Subgroups — C₄₇×#29695 #26069393

Order 12032.

1024 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#479	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2851	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2058	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2057	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2043	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2036	C₂	1	2	yes	maximal
9	C₄₇×#2035	C₂	1	2	yes	maximal
10	C₄₇×#1805	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic
12	C₄₇×#533	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₄₇	—	2	1	no	—
16	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
20	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
21	C₂×#117×C₄₇	—	2	1	no	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#479	—	2	8	no	—
24	C₂×#107×C₄₇	C₂²	1	2	yes	—
25	C₂×#106×C₄₇	C₂²	1	2	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
27	C₂×#103×C₄₇	C₂²	1	2	yes	—
28	C₂×#103×C₄₇	C₂²	1	2	yes	—
29	C₂×#103×C₄₇	C₂²	1	2	yes	—
30	C₂×#103×C₄₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
32	C₄₇×#389	C₂²	1	1	yes	characteristic
33	C₄₇×#389	C₂²	1	1	yes	characteristic
34	C₄₇×#387	—	2	1	no	—
35	C₄₇×#387	—	2	1	no	—
36	C₄₇×#385	—	2	1	no	—
37	C₄₇×#385	—	2	1	no	—
38	C₄₇×#382	C₂²	1	1	yes	characteristic
39	C₄₇×#380	C₂²	1	1	yes	characteristic
40	C₄₇×#380	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₄₇×#336	C₂²	1	1	yes	characteristic
45	C₂²×Q₈×C₄₇	—	2	1	no	—
46	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	C₄⋊Q₈×C₄₇	—	2	4	no	—
53	C₄⋊Q₈×C₄₇	—	2	4	no	—
54	#125×C₄₇	—	2	8	no	—
55	#125×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	—	2	8	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	C₄×Q₈×C₄₇	—	2	8	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	D₄	1	8	yes	—
62	#117×C₄₇	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	—	2	4	no	—
82	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	#107×C₄₇	—	2	4	no	—
87	#106×C₄₇	—	2	4	no	—
88	C₄⋊C₈×C₄₇	—	2	4	no	—
89	#103×C₄₇	—	2	4	no	—
90	#103×C₄₇	—	2	4	no	—
91	#103×C₄₇	—	4	2	no	—
92	#103×C₄₇	—	4	2	no	—
93	C₂²⋊C₈×C₄₇	—	4	2	no	—
94	#95×C₄₇	—	2	1	no	—
95	#95×C₄₇	—	2	1	no	—
96	#95×C₄₇	—	2	1	no	—
97	#95×C₄₇	—	2	1	no	—
98	#95×C₄₇	—	2	1	no	—
99	#95×C₄₇	—	2	1	no	—
100	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂×Q₈×C₄₇	—	2	4	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	4	2	no	—
108	C₂×Q₈×C₄₇	—	4	2	no	—
109	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	4	1	no	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	2	8	no	—
141	C₄⋊C₄×C₄₇	—	2	4	no	—
142	C₄⋊C₄×C₄₇	—	2	8	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₄⋊C₄×C₄₇	—	2	1	no	—
148	C₄⋊C₄×C₄₇	—	2	1	no	—
149	C₄⋊C₄×C₄₇	—	2	1	no	—
150	C₄⋊C₄×C₄₇	—	4	2	no	—
151	C₄⋊C₄×C₄₇	—	4	2	no	—
152	C₄⋊C₄×C₄₇	—	4	2	no	—
153	C₄⋊C₄×C₄₇	—	4	2	no	—
154	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
155	C₂²⋊C₄×C₄₇	—	2	8	no	—
156	C₂²⋊C₄×C₄₇	—	4	2	no	—
157	C₂²⋊C₄×C₄₇	—	4	2	no	—
158	C₄²×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	8	no	—
161	C₄²×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	C₂×D₄	1	4	yes	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	1	no	—
166	C₂³×C₄₇	—	2	1	no	—
167	C₂³×C₄₇	—	2	1	no	—
168	C₂³×C₄₇	—	2	1	no	—
169	C₂³×C₄₇	#137	1	2	yes	—
170	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
171	Q₈×C₄₇	—	2	4	no	—
172	Q₈×C₄₇	—	2	4	no	—
173	Q₈×C₄₇	—	4	8	no	—
174	Q₈×C₄₇	—	4	2	no	—
175	Q₈×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	2	8	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	4	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	1	no	—
190	C₂×C₄×C₄₇	—	4	4	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	1	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	#120	1	2	yes	—
210	C₂×C₄×C₄₇	#120	1	2	yes	—
211	C₂×C₄×C₄₇	#135	1	2	yes	—
212	C₂×C₄×C₄₇	#137	1	2	yes	—
213	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
214	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
216	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
217	C₈×C₄₇	—	4	2	no	—
218	C₈×C₄₇	—	4	2	no	—
219	#29695	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	2	2	no	—
223	C₂²×C₄₇	—	4	1	no	—
224	C₂²×C₄₇	—	4	1	no	—
225	C₂²×C₄₇	—	4	1	no	—
226	C₂²×C₄₇	—	4	1	no	—
227	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
228	C₂²×C₄₇	#536	1	1	yes	characteristic
229	C₂²×C₄₇	#537	1	1	yes	characteristic
230	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
233	C₂²×C₄₇	#575	1	1	yes	characteristic
234	C₄×C₄₇	—	2	2	no	—
235	C₄×C₄₇	—	2	2	no	—
236	C₄×C₄₇	—	2	2	no	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	4	1	no	—
239	C₄×C₄₇	—	4	4	no	—
240	C₄×C₄₇	—	4	4	no	—
241	C₄×C₄₇	—	8	1	no	—
242	C₄×C₄₇	—	8	1	no	—
243	C₄×C₄₇	—	8	1	no	—
244	C₄×C₄₇	—	8	1	no	—
245	C₄×C₄₇	#536	1	2	yes	—
246	C₄×C₄₇	#537	1	2	yes	—
247	C₂×#533	C₂×C₄₇	1	1	yes	characteristic
248	C₂×#479	C₂×C₄₇	1	2	yes	complemented
249	#2851	C₂×C₄₇	1	1	yes	characteristic
250	#2058	C₂×C₄₇	1	1	yes	characteristic, complemented
251	#2057	C₂×C₄₇	1	1	yes	characteristic, complemented
252	#2043	C₂×C₄₇	1	1	yes	characteristic, complemented
253	#2043	C₂×C₄₇	1	1	yes	characteristic, complemented
254	#2036	C₂×C₄₇	1	2	yes	—
255	#2035	C₂×C₄₇	1	2	yes	—
256	#1805	C₂×C₄₇	1	2	yes	complemented
257	#1797	C₂×C₄₇	1	1	yes	characteristic
258	C₂×C₄₇	—	4	2	no	—
259	C₂×C₄₇	#2616	1	1	yes	characteristic
260	C₂×C₄₇	#3002	1	1	yes	characteristic
261	C₂×C₄₇	#3004	1	1	yes	characteristic
262	C₂×C₄₇	#3231	1	1	yes	characteristic
263	C₂×C₄₇	#3236	1	1	yes	characteristic
264	C₂×C₄₇	#3248	1	1	yes	characteristic
265	C₂×C₄₇	#3252	1	1	yes	characteristic
266	#533	—	2	8	no	—
267	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
268	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×#125	—	2	1	no	—
270	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
271	C₂×C₂²⋊Q₈	—	2	1	no	—
272	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
273	C₂×C₄×Q₈	—	2	1	no	—
274	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
275	C₂×#117	—	2	1	no	—
276	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
277	#479	—	2	8	no	—
278	C₂×#107	C₂²×C₄₇	1	2	yes	—
279	C₂×#106	C₂²×C₄₇	1	2	yes	—
280	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
281	C₂×#103	C₂²×C₄₇	1	2	yes	—
282	C₂×#103	C₂²×C₄₇	1	2	yes	—
283	C₂×#103	C₂²×C₄₇	1	2	yes	—
284	C₂×#103	C₂²×C₄₇	1	2	yes	—
285	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
286	#389	C₂²×C₄₇	1	1	yes	characteristic
287	#389	C₂²×C₄₇	1	1	yes	characteristic
288	#387	—	2	1	no	—
289	#387	—	2	1	no	—
290	#385	—	2	1	no	—
291	#385	—	2	1	no	—
292	#382	C₂²×C₄₇	1	1	yes	characteristic
293	#380	C₂²×C₄₇	1	1	yes	characteristic
294	#380	C₂²×C₄₇	1	1	yes	characteristic
295	#340	C₂²×C₄₇	1	2	yes	—
296	#340	C₂²×C₄₇	1	2	yes	—
297	#336	C₂²×C₄₇	1	1	yes	characteristic
298	#336	C₂²×C₄₇	1	1	yes	characteristic
299	C₄₇	#29695	1	1	yes	characteristic, direct product factor, Sylow
300	C₂²×Q₈	—	2	1	no	—
301	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
302	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
303	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
306	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
307	C₄⋊Q₈	—	2	4	no	—
308	C₄⋊Q₈	—	2	4	no	—
309	#125	—	2	8	no	—
310	#125	—	2	4	no	—
311	C₂²⋊Q₈	—	2	8	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	4	no	—
314	C₄×Q₈	—	2	8	no	—
315	C₄×Q₈	—	2	4	no	—
316	C₄×Q₈	D₄×C₄₇	1	8	yes	—
317	#117	—	2	8	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	2	no	—
322	C₂×C₄⋊C₄	—	2	2	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	2	1	no	—
325	C₂×C₄⋊C₄	—	2	1	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₄²	—	2	2	no	—
336	C₂×C₄²	—	2	4	no	—
337	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
338	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
339	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
341	#107	—	2	4	no	—
342	#106	—	2	4	no	—
343	C₄⋊C₈	—	2	4	no	—
344	#103	—	2	4	no	—
345	#103	—	2	4	no	—
346	#103	—	4	2	no	—
347	#103	—	4	2	no	—
348	C₂²⋊C₈	—	4	2	no	—
349	#95	—	2	1	no	—
350	#95	—	2	1	no	—
351	#95	—	2	1	no	—
352	#95	—	2	1	no	—
353	#95	—	2	1	no	—
354	#95	—	2	1	no	—
355	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	2	no	—
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	4	2	no	—
363	C₂×Q₈	—	4	2	no	—
364	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	4	1	no	—
381	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	4	2	no	—
407	C₄⋊C₄	—	4	2	no	—
408	C₄⋊C₄	—	4	2	no	—
409	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	8	no	—
416	C₄²	—	2	2	no	—
417	C₄²	C₂×D₄×C₄₇	1	4	yes	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	1	no	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	#137×C₄₇	1	2	yes	—
425	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	2	4	no	—
428	Q₈	—	4	8	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	2	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	4	4	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	#120×C₄₇	1	2	yes	—
465	C₂×C₄	#120×C₄₇	1	2	yes	—
466	C₂×C₄	#135×C₄₇	1	2	yes	—
467	C₂×C₄	#137×C₄₇	1	2	yes	—
468	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
469	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
470	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
471	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
472	C₈	—	4	2	no	—
473	C₈	—	4	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	2	2	no	—
477	C₂²	—	4	1	no	—
478	C₂²	—	4	1	no	—
479	C₂²	—	4	1	no	—
480	C₂²	—	4	1	no	—
481	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
482	C₂²	C₄₇×#536	1	1	yes	characteristic
483	C₂²	C₄₇×#537	1	1	yes	characteristic
484	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
485	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
486	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
487	C₂²	C₄₇×#575	1	1	yes	characteristic
488	C₄	—	2	2	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	2	no	—
491	C₄	—	2	2	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	4	no	—
494	C₄	—	4	4	no	—
495	C₄	—	8	1	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	1	no	—
498	C₄	—	8	1	no	—
499	C₄	C₄₇×#536	1	2	yes	—
500	C₄	C₄₇×#537	1	2	yes	—
501	C₂	—	4	2	no	—
502	C₂	C₄₇×#2616	1	1	yes	characteristic
503	C₂	C₄₇×#3002	1	1	yes	characteristic
504	C₂	C₄₇×#3004	1	1	yes	characteristic
505	C₂	C₄₇×#3231	1	1	yes	characteristic
506	C₂	C₄₇×#3236	1	1	yes	characteristic
507	C₂	C₄₇×#3248	1	1	yes	characteristic
508	C₂	C₄₇×#3252	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂⁴×C₄₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#479	C₂	semidirect
4. C₄₇×#2058	C₂	semidirect
5. C₄₇×#2057	C₂	semidirect
6. C₄₇×#2043	C₂	semidirect
7. C₄₇×#2043	C₂	semidirect
10. C₄₇×#1805	C₂	semidirect
219. #29695	C₄₇	direct (N × H)
248. C₂×#479	C₂×C₄₇	semidirect
250. #2058	C₂×C₄₇	semidirect
251. #2057	C₂×C₄₇	semidirect
252. #2043	C₂×C₄₇	semidirect
253. #2043	C₂×C₄₇	semidirect
256. #1805	C₂×C₄₇	semidirect
299. C₄₇	#29695	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#533	2
C₂×C₄₇×#479	2
C₄₇×#2851	2
C₄₇×#2058	2
C₄₇×#2057	2
C₄₇×#2043	2
C₄₇×#2036	2
C₄₇×#2035	2
C₄₇×#1805	2
C₄₇×#1797	2
#29695	47

Subgroups — C47×#29695 #26069393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29695 #26069393