Subgroups — C₄₇×#29700 #26069398

Order 12032.

1068 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#540	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#478	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2059	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2041	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2034	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2033	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1802	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#540	—	2	8	no	—
11	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#123×C₄₇	—	2	2	no	—
15	C₂×#121×C₄₇	—	2	2	no	—
16	C₂×#121×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
18	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#478	—	2	8	no	—
20	C₂×#107×C₄₇	C₂²	1	2	yes	—
21	C₂×#106×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#102×C₄₇	C₂²	1	2	yes	—
24	C₂×#102×C₄₇	C₂²	1	2	yes	—
25	C₂×#102×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#398	—	2	2	no	—
30	C₄₇×#396	—	2	2	no	—
31	C₄₇×#389	C₂²	1	2	yes	—
32	C₄₇×#384	C₂²	1	1	yes	characteristic
33	C₄₇×#380	C₂²	1	2	yes	—
34	C₄₇×#340	C₂²	1	2	yes	—
35	C₄₇×#340	C₂²	1	2	yes	—
36	C₄₇×#336	C₂²	1	2	yes	—
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	2	2	no	—
39	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
44	#127×C₄₇	—	2	4	no	—
45	#125×C₄₇	—	2	4	no	—
46	#125×C₄₇	—	2	4	no	—
47	#123×C₄₇	—	2	16	no	—
48	#121×C₄₇	—	2	16	no	—
49	#121×C₄₇	—	2	4	no	—
50	#121×C₄₇	—	2	4	no	—
51	C₄×D₄×C₄₇	—	2	4	no	—
52	C₄×D₄×C₄₇	D₄	1	8	yes	—
53	#117×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	#107×C₄₇	—	2	4	no	—
69	#106×C₄₇	—	2	4	no	—
70	C₄⋊C₈×C₄₇	—	2	4	no	—
71	#102×C₄₇	—	2	4	no	—
72	#102×C₄₇	—	2	4	no	—
73	#102×C₄₇	—	4	2	no	—
74	#102×C₄₇	—	4	2	no	—
75	C₂²⋊C₈×C₄₇	—	4	1	no	—
76	C₂²⋊C₈×C₄₇	—	4	1	no	—
77	#95×C₄₇	—	2	2	no	—
78	#95×C₄₇	—	2	2	no	—
79	C₂⁴×C₄₇	—	2	2	no	—
80	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂×D₄×C₄₇	—	2	8	no	—
82	C₂×D₄×C₄₇	—	2	8	no	—
83	C₂×D₄×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	8	2	no	—
89	C₂×D₄×C₄₇	—	8	2	no	—
90	C₂×D₄×C₄₇	—	8	2	no	—
91	C₂×D₄×C₄₇	—	8	2	no	—
92	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	8	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	8	2	no	—
102	C₂²×C₄×C₄₇	—	8	2	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	8	no	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	4	4	no	—
121	C₄⋊C₄×C₄₇	—	8	2	no	—
122	C₄⋊C₄×C₄₇	—	8	2	no	—
123	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
124	C₂²⋊C₄×C₄₇	—	2	8	no	—
125	C₂²⋊C₄×C₄₇	—	2	8	no	—
126	C₂²⋊C₄×C₄₇	—	2	4	no	—
127	C₂²⋊C₄×C₄₇	—	8	2	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	C₂×D₄	1	4	yes	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	—	2	1	no	—
133	C₂³×C₄₇	—	2	1	no	—
134	C₂³×C₄₇	—	2	2	no	—
135	C₂³×C₄₇	—	2	2	no	—
136	C₂³×C₄₇	—	4	2	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	D₄×C₄₇	—	2	4	no	—
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	8	8	no	—
148	D₄×C₄₇	—	8	8	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	8	8	no	—
169	C₂×C₄×C₄₇	#120	1	4	yes	—
170	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	—	4	2	no	—
176	#29700	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₇	—	4	1	no	—
178	C₂²×C₄₇	—	4	4	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	—	4	1	no	—
181	C₂²×C₄₇	—	4	1	no	—
182	C₂²×C₄₇	—	4	4	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
190	C₂²×C₄₇	#536	1	1	yes	characteristic
191	C₂²×C₄₇	#537	1	1	yes	characteristic
192	C₂²×C₄₇	#576	1	2	yes	—
193	C₂²×C₄₇	#577	1	2	yes	—
194	C₄×C₄₇	—	2	4	no	—
195	C₄×C₄₇	—	4	1	no	—
196	C₄×C₄₇	—	4	2	no	—
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	—	8	2	no	—
199	C₄×C₄₇	—	8	2	no	—
200	C₄×C₄₇	#536	1	2	yes	—
201	C₄×C₄₇	#537	1	2	yes	—
202	C₂×#540	C₂×C₄₇	1	1	yes	characteristic
203	C₂×#478	C₂×C₄₇	1	2	yes	complemented
204	#2629	C₂×C₄₇	1	1	yes	characteristic, complemented
205	#2059	C₂×C₄₇	1	2	yes	complemented
206	#2041	C₂×C₄₇	1	2	yes	complemented
207	#2034	C₂×C₄₇	1	2	yes	complemented
208	#2033	C₂×C₄₇	1	2	yes	complemented
209	#1802	C₂×C₄₇	1	2	yes	complemented
210	#1798	C₂×C₄₇	1	1	yes	characteristic, complemented
211	C₂×C₄₇	—	8	1	no	—
212	C₂×C₄₇	—	8	4	no	—
213	C₂×C₄₇	#2616	1	1	yes	characteristic
214	C₂×C₄₇	#3012	1	2	yes	—
215	C₂×C₄₇	#3241	1	2	yes	—
216	C₂×C₄₇	#3259	1	1	yes	characteristic
217	C₂×C₄₇	#3260	1	1	yes	characteristic
218	#540	—	2	8	no	—
219	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
220	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
221	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
222	C₂×#123	—	2	2	no	—
223	C₂×#121	—	2	2	no	—
224	C₂×#121	C₂²×C₄₇	1	2	yes	—
225	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
226	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
227	#478	—	2	8	no	—
228	C₂×#107	C₂²×C₄₇	1	2	yes	—
229	C₂×#106	C₂²×C₄₇	1	2	yes	—
230	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
231	C₂×#102	C₂²×C₄₇	1	2	yes	—
232	C₂×#102	C₂²×C₄₇	1	2	yes	—
233	C₂×#102	C₂²×C₄₇	1	2	yes	—
234	C₂×#102	C₂²×C₄₇	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
236	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
237	#398	—	2	2	no	—
238	#396	—	2	2	no	—
239	#389	C₂²×C₄₇	1	2	yes	—
240	#384	C₂²×C₄₇	1	1	yes	characteristic
241	#380	C₂²×C₄₇	1	2	yes	—
242	#340	C₂²×C₄₇	1	2	yes	—
243	#340	C₂²×C₄₇	1	2	yes	—
244	#336	C₂²×C₄₇	1	2	yes	—
245	C₄₇	#29700	1	1	yes	characteristic, direct product factor, Sylow
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	—	2	2	no	—
248	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
252	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
253	#127	—	2	4	no	—
254	#125	—	2	4	no	—
255	#125	—	2	4	no	—
256	#123	—	2	16	no	—
257	#121	—	2	16	no	—
258	#121	—	2	4	no	—
259	#121	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	D₄×C₄₇	1	8	yes	—
262	#117	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	2	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
275	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
277	#107	—	2	4	no	—
278	#106	—	2	4	no	—
279	C₄⋊C₈	—	2	4	no	—
280	#102	—	2	4	no	—
281	#102	—	2	4	no	—
282	#102	—	4	2	no	—
283	#102	—	4	2	no	—
284	C₂²⋊C₈	—	4	1	no	—
285	C₂²⋊C₈	—	4	1	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	C₂⁴	—	2	2	no	—
289	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
290	C₂×D₄	—	2	8	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	8	2	no	—
298	C₂×D₄	—	8	2	no	—
299	C₂×D₄	—	8	2	no	—
300	C₂×D₄	—	8	2	no	—
301	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	8	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	8	2	no	—
311	C₂²×C₄	—	8	2	no	—
312	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
314	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₄⋊C₄	—	2	8	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	4	no	—
330	C₄⋊C₄	—	8	2	no	—
331	C₄⋊C₄	—	8	2	no	—
332	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
333	C₂²⋊C₄	—	2	8	no	—
334	C₂²⋊C₄	—	2	8	no	—
335	C₂²⋊C₄	—	2	4	no	—
336	C₂²⋊C₄	—	8	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	C₂×D₄×C₄₇	1	4	yes	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	4	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	8	8	no	—
357	D₄	—	8	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	8	8	no	—
378	C₂×C₄	#120×C₄₇	1	4	yes	—
379	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
380	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
381	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
382	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
383	C₈	—	4	2	no	—
384	C₈	—	4	2	no	—
385	C₂²	—	4	1	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	1	no	—
389	C₂²	—	4	1	no	—
390	C₂²	—	4	4	no	—
391	C₂²	—	4	2	no	—
392	C₂²	—	4	4	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
398	C₂²	C₄₇×#536	1	1	yes	characteristic
399	C₂²	C₄₇×#537	1	1	yes	characteristic
400	C₂²	C₄₇×#576	1	2	yes	—
401	C₂²	C₄₇×#577	1	2	yes	—
402	C₄	—	2	4	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	2	no	—
405	C₄	—	4	4	no	—
406	C₄	—	8	2	no	—
407	C₄	—	8	2	no	—
408	C₄	C₄₇×#536	1	2	yes	—
409	C₄	C₄₇×#537	1	2	yes	—
410	C₂	—	8	1	no	—
411	C₂	—	8	4	no	—
412	C₂	C₄₇×#2616	1	1	yes	characteristic
413	C₂	C₄₇×#3012	1	2	yes	—
414	C₂	C₄₇×#3241	1	2	yes	—
415	C₂	C₄₇×#3259	1	1	yes	characteristic
416	C₂	C₄₇×#3260	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#540	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#478	C₂	semidirect
3. C₄₇×#2629	C₂	semidirect
4. C₄₇×#2059	C₂	semidirect
5. C₄₇×#2041	C₂	semidirect
6. C₄₇×#2034	C₂	semidirect
7. C₄₇×#2033	C₂	semidirect
8. C₄₇×#1802	C₂	semidirect
9. C₄₇×#1798	C₂	semidirect
176. #29700	C₄₇	direct (N × H)
203. C₂×#478	C₂×C₄₇	semidirect
204. #2629	C₂×C₄₇	semidirect
205. #2059	C₂×C₄₇	semidirect
206. #2041	C₂×C₄₇	semidirect
207. #2034	C₂×C₄₇	semidirect
208. #2033	C₂×C₄₇	semidirect
209. #1802	C₂×C₄₇	semidirect
210. #1798	C₂×C₄₇	semidirect
245. C₄₇	#29700	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×#540	2
C₂×C₄₇×#478	2
C₄₇×#2629	2
C₄₇×#2059	2
C₄₇×#2041	2
C₄₇×#2034	2
C₄₇×#2033	2
C₄₇×#1802	2
C₄₇×#1798	2
#29700	47

Subgroups — C47×#29700 #26069398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29700 #26069398