Subgroups — #15771899

Order 3328.

330 conjugacy classes of subgroups.

The subgroup lattice has 162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88038	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₆×D₁₃	C₂	1	1	yes	maximal, characteristic
3	#13113118	C₂	1	1	yes	maximal, characteristic
4	#13112753	C₂	1	1	yes	maximal, characteristic, complemented
5	#13112752	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₆×#1055	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88038	C₄	1	2	yes	—
9	C₂×C₁₆×D₁₃	C₄	1	2	yes	—
10	#11718346	C₄	1	2	yes	—
11	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
13	C₄×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
14	C₈²×C₁₃	C₂²	1	1	yes	characteristic
15	#11718094	C₄	1	2	yes	—
16	C₁₆×Dic₁₃	C₄	1	2	yes	—
17	C₄×#6090	C₂²	1	1	yes	characteristic
18	C₄×#6090	C₂²	1	1	yes	characteristic
19	#11718046	C₄	1	2	yes	—
20	C₈×#1055	C₂²	1	1	yes	characteristic
21	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
25	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	#88060	C₈	1	4	yes	—
29	#88054	C₈	1	4	yes	—
30	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₂×#6090	C₂×C₄	1	2	yes	—
33	C₂×#6090	C₂×C₄	1	2	yes	—
34	C₄×#1055	C₂×C₄	1	1	yes	characteristic
35	C₄×#1055	C₂×C₄	1	2	yes	—
36	#88038	C₈	1	8	yes	complemented
37	C₁₆×D₁₃	C₈	1	8	yes	complemented
38	#11399	—	13	1	no	maximal, Sylow
39	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
40	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
42	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
46	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
47	C₂×#1055	C₄²	1	1	yes	characteristic
48	C₂×#1055	C₄²	1	1	yes	characteristic
49	C₂×#1055	C₂×C₈	1	4	yes	—
50	C₈×D₁₃	C₂×C₈	1	4	yes	—
51	C₈×D₁₃	C₂×C₈	1	4	yes	—
52	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
53	C₁₃×C₁₆	C₂×C₈	1	4	yes	—
54	#6090	C₂×C₈	1	4	yes	—
55	#6090	C₂×C₈	1	4	yes	—
56	C₄×M₃₂	—	13	1	no	—
57	C₂×C₄×C₁₆	—	13	1	no	—
58	#1450	—	13	1	no	—
59	#1311	—	13	1	no	—
60	#1311	—	13	1	no	—
61	C₈×C₁₆	—	13	1	no	—
62	C₈×C₁₆	D₁₃	1	1	yes	characteristic, complemented
63	C₂²×D₁₃	C₄×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
65	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
66	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
67	C₂×Dic₁₃	C₄×C₈	1	1	yes	characteristic
68	C₄×D₁₃	—	2	4	no	—
69	C₄×D₁₃	C₄×C₈	1	2	yes	—
70	C₄×D₁₃	C₄×C₈	1	2	yes	—
71	C₈×C₁₃	—	2	4	no	—
72	C₈×C₁₃	C₂²×C₈	1	2	yes	—
73	C₈×C₁₃	C₂²×C₈	1	2	yes	—
74	#1055	—	2	4	no	—
75	#1055	C₄×C₈	1	2	yes	—
76	#1055	C₄×C₈	1	2	yes	—
77	C₂×M₃₂	—	13	2	no	—
78	C₂²×C₁₆	—	13	2	no	—
79	#431	—	13	2	no	—
80	C₂×C₄×C₈	—	13	1	no	—
81	#346	—	13	2	no	—
82	C₄×C₁₆	—	13	2	no	—
83	C₄×C₁₆	—	13	1	no	—
84	C₄×C₁₆	—	13	1	no	—
85	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
86	C₄×C₁₆	C₂×D₁₃	1	1	yes	characteristic
87	#322	—	13	2	no	—
88	C₈²	—	13	1	no	—
89	C₈²	C₂×D₁₃	1	1	yes	characteristic
90	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
91	C₂×D₁₃	—	2	2	no	—
92	C₂×D₁₃	C₈²	1	2	yes	—
93	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
94	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
95	C₄×C₁₃	#504	1	4	yes	—
96	Dic₁₃	—	2	2	no	—
97	Dic₁₃	C₈²	1	2	yes	—
98	C₂²×C₈	—	13	1	no	—
99	C₂²×C₈	—	13	1	no	—
100	C₂×C₄²	—	13	1	no	—
101	M₃₂	—	13	8	no	—
102	C₂×C₁₆	—	13	2	no	—
103	C₂×C₁₆	—	13	2	no	—
104	C₂×C₁₆	—	13	8	no	—
105	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
106	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
107	C₄⋊C₈	—	13	4	no	—
108	C₂²⋊C₈	—	13	4	no	—
109	C₄×C₈	—	13	1	no	—
110	C₄×C₈	—	13	1	no	—
111	C₄×C₈	—	13	2	no	—
112	C₄×C₈	—	13	1	no	—
113	C₄×C₈	C₄×D₁₃	1	2	yes	—
114	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
115	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
116	C₂×C₁₃	#2108	1	2	yes	—
117	D₁₃	—	2	2	no	—
118	C₂²×C₄	—	13	1	no	—
119	C₂²×C₄	—	13	2	no	—
120	C₂×C₈	—	13	1	no	—
121	C₂×C₈	—	13	1	no	—
122	C₂×C₈	—	13	4	no	—
123	C₂×C₈	—	13	4	no	—
124	C₂×C₈	—	13	4	no	—
125	C₂×C₈	C₈×D₁₃	1	4	yes	—
126	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
127	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
128	C₄²	—	13	1	no	—
129	C₄²	—	13	2	no	—
130	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
131	C₁₆	—	13	4	no	—
132	C₁₆	—	13	4	no	—
133	C₁₆	C₈×D₁₃	1	4	yes	—
134	C₁₆	C₈×D₁₃	1	4	yes	—
135	C₁₃	#11399	1	1	yes	characteristic, complemented, Sylow
136	C₂³	—	13	1	no	—
137	C₂×C₄	—	13	1	no	—
138	C₂×C₄	—	13	2	no	—
139	C₂×C₄	—	13	2	no	—
140	C₂×C₄	—	13	2	no	—
141	C₂×C₄	—	26	4	no	—
142	C₂×C₄	C₄²×D₁₃	1	1	yes	characteristic
143	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
144	C₈	—	2	4	no	—
145	C₈	—	13	2	no	—
146	C₈	—	13	2	no	—
147	C₈	—	26	4	no	—
148	C₈	C₂×C₈×D₁₃	1	2	yes	—
149	C₈	C₂×C₈×D₁₃	1	2	yes	—
150	C₂²	—	13	2	no	—
151	C₂²	—	26	2	no	—
152	C₂²	C₄×C₈×D₁₃	1	1	yes	characteristic
153	C₄	—	13	2	no	—
154	C₄	—	26	2	no	—
155	C₄	C₄×C₈×D₁₃	1	1	yes	characteristic
156	C₄	C₄×C₈×D₁₃	1	1	yes	characteristic
157	C₄	#11718562	1	4	yes	—
158	C₂	—	26	2	no	—
159	C₂	C₈²×D₁₃	1	1	yes	characteristic
160	C₂	#13116431	1	2	yes	—

	subgroup	G/H
center	C₄×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₈²
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₈×C₁₃×C₁₆	C₂
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂²×D₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₈×C₁₆	D₁₃
hypocenter	C₁₃	#11399
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₁₆ ◁ C₈×C₁₆

Complements

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

N	H ≅ G/N	type
4. #13112753	C₂	semidirect
5. #13112752	C₂	semidirect
6. C₁₆×#1055	C₂	semidirect
7. C₈×C₁₃×C₁₆	C₂	semidirect
36. #88038	C₈	semidirect
37. C₁₆×D₁₃	C₈	semidirect
62. C₈×C₁₆	D₁₃	semidirect
135. C₁₃	#11399	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88038	2
C₄×C₁₆×D₁₃	2
#13113118	2
#13112753	2
#13112752	2
C₁₆×#1055	2
C₈×C₁₃×C₁₆	2
#11399	13