Subgroups — #20241652

Order 6016.

608 conjugacy classes of subgroups.

The subgroup lattice has 262 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×Dic₄₇⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄₇⋊#95	C₂	1	2	yes	maximal
4	C₂×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
5	C₂×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×Dic₄₇	C₂²	1	2	yes	—
7	C₂³×Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄⋊Dic₄₇	—	2	2	no	—
9	C₂×C₄⋊Dic₄₇	—	2	4	no	—
10	C₂×Dic₄₇⋊C₄	—	2	4	no	—
11	C₂×Dic₄₇⋊C₄	—	2	4	no	—
12	C₂×Dic₄₇⋊C₄	—	2	4	no	—
13	C₄₇⋊#95	—	2	4	no	—
14	C₄₇⋊#95	C₄	1	4	yes	complemented
15	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
18	#95×C₄₇	—	2	2	no	—
19	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₄₇	—	2	2	no	—
21	C₂²×C₄×C₄₇	—	2	2	no	—
22	C₂²×C₄×C₄₇	—	2	2	no	—
23	C₂²×C₄×C₄₇	—	2	2	no	—
24	C₂²×C₄×C₄₇	—	2	2	no	—
25	C₂²×C₄×C₄₇	—	2	1	no	—
26	C₂²×C₄×C₄₇	—	2	1	no	—
27	C₂²×C₄×C₄₇	—	2	1	no	—
28	C₂²×C₄×C₄₇	—	2	1	no	—
29	C₂²×C₄×C₄₇	—	2	2	no	—
30	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
31	C₂²×C₄×C₄₇	D₄	1	2	yes	—
32	C₂²×C₄×C₄₇	D₄	1	2	yes	—
33	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
34	C₂²×C₄×C₄₇	Q₈	1	2	yes	—
35	C₂²×Dic₄₇	—	2	2	no	—
36	C₂²×Dic₄₇	—	2	2	no	—
37	C₂²×Dic₄₇	—	2	2	no	—
38	C₂²×Dic₄₇	—	2	2	no	—
39	C₂²×Dic₄₇	—	2	2	no	—
40	C₂²×Dic₄₇	—	2	2	no	—
41	C₂²×Dic₄₇	—	2	2	no	—
42	C₂²×Dic₄₇	—	2	2	no	—
43	C₂²×Dic₄₇	—	2	2	no	—
44	C₂²×Dic₄₇	—	2	2	no	—
45	C₂²×Dic₄₇	C₂×C₄	1	4	yes	—
46	C₂²×Dic₄₇	D₄	1	4	yes	—
47	C₂²×Dic₄₇	D₄	1	4	yes	—
48	C₂²×Dic₄₇	Q₈	1	4	yes	—
49	C₄⋊Dic₄₇	—	2	8	no	—
50	Dic₄₇⋊C₄	—	2	16	no	—
51	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
52	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
53	C₂³×C₄₇	C₂×D₄	1	2	yes	—
54	C₂³×C₄₇	C₂×D₄	1	2	yes	—
55	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
57	C₂³×C₄₇	C₂×Q₈	1	1	yes	characteristic
58	C₂³×C₄₇	C₂×Q₈	1	2	yes	—
59	C₂³×C₄₇	#41	1	1	yes	characteristic
60	C₂³×C₄₇	#41	1	1	yes	characteristic
61	C₂³×C₄₇	#41	1	2	yes	—
62	C₂×C₄×C₄₇	—	2	4	no	—
63	C₂×C₄×C₄₇	—	2	2	no	—
64	C₂×C₄×C₄₇	—	2	4	no	—
65	C₂×C₄×C₄₇	—	2	2	no	—
66	C₂×C₄×C₄₇	—	2	4	no	—
67	C₂×C₄×C₄₇	—	2	2	no	—
68	C₂×C₄×C₄₇	—	2	4	no	—
69	C₂×C₄×C₄₇	—	2	2	no	—
70	C₂×C₄×C₄₇	—	4	1	no	—
71	C₂×C₄×C₄₇	—	4	2	no	—
72	C₂×C₄×C₄₇	—	4	1	no	—
73	C₂×C₄×C₄₇	—	4	2	no	—
74	C₂×C₄×C₄₇	—	4	1	no	—
75	C₂×C₄×C₄₇	—	4	1	no	—
76	C₂×C₄×C₄₇	C₄⋊C₄	1	4	yes	complemented
77	C₂×Dic₄₇	—	2	4	no	—
78	C₂×Dic₄₇	—	2	4	no	—
79	C₂×Dic₄₇	—	2	4	no	—
80	C₂×Dic₄₇	—	2	4	no	—
81	C₂×Dic₄₇	—	2	4	no	—
82	C₂×Dic₄₇	—	2	4	no	—
83	C₂×Dic₄₇	—	2	4	no	—
84	C₂×Dic₄₇	—	2	4	no	—
85	C₂×Dic₄₇	—	2	4	no	—
86	C₂×Dic₄₇	—	4	2	no	—
87	C₂×Dic₄₇	—	4	2	no	—
88	C₂×Dic₄₇	—	4	2	no	—
89	C₂×Dic₄₇	—	4	2	no	—
90	C₂×Dic₄₇	C₄⋊C₄	1	8	yes	complemented
91	C₂²×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
92	C₂²×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄₇	C₄×D₄	1	2	yes	—
94	C₂²×C₄₇	C₄×D₄	1	1	yes	characteristic
95	C₂²×C₄₇	C₄×Q₈	1	1	yes	characteristic
96	C₂²×C₄₇	#120	1	1	yes	characteristic
97	C₂²×C₄₇	#120	1	2	yes	—
98	C₂²×C₄₇	#121	1	2	yes	—
99	C₂²×C₄₇	#121	1	1	yes	characteristic
100	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
101	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
102	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
103	C₂²×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
104	C₂²×C₄₇	C₂²⋊Q₈	1	2	yes	—
105	C₂²×C₄₇	#123	1	1	yes	characteristic
106	C₂²×C₄₇	#123	1	2	yes	—
107	C₂²×C₄₇	#125	1	2	yes	—
108	C₂²×C₄₇	#125	1	1	yes	characteristic
109	C₂²×C₄₇	#127	1	1	yes	characteristic
110	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
111	C₂²×C₄₇	C₄⋊Q₈	1	2	yes	—
112	C₂²×C₄₇	C₄⋊Q₈	1	2	yes	—
113	C₂²×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
114	C₄×C₄₇	—	2	4	no	—
115	C₄×C₄₇	—	4	2	no	—
116	C₄×C₄₇	—	4	2	no	—
117	Dic₄₇	—	2	8	no	—
118	Dic₄₇	—	4	4	no	—
119	#1444	—	47	1	no	maximal, Sylow
120	C₂×C₄₇	#384	1	1	yes	characteristic
121	C₂×C₄₇	#385	1	1	yes	characteristic
122	C₂×C₄₇	#385	1	2	yes	—
123	C₂×C₄₇	#389	1	2	yes	—
124	C₂×C₄₇	#389	1	1	yes	characteristic
125	C₂×C₄₇	#392	1	1	yes	characteristic
126	C₂×C₄₇	#395	1	1	yes	characteristic
127	C₂×C₄₇	#395	1	2	yes	—
128	C₂×C₄₇	#398	1	1	yes	characteristic
129	C₂×C₄₇	#398	1	2	yes	—
130	C₂×C₄₇	#399	1	1	yes	characteristic
131	C₂²×C₄⋊C₄	—	47	2	no	—
132	C₂²×C₄⋊C₄	—	47	1	no	—
133	C₂×#95	—	47	1	no	—
134	C₂×#95	—	47	2	no	—
135	C₂×#95	D₄₇	1	1	yes	characteristic
136	C₄₇	#1444	1	1	yes	characteristic, complemented, Sylow
137	C₂³×C₄	—	47	2	no	—
138	C₂³×C₄	—	47	2	no	—
139	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
140	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
141	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
142	C₂×C₄⋊C₄	—	94	4	no	—
143	C₂×C₄⋊C₄	—	94	4	no	—
144	C₂×C₄⋊C₄	—	94	4	no	—
145	C₂×C₄⋊C₄	—	94	4	no	—
146	C₂×C₄⋊C₄	—	94	2	no	—
147	#95	—	2	2	no	—
148	#95	—	47	4	no	—
149	#95	—	94	4	no	—
150	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
151	C₂²×C₄	—	2	2	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	—	2	1	no	—
154	C₂²×C₄	—	2	1	no	—
155	C₂²×C₄	—	2	2	no	—
156	C₂²×C₄	—	2	2	no	—
157	C₂²×C₄	—	2	2	no	—
158	C₂²×C₄	—	2	2	no	—
159	C₂²×C₄	—	2	1	no	—
160	C₂²×C₄	—	2	1	no	—
161	C₂²×C₄	—	47	4	no	—
162	C₂²×C₄	—	47	4	no	—
163	C₂²×C₄	—	47	4	no	—
164	C₂²×C₄	—	47	4	no	—
165	C₂²×C₄	—	94	2	no	—
166	C₂²×C₄	—	94	2	no	—
167	C₂²×C₄	—	94	2	no	—
168	C₂²×C₄	—	94	2	no	—
169	C₂²×C₄	—	94	2	no	—
170	C₂²×C₄	—	94	2	no	—
171	C₂²×C₄	—	94	2	no	—
172	C₂²×C₄	—	94	2	no	—
173	C₂²×C₄	—	94	2	no	—
174	C₂²×C₄	—	94	2	no	—
175	C₂²×C₄	Dic₉₄	1	2	yes	—
176	C₂²×C₄	Dic₉₄	1	2	yes	—
177	C₂²×C₄	C₄×D₄₇	1	2	yes	—
178	C₂²×C₄	D₁₈₈	1	2	yes	—
179	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
180	C₄⋊C₄	—	94	16	no	—
181	C₄⋊C₄	—	94	8	no	—
182	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
183	C₂³	C₂×Dic₉₄	1	1	yes	characteristic
184	C₂³	C₂×C₄×D₄₇	1	1	yes	characteristic
185	C₂³	C₂×D₁₈₈	1	1	yes	characteristic
186	C₂³	#10625350	1	1	yes	characteristic
187	C₂³	#10625350	1	1	yes	characteristic
188	C₂³	D₄×D₄₇	1	2	yes	—
189	C₂³	D₄×D₄₇	1	2	yes	—
190	C₂³	#10625352	1	2	yes	—
191	C₂³	Q₈×D₄₇	1	2	yes	—
192	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
193	C₂×C₄	—	2	4	no	—
194	C₂×C₄	—	2	2	no	—
195	C₂×C₄	—	2	4	no	—
196	C₂×C₄	—	2	2	no	—
197	C₂×C₄	—	2	4	no	—
198	C₂×C₄	—	2	2	no	—
199	C₂×C₄	—	2	4	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	4	1	no	—
202	C₂×C₄	—	4	2	no	—
203	C₂×C₄	—	4	1	no	—
204	C₂×C₄	—	4	2	no	—
205	C₂×C₄	—	4	1	no	—
206	C₂×C₄	—	4	1	no	—
207	C₂×C₄	—	47	8	no	—
208	C₂×C₄	—	94	4	no	—
209	C₂×C₄	—	94	4	no	—
210	C₂×C₄	—	94	4	no	—
211	C₂×C₄	—	94	4	no	—
212	C₂×C₄	—	94	4	no	—
213	C₂×C₄	—	94	4	no	—
214	C₂×C₄	—	94	4	no	—
215	C₂×C₄	—	94	4	no	—
216	C₂×C₄	—	94	4	no	—
217	C₂×C₄	—	188	2	no	—
218	C₂×C₄	—	188	2	no	—
219	C₂×C₄	—	188	2	no	—
220	C₂×C₄	—	188	2	no	—
221	C₂×C₄	Dic₄₇⋊C₄	1	4	yes	complemented
222	C₂²	C₄⋊C₄×D₄₇	1	2	yes	—
223	C₂²	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
224	C₂²	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
225	C₂²	C₄×D₁₈₈	1	1	yes	characteristic
226	C₂²	C₄×Dic₉₄	1	1	yes	characteristic
227	C₂²	#13093992	1	1	yes	characteristic
228	C₂²	#13093994	1	2	yes	—
229	C₂²	#13093997	1	2	yes	—
230	C₂²	#13093998	1	1	yes	characteristic
231	C₂²	#13094001	1	2	yes	—
232	C₂²	#13094001	1	2	yes	—
233	C₂²	#13094002	1	2	yes	—
234	C₂²	#13094003	1	1	yes	characteristic
235	C₂²	#13094004	1	2	yes	—
236	C₂²	#13094005	1	1	yes	characteristic
237	C₂²	#13094006	1	2	yes	—
238	C₂²	#13094014	1	2	yes	—
239	C₂²	#13094016	1	1	yes	characteristic
240	C₂²	#13094020	1	1	yes	characteristic
241	C₂²	#13094022	1	1	yes	characteristic
242	C₂²	#13094023	1	2	yes	—
243	C₂²	#13094023	1	2	yes	—
244	C₂²	#13094024	1	1	yes	characteristic
245	C₄	—	2	4	no	—
246	C₄	—	4	2	no	—
247	C₄	—	4	2	no	—
248	C₄	—	94	8	no	—
249	C₄	—	188	4	no	—
250	C₂	#15688992	1	1	yes	characteristic
251	C₂	#15688995	1	1	yes	characteristic
252	C₂	#15688997	1	2	yes	—
253	C₂	#15689020	1	2	yes	—
254	C₂	#15689021	1	1	yes	characteristic
255	C₂	#15689032	1	1	yes	characteristic
256	C₂	#15689043	1	1	yes	characteristic
257	C₂	#15689044	1	2	yes	—
258	C₂	#15689053	1	1	yes	characteristic
259	C₂	#15689057	1	2	yes	—
260	C₂	#15689059	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂⁴	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂²×C₄
Fitting	C₂×#95×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂³
hypercenter	C₂×#95	D₄₇
hypocenter	C₄₇	#1444
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂×#95

Complements

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

N	H ≅ G/N	type
14. C₄₇⋊#95	C₄	semidirect
76. C₂×C₄×C₄₇	C₄⋊C₄	semidirect
90. C₂×Dic₄₇	C₄⋊C₄	semidirect
136. C₄₇	#1444	semidirect
221. C₂×C₄	Dic₄₇⋊C₄	semidirect