Subgroups — #20246307

Order 6016.

552 conjugacy classes of subgroups.

The subgroup lattice has 258 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#13093989	C₂	1	1	yes	maximal, characteristic
3	C₂×#13093989	C₂	1	1	yes	maximal, characteristic
4	#15689022	C₂	1	1	yes	maximal, characteristic
5	#15689020	C₂	1	2	yes	maximal
6	#15689018	C₂	1	2	yes	maximal
7	#15688988	C₂	1	1	yes	maximal, characteristic
8	#15688987	C₂	1	2	yes	maximal
9	C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal
10	C₄×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#389	C₂	1	1	yes	maximal, characteristic
12	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
13	C₄×Dic₉₄	—	2	4	no	—
14	#13093989	—	2	4	no	—
15	#13093989	C₄	1	8	yes	complemented
16	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
17	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
21	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
22	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
23	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
25	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
26	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
28	C₄₇⋊#95	C₂²	1	1	yes	characteristic
29	C₄₇⋊#95	C₂²	1	1	yes	characteristic
30	C₄₇⋊#95	C₂²	1	2	yes	—
31	C₄₇⋊#95	C₂²	1	2	yes	—
32	C₄₇⋊#95	C₂²	1	2	yes	—
33	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
37	#95×C₄₇	C₂²	1	2	yes	—
38	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
44	C₂²×Dic₄₇	C₂³	1	2	yes	—
45	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
46	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
47	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
48	C₂²×Dic₄₇	C₂³	1	2	yes	—
49	C₂×Dic₉₄	C₂×C₄	1	4	yes	—
50	C₂×Dic₉₄	D₄	1	4	yes	—
51	C₂×Dic₉₄	Q₈	1	4	yes	—
52	C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
55	C₄²×C₄₇	—	2	2	no	—
56	C₄⋊Dic₄₇	—	2	2	no	—
57	C₄⋊Dic₄₇	—	2	4	no	—
58	Dic₄₇⋊C₄	—	2	2	no	—
59	Dic₄₇⋊C₄	—	2	4	no	—
60	Dic₄₇⋊C₄	—	2	4	no	—
61	Dic₄₇⋊C₄	—	2	2	no	—
62	Dic₄₇⋊C₄	C₂×C₄	1	8	yes	—
63	C₄×Dic₄₇	—	2	2	no	—
64	C₄×Dic₄₇	—	2	4	no	—
65	C₄×Dic₄₇	—	2	4	no	—
66	C₄×Dic₄₇	C₂×C₄	1	4	yes	—
67	C₄×Dic₄₇	C₂×C₄	1	8	yes	—
68	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
69	C₂×C₄×C₄₇	—	2	1	no	—
70	C₂×C₄×C₄₇	—	2	2	no	—
71	C₂×C₄×C₄₇	—	2	2	no	—
72	C₂×C₄×C₄₇	—	2	1	no	—
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	2	1	no	—
75	C₂×C₄×C₄₇	—	2	1	no	—
76	C₂×C₄×C₄₇	—	2	2	no	—
77	C₂×C₄×C₄₇	—	2	2	no	—
78	C₂×C₄×C₄₇	—	2	1	no	—
79	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
80	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
81	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₄₇	C₂×Q₈	1	2	yes	—
83	C₂×C₄×C₄₇	#41	1	2	yes	—
84	C₂×Dic₄₇	—	2	1	no	—
85	C₂×Dic₄₇	—	2	1	no	—
86	C₂×Dic₄₇	—	2	1	no	—
87	C₂×Dic₄₇	—	2	1	no	—
88	C₂×Dic₄₇	—	2	1	no	—
89	C₂×Dic₄₇	—	2	1	no	—
90	C₂×Dic₄₇	—	2	1	no	—
91	C₂×Dic₄₇	—	2	2	no	—
92	C₂×Dic₄₇	—	2	1	no	—
93	C₂×Dic₄₇	—	2	2	no	—
94	C₂×Dic₄₇	—	2	1	no	—
95	C₂×Dic₄₇	—	2	2	no	—
96	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂×Dic₄₇	C₂²×C₄	1	2	yes	—
98	C₂×Dic₄₇	C₂²×C₄	1	4	yes	—
99	C₂×Dic₄₇	C₂×D₄	1	4	yes	—
100	C₂×Dic₄₇	C₂×Q₈	1	4	yes	—
101	C₂×Dic₄₇	#41	1	2	yes	—
102	Dic₉₄	C₄⋊C₄	1	16	yes	complemented
103	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
104	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
105	C₂²×C₄₇	C₂²×Q₈	1	1	yes	characteristic
106	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
107	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
108	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
109	C₂²×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
110	C₄×C₄₇	—	2	4	no	—
111	C₄×C₄₇	—	2	2	no	—
112	C₄×C₄₇	—	4	2	no	—
113	C₄×C₄₇	—	4	1	no	—
114	C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
115	Dic₄₇	—	2	2	no	—
116	Dic₄₇	—	2	2	no	—
117	Dic₄₇	—	2	2	no	—
118	Dic₄₇	—	4	1	no	—
119	Dic₄₇	—	4	2	no	—
120	Dic₄₇	C₂×C₄⋊C₄	1	8	yes	—
121	#2351	—	47	1	no	maximal, Sylow
122	C₂×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
123	C₂×C₄₇	C₄×#41	1	1	yes	characteristic
124	C₂×C₄₇	#519	1	1	yes	characteristic
125	C₂×C₄₇	#548	1	1	yes	characteristic
126	C₂×C₄₇	#548	1	1	yes	characteristic
127	C₂×C₄₇	#557	1	1	yes	characteristic
128	C₂×C₄₇	#557	1	1	yes	characteristic
129	C₂×C₄×Q₈	—	47	1	no	—
130	C₂×C₄×Q₈	—	47	1	no	—
131	C₂×C₄×Q₈	—	47	1	no	—
132	#389	—	47	2	no	—
133	#389	—	47	1	no	—
134	#389	—	47	2	no	—
135	#389	D₄₇	1	1	yes	characteristic
136	#382	—	47	1	no	—
137	#382	—	47	2	no	—
138	C₄×C₄⋊C₄	—	47	2	no	—
139	C₄×C₄⋊C₄	—	47	1	no	—
140	C₄₇	#2351	1	1	yes	characteristic, complemented, Sylow
141	C₂²×Q₈	—	47	1	no	—
142	C₄×Q₈	—	47	8	no	—
143	C₄×Q₈	—	94	4	no	—
144	C₄×Q₈	—	94	4	no	—
145	C₂×C₄⋊C₄	—	47	2	no	—
146	C₂×C₄⋊C₄	—	47	2	no	—
147	C₂×C₄⋊C₄	—	47	2	no	—
148	C₂×C₄⋊C₄	—	47	1	no	—
149	C₂×C₄⋊C₄	—	47	1	no	—
150	C₂×C₄⋊C₄	—	47	1	no	—
151	C₂×C₄⋊C₄	—	47	2	no	—
152	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
153	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
154	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
155	C₂×C₄²	—	47	2	no	—
156	C₂×C₄²	—	47	1	no	—
157	C₂×C₄²	—	47	2	no	—
158	C₂×C₄²	—	47	2	no	—
159	C₂×C₄²	—	47	1	no	—
160	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
161	#95	—	47	1	no	—
162	#95	—	47	2	no	—
163	#95	—	47	1	no	—
164	#95	—	47	2	no	—
165	#95	—	47	2	no	—
166	#95	C₂×D₄₇	1	2	yes	—
167	C₂×Q₈	—	47	4	no	—
168	C₂×Q₈	—	47	4	no	—
169	C₂×Q₈	—	47	4	no	—
170	C₂²×C₄	—	47	2	no	—
171	C₂²×C₄	—	47	1	no	—
172	C₂²×C₄	—	47	1	no	—
173	C₂²×C₄	—	47	1	no	—
174	C₂²×C₄	—	47	2	no	—
175	C₂²×C₄	—	47	1	no	—
176	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
177	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
178	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
179	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
180	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
181	C₄⋊C₄	—	2	2	no	—
182	C₄⋊C₄	—	2	4	no	—
183	C₄⋊C₄	—	47	8	no	—
184	C₄⋊C₄	—	94	2	no	—
185	C₄⋊C₄	—	94	4	no	—
186	C₄⋊C₄	—	94	4	no	—
187	C₄⋊C₄	—	94	4	no	—
188	C₄⋊C₄	—	94	2	no	—
189	C₄⋊C₄	—	94	2	no	—
190	C₄⋊C₄	C₄×D₄₇	1	4	yes	—
191	C₄²	—	2	2	no	—
192	C₄²	—	47	8	no	—
193	C₄²	—	47	4	no	—
194	C₄²	—	94	4	no	—
195	C₄²	—	94	4	no	—
196	C₄²	—	94	2	no	—
197	C₂³	C₂³×D₄₇	1	1	yes	characteristic
198	Q₈	—	47	16	no	—
199	C₂×C₄	—	2	1	no	—
200	C₂×C₄	—	2	2	no	—
201	C₂×C₄	—	2	2	no	—
202	C₂×C₄	—	2	1	no	—
203	C₂×C₄	—	2	1	no	—
204	C₂×C₄	—	2	2	no	—
205	C₂×C₄	—	2	1	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	1	no	—
209	C₂×C₄	—	47	4	no	—
210	C₂×C₄	—	47	4	no	—
211	C₂×C₄	—	47	4	no	—
212	C₂×C₄	—	47	2	no	—
213	C₂×C₄	—	47	2	no	—
214	C₂×C₄	—	47	2	no	—
215	C₂×C₄	—	94	1	no	—
216	C₂×C₄	—	94	1	no	—
217	C₂×C₄	—	94	1	no	—
218	C₂×C₄	—	94	1	no	—
219	C₂×C₄	—	94	1	no	—
220	C₂×C₄	—	94	1	no	—
221	C₂×C₄	—	94	1	no	—
222	C₂×C₄	—	94	2	no	—
223	C₂×C₄	—	94	2	no	—
224	C₂×C₄	—	94	1	no	—
225	C₂×C₄	—	94	1	no	—
226	C₂×C₄	—	94	2	no	—
227	C₂×C₄	C₂×C₄×D₄₇	1	4	yes	—
228	C₂×C₄	C₂×C₄×D₄₇	1	2	yes	—
229	C₂×C₄	D₄×D₄₇	1	2	yes	—
230	C₂×C₄	#10625352	1	2	yes	—
231	C₂×C₄	Q₈×D₄₇	1	2	yes	—
232	C₂²	C₂²×C₄×D₄₇	1	1	yes	characteristic
233	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
234	C₂²	C₂×Q₈×D₄₇	1	1	yes	characteristic
235	C₂²	#41×D₄₇	1	1	yes	characteristic
236	C₂²	C₂×#10625352	1	1	yes	characteristic
237	C₂²	#13094071	1	1	yes	characteristic
238	C₂²	#13094072	1	1	yes	characteristic
239	C₄	—	2	2	no	—
240	C₄	—	2	4	no	—
241	C₄	—	4	2	no	—
242	C₄	—	4	1	no	—
243	C₄	—	47	8	no	—
244	C₄	—	94	2	no	—
245	C₄	—	94	2	no	—
246	C₄	—	94	2	no	—
247	C₄	—	188	1	no	—
248	C₄	—	188	2	no	—
249	C₄	C₄⋊C₄×D₄₇	1	4	yes	—
250	C₂	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
251	C₂	C₄×#10625352	1	1	yes	characteristic
252	C₂	#15689599	1	1	yes	characteristic
253	C₂	#15689779	1	1	yes	characteristic
254	C₂	#15689783	1	1	yes	characteristic
255	C₂	#15689848	1	1	yes	characteristic
256	C₂	#15689850	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₄₇×#389	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	#389	D₄₇
hypocenter	C₄₇	#2351
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #389

Complements

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

N	H ≅ G/N	type
15. #13093989	C₄	semidirect
102. Dic₉₄	C₄⋊C₄	semidirect
140. C₄₇	#2351	semidirect