Subgroups — C₄₇×#18832 #26058530

Order 12032.

928 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1650	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1647	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1628	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1625	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1556	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1496	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1488	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#556	C₂²	1	2	yes	—
13	C₄₇×#555	—	2	1	no	—
14	C₄₇×#554	—	2	1	no	—
15	C₄₇×#553	—	2	2	no	—
16	C₄₇×#548	—	2	2	no	—
17	C₄₇×#547	C₂²	1	2	yes	—
18	C₄₇×#542	—	2	2	no	—
19	C₄₇×#537	—	2	1	no	—
20	C₄₇×#533	—	2	1	no	—
21	C₄₇×#532	—	2	1	no	—
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#520	—	2	1	no	—
26	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#500	C₂²	1	2	yes	—
28	C₄₇×#496	—	2	1	no	—
29	C₄₇×#489	—	2	1	no	—
30	C₄₇×#486	C₂²	1	2	yes	—
31	C₄₇×#482	—	2	1	no	—
32	C₄₇×#480	—	2	2	no	—
33	C₄₇×#475	C₂²	1	1	yes	characteristic
34	C₄₇×#474	—	2	2	no	—
35	C₄₇×#474	C₂²	1	1	yes	characteristic
36	C₄₇×#461	C₂²	1	2	yes	—
37	C₄₇×#460	C₂²	1	1	yes	characteristic
38	C₄₇×#459	C₂²	1	1	yes	characteristic
39	C₄₇×#459	C₂²	1	2	yes	—
40	C₄₇×#449	—	2	1	no	—
41	C₄₇×#449	—	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×#332	C₂²	1	2	yes	—
48	C₄₇×#332	C₂²	1	2	yes	—
49	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₄₇	—	2	2	no	—
54	C₂×#41×C₄₇	—	2	1	no	—
55	C₂×#41×C₄₇	—	2	1	no	—
56	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
57	C₂²×Q₈×C₄₇	—	2	1	no	—
58	C₂×SD₁₆×C₄₇	—	2	1	no	—
59	C₂×SD₁₆×C₄₇	—	2	2	no	—
60	C₂×D₈×C₄₇	—	2	1	no	—
61	C₂×D₈×C₄₇	—	2	2	no	—
62	C₄⋊Q₈×C₄₇	—	2	1	no	—
63	C₄⋊Q₈×C₄₇	—	2	1	no	—
64	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
65	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
67	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
68	#127×C₄₇	D₄	1	1	yes	characteristic
69	#127×C₄₇	C₂³	1	1	yes	characteristic
70	#126×C₄₇	—	2	4	no	—
71	#125×C₄₇	—	2	2	no	—
72	#124×C₄₇	—	2	4	no	—
73	#124×C₄₇	—	2	2	no	—
74	#124×C₄₇	—	2	1	no	—
75	#124×C₄₇	—	2	1	no	—
76	#123×C₄₇	—	2	4	no	—
77	C₂²⋊Q₈×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	—	2	4	no	—
79	C₂²⋊Q₈×C₄₇	—	2	2	no	—
80	C₂²⋊Q₈×C₄₇	—	2	2	no	—
81	#121×C₄₇	—	2	2	no	—
82	#121×C₄₇	—	2	2	no	—
83	#121×C₄₇	—	2	4	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	1	no	—
87	#121×C₄₇	—	2	1	no	—
88	#121×C₄₇	D₄	1	2	yes	—
89	C₄×Q₈×C₄₇	—	2	2	no	—
90	C₄×Q₈×C₄₇	—	2	2	no	—
91	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₄×D₄×C₄₇	—	2	4	no	—
95	C₄×D₄×C₄₇	—	2	2	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	—	2	1	no	—
100	C₄×D₄×C₄₇	—	2	1	no	—
101	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
102	C₄×D₄×C₄₇	C₂³	1	2	yes	—
103	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
104	#117×C₄₇	—	2	2	no	—
105	#117×C₄₇	—	2	2	no	—
106	#117×C₄₇	—	2	1	no	—
107	#117×C₄₇	D₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
111	C₂×C₄²×C₄₇	—	2	1	no	—
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	#107×C₄₇	—	2	4	no	—
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	2	yes	—
118	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
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	2	no	—
124	#102×C₄₇	—	2	1	no	—
125	#102×C₄₇	—	2	1	no	—
126	#102×C₄₇	—	2	4	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	#41×C₄₇	—	4	1	no	—
134	#41×C₄₇	—	4	1	no	—
135	#41×C₄₇	—	4	2	no	—
136	#41×C₄₇	—	4	2	no	—
137	#41×C₄₇	—	8	2	no	—
138	#41×C₄₇	—	8	2	no	—
139	#41×C₄₇	—	8	2	no	—
140	C₂×Q₈×C₄₇	—	2	1	no	—
141	C₂×Q₈×C₄₇	—	2	2	no	—
142	C₂×Q₈×C₄₇	—	2	2	no	—
143	C₂×Q₈×C₄₇	—	2	1	no	—
144	C₂×Q₈×C₄₇	—	8	2	no	—
145	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂×D₄×C₄₇	—	2	1	no	—
147	C₂×D₄×C₄₇	—	2	2	no	—
148	C₂×D₄×C₄₇	—	2	4	no	—
149	C₂×D₄×C₄₇	—	2	1	no	—
150	C₂×D₄×C₄₇	—	2	1	no	—
151	C₂×D₄×C₄₇	—	2	1	no	—
152	C₂×D₄×C₄₇	—	2	1	no	—
153	C₂×D₄×C₄₇	—	2	1	no	—
154	C₂×D₄×C₄₇	—	4	1	no	—
155	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
157	C₂²×C₄×C₄₇	—	2	4	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	2	1	no	—
160	C₂²×C₄×C₄₇	—	2	1	no	—
161	C₂²×C₄×C₄₇	—	2	1	no	—
162	C₂²×C₄×C₄₇	—	2	2	no	—
163	C₂²×C₄×C₄₇	—	4	1	no	—
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
167	SD₁₆×C₄₇	—	4	2	no	—
168	SD₁₆×C₄₇	—	8	2	no	—
169	D₈×C₄₇	—	4	2	no	—
170	D₈×C₄₇	—	8	2	no	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	4	no	—
176	C₄⋊C₄×C₄₇	—	2	4	no	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	—	2	2	no	—
179	C₄⋊C₄×C₄₇	—	2	1	no	—
180	C₄⋊C₄×C₄₇	—	2	1	no	—
181	C₄⋊C₄×C₄₇	—	2	2	no	—
182	C₄⋊C₄×C₄₇	—	2	1	no	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
189	C₂²⋊C₄×C₄₇	—	2	4	no	—
190	C₂²⋊C₄×C₄₇	—	2	4	no	—
191	C₂²⋊C₄×C₄₇	—	2	4	no	—
192	C₂²⋊C₄×C₄₇	—	2	1	no	—
193	C₂²⋊C₄×C₄₇	—	2	1	no	—
194	C₂²⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	1	no	—
196	C₂²⋊C₄×C₄₇	—	2	2	no	—
197	C₂²⋊C₄×C₄₇	—	4	1	no	—
198	C₂²⋊C₄×C₄₇	—	4	1	no	—
199	C₄²×C₄₇	—	2	4	no	—
200	C₄²×C₄₇	—	2	1	no	—
201	C₄²×C₄₇	—	2	1	no	—
202	C₄²×C₄₇	—	2	1	no	—
203	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
207	C₂³×C₄₇	—	2	1	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	—	4	1	no	—
210	C₂³×C₄₇	#120	1	1	yes	characteristic
211	Q₈×C₄₇	—	2	1	no	—
212	Q₈×C₄₇	—	2	1	no	—
213	Q₈×C₄₇	—	4	2	no	—
214	Q₈×C₄₇	—	4	2	no	—
215	Q₈×C₄₇	—	4	2	no	—
216	Q₈×C₄₇	—	4	2	no	—
217	Q₈×C₄₇	—	8	2	no	—
218	D₄×C₄₇	—	2	1	no	—
219	D₄×C₄₇	—	2	1	no	—
220	D₄×C₄₇	—	2	2	no	—
221	D₄×C₄₇	—	2	2	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	4	no	—
227	D₄×C₄₇	—	4	1	no	—
228	D₄×C₄₇	—	4	1	no	—
229	D₄×C₄₇	—	4	2	no	—
230	D₄×C₄₇	—	8	4	no	—
231	D₄×C₄₇	—	8	2	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	4	1	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	2	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	—	4	1	no	—
247	C₂×C₄×C₄₇	—	8	2	no	—
248	C₂×C₄×C₄₇	—	8	2	no	—
249	C₂×C₄×C₄₇	—	8	4	no	—
250	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
251	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
252	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
256	C₈×C₄₇	—	4	2	no	—
257	C₈×C₄₇	—	4	1	no	—
258	C₈×C₄₇	—	4	1	no	—
259	C₈×C₄₇	—	4	2	no	—
260	#18832	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	1	no	—
264	C₂²×C₄₇	—	4	1	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	1	no	—
267	C₂²×C₄₇	—	4	2	no	—
268	C₂²×C₄₇	—	4	1	no	—
269	C₂²×C₄₇	—	4	2	no	—
270	C₂²×C₄₇	—	8	1	no	—
271	C₂²×C₄₇	—	8	1	no	—
272	C₂²×C₄₇	—	8	1	no	—
273	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	4	1	no	—
279	C₄×C₄₇	—	4	2	no	—
280	C₄×C₄₇	—	4	1	no	—
281	C₄×C₄₇	—	4	4	no	—
282	C₄×C₄₇	—	4	1	no	—
283	C₄×C₄₇	—	8	1	no	—
284	C₄×C₄₇	#575	1	1	yes	characteristic
285	C₄×C₄₇	#575	1	1	yes	characteristic
286	C₄×C₄₇	#576	1	2	yes	—
287	#3511	C₂×C₄₇	1	1	yes	characteristic, complemented
288	#3226	C₂×C₄₇	1	1	yes	characteristic, complemented
289	#3214	C₂×C₄₇	1	1	yes	characteristic, complemented
290	#3115	C₂×C₄₇	1	1	yes	characteristic, complemented
291	#1650	C₂×C₄₇	1	2	yes	complemented
292	#1647	C₂×C₄₇	1	2	yes	complemented
293	#1628	C₂×C₄₇	1	2	yes	complemented
294	#1625	C₂×C₄₇	1	2	yes	complemented
295	#1556	C₂×C₄₇	1	1	yes	characteristic, complemented
296	#1496	C₂×C₄₇	1	1	yes	characteristic, complemented
297	#1488	C₂×C₄₇	1	1	yes	characteristic, complemented
298	C₂×C₄₇	—	4	1	no	—
299	C₂×C₄₇	—	8	1	no	—
300	C₂×C₄₇	—	8	2	no	—
301	C₂×C₄₇	—	16	1	no	—
302	C₂×C₄₇	#3005	1	1	yes	characteristic
303	C₂×C₄₇	#3008	1	1	yes	characteristic
304	C₂×C₄₇	#3020	1	1	yes	characteristic
305	#556	C₂²×C₄₇	1	2	yes	—
306	#555	—	2	1	no	—
307	#554	—	2	1	no	—
308	#553	—	2	2	no	—
309	#548	—	2	2	no	—
310	#547	C₂²×C₄₇	1	2	yes	—
311	#542	—	2	2	no	—
312	#537	—	2	1	no	—
313	#533	—	2	1	no	—
314	#532	—	2	1	no	—
315	#532	C₂²×C₄₇	1	1	yes	characteristic
316	#532	C₂²×C₄₇	1	1	yes	characteristic
317	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
318	#520	—	2	1	no	—
319	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
320	#500	C₂²×C₄₇	1	2	yes	—
321	#496	—	2	1	no	—
322	#489	—	2	1	no	—
323	#486	C₂²×C₄₇	1	2	yes	—
324	#482	—	2	1	no	—
325	#480	—	2	2	no	—
326	#475	C₂²×C₄₇	1	1	yes	characteristic
327	#474	—	2	2	no	—
328	#474	C₂²×C₄₇	1	1	yes	characteristic
329	#461	C₂²×C₄₇	1	2	yes	—
330	#460	C₂²×C₄₇	1	1	yes	characteristic
331	#459	C₂²×C₄₇	1	1	yes	characteristic
332	#459	C₂²×C₄₇	1	2	yes	—
333	#449	—	2	1	no	—
334	#449	—	2	2	no	—
335	#442	—	2	1	no	—
336	#440	—	2	1	no	—
337	#432	C₂²×C₄₇	1	1	yes	characteristic
338	#432	C₂²×C₄₇	1	1	yes	characteristic
339	#431	C₂²×C₄₇	1	1	yes	characteristic
340	#332	C₂²×C₄₇	1	2	yes	—
341	#332	C₂²×C₄₇	1	2	yes	—
342	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
343	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
344	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
345	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
346	C₄₇	#18832	1	1	yes	characteristic, direct product factor, Sylow
347	C₂×#41	—	2	2	no	—
348	C₂×#41	—	2	1	no	—
349	C₂×#41	—	2	1	no	—
350	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
351	C₂²×Q₈	—	2	1	no	—
352	C₂×SD₁₆	—	2	1	no	—
353	C₂×SD₁₆	—	2	2	no	—
354	C₂×D₈	—	2	1	no	—
355	C₂×D₈	—	2	2	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
359	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
360	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
361	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
362	#127	D₄×C₄₇	1	1	yes	characteristic
363	#127	C₂³×C₄₇	1	1	yes	characteristic
364	#126	—	2	4	no	—
365	#125	—	2	2	no	—
366	#124	—	2	4	no	—
367	#124	—	2	2	no	—
368	#124	—	2	1	no	—
369	#124	—	2	1	no	—
370	#123	—	2	4	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	4	no	—
373	C₂²⋊Q₈	—	2	2	no	—
374	C₂²⋊Q₈	—	2	2	no	—
375	#121	—	2	2	no	—
376	#121	—	2	2	no	—
377	#121	—	2	4	no	—
378	#121	—	2	2	no	—
379	#121	—	2	1	no	—
380	#121	—	2	1	no	—
381	#121	—	2	1	no	—
382	#121	D₄×C₄₇	1	2	yes	—
383	C₄×Q₈	—	2	2	no	—
384	C₄×Q₈	—	2	2	no	—
385	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
386	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
387	C₄×D₄	—	2	2	no	—
388	C₄×D₄	—	2	4	no	—
389	C₄×D₄	—	2	2	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	—	2	1	no	—
393	C₄×D₄	—	2	1	no	—
394	C₄×D₄	—	2	1	no	—
395	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
396	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
397	C₄×D₄	C₂³×C₄₇	1	2	yes	—
398	#117	—	2	2	no	—
399	#117	—	2	2	no	—
400	#117	—	2	1	no	—
401	#117	D₄×C₄₇	1	1	yes	characteristic
402	C₂×C₄⋊C₄	—	2	1	no	—
403	C₂×C₄⋊C₄	—	2	2	no	—
404	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
407	#107	—	2	1	no	—
408	#107	—	2	4	no	—
409	#106	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
414	#103	—	2	1	no	—
415	#103	—	2	2	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	#102	—	2	2	no	—
420	#102	—	2	4	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	—	2	1	no	—
424	#97	—	2	1	no	—
425	#97	—	2	1	no	—
426	C₄×C₈	C₂³×C₄₇	1	2	yes	—
427	#41	—	4	1	no	—
428	#41	—	4	1	no	—
429	#41	—	4	2	no	—
430	#41	—	4	2	no	—
431	#41	—	8	2	no	—
432	#41	—	8	2	no	—
433	#41	—	8	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	—	2	2	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	8	2	no	—
439	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	4	1	no	—
449	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
450	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
451	C₂²×C₄	—	2	4	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
460	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
461	SD₁₆	—	4	2	no	—
462	SD₁₆	—	8	2	no	—
463	D₈	—	4	2	no	—
464	D₈	—	8	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
480	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	4	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₄²	—	2	4	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
499	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
500	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	2	2	no	—
503	C₂³	—	4	1	no	—
504	C₂³	#120×C₄₇	1	1	yes	characteristic
505	Q₈	—	2	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	2	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	4	2	no	—
511	Q₈	—	8	2	no	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	4	no	—
521	D₄	—	4	1	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	2	no	—
524	D₄	—	8	4	no	—
525	D₄	—	8	2	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	2	no	—
543	C₂×C₄	—	8	4	no	—
544	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
545	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
546	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
550	C₈	—	4	2	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	2	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	2	1	no	—
556	C₂²	—	2	1	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	2	no	—
563	C₂²	—	8	1	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	1	no	—
576	C₄	—	8	1	no	—
577	C₄	C₄₇×#575	1	1	yes	characteristic
578	C₄	C₄₇×#575	1	1	yes	characteristic
579	C₄	C₄₇×#576	1	2	yes	—
580	C₂	—	4	1	no	—
581	C₂	—	8	1	no	—
582	C₂	—	8	2	no	—
583	C₂	—	16	1	no	—
584	C₂	C₄₇×#3005	1	1	yes	characteristic
585	C₂	C₄₇×#3008	1	1	yes	characteristic
586	C₂	C₄₇×#3020	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×#3511	C₂	semidirect
2. C₄₇×#3226	C₂	semidirect
3. C₄₇×#3214	C₂	semidirect
4. C₄₇×#3115	C₂	semidirect
5. C₄₇×#1650	C₂	semidirect
6. C₄₇×#1647	C₂	semidirect
7. C₄₇×#1628	C₂	semidirect
8. C₄₇×#1625	C₂	semidirect
9. C₄₇×#1556	C₂	semidirect
10. C₄₇×#1496	C₂	semidirect
11. C₄₇×#1488	C₂	semidirect
260. #18832	C₄₇	direct (N × H)
287. #3511	C₂×C₄₇	semidirect
288. #3226	C₂×C₄₇	semidirect
289. #3214	C₂×C₄₇	semidirect
290. #3115	C₂×C₄₇	semidirect
291. #1650	C₂×C₄₇	semidirect
292. #1647	C₂×C₄₇	semidirect
293. #1628	C₂×C₄₇	semidirect
294. #1625	C₂×C₄₇	semidirect
295. #1556	C₂×C₄₇	semidirect
296. #1496	C₂×C₄₇	semidirect
297. #1488	C₂×C₄₇	semidirect
346. C₄₇	#18832	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×#3511	2
C₄₇×#3226	2
C₄₇×#3214	2
C₄₇×#3115	2
C₄₇×#1650	2
C₄₇×#1647	2
C₄₇×#1628	2
C₄₇×#1625	2
C₄₇×#1556	2
C₄₇×#1496	2
C₄₇×#1488	2
#18832	47

Subgroups — C47×#18832 #26058530

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18832 #26058530