Subgroups — C₄₇×#25704 #26065402

Order 12032.

1102 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#555	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2033	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1854	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#555	—	2	4	no	—
11	C₄₇×#555	—	2	4	no	—
12	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₇	—	2	2	no	—
15	C₂×#121×C₄₇	—	2	1	no	—
16	C₂×#121×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	—	2	1	no	—
20	C₂×#117×C₄₇	C₂²	1	2	yes	—
21	C₄₇×#500	—	2	4	no	—
22	C₄₇×#476	—	2	4	no	—
23	C₂×#107×C₄₇	C₂²	1	4	yes	—
24	C₂×#106×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×#102×C₄₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#393	—	2	2	no	—
31	C₄₇×#390	—	2	1	no	—
32	C₄₇×#382	—	2	1	no	—
33	C₄₇×#380	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#340	C₂²	1	2	yes	—
36	C₄₇×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₇	—	2	1	no	—
38	C₂²×Q₈×C₄₇	—	2	1	no	—
39	C₂²×D₄×C₄₇	—	2	2	no	—
40	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
46	C₄⋊Q₈×C₄₇	—	2	2	no	—
47	C₄⋊Q₈×C₄₇	—	2	2	no	—
48	C₄⋊Q₈×C₄₇	—	2	2	no	—
49	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
50	#124×C₄₇	—	2	16	no	—
51	#121×C₄₇	—	2	8	no	—
52	#121×C₄₇	—	2	4	no	—
53	#121×C₄₇	—	2	4	no	—
54	C₄×D₄×C₄₇	—	2	2	no	—
55	C₄×D₄×C₄₇	—	2	2	no	—
56	C₄×D₄×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	D₄	1	4	yes	—
58	#117×C₄₇	—	2	8	no	—
59	#117×C₄₇	—	2	4	no	—
60	#117×C₄₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
72	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
73	C₂×C₄²×C₄₇	—	2	2	no	—
74	C₂×C₄²×C₄₇	—	2	1	no	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	#107×C₄₇	—	2	8	no	—
77	#106×C₄₇	—	2	4	no	—
78	C₄⋊C₈×C₄₇	—	2	2	no	—
79	#102×C₄₇	—	2	4	no	—
80	#102×C₄₇	—	2	4	no	—
81	C₂²⋊C₈×C₄₇	—	2	8	no	—
82	C₄×C₈×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	1	no	—
84	#95×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	1	no	—
86	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
87	C₂×Q₈×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	—	4	2	no	—
89	C₂×Q₈×C₄₇	—	8	2	no	—
90	C₂×Q₈×C₄₇	—	8	2	no	—
91	C₂×D₄×C₄₇	—	2	8	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	8	4	no	—
99	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	4	no	—
119	C₂×C₈×C₄₇	#41	1	4	yes	—
120	C₄⋊C₄×C₄₇	—	2	4	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	4	2	no	—
129	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
131	C₂²⋊C₄×C₄₇	—	2	8	no	—
132	C₂²⋊C₄×C₄₇	—	2	8	no	—
133	C₂²⋊C₄×C₄₇	—	2	4	no	—
134	C₂²⋊C₄×C₄₇	—	2	4	no	—
135	C₂²⋊C₄×C₄₇	—	8	4	no	—
136	C₄²×C₄₇	—	2	8	no	—
137	C₄²×C₄₇	—	4	2	no	—
138	C₄²×C₄₇	C₂×D₄	1	2	yes	—
139	C₄²×C₄₇	C₂×D₄	1	2	yes	—
140	C₂³×C₄₇	—	2	2	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	4	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	4	no	—
146	C₂³×C₄₇	—	4	2	no	—
147	C₂³×C₄₇	—	4	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₇	—	8	4	no	—
152	Q₈×C₄₇	—	8	4	no	—
153	D₄×C₄₇	—	2	2	no	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	—	4	2	no	—
156	D₄×C₄₇	—	4	4	no	—
157	D₄×C₄₇	—	8	8	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	4	no	—
175	C₂×C₄×C₄₇	#120	1	2	yes	—
176	C₂×C₄×C₄₇	#120	1	2	yes	—
177	C₂×C₄×C₄₇	#135	1	2	yes	—
178	C₂×C₄×C₄₇	#137	1	2	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
183	C₈×C₄₇	—	2	4	no	—
184	C₈×C₄₇	—	4	2	no	—
185	#25704	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
197	C₂²×C₄₇	#547	1	2	yes	—
198	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
200	C₂²×C₄₇	#576	1	2	yes	—
201	C₄×C₄₇	—	2	2	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	4	4	no	—
205	C₄×C₄₇	—	8	2	no	—
206	C₄×C₄₇	—	8	2	no	—
207	C₄×C₄₇	#452	1	4	yes	—
208	C₄×C₄₇	#532	1	1	yes	characteristic
209	C₄×C₄₇	#536	1	1	yes	characteristic
210	C₄×C₄₇	#548	1	2	yes	—
211	C₂×#555	C₂×C₄₇	1	1	yes	characteristic
212	C₂×#500	C₂×C₄₇	1	1	yes	characteristic, complemented
213	C₂×#476	C₂×C₄₇	1	1	yes	characteristic, complemented
214	#2563	C₂×C₄₇	1	1	yes	characteristic, complemented
215	#2033	C₂×C₄₇	1	4	yes	complemented
216	#1987	C₂×C₄₇	1	1	yes	characteristic, complemented
217	#1954	C₂×C₄₇	1	1	yes	characteristic, complemented
218	#1854	C₂×C₄₇	1	4	yes	complemented
219	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
220	C₂×C₄₇	—	8	2	no	—
221	C₂×C₄₇	—	8	2	no	—
222	C₂×C₄₇	#2432	1	1	yes	characteristic
223	C₂×C₄₇	C₂×#452	1	1	yes	characteristic
224	C₂×C₄₇	#3008	1	1	yes	characteristic
225	C₂×C₄₇	#3341	1	2	yes	—
226	C₂×C₄₇	#3357	1	2	yes	—
227	#555	—	2	4	no	—
228	#555	—	2	4	no	—
229	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
231	C₂×#124	—	2	2	no	—
232	C₂×#121	—	2	1	no	—
233	C₂×#121	C₂²×C₄₇	1	2	yes	—
234	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
235	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
236	C₂×#117	—	2	1	no	—
237	C₂×#117	C₂²×C₄₇	1	2	yes	—
238	#500	—	2	4	no	—
239	#476	—	2	4	no	—
240	C₂×#107	C₂²×C₄₇	1	4	yes	—
241	C₂×#106	C₂²×C₄₇	1	2	yes	—
242	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×#102	C₂²×C₄₇	1	2	yes	—
244	C₂×#102	C₂²×C₄₇	1	2	yes	—
245	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
246	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
247	#393	—	2	2	no	—
248	#390	—	2	1	no	—
249	#382	—	2	1	no	—
250	#380	C₂²×C₄₇	1	4	yes	—
251	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
252	#340	C₂²×C₄₇	1	2	yes	—
253	#340	C₂²×C₄₇	1	4	yes	—
254	C₄₇	#25704	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
259	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
260	C₂³×C₄	—	2	1	no	—
261	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
262	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
263	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₄⋊Q₈	—	2	2	no	—
267	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
268	#124	—	2	16	no	—
269	#121	—	2	8	no	—
270	#121	—	2	4	no	—
271	#121	—	2	4	no	—
272	C₄×D₄	—	2	2	no	—
273	C₄×D₄	—	2	2	no	—
274	C₄×D₄	—	2	2	no	—
275	C₄×D₄	D₄×C₄₇	1	4	yes	—
276	#117	—	2	8	no	—
277	#117	—	2	4	no	—
278	#117	—	2	4	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	—	2	1	no	—
289	C₂×C₂²⋊C₄	—	2	4	no	—
290	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
291	C₂×C₄²	—	2	2	no	—
292	C₂×C₄²	—	2	1	no	—
293	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
294	#107	—	2	8	no	—
295	#106	—	2	4	no	—
296	C₄⋊C₈	—	2	2	no	—
297	#102	—	2	4	no	—
298	#102	—	2	4	no	—
299	C₂²⋊C₈	—	2	8	no	—
300	C₄×C₈	—	2	2	no	—
301	#95	—	2	1	no	—
302	#95	—	2	4	no	—
303	C₂⁴	—	2	1	no	—
304	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
305	C₂×Q₈	—	2	4	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂×Q₈	—	8	2	no	—
308	C₂×Q₈	—	8	2	no	—
309	C₂×D₄	—	2	8	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	8	4	no	—
317	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	4	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	—	4	2	no	—
329	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
330	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	2	4	no	—
337	C₂×C₈	#41×C₄₇	1	4	yes	—
338	C₄⋊C₄	—	2	4	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
348	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
349	C₂²⋊C₄	—	2	8	no	—
350	C₂²⋊C₄	—	2	8	no	—
351	C₂²⋊C₄	—	2	4	no	—
352	C₂²⋊C₄	—	2	4	no	—
353	C₂²⋊C₄	—	8	4	no	—
354	C₄²	—	2	8	no	—
355	C₄²	—	4	2	no	—
356	C₄²	C₂×D₄×C₄₇	1	2	yes	—
357	C₄²	C₂×D₄×C₄₇	1	2	yes	—
358	C₂³	—	2	2	no	—
359	C₂³	—	2	2	no	—
360	C₂³	—	2	4	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	2	2	no	—
363	C₂³	—	2	4	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
369	Q₈	—	8	4	no	—
370	Q₈	—	8	4	no	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	4	4	no	—
374	D₄	—	4	2	no	—
375	D₄	—	8	8	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	4	no	—
384	C₂×C₄	—	4	8	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	#120×C₄₇	1	2	yes	—
394	C₂×C₄	#120×C₄₇	1	2	yes	—
395	C₂×C₄	#135×C₄₇	1	2	yes	—
396	C₂×C₄	#137×C₄₇	1	2	yes	—
397	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
400	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
401	C₈	—	2	4	no	—
402	C₈	—	4	2	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	4	2	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	4	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
414	C₂²	C₄₇×#547	1	2	yes	—
415	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
416	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
417	C₂²	C₄₇×#576	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	8	2	no	—
423	C₄	—	8	2	no	—
424	C₄	C₄₇×#452	1	4	yes	—
425	C₄	C₄₇×#532	1	1	yes	characteristic
426	C₄	C₄₇×#536	1	1	yes	characteristic
427	C₄	C₄₇×#548	1	2	yes	—
428	C₂	—	8	2	no	—
429	C₂	—	8	2	no	—
430	C₂	C₄₇×#2432	1	1	yes	characteristic
431	C₂	C₂×C₄₇×#452	1	1	yes	characteristic
432	C₂	C₄₇×#3008	1	1	yes	characteristic
433	C₂	C₄₇×#3341	1	2	yes	—
434	C₂	C₄₇×#3357	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#555	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#500	C₂	semidirect
3. C₂×C₄₇×#476	C₂	semidirect
4. C₄₇×#2563	C₂	semidirect
5. C₄₇×#2033	C₂	semidirect
6. C₄₇×#1987	C₂	semidirect
7. C₄₇×#1954	C₂	semidirect
8. C₄₇×#1854	C₂	semidirect
9. C₄×#102×C₄₇	C₂	semidirect
185. #25704	C₄₇	direct (N × H)
212. C₂×#500	C₂×C₄₇	semidirect
213. C₂×#476	C₂×C₄₇	semidirect
214. #2563	C₂×C₄₇	semidirect
215. #2033	C₂×C₄₇	semidirect
216. #1987	C₂×C₄₇	semidirect
217. #1954	C₂×C₄₇	semidirect
218. #1854	C₂×C₄₇	semidirect
219. C₄×#102	C₂×C₄₇	semidirect
254. C₄₇	#25704	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×#555	2
C₂×C₄₇×#500	2
C₂×C₄₇×#476	2
C₄₇×#2563	2
C₄₇×#2033	2
C₄₇×#1987	2
C₄₇×#1954	2
C₄₇×#1854	2
C₄×#102×C₄₇	2
#25704	47

Subgroups — C47×#25704 #26065402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25704 #26065402