Subgroups — C₄₇×#26042 #26065740

Order 12032.

810 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#475	C₂	1	2	yes	maximal
2	C₄₇×#2551	C₂	1	1	yes	maximal, characteristic
3	Q₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2088	C₂	1	2	yes	maximal
5	C₄₇×#2058	C₂	1	2	yes	maximal
6	C₄₇×#1948	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic
8	C₄₇×#1865	C₂	1	2	yes	maximal
9	C₄₇×#1844	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#1803	C₂	1	1	yes	maximal, characteristic
11	C₄×#103×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#475	—	2	8	no	—
17	C₂×#106×C₄₇	C₂²	1	2	yes	—
18	C₂×#106×C₄₇	C₂²	1	2	yes	—
19	C₂×#106×C₄₇	C₂²	1	2	yes	—
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#395	—	2	2	no	—
27	C₄₇×#389	—	2	2	no	—
28	C₄₇×#389	—	2	1	no	—
29	C₄₇×#389	C₂²	1	2	yes	—
30	C₄₇×#389	C₂²	1	2	yes	—
31	C₄₇×#384	—	2	1	no	—
32	C₄₇×#384	C₂²	1	1	yes	characteristic
33	C₄₇×#384	C₂²	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#340	C₂²	1	1	yes	characteristic
38	C₄₇×#340	C₂²	1	1	yes	characteristic
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
47	C₄⋊Q₈×C₄₇	—	2	4	no	—
48	C₄⋊Q₈×C₄₇	—	4	2	no	—
49	C₄⋊Q₈×C₄₇	—	4	4	no	—
50	C₄×Q₈×C₄₇	—	2	2	no	—
51	C₄×Q₈×C₄₇	—	2	4	no	—
52	C₄×Q₈×C₄₇	—	4	2	no	—
53	C₄×Q₈×C₄₇	Q₈	1	4	yes	complemented
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
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	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	#106×C₄₇	—	2	4	no	—
76	#106×C₄₇	—	2	4	no	—
77	#106×C₄₇	—	4	2	no	—
78	C₄⋊C₈×C₄₇	—	2	4	no	—
79	C₄⋊C₈×C₄₇	—	2	2	no	—
80	#103×C₄₇	—	2	4	no	—
81	#103×C₄₇	D₄	1	4	yes	—
82	#103×C₄₇	Q₈	1	4	yes	complemented
83	C₄×C₈×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	2	no	—
85	#95×C₄₇	—	2	1	no	—
86	#95×C₄₇	—	2	2	no	—
87	#95×C₄₇	D₄	1	2	yes	—
88	C₂×Q₈×C₄₇	—	2	1	no	—
89	C₂×Q₈×C₄₇	—	2	1	no	—
90	C₂×Q₈×C₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	4	4	no	—
92	C₂×Q₈×C₄₇	—	4	4	no	—
93	C₂×Q₈×C₄₇	—	8	2	no	—
94	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
95	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
96	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	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	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂×C₈×C₄₇	—	2	1	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	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	4	4	no	—
127	C₄⋊C₄×C₄₇	—	4	4	no	—
128	C₄⋊C₄×C₄₇	—	4	4	no	—
129	C₄⋊C₄×C₄₇	—	4	2	no	—
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	—	8	1	no	—
132	C₄⋊C₄×C₄₇	—	8	1	no	—
133	C₄⋊C₄×C₄₇	—	8	2	no	—
134	C₄⋊C₄×C₄₇	SD₁₆	1	4	yes	—
135	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
137	C₄⋊C₄×C₄₇	C₂×Q₈	1	2	yes	—
138	C₄²×C₄₇	—	2	4	no	—
139	C₄²×C₄₇	—	2	2	no	—
140	C₄²×C₄₇	—	2	2	no	—
141	C₄²×C₄₇	—	4	4	no	—
142	C₄²×C₄₇	—	4	2	no	—
143	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
144	C₄²×C₄₇	#41	1	2	yes	—
145	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	Q₈×C₄₇	—	2	2	no	—
147	Q₈×C₄₇	—	2	2	no	—
148	Q₈×C₄₇	—	2	2	no	—
149	Q₈×C₄₇	—	8	8	no	—
150	Q₈×C₄₇	C₄⋊Q₈	1	4	yes	complemented
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	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	2	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	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	C₂²⋊Q₈	1	2	yes	—
177	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
179	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
180	C₂×C₄×C₄₇	#137	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	2	no	—
189	C₈×C₄₇	—	4	2	no	—
190	#26042	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
191	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
192	C₂²×C₄₇	D₄²	1	1	yes	characteristic
193	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
194	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
196	C₂²×C₄₇	#577	1	1	yes	characteristic
197	C₂²×C₄₇	#577	1	1	yes	characteristic
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	2	4	no	—
200	C₄×C₄₇	—	2	4	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	—	4	2	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	4	2	no	—
205	C₄×C₄₇	—	8	2	no	—
206	C₄×C₄₇	—	8	2	no	—
207	C₄×C₄₇	#475	1	4	yes	complemented
208	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
209	C₄×C₄₇	#544	1	1	yes	characteristic
210	C₄×C₄₇	#547	1	1	yes	characteristic
211	C₄×C₄₇	#554	1	1	yes	characteristic
212	C₂×#475	C₂×C₄₇	1	2	yes	—
213	#2551	C₂×C₄₇	1	1	yes	characteristic
214	Q₈×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
215	#2088	C₂×C₄₇	1	2	yes	—
216	#2058	C₂×C₄₇	1	2	yes	—
217	#1948	C₂×C₄₇	1	1	yes	characteristic
218	#1939	C₂×C₄₇	1	1	yes	characteristic
219	#1865	C₂×C₄₇	1	2	yes	—
220	#1844	C₂×C₄₇	1	1	yes	characteristic
221	#1803	C₂×C₄₇	1	1	yes	characteristic
222	C₄×#103	C₂×C₄₇	1	1	yes	characteristic
223	C₂×C₄₇	#2440	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#475	1	1	yes	characteristic
225	C₂×C₄₇	#3084	1	1	yes	characteristic
226	C₂×C₄₇	#3278	1	1	yes	characteristic
227	C₂×C₄₇	D₄×SD₁₆	1	1	yes	characteristic
228	C₂×C₄₇	Q₈×SD₁₆	1	1	yes	characteristic
229	C₂×C₄₇	#3387	1	1	yes	characteristic
230	C₂×C₄⋊Q₈	—	2	1	no	—
231	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
232	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
233	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
234	#475	—	2	8	no	—
235	C₂×#106	C₂²×C₄₇	1	2	yes	—
236	C₂×#106	C₂²×C₄₇	1	2	yes	—
237	C₂×#106	C₂²×C₄₇	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
239	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
240	C₂×#103	C₂²×C₄₇	1	2	yes	—
241	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
242	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
244	#395	—	2	2	no	—
245	#389	—	2	1	no	—
246	#389	—	2	2	no	—
247	#389	C₂²×C₄₇	1	2	yes	—
248	#389	C₂²×C₄₇	1	2	yes	—
249	#384	—	2	1	no	—
250	#384	C₂²×C₄₇	1	1	yes	characteristic
251	#384	C₂²×C₄₇	1	1	yes	characteristic
252	C₄×C₄⋊C₄	—	2	1	no	—
253	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
255	#340	C₂²×C₄₇	1	1	yes	characteristic
256	#340	C₂²×C₄₇	1	2	yes	—
257	#340	C₂²×C₄₇	1	1	yes	characteristic
258	#340	C₂²×C₄₇	1	2	yes	—
259	#336	C₂²×C₄₇	1	2	yes	—
260	C₄₇	#26042	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×Q₈	—	2	2	no	—
262	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
264	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
266	C₄⋊Q₈	—	2	4	no	—
267	C₄⋊Q₈	—	4	2	no	—
268	C₄⋊Q₈	—	4	4	no	—
269	C₄×Q₈	—	2	2	no	—
270	C₄×Q₈	—	2	4	no	—
271	C₄×Q₈	—	4	2	no	—
272	C₄×Q₈	Q₈×C₄₇	1	4	yes	complemented
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
283	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
288	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂×C₄²	—	2	1	no	—
290	C₂×C₄²	—	2	2	no	—
291	C₂×C₄²	—	2	1	no	—
292	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
293	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
294	#106	—	2	4	no	—
295	#106	—	2	4	no	—
296	#106	—	4	2	no	—
297	C₄⋊C₈	—	2	4	no	—
298	C₄⋊C₈	—	2	2	no	—
299	#103	—	2	4	no	—
300	#103	D₄×C₄₇	1	4	yes	—
301	#103	Q₈×C₄₇	1	4	yes	complemented
302	C₄×C₈	—	2	2	no	—
303	#95	—	2	2	no	—
304	#95	—	2	1	no	—
305	#95	—	2	2	no	—
306	#95	D₄×C₄₇	1	2	yes	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	—	2	1	no	—
310	C₂×Q₈	—	4	4	no	—
311	C₂×Q₈	—	4	4	no	—
312	C₂×Q₈	—	8	2	no	—
313	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
314	C₂×Q₈	C₂×Q₈×C₄₇	1	2	yes	—
315	C₂×Q₈	C₂×Q₈×C₄₇	1	2	yes	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	1	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
323	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
335	C₂×C₈	C₂×Q₈×C₄₇	1	2	yes	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	4	4	no	—
346	C₄⋊C₄	—	4	4	no	—
347	C₄⋊C₄	—	4	4	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	8	1	no	—
351	C₄⋊C₄	—	8	1	no	—
352	C₄⋊C₄	—	8	2	no	—
353	C₄⋊C₄	SD₁₆×C₄₇	1	4	yes	—
354	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
355	C₄⋊C₄	C₂×Q₈×C₄₇	1	2	yes	—
356	C₄⋊C₄	C₂×Q₈×C₄₇	1	2	yes	—
357	C₄²	—	2	4	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	4	4	no	—
361	C₄²	—	4	2	no	—
362	C₄²	C₂×Q₈×C₄₇	1	2	yes	—
363	C₄²	#41×C₄₇	1	2	yes	—
364	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	2	2	no	—
367	Q₈	—	2	2	no	—
368	Q₈	—	8	8	no	—
369	Q₈	C₄⋊Q₈×C₄₇	1	4	yes	complemented
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
396	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
397	C₂×C₄	C₂×SD₁₆×C₄₇	1	4	yes	—
398	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
399	C₂×C₄	#137×C₄₇	1	2	yes	—
400	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
403	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
404	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
405	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
406	C₈	—	2	2	no	—
407	C₈	—	2	2	no	—
408	C₈	—	4	2	no	—
409	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
410	C₂²	D₄²×C₄₇	1	1	yes	characteristic
411	C₂²	D₄×Q₈×C₄₇	1	1	yes	characteristic
412	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
413	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
414	C₂²	C₄₇×#577	1	1	yes	characteristic
415	C₂²	C₄₇×#577	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	4	no	—
418	C₄	—	2	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	2	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₄₇×#475	1	4	yes	complemented
426	C₄	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
427	C₄	C₄₇×#544	1	1	yes	characteristic
428	C₄	C₄₇×#547	1	1	yes	characteristic
429	C₄	C₄₇×#554	1	1	yes	characteristic
430	C₂	C₄₇×#2440	1	1	yes	characteristic
431	C₂	C₂×C₄₇×#475	1	1	yes	characteristic
432	C₂	C₄₇×#3084	1	1	yes	characteristic
433	C₂	C₄₇×#3278	1	1	yes	characteristic
434	C₂	D₄×SD₁₆×C₄₇	1	1	yes	characteristic
435	C₂	Q₈×SD₁₆×C₄₇	1	1	yes	characteristic
436	C₂	C₄₇×#3387	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
53. C₄×Q₈×C₄₇	Q₈	semidirect
82. #103×C₄₇	Q₈	semidirect
150. Q₈×C₄₇	C₄⋊Q₈	semidirect
190. #26042	C₄₇	direct (N × H)
207. C₄×C₄₇	#475	semidirect
260. C₄₇	#26042	direct (N × H)
272. C₄×Q₈	Q₈×C₄₇	semidirect
301. #103	Q₈×C₄₇	semidirect
369. Q₈	C₄⋊Q₈×C₄₇	semidirect
425. C₄	C₄₇×#475	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#475	2
C₄₇×#2551	2
Q₈×C₄⋊C₄×C₄₇	2
C₄₇×#2088	2
C₄₇×#2058	2
C₄₇×#1948	2
C₄₇×#1939	2
C₄₇×#1865	2
C₄₇×#1844	2
C₄₇×#1803	2
C₄×#103×C₄₇	2
#26042	47

Subgroups — C47×#26042 #26065740

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#26042 #26065740