Subgroups — #26258741

Order 12032.

846 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	C₂×#15689398	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253043	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252936	C₂	1	2	yes	maximal
4	#20251988	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244750	C₂	1	2	yes	maximal, complemented
6	#20244604	C₂	1	2	yes	maximal, complemented
7	#20244249	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244136	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243755	C₂	1	2	yes	maximal, complemented
10	#20243452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#443	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094054	C₂²	1	2	yes	—
13	C₂²×Dic₁₈₈	C₂²	1	1	yes	characteristic
14	#15689694	C₂²	1	2	yes	—
15	#15689606	C₂²	1	2	yes	—
16	#15689398	—	2	4	no	—
17	#15689381	—	2	2	no	—
18	#15689364	—	2	1	no	—
19	#15689364	—	2	1	no	—
20	#15689343	—	2	2	no	—
21	#15689336	—	2	2	no	—
22	#15689331	—	2	2	no	—
23	#15689326	—	2	2	no	—
24	C₂×#13093960	C₂²	1	1	yes	characteristic
25	#15689165	—	2	2	no	—
26	#15689165	C₂²	1	2	yes	—
27	#15689161	—	2	1	no	—
28	#15689161	C₂²	1	1	yes	characteristic
29	C₂×#13093958	—	2	1	no	—
30	C₂×#13093958	C₂²	1	1	yes	characteristic
31	#15689149	C₂²	1	2	yes	—
32	#15689133	C₂²	1	2	yes	—
33	#15689124	C₂²	1	2	yes	—
34	C₂×#13093949	C₂²	1	2	yes	—
35	C₂×#13093942	C₂²	1	2	yes	—
36	#15689029	C₂²	1	2	yes	—
37	#15688891	C₂²	1	2	yes	—
38	#15688883	C₂²	1	2	yes	—
39	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#443	—	2	4	no	—
43	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#104×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂²×Dic₉₄	C₂³	1	2	yes	—
48	#13094054	—	2	4	no	—
49	#13094054	—	2	4	no	—
50	C₂×Dic₁₈₈	—	2	1	no	—
51	C₂×Dic₁₈₈	—	2	1	no	—
52	C₂×Dic₁₈₈	—	2	2	no	—
53	C₂×Dic₁₈₈	—	2	2	no	—
54	C₂×#10625337	—	2	2	no	—
55	C₂×#10625335	—	2	2	no	—
56	C₂×#10625329	C₂³	1	2	yes	—
57	#13094022	—	2	2	no	—
58	#13094011	—	2	2	no	—
59	#13094005	—	4	2	no	—
60	#13094003	—	2	2	no	—
61	#13094003	—	2	2	no	—
62	Q₈×Dic₄₇	—	2	2	no	—
63	D₄×Dic₄₇	—	2	2	no	—
64	D₄×Dic₄₇	—	4	2	no	—
65	#13093983	—	2	2	no	—
66	#13093983	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₄₇	—	2	2	no	—
68	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
69	#13093960	—	2	2	no	—
70	#13093958	—	2	1	no	—
71	#13093958	—	2	1	no	—
72	#13093958	—	2	2	no	—
73	#13093958	D₄	1	1	yes	characteristic
74	#13093958	D₄	1	1	yes	characteristic
75	#13093956	—	2	2	no	—
76	#13093956	D₄	1	2	yes	—
77	Dic₄₇⋊C₈	—	2	2	no	—
78	Dic₄₇⋊C₈	—	2	2	no	—
79	#13093949	—	2	2	no	—
80	#13093949	—	2	2	no	—
81	#13093949	—	2	2	no	—
82	#13093949	—	2	2	no	—
83	#13093948	—	2	2	no	—
84	#13093945	—	2	2	no	—
85	#13093942	—	2	4	no	—
86	C₄₇⋊#95	—	4	2	no	—
87	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
89	#135×C₄₇	—	2	2	no	—
90	#135×C₄₇	—	2	2	no	—
91	C₂×Q₁₆×C₄₇	D₄	1	1	yes	characteristic
92	C₂×SD₁₆×C₄₇	D₄	1	1	yes	characteristic
93	C₂×SD₁₆×C₄₇	D₄	1	1	yes	characteristic
94	C₂×D₈×C₄₇	D₄	1	1	yes	characteristic
95	#131×C₄₇	—	2	2	no	—
96	#131×C₄₇	—	2	2	no	—
97	#131×C₄₇	—	2	2	no	—
98	#131×C₄₇	D₄	1	4	yes	—
99	C₂×M₁₆×C₄₇	—	2	1	no	—
100	C₂×M₁₆×C₄₇	—	2	1	no	—
101	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	—	2	1	no	—
104	C₂²×C₈×C₄₇	—	2	1	no	—
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
108	#108×C₄₇	—	2	2	no	—
109	#104×C₄₇	—	2	2	no	—
110	#104×C₄₇	—	2	2	no	—
111	C₄×C₈×C₄₇	—	2	2	no	—
112	#41×C₄₇	—	2	1	no	—
113	#41×C₄₇	—	2	1	no	—
114	#41×C₄₇	—	2	1	no	—
115	#41×C₄₇	—	2	1	no	—
116	#41×C₄₇	—	2	1	no	—
117	#41×C₄₇	—	2	1	no	—
118	#41×C₄₇	C₂×D₄	1	2	yes	—
119	#41×C₄₇	#41	1	2	yes	—
120	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×D₄×C₄₇	—	2	1	no	—
123	C₂×D₄×C₄₇	—	2	1	no	—
124	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	—	2	1	no	—
129	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₂²×Dic₄₇	—	2	2	no	—
131	C₂²×Dic₄₇	—	2	2	no	—
132	C₂²×Dic₄₇	—	4	2	no	—
133	C₂×Dic₉₄	—	2	2	no	—
134	C₂×Dic₉₄	—	2	2	no	—
135	C₂×Dic₉₄	—	2	2	no	—
136	C₂×Dic₉₄	—	2	2	no	—
137	C₂×Dic₉₄	—	2	2	no	—
138	C₂×Dic₉₄	—	2	2	no	—
139	Q₁₆×C₄₇	—	2	2	no	—
140	SD₁₆×C₄₇	—	2	2	no	—
141	SD₁₆×C₄₇	—	2	2	no	—
142	D₈×C₄₇	—	2	2	no	—
143	M₁₆×C₄₇	—	2	1	no	—
144	M₁₆×C₄₇	—	2	4	no	—
145	M₁₆×C₄₇	—	2	1	no	—
146	M₁₆×C₄₇	—	2	1	no	—
147	M₁₆×C₄₇	—	4	2	no	—
148	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₄₇	—	2	1	no	—
150	C₂×C₈×C₄₇	—	2	1	no	—
151	C₂×C₈×C₄₇	—	2	1	no	—
152	C₂×C₈×C₄₇	—	2	4	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	4	2	no	—
155	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
160	C₂×C₈×C₄₇	#41	1	2	yes	—
161	C₄²×C₄₇	—	2	1	no	—
162	C₄²×C₄₇	—	2	1	no	—
163	C₂²⋊Dic₄₇	—	2	2	no	—
164	C₂²⋊Dic₄₇	—	4	2	no	—
165	C₂²⋊Dic₄₇	—	4	2	no	—
166	C₂²⋊Dic₄₇	—	4	2	no	—
167	#10625337	—	4	4	no	—
168	#10625335	—	4	4	no	—
169	C₄⋊Dic₄₇	—	2	2	no	—
170	C₄⋊Dic₄₇	—	2	2	no	—
171	C₄⋊Dic₄₇	—	4	2	no	—
172	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
173	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
174	Dic₄₇⋊C₄	—	4	2	no	—
175	Dic₄₇⋊C₄	—	4	2	no	—
176	C₄×Dic₄₇	—	2	2	no	—
177	C₄×Dic₄₇	—	4	2	no	—
178	#10625329	—	2	2	no	—
179	#10625329	—	2	2	no	—
180	C₂×C₄₇⋊C₈	—	2	2	no	—
181	Dic₁₈₈	—	4	2	no	—
182	Dic₁₈₈	—	4	2	no	—
183	C₂³×C₄₇	—	2	1	no	—
184	C₂³×C₄₇	—	2	1	no	—
185	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
186	Q₈×C₄₇	—	2	1	no	—
187	Q₈×C₄₇	—	2	1	no	—
188	Q₈×C₄₇	—	2	1	no	—
189	Q₈×C₄₇	#121	1	2	yes	—
190	D₄×C₄₇	—	2	2	no	—
191	D₄×C₄₇	—	2	2	no	—
192	D₄×C₄₇	—	2	1	no	—
193	D₄×C₄₇	—	2	1	no	—
194	D₄×C₄₇	—	2	1	no	—
195	D₄×C₄₇	—	4	1	no	—
196	D₄×C₄₇	—	4	1	no	—
197	D₄×C₄₇	#121	1	2	yes	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	—	2	2	no	—
215	C₂×Dic₄₇	—	4	2	no	—
216	C₂×Dic₄₇	—	4	2	no	—
217	C₂×Dic₄₇	—	4	2	no	—
218	C₂×Dic₄₇	—	4	2	no	—
219	C₂×Dic₄₇	—	8	2	no	—
220	C₂×Dic₄₇	—	16	2	no	—
221	Dic₉₄	—	4	2	no	—
222	Dic₉₄	—	4	2	no	—
223	Dic₉₄	—	4	2	no	—
224	Dic₉₄	—	4	2	no	—
225	C₈×C₄₇	—	2	2	no	—
226	C₈×C₄₇	—	2	1	no	—
227	C₈×C₄₇	—	2	1	no	—
228	C₈×C₄₇	—	4	1	no	—
229	C₈×C₄₇	#121	1	2	yes	—
230	C₈×C₄₇	#121	1	2	yes	—
231	C₄₇⋊C₈	—	4	2	no	—
232	#24798	—	47	1	no	maximal, Sylow
233	C₂²×C₄₇	—	2	1	no	—
234	C₂²×C₄₇	—	2	1	no	—
235	C₂²×C₄₇	—	2	2	no	—
236	C₂²×C₄₇	—	4	1	no	—
237	C₂²×C₄₇	—	4	1	no	—
238	C₂²×C₄₇	—	4	1	no	—
239	C₂²×C₄₇	—	4	1	no	—
240	C₂²×C₄₇	—	4	1	no	—
241	C₂²×C₄₇	#537	1	1	yes	characteristic
242	C₂²×C₄₇	D₄²	1	1	yes	characteristic
243	C₂²×C₄₇	#553	1	1	yes	characteristic
244	C₄×C₄₇	—	2	2	no	—
245	C₄×C₄₇	—	4	2	no	—
246	C₄×C₄₇	—	4	1	no	—
247	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
248	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
249	C₄×C₄₇	#547	1	1	yes	characteristic
250	C₄×C₄₇	#548	1	1	yes	characteristic
251	Dic₄₇	—	4	2	no	—
252	Dic₄₇	—	4	2	no	—
253	Dic₄₇	—	8	2	no	—
254	Dic₄₇	—	8	2	no	—
255	C₂×#473	—	47	1	no	—
256	#3059	—	47	1	no	—
257	#3046	—	47	2	no	—
258	C₂×#443	D₄₇	1	1	yes	characteristic
259	#2913	—	47	1	no	—
260	#2064	—	47	2	no	—
261	#2038	—	47	2	no	—
262	#1969	—	47	1	no	—
263	#1945	—	47	1	no	—
264	#1882	—	47	2	no	—
265	#1816	—	47	1	no	—
266	C₂×C₄₇	—	2	1	no	—
267	C₂×C₄₇	—	2	1	no	—
268	C₂×C₄₇	—	4	2	no	—
269	C₂×C₄₇	—	8	1	no	—
270	C₂×C₄₇	#2416	1	1	yes	characteristic
271	C₂×C₄₇	#3290	1	1	yes	characteristic
272	C₂×C₄₇	#3293	1	1	yes	characteristic
273	C₂×#137	—	47	2	no	—
274	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
275	C₂²×Q₁₆	—	47	1	no	—
276	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
277	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
278	#536	—	47	2	no	—
279	#520	—	47	2	no	—
280	#473	—	94	4	no	—
281	#470	—	94	2	no	—
282	#467	—	94	1	no	—
283	#467	—	94	1	no	—
284	#464	—	94	2	no	—
285	#463	—	94	2	no	—
286	#462	—	94	2	no	—
287	#461	—	94	2	no	—
288	#443	—	2	4	no	—
289	C₂×#108	—	47	1	no	—
290	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
291	#428	—	47	2	no	—
292	#428	—	94	2	no	—
293	#427	—	47	1	no	—
294	#427	—	94	1	no	—
295	C₂×#107	—	47	1	no	—
296	C₂×#107	—	94	1	no	—
297	#424	—	47	2	no	—
298	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
299	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
300	#419	—	47	2	no	—
301	#417	—	47	2	no	—
302	C₂×#103	—	47	2	no	—
303	C₂×#101	—	47	2	no	—
304	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
305	#391	—	47	2	no	—
306	#343	—	47	2	no	—
307	#339	—	47	2	no	—
308	C₄₇	#24798	1	1	yes	characteristic, complemented, Sylow
309	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
310	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
311	C₂²×Q₈	—	47	2	no	—
312	#137	—	94	4	no	—
313	#137	—	94	4	no	—
314	#135	—	2	2	no	—
315	#135	—	2	2	no	—
316	C₂×Q₁₆	—	94	2	no	—
317	C₂×Q₁₆	—	94	1	no	—
318	C₂×Q₁₆	—	94	1	no	—
319	C₂×Q₁₆	—	94	2	no	—
320	C₂×Q₁₆	—	94	2	no	—
321	C₂×Q₁₆	D₁₈₈	1	1	yes	characteristic
322	C₂×SD₁₆	—	94	2	no	—
323	C₂×SD₁₆	D₁₈₈	1	1	yes	characteristic
324	C₂×SD₁₆	D₁₈₈	1	1	yes	characteristic
325	C₂×D₈	D₁₈₈	1	1	yes	characteristic
326	#131	—	2	2	no	—
327	#131	—	2	2	no	—
328	#131	—	2	2	no	—
329	#131	C₂²⋊D₄₇	1	4	yes	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	47	2	no	—
333	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	—	2	1	no	—
337	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
338	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
339	C₄⋊Q₈	—	94	2	no	—
340	#124	—	94	2	no	—
341	#123	—	188	2	no	—
342	C₂²⋊Q₈	—	94	2	no	—
343	C₂²⋊Q₈	—	94	2	no	—
344	C₄×Q₈	—	94	2	no	—
345	C₄×D₄	—	94	2	no	—
346	C₄×D₄	—	188	2	no	—
347	#117	—	47	2	no	—
348	#117	—	94	2	no	—
349	C₂×C₄⋊C₄	—	47	2	no	—
350	C₂×C₄⋊C₄	—	94	2	no	—
351	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
352	#108	—	2	2	no	—
353	#108	—	94	2	no	—
354	#107	—	47	1	no	—
355	#107	—	47	1	no	—
356	#107	—	94	2	no	—
357	#107	—	94	1	no	—
358	#107	—	94	1	no	—
359	#106	—	47	2	no	—
360	#106	—	94	2	no	—
361	C₄⋊C₈	—	94	2	no	—
362	C₄⋊C₈	—	94	2	no	—
363	#104	—	2	2	no	—
364	#104	—	2	2	no	—
365	#103	—	94	2	no	—
366	#103	—	94	2	no	—
367	#103	—	94	2	no	—
368	#103	—	94	2	no	—
369	#103	—	94	2	no	—
370	#102	—	94	2	no	—
371	#101	—	94	4	no	—
372	C₄×C₈	—	2	2	no	—
373	#95	—	188	2	no	—
374	#41	—	2	1	no	—
375	#41	—	2	1	no	—
376	#41	—	2	1	no	—
377	#41	—	2	1	no	—
378	#41	—	2	1	no	—
379	#41	—	2	1	no	—
380	#41	#10625350	1	2	yes	—
381	#41	C₂×C₂²⋊D₄₇	1	2	yes	—
382	C₂×Q₈	—	94	2	no	—
383	C₂×Q₈	—	94	2	no	—
384	C₂×Q₈	—	94	2	no	—
385	C₂×Q₈	—	94	2	no	—
386	C₂×Q₈	—	94	2	no	—
387	C₂×Q₈	—	94	2	no	—
388	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
389	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
393	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	94	2	no	—
398	C₂²×C₄	—	94	2	no	—
399	C₂²×C₄	—	188	2	no	—
400	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
401	Q₁₆	—	2	2	no	—
402	Q₁₆	—	188	4	no	—
403	Q₁₆	—	188	2	no	—
404	Q₁₆	—	188	2	no	—
405	SD₁₆	—	2	2	no	—
406	SD₁₆	—	2	2	no	—
407	SD₁₆	—	188	4	no	—
408	D₈	—	2	2	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	4	no	—
411	M₁₆	—	2	1	no	—
412	M₁₆	—	2	1	no	—
413	M₁₆	—	4	2	no	—
414	M₁₆	—	94	2	no	—
415	M₁₆	—	94	2	no	—
416	M₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	4	no	—
421	C₂×C₈	—	2	1	no	—
422	C₂×C₈	—	4	2	no	—
423	C₂×C₈	—	94	2	no	—
424	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
425	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
426	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
427	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
428	C₂×C₈	#10625352	1	2	yes	—
429	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
430	C₄⋊C₄	—	47	2	no	—
431	C₄⋊C₄	—	47	2	no	—
432	C₄⋊C₄	—	94	2	no	—
433	C₄⋊C₄	—	94	2	no	—
434	C₄⋊C₄	—	188	2	no	—
435	C₄⋊C₄	—	188	2	no	—
436	C₄⋊C₄	—	188	2	no	—
437	C₂²⋊C₄	—	94	2	no	—
438	C₂²⋊C₄	—	188	2	no	—
439	C₂²⋊C₄	—	188	2	no	—
440	C₂²⋊C₄	—	188	2	no	—
441	C₄²	—	2	1	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	94	2	no	—
444	C₄²	—	188	2	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	2	1	no	—
447	C₂³	#13094070	1	1	yes	characteristic
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	2	1	no	—
451	Q₈	—	188	2	no	—
452	Q₈	—	188	2	no	—
453	Q₈	—	188	2	no	—
454	Q₈	—	188	2	no	—
455	Q₈	#13093998	1	2	yes	—
456	D₄	—	2	2	no	—
457	D₄	—	2	2	no	—
458	D₄	—	2	1	no	—
459	D₄	—	2	1	no	—
460	D₄	—	2	1	no	—
461	D₄	—	4	1	no	—
462	D₄	—	4	1	no	—
463	D₄	#13093998	1	2	yes	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	94	2	no	—
474	C₂×C₄	—	94	2	no	—
475	C₂×C₄	—	376	2	no	—
476	C₂×C₄	—	188	2	no	—
477	C₂×C₄	—	188	2	no	—
478	C₂×C₄	—	188	2	no	—
479	C₂×C₄	—	188	2	no	—
480	C₂×C₄	—	752	2	no	—
481	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
482	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
484	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
485	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
486	C₂×C₄	#13094071	1	1	yes	characteristic
487	C₈	—	2	2	no	—
488	C₈	—	2	1	no	—
489	C₈	—	2	1	no	—
490	C₈	—	4	1	no	—
491	C₈	—	188	2	no	—
492	C₈	#13093996	1	2	yes	—
493	C₈	#13093996	1	2	yes	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	2	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	—	4	1	no	—
501	C₂²	—	4	1	no	—
502	C₂²	#15689701	1	1	yes	characteristic
503	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
504	C₂²	#15689819	1	1	yes	characteristic
505	C₄	—	2	2	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	1	no	—
508	C₄	—	376	2	no	—
509	C₄	—	376	2	no	—
510	C₄	—	188	2	no	—
511	C₄	—	188	2	no	—
512	C₄	C₂×#13093996	1	1	yes	characteristic
513	C₄	C₂×#13093998	1	1	yes	characteristic
514	C₄	#15689777	1	1	yes	characteristic
515	C₄	#15689782	1	1	yes	characteristic
516	C₂	—	2	1	no	—
517	C₂	—	2	1	no	—
518	C₂	—	4	2	no	—
519	C₂	—	8	1	no	—
520	C₂	#20246828	1	1	yes	characteristic
521	C₂	#20255175	1	1	yes	characteristic
522	C₂	#20255193	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₈₈
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#443	C₂
socle	C₂²×C₄₇	D₄²
prime radical	C₂×#135×C₄₇	C₂²
hypercenter	C₂×#443	D₄₇
hypocenter	C₄₇	#24798
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. C₂×#15689398	C₂	semidirect
2. #20253043	C₂	semidirect
4. #20251988	C₂	semidirect
5. #20244750	C₂	semidirect
6. #20244604	C₂	semidirect
7. #20244249	C₂	semidirect
8. #20244136	C₂	semidirect
9. #20243755	C₂	semidirect
10. #20243452	C₂	semidirect
308. C₄₇	#24798	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689398	2
#20253043	2
#20252936	2
#20251988	2
#20244750	2
#20244604	2
#20244249	2
#20244136	2
#20243755	2
#20243452	2
C₂×C₄₇×#443	2
#24798	47