Subgroups — #15771948

Order 3328.

306 conjugacy classes of subgroups.

The subgroup lattice has 154 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116635	C₂	1	2	yes	maximal
2	#13112754	C₂	1	2	yes	maximal, complemented
3	C₈×#6090	C₂	1	2	yes	maximal, complemented
4	C₂×C₈²×C₁₃	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₈²×C₁₃	C₄	1	1	yes	characteristic
9	C₈²×C₁₃	C₄	1	1	yes	characteristic
10	C₈²×C₁₃	C₂²	1	1	yes	characteristic
11	C₈²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²⋊#6090	C₄	1	4	yes	—
13	C₄⋊#6090	C₄	1	4	yes	—
14	C₄×#6090	C₂²	1	4	yes	—
15	C₂²×C₈×C₁₃	C₈	1	2	yes	—
16	C₂²×C₈×C₁₃	C₈	1	2	yes	—
17	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈×C₁₃	C₈	1	2	yes	—
20	C₄×C₈×C₁₃	C₈	1	2	yes	—
21	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
23	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
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	C₂³	1	1	yes	characteristic
28	C₂×#6090	C₂×C₄	1	8	yes	—
29	#11410	—	13	1	no	maximal, Sylow
30	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
32	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₈×C₁₃	—	2	4	no	—
34	C₂×C₈×C₁₃	—	2	4	no	—
35	C₂×C₈×C₁₃	C₁₆	1	8	yes	complemented
36	C₂×C₈×C₁₃	C₄²	1	2	yes	—
37	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
38	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
39	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
41	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
42	C₄²×C₁₃	C₄²	1	1	yes	characteristic
43	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
44	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
45	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
46	#6090	—	2	8	no	—
47	#2162	—	13	2	no	—
48	C₂×C₈²	D₁₃	1	1	yes	characteristic
49	#1312	—	13	2	no	—
50	C₈×C₁₆	—	13	2	no	—
51	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
52	C₂×C₄×C₁₃	—	2	2	no	—
53	C₂×C₄×C₁₃	—	2	2	no	—
54	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	C₂×C₁₆	1	4	yes	—
58	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
61	C₈×C₁₃	—	2	2	no	—
62	C₈×C₁₃	—	2	2	no	—
63	C₈×C₁₃	C₂×C₁₆	1	4	yes	—
64	C₈×C₁₃	C₂×C₁₆	1	4	yes	—
65	C₈×C₁₃	M₃₂	1	4	yes	—
66	C₈×C₁₃	#131	1	4	yes	—
67	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
68	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
69	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
70	C₄⋊C₁₆	—	13	4	no	—
71	C₂²⋊C₁₆	—	13	4	no	—
72	C₄×C₁₆	—	13	4	no	—
73	C₈²	Dic₁₃	1	1	yes	characteristic
74	C₈²	Dic₁₃	1	1	yes	characteristic
75	C₈²	C₂×D₁₃	1	1	yes	characteristic
76	C₈²	C₂×D₁₃	1	1	yes	characteristic
77	C₂²×C₁₃	—	2	1	no	—
78	C₂²×C₁₃	—	2	1	no	—
79	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
80	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
81	C₄×C₁₃	—	2	1	no	—
82	C₄×C₁₃	—	2	1	no	—
83	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
84	C₄×C₁₃	#405	1	2	yes	—
85	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
86	C₄×C₁₃	C₂×M₃₂	1	2	yes	—
87	C₂²×C₈	#1055	1	2	yes	—
88	C₂²×C₈	#1055	1	2	yes	—
89	C₂²×C₈	C₄×D₁₃	1	2	yes	—
90	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
91	C₂×C₁₆	—	13	8	no	—
92	C₄×C₈	#1055	1	2	yes	—
93	C₄×C₈	#1055	1	2	yes	—
94	C₄×C₈	C₄×D₁₃	1	2	yes	—
95	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
96	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
97	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
98	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
99	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
100	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
101	C₂×C₁₃	—	2	2	no	—
102	C₂×C₁₃	#1450	1	1	yes	characteristic
103	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
104	C₂×C₁₃	C₄×M₃₂	1	1	yes	characteristic
105	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
106	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
107	C₂²×C₄	C₄×Dic₁₃	1	1	yes	characteristic
108	C₂×C₈	—	2	4	no	—
109	C₂×C₈	—	2	4	no	—
110	C₂×C₈	#6090	1	8	yes	complemented
111	C₂×C₈	C₂×#1055	1	2	yes	—
112	C₂×C₈	C₂×#1055	1	2	yes	—
113	C₂×C₈	C₂×#1055	1	2	yes	—
114	C₂×C₈	C₂×#1055	1	2	yes	—
115	C₂×C₈	C₄×Dic₁₃	1	2	yes	—
116	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
117	C₄²	C₂×#1055	1	1	yes	characteristic
118	C₄²	C₂×#1055	1	1	yes	characteristic
119	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
120	C₄²	C₂²×Dic₁₃	1	1	yes	characteristic
121	C₁₆	—	26	8	no	—
122	C₁₃	#11410	1	1	yes	characteristic, complemented, Sylow
123	C₂³	C₄×#1055	1	1	yes	characteristic
124	C₂×C₄	—	2	2	no	—
125	C₂×C₄	—	2	2	no	—
126	C₂×C₄	C₄×#1055	1	1	yes	characteristic
127	C₂×C₄	C₄×#1055	1	1	yes	characteristic
128	C₂×C₄	C₄×#1055	1	1	yes	characteristic
129	C₂×C₄	C₂×#6090	1	4	yes	—
130	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
131	C₂×C₄	C₂²×#1055	1	1	yes	characteristic
132	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
133	C₈	—	2	2	no	—
134	C₈	—	2	2	no	—
135	C₈	C₂×#6090	1	4	yes	—
136	C₈	C₂×#6090	1	4	yes	—
137	C₈	#88052	1	4	yes	—
138	C₈	#88155	1	4	yes	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	C₄×#6090	1	2	yes	—
142	C₂²	C₂×C₄×#1055	1	1	yes	characteristic
143	C₄	—	2	1	no	—
144	C₄	—	2	1	no	—
145	C₄	C₄×#6090	1	2	yes	—
146	C₄	C₂²×#6090	1	2	yes	—
147	C₄	C₂×#88052	1	2	yes	—
148	C₄	#11718762	1	2	yes	—
149	C₂	—	2	2	no	—
150	C₂	#13113119	1	1	yes	characteristic
151	C₂	C₂×C₄×#6090	1	1	yes	characteristic
152	C₂	C₄×#88052	1	1	yes	characteristic

	subgroup	G/H
center	C₈²	C₂×D₁₃
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₄×C₈	C₂²×D₁₃
Fitting	C₂×C₈²×C₁₃	C₂
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₄×C₈×C₁₃	C₂³
hypercenter	C₂×C₈²	D₁₃
hypocenter	C₁₃	#11410
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈² ◁ C₂×C₈²

Complements

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

N	H ≅ G/N	type
2. #13112754	C₂	semidirect
3. C₈×#6090	C₂	semidirect
35. C₂×C₈×C₁₃	C₁₆	semidirect
110. C₂×C₈	#6090	semidirect
122. C₁₃	#11410	semidirect

Maximal subgroups

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

subgroup	index
#13116635	2
#13112754	2
C₈×#6090	2
C₂×C₈²×C₁₃	2
#11410	13