Subgroups — M₃₂×#3624 #17957983

Order 4352.

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	#14544990	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×#3624	C₂	1	1	yes	maximal, characteristic
3	#14543695	C₂	1	2	yes	maximal, complemented
4	C₁₆×#3624	C₂	1	2	yes	maximal, complemented
5	M₃₂×Dic₁₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587538	C₄	1	2	yes	—
7	C₂×C₄×#3624	C₄	1	2	yes	—
8	#11763698	C₄	1	2	yes	—
9	#11763695	C₂²	1	2	yes	—
10	C₈×#3624	C₄	1	2	yes	—
11	C₈×#3624	C₂²	1	1	yes	characteristic
12	C₈×#3624	C₂²	1	1	yes	characteristic
13	C₂×#10587483	C₄	1	1	yes	characteristic
14	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
15	#11762584	C₄	1	2	yes	—
16	C₁₆×Dic₁₇	C₂²	1	2	yes	—
17	C₂×C₁₇×M₃₂	C₄	1	1	yes	characteristic
18	C₂²×#3624	C₈	1	4	yes	—
19	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
22	C₄×#3624	C₈	1	4	yes	—
23	C₄×#3624	C₂×C₄	1	2	yes	—
24	C₄×#3624	C₂×C₄	1	2	yes	—
25	#10587538	C₈	1	8	yes	complemented
26	C₂×#63216	C₂×C₄	1	4	yes	—
27	C₁₇×M₃₂	C₈	1	4	yes	complemented
28	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
29	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
30	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
33	#10587483	C₈	1	4	yes	complemented
34	C₂×#63214	C₂×C₄	1	2	yes	—
35	C₂²×C₄×C₁₇	C₄²	1	1	yes	characteristic
36	C₂²×Dic₁₇	C₂×C₈	1	2	yes	—
37	C₂×#3624	—	2	8	no	—
38	C₂×#3624	C₂×C₈	1	4	yes	—
39	C₂×#3624	C₂×C₈	1	4	yes	—
40	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
41	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
42	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
43	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
44	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
45	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
46	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
47	C₂×#3622	C₄²	1	1	yes	characteristic
48	C₂×#3622	C₂×C₈	1	4	yes	—
49	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
50	#63216	C₂×C₈	1	8	yes	complemented
51	C₁₆×C₁₇	C₂×C₈	1	4	yes	complemented
52	#63214	C₂×C₈	1	4	yes	complemented
53	C₈×M₃₂	—	17	1	no	maximal, Sylow
54	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₄×C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
57	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
58	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
59	C₂×Dic₁₇	—	2	4	no	—
60	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
61	C₂×Dic₁₇	C₂²×C₈	1	2	yes	—
62	#3624	—	2	4	no	—
63	#3624	M₃₂	1	8	yes	direct product factor
64	C₈×C₁₇	C₄×C₈	1	2	yes	—
65	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
66	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
67	#3622	C₄×C₈	1	2	yes	—
68	#3622	C₂²×C₈	1	2	yes	—
69	C₄×M₃₂	—	17	1	no	—
70	C₄×M₃₂	—	17	1	no	—
71	C₂×C₈²	—	17	1	no	—
72	#1311	—	17	2	no	—
73	C₈×C₁₆	—	17	2	no	—
74	C₂²×C₁₇	—	2	2	no	—
75	C₂²×C₁₇	C₈²	1	2	yes	—
76	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
77	C₄×C₁₇	C₈²	1	2	yes	—
78	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
79	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
80	Dic₁₇	—	2	2	no	—
81	Dic₁₇	C₂×M₃₂	1	4	yes	—
82	C₂×M₃₂	—	17	2	no	—
83	C₂×M₃₂	—	17	1	no	—
84	C₂×M₃₂	#595	1	1	yes	characteristic
85	C₂×C₄×C₈	—	17	2	no	—
86	C₂×C₄×C₈	—	17	1	no	—
87	#346	—	17	2	no	—
88	#346	—	17	2	no	—
89	C₄×C₁₆	—	17	2	no	—
90	C₄×C₁₆	—	17	2	no	—
91	C₈²	—	17	1	no	—
92	C₈²	—	17	1	no	—
93	C₈²	—	17	2	no	—
94	C₂×C₁₇	—	2	2	no	—
95	C₂×C₁₇	C₂×C₈²	1	1	yes	characteristic
96	C₂×C₁₇	C₄×M₃₂	1	2	yes	—
97	C₂²×C₈	—	17	1	no	—
98	C₂²×C₈	—	17	4	no	—
99	C₂²×C₈	C₂×#595	1	1	yes	characteristic
100	C₂×C₄²	—	17	1	no	—
101	M₃₂	—	17	8	no	—
102	M₃₂	—	17	4	no	—
103	M₃₂	#3624	1	4	yes	direct product factor
104	C₂×C₁₆	—	17	4	no	—
105	C₂×C₁₆	—	17	2	no	—
106	C₂×C₁₆	C₂×#595	1	2	yes	—
107	C₄×C₈	—	17	2	no	—
108	C₄×C₈	—	17	2	no	—
109	C₄×C₈	—	17	4	no	—
110	C₄×C₈	—	17	1	no	—
111	C₄×C₈	—	17	1	no	—
112	C₄×C₈	—	17	1	no	—
113	C₄×C₈	—	17	1	no	—
114	C₁₇	C₈×M₃₂	1	1	yes	characteristic, complemented, Sylow
115	C₂²×C₄	—	17	2	no	—
116	C₂²×C₄	C₄×#595	1	1	yes	characteristic
117	C₂×C₈	—	17	4	no	—
118	C₂×C₈	—	17	1	no	—
119	C₂×C₈	—	17	1	no	—
120	C₂×C₈	—	17	4	no	—
121	C₂×C₈	—	17	4	no	—
122	C₂×C₈	—	34	8	no	—
123	C₂×C₈	#63242	1	2	yes	—
124	C₂×C₈	C₄×#595	1	1	yes	characteristic
125	C₂×C₈	C₂×#3624	1	2	yes	—
126	C₂×C₈	C₂²×#595	1	1	yes	characteristic
127	C₄²	—	17	1	no	—
128	C₄²	—	17	1	no	—
129	C₄²	—	17	2	no	—
130	C₁₆	—	17	8	no	—
131	C₁₆	—	17	4	no	—
132	C₁₆	C₂×#3624	1	4	yes	complemented
133	C₂³	C₈×#595	1	1	yes	characteristic
134	C₂×C₄	—	17	2	no	—
135	C₂×C₄	—	17	2	no	—
136	C₂×C₄	—	34	4	no	—
137	C₂×C₄	C₈×#595	1	2	yes	—
138	C₂×C₄	C₈×#595	1	1	yes	characteristic
139	C₂×C₄	C₄×#3624	1	2	yes	—
140	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
141	C₈	—	17	8	no	—
142	C₈	—	17	2	no	—
143	C₈	—	17	2	no	—
144	C₈	—	34	4	no	—
145	C₈	C₄×#3624	1	2	yes	—
146	C₈	C₂×#63242	1	1	yes	characteristic
147	C₈	C₂²×#3624	1	1	yes	characteristic
148	C₂²	—	2	2	no	—
149	C₂²	C₈×#3624	1	2	yes	—
150	C₂²	C₂×C₈×#595	1	1	yes	characteristic
151	C₄	—	17	4	no	—
152	C₄	—	34	2	no	—
153	C₄	C₈×#3624	1	2	yes	—
154	C₄	C₂×C₈×#595	1	1	yes	characteristic
155	C₄	C₂×C₄×#3624	1	1	yes	characteristic
156	C₂	—	2	2	no	—
157	C₂	C₂×C₈×#3624	1	1	yes	characteristic
158	C₂	M₃₂×#595	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂²×#595
commutator	C₂×C₁₇	C₂×C₈²
Fitting	C₂×C₁₇×M₃₂	C₄
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂³×C₁₇	C₄×C₈
cosocle	C₈×Dic₁₇	C₂³
hypercenter	C₂×M₃₂	#595
hypocenter	C₁₇	C₈×M₃₂
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
3. #14543695	C₂	semidirect
4. C₁₆×#3624	C₂	semidirect
25. #10587538	C₈	semidirect
27. C₁₇×M₃₂	C₈	semidirect
33. #10587483	C₈	semidirect
50. #63216	C₂×C₈	semidirect
51. C₁₆×C₁₇	C₂×C₈	semidirect
52. #63214	C₂×C₈	semidirect
63. #3624	M₃₂	direct (N × H)
103. M₃₂	#3624	direct (N × H)
114. C₁₇	C₈×M₃₂	semidirect
132. C₁₆	C₂×#3624	semidirect

Maximal subgroups

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

subgroup	index
#14544990	2
C₂×C₈×#3624	2
#14543695	2
C₁₆×#3624	2
M₃₂×Dic₁₇	2
C₈×M₃₂	17

Subgroups — M32×#3624 #17957983

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×#3624 #17957983