Subgroups — #14672382

Order 2816.

374 conjugacy classes of subgroups.

The subgroup lattice has 182 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
2	#13068776	C₂	1	1	yes	maximal, characteristic
3	#13066708	C₂	1	4	yes	maximal
4	C₂×C₁₁×#346	C₂	1	1	yes	maximal, characteristic
5	C₂×#66923	—	2	1	no	—
6	C₂²×C₁₁×C₁₆	C₂²	1	2	yes	—
7	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
8	C₂×#66882	—	2	1	no	—
9	C₂×#66882	C₂²	1	2	yes	—
10	C₂×#66882	C₂²	1	2	yes	—
11	C₂×#66881	—	2	1	no	—
12	#10622548	—	2	1	no	—
13	#10622296	—	2	2	no	—
14	#10622296	C₄	1	4	yes	complemented
15	C₁₁×#346	—	2	2	no	—
16	C₂²×C₈×C₁₁	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
19	C₂×C₄⋊Dic₁₁	—	2	2	no	—
20	C₂×C₄⋊Dic₁₁	—	2	2	no	—
21	C₂×C₄⋊Dic₁₁	—	4	2	no	—
22	C₂×Dic₁₁⋊C₄	—	4	2	no	—
23	#66923	—	2	4	no	—
24	#66923	—	4	2	no	—
25	C₂×C₁₁×C₁₆	—	2	2	no	—
26	C₂×C₁₁×C₁₆	—	2	2	no	—
27	C₂×C₁₁×C₁₆	Q₈	1	4	yes	—
28	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
29	C₄×C₈×C₁₁	D₄	1	2	yes	—
30	#66882	—	2	2	no	—
31	#66882	—	2	4	no	—
32	#66882	—	4	2	no	—
33	#66882	C₂×C₄	1	4	yes	—
34	#66881	—	2	4	no	—
35	#13284	—	11	1	no	maximal, Sylow
36	C₂²×C₄×C₁₁	D₈	1	2	yes	—
37	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
38	C₂²×Dic₁₁	—	4	2	no	—
39	C₂²×Dic₁₁	—	4	2	no	—
40	C₂×C₈×C₁₁	C₂²⋊C₄	1	2	yes	—
41	C₂×C₈×C₁₁	SD₁₆	1	2	yes	—
42	C₂×C₈×C₁₁	Q₁₆	1	2	yes	—
43	C₂×C₈×C₁₁	C₂²×C₄	1	1	yes	characteristic
44	C₂×C₈×C₁₁	C₂×D₄	1	1	yes	characteristic
45	C₂×C₈×C₁₁	C₂×Q₈	1	2	yes	—
46	C₂×C₈×C₁₁	#41	1	2	yes	—
47	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
48	C₄²×C₁₁	SD₁₆	1	2	yes	—
49	C₄⋊Dic₁₁	—	2	4	no	—
50	C₄⋊Dic₁₁	—	4	2	no	—
51	C₄⋊Dic₁₁	—	4	2	no	—
52	C₄⋊Dic₁₁	—	4	2	no	—
53	C₄⋊Dic₁₁	—	8	4	no	—
54	Dic₁₁⋊C₄	—	4	8	no	—
55	C₁₁×C₁₆	—	2	4	no	—
56	C₂×#499	—	11	1	no	—
57	C₂×#346	D₁₁	1	1	yes	characteristic
58	#1845	—	11	1	no	—
59	#1380	—	11	4	no	—
60	C₂³×C₁₁	C₂×D₈	1	1	yes	characteristic
61	C₂×C₄×C₁₁	—	2	2	no	—
62	C₂×C₄×C₁₁	—	2	2	no	—
63	C₂×C₄×C₁₁	#102	1	4	yes	—
64	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×C₁₁	#124	1	1	yes	characteristic
66	C₂×C₄×C₁₁	C₄⋊Q₈	1	1	yes	characteristic
67	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
68	C₂×C₄×C₁₁	C₂×SD₁₆	1	1	yes	characteristic
69	C₂×C₄×C₁₁	C₂×Q₁₆	1	1	yes	characteristic
70	C₂×Dic₁₁	—	4	4	no	—
71	C₂×Dic₁₁	—	8	2	no	—
72	C₂×Dic₁₁	—	8	2	no	—
73	C₂×Dic₁₁	—	8	2	no	—
74	C₂×Dic₁₁	—	8	4	no	—
75	C₈×C₁₁	#103	1	4	yes	—
76	C₈×C₁₁	C₄×Q₈	1	2	yes	—
77	C₈×C₁₁	C₂²⋊Q₈	1	2	yes	—
78	C₂×#125	—	22	1	no	—
79	C₂²×C₁₆	C₂×D₁₁	1	2	yes	—
80	#499	—	11	4	no	—
81	#499	—	22	2	no	—
82	C₂×#107	—	11	2	no	—
83	C₂×#107	—	11	2	no	—
84	C₂×#107	—	22	1	no	—
85	C₂×#106	—	22	1	no	—
86	C₂×C₄×C₈	C₂×D₁₁	1	1	yes	characteristic
87	#384	—	22	1	no	—
88	#346	—	2	2	no	—
89	C₂²×C₁₁	C₂×#102	1	1	yes	characteristic
90	C₂²×C₁₁	#486	1	1	yes	characteristic
91	C₂²×C₁₁	#500	1	1	yes	characteristic
92	C₂²×C₁₁	#509	1	2	yes	—
93	C₂²×C₁₁	#510	1	2	yes	—
94	C₄×C₁₁	—	2	4	no	—
95	C₄×C₁₁	#391	1	1	yes	characteristic
96	C₄×C₁₁	C₂×#103	1	1	yes	characteristic
97	C₄×C₁₁	#487	1	1	yes	characteristic
98	C₄×C₁₁	#498	1	1	yes	characteristic
99	Dic₁₁	—	8	4	no	—
100	Dic₁₁	—	16	2	no	—
101	C₂²×C₈	D₄₄	1	1	yes	characteristic
102	C₂²×C₈	C₂²×D₁₁	1	1	yes	characteristic
103	#125	—	22	4	no	—
104	#125	—	44	2	no	—
105	C₂×C₄⋊C₄	—	22	2	no	—
106	C₂×C₄⋊C₄	—	22	2	no	—
107	C₂×C₄⋊C₄	—	44	2	no	—
108	C₂×C₄⋊C₄	—	44	2	no	—
109	C₂×C₄²	D₄₄	1	1	yes	characteristic
110	C₂×C₁₆	—	2	2	no	—
111	C₂×C₁₆	—	2	2	no	—
112	C₂×C₁₆	Dic₂₂	1	4	yes	—
113	#107	—	11	4	no	—
114	#107	—	22	2	no	—
115	#107	—	22	4	no	—
116	#107	—	44	2	no	—
117	#106	—	22	4	no	—
118	C₄×C₈	C₄×D₁₁	1	2	yes	—
119	C₄×C₈	C₂²⋊D₁₁	1	2	yes	—
120	C₂×C₁₁	#1990	1	1	yes	characteristic
121	C₂×C₁₁	#2139	1	2	yes	—
122	C₂×C₁₁	#2244	1	1	yes	characteristic
123	C₂×C₁₁	#2245	1	1	yes	characteristic
124	C₂×C₁₁	#2255	1	2	yes	—
125	C₂²×C₄	—	44	2	no	—
126	C₂²×C₄	—	44	2	no	—
127	C₂²×C₄	D₈₈	1	2	yes	—
128	C₂²×C₄	C₂×D₄₄	1	1	yes	characteristic
129	C₂×C₈	#4314	1	2	yes	—
130	C₂×C₈	Dic₄₄	1	2	yes	—
131	C₂×C₈	(C₂×D₁₁)⋊C₄	1	2	yes	—
132	C₂×C₈	C₂×Dic₂₂	1	2	yes	—
133	C₂×C₈	C₂×C₄×D₁₁	1	1	yes	characteristic
134	C₂×C₈	#4339	1	2	yes	—
135	C₂×C₈	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
136	C₄⋊C₄	—	22	4	no	—
137	C₄⋊C₄	—	44	8	no	—
138	C₄⋊C₄	—	44	2	no	—
139	C₄⋊C₄	—	44	2	no	—
140	C₄⋊C₄	—	44	2	no	—
141	C₄⋊C₄	—	88	4	no	—
142	C₄²	#4314	1	2	yes	—
143	C₄²	(C₂×D₁₁)⋊C₄	1	2	yes	—
144	C₁₆	—	2	4	no	—
145	C₁₁	#13284	1	1	yes	characteristic, complemented, Sylow
146	C₂³	C₂×D₈₈	1	1	yes	characteristic
147	C₂×C₄	—	2	2	no	—
148	C₂×C₄	—	2	2	no	—
149	C₂×C₄	—	44	4	no	—
150	C₂×C₄	—	88	2	no	—
151	C₂×C₄	—	88	2	no	—
152	C₂×C₄	—	88	4	no	—
153	C₂×C₄	—	88	2	no	—
154	C₂×C₄	#66885	1	4	yes	—
155	C₂×C₄	#66922	1	1	yes	characteristic
156	C₂×C₄	#66928	1	1	yes	characteristic
157	C₂×C₄	C₂×#4314	1	1	yes	characteristic
158	C₂×C₄	C₂×#4314	1	1	yes	characteristic
159	C₂×C₄	C₂×Dic₄₄	1	1	yes	characteristic
160	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
161	C₈	#66880	1	4	yes	—
162	C₈	C₄×Dic₂₂	1	2	yes	—
163	C₈	#66977	1	2	yes	—
164	C₂²	#10622295	1	1	yes	characteristic
165	C₂²	#10622307	1	1	yes	characteristic
166	C₂²	#10622521	1	2	yes	—
167	C₂²	#10622522	1	2	yes	—
168	C₂²	C₂×#66885	1	1	yes	characteristic
169	C₄	—	2	4	no	—
170	C₄	—	88	4	no	—
171	C₄	—	176	2	no	—
172	C₄	#10622293	1	1	yes	characteristic
173	C₄	#10622294	1	1	yes	characteristic
174	C₄	#10622542	1	1	yes	characteristic
175	C₄	C₂×#66880	1	1	yes	characteristic
176	C₂	#13069577	1	1	yes	characteristic
177	C₂	#13070329	1	2	yes	—
178	C₂	#13070858	1	1	yes	characteristic
179	C₂	#13070862	1	1	yes	characteristic
180	C₂	#13070902	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₈₈
commutator	C₂×C₈×C₁₁	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₁
Fitting	C₂×C₁₁×#346	C₂
socle, prime radical	C₂³×C₁₁	C₂×D₈
cosocle	C₂²×C₈×C₁₁	C₂³
hypercenter	C₂×#346	D₁₁
hypocenter	C₁₁	#13284
LCS	G ▷ C₂×C₈×C₁₁ ▷ C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
14. #10622296	C₄	semidirect
145. C₁₁	#13284	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
#13068776	2
#13066708	2
C₂×C₁₁×#346	2
#13284	11