Subgroups — #26222249

Order 12032.

1282 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258099	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252736	C₂	1	1	yes	maximal, characteristic
3	#20252289	C₂	1	2	yes	maximal, complemented
4	#20243772	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243753	C₂	1	2	yes	maximal, complemented
6	#20243627	C₂	1	2	yes	maximal, complemented
7	#20243607	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243351	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243232	C₂	1	2	yes	maximal, complemented
10	#20243188	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689959	C₂²	1	1	yes	characteristic
13	#15689921	C₂²	1	2	yes	—
14	#15689890	C₂²	1	1	yes	characteristic
15	#15689889	—	2	2	no	—
16	#15689889	C₂²	1	2	yes	—
17	#15689888	—	2	4	no	—
18	C₂×#13094030	—	2	2	no	—
19	C₂×#13094030	C₂²	1	2	yes	—
20	#131×D₄₇	—	2	4	no	—
21	#15689305	C₄	1	2	yes	complemented
22	#15689300	C₄	1	2	yes	complemented
23	#15689295	C₄	1	2	yes	complemented
24	#15689290	C₄	1	2	yes	complemented
25	#15689243	—	2	4	no	—
26	#15689238	—	2	4	no	—
27	#15689171	C₂²	1	2	yes	complemented
28	#15689140	C₂²	1	2	yes	complemented
29	#15689139	C₂²	1	2	yes	—
30	C₂×#13093952	C₂²	1	2	yes	—
31	#15689120	C₂²	1	2	yes	—
32	#15689107	C₂²	1	1	yes	characteristic
33	#15689097	C₂²	1	1	yes	characteristic
34	#15689078	C₂²	1	2	yes	complemented
35	#15688894	C₂²	1	2	yes	complemented
36	#15688888	C₂²	1	2	yes	complemented
37	#15688883	C₂²	1	2	yes	complemented
38	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₄₇×#435	—	2	2	no	—
42	C₄₇×#435	—	2	2	no	—
43	C₄₇×#423	C₂²	1	1	yes	characteristic, complemented
44	C₄₇×#408	C₂²	1	1	yes	characteristic
45	C₄₇×#408	C₂²	1	1	yes	characteristic, complemented
46	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic, complemented
47	#13094072	C₂×C₄	1	2	yes	—
48	#13094071	—	2	2	no	—
49	#13094070	—	2	2	no	—
50	#13094069	—	2	2	no	—
51	#13094069	C₂×C₄	1	2	yes	—
52	C₂×#10625350	—	2	2	no	—
53	C₂×#10625350	C₂³	1	2	yes	—
54	#41×D₄₇	—	2	4	no	—
55	#13094055	C₂×C₄	1	4	yes	—
56	#13094054	—	2	2	no	—
57	#13094050	C₂×C₄	1	4	yes	—
58	#13094049	—	2	2	no	—
59	#13094044	—	2	4	no	—
60	#13094032	—	2	8	no	—
61	#13094032	—	2	4	no	—
62	#13094031	—	2	4	no	—
63	#13094030	—	2	4	no	—
64	#13094030	—	2	4	no	—
65	#13094030	—	2	2	no	—
66	#13094030	—	2	4	no	—
67	#13094030	—	2	2	no	—
68	#13094030	D₄	1	4	yes	complemented
69	#13094030	D₄	1	4	yes	complemented
70	C₂×#10625329	—	2	2	no	—
71	C₂×#10625329	C₂³	1	2	yes	—
72	C₂×#10625329	C₂³	1	2	yes	—
73	C₂×#10625324	—	2	4	no	—
74	C₂×#10625324	—	2	2	no	—
75	M₁₆×D₄₇	—	2	8	no	—
76	M₁₆×D₄₇	—	2	4	no	—
77	C₂×C₈×D₄₇	—	2	4	no	—
78	C₂×C₈×D₄₇	—	2	2	no	—
79	#13093983	C₂³	1	2	yes	—
80	#13093959	—	2	4	no	—
81	#13093952	C₂×C₄	1	4	yes	—
82	#13093952	C₂×C₄	1	4	yes	—
83	#13093951	—	2	4	no	—
84	#13093950	—	2	4	no	—
85	#13093949	—	2	2	no	—
86	#13093946	—	2	2	no	—
87	#13093943	C₂×C₄	1	2	yes	—
88	#13093941	C₂×C₄	1	2	yes	—
89	#13093939	—	2	2	no	—
90	#13093934	—	2	2	no	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
94	#131×C₄₇	—	2	2	no	—
95	#131×C₄₇	—	2	2	no	—
96	#131×C₄₇	—	2	2	no	—
97	#131×C₄₇	—	2	2	no	—
98	C₂×M₁₆×C₄₇	—	2	1	no	—
99	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
100	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	—	2	1	no	—
103	C₂²×C₈×C₄₇	D₄	1	2	yes	—
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
107	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
108	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
109	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
110	#121×C₄₇	—	2	2	no	—
111	C₄×D₄×C₄₇	—	2	2	no	—
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₇	—	2	2	no	—
114	C₂²⋊C₈×C₄₇	—	2	2	no	—
115	C₂²⋊C₈×C₄₇	—	2	2	no	—
116	#97×C₄₇	—	2	1	no	—
117	#97×C₄₇	—	2	1	no	—
118	#41×C₄₇	—	2	2	no	—
119	#41×C₄₇	—	2	2	no	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	2	no	—
122	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₄₇	—	2	1	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₇	#41	1	2	yes	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₇	—	2	4	no	—
134	C₂×C₂²⋊D₄₇	—	2	2	no	—
135	#10625354	—	2	4	no	—
136	Q₈×D₄₇	—	2	4	no	—
137	#10625352	—	2	8	no	—
138	#10625352	—	2	4	no	—
139	D₄×D₄₇	—	2	8	no	—
140	D₄×D₄₇	—	2	4	no	—
141	#10625350	—	2	4	no	—
142	#10625350	—	2	4	no	—
143	#10625350	—	2	4	no	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	C₂²×C₄	1	4	yes	—
147	#10625350	C₂×D₄	1	4	yes	—
148	C₂×D₁₈₈	—	2	2	no	—
149	C₂×D₁₈₈	#41	1	2	yes	—
150	C₂×C₄×D₄₇	—	2	4	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×Dic₉₄	—	2	2	no	—
153	C₂×Dic₉₄	#41	1	2	yes	—
154	M₁₆×C₄₇	—	2	2	no	—
155	M₁₆×C₄₇	—	2	4	no	—
156	M₁₆×C₄₇	—	2	2	no	—
157	M₁₆×C₄₇	—	4	1	no	—
158	M₁₆×C₄₇	—	4	1	no	—
159	C₂×C₈×C₄₇	—	2	2	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	2	1	no	—
162	C₂×C₈×C₄₇	—	2	1	no	—
163	C₂×C₈×C₄₇	—	2	2	no	—
164	C₂×C₈×C₄₇	—	4	2	no	—
165	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
166	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
167	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₂²⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	2	2	no	—
173	C₄²×C₄₇	—	2	1	no	—
174	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
176	C₂²⋊Dic₄₇	—	2	2	no	—
177	#10625337	—	2	4	no	—
178	#10625336	—	2	4	no	—
179	#10625335	—	2	4	no	—
180	#10625334	—	2	4	no	—
181	C₄⋊Dic₄₇	—	2	2	no	—
182	C₄×Dic₄₇	—	2	2	no	—
183	#10625329	—	2	4	no	—
184	#10625329	—	2	2	no	—
185	#10625329	—	2	2	no	—
186	#10625329	C₂²×C₄	1	4	yes	—
187	#10625329	C₂×D₄	1	4	yes	—
188	C₂×C₄₇⋊C₈	—	2	4	no	—
189	C₂×C₄₇⋊C₈	—	2	2	no	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	#10625324	—	2	8	no	—
192	#10625324	—	2	4	no	—
193	#10625324	—	2	4	no	—
194	C₈×D₄₇	—	2	8	no	—
195	C₈×D₄₇	—	2	4	no	—
196	C₈×D₄₇	—	2	4	no	—
197	C₂³×C₄₇	—	2	1	no	—
198	C₂³×C₄₇	C₄×D₄	1	2	yes	—
199	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂²×D₄₇	—	2	4	no	—
201	C₂²×D₄₇	—	2	2	no	—
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	2	2	no	—
204	D₄×C₄₇	—	2	4	no	—
205	D₄×C₄₇	—	2	2	no	—
206	D₄×C₄₇	—	2	2	no	—
207	D₄×C₄₇	—	4	2	no	—
208	D₄×C₄₇	—	8	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	4	1	no	—
215	C₂×C₄×C₄₇	—	4	1	no	—
216	C₂×C₄×C₄₇	—	8	1	no	—
217	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
218	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
222	C₂²⋊D₄₇	—	2	8	no	—
223	C₂²⋊D₄₇	—	2	4	no	—
224	C₂²⋊D₄₇	—	2	4	no	—
225	C₂×Dic₄₇	—	2	4	no	—
226	C₂×Dic₄₇	—	2	2	no	—
227	C₂×Dic₄₇	—	4	2	no	—
228	D₁₈₈	—	2	4	no	—
229	D₁₈₈	—	2	2	no	—
230	D₁₈₈	C₄×D₄	1	4	yes	—
231	C₄×D₄₇	—	2	8	no	—
232	C₄×D₄₇	—	2	4	no	—
233	C₄×D₄₇	—	2	4	no	—
234	Dic₉₄	—	2	4	no	—
235	Dic₉₄	—	2	2	no	—
236	Dic₉₄	C₄×D₄	1	4	yes	—
237	C₈×C₄₇	—	2	2	no	—
238	C₈×C₄₇	—	4	1	no	—
239	C₈×C₄₇	—	4	1	no	—
240	C₈×C₄₇	#120	1	1	yes	characteristic
241	C₈×C₄₇	#120	1	2	yes	—
242	C₈×C₄₇	#120	1	1	yes	characteristic
243	C₄₇⋊C₈	—	2	4	no	—
244	C₄₇⋊C₈	—	2	4	no	—
245	#21478	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	4	1	no	—
248	C₂²×C₄₇	—	4	2	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	4	1	no	—
251	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
252	C₂²×C₄₇	#525	1	2	yes	—
253	C₂×D₄₇	—	2	4	no	—
254	C₂×D₄₇	—	8	2	no	—
255	C₂×D₄₇	—	8	4	no	—
256	C₄×C₄₇	—	2	2	no	—
257	C₄×C₄₇	—	4	1	no	—
258	C₄×C₄₇	—	4	1	no	—
259	C₄×C₄₇	—	4	1	no	—
260	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
261	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
262	C₄×C₄₇	#525	1	1	yes	characteristic
263	Dic₄₇	—	2	4	no	—
264	Dic₄₇	—	8	2	no	—
265	#3573	—	47	1	no	—
266	#3018	—	47	1	no	—
267	#2955	—	47	2	no	—
268	#2932	D₄₇	1	1	yes	characteristic, complemented
269	#1884	—	47	1	no	—
270	#1881	—	47	2	no	—
271	#1861	—	47	2	no	—
272	#1858	—	47	1	no	—
273	#1794	—	47	1	no	—
274	#1765	—	47	2	no	—
275	#1757	—	47	1	no	—
276	C₂×C₄₇	—	2	2	no	—
277	C₂×C₄₇	—	2	1	no	—
278	C₂×C₄₇	—	4	2	no	—
279	C₂×C₄₇	—	8	1	no	—
280	C₂×C₄₇	C₄×#120	1	1	yes	characteristic
281	D₄₇	—	4	4	no	—
282	#585	—	47	1	no	—
283	#575	—	47	2	no	—
284	#568	—	47	1	no	—
285	#568	—	47	2	no	—
286	#568	—	94	4	no	—
287	#568	—	94	2	no	—
288	C₂×#131	—	47	2	no	—
289	C₂×#131	—	94	4	no	—
290	C₂×#131	—	94	2	no	—
291	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
292	C₂×#131	C₂×D₄₇	1	1	yes	characteristic, complemented
293	#532	C₂×D₄₇	1	1	yes	characteristic
294	#456	—	47	2	no	—
295	#455	—	47	2	no	—
296	#454	—	47	2	no	—
297	#453	—	47	2	no	—
298	#444	—	94	4	no	—
299	#443	—	94	4	no	—
300	#435	—	2	2	no	—
301	#435	—	2	2	no	—
302	#430	—	47	2	no	—
303	#423	C₂×D₄₇	1	1	yes	characteristic, complemented
304	#421	—	47	2	no	—
305	#421	—	47	2	no	—
306	C₂×#104	—	47	2	no	—
307	#416	—	47	2	no	—
308	#413	—	47	1	no	—
309	#410	—	47	1	no	—
310	#408	C₂×D₄₇	1	1	yes	characteristic
311	#408	C₂×D₄₇	1	1	yes	characteristic, complemented
312	#405	—	47	2	no	—
313	C₂×#97	C₂×D₄₇	1	1	yes	characteristic, complemented
314	#344	—	47	2	no	—
315	#341	—	47	2	no	—
316	#339	—	47	2	no	—
317	C₄₇	#21478	1	1	yes	characteristic, complemented, Sylow
318	2₋¹⁺⁴	—	47	2	no	—
319	2₋¹⁺⁴	—	94	2	no	—
320	H(5,𝔽₂)	—	47	2	no	—
321	H(5,𝔽₂)	—	94	2	no	—
322	H(5,𝔽₂)	—	94	2	no	—
323	C₂×#41	—	47	2	no	—
324	C₂×#41	—	94	4	no	—
325	C₂×#41	—	94	2	no	—
326	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
328	#137	—	47	4	no	—
329	#137	—	94	2	no	—
330	AGL(1,ℤ/8)	—	47	4	no	—
331	AGL(1,ℤ/8)	—	94	2	no	—
332	#135	—	94	4	no	—
333	#131	—	2	2	no	—
334	#131	—	2	2	no	—
335	#131	—	2	2	no	—
336	#131	—	2	2	no	—
337	#131	—	47	4	no	—
338	#131	—	47	4	no	—
339	#131	—	94	4	no	—
340	#131	—	94	4	no	—
341	#131	—	94	4	no	—
342	#131	—	94	8	no	—
343	#131	—	94	4	no	—
344	#131	—	94	2	no	—
345	#131	—	94	2	no	—
346	#131	—	94	4	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	47	2	no	—
349	C₂×M₁₆	—	47	2	no	—
350	C₂×M₁₆	—	94	4	no	—
351	C₂×M₁₆	—	94	4	no	—
352	C₂×M₁₆	—	94	8	no	—
353	C₂×M₁₆	—	94	2	no	—
354	C₂×M₁₆	—	94	2	no	—
355	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
356	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
357	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
358	C₂²×C₈	—	2	1	no	—
359	C₂²×C₈	—	94	4	no	—
360	C₂²×C₈	—	94	2	no	—
361	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
362	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
363	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
364	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
365	#127	C₄×D₄₇	1	1	yes	characteristic
366	#124	C₄×D₄₇	1	1	yes	characteristic
367	#124	C₄×D₄₇	1	1	yes	characteristic
368	#121	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	#117	—	47	2	no	—
371	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
372	#108	—	94	4	no	—
373	C₄⋊C₈	—	2	2	no	—
374	#104	—	47	4	no	—
375	#104	—	47	4	no	—
376	#104	—	94	4	no	—
377	#104	—	94	4	no	—
378	#103	—	94	2	no	—
379	#102	—	94	2	no	—
380	#101	—	47	2	no	—
381	#100	—	47	2	no	—
382	#99	—	94	2	no	—
383	C₂²⋊C₈	—	2	2	no	—
384	C₂²⋊C₈	—	2	2	no	—
385	#97	—	2	1	no	—
386	#97	—	2	1	no	—
387	#97	—	94	2	no	—
388	C₄×C₈	—	94	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	—	47	4	no	—
394	#41	—	47	4	no	—
395	#41	—	94	4	no	—
396	#41	—	94	4	no	—
397	#41	—	94	4	no	—
398	#41	—	94	8	no	—
399	#41	—	94	4	no	—
400	#41	—	94	4	no	—
401	#41	—	94	2	no	—
402	#41	—	94	2	no	—
403	C₂×Q₈	—	47	2	no	—
404	C₂×Q₈	—	94	2	no	—
405	C₂×Q₈	—	94	4	no	—
406	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
407	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	47	2	no	—
411	C₂×D₄	—	94	2	no	—
412	C₂×D₄	—	94	4	no	—
413	C₂×D₄	—	94	8	no	—
414	C₂×D₄	—	94	4	no	—
415	C₂×D₄	—	94	2	no	—
416	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
417	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
418	C₂×D₄	#10625350	1	2	yes	—
419	C₂²×C₄	—	2	1	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	94	4	no	—
422	C₂²×C₄	—	94	2	no	—
423	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
424	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
425	Q₁₆	—	94	4	no	—
426	SD₁₆	—	94	4	no	—
427	SD₁₆	—	94	4	no	—
428	D₈	—	94	4	no	—
429	M₁₆	—	2	2	no	—
430	M₁₆	—	2	4	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	4	1	no	—
433	M₁₆	—	4	1	no	—
434	M₁₆	—	47	4	no	—
435	M₁₆	—	47	4	no	—
436	M₁₆	—	94	8	no	—
437	M₁₆	—	94	4	no	—
438	M₁₆	—	94	2	no	—
439	M₁₆	—	94	2	no	—
440	M₁₆	—	94	4	no	—
441	M₁₆	—	94	4	no	—
442	C₂×C₈	—	2	2	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	2	no	—
447	C₂×C₈	—	4	2	no	—
448	C₂×C₈	—	94	8	no	—
449	C₂×C₈	—	94	4	no	—
450	C₂×C₈	—	94	2	no	—
451	C₂×C₈	—	94	2	no	—
452	C₂×C₈	—	94	4	no	—
453	C₂×C₈	—	94	4	no	—
454	C₂×C₈	D₄×D₄₇	1	2	yes	—
455	C₂×C₈	D₄×D₄₇	1	2	yes	—
456	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
457	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
458	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	—	94	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	94	2	no	—
464	C₄²	—	2	1	no	—
465	C₄²	—	94	2	no	—
466	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
467	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
468	C₂³	—	2	1	no	—
469	C₂³	—	94	4	no	—
470	C₂³	—	94	2	no	—
471	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
472	C₂³	C₂×#10625350	1	1	yes	characteristic
473	Q₈	—	2	2	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	47	4	no	—
476	Q₈	—	94	4	no	—
477	Q₈	—	94	2	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	4	2	no	—
482	D₄	—	8	2	no	—
483	D₄	—	47	4	no	—
484	D₄	—	94	4	no	—
485	D₄	—	94	8	no	—
486	D₄	—	94	4	no	—
487	D₄	—	94	4	no	—
488	D₄	—	94	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	4	1	no	—
495	C₂×C₄	—	4	1	no	—
496	C₂×C₄	—	8	1	no	—
497	C₂×C₄	—	94	8	no	—
498	C₂×C₄	—	94	4	no	—
499	C₂×C₄	—	94	2	no	—
500	C₂×C₄	—	94	4	no	—
501	C₂×C₄	—	94	4	no	—
502	C₂×C₄	—	188	2	no	—
503	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
504	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
506	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
507	C₂×C₄	#41×D₄₇	1	2	yes	—
508	C₈	—	2	2	no	—
509	C₈	—	4	1	no	—
510	C₈	—	4	1	no	—
511	C₈	—	94	4	no	—
512	C₈	—	94	4	no	—
513	C₈	#13093992	1	1	yes	characteristic
514	C₈	#13093992	1	1	yes	characteristic
515	C₈	#13093992	1	2	yes	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	1	no	—
518	C₂²	—	4	2	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	94	4	no	—
522	C₂²	—	376	2	no	—
523	C₂²	—	376	4	no	—
524	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
525	C₂²	#15689632	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	94	4	no	—
531	C₄	—	376	2	no	—
532	C₄	C₄×D₄×D₄₇	1	2	yes	—
533	C₄	C₂×#13093992	1	1	yes	characteristic
534	C₄	#15689630	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	2	no	—
537	C₂	—	4	2	no	—
538	C₂	—	8	1	no	—
539	C₂	—	188	4	no	—
540	C₂	C₄×#13093992	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×#13093992
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2932	C₂
socle	C₂×C₄₇	C₄×#120
prime radical	#20252736	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2932	D₄₇
hypocenter	C₄₇	#21478
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₈ ◁ #2932

Complements

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

N	H ≅ G/N	type
1. #20258099	C₂	semidirect
3. #20252289	C₂	semidirect
4. #20243772	C₂	semidirect
5. #20243753	C₂	semidirect
6. #20243627	C₂	semidirect
7. #20243607	C₂	semidirect
8. #20243351	C₂	semidirect
9. #20243232	C₂	semidirect
10. #20243188	C₂	semidirect
11. C₄₇×#2932	C₂	semidirect
21. #15689305	C₄	semidirect
22. #15689300	C₄	semidirect
23. #15689295	C₄	semidirect
24. #15689290	C₄	semidirect
27. #15689171	C₂²	semidirect
28. #15689140	C₂²	semidirect
34. #15689078	C₂²	semidirect
35. #15688894	C₂²	semidirect
36. #15688888	C₂²	semidirect
37. #15688883	C₂²	semidirect
39. C₂×#131×C₄₇	C₂²	semidirect
43. C₄₇×#423	C₂²	semidirect
45. C₄₇×#408	C₂²	semidirect
46. C₂×#97×C₄₇	C₂²	semidirect
68. #13094030	D₄	semidirect
69. #13094030	D₄	semidirect
268. #2932	D₄₇	semidirect
292. C₂×#131	C₂×D₄₇	semidirect
303. #423	C₂×D₄₇	semidirect
311. #408	C₂×D₄₇	semidirect
313. C₂×#97	C₂×D₄₇	semidirect
317. C₄₇	#21478	semidirect

Maximal subgroups

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

subgroup	index
#20258099	2
#20252736	2
#20252289	2
#20243772	2
#20243753	2
#20243627	2
#20243607	2
#20243351	2
#20243232	2
#20243188	2
C₄₇×#2932	2
#21478	47