Subgroups — M₃₂×#1057 #16786578

Order 3328.

354 conjugacy classes of subgroups.

The subgroup lattice has 160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131042	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#1057	C₂	1	1	yes	maximal, characteristic
3	#13129747	C₂	1	2	yes	maximal, complemented
4	C₁₆×#1057	C₂	1	2	yes	maximal, complemented
5	M₃₂×Dic₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄×#1057	C₄	1	2	yes	—
7	C₂×#88106	C₄	1	2	yes	—
8	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
9	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
10	C₂×#88052	C₄	1	1	yes	characteristic
11	#11718258	C₄	1	2	yes	—
12	#11718257	C₂²	1	2	yes	—
13	C₈×#1057	C₄	1	2	yes	—
14	C₈×#1057	C₂²	1	1	yes	characteristic
15	C₈×#1057	C₂²	1	1	yes	characteristic
16	#11718094	C₄	1	2	yes	—
17	C₁₆×Dic₁₃	C₂²	1	2	yes	—
18	C₂²×#1057	C₈	1	4	yes	—
19	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
22	C₄×#1057	C₈	1	4	yes	—
23	C₄×#1057	C₂×C₄	1	2	yes	—
24	C₄×#1057	C₂×C₄	1	2	yes	—
25	#88106	C₈	1	8	yes	complemented
26	C₂×#6092	C₂×C₄	1	4	yes	—
27	C₁₃×M₃₂	C₈	1	4	yes	complemented
28	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
29	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
33	#88052	C₈	1	4	yes	complemented
34	C₂×#6090	C₂×C₄	1	2	yes	—
35	C₈×M₃₂	—	13	1	no	maximal, Sylow
36	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
37	C₂²×Dic₁₃	C₂×C₈	1	2	yes	—
38	C₂×#1057	—	2	8	no	—
39	C₂×#1057	C₂×C₈	1	4	yes	—
40	C₂×#1057	C₂×C₈	1	4	yes	—
41	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
46	C₄×Dic₁₃	C₂×C₈	1	2	yes	—
47	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
48	C₂×#1055	C₄²	1	1	yes	characteristic
49	C₂×#1055	C₂×C₈	1	4	yes	—
50	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
51	#6092	C₂×C₈	1	8	yes	complemented
52	C₁₃×C₁₆	C₂×C₈	1	4	yes	complemented
53	#6090	C₂×C₈	1	4	yes	complemented
54	C₄×M₃₂	—	13	1	no	—
55	C₄×M₃₂	—	13	1	no	—
56	C₂×C₈²	—	13	1	no	—
57	#1311	—	13	2	no	—
58	C₈×C₁₆	—	13	2	no	—
59	C₂³×C₁₃	C₄×C₈	1	1	yes	characteristic
60	C₂×C₄×C₁₃	C₄×C₈	1	1	yes	characteristic
61	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
62	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×Dic₁₃	—	2	4	no	—
65	C₂×Dic₁₃	C₄×C₈	1	2	yes	—
66	C₂×Dic₁₃	C₂²×C₈	1	2	yes	—
67	#1057	—	2	4	no	—
68	#1057	M₃₂	1	8	yes	direct product factor
69	C₈×C₁₃	C₄×C₈	1	2	yes	—
70	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
71	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	#1055	C₄×C₈	1	2	yes	—
73	#1055	C₂²×C₈	1	2	yes	—
74	C₂×M₃₂	—	13	2	no	—
75	C₂×M₃₂	—	13	1	no	—
76	C₂×M₃₂	#261	1	1	yes	characteristic
77	C₂×C₄×C₈	—	13	2	no	—
78	C₂×C₄×C₈	—	13	1	no	—
79	#346	—	13	2	no	—
80	#346	—	13	2	no	—
81	C₄×C₁₆	—	13	2	no	—
82	C₄×C₁₆	—	13	2	no	—
83	C₈²	—	13	1	no	—
84	C₈²	—	13	1	no	—
85	C₈²	—	13	2	no	—
86	C₂²×C₁₃	—	2	2	no	—
87	C₂²×C₁₃	C₈²	1	2	yes	—
88	C₂²×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
89	C₄×C₁₃	C₈²	1	2	yes	—
90	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
91	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
92	Dic₁₃	—	2	2	no	—
93	Dic₁₃	C₂×M₃₂	1	4	yes	—
94	C₂²×C₈	—	13	1	no	—
95	C₂²×C₈	—	13	4	no	—
96	C₂²×C₈	C₂×#261	1	1	yes	characteristic
97	C₂×C₄²	—	13	1	no	—
98	M₃₂	—	13	8	no	—
99	M₃₂	—	13	4	no	—
100	M₃₂	#1057	1	4	yes	direct product factor
101	C₂×C₁₆	—	13	4	no	—
102	C₂×C₁₆	—	13	2	no	—
103	C₂×C₁₆	C₂×#261	1	2	yes	—
104	C₄×C₈	—	13	4	no	—
105	C₄×C₈	—	13	2	no	—
106	C₄×C₈	—	13	2	no	—
107	C₄×C₈	—	13	1	no	—
108	C₄×C₈	—	13	1	no	—
109	C₄×C₈	—	13	1	no	—
110	C₄×C₈	—	13	1	no	—
111	C₂×C₁₃	—	2	2	no	—
112	C₂×C₁₃	C₂×C₈²	1	1	yes	characteristic
113	C₂×C₁₃	C₄×M₃₂	1	2	yes	—
114	C₂²×C₄	—	13	2	no	—
115	C₂²×C₄	C₄×#261	1	1	yes	characteristic
116	C₂×C₈	—	13	4	no	—
117	C₂×C₈	—	13	4	no	—
118	C₂×C₈	—	13	1	no	—
119	C₂×C₈	—	13	1	no	—
120	C₂×C₈	—	13	4	no	—
121	C₂×C₈	—	26	8	no	—
122	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
123	C₂×C₈	C₄×#261	1	1	yes	characteristic
124	C₂×C₈	C₂×#1057	1	2	yes	—
125	C₂×C₈	C₂²×#261	1	1	yes	characteristic
126	C₄²	—	13	2	no	—
127	C₄²	—	13	1	no	—
128	C₄²	—	13	1	no	—
129	C₁₆	—	13	8	no	—
130	C₁₆	—	13	4	no	—
131	C₁₆	C₂×#1057	1	4	yes	complemented
132	C₁₃	C₈×M₃₂	1	1	yes	characteristic, complemented, Sylow
133	C₂³	C₈×#261	1	1	yes	characteristic
134	C₂×C₄	—	13	2	no	—
135	C₂×C₄	—	13	2	no	—
136	C₂×C₄	—	26	4	no	—
137	C₂×C₄	C₈×#261	1	1	yes	characteristic
138	C₂×C₄	C₈×#261	1	2	yes	—
139	C₂×C₄	C₄×#1057	1	2	yes	—
140	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
141	C₈	—	13	8	no	—
142	C₈	—	13	2	no	—
143	C₈	—	13	2	no	—
144	C₈	—	26	4	no	—
145	C₈	C₄×#1057	1	2	yes	—
146	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
147	C₈	C₂²×#1057	1	1	yes	characteristic
148	C₂²	—	2	2	no	—
149	C₂²	C₈×#1057	1	2	yes	—
150	C₂²	C₂×C₈×#261	1	1	yes	characteristic
151	C₄	—	13	4	no	—
152	C₄	—	26	2	no	—
153	C₄	C₈×#1057	1	2	yes	—
154	C₄	C₂×C₈×#261	1	1	yes	characteristic
155	C₄	C₂×C₄×#1057	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	C₂×C₈×#1057	1	1	yes	characteristic
158	C₂	M₃₂×#261	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#261
commutator	C₂×C₁₃	C₂×C₈²
Fitting	C₂×C₁₃×M₃₂	C₄
socle	C₂²×C₁₃	C₂×C₄×C₈
prime radical	C₂³×C₁₃	C₄×C₈
cosocle	C₈×Dic₁₃	C₂³
hypercenter	C₂×M₃₂	#261
hypocenter	C₁₃	C₈×M₃₂
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #13129747	C₂	semidirect
4. C₁₆×#1057	C₂	semidirect
25. #88106	C₈	semidirect
27. C₁₃×M₃₂	C₈	semidirect
33. #88052	C₈	semidirect
51. #6092	C₂×C₈	semidirect
52. C₁₃×C₁₆	C₂×C₈	semidirect
53. #6090	C₂×C₈	semidirect
68. #1057	M₃₂	direct (N × H)
100. M₃₂	#1057	direct (N × H)
131. C₁₆	C₂×#1057	semidirect
132. C₁₃	C₈×M₃₂	semidirect

Maximal subgroups

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

subgroup	index
#13131042	2
C₂×C₈×#1057	2
#13129747	2
C₁₆×#1057	2
M₃₂×Dic₁₃	2
C₈×M₃₂	13

Subgroups — M32×#1057 #16786578

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×#1057 #16786578