Subgroups — C₈×#13094018 #26224491

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 240 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094018	C₂	1	1	yes	maximal, characteristic
2	#20243994	C₂	1	3	yes	maximal
3	#20243945	C₂	1	3	yes	maximal, complemented
4	#20243531	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×Dic₄₇⋊C₄	C₂	1	3	yes	maximal, complemented
6	C₈×(C₂×D₄₇)⋊C₄	C₂	1	3	yes	maximal
7	C₄²×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
9	C₂×#13094018	C₄	1	1	yes	characteristic
10	C₂×Dic₄₇⋊C₈	C₂²	1	3	yes	—
11	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	3	yes	—
12	C₂×C₈×Dic₄₇	C₂²	1	3	yes	—
13	#15689014	C₄	1	3	yes	—
14	#15689007	C₄	1	3	yes	—
15	#15688991	C₄	1	1	yes	characteristic
16	C₄×Dic₄₇⋊C₄	C₂²	1	3	yes	—
17	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	3	yes	—
18	#15688878	C₂²	1	3	yes	—
19	#15688878	C₂²	1	3	yes	—
20	#15688877	C₂²	1	3	yes	—
21	#15688877	C₂²	1	3	yes	—
22	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	—
23	C₂×C₄×C₈×C₄₇	C₂²	1	3	yes	—
24	C₄³×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
26	C₂²×C₄₇⋊C₈	C₂³	1	3	yes	—
27	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
28	C₂×C₈×D₄₇	—	2	6	no	—
29	#13094018	C₈	1	8	yes	direct product factor
30	C₂×Dic₄₇⋊C₄	C₂×C₄	1	3	yes	—
31	C₂×Dic₄₇⋊C₄	C₂×C₄	1	3	yes	—
32	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	3	yes	—
33	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	3	yes	—
34	C₂×C₄×Dic₄₇	C₂³	1	3	yes	—
35	Dic₄₇⋊C₈	—	2	6	no	—
36	(C₂×D₄₇)⋊C₈	—	2	6	no	—
37	C₈×Dic₄₇	—	2	6	no	—
38	C₄₇⋊#95	C₂×C₄	1	3	yes	—
39	C₄₇⋊#95	C₂×C₄	1	3	yes	—
40	C₄₇⋊#95	C₂×C₄	1	3	yes	—
41	C₄₇⋊#95	C₂×C₄	1	3	yes	—
42	C₂²×C₈×C₄₇	C₂³	1	3	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₄²×C₄₇	C₂×C₄	1	3	yes	—
45	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₇	C₂³	1	3	yes	—
47	C₄×C₈×C₄₇	—	2	6	no	—
48	C₄×C₈×C₄₇	—	2	6	no	—
49	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
50	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
51	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
52	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
53	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
54	C₂²×Dic₄₇	C₂²×C₄	1	3	yes	—
55	C₂²×Dic₄₇	C₂²×C₄	1	3	yes	—
56	C₂×C₄×D₄₇	—	2	3	no	—
57	C₂×C₄×D₄₇	—	2	3	no	—
58	C₂×C₈×C₄₇	—	2	3	no	—
59	C₂×C₈×C₄₇	—	2	3	no	—
60	C₂×C₈×C₄₇	#41	1	6	yes	—
61	C₂×C₈×C₄₇	#41	1	6	yes	—
62	C₄²×C₄₇	—	2	6	no	—
63	C₄²×C₄₇	—	2	3	no	—
64	C₄²×C₄₇	—	2	3	no	—
65	C₄²×C₄₇	C₂×C₈	1	4	yes	complemented
66	(C₂×D₄₇)⋊C₄	—	2	6	no	—
67	(C₂×D₄₇)⋊C₄	C₂×C₈	1	12	yes	—
68	Dic₄₇⋊C₄	—	2	6	no	—
69	Dic₄₇⋊C₄	C₂×C₈	1	12	yes	complemented
70	C₄×Dic₄₇	—	2	3	no	—
71	C₄×Dic₄₇	—	2	3	no	—
72	C₂×C₄₇⋊C₈	—	2	3	no	—
73	C₂×C₄₇⋊C₈	—	2	3	no	—
74	C₂×C₄₇⋊C₈	—	2	3	no	—
75	C₂×C₄₇⋊C₈	—	2	3	no	—
76	C₈×D₄₇	—	4	4	no	—
77	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
78	C₂²×D₄₇	—	2	3	no	—
79	C₂²×D₄₇	—	2	3	no	—
80	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
81	C₂×C₄×C₄₇	—	2	3	no	—
82	C₂×C₄×C₄₇	—	2	3	no	—
83	C₂×C₄×C₄₇	—	2	3	no	—
84	C₂×C₄×C₄₇	—	2	3	no	—
85	C₂×C₄×C₄₇	C₂²×C₈	1	6	yes	—
86	C₂×C₄×C₄₇	#131	1	6	yes	—
87	C₂×C₄×C₄₇	C₂×#41	1	3	yes	—
88	C₂×C₄×C₄₇	C₂×#41	1	3	yes	—
89	C₂×Dic₄₇	—	2	3	no	—
90	C₂×Dic₄₇	—	2	3	no	—
91	C₂×Dic₄₇	—	2	3	no	—
92	C₂×Dic₄₇	—	2	3	no	—
93	C₂×Dic₄₇	—	2	3	no	—
94	C₂×Dic₄₇	—	2	3	no	—
95	C₂×Dic₄₇	C₂²×C₈	1	6	yes	—
96	C₄×D₄₇	—	4	1	no	—
97	C₄×D₄₇	—	4	3	no	—
98	C₈×C₄₇	—	2	6	no	—
99	C₈×C₄₇	#126	1	4	yes	complemented
100	C₄₇⋊C₈	—	4	1	no	—
101	C₄₇⋊C₈	—	4	3	no	—
102	C₈×#126	—	47	1	no	maximal, Sylow
103	C₂²×C₄₇	C₄×#41	1	3	yes	—
104	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
105	C₂²×C₄₇	C₂×#131	1	3	yes	—
106	C₂×D₄₇	—	2	6	no	—
107	C₂×D₄₇	—	4	1	no	—
108	C₂×D₄₇	—	4	3	no	—
109	C₄×C₄₇	—	2	6	no	—
110	C₄×C₄₇	—	2	6	no	—
111	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
112	C₄×C₄₇	#529	1	3	yes	—
113	Dic₄₇	—	2	6	no	—
114	Dic₄₇	—	4	1	no	—
115	Dic₄₇	—	4	3	no	—
116	C₄×#126	—	47	1	no	—
117	#1923	—	47	3	no	—
118	#1916	—	47	3	no	—
119	#1839	—	47	1	no	—
120	C₈×C₄⋊C₄	—	47	3	no	—
121	C₈×C₂²⋊C₄	—	47	3	no	—
122	C₄²×C₈	D₄₇	1	1	yes	characteristic, complemented
123	C₂×C₄₇	C₄×#126	1	1	yes	characteristic
124	C₂×C₄₇	C₈×#41	1	3	yes	—
125	C₂×C₄₇	#2966	1	3	yes	—
126	D₄₇	—	4	2	no	—
127	C₂³×C₈	—	47	1	no	—
128	C₂×#126	—	47	1	no	—
129	C₂×C₄⋊C₈	—	47	3	no	—
130	C₂×C₂²⋊C₈	—	47	3	no	—
131	C₂×C₄×C₈	—	47	3	no	—
132	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	—
133	C₂×C₄×C₈	C₂×D₄₇	1	3	yes	—
134	#388	—	47	3	no	—
135	#387	—	47	3	no	—
136	#383	—	47	1	no	—
137	C₄×C₄⋊C₄	—	47	3	no	—
138	C₄×C₂²⋊C₄	—	47	3	no	—
139	C₄³	C₂×D₄₇	1	1	yes	characteristic
140	#336	—	47	3	no	—
141	#336	—	47	3	no	—
142	#336	—	47	3	no	—
143	#336	—	47	3	no	—
144	C₄₇	C₈×#126	1	1	yes	characteristic, complemented, Sylow
145	C₂³×C₄	—	47	1	no	—
146	C₂²×C₈	—	47	1	no	—
147	C₂²×C₈	—	47	3	no	—
148	C₂²×C₈	—	94	6	no	—
149	C₂²×C₈	C₂²×D₄₇	1	3	yes	—
150	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
151	#126	—	47	8	no	—
152	C₂×C₄⋊C₄	—	47	3	no	—
153	C₂×C₄⋊C₄	—	47	3	no	—
154	C₂×C₂²⋊C₄	—	47	3	no	—
155	C₂×C₂²⋊C₄	—	47	3	no	—
156	C₂×C₄²	—	47	3	no	—
157	C₂×C₄²	C₄×D₄₇	1	3	yes	—
158	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
159	C₂×C₄²	C₂²×D₄₇	1	3	yes	—
160	C₄⋊C₈	—	94	6	no	—
161	C₂²⋊C₈	—	94	6	no	—
162	C₄×C₈	—	2	6	no	—
163	C₄×C₈	—	2	6	no	—
164	C₄×C₈	—	94	6	no	—
165	#95	—	47	3	no	—
166	#95	—	47	3	no	—
167	#95	—	47	3	no	—
168	#95	—	47	3	no	—
169	C₂⁴	—	47	1	no	—
170	C₂²×C₄	—	47	3	no	—
171	C₂²×C₄	—	47	1	no	—
172	C₂²×C₄	—	47	3	no	—
173	C₂²×C₄	—	94	3	no	—
174	C₂²×C₄	—	94	3	no	—
175	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
176	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
177	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
178	C₂×C₈	—	2	3	no	—
179	C₂×C₈	—	2	3	no	—
180	C₂×C₈	—	94	3	no	—
181	C₂×C₈	—	94	3	no	—
182	C₂×C₈	—	94	3	no	—
183	C₂×C₈	—	94	3	no	—
184	C₂×C₈	—	188	4	no	—
185	C₂×C₈	#10625350	1	6	yes	—
186	C₂×C₈	#10625350	1	6	yes	—
187	C₄⋊C₄	—	47	12	no	—
188	C₄⋊C₄	—	94	6	no	—
189	C₂²⋊C₄	—	47	12	no	—
190	C₂²⋊C₄	—	94	6	no	—
191	C₄²	—	2	6	no	—
192	C₄²	—	2	3	no	—
193	C₄²	—	2	3	no	—
194	C₄²	—	94	3	no	—
195	C₄²	—	94	3	no	—
196	C₄²	C₈×D₄₇	1	4	yes	complemented
197	C₂³	—	47	2	no	—
198	C₂³	—	94	3	no	—
199	C₂³	—	94	3	no	—
200	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
201	C₂×C₄	—	2	3	no	—
202	C₂×C₄	—	2	3	no	—
203	C₂×C₄	—	2	3	no	—
204	C₂×C₄	—	2	3	no	—
205	C₂×C₄	—	47	6	no	—
206	C₂×C₄	—	94	3	no	—
207	C₂×C₄	—	94	3	no	—
208	C₂×C₄	—	94	3	no	—
209	C₂×C₄	—	94	3	no	—
210	C₂×C₄	—	94	3	no	—
211	C₂×C₄	—	94	3	no	—
212	C₂×C₄	—	188	1	no	—
213	C₂×C₄	—	188	3	no	—
214	C₂×C₄	C₂×C₈×D₄₇	1	6	yes	—
215	C₂×C₄	#13094030	1	6	yes	—
216	C₂×C₄	C₂×#10625350	1	3	yes	—
217	C₂×C₄	C₂×#10625350	1	3	yes	—
218	C₈	—	2	6	no	—
219	C₈	—	188	1	no	—
220	C₈	—	188	3	no	—
221	C₈	#13094018	1	4	yes	direct product factor
222	C₂²	—	94	6	no	—
223	C₂²	—	188	1	no	—
224	C₂²	—	188	3	no	—
225	C₂²	C₄×#10625350	1	3	yes	—
226	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
227	C₂²	C₂×#13094030	1	3	yes	—
228	C₄	—	2	6	no	—
229	C₄	—	2	6	no	—
230	C₄	—	94	6	no	—
231	C₄	—	188	1	no	—
232	C₄	—	188	3	no	—
233	C₄	C₂×#13094018	1	1	yes	characteristic
234	C₄	#15689657	1	3	yes	—
235	C₂	—	188	2	no	—
236	C₂	C₄×#13094018	1	1	yes	characteristic
237	C₂	C₈×#10625350	1	3	yes	—
238	C₂	#20252363	1	3	yes	—

	subgroup	G/H
center	C₂²×C₈	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄²×C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄²×C₈	D₄₇
hypocenter	C₄₇	C₈×#126
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₈ ◁ C₄²×C₈

Complements

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

N	H ≅ G/N	type
3. #20243945	C₂	semidirect
4. #20243531	C₂	semidirect
5. C₈×Dic₄₇⋊C₄	C₂	semidirect
7. C₄²×C₈×C₄₇	C₂	semidirect
29. #13094018	C₈	direct (N × H)
65. C₄²×C₄₇	C₂×C₈	semidirect
69. Dic₄₇⋊C₄	C₂×C₈	semidirect
99. C₈×C₄₇	#126	semidirect
122. C₄²×C₈	D₄₇	semidirect
144. C₄₇	C₈×#126	semidirect
196. C₄²	C₈×D₄₇	semidirect
221. C₈	#13094018	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×#13094018	2
#20243994	2
#20243945	2
#20243531	2
C₈×Dic₄₇⋊C₄	2
C₈×(C₂×D₄₇)⋊C₄	2
C₄²×C₈×C₄₇	2
C₈×#126	47

Subgroups — C8×#13094018 #26224491

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13094018 #26224491