Subgroups — #26104206

Order 12032.

2886 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄₇⋊#95	C₂	1	4	yes	maximal
3	C₂²×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic
4	C₂²×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
6	C₂⁴×Dic₄₇	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	—	2	8	no	—
8	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
9	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
10	C₂²×C₄⋊Dic₄₇	C₄	1	4	yes	complemented
11	C₂×C₄₇⋊#95	—	2	8	no	—
12	C₂×C₄₇⋊#95	—	2	8	no	—
13	C₂×C₄₇⋊#95	—	2	8	no	—
14	C₂×C₄₇⋊#95	—	2	2	no	—
15	C₂×C₄₇⋊#95	—	2	2	no	—
16	C₂×C₄₇⋊#95	C₄	1	4	yes	complemented
17	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
18	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#95×C₄₇	—	2	2	no	—
20	C₂×#95×C₄₇	—	2	2	no	—
21	C₂×#95×C₄₇	C₄	1	4	yes	complemented
22	C₂³×Dic₄₇	—	2	2	no	—
23	C₂³×Dic₄₇	—	2	2	no	—
24	C₂³×Dic₄₇	—	2	4	no	—
25	C₂³×Dic₄₇	—	2	4	no	—
26	C₂³×Dic₄₇	—	2	4	no	—
27	C₂³×Dic₄₇	—	2	4	no	—
28	C₂³×Dic₄₇	—	2	4	no	—
29	C₂³×Dic₄₇	—	2	2	no	—
30	C₂³×Dic₄₇	—	2	2	no	—
31	C₂³×Dic₄₇	—	2	2	no	—
32	C₂³×Dic₄₇	—	2	2	no	—
33	C₂³×Dic₄₇	—	2	4	no	—
34	C₂³×Dic₄₇	—	2	4	no	—
35	C₂³×Dic₄₇	—	2	4	no	—
36	C₂³×Dic₄₇	—	2	4	no	—
37	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
38	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
39	C₂³×Dic₄₇	D₄	1	8	yes	—
40	C₂³×Dic₄₇	D₄	1	4	yes	—
41	C₂³×Dic₄₇	Q₈	1	4	yes	—
42	C₂×C₄⋊Dic₄₇	—	2	16	no	—
43	C₂×C₄⋊Dic₄₇	—	2	16	no	—
44	C₂×C₄⋊Dic₄₇	—	2	8	no	—
45	C₂×C₄⋊Dic₄₇	—	2	16	no	—
46	C₄₇⋊#95	—	2	32	no	—
47	C₄₇⋊#95	—	2	8	no	—
48	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	—	2	4	no	—
50	C₂³×C₄×C₄₇	—	2	4	no	—
51	C₂³×C₄×C₄₇	—	2	4	no	—
52	C₂³×C₄×C₄₇	—	2	4	no	—
53	C₂³×C₄×C₄₇	—	2	2	no	—
54	C₂³×C₄×C₄₇	—	2	2	no	—
55	C₂³×C₄×C₄₇	—	2	2	no	—
56	C₂³×C₄×C₄₇	—	2	2	no	—
57	C₂³×C₄×C₄₇	—	2	4	no	—
58	C₂³×C₄×C₄₇	—	2	4	no	—
59	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
60	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
61	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂³×C₄×C₄₇	D₄	1	4	yes	—
64	C₂³×C₄×C₄₇	D₄	1	2	yes	—
65	C₂³×C₄×C₄₇	D₄	1	2	yes	—
66	C₂³×C₄×C₄₇	D₄	1	2	yes	—
67	C₂³×C₄×C₄₇	Q₈	1	4	yes	—
68	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
69	#95×C₄₇	—	2	8	no	—
70	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
71	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
74	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
77	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
78	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
79	C₂⁴×C₄₇	C₂×Q₈	1	1	yes	characteristic
80	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
81	C₂⁴×C₄₇	C₂×Q₈	1	2	yes	—
82	C₂⁴×C₄₇	#41	1	4	yes	—
83	C₂⁴×C₄₇	#41	1	2	yes	—
84	C₂⁴×C₄₇	#41	1	2	yes	—
85	C₂⁴×C₄₇	#41	1	2	yes	—
86	C₂⁴×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	8	no	—
90	C₂²×C₄×C₄₇	—	2	8	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	8	no	—
94	C₂²×C₄×C₄₇	—	2	8	no	—
95	C₂²×C₄×C₄₇	—	2	4	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	2	4	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	8	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	—	2	8	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	8	no	—
107	C₂²×C₄×C₄₇	—	2	8	no	—
108	C₂²×C₄×C₄₇	—	2	8	no	—
109	C₂²×C₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	—	4	4	no	—
112	C₂²×C₄×C₄₇	—	4	4	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	—	4	4	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	4	4	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
120	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
123	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
125	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₄⋊C₄	1	8	yes	complemented
127	C₂²×Dic₄₇	—	2	4	no	—
128	C₂²×Dic₄₇	—	2	4	no	—
129	C₂²×Dic₄₇	—	2	4	no	—
130	C₂²×Dic₄₇	—	2	4	no	—
131	C₂²×Dic₄₇	—	2	8	no	—
132	C₂²×Dic₄₇	—	2	8	no	—
133	C₂²×Dic₄₇	—	2	8	no	—
134	C₂²×Dic₄₇	—	2	8	no	—
135	C₂²×Dic₄₇	—	2	8	no	—
136	C₂²×Dic₄₇	—	2	8	no	—
137	C₂²×Dic₄₇	—	2	8	no	—
138	C₂²×Dic₄₇	—	2	8	no	—
139	C₂²×Dic₄₇	—	2	4	no	—
140	C₂²×Dic₄₇	—	2	4	no	—
141	C₂²×Dic₄₇	—	2	8	no	—
142	C₂²×Dic₄₇	—	2	8	no	—
143	C₂²×Dic₄₇	—	2	4	no	—
144	C₂²×Dic₄₇	—	2	4	no	—
145	C₂²×Dic₄₇	—	2	8	no	—
146	C₂²×Dic₄₇	—	2	8	no	—
147	C₂²×Dic₄₇	—	2	8	no	—
148	C₂²×Dic₄₇	—	2	8	no	—
149	C₂²×Dic₄₇	—	4	4	no	—
150	C₂²×Dic₄₇	—	4	2	no	—
151	C₂²×Dic₄₇	—	4	4	no	—
152	C₂²×Dic₄₇	—	4	4	no	—
153	C₂²×Dic₄₇	—	4	4	no	—
154	C₂²×Dic₄₇	—	4	4	no	—
155	C₂²×Dic₄₇	—	4	4	no	—
156	C₂²×Dic₄₇	—	4	4	no	—
157	C₂²×Dic₄₇	—	4	4	no	—
158	C₂²×Dic₄₇	—	4	4	no	—
159	C₂²×Dic₄₇	—	4	2	no	—
160	C₂²×Dic₄₇	—	4	4	no	—
161	C₂²×Dic₄₇	—	4	4	no	—
162	C₂²×Dic₄₇	—	4	2	no	—
163	C₂²×Dic₄₇	—	4	2	no	—
164	C₂²×Dic₄₇	—	4	2	no	—
165	C₂²×Dic₄₇	—	4	4	no	—
166	C₂²×Dic₄₇	—	4	2	no	—
167	C₂²×Dic₄₇	—	4	2	no	—
168	C₂²×Dic₄₇	—	4	2	no	—
169	C₂²×Dic₄₇	C₂²⋊C₄	1	8	yes	—
170	C₂²×Dic₄₇	C₄⋊C₄	1	8	yes	complemented
171	C₄⋊Dic₄₇	—	2	32	no	—
172	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
173	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
174	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
175	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
178	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
179	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
182	C₂³×C₄₇	#117	1	2	yes	—
183	C₂³×C₄₇	#117	1	2	yes	—
184	C₂³×C₄₇	#117	1	2	yes	—
185	C₂³×C₄₇	C₄×D₄	1	4	yes	—
186	C₂³×C₄₇	C₄×D₄	1	2	yes	—
187	C₂³×C₄₇	C₄×D₄	1	4	yes	—
188	C₂³×C₄₇	C₄×D₄	1	2	yes	—
189	C₂³×C₄₇	C₄×D₄	1	2	yes	—
190	C₂³×C₄₇	C₄×D₄	1	2	yes	—
191	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
192	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
193	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
194	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
195	C₂³×C₄₇	#120	1	2	yes	—
196	C₂³×C₄₇	#120	1	2	yes	—
197	C₂³×C₄₇	#120	1	4	yes	—
198	C₂³×C₄₇	#121	1	2	yes	—
199	C₂³×C₄₇	#121	1	4	yes	—
200	C₂³×C₄₇	#121	1	4	yes	—
201	C₂³×C₄₇	#121	1	2	yes	—
202	C₂³×C₄₇	#121	1	2	yes	—
203	C₂³×C₄₇	#121	1	2	yes	—
204	C₂³×C₄₇	#121	1	4	yes	—
205	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
206	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
207	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
208	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
209	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
210	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
211	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
212	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
213	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
214	C₂³×C₄₇	#123	1	2	yes	—
215	C₂³×C₄₇	#123	1	4	yes	—
216	C₂³×C₄₇	#123	1	2	yes	—
217	C₂³×C₄₇	#123	1	4	yes	—
218	C₂³×C₄₇	#123	1	4	yes	—
219	C₂³×C₄₇	#124	1	4	yes	—
220	C₂³×C₄₇	#124	1	1	yes	characteristic
221	C₂³×C₄₇	#124	1	1	yes	characteristic
222	C₂³×C₄₇	#124	1	1	yes	characteristic
223	C₂³×C₄₇	#124	1	1	yes	characteristic
224	C₂³×C₄₇	#125	1	4	yes	—
225	C₂³×C₄₇	#125	1	2	yes	—
226	C₂³×C₄₇	#125	1	4	yes	—
227	C₂³×C₄₇	#125	1	2	yes	—
228	C₂³×C₄₇	#126	1	4	yes	—
229	C₂³×C₄₇	#126	1	4	yes	—
230	C₂³×C₄₇	#127	1	1	yes	characteristic
231	C₂³×C₄₇	#127	1	1	yes	characteristic
232	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
233	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
234	C₂³×C₄₇	C₄⋊Q₈	1	4	yes	—
235	C₂³×C₄₇	C₄⋊Q₈	1	2	yes	—
236	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
237	C₂×C₄×C₄₇	—	2	8	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	8	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	8	no	—
242	C₂×C₄×C₄₇	—	2	8	no	—
243	C₂×C₄×C₄₇	—	2	8	no	—
244	C₂×C₄×C₄₇	—	2	8	no	—
245	C₂×C₄×C₄₇	—	2	8	no	—
246	C₂×C₄×C₄₇	—	2	16	no	—
247	C₂×C₄×C₄₇	—	4	4	no	—
248	C₂×C₄×C₄₇	—	4	8	no	—
249	C₂×C₄×C₄₇	—	4	4	no	—
250	C₂×C₄×C₄₇	—	4	4	no	—
251	C₂×C₄×C₄₇	—	4	4	no	—
252	C₂×C₄×C₄₇	—	4	8	no	—
253	C₂×C₄×C₄₇	—	4	8	no	—
254	C₂×C₄×C₄₇	—	4	4	no	—
255	C₂×C₄×C₄₇	—	4	4	no	—
256	C₂×C₄×C₄₇	#95	1	8	yes	complemented
257	C₂×Dic₄₇	—	2	8	no	—
258	C₂×Dic₄₇	—	2	8	no	—
259	C₂×Dic₄₇	—	2	16	no	—
260	C₂×Dic₄₇	—	2	16	no	—
261	C₂×Dic₄₇	—	4	4	no	—
262	C₂×Dic₄₇	—	4	8	no	—
263	C₂×Dic₄₇	—	4	8	no	—
264	C₂×Dic₄₇	—	4	4	no	—
265	C₂×Dic₄₇	—	4	4	no	—
266	C₂×Dic₄₇	—	4	4	no	—
267	C₂×Dic₄₇	—	4	8	no	—
268	C₂×Dic₄₇	—	4	8	no	—
269	C₂×Dic₄₇	—	4	4	no	—
270	C₂×Dic₄₇	—	4	4	no	—
271	C₂×Dic₄₇	—	4	8	no	—
272	C₂×Dic₄₇	—	4	8	no	—
273	C₂×Dic₄₇	—	4	8	no	—
274	C₂×Dic₄₇	—	4	8	no	—
275	C₂×Dic₄₇	—	4	4	no	—
276	C₂×Dic₄₇	—	4	4	no	—
277	#7557	—	47	1	no	maximal, Sylow
278	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
279	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
280	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
281	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
282	C₂²×C₄₇	#379	1	1	yes	characteristic
283	C₂²×C₄₇	#380	1	2	yes	—
284	C₂²×C₄₇	#380	1	2	yes	—
285	C₂²×C₄₇	#380	1	2	yes	—
286	C₂²×C₄₇	#381	1	1	yes	characteristic
287	C₂²×C₄₇	#382	1	1	yes	characteristic
288	C₂²×C₄₇	#382	1	1	yes	characteristic
289	C₂²×C₄₇	#384	1	1	yes	characteristic
290	C₂²×C₄₇	#384	1	1	yes	characteristic
291	C₂²×C₄₇	#385	1	2	yes	—
292	C₂²×C₄₇	#385	1	4	yes	—
293	C₂²×C₄₇	#385	1	2	yes	—
294	C₂²×C₄₇	#385	1	4	yes	—
295	C₂²×C₄₇	#386	1	2	yes	—
296	C₂²×C₄₇	#386	1	4	yes	—
297	C₂²×C₄₇	#386	1	2	yes	—
298	C₂²×C₄₇	#387	1	4	yes	—
299	C₂²×C₄₇	#387	1	4	yes	—
300	C₂²×C₄₇	#387	1	4	yes	—
301	C₂²×C₄₇	#387	1	4	yes	—
302	C₂²×C₄₇	#388	1	4	yes	—
303	C₂²×C₄₇	#388	1	4	yes	—
304	C₂²×C₄₇	#389	1	2	yes	—
305	C₂²×C₄₇	#389	1	4	yes	—
306	C₂²×C₄₇	#389	1	2	yes	—
307	C₂²×C₄₇	#389	1	2	yes	—
308	C₂²×C₄₇	#389	1	2	yes	—
309	C₂²×C₄₇	#389	1	4	yes	—
310	C₂²×C₄₇	#390	1	1	yes	characteristic
311	C₂²×C₄₇	#390	1	1	yes	characteristic
312	C₂²×C₄₇	#390	1	1	yes	characteristic
313	C₂²×C₄₇	#390	1	1	yes	characteristic
314	C₂²×C₄₇	#391	1	4	yes	—
315	C₂²×C₄₇	#391	1	1	yes	characteristic
316	C₂²×C₄₇	#391	1	1	yes	characteristic
317	C₂²×C₄₇	#391	1	1	yes	characteristic
318	C₂²×C₄₇	#391	1	1	yes	characteristic
319	C₂²×C₄₇	#392	1	2	yes	—
320	C₂²×C₄₇	#392	1	2	yes	—
321	C₂²×C₄₇	#393	1	2	yes	—
322	C₂²×C₄₇	#393	1	2	yes	—
323	C₂²×C₄₇	#394	1	4	yes	—
324	C₂²×C₄₇	#394	1	2	yes	—
325	C₂²×C₄₇	#394	1	2	yes	—
326	C₂²×C₄₇	#395	1	2	yes	—
327	C₂²×C₄₇	#395	1	4	yes	—
328	C₂²×C₄₇	#395	1	2	yes	—
329	C₂²×C₄₇	#396	1	4	yes	—
330	C₂²×C₄₇	#396	1	4	yes	—
331	C₂²×C₄₇	#397	1	2	yes	—
332	C₂²×C₄₇	#397	1	2	yes	—
333	C₂²×C₄₇	#398	1	2	yes	—
334	C₂²×C₄₇	#398	1	4	yes	—
335	C₂²×C₄₇	#398	1	2	yes	—
336	C₂²×C₄₇	#398	1	4	yes	—
337	C₂²×C₄₇	#398	1	4	yes	—
338	C₂²×C₄₇	#399	1	2	yes	—
339	C₂²×C₄₇	#399	1	2	yes	—
340	C₂²×C₄₇	#400	1	2	yes	—
341	C₂²×C₄₇	#400	1	2	yes	—
342	C₂²×C₄₇	#400	1	4	yes	—
343	C₄×C₄₇	—	2	8	no	—
344	C₄×C₄₇	—	4	8	no	—
345	Dic₄₇	—	4	8	no	—
346	Dic₄₇	—	4	8	no	—
347	C₂³×C₄⋊C₄	—	47	1	no	—
348	C₂²×#95	—	47	1	no	—
349	C₂²×#95	—	47	4	no	—
350	C₂²×#95	D₄₇	1	1	yes	characteristic
351	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
352	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
353	C₂×C₄₇	C₄⋊#95	1	1	yes	characteristic
354	C₂×C₄₇	#1436	1	4	yes	—
355	C₂×C₄₇	#1438	1	1	yes	characteristic
356	C₂×C₄₇	#1439	1	2	yes	—
357	C₂×C₄₇	#1439	1	2	yes	—
358	C₂×C₄₇	#1441	1	4	yes	—
359	C₂×C₄₇	#1441	1	2	yes	—
360	C₂×C₄₇	#1441	1	2	yes	—
361	C₂×C₄₇	#1442	1	2	yes	—
362	C₂×C₄₇	#1442	1	2	yes	—
363	C₂×C₄₇	#1444	1	2	yes	—
364	C₂×C₄₇	#1444	1	2	yes	—
365	C₂×C₄₇	#1445	1	1	yes	characteristic
366	C₂×C₄₇	#1445	1	1	yes	characteristic
367	C₂×C₄₇	#1446	1	1	yes	characteristic
368	C₂⁴×C₄	—	47	2	no	—
369	C₂⁴×C₄	—	47	2	no	—
370	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
371	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
372	C₂²×C₄⋊C₄	—	47	4	no	—
373	C₂²×C₄⋊C₄	—	94	8	no	—
374	C₂²×C₄⋊C₄	—	94	2	no	—
375	C₂²×C₄⋊C₄	—	94	2	no	—
376	C₂×#95	—	2	2	no	—
377	C₂×#95	—	2	2	no	—
378	C₂×#95	—	47	4	no	—
379	C₂×#95	—	94	8	no	—
380	C₂×#95	—	94	8	no	—
381	C₂×#95	—	94	8	no	—
382	C₂×#95	—	94	2	no	—
383	C₂×#95	—	94	2	no	—
384	C₂×#95	Dic₄₇	1	4	yes	complemented
385	C₄₇	#7557	1	1	yes	characteristic, complemented, Sylow
386	C₂⁵	C₂²×D₄₇	1	1	yes	characteristic
387	C₂³×C₄	—	2	4	no	—
388	C₂³×C₄	—	2	4	no	—
389	C₂³×C₄	—	2	2	no	—
390	C₂³×C₄	—	2	2	no	—
391	C₂³×C₄	—	2	4	no	—
392	C₂³×C₄	—	2	4	no	—
393	C₂³×C₄	—	2	4	no	—
394	C₂³×C₄	—	2	4	no	—
395	C₂³×C₄	—	2	2	no	—
396	C₂³×C₄	—	2	2	no	—
397	C₂³×C₄	—	47	4	no	—
398	C₂³×C₄	—	47	4	no	—
399	C₂³×C₄	—	47	8	no	—
400	C₂³×C₄	—	47	4	no	—
401	C₂³×C₄	—	47	4	no	—
402	C₂³×C₄	—	94	2	no	—
403	C₂³×C₄	—	94	2	no	—
404	C₂³×C₄	—	94	4	no	—
405	C₂³×C₄	—	94	4	no	—
406	C₂³×C₄	—	94	4	no	—
407	C₂³×C₄	—	94	4	no	—
408	C₂³×C₄	—	94	4	no	—
409	C₂³×C₄	—	94	4	no	—
410	C₂³×C₄	—	94	4	no	—
411	C₂³×C₄	—	94	2	no	—
412	C₂³×C₄	—	94	4	no	—
413	C₂³×C₄	—	94	2	no	—
414	C₂³×C₄	—	94	4	no	—
415	C₂³×C₄	—	94	2	no	—
416	C₂³×C₄	—	94	2	no	—
417	C₂³×C₄	Dic₉₄	1	4	yes	—
418	C₂³×C₄	Dic₉₄	1	2	yes	—
419	C₂³×C₄	C₄×D₄₇	1	2	yes	—
420	C₂³×C₄	C₄×D₄₇	1	2	yes	—
421	C₂³×C₄	D₁₈₈	1	4	yes	—
422	C₂³×C₄	D₁₈₈	1	2	yes	—
423	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
424	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
425	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
426	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
427	C₂×C₄⋊C₄	—	94	16	no	—
428	C₂×C₄⋊C₄	—	94	16	no	—
429	C₂×C₄⋊C₄	—	94	16	no	—
430	C₂×C₄⋊C₄	—	94	8	no	—
431	#95	—	2	8	no	—
432	#95	—	94	32	no	—
433	#95	—	94	8	no	—
434	C₂⁴	C₂×Dic₉₄	1	1	yes	characteristic
435	C₂⁴	C₂×Dic₉₄	1	2	yes	—
436	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
437	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
438	C₂⁴	C₂×D₁₈₈	1	1	yes	characteristic
439	C₂⁴	C₂×D₁₈₈	1	2	yes	—
440	C₂⁴	#10625350	1	2	yes	—
441	C₂⁴	#10625350	1	2	yes	—
442	C₂⁴	D₄×D₄₇	1	4	yes	—
443	C₂⁴	D₄×D₄₇	1	2	yes	—
444	C₂⁴	#10625352	1	4	yes	—
445	C₂⁴	#10625352	1	2	yes	—
446	C₂⁴	Q₈×D₄₇	1	2	yes	—
447	C₂⁴	#10625354	1	2	yes	—
448	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
449	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
450	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	4	no	—
453	C₂²×C₄	—	2	8	no	—
454	C₂²×C₄	—	2	8	no	—
455	C₂²×C₄	—	2	4	no	—
456	C₂²×C₄	—	2	4	no	—
457	C₂²×C₄	—	2	8	no	—
458	C₂²×C₄	—	2	8	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	4	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	8	no	—
464	C₂²×C₄	—	2	8	no	—
465	C₂²×C₄	—	2	8	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	8	no	—
469	C₂²×C₄	—	2	8	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	4	2	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	2	no	—
481	C₂²×C₄	—	4	4	no	—
482	C₂²×C₄	—	4	2	no	—
483	C₂²×C₄	—	47	8	no	—
484	C₂²×C₄	—	47	8	no	—
485	C₂²×C₄	—	94	4	no	—
486	C₂²×C₄	—	94	4	no	—
487	C₂²×C₄	—	94	4	no	—
488	C₂²×C₄	—	94	4	no	—
489	C₂²×C₄	—	94	8	no	—
490	C₂²×C₄	—	94	8	no	—
491	C₂²×C₄	—	94	8	no	—
492	C₂²×C₄	—	94	8	no	—
493	C₂²×C₄	—	94	8	no	—
494	C₂²×C₄	—	94	8	no	—
495	C₂²×C₄	—	94	8	no	—
496	C₂²×C₄	—	94	8	no	—
497	C₂²×C₄	—	94	4	no	—
498	C₂²×C₄	—	94	8	no	—
499	C₂²×C₄	—	94	4	no	—
500	C₂²×C₄	—	94	8	no	—
501	C₂²×C₄	—	94	4	no	—
502	C₂²×C₄	—	94	8	no	—
503	C₂²×C₄	—	94	4	no	—
504	C₂²×C₄	—	94	8	no	—
505	C₂²×C₄	—	94	8	no	—
506	C₂²×C₄	—	94	8	no	—
507	C₂²×C₄	—	188	2	no	—
508	C₂²×C₄	—	188	4	no	—
509	C₂²×C₄	—	188	4	no	—
510	C₂²×C₄	—	188	4	no	—
511	C₂²×C₄	—	188	4	no	—
512	C₂²×C₄	—	188	4	no	—
513	C₂²×C₄	—	188	4	no	—
514	C₂²×C₄	—	188	4	no	—
515	C₂²×C₄	—	188	4	no	—
516	C₂²×C₄	—	188	2	no	—
517	C₂²×C₄	—	188	4	no	—
518	C₂²×C₄	—	188	4	no	—
519	C₂²×C₄	—	188	4	no	—
520	C₂²×C₄	—	188	2	no	—
521	C₂²×C₄	—	188	2	no	—
522	C₂²×C₄	—	188	2	no	—
523	C₂²×C₄	—	188	4	no	—
524	C₂²×C₄	—	188	2	no	—
525	C₂²×C₄	—	188	2	no	—
526	C₂²×C₄	—	188	2	no	—
527	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
528	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
529	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
530	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
531	C₂²×C₄	C₄⋊Dic₄₇	1	8	yes	complemented
532	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
533	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
534	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
535	C₄⋊C₄	—	94	32	no	—
536	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
537	C₂³	C₂²⋊C₄×D₄₇	1	2	yes	—
538	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
539	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
540	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
541	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
542	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
543	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
544	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
545	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
546	C₂³	#13093980	1	2	yes	—
547	C₂³	#13093982	1	2	yes	—
548	C₂³	#13093983	1	2	yes	—
549	C₂³	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
550	C₂³	#13093986	1	2	yes	—
551	C₂³	D₄×Dic₄₇	1	4	yes	—
552	C₂³	D₄×Dic₄₇	1	2	yes	—
553	C₂³	C₄×D₁₈₈	1	2	yes	—
554	C₂³	C₄×D₁₈₈	1	2	yes	—
555	C₂³	#13093989	1	2	yes	—
556	C₂³	C₄×Dic₉₄	1	2	yes	—
557	C₂³	C₄×Dic₉₄	1	2	yes	—
558	C₂³	Q₈×Dic₄₇	1	2	yes	—
559	C₂³	#13093992	1	2	yes	—
560	C₂³	#13093994	1	2	yes	—
561	C₂³	#13093994	1	4	yes	—
562	C₂³	#13093995	1	2	yes	—
563	C₂³	#13093996	1	4	yes	—
564	C₂³	#13093997	1	4	yes	—
565	C₂³	#13093998	1	2	yes	—
566	C₂³	#13093998	1	2	yes	—
567	C₂³	#13093999	1	2	yes	—
568	C₂³	#13093999	1	4	yes	—
569	C₂³	#13094000	1	2	yes	—
570	C₂³	#13094001	1	4	yes	—
571	C₂³	#13094001	1	4	yes	—
572	C₂³	#13094001	1	4	yes	—
573	C₂³	#13094002	1	4	yes	—
574	C₂³	#13094003	1	2	yes	—
575	C₂³	#13094003	1	2	yes	—
576	C₂³	#13094004	1	2	yes	—
577	C₂³	#13094004	1	4	yes	—
578	C₂³	#13094005	1	2	yes	—
579	C₂³	#13094006	1	4	yes	—
580	C₂³	#13094008	1	2	yes	—
581	C₂³	#13094008	1	4	yes	—
582	C₂³	#13094009	1	4	yes	—
583	C₂³	#13094010	1	4	yes	—
584	C₂³	#13094011	1	1	yes	characteristic
585	C₂³	#13094012	1	1	yes	characteristic
586	C₂³	#13094012	1	1	yes	characteristic
587	C₂³	#13094013	1	1	yes	characteristic
588	C₂³	#13094014	1	4	yes	—
589	C₂³	#13094015	1	2	yes	—
590	C₂³	#13094015	1	4	yes	—
591	C₂³	#13094016	1	2	yes	—
592	C₂³	#13094017	1	4	yes	—
593	C₂³	#13094019	1	4	yes	—
594	C₂³	#13094020	1	1	yes	characteristic
595	C₂³	#13094021	1	1	yes	characteristic
596	C₂³	#13094022	1	1	yes	characteristic
597	C₂³	#13094023	1	2	yes	—
598	C₂³	#13094023	1	4	yes	—
599	C₂³	#13094024	1	2	yes	—
600	C₂³	#13094024	1	1	yes	characteristic
601	C₂×C₄	—	2	8	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	8	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	2	8	no	—
607	C₂×C₄	—	2	8	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	2	8	no	—
610	C₂×C₄	—	2	16	no	—
611	C₂×C₄	—	4	4	no	—
612	C₂×C₄	—	4	8	no	—
613	C₂×C₄	—	4	4	no	—
614	C₂×C₄	—	4	4	no	—
615	C₂×C₄	—	4	4	no	—
616	C₂×C₄	—	4	8	no	—
617	C₂×C₄	—	4	8	no	—
618	C₂×C₄	—	4	4	no	—
619	C₂×C₄	—	4	4	no	—
620	C₂×C₄	—	94	8	no	—
621	C₂×C₄	—	94	8	no	—
622	C₂×C₄	—	94	16	no	—
623	C₂×C₄	—	94	16	no	—
624	C₂×C₄	—	188	4	no	—
625	C₂×C₄	—	188	8	no	—
626	C₂×C₄	—	188	8	no	—
627	C₂×C₄	—	188	4	no	—
628	C₂×C₄	—	188	4	no	—
629	C₂×C₄	—	188	4	no	—
630	C₂×C₄	—	188	8	no	—
631	C₂×C₄	—	188	8	no	—
632	C₂×C₄	—	188	4	no	—
633	C₂×C₄	—	188	4	no	—
634	C₂×C₄	—	188	8	no	—
635	C₂×C₄	—	188	8	no	—
636	C₂×C₄	—	188	8	no	—
637	C₂×C₄	—	188	8	no	—
638	C₂×C₄	—	188	4	no	—
639	C₂×C₄	—	188	4	no	—
640	C₂×C₄	C₄₇⋊#95	1	8	yes	complemented
641	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
642	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
643	C₂²	C₄×C₄⋊Dic₄₇	1	2	yes	—
644	C₂²	C₄⋊C₄×Dic₄₇	1	2	yes	—
645	C₂²	#15688978	1	1	yes	characteristic
646	C₂²	#15688980	1	2	yes	—
647	C₂²	#15688981	1	2	yes	—
648	C₂²	#15688983	1	2	yes	—
649	C₂²	#15688984	1	1	yes	characteristic
650	C₂²	#15688988	1	1	yes	characteristic
651	C₂²	#15688989	1	1	yes	characteristic
652	C₂²	#15688992	1	1	yes	characteristic
653	C₂²	#15688993	1	1	yes	characteristic
654	C₂²	#15688995	1	2	yes	—
655	C₂²	#15688997	1	4	yes	—
656	C₂²	#15688998	1	2	yes	—
657	C₂²	#15688998	1	4	yes	—
658	C₂²	#15689000	1	2	yes	—
659	C₂²	#15689001	1	4	yes	—
660	C₂²	#15689003	1	2	yes	—
661	C₂²	#15689006	1	4	yes	—
662	C₂²	#15689008	1	4	yes	—
663	C₂²	#15689009	1	4	yes	—
664	C₂²	#15689010	1	4	yes	—
665	C₂²	#15689015	1	4	yes	—
666	C₂²	#15689016	1	4	yes	—
667	C₂²	#15689019	1	2	yes	—
668	C₂²	#15689020	1	4	yes	—
669	C₂²	#15689021	1	2	yes	—
670	C₂²	#15689021	1	2	yes	—
671	C₂²	#15689022	1	2	yes	—
672	C₂²	#15689022	1	4	yes	—
673	C₂²	#15689024	1	1	yes	characteristic
674	C₂²	#15689025	1	1	yes	characteristic
675	C₂²	#15689025	1	1	yes	characteristic
676	C₂²	#15689026	1	1	yes	characteristic
677	C₂²	#15689027	1	4	yes	—
678	C₂²	#15689028	1	1	yes	characteristic
679	C₂²	#15689029	1	1	yes	characteristic
680	C₂²	#15689029	1	1	yes	characteristic
681	C₂²	#15689030	1	1	yes	characteristic
682	C₂²	#15689032	1	2	yes	—
683	C₂²	#15689033	1	2	yes	—
684	C₂²	#15689035	1	2	yes	—
685	C₂²	#15689036	1	2	yes	—
686	C₂²	#15689039	1	4	yes	—
687	C₂²	#15689040	1	2	yes	—
688	C₂²	#15689041	1	2	yes	—
689	C₂²	#15689043	1	2	yes	—
690	C₂²	#15689044	1	4	yes	—
691	C₂²	#15689044	1	2	yes	—
692	C₂²	#15689045	1	4	yes	—
693	C₂²	#15689046	1	4	yes	—
694	C₂²	#15689048	1	2	yes	—
695	C₂²	#15689050	1	2	yes	—
696	C₂²	#15689053	1	2	yes	—
697	C₂²	#15689055	1	4	yes	—
698	C₂²	#15689055	1	2	yes	—
699	C₂²	#15689056	1	4	yes	—
700	C₂²	#15689057	1	4	yes	—
701	C₂²	#15689059	1	2	yes	—
702	C₂²	#15689060	1	2	yes	—
703	C₂²	#15689062	1	2	yes	—
704	C₂²	#15689063	1	2	yes	—
705	C₂²	#15689065	1	4	yes	—
706	C₄	—	2	8	no	—
707	C₄	—	4	8	no	—
708	C₄	—	188	8	no	—
709	C₄	—	188	8	no	—
710	C₂	#20241610	1	1	yes	characteristic
711	C₂	#20241617	1	1	yes	characteristic
712	C₂	#20241618	1	1	yes	characteristic
713	C₂	#20241622	1	4	yes	—
714	C₂	#20241628	1	1	yes	characteristic
715	C₂	#20241633	1	2	yes	—
716	C₂	#20241634	1	2	yes	—
717	C₂	#20241640	1	4	yes	—
718	C₂	#20241641	1	2	yes	—
719	C₂	#20241642	1	2	yes	—
720	C₂	#20241644	1	2	yes	—
721	C₂	#20241645	1	2	yes	—
722	C₂	#20241652	1	2	yes	—
723	C₂	#20241653	1	2	yes	—
724	C₂	#20241655	1	1	yes	characteristic
725	C₂	#20241657	1	1	yes	characteristic
726	C₂	#20241658	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂⁵	C₂²×D₄₇
commutator	C₂³×C₄₇	C₂×C₄²
Fitting	C₂²×#95×C₄₇	C₂
socle, prime radical, cosocle	C₂⁵×C₄₇	C₂³
hypercenter	C₂²×#95	D₄₇
hypocenter	C₄₇	#7557
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁵ ◁ C₂²×#95

Complements

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

N	H ≅ G/N	type
10. C₂²×C₄⋊Dic₄₇	C₄	semidirect
16. C₂×C₄₇⋊#95	C₄	semidirect
21. C₂×#95×C₄₇	C₄	semidirect
126. C₂²×C₄×C₄₇	C₄⋊C₄	semidirect
170. C₂²×Dic₄₇	C₄⋊C₄	semidirect
256. C₂×C₄×C₄₇	#95	semidirect
384. C₂×#95	Dic₄₇	semidirect
385. C₄₇	#7557	semidirect
531. C₂²×C₄	C₄⋊Dic₄₇	semidirect
640. C₂×C₄	C₄₇⋊#95	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊Dic₄₇	2
C₂²×C₄₇⋊#95	2
C₂²×#95×C₄₇	2
#7557	47