Subgroups — #15752295

Order 3328.

582 conjugacy classes of subgroups.

The subgroup lattice has 146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#88043	C₂	1	2	yes	maximal
2	C₂×#11718046	C₂	1	2	yes	maximal
3	C₂×#11718047	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
5	C₄×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#97	C₄	1	4	yes	—
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
9	C₄³×C₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88043	C₄	1	8	yes	—
11	C₂×C₄×#1055	C₂²	1	2	yes	—
12	C₂×C₄×#1055	C₂²	1	2	yes	—
13	#11718047	C₄	1	4	yes	complemented
14	#11718046	C₄	1	8	yes	complemented
15	C₈×#1055	C₄	1	4	yes	complemented
16	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
19	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
20	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
21	C₂²×#1055	C₂×C₄	1	4	yes	—
22	C₂²×#1055	C₂×C₄	1	4	yes	—
23	C₁₃×#97	—	2	8	no	—
24	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	—
26	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
27	#88043	—	2	16	no	—
28	C₄×#1055	C₂×C₄	1	4	yes	—
29	C₄×#1055	C₂×C₄	1	4	yes	—
30	C₄×#1055	C₂×C₄	1	4	yes	—
31	C₄×#1055	C₂×C₄	1	4	yes	—
32	#7846	—	13	1	no	maximal, Sylow
33	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
34	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
35	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×C₈×C₁₃	—	2	4	no	—
37	C₂×C₈×C₁₃	C₄²	1	4	yes	—
38	C₂×C₈×C₁₃	C₄²	1	4	yes	—
39	C₂×C₈×C₁₃	M₁₆	1	8	yes	—
40	C₄²×C₁₃	—	2	4	no	—
41	C₄²×C₁₃	—	2	8	no	—
42	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
43	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
44	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×#1055	—	2	8	no	—
46	C₂×#1055	C₄²	1	8	yes	—
47	C₂×#1055	C₄²	1	8	yes	—
48	C₂×#1055	M₁₆	1	16	yes	—
49	C₄×#97	—	13	2	no	—
50	C₄×#97	D₁₃	1	1	yes	characteristic
51	C₂×#322	—	13	1	no	—
52	C₂×#322	—	13	2	no	—
53	C₂×C₈²	—	13	1	no	—
54	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₃	—	2	8	no	—
56	C₂×C₄×C₁₃	—	2	4	no	—
57	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
58	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
60	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
62	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
63	C₈×C₁₃	—	2	4	no	—
64	C₈×C₁₃	#97	1	8	yes	complemented
65	#1055	—	2	8	no	—
66	#1055	#97	1	16	yes	complemented
67	C₂×#97	—	13	8	no	—
68	C₂×#97	Dic₁₃	1	4	yes	—
69	C₂×C₄×C₈	—	13	2	no	—
70	C₂×C₄×C₈	—	13	2	no	—
71	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
72	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
73	C₄³	C₂×D₁₃	1	1	yes	characteristic
74	#322	—	13	8	no	—
75	#322	—	13	4	no	—
76	C₈²	—	13	4	no	—
77	C₂²×C₁₃	C₄³	1	1	yes	characteristic
78	C₂²×C₁₃	C₄×M₁₆	1	4	yes	—
79	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
80	C₄×C₁₃	—	4	4	no	—
81	C₄×C₁₃	C₂×#97	1	2	yes	—
82	C₄×C₁₃	C₂×#97	1	4	yes	—
83	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
84	C₄×C₁₃	C₄×M₁₆	1	4	yes	—
85	C₂²×C₈	—	13	4	no	—
86	C₂²×C₈	—	13	4	no	—
87	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
88	C₂²×C₈	C₂×Dic₁₃	1	2	yes	—
89	C₂×C₄²	C₄×D₁₃	1	4	yes	—
90	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
91	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
92	#97	—	2	8	no	—
93	#97	—	26	16	no	—
94	C₄×C₈	—	13	4	no	—
95	C₄×C₈	—	13	4	no	—
96	C₄×C₈	—	13	4	no	—
97	C₄×C₈	—	13	4	no	—
98	C₄×C₈	C₄×D₁₃	1	2	yes	—
99	C₄×C₈	C₄×D₁₃	1	4	yes	—
100	C₄×C₈	C₄×D₁₃	1	2	yes	—
101	C₂×C₁₃	#1455	1	4	yes	—
102	C₂×C₁₃	C₄×#97	1	2	yes	—
103	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
104	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
105	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
106	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
107	C₂×C₈	—	2	4	no	—
108	C₂×C₈	—	13	8	no	—
109	C₂×C₈	—	13	16	no	—
110	C₂×C₈	—	13	8	no	—
111	C₂×C₈	—	26	8	no	—
112	C₂×C₈	#6099	1	8	yes	—
113	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
114	C₂×C₈	C₄×Dic₁₃	1	4	yes	—
115	C₄²	—	2	8	no	—
116	C₄²	—	2	4	no	—
117	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
118	C₄²	C₂×C₄×D₁₃	1	2	yes	—
119	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
120	C₁₃	#7846	1	1	yes	characteristic, complemented, Sylow
121	C₂³	C₂×C₄×Dic₁₃	1	1	yes	characteristic
122	C₂×C₄	—	2	8	no	—
123	C₂×C₄	—	2	4	no	—
124	C₂×C₄	C₄²×D₁₃	1	2	yes	—
125	C₂×C₄	C₄²×D₁₃	1	2	yes	—
126	C₂×C₄	M₁₆×D₁₃	1	8	yes	—
127	C₂×C₄	C₂×#6099	1	4	yes	—
128	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
129	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
130	C₈	—	2	4	no	—
131	C₈	—	13	16	no	—
132	C₈	—	26	8	no	—
133	C₈	#88043	1	8	yes	complemented
134	C₂²	C₄×#6099	1	2	yes	—
135	C₂²	C₄²×Dic₁₃	1	1	yes	characteristic
136	C₂²	M₁₆×Dic₁₃	1	4	yes	—
137	C₄	—	4	4	no	—
138	C₄	D₁₃×#97	1	4	yes	—
139	C₄	#11718368	1	4	yes	—
140	C₄	C₂×#88043	1	2	yes	—
141	C₄	C₄×#6099	1	2	yes	—
142	C₂	#13113139	1	4	yes	—
143	C₂	#97×Dic₁₃	1	2	yes	—
144	C₂	C₄×#88043	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₃
commutator	C₂²×C₁₃	C₄³
Fitting	C₄×C₁₃×#97	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₄²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	C₄×#97	D₁₃
hypocenter	C₁₃	#7846
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄² ◁ C₄×#97

Complements

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

N	H ≅ G/N	type
13. #11718047	C₄	semidirect
14. #11718046	C₄	semidirect
15. C₈×#1055	C₄	semidirect
64. C₈×C₁₃	#97	semidirect
66. #1055	#97	semidirect
120. C₁₃	#7846	semidirect
133. C₈	#88043	semidirect

Maximal subgroups

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

subgroup	index
C₄×#88043	2
C₂×#11718046	2
C₂×#11718047	2
C₂×C₈×#1055	2
C₄×C₁₃×#97	2
#7846	13