Subgroups — #26258763

Order 12032.

842 conjugacy classes of subgroups.

The subgroup lattice has 514 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	#20251983	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244750	C₂	1	2	yes	maximal, complemented
6	#20244604	C₂	1	2	yes	maximal, complemented
7	#20244259	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244141	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243755	C₂	1	2	yes	maximal, complemented
10	#20243447	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#444	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	1	no	—
18	#15689381	—	2	1	no	—
19	#15689364	—	2	2	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×#13093956	—	2	1	no	—
30	C₂×#13093956	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×#444	—	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×#97×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	2	no	—
71	#13093958	D₄	1	2	yes	—
72	#13093956	—	2	1	no	—
73	#13093956	—	2	1	no	—
74	#13093956	—	2	2	no	—
75	#13093956	D₄	1	1	yes	characteristic
76	#13093956	D₄	1	1	yes	characteristic
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	#97×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	1	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	—	4	2	no	—
215	C₂×Dic₄₇	—	4	2	no	—
216	C₂×Dic₄₇	—	4	2	no	—
217	C₂×Dic₄₇	—	4	2	no	—
218	C₂×Dic₄₇	—	8	2	no	—
219	C₂×Dic₄₇	—	16	2	no	—
220	Dic₉₄	—	4	2	no	—
221	Dic₉₄	—	4	2	no	—
222	Dic₉₄	—	4	2	no	—
223	Dic₉₄	—	4	2	no	—
224	C₈×C₄₇	—	2	2	no	—
225	C₈×C₄₇	—	2	1	no	—
226	C₈×C₄₇	—	2	1	no	—
227	C₈×C₄₇	—	4	1	no	—
228	C₈×C₄₇	#121	1	2	yes	—
229	C₈×C₄₇	#121	1	2	yes	—
230	C₄₇⋊C₈	—	4	2	no	—
231	#24800	—	47	1	no	maximal, Sylow
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	2	no	—
234	C₂²×C₄₇	—	4	2	no	—
235	C₂²×C₄₇	—	4	1	no	—
236	C₂²×C₄₇	—	4	2	no	—
237	C₂²×C₄₇	#537	1	1	yes	characteristic
238	C₂²×C₄₇	D₄²	1	1	yes	characteristic
239	C₂²×C₄₇	#553	1	1	yes	characteristic
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	4	1	no	—
242	C₄×C₄₇	—	8	1	no	—
243	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
244	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
245	C₄×C₄₇	#547	1	1	yes	characteristic
246	C₄×C₄₇	#548	1	1	yes	characteristic
247	Dic₄₇	—	4	2	no	—
248	Dic₄₇	—	4	2	no	—
249	Dic₄₇	—	8	2	no	—
250	Dic₄₇	—	8	2	no	—
251	C₂×#473	—	47	1	no	—
252	#3059	—	47	1	no	—
253	#3046	—	47	2	no	—
254	C₂×#444	D₄₇	1	1	yes	characteristic
255	#2912	—	47	1	no	—
256	#2064	—	47	2	no	—
257	#2038	—	47	2	no	—
258	#1971	—	47	1	no	—
259	#1946	—	47	1	no	—
260	#1882	—	47	2	no	—
261	#1815	—	47	1	no	—
262	C₂×C₄₇	—	2	1	no	—
263	C₂×C₄₇	—	2	1	no	—
264	C₂×C₄₇	—	4	2	no	—
265	C₂×C₄₇	—	8	1	no	—
266	C₂×C₄₇	#2416	1	1	yes	characteristic
267	C₂×C₄₇	#3289	1	2	yes	—
268	C₂×#137	—	47	2	no	—
269	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
270	C₂²×Q₁₆	—	47	1	no	—
271	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
272	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
273	#536	—	47	2	no	—
274	#520	—	47	2	no	—
275	#473	—	94	4	no	—
276	#470	—	94	1	no	—
277	#470	—	94	1	no	—
278	#467	—	94	2	no	—
279	#464	—	94	2	no	—
280	#463	—	94	2	no	—
281	#462	—	94	2	no	—
282	#461	—	94	2	no	—
283	#444	—	2	4	no	—
284	C₂×#108	—	47	1	no	—
285	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
286	#428	—	47	2	no	—
287	#428	—	94	2	no	—
288	#427	—	47	1	no	—
289	#427	—	94	1	no	—
290	C₂×#106	—	47	1	no	—
291	C₂×#106	—	94	1	no	—
292	#424	—	47	2	no	—
293	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
294	C₂×#104	C₂×D₄₇	1	1	yes	characteristic
295	#419	—	47	2	no	—
296	#417	—	47	2	no	—
297	C₂×#103	—	47	2	no	—
298	C₂×#101	—	47	2	no	—
299	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
300	#391	—	47	2	no	—
301	#343	—	47	2	no	—
302	#339	—	47	2	no	—
303	C₄₇	#24800	1	1	yes	characteristic, complemented, Sylow
304	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
305	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
306	C₂²×Q₈	—	47	2	no	—
307	#137	—	94	4	no	—
308	#137	—	94	4	no	—
309	#135	—	2	2	no	—
310	#135	—	2	2	no	—
311	C₂×Q₁₆	—	94	2	no	—
312	C₂×Q₁₆	—	94	1	no	—
313	C₂×Q₁₆	—	94	1	no	—
314	C₂×Q₁₆	—	94	2	no	—
315	C₂×Q₁₆	—	94	2	no	—
316	C₂×Q₁₆	D₁₈₈	1	1	yes	characteristic
317	C₂×SD₁₆	—	94	2	no	—
318	C₂×SD₁₆	D₁₈₈	1	1	yes	characteristic
319	C₂×SD₁₆	D₁₈₈	1	1	yes	characteristic
320	C₂×D₈	D₁₈₈	1	1	yes	characteristic
321	#131	—	2	2	no	—
322	#131	—	2	2	no	—
323	#131	—	2	2	no	—
324	#131	C₂²⋊D₄₇	1	4	yes	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	47	2	no	—
328	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
329	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
333	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₄⋊Q₈	—	94	2	no	—
335	#124	—	94	2	no	—
336	#123	—	188	2	no	—
337	C₂²⋊Q₈	—	94	2	no	—
338	C₂²⋊Q₈	—	94	2	no	—
339	C₄×Q₈	—	94	2	no	—
340	C₄×D₄	—	94	2	no	—
341	C₄×D₄	—	188	2	no	—
342	#117	—	47	2	no	—
343	#117	—	94	2	no	—
344	C₂×C₄⋊C₄	—	47	2	no	—
345	C₂×C₄⋊C₄	—	94	2	no	—
346	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
347	#108	—	2	2	no	—
348	#108	—	94	2	no	—
349	#107	—	47	2	no	—
350	#107	—	94	2	no	—
351	#106	—	47	1	no	—
352	#106	—	47	1	no	—
353	#106	—	94	2	no	—
354	#106	—	94	1	no	—
355	#106	—	94	1	no	—
356	C₄⋊C₈	—	94	2	no	—
357	C₄⋊C₈	—	94	2	no	—
358	#104	—	2	2	no	—
359	#104	—	2	2	no	—
360	#103	—	94	2	no	—
361	#103	—	94	2	no	—
362	#103	—	94	2	no	—
363	#103	—	94	2	no	—
364	#103	—	94	2	no	—
365	#102	—	94	2	no	—
366	#101	—	94	4	no	—
367	#97	—	2	2	no	—
368	#95	—	188	2	no	—
369	#41	—	2	1	no	—
370	#41	—	2	1	no	—
371	#41	—	2	1	no	—
372	#41	—	2	1	no	—
373	#41	—	2	1	no	—
374	#41	—	2	1	no	—
375	#41	#10625350	1	2	yes	—
376	#41	C₂×C₂²⋊D₄₇	1	2	yes	—
377	C₂×Q₈	—	94	2	no	—
378	C₂×Q₈	—	94	2	no	—
379	C₂×Q₈	—	94	2	no	—
380	C₂×Q₈	—	94	2	no	—
381	C₂×Q₈	—	94	2	no	—
382	C₂×Q₈	—	94	2	no	—
383	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
384	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
388	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	94	2	no	—
393	C₂²×C₄	—	94	2	no	—
394	C₂²×C₄	—	188	2	no	—
395	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
396	Q₁₆	—	2	2	no	—
397	Q₁₆	—	188	4	no	—
398	Q₁₆	—	188	2	no	—
399	Q₁₆	—	188	2	no	—
400	SD₁₆	—	2	2	no	—
401	SD₁₆	—	2	2	no	—
402	SD₁₆	—	188	4	no	—
403	D₈	—	2	2	no	—
404	M₁₆	—	2	1	no	—
405	M₁₆	—	2	4	no	—
406	M₁₆	—	2	1	no	—
407	M₁₆	—	2	1	no	—
408	M₁₆	—	4	2	no	—
409	M₁₆	—	94	2	no	—
410	M₁₆	—	94	2	no	—
411	M₁₆	C₂×C₂²⋊D₄₇	1	2	yes	—
412	C₂×C₈	—	2	1	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	4	2	no	—
418	C₂×C₈	—	94	2	no	—
419	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
420	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
421	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
422	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
423	C₂×C₈	#10625352	1	2	yes	—
424	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
425	C₄⋊C₄	—	47	2	no	—
426	C₄⋊C₄	—	47	2	no	—
427	C₄⋊C₄	—	94	2	no	—
428	C₄⋊C₄	—	94	2	no	—
429	C₄⋊C₄	—	188	2	no	—
430	C₄⋊C₄	—	188	2	no	—
431	C₄⋊C₄	—	188	2	no	—
432	C₂²⋊C₄	—	94	2	no	—
433	C₂²⋊C₄	—	188	2	no	—
434	C₂²⋊C₄	—	188	2	no	—
435	C₂²⋊C₄	—	188	2	no	—
436	C₄²	—	2	1	no	—
437	C₄²	—	2	1	no	—
438	C₄²	—	94	2	no	—
439	C₄²	—	188	2	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	#13094070	1	1	yes	characteristic
443	Q₈	—	2	1	no	—
444	Q₈	—	2	1	no	—
445	Q₈	—	2	1	no	—
446	Q₈	—	188	2	no	—
447	Q₈	—	188	2	no	—
448	Q₈	—	188	2	no	—
449	Q₈	—	188	2	no	—
450	Q₈	#13093998	1	2	yes	—
451	D₄	—	2	2	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	1	no	—
454	D₄	—	2	1	no	—
455	D₄	—	2	1	no	—
456	D₄	—	4	1	no	—
457	D₄	—	4	1	no	—
458	D₄	#13093998	1	2	yes	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	1	no	—
467	C₂×C₄	—	94	2	no	—
468	C₂×C₄	—	94	2	no	—
469	C₂×C₄	—	376	2	no	—
470	C₂×C₄	—	188	2	no	—
471	C₂×C₄	—	188	2	no	—
472	C₂×C₄	—	188	2	no	—
473	C₂×C₄	—	188	2	no	—
474	C₂×C₄	—	752	2	no	—
475	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
476	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
477	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
478	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
479	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
480	C₂×C₄	#13094071	1	1	yes	characteristic
481	C₈	—	2	2	no	—
482	C₈	—	2	1	no	—
483	C₈	—	2	1	no	—
484	C₈	—	4	1	no	—
485	C₈	—	188	2	no	—
486	C₈	#13093996	1	2	yes	—
487	C₈	#13093996	1	2	yes	—
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	1	no	—
492	C₂²	—	4	2	no	—
493	C₂²	#15689701	1	1	yes	characteristic
494	C₂²	D₄×D₁₈₈	1	1	yes	characteristic
495	C₂²	#15689819	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	4	1	no	—
498	C₄	—	8	1	no	—
499	C₄	—	376	2	no	—
500	C₄	—	376	2	no	—
501	C₄	—	188	2	no	—
502	C₄	—	188	2	no	—
503	C₄	C₂×#13093996	1	1	yes	characteristic
504	C₄	C₂×#13093998	1	1	yes	characteristic
505	C₄	#15689777	1	1	yes	characteristic
506	C₄	#15689782	1	1	yes	characteristic
507	C₂	—	2	1	no	—
508	C₂	—	2	1	no	—
509	C₂	—	4	2	no	—
510	C₂	—	8	1	no	—
511	C₂	#20246828	1	1	yes	characteristic
512	C₂	#20255164	1	2	yes	—

	subgroup	G/H
center	C₂²	D₄×D₁₈₈
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#444	C₂
socle	C₂²×C₄₇	D₄²
prime radical	C₂×#135×C₄₇	C₂²
hypercenter	C₂×#444	D₄₇
hypocenter	C₄₇	#24800
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#444

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. #20251983	C₂	semidirect
5. #20244750	C₂	semidirect
6. #20244604	C₂	semidirect
7. #20244259	C₂	semidirect
8. #20244141	C₂	semidirect
9. #20243755	C₂	semidirect
10. #20243447	C₂	semidirect
303. C₄₇	#24800	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
#20251983	2
#20244750	2
#20244604	2
#20244259	2
#20244141	2
#20243755	2
#20243447	2
C₂×C₄₇×#444	2
#24800	47