Subgroups — C₄₇×#25700 #26065398

Order 12032.

1122 conjugacy classes of subgroups.

The subgroup lattice has 442 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×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#474	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2547	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2034	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	1	no	—
15	C₂×#124×C₄₇	—	2	2	no	—
16	C₂×#121×C₄₇	—	2	1	no	—
17	C₂×#121×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₇	—	2	1	no	—
21	C₂×#117×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#498	—	2	4	no	—
23	C₄₇×#474	—	2	4	no	—
24	C₂×#107×C₄₇	C₂²	1	2	yes	—
25	C₂×#106×C₄₇	C₂²	1	4	yes	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₇	C₂²	1	2	yes	—
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#397	—	2	2	no	—
32	C₄₇×#391	—	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	#124×C₄₇	—	4	4	no	—
52	#121×C₄₇	—	2	8	no	—
53	#121×C₄₇	—	2	4	no	—
54	#121×C₄₇	—	2	4	no	—
55	C₄×D₄×C₄₇	—	2	2	no	—
56	C₄×D₄×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	—	2	2	no	—
58	C₄×D₄×C₄₇	D₄	1	4	yes	—
59	#117×C₄₇	—	2	8	no	—
60	#117×C₄₇	—	2	4	no	—
61	#117×C₄₇	—	2	4	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
73	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
74	C₂×C₄²×C₄₇	—	2	2	no	—
75	C₂×C₄²×C₄₇	—	2	1	no	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#107×C₄₇	—	2	4	no	—
78	#106×C₄₇	—	2	8	no	—
79	C₄⋊C₈×C₄₇	—	2	2	no	—
80	#102×C₄₇	—	2	4	no	—
81	#102×C₄₇	—	2	4	no	—
82	C₂²⋊C₈×C₄₇	—	2	8	no	—
83	C₄×C₈×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	1	no	—
85	#95×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	1	no	—
87	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
88	C₂×Q₈×C₄₇	—	2	4	no	—
89	C₂×Q₈×C₄₇	—	4	2	no	—
90	C₂×Q₈×C₄₇	—	4	2	no	—
91	C₂×Q₈×C₄₇	—	4	2	no	—
92	C₂×Q₈×C₄₇	—	8	2	no	—
93	C₂×D₄×C₄₇	—	2	8	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	8	4	no	—
101	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	4	no	—
108	C₂²×C₄×C₄₇	—	2	4	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	4	2	no	—
112	C₂²×C₄×C₄₇	—	4	2	no	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	4	no	—
121	C₂×C₈×C₄₇	#41	1	4	yes	—
122	C₄⋊C₄×C₄₇	—	2	4	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	1	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	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
132	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²⋊C₄×C₄₇	—	2	8	no	—
134	C₂²⋊C₄×C₄₇	—	2	8	no	—
135	C₂²⋊C₄×C₄₇	—	2	4	no	—
136	C₂²⋊C₄×C₄₇	—	2	4	no	—
137	C₂²⋊C₄×C₄₇	—	4	8	no	—
138	C₄²×C₄₇	—	2	8	no	—
139	C₄²×C₄₇	—	4	2	no	—
140	C₄²×C₄₇	C₂×D₄	1	2	yes	—
141	C₄²×C₄₇	C₂×D₄	1	2	yes	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	2	4	no	—
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	Q₈×C₄₇	—	8	4	no	—
154	Q₈×C₄₇	—	8	4	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	4	4	no	—
159	D₄×C₄₇	—	8	8	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	8	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	#120	1	2	yes	—
179	C₂×C₄×C₄₇	#120	1	2	yes	—
180	C₂×C₄×C₄₇	#135	1	2	yes	—
181	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
185	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
186	C₈×C₄₇	—	2	4	no	—
187	C₈×C₄₇	—	4	2	no	—
188	#25700	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₇	—	4	4	no	—
190	C₂²×C₄₇	—	4	4	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	—	8	2	no	—
199	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
200	C₂²×C₄₇	#547	1	2	yes	—
201	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
202	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
203	C₂²×C₄₇	#577	1	2	yes	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	4	2	no	—
206	C₄×C₄₇	—	4	2	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	8	2	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	#449	1	4	yes	—
211	C₄×C₄₇	#532	1	1	yes	characteristic
212	C₄×C₄₇	#536	1	1	yes	characteristic
213	C₄×C₄₇	#548	1	2	yes	—
214	C₂×#555	C₂×C₄₇	1	1	yes	characteristic
215	C₂×#498	C₂×C₄₇	1	1	yes	characteristic, complemented
216	C₂×#474	C₂×C₄₇	1	1	yes	characteristic, complemented
217	#2547	C₂×C₄₇	1	1	yes	characteristic, complemented
218	#2034	C₂×C₄₇	1	4	yes	complemented
219	#1987	C₂×C₄₇	1	1	yes	characteristic, complemented
220	#1954	C₂×C₄₇	1	1	yes	characteristic, complemented
221	#1854	C₂×C₄₇	1	4	yes	complemented
222	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
223	C₂×C₄₇	—	8	2	no	—
224	C₂×C₄₇	—	8	2	no	—
225	C₂×C₄₇	#2432	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#449	1	1	yes	characteristic
227	C₂×C₄₇	#3009	1	1	yes	characteristic
228	C₂×C₄₇	#3340	1	2	yes	—
229	C₂×C₄₇	#3354	1	2	yes	—
230	#555	—	2	4	no	—
231	#555	—	2	4	no	—
232	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
234	C₂×#124	—	2	1	no	—
235	C₂×#124	—	2	2	no	—
236	C₂×#121	—	2	1	no	—
237	C₂×#121	C₂²×C₄₇	1	2	yes	—
238	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
239	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
240	C₂×#117	—	2	1	no	—
241	C₂×#117	C₂²×C₄₇	1	2	yes	—
242	#498	—	2	4	no	—
243	#474	—	2	4	no	—
244	C₂×#107	C₂²×C₄₇	1	2	yes	—
245	C₂×#106	C₂²×C₄₇	1	4	yes	—
246	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
247	C₂×#102	C₂²×C₄₇	1	2	yes	—
248	C₂×#102	C₂²×C₄₇	1	2	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
250	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
251	#397	—	2	2	no	—
252	#391	—	2	1	no	—
253	#380	C₂²×C₄₇	1	4	yes	—
254	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
255	#340	C₂²×C₄₇	1	2	yes	—
256	#340	C₂²×C₄₇	1	4	yes	—
257	C₄₇	#25700	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×Q₈	—	2	1	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×D₄	—	2	2	no	—
261	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
262	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
265	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
266	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
271	#124	—	2	16	no	—
272	#124	—	4	4	no	—
273	#121	—	2	8	no	—
274	#121	—	2	4	no	—
275	#121	—	2	4	no	—
276	C₄×D₄	—	2	2	no	—
277	C₄×D₄	—	2	2	no	—
278	C₄×D₄	—	2	2	no	—
279	C₄×D₄	D₄×C₄₇	1	4	yes	—
280	#117	—	2	8	no	—
281	#117	—	2	4	no	—
282	#117	—	2	4	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
286	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
290	C₂×C₂²⋊C₄	—	2	2	no	—
291	C₂×C₂²⋊C₄	—	2	2	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	4	no	—
294	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
295	C₂×C₄²	—	2	2	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
298	#107	—	2	4	no	—
299	#106	—	2	8	no	—
300	C₄⋊C₈	—	2	2	no	—
301	#102	—	2	4	no	—
302	#102	—	2	4	no	—
303	C₂²⋊C₈	—	2	8	no	—
304	C₄×C₈	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	4	no	—
307	C₂⁴	—	2	1	no	—
308	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	8	2	no	—
314	C₂×D₄	—	2	8	no	—
315	C₂×D₄	—	2	2	no	—
316	C₂×D₄	—	2	2	no	—
317	C₂×D₄	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	4	no	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	4	no	—
342	C₂×C₈	#41×C₄₇	1	4	yes	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
353	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
354	C₂²⋊C₄	—	2	8	no	—
355	C₂²⋊C₄	—	2	8	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	4	no	—
358	C₂²⋊C₄	—	4	8	no	—
359	C₄²	—	2	8	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×D₄×C₄₇	1	2	yes	—
362	C₄²	C₂×D₄×C₄₇	1	2	yes	—
363	C₂³	—	2	2	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	2	no	—
367	C₂³	—	2	2	no	—
368	C₂³	—	2	4	no	—
369	C₂³	—	4	2	no	—
370	C₂³	—	4	1	no	—
371	C₂³	—	4	1	no	—
372	C₂³	—	4	2	no	—
373	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
374	Q₈	—	8	4	no	—
375	Q₈	—	8	4	no	—
376	D₄	—	2	2	no	—
377	D₄	—	2	2	no	—
378	D₄	—	4	4	no	—
379	D₄	—	4	2	no	—
380	D₄	—	8	8	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	8	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	#120×C₄₇	1	2	yes	—
400	C₂×C₄	#120×C₄₇	1	2	yes	—
401	C₂×C₄	#135×C₄₇	1	2	yes	—
402	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
403	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
406	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
407	C₈	—	2	4	no	—
408	C₈	—	4	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	4	4	no	—
411	C₂²	—	4	2	no	—
412	C₂²	—	4	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	8	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
420	C₂²	C₄₇×#547	1	2	yes	—
421	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
422	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
423	C₂²	C₄₇×#577	1	2	yes	—
424	C₄	—	2	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	8	2	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄₇×#449	1	4	yes	—
431	C₄	C₄₇×#532	1	1	yes	characteristic
432	C₄	C₄₇×#536	1	1	yes	characteristic
433	C₄	C₄₇×#548	1	2	yes	—
434	C₂	—	8	2	no	—
435	C₂	—	8	2	no	—
436	C₂	C₄₇×#2432	1	1	yes	characteristic
437	C₂	C₂×C₄₇×#449	1	1	yes	characteristic
438	C₂	C₄₇×#3009	1	1	yes	characteristic
439	C₂	C₄₇×#3340	1	2	yes	—
440	C₂	C₄₇×#3354	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×#498	C₂	semidirect
3. C₂×C₄₇×#474	C₂	semidirect
4. C₄₇×#2547	C₂	semidirect
5. C₄₇×#2034	C₂	semidirect
6. C₄₇×#1987	C₂	semidirect
7. C₄₇×#1954	C₂	semidirect
8. C₄₇×#1854	C₂	semidirect
9. C₄×#102×C₄₇	C₂	semidirect
188. #25700	C₄₇	direct (N × H)
215. C₂×#498	C₂×C₄₇	semidirect
216. C₂×#474	C₂×C₄₇	semidirect
217. #2547	C₂×C₄₇	semidirect
218. #2034	C₂×C₄₇	semidirect
219. #1987	C₂×C₄₇	semidirect
220. #1954	C₂×C₄₇	semidirect
221. #1854	C₂×C₄₇	semidirect
222. C₄×#102	C₂×C₄₇	semidirect
257. C₄₇	#25700	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×#498	2
C₂×C₄₇×#474	2
C₄₇×#2547	2
C₄₇×#2034	2
C₄₇×#1987	2
C₄₇×#1954	2
C₄₇×#1854	2
C₄×#102×C₄₇	2
#25700	47

Subgroups — C47×#25700 #26065398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25700 #26065398