Subgroups — C₄₇×#29116 #26068814

Order 12032.

962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2628	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#2309	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2073	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2023	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1936	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1934	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1825	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1786	C₂	1	2	yes	maximal
9	C₄₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#102×C₄₇	C₂²	1	2	yes	—
15	C₂×#102×C₄₇	C₂²	1	2	yes	—
16	C₂×#102×C₄₇	C₂²	1	2	yes	—
17	C₂×#102×C₄₇	C₂²	1	2	yes	—
18	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
21	C₄₇×#400	—	2	1	no	—
22	C₄₇×#399	—	2	1	no	—
23	C₄₇×#395	—	2	1	no	—
24	C₄₇×#393	—	2	1	no	—
25	C₄₇×#390	—	2	1	no	—
26	C₄₇×#390	—	2	1	no	—
27	C₄₇×#390	C₂²	1	2	yes	—
28	C₄₇×#390	C₂²	1	2	yes	—
29	C₄₇×#389	C₂²	1	2	yes	complemented
30	C₄₇×#382	C₂²	1	1	yes	characteristic, complemented
31	C₄₇×#380	C₂²	1	2	yes	—
32	C₄₇×#379	—	2	1	no	—
33	C₄₇×#379	—	2	1	no	—
34	C₄₇×#340	C₂²	1	2	yes	complemented
35	C₄₇×#340	C₂²	1	2	yes	complemented
36	C₄₇×#340	C₂²	1	2	yes	complemented
37	C₄₇×#340	C₂²	1	2	yes	complemented
38	C₄₇×#336	C₂²	1	2	yes	complemented
39	C₂⁵×C₄₇	—	2	1	no	—
40	C₂²×Q₈×C₄₇	—	2	1	no	—
41	C₂²×D₄×C₄₇	—	2	4	no	—
42	C₂²×D₄×C₄₇	—	2	1	no	—
43	C₂²×D₄×C₄₇	—	2	4	no	—
44	C₂²×D₄×C₄₇	—	4	1	no	—
45	C₂²×D₄×C₄₇	—	4	1	no	—
46	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₄₇	—	4	1	no	—
51	C₄⋊Q₈×C₄₇	—	4	1	no	—
52	#117×C₄₇	—	2	4	no	—
53	#117×C₄₇	—	4	1	no	—
54	#117×C₄₇	—	4	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
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	1	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	#102×C₄₇	—	2	4	no	—
74	#102×C₄₇	—	2	4	no	—
75	#102×C₄₇	—	4	2	no	—
76	#102×C₄₇	—	4	2	no	—
77	C₂²⋊C₈×C₄₇	—	2	4	no	—
78	#97×C₄₇	—	4	1	no	—
79	C₄×C₈×C₄₇	—	4	1	no	—
80	#95×C₄₇	—	2	2	no	—
81	#95×C₄₇	—	2	1	no	—
82	#95×C₄₇	—	2	1	no	—
83	#95×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂⁴×C₄₇	—	4	2	no	—
87	C₂⁴×C₄₇	—	4	2	no	—
88	C₂⁴×C₄₇	—	8	2	no	—
89	C₂⁴×C₄₇	—	8	2	no	—
90	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂×Q₈×C₄₇	—	4	2	no	—
92	C₂×Q₈×C₄₇	—	8	2	no	—
93	C₂×D₄×C₄₇	—	2	4	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	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	4	8	no	—
100	C₂×D₄×C₄₇	—	4	8	no	—
101	C₂×D₄×C₄₇	—	4	2	no	—
102	C₂×D₄×C₄₇	—	4	2	no	—
103	C₂×D₄×C₄₇	#41	1	4	yes	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	4	yes	—
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	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	4	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	1	no	—
129	C₄⋊C₄×C₄₇	—	4	1	no	—
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	—	8	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	1	no	—
133	C₂²⋊C₄×C₄₇	—	4	1	no	—
134	C₂²⋊C₄×C₄₇	—	4	2	no	—
135	C₂²⋊C₄×C₄₇	—	8	2	no	—
136	C₂²⋊C₄×C₄₇	—	8	2	no	—
137	C₂²⋊C₄×C₄₇	—	8	2	no	—
138	C₂²⋊C₄×C₄₇	—	8	2	no	—
139	C₂²⋊C₄×C₄₇	—	8	2	no	—
140	C₄²×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	1	no	—
142	C₄²×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	—	2	1	no	—
144	C₄²×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	2	1	no	—
146	C₂³×C₄₇	—	2	1	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	2	4	no	—
150	C₂³×C₄₇	—	4	8	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	4	2	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	4	2	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	—	8	8	no	—
158	C₂³×C₄₇	—	8	8	no	—
159	C₂³×C₄₇	—	8	4	no	—
160	C₂³×C₄₇	—	8	4	no	—
161	C₂³×C₄₇	#124	1	2	yes	—
162	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	Q₈×C₄₇	—	8	4	no	—
164	D₄×C₄₇	—	2	4	no	—
165	D₄×C₄₇	—	2	4	no	—
166	D₄×C₄₇	—	4	8	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	#124	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
192	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
193	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
194	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	—	4	2	no	—
197	#29116	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	—	2	4	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	1	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	4	4	no	—
205	C₂²×C₄₇	—	4	4	no	—
206	C₂²×C₄₇	—	8	16	no	—
207	C₂²×C₄₇	—	8	2	no	—
208	C₂²×C₄₇	—	8	2	no	—
209	C₂²×C₄₇	—	8	2	no	—
210	C₂²×C₄₇	—	8	2	no	—
211	C₂²×C₄₇	#525	1	1	yes	characteristic
212	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
213	C₂²×C₄₇	#534	1	1	yes	characteristic
214	C₂²×C₄₇	#576	1	2	yes	—
215	C₂²×C₄₇	#577	1	2	yes	—
216	C₄×C₄₇	—	2	2	no	—
217	C₄×C₄₇	—	4	1	no	—
218	C₄×C₄₇	—	4	1	no	—
219	C₄×C₄₇	—	4	1	no	—
220	C₄×C₄₇	—	4	1	no	—
221	C₄×C₄₇	—	8	2	no	—
222	C₄×C₄₇	—	8	2	no	—
223	C₄×C₄₇	—	8	2	no	—
224	C₄×C₄₇	#551	1	2	yes	—
225	C₄×C₄₇	#551	1	2	yes	—
226	#2628	C₂×C₄₇	1	1	yes	characteristic, complemented
227	#2309	C₂×C₄₇	1	1	yes	characteristic
228	#2073	C₂×C₄₇	1	2	yes	complemented
229	#2023	C₂×C₄₇	1	2	yes	complemented
230	#1936	C₂×C₄₇	1	2	yes	complemented
231	#1934	C₂×C₄₇	1	2	yes	complemented
232	#1825	C₂×C₄₇	1	2	yes	complemented
233	#1786	C₂×C₄₇	1	2	yes	—
234	#1750	C₂×C₄₇	1	1	yes	characteristic, complemented
235	C₂×C₄₇	—	4	2	no	—
236	C₂×C₄₇	—	8	4	no	—
237	C₂×C₄₇	#2561	1	1	yes	characteristic
238	C₂×C₄₇	#3118	1	2	yes	—
239	C₂×C₄₇	#3136	1	2	yes	—
240	C₂×C₄₇	#3199	1	1	yes	characteristic
241	C₂×C₄₇	#3200	1	1	yes	characteristic
242	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
244	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
245	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
246	C₂×#102	C₂²×C₄₇	1	2	yes	—
247	C₂×#102	C₂²×C₄₇	1	2	yes	—
248	C₂×#102	C₂²×C₄₇	1	2	yes	—
249	C₂×#102	C₂²×C₄₇	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
251	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic, complemented
252	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
253	#400	—	2	1	no	—
254	#399	—	2	1	no	—
255	#395	—	2	1	no	—
256	#393	—	2	1	no	—
257	#390	—	2	1	no	—
258	#390	—	2	1	no	—
259	#390	C₂²×C₄₇	1	2	yes	—
260	#390	C₂²×C₄₇	1	2	yes	—
261	#389	C₂²×C₄₇	1	2	yes	complemented
262	#382	C₂²×C₄₇	1	1	yes	characteristic, complemented
263	#380	C₂²×C₄₇	1	2	yes	—
264	#379	—	2	1	no	—
265	#379	—	2	1	no	—
266	#340	C₂²×C₄₇	1	2	yes	complemented
267	#340	C₂²×C₄₇	1	2	yes	complemented
268	#340	C₂²×C₄₇	1	2	yes	complemented
269	#340	C₂²×C₄₇	1	2	yes	complemented
270	#336	C₂²×C₄₇	1	2	yes	complemented
271	C₄₇	#29116	1	1	yes	characteristic, direct product factor, Sylow
272	C₂⁵	—	2	1	no	—
273	C₂²×Q₈	—	2	1	no	—
274	C₂²×D₄	—	2	4	no	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	—	2	4	no	—
277	C₂²×D₄	—	4	1	no	—
278	C₂²×D₄	—	4	1	no	—
279	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
280	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
281	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
282	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
283	C₄⋊Q₈	—	4	1	no	—
284	C₄⋊Q₈	—	4	1	no	—
285	#117	—	2	4	no	—
286	#117	—	4	1	no	—
287	#117	—	4	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
291	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	1	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
302	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
305	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
306	#102	—	2	4	no	—
307	#102	—	2	4	no	—
308	#102	—	4	2	no	—
309	#102	—	4	2	no	—
310	C₂²⋊C₈	—	2	4	no	—
311	#97	—	4	1	no	—
312	C₄×C₈	—	4	1	no	—
313	#95	—	2	2	no	—
314	#95	—	2	1	no	—
315	#95	—	2	1	no	—
316	#95	—	2	2	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	2	no	—
319	C₂⁴	—	4	2	no	—
320	C₂⁴	—	4	2	no	—
321	C₂⁴	—	8	2	no	—
322	C₂⁴	—	8	2	no	—
323	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
324	C₂×Q₈	—	4	2	no	—
325	C₂×Q₈	—	8	2	no	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	8	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	2	no	—
336	C₂×D₄	#41×C₄₇	1	4	yes	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
348	C₂²×C₄	#41×C₄₇	1	4	yes	—
349	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	2	no	—
364	C₄⋊C₄	—	8	2	no	—
365	C₂²⋊C₄	—	4	1	no	—
366	C₂²⋊C₄	—	4	1	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	8	2	no	—
369	C₂²⋊C₄	—	8	2	no	—
370	C₂²⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	8	2	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₄²	—	2	1	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	—	4	2	no	—
378	C₂³	—	2	1	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	4	no	—
383	C₂³	—	4	8	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	8	8	no	—
391	C₂³	—	8	8	no	—
392	C₂³	—	8	4	no	—
393	C₂³	—	8	4	no	—
394	C₂³	#124×C₄₇	1	2	yes	—
395	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
396	Q₈	—	8	4	no	—
397	D₄	—	2	4	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	8	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	#124×C₄₇	1	2	yes	—
424	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
425	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
426	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	8	16	no	—
439	C₂²	—	8	2	no	—
440	C₂²	—	8	2	no	—
441	C₂²	—	8	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	C₄₇×#525	1	1	yes	characteristic
444	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
445	C₂²	C₄₇×#534	1	1	yes	characteristic
446	C₂²	C₄₇×#576	1	2	yes	—
447	C₂²	C₄₇×#577	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	1	no	—
450	C₄	—	4	1	no	—
451	C₄	—	4	1	no	—
452	C₄	—	4	1	no	—
453	C₄	—	8	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	2	no	—
456	C₄	C₄₇×#551	1	2	yes	—
457	C₄	C₄₇×#551	1	2	yes	—
458	C₂	—	4	2	no	—
459	C₂	—	8	4	no	—
460	C₂	C₄₇×#2561	1	1	yes	characteristic
461	C₂	C₄₇×#3118	1	2	yes	—
462	C₂	C₄₇×#3136	1	2	yes	—
463	C₂	C₄₇×#3199	1	1	yes	characteristic
464	C₂	C₄₇×#3200	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
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
1. C₄₇×#2628	C₂	semidirect
3. C₄₇×#2073	C₂	semidirect
4. C₄₇×#2023	C₂	semidirect
5. C₄₇×#1936	C₂	semidirect
6. C₄₇×#1934	C₂	semidirect
7. C₄₇×#1825	C₂	semidirect
9. C₄₇×#1750	C₂	semidirect
11. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
19. C₂×#97×C₄₇	C₂²	semidirect
20. C₂×C₄×C₈×C₄₇	C₂²	semidirect
29. C₄₇×#389	C₂²	semidirect
30. C₄₇×#382	C₂²	semidirect
34. C₄₇×#340	C₂²	semidirect
35. C₄₇×#340	C₂²	semidirect
36. C₄₇×#340	C₂²	semidirect
37. C₄₇×#340	C₂²	semidirect
38. C₄₇×#336	C₂²	semidirect
197. #29116	C₄₇	direct (N × H)
226. #2628	C₂×C₄₇	semidirect
228. #2073	C₂×C₄₇	semidirect
229. #2023	C₂×C₄₇	semidirect
230. #1936	C₂×C₄₇	semidirect
231. #1934	C₂×C₄₇	semidirect
232. #1825	C₂×C₄₇	semidirect
234. #1750	C₂×C₄₇	semidirect
243. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
251. C₂×#97	C₂²×C₄₇	semidirect
252. C₂×C₄×C₈	C₂²×C₄₇	semidirect
261. #389	C₂²×C₄₇	semidirect
262. #382	C₂²×C₄₇	semidirect
266. #340	C₂²×C₄₇	semidirect
267. #340	C₂²×C₄₇	semidirect
268. #340	C₂²×C₄₇	semidirect
269. #340	C₂²×C₄₇	semidirect
270. #336	C₂²×C₄₇	semidirect
271. C₄₇	#29116	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2628	2
C₄₇×#2309	2
C₄₇×#2073	2
C₄₇×#2023	2
C₄₇×#1936	2
C₄₇×#1934	2
C₄₇×#1825	2
C₄₇×#1786	2
C₄₇×#1750	2
#29116	47

Subgroups — C47×#29116 #26068814

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29116 #26068814