Subgroups — #15777930

Order 3328.

354 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×#88052	C₂	1	1	yes	maximal, characteristic
2	C₄×#88055	C₂	1	1	yes	maximal, characteristic
3	#13112915	C₂	1	4	yes	maximal
4	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88055	C₄	1	2	yes	—
8	C₂×#88055	C₂²	1	2	yes	—
9	C₂×#88052	C₂²	1	2	yes	—
10	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×#1055	C₄	1	1	yes	characteristic
12	C₁₃×#346	C₄	1	2	yes	complemented
13	C₄×C₁₃×C₁₆	C₄	1	2	yes	complemented
14	#11718053	C₄	1	2	yes	complemented
15	C₄×#6090	C₄	1	2	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₃	—	2	2	no	—
20	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
21	C₂²×#1055	C₂×C₄	1	2	yes	—
22	C₁₃×M₃₂	—	2	4	no	—
23	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
24	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	#88055	—	2	4	no	—
29	#88055	C₈	1	8	yes	—
30	#88052	—	2	4	no	—
31	C₂×#6090	C₂×C₄	1	4	yes	—
32	C₄×#1055	—	2	2	no	—
33	#12594	—	13	1	no	maximal, Sylow
34	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×Dic₁₃	—	2	2	no	—
37	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
38	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₂×C₈	1	4	yes	—
40	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	#41	1	4	yes	—
43	C₄²×C₁₃	C₄²	1	1	yes	characteristic
44	C₄²×C₁₃	C₄²	1	1	yes	characteristic
45	C₄²×C₁₃	M₁₆	1	2	yes	—
46	C₄×Dic₁₃	—	2	2	no	—
47	C₄×Dic₁₃	—	4	4	no	—
48	C₄×Dic₁₃	C₂×C₈	1	4	yes	—
49	C₂×#1055	—	2	2	no	—
50	C₂×#1055	—	2	2	no	—
51	C₂×#1055	C₂×C₈	1	4	yes	—
52	C₁₃×C₁₆	—	2	4	no	—
53	#6090	—	2	4	no	—
54	C₄×M₃₂	—	13	1	no	—
55	C₄×M₃₂	D₁₃	1	1	yes	characteristic
56	C₄×#97	—	13	1	no	—
57	#1375	—	13	4	no	—
58	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
59	C₂×C₄×C₁₃	—	2	4	no	—
60	C₂×C₄×C₁₃	#97	1	2	yes	—
61	C₂×C₄×C₁₃	#97	1	2	yes	—
62	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
63	C₂×C₄×C₁₃	#117	1	2	yes	—
64	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
65	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
66	C₂×Dic₁₃	—	2	4	no	—
67	C₂×Dic₁₃	—	4	4	no	—
68	C₈×C₁₃	C₄×C₈	1	2	yes	—
69	C₈×C₁₃	C₄×C₈	1	2	yes	—
70	C₈×C₁₃	#117	1	2	yes	—
71	C₈×C₁₃	#117	1	2	yes	—
72	#1055	—	2	4	no	—
73	C₂×M₃₂	—	13	2	no	—
74	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
75	C₂×#97	—	13	2	no	—
76	C₂×#97	—	13	2	no	—
77	C₂×C₄×C₈	—	13	1	no	—
78	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
79	C₄³	—	13	1	no	—
80	#346	—	13	2	no	—
81	#346	Dic₁₃	1	2	yes	complemented
82	C₄×C₁₆	—	13	2	no	—
83	C₄×C₁₆	Dic₁₃	1	2	yes	complemented
84	C₂²×C₁₃	—	2	2	no	—
85	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
86	C₂²×C₁₃	#431	1	2	yes	—
87	C₄×C₁₃	—	2	2	no	—
88	C₄×C₁₃	#347	1	4	yes	—
89	C₄×C₁₃	#376	1	1	yes	characteristic
90	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
91	C₄×C₁₃	#431	1	2	yes	—
92	Dic₁₃	—	4	4	no	—
93	C₂²×C₈	—	13	2	no	—
94	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
95	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
96	C₂×C₄²	—	13	2	no	—
97	C₂×C₄²	—	26	2	no	—
98	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
99	M₃₂	—	2	4	no	—
100	M₃₂	—	26	4	no	—
101	C₂×C₁₆	—	13	4	no	—
102	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
103	#97	—	13	8	no	—
104	#97	—	26	4	no	—
105	C₄×C₈	—	26	2	no	—
106	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
107	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
108	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
109	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
110	C₂×C₁₃	—	2	2	no	—
111	C₂×C₁₃	#1744	1	1	yes	characteristic
112	C₂×C₁₃	C₂×#347	1	2	yes	—
113	C₂²×C₄	—	26	2	no	—
114	C₂²×C₄	#6094	1	2	yes	—
115	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
116	C₂×C₈	—	13	4	no	—
117	C₂×C₈	—	26	2	no	—
118	C₂×C₈	—	26	2	no	—
119	C₂×C₈	C₈×D₁₃	1	4	yes	—
120	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
121	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
122	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
123	C₂×C₈	#6127	1	4	yes	—
124	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
125	C₄²	—	13	4	no	—
126	C₄²	—	26	2	no	—
127	C₄²	—	52	4	no	—
128	C₄²	#6094	1	2	yes	—
129	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
130	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
131	C₁₆	—	2	4	no	—
132	C₁₆	—	26	4	no	—
133	C₁₃	#12594	1	1	yes	characteristic, complemented, Sylow
134	C₂³	C₂×#6094	1	1	yes	characteristic
135	C₂×C₄	—	2	4	no	—
136	C₂×C₄	—	26	4	no	—
137	C₂×C₄	—	52	4	no	—
138	C₂×C₄	#88055	1	2	yes	—
139	C₂×C₄	#88055	1	2	yes	—
140	C₂×C₄	#88126	1	2	yes	—
141	C₂×C₄	C₂×C₈×D₁₃	1	2	yes	—
142	C₂×C₄	C₂×#6094	1	1	yes	characteristic
143	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
144	C₈	—	26	4	no	—
145	C₈	C₈×Dic₁₃	1	2	yes	—
146	C₈	C₈×Dic₁₃	1	2	yes	—
147	C₈	#88126	1	2	yes	—
148	C₈	#88180	1	2	yes	—
149	C₂²	—	2	2	no	—
150	C₂²	#11718346	1	2	yes	—
151	C₂²	C₂×#88055	1	1	yes	characteristic
152	C₄	—	2	2	no	—
153	C₄	—	52	4	no	—
154	C₄	#11718104	1	4	yes	—
155	C₄	#11718346	1	2	yes	—
156	C₄	#11718593	1	1	yes	characteristic
157	C₄	C₂×C₈×Dic₁₃	1	1	yes	characteristic
158	C₂	—	2	2	no	—
159	C₂	#13114581	1	1	yes	characteristic
160	C₂	C₂×#11718104	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₁₃
commutator	C₄×C₁₃	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄×M₃₂	D₁₃
hypocenter	C₁₃	#12594
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
12. C₁₃×#346	C₄	semidirect
13. C₄×C₁₃×C₁₆	C₄	semidirect
14. #11718053	C₄	semidirect
15. C₄×#6090	C₄	semidirect
81. #346	Dic₁₃	semidirect
83. C₄×C₁₆	Dic₁₃	semidirect
133. C₁₃	#12594	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88052	2
C₄×#88055	2
#13112915	2
C₄×C₁₃×M₃₂	2
#12594	13