Subgroups — #26265814

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689323	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20248387	C₂	1	1	yes	maximal, characteristic
4	#20244759	C₂	1	2	yes	maximal, complemented
5	#20244703	C₂	1	2	yes	maximal, complemented
6	#20244245	C₂	1	2	yes	maximal, complemented
7	#20244193	C₂	1	1	yes	maximal, characteristic
8	#20244149	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244070	C₂	1	2	yes	maximal, complemented
10	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2582	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625336	C₂²	1	2	yes	—
13	C₂×#13094021	C₂²	1	1	yes	characteristic
14	C₂×#13094013	—	2	1	no	—
15	#15689323	—	2	4	no	—
16	Q₈×C₄₇⋊C₈	—	2	4	no	—
17	C₂×#13093955	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	1	yes	characteristic
21	C₂×#13093948	C₂²	1	1	yes	characteristic
22	C₂×#13093944	C₂²	1	2	yes	—
23	C₂×#13093944	C₂²	1	2	yes	—
24	C₂×#13093944	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
27	#15689040	—	2	2	no	—
28	#15689025	C₂²	1	2	yes	—
29	#15689025	C₂²	1	2	yes	—
30	#15689024	—	2	1	no	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688885	C₂²	1	1	yes	characteristic
33	#15688885	C₂²	1	1	yes	characteristic
34	#15688885	C₂²	1	2	yes	—
35	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#398	—	2	2	no	—
38	C₄₇×#391	—	2	1	no	—
39	C₄₇×#391	C₂²	1	2	yes	—
40	C₄₇×#389	—	2	1	no	—
41	C₄₇×#389	C₂²	1	2	yes	—
42	C₄₇×#384	C₂²	1	1	yes	characteristic
43	C₂²×D₁₈₈	—	2	1	no	—
44	C₂²×D₁₈₈	—	2	1	no	—
45	C₂²×D₁₈₈	C₂³	1	2	yes	—
46	C₂×#10625336	—	2	4	no	—
47	C₂×#10625336	—	2	4	no	—
48	C₂×#10625336	—	4	2	no	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	#13094021	—	2	2	no	—
53	#13094021	—	2	2	no	—
54	#13094013	—	4	4	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
59	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
60	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	#13093955	—	4	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
64	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
65	#13093948	—	2	2	no	—
66	#13093948	—	2	2	no	—
67	#13093944	—	2	4	no	—
68	#13093944	—	2	4	no	—
69	#13093944	—	4	2	no	—
70	C₄×C₄₇⋊C₈	—	2	2	no	—
71	C₄×C₄₇⋊C₈	—	2	4	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
74	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₄×Q₈×C₄₇	—	2	2	no	—
77	C₄×Q₈×C₄₇	—	2	2	no	—
78	C₄×Q₈×C₄₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	#95×C₄₇	—	2	2	no	—
93	C₂³×D₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	2	1	no	—
99	C₂×Q₈×C₄₇	—	2	1	no	—
100	C₂×Q₈×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	SD₁₆	1	4	yes	complemented
102	C₂×Q₈×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	1	no	—
112	C₂²×Dic₄₇	—	2	1	no	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	—	2	2	no	—
115	C₂×D₁₈₈	—	2	2	no	—
116	C₂×D₁₈₈	—	2	2	no	—
117	C₂×D₁₈₈	—	2	2	no	—
118	C₂×D₁₈₈	—	2	2	no	—
119	C₂×D₁₈₈	—	4	2	no	—
120	C₂×D₁₈₈	—	4	2	no	—
121	C₂×D₁₈₈	—	4	2	no	—
122	C₂×D₁₈₈	—	4	2	no	—
123	C₂×D₁₈₈	—	8	1	no	—
124	C₂×D₁₈₈	—	8	1	no	—
125	C₄⋊C₄×C₄₇	—	2	4	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	2	no	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₄⋊C₄×C₄₇	—	8	1	no	—
134	C₄⋊C₄×C₄₇	—	8	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	4	2	no	—
138	C₄²×C₄₇	C₂×D₄	1	2	yes	—
139	C₄²×C₄₇	#41	1	2	yes	—
140	#10625336	—	4	8	no	—
141	(C₂×D₄₇)⋊C₄	—	4	4	no	—
142	(C₂×D₄₇)⋊C₄	—	4	4	no	—
143	(C₂×D₄₇)⋊C₄	—	8	2	no	—
144	(C₂×D₄₇)⋊C₄	—	8	2	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	—	2	1	no	—
147	C₄⋊Dic₄₇	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄×Dic₄₇	—	4	2	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
158	C₂×C₄₇⋊C₈	#41	1	2	yes	—
159	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂²×D₄₇	—	4	2	no	—
161	C₂²×D₄₇	—	4	2	no	—
162	C₂²×D₄₇	—	4	2	no	—
163	C₂²×D₄₇	—	4	2	no	—
164	C₂²×D₄₇	—	4	2	no	—
165	C₂²×D₄₇	—	4	2	no	—
166	C₂²×D₄₇	—	4	2	no	—
167	Q₈×C₄₇	—	2	8	no	—
168	Q₈×C₄₇	—	2	2	no	—
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	4	1	no	—
171	Q₈×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	1	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	1	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	#121	1	2	yes	—
189	C₂×C₄×C₄₇	#121	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
191	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
192	C₂×C₄×C₄₇	#135	1	2	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	C₂×#41	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
198	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	1	no	—
203	C₂×Dic₄₇	—	4	1	no	—
204	C₂×Dic₄₇	—	4	1	no	—
205	D₁₈₈	—	4	2	no	—
206	D₁₈₈	—	4	2	no	—
207	D₁₈₈	—	4	2	no	—
208	D₁₈₈	—	4	2	no	—
209	D₁₈₈	—	8	4	no	—
210	D₁₈₈	—	8	4	no	—
211	C₄₇⋊C₈	—	2	4	no	—
212	C₄₇⋊C₈	—	2	2	no	—
213	C₄₇⋊C₈	—	4	1	no	—
214	#25295	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
216	C₂²×C₄₇	#548	1	1	yes	characteristic
217	C₂²×C₄₇	#550	1	1	yes	characteristic
218	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
220	C₂²×C₄₇	#576	1	1	yes	characteristic
221	C₂²×C₄₇	#577	1	1	yes	characteristic
222	C₂×D₄₇	—	8	2	no	—
223	C₂×D₄₇	—	8	2	no	—
224	C₂×D₄₇	—	8	2	no	—
225	C₂×D₄₇	—	8	2	no	—
226	C₂×D₄₇	—	8	2	no	—
227	C₂×D₄₇	—	8	2	no	—
228	C₂×D₄₇	—	8	2	no	—
229	C₄×C₄₇	—	2	4	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	4	2	no	—
232	C₄×C₄₇	—	4	2	no	—
233	C₄×C₄₇	—	8	2	no	—
234	C₄×C₄₇	—	8	1	no	—
235	C₄×C₄₇	#465	1	4	yes	—
236	C₄×C₄₇	#529	1	1	yes	characteristic
237	C₄×C₄₇	#542	1	1	yes	characteristic
238	C₄×C₄₇	#546	1	1	yes	characteristic
239	C₄×C₄₇	#548	1	1	yes	characteristic
240	Dic₄₇	—	8	1	no	—
241	Dic₄₇	—	8	1	no	—
242	C₂×#460	—	47	1	no	—
243	C₂×C₈×Q₈	—	47	1	no	—
244	#2582	D₄₇	1	1	yes	characteristic, complemented
245	#2548	—	47	1	no	—
246	#2065	—	47	2	no	—
247	#2055	—	47	2	no	—
248	#1968	—	47	2	no	—
249	#1957	—	47	1	no	—
250	#1948	—	47	1	no	—
251	#1934	—	47	2	no	—
252	C₄×#103	—	47	1	no	—
253	C₂×C₄₇	#2426	1	1	yes	characteristic
254	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
255	C₂×C₄₇	#3062	1	1	yes	characteristic
256	C₂×C₄₇	#3362	1	1	yes	characteristic
257	C₂×C₄₇	#3365	1	1	yes	characteristic
258	C₂×C₄₇	#3392	1	1	yes	characteristic
259	C₂×C₄₇	#3396	1	1	yes	characteristic
260	D₄₇	—	16	2	no	—
261	C₂²×SD₁₆	—	47	2	no	—
262	C₂×#127	—	47	1	no	—
263	C₂×#124	—	94	1	no	—
264	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
266	#460	—	94	4	no	—
267	C₈×Q₈	—	94	4	no	—
268	C₂×#106	—	47	2	no	—
269	C₂×C₄⋊C₈	—	47	1	no	—
270	C₂×C₄⋊C₈	—	47	2	no	—
271	C₂×#103	—	47	1	no	—
272	C₂×#103	—	47	1	no	—
273	C₂×#102	—	47	2	no	—
274	C₂×#102	—	47	2	no	—
275	C₂×#102	—	47	2	no	—
276	C₂×C₄×C₈	—	47	2	no	—
277	C₂×C₄×C₈	—	47	1	no	—
278	#398	—	2	2	no	—
279	#394	—	94	2	no	—
280	#391	—	2	1	no	—
281	#391	C₂×D₄₇	1	2	yes	—
282	#390	—	47	2	no	—
283	#390	—	47	2	no	—
284	#390	—	94	1	no	—
285	#389	—	2	1	no	—
286	#389	C₂×D₄₇	1	2	yes	—
287	#384	C₂×D₄₇	1	1	yes	characteristic
288	C₄×C₄⋊C₄	—	47	1	no	—
289	#340	—	47	2	no	—
290	#340	—	47	1	no	—
291	#340	—	47	1	no	—
292	C₄₇	#25295	1	1	yes	characteristic, complemented, Sylow
293	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
294	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×D₄	—	47	2	no	—
296	C₂²×D₄	—	94	1	no	—
297	C₂²×D₄	—	94	1	no	—
298	C₂×SD₁₆	—	94	4	no	—
299	C₂×SD₁₆	—	94	4	no	—
300	C₂×SD₁₆	—	188	2	no	—
301	C₂²×C₈	—	47	2	no	—
302	C₂²×C₈	—	47	1	no	—
303	C₂²×C₈	—	47	1	no	—
304	#127	—	94	2	no	—
305	#127	—	94	2	no	—
306	#124	—	188	4	no	—
307	C₄×Q₈	—	2	2	no	—
308	C₄×Q₈	—	2	2	no	—
309	C₄×Q₈	—	2	2	no	—
310	C₄×Q₈	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	47	1	no	—
316	C₂×C₄⋊C₄	—	47	1	no	—
317	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	2	yes	—
319	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
321	C₂×C₂²⋊C₄	—	94	2	no	—
322	C₂×C₂²⋊C₄	—	94	2	no	—
323	C₂×C₂²⋊C₄	—	94	2	no	—
324	C₂×C₂²⋊C₄	—	94	2	no	—
325	C₂×C₄²	—	2	1	no	—
326	C₂×C₄²	—	94	1	no	—
327	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
328	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
329	#106	—	188	2	no	—
330	C₄⋊C₈	—	47	4	no	—
331	C₄⋊C₈	—	94	4	no	—
332	#103	—	94	2	no	—
333	#103	—	94	2	no	—
334	#102	—	94	4	no	—
335	#102	—	94	4	no	—
336	#102	—	188	2	no	—
337	C₄×C₈	—	94	4	no	—
338	C₄×C₈	—	94	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	—	2	2	no	—
342	#95	—	94	1	no	—
343	C₂⁴	—	94	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	1	no	—
349	C₂×Q₈	—	2	1	no	—
350	C₂×Q₈	—	2	1	no	—
351	C₂×Q₈	#10625336	1	4	yes	complemented
352	C₂×Q₈	#10625354	1	2	yes	—
353	C₂×D₄	—	94	2	no	—
354	C₂×D₄	—	94	2	no	—
355	C₂×D₄	—	94	2	no	—
356	C₂×D₄	—	94	2	no	—
357	C₂×D₄	—	94	2	no	—
358	C₂×D₄	—	94	2	no	—
359	C₂×D₄	—	376	1	no	—
360	C₂×D₄	—	376	1	no	—
361	C₂×D₄	—	188	2	no	—
362	C₂×D₄	—	188	2	no	—
363	C₂×D₄	—	188	2	no	—
364	C₂×D₄	—	188	2	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	1	no	—
370	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
371	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
372	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
373	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
375	SD₁₆	—	188	8	no	—
376	C₂×C₈	—	47	4	no	—
377	C₂×C₈	—	47	2	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	94	1	no	—
382	C₂×C₈	—	94	1	no	—
383	C₂×C₈	—	94	1	no	—
384	C₂×C₈	—	94	1	no	—
385	C₄⋊C₄	—	2	4	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	8	1	no	—
394	C₄⋊C₄	—	8	2	no	—
395	C₄⋊C₄	—	94	1	no	—
396	C₄⋊C₄	—	94	1	no	—
397	C₄⋊C₄	—	94	1	no	—
398	C₄⋊C₄	—	94	1	no	—
399	C₂²⋊C₄	—	376	2	no	—
400	C₂²⋊C₄	—	376	2	no	—
401	C₂²⋊C₄	—	188	4	no	—
402	C₂²⋊C₄	—	188	4	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	4	2	no	—
406	C₄²	—	188	2	no	—
407	C₄²	D₄×D₄₇	1	2	yes	—
408	C₄²	#10625352	1	2	yes	—
409	C₂³	—	188	2	no	—
410	C₂³	—	188	2	no	—
411	C₂³	—	188	2	no	—
412	C₂³	—	188	2	no	—
413	C₂³	—	188	2	no	—
414	C₂³	—	188	2	no	—
415	C₂³	—	188	2	no	—
416	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
417	Q₈	—	2	8	no	—
418	Q₈	—	2	2	no	—
419	Q₈	—	2	2	no	—
420	Q₈	—	4	1	no	—
421	Q₈	—	4	1	no	—
422	D₄	—	376	4	no	—
423	D₄	—	376	4	no	—
424	D₄	—	188	2	no	—
425	D₄	—	188	2	no	—
426	D₄	—	188	2	no	—
427	D₄	—	188	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	188	1	no	—
445	C₂×C₄	—	188	1	no	—
446	C₂×C₄	—	188	1	no	—
447	C₂×C₄	—	188	1	no	—
448	C₂×C₄	—	188	1	no	—
449	C₂×C₄	—	188	1	no	—
450	C₂×C₄	#13093996	1	2	yes	—
451	C₂×C₄	#13093996	1	2	yes	—
452	C₂×C₄	C₂×#10625336	1	4	yes	—
453	C₂×C₄	C₂×#10625336	1	2	yes	—
454	C₂×C₄	#13094044	1	2	yes	—
455	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
456	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
458	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
459	C₂×C₄	#13094070	1	1	yes	characteristic
460	C₂×C₄	#13094072	1	1	yes	characteristic
461	C₈	—	94	4	no	—
462	C₈	—	94	2	no	—
463	C₈	—	188	1	no	—
464	C₂²	—	376	2	no	—
465	C₂²	—	376	2	no	—
466	C₂²	—	376	2	no	—
467	C₂²	—	376	2	no	—
468	C₂²	—	376	2	no	—
469	C₂²	—	376	2	no	—
470	C₂²	—	376	2	no	—
471	C₂²	C₂×#13093996	1	1	yes	characteristic
472	C₂²	#15689784	1	1	yes	characteristic
473	C₂²	#15689792	1	1	yes	characteristic
474	C₂²	C₂²×#10625336	1	1	yes	characteristic
475	C₂²	C₂×#13094044	1	1	yes	characteristic
476	C₂²	#15689926	1	1	yes	characteristic
477	C₂²	#15689931	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	2	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	1	no	—
484	C₄	—	376	1	no	—
485	C₄	—	376	1	no	—
486	C₄	#15689354	1	4	yes	—
487	C₄	#15689659	1	1	yes	characteristic
488	C₄	#15689746	1	1	yes	characteristic
489	C₄	#15689764	1	1	yes	characteristic
490	C₄	#15689783	1	1	yes	characteristic
491	C₂	—	752	2	no	—
492	C₂	#20246956	1	1	yes	characteristic
493	C₂	C₂×#15689354	1	1	yes	characteristic
494	C₂	#20253070	1	1	yes	characteristic
495	C₂	#20256059	1	1	yes	characteristic
496	C₂	#20256084	1	1	yes	characteristic
497	C₂	#20256365	1	1	yes	characteristic
498	C₂	#20256396	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2582	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#13094021	C₂²
hypercenter	#2582	D₄₇
hypocenter	C₄₇	#25295
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈ ◁ #2582

Complements

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

N	H ≅ G/N	type
2. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20244759	C₂	semidirect
5. #20244703	C₂	semidirect
6. #20244245	C₂	semidirect
8. #20244149	C₂	semidirect
9. #20244070	C₂	semidirect
10. C₄×#13093948	C₂	semidirect
11. C₄₇×#2582	C₂	semidirect
101. C₂×Q₈×C₄₇	SD₁₆	semidirect
244. #2582	D₄₇	semidirect
292. C₄₇	#25295	semidirect
351. C₂×Q₈	#10625336	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689323	2
C₂×Q₈×C₄₇⋊C₈	2
#20248387	2
#20244759	2
#20244703	2
#20244245	2
#20244193	2
#20244149	2
#20244070	2
C₄×#13093948	2
C₄₇×#2582	2
#25295	47