Subgroups — #26267296

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253838	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689383	C₂	1	2	yes	maximal, complemented
3	#20252860	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252131	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244681	C₂	1	2	yes	maximal, complemented
6	#20244500	C₂	1	2	yes	maximal, complemented
7	#20244229	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244164	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243899	C₂	1	2	yes	maximal, complemented
10	C₄×#13093943	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094055	C₂²	1	2	yes	—
13	C₂×#13094050	C₂²	1	2	yes	—
14	C₂×#13094050	C₂²	1	2	yes	—
15	C₂×#13094030	C₂²	1	2	yes	—
16	#15689673	C₂²	1	1	yes	characteristic
17	#15689510	—	2	2	no	—
18	#15689499	—	2	1	no	—
19	#15689495	—	2	1	no	—
20	#15689383	—	2	8	no	—
21	#15689345	—	2	2	no	—
22	#15689333	—	2	1	no	—
23	#15689323	—	2	1	no	—
24	#15689200	—	2	1	no	—
25	#15689193	—	2	2	no	—
26	#15689188	—	2	1	no	—
27	C₂×#13093960	C₂²	1	2	yes	—
28	#15689147	C₂²	1	1	yes	characteristic
29	#15689122	C₂²	1	2	yes	—
30	C₂×#13093943	C₂²	1	1	yes	characteristic
31	C₂×#13093943	C₂²	1	1	yes	characteristic
32	C₂×#13093941	C₂²	1	2	yes	—
33	C₂×#13093941	C₂²	1	2	yes	—
34	#15689089	C₂²	1	2	yes	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	#15688892	C₂²	1	1	yes	characteristic
38	#15688892	C₂²	1	1	yes	characteristic
39	#15688888	C₂²	1	2	yes	—
40	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
41	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#460	—	2	1	no	—
44	C₄₇×#460	—	2	2	no	—
45	C₄₇×#460	—	2	1	no	—
46	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#102×C₄₇	C₂²	1	2	yes	—
48	C₂×#10625350	C₂³	1	2	yes	—
49	#13094055	—	2	4	no	—
50	#13094055	—	4	2	no	—
51	#13094050	—	2	4	no	—
52	#13094050	—	2	4	no	—
53	#13094050	—	4	2	no	—
54	#13094050	—	4	2	no	—
55	C₂×#10625337	—	2	2	no	—
56	C₂×#10625335	—	2	2	no	—
57	C₂×#10625335	—	2	2	no	—
58	C₂×#10625336	—	2	2	no	—
59	C₂×#10625334	—	2	2	no	—
60	C₂×#10625334	—	2	2	no	—
61	#13094030	—	2	4	no	—
62	#13094030	—	4	2	no	—
63	C₂×#10625329	C₂³	1	1	yes	characteristic
64	C₂×#10625329	C₂³	1	2	yes	—
65	C₂×#10625329	C₂³	1	1	yes	characteristic
66	C₂×#10625329	C₂³	1	1	yes	characteristic
67	C₂×#10625329	C₂³	1	1	yes	characteristic
68	C₂×#10625324	—	2	2	no	—
69	C₂×C₈×D₄₇	—	2	2	no	—
70	#13094024	D₄	1	1	yes	characteristic
71	#13094021	D₄	1	1	yes	characteristic
72	#13094012	D₄	1	2	yes	—
73	#13093998	—	2	1	no	—
74	#13093998	—	2	1	no	—
75	C₄×D₁₈₈	—	2	1	no	—
76	C₄×D₁₈₈	—	2	1	no	—
77	#13093960	—	2	4	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
80	#13093947	—	2	2	no	—
81	#13093944	—	2	2	no	—
82	#13093943	—	2	2	no	—
83	#13093943	D₄	1	4	yes	complemented
84	#13093941	—	2	4	no	—
85	#13093941	—	4	2	no	—
86	(C₂×D₄₇)⋊C₈	—	2	2	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	#13093935	—	2	1	no	—
89	#13093935	—	2	1	no	—
90	C₄×C₄₇⋊C₈	—	2	1	no	—
91	C₄×C₄₇⋊C₈	—	2	1	no	—
92	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	—	2	1	no	—
94	C₂²×D₄×C₄₇	—	2	1	no	—
95	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
96	C₂×SD₁₆×C₄₇	—	2	4	no	—
97	C₂×SD₁₆×C₄₇	—	2	2	no	—
98	C₂×SD₁₆×C₄₇	—	2	2	no	—
99	C₂×SD₁₆×C₄₇	—	4	2	no	—
100	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
101	#127×C₄₇	—	2	1	no	—
102	#127×C₄₇	—	2	1	no	—
103	#127×C₄₇	—	2	1	no	—
104	#127×C₄₇	—	2	1	no	—
105	C₄×Q₈×C₄₇	—	2	1	no	—
106	C₄×Q₈×C₄₇	—	2	1	no	—
107	C₄×Q₈×C₄₇	—	2	1	no	—
108	C₄×Q₈×C₄₇	—	2	1	no	—
109	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₇	—	2	1	no	—
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
114	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
115	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
116	#102×C₄₇	—	2	2	no	—
117	#102×C₄₇	—	2	2	no	—
118	C₂⁴×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	1	no	—
120	C₂×Q₈×C₄₇	—	2	1	no	—
121	C₂×Q₈×C₄₇	—	2	1	no	—
122	C₂×Q₈×C₄₇	—	2	1	no	—
123	C₂×Q₈×C₄₇	—	2	1	no	—
124	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	4	1	no	—
132	C₂×D₄×C₄₇	—	4	1	no	—
133	C₂×D₄×C₄₇	—	4	1	no	—
134	C₂×D₄×C₄₇	—	4	1	no	—
135	C₂×D₄×C₄₇	—	8	2	no	—
136	C₂×D₄×C₄₇	—	8	2	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂×C₂²⋊D₄₇	—	2	2	no	—
143	#10625350	—	2	2	no	—
144	#10625350	—	2	2	no	—
145	#10625350	—	2	2	no	—
146	#10625350	—	2	2	no	—
147	C₂×D₁₈₈	—	2	1	no	—
148	C₂×D₁₈₈	—	2	1	no	—
149	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
152	SD₁₆×C₄₇	—	4	4	no	—
153	SD₁₆×C₄₇	—	4	4	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
157	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
158	C₄⋊C₄×C₄₇	—	2	1	no	—
159	C₄⋊C₄×C₄₇	—	2	1	no	—
160	C₄⋊C₄×C₄₇	—	4	1	no	—
161	C₄⋊C₄×C₄₇	—	4	1	no	—
162	C₄²×C₄₇	—	4	1	no	—
163	C₄²×C₄₇	—	4	1	no	—
164	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
166	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
168	#10625337	—	4	4	no	—
169	#10625336	—	4	4	no	—
170	#10625335	—	4	4	no	—
171	#10625335	—	4	4	no	—
172	#10625334	—	4	4	no	—
173	#10625334	—	4	4	no	—
174	(C₂×D₄₇)⋊C₄	—	2	2	no	—
175	(C₂×D₄₇)⋊C₄	—	2	2	no	—
176	C₄⋊Dic₄₇	—	2	1	no	—
177	C₄⋊Dic₄₇	—	2	1	no	—
178	#10625329	—	2	1	no	—
179	#10625329	—	2	1	no	—
180	#10625329	—	2	1	no	—
181	#10625329	—	2	2	no	—
182	#10625329	—	2	1	no	—
183	#10625329	—	2	1	no	—
184	#10625329	—	2	2	no	—
185	#10625329	C₂×D₄	1	2	yes	—
186	#10625329	C₂×D₄	1	2	yes	—
187	#10625329	#41	1	2	yes	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	2	no	—
193	#10625324	—	4	4	no	—
194	C₈×D₄₇	—	4	4	no	—
195	C₂³×C₄₇	—	4	2	no	—
196	C₂³×C₄₇	—	4	2	no	—
197	C₂³×C₄₇	—	4	2	no	—
198	C₂³×C₄₇	—	8	2	no	—
199	C₂³×C₄₇	—	8	2	no	—
200	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂²×D₄₇	—	2	2	no	—
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	2	2	no	—
204	Q₈×C₄₇	—	4	1	no	—
205	Q₈×C₄₇	—	4	1	no	—
206	D₄×C₄₇	—	4	2	no	—
207	D₄×C₄₇	—	4	2	no	—
208	D₄×C₄₇	—	4	2	no	—
209	D₄×C₄₇	—	4	2	no	—
210	D₄×C₄₇	—	8	2	no	—
211	D₄×C₄₇	—	8	2	no	—
212	D₄×C₄₇	—	8	2	no	—
213	D₄×C₄₇	—	8	2	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	4	1	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	4	1	no	—
219	C₂×C₄×C₄₇	—	4	1	no	—
220	C₂×C₄×C₄₇	—	8	1	no	—
221	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²⋊D₄₇	—	4	2	no	—
232	C₂²⋊D₄₇	—	4	2	no	—
233	C₂×Dic₄₇	—	2	2	no	—
234	D₁₈₈	—	2	2	no	—
235	D₁₈₈	—	2	2	no	—
236	D₁₈₈	—	4	2	no	—
237	D₁₈₈	—	8	1	no	—
238	C₄×D₄₇	—	4	2	no	—
239	C₄×D₄₇	—	4	2	no	—
240	Dic₉₄	—	2	2	no	—
241	Dic₉₄	—	2	2	no	—
242	C₈×C₄₇	—	2	2	no	—
243	C₈×C₄₇	—	2	2	no	—
244	C₄₇⋊C₈	—	2	2	no	—
245	C₄₇⋊C₈	—	2	2	no	—
246	C₄₇⋊C₈	—	2	2	no	—
247	C₄₇⋊C₈	—	4	2	no	—
248	C₄₇⋊C₈	—	4	1	no	—
249	#25407	—	47	1	no	maximal, Sylow
250	C₂²×C₄₇	—	2	1	no	—
251	C₂²×C₄₇	—	2	1	no	—
252	C₂²×C₄₇	—	8	2	no	—
253	C₂²×C₄₇	—	8	2	no	—
254	C₂²×C₄₇	—	8	2	no	—
255	C₂²×C₄₇	—	16	2	no	—
256	C₂²×C₄₇	—	16	2	no	—
257	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
258	C₂²×C₄₇	#532	1	1	yes	characteristic
259	C₂²×C₄₇	#540	1	1	yes	characteristic
260	C₂×D₄₇	—	4	2	no	—
261	C₂×D₄₇	—	4	2	no	—
262	C₂×D₄₇	—	4	2	no	—
263	C₄×C₄₇	—	2	1	no	—
264	C₄×C₄₇	—	2	1	no	—
265	C₄×C₄₇	—	2	1	no	—
266	C₄×C₄₇	—	4	2	no	—
267	C₄×C₄₇	—	8	1	no	—
268	C₄×C₄₇	#471	1	2	yes	complemented
269	C₄×C₄₇	D₄²	1	1	yes	characteristic
270	C₄×C₄₇	D₄²	1	1	yes	characteristic
271	C₄×C₄₇	#546	1	1	yes	characteristic
272	C₄×C₄₇	#550	1	1	yes	characteristic
273	Dic₄₇	—	4	2	no	—
274	#3151	—	47	1	no	—
275	C₂×#471	—	47	2	no	—
276	#3037	—	47	1	no	—
277	C₂×#460	D₄₇	1	1	yes	characteristic, complemented
278	#2935	—	47	1	no	—
279	#2051	—	47	2	no	—
280	#2019	—	47	2	no	—
281	#1965	—	47	1	no	—
282	#1950	—	47	1	no	—
283	#1907	—	47	2	no	—
284	C₄×#101	—	47	1	no	—
285	C₂×C₄₇	—	2	1	no	—
286	C₂×C₄₇	—	2	1	no	—
287	C₂×C₄₇	—	16	2	no	—
288	C₂×C₄₇	#2428	1	1	yes	characteristic
289	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
290	C₂×C₄₇	#3068	1	1	yes	characteristic
291	D₄₇	—	8	2	no	—
292	C₂×#137	—	47	2	no	—
293	C₂×AGL(1,ℤ/8)	—	47	2	no	—
294	C₂×AGL(1,ℤ/8)	—	47	2	no	—
295	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
296	C₂×#131	—	47	2	no	—
297	#532	—	47	1	no	—
298	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
299	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
300	#496	—	94	2	no	—
301	#493	—	94	1	no	—
302	#492	—	94	1	no	—
303	#471	—	94	8	no	—
304	#464	—	94	2	no	—
305	#462	—	94	1	no	—
306	#460	—	2	1	no	—
307	#460	—	2	2	no	—
308	#460	—	2	1	no	—
309	#460	—	94	1	no	—
310	#436	—	94	1	no	—
311	#435	—	94	2	no	—
312	C₈×D₄	—	94	1	no	—
313	C₂×#108	—	47	2	no	—
314	#423	—	47	1	no	—
315	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
316	#417	—	47	2	no	—
317	C₂×#102	C₂×D₄₇	1	2	yes	—
318	C₂×#101	—	47	1	no	—
319	C₂×#101	—	47	1	no	—
320	C₂×#100	—	47	2	no	—
321	C₂×#100	—	47	2	no	—
322	#408	—	47	2	no	—
323	C₄×M₁₆	—	47	1	no	—
324	C₄×M₁₆	—	47	1	no	—
325	#343	—	47	1	no	—
326	#343	—	47	1	no	—
327	#341	—	47	2	no	—
328	C₄₇	#25407	1	1	yes	characteristic, complemented, Sylow
329	C₂×#41	—	47	2	no	—
330	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
331	C₂²×D₄	—	2	1	no	—
332	C₂²×D₄	—	2	1	no	—
333	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
334	#137	—	94	4	no	—
335	#137	—	188	2	no	—
336	AGL(1,ℤ/8)	—	94	4	no	—
337	AGL(1,ℤ/8)	—	94	4	no	—
338	AGL(1,ℤ/8)	—	188	2	no	—
339	AGL(1,ℤ/8)	—	188	2	no	—
340	C₂×Q₁₆	—	94	2	no	—
341	C₂×SD₁₆	—	2	4	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	—	4	2	no	—
345	C₂×SD₁₆	—	94	2	no	—
346	C₂×SD₁₆	—	94	2	no	—
347	C₂×SD₁₆	—	94	2	no	—
348	C₂×D₈	—	94	2	no	—
349	C₂×D₈	—	94	2	no	—
350	#131	—	94	4	no	—
351	#131	—	188	2	no	—
352	C₂×M₁₆	—	47	1	no	—
353	C₂×M₁₆	—	47	1	no	—
354	C₂×M₁₆	—	47	1	no	—
355	C₂×M₁₆	—	47	2	no	—
356	C₂×M₁₆	—	47	1	no	—
357	C₂×M₁₆	—	94	2	no	—
358	C₂²×C₈	—	94	2	no	—
359	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
360	C₄⋊Q₈	—	47	1	no	—
361	#127	—	2	1	no	—
362	#127	—	2	1	no	—
363	#127	—	2	1	no	—
364	#127	—	2	1	no	—
365	#127	—	47	1	no	—
366	#124	—	47	2	no	—
367	#121	—	94	1	no	—
368	#121	—	94	1	no	—
369	C₄×Q₈	—	2	1	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×D₄	—	94	1	no	—
374	C₄×D₄	—	94	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
377	C₂×C₄²	—	2	1	no	—
378	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
379	#108	—	94	4	no	—
380	C₄⋊C₈	—	94	1	no	—
381	C₄⋊C₈	—	94	1	no	—
382	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
383	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
384	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
385	#103	—	94	2	no	—
386	#102	—	2	2	no	—
387	#102	—	2	2	no	—
388	#102	—	94	2	no	—
389	#101	—	47	4	no	—
390	#101	—	94	2	no	—
391	#100	—	94	4	no	—
392	#100	—	188	2	no	—
393	C₂²⋊C₈	—	94	2	no	—
394	C₂²⋊C₈	—	94	2	no	—
395	#97	—	94	1	no	—
396	#97	—	94	1	no	—
397	C₄×C₈	—	94	1	no	—
398	C₄×C₈	—	94	1	no	—
399	C₂⁴	—	2	2	no	—
400	#41	—	94	2	no	—
401	#41	—	94	2	no	—
402	#41	—	94	2	no	—
403	#41	—	94	2	no	—
404	C₂×Q₈	—	2	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	47	2	no	—
410	C₂×Q₈	D₄×D₄₇	1	2	yes	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	2	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	8	2	no	—
422	C₂×D₄	—	8	2	no	—
423	C₂×D₄	—	47	2	no	—
424	C₂×D₄	—	94	2	no	—
425	C₂×D₄	—	94	1	no	—
426	C₂×D₄	—	94	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	94	2	no	—
430	C₂²×C₄	#10625352	1	1	yes	characteristic
431	C₂²×C₄	#10625352	1	1	yes	characteristic
432	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
433	Q₁₆	—	188	4	no	—
434	SD₁₆	—	4	4	no	—
435	SD₁₆	—	4	4	no	—
436	SD₁₆	—	188	4	no	—
437	SD₁₆	—	188	4	no	—
438	SD₁₆	—	188	4	no	—
439	D₈	—	188	4	no	—
440	D₈	—	188	4	no	—
441	M₁₆	—	47	2	no	—
442	M₁₆	—	47	2	no	—
443	M₁₆	—	47	2	no	—
444	M₁₆	—	94	1	no	—
445	M₁₆	—	94	1	no	—
446	M₁₆	—	94	1	no	—
447	M₁₆	—	94	2	no	—
448	M₁₆	—	94	1	no	—
449	M₁₆	—	94	1	no	—
450	M₁₆	—	94	2	no	—
451	M₁₆	—	188	4	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	94	1	no	—
455	C₂×C₈	—	94	1	no	—
456	C₂×C₈	—	94	1	no	—
457	C₂×C₈	—	94	2	no	—
458	C₂×C₈	—	94	1	no	—
459	C₂×C₈	—	188	4	no	—
460	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
461	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	2	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	94	1	no	—
467	C₄⋊C₄	—	94	1	no	—
468	C₂²⋊C₄	—	94	2	no	—
469	C₂²⋊C₄	—	94	2	no	—
470	C₄²	—	4	1	no	—
471	C₄²	—	4	1	no	—
472	C₄²	D₄×D₄₇	1	1	yes	characteristic
473	C₄²	D₄×D₄₇	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
475	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
476	C₂³	—	4	2	no	—
477	C₂³	—	4	2	no	—
478	C₂³	—	4	2	no	—
479	C₂³	—	8	2	no	—
480	C₂³	—	8	2	no	—
481	C₂³	—	94	2	no	—
482	C₂³	C₂×#10625352	1	1	yes	characteristic
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	4	1	no	—
487	Q₈	—	94	2	no	—
488	Q₈	—	94	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	2	no	—
492	D₄	—	4	2	no	—
493	D₄	—	8	2	no	—
494	D₄	—	8	2	no	—
495	D₄	—	8	2	no	—
496	D₄	—	8	2	no	—
497	D₄	—	94	2	no	—
498	D₄	—	94	2	no	—
499	D₄	—	376	1	no	—
500	D₄	—	188	2	no	—
501	D₄	—	188	2	no	—
502	D₄	—	188	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	8	1	no	—
510	C₂×C₄	—	94	2	no	—
511	C₂×C₄	—	188	2	no	—
512	C₂×C₄	—	188	2	no	—
513	C₂×C₄	#13093995	1	1	yes	characteristic
514	C₂×C₄	#13093995	1	1	yes	characteristic
515	C₂×C₄	#13093995	1	1	yes	characteristic
516	C₂×C₄	#13093995	1	1	yes	characteristic
517	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
518	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
520	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
521	C₂×C₄	#13094069	1	1	yes	characteristic
522	C₂×C₄	#13094070	1	1	yes	characteristic
523	C₈	—	2	2	no	—
524	C₈	—	2	2	no	—
525	C₈	—	94	2	no	—
526	C₈	—	94	2	no	—
527	C₈	—	94	2	no	—
528	C₈	—	188	2	no	—
529	C₈	—	188	1	no	—
530	C₂²	—	2	1	no	—
531	C₂²	—	2	1	no	—
532	C₂²	—	8	2	no	—
533	C₂²	—	8	2	no	—
534	C₂²	—	8	2	no	—
535	C₂²	—	16	2	no	—
536	C₂²	—	16	2	no	—
537	C₂²	—	188	2	no	—
538	C₂²	—	188	2	no	—
539	C₂²	—	188	2	no	—
540	C₂²	C₂×#13093995	1	1	yes	characteristic
541	C₂²	#15689668	1	1	yes	characteristic
542	C₂²	#15689726	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	1	no	—
545	C₄	—	2	1	no	—
546	C₄	—	4	2	no	—
547	C₄	—	8	1	no	—
548	C₄	—	188	2	no	—
549	C₄	#15689383	1	2	yes	complemented
550	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
551	C₄	#15689757	1	1	yes	characteristic
552	C₄	#15689770	1	1	yes	characteristic
553	C₄	#15689792	1	1	yes	characteristic
554	C₂	—	2	1	no	—
555	C₂	—	2	1	no	—
556	C₂	—	16	2	no	—
557	C₂	—	376	2	no	—
558	C₂	#20246972	1	1	yes	characteristic
559	C₂	C₂×#15689383	1	1	yes	characteristic
560	C₂	#20253112	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093995
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#460	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#20253838	C₂
hypercenter	C₂×#460	D₄₇
hypocenter	C₄₇	#25407
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. C₂×#15689383	C₂	semidirect
3. #20252860	C₂	semidirect
4. #20252131	C₂	semidirect
5. #20244681	C₂	semidirect
6. #20244500	C₂	semidirect
7. #20244229	C₂	semidirect
8. #20244164	C₂	semidirect
9. #20243899	C₂	semidirect
10. C₄×#13093943	C₂	semidirect
11. C₂×C₄₇×#460	C₂	semidirect
83. #13093943	D₄	semidirect
268. C₄×C₄₇	#471	semidirect
277. C₂×#460	D₄₇	semidirect
328. C₄₇	#25407	semidirect
549. C₄	#15689383	semidirect

Maximal subgroups

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

subgroup	index
#20253838	2
C₂×#15689383	2
#20252860	2
#20252131	2
#20244681	2
#20244500	2
#20244229	2
#20244164	2
#20243899	2
C₄×#13093943	2
C₂×C₄₇×#460	2
#25407	47