Subgroups — #26131285

Order 12032.

338 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	M₃₂×Dic₄₇	C₂	1	2	yes	maximal
2	#20243076	C₂	1	1	yes	maximal, characteristic
3	#20241468	C₂	1	1	yes	maximal, characteristic
4	#20241467	C₂	1	2	yes	maximal
5	C₄₇×#1375	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093964	C₂²	1	2	yes	—
7	C₂×#13093934	C₄	1	1	yes	characteristic
8	C₂×#13093934	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
10	C₂×C₈×Dic₄₇	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
12	#15688969	C₄	1	1	yes	characteristic
13	#15688898	C₄	1	4	yes	complemented
14	C₁₆×Dic₄₇	C₄	1	4	yes	complemented
15	C₂×M₃₂×C₄₇	C₂²	1	2	yes	—
16	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
21	#13093964	—	2	2	no	—
22	#13093964	—	2	2	no	—
23	C₂×C₄₇⋊C₁₆	C₂×C₄	1	4	yes	—
24	#13093934	—	2	1	no	—
25	#13093934	—	2	1	no	—
26	#13093934	—	2	2	no	—
27	C₄×C₄₇⋊C₈	C₈	1	4	yes	—
28	C₈×Dic₄₇	C₈	1	4	yes	—
29	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
30	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
31	C₄₇⋊#95	—	2	2	no	—
32	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
34	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
35	M₃₂×C₄₇	—	2	2	no	—
36	M₃₂×C₄₇	—	2	2	no	—
37	C₂×C₁₆×C₄₇	C₂×C₄	1	4	yes	—
38	#97×C₄₇	—	2	2	no	—
39	C₂²×C₄×C₄₇	—	2	1	no	—
40	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
41	C₂²×Dic₄₇	—	2	1	no	—
42	C₂²×Dic₄₇	M₁₆	1	2	yes	—
43	C₂×C₈×C₄₇	—	2	1	no	—
44	C₂×C₈×C₄₇	—	2	1	no	—
45	C₂×C₈×C₄₇	C₂×C₈	1	2	yes	—
46	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
47	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
48	C₂×C₈×C₄₇	#41	1	2	yes	—
49	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
50	C₄²×C₄₇	—	2	1	no	—
51	C₄²×C₄₇	C₂×C₈	1	2	yes	—
52	C₄×Dic₄₇	—	2	1	no	—
53	C₄×Dic₄₇	C₄²	1	2	yes	—
54	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
55	C₄×Dic₄₇	M₁₆	1	2	yes	—
56	C₂×C₄₇⋊C₈	—	2	1	no	—
57	C₂×C₄₇⋊C₈	—	2	1	no	—
58	C₂×C₄₇⋊C₈	C₄²	1	1	yes	characteristic
59	C₂×C₄₇⋊C₈	C₄²	1	1	yes	characteristic
60	C₂×C₄₇⋊C₈	C₂×C₈	1	2	yes	—
61	C₂×C₄₇⋊C₈	C₂×C₈	1	2	yes	—
62	C₂×C₄₇⋊C₈	C₂×C₈	1	2	yes	—
63	C₁₆×C₄₇	—	2	4	no	—
64	C₄₇⋊C₁₆	—	2	4	no	—
65	C₂³×C₄₇	C₂×M₁₆	1	1	yes	characteristic
66	C₂×C₄×C₄₇	—	2	2	no	—
67	C₂×C₄×C₄₇	—	4	2	no	—
68	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
69	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
70	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
71	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
72	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
73	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
74	C₂×Dic₄₇	—	2	2	no	—
75	C₂×Dic₄₇	—	4	2	no	—
76	C₂×Dic₄₇	—	4	2	no	—
77	C₂×Dic₄₇	#97	1	4	yes	—
78	C₈×C₄₇	—	2	2	no	—
79	C₈×C₄₇	#117	1	2	yes	—
80	C₈×C₄₇	#117	1	2	yes	—
81	C₄₇⋊C₈	—	2	2	no	—
82	C₄₇⋊C₈	C₄×C₈	1	2	yes	—
83	C₄₇⋊C₈	C₄×C₈	1	2	yes	—
84	#12593	—	47	1	no	maximal, Sylow
85	C₂²×C₄₇	—	2	2	no	—
86	C₂²×C₄₇	C₂×#97	1	1	yes	characteristic
87	C₂²×C₄₇	#431	1	1	yes	characteristic
88	C₂²×C₄₇	#431	1	1	yes	characteristic
89	C₄×C₄₇	—	4	2	no	—
90	C₄×C₄₇	#376	1	1	yes	characteristic
91	C₄×C₄₇	C₂×C₄×C₈	1	1	yes	characteristic
92	C₄×C₄₇	#431	1	1	yes	characteristic
93	C₄×C₄₇	#431	1	1	yes	characteristic
94	Dic₄₇	—	2	4	no	—
95	Dic₄₇	—	4	2	no	—
96	C₄×M₃₂	—	47	2	no	—
97	#1726	—	47	1	no	—
98	#1375	—	47	2	no	—
99	#1375	—	47	1	no	—
100	#1375	D₄₇	1	1	yes	characteristic
101	C₂×C₄₇	—	2	1	no	—
102	C₂×C₄₇	—	2	1	no	—
103	C₂×C₄₇	#1744	1	1	yes	characteristic
104	C₂×C₄₇	#2110	1	2	yes	—
105	C₂×M₃₂	—	47	2	no	—
106	C₂×M₃₂	C₂×D₄₇	1	2	yes	—
107	C₂×#97	—	47	1	no	—
108	C₂×#97	—	47	1	no	—
109	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
110	C₂×C₄×C₈	—	47	1	no	—
111	C₂×C₄×C₈	—	47	1	no	—
112	C₂×C₄×C₈	—	47	1	no	—
113	#376	—	47	1	no	—
114	#346	—	47	4	no	—
115	C₄×C₁₆	—	47	4	no	—
116	C₄₇	#12593	1	1	yes	characteristic, complemented, Sylow
117	C₂²×C₈	—	47	1	no	—
118	C₂²×C₈	—	47	1	no	—
119	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
120	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
121	C₂×C₄²	—	47	1	no	—
122	C₂×C₄²	—	47	1	no	—
123	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
124	M₃₂	—	2	2	no	—
125	M₃₂	—	2	2	no	—
126	M₃₂	—	94	2	no	—
127	M₃₂	—	94	2	no	—
128	C₂×C₁₆	—	47	4	no	—
129	C₂×C₁₆	C₄×D₄₇	1	4	yes	—
130	#97	—	2	2	no	—
131	#97	—	94	2	no	—
132	#97	—	94	1	no	—
133	#97	—	94	1	no	—
134	C₄×C₈	—	47	4	no	—
135	C₄×C₈	—	47	2	no	—
136	C₄×C₈	—	47	2	no	—
137	C₄×C₈	—	47	4	no	—
138	#95	—	94	2	no	—
139	C₂²×C₄	—	2	1	no	—
140	C₂²×C₄	—	47	2	no	—
141	C₂²×C₄	—	94	1	no	—
142	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
143	C₂×C₈	—	2	1	no	—
144	C₂×C₈	—	2	1	no	—
145	C₂×C₈	—	47	1	no	—
146	C₂×C₈	—	47	1	no	—
147	C₂×C₈	—	47	2	no	—
148	C₂×C₈	—	47	2	no	—
149	C₂×C₈	—	47	2	no	—
150	C₂×C₈	—	94	1	no	—
151	C₂×C₈	—	94	1	no	—
152	C₂×C₈	C₈×D₄₇	1	2	yes	—
153	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
154	C₂×C₈	#10625352	1	1	yes	characteristic
155	C₂×C₈	#10625352	1	2	yes	—
156	C₂×C₈	#10625354	1	1	yes	characteristic
157	C₄²	—	2	1	no	—
158	C₄²	—	47	2	no	—
159	C₄²	—	47	2	no	—
160	C₄²	—	47	2	no	—
161	C₄²	—	94	1	no	—
162	C₄²	C₈×D₄₇	1	2	yes	—
163	C₁₆	—	2	4	no	—
164	C₁₆	—	94	4	no	—
165	C₂³	M₁₆×D₄₇	1	1	yes	characteristic
166	C₂×C₄	—	2	2	no	—
167	C₂×C₄	—	4	2	no	—
168	C₂×C₄	—	47	4	no	—
169	C₂×C₄	—	94	2	no	—
170	C₂×C₄	—	188	2	no	—
171	C₂×C₄	—	188	2	no	—
172	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
173	C₂×C₄	#13093980	1	1	yes	characteristic
174	C₂×C₄	#13093982	1	1	yes	characteristic
175	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
176	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
177	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
178	C₈	—	2	2	no	—
179	C₈	—	47	2	no	—
180	C₈	—	47	2	no	—
181	C₈	—	94	2	no	—
182	C₈	#13093980	1	2	yes	—
183	C₈	#13093982	1	2	yes	—
184	C₂²	—	2	2	no	—
185	C₂²	#97×D₄₇	1	1	yes	characteristic
186	C₂²	#15689173	1	1	yes	characteristic
187	C₂²	#15689175	1	1	yes	characteristic
188	C₄	—	4	2	no	—
189	C₄	—	94	4	no	—
190	C₄	—	188	2	no	—
191	C₄	#15688968	1	1	yes	characteristic
192	C₄	C₄×C₈×D₄₇	1	1	yes	characteristic
193	C₄	#15689173	1	1	yes	characteristic
194	C₄	#15689175	1	1	yes	characteristic
195	C₂	—	2	1	no	—
196	C₂	—	2	1	no	—
197	C₂	#20243132	1	1	yes	characteristic
198	C₂	#20244991	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₄²×D₄₇
commutator	C₄×C₄₇	C₂×C₄×C₈
Frattini	C₂²×C₈	C₂²×D₄₇
Fitting	C₄₇×#1375	C₂
socle	C₂²×C₄₇	C₂×#97
prime radical	C₂³×C₄₇	C₂×M₁₆
cosocle	C₂²×C₈×C₄₇	C₂³
hypercenter	#1375	D₄₇
hypocenter	C₄₇	#12593
LCS	G ▷ C₄×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #1375

Complements

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

N	H ≅ G/N	type
13. #15688898	C₄	semidirect
14. C₁₆×Dic₄₇	C₄	semidirect
116. C₄₇	#12593	semidirect

Maximal subgroups

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

subgroup	index
M₃₂×Dic₄₇	2
#20243076	2
#20241468	2
#20241467	2
C₄₇×#1375	2
#12593	47