Subgroups — C₄₇×#18857 #26058555

Order 12032.

956 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3109	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1635	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1634	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1625	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1624	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1559	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#559	—	2	2	no	—
13	C₄₇×#556	—	2	1	no	—
14	C₄₇×#555	C₂²	1	2	yes	—
15	C₄₇×#553	—	2	2	no	—
16	C₄₇×#550	—	2	1	no	—
17	C₄₇×#547	C₂²	1	2	yes	—
18	C₄₇×#538	—	2	2	no	—
19	C₄₇×#535	—	2	1	no	—
20	C₄₇×#533	C₂²	1	1	yes	characteristic
21	C₄₇×#532	C₂²	1	1	yes	characteristic
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₄₇×#525	—	2	2	no	—
24	C₄₇×#520	—	2	1	no	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#494	C₂²	1	1	yes	characteristic, complemented
27	C₄₇×#492	C₂²	1	1	yes	characteristic, complemented
28	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
30	C₄₇×#481	—	2	1	no	—
31	C₄₇×#476	—	2	1	no	—
32	C₄₇×#476	C₂²	1	2	yes	—
33	C₄₇×#476	C₂²	1	2	yes	complemented
34	C₄₇×#469	—	2	2	no	—
35	C₄₇×#464	—	2	2	no	—
36	C₄₇×#459	—	2	1	no	—
37	C₄₇×#459	C₂²	1	2	yes	—
38	C₄₇×#459	C₂²	1	2	yes	complemented
39	C₄₇×#452	—	2	2	no	—
40	C₄₇×#447	—	2	1	no	—
41	C₄₇×#442	—	2	2	no	—
42	C₄₇×#432	C₂²	1	1	yes	characteristic
43	C₄₇×#431	C₂²	1	1	yes	characteristic
44	C₄₇×#423	C₂²	1	1	yes	characteristic
45	C₄₇×#333	C₂²	1	2	yes	complemented
46	C₄₇×#332	C₂²	1	2	yes	complemented
47	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
48	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
49	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
51	C₂×#41×C₄₇	—	2	2	no	—
52	C₂×#41×C₄₇	—	2	1	no	—
53	C₂×#41×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	C₂×Q₁₆×C₄₇	—	2	2	no	—
57	C₂×SD₁₆×C₄₇	—	2	2	no	—
58	C₂×D₈×C₄₇	—	2	2	no	—
59	C₂×D₈×C₄₇	—	2	2	no	—
60	C₂×M₁₆×C₄₇	—	2	1	no	—
61	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
65	#127×C₄₇	—	2	2	no	—
66	#127×C₄₇	D₄	1	1	yes	characteristic
67	#127×C₄₇	C₂³	1	1	yes	characteristic
68	#126×C₄₇	—	2	4	no	—
69	#125×C₄₇	—	2	1	no	—
70	#124×C₄₇	—	2	2	no	—
71	#124×C₄₇	—	2	4	no	—
72	#124×C₄₇	—	2	1	no	—
73	#124×C₄₇	—	2	1	no	—
74	#123×C₄₇	—	2	4	no	—
75	#123×C₄₇	—	2	4	no	—
76	C₂²⋊Q₈×C₄₇	—	2	1	no	—
77	C₂²⋊Q₈×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
79	#121×C₄₇	—	2	4	no	—
80	#121×C₄₇	—	2	2	no	—
81	#121×C₄₇	—	2	2	no	—
82	#121×C₄₇	—	2	2	no	—
83	#121×C₄₇	—	2	1	no	—
84	#121×C₄₇	—	2	1	no	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	D₄	1	2	yes	—
87	#120×C₄₇	—	2	4	no	—
88	C₄×Q₈×C₄₇	—	2	2	no	—
89	C₄×Q₈×C₄₇	—	2	1	no	—
90	C₄×Q₈×C₄₇	D₄	1	2	yes	—
91	C₄×D₄×C₄₇	—	2	4	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	4	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	D₄	1	2	yes	—
100	C₄×D₄×C₄₇	C₂³	1	2	yes	—
101	C₄×D₄×C₄₇	C₂³	1	2	yes	—
102	#117×C₄₇	—	2	1	no	—
103	#117×C₄₇	—	2	2	no	—
104	#117×C₄₇	—	2	2	no	—
105	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	#106×C₄₇	—	2	2	no	—
110	#106×C₄₇	—	2	2	no	—
111	C₄⋊C₈×C₄₇	—	2	1	no	—
112	C₄⋊C₈×C₄₇	—	2	1	no	—
113	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
114	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
115	#103×C₄₇	—	2	2	no	—
116	#102×C₄₇	—	2	2	no	—
117	#102×C₄₇	—	2	2	no	—
118	#102×C₄₇	—	2	2	no	—
119	#102×C₄₇	—	2	2	no	—
120	#102×C₄₇	—	2	2	no	—
121	C₂²⋊C₈×C₄₇	—	2	1	no	—
122	C₂²⋊C₈×C₄₇	—	2	1	no	—
123	#97×C₄₇	—	2	1	no	—
124	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂⁴×C₄₇	—	2	1	no	—
127	#41×C₄₇	—	4	4	no	—
128	#41×C₄₇	—	8	2	no	—
129	#41×C₄₇	—	8	2	no	—
130	#41×C₄₇	—	8	2	no	—
131	C₂×Q₈×C₄₇	—	2	1	no	—
132	C₂×Q₈×C₄₇	—	2	1	no	—
133	C₂×Q₈×C₄₇	—	2	1	no	—
134	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	4	no	—
137	C₂×D₄×C₄₇	—	2	4	no	—
138	C₂×D₄×C₄₇	—	2	1	no	—
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	1	no	—
141	C₂×D₄×C₄₇	—	2	1	no	—
142	C₂×D₄×C₄₇	—	2	1	no	—
143	C₂×D₄×C₄₇	—	2	1	no	—
144	C₂×D₄×C₄₇	—	4	2	no	—
145	C₂×D₄×C₄₇	—	4	1	no	—
146	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	2	no	—
151	C₂²×C₄×C₄₇	—	2	2	no	—
152	C₂²×C₄×C₄₇	—	2	2	no	—
153	C₂²×C₄×C₄₇	—	4	1	no	—
154	C₂²×C₄×C₄₇	—	8	1	no	—
155	C₂²×C₄×C₄₇	—	8	1	no	—
156	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	Q₁₆×C₄₇	—	8	2	no	—
160	SD₁₆×C₄₇	—	8	2	no	—
161	D₈×C₄₇	—	4	4	no	—
162	D₈×C₄₇	—	8	2	no	—
163	M₁₆×C₄₇	—	8	1	no	—
164	C₂×C₈×C₄₇	—	2	1	no	—
165	C₂×C₈×C₄₇	—	2	2	no	—
166	C₂×C₈×C₄₇	—	2	1	no	—
167	C₂×C₈×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	4	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	2	1	no	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	1	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
178	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
181	C₂²⋊C₄×C₄₇	—	2	4	no	—
182	C₂²⋊C₄×C₄₇	—	2	4	no	—
183	C₂²⋊C₄×C₄₇	—	2	4	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	2	2	no	—
189	C₂²⋊C₄×C₄₇	—	4	1	no	—
190	C₂²⋊C₄×C₄₇	—	4	1	no	—
191	C₄²×C₄₇	—	2	4	no	—
192	C₄²×C₄₇	—	2	2	no	—
193	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
196	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	4	2	no	—
200	C₂³×C₄₇	—	4	1	no	—
201	C₂³×C₄₇	—	8	1	no	—
202	C₂³×C₄₇	—	8	1	no	—
203	C₂³×C₄₇	#120	1	1	yes	characteristic
204	Q₈×C₄₇	—	4	2	no	—
205	Q₈×C₄₇	—	4	2	no	—
206	Q₈×C₄₇	—	4	2	no	—
207	Q₈×C₄₇	—	4	1	no	—
208	Q₈×C₄₇	—	4	1	no	—
209	D₄×C₄₇	—	2	2	no	—
210	D₄×C₄₇	—	2	2	no	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	2	2	no	—
213	D₄×C₄₇	—	4	2	no	—
214	D₄×C₄₇	—	4	2	no	—
215	D₄×C₄₇	—	4	2	no	—
216	D₄×C₄₇	—	4	4	no	—
217	D₄×C₄₇	—	4	2	no	—
218	D₄×C₄₇	—	4	1	no	—
219	D₄×C₄₇	—	4	1	no	—
220	D₄×C₄₇	—	8	1	no	—
221	D₄×C₄₇	—	8	4	no	—
222	D₄×C₄₇	—	8	4	no	—
223	D₄×C₄₇	—	8	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	1	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	4	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	8	2	no	—
237	C₂×C₄×C₄₇	—	8	2	no	—
238	C₂×C₄×C₄₇	—	8	1	no	—
239	C₂×C₄×C₄₇	—	8	4	no	—
240	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
241	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
242	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₄₇	—	4	1	no	—
247	C₈×C₄₇	—	4	1	no	—
248	C₈×C₄₇	—	4	2	no	—
249	C₈×C₄₇	—	4	2	no	—
250	#18857	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂²×C₄₇	—	2	1	no	—
252	C₂²×C₄₇	—	2	1	no	—
253	C₂²×C₄₇	—	2	1	no	—
254	C₂²×C₄₇	—	4	2	no	—
255	C₂²×C₄₇	—	4	2	no	—
256	C₂²×C₄₇	—	4	2	no	—
257	C₂²×C₄₇	—	4	2	no	—
258	C₂²×C₄₇	—	4	2	no	—
259	C₂²×C₄₇	—	4	2	no	—
260	C₂²×C₄₇	—	8	4	no	—
261	C₂²×C₄₇	—	8	1	no	—
262	C₂²×C₄₇	—	8	1	no	—
263	C₂²×C₄₇	—	8	1	no	—
264	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
265	C₄×C₄₇	—	2	1	no	—
266	C₄×C₄₇	—	2	1	no	—
267	C₄×C₄₇	—	2	1	no	—
268	C₄×C₄₇	—	2	1	no	—
269	C₄×C₄₇	—	4	2	no	—
270	C₄×C₄₇	—	4	2	no	—
271	C₄×C₄₇	—	4	2	no	—
272	C₄×C₄₇	—	4	2	no	—
273	C₄×C₄₇	—	8	1	no	—
274	C₄×C₄₇	#575	1	2	yes	—
275	C₄×C₄₇	#576	1	1	yes	characteristic
276	C₄×C₄₇	#577	1	1	yes	characteristic
277	#3506	C₂×C₄₇	1	1	yes	characteristic, complemented
278	#3253	C₂×C₄₇	1	1	yes	characteristic, complemented
279	#3210	C₂×C₄₇	1	1	yes	characteristic, complemented
280	#3109	C₂×C₄₇	1	1	yes	characteristic, complemented
281	#1635	C₂×C₄₇	1	2	yes	complemented
282	#1634	C₂×C₄₇	1	2	yes	complemented
283	#1625	C₂×C₄₇	1	2	yes	complemented
284	#1624	C₂×C₄₇	1	2	yes	complemented
285	#1559	C₂×C₄₇	1	1	yes	characteristic, complemented
286	#1496	C₂×C₄₇	1	1	yes	characteristic, complemented
287	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
288	C₂×C₄₇	—	4	1	no	—
289	C₂×C₄₇	—	8	2	no	—
290	C₂×C₄₇	—	8	2	no	—
291	C₂×C₄₇	—	16	1	no	—
292	C₂×C₄₇	#3005	1	1	yes	characteristic
293	C₂×C₄₇	#3012	1	1	yes	characteristic
294	C₂×C₄₇	#3021	1	1	yes	characteristic
295	#559	—	2	2	no	—
296	#556	—	2	1	no	—
297	#555	C₂²×C₄₇	1	2	yes	—
298	#553	—	2	2	no	—
299	#550	—	2	1	no	—
300	#547	C₂²×C₄₇	1	2	yes	—
301	#538	—	2	2	no	—
302	#535	—	2	1	no	—
303	#533	C₂²×C₄₇	1	1	yes	characteristic
304	#532	C₂²×C₄₇	1	1	yes	characteristic
305	#532	C₂²×C₄₇	1	1	yes	characteristic
306	#525	—	2	2	no	—
307	#520	—	2	1	no	—
308	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
309	#494	C₂²×C₄₇	1	1	yes	characteristic, complemented
310	#492	C₂²×C₄₇	1	1	yes	characteristic, complemented
311	#487	C₂²×C₄₇	1	1	yes	characteristic, complemented
312	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
313	#481	—	2	1	no	—
314	#476	—	2	1	no	—
315	#476	C₂²×C₄₇	1	2	yes	—
316	#476	C₂²×C₄₇	1	2	yes	complemented
317	#469	—	2	2	no	—
318	#464	—	2	2	no	—
319	#459	—	2	1	no	—
320	#459	C₂²×C₄₇	1	2	yes	—
321	#459	C₂²×C₄₇	1	2	yes	complemented
322	#452	—	2	2	no	—
323	#447	—	2	1	no	—
324	#442	—	2	2	no	—
325	#432	C₂²×C₄₇	1	1	yes	characteristic
326	#431	C₂²×C₄₇	1	1	yes	characteristic
327	#423	C₂²×C₄₇	1	1	yes	characteristic
328	#333	C₂²×C₄₇	1	2	yes	complemented
329	#332	C₂²×C₄₇	1	2	yes	complemented
330	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
331	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
332	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
333	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
334	C₄₇	#18857	1	1	yes	characteristic, direct product factor, Sylow
335	C₂×#41	—	2	2	no	—
336	C₂×#41	—	2	1	no	—
337	C₂×#41	—	2	1	no	—
338	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
339	C₂³×C₄	—	2	1	no	—
340	C₂×Q₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×D₈	—	2	2	no	—
343	C₂×D₈	—	2	2	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
346	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
347	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
349	#127	—	2	2	no	—
350	#127	D₄×C₄₇	1	1	yes	characteristic
351	#127	C₂³×C₄₇	1	1	yes	characteristic
352	#126	—	2	4	no	—
353	#125	—	2	1	no	—
354	#124	—	2	2	no	—
355	#124	—	2	4	no	—
356	#124	—	2	1	no	—
357	#124	—	2	1	no	—
358	#123	—	2	4	no	—
359	#123	—	2	4	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	D₄×C₄₇	1	2	yes	—
363	#121	—	2	4	no	—
364	#121	—	2	2	no	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#121	—	2	1	no	—
368	#121	—	2	1	no	—
369	#121	—	2	1	no	—
370	#121	D₄×C₄₇	1	2	yes	—
371	#120	—	2	4	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	D₄×C₄₇	1	2	yes	—
375	C₄×D₄	—	2	4	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	D₄×C₄₇	1	2	yes	—
384	C₄×D₄	C₂³×C₄₇	1	2	yes	—
385	C₄×D₄	C₂³×C₄₇	1	2	yes	—
386	#117	—	2	1	no	—
387	#117	—	2	2	no	—
388	#117	—	2	2	no	—
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
391	C₂×C₂²⋊C₄	—	2	1	no	—
392	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
393	#106	—	2	2	no	—
394	#106	—	2	2	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
398	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
399	#103	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#102	—	2	2	no	—
404	#102	—	2	2	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	#97	—	2	1	no	—
408	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
409	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
410	C₂⁴	—	2	1	no	—
411	#41	—	4	4	no	—
412	#41	—	8	2	no	—
413	#41	—	8	2	no	—
414	#41	—	8	2	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
419	C₂×D₄	—	2	2	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	4	no	—
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	2	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
431	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	8	1	no	—
439	C₂²×C₄	—	8	1	no	—
440	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
441	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
443	Q₁₆	—	8	2	no	—
444	SD₁₆	—	8	2	no	—
445	D₈	—	4	4	no	—
446	D₈	—	8	2	no	—
447	M₁₆	—	8	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	2	no	—
452	C₄⋊C₄	—	2	4	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	2	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
463	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
464	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	2	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₄²	—	2	4	no	—
476	C₄²	—	2	2	no	—
477	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
478	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
480	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	4	2	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	8	1	no	—
486	C₂³	—	8	1	no	—
487	C₂³	#120×C₄₇	1	1	yes	characteristic
488	Q₈	—	4	2	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	1	no	—
492	Q₈	—	4	1	no	—
493	D₄	—	2	2	no	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	4	2	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	1	no	—
503	D₄	—	4	1	no	—
504	D₄	—	8	1	no	—
505	D₄	—	8	4	no	—
506	D₄	—	8	4	no	—
507	D₄	—	8	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	4	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	8	2	no	—
521	C₂×C₄	—	8	2	no	—
522	C₂×C₄	—	8	1	no	—
523	C₂×C₄	—	8	4	no	—
524	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
525	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
526	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
527	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
528	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
529	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
530	C₈	—	4	1	no	—
531	C₈	—	4	1	no	—
532	C₈	—	4	2	no	—
533	C₈	—	4	2	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	4	2	no	—
538	C₂²	—	4	2	no	—
539	C₂²	—	4	2	no	—
540	C₂²	—	4	2	no	—
541	C₂²	—	4	2	no	—
542	C₂²	—	4	2	no	—
543	C₂²	—	8	4	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	—	8	1	no	—
547	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	4	2	no	—
555	C₄	—	4	2	no	—
556	C₄	—	8	1	no	—
557	C₄	C₄₇×#575	1	2	yes	—
558	C₄	C₄₇×#576	1	1	yes	characteristic
559	C₄	C₄₇×#577	1	1	yes	characteristic
560	C₂	—	4	1	no	—
561	C₂	—	8	2	no	—
562	C₂	—	8	2	no	—
563	C₂	—	16	1	no	—
564	C₂	C₄₇×#3005	1	1	yes	characteristic
565	C₂	C₄₇×#3012	1	1	yes	characteristic
566	C₂	C₄₇×#3021	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×#3506	C₂	semidirect
2. C₄₇×#3253	C₂	semidirect
3. C₄₇×#3210	C₂	semidirect
4. C₄₇×#3109	C₂	semidirect
5. C₄₇×#1635	C₂	semidirect
6. C₄₇×#1634	C₂	semidirect
7. C₄₇×#1625	C₂	semidirect
8. C₄₇×#1624	C₂	semidirect
9. C₄₇×#1559	C₂	semidirect
10. C₄₇×#1496	C₂	semidirect
11. C₄₇×#1486	C₂	semidirect
26. C₄₇×#494	C₂²	semidirect
27. C₄₇×#492	C₂²	semidirect
28. C₄₇×#487	C₂²	semidirect
29. C₄₇×#486	C₂²	semidirect
33. C₄₇×#476	C₂²	semidirect
38. C₄₇×#459	C₂²	semidirect
45. C₄₇×#333	C₂²	semidirect
46. C₄₇×#332	C₂²	semidirect
49. C₄₇×D₄⋊C₈	C₂²	semidirect
50. C₄₇×D₄⋊C₈	C₂²	semidirect
250. #18857	C₄₇	direct (N × H)
277. #3506	C₂×C₄₇	semidirect
278. #3253	C₂×C₄₇	semidirect
279. #3210	C₂×C₄₇	semidirect
280. #3109	C₂×C₄₇	semidirect
281. #1635	C₂×C₄₇	semidirect
282. #1634	C₂×C₄₇	semidirect
283. #1625	C₂×C₄₇	semidirect
284. #1624	C₂×C₄₇	semidirect
285. #1559	C₂×C₄₇	semidirect
286. #1496	C₂×C₄₇	semidirect
287. #1486	C₂×C₄₇	semidirect
309. #494	C₂²×C₄₇	semidirect
310. #492	C₂²×C₄₇	semidirect
311. #487	C₂²×C₄₇	semidirect
312. #486	C₂²×C₄₇	semidirect
316. #476	C₂²×C₄₇	semidirect
321. #459	C₂²×C₄₇	semidirect
328. #333	C₂²×C₄₇	semidirect
329. #332	C₂²×C₄₇	semidirect
332. D₄⋊C₈	C₂²×C₄₇	semidirect
333. D₄⋊C₈	C₂²×C₄₇	semidirect
334. C₄₇	#18857	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×#3506	2
C₄₇×#3253	2
C₄₇×#3210	2
C₄₇×#3109	2
C₄₇×#1635	2
C₄₇×#1634	2
C₄₇×#1625	2
C₄₇×#1624	2
C₄₇×#1559	2
C₄₇×#1496	2
C₄₇×#1486	2
#18857	47

Subgroups — C47×#18857 #26058555

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18857 #26058555