Subgroups — C₄₇×#21803 #26061501

Order 12032.

2054 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1982	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1957	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1786	C₂	1	4	yes	maximal, complemented
7	C₂³×D₄×C₄₇	—	2	1	no	—
8	C₂³×D₄×C₄₇	—	2	1	no	—
9	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
10	C₂×#127×C₄₇	—	2	1	no	—
11	C₂×#127×C₄₇	—	2	1	no	—
12	C₂×#127×C₄₇	—	2	4	no	—
13	C₂×#127×C₄₇	C₄	1	8	yes	complemented
14	C₂×#127×C₄₇	C₂²	1	2	yes	—
15	C₂×#127×C₄₇	C₂²	1	2	yes	—
16	C₂×#117×C₄₇	—	2	1	no	—
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#431	—	2	4	no	—
19	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
20	C₂×#102×C₄₇	C₂²	1	16	yes	complemented
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
23	C₄₇×#384	C₂²	1	2	yes	complemented
24	C₄₇×#382	—	2	1	no	—
25	C₄₇×#380	—	2	1	no	—
26	C₄₇×#380	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
29	C₂⁵×C₄₇	—	2	2	no	—
30	C₂²×D₄×C₄₇	—	2	8	no	—
31	C₂²×D₄×C₄₇	—	2	8	no	—
32	C₂²×D₄×C₄₇	—	2	2	no	—
33	C₂²×D₄×C₄₇	—	2	4	no	—
34	C₂²×D₄×C₄₇	—	2	2	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	4	8	no	—
39	C₂²×D₄×C₄₇	—	4	8	no	—
40	C₂²×D₄×C₄₇	—	4	4	no	—
41	C₂²×D₄×C₄₇	—	4	4	no	—
42	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
43	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
48	#127×C₄₇	—	2	8	no	—
49	#127×C₄₇	—	2	8	no	—
50	#127×C₄₇	—	2	4	no	—
51	#127×C₄₇	—	2	4	no	—
52	#127×C₄₇	C₂×C₄	1	8	yes	—
53	#127×C₄₇	C₂×C₄	1	8	yes	—
54	#117×C₄₇	—	4	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	D₄	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₄₇	—	2	4	no	—
67	#102×C₄₇	—	4	16	no	—
68	C₂²⋊C₈×C₄₇	—	2	4	no	—
69	C₄×C₈×C₄₇	—	2	4	no	—
70	#95×C₄₇	—	2	2	no	—
71	#95×C₄₇	—	2	2	no	—
72	C₂⁴×C₄₇	—	2	8	no	—
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	—	4	8	no	—
75	C₂⁴×C₄₇	—	4	8	no	—
76	C₂⁴×C₄₇	—	4	4	no	—
77	C₂⁴×C₄₇	—	4	4	no	—
78	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂×D₄×C₄₇	—	2	8	no	—
80	C₂×D₄×C₄₇	—	2	8	no	—
81	C₂×D₄×C₄₇	—	2	8	no	—
82	C₂×D₄×C₄₇	—	2	8	no	—
83	C₂×D₄×C₄₇	—	2	8	no	—
84	C₂×D₄×C₄₇	—	2	4	no	—
85	C₂×D₄×C₄₇	—	2	16	no	—
86	C₂×D₄×C₄₇	—	4	16	no	—
87	C₂×D₄×C₄₇	—	4	8	no	—
88	C₂×D₄×C₄₇	—	4	8	no	—
89	C₂×D₄×C₄₇	—	4	16	no	—
90	C₂×D₄×C₄₇	—	4	32	no	—
91	C₂×D₄×C₄₇	—	4	32	no	—
92	C₂×D₄×C₄₇	—	4	4	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	4	no	—
95	C₂×D₄×C₄₇	—	4	4	no	—
96	C₂×D₄×C₄₇	—	4	8	no	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	D₈	1	4	yes	—
104	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	—	2	8	no	—
115	C₄⋊C₄×C₄₇	—	2	8	no	—
116	C₄⋊C₄×C₄₇	—	4	4	no	—
117	C₄⋊C₄×C₄₇	—	4	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	4	no	—
119	C₄²×C₄₇	—	4	4	no	—
120	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
121	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	8	no	—
129	C₂³×C₄₇	—	4	16	no	—
130	C₂³×C₄₇	—	4	16	no	—
131	C₂³×C₄₇	—	4	8	no	—
132	C₂³×C₄₇	—	4	4	no	—
133	C₂³×C₄₇	—	4	4	no	—
134	C₂³×C₄₇	—	4	8	no	—
135	C₂³×C₄₇	—	4	16	no	—
136	C₂³×C₄₇	—	8	16	no	—
137	C₂³×C₄₇	—	8	16	no	—
138	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
139	C₂³×C₄₇	C₂×D₈	1	2	yes	—
140	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
141	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₄₇	—	2	16	no	—
143	D₄×C₄₇	—	4	16	no	—
144	D₄×C₄₇	—	4	16	no	—
145	D₄×C₄₇	—	4	8	no	—
146	D₄×C₄₇	—	4	16	no	—
147	D₄×C₄₇	—	4	16	no	—
148	D₄×C₄₇	—	4	16	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	#102	1	16	yes	complemented
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
167	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
171	C₈×C₄₇	—	4	4	no	—
172	#21803	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	2	4	no	—
177	C₂²×C₄₇	—	4	8	no	—
178	C₂²×C₄₇	—	4	8	no	—
179	C₂²×C₄₇	—	4	8	no	—
180	C₂²×C₄₇	—	8	32	no	—
181	C₂²×C₄₇	—	8	8	no	—
182	C₂²×C₄₇	—	8	8	no	—
183	C₂²×C₄₇	C₂×#102	1	4	yes	—
184	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×C₄₇	#535	1	2	yes	—
186	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
187	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	8	4	no	—
192	C₄×C₄₇	C₂×#102	1	4	yes	—
193	C₄×C₄₇	C₂×#102	1	4	yes	—
194	C₄×C₄₇	#418	1	4	yes	—
195	C₄×C₄₇	#518	1	2	yes	—
196	C₄×C₄₇	#535	1	2	yes	—
197	C₂²×#127	C₂×C₄₇	1	1	yes	characteristic
198	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
199	#2285	C₂×C₄₇	1	1	yes	characteristic, complemented
200	#1982	C₂×C₄₇	1	4	yes	complemented
201	#1957	C₂×C₄₇	1	4	yes	complemented
202	#1786	C₂×C₄₇	1	4	yes	complemented
203	C₂×C₄₇	—	2	4	no	—
204	C₂×C₄₇	—	8	8	no	—
205	C₂×C₄₇	#2309	1	1	yes	characteristic
206	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
207	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
208	C₂×C₄₇	#3205	1	2	yes	—
209	C₂×C₄₇	#3208	1	2	yes	—
210	C₂³×D₄	—	2	1	no	—
211	C₂³×D₄	—	2	1	no	—
212	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
213	C₂×#127	—	2	1	no	—
214	C₂×#127	—	2	1	no	—
215	C₂×#127	—	2	4	no	—
216	C₂×#127	C₄×C₄₇	1	8	yes	complemented
217	C₂×#127	C₂²×C₄₇	1	2	yes	—
218	C₂×#127	C₂²×C₄₇	1	2	yes	—
219	C₂×#117	—	2	1	no	—
220	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
221	#431	—	2	4	no	—
222	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
223	C₂×#102	C₂²×C₄₇	1	16	yes	complemented
224	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
225	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	complemented
226	#384	C₂²×C₄₇	1	2	yes	complemented
227	#382	—	2	1	no	—
228	#380	—	2	1	no	—
229	#380	C₂²×C₄₇	1	2	yes	—
230	C₄×C₄⋊C₄	—	2	1	no	—
231	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
232	C₄₇	#21803	1	1	yes	characteristic, direct product factor, Sylow
233	C₂⁵	—	2	2	no	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	—	2	8	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	—	2	4	no	—
238	C₂²×D₄	—	2	2	no	—
239	C₂²×D₄	—	2	2	no	—
240	C₂²×D₄	—	2	2	no	—
241	C₂²×D₄	—	2	2	no	—
242	C₂²×D₄	—	4	8	no	—
243	C₂²×D₄	—	4	8	no	—
244	C₂²×D₄	—	4	4	no	—
245	C₂²×D₄	—	4	4	no	—
246	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
247	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
248	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
249	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
250	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
252	#127	—	2	8	no	—
253	#127	—	2	8	no	—
254	#127	—	2	4	no	—
255	#127	—	2	4	no	—
256	#127	C₂×C₄×C₄₇	1	8	yes	—
257	#127	C₂×C₄×C₄₇	1	8	yes	—
258	#117	—	4	4	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
265	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₄₇	1	4	yes	—
268	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
270	C₄⋊C₈	—	2	4	no	—
271	#102	—	4	16	no	—
272	C₂²⋊C₈	—	2	4	no	—
273	C₄×C₈	—	2	4	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	C₂⁴	—	2	8	no	—
277	C₂⁴	—	2	4	no	—
278	C₂⁴	—	4	8	no	—
279	C₂⁴	—	4	8	no	—
280	C₂⁴	—	4	4	no	—
281	C₂⁴	—	4	4	no	—
282	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
283	C₂×D₄	—	2	8	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	8	no	—
286	C₂×D₄	—	2	8	no	—
287	C₂×D₄	—	2	8	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	16	no	—
290	C₂×D₄	—	4	16	no	—
291	C₂×D₄	—	4	8	no	—
292	C₂×D₄	—	4	8	no	—
293	C₂×D₄	—	4	16	no	—
294	C₂×D₄	—	4	32	no	—
295	C₂×D₄	—	4	4	no	—
296	C₂×D₄	—	4	4	no	—
297	C₂×D₄	—	4	4	no	—
298	C₂×D₄	—	4	4	no	—
299	C₂×D₄	—	4	8	no	—
300	C₂×D₄	—	4	32	no	—
301	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
306	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
307	C₂²×C₄	D₈×C₄₇	1	4	yes	—
308	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
315	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
317	C₂×C₈	—	2	4	no	—
318	C₂×C₈	—	2	8	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₄²	—	4	4	no	—
324	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
325	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
326	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
327	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
328	C₄²	C₂×D₄×C₄₇	1	2	yes	—
329	C₄²	C₂×D₄×C₄₇	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	8	no	—
333	C₂³	—	4	16	no	—
334	C₂³	—	4	16	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	8	no	—
339	C₂³	—	4	16	no	—
340	C₂³	—	8	16	no	—
341	C₂³	—	8	16	no	—
342	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
343	C₂³	C₂×D₈×C₄₇	1	2	yes	—
344	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
345	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
346	D₄	—	2	16	no	—
347	D₄	—	4	16	no	—
348	D₄	—	4	16	no	—
349	D₄	—	4	8	no	—
350	D₄	—	4	16	no	—
351	D₄	—	4	16	no	—
352	D₄	—	4	16	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	#102×C₄₇	1	16	yes	complemented
362	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
367	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
368	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
369	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
370	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
371	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
372	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
374	C₂×C₄	H(5,𝔽₂)×C₄₇	1	4	yes	—
375	C₈	—	4	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	4	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	4	8	no	—
381	C₂²	—	4	8	no	—
382	C₂²	—	4	8	no	—
383	C₂²	—	8	32	no	—
384	C₂²	—	8	8	no	—
385	C₂²	—	8	8	no	—
386	C₂²	C₂×#102×C₄₇	1	4	yes	—
387	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
388	C₂²	C₄₇×#535	1	2	yes	—
389	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
390	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
391	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	8	4	no	—
395	C₄	C₂×#102×C₄₇	1	4	yes	—
396	C₄	C₂×#102×C₄₇	1	4	yes	—
397	C₄	C₄₇×#418	1	4	yes	—
398	C₄	C₄₇×#518	1	2	yes	—
399	C₄	C₄₇×#535	1	2	yes	—
400	C₂	—	2	4	no	—
401	C₂	—	8	8	no	—
402	C₂	C₄₇×#2309	1	1	yes	characteristic
403	C₂	C₂²×#102×C₄₇	1	1	yes	characteristic
404	C₂	C₂×C₄₇×#418	1	1	yes	characteristic
405	C₂	C₄₇×#3205	1	2	yes	—
406	C₂	C₄₇×#3208	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#127×C₄₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#431	C₂	semidirect
3. C₄₇×#2285	C₂	semidirect
4. C₄₇×#1982	C₂	semidirect
5. C₄₇×#1957	C₂	semidirect
6. C₄₇×#1786	C₂	semidirect
13. C₂×#127×C₄₇	C₄	semidirect
19. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
20. C₂×#102×C₄₇	C₂²	semidirect
22. C₂×C₄×C₈×C₄₇	C₂²	semidirect
23. C₄₇×#384	C₂²	semidirect
28. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
157. C₂×C₄×C₄₇	#102	semidirect
172. #21803	C₄₇	direct (N × H)
198. C₂×#431	C₂×C₄₇	semidirect
199. #2285	C₂×C₄₇	semidirect
200. #1982	C₂×C₄₇	semidirect
201. #1957	C₂×C₄₇	semidirect
202. #1786	C₂×C₄₇	semidirect
216. C₂×#127	C₄×C₄₇	semidirect
222. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
223. C₂×#102	C₂²×C₄₇	semidirect
225. C₂×C₄×C₈	C₂²×C₄₇	semidirect
226. #384	C₂²×C₄₇	semidirect
231. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
232. C₄₇	#21803	direct (N × H)
361. C₂×C₄	#102×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₄₇	2
C₂×C₄₇×#431	2
C₄₇×#2285	2
C₄₇×#1982	2
C₄₇×#1957	2
C₄₇×#1786	2
#21803	47

Subgroups — C47×#21803 #26061501

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21803 #26061501