Subgroups — #27096916

Order 12032.

1818 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257189	C₂	1	2	yes	maximal, complemented
2	#20256349	C₂	1	4	yes	maximal, complemented
3	#20256292	C₂	1	4	yes	maximal, complemented
4	#20256257	C₂	1	2	yes	maximal, complemented
5	#20256252	C₂	1	4	yes	maximal, complemented
6	#20256240	C₂	1	2	yes	maximal, complemented
7	#20253928	C₂	1	2	yes	maximal, complemented
8	#20253222	C₂	1	4	yes	maximal, complemented
9	#20253181	C₂	1	2	yes	maximal, complemented
10	#20252322	C₂	1	1	yes	maximal, characteristic, complemented
11	#20252239	C₂	1	2	yes	maximal
12	C₂×C₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic
13	C₄₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
15	#15689834	C₂²	1	4	yes	complemented
16	#15689833	—	2	2	no	—
17	#15689833	—	2	4	no	—
18	#15689829	C₂²	1	8	yes	complemented
19	Q₈×D₁₈₈	—	2	2	no	—
20	#15689788	C₂²	1	4	yes	complemented
21	#15689751	C₂²	1	4	yes	—
22	#15689748	—	2	4	no	—
23	#15689680	C₂²	1	1	yes	characteristic
24	C₂²⋊Q₈×D₄₇	—	2	4	no	—
25	#15689597	C₂²	1	4	yes	—
26	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
27	#15689530	C₂²	1	8	yes	complemented
28	#15689527	C₂²	1	4	yes	complemented
29	#15689524	C₂²	1	4	yes	complemented
30	#15689426	C₂²	1	8	yes	complemented
31	#15689422	C₂²	1	8	yes	complemented
32	#15689420	C₂²	1	8	yes	complemented
33	#15689412	C₂²	1	8	yes	complemented
34	#15689410	C₂²	1	4	yes	complemented
35	#15689402	C₂²	1	8	yes	complemented
36	#15689400	C₂²	1	4	yes	complemented
37	#15689253	C₂²	1	2	yes	complemented
38	#15689253	C₂²	1	2	yes	complemented
39	C₈×Dic₉₄	C₂²	1	2	yes	complemented
40	C₈×Dic₉₄	C₂²	1	2	yes	complemented
41	#15689234	C₂²	1	8	yes	—
42	C₄×D₃₇₆	C₂²	1	2	yes	—
43	C₄×D₃₇₆	C₂²	1	2	yes	—
44	C₄×D₃₇₆	C₂²	1	2	yes	—
45	C₄×D₃₇₆	C₂²	1	2	yes	—
46	#15689205	C₂²	1	4	yes	—
47	#15689205	C₂²	1	4	yes	—
48	#15689166	C₂²	1	4	yes	—
49	C₂×#13093958	C₂²	1	1	yes	characteristic
50	#15689149	C₂²	1	2	yes	—
51	#15689147	C₂²	1	1	yes	characteristic
52	#15689127	C₂²	1	4	yes	—
53	C₂×#13093946	C₂²	1	2	yes	—
54	#15689078	C₂²	1	2	yes	—
55	C₄₇×#533	C₂²	1	2	yes	—
56	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
57	C₄₇×#500	C₂²	1	1	yes	characteristic, complemented
58	C₄₇×#499	C₂²	1	2	yes	complemented
59	C₄₇×#499	C₂²	1	2	yes	complemented
60	C₄₇×#498	C₂²	1	2	yes	complemented
61	C₄₇×#427	C₂²	1	2	yes	—
62	C₄₇×#427	C₂²	1	2	yes	—
63	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
64	C₂×Q₈×D₄₇	—	2	4	no	—
65	C₂²×D₁₈₈	C₂³	1	2	yes	—
66	C₂²×C₄×D₄₇	—	2	2	no	—
67	C₂×D₃₇₆	Q₈	1	8	yes	complemented
68	C₂×D₃₇₆	C₂³	1	2	yes	—
69	C₂×D₃₇₆	C₂³	1	2	yes	—
70	C₂×#10625329	C₂³	1	2	yes	—
71	#13094024	—	2	4	no	—
72	#13094024	D₄	1	1	yes	characteristic
73	#13094024	D₄	1	1	yes	characteristic
74	#13094023	C₂³	1	8	yes	—
75	#13094016	—	2	4	no	—
76	#13094016	D₄	1	2	yes	—
77	#13094015	C₂³	1	8	yes	—
78	#13094004	—	2	4	no	—
79	#13094004	—	2	8	no	—
80	#13094003	D₄	1	2	yes	—
81	#13094003	D₄	1	2	yes	—
82	#13094002	—	2	8	no	—
83	#13094002	—	2	8	no	—
84	#13094002	—	2	8	no	—
85	#13094001	—	2	8	no	—
86	#13094000	—	2	4	no	—
87	#13094000	—	2	8	no	—
88	C₄×Dic₉₄	C₂³	1	2	yes	—
89	C₄×Dic₉₄	C₂³	1	2	yes	—
90	C₄×D₁₈₈	—	2	2	no	—
91	C₄×D₁₈₈	—	2	2	no	—
92	C₄×D₁₈₈	—	2	4	no	—
93	C₄×D₁₈₈	—	2	4	no	—
94	C₄×D₁₈₈	C₂³	1	4	yes	—
95	C₄×D₁₈₈	C₂³	1	4	yes	—
96	#13093986	C₂³	1	8	yes	—
97	#13093986	C₂³	1	8	yes	—
98	#13093983	C₂³	1	2	yes	—
99	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
100	C₄⋊C₄×D₄₇	—	2	4	no	—
101	C₄⋊C₄×D₄₇	—	2	8	no	—
102	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
103	C₂²⋊C₄×D₄₇	—	2	8	no	—
104	#13093958	C₂³	1	2	yes	—
105	#13093958	C₂³	1	2	yes	—
106	#13093957	C₂³	1	8	yes	—
107	#13093955	C₂³	1	8	yes	—
108	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
109	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
110	Dic₄₇⋊C₈	C₂³	1	4	yes	—
111	Dic₄₇⋊C₈	C₂³	1	4	yes	—
112	#13093946	C₂³	1	4	yes	—
113	#13093946	C₂³	1	4	yes	—
114	#13093944	C₂³	1	8	yes	—
115	#13093944	C₂³	1	8	yes	—
116	#13093934	C₂³	1	4	yes	—
117	C₈×Dic₄₇	C₂³	1	4	yes	—
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
120	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
121	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
122	#125×C₄₇	C₂³	1	4	yes	—
123	C₂²⋊Q₈×C₄₇	—	2	2	no	—
124	C₂²⋊Q₈×C₄₇	—	2	2	no	—
125	C₄×Q₈×C₄₇	—	2	2	no	—
126	C₄×Q₈×C₄₇	—	2	2	no	—
127	#117×C₄₇	C₂³	1	4	yes	—
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	#107×C₄₇	C₂³	1	2	yes	—
130	#107×C₄₇	C₂³	1	2	yes	—
131	#107×C₄₇	C₂³	1	2	yes	—
132	#107×C₄₇	C₂³	1	2	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	—	2	2	no	—
140	C₂×Q₈×C₄₇	—	2	2	no	—
141	C₂×Q₈×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²×Dic₄₇	—	2	2	no	—
146	Q₈×D₄₇	—	8	8	no	—
147	C₂×D₁₈₈	—	2	2	no	—
148	C₂×D₁₈₈	—	2	4	no	—
149	C₂×D₁₈₈	C₂×Q₈	1	8	yes	complemented
150	C₂×D₁₈₈	C₂⁴	1	4	yes	—
151	C₂×C₄×D₄₇	—	2	4	no	—
152	C₂×C₄×D₄₇	—	2	4	no	—
153	C₂×C₄×D₄₇	—	2	8	no	—
154	C₂×C₄×D₄₇	—	2	8	no	—
155	C₂×C₄×D₄₇	—	8	4	no	—
156	C₂×Dic₉₄	—	2	8	no	—
157	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
158	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
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	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₄⋊C₄×C₄₇	—	2	4	no	—
166	C₄⋊C₄×C₄₇	—	2	4	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	2	no	—
169	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
170	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
171	C₂²⋊C₄×C₄₇	—	2	4	no	—
172	C₄²×C₄₇	—	2	4	no	—
173	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
176	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
177	C₂²⋊Dic₄₇	C₂×D₄	1	4	yes	—
178	(C₂×D₄₇)⋊C₄	—	2	4	no	—
179	(C₂×D₄₇)⋊C₄	—	2	4	no	—
180	(C₂×D₄₇)⋊C₄	—	2	8	no	—
181	(C₂×D₄₇)⋊C₄	—	2	8	no	—
182	C₄⋊Dic₄₇	—	2	2	no	—
183	C₄⋊Dic₄₇	—	2	8	no	—
184	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
185	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
186	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
187	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
188	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
189	Dic₄₇⋊C₄	—	2	8	no	—
190	Dic₄₇⋊C₄	—	2	8	no	—
191	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
192	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
193	C₄×Dic₄₇	C₂⁴	1	4	yes	—
194	#10625329	—	2	4	no	—
195	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
196	D₃₇₆	C₂×Q₈	1	8	yes	complemented
197	D₃₇₆	C₂×Q₈	1	8	yes	complemented
198	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	C₂²×D₄₇	—	2	4	no	—
200	C₂²×D₄₇	—	2	8	no	—
201	C₂²×D₄₇	—	8	2	no	—
202	C₂²×D₄₇	—	8	2	no	—
203	Q₈×C₄₇	—	4	4	no	—
204	Q₈×C₄₇	—	8	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
215	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
216	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
217	C₂×Dic₄₇	—	2	4	no	—
218	C₂×Dic₄₇	—	8	2	no	—
219	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
220	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
221	D₁₈₈	—	2	8	no	—
222	D₁₈₈	—	2	4	no	—
223	D₁₈₈	C₂²×Q₈	1	8	yes	—
224	C₄×D₄₇	—	4	8	no	—
225	C₄×D₄₇	—	8	8	no	—
226	C₄×D₄₇	—	8	8	no	—
227	C₄×D₄₇	—	8	4	no	—
228	Dic₉₄	—	2	4	no	—
229	Dic₉₄	—	4	2	no	—
230	Dic₉₄	—	8	8	no	—
231	C₈×C₄₇	—	2	1	no	—
232	C₈×C₄₇	—	2	1	no	—
233	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
234	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
235	C₄₇⋊C₈	—	2	4	no	—
236	#61370	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	2	1	no	—
239	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
240	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
241	C₂×D₄₇	—	2	8	no	—
242	C₂×D₄₇	—	4	4	no	—
243	C₂×D₄₇	—	4	4	no	—
244	C₂×D₄₇	—	8	8	no	—
245	C₄×C₄₇	—	2	1	no	—
246	C₄×C₄₇	—	2	1	no	—
247	C₄×C₄₇	—	2	1	no	—
248	C₄×C₄₇	—	4	4	no	—
249	C₄×C₄₇	—	4	4	no	—
250	C₄×C₄₇	D₄×Q₈	1	2	yes	—
251	C₄×C₄₇	#576	1	2	yes	—
252	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
253	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	Dic₄₇	—	2	4	no	—
255	Dic₄₇	—	2	4	no	—
256	Dic₄₇	—	4	4	no	—
257	#3501	—	47	2	no	—
258	#3389	—	47	4	no	—
259	#3384	—	47	4	no	—
260	#3380	—	47	2	no	—
261	#3380	—	47	4	no	—
262	Q₈×D₈	—	47	2	no	—
263	#3164	—	47	2	no	—
264	#3160	D₄₇	1	1	yes	characteristic, complemented
265	#3081	—	47	4	no	—
266	#3077	—	47	2	no	—
267	#2960	—	47	1	no	—
268	#2948	—	47	2	no	—
269	C₂×C₄×D₈	—	47	1	no	—
270	C₂×C₄₇	—	2	2	no	—
271	C₂×C₄₇	C₂×D₄×Q₈	1	1	yes	characteristic
272	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
273	C₂×C₄₇	#3584	1	1	yes	characteristic
274	D₄₇	—	4	8	no	—
275	C₂²×D₈	—	47	1	no	—
276	#554	—	47	4	no	—
277	#554	—	47	8	no	—
278	#554	—	94	4	no	—
279	#554	—	94	2	no	—
280	D₄×Q₈	—	47	4	no	—
281	D₄×Q₈	—	94	2	no	—
282	#544	—	47	4	no	—
283	#543	—	94	4	no	—
284	#533	—	47	1	no	—
285	#533	C₂×D₄₇	1	2	yes	—
286	C₂×C₂²⋊Q₈	—	94	4	no	—
287	#518	—	47	4	no	—
288	C₂×C₄×D₄	—	47	2	no	—
289	#501	—	47	8	no	—
290	#500	—	47	4	no	—
291	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
292	#500	C₂×D₄₇	1	1	yes	characteristic, complemented
293	#499	—	47	4	no	—
294	#499	C₂×D₄₇	1	2	yes	complemented
295	#499	C₂×D₄₇	1	2	yes	complemented
296	#498	C₂×D₄₇	1	2	yes	complemented
297	#478	—	47	8	no	—
298	#478	—	47	8	no	—
299	#478	—	47	8	no	—
300	#476	—	47	4	no	—
301	#476	—	47	8	no	—
302	#474	—	47	4	no	—
303	#474	—	47	8	no	—
304	#446	—	47	2	no	—
305	#446	—	47	2	no	—
306	C₈×Q₈	—	47	2	no	—
307	C₈×Q₈	—	47	2	no	—
308	#442	—	47	8	no	—
309	C₄×D₈	—	47	4	no	—
310	C₄×D₈	—	47	4	no	—
311	C₄×D₈	—	47	2	no	—
312	C₄×D₈	—	47	2	no	—
313	C₄×D₈	—	47	2	no	—
314	C₄×D₈	—	47	2	no	—
315	#428	—	47	4	no	—
316	#427	C₂×D₄₇	1	2	yes	—
317	#427	C₂×D₄₇	1	2	yes	—
318	C₂×#107	—	47	1	no	—
319	#424	—	47	2	no	—
320	#423	—	47	1	no	—
321	#418	—	47	4	no	—
322	C₂×#102	—	47	2	no	—
323	#405	—	47	2	no	—
324	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
325	C₄₇	#61370	1	1	yes	characteristic, complemented, Sylow
326	C₂²×Q₈	—	94	4	no	—
327	C₂²×D₄	—	47	2	no	—
328	C₂³×C₄	—	94	2	no	—
329	C₂×D₈	—	47	8	no	—
330	C₂×D₈	—	47	2	no	—
331	C₂×D₈	—	47	2	no	—
332	C₂×M₁₆	—	47	2	no	—
333	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	C₄⋊Q₈	—	47	8	no	—
336	C₄⋊Q₈	—	47	1	no	—
337	C₄⋊Q₈	—	47	1	no	—
338	C₄⋊Q₈	—	94	4	no	—
339	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
340	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
341	#125	—	47	8	no	—
342	#125	—	47	2	no	—
343	#125	—	94	4	no	—
344	#125	C₂²×D₄₇	1	4	yes	—
345	C₂²⋊Q₈	—	2	2	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	47	2	no	—
348	C₂²⋊Q₈	—	47	2	no	—
349	C₂²⋊Q₈	—	94	8	no	—
350	C₂²⋊Q₈	—	94	8	no	—
351	C₂²⋊Q₈	—	94	8	no	—
352	C₂²⋊Q₈	—	94	8	no	—
353	C₂²⋊Q₈	—	94	4	no	—
354	C₂²⋊Q₈	—	94	8	no	—
355	C₂²⋊Q₈	—	94	4	no	—
356	C₂²⋊Q₈	—	94	8	no	—
357	C₄×Q₈	—	2	2	no	—
358	C₄×Q₈	—	2	2	no	—
359	C₄×Q₈	—	47	2	no	—
360	C₄×Q₈	—	47	2	no	—
361	C₄×D₄	—	47	8	no	—
362	C₄×D₄	—	47	8	no	—
363	C₄×D₄	—	47	4	no	—
364	C₄×D₄	—	47	4	no	—
365	C₄×D₄	—	94	4	no	—
366	C₄×D₄	—	94	4	no	—
367	C₄×D₄	—	94	2	no	—
368	C₄×D₄	—	94	2	no	—
369	#117	—	47	2	no	—
370	#117	C₂²×D₄₇	1	4	yes	—
371	C₂×C₄⋊C₄	—	47	2	no	—
372	C₂×C₄⋊C₄	—	94	8	no	—
373	C₂×C₄⋊C₄	—	94	4	no	—
374	C₂×C₂²⋊C₄	—	94	8	no	—
375	C₂×C₂²⋊C₄	—	94	2	no	—
376	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
377	#107	—	47	2	no	—
378	#107	—	47	2	no	—
379	#107	—	47	8	no	—
380	#107	C₂²×D₄₇	1	2	yes	—
381	#107	C₂²×D₄₇	1	2	yes	—
382	#107	C₂²×D₄₇	1	2	yes	—
383	#107	C₂²×D₄₇	1	2	yes	—
384	#106	—	47	8	no	—
385	#106	C₂²×D₄₇	1	4	yes	—
386	#106	C₂²×D₄₇	1	4	yes	—
387	C₄⋊C₈	—	47	4	no	—
388	C₄⋊C₈	—	47	4	no	—
389	C₄⋊C₈	—	47	2	no	—
390	C₄⋊C₈	—	47	2	no	—
391	#102	—	47	4	no	—
392	#102	—	47	4	no	—
393	#102	—	47	8	no	—
394	#102	—	47	8	no	—
395	#97	—	47	4	no	—
396	C₄×C₈	—	47	4	no	—
397	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
399	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
400	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
401	C₂⁴	—	94	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	47	2	no	—
405	C₂×Q₈	—	47	2	no	—
406	C₂×Q₈	—	94	8	no	—
407	C₂×Q₈	—	376	8	no	—
408	C₂×D₄	—	47	8	no	—
409	C₂×D₄	—	47	4	no	—
410	C₂×D₄	—	94	2	no	—
411	C₂×D₄	—	94	4	no	—
412	C₂²×C₄	—	94	8	no	—
413	C₂²×C₄	—	94	8	no	—
414	C₂²×C₄	—	94	2	no	—
415	C₂²×C₄	—	94	4	no	—
416	C₂²×C₄	—	94	4	no	—
417	C₂²×C₄	—	376	4	no	—
418	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
419	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
420	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
421	D₈	—	47	8	no	—
422	D₈	—	47	8	no	—
423	M₁₆	—	94	4	no	—
424	C₂×C₈	—	2	2	no	—
425	C₂×C₈	—	47	4	no	—
426	C₂×C₈	Q₈×D₄₇	1	4	yes	complemented
427	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
428	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
429	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
430	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
431	C₄⋊C₄	—	2	4	no	—
432	C₄⋊C₄	—	2	2	no	—
433	C₄⋊C₄	—	2	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	47	4	no	—
436	C₄⋊C₄	—	47	4	no	—
437	C₄⋊C₄	—	47	2	no	—
438	C₄⋊C₄	—	47	2	no	—
439	C₄⋊C₄	—	47	2	no	—
440	C₄⋊C₄	—	47	2	no	—
441	C₄⋊C₄	—	47	4	no	—
442	C₄⋊C₄	—	94	8	no	—
443	C₄⋊C₄	—	94	8	no	—
444	C₄⋊C₄	—	94	8	no	—
445	C₄⋊C₄	—	94	2	no	—
446	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
447	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
448	C₂²⋊C₄	—	2	4	no	—
449	C₂²⋊C₄	—	47	4	no	—
450	C₂²⋊C₄	—	94	8	no	—
451	C₂²⋊C₄	—	94	8	no	—
452	C₂²⋊C₄	—	94	4	no	—
453	C₂²⋊C₄	—	94	4	no	—
454	C₄²	—	2	4	no	—
455	C₄²	—	47	4	no	—
456	C₄²	D₄×D₄₇	1	1	yes	characteristic
457	C₄²	D₄×D₄₇	1	1	yes	characteristic
458	C₄²	C₂³×D₄₇	1	1	yes	characteristic
459	C₄²	C₂³×D₄₇	1	1	yes	characteristic
460	C₂³	—	94	8	no	—
461	C₂³	—	94	4	no	—
462	C₂³	—	376	2	no	—
463	C₂³	—	376	2	no	—
464	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
465	Q₈	—	4	4	no	—
466	Q₈	—	8	2	no	—
467	Q₈	—	94	4	no	—
468	Q₈	—	376	8	no	—
469	Q₈	—	188	2	no	—
470	D₄	—	47	8	no	—
471	D₄	—	94	8	no	—
472	D₄	—	94	4	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	47	4	no	—
478	C₂×C₄	—	47	4	no	—
479	C₂×C₄	—	94	4	no	—
480	C₂×C₄	—	376	4	no	—
481	C₂×C₄	—	376	8	no	—
482	C₂×C₄	—	376	8	no	—
483	C₂×C₄	—	376	2	no	—
484	C₂×C₄	—	188	8	no	—
485	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
488	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
489	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
490	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
491	C₂×C₄	#13094072	1	2	yes	—
492	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
493	C₈	—	2	1	no	—
494	C₈	—	2	1	no	—
495	C₈	—	94	4	no	—
496	C₈	C₂×Q₈×D₄₇	1	2	yes	—
497	C₈	C₂×Q₈×D₄₇	1	2	yes	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	94	8	no	—
501	C₂²	—	376	8	no	—
502	C₂²	—	188	4	no	—
503	C₂²	—	188	4	no	—
504	C₂²	#15689788	1	2	yes	—
505	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	2	1	no	—
509	C₄	—	4	4	no	—
510	C₄	—	4	4	no	—
511	C₄	—	94	4	no	—
512	C₄	—	94	4	no	—
513	C₄	—	188	4	no	—
514	C₄	#15689788	1	2	yes	—
515	C₄	#15689925	1	2	yes	—
516	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
517	C₄	C₂×#13094072	1	1	yes	characteristic
518	C₂	—	2	2	no	—
519	C₂	—	188	8	no	—
520	C₂	C₂×#15689788	1	1	yes	characteristic
521	C₂	C₂×#15689925	1	1	yes	characteristic
522	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3160	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂²×D₃₇₆	C₂²
hypercenter	#3160	D₄₇
hypocenter	C₄₇	#61370
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
1. #20257189	C₂	semidirect
2. #20256349	C₂	semidirect
3. #20256292	C₂	semidirect
4. #20256257	C₂	semidirect
5. #20256252	C₂	semidirect
6. #20256240	C₂	semidirect
7. #20253928	C₂	semidirect
8. #20253222	C₂	semidirect
9. #20253181	C₂	semidirect
10. #20252322	C₂	semidirect
13. C₄₇×#3160	C₂	semidirect
15. #15689834	C₂²	semidirect
18. #15689829	C₂²	semidirect
20. #15689788	C₂²	semidirect
27. #15689530	C₂²	semidirect
28. #15689527	C₂²	semidirect
29. #15689524	C₂²	semidirect
30. #15689426	C₂²	semidirect
31. #15689422	C₂²	semidirect
32. #15689420	C₂²	semidirect
33. #15689412	C₂²	semidirect
34. #15689410	C₂²	semidirect
35. #15689402	C₂²	semidirect
36. #15689400	C₂²	semidirect
37. #15689253	C₂²	semidirect
38. #15689253	C₂²	semidirect
39. C₈×Dic₉₄	C₂²	semidirect
40. C₈×Dic₉₄	C₂²	semidirect
56. C₄₇×#500	C₂²	semidirect
57. C₄₇×#500	C₂²	semidirect
58. C₄₇×#499	C₂²	semidirect
59. C₄₇×#499	C₂²	semidirect
60. C₄₇×#498	C₂²	semidirect
67. C₂×D₃₇₆	Q₈	semidirect
149. C₂×D₁₈₈	C₂×Q₈	semidirect
160. C₂×C₈×C₄₇	C₂×Q₈	semidirect
196. D₃₇₆	C₂×Q₈	semidirect
197. D₃₇₆	C₂×Q₈	semidirect
264. #3160	D₄₇	semidirect
291. #500	C₂×D₄₇	semidirect
292. #500	C₂×D₄₇	semidirect
294. #499	C₂×D₄₇	semidirect
295. #499	C₂×D₄₇	semidirect
296. #498	C₂×D₄₇	semidirect
325. C₄₇	#61370	semidirect
426. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20257189	2
#20256349	2
#20256292	2
#20256257	2
#20256252	2
#20256240	2
#20253928	2
#20253222	2
#20253181	2
#20252322	2
#20252239	2
C₂×C₄×D₃₇₆	2
C₄₇×#3160	2
#61370	47