Subgroups — #26252221

Order 12032.

1290 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20258162	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253108	C₂	1	2	yes	maximal, complemented
3	#20252736	C₂	1	2	yes	maximal, complemented
4	#20244675	C₂	1	2	yes	maximal, complemented
5	#20244492	C₂	1	2	yes	maximal, complemented
6	#20244281	C₂	1	2	yes	maximal, complemented
7	#20243438	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243338	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2932	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689959	C₂²	1	2	yes	—
11	#15689940	—	2	2	no	—
12	#15689935	—	2	4	no	—
13	#15689928	—	2	2	no	—
14	#15689923	—	2	2	no	—
15	#15689923	C₂²	1	2	yes	—
16	#15689921	C₂²	1	4	yes	complemented
17	C₂×#13094046	—	2	2	no	—
18	C₂×#13094046	C₂²	1	2	yes	—
19	#15689398	—	2	2	no	—
20	#15689393	—	2	2	no	—
21	#15689386	—	2	4	no	—
22	#15689305	—	2	2	no	—
23	#15689300	—	2	2	no	—
24	#15689295	—	2	2	no	—
25	#15689290	—	2	2	no	—
26	C₂×#13093960	C₂²	1	2	yes	complemented
27	C₂×#13093952	C₂²	1	4	yes	complemented
28	#15689107	C₂²	1	2	yes	—
29	#15689105	C₂²	1	4	yes	complemented
30	#15689089	C₂²	1	4	yes	complemented
31	C₄₇⋊#338	C₂²	1	2	yes	complemented
32	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic, complemented
34	C₄₇×#532	C₂²	1	1	yes	characteristic
35	C₄₇×#435	—	2	2	no	—
36	C₄₇×#435	—	2	2	no	—
37	C₄₇×#423	C₂²	1	1	yes	characteristic, complemented
38	C₄₇×#408	C₂²	1	1	yes	characteristic
39	C₄₇×#408	C₂²	1	1	yes	characteristic, complemented
40	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic, complemented
41	#13094072	—	2	2	no	—
42	#13094071	—	2	4	no	—
43	#13094070	—	2	4	no	—
44	#13094069	—	2	2	no	—
45	#13094069	—	2	4	no	—
46	C₂×#10625350	—	2	4	no	—
47	C₂×#10625350	C₂³	1	4	yes	—
48	#41×D₄₇	—	4	4	no	—
49	#13094057	—	2	8	no	—
50	#13094057	—	2	4	no	—
51	#13094055	—	2	4	no	—
52	#13094054	—	2	4	no	—
53	#13094052	—	2	8	no	—
54	#13094052	—	2	4	no	—
55	#13094050	—	2	4	no	—
56	#13094049	—	2	4	no	—
57	#13094046	—	2	4	no	—
58	#13094046	—	2	4	no	—
59	#13094046	—	2	2	no	—
60	#13094046	—	2	4	no	—
61	#13094046	—	2	2	no	—
62	#13094046	—	2	2	no	—
63	#13094046	—	2	2	no	—
64	#13094044	—	4	4	no	—
65	C₂×Dic₁₈₈	—	2	2	no	—
66	C₂×Dic₁₈₈	D₄	1	2	yes	complemented
67	C₂×#10625325	—	2	4	no	—
68	C₂×#10625325	D₄	1	4	yes	complemented
69	C₂×D₃₇₆	—	2	2	no	—
70	C₂×D₃₇₆	D₄	1	2	yes	complemented
71	C₂×#10625329	C₂³	1	4	yes	—
72	#13093960	—	2	2	no	—
73	#13093960	—	2	2	no	—
74	#13093952	—	2	4	no	—
75	#13093952	—	2	4	no	—
76	#13093943	—	2	2	no	—
77	#13093942	—	2	4	no	—
78	#13093941	—	2	2	no	—
79	#13093940	—	2	4	no	—
80	(C₂×D₄₇)⋊C₈	—	4	4	no	—
81	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
83	#131×C₄₇	—	2	2	no	—
84	#131×C₄₇	—	2	2	no	—
85	#131×C₄₇	—	2	2	no	—
86	#131×C₄₇	—	2	2	no	—
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
89	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	—	2	1	no	—
92	C₂²×C₈×C₄₇	D₄	1	2	yes	—
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
96	#127×C₄₇	D₄	1	1	yes	characteristic
97	#124×C₄₇	D₄	1	1	yes	characteristic
98	#124×C₄₇	D₄	1	1	yes	characteristic
99	#121×C₄₇	—	2	2	no	—
100	C₄×D₄×C₄₇	—	2	2	no	—
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₇	—	2	2	no	—
103	C₂²⋊C₈×C₄₇	—	2	2	no	—
104	C₂²⋊C₈×C₄₇	—	2	2	no	—
105	#97×C₄₇	—	2	1	no	—
106	#97×C₄₇	—	2	1	no	—
107	#41×C₄₇	—	2	2	no	—
108	#41×C₄₇	—	2	2	no	—
109	#41×C₄₇	—	2	2	no	—
110	#41×C₄₇	—	2	2	no	—
111	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂×D₄×C₄₇	—	2	1	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×D₄×C₄₇	#41	1	2	yes	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₂×C₂²⋊D₄₇	—	2	4	no	—
123	C₂×C₂²⋊D₄₇	—	4	4	no	—
124	#10625354	—	4	4	no	—
125	Q₈×D₄₇	—	4	4	no	—
126	#10625352	—	4	4	no	—
127	#10625352	—	4	8	no	—
128	D₄×D₄₇	—	4	4	no	—
129	D₄×D₄₇	—	4	8	no	—
130	#10625350	—	2	8	no	—
131	#10625350	—	2	4	no	—
132	#10625350	—	2	4	no	—
133	#10625350	—	2	4	no	—
134	#10625350	—	2	4	no	—
135	#10625350	—	4	4	no	—
136	#10625350	—	4	4	no	—
137	C₂×D₁₈₈	—	2	4	no	—
138	C₂×D₁₈₈	C₂×D₄	1	4	yes	—
139	C₂×C₄×D₄₇	—	2	4	no	—
140	C₂×C₄×D₄₇	—	4	4	no	—
141	C₂×Dic₉₄	—	2	4	no	—
142	C₂×Dic₉₄	C₂×D₄	1	4	yes	—
143	M₁₆×C₄₇	—	2	2	no	—
144	M₁₆×C₄₇	—	2	4	no	—
145	M₁₆×C₄₇	—	2	2	no	—
146	M₁₆×C₄₇	—	4	1	no	—
147	M₁₆×C₄₇	—	4	1	no	—
148	C₂×C₈×C₄₇	—	2	2	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	—	2	1	no	—
151	C₂×C₈×C₄₇	—	2	1	no	—
152	C₂×C₈×C₄₇	—	2	2	no	—
153	C₂×C₈×C₄₇	—	4	2	no	—
154	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
155	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
156	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₂²⋊C₄×C₄₇	—	2	2	no	—
161	C₂²⋊C₄×C₄₇	—	2	2	no	—
162	C₄²×C₄₇	—	2	1	no	—
163	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
165	#10625337	—	4	4	no	—
166	#10625336	—	4	4	no	—
167	#10625335	—	4	4	no	—
168	#10625334	—	4	4	no	—
169	#10625329	—	2	4	no	—
170	#10625329	—	2	4	no	—
171	C₂×C₄₇⋊C₈	—	2	4	no	—
172	Dic₁₈₈	—	2	4	no	—
173	Dic₁₈₈	—	2	2	no	—
174	Dic₁₈₈	—	2	2	no	—
175	D₃₇₆	—	2	4	no	—
176	D₃₇₆	—	2	2	no	—
177	D₃₇₆	—	2	2	no	—
178	#10625325	—	2	8	no	—
179	#10625325	—	2	4	no	—
180	#10625325	—	2	4	no	—
181	C₂³×C₄₇	—	2	1	no	—
182	C₂³×C₄₇	#121	1	2	yes	—
183	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂²×D₄₇	—	2	4	no	—
185	C₂²×D₄₇	—	4	4	no	—
186	Q₈×C₄₇	—	2	2	no	—
187	Q₈×C₄₇	—	2	2	no	—
188	D₄×C₄₇	—	2	4	no	—
189	D₄×C₄₇	—	2	2	no	—
190	D₄×C₄₇	—	2	2	no	—
191	D₄×C₄₇	—	4	2	no	—
192	D₄×C₄₇	—	8	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	8	1	no	—
201	C₂×C₄×C₄₇	#121	1	2	yes	—
202	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
206	C₂²⋊D₄₇	—	4	8	no	—
207	C₂²⋊D₄₇	—	4	4	no	—
208	C₂²⋊D₄₇	—	4	4	no	—
209	C₂×Dic₄₇	—	2	4	no	—
210	C₂×Dic₄₇	—	4	4	no	—
211	D₁₈₈	—	2	4	no	—
212	D₁₈₈	—	2	4	no	—
213	D₁₈₈	—	4	4	no	—
214	C₄×D₄₇	—	4	8	no	—
215	C₄×D₄₇	—	4	4	no	—
216	C₄×D₄₇	—	4	4	no	—
217	Dic₉₄	—	2	4	no	—
218	Dic₉₄	—	2	4	no	—
219	Dic₉₄	—	4	4	no	—
220	C₈×C₄₇	—	2	2	no	—
221	C₈×C₄₇	—	4	1	no	—
222	C₈×C₄₇	—	4	1	no	—
223	C₈×C₄₇	#120	1	1	yes	characteristic
224	C₈×C₄₇	#120	1	2	yes	—
225	C₈×C₄₇	#120	1	1	yes	characteristic
226	C₄₇⋊C₈	—	4	4	no	—
227	#24288	—	47	1	no	maximal, Sylow
228	C₂²×C₄₇	—	2	2	no	—
229	C₂²×C₄₇	—	4	1	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	1	no	—
233	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
234	C₂²×C₄₇	#546	1	2	yes	—
235	C₂×D₄₇	—	4	4	no	—
236	C₂×D₄₇	—	8	4	no	—
237	C₂×D₄₇	—	16	4	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	4	1	no	—
240	C₄×C₄₇	—	4	1	no	—
241	C₄×C₄₇	—	4	1	no	—
242	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
243	C₄×C₄₇	#535	1	1	yes	characteristic
244	C₄×C₄₇	D₄²	1	2	yes	—
245	Dic₄₇	—	4	4	no	—
246	#3584	—	47	1	no	—
247	#3067	—	47	2	no	—
248	#3018	—	47	2	no	—
249	#2932	D₄₇	1	1	yes	characteristic, complemented
250	#2050	—	47	2	no	—
251	#2017	—	47	2	no	—
252	#1975	—	47	2	no	—
253	#1813	—	47	1	no	—
254	#1791	—	47	2	no	—
255	C₂×C₄₇	—	2	1	no	—
256	C₂×C₄₇	—	2	2	no	—
257	C₂×C₄₇	—	4	2	no	—
258	C₂×C₄₇	—	8	1	no	—
259	C₂×C₄₇	#2408	1	1	yes	characteristic
260	D₄₇	—	8	4	no	—
261	#585	—	47	2	no	—
262	#578	—	94	2	no	—
263	#577	—	94	4	no	—
264	#576	—	94	2	no	—
265	#575	—	47	4	no	—
266	#575	—	47	2	no	—
267	#575	—	94	2	no	—
268	C₂×#135	—	47	2	no	—
269	C₂×#135	—	94	2	no	—
270	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
271	C₂×#131	C₂×D₄₇	1	1	yes	characteristic, complemented
272	#532	C₂×D₄₇	1	1	yes	characteristic
273	#473	—	94	2	no	—
274	#472	—	94	2	no	—
275	#471	—	94	4	no	—
276	#456	—	94	2	no	—
277	#455	—	94	2	no	—
278	#454	—	94	2	no	—
279	#453	—	94	2	no	—
280	#435	—	2	2	no	—
281	#435	—	2	2	no	—
282	C₂×#108	—	47	2	no	—
283	#423	C₂×D₄₇	1	1	yes	characteristic, complemented
284	C₂×#104	—	47	4	no	—
285	#413	—	47	2	no	—
286	#413	—	47	4	no	—
287	#408	—	47	4	no	—
288	#408	C₂×D₄₇	1	1	yes	characteristic
289	#408	C₂×D₄₇	1	1	yes	characteristic, complemented
290	C₂×#97	C₂×D₄₇	1	1	yes	characteristic, complemented
291	#338	—	47	2	no	—
292	C₄₇	#24288	1	1	yes	characteristic, complemented, Sylow
293	2₋¹⁺⁴	—	94	4	no	—
294	2₋¹⁺⁴	—	94	2	no	—
295	H(5,𝔽₂)	—	94	4	no	—
296	H(5,𝔽₂)	—	94	4	no	—
297	H(5,𝔽₂)	—	94	2	no	—
298	C₂×#41	—	47	4	no	—
299	C₂×#41	—	94	4	no	—
300	C₂×#41	—	188	4	no	—
301	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
302	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
303	#137	—	94	4	no	—
304	#137	—	94	8	no	—
305	#137	—	94	4	no	—
306	#137	—	94	4	no	—
307	AGL(1,ℤ/8)	—	94	4	no	—
308	AGL(1,ℤ/8)	—	94	8	no	—
309	AGL(1,ℤ/8)	—	94	4	no	—
310	AGL(1,ℤ/8)	—	94	4	no	—
311	#135	—	94	4	no	—
312	#135	—	94	4	no	—
313	#135	—	94	2	no	—
314	#135	—	94	2	no	—
315	#135	—	94	2	no	—
316	#135	—	94	2	no	—
317	#135	—	94	4	no	—
318	#135	—	188	4	no	—
319	C₂×Q₁₆	—	47	2	no	—
320	C₂×Q₁₆	—	94	2	no	—
321	C₂×SD₁₆	—	47	4	no	—
322	C₂×SD₁₆	—	94	4	no	—
323	C₂×D₈	—	47	2	no	—
324	C₂×D₈	—	94	2	no	—
325	#131	—	2	2	no	—
326	#131	—	2	2	no	—
327	#131	—	2	2	no	—
328	#131	—	2	2	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	47	4	no	—
331	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
332	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
333	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
336	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
337	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
338	C₄⋊Q₈	D₁₈₈	1	1	yes	characteristic
339	#127	D₁₈₈	1	1	yes	characteristic
340	#124	D₁₈₈	1	1	yes	characteristic
341	#124	D₁₈₈	1	1	yes	characteristic
342	#121	—	2	2	no	—
343	C₄×D₄	—	2	2	no	—
344	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
345	#108	—	94	2	no	—
346	#108	—	94	2	no	—
347	C₄⋊C₈	—	2	2	no	—
348	#104	—	94	4	no	—
349	#104	—	94	4	no	—
350	#101	—	94	4	no	—
351	#101	—	94	2	no	—
352	#100	—	94	4	no	—
353	#100	—	94	2	no	—
354	C₂²⋊C₈	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₂²⋊C₈	—	188	4	no	—
357	#97	—	2	1	no	—
358	#97	—	2	1	no	—
359	#41	—	2	2	no	—
360	#41	—	2	2	no	—
361	#41	—	2	2	no	—
362	#41	—	2	2	no	—
363	#41	—	94	8	no	—
364	#41	—	94	4	no	—
365	#41	—	94	4	no	—
366	#41	—	94	4	no	—
367	#41	—	94	4	no	—
368	#41	—	188	4	no	—
369	#41	—	188	8	no	—
370	#41	—	188	4	no	—
371	#41	—	188	4	no	—
372	#41	—	188	4	no	—
373	C₂×Q₈	—	47	4	no	—
374	C₂×Q₈	—	94	4	no	—
375	C₂×Q₈	—	188	4	no	—
376	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
377	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
378	C₂×D₄	—	2	1	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	47	4	no	—
381	C₂×D₄	—	94	4	no	—
382	C₂×D₄	—	94	4	no	—
383	C₂×D₄	—	188	4	no	—
384	C₂×D₄	—	188	8	no	—
385	C₂×D₄	—	188	4	no	—
386	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
387	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
388	C₂×D₄	#10625350	1	2	yes	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	94	4	no	—
392	C₂²×C₄	—	188	4	no	—
393	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
394	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
395	Q₁₆	—	94	4	no	—
396	Q₁₆	—	94	2	no	—
397	Q₁₆	—	94	2	no	—
398	Q₁₆	—	188	4	no	—
399	SD₁₆	—	94	8	no	—
400	SD₁₆	—	94	4	no	—
401	SD₁₆	—	94	4	no	—
402	SD₁₆	—	188	4	no	—
403	SD₁₆	—	188	4	no	—
404	D₈	—	94	4	no	—
405	D₈	—	94	2	no	—
406	D₈	—	94	2	no	—
407	D₈	—	188	4	no	—
408	M₁₆	—	2	2	no	—
409	M₁₆	—	2	4	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	4	1	no	—
412	M₁₆	—	4	1	no	—
413	M₁₆	—	94	4	no	—
414	M₁₆	—	94	4	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	4	2	no	—
421	C₂×C₈	—	94	4	no	—
422	C₂×C₈	D₄×D₄₇	1	2	yes	—
423	C₂×C₈	D₄×D₄₇	1	2	yes	—
424	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
425	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
426	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
427	C₄⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	2	2	no	—
429	C₂²⋊C₄	—	2	2	no	—
430	C₄²	—	2	1	no	—
431	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
432	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
433	C₂³	—	2	1	no	—
434	C₂³	—	94	4	no	—
435	C₂³	—	188	4	no	—
436	C₂³	#13093998	1	2	yes	—
437	C₂³	C₂×#10625350	1	1	yes	characteristic
438	Q₈	—	2	2	no	—
439	Q₈	—	2	2	no	—
440	Q₈	—	94	4	no	—
441	Q₈	—	94	4	no	—
442	Q₈	—	188	4	no	—
443	D₄	—	2	4	no	—
444	D₄	—	2	2	no	—
445	D₄	—	2	2	no	—
446	D₄	—	4	2	no	—
447	D₄	—	8	2	no	—
448	D₄	—	94	4	no	—
449	D₄	—	94	4	no	—
450	D₄	—	188	4	no	—
451	D₄	—	188	8	no	—
452	D₄	—	188	4	no	—
453	D₄	—	188	4	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	8	1	no	—
462	C₂×C₄	—	94	4	no	—
463	C₂×C₄	—	188	8	no	—
464	C₂×C₄	—	188	4	no	—
465	C₂×C₄	—	188	4	no	—
466	C₂×C₄	—	188	4	no	—
467	C₂×C₄	#13093998	1	2	yes	—
468	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
469	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
470	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
471	C₂×C₄	#13094070	1	2	yes	—
472	C₈	—	2	2	no	—
473	C₈	—	4	1	no	—
474	C₈	—	4	1	no	—
475	C₈	—	188	4	no	—
476	C₈	#13093992	1	1	yes	characteristic
477	C₈	#13093992	1	1	yes	characteristic
478	C₈	#13093992	1	2	yes	—
479	C₂²	—	2	2	no	—
480	C₂²	—	4	1	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	376	4	no	—
485	C₂²	—	188	4	no	—
486	C₂²	—	752	4	no	—
487	C₂²	C₂×#13093998	1	1	yes	characteristic
488	C₂²	#15689769	1	2	yes	—
489	C₄	—	2	2	no	—
490	C₄	—	4	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	188	4	no	—
494	C₄	C₂×#13093992	1	1	yes	characteristic
495	C₄	#15689687	1	1	yes	characteristic
496	C₄	D₄×D₁₈₈	1	2	yes	—
497	C₂	—	2	1	no	—
498	C₂	—	2	2	no	—
499	C₂	—	4	2	no	—
500	C₂	—	8	1	no	—
501	C₂	—	376	4	no	—
502	C₂	#20246744	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689687
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2932	C₂
socle	C₂×C₄₇	#2408
hypercenter	#2932	D₄₇
hypocenter	C₄₇	#24288
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #2932

Complements

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

N	H ≅ G/N	type
1. #20258162	C₂	semidirect
2. #20253108	C₂	semidirect
3. #20252736	C₂	semidirect
4. #20244675	C₂	semidirect
5. #20244492	C₂	semidirect
6. #20244281	C₂	semidirect
7. #20243438	C₂	semidirect
8. #20243338	C₂	semidirect
9. C₄₇×#2932	C₂	semidirect
16. #15689921	C₂²	semidirect
26. C₂×#13093960	C₂²	semidirect
27. C₂×#13093952	C₂²	semidirect
29. #15689105	C₂²	semidirect
30. #15689089	C₂²	semidirect
31. C₄₇⋊#338	C₂²	semidirect
33. C₂×#131×C₄₇	C₂²	semidirect
37. C₄₇×#423	C₂²	semidirect
39. C₄₇×#408	C₂²	semidirect
40. C₂×#97×C₄₇	C₂²	semidirect
66. C₂×Dic₁₈₈	D₄	semidirect
68. C₂×#10625325	D₄	semidirect
70. C₂×D₃₇₆	D₄	semidirect
249. #2932	D₄₇	semidirect
271. C₂×#131	C₂×D₄₇	semidirect
283. #423	C₂×D₄₇	semidirect
289. #408	C₂×D₄₇	semidirect
290. C₂×#97	C₂×D₄₇	semidirect
292. C₄₇	#24288	semidirect

Maximal subgroups

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

subgroup	index
#20258162	2
#20253108	2
#20252736	2
#20244675	2
#20244492	2
#20244281	2
#20243438	2
#20243338	2
C₄₇×#2932	2
#24288	47