Subgroups — #15777748

Order 3328.

402 conjugacy classes of subgroups.

The subgroup lattice has 206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718058	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718104	C₂	1	2	yes	maximal
3	M₃₂×Dic₁₃	C₂	1	2	yes	maximal
4	#13114524	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×#347	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
7	C₂×C₁₃×#97	C₂²	1	1	yes	characteristic
8	C₂×#88055	C₄	1	1	yes	characteristic
9	C₂×#88055	C₂²	1	1	yes	characteristic
10	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
12	C₂×#88052	C₂²	1	2	yes	—
13	#11718593	C₄	1	1	yes	characteristic
14	C₂×C₄×#1055	C₄	1	1	yes	characteristic
15	C₁₃×#347	C₄	1	4	yes	complemented
16	#11718104	C₄	1	8	yes	complemented
17	#11718094	C₄	1	4	yes	complemented
18	C₁₆×Dic₁₃	C₄	1	4	yes	complemented
19	#11718058	C₄	1	4	yes	complemented
20	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
22	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
26	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
27	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
28	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
29	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
30	C₁₃×#97	C₂×C₄	1	2	yes	—
31	C₁₃×#97	C₂×C₄	1	2	yes	—
32	#88071	—	2	2	no	—
33	#88055	—	2	2	no	—
34	#88055	C₂×C₄	1	4	yes	—
35	C₈×Dic₁₃	—	2	2	no	—
36	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
37	C₈×Dic₁₃	C₂×C₄	1	2	yes	—
38	#88052	C₂×C₄	1	4	yes	—
39	#88052	C₂×C₄	1	4	yes	—
40	C₂×#6090	C₂×C₄	1	4	yes	—
41	C₄×#1055	—	2	2	no	—
42	#12541	—	13	1	no	maximal, Sylow
43	C₂²×C₄×C₁₃	—	2	1	no	—
44	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂²×Dic₁₃	—	2	1	no	—
46	C₂²×Dic₁₃	M₁₆	1	2	yes	—
47	C₂×C₈×C₁₃	—	2	1	no	—
48	C₂×C₈×C₁₃	—	2	1	no	—
49	C₂×C₈×C₁₃	C₄²	1	2	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
51	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
52	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
53	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
54	C₄²×C₁₃	—	2	1	no	—
55	C₄²×C₁₃	C₄²	1	2	yes	—
56	C₄×Dic₁₃	—	2	1	no	—
57	C₄×Dic₁₃	C₄²	1	2	yes	—
58	C₄×Dic₁₃	C₄²	1	2	yes	—
59	C₄×Dic₁₃	M₁₆	1	2	yes	—
60	C₂×#1055	—	2	1	no	—
61	C₂×#1055	—	2	1	no	—
62	C₂×#1055	C₄²	1	2	yes	—
63	C₂×#1055	C₄²	1	1	yes	characteristic
64	C₂×#1055	C₄²	1	1	yes	characteristic
65	C₂×#1055	M₁₆	1	2	yes	—
66	C₂×#1055	M₁₆	1	2	yes	—
67	C₁₃×C₁₆	C₄²	1	8	yes	—
68	#6090	C₄²	1	8	yes	—
69	C₂×#347	—	13	2	no	—
70	C₂×#347	—	13	1	no	—
71	C₂×#347	D₁₃	1	1	yes	characteristic
72	C₄×M₃₂	—	13	2	no	—
73	#1726	—	13	1	no	—
74	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
75	C₂×C₄×C₁₃	—	2	2	no	—
76	C₂×C₄×C₁₃	—	4	2	no	—
77	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
78	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
79	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
80	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
81	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
82	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
83	C₂×Dic₁₃	—	2	2	no	—
84	C₂×Dic₁₃	—	4	2	no	—
85	C₂×Dic₁₃	—	4	2	no	—
86	C₂×Dic₁₃	#97	1	4	yes	—
87	C₈×C₁₃	—	2	2	no	—
88	C₈×C₁₃	C₂×C₄²	1	2	yes	—
89	C₈×C₁₃	C₂×C₄²	1	2	yes	—
90	#1055	—	2	2	no	—
91	#1055	#97	1	2	yes	—
92	#1055	#97	1	2	yes	—
93	C₂×M₃₂	—	13	2	no	—
94	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
95	C₂×#97	—	13	1	no	—
96	C₂×#97	—	13	1	no	—
97	C₂×#97	C₂×D₁₃	1	1	yes	characteristic
98	C₂×C₄×C₈	—	13	1	no	—
99	C₂×C₄×C₈	—	13	1	no	—
100	C₂×C₄×C₈	—	13	1	no	—
101	#376	—	13	1	no	—
102	#347	—	13	8	no	—
103	#347	—	13	4	no	—
104	#347	Dic₁₃	1	4	yes	complemented
105	#346	—	13	4	no	—
106	C₄×C₁₆	—	13	4	no	—
107	C₂²×C₁₃	—	2	2	no	—
108	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
109	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
110	C₂²×C₁₃	C₄×M₁₆	1	1	yes	characteristic
111	C₄×C₁₃	—	4	2	no	—
112	C₄×C₁₃	C₄³	1	1	yes	characteristic
113	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
114	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
115	C₄×C₁₃	C₄×M₁₆	1	1	yes	characteristic
116	Dic₁₃	—	2	4	no	—
117	Dic₁₃	—	4	2	no	—
118	C₂²×C₈	—	13	1	no	—
119	C₂²×C₈	—	13	1	no	—
120	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
121	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
122	C₂×C₄²	—	13	1	no	—
123	C₂×C₄²	—	13	1	no	—
124	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
125	M₃₂	—	13	4	no	—
126	M₃₂	—	13	4	no	—
127	M₃₂	C₄×D₁₃	1	4	yes	—
128	M₃₂	C₂×Dic₁₃	1	4	yes	—
129	C₂×C₁₆	—	13	4	no	—
130	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
131	#97	—	13	4	no	—
132	#97	—	26	2	no	—
133	#97	C₄×D₁₃	1	2	yes	—
134	#97	C₂×Dic₁₃	1	2	yes	—
135	C₄×C₈	—	13	2	no	—
136	C₄×C₈	—	13	2	no	—
137	C₄×C₈	—	26	2	no	—
138	C₄×C₈	—	26	2	no	—
139	#95	—	26	2	no	—
140	C₂×C₁₃	—	2	1	no	—
141	C₂×C₁₃	—	2	1	no	—
142	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
143	C₂×C₁₃	#2110	1	2	yes	—
144	C₂²×C₄	—	2	1	no	—
145	C₂²×C₄	—	13	2	no	—
146	C₂²×C₄	—	26	1	no	—
147	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
148	C₂×C₈	—	2	1	no	—
149	C₂×C₈	—	2	1	no	—
150	C₂×C₈	—	13	1	no	—
151	C₂×C₈	—	13	1	no	—
152	C₂×C₈	—	13	2	no	—
153	C₂×C₈	—	13	2	no	—
154	C₂×C₈	—	13	2	no	—
155	C₂×C₈	—	26	1	no	—
156	C₂×C₈	—	26	1	no	—
157	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
158	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
159	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
160	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
161	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
162	C₄²	—	2	1	no	—
163	C₄²	—	13	2	no	—
164	C₄²	—	13	2	no	—
165	C₄²	—	13	2	no	—
166	C₄²	—	26	1	no	—
167	C₄²	C₄×Dic₁₃	1	2	yes	—
168	C₁₆	—	13	8	no	—
169	C₁₆	C₄×Dic₁₃	1	8	yes	—
170	C₁₃	#12541	1	1	yes	characteristic, complemented, Sylow
171	C₂³	M₁₆×D₁₃	1	1	yes	characteristic
172	C₂×C₄	—	2	2	no	—
173	C₂×C₄	—	4	2	no	—
174	C₂×C₄	—	13	4	no	—
175	C₂×C₄	—	26	2	no	—
176	C₂×C₄	—	52	2	no	—
177	C₂×C₄	—	52	2	no	—
178	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
179	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
180	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
181	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
182	C₂×C₄	M₁₆×D₁₃	1	1	yes	characteristic
183	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
184	C₈	—	2	2	no	—
185	C₈	—	13	2	no	—
186	C₈	—	13	2	no	—
187	C₈	—	26	2	no	—
188	C₈	C₄²×D₁₃	1	2	yes	—
189	C₈	C₂×C₄×Dic₁₃	1	2	yes	—
190	C₂²	—	2	2	no	—
191	C₂²	D₁₃×#97	1	1	yes	characteristic
192	C₂²	#11718368	1	1	yes	characteristic
193	C₂²	M₁₆×Dic₁₃	1	1	yes	characteristic
194	C₄	—	4	2	no	—
195	C₄	—	26	4	no	—
196	C₄	—	52	2	no	—
197	C₄	D₁₃×#97	1	1	yes	characteristic
198	C₄	#11718368	1	1	yes	characteristic
199	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
200	C₄	M₁₆×Dic₁₃	1	1	yes	characteristic
201	C₂	—	2	1	no	—
202	C₂	—	2	1	no	—
203	C₂	#97×Dic₁₃	1	1	yes	characteristic
204	C₂	#13116439	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₁₃
commutator	C₄×C₁₃	C₄³
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₁₃×#347	C₂
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×#347	D₁₃
hypocenter	C₁₃	#12541
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#347

Complements

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

N	H ≅ G/N	type
15. C₁₃×#347	C₄	semidirect
16. #11718104	C₄	semidirect
17. #11718094	C₄	semidirect
18. C₁₆×Dic₁₃	C₄	semidirect
19. #11718058	C₄	semidirect
104. #347	Dic₁₃	semidirect
170. C₁₃	#12541	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718058	2
C₂×#11718104	2
M₃₂×Dic₁₃	2
#13114524	2
C₂×C₁₃×#347	2
#12541	13