Subgroups — C₄₇×#20961 #26060659

Order 12032.

1998 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#535	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#410	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2309	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1889	C₂	1	8	yes	maximal, complemented
6	C₄₇×#1740	C₂	1	2	yes	maximal, complemented
7	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₄₇×#535	—	2	4	no	—
10	C₄₇×#535	C₄	1	8	yes	complemented
11	C₂×#127×C₄₇	—	2	1	no	—
12	C₂×#124×C₄₇	—	2	1	no	—
13	C₂×#121×C₄₇	—	2	2	no	—
14	C₂×#120×C₄₇	C₂²	1	4	yes	—
15	C₄₇×#520	—	2	4	no	—
16	C₄₇×#519	—	2	1	no	—
17	C₄₇×#518	—	2	1	no	—
18	C₄₇×#518	C₂²	1	4	yes	—
19	C₄×#41×C₄₇	—	2	4	no	—
20	C₂×#117×C₄₇	—	2	2	no	—
21	C₂×#117×C₄₇	C₂²	1	2	yes	—
22	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#117×C₄₇	C₂²	1	2	yes	—
24	C₄₇×#410	—	2	4	no	—
25	C₂×#99×C₄₇	C₂²	1	4	yes	—
26	C₄₇×#390	—	2	4	no	—
27	C₄₇×#390	—	2	4	no	—
28	C₄₇×#379	C₂²	1	8	yes	—
29	C₄₇×#342	C₂²	1	8	yes	—
30	C₂⁵×C₄₇	C₂³	1	2	yes	—
31	C₂×#41×C₄₇	—	2	2	no	—
32	C₂×#41×C₄₇	—	2	2	no	—
33	C₂×#41×C₄₇	—	2	4	no	—
34	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
35	C₂×#41×C₄₇	D₄	1	4	yes	—
36	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
37	C₂²×D₄×C₄₇	—	2	4	no	—
38	C₂²×D₄×C₄₇	—	2	1	no	—
39	C₂²×D₄×C₄₇	—	2	1	no	—
40	C₂²×D₄×C₄₇	—	2	2	no	—
41	C₂²×D₄×C₄₇	—	2	2	no	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	—	2	4	no	—
44	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
45	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	#127×C₄₇	—	2	8	no	—
50	#124×C₄₇	—	2	8	no	—
51	#121×C₄₇	—	2	16	no	—
52	#120×C₄₇	—	2	8	no	—
53	#120×C₄₇	C₂×C₄	1	16	yes	complemented
54	C₄×Q₈×C₄₇	—	2	8	no	—
55	C₄×D₄×C₄₇	—	2	8	no	—
56	C₄×D₄×C₄₇	—	2	16	no	—
57	#117×C₄₇	—	2	4	no	—
58	#117×C₄₇	—	2	4	no	—
59	#117×C₄₇	—	2	2	no	—
60	#117×C₄₇	—	2	4	no	—
61	#117×C₄₇	—	2	2	no	—
62	#117×C₄₇	—	2	2	no	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	—	2	2	no	—
65	#117×C₄₇	—	2	4	no	—
66	#117×C₄₇	—	2	4	no	—
67	#117×C₄₇	C₂×C₄	1	4	yes	complemented
68	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	complemented
72	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
75	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
77	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	—	2	4	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	D₄	1	4	yes	complemented
82	#99×C₄₇	—	2	8	no	—
83	C₂⁴×C₄₇	—	2	4	no	—
84	C₂⁴×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂⁴×C₄₇	—	2	4	no	—
87	C₂⁴×C₄₇	—	8	4	no	—
88	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
89	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
90	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
91	#41×C₄₇	—	2	8	no	—
92	#41×C₄₇	—	2	8	no	—
93	#41×C₄₇	—	2	8	no	—
94	#41×C₄₇	—	2	8	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	complemented
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	16	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	—	2	8	no	—
104	C₂×D₄×C₄₇	—	2	8	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	4	1	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	—	4	1	no	—
110	C₂×D₄×C₄₇	—	4	4	no	—
111	C₂×D₄×C₄₇	—	4	4	no	—
112	C₂×D₄×C₄₇	—	4	2	no	—
113	C₂×D₄×C₄₇	—	4	2	no	—
114	C₂×D₄×C₄₇	—	8	8	no	—
115	C₂×D₄×C₄₇	C₂²⋊C₄	1	4	yes	complemented
116	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
117	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	8	no	—
123	C₂²×C₄×C₄₇	—	2	4	no	—
124	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	complemented
125	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
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	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	4	yes	—
134	C₄⋊C₄×C₄₇	—	2	8	no	—
135	C₄⋊C₄×C₄₇	—	2	4	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₄⋊C₄×C₄₇	—	2	4	no	—
138	C₄⋊C₄×C₄₇	—	4	4	no	—
139	C₂²⋊C₄×C₄₇	—	2	8	no	—
140	C₂²⋊C₄×C₄₇	—	2	4	no	—
141	C₂²⋊C₄×C₄₇	—	2	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₂²⋊C₄×C₄₇	—	2	16	no	—
144	C₂²⋊C₄×C₄₇	—	2	4	no	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	8	16	no	—
147	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
148	C₄²×C₄₇	—	2	8	no	—
149	C₄²×C₄₇	—	2	4	no	—
150	C₄²×C₄₇	—	2	4	no	—
151	C₄²×C₄₇	—	2	4	no	—
152	C₄²×C₄₇	—	4	4	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	4	no	—
156	C₂³×C₄₇	—	2	8	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	—	4	4	no	—
159	C₂³×C₄₇	—	4	16	no	—
160	C₂³×C₄₇	—	4	8	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	4	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	—	8	4	no	—
165	C₂³×C₄₇	—	8	4	no	—
166	C₂³×C₄₇	—	8	8	no	—
167	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
168	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
171	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	C₂³×C₄₇	C₂×#41	1	2	yes	—
173	Q₈×C₄₇	—	2	8	no	—
174	D₄×C₄₇	—	2	8	no	—
175	D₄×C₄₇	—	2	8	no	—
176	D₄×C₄₇	—	2	8	no	—
177	D₄×C₄₇	—	4	4	no	—
178	D₄×C₄₇	—	4	4	no	—
179	D₄×C₄₇	—	4	8	no	—
180	D₄×C₄₇	—	8	16	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	8	no	—
184	C₂×C₄×C₄₇	—	2	8	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	—	4	4	no	—
188	C₂×C₄×C₄₇	—	4	8	no	—
189	C₂×C₄×C₄₇	—	4	8	no	—
190	C₂×C₄×C₄₇	—	4	4	no	—
191	C₂×C₄×C₄₇	—	8	8	no	—
192	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
193	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
194	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
195	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
196	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
197	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
198	C₂×C₄×C₄₇	#120	1	2	yes	—
199	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
200	C₂×C₄×C₄₇	#121	1	4	yes	—
201	C₂×C₄×C₄₇	#121	1	4	yes	—
202	C₂×C₄×C₄₇	#123	1	2	yes	—
203	C₂×C₄×C₄₇	#123	1	2	yes	—
204	#20961	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	2	4	no	—
208	C₂²×C₄₇	—	4	1	no	—
209	C₂²×C₄₇	—	4	1	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	4	no	—
212	C₂²×C₄₇	—	4	8	no	—
213	C₂²×C₄₇	—	4	16	no	—
214	C₂²×C₄₇	—	4	4	no	—
215	C₂²×C₄₇	—	4	4	no	—
216	C₂²×C₄₇	—	8	2	no	—
217	C₂²×C₄₇	—	8	8	no	—
218	C₂²×C₄₇	—	8	4	no	—
219	C₂²×C₄₇	—	8	4	no	—
220	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
222	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×#121	1	2	yes	—
224	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
225	C₄×C₄₇	—	2	4	no	—
226	C₄×C₄₇	—	4	4	no	—
227	C₄×C₄₇	—	4	8	no	—
228	C₄×C₄₇	—	8	4	no	—
229	C₄×C₄₇	#386	1	2	yes	—
230	C₄×C₄₇	#386	1	2	yes	—
231	C₄×C₄₇	#386	1	4	yes	—
232	C₂×#535	C₂×C₄₇	1	1	yes	characteristic
233	#3428	C₂×C₄₇	1	1	yes	characteristic, complemented
234	C₂×#410	C₂×C₄₇	1	1	yes	characteristic, complemented
235	#2309	C₂×C₄₇	1	2	yes	complemented
236	#1889	C₂×C₄₇	1	8	yes	complemented
237	#1740	C₂×C₄₇	1	2	yes	complemented
238	C₂×C₄₇	—	2	1	no	—
239	C₂×C₄₇	—	2	2	no	—
240	C₂×C₄₇	—	2	2	no	—
241	C₂×C₄₇	—	2	1	no	—
242	C₂×C₄₇	—	4	4	no	—
243	C₂×C₄₇	—	8	4	no	—
244	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
245	C₂×C₄₇	#3027	1	2	yes	—
246	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
247	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
248	#535	—	2	4	no	—
249	#535	C₄×C₄₇	1	8	yes	complemented
250	C₂×#127	—	2	1	no	—
251	C₂×#124	—	2	1	no	—
252	C₂×#121	—	2	2	no	—
253	C₂×#120	C₂²×C₄₇	1	4	yes	—
254	#520	—	2	4	no	—
255	#519	—	2	1	no	—
256	#518	—	2	1	no	—
257	#518	C₂²×C₄₇	1	4	yes	—
258	C₄×#41	—	2	4	no	—
259	C₂×#117	—	2	2	no	—
260	C₂×#117	C₂²×C₄₇	1	2	yes	—
261	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
262	C₂×#117	C₂²×C₄₇	1	2	yes	—
263	#410	—	2	4	no	—
264	C₂×#99	C₂²×C₄₇	1	4	yes	—
265	#390	—	2	4	no	—
266	#390	—	2	4	no	—
267	#379	C₂²×C₄₇	1	8	yes	—
268	#342	C₂²×C₄₇	1	8	yes	—
269	C₄₇	#20961	1	1	yes	characteristic, direct product factor, Sylow
270	C₂⁵	C₂³×C₄₇	1	2	yes	—
271	C₂×#41	—	2	2	no	—
272	C₂×#41	—	2	2	no	—
273	C₂×#41	—	2	4	no	—
274	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
275	C₂×#41	D₄×C₄₇	1	4	yes	—
276	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
277	C₂²×D₄	—	2	4	no	—
278	C₂²×D₄	—	2	1	no	—
279	C₂²×D₄	—	2	1	no	—
280	C₂²×D₄	—	2	2	no	—
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂²×D₄	—	2	4	no	—
284	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	complemented
285	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
286	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
287	C₂³×C₄	D₄×C₄₇	1	2	yes	—
288	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
289	#127	—	2	8	no	—
290	#124	—	2	8	no	—
291	#121	—	2	16	no	—
292	#120	—	2	8	no	—
293	#120	C₂×C₄×C₄₇	1	16	yes	complemented
294	C₄×Q₈	—	2	8	no	—
295	C₄×D₄	—	2	8	no	—
296	C₄×D₄	—	2	16	no	—
297	#117	—	2	4	no	—
298	#117	—	2	4	no	—
299	#117	—	2	2	no	—
300	#117	—	2	4	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	4	no	—
306	#117	—	2	4	no	—
307	#117	C₂×C₄×C₄₇	1	4	yes	complemented
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	complemented
312	C₂×C₂²⋊C₄	—	2	4	no	—
313	C₂×C₂²⋊C₄	—	2	4	no	—
314	C₂×C₂²⋊C₄	—	2	16	no	—
315	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
316	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
317	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
318	C₂×C₄²	—	2	4	no	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	D₄×C₄₇	1	4	yes	complemented
322	#99	—	2	8	no	—
323	C₂⁴	—	2	4	no	—
324	C₂⁴	—	2	2	no	—
325	C₂⁴	—	2	2	no	—
326	C₂⁴	—	2	4	no	—
327	C₂⁴	—	8	4	no	—
328	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
329	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
330	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
331	#41	—	2	8	no	—
332	#41	—	2	8	no	—
333	#41	—	2	8	no	—
334	#41	—	2	8	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	C₂²⋊C₄×C₄₇	1	4	yes	complemented
338	C₂×D₄	—	2	4	no	—
339	C₂×D₄	—	2	4	no	—
340	C₂×D₄	—	2	16	no	—
341	C₂×D₄	—	2	4	no	—
342	C₂×D₄	—	2	4	no	—
343	C₂×D₄	—	2	8	no	—
344	C₂×D₄	—	2	8	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	4	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	2	no	—
354	C₂×D₄	—	8	8	no	—
355	C₂×D₄	C₂²⋊C₄×C₄₇	1	4	yes	complemented
356	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
357	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	8	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	complemented
365	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
366	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
367	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
368	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
373	C₂²×C₄	#41×C₄₇	1	4	yes	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	2	4	no	—
381	C₂²⋊C₄	—	2	4	no	—
382	C₂²⋊C₄	—	2	2	no	—
383	C₂²⋊C₄	—	2	16	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	8	16	no	—
387	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
388	C₄²	—	2	8	no	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	4	no	—
391	C₄²	—	2	4	no	—
392	C₄²	—	4	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	4	no	—
396	C₂³	—	2	8	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	16	no	—
400	C₂³	—	4	8	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	4	no	—
403	C₂³	—	4	2	no	—
404	C₂³	—	8	4	no	—
405	C₂³	—	8	4	no	—
406	C₂³	—	8	8	no	—
407	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
408	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
409	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
410	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
411	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
412	C₂³	C₂×#41×C₄₇	1	2	yes	—
413	Q₈	—	2	8	no	—
414	D₄	—	2	8	no	—
415	D₄	—	2	8	no	—
416	D₄	—	2	8	no	—
417	D₄	—	4	4	no	—
418	D₄	—	4	4	no	—
419	D₄	—	4	8	no	—
420	D₄	—	8	16	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	—	4	8	no	—
429	C₂×C₄	—	4	8	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	8	8	no	—
432	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
433	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
434	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
435	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
436	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
437	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
438	C₂×C₄	#120×C₄₇	1	2	yes	—
439	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
440	C₂×C₄	#121×C₄₇	1	4	yes	—
441	C₂×C₄	#121×C₄₇	1	4	yes	—
442	C₂×C₄	#123×C₄₇	1	2	yes	—
443	C₂×C₄	#123×C₄₇	1	2	yes	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	8	no	—
452	C₂²	—	4	16	no	—
453	C₂²	—	4	4	no	—
454	C₂²	—	4	4	no	—
455	C₂²	—	8	2	no	—
456	C₂²	—	8	8	no	—
457	C₂²	—	8	4	no	—
458	C₂²	—	8	4	no	—
459	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
460	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
461	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
462	C₂²	C₂×#121×C₄₇	1	2	yes	—
463	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
464	C₄	—	2	4	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	8	no	—
467	C₄	—	8	4	no	—
468	C₄	C₄₇×#386	1	2	yes	—
469	C₄	C₄₇×#386	1	2	yes	—
470	C₄	C₄₇×#386	1	4	yes	—
471	C₂	—	2	1	no	—
472	C₂	—	2	2	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	4	no	—
476	C₂	—	8	4	no	—
477	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
478	C₂	C₄₇×#3027	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#535	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#3428	C₂	semidirect
3. C₂×C₄₇×#410	C₂	semidirect
4. C₄₇×#2309	C₂	semidirect
5. C₄₇×#1889	C₂	semidirect
6. C₄₇×#1740	C₂	semidirect
10. C₄₇×#535	C₄	semidirect
44. C₂²×D₄×C₄₇	C₂×C₄	semidirect
53. #120×C₄₇	C₂×C₄	semidirect
67. #117×C₄₇	C₂×C₄	semidirect
71. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
81. C₂×C₄²×C₄₇	D₄	semidirect
97. C₂×Q₈×C₄₇	C₂²⋊C₄	semidirect
115. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
124. C₂²×C₄×C₄₇	C₂²⋊C₄	semidirect
204. #20961	C₄₇	direct (N × H)
233. #3428	C₂×C₄₇	semidirect
234. C₂×#410	C₂×C₄₇	semidirect
235. #2309	C₂×C₄₇	semidirect
236. #1889	C₂×C₄₇	semidirect
237. #1740	C₂×C₄₇	semidirect
249. #535	C₄×C₄₇	semidirect
269. C₄₇	#20961	direct (N × H)
284. C₂²×D₄	C₂×C₄×C₄₇	semidirect
293. #120	C₂×C₄×C₄₇	semidirect
307. #117	C₂×C₄×C₄₇	semidirect
311. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
321. C₂×C₄²	D₄×C₄₇	semidirect
337. C₂×Q₈	C₂²⋊C₄×C₄₇	semidirect
355. C₂×D₄	C₂²⋊C₄×C₄₇	semidirect
364. C₂²×C₄	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#535	2
C₄₇×#3428	2
C₂×C₄₇×#410	2
C₄₇×#2309	2
C₄₇×#1889	2
C₄₇×#1740	2
#20961	47

Subgroups — C47×#20961 #26060659

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20961 #26060659