Subgroups — C₄₇×#29850 #26069548

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#488	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2629	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2620	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2066	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2065	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2035	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2034	C₂	1	2	yes	maximal
9	C₄₇×#1992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1959	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#488	—	2	4	no	—
18	C₄₇×#433	—	2	4	no	—
19	C₂×#106×C₄₇	C₂²	1	2	yes	—
20	C₂×#106×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×#103×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#102×C₄₇	C₂²	1	2	yes	—
25	C₂×#102×C₄₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
27	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#398	—	2	2	no	—
30	C₄₇×#396	—	2	2	no	—
31	C₄₇×#396	—	2	2	no	—
32	C₄₇×#394	—	2	2	no	—
33	C₄₇×#391	C₂²	1	1	yes	characteristic
34	C₄₇×#390	C₂²	1	1	yes	characteristic
35	C₄₇×#389	C₂²	1	2	yes	—
36	C₄₇×#384	C₂²	1	1	yes	characteristic
37	C₄₇×#384	C₂²	1	1	yes	characteristic
38	C₄₇×#380	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×D₄×C₄₇	—	2	1	no	—
43	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
47	#125×C₄₇	—	2	2	no	—
48	#125×C₄₇	—	2	2	no	—
49	#124×C₄₇	—	2	2	no	—
50	#124×C₄₇	—	2	2	no	—
51	C₂²⋊Q₈×C₄₇	—	4	2	no	—
52	#121×C₄₇	—	4	2	no	—
53	#117×C₄₇	—	2	2	no	—
54	#117×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	#106×C₄₇	—	4	2	no	—
74	#106×C₄₇	—	4	2	no	—
75	C₄⋊C₈×C₄₇	—	2	4	no	—
76	#103×C₄₇	—	2	4	no	—
77	#103×C₄₇	—	4	2	no	—
78	#102×C₄₇	—	2	4	no	—
79	#102×C₄₇	—	4	2	no	—
80	C₂²⋊C₈×C₄₇	—	2	4	no	—
81	#97×C₄₇	—	2	2	no	—
82	C₄×C₈×C₄₇	D₄	1	4	yes	complemented
83	#95×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	2	no	—
85	#95×C₄₇	—	2	2	no	—
86	C₂⁴×C₄₇	—	2	1	no	—
87	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
88	C₂×Q₈×C₄₇	—	2	1	no	—
89	C₂×Q₈×C₄₇	—	2	1	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	—	8	2	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	4	4	no	—
126	C₄⋊C₄×C₄₇	—	8	2	no	—
127	C₄⋊C₄×C₄₇	—	8	2	no	—
128	C₄⋊C₄×C₄₇	—	8	2	no	—
129	C₂²⋊C₄×C₄₇	—	2	4	no	—
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	2	no	—
132	C₂²⋊C₄×C₄₇	—	4	4	no	—
133	C₂²⋊C₄×C₄₇	—	8	2	no	—
134	C₂²⋊C₄×C₄₇	—	8	2	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	C₂×D₄	1	2	yes	—
138	C₄²×C₄₇	#41	1	2	yes	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	1	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	—	2	2	no	—
144	C₂³×C₄₇	—	4	1	no	—
145	C₂³×C₄₇	—	4	1	no	—
146	C₂³×C₄₇	—	4	1	no	—
147	C₂³×C₄₇	—	4	2	no	—
148	C₂³×C₄₇	—	4	2	no	—
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₇	—	4	2	no	—
151	Q₈×C₄₇	—	4	2	no	—
152	D₄×C₄₇	—	4	2	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	8	4	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	#121	1	4	yes	—
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
182	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
183	C₈×C₄₇	—	2	4	no	—
184	C₈×C₄₇	—	4	2	no	—
185	#29850	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
186	C₂²×C₄₇	—	4	1	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	1	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	8	1	no	—
192	C₂²×C₄₇	—	8	1	no	—
193	C₂²×C₄₇	—	8	1	no	—
194	C₂²×C₄₇	—	8	2	no	—
195	C₂²×C₄₇	—	8	2	no	—
196	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
197	C₂²×C₄₇	#535	1	1	yes	characteristic
198	C₂²×C₄₇	#536	1	1	yes	characteristic
199	C₂²×C₄₇	#577	1	2	yes	—
200	C₂²×C₄₇	#577	1	2	yes	—
201	C₄×C₄₇	—	2	4	no	—
202	C₄×C₄₇	—	4	1	no	—
203	C₄×C₄₇	—	4	2	no	—
204	C₄×C₄₇	—	8	1	no	—
205	C₄×C₄₇	—	8	2	no	—
206	C₄×C₄₇	—	8	1	no	—
207	C₄×C₄₇	—	8	1	no	—
208	C₄×C₄₇	—	8	2	no	—
209	C₄×C₄₇	#537	1	2	yes	—
210	C₄×C₄₇	#542	1	2	yes	—
211	C₂×#488	C₂×C₄₇	1	1	yes	characteristic, complemented
212	C₂×#433	C₂×C₄₇	1	1	yes	characteristic, complemented
213	#2629	C₂×C₄₇	1	1	yes	characteristic, complemented
214	#2620	C₂×C₄₇	1	1	yes	characteristic
215	#2066	C₂×C₄₇	1	2	yes	complemented
216	#2065	C₂×C₄₇	1	2	yes	complemented
217	#2035	C₂×C₄₇	1	2	yes	complemented
218	#2034	C₂×C₄₇	1	2	yes	—
219	#1992	C₂×C₄₇	1	1	yes	characteristic, complemented
220	#1959	C₂×C₄₇	1	1	yes	characteristic, complemented
221	#1844	C₂×C₄₇	1	1	yes	characteristic, complemented
222	C₂×C₄₇	—	8	1	no	—
223	C₂×C₄₇	—	16	1	no	—
224	C₂×C₄₇	#2620	1	1	yes	characteristic
225	C₂×C₄₇	#3060	1	2	yes	—
226	C₂×C₄₇	#3221	1	1	yes	characteristic
227	C₂×C₄₇	#3222	1	1	yes	characteristic
228	C₂×C₄₇	#3244	1	2	yes	—
229	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
230	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
232	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
233	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
234	#488	—	2	4	no	—
235	#433	—	2	4	no	—
236	C₂×#106	C₂²×C₄₇	1	2	yes	—
237	C₂×#106	C₂²×C₄₇	1	2	yes	—
238	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
239	C₂×#103	C₂²×C₄₇	1	2	yes	—
240	C₂×#103	C₂²×C₄₇	1	2	yes	—
241	C₂×#102	C₂²×C₄₇	1	2	yes	—
242	C₂×#102	C₂²×C₄₇	1	2	yes	—
243	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
244	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
245	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
246	#398	—	2	2	no	—
247	#396	—	2	2	no	—
248	#396	—	2	2	no	—
249	#394	—	2	2	no	—
250	#391	C₂²×C₄₇	1	1	yes	characteristic
251	#390	C₂²×C₄₇	1	1	yes	characteristic
252	#389	C₂²×C₄₇	1	2	yes	—
253	#384	C₂²×C₄₇	1	1	yes	characteristic
254	#384	C₂²×C₄₇	1	1	yes	characteristic
255	#380	C₂²×C₄₇	1	2	yes	—
256	#340	C₂²×C₄₇	1	2	yes	—
257	#340	C₂²×C₄₇	1	2	yes	—
258	C₄₇	#29850	1	1	yes	characteristic, direct product factor, Sylow
259	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
260	C₂²×D₄	—	2	1	no	—
261	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
262	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
264	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
265	#125	—	2	2	no	—
266	#125	—	2	2	no	—
267	#124	—	2	2	no	—
268	#124	—	2	2	no	—
269	C₂²⋊Q₈	—	4	2	no	—
270	#121	—	4	2	no	—
271	#117	—	2	2	no	—
272	#117	—	2	2	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	—	2	2	no	—
276	C₂×C₄⋊C₄	—	2	2	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
280	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
282	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
283	C₂×C₂²⋊C₄	—	2	1	no	—
284	C₂×C₂²⋊C₄	—	2	1	no	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	2	no	—
287	C₂×C₂²⋊C₄	—	2	2	no	—
288	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
289	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
291	#106	—	4	2	no	—
292	#106	—	4	2	no	—
293	C₄⋊C₈	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	4	2	no	—
296	#102	—	2	4	no	—
297	#102	—	4	2	no	—
298	C₂²⋊C₈	—	2	4	no	—
299	#97	—	2	2	no	—
300	C₄×C₈	D₄×C₄₇	1	4	yes	complemented
301	#95	—	2	2	no	—
302	#95	—	2	2	no	—
303	#95	—	2	2	no	—
304	C₂⁴	—	2	1	no	—
305	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	2	2	no	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	8	2	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	1	no	—
325	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	8	2	no	—
345	C₄⋊C₄	—	8	2	no	—
346	C₄⋊C₄	—	8	2	no	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	2	no	—
349	C₂²⋊C₄	—	4	2	no	—
350	C₂²⋊C₄	—	4	4	no	—
351	C₂²⋊C₄	—	8	2	no	—
352	C₂²⋊C₄	—	8	2	no	—
353	C₄²	—	2	1	no	—
354	C₄²	—	2	1	no	—
355	C₄²	C₂×D₄×C₄₇	1	2	yes	—
356	C₄²	#41×C₄₇	1	2	yes	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	8	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	#121×C₄₇	1	4	yes	—
397	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
398	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
399	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
400	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
401	C₈	—	2	4	no	—
402	C₈	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	8	2	no	—
413	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
414	C₂²	C₄₇×#535	1	1	yes	characteristic
415	C₂²	C₄₇×#536	1	1	yes	characteristic
416	C₂²	C₄₇×#577	1	2	yes	—
417	C₂²	C₄₇×#577	1	2	yes	—
418	C₄	—	2	4	no	—
419	C₄	—	4	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	1	no	—
426	C₄	C₄₇×#537	1	2	yes	—
427	C₄	C₄₇×#542	1	2	yes	—
428	C₂	—	8	1	no	—
429	C₂	—	16	1	no	—
430	C₂	C₄₇×#2620	1	1	yes	characteristic
431	C₂	C₄₇×#3060	1	2	yes	—
432	C₂	C₄₇×#3221	1	1	yes	characteristic
433	C₂	C₄₇×#3222	1	1	yes	characteristic
434	C₂	C₄₇×#3244	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#121×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#488	C₂	semidirect
2. C₂×C₄₇×#433	C₂	semidirect
3. C₄₇×#2629	C₂	semidirect
5. C₄₇×#2066	C₂	semidirect
6. C₄₇×#2065	C₂	semidirect
7. C₄₇×#2035	C₂	semidirect
9. C₄₇×#1992	C₂	semidirect
10. C₄₇×#1959	C₂	semidirect
11. C₄₇×#1844	C₂	semidirect
82. C₄×C₈×C₄₇	D₄	semidirect
185. #29850	C₄₇	direct (N × H)
211. C₂×#488	C₂×C₄₇	semidirect
212. C₂×#433	C₂×C₄₇	semidirect
213. #2629	C₂×C₄₇	semidirect
215. #2066	C₂×C₄₇	semidirect
216. #2065	C₂×C₄₇	semidirect
217. #2035	C₂×C₄₇	semidirect
219. #1992	C₂×C₄₇	semidirect
220. #1959	C₂×C₄₇	semidirect
221. #1844	C₂×C₄₇	semidirect
258. C₄₇	#29850	direct (N × H)
300. C₄×C₈	D₄×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×#488	2
C₂×C₄₇×#433	2
C₄₇×#2629	2
C₄₇×#2620	2
C₄₇×#2066	2
C₄₇×#2065	2
C₄₇×#2035	2
C₄₇×#2034	2
C₄₇×#1992	2
C₄₇×#1959	2
C₄₇×#1844	2
#29850	47

Subgroups — C47×#29850 #26069548

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29850 #26069548