Subgroups — #20251987

Order 6016.

476 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13094032	C₂	1	1	yes	maximal, characteristic
2	#15689604	C₂	1	1	yes	maximal, characteristic
3	#15689603	C₂	1	1	yes	maximal, characteristic
4	#15689165	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689164	C₂	1	2	yes	maximal, complemented
6	#15689162	C₂	1	2	yes	maximal, complemented
7	#15689159	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689158	C₂	1	2	yes	maximal, complemented
9	C₂×#13093957	C₂	1	1	yes	maximal, characteristic, complemented
10	#107×D₄₇	C₂	1	2	yes	maximal, complemented
11	C₄₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#10625350	C₂²	1	1	yes	characteristic
13	#13094032	C₄	1	8	yes	complemented
14	C₂×#10625324	C₂²	1	2	yes	—
15	C₂²×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₄₇	C₂²	1	2	yes	—
17	C₄×Dic₉₄	—	2	1	no	—
18	#13093989	—	2	1	no	—
19	C₄×D₁₈₈	—	2	1	no	—
20	#13093986	—	2	1	no	—
21	C₄×C₂²⋊D₄₇	—	2	2	no	—
22	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
23	#13093983	C₂²	1	1	yes	characteristic
24	#13093982	C₂²	1	2	yes	—
25	#13093982	C₂²	1	2	yes	—
26	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
28	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
29	#13093958	C₂²	1	2	yes	—
30	#13093957	C₂²	1	1	yes	characteristic
31	#13093957	C₂²	1	2	yes	—
32	#13093957	C₂²	1	2	yes	—
33	#13093957	C₂²	1	1	yes	characteristic
34	#13093956	C₂²	1	2	yes	—
35	#13093955	C₂²	1	1	yes	characteristic
36	#13093955	C₂²	1	1	yes	characteristic
37	C₂×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	#117×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	#107×C₄₇	C₂²	1	2	yes	—
41	#106×C₄₇	C₂²	1	2	yes	—
42	C₂²×C₄×C₄₇	—	2	1	no	—
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×C₂²⋊D₄₇	D₄	1	2	yes	—
45	C₂²×Dic₄₇	—	2	1	no	—
46	#10625350	C₂×C₄	1	4	yes	—
47	#10625350	Q₈	1	4	yes	—
48	C₂×D₁₈₈	D₄	1	1	yes	characteristic
49	C₂×C₄×D₄₇	—	2	2	no	—
50	C₂×C₄×D₄₇	—	2	2	no	—
51	C₂×C₄×D₄₇	C₂³	1	2	yes	—
52	C₂×Dic₉₄	D₄	1	1	yes	characteristic
53	M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
54	C₂×C₈×C₄₇	C₂³	1	2	yes	—
55	C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
58	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²⋊C₄×C₄₇	—	2	1	no	—
60	C₄²×C₄₇	—	2	1	no	—
61	C₂²⋊Dic₄₇	—	2	1	no	—
62	(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₄⋊Dic₄₇	—	2	1	no	—
65	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊Dic₄₇	C₂³	1	2	yes	—
68	Dic₄₇⋊C₄	—	2	2	no	—
69	Dic₄₇⋊C₄	—	2	2	no	—
70	C₄×Dic₄₇	—	2	1	no	—
71	C₄×Dic₄₇	—	2	2	no	—
72	C₄×Dic₄₇	—	2	2	no	—
73	C₂×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
74	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	#10625324	C₂×C₄	1	8	yes	complemented
77	C₈×D₄₇	C₂×C₄	1	8	yes	complemented
78	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×D₄₇	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₄₇	—	2	1	no	—
81	C₂×C₄×C₄₇	—	2	2	no	—
82	C₂×C₄×C₄₇	—	2	1	no	—
83	C₂×C₄×C₄₇	—	8	1	no	—
84	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
87	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂²⋊D₄₇	C₄⋊C₄	1	8	yes	—
89	C₂×Dic₄₇	—	2	1	no	—
90	C₂×Dic₄₇	—	2	1	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	8	1	no	—
93	C₂×Dic₄₇	C₂×D₄	1	2	yes	—
94	D₁₈₈	C₄⋊C₄	1	4	yes	—
95	C₄×D₄₇	—	8	2	no	—
96	C₄×D₄₇	—	8	2	no	—
97	C₄×D₄₇	C₂²×C₄	1	4	yes	—
98	C₄×D₄₇	C₂×Q₈	1	4	yes	—
99	Dic₉₄	C₄⋊C₄	1	4	yes	—
100	C₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
102	C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
103	C₂²×C₄₇	—	2	1	no	—
104	C₂²×C₄₇	—	2	1	no	—
105	C₂²×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
106	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
107	C₂×D₄₇	—	2	2	no	—
108	C₂×D₄₇	—	2	2	no	—
109	C₂×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
110	C₄×C₄₇	—	4	1	no	—
111	C₄×C₄₇	—	4	2	no	—
112	C₄×C₄₇	—	4	1	no	—
113	C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
114	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
115	C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
116	Dic₄₇	—	4	1	no	—
117	Dic₄₇	—	4	2	no	—
118	Dic₄₇	—	4	1	no	—
119	Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
120	#2913	—	47	1	no	maximal, Sylow
121	C₂×C₄₇	—	2	2	no	—
122	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄₇	#576	1	1	yes	characteristic
124	C₂×C₄₇	#578	1	1	yes	characteristic
125	D₄₇	—	2	4	no	—
126	C₂×#131	—	47	1	no	—
127	#520	—	47	1	no	—
128	#520	—	47	1	no	—
129	#428	—	47	1	no	—
130	#428	—	47	2	no	—
131	#428	—	47	2	no	—
132	#428	D₄₇	1	1	yes	characteristic, complemented
133	#427	—	47	1	no	—
134	#427	—	47	2	no	—
135	C₂×#107	—	47	1	no	—
136	C₂×#107	—	47	2	no	—
137	C₄₇	#2913	1	1	yes	characteristic, complemented, Sylow
138	C₂×#41	—	47	1	no	—
139	#131	—	47	8	no	—
140	C₂×M₁₆	—	47	2	no	—
141	C₂×M₁₆	C₂×D₄₇	1	1	yes	characteristic
142	C₂²×C₈	—	47	1	no	—
143	C₂²×C₈	—	47	2	no	—
144	C₄×Q₈	—	94	1	no	—
145	C₄×Q₈	—	94	1	no	—
146	C₄×D₄	—	94	1	no	—
147	C₄×D₄	—	94	2	no	—
148	C₄×D₄	—	94	1	no	—
149	C₄×D₄	—	94	2	no	—
150	#117	—	47	1	no	—
151	#117	—	47	2	no	—
152	#117	—	47	2	no	—
153	#117	C₂×D₄₇	1	1	yes	characteristic
154	C₂×C₄⋊C₄	—	47	1	no	—
155	C₂×C₄⋊C₄	—	47	2	no	—
156	C₂×C₄⋊C₄	—	47	2	no	—
157	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
158	#107	—	47	2	no	—
159	#107	—	47	1	no	—
160	#107	—	47	2	no	—
161	#107	—	47	2	no	—
162	#107	—	47	1	no	—
163	#107	C₂×D₄₇	1	2	yes	—
164	#106	—	47	2	no	—
165	#106	—	47	1	no	—
166	#106	—	47	1	no	—
167	#106	C₂×D₄₇	1	2	yes	—
168	#41	—	47	4	no	—
169	#41	—	47	4	no	—
170	C₂×Q₈	—	47	1	no	—
171	C₂×D₄	—	47	2	no	—
172	C₂×D₄	—	47	1	no	—
173	C₂²×C₄	—	2	1	no	—
174	C₂²×C₄	—	47	2	no	—
175	C₂²×C₄	—	94	2	no	—
176	C₂²×C₄	—	94	2	no	—
177	C₂²×C₄	—	94	1	no	—
178	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
179	M₁₆	—	47	8	no	—
180	M₁₆	C₄×D₄₇	1	4	yes	complemented
181	C₂×C₈	—	47	4	no	—
182	C₂×C₈	—	47	1	no	—
183	C₂×C₈	—	47	1	no	—
184	C₂×C₈	—	47	8	no	—
185	C₂×C₈	C₂²×D₄₇	1	2	yes	—
186	C₄⋊C₄	—	2	1	no	—
187	C₄⋊C₄	—	47	1	no	—
188	C₄⋊C₄	—	47	1	no	—
189	C₄⋊C₄	—	47	2	no	—
190	C₄⋊C₄	—	94	2	no	—
191	C₄⋊C₄	—	94	2	no	—
192	C₄⋊C₄	—	94	1	no	—
193	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
194	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
195	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
196	C₂²⋊C₄	—	2	1	no	—
197	C₂²⋊C₄	—	94	2	no	—
198	C₂²⋊C₄	—	94	2	no	—
199	C₂²⋊C₄	—	94	1	no	—
200	C₄²	—	2	1	no	—
201	C₄²	—	94	2	no	—
202	C₄²	—	94	2	no	—
203	C₄²	—	94	1	no	—
204	C₂³	—	47	2	no	—
205	C₂³	D₄×D₄₇	1	1	yes	characteristic
206	Q₈	—	47	4	no	—
207	D₄	—	47	8	no	—
208	D₄	—	47	4	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	8	1	no	—
213	C₂×C₄	—	47	2	no	—
214	C₂×C₄	—	47	4	no	—
215	C₂×C₄	—	47	4	no	—
216	C₂×C₄	—	94	1	no	—
217	C₂×C₄	—	94	1	no	—
218	C₂×C₄	—	94	2	no	—
219	C₂×C₄	—	376	2	no	—
220	C₂×C₄	—	376	2	no	—
221	C₂×C₄	—	376	1	no	—
222	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
223	C₂×C₄	D₄×D₄₇	1	1	yes	characteristic
224	C₂×C₄	Q₈×D₄₇	1	2	yes	—
225	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
226	C₈	—	47	2	no	—
227	C₈	—	47	2	no	—
228	C₈	C₂×C₄×D₄₇	1	4	yes	—
229	C₂²	—	2	1	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	47	4	no	—
232	C₂²	—	94	2	no	—
233	C₂²	—	94	2	no	—
234	C₂²	C₄⋊C₄×D₄₇	1	2	yes	—
235	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
236	C₄	—	4	2	no	—
237	C₄	—	4	1	no	—
238	C₄	—	4	1	no	—
239	C₄	—	47	4	no	—
240	C₄	—	188	1	no	—
241	C₄	—	188	2	no	—
242	C₄	—	188	1	no	—
243	C₄	C₄⋊C₄×D₄₇	1	2	yes	—
244	C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
245	C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
246	C₂	—	2	2	no	—
247	C₂	—	94	4	no	—
248	C₂	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
249	C₂	#15689927	1	1	yes	characteristic
250	C₂	#15689939	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₄₇×#428	C₂
socle	C₂²×C₄₇	C₂²×D₄
hypercenter	#428	D₄₇
hypocenter	C₄₇	#2913
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #428

Complements

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

N	H ≅ G/N	type
4. #15689165	C₂	semidirect
5. #15689164	C₂	semidirect
6. #15689162	C₂	semidirect
7. #15689159	C₂	semidirect
8. #15689158	C₂	semidirect
9. C₂×#13093957	C₂	semidirect
10. #107×D₄₇	C₂	semidirect
11. C₄₇×#428	C₂	semidirect
13. #13094032	C₄	semidirect
53. M₁₆×C₄₇	C₂×C₄	semidirect
73. C₂×C₄₇⋊C₈	C₂×C₄	semidirect
76. #10625324	C₂×C₄	semidirect
77. C₈×D₄₇	C₂×C₄	semidirect
132. #428	D₄₇	semidirect
137. C₄₇	#2913	semidirect
180. M₁₆	C₄×D₄₇	semidirect