Subgroups — C₄₇×#22188 #26061886

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#470	C₂	1	1	yes	maximal, characteristic
2	C₄×C₂²⋊Q₈×C₄₇	C₂	1	2	yes	maximal
3	C₄₇×#1927	C₂	1	2	yes	maximal, complemented
4	C₄₇×#1920	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1894	C₂	1	2	yes	maximal
6	C₄₇×#1878	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1863	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#470	C₄	1	8	yes	complemented
17	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#103×C₄₇	C₂²	1	2	yes	—
21	C₂×#103×C₄₇	C₂²	1	2	yes	—
22	C₂×#103×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#391	C₂²	1	2	yes	—
24	C₄₇×#389	C₂²	1	2	yes	—
25	C₄₇×#387	—	2	2	no	—
26	C₄₇×#385	—	2	2	no	—
27	C₄₇×#380	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
29	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
31	C₄₇×#340	C₂²	1	2	yes	—
32	C₄₇×#340	C₂²	1	2	yes	—
33	C₄₇×#340	C₂²	1	2	yes	—
34	C₄₇×#336	C₂²	1	2	yes	—
35	C₄₇×#336	C₂²	1	2	yes	—
36	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂×Q₁₆×C₄₇	—	4	1	no	—
41	C₂×Q₁₆×C₄₇	—	4	1	no	—
42	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
43	C₂×M₁₆×C₄₇	—	2	2	no	—
44	C₂×M₁₆×C₄₇	—	4	1	no	—
45	C₂×M₁₆×C₄₇	—	4	1	no	—
46	C₂×M₁₆×C₄₇	—	4	1	no	—
47	C₂×M₁₆×C₄₇	—	4	1	no	—
48	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
52	C₂²⋊Q₈×C₄₇	—	2	4	no	—
53	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
54	C₄×Q₈×C₄₇	—	4	2	no	—
55	C₄×Q₈×C₄₇	—	4	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
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×C₄²×C₄₇	—	2	2	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	—	4	1	no	—
67	C₂×C₄²×C₄₇	—	4	1	no	—
68	C₂×C₄²×C₄₇	D₄	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	#107×C₄₇	—	4	1	no	—
71	#106×C₄₇	—	4	1	no	—
72	#106×C₄₇	C₂×C₄	1	4	yes	complemented
73	#103×C₄₇	—	4	2	no	—
74	#103×C₄₇	—	4	2	no	—
75	#103×C₄₇	C₂×C₄	1	8	yes	complemented
76	#95×C₄₇	—	2	2	no	—
77	#95×C₄₇	—	2	2	no	—
78	#95×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	—	4	1	no	—
99	C₂²×C₄×C₄₇	—	4	2	no	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	Q₁₆×C₄₇	—	4	4	no	—
107	M₁₆×C₄₇	—	4	4	no	—
108	M₁₆×C₄₇	—	4	4	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₄₇	—	2	8	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	4	4	no	—
125	C₄⋊C₄×C₄₇	—	4	4	no	—
126	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
127	C₂²⋊C₄×C₄₇	—	2	8	no	—
128	C₂²⋊C₄×C₄₇	—	4	4	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	4	2	no	—
132	C₄²×C₄₇	—	4	4	no	—
133	C₄²×C₄₇	—	4	4	no	—
134	C₂³×C₄₇	—	2	1	no	—
135	C₂³×C₄₇	—	2	1	no	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	C₄×D₄	1	2	yes	—
139	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₄₇	—	2	4	no	—
141	Q₈×C₄₇	—	2	4	no	—
142	Q₈×C₄₇	—	4	2	no	—
143	Q₈×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	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	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	4	4	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	—	4	2	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	#137	1	4	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
177	C₈×C₄₇	—	2	2	no	—
178	C₈×C₄₇	—	2	2	no	—
179	C₈×C₄₇	—	4	2	no	—
180	#22188	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
181	C₂²×C₄₇	—	2	2	no	—
182	C₂²×C₄₇	—	2	4	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	1	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₇	#534	1	1	yes	characteristic
188	C₂²×C₄₇	#537	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×#137	1	2	yes	—
190	C₂²×C₄₇	#575	1	2	yes	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	2	4	no	—
193	C₄×C₄₇	—	4	4	no	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	—	4	4	no	—
196	C₄×C₄₇	—	8	2	no	—
197	C₄×C₄₇	—	8	2	no	—
198	C₄×C₄₇	#518	1	1	yes	characteristic
199	C₄×C₄₇	#520	1	1	yes	characteristic
200	C₄×C₄₇	#538	1	1	yes	characteristic
201	C₄×C₄₇	#539	1	1	yes	characteristic
202	C₂×#470	C₂×C₄₇	1	1	yes	characteristic
203	C₄×C₂²⋊Q₈	C₂×C₄₇	1	2	yes	—
204	#1927	C₂×C₄₇	1	2	yes	complemented
205	#1920	C₂×C₄₇	1	2	yes	complemented
206	#1894	C₂×C₄₇	1	2	yes	—
207	#1878	C₂×C₄₇	1	2	yes	complemented
208	#1863	C₂×C₄₇	1	2	yes	complemented
209	#1809	C₂×C₄₇	1	1	yes	characteristic
210	#1728	C₂×C₄₇	1	1	yes	characteristic
211	C₂×C₄₇	—	4	2	no	—
212	C₂×C₄₇	#2325	1	1	yes	characteristic
213	C₂×C₄₇	C₄×#137	1	2	yes	—
214	C₂×C₄₇	#3195	1	1	yes	characteristic
215	C₂×C₄₇	#3197	1	1	yes	characteristic
216	C₂×C₄₇	#3252	1	2	yes	—
217	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
219	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
220	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
222	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
223	#470	C₄×C₄₇	1	8	yes	complemented
224	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
225	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
226	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
227	C₂×#103	C₂²×C₄₇	1	2	yes	—
228	C₂×#103	C₂²×C₄₇	1	2	yes	—
229	C₂×#103	C₂²×C₄₇	1	2	yes	—
230	#391	C₂²×C₄₇	1	2	yes	—
231	#389	C₂²×C₄₇	1	2	yes	—
232	#387	—	2	2	no	—
233	#385	—	2	2	no	—
234	#380	C₂²×C₄₇	1	2	yes	—
235	C₄×C₄⋊C₄	—	2	2	no	—
236	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
237	C₄×C₂²⋊C₄	—	2	2	no	—
238	#340	C₂²×C₄₇	1	2	yes	—
239	#340	C₂²×C₄₇	1	2	yes	—
240	#340	C₂²×C₄₇	1	2	yes	—
241	#336	C₂²×C₄₇	1	2	yes	—
242	#336	C₂²×C₄₇	1	2	yes	—
243	C₄₇	#22188	1	1	yes	characteristic, direct product factor, Sylow
244	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
245	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
246	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
247	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
248	C₂×Q₁₆	—	4	1	no	—
249	C₂×Q₁₆	—	4	1	no	—
250	C₂×Q₁₆	C₂×C₄×C₄₇	1	4	yes	complemented
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	4	1	no	—
253	C₂×M₁₆	—	4	1	no	—
254	C₂×M₁₆	—	4	1	no	—
255	C₂×M₁₆	—	4	1	no	—
256	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
257	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
260	C₂²⋊Q₈	—	2	4	no	—
261	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	—
262	C₄×Q₈	—	4	2	no	—
263	C₄×Q₈	—	4	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	C₂³×C₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
270	C₂×C₂²⋊C₄	—	2	2	no	—
271	C₂×C₂²⋊C₄	—	2	2	no	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	—	2	2	no	—
274	C₂×C₄²	—	4	1	no	—
275	C₂×C₄²	—	4	1	no	—
276	C₂×C₄²	D₄×C₄₇	1	2	yes	—
277	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
278	#107	—	4	1	no	—
279	#106	—	4	1	no	—
280	#106	C₂×C₄×C₄₇	1	4	yes	complemented
281	#103	—	4	2	no	—
282	#103	—	4	2	no	—
283	#103	C₂×C₄×C₄₇	1	8	yes	complemented
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
309	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
312	C₂²×C₄	#41×C₄₇	1	2	yes	—
313	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
314	Q₁₆	—	4	4	no	—
315	M₁₆	—	4	4	no	—
316	M₁₆	—	4	4	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
325	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	4	no	—
333	C₄⋊C₄	—	4	4	no	—
334	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
335	C₂²⋊C₄	—	2	8	no	—
336	C₂²⋊C₄	—	4	4	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	4	2	no	—
340	C₄²	—	4	4	no	—
341	C₄²	—	4	4	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	C₄×D₄×C₄₇	1	2	yes	—
347	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
348	Q₈	—	2	4	no	—
349	Q₈	—	2	4	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	4	4	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	C₄×D₄×C₄₇	1	2	yes	—
378	C₂×C₄	#137×C₄₇	1	4	yes	—
379	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
383	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
384	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	1	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
394	C₂²	C₄₇×#534	1	1	yes	characteristic
395	C₂²	C₄₇×#537	1	1	yes	characteristic
396	C₂²	C₂×#137×C₄₇	1	2	yes	—
397	C₂²	C₄₇×#575	1	2	yes	—
398	C₄	—	2	2	no	—
399	C₄	—	2	4	no	—
400	C₄	—	4	4	no	—
401	C₄	—	4	2	no	—
402	C₄	—	4	4	no	—
403	C₄	—	8	2	no	—
404	C₄	—	8	2	no	—
405	C₄	C₄₇×#518	1	1	yes	characteristic
406	C₄	C₄₇×#520	1	1	yes	characteristic
407	C₄	C₄₇×#538	1	1	yes	characteristic
408	C₄	C₄₇×#539	1	1	yes	characteristic
409	C₂	—	4	2	no	—
410	C₂	C₄₇×#2325	1	1	yes	characteristic
411	C₂	C₄×#137×C₄₇	1	2	yes	—
412	C₂	C₄₇×#3195	1	1	yes	characteristic
413	C₂	C₄₇×#3197	1	1	yes	characteristic
414	C₂	C₄₇×#3252	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	C₂⁴×C₄₇	C₂×D₄
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
3. C₄₇×#1927	C₂	semidirect
4. C₄₇×#1920	C₂	semidirect
6. C₄₇×#1878	C₂	semidirect
7. C₄₇×#1863	C₂	semidirect
16. C₄₇×#470	C₄	semidirect
42. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
72. #106×C₄₇	C₂×C₄	semidirect
75. #103×C₄₇	C₂×C₄	semidirect
180. #22188	C₄₇	direct (N × H)
204. #1927	C₂×C₄₇	semidirect
205. #1920	C₂×C₄₇	semidirect
207. #1878	C₂×C₄₇	semidirect
208. #1863	C₂×C₄₇	semidirect
223. #470	C₄×C₄₇	semidirect
243. C₄₇	#22188	direct (N × H)
250. C₂×Q₁₆	C₂×C₄×C₄₇	semidirect
280. #106	C₂×C₄×C₄₇	semidirect
283. #103	C₂×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#470	2
C₄×C₂²⋊Q₈×C₄₇	2
C₄₇×#1927	2
C₄₇×#1920	2
C₄₇×#1894	2
C₄₇×#1878	2
C₄₇×#1863	2
C₄₇×#1809	2
C₄₇×#1728	2
#22188	47

Subgroups — C47×#22188 #26061886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#22188 #26061886