Subgroups — #26185992

Order 12032.

660 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252506	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13094044	C₂	1	1	yes	maximal, characteristic
4	#20242256	C₂	1	2	yes	maximal, complemented
5	#20242249	C₂	1	2	yes	maximal, complemented
6	#20242228	C₂	1	2	yes	maximal, complemented
7	#20242221	C₂	1	2	yes	maximal, complemented
8	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241776	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₄	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689250	C₂²	1	2	yes	—
15	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
16	C₄×#10625337	C₄	1	1	yes	characteristic
17	C₄×#10625337	C₂²	1	1	yes	characteristic
18	C₄×#10625336	C₄	1	1	yes	characteristic
19	C₄×#10625336	C₂²	1	1	yes	characteristic
20	C₄×#10625335	C₄	1	1	yes	characteristic
21	C₄×#10625335	C₂²	1	1	yes	characteristic
22	C₄×#10625334	C₄	1	1	yes	characteristic
23	C₄×#10625334	C₂²	1	1	yes	characteristic
24	#15689200	C₂²	1	2	yes	—
25	#15689194	—	2	2	no	—
26	D₄×C₄₇⋊C₈	—	2	2	no	—
27	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	#15689179	—	2	1	no	—
29	#15689176	—	2	1	no	—
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689159	C₄	1	1	yes	characteristic
32	#15689145	—	2	1	no	—
33	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
34	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	#15689119	C₄	1	1	yes	characteristic
36	#15689117	C₄	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688873	C₂²	1	2	yes	—
39	#15688873	C₂²	1	2	yes	—
40	#15688855	C₂²	1	2	yes	—
41	#15688852	C₂²	1	2	yes	—
42	#15688845	C₂²	1	2	yes	—
43	#15688844	C₂²	1	2	yes	—
44	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	#13094044	—	2	4	no	—
51	C₂×#10625337	C₂×C₄	1	1	yes	characteristic
52	C₂×#10625335	C₂×C₄	1	1	yes	characteristic
53	C₂×#10625336	C₂×C₄	1	1	yes	characteristic
54	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
55	C₂×#10625324	—	2	2	no	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	2	no	—
58	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
61	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
62	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
63	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
64	C₄×C₂²⋊D₄₇	—	2	1	no	—
65	C₄×C₂²⋊D₄₇	—	2	1	no	—
66	#13093983	C₂×C₄	1	1	yes	characteristic
67	#13093981	—	2	1	no	—
68	C₄²×D₄₇	—	2	1	no	—
69	#13093957	C₂×C₄	1	1	yes	characteristic
70	#13093957	C₂×C₄	1	1	yes	characteristic
71	#13093955	C₂×C₄	1	1	yes	characteristic
72	#13093955	C₂×C₄	1	1	yes	characteristic
73	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
74	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
75	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
76	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	#13093948	C₂×C₄	1	1	yes	characteristic
80	#13093948	C₂×C₄	1	1	yes	characteristic
81	#13093947	C₂×C₄	1	1	yes	characteristic
82	#13093947	C₂×C₄	1	1	yes	characteristic
83	#13093945	C₂×C₄	1	1	yes	characteristic
84	#13093945	C₂×C₄	1	1	yes	characteristic
85	#13093944	C₂×C₄	1	1	yes	characteristic
86	#13093944	C₂×C₄	1	1	yes	characteristic
87	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
88	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
89	(C₂×D₄₇)⋊C₈	—	2	2	no	—
90	#13093934	—	2	2	no	—
91	C₄×C₄₇⋊C₈	—	2	2	no	—
92	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
93	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
97	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	—	2	1	no	—
99	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₄₇	—	2	1	no	—
102	C₄×D₄×C₄₇	—	2	1	no	—
103	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
105	#117×C₄₇	—	2	1	no	—
106	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₄₇	—	2	1	no	—
110	C₄⋊C₈×C₄₇	—	2	1	no	—
111	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
112	C₂²⋊C₈×C₄₇	—	2	1	no	—
113	C₄×C₈×C₄₇	C₂³	1	2	yes	—
114	#41×C₄₇	—	2	2	no	—
115	#41×C₄₇	M₁₆	1	4	yes	complemented
116	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×D₄×C₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₇	—	2	1	no	—
126	#10625350	—	2	2	no	—
127	#10625350	—	2	2	no	—
128	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₄×D₄₇	—	2	1	no	—
130	C₂×C₄×D₄₇	—	2	1	no	—
131	C₂×C₄×D₄₇	—	2	1	no	—
132	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	8	1	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²⋊C₄×C₄₇	—	2	1	no	—
141	C₂²⋊C₄×C₄₇	—	2	1	no	—
142	C₂²⋊C₄×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	—	2	1	no	—
144	C₄²×C₄₇	—	2	1	no	—
145	C₄²×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₄²×C₄₇	#41	1	1	yes	characteristic
149	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
150	C₂²⋊Dic₄₇	—	2	1	no	—
151	#10625337	—	2	2	no	—
152	#10625336	—	2	2	no	—
153	#10625335	—	2	2	no	—
154	#10625334	—	2	2	no	—
155	(C₂×D₄₇)⋊C₄	—	2	1	no	—
156	(C₂×D₄₇)⋊C₄	—	2	1	no	—
157	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
159	Dic₄₇⋊C₄	—	2	1	no	—
160	Dic₄₇⋊C₄	—	2	1	no	—
161	C₄×Dic₄₇	—	2	1	no	—
162	C₄×Dic₄₇	—	2	1	no	—
163	C₄×Dic₄₇	—	2	1	no	—
164	C₂×C₄₇⋊C₈	—	2	2	no	—
165	C₂×C₄₇⋊C₈	—	2	2	no	—
166	C₂×C₄₇⋊C₈	—	2	2	no	—
167	C₂×C₄₇⋊C₈	—	8	2	no	—
168	C₂×C₄₇⋊C₈	—	8	1	no	—
169	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
174	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
175	#10625324	—	8	2	no	—
176	C₂³×C₄₇	—	2	1	no	—
177	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
178	C₂²×D₄₇	—	2	1	no	—
179	Q₈×C₄₇	—	2	1	no	—
180	Q₈×C₄₇	C₂×M₁₆	1	2	yes	—
181	D₄×C₄₇	—	2	4	no	—
182	D₄×C₄₇	—	2	1	no	—
183	D₄×C₄₇	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	1	no	—
190	C₂×C₄×C₄₇	—	4	1	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	—	4	1	no	—
193	C₂×C₄×C₄₇	—	8	1	no	—
194	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
198	C₂×C₄×C₄₇	#131	1	2	yes	—
199	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
202	C₂²⋊D₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	2	1	no	—
204	C₂×Dic₄₇	—	2	1	no	—
205	C₂×Dic₄₇	—	2	1	no	—
206	D₁₈₈	—	2	1	no	—
207	D₁₈₈	—	2	1	no	—
208	C₄×D₄₇	—	4	1	no	—
209	C₄×D₄₇	—	4	1	no	—
210	C₄×D₄₇	—	4	2	no	—
211	C₄×D₄₇	—	8	1	no	—
212	Dic₉₄	—	2	1	no	—
213	Dic₉₄	—	2	1	no	—
214	C₈×C₄₇	—	4	2	no	—
215	C₈×C₄₇	—	4	2	no	—
216	C₄₇⋊C₈	—	2	1	no	—
217	C₄₇⋊C₈	—	2	1	no	—
218	C₄₇⋊C₈	—	2	1	no	—
219	C₄₇⋊C₈	—	2	1	no	—
220	C₄₇⋊C₈	—	2	2	no	—
221	C₄₇⋊C₈	—	2	2	no	—
222	C₄₇⋊C₈	—	4	2	no	—
223	#17882	—	47	1	no	maximal, Sylow
224	C₂²×C₄₇	—	2	1	no	—
225	C₂²×C₄₇	—	2	1	no	—
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	4	1	no	—
228	C₂²×C₄₇	—	4	1	no	—
229	C₂²×C₄₇	#435	1	2	yes	—
230	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
231	C₂×D₄₇	—	4	1	no	—
232	C₂×D₄₇	—	4	1	no	—
233	C₂×D₄₇	—	4	1	no	—
234	C₄×C₄₇	—	2	2	no	—
235	C₄×C₄₇	—	2	1	no	—
236	C₄×C₄₇	—	2	1	no	—
237	C₄×C₄₇	—	2	1	no	—
238	C₄×C₄₇	—	4	1	no	—
239	C₄×C₄₇	—	4	1	no	—
240	C₄×C₄₇	#435	1	2	yes	—
241	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
242	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
243	C₄×C₄₇	#577	1	1	yes	characteristic
244	C₄×C₄₇	#577	1	1	yes	characteristic
245	Dic₄₇	—	4	1	no	—
246	Dic₄₇	—	4	1	no	—
247	Dic₄₇	—	4	1	no	—
248	#2989	—	47	1	no	—
249	#2988	—	47	1	no	—
250	C₄×#135	—	47	1	no	—
251	#1587	—	47	2	no	—
252	#1586	—	47	2	no	—
253	#1583	—	47	2	no	—
254	#1582	—	47	2	no	—
255	C₂×#334	—	47	1	no	—
256	#1477	—	47	1	no	—
257	#1477	D₄₇	1	1	yes	characteristic, complemented
258	#1452	—	47	1	no	—
259	C₂×C₄₇	—	2	2	no	—
260	C₂×C₄₇	—	4	2	no	—
261	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
262	C₂×C₄₇	#2952	1	1	yes	characteristic
263	C₂×C₄₇	#2957	1	1	yes	characteristic
264	D₄₇	—	8	1	no	—
265	C₂×#135	—	47	1	no	—
266	C₄×#41	—	47	1	no	—
267	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
268	#446	—	47	2	no	—
269	C₈×Q₈	—	47	2	no	—
270	C₄×Q₁₆	—	47	1	no	—
271	C₄×Q₁₆	—	47	1	no	—
272	C₄×SD₁₆	—	47	1	no	—
273	C₄×SD₁₆	—	47	1	no	—
274	C₄×SD₁₆	—	47	1	no	—
275	C₄×SD₁₆	—	47	1	no	—
276	C₄×D₈	—	47	1	no	—
277	C₄×D₈	—	47	1	no	—
278	#436	—	47	2	no	—
279	#435	—	94	2	no	—
280	C₈×D₄	—	47	2	no	—
281	C₈×D₄	—	94	2	no	—
282	#432	—	94	1	no	—
283	#431	—	47	1	no	—
284	#431	—	94	1	no	—
285	#431	C₂×D₄₇	1	1	yes	characteristic
286	#427	—	47	1	no	—
287	#423	—	94	1	no	—
288	C₂×C₄⋊C₈	—	47	1	no	—
289	C₂×C₄⋊C₈	—	94	1	no	—
290	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
291	#416	—	47	1	no	—
292	#416	—	47	1	no	—
293	C₂×C₄×C₈	—	47	1	no	—
294	#334	—	47	2	no	—
295	#334	—	47	2	no	—
296	Q₈⋊C₈	—	47	2	no	—
297	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
298	D₄⋊C₈	—	47	2	no	—
299	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
300	#322	—	47	2	no	—
301	#322	—	47	2	no	—
302	C₄₇	#17882	1	1	yes	characteristic, complemented, Sylow
303	C₂×#41	—	47	1	no	—
304	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
305	#135	—	94	4	no	—
306	C₂×Q₁₆	—	47	1	no	—
307	C₂×SD₁₆	—	47	1	no	—
308	C₂×SD₁₆	—	47	1	no	—
309	C₂×D₈	—	47	1	no	—
310	C₂×M₁₆	—	94	2	no	—
311	C₂²×C₈	—	2	1	no	—
312	C₂²×C₈	—	47	1	no	—
313	C₂²×C₈	—	47	1	no	—
314	C₂²×C₈	—	94	2	no	—
315	C₂²×C₈	—	94	1	no	—
316	C₄×Q₈	—	47	1	no	—
317	C₄×Q₈	—	47	1	no	—
318	C₄×Q₈	C₄×D₄₇	1	1	yes	characteristic
319	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
320	C₄×D₄	—	2	1	no	—
321	C₄×D₄	—	2	1	no	—
322	C₄×D₄	—	47	1	no	—
323	C₄×D₄	—	47	1	no	—
324	C₄×D₄	—	94	1	no	—
325	C₄×D₄	—	94	1	no	—
326	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
327	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
328	#117	—	2	1	no	—
329	#117	—	47	1	no	—
330	#117	—	94	1	no	—
331	#117	C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	94	1	no	—
334	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
335	#107	—	47	1	no	—
336	#107	—	47	1	no	—
337	#106	—	47	1	no	—
338	#106	—	47	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	—	47	1	no	—
342	C₄⋊C₈	—	47	1	no	—
343	C₄⋊C₈	—	47	2	no	—
344	C₄⋊C₈	—	94	2	no	—
345	C₄⋊C₈	—	94	2	no	—
346	C₄⋊C₈	—	94	1	no	—
347	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
348	#103	—	47	1	no	—
349	#103	—	47	1	no	—
350	#103	—	47	1	no	—
351	#103	—	47	1	no	—
352	#102	—	47	1	no	—
353	#102	—	47	1	no	—
354	#102	—	47	1	no	—
355	#102	—	47	1	no	—
356	C₂²⋊C₈	—	2	1	no	—
357	C₂²⋊C₈	—	47	2	no	—
358	C₂²⋊C₈	—	94	2	no	—
359	C₂²⋊C₈	—	94	2	no	—
360	#97	—	94	2	no	—
361	C₄×C₈	—	47	1	no	—
362	C₄×C₈	—	47	1	no	—
363	C₄×C₈	—	47	1	no	—
364	C₄×C₈	—	47	1	no	—
365	C₄×C₈	—	47	2	no	—
366	C₄×C₈	—	94	2	no	—
367	C₄×C₈	C₂²×D₄₇	1	2	yes	—
368	#41	—	2	2	no	—
369	#41	—	94	2	no	—
370	#41	—	94	2	no	—
371	#41	#10625324	1	4	yes	complemented
372	C₂×Q₈	—	47	1	no	—
373	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	47	1	no	—
376	C₂×D₄	—	94	1	no	—
377	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	94	1	no	—
382	C₂²×C₄	—	94	1	no	—
383	C₂²×C₄	—	94	1	no	—
384	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
386	C₂²×C₄	#10625352	1	1	yes	characteristic
387	Q₁₆	—	94	2	no	—
388	SD₁₆	—	94	2	no	—
389	SD₁₆	—	94	2	no	—
390	D₈	—	94	2	no	—
391	M₁₆	—	376	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	8	1	no	—
395	C₂×C₈	—	47	1	no	—
396	C₂×C₈	—	47	1	no	—
397	C₂×C₈	—	47	1	no	—
398	C₂×C₈	—	47	1	no	—
399	C₂×C₈	—	47	2	no	—
400	C₂×C₈	—	47	2	no	—
401	C₂×C₈	—	94	2	no	—
402	C₂×C₈	—	94	2	no	—
403	C₂×C₈	—	94	2	no	—
404	C₂×C₈	—	376	2	no	—
405	C₂×C₈	—	376	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	1	no	—
408	C₄⋊C₄	—	47	1	no	—
409	C₄⋊C₄	—	47	1	no	—
410	C₄⋊C₄	—	94	1	no	—
411	C₄⋊C₄	—	94	1	no	—
412	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
413	C₄⋊C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	2	1	no	—
416	C₂²⋊C₄	—	2	1	no	—
417	C₂²⋊C₄	—	94	1	no	—
418	C₂²⋊C₄	—	94	1	no	—
419	C₂²⋊C₄	—	94	1	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	94	1	no	—
424	C₄²	—	94	1	no	—
425	C₄²	—	94	1	no	—
426	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
427	C₄²	D₄×D₄₇	1	1	yes	characteristic
428	C₄²	#10625352	1	1	yes	characteristic
429	C₄²	C₂³×D₄₇	1	1	yes	characteristic
430	C₂³	—	2	1	no	—
431	C₂³	—	94	1	no	—
432	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
433	Q₈	—	2	1	no	—
434	Q₈	—	94	1	no	—
435	Q₈	—	94	1	no	—
436	Q₈	C₂×#10625324	1	2	yes	—
437	D₄	—	2	4	no	—
438	D₄	—	2	1	no	—
439	D₄	—	94	1	no	—
440	D₄	—	94	1	no	—
441	D₄	—	188	2	no	—
442	D₄	C₂×#10625324	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	8	1	no	—
453	C₂×C₄	—	94	1	no	—
454	C₂×C₄	—	94	1	no	—
455	C₂×C₄	—	94	1	no	—
456	C₂×C₄	—	376	1	no	—
457	C₂×C₄	—	188	1	no	—
458	C₂×C₄	—	188	1	no	—
459	C₂×C₄	—	188	2	no	—
460	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
461	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
462	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
463	C₂×C₄	C₂×#10625324	1	2	yes	—
464	C₂×C₄	#13094032	1	2	yes	—
465	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
466	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
468	C₈	—	4	2	no	—
469	C₈	—	4	2	no	—
470	C₈	—	94	1	no	—
471	C₈	—	94	1	no	—
472	C₈	—	94	1	no	—
473	C₈	—	94	1	no	—
474	C₈	—	94	2	no	—
475	C₈	—	94	2	no	—
476	C₈	—	188	2	no	—
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	1	no	—
482	C₂²	—	188	1	no	—
483	C₂²	—	188	1	no	—
484	C₂²	—	188	1	no	—
485	C₂²	#15689191	1	2	yes	—
486	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
487	C₄	—	2	1	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	2	2	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	188	1	no	—
494	C₄	—	188	1	no	—
495	C₄	—	188	1	no	—
496	C₄	#15689191	1	2	yes	—
497	C₄	C₂²×#10625324	1	1	yes	characteristic
498	C₄	C₂×#13094032	1	1	yes	characteristic
499	C₄	#15689932	1	1	yes	characteristic
500	C₄	#15689933	1	1	yes	characteristic
501	C₂	—	2	2	no	—
502	C₂	—	4	2	no	—
503	C₂	—	376	1	no	—
504	C₂	C₂×#15689191	1	1	yes	characteristic
505	C₂	#20252267	1	1	yes	characteristic
506	C₂	#20252301	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1477	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094044	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1477	D₄₇
hypocenter	C₄₇	#17882
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
1. #20252506	C₂	semidirect
2. #20252499	C₂	semidirect
4. #20242256	C₂	semidirect
5. #20242249	C₂	semidirect
6. #20242228	C₂	semidirect
7. #20242221	C₂	semidirect
8. C₂×#15688873	C₂	semidirect
9. #20241776	C₂	semidirect
10. #20241681	C₂	semidirect
11. C₄₇×#1477	C₂	semidirect
115. #41×C₄₇	M₁₆	semidirect
257. #1477	D₄₇	semidirect
302. C₄₇	#17882	semidirect
371. #41	#10625324	semidirect

Maximal subgroups

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

subgroup	index
#20252506	2
#20252499	2
C₄×#13094044	2
#20242256	2
#20242249	2
#20242228	2
#20242221	2
C₂×#15688873	2
#20241776	2
#20241681	2
C₄₇×#1477	2
#17882	47