Subgroups — #26266407

Order 12032.

874 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
2	#20248562	C₂	1	1	yes	maximal, characteristic
3	#20248306	C₂	1	1	yes	maximal, characteristic
4	#20244817	C₂	1	2	yes	maximal, complemented
5	#20244590	C₂	1	2	yes	maximal, complemented
6	#20244350	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244147	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243808	C₂	1	2	yes	maximal, complemented
9	#20243414	C₂	1	2	yes	maximal, complemented
10	C₄×#13093948	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₂×#13094000	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	#15689188	—	2	4	no	—
16	C₂×#13093958	C₂²	1	2	yes	—
17	C₂×#13093948	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	#15689045	—	2	2	no	—
22	#15689034	—	2	2	no	—
23	#15689025	—	2	1	no	—
24	#15689024	—	2	1	no	—
25	#15689021	—	2	1	no	—
26	#15688993	C₂²	1	1	yes	characteristic
27	#15688988	—	2	1	no	—
28	#15688980	C₂²	1	2	yes	—
29	#15688980	C₂²	1	2	yes	—
30	#15688980	C₂²	1	2	yes	—
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688886	C₂²	1	2	yes	—
33	#15688885	C₂²	1	1	yes	characteristic
34	#15688885	C₂²	1	1	yes	characteristic
35	#15688885	C₂²	1	2	yes	—
36	#15688885	C₂²	1	2	yes	—
37	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#477	—	2	4	no	—
40	C₂×#107×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#103×C₄₇	C₂²	1	2	yes	—
43	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂×C₈×D₄₇	—	2	4	no	—
48	C₂×C₈×D₄₇	—	2	4	no	—
49	C₂×C₈×D₄₇	—	4	2	no	—
50	#13094000	—	2	4	no	—
51	#13094000	—	4	2	no	—
52	C₄×D₁₈₈	—	2	2	no	—
53	C₄×D₁₈₈	—	2	2	no	—
54	C₂×C₄⋊Dic₄₇	—	2	1	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×Dic₄₇⋊C₄	—	2	2	no	—
61	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
64	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
65	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	#13093958	—	4	2	no	—
68	#13093948	—	2	2	no	—
69	#13093948	—	2	2	no	—
70	(C₂×D₄₇)⋊C₈	—	2	4	no	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₂²×Q₈×C₄₇	—	2	1	no	—
77	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
79	C₄⋊Q₈×C₄₇	—	2	2	no	—
80	C₄⋊Q₈×C₄₇	—	2	2	no	—
81	C₄×Q₈×C₄₇	—	2	2	no	—
82	C₄×Q₈×C₄₇	—	2	2	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
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	1	yes	characteristic
89	#107×C₄₇	—	2	4	no	—
90	C₄⋊C₈×C₄₇	D₄	1	4	yes	—
91	#103×C₄₇	—	2	4	no	—
92	C₂³×D₄₇	C₂×D₄	1	2	yes	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	2	1	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	4	2	no	—
99	C₂×Q₈×C₄₇	—	8	1	no	—
100	C₂×Q₈×C₄₇	—	8	1	no	—
101	C₂×Q₈×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₂²×Dic₄₇	—	2	1	no	—
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
112	C₂×D₁₈₈	—	2	2	no	—
113	C₂×D₁₈₈	—	2	2	no	—
114	C₂×D₁₈₈	Q₁₆	1	4	yes	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×C₄×D₄₇	—	2	2	no	—
117	C₂×C₄×D₄₇	—	2	2	no	—
118	C₂×C₄×D₄₇	—	2	2	no	—
119	C₂×C₄×D₄₇	—	2	2	no	—
120	C₂×C₄×D₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₄⋊C₄×C₄₇	—	4	2	no	—
129	C₄⋊C₄×C₄₇	—	4	2	no	—
130	C₄²×C₄₇	—	4	2	no	—
131	C₄²×C₄₇	C₂×D₄	1	2	yes	—
132	C₄²×C₄₇	#41	1	2	yes	—
133	(C₂×D₄₇)⋊C₄	—	2	4	no	—
134	(C₂×D₄₇)⋊C₄	—	4	4	no	—
135	(C₂×D₄₇)⋊C₄	—	8	2	no	—
136	(C₂×D₄₇)⋊C₄	—	8	2	no	—
137	(C₂×D₄₇)⋊C₄	—	8	2	no	—
138	C₄⋊Dic₄₇	—	2	2	no	—
139	C₄⋊Dic₄₇	—	2	1	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	—	2	2	no	—
142	C₄⋊Dic₄₇	—	2	1	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	2	1	no	—
145	C₄⋊Dic₄₇	—	4	2	no	—
146	C₄⋊Dic₄₇	—	8	1	no	—
147	Dic₄₇⋊C₄	—	4	4	no	—
148	C₄×Dic₄₇	—	4	2	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	#41	1	2	yes	—
155	C₈×D₄₇	—	4	8	no	—
156	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
157	C₂²×D₄₇	—	2	2	no	—
158	C₂²×D₄₇	—	2	2	no	—
159	C₂²×D₄₇	—	2	2	no	—
160	C₂²×D₄₇	—	2	2	no	—
161	C₂²×D₄₇	—	2	2	no	—
162	C₂²×D₄₇	—	2	2	no	—
163	C₂²×D₄₇	C₂×Q₁₆	1	4	yes	—
164	Q₈×C₄₇	—	2	2	no	—
165	Q₈×C₄₇	—	2	2	no	—
166	Q₈×C₄₇	—	4	1	no	—
167	Q₈×C₄₇	—	4	1	no	—
168	Q₈×C₄₇	—	8	4	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	1	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	#121	1	2	yes	—
181	C₂×C₄×C₄₇	#121	1	2	yes	—
182	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
183	C₂×C₄×C₄₇	#135	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
190	C₂×Dic₄₇	—	2	2	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	1	no	—
195	C₂×Dic₄₇	—	4	1	no	—
196	C₂×Dic₄₇	—	4	1	no	—
197	C₂×Dic₄₇	—	4	1	no	—
198	C₂×Dic₄₇	—	4	2	no	—
199	C₂×Dic₄₇	—	4	2	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	D₁₈₈	—	2	8	no	—
203	C₄×D₄₇	—	4	2	no	—
204	C₄×D₄₇	—	4	2	no	—
205	C₄×D₄₇	—	4	2	no	—
206	C₄×D₄₇	—	4	2	no	—
207	C₈×C₄₇	—	2	4	no	—
208	C₄₇⋊C₈	—	2	2	no	—
209	C₄₇⋊C₈	—	4	1	no	—
210	#25340	—	47	1	no	maximal, Sylow
211	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
212	C₂²×C₄₇	#546	1	1	yes	characteristic
213	C₂²×C₄₇	#547	1	1	yes	characteristic
214	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
216	C₂²×C₄₇	#576	1	1	yes	characteristic
217	C₂²×C₄₇	#577	1	1	yes	characteristic
218	C₂×D₄₇	—	2	4	no	—
219	C₂×D₄₇	—	2	4	no	—
220	C₂×D₄₇	—	2	4	no	—
221	C₂×D₄₇	—	4	2	no	—
222	C₂×D₄₇	—	4	2	no	—
223	C₂×D₄₇	—	4	2	no	—
224	C₂×D₄₇	—	4	2	no	—
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	—	8	1	no	—
228	C₄×C₄₇	—	8	2	no	—
229	C₄×C₄₇	#467	1	4	yes	—
230	C₄×C₄₇	#529	1	1	yes	characteristic
231	C₄×C₄₇	#542	1	1	yes	characteristic
232	C₄×C₄₇	#546	1	1	yes	characteristic
233	C₄×C₄₇	#548	1	1	yes	characteristic
234	Dic₄₇	—	4	2	no	—
235	Dic₄₇	—	8	1	no	—
236	Dic₄₇	—	8	2	no	—
237	Dic₄₇	—	8	1	no	—
238	C₂×#477	D₄₇	1	1	yes	characteristic, complemented
239	C₂×C₈×D₄	—	47	1	no	—
240	#2563	—	47	1	no	—
241	#2538	—	47	1	no	—
242	#2076	—	47	2	no	—
243	#2036	—	47	2	no	—
244	#1990	—	47	1	no	—
245	#1947	—	47	1	no	—
246	#1892	—	47	2	no	—
247	#1808	—	47	2	no	—
248	C₄×#103	—	47	1	no	—
249	C₂×C₄₇	#2427	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
251	C₂×C₄₇	#3062	1	1	yes	characteristic
252	C₂×C₄₇	#3299	1	1	yes	characteristic
253	C₂×C₄₇	#3305	1	1	yes	characteristic
254	C₂×C₄₇	#3338	1	1	yes	characteristic
255	C₂×C₄₇	#3340	1	1	yes	characteristic
256	D₄₇	—	4	4	no	—
257	C₂³×C₈	—	47	2	no	—
258	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
259	C₂×C₂²⋊Q₈	—	47	2	no	—
260	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₄×D₄	—	47	1	no	—
262	#477	—	2	4	no	—
263	C₈×D₄	—	94	4	no	—
264	C₂×#107	—	47	2	no	—
265	C₂×#107	C₂×D₄₇	1	2	yes	—
266	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
267	C₂×#103	—	47	1	no	—
268	C₂×#103	—	47	1	no	—
269	C₂×#103	C₂×D₄₇	1	2	yes	—
270	C₂×C₂²⋊C₈	—	47	2	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	#396	—	94	2	no	—
273	#393	—	94	2	no	—
274	#390	—	94	1	no	—
275	#390	—	94	1	no	—
276	#389	—	94	1	no	—
277	#384	—	47	1	no	—
278	#382	—	94	1	no	—
279	#380	—	47	2	no	—
280	#380	—	47	2	no	—
281	#380	—	47	2	no	—
282	C₄×C₄⋊C₄	—	47	1	no	—
283	#340	—	47	2	no	—
284	#340	—	47	1	no	—
285	#340	—	47	2	no	—
286	#340	—	47	1	no	—
287	#340	—	47	2	no	—
288	C₄₇	#25340	1	1	yes	characteristic, complemented, Sylow
289	C₂²×Q₈	—	2	1	no	—
290	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂²×D₄	—	47	1	no	—
292	C₂³×C₄	—	47	2	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	47	1	no	—
295	C₂²×C₈	—	94	4	no	—
296	C₂²×C₈	—	94	4	no	—
297	C₂²×C₈	—	188	2	no	—
298	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	2	no	—
301	C₂²⋊Q₈	—	94	4	no	—
302	C₂²⋊Q₈	—	188	2	no	—
303	C₄×Q₈	—	2	2	no	—
304	C₄×Q₈	—	2	2	no	—
305	C₄×D₄	—	94	2	no	—
306	C₄×D₄	—	94	2	no	—
307	C₂×C₄⋊C₄	—	2	1	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	47	1	no	—
310	C₂×C₄⋊C₄	—	47	2	no	—
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₄⋊C₄	—	94	1	no	—
314	C₂×C₄⋊C₄	—	94	2	no	—
315	C₂×C₄⋊C₄	—	94	1	no	—
316	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
318	C₂×C₂²⋊C₄	—	47	2	no	—
319	C₂×C₂²⋊C₄	—	94	2	no	—
320	C₂×C₂²⋊C₄	—	94	2	no	—
321	C₂×C₂²⋊C₄	—	94	2	no	—
322	C₂×C₂²⋊C₄	—	94	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	94	1	no	—
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	#107	—	2	4	no	—
327	#107	—	188	2	no	—
328	C₄⋊C₈	C₂²⋊D₄₇	1	4	yes	—
329	#103	—	2	4	no	—
330	#103	—	94	2	no	—
331	#103	—	94	2	no	—
332	C₂²⋊C₈	—	94	4	no	—
333	C₄×C₈	—	94	2	no	—
334	#95	—	94	2	no	—
335	#95	—	94	2	no	—
336	#95	—	94	2	no	—
337	#95	—	94	1	no	—
338	C₂⁴	—	47	2	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	4	2	no	—
345	C₂×Q₈	—	8	1	no	—
346	C₂×Q₈	—	8	1	no	—
347	C₂×Q₈	#10625354	1	2	yes	—
348	C₂×D₄	—	47	4	no	—
349	C₂×D₄	—	94	2	no	—
350	C₂×D₄	—	94	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	47	2	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	94	2	no	—
357	C₂²×C₄	—	94	2	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	94	2	no	—
361	C₂²×C₄	—	94	1	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	94	2	no	—
364	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	47	2	no	—
370	C₂×C₈	—	94	1	no	—
371	C₂×C₈	—	94	1	no	—
372	C₂×C₈	—	94	1	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	188	8	no	—
376	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	4	2	no	—
382	C₄⋊C₄	—	4	2	no	—
383	C₄⋊C₄	—	94	2	no	—
384	C₄⋊C₄	—	94	1	no	—
385	C₄⋊C₄	—	94	1	no	—
386	C₄⋊C₄	—	94	2	no	—
387	C₄⋊C₄	—	94	1	no	—
388	C₄⋊C₄	—	94	2	no	—
389	C₄⋊C₄	—	94	1	no	—
390	C₄⋊C₄	—	376	1	no	—
391	C₄⋊C₄	—	188	4	no	—
392	C₄⋊C₄	—	188	2	no	—
393	C₂²⋊C₄	—	94	4	no	—
394	C₂²⋊C₄	—	376	2	no	—
395	C₂²⋊C₄	—	376	2	no	—
396	C₂²⋊C₄	—	376	2	no	—
397	C₂²⋊C₄	—	188	4	no	—
398	C₄²	—	4	2	no	—
399	C₄²	—	188	2	no	—
400	C₄²	#10625352	1	2	yes	—
401	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
402	C₂³	—	47	4	no	—
403	C₂³	—	94	2	no	—
404	C₂³	—	94	2	no	—
405	C₂³	—	94	2	no	—
406	C₂³	—	94	2	no	—
407	C₂³	—	94	2	no	—
408	C₂³	—	94	2	no	—
409	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
410	Q₈	—	2	2	no	—
411	Q₈	—	2	2	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	1	no	—
414	Q₈	—	8	4	no	—
415	D₄	—	94	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	94	2	no	—
428	C₂×C₄	—	94	2	no	—
429	C₂×C₄	—	94	2	no	—
430	C₂×C₄	—	188	2	no	—
431	C₂×C₄	—	188	1	no	—
432	C₂×C₄	—	188	1	no	—
433	C₂×C₄	—	188	1	no	—
434	C₂×C₄	—	188	1	no	—
435	C₂×C₄	—	188	2	no	—
436	C₂×C₄	—	188	1	no	—
437	C₂×C₄	—	188	2	no	—
438	C₂×C₄	—	188	1	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	2	no	—
441	C₂×C₄	—	188	2	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	#13093995	1	2	yes	—
444	C₂×C₄	#13093995	1	2	yes	—
445	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
446	C₂×C₄	#13094047	1	2	yes	—
447	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
448	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
450	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
451	C₂×C₄	#13094070	1	1	yes	characteristic
452	C₂×C₄	#13094072	1	1	yes	characteristic
453	C₈	—	2	4	no	—
454	C₈	—	94	2	no	—
455	C₈	—	188	1	no	—
456	C₂²	—	94	4	no	—
457	C₂²	—	94	4	no	—
458	C₂²	—	94	4	no	—
459	C₂²	—	188	2	no	—
460	C₂²	—	188	2	no	—
461	C₂²	—	188	2	no	—
462	C₂²	—	188	2	no	—
463	C₂²	C₂×#13093995	1	1	yes	characteristic
464	C₂²	#15689764	1	1	yes	characteristic
465	C₂²	#15689775	1	1	yes	characteristic
466	C₂²	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
467	C₂²	C₂×#13094047	1	1	yes	characteristic
468	C₂²	#15689927	1	1	yes	characteristic
469	C₂²	#15689933	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	8	2	no	—
473	C₄	—	8	1	no	—
474	C₄	—	376	1	no	—
475	C₄	—	376	2	no	—
476	C₄	—	376	1	no	—
477	C₄	—	188	2	no	—
478	C₄	#15689361	1	4	yes	—
479	C₄	#15689659	1	1	yes	characteristic
480	C₄	#15689746	1	1	yes	characteristic
481	C₄	#15689761	1	1	yes	characteristic
482	C₄	#15689784	1	1	yes	characteristic
483	C₂	—	188	4	no	—
484	C₂	#20246961	1	1	yes	characteristic
485	C₂	C₂×#15689361	1	1	yes	characteristic
486	C₂	#20253062	1	1	yes	characteristic
487	C₂	#20255261	1	1	yes	characteristic
488	C₂	#20255335	1	1	yes	characteristic
489	C₂	#20255779	1	1	yes	characteristic
490	C₂	#20255804	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#477	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₁₈₈	D₄
hypercenter	C₂×#477	D₄₇
hypocenter	C₄₇	#25340
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#477

Complements

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

N	H ≅ G/N	type
4. #20244817	C₂	semidirect
5. #20244590	C₂	semidirect
6. #20244350	C₂	semidirect
7. #20244147	C₂	semidirect
8. #20243808	C₂	semidirect
9. #20243414	C₂	semidirect
10. C₄×#13093948	C₂	semidirect
11. C₂×C₄₇×#477	C₂	semidirect
238. C₂×#477	D₄₇	semidirect
288. C₄₇	#25340	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689188	2
#20248562	2
#20248306	2
#20244817	2
#20244590	2
#20244350	2
#20244147	2
#20243808	2
#20243414	2
C₄×#13093948	2
C₂×C₄₇×#477	2
#25340	47