Subgroups — #15750606

Order 3328.

202 conjugacy classes of subgroups.

The subgroup lattice has 140 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88034	C₂	1	2	yes	maximal
2	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₃×C₁₆	C₄	1	1	yes	characteristic
4	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₄×C₁₃×C₁₆	—	2	2	no	—
7	C₂×#88034	—	2	2	no	—
8	C₂×#88034	—	2	2	no	—
9	C₂×#88034	C₄	1	4	yes	complemented
10	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
11	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
12	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
13	C₂×C₁₃×C₁₆	—	2	1	no	—
14	C₂×C₁₃×C₁₆	—	2	1	no	—
15	C₂×C₁₃×C₁₆	C₈	1	2	yes	—
16	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
17	C₂×C₁₃×C₁₆	D₄	1	1	yes	characteristic
18	C₂×C₁₃×C₁₆	D₄	1	2	yes	—
19	C₂×C₁₃×C₁₆	Q₈	1	1	yes	characteristic
20	C₄×C₈×C₁₃	—	2	1	no	—
21	C₄×C₈×C₁₃	—	2	1	no	—
22	#88034	—	2	4	no	—
23	#7465	—	13	1	no	maximal, Sylow
24	C₂²×C₄×C₁₃	C₁₆	1	2	yes	—
25	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₈×C₁₃	—	2	1	no	—
27	C₂×C₈×C₁₃	—	2	1	no	—
28	C₂×C₈×C₁₃	C₁₆	1	2	yes	—
29	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
30	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
32	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
33	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
34	C₂×C₈×C₁₃	M₁₆	1	1	yes	characteristic
35	C₄²×C₁₃	—	2	1	no	—
36	C₄²×C₁₃	—	2	1	no	—
37	C₁₃×C₁₆	—	2	2	no	—
38	C₁₃×C₁₆	C₂²⋊C₄	1	2	yes	—
39	C₁₃×C₁₆	C₄⋊C₄	1	2	yes	—
40	C₂²×C₃₂	—	13	2	no	—
41	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
42	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
43	C₂×C₄×C₁₃	—	2	2	no	—
44	C₂×C₄×C₁₃	—	2	2	no	—
45	C₂×C₄×C₁₃	C₃₂	1	4	yes	complemented
46	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
47	C₂×C₄×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
48	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
49	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
51	C₂×C₄×C₁₃	M₃₂	1	1	yes	characteristic
52	C₈×C₁₃	—	2	2	no	—
53	C₈×C₁₃	#95	1	1	yes	characteristic
54	C₈×C₁₃	#97	1	1	yes	characteristic
55	C₈×C₁₃	C₂²⋊C₈	1	1	yes	characteristic
56	C₈×C₁₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂²×C₁₆	Dic₁₃	1	1	yes	characteristic
58	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
59	C₂×C₄×C₈	Dic₁₃	1	1	yes	characteristic
60	C₂×C₃₂	—	13	4	no	—
61	C₂×C₃₂	—	26	2	no	—
62	C₂×C₃₂	—	26	2	no	—
63	C₄×C₁₆	—	2	2	no	—
64	C₂²×C₁₃	C₄×C₁₆	1	1	yes	characteristic
65	C₂²×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
66	C₂²×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
67	C₂²×C₁₃	C₂×C₃₂	1	2	yes	—
68	C₂²×C₁₃	M₆₄	1	2	yes	—
69	C₄×C₁₃	—	2	4	no	—
70	C₄×C₁₃	#336	1	1	yes	characteristic
71	C₄×C₁₃	#346	1	1	yes	characteristic
72	C₄×C₁₃	C₂²⋊C₁₆	1	1	yes	characteristic
73	C₄×C₁₃	C₄⋊C₁₆	1	1	yes	characteristic
74	C₂²×C₈	#1055	1	1	yes	characteristic
75	C₂²×C₈	C₂×Dic₁₃	1	1	yes	characteristic
76	C₂×C₄²	#1055	1	1	yes	characteristic
77	C₂×C₁₆	—	2	1	no	—
78	C₂×C₁₆	—	2	1	no	—
79	C₂×C₁₆	#1055	1	2	yes	—
80	C₂×C₁₆	Dic₂₆	1	1	yes	characteristic
81	C₂×C₁₆	C₄×D₁₃	1	2	yes	—
82	C₂×C₁₆	D₅₂	1	1	yes	characteristic
83	C₂×C₁₆	C₂²⋊D₁₃	1	2	yes	—
84	C₄×C₈	—	2	1	no	—
85	C₄×C₈	—	2	1	no	—
86	C₃₂	—	26	4	no	—
87	C₂×C₁₃	#1374	1	1	yes	characteristic
88	C₂×C₁₃	C₄×C₃₂	1	1	yes	characteristic
89	C₂×C₁₃	#1397	1	1	yes	characteristic
90	C₂×C₁₃	C₂²⋊C₃₂	1	2	yes	—
91	C₂×C₁₃	C₄⋊C₃₂	1	2	yes	—
92	C₂²×C₄	#6090	1	2	yes	—
93	C₂²×C₄	C₂×#1055	1	1	yes	characteristic
94	C₂×C₈	—	2	1	no	—
95	C₂×C₈	—	2	1	no	—
96	C₂×C₈	#6090	1	2	yes	—
97	C₂×C₈	C₂×#1055	1	1	yes	characteristic
98	C₂×C₈	#6099	1	1	yes	characteristic
99	C₂×C₈	#6099	1	1	yes	characteristic
100	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
101	C₂×C₈	C₄⋊Dic₁₃	1	1	yes	characteristic
102	C₂×C₈	C₂²⋊Dic₁₃	1	1	yes	characteristic
103	C₄²	—	2	1	no	—
104	C₄²	—	2	1	no	—
105	C₁₆	—	2	2	no	—
106	C₁₆	#6101	1	2	yes	—
107	C₁₆	#6103	1	2	yes	—
108	C₁₃	#7465	1	1	yes	characteristic, complemented, Sylow
109	C₂³	C₂×#6090	1	1	yes	characteristic
110	C₂×C₄	—	2	2	no	—
111	C₂×C₄	—	2	2	no	—
112	C₂×C₄	#88034	1	4	yes	complemented
113	C₂×C₄	C₄×#1055	1	1	yes	characteristic
114	C₂×C₄	C₄⋊#1055	1	1	yes	characteristic
115	C₂×C₄	C₂×#6090	1	1	yes	characteristic
116	C₂×C₄	#88052	1	1	yes	characteristic
117	C₂×C₄	#88052	1	1	yes	characteristic
118	C₂×C₄	C₂²⋊#1055	1	1	yes	characteristic
119	C₈	—	2	2	no	—
120	C₈	#88043	1	1	yes	characteristic
121	C₈	C₄⋊#1055	1	1	yes	characteristic
122	C₈	C₂²⋊#1055	1	1	yes	characteristic
123	C₈	#88071	1	1	yes	characteristic
124	C₂²	C₄×#6090	1	1	yes	characteristic
125	C₂²	C₄⋊#6090	1	1	yes	characteristic
126	C₂²	C₂×#88034	1	2	yes	—
127	C₂²	#11718091	1	2	yes	—
128	C₂²	C₂²⋊#6090	1	1	yes	characteristic
129	C₄	—	2	4	no	—
130	C₄	#11718053	1	1	yes	characteristic
131	C₄	C₄⋊#6090	1	1	yes	characteristic
132	C₄	#11718116	1	1	yes	characteristic
133	C₄	C₂²⋊#6090	1	1	yes	characteristic
134	C₂	#13112914	1	1	yes	characteristic
135	C₂	C₄×#88034	1	1	yes	characteristic
136	C₂	#13112970	1	1	yes	characteristic
137	C₂	C₂²⋊#88034	1	2	yes	—
138	C₂	C₄⋊#88034	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₁₆	C₂×D₁₃
commutator	C₂×C₁₃	C₄×C₃₂
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂²×C₁₃×C₁₆	C₂²
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	#7465
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₁₆ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
9. C₂×#88034	C₄	semidirect
45. C₂×C₄×C₁₃	C₃₂	semidirect
108. C₁₃	#7465	semidirect
112. C₂×C₄	#88034	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#88034	2
C₂×C₄×C₁₃×C₁₆	2
#7465	13