Subgroups — #27086137

Order 12032.

1878 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20256780	C₂	1	2	yes	maximal, complemented
2	#20254048	C₂	1	2	yes	maximal, complemented
3	#20254039	C₂	1	2	yes	maximal, complemented
4	#20254030	C₂	1	4	yes	maximal, complemented
5	#20254018	C₂	1	4	yes	maximal, complemented
6	#20254007	C₂	1	4	yes	maximal, complemented
7	#20253816	C₂	1	1	yes	maximal, characteristic, complemented
8	#20253736	C₂	1	2	yes	maximal, complemented
9	#20252998	C₂	1	2	yes	maximal, complemented
10	#20252970	C₂	1	2	yes	maximal, complemented
11	#20252188	C₂	1	2	yes	maximal, complemented
12	#20252159	C₂	1	2	yes	maximal, complemented
13	C₂×#15689077	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#13094046	C₂²	1	2	yes	—
16	C₂×#13094046	C₂²	1	2	yes	—
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	#15689747	C₂²	1	8	yes	—
20	#15689736	C₂²	1	4	yes	—
21	#15689729	C₂²	1	4	yes	—
22	#15689722	—	2	4	no	—
23	#15689713	—	2	4	no	—
24	#15689673	C₂²	1	2	yes	—
25	#15689660	—	2	8	no	—
26	#15689635	C₂²	1	4	yes	—
27	#15689591	C₂²	1	4	yes	—
28	C₂×#13093981	C₂²	1	1	yes	characteristic
29	#15689507	C₂²	1	2	yes	complemented
30	#15689507	C₂²	1	2	yes	complemented
31	#15689503	C₂²	1	1	yes	characteristic, complemented
32	#15689500	C₂²	1	1	yes	characteristic, complemented
33	#15689496	C₂²	1	2	yes	complemented
34	#15689493	C₂²	1	4	yes	complemented
35	#15689489	C₂²	1	4	yes	complemented
36	#15689485	C₂²	1	8	yes	complemented
37	#15689382	C₂²	1	4	yes	—
38	#15689377	C₂²	1	4	yes	—
39	#15689370	C₂²	1	8	yes	—
40	#15689365	C₂²	1	4	yes	—
41	#15689360	C₂²	1	4	yes	—
42	#15689353	C₂²	1	8	yes	—
43	#15689234	C₂²	1	4	yes	complemented
44	#15689229	C₂²	1	4	yes	complemented
45	#15689222	C₂²	1	8	yes	complemented
46	#15689217	C₂²	1	4	yes	complemented
47	#15689210	C₂²	1	8	yes	complemented
48	#15689205	C₂²	1	4	yes	complemented
49	#15689117	C₂²	1	4	yes	—
50	#15689117	C₂²	1	4	yes	—
51	#15689077	C₂²	1	2	yes	—
52	#15689077	C₂²	1	2	yes	—
53	#15689077	C₂²	1	2	yes	—
54	#15689077	C₂²	1	2	yes	—
55	C₂×#13093935	C₂²	1	1	yes	characteristic
56	C₂×#13093934	C₂²	1	1	yes	characteristic
57	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
58	C₄₇×#533	C₂²	1	2	yes	—
59	C₄₇×#500	C₂²	1	2	yes	complemented
60	C₄₇×#499	C₂²	1	2	yes	complemented
61	C₄₇×#499	C₂²	1	2	yes	complemented
62	C₄₇×#498	C₂²	1	2	yes	complemented
63	C₄₇×#427	C₂²	1	2	yes	—
64	C₄₇×#427	C₂²	1	2	yes	—
65	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
66	C₂×#10625350	C₂³	1	4	yes	—
67	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
68	#13094046	—	2	8	no	—
69	#13094046	—	2	8	no	—
70	C₂×Dic₁₈₈	C₂³	1	2	yes	—
71	C₂×Dic₁₈₈	C₂³	1	2	yes	—
72	C₂×#10625325	C₂³	1	4	yes	—
73	C₂×#10625325	C₂³	1	4	yes	—
74	C₂×D₃₇₆	C₂³	1	2	yes	—
75	C₂×D₃₇₆	C₂³	1	2	yes	—
76	C₂×#10625324	—	2	4	no	—
77	C₂×#10625324	C₂³	1	2	yes	—
78	C₂×#10625324	C₂³	1	2	yes	—
79	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×C₈×D₄₇	—	2	4	no	—
82	C₂×C₈×D₄₇	C₂³	1	2	yes	—
83	C₂×C₈×D₄₇	C₂³	1	2	yes	—
84	#13094024	C₂³	1	2	yes	—
85	#13094021	C₂³	1	2	yes	—
86	#13094019	—	2	8	no	—
87	#13094019	—	2	8	no	—
88	#13094015	—	2	8	no	—
89	#13094013	—	2	8	no	—
90	#13094012	C₂³	1	4	yes	—
91	#13094009	—	2	8	no	—
92	#13094009	—	2	8	no	—
93	#13094008	—	2	4	no	—
94	#13094004	C₂³	1	8	yes	—
95	#13094000	—	2	8	no	—
96	#13093999	—	2	8	no	—
97	#13093999	C₂³	1	8	yes	—
98	#13093998	—	2	4	no	—
99	#13093994	—	2	4	no	—
100	#13093989	C₂³	1	8	yes	—
101	C₄×D₁₈₈	—	2	8	no	—
102	C₄×D₁₈₈	—	2	4	no	—
103	#13093986	C₂³	1	8	yes	—
104	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
105	#13093981	—	2	4	no	—
106	#13093981	D₄	1	4	yes	—
107	#13093981	C₂³	1	2	yes	—
108	#13093981	C₂³	1	2	yes	—
109	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
110	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
111	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
112	C₄²×D₄₇	—	2	4	no	—
113	#13093947	C₂³	1	8	yes	—
114	#13093947	C₂³	1	8	yes	—
115	#13093944	C₂³	1	8	yes	—
116	#13093944	C₂³	1	8	yes	—
117	#13093935	C₂³	1	2	yes	—
118	#13093935	C₂³	1	2	yes	—
119	#13093934	C₂³	1	2	yes	—
120	#13093934	C₂³	1	2	yes	—
121	C₈×Dic₄₇	C₂³	1	2	yes	—
122	C₈×Dic₄₇	C₂³	1	2	yes	—
123	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
126	#125×C₄₇	C₂³	1	4	yes	—
127	C₂²⋊Q₈×C₄₇	—	2	4	no	—
128	C₄×Q₈×C₄₇	—	2	4	no	—
129	#117×C₄₇	C₂³	1	4	yes	—
130	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
131	#107×C₄₇	C₂³	1	4	yes	—
132	#107×C₄₇	C₂³	1	4	yes	—
133	#106×C₄₇	C₂³	1	4	yes	—
134	#106×C₄₇	C₂³	1	4	yes	—
135	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
136	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
137	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
138	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
139	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×Q₈×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂×C₂²⋊D₄₇	—	2	4	no	—
144	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
146	#10625350	—	2	8	no	—
147	#10625350	—	2	8	no	—
148	C₂×D₁₈₈	—	2	8	no	—
149	C₂×D₁₈₈	—	2	4	no	—
150	C₂×D₁₈₈	C₂⁴	1	4	yes	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×C₄×D₄₇	—	2	4	no	—
154	C₂×C₄×D₄₇	—	2	8	no	—
155	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
156	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
157	C₂×Dic₉₄	C₂⁴	1	4	yes	—
158	C₂×C₈×C₄₇	#41	1	4	yes	—
159	C₂×C₈×C₄₇	#41	1	4	yes	—
160	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
162	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
163	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₄⋊C₄×C₄₇	—	2	8	no	—
165	C₄⋊C₄×C₄₇	—	2	4	no	—
166	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
167	C₂²⋊C₄×C₄₇	—	2	4	no	—
168	C₄²×C₄₇	—	2	4	no	—
169	C₄²×C₄₇	C₂×D₄	1	2	yes	—
170	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
172	(C₂×D₄₇)⋊C₄	—	2	8	no	—
173	(C₂×D₄₇)⋊C₄	—	2	8	no	—
174	(C₂×D₄₇)⋊C₄	—	2	8	no	—
175	(C₂×D₄₇)⋊C₄	—	2	8	no	—
176	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
177	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
178	C₄⋊Dic₄₇	—	2	4	no	—
179	C₄⋊Dic₄₇	—	2	8	no	—
180	Dic₄₇⋊C₄	—	2	8	no	—
181	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
182	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
183	C₄×Dic₄₇	—	2	8	no	—
184	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
185	C₄×Dic₄₇	C₂⁴	1	2	yes	—
186	C₂×C₄₇⋊C₈	—	2	2	no	—
187	C₂×C₄₇⋊C₈	—	2	2	no	—
188	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
189	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
190	Dic₁₈₈	—	2	4	no	—
191	Dic₁₈₈	—	2	4	no	—
192	D₃₇₆	—	2	4	no	—
193	D₃₇₆	—	2	4	no	—
194	#10625325	—	2	8	no	—
195	#10625325	—	2	8	no	—
196	#10625324	—	2	4	no	—
197	#10625324	—	2	4	no	—
198	C₈×D₄₇	—	2	4	no	—
199	C₈×D₄₇	—	2	4	no	—
200	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂²×D₄₇	—	2	2	no	—
202	C₂²×D₄₇	—	2	4	no	—
203	C₂²×D₄₇	—	4	2	no	—
204	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
205	Q₈×C₄₇	—	8	4	no	—
206	C₂×C₄×C₄₇	—	2	8	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
212	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
213	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
214	C₂²⋊D₄₇	—	4	8	no	—
215	C₂×Dic₄₇	—	2	2	no	—
216	C₂×Dic₄₇	—	2	4	no	—
217	C₂×Dic₄₇	—	4	2	no	—
218	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
219	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
220	D₁₈₈	—	2	4	no	—
221	D₁₈₈	—	2	4	no	—
222	D₁₈₈	—	8	4	no	—
223	D₁₈₈	—	8	8	no	—
224	C₄×D₄₇	—	2	4	no	—
225	C₄×D₄₇	—	2	2	no	—
226	C₄×D₄₇	—	2	2	no	—
227	C₄×D₄₇	—	4	8	no	—
228	C₄×D₄₇	—	8	8	no	—
229	Dic₉₄	—	2	4	no	—
230	Dic₉₄	—	2	4	no	—
231	C₈×C₄₇	C₂×#41	1	2	yes	—
232	C₈×C₄₇	C₂×#41	1	2	yes	—
233	C₈×C₄₇	C₂×#41	1	2	yes	—
234	C₈×C₄₇	C₂×#41	1	2	yes	—
235	C₄₇⋊C₈	—	2	2	no	—
236	C₄₇⋊C₈	—	2	2	no	—
237	#60682	—	47	1	no	maximal, Sylow
238	C₂²×C₄₇	—	2	2	no	—
239	C₂²×C₄₇	#532	1	2	yes	—
240	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
241	C₂×D₄₇	—	2	4	no	—
242	C₂×D₄₇	—	2	2	no	—
243	C₂×D₄₇	—	4	4	no	—
244	C₂×D₄₇	—	4	8	no	—
245	C₂×D₄₇	—	4	4	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	4	8	no	—
249	C₄×C₄₇	#532	1	2	yes	—
250	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
251	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
252	Dic₄₇	—	2	4	no	—
253	Dic₄₇	—	2	2	no	—
254	Dic₄₇	—	4	4	no	—
255	#3455	—	47	2	no	—
256	#3177	—	47	2	no	—
257	#3176	—	47	2	no	—
258	#3175	—	47	4	no	—
259	#3174	—	47	4	no	—
260	#3173	—	47	4	no	—
261	#3160	D₄₇	1	1	yes	characteristic, complemented
262	#3147	—	47	1	no	—
263	#3135	—	47	2	no	—
264	#3054	—	47	2	no	—
265	#3050	—	47	2	no	—
266	#2943	—	47	2	no	—
267	C₄×#135	—	47	2	no	—
268	C₂×#405	—	47	1	no	—
269	C₂×C₄₇	—	2	2	no	—
270	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
271	C₂×C₄₇	#3584	1	2	yes	—
272	D₄₇	—	4	2	no	—
273	D₄₇	—	8	4	no	—
274	C₂×#135	—	47	2	no	—
275	C₂×#135	—	47	2	no	—
276	C₂²×M₁₆	—	47	1	no	—
277	C₂³×C₈	—	47	1	no	—
278	#542	—	47	8	no	—
279	#541	—	47	4	no	—
280	#540	—	47	4	no	—
281	#539	—	94	4	no	—
282	#538	—	94	4	no	—
283	#533	C₂×D₄₇	1	2	yes	—
284	#532	—	47	2	no	—
285	#529	—	94	8	no	—
286	#525	—	47	4	no	—
287	C₄×#41	—	47	4	no	—
288	C₂×#117	—	47	1	no	—
289	#500	C₂×D₄₇	1	2	yes	complemented
290	#499	C₂×D₄₇	1	2	yes	complemented
291	#499	C₂×D₄₇	1	2	yes	complemented
292	#498	C₂×D₄₇	1	2	yes	complemented
293	#495	—	47	2	no	—
294	#495	—	47	2	no	—
295	#494	—	47	1	no	—
296	#493	—	47	1	no	—
297	#492	—	47	2	no	—
298	#491	—	47	4	no	—
299	#490	—	47	4	no	—
300	#489	—	47	8	no	—
301	#470	—	47	4	no	—
302	#469	—	47	4	no	—
303	#468	—	47	8	no	—
304	#467	—	47	4	no	—
305	#466	—	47	4	no	—
306	#465	—	47	8	no	—
307	#442	—	47	4	no	—
308	#441	—	47	4	no	—
309	#440	—	47	8	no	—
310	C₄×Q₁₆	—	47	4	no	—
311	C₄×SD₁₆	—	47	8	no	—
312	C₄×D₈	—	47	4	no	—
313	#427	C₂×D₄₇	1	2	yes	—
314	#427	C₂×D₄₇	1	2	yes	—
315	#416	—	47	4	no	—
316	#416	—	47	4	no	—
317	#405	—	47	2	no	—
318	#405	—	47	2	no	—
319	#405	—	47	2	no	—
320	#405	—	47	2	no	—
321	C₂×#97	—	47	1	no	—
322	C₂×#97	—	47	1	no	—
323	C₂×C₄×C₈	—	47	1	no	—
324	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
325	C₄₇	#60682	1	1	yes	characteristic, complemented, Sylow
326	C₂×#41	—	47	4	no	—
327	C₂³×C₄	—	47	1	no	—
328	#135	—	94	8	no	—
329	#135	—	94	8	no	—
330	C₂×Q₁₆	—	47	2	no	—
331	C₂×Q₁₆	—	47	2	no	—
332	C₂×SD₁₆	—	47	4	no	—
333	C₂×SD₁₆	—	47	4	no	—
334	C₂×D₈	—	47	2	no	—
335	C₂×D₈	—	47	2	no	—
336	C₂×M₁₆	—	47	2	no	—
337	C₂×M₁₆	—	47	2	no	—
338	C₂×M₁₆	—	94	4	no	—
339	C₂²×C₈	—	47	1	no	—
340	C₂²×C₈	—	47	1	no	—
341	C₂²×C₈	—	47	2	no	—
342	C₂²×C₈	—	47	2	no	—
343	C₂²×C₈	—	94	4	no	—
344	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
345	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊Q₈	—	47	2	no	—
347	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
348	#127	—	47	2	no	—
349	#126	—	94	8	no	—
350	#126	—	94	8	no	—
351	#125	—	94	8	no	—
352	#125	C₂²×D₄₇	1	4	yes	—
353	#124	—	47	4	no	—
354	#124	—	94	8	no	—
355	#123	—	94	4	no	—
356	#123	—	94	8	no	—
357	#123	—	94	8	no	—
358	C₂²⋊Q₈	—	2	4	no	—
359	C₂²⋊Q₈	—	47	8	no	—
360	C₂²⋊Q₈	—	94	8	no	—
361	#121	—	47	8	no	—
362	#121	—	94	8	no	—
363	#121	—	94	4	no	—
364	#120	—	94	4	no	—
365	C₄×Q₈	—	2	4	no	—
366	C₄×Q₈	—	47	8	no	—
367	C₄×D₄	—	47	8	no	—
368	C₄×D₄	—	94	8	no	—
369	C₄×D₄	—	94	8	no	—
370	C₄×D₄	—	94	4	no	—
371	#117	—	47	4	no	—
372	#117	—	47	2	no	—
373	#117	—	47	2	no	—
374	#117	—	94	4	no	—
375	#117	C₂²×D₄₇	1	4	yes	—
376	C₂×C₄⋊C₄	—	47	2	no	—
377	C₂×C₂²⋊C₄	—	47	2	no	—
378	C₂×C₄²	—	47	1	no	—
379	C₂×C₄²	—	94	4	no	—
380	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
381	#107	C₂²×D₄₇	1	4	yes	—
382	#107	C₂²×D₄₇	1	4	yes	—
383	#106	C₂²×D₄₇	1	4	yes	—
384	#106	C₂²×D₄₇	1	4	yes	—
385	#103	—	47	8	no	—
386	#103	—	47	8	no	—
387	#102	—	47	8	no	—
388	#102	—	47	8	no	—
389	#97	—	47	2	no	—
390	#97	—	47	2	no	—
391	#97	—	47	2	no	—
392	#97	—	47	2	no	—
393	C₄×C₈	—	47	2	no	—
394	C₄×C₈	—	47	2	no	—
395	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
396	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
397	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
399	C₂⁴	—	47	1	no	—
400	#41	—	94	8	no	—
401	#41	—	94	8	no	—
402	C₂×Q₈	—	2	4	no	—
403	C₂×Q₈	—	47	4	no	—
404	C₂×D₄	—	47	4	no	—
405	C₂×D₄	—	94	8	no	—
406	C₂×D₄	—	94	4	no	—
407	C₂×D₄	—	94	4	no	—
408	C₂²×C₄	—	47	1	no	—
409	C₂²×C₄	—	47	2	no	—
410	C₂²×C₄	—	47	2	no	—
411	C₂²×C₄	—	47	2	no	—
412	C₂²×C₄	—	94	8	no	—
413	C₂²×C₄	—	94	2	no	—
414	C₂²×C₄	—	94	2	no	—
415	C₂²×C₄	—	94	4	no	—
416	C₂²×C₄	D₄×D₄₇	1	2	yes	—
417	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
418	Q₁₆	—	94	4	no	—
419	Q₁₆	—	94	4	no	—
420	SD₁₆	—	94	8	no	—
421	SD₁₆	—	94	8	no	—
422	D₈	—	94	4	no	—
423	D₈	—	94	4	no	—
424	M₁₆	—	94	4	no	—
425	M₁₆	—	94	4	no	—
426	C₂×C₈	—	47	2	no	—
427	C₂×C₈	—	47	2	no	—
428	C₂×C₈	—	94	2	no	—
429	C₂×C₈	—	94	2	no	—
430	C₂×C₈	—	94	4	no	—
431	C₂×C₈	—	94	4	no	—
432	C₂×C₈	#10625354	1	4	yes	—
433	C₂×C₈	#10625354	1	4	yes	—
434	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
435	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
436	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
437	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	47	4	no	—
441	C₄⋊C₄	—	47	4	no	—
442	C₄⋊C₄	—	94	8	no	—
443	C₄⋊C₄	—	94	8	no	—
444	C₄⋊C₄	—	94	4	no	—
445	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
446	C₂²⋊C₄	—	2	4	no	—
447	C₂²⋊C₄	—	47	4	no	—
448	C₂²⋊C₄	—	47	4	no	—
449	C₂²⋊C₄	—	94	8	no	—
450	C₂²⋊C₄	—	94	8	no	—
451	C₂²⋊C₄	—	94	8	no	—
452	C₂²⋊C₄	—	94	8	no	—
453	C₄²	—	2	4	no	—
454	C₄²	—	47	2	no	—
455	C₄²	—	47	2	no	—
456	C₄²	—	94	8	no	—
457	C₄²	D₄×D₄₇	1	2	yes	—
458	C₄²	C₂³×D₄₇	1	1	yes	characteristic
459	C₄²	C₂³×D₄₇	1	1	yes	characteristic
460	C₂³	—	47	2	no	—
461	C₂³	—	94	2	no	—
462	C₂³	—	94	4	no	—
463	C₂³	—	188	2	no	—
464	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
465	Q₈	—	8	4	no	—
466	Q₈	—	94	4	no	—
467	Q₈	—	94	4	no	—
468	D₄	—	94	4	no	—
469	D₄	—	94	4	no	—
470	D₄	—	376	4	no	—
471	D₄	—	376	8	no	—
472	D₄	—	188	8	no	—
473	C₂×C₄	—	2	8	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	47	4	no	—
476	C₂×C₄	—	47	2	no	—
477	C₂×C₄	—	94	2	no	—
478	C₂×C₄	—	94	4	no	—
479	C₂×C₄	—	94	2	no	—
480	C₂×C₄	—	94	2	no	—
481	C₂×C₄	—	94	4	no	—
482	C₂×C₄	—	376	8	no	—
483	C₂×C₄	—	188	2	no	—
484	C₂×C₄	—	188	8	no	—
485	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
486	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
487	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
488	C₂×C₄	C₂×#10625354	1	2	yes	—
489	C₂×C₄	C₂×#10625354	1	2	yes	—
490	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
491	C₈	—	94	2	no	—
492	C₈	—	94	2	no	—
493	C₈	C₂×#10625354	1	2	yes	—
494	C₈	C₂×#10625354	1	2	yes	—
495	C₈	C₂×#10625354	1	2	yes	—
496	C₈	C₂×#10625354	1	2	yes	—
497	C₂²	—	2	2	no	—
498	C₂²	—	94	4	no	—
499	C₂²	—	94	2	no	—
500	C₂²	—	188	4	no	—
501	C₂²	—	188	8	no	—
502	C₂²	—	188	4	no	—
503	C₂²	#15689674	1	2	yes	—
504	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
505	C₄	—	2	2	no	—
506	C₄	—	2	2	no	—
507	C₄	—	4	8	no	—
508	C₄	—	94	4	no	—
509	C₄	—	94	2	no	—
510	C₄	—	188	4	no	—
511	C₄	#15689674	1	2	yes	—
512	C₄	C₂²×#10625354	1	1	yes	characteristic
513	C₄	C₂²×#10625354	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	376	4	no	—
516	C₂	—	188	2	no	—
517	C₂	C₂×#15689674	1	1	yes	characteristic
518	C₂	#20258157	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3160	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3160	D₄₇
hypocenter	C₄₇	#60682
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #20256780	C₂	semidirect
2. #20254048	C₂	semidirect
3. #20254039	C₂	semidirect
4. #20254030	C₂	semidirect
5. #20254018	C₂	semidirect
6. #20254007	C₂	semidirect
7. #20253816	C₂	semidirect
8. #20253736	C₂	semidirect
9. #20252998	C₂	semidirect
10. #20252970	C₂	semidirect
11. #20252188	C₂	semidirect
12. #20252159	C₂	semidirect
13. C₂×#15689077	C₂	semidirect
14. C₄₇×#3160	C₂	semidirect
29. #15689507	C₂²	semidirect
30. #15689507	C₂²	semidirect
31. #15689503	C₂²	semidirect
32. #15689500	C₂²	semidirect
33. #15689496	C₂²	semidirect
34. #15689493	C₂²	semidirect
35. #15689489	C₂²	semidirect
36. #15689485	C₂²	semidirect
43. #15689234	C₂²	semidirect
44. #15689229	C₂²	semidirect
45. #15689222	C₂²	semidirect
46. #15689217	C₂²	semidirect
47. #15689210	C₂²	semidirect
48. #15689205	C₂²	semidirect
59. C₄₇×#500	C₂²	semidirect
60. C₄₇×#499	C₂²	semidirect
61. C₄₇×#499	C₂²	semidirect
62. C₄₇×#498	C₂²	semidirect
261. #3160	D₄₇	semidirect
289. #500	C₂×D₄₇	semidirect
290. #499	C₂×D₄₇	semidirect
291. #499	C₂×D₄₇	semidirect
292. #498	C₂×D₄₇	semidirect
325. C₄₇	#60682	semidirect

Maximal subgroups

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

subgroup	index
#20256780	2
#20254048	2
#20254039	2
#20254030	2
#20254018	2
#20254007	2
#20253816	2
#20253736	2
#20252998	2
#20252970	2
#20252188	2
#20252159	2
C₂×#15689077	2
C₄₇×#3160	2
#60682	47