Subgroups — C₄₇×#20954 #26060652

Order 12032.

1694 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#536	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2896	C₂	1	2	yes	maximal
4	C₂²×#101×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1888	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1886	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1733	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
9	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
11	C₄₇×#536	—	2	4	no	—
12	C₄₇×#536	C₄	1	8	yes	complemented
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	2	yes	—
14	C₂×#124×C₄₇	C₂²	1	2	yes	—
15	C₂×#123×C₄₇	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
17	C₄₇×#519	—	2	2	no	—
18	C₄₇×#519	—	2	4	no	—
19	C₄₇×#519	C₂²	1	4	yes	—
20	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
21	C₂×#117×C₄₇	—	2	2	no	—
22	C₂×#117×C₄₇	C₂²	1	2	yes	—
23	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#419	C₂²	1	4	yes	—
25	C₄₇×#418	C₂²	1	4	yes	—
26	C₄₇×#417	—	2	4	no	—
27	C₄₇×#416	—	2	4	no	—
28	C₂×#101×C₄₇	—	2	4	no	—
29	C₂×#101×C₄₇	C₂²	1	4	yes	—
30	C₄₇×#339	C₂²	1	8	yes	—
31	C₂×#41×C₄₇	—	2	2	no	—
32	C₂×#41×C₄₇	—	2	2	no	—
33	C₂×#41×C₄₇	—	2	2	no	—
34	C₂×#41×C₄₇	—	2	4	no	—
35	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₄₇	—	2	2	no	—
37	C₂²×Q₈×C₄₇	—	2	2	no	—
38	C₂²×Q₈×C₄₇	—	2	4	no	—
39	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
40	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
41	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
42	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
44	C₂²×D₄×C₄₇	—	2	1	no	—
45	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	—	2	1	no	—
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	—	2	4	no	—
51	C₂×M₁₆×C₄₇	—	2	4	no	—
52	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
53	C₂²×C₈×C₄₇	—	2	2	no	—
54	C₄⋊Q₈×C₄₇	—	2	4	no	—
55	C₄⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
56	#124×C₄₇	—	2	4	no	—
57	#124×C₄₇	C₂×C₄	1	8	yes	complemented
58	#123×C₄₇	—	2	16	no	—
59	C₂²⋊Q₈×C₄₇	—	2	16	no	—
60	C₄×Q₈×C₄₇	—	2	16	no	—
61	C₄×Q₈×C₄₇	—	2	16	no	—
62	#117×C₄₇	—	2	8	no	—
63	#117×C₄₇	—	2	8	no	—
64	#117×C₄₇	—	2	2	no	—
65	#117×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	2	no	—
67	#117×C₄₇	C₂×C₄	1	4	yes	—
68	#117×C₄₇	D₄	1	4	yes	—
69	#117×C₄₇	C₂³	1	4	yes	—
70	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
73	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂×C₄²×C₄₇	—	2	4	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	#103×C₄₇	—	2	8	no	—
81	#102×C₄₇	—	2	8	no	—
82	#101×C₄₇	—	2	8	no	—
83	C₂⁴×C₄₇	—	2	1	no	—
84	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
85	#41×C₄₇	—	2	8	no	—
86	#41×C₄₇	—	2	8	no	—
87	#41×C₄₇	—	4	4	no	—
88	#41×C₄₇	—	4	4	no	—
89	C₂×Q₈×C₄₇	—	2	8	no	—
90	C₂×Q₈×C₄₇	—	2	8	no	—
91	C₂×Q₈×C₄₇	—	2	4	no	—
92	C₂×Q₈×C₄₇	—	2	8	no	—
93	C₂×Q₈×C₄₇	—	2	8	no	—
94	C₂×Q₈×C₄₇	—	2	4	no	—
95	C₂×Q₈×C₄₇	—	2	4	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	4	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²⋊C₄	1	8	yes	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
104	C₂×D₄×C₄₇	—	2	4	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	4	1	no	—
109	C₂×D₄×C₄₇	—	4	1	no	—
110	C₂×D₄×C₄₇	—	4	2	no	—
111	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	4	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	4	no	—
119	C₂²×C₄×C₄₇	—	4	2	no	—
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	#41	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
130	M₁₆×C₄₇	—	2	4	no	—
131	M₁₆×C₄₇	—	2	4	no	—
132	M₁₆×C₄₇	—	4	4	no	—
133	C₂×C₈×C₄₇	—	2	4	no	—
134	C₂×C₈×C₄₇	—	4	4	no	—
135	C₄⋊C₄×C₄₇	—	2	16	no	—
136	C₄⋊C₄×C₄₇	—	2	4	no	—
137	C₄⋊C₄×C₄₇	—	2	16	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
140	C₂²⋊C₄×C₄₇	—	2	4	no	—
141	C₂²⋊C₄×C₄₇	—	2	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	4	no	—
143	C₂²⋊C₄×C₄₇	—	2	16	no	—
144	C₄²×C₄₇	—	2	16	no	—
145	C₄²×C₄₇	—	2	4	no	—
146	C₄²×C₄₇	—	2	4	no	—
147	C₄²×C₄₇	—	2	2	no	—
148	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	4	2	no	—
151	C₂³×C₄₇	—	4	4	no	—
152	C₂³×C₄₇	—	4	1	no	—
153	C₂³×C₄₇	—	4	1	no	—
154	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂³×C₄₇	#120	1	1	yes	characteristic
156	C₂³×C₄₇	#120	1	1	yes	characteristic
157	C₂³×C₄₇	#123	1	2	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₇	—	2	8	no	—
160	Q₈×C₄₇	—	2	8	no	—
161	Q₈×C₄₇	—	2	16	no	—
162	Q₈×C₄₇	—	2	4	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	2	4	no	—
165	D₄×C₄₇	—	4	4	no	—
166	D₄×C₄₇	—	4	4	no	—
167	D₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	8	no	—
171	C₂×C₄×C₄₇	—	2	8	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	8	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	8	no	—
180	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
181	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
183	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
184	C₂×C₄×C₄₇	#120	1	2	yes	—
185	C₂×C₄×C₄₇	#121	1	4	yes	—
186	C₂×C₄×C₄₇	#121	1	4	yes	—
187	C₂×C₄×C₄₇	#123	1	2	yes	—
188	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
192	C₈×C₄₇	—	4	4	no	—
193	#20954	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	4	4	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	8	2	no	—
202	C₂²×C₄₇	—	8	2	no	—
203	C₂²×C₄₇	#386	1	2	yes	—
204	C₂²×C₄₇	#386	1	2	yes	—
205	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
208	C₄×C₄₇	—	2	8	no	—
209	C₄×C₄₇	—	4	4	no	—
210	C₄×C₄₇	—	4	8	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	#386	1	4	yes	—
213	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
214	C₄×C₄₇	C₂×#121	1	2	yes	—
215	C₂×#536	C₂×C₄₇	1	1	yes	characteristic
216	C₂×#519	C₂×C₄₇	1	1	yes	characteristic, complemented
217	#2896	C₂×C₄₇	1	2	yes	—
218	C₂²×#101	C₂×C₄₇	1	1	yes	characteristic, complemented
219	#1888	C₂×C₄₇	1	4	yes	complemented
220	#1886	C₂×C₄₇	1	4	yes	complemented
221	#1733	C₂×C₄₇	1	2	yes	complemented
222	C₂×C₄₇	—	2	1	no	—
223	C₂×C₄₇	—	2	1	no	—
224	C₂×C₄₇	—	2	2	no	—
225	C₂×C₄₇	—	2	2	no	—
226	C₂×C₄₇	—	8	2	no	—
227	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
228	C₂×C₄₇	#3020	1	2	yes	—
229	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
230	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
231	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
232	#536	—	2	4	no	—
233	#536	C₄×C₄₇	1	8	yes	complemented
234	C₂×C₄⋊Q₈	C₂²×C₄₇	1	2	yes	—
235	C₂×#124	C₂²×C₄₇	1	2	yes	—
236	C₂×#123	—	2	2	no	—
237	C₂×C₂²⋊Q₈	—	2	2	no	—
238	#519	—	2	2	no	—
239	#519	—	2	4	no	—
240	#519	C₂²×C₄₇	1	4	yes	—
241	C₂×C₄×Q₈	—	2	4	no	—
242	C₂×#117	—	2	2	no	—
243	C₂×#117	C₂²×C₄₇	1	2	yes	—
244	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
245	#419	C₂²×C₄₇	1	4	yes	—
246	#418	C₂²×C₄₇	1	4	yes	—
247	#417	—	2	4	no	—
248	#416	—	2	4	no	—
249	C₂×#101	—	2	4	no	—
250	C₂×#101	C₂²×C₄₇	1	4	yes	—
251	#339	C₂²×C₄₇	1	8	yes	—
252	C₄₇	#20954	1	1	yes	characteristic, direct product factor, Sylow
253	C₂×#41	—	2	2	no	—
254	C₂×#41	—	2	2	no	—
255	C₂×#41	—	2	2	no	—
256	C₂×#41	—	2	4	no	—
257	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
258	C₂²×Q₈	—	2	2	no	—
259	C₂²×Q₈	—	2	2	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
262	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
263	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
264	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
265	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
268	C₂³×C₄	—	2	1	no	—
269	C₂³×C₄	D₄×C₄₇	1	2	yes	—
270	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	2	4	no	—
273	C₂×M₁₆	—	2	4	no	—
274	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
275	C₂²×C₈	—	2	2	no	—
276	C₄⋊Q₈	—	2	4	no	—
277	C₄⋊Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
278	#124	—	2	4	no	—
279	#124	C₂×C₄×C₄₇	1	8	yes	complemented
280	#123	—	2	16	no	—
281	C₂²⋊Q₈	—	2	16	no	—
282	C₄×Q₈	—	2	16	no	—
283	C₄×Q₈	—	2	16	no	—
284	#117	—	2	8	no	—
285	#117	—	2	8	no	—
286	#117	—	2	2	no	—
287	#117	—	2	2	no	—
288	#117	—	2	2	no	—
289	#117	C₂×C₄×C₄₇	1	4	yes	—
290	#117	D₄×C₄₇	1	4	yes	—
291	#117	C₂³×C₄₇	1	4	yes	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	1	no	—
298	C₂×C₂²⋊C₄	—	2	4	no	—
299	C₂×C₄²	—	2	4	no	—
300	C₂×C₄²	—	2	2	no	—
301	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
302	#103	—	2	8	no	—
303	#102	—	2	8	no	—
304	#101	—	2	8	no	—
305	C₂⁴	—	2	1	no	—
306	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
307	#41	—	2	8	no	—
308	#41	—	2	8	no	—
309	#41	—	4	4	no	—
310	#41	—	4	4	no	—
311	C₂×Q₈	—	2	8	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	4	no	—
314	C₂×Q₈	—	2	8	no	—
315	C₂×Q₈	—	2	8	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₂²⋊C₄×C₄₇	1	8	yes	—
323	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
324	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
325	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
326	C₂×D₄	—	2	4	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	1	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	1	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	4	no	—
337	C₂²×C₄	—	2	4	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	4	2	no	—
342	C₂²×C₄	—	4	2	no	—
343	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
344	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
345	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
346	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
349	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
350	C₂²×C₄	#41×C₄₇	1	4	yes	—
351	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
352	M₁₆	—	2	4	no	—
353	M₁₆	—	2	4	no	—
354	M₁₆	—	4	4	no	—
355	C₂×C₈	—	2	4	no	—
356	C₂×C₈	—	4	4	no	—
357	C₄⋊C₄	—	2	16	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	16	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
362	C₂²⋊C₄	—	2	4	no	—
363	C₂²⋊C₄	—	2	4	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	16	no	—
366	C₄²	—	2	16	no	—
367	C₄²	—	2	4	no	—
368	C₄²	—	2	4	no	—
369	C₄²	—	2	2	no	—
370	C₄²	C₂²×C₄×C₄₇	1	4	yes	—
371	C₂³	—	2	2	no	—
372	C₂³	—	4	2	no	—
373	C₂³	—	4	4	no	—
374	C₂³	—	4	1	no	—
375	C₂³	—	4	1	no	—
376	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
377	C₂³	#120×C₄₇	1	1	yes	characteristic
378	C₂³	#120×C₄₇	1	1	yes	characteristic
379	C₂³	#123×C₄₇	1	2	yes	—
380	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
381	Q₈	—	2	8	no	—
382	Q₈	—	2	8	no	—
383	Q₈	—	2	16	no	—
384	Q₈	—	2	4	no	—
385	Q₈	—	4	2	no	—
386	D₄	—	2	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	4	no	—
389	D₄	—	4	2	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	8	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	8	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	8	no	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
404	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
405	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
406	C₂×C₄	#120×C₄₇	1	2	yes	—
407	C₂×C₄	#121×C₄₇	1	4	yes	—
408	C₂×C₄	#121×C₄₇	1	4	yes	—
409	C₂×C₄	#123×C₄₇	1	2	yes	—
410	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
412	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
414	C₈	—	4	4	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	4	no	—
421	C₂²	—	4	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₄₇×#386	1	2	yes	—
425	C₂²	C₄₇×#386	1	2	yes	—
426	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
427	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
428	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
429	C₄	—	2	8	no	—
430	C₄	—	4	4	no	—
431	C₄	—	4	2	no	—
432	C₄	—	4	8	no	—
433	C₄	C₄₇×#386	1	4	yes	—
434	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
435	C₄	C₂×#121×C₄₇	1	2	yes	—
436	C₂	—	2	1	no	—
437	C₂	—	2	1	no	—
438	C₂	—	2	2	no	—
439	C₂	—	2	2	no	—
440	C₂	—	8	2	no	—
441	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
442	C₂	C₄₇×#3020	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#519	C₂	semidirect
4. C₂²×#101×C₄₇	C₂	semidirect
5. C₄₇×#1888	C₂	semidirect
6. C₄₇×#1886	C₂	semidirect
7. C₄₇×#1733	C₂	semidirect
12. C₄₇×#536	C₄	semidirect
55. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
57. #124×C₄₇	C₂×C₄	semidirect
193. #20954	C₄₇	direct (N × H)
216. C₂×#519	C₂×C₄₇	semidirect
218. C₂²×#101	C₂×C₄₇	semidirect
219. #1888	C₂×C₄₇	semidirect
220. #1886	C₂×C₄₇	semidirect
221. #1733	C₂×C₄₇	semidirect
233. #536	C₄×C₄₇	semidirect
252. C₄₇	#20954	direct (N × H)
277. C₄⋊Q₈	C₂×C₄×C₄₇	semidirect
279. #124	C₂×C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#536	2
C₂×C₄₇×#519	2
C₄₇×#2896	2
C₂²×#101×C₄₇	2
C₄₇×#1888	2
C₄₇×#1886	2
C₄₇×#1733	2
#20954	47

Subgroups — C47×#20954 #26060652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20954 #26060652