Subgroups — C₄₇×#29817 #26069515

Order 12032.

866 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2621	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2620	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2056	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2055	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2001	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2000	C₂	1	2	yes	maximal
9	C₄₇×#1958	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1836	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
18	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#497	—	2	4	no	—
21	C₄₇×#433	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
28	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#398	—	2	2	no	—
31	C₄₇×#397	—	2	2	no	—
32	C₄₇×#396	—	2	2	no	—
33	C₄₇×#394	—	2	2	no	—
34	C₄₇×#391	C₂²	1	2	yes	—
35	C₄₇×#391	C₂²	1	1	yes	characteristic
36	C₄₇×#390	C₂²	1	1	yes	characteristic
37	C₄₇×#384	C₂²	1	1	yes	characteristic
38	C₄₇×#382	C₂²	1	1	yes	characteristic
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×Q₈×C₄₇	C₂³	1	2	yes	—
43	C₂²×D₄×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₄₇	—	2	4	no	—
47	C₂×Q₁₆×C₄₇	—	4	2	no	—
48	C₂×Q₁₆×C₄₇	—	4	2	no	—
49	C₂×SD₁₆×C₄₇	—	2	4	no	—
50	C₂×SD₁₆×C₄₇	—	4	2	no	—
51	C₂×SD₁₆×C₄₇	—	4	2	no	—
52	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₄⋊Q₈×C₄₇	—	2	2	no	—
56	#124×C₄₇	—	2	2	no	—
57	#124×C₄₇	—	2	2	no	—
58	C₂²⋊Q₈×C₄₇	—	4	2	no	—
59	C₂²⋊Q₈×C₄₇	—	4	2	no	—
60	C₂²⋊Q₈×C₄₇	—	4	2	no	—
61	#121×C₄₇	—	4	2	no	—
62	#117×C₄₇	—	2	2	no	—
63	#117×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	—	2	4	no	—
81	#103×C₄₇	—	4	2	no	—
82	#103×C₄₇	—	4	2	no	—
83	#103×C₄₇	—	4	2	no	—
84	#102×C₄₇	—	4	2	no	—
85	C₂²⋊C₈×C₄₇	—	2	4	no	—
86	#97×C₄₇	D₄	1	4	yes	complemented
87	C₄×C₈×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	4	no	—
91	C₂⁴×C₄₇	—	2	1	no	—
92	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	—	8	2	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	Q₁₆×C₄₇	—	4	8	no	—
123	SD₁₆×C₄₇	—	4	8	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	2	no	—
127	C₂×C₈×C₄₇	—	2	2	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₄₇	—	2	4	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₄⋊C₄×C₄₇	—	4	2	no	—
136	C₄⋊C₄×C₄₇	—	4	4	no	—
137	C₄⋊C₄×C₄₇	—	4	4	no	—
138	C₄⋊C₄×C₄₇	—	8	2	no	—
139	C₂²⋊C₄×C₄₇	—	2	4	no	—
140	C₂²⋊C₄×C₄₇	—	4	2	no	—
141	C₂²⋊C₄×C₄₇	—	4	4	no	—
142	C₂²⋊C₄×C₄₇	—	4	2	no	—
143	C₂²⋊C₄×C₄₇	—	4	4	no	—
144	C₂²⋊C₄×C₄₇	—	8	2	no	—
145	C₄²×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	C₂×D₄	1	2	yes	—
148	C₄²×C₄₇	#41	1	2	yes	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	2	1	no	—
151	C₂³×C₄₇	—	2	1	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	2	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	1	no	—
156	C₂³×C₄₇	—	4	1	no	—
157	C₂³×C₄₇	—	4	2	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	Q₈×C₄₇	—	4	2	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	8	4	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	1	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	#121	1	4	yes	—
193	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
196	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
197	C₈×C₄₇	—	2	4	no	—
198	C₈×C₄₇	—	4	2	no	—
199	#29817	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	—	4	1	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	8	1	no	—
206	C₂²×C₄₇	—	8	1	no	—
207	C₂²×C₄₇	—	8	1	no	—
208	C₂²×C₄₇	—	8	2	no	—
209	C₂²×C₄₇	—	8	2	no	—
210	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
211	C₂²×C₄₇	#535	1	1	yes	characteristic
212	C₂²×C₄₇	#535	1	1	yes	characteristic
213	C₂²×C₄₇	#577	1	2	yes	—
214	C₂²×C₄₇	#578	1	2	yes	—
215	C₄×C₄₇	—	2	4	no	—
216	C₄×C₄₇	—	4	1	no	—
217	C₄×C₄₇	—	4	2	no	—
218	C₄×C₄₇	—	8	1	no	—
219	C₄×C₄₇	—	8	2	no	—
220	C₄×C₄₇	—	8	1	no	—
221	C₄×C₄₇	—	8	1	no	—
222	C₄×C₄₇	—	8	2	no	—
223	C₄×C₄₇	#535	1	2	yes	—
224	C₄×C₄₇	#540	1	2	yes	—
225	C₂×#497	C₂×C₄₇	1	1	yes	characteristic, complemented
226	C₂×#433	C₂×C₄₇	1	1	yes	characteristic, complemented
227	#2621	C₂×C₄₇	1	1	yes	characteristic, complemented
228	#2620	C₂×C₄₇	1	1	yes	characteristic
229	#2056	C₂×C₄₇	1	2	yes	complemented
230	#2055	C₂×C₄₇	1	2	yes	complemented
231	#2001	C₂×C₄₇	1	2	yes	complemented
232	#2000	C₂×C₄₇	1	2	yes	—
233	#1958	C₂×C₄₇	1	1	yes	characteristic, complemented
234	#1956	C₂×C₄₇	1	1	yes	characteristic, complemented
235	#1836	C₂×C₄₇	1	1	yes	characteristic, complemented
236	C₂×C₄₇	—	8	1	no	—
237	C₂×C₄₇	—	16	1	no	—
238	C₂×C₄₇	#2619	1	1	yes	characteristic
239	C₂×C₄₇	#3063	1	2	yes	—
240	C₂×C₄₇	#3222	1	1	yes	characteristic
241	C₂×C₄₇	#3223	1	1	yes	characteristic
242	C₂×C₄₇	#3225	1	2	yes	—
243	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
244	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
245	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
246	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
247	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
249	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
251	#497	—	2	4	no	—
252	#433	—	2	4	no	—
253	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
254	C₂×#103	C₂²×C₄₇	1	2	yes	—
255	C₂×#103	C₂²×C₄₇	1	2	yes	—
256	C₂×#103	C₂²×C₄₇	1	2	yes	—
257	C₂×#102	C₂²×C₄₇	1	2	yes	—
258	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
259	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
261	#398	—	2	2	no	—
262	#397	—	2	2	no	—
263	#396	—	2	2	no	—
264	#394	—	2	2	no	—
265	#391	C₂²×C₄₇	1	2	yes	—
266	#391	C₂²×C₄₇	1	1	yes	characteristic
267	#390	C₂²×C₄₇	1	1	yes	characteristic
268	#384	C₂²×C₄₇	1	1	yes	characteristic
269	#382	C₂²×C₄₇	1	1	yes	characteristic
270	#340	C₂²×C₄₇	1	2	yes	—
271	#340	C₂²×C₄₇	1	2	yes	—
272	C₄₇	#29817	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
274	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
275	C₂²×D₄	—	2	1	no	—
276	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
277	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
278	C₂×Q₁₆	—	2	4	no	—
279	C₂×Q₁₆	—	4	2	no	—
280	C₂×Q₁₆	—	4	2	no	—
281	C₂×SD₁₆	—	2	4	no	—
282	C₂×SD₁₆	—	4	2	no	—
283	C₂×SD₁₆	—	4	2	no	—
284	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
285	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
286	C₄⋊Q₈	—	2	2	no	—
287	C₄⋊Q₈	—	2	2	no	—
288	#124	—	2	2	no	—
289	#124	—	2	2	no	—
290	C₂²⋊Q₈	—	4	2	no	—
291	C₂²⋊Q₈	—	4	2	no	—
292	C₂²⋊Q₈	—	4	2	no	—
293	#121	—	4	2	no	—
294	#117	—	2	2	no	—
295	#117	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	1	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	2	2	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
301	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
303	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	2	1	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	1	no	—
307	C₂×C₂²⋊C₄	—	2	2	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
310	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
311	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
312	C₄⋊C₈	—	2	4	no	—
313	#103	—	4	2	no	—
314	#103	—	4	2	no	—
315	#103	—	4	2	no	—
316	#102	—	4	2	no	—
317	C₂²⋊C₈	—	2	4	no	—
318	#97	D₄×C₄₇	1	4	yes	complemented
319	C₄×C₈	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	4	no	—
323	C₂⁴	—	2	1	no	—
324	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
353	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
354	Q₁₆	—	4	8	no	—
355	SD₁₆	—	4	8	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	4	2	no	—
368	C₄⋊C₄	—	4	4	no	—
369	C₄⋊C₄	—	4	4	no	—
370	C₄⋊C₄	—	8	2	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	4	2	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	8	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	C₂×D₄×C₄₇	1	2	yes	—
380	C₄²	#41×C₄₇	1	2	yes	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	1	no	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	1	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
392	Q₈	—	4	2	no	—
393	Q₈	—	4	2	no	—
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	4	2	no	—
398	D₄	—	4	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	8	4	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	#121×C₄₇	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
426	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
427	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
428	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
429	C₈	—	2	4	no	—
430	C₈	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	1	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	8	2	no	—
437	C₂²	—	8	1	no	—
438	C₂²	—	8	1	no	—
439	C₂²	—	8	1	no	—
440	C₂²	—	8	2	no	—
441	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
442	C₂²	C₄₇×#535	1	1	yes	characteristic
443	C₂²	C₄₇×#535	1	1	yes	characteristic
444	C₂²	C₄₇×#577	1	2	yes	—
445	C₂²	C₄₇×#578	1	2	yes	—
446	C₄	—	2	4	no	—
447	C₄	—	4	2	no	—
448	C₄	—	4	1	no	—
449	C₄	—	8	1	no	—
450	C₄	—	8	2	no	—
451	C₄	—	8	1	no	—
452	C₄	—	8	1	no	—
453	C₄	—	8	2	no	—
454	C₄	C₄₇×#535	1	2	yes	—
455	C₄	C₄₇×#540	1	2	yes	—
456	C₂	—	8	1	no	—
457	C₂	—	16	1	no	—
458	C₂	C₄₇×#2619	1	1	yes	characteristic
459	C₂	C₄₇×#3063	1	2	yes	—
460	C₂	C₄₇×#3222	1	1	yes	characteristic
461	C₂	C₄₇×#3223	1	1	yes	characteristic
462	C₂	C₄₇×#3225	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×#497	C₂	semidirect
2. C₂×C₄₇×#433	C₂	semidirect
3. C₄₇×#2621	C₂	semidirect
5. C₄₇×#2056	C₂	semidirect
6. C₄₇×#2055	C₂	semidirect
7. C₄₇×#2001	C₂	semidirect
9. C₄₇×#1958	C₂	semidirect
10. C₄₇×#1956	C₂	semidirect
11. C₄₇×#1836	C₂	semidirect
86. #97×C₄₇	D₄	semidirect
199. #29817	C₄₇	direct (N × H)
225. C₂×#497	C₂×C₄₇	semidirect
226. C₂×#433	C₂×C₄₇	semidirect
227. #2621	C₂×C₄₇	semidirect
229. #2056	C₂×C₄₇	semidirect
230. #2055	C₂×C₄₇	semidirect
231. #2001	C₂×C₄₇	semidirect
233. #1958	C₂×C₄₇	semidirect
234. #1956	C₂×C₄₇	semidirect
235. #1836	C₂×C₄₇	semidirect
272. C₄₇	#29817	direct (N × H)
318. #97	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×#497	2
C₂×C₄₇×#433	2
C₄₇×#2621	2
C₄₇×#2620	2
C₄₇×#2056	2
C₄₇×#2055	2
C₄₇×#2001	2
C₄₇×#2000	2
C₄₇×#1958	2
C₄₇×#1956	2
C₄₇×#1836	2
#29817	47

Subgroups — C47×#29817 #26069515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29817 #26069515