Subgroups — C₄₇×#18818 #26058516

Order 12032.

1004 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3216	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1641	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1640	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1621	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1620	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1555	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#559	—	2	1	no	—
13	C₄₇×#559	C₂²	1	2	yes	—
14	C₄₇×#550	—	2	1	no	—
15	C₄₇×#550	C₂²	1	2	yes	—
16	C₄₇×#546	—	2	2	no	—
17	C₄₇×#546	—	2	2	no	—
18	C₄₇×#540	—	2	2	no	—
19	C₄₇×#535	—	2	1	no	—
20	C₄₇×#533	C₂²	1	1	yes	characteristic
21	C₄₇×#532	—	2	1	no	—
22	C₄₇×#532	—	2	1	no	—
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#518	—	2	1	no	—
26	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#497	—	2	1	no	—
28	C₄₇×#493	C₂²	1	2	yes	—
29	C₄₇×#489	—	2	1	no	—
30	C₄₇×#486	C₂²	1	2	yes	—
31	C₄₇×#482	—	2	1	no	—
32	C₄₇×#475	C₂²	1	1	yes	characteristic, complemented
33	C₄₇×#474	C₂²	1	1	yes	characteristic, complemented
34	C₄₇×#462	C₂²	1	2	yes	complemented
35	C₄₇×#460	C₂²	1	1	yes	characteristic, complemented
36	C₄₇×#460	C₂²	1	2	yes	complemented
37	C₄₇×#459	—	2	2	no	—
38	C₄₇×#459	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#452	—	2	2	no	—
40	C₄₇×#449	—	2	1	no	—
41	C₄₇×#447	—	2	2	no	—
42	C₄₇×#442	—	2	1	no	—
43	C₄₇×#440	—	2	1	no	—
44	C₄₇×#432	C₂²	1	1	yes	characteristic
45	C₄₇×#432	C₂²	1	1	yes	characteristic
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₄₇×#331	C₂²	1	2	yes	—
48	C₄₇×#331	C₂²	1	2	yes	—
49	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
50	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
51	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	—	2	1	no	—
56	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₇	—	2	1	no	—
58	C₂²×D₄×C₄₇	—	2	1	no	—
59	C₂²×D₄×C₄₇	D₄	1	2	yes	—
60	C₂×Q₁₆×C₄₇	—	2	2	no	—
61	C₂×SD₁₆×C₄₇	—	2	1	no	—
62	C₂×SD₁₆×C₄₇	—	2	2	no	—
63	C₂×D₈×C₄₇	—	2	1	no	—
64	C₂×D₈×C₄₇	—	2	4	no	—
65	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
68	#127×C₄₇	—	2	2	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	—	2	1	no	—
71	#127×C₄₇	D₄	1	2	yes	—
72	#127×C₄₇	C₂³	1	1	yes	characteristic
73	#127×C₄₇	C₂³	1	2	yes	—
74	#125×C₄₇	—	2	1	no	—
75	#124×C₄₇	—	2	2	no	—
76	#124×C₄₇	—	2	2	no	—
77	#124×C₄₇	—	2	2	no	—
78	#124×C₄₇	—	2	1	no	—
79	#123×C₄₇	—	2	4	no	—
80	#123×C₄₇	—	2	4	no	—
81	C₂²⋊Q₈×C₄₇	—	2	1	no	—
82	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	2	no	—
86	#121×C₄₇	—	2	4	no	—
87	#121×C₄₇	—	2	4	no	—
88	#121×C₄₇	—	2	2	no	—
89	#121×C₄₇	—	2	1	no	—
90	#121×C₄₇	—	2	1	no	—
91	#120×C₄₇	—	2	4	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
95	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₄₇	—	2	2	no	—
97	C₄×D₄×C₄₇	—	2	2	no	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₄×D₄×C₄₇	—	2	1	no	—
100	C₄×D₄×C₄₇	—	2	1	no	—
101	C₄×D₄×C₄₇	—	2	2	no	—
102	C₄×D₄×C₄₇	—	2	2	no	—
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
107	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
108	#117×C₄₇	—	2	1	no	—
109	#117×C₄₇	—	2	1	no	—
110	#117×C₄₇	D₄	1	1	yes	characteristic
111	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
112	C₂×C₄²×C₄₇	—	2	1	no	—
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	#107×C₄₇	—	2	1	no	—
115	#106×C₄₇	—	2	1	no	—
116	C₄⋊C₈×C₄₇	—	2	1	no	—
117	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
118	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
119	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
120	#103×C₄₇	—	2	1	no	—
121	#103×C₄₇	—	2	2	no	—
122	#102×C₄₇	—	2	1	no	—
123	#102×C₄₇	—	2	4	no	—
124	#102×C₄₇	—	2	2	no	—
125	#102×C₄₇	—	2	1	no	—
126	#102×C₄₇	—	2	1	no	—
127	C₂²⋊C₈×C₄₇	—	2	1	no	—
128	C₂²⋊C₈×C₄₇	—	2	1	no	—
129	C₂²⋊C₈×C₄₇	—	2	1	no	—
130	#97×C₄₇	—	2	1	no	—
131	#97×C₄₇	—	2	1	no	—
132	C₄×C₈×C₄₇	C₂³	1	2	yes	—
133	C₂⁴×C₄₇	—	2	2	no	—
134	#41×C₄₇	—	4	1	no	—
135	#41×C₄₇	—	4	1	no	—
136	#41×C₄₇	—	8	2	no	—
137	#41×C₄₇	—	8	2	no	—
138	#41×C₄₇	—	8	2	no	—
139	#41×C₄₇	—	8	4	no	—
140	C₂×Q₈×C₄₇	—	2	1	no	—
141	C₂×Q₈×C₄₇	—	2	1	no	—
142	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
144	C₂×D₄×C₄₇	—	2	1	no	—
145	C₂×D₄×C₄₇	—	2	4	no	—
146	C₂×D₄×C₄₇	—	2	4	no	—
147	C₂×D₄×C₄₇	—	2	2	no	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	1	no	—
153	C₂×D₄×C₄₇	—	2	1	no	—
154	C₂×D₄×C₄₇	—	2	1	no	—
155	C₂×D₄×C₄₇	—	4	2	no	—
156	C₂×D₄×C₄₇	—	4	2	no	—
157	C₂×D₄×C₄₇	—	4	1	no	—
158	C₂×D₄×C₄₇	—	8	2	no	—
159	C₂×D₄×C₄₇	—	8	2	no	—
160	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
162	C₂²×C₄×C₄₇	—	2	4	no	—
163	C₂²×C₄×C₄₇	—	2	4	no	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	1	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	4	1	no	—
168	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
171	Q₁₆×C₄₇	—	8	2	no	—
172	SD₁₆×C₄₇	—	4	2	no	—
173	SD₁₆×C₄₇	—	8	2	no	—
174	D₈×C₄₇	—	4	2	no	—
175	D₈×C₄₇	—	8	4	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	2	no	—
178	C₂×C₈×C₄₇	—	2	2	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₄⋊C₄×C₄₇	—	2	1	no	—
181	C₄⋊C₄×C₄₇	—	2	1	no	—
182	C₄⋊C₄×C₄₇	—	2	1	no	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	—	2	1	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	1	no	—
188	C₄⋊C₄×C₄₇	—	2	1	no	—
189	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
190	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
192	C₂²⋊C₄×C₄₇	—	2	4	no	—
193	C₂²⋊C₄×C₄₇	—	2	4	no	—
194	C₂²⋊C₄×C₄₇	—	2	4	no	—
195	C₂²⋊C₄×C₄₇	—	2	4	no	—
196	C₂²⋊C₄×C₄₇	—	2	1	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	—	2	1	no	—
199	C₂²⋊C₄×C₄₇	—	2	1	no	—
200	C₂²⋊C₄×C₄₇	—	4	1	no	—
201	C₂²⋊C₄×C₄₇	—	4	1	no	—
202	C₄²×C₄₇	—	2	1	no	—
203	C₄²×C₄₇	—	2	1	no	—
204	C₄²×C₄₇	—	2	1	no	—
205	C₄²×C₄₇	—	2	2	no	—
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂³×C₄₇	—	2	4	no	—
211	C₂³×C₄₇	—	2	1	no	—
212	C₂³×C₄₇	—	4	4	no	—
213	C₂³×C₄₇	—	4	1	no	—
214	C₂³×C₄₇	—	8	2	no	—
215	C₂³×C₄₇	—	8	2	no	—
216	C₂³×C₄₇	#120	1	1	yes	characteristic
217	Q₈×C₄₇	—	2	1	no	—
218	Q₈×C₄₇	—	2	1	no	—
219	Q₈×C₄₇	—	2	2	no	—
220	Q₈×C₄₇	—	2	2	no	—
221	Q₈×C₄₇	—	4	2	no	—
222	Q₈×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	2	1	no	—
224	D₄×C₄₇	—	2	1	no	—
225	D₄×C₄₇	—	4	4	no	—
226	D₄×C₄₇	—	4	4	no	—
227	D₄×C₄₇	—	4	4	no	—
228	D₄×C₄₇	—	4	2	no	—
229	D₄×C₄₇	—	4	2	no	—
230	D₄×C₄₇	—	4	2	no	—
231	D₄×C₄₇	—	4	2	no	—
232	D₄×C₄₇	—	4	1	no	—
233	D₄×C₄₇	—	4	1	no	—
234	D₄×C₄₇	—	4	2	no	—
235	D₄×C₄₇	—	4	2	no	—
236	D₄×C₄₇	—	4	2	no	—
237	D₄×C₄₇	—	8	2	no	—
238	D₄×C₄₇	—	8	4	no	—
239	D₄×C₄₇	—	8	4	no	—
240	D₄×C₄₇	—	8	2	no	—
241	C₂×C₄×C₄₇	—	2	1	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	4	1	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	4	1	no	—
254	C₂×C₄×C₄₇	—	8	2	no	—
255	C₂×C₄×C₄₇	—	8	4	no	—
256	C₂×C₄×C₄₇	—	8	4	no	—
257	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
258	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
259	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
262	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
263	C₈×C₄₇	—	4	2	no	—
264	C₈×C₄₇	—	4	1	no	—
265	C₈×C₄₇	—	4	1	no	—
266	C₈×C₄₇	—	4	2	no	—
267	#18818	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂²×C₄₇	—	2	1	no	—
269	C₂²×C₄₇	—	2	1	no	—
270	C₂²×C₄₇	—	2	1	no	—
271	C₂²×C₄₇	—	4	1	no	—
272	C₂²×C₄₇	—	4	4	no	—
273	C₂²×C₄₇	—	4	1	no	—
274	C₂²×C₄₇	—	4	4	no	—
275	C₂²×C₄₇	—	4	1	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	8	1	no	—
278	C₂²×C₄₇	—	8	1	no	—
279	C₂²×C₄₇	—	8	1	no	—
280	C₂²×C₄₇	—	16	4	no	—
281	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
282	C₄×C₄₇	—	2	1	no	—
283	C₄×C₄₇	—	2	1	no	—
284	C₄×C₄₇	—	2	1	no	—
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	4	1	no	—
287	C₄×C₄₇	—	4	1	no	—
288	C₄×C₄₇	—	4	2	no	—
289	C₄×C₄₇	—	4	1	no	—
290	C₄×C₄₇	—	4	2	no	—
291	C₄×C₄₇	—	8	1	no	—
292	C₄×C₄₇	#575	1	1	yes	characteristic
293	C₄×C₄₇	#575	1	1	yes	characteristic
294	C₄×C₄₇	#576	1	2	yes	—
295	#3508	C₂×C₄₇	1	1	yes	characteristic, complemented
296	#3216	C₂×C₄₇	1	1	yes	characteristic, complemented
297	#3205	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#3115	C₂×C₄₇	1	1	yes	characteristic, complemented
299	#1641	C₂×C₄₇	1	2	yes	complemented
300	#1640	C₂×C₄₇	1	2	yes	complemented
301	#1621	C₂×C₄₇	1	2	yes	complemented
302	#1620	C₂×C₄₇	1	2	yes	complemented
303	#1555	C₂×C₄₇	1	1	yes	characteristic, complemented
304	#1497	C₂×C₄₇	1	1	yes	characteristic, complemented
305	#1488	C₂×C₄₇	1	1	yes	characteristic, complemented
306	C₂×C₄₇	—	4	1	no	—
307	C₂×C₄₇	—	8	1	no	—
308	C₂×C₄₇	—	8	4	no	—
309	C₂×C₄₇	—	16	1	no	—
310	C₂×C₄₇	#3005	1	1	yes	characteristic
311	C₂×C₄₇	#3008	1	1	yes	characteristic
312	C₂×C₄₇	#3019	1	1	yes	characteristic
313	#559	—	2	1	no	—
314	#559	C₂²×C₄₇	1	2	yes	—
315	#550	—	2	1	no	—
316	#550	C₂²×C₄₇	1	2	yes	—
317	#546	—	2	2	no	—
318	#546	—	2	2	no	—
319	#540	—	2	2	no	—
320	#535	—	2	1	no	—
321	#533	C₂²×C₄₇	1	1	yes	characteristic
322	#532	—	2	1	no	—
323	#532	—	2	1	no	—
324	#532	C₂²×C₄₇	1	1	yes	characteristic
325	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
326	#518	—	2	1	no	—
327	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
328	#497	—	2	1	no	—
329	#493	C₂²×C₄₇	1	2	yes	—
330	#489	—	2	1	no	—
331	#486	C₂²×C₄₇	1	2	yes	—
332	#482	—	2	1	no	—
333	#475	C₂²×C₄₇	1	1	yes	characteristic, complemented
334	#474	C₂²×C₄₇	1	1	yes	characteristic, complemented
335	#462	C₂²×C₄₇	1	2	yes	complemented
336	#460	C₂²×C₄₇	1	1	yes	characteristic, complemented
337	#460	C₂²×C₄₇	1	2	yes	complemented
338	#459	—	2	2	no	—
339	#459	C₂²×C₄₇	1	1	yes	characteristic, complemented
340	#452	—	2	2	no	—
341	#449	—	2	1	no	—
342	#447	—	2	2	no	—
343	#442	—	2	1	no	—
344	#440	—	2	1	no	—
345	#432	C₂²×C₄₇	1	1	yes	characteristic
346	#432	C₂²×C₄₇	1	1	yes	characteristic
347	#431	C₂²×C₄₇	1	1	yes	characteristic
348	#331	C₂²×C₄₇	1	2	yes	—
349	#331	C₂²×C₄₇	1	2	yes	—
350	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
351	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
352	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
353	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
354	C₄₇	#18818	1	1	yes	characteristic, direct product factor, Sylow
355	C₂×#41	—	2	2	no	—
356	C₂×#41	—	2	2	no	—
357	C₂×#41	—	2	1	no	—
358	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
359	C₂²×D₄	—	2	1	no	—
360	C₂²×D₄	—	2	1	no	—
361	C₂²×D₄	D₄×C₄₇	1	2	yes	—
362	C₂×Q₁₆	—	2	2	no	—
363	C₂×SD₁₆	—	2	1	no	—
364	C₂×SD₁₆	—	2	2	no	—
365	C₂×D₈	—	2	1	no	—
366	C₂×D₈	—	2	4	no	—
367	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
368	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
370	#127	—	2	2	no	—
371	#127	—	2	1	no	—
372	#127	—	2	1	no	—
373	#127	D₄×C₄₇	1	2	yes	—
374	#127	C₂³×C₄₇	1	1	yes	characteristic
375	#127	C₂³×C₄₇	1	2	yes	—
376	#125	—	2	1	no	—
377	#124	—	2	2	no	—
378	#124	—	2	2	no	—
379	#124	—	2	2	no	—
380	#124	—	2	1	no	—
381	#123	—	2	4	no	—
382	#123	—	2	4	no	—
383	C₂²⋊Q₈	—	2	1	no	—
384	C₂²⋊Q₈	D₄×C₄₇	1	2	yes	—
385	#121	—	2	2	no	—
386	#121	—	2	2	no	—
387	#121	—	2	2	no	—
388	#121	—	2	4	no	—
389	#121	—	2	4	no	—
390	#121	—	2	2	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	#120	—	2	4	no	—
394	C₄×Q₈	—	2	1	no	—
395	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
396	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
397	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
398	C₄×D₄	—	2	2	no	—
399	C₄×D₄	—	2	2	no	—
400	C₄×D₄	—	2	2	no	—
401	C₄×D₄	—	2	1	no	—
402	C₄×D₄	—	2	1	no	—
403	C₄×D₄	—	2	2	no	—
404	C₄×D₄	—	2	2	no	—
405	C₄×D₄	—	2	2	no	—
406	C₄×D₄	—	2	1	no	—
407	C₄×D₄	—	2	1	no	—
408	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
409	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
410	#117	—	2	1	no	—
411	#117	—	2	1	no	—
412	#117	D₄×C₄₇	1	1	yes	characteristic
413	C₂×C₂²⋊C₄	—	2	4	no	—
414	C₂×C₄²	—	2	1	no	—
415	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
416	#107	—	2	1	no	—
417	#106	—	2	1	no	—
418	C₄⋊C₈	—	2	1	no	—
419	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
420	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
422	#103	—	2	1	no	—
423	#103	—	2	2	no	—
424	#102	—	2	1	no	—
425	#102	—	2	4	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	2	no	—
429	C₂²⋊C₈	—	2	1	no	—
430	C₂²⋊C₈	—	2	1	no	—
431	C₂²⋊C₈	—	2	1	no	—
432	#97	—	2	1	no	—
433	#97	—	2	1	no	—
434	C₄×C₈	C₂³×C₄₇	1	2	yes	—
435	C₂⁴	—	2	2	no	—
436	#41	—	4	1	no	—
437	#41	—	4	1	no	—
438	#41	—	8	2	no	—
439	#41	—	8	2	no	—
440	#41	—	8	2	no	—
441	#41	—	8	4	no	—
442	C₂×Q₈	—	2	1	no	—
443	C₂×Q₈	—	2	1	no	—
444	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
445	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	4	2	no	—
458	C₂×D₄	—	4	2	no	—
459	C₂×D₄	—	4	1	no	—
460	C₂×D₄	—	8	2	no	—
461	C₂×D₄	—	8	2	no	—
462	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
463	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
464	C₂²×C₄	—	2	4	no	—
465	C₂²×C₄	—	2	4	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
472	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
473	Q₁₆	—	8	2	no	—
474	SD₁₆	—	4	2	no	—
475	SD₁₆	—	8	2	no	—
476	D₈	—	4	2	no	—
477	D₈	—	8	4	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
492	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
493	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
494	C₂²⋊C₄	—	2	4	no	—
495	C₂²⋊C₄	—	2	4	no	—
496	C₂²⋊C₄	—	2	4	no	—
497	C₂²⋊C₄	—	2	4	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	4	1	no	—
503	C₂²⋊C₄	—	4	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	2	1	no	—
507	C₄²	—	2	2	no	—
508	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
509	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
510	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
511	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
512	C₂³	—	2	4	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	4	4	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	8	2	no	—
517	C₂³	—	8	2	no	—
518	C₂³	#120×C₄₇	1	1	yes	characteristic
519	Q₈	—	2	1	no	—
520	Q₈	—	2	1	no	—
521	Q₈	—	2	2	no	—
522	Q₈	—	2	2	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	D₄	—	2	1	no	—
526	D₄	—	2	1	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	2	no	—
533	D₄	—	4	2	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	8	2	no	—
540	D₄	—	8	4	no	—
541	D₄	—	8	4	no	—
542	D₄	—	8	2	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	4	no	—
558	C₂×C₄	—	8	4	no	—
559	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
560	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
561	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
562	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
563	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
564	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
565	C₈	—	4	2	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	2	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	2	1	no	—
571	C₂²	—	2	1	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	4	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	4	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	4	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	16	4	no	—
582	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	2	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	8	1	no	—
593	C₄	C₄₇×#575	1	1	yes	characteristic
594	C₄	C₄₇×#575	1	1	yes	characteristic
595	C₄	C₄₇×#576	1	2	yes	—
596	C₂	—	4	1	no	—
597	C₂	—	8	4	no	—
598	C₂	—	8	1	no	—
599	C₂	—	16	1	no	—
600	C₂	C₄₇×#3005	1	1	yes	characteristic
601	C₂	C₄₇×#3008	1	1	yes	characteristic
602	C₂	C₄₇×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ 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
1. C₄₇×#3508	C₂	semidirect
2. C₄₇×#3216	C₂	semidirect
3. C₄₇×#3205	C₂	semidirect
4. C₄₇×#3115	C₂	semidirect
5. C₄₇×#1641	C₂	semidirect
6. C₄₇×#1640	C₂	semidirect
7. C₄₇×#1621	C₂	semidirect
8. C₄₇×#1620	C₂	semidirect
9. C₄₇×#1555	C₂	semidirect
10. C₄₇×#1497	C₂	semidirect
11. C₄₇×#1488	C₂	semidirect
32. C₄₇×#475	C₂²	semidirect
33. C₄₇×#474	C₂²	semidirect
34. C₄₇×#462	C₂²	semidirect
35. C₄₇×#460	C₂²	semidirect
36. C₄₇×#460	C₂²	semidirect
38. C₄₇×#459	C₂²	semidirect
49. C₄₇×Q₈⋊C₈	C₂²	semidirect
50. C₄₇×Q₈⋊C₈	C₂²	semidirect
51. C₄₇×Q₈⋊C₈	C₂²	semidirect
52. C₄₇×D₄⋊C₈	C₂²	semidirect
267. #18818	C₄₇	direct (N × H)
295. #3508	C₂×C₄₇	semidirect
296. #3216	C₂×C₄₇	semidirect
297. #3205	C₂×C₄₇	semidirect
298. #3115	C₂×C₄₇	semidirect
299. #1641	C₂×C₄₇	semidirect
300. #1640	C₂×C₄₇	semidirect
301. #1621	C₂×C₄₇	semidirect
302. #1620	C₂×C₄₇	semidirect
303. #1555	C₂×C₄₇	semidirect
304. #1497	C₂×C₄₇	semidirect
305. #1488	C₂×C₄₇	semidirect
333. #475	C₂²×C₄₇	semidirect
334. #474	C₂²×C₄₇	semidirect
335. #462	C₂²×C₄₇	semidirect
336. #460	C₂²×C₄₇	semidirect
337. #460	C₂²×C₄₇	semidirect
339. #459	C₂²×C₄₇	semidirect
350. Q₈⋊C₈	C₂²×C₄₇	semidirect
351. Q₈⋊C₈	C₂²×C₄₇	semidirect
352. Q₈⋊C₈	C₂²×C₄₇	semidirect
353. D₄⋊C₈	C₂²×C₄₇	semidirect
354. C₄₇	#18818	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×#3508	2
C₄₇×#3216	2
C₄₇×#3205	2
C₄₇×#3115	2
C₄₇×#1641	2
C₄₇×#1640	2
C₄₇×#1621	2
C₄₇×#1620	2
C₄₇×#1555	2
C₄₇×#1497	2
C₄₇×#1488	2
#18818	47

Subgroups — C47×#18818 #26058516

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18818 #26058516