Subgroups — C₄₇×#18309 #26058007

Order 12032.

1168 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3449	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3227	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2628	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1616	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1613	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1517	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₄₇	—	2	1	no	—
9	C₄₇×#537	—	2	1	no	—
10	C₄₇×#537	C₂²	1	2	yes	—
11	C₄₇×#536	—	2	2	no	—
12	C₄₇×#535	—	2	2	no	—
13	C₄₇×#534	—	2	1	no	—
14	C₄₇×#534	C₂²	1	2	yes	—
15	C₄₇×#532	—	2	1	no	—
16	C₄₇×#532	C₂²	1	2	yes	—
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
18	C₄₇×#525	—	2	4	no	—
19	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#498	—	2	2	no	—
21	C₄₇×#486	—	2	2	no	—
22	C₄₇×#481	C₂²	1	8	yes	complemented
23	C₄₇×#476	—	2	4	no	—
24	C₄₇×#431	C₂²	1	2	yes	complemented
25	C₄₇×#400	C₂²	1	2	yes	complemented
26	C₄₇×#399	C₂²	1	2	yes	—
27	C₄₇×#395	—	2	1	no	—
28	C₄₇×#393	—	2	1	no	—
29	C₄₇×#389	—	2	1	no	—
30	C₄₇×#382	C₂²	1	1	yes	characteristic, complemented
31	C₄₇×#380	—	2	1	no	—
32	C₄₇×#327	C₂²	1	8	yes	complemented
33	C₄₇×#324	C₂²	1	2	yes	complemented
34	C₄₇×#323	C₂²	1	2	yes	—
35	C₂×#41×C₄₇	—	2	2	no	—
36	C₂×#41×C₄₇	—	2	2	no	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	—	4	4	no	—
40	C₂×#41×C₄₇	—	4	4	no	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	—	2	1	no	—
43	C₂²×D₄×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₄₇	—	2	1	no	—
48	C₄⋊Q₈×C₄₇	—	2	2	no	—
49	C₄⋊Q₈×C₄₇	—	2	2	no	—
50	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
51	#127×C₄₇	—	2	1	no	—
52	#127×C₄₇	D₄	1	2	yes	—
53	#124×C₄₇	—	2	2	no	—
54	#124×C₄₇	—	2	2	no	—
55	#123×C₄₇	—	2	4	no	—
56	#123×C₄₇	—	2	4	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	#121×C₄₇	—	2	4	no	—
60	#121×C₄₇	—	2	4	no	—
61	#121×C₄₇	—	2	2	no	—
62	#121×C₄₇	—	2	2	no	—
63	#121×C₄₇	—	2	2	no	—
64	#121×C₄₇	C₂³	1	4	yes	—
65	#120×C₄₇	—	2	4	no	—
66	#120×C₄₇	—	2	4	no	—
67	C₄×D₄×C₄₇	—	2	2	no	—
68	C₄×D₄×C₄₇	—	2	2	no	—
69	C₄×D₄×C₄₇	—	2	2	no	—
70	C₄×D₄×C₄₇	D₄	1	4	yes	—
71	#117×C₄₇	—	2	2	no	—
72	#117×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#106×C₄₇	—	2	8	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	#102×C₄₇	—	2	8	no	—
87	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
88	C₄×C₈×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	1	no	—
91	#95×C₄₇	—	2	2	no	—
92	#95×C₄₇	C₂³	1	2	yes	—
93	C₂⁴×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
95	#41×C₄₇	—	4	4	no	—
96	#41×C₄₇	—	4	8	no	—
97	#41×C₄₇	—	4	8	no	—
98	#41×C₄₇	—	4	4	no	—
99	#41×C₄₇	—	4	4	no	—
100	#41×C₄₇	—	4	4	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	4	4	no	—
104	C₂×Q₈×C₄₇	—	4	2	no	—
105	C₂×Q₈×C₄₇	—	8	2	no	—
106	C₂×D₄×C₄₇	—	2	4	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	2	4	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	4	4	no	—
114	C₂×D₄×C₄₇	—	4	4	no	—
115	C₂×D₄×C₄₇	—	4	4	no	—
116	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	4	8	no	—
126	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₈×C₄₇	—	2	4	no	—
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	4	1	no	—
141	C₄⋊C₄×C₄₇	—	4	1	no	—
142	C₄⋊C₄×C₄₇	—	4	2	no	—
143	C₄⋊C₄×C₄₇	—	8	2	no	—
144	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	2	4	no	—
147	C₂²⋊C₄×C₄₇	—	2	2	no	—
148	C₂²⋊C₄×C₄₇	—	2	4	no	—
149	C₂²⋊C₄×C₄₇	—	2	2	no	—
150	C₂²⋊C₄×C₄₇	—	2	4	no	—
151	C₂²⋊C₄×C₄₇	—	8	2	no	—
152	C₄²×C₄₇	—	2	1	no	—
153	C₄²×C₄₇	—	2	1	no	—
154	C₄²×C₄₇	C₂×D₄	1	2	yes	—
155	C₄²×C₄₇	C₂×D₄	1	2	yes	—
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	—	2	1	no	—
158	C₂³×C₄₇	—	2	4	no	—
159	C₂³×C₄₇	—	4	1	no	—
160	C₂³×C₄₇	—	4	1	no	—
161	C₂³×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	—	8	2	no	—
163	C₂³×C₄₇	—	8	2	no	—
164	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
165	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₇	—	4	4	no	—
167	Q₈×C₄₇	—	4	4	no	—
168	Q₈×C₄₇	—	8	4	no	—
169	D₄×C₄₇	—	4	4	no	—
170	D₄×C₄₇	—	4	4	no	—
171	D₄×C₄₇	—	4	8	no	—
172	D₄×C₄₇	—	4	4	no	—
173	D₄×C₄₇	—	4	4	no	—
174	D₄×C₄₇	—	4	4	no	—
175	D₄×C₄₇	—	8	2	no	—
176	D₄×C₄₇	—	8	2	no	—
177	D₄×C₄₇	—	8	2	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	4	no	—
185	C₂×C₄×C₄₇	—	4	1	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	8	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	8	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	#120	1	2	yes	—
199	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
200	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
203	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
204	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
205	C₈×C₄₇	—	4	4	no	—
206	#18309	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₇	—	2	1	no	—
208	C₂²×C₄₇	—	2	1	no	—
209	C₂²×C₄₇	—	2	2	no	—
210	C₂²×C₄₇	—	4	2	no	—
211	C₂²×C₄₇	—	4	1	no	—
212	C₂²×C₄₇	—	4	1	no	—
213	C₂²×C₄₇	—	4	4	no	—
214	C₂²×C₄₇	—	4	4	no	—
215	C₂²×C₄₇	—	4	4	no	—
216	C₂²×C₄₇	—	8	1	no	—
217	C₂²×C₄₇	—	8	8	no	—
218	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
219	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	2	2	no	—
223	C₄×C₄₇	—	2	2	no	—
224	C₄×C₄₇	—	4	4	no	—
225	C₄×C₄₇	—	4	1	no	—
226	C₄×C₄₇	—	4	1	no	—
227	C₄×C₄₇	—	8	2	no	—
228	C₄×C₄₇	—	8	2	no	—
229	C₄×C₄₇	#450	1	2	yes	—
230	C₄×C₄₇	#450	1	2	yes	—
231	#3449	C₂×C₄₇	1	1	yes	characteristic
232	#3227	C₂×C₄₇	1	2	yes	complemented
233	#2628	C₂×C₄₇	1	1	yes	characteristic, complemented
234	#1616	C₂×C₄₇	1	4	yes	complemented
235	#1613	C₂×C₄₇	1	4	yes	complemented
236	#1517	C₂×C₄₇	1	2	yes	complemented
237	#1458	C₂×C₄₇	1	1	yes	characteristic, complemented
238	C₂×C₄₇	—	2	1	no	—
239	C₂×C₄₇	—	2	1	no	—
240	C₂×C₄₇	—	4	2	no	—
241	C₂×C₄₇	—	8	4	no	—
242	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
243	C₂×C₄₇	#3021	1	1	yes	characteristic
244	C₂×C₄₇	#3028	1	1	yes	characteristic
245	C₂²×#41	—	2	1	no	—
246	#537	—	2	1	no	—
247	#537	C₂²×C₄₇	1	2	yes	—
248	#536	—	2	2	no	—
249	#535	—	2	2	no	—
250	#534	—	2	1	no	—
251	#534	C₂²×C₄₇	1	2	yes	—
252	#532	—	2	1	no	—
253	#532	C₂²×C₄₇	1	2	yes	—
254	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
255	#525	—	2	4	no	—
256	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
257	#498	—	2	2	no	—
258	#486	—	2	2	no	—
259	#481	C₂²×C₄₇	1	8	yes	complemented
260	#476	—	2	4	no	—
261	#431	C₂²×C₄₇	1	2	yes	complemented
262	#400	C₂²×C₄₇	1	2	yes	complemented
263	#399	C₂²×C₄₇	1	2	yes	—
264	#395	—	2	1	no	—
265	#393	—	2	1	no	—
266	#389	—	2	1	no	—
267	#382	C₂²×C₄₇	1	1	yes	characteristic, complemented
268	#380	—	2	1	no	—
269	#327	C₂²×C₄₇	1	8	yes	complemented
270	#324	C₂²×C₄₇	1	2	yes	complemented
271	#323	C₂²×C₄₇	1	2	yes	—
272	C₄₇	#18309	1	1	yes	characteristic, direct product factor, Sylow
273	C₂×#41	—	2	2	no	—
274	C₂×#41	—	2	2	no	—
275	C₂×#41	—	2	2	no	—
276	C₂×#41	—	2	2	no	—
277	C₂×#41	—	4	4	no	—
278	C₂×#41	—	4	4	no	—
279	C₂²×Q₈	—	2	1	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×D₄	—	2	1	no	—
282	C₂²×D₄	—	2	2	no	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
285	C₄⋊Q₈	—	2	1	no	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
289	#127	—	2	1	no	—
290	#127	D₄×C₄₇	1	2	yes	—
291	#124	—	2	2	no	—
292	#124	—	2	2	no	—
293	#123	—	2	4	no	—
294	#123	—	2	4	no	—
295	C₂²⋊Q₈	—	2	4	no	—
296	C₂²⋊Q₈	—	2	4	no	—
297	#121	—	2	4	no	—
298	#121	—	2	4	no	—
299	#121	—	2	2	no	—
300	#121	—	2	2	no	—
301	#121	—	2	2	no	—
302	#121	C₂³×C₄₇	1	4	yes	—
303	#120	—	2	4	no	—
304	#120	—	2	4	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	—	2	2	no	—
307	C₄×D₄	—	2	2	no	—
308	C₄×D₄	D₄×C₄₇	1	4	yes	—
309	#117	—	2	2	no	—
310	#117	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	2	2	no	—
318	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
320	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
321	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
322	#106	—	2	8	no	—
323	C₄⋊C₈	—	2	2	no	—
324	#102	—	2	8	no	—
325	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
326	C₄×C₈	—	2	2	no	—
327	#95	—	2	2	no	—
328	#95	—	2	1	no	—
329	#95	—	2	2	no	—
330	#95	C₂³×C₄₇	1	2	yes	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
333	#41	—	4	4	no	—
334	#41	—	4	8	no	—
335	#41	—	4	8	no	—
336	#41	—	4	4	no	—
337	#41	—	4	4	no	—
338	#41	—	4	4	no	—
339	C₂×Q₈	—	2	2	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	—	4	2	no	—
343	C₂×Q₈	—	8	2	no	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	2	no	—
346	C₂×D₄	—	2	4	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	2	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	4	no	—
352	C₂×D₄	—	4	4	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	4	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	4	8	no	—
364	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
365	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
371	C₂×C₈	—	2	4	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	2	2	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	2	no	—
381	C₄⋊C₄	—	8	2	no	—
382	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
383	C₂²⋊C₄	—	2	4	no	—
384	C₂²⋊C₄	—	2	4	no	—
385	C₂²⋊C₄	—	2	2	no	—
386	C₂²⋊C₄	—	2	4	no	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	8	2	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	C₂×D₄×C₄₇	1	2	yes	—
393	C₄²	C₂×D₄×C₄₇	1	2	yes	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	1	no	—
398	C₂³	—	4	1	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	8	2	no	—
401	C₂³	—	8	2	no	—
402	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
403	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
404	Q₈	—	4	4	no	—
405	Q₈	—	4	4	no	—
406	Q₈	—	8	4	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	4	no	—
409	D₄	—	4	8	no	—
410	D₄	—	4	4	no	—
411	D₄	—	4	4	no	—
412	D₄	—	4	4	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	D₄	—	8	2	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	8	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	8	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	#120×C₄₇	1	2	yes	—
437	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
438	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
439	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
440	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
441	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
443	C₈	—	4	4	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	2	no	—
447	C₂²	—	4	2	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	4	no	—
452	C₂²	—	4	4	no	—
453	C₂²	—	8	1	no	—
454	C₂²	—	8	8	no	—
455	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
456	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
457	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
458	C₄	—	2	2	no	—
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	4	4	no	—
462	C₄	—	4	1	no	—
463	C₄	—	4	1	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₄₇×#450	1	2	yes	—
467	C₄	C₄₇×#450	1	2	yes	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	4	2	no	—
471	C₂	—	8	4	no	—
472	C₂	C₂×C₄₇×#450	1	1	yes	characteristic
473	C₂	C₄₇×#3021	1	1	yes	characteristic
474	C₂	C₄₇×#3028	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#3449	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#3227	C₂	semidirect
3. C₄₇×#2628	C₂	semidirect
4. C₄₇×#1616	C₂	semidirect
5. C₄₇×#1613	C₂	semidirect
6. C₄₇×#1517	C₂	semidirect
7. C₄₇×#1458	C₂	semidirect
17. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
22. C₄₇×#481	C₂²	semidirect
24. C₄₇×#431	C₂²	semidirect
25. C₄₇×#400	C₂²	semidirect
30. C₄₇×#382	C₂²	semidirect
32. C₄₇×#327	C₂²	semidirect
33. C₄₇×#324	C₂²	semidirect
206. #18309	C₄₇	direct (N × H)
232. #3227	C₂×C₄₇	semidirect
233. #2628	C₂×C₄₇	semidirect
234. #1616	C₂×C₄₇	semidirect
235. #1613	C₂×C₄₇	semidirect
236. #1517	C₂×C₄₇	semidirect
237. #1458	C₂×C₄₇	semidirect
254. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
259. #481	C₂²×C₄₇	semidirect
261. #431	C₂²×C₄₇	semidirect
262. #400	C₂²×C₄₇	semidirect
267. #382	C₂²×C₄₇	semidirect
269. #327	C₂²×C₄₇	semidirect
270. #324	C₂²×C₄₇	semidirect
272. C₄₇	#18309	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×#3449	2
C₄₇×#3227	2
C₄₇×#2628	2
C₄₇×#1616	2
C₄₇×#1613	2
C₄₇×#1517	2
C₄₇×#1458	2
#18309	47

Subgroups — C47×#18309 #26058007

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18309 #26058007