Subgroups — C₄₇⋊#7050 #26102890

Order 12032.

332 conjugacy classes of subgroups.

The subgroup lattice has 184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243540	C₂	1	2	yes	maximal
2	C₄₇×#1842	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
4	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
5	C₂×C₄⋊(C₄₇⋊C₈)	C₄	1	4	yes	—
6	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
7	C₂×C₄⋊C₈×C₄₇	C₄	1	2	yes	—
8	C₄³×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄₇⋊C₈	—	2	4	no	—
10	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
11	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
12	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
13	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
14	C₄⋊(C₄₇⋊C₈)	—	4	4	no	—
15	C₂²×C₈×C₄₇	—	2	2	no	—
16	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
17	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
18	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
19	C₂×C₄²×C₄₇	D₄	1	2	yes	—
20	C₂×C₄²×C₄₇	Q₈	1	1	yes	characteristic
21	C₄⋊C₈×C₄₇	—	4	2	no	—
22	C₄⋊C₈×C₄₇	—	4	2	no	—
23	C₄⋊C₈×C₄₇	—	4	2	no	—
24	C₂²×C₄×C₄₇	C₄²	1	1	yes	characteristic
25	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
26	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
27	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
28	C₂²×C₄×C₄₇	C₄⋊C₄	1	1	yes	characteristic
29	C₂×C₈×C₄₇	—	4	2	no	—
30	C₂×C₈×C₄₇	—	4	4	no	—
31	C₄²×C₄₇	—	2	1	no	—
32	C₄²×C₄₇	—	2	2	no	—
33	C₄²×C₄₇	—	2	2	no	—
34	C₄²×C₄₇	—	2	1	no	—
35	C₄²×C₄₇	—	4	1	no	—
36	C₄²×C₄₇	D₈	1	1	yes	characteristic
37	C₄²×C₄₇	D₈	1	2	yes	—
38	C₄²×C₄₇	SD₁₆	1	2	yes	—
39	C₄²×C₄₇	SD₁₆	1	2	yes	—
40	C₄²×C₄₇	SD₁₆	1	2	yes	—
41	C₄²×C₄₇	Q₁₆	1	1	yes	characteristic
42	C₄²×C₄₇	Q₁₆	1	2	yes	—
43	C₂×C₄₇⋊C₈	—	4	4	no	—
44	C₂×C₄₇⋊C₈	—	4	4	no	—
45	C₂×C₄₇⋊C₈	—	4	4	no	—
46	C₂³×C₄₇	#95	1	1	yes	characteristic
47	C₂×C₄×C₄₇	—	2	2	no	—
48	C₂×C₄×C₄₇	—	2	1	no	—
49	C₂×C₄×C₄₇	—	2	2	no	—
50	C₂×C₄×C₄₇	—	2	1	no	—
51	C₂×C₄×C₄₇	—	2	2	no	—
52	C₂×C₄×C₄₇	—	2	1	no	—
53	C₂×C₄×C₄₇	#100	1	2	yes	—
54	C₂×C₄×C₄₇	#100	1	1	yes	characteristic
55	C₂×C₄×C₄₇	#101	1	2	yes	—
56	C₂×C₄×C₄₇	#101	1	1	yes	characteristic
57	C₂×C₄×C₄₇	#102	1	2	yes	—
58	C₂×C₄×C₄₇	#102	1	2	yes	—
59	C₂×C₄×C₄₇	#102	1	2	yes	—
60	C₂×C₄×C₄₇	#103	1	2	yes	—
61	C₂×C₄×C₄₇	#103	1	2	yes	—
62	C₂×C₄×C₄₇	#103	1	2	yes	—
63	C₂×C₄×C₄₇	#106	1	2	yes	—
64	C₂×C₄×C₄₇	#106	1	1	yes	characteristic
65	C₂×C₄×C₄₇	#107	1	2	yes	—
66	C₂×C₄×C₄₇	#107	1	1	yes	characteristic
67	C₈×C₄₇	—	8	2	no	—
68	C₄₇⋊C₈	—	8	4	no	—
69	#7050	—	47	1	no	maximal, Sylow
70	C₂²×C₄₇	#338	1	1	yes	characteristic
71	C₂²×C₄₇	#340	1	2	yes	—
72	C₂²×C₄₇	#340	1	1	yes	characteristic
73	C₂²×C₄₇	#343	1	2	yes	—
74	C₂²×C₄₇	#343	1	1	yes	characteristic
75	C₄×C₄₇	—	2	2	no	—
76	C₄×C₄₇	—	2	1	no	—
77	C₄×C₄₇	—	2	2	no	—
78	C₄×C₄₇	—	2	1	no	—
79	C₄×C₄₇	—	4	1	no	—
80	C₄×C₄₇	#331	1	2	yes	—
81	C₄×C₄₇	#331	1	1	yes	characteristic
82	C₄×C₄₇	#332	1	2	yes	—
83	C₄×C₄₇	#332	1	2	yes	—
84	C₄×C₄₇	#332	1	2	yes	—
85	C₄×C₄₇	#333	1	2	yes	—
86	C₄×C₄₇	#333	1	1	yes	characteristic
87	#1842	—	47	2	no	—
88	#1842	D₄₇	1	1	yes	characteristic
89	C₂×C₄₇	#1292	1	2	yes	—
90	C₂×C₄₇	#1292	1	1	yes	characteristic
91	C₂×C₄₇	#1296	1	1	yes	characteristic
92	C₂×C₄₇	#1296	1	2	yes	—
93	C₂×C₄₇	#1309	1	1	yes	characteristic
94	C₂×C₄⋊C₈	—	2	2	no	—
95	C₂×C₄⋊C₈	—	47	4	no	—
96	C₂×C₄⋊C₈	—	94	2	no	—
97	C₂×C₄⋊C₈	—	94	2	no	—
98	C₂×C₄⋊C₈	Dic₄₇	1	2	yes	—
99	C₄³	C₂×D₄₇	1	1	yes	characteristic
100	C₄₇	#7050	1	1	yes	characteristic, complemented, Sylow
101	C₂²×C₈	—	2	2	no	—
102	C₂²×C₈	—	94	4	no	—
103	C₂×C₄²	Dic₉₄	1	1	yes	characteristic
104	C₂×C₄²	C₄×D₄₇	1	2	yes	—
105	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
106	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
107	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
108	C₄⋊C₈	—	4	2	no	—
109	C₄⋊C₈	—	4	2	no	—
110	C₄⋊C₈	—	4	2	no	—
111	C₄⋊C₈	—	188	4	no	—
112	C₄⋊C₈	—	188	2	no	—
113	C₄⋊C₈	—	188	2	no	—
114	C₄⋊C₈	—	188	2	no	—
115	C₄⋊C₈	—	188	2	no	—
116	C₂²×C₄	C₄×Dic₄₇	1	1	yes	characteristic
117	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
118	C₂²×C₄	C₄⋊Dic₄₇	1	1	yes	characteristic
119	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
120	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
121	C₂×C₈	—	4	2	no	—
122	C₂×C₈	—	4	4	no	—
123	C₂×C₈	—	188	4	no	—
124	C₂×C₈	—	188	4	no	—
125	C₂×C₈	—	188	4	no	—
126	C₄²	—	2	2	no	—
127	C₄²	—	2	1	no	—
128	C₄²	—	2	2	no	—
129	C₄²	—	2	1	no	—
130	C₄²	—	4	1	no	—
131	C₄²	#10625325	1	2	yes	—
132	C₄²	D₃₇₆	1	1	yes	characteristic
133	C₄²	Dic₁₈₈	1	1	yes	characteristic
134	C₄²	#10625334	1	2	yes	—
135	C₄²	#10625335	1	2	yes	—
136	C₄²	#10625336	1	2	yes	—
137	C₄²	#10625337	1	2	yes	—
138	C₂³	C₄₇⋊#95	1	1	yes	characteristic
139	C₂×C₄	—	2	2	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	2	2	no	—
142	C₂×C₄	—	2	1	no	—
143	C₂×C₄	—	2	2	no	—
144	C₂×C₄	—	2	1	no	—
145	C₂×C₄	#13093940	1	2	yes	—
146	C₂×C₄	#13093941	1	1	yes	characteristic
147	C₂×C₄	#13093942	1	2	yes	—
148	C₂×C₄	#13093943	1	1	yes	characteristic
149	C₂×C₄	#13093944	1	2	yes	—
150	C₂×C₄	#13093945	1	2	yes	—
151	C₂×C₄	#13093946	1	2	yes	—
152	C₂×C₄	#13093947	1	2	yes	—
153	C₂×C₄	#13093948	1	2	yes	—
154	C₂×C₄	#13093949	1	2	yes	—
155	C₂×C₄	#13093955	1	2	yes	—
156	C₂×C₄	#13093956	1	1	yes	characteristic
157	C₂×C₄	#13093957	1	2	yes	—
158	C₂×C₄	#13093958	1	1	yes	characteristic
159	C₈	—	8	2	no	—
160	C₈	—	376	4	no	—
161	C₂²	C₄₇⋊#338	1	1	yes	characteristic
162	C₂²	#15688885	1	2	yes	—
163	C₂²	#15688886	1	1	yes	characteristic
164	C₂²	#15688891	1	2	yes	—
165	C₂²	#15688892	1	1	yes	characteristic
166	C₄	—	2	2	no	—
167	C₄	—	2	2	no	—
168	C₄	—	2	1	no	—
169	C₄	—	2	1	no	—
170	C₄	—	4	1	no	—
171	C₄	#15688866	1	2	yes	—
172	C₄	#15688867	1	1	yes	characteristic
173	C₄	#15688868	1	2	yes	—
174	C₄	#15688869	1	2	yes	—
175	C₄	#15688870	1	2	yes	—
176	C₄	#15688871	1	2	yes	—
177	C₄	#15688872	1	1	yes	characteristic
178	C₂	#20241262	1	2	yes	—
179	C₂	#20241263	1	1	yes	characteristic
180	C₂	#20241271	1	1	yes	characteristic
181	C₂	#20241272	1	2	yes	—
182	C₂	C₄₇⋊#1309	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₄₇⋊#95
commutator	C₂²×C₄×C₄₇	C₄²
Frattini	C₄³	C₂×D₄₇
Fitting	C₄₇×#1842	C₂
socle, prime radical	C₂³×C₄₇	#95
cosocle	C₄³×C₄₇	C₂²
hypercenter	#1842	D₄₇
hypocenter	C₄₇	#7050
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #1842

Complements

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

N	H ≅ G/N	type
100. C₄₇	#7050	semidirect

Maximal subgroups

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

subgroup	index
#20243540	2
C₄₇×#1842	2
#7050	47

Subgroups — C47⋊#7050 #26102890

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇⋊#7050 #26102890