Subgroups — #16807383

Order 3328.

444 conjugacy classes of subgroups.

The subgroup lattice has 208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131253	C₂	1	4	yes	maximal, complemented
2	#13131252	C₂	1	4	yes	maximal, complemented
3	#13131202	C₂	1	2	yes	maximal
4	#13131201	C₂	1	2	yes	maximal
5	#13131198	C₂	1	2	yes	maximal
6	#13123769	C₂	1	1	yes	maximal, characteristic
7	#11719222	C₄	1	1	yes	characteristic
8	C₁₃×#424	C₄	1	1	yes	characteristic
9	#11718783	C₂²	1	1	yes	characteristic
10	#11718779	C₄	1	1	yes	characteristic
11	#11718763	C₄	1	1	yes	characteristic
12	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
13	#11718658	C₂²	1	1	yes	characteristic
14	#11718491	C₂²	1	4	yes	—
15	#11718489	C₄	1	4	yes	—
16	C₂²⋊#6092	C₂²	1	4	yes	—
17	#11718260	C₂²	1	2	yes	—
18	#11718260	C₂²	1	2	yes	—
19	#11718260	C₂²	1	4	yes	—
20	#11718258	C₂²	1	4	yes	—
21	#11718258	C₂²	1	2	yes	—
22	#11718257	C₂²	1	2	yes	—
23	#11718231	C₂²	1	2	yes	—
24	C₄⋊#6092	C₂²	1	4	yes	—
25	C₄×#6092	C₂²	1	2	yes	—
26	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
29	#88180	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₂×#6099	C₂×C₄	1	1	yes	characteristic
32	C₂²×#1055	C₂³	1	1	yes	characteristic
33	#88144	C₈	1	2	yes	—
34	#88142	C₈	1	2	yes	—
35	#88132	C₈	1	4	yes	—
36	C₄×Dic₂₆	C₂×C₄	1	4	yes	—
37	C₂×#6092	C₂³	1	4	yes	—
38	C₂×#6092	C₂³	1	4	yes	—
39	C₁₃×C₄⋊C₈	C₂×C₄	1	4	yes	—
40	#88055	C₂×C₄	1	2	yes	—
41	#88054	C₂×C₄	1	4	yes	—
42	#88054	C₂×C₄	1	4	yes	—
43	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
44	C₈×Dic₁₃	C₂³	1	2	yes	—
45	C₈×Dic₁₃	C₂³	1	2	yes	—
46	#88043	C₂×C₄	1	2	yes	—
47	C₄×#1055	C₂³	1	2	yes	—
48	#33501	—	13	1	no	maximal, Sylow
49	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
51	C₂×Dic₂₆	C₂×C₈	1	4	yes	—
52	C₁₃×M₁₆	—	4	1	no	—
53	C₂×C₈×C₁₃	—	4	1	no	—
54	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
55	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
56	C₁₃×C₄⋊C₄	C₂×C₈	1	2	yes	—
57	C₁₃×C₂²⋊C₄	C₂×C₈	1	2	yes	—
58	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
59	C₂²⋊Dic₁₃	C₂×C₈	1	2	yes	—
60	C₄⋊Dic₁₃	C₂×C₈	1	4	yes	—
61	C₄⋊Dic₁₃	C₂×C₈	1	2	yes	—
62	#6101	C₂×C₈	1	4	yes	—
63	#6101	C₂×C₈	1	4	yes	—
64	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
65	C₄×Dic₁₃	C₂×C₈	1	1	yes	characteristic
66	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
67	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
68	#6099	—	4	1	no	—
69	C₂×#1055	—	2	2	no	—
70	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
71	C₂×#1055	C₂²×C₄	1	2	yes	—
72	C₂×#1055	C₂⁴	1	1	yes	characteristic
73	#6092	—	2	4	no	—
74	#6092	—	2	4	no	—
75	#2960	—	13	1	no	—
76	#2183	—	13	4	no	—
77	#2183	—	13	4	no	—
78	#2164	—	13	2	no	—
79	#2164	—	13	2	no	—
80	#2163	—	13	2	no	—
81	C₂³×C₁₃	C₂²×C₈	1	1	yes	characteristic
82	C₂×C₄×C₁₃	—	2	1	no	—
83	C₂×C₄×C₁₃	—	2	1	no	—
84	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
85	C₂×C₄×C₁₃	C₂²×C₈	1	4	yes	—
86	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
87	C₂×Dic₁₃	—	4	2	no	—
88	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
89	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
90	C₂×Dic₁₃	C₂²×C₈	1	4	yes	—
91	Dic₂₆	—	4	4	no	—
92	C₈×C₁₃	—	2	2	no	—
93	C₈×C₁₃	—	2	2	no	—
94	#1055	—	2	1	no	—
95	#1055	—	2	2	no	—
96	#1055	2₋¹⁺⁴	1	2	yes	—
97	#533	—	13	1	no	—
98	#446	—	13	4	no	—
99	C₈×Q₈	—	13	4	no	—
100	#424	—	13	1	no	—
101	#424	#261	1	1	yes	characteristic
102	#423	—	13	1	no	—
103	#405	—	13	1	no	—
104	#405	—	13	1	no	—
105	C₂×C₄×C₈	—	13	1	no	—
106	C₄⋊C₁₆	—	13	4	no	—
107	C₄⋊C₁₆	—	13	2	no	—
108	C₄⋊C₁₆	—	13	2	no	—
109	C₄⋊C₁₆	—	13	4	no	—
110	C₂²⋊C₁₆	—	13	4	no	—
111	#346	—	13	2	no	—
112	#346	—	13	4	no	—
113	#346	—	13	2	no	—
114	C₄×C₁₆	—	13	2	no	—
115	C₄×C₁₆	—	13	2	no	—
116	C₂²×C₁₃	—	2	2	no	—
117	C₂²×C₁₃	—	2	1	no	—
118	C₂²×C₁₃	C₂³×C₈	1	1	yes	characteristic
119	C₄×C₁₃	—	2	4	no	—
120	C₄×C₁₃	—	2	1	no	—
121	C₄×C₁₃	#519	1	1	yes	characteristic
122	C₄×C₁₃	#568	1	1	yes	characteristic
123	Dic₁₃	—	2	2	no	—
124	Dic₁₃	—	2	4	no	—
125	Dic₁₃	—	2	2	no	—
126	C₂×M₁₆	—	13	1	no	—
127	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
128	C₂²×C₈	—	13	1	no	—
129	C₂²×C₈	C₂×#261	1	1	yes	characteristic
130	C₄⋊Q₈	—	13	2	no	—
131	#125	—	13	2	no	—
132	C₂²⋊Q₈	—	13	4	no	—
133	C₄×Q₈	—	13	4	no	—
134	#117	—	13	1	no	—
135	#117	C₂×#261	1	1	yes	characteristic
136	C₂×C₄²	—	13	1	no	—
137	C₂×C₁₆	—	13	4	no	—
138	C₂×C₁₆	—	13	4	no	—
139	C₄⋊C₈	—	13	4	no	—
140	C₄⋊C₈	—	13	4	no	—
141	C₄⋊C₈	C₂×#261	1	4	yes	—
142	#97	—	13	2	no	—
143	#97	—	13	2	no	—
144	C₄×C₈	—	13	2	no	—
145	C₄×C₈	—	13	2	no	—
146	C₄×C₈	—	13	2	no	—
147	C₄×C₈	—	13	2	no	—
148	C₂×C₁₃	—	4	1	no	—
149	C₂×C₁₃	#2982	1	1	yes	characteristic
150	C₂×C₁₃	#3407	1	2	yes	—
151	C₂×Q₈	—	13	4	no	—
152	C₂²×C₄	—	13	2	no	—
153	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
154	M₁₆	—	4	1	no	—
155	M₁₆	—	52	1	no	—
156	C₂×C₈	—	4	1	no	—
157	C₂×C₈	—	13	1	no	—
158	C₂×C₈	—	13	1	no	—
159	C₂×C₈	—	13	2	no	—
160	C₂×C₈	—	26	2	no	—
161	C₂×C₈	C₂²×#261	1	2	yes	—
162	C₂×C₈	C₂²×#261	1	2	yes	—
163	C₄⋊C₄	—	13	2	no	—
164	C₄⋊C₄	—	13	4	no	—
165	C₄⋊C₄	—	13	4	no	—
166	C₄⋊C₄	—	13	4	no	—
167	C₄⋊C₄	D₁₃⋊C₈	1	2	yes	—
168	C₂²⋊C₄	—	13	2	no	—
169	C₂²⋊C₄	D₁₃⋊C₈	1	2	yes	—
170	C₄²	—	13	1	no	—
171	C₄²	—	13	1	no	—
172	C₄²	—	13	2	no	—
173	C₄²	—	13	2	no	—
174	C₄²	C₂²×#261	1	2	yes	—
175	C₁₆	—	26	4	no	—
176	C₁₆	—	26	4	no	—
177	C₁₃	#33501	1	1	yes	characteristic, complemented, Sylow
178	C₂³	C₂×D₁₃⋊C₈	1	1	yes	characteristic
179	Q₈	—	52	4	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	1	no	—
182	C₂×C₄	—	13	2	no	—
183	C₂×C₄	—	13	2	no	—
184	C₂×C₄	—	13	4	no	—
185	C₂×C₄	—	52	2	no	—
186	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
187	C₂×C₄	C₂×D₁₃⋊C₈	1	4	yes	—
188	C₂×C₄	C₂³×#261	1	1	yes	characteristic
189	C₈	—	2	2	no	—
190	C₈	—	2	2	no	—
191	C₈	—	13	2	no	—
192	C₈	—	26	2	no	—
193	C₈	—	26	1	no	—
194	C₂²	—	2	2	no	—
195	C₂²	—	2	1	no	—
196	C₂²	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
197	C₄	—	2	4	no	—
198	C₄	—	2	1	no	—
199	C₄	—	26	2	no	—
200	C₄	—	26	2	no	—
201	C₄	—	26	4	no	—
202	C₄	#11719621	1	1	yes	characteristic
203	C₄	#11719627	1	1	yes	characteristic
204	C₂	—	4	1	no	—
205	C₂	#13131731	1	1	yes	characteristic
206	C₂	#13131804	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂³×C₈
Fitting	C₁₃×#424	C₄
prime radical	C₂³×C₁₃	C₂²×C₈
cosocle	C₂×#1055	C₂⁴
hypercenter	#424	#261
hypocenter	C₁₃	#33501
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #424

Complements

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

N	H ≅ G/N	type
1. #13131253	C₂	semidirect
2. #13131252	C₂	semidirect
177. C₁₃	#33501	semidirect

Maximal subgroups

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

subgroup	index
#13131253	2
#13131252	2
#13131202	2
#13131201	2
#13131198	2
#13123769	2
#33501	13