	C₂²×C₄⋊C₄	1	1	yes	characteristic
90	C₂²×C₁₁	C₂²×C₄⋊C₄	1	2	yes	—
91	C₂²×C₁₁	C₂×#117	1	4	yes	—
92	C₂²×C₁₁	C₂×#124	1	4	yes	—
93	C₂²×C₁₁	C₂×#125	1	4	yes	—
94	C₂²×C₁₁	C₂×#127	1	1	yes	characteristic
95	C₂²×C₁₁	C₂×C₄⋊Q₈	1	2	yes	—
96	C₂²×C₁₁	C₂×C₄⋊Q₈	1	1	yes	characteristic
97	C₂²×C₁₁	#532	1	8	yes	—
98	C₂²×C₁₁	#533	1	8	yes	—
99	C₄×C₁₁	—	2	16	no	—
100	C₄×C₁₁	#382	1	16	yes	complemented
101	C₄×C₁₁	#384	1	8	yes	—
102	Dic₁₁	—	8	8	no	—
103	C₂³×C₄	—	11	8	no	—
104	C₂³×C₄	C₂²×D₁₁	1	4	yes	—
105	C₂³×C₄	C₂²×D₁₁	1	1	yes	characteristic
106	C₂³×C₄	C₂²×D₁₁	1	2	yes	—
107	C₂×C₄⋊C₄	—	22	16	no	—
108	C₂×C₄⋊C₄	—	22	8	no	—
109	C₂×C₄⋊C₄	—	22	16	no	—
110	C₂×C₄⋊C₄	—	22	32	no	—
111	C₂×C₄²	—	2	16	no	—
112	C₂×C₄²	Dic₂₂	1	4	yes	—
113	C₂×C₄²	Dic₂₂	1	8	yes	—
114	C₂×C₄²	D₄₄	1	4	yes	—
115	C₂×C₄²	D₄₄	1	8	yes	—
116	C₂×C₄²	C₂×Dic₁₁	1	16	yes	—
117	C₂×C₄²	C₂×Dic₁₁	1	4	yes	—
118	C₂×C₄²	C₂×Dic₁₁	1	8	yes	—
119	#95	—	22	32	no	—
120	C₂×C₁₁	C₂×#382	1	2	yes	—
121	C₂×C₁₁	C₂×#384	1	1	yes	characteristic
122	C₂×C₁₁	#2285	1	4	yes	—
123	C₂×C₁₁	#2858	1	2	yes	—
124	C₂×C₁₁	#2859	1	4	yes	—
125	C₂×C₁₁	#2862	1	2	yes	—
126	C₂⁴	C₂³×D₁₁	1	1	yes	characteristic
127	C₂²×C₄	—	2	16	no	—
128	C₂²×C₄	—	22	16	no	—
129	C₂²×C₄	—	22	8	no	—
130	C₂²×C₄	—	22	32	no	—
131	C₂²×C₄	C₂×Dic₂₂	1	8	yes	—
132	C₂²×C₄	C₂×Dic₂₂	1	2	yes	—
133	C₂²×C₄	C₂×Dic₂₂	1	4	yes	—
134	C₂²×C₄	C₂×Dic₂₂	1	4	yes	—
135	C₂²×C₄	C₂×D₄₄	1	8	yes	—
136	C₂²×C₄	C₂×D₄₄	1	2	yes	—
137	C₂²×C₄	C₂×D₄₄	1	4	yes	—
138	C₂²×C₄	C₂×D₄₄	1	4	yes	—
139	C₂²×C₄	#4339	1	16	yes	—
140	C₂²×C₄	C₂²×Dic₁₁	1	8	yes	—
141	C₂²×C₄	C₂²×Dic₁₁	1	2	yes	—
142	C₂²×C₄	C₂²×Dic₁₁	1	4	yes	—
143	C₄⋊C₄	—	44	16	no	—
144	C₄⋊C₄	—	44	32	no	—
145	C₄²	—	2	32	no	—
146	C₄²	C₄⋊Dic₁₁	1	16	yes	—
147	C₄²	C₄⋊Dic₁₁	1	32	yes	complemented
148	C₁₁	#14687	1	1	yes	characteristic, complemented, Sylow
149	C₂³	C₂²×Dic₂₂	1	1	yes	characteristic
150	C₂³	C₂²×Dic₂₂	1	2	yes	—
151	C₂³	C₂²×D₄₄	1	1	yes	characteristic
152	C₂³	C₂²×D₄₄	1	2	yes	—
153	C₂³	C₂×#4339	1	8	yes	—
154	C₂³	C₂³×Dic₁₁	1	1	yes	characteristic
155	C₂×C₄	—	2	16	no	—
156	C₂×C₄	—	2	16	no	—
157	C₂×C₄	—	2	16	no	—
158	C₂×C₄	—	44	8	no	—
159	C₂×C₄	—	44	16	no	—
160	C₂×C₄	—	44	32	no	—
161	C₂×C₄	#66922	1	4	yes	—
162	C₂×C₄	#66922	1	8	yes	—
163	C₂×C₄	#66923	1	16	yes	—
164	C₂×C₄	#66927	1	4	yes	—
165	C₂×C₄	#66928	1	16	yes	—
166	C₂×C₄	C₂×C₄⋊Dic₁₁	1	16	yes	—
167	C₂×C₄	C₂×C₄⋊Dic₁₁	1	4	yes	—
168	C₂×C₄	C₂×C₄⋊Dic₁₁	1	8	yes	—
169	C₂×C₄	C₂×C₄⋊Dic₁₁	1	8	yes	—
170	C₂×C₄	#66979	1	16	yes	—
171	C₂²	C₂×#66922	1	1	yes	characteristic
172	C₂²	C₂×#66922	1	2	yes	—
173	C₂²	C₂×#66923	1	4	yes	—
174	C₂²	#10623001	1	8	yes	—
175	C₂²	C₂×#66927	1	1	yes	characteristic
176	C₂²	C₂×#66928	1	4	yes	—
177	C₂²	#10623008	1	8	yes	—
178	C₂²	C₂²×C₄⋊Dic₁₁	1	1	yes	characteristic
179	C₂²	C₂²×C₄⋊Dic₁₁	1	2	yes	—
180	C₂²	C₂×#66979	1	4	yes	—
181	C₄	—	2	16	no	—
182	C₄	—	88	8	no	—
183	C₄	#10622548	1	8	yes	—
184	C₄	#10622549	1	16	yes	complemented
185	C₂	C₂×#10622549	1	2	yes	—
186	C₂	C₂×#10622548	1	1	yes	characteristic
187	C₂	#13071023	1	4	yes	—
188	C₂	#13076973	1	2	yes	—
189	C₂	#13076979	1	4	yes	—
190	C₂	#13076994	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂⁴	C₂³×D₁₁
commutator	C₂³×C₁₁	C₂³×C₄
Fitting	C₂×C₄³×C₁₁	C₂
socle, prime radical, cosocle	C₂⁴×C₁₁	C₂⁴
hypercenter	C₂×C₄³	D₁₁
hypocenter	C₁₁	#14687
LCS	G ▷ C₂³×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂⁴ ◁ C₂×C₄³

Complements

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

N	H ≅ G/N	type
10. C₄³×C₁₁	C₄	semidirect
51. C₄²×C₁₁	C₄⋊C₄	semidirect
88. C₄³	Dic₁₁	semidirect
100. C₄×C₁₁	#382	semidirect
147. C₄²	C₄⋊Dic₁₁	semidirect
148. C₁₁	#14687	semidirect
184. C₄	#10622549	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10622548	2
C₂×#10622549	2
#13066846	2
C₂×C₄³×C₁₁	2
#14687	11