Subgroups — #26223174

Order 12032.

938 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689390	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094050	C₂	1	2	yes	maximal, complemented
3	#20251813	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244299	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244166	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244047	C₂	1	2	yes	maximal, complemented
7	#20243899	C₂	1	2	yes	maximal, complemented
8	#20243448	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243294	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093941	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094050	C₂²	1	2	yes	—
13	C₂×#13094030	C₂²	1	1	yes	characteristic
14	C₂×#13094030	C₂²	1	1	yes	characteristic
15	C₄×#10625350	C₂²	1	1	yes	characteristic
16	#15689390	C₄	1	8	yes	complemented
17	#15689233	—	2	2	no	—
18	#15689223	—	2	2	no	—
19	C₄×#10625335	—	2	2	no	—
20	C₄×#10625334	—	2	2	no	—
21	C₂×#13093960	C₂²	1	1	yes	characteristic
22	C₂×#13093960	C₂²	1	1	yes	characteristic
23	#15689163	C₂²	1	2	yes	—
24	#15689128	C₂²	1	2	yes	—
25	#15689122	C₂²	1	2	yes	—
26	C₂×#13093941	C₂²	1	2	yes	—
27	C₂×#13093941	C₂²	1	2	yes	—
28	#15689080	—	2	1	no	—
29	#15689080	—	2	1	no	—
30	#15689078	C₂²	1	1	yes	characteristic
31	#15689078	C₂²	1	1	yes	characteristic
32	C₄×#10625329	C₂²	1	2	yes	—
33	C₄×#10625329	C₂²	1	1	yes	characteristic
34	#15689075	—	2	1	no	—
35	#97×D₄₇	—	2	1	no	—
36	#15688892	C₂²	1	2	yes	—
37	#15688892	C₂²	1	2	yes	—
38	#15688888	C₂²	1	2	yes	—
39	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#442	—	2	1	no	—
42	C₄₇×#442	—	2	1	no	—
43	C₄₇×#442	—	2	1	no	—
44	C₄₇×#442	—	2	1	no	—
45	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×#102×C₄₇	C₂²	1	2	yes	—
47	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
48	C₂×#10625350	C₂³	1	1	yes	characteristic
49	#13094050	—	2	4	no	—
50	#13094050	C₂×C₄	1	8	yes	complemented
51	C₂×#10625335	—	2	2	no	—
52	C₂×#10625334	—	2	2	no	—
53	#13094030	—	2	2	no	—
54	#13094030	—	2	2	no	—
55	#13094030	—	2	2	no	—
56	#13094030	C₂×C₄	1	4	yes	complemented
57	C₂×#10625329	C₂³	1	2	yes	—
58	C₂×#10625329	C₂³	1	1	yes	characteristic
59	C₂×#10625329	C₂³	1	2	yes	—
60	C₂×#10625329	C₂³	1	1	yes	characteristic
61	C₂×#10625324	—	2	1	no	—
62	C₂×#10625324	—	2	1	no	—
63	C₂×C₈×D₄₇	—	2	1	no	—
64	C₂×C₈×D₄₇	—	2	1	no	—
65	C₄×Dic₉₄	D₄	1	2	yes	—
66	C₄×D₁₈₈	D₄	1	2	yes	—
67	C₄×C₂²⋊D₄₇	—	2	2	no	—
68	#13093983	C₂³	1	1	yes	characteristic
69	#13093981	—	2	1	no	—
70	C₄²×D₄₇	—	2	1	no	—
71	#13093960	—	2	2	no	—
72	#13093960	C₂×C₄	1	4	yes	complemented
73	#13093957	—	2	2	no	—
74	#13093955	—	2	2	no	—
75	#13093947	—	2	2	no	—
76	#13093945	—	2	2	no	—
77	#13093945	—	2	2	no	—
78	#13093944	—	2	2	no	—
79	#13093941	—	2	4	no	—
80	#13093941	C₂×C₄	1	8	yes	complemented
81	#13093935	—	2	2	no	—
82	#13093935	—	2	1	no	—
83	#13093934	—	2	1	no	—
84	#13093934	—	2	1	no	—
85	C₄×C₄₇⋊C₈	—	2	1	no	—
86	C₄×C₄₇⋊C₈	—	2	2	no	—
87	C₈×Dic₄₇	—	2	1	no	—
88	C₈×Dic₄₇	—	2	1	no	—
89	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
90	C₂³×C₄×C₄₇	—	2	2	no	—
91	C₂×D₈×C₄₇	—	2	1	no	—
92	C₂×D₈×C₄₇	—	2	1	no	—
93	C₂×D₈×C₄₇	—	2	2	no	—
94	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
95	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₄₇	—	2	2	no	—
98	C₄×D₄×C₄₇	—	2	2	no	—
99	C₄×D₄×C₄₇	—	2	2	no	—
100	C₄×D₄×C₄₇	—	2	2	no	—
101	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
102	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	#106×C₄₇	—	2	1	no	—
105	#106×C₄₇	—	2	1	no	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	#97×C₄₇	D₄	1	1	yes	characteristic
109	#97×C₄₇	D₄	1	1	yes	characteristic
110	#97×C₄₇	D₄	1	1	yes	characteristic
111	#97×C₄₇	D₄	1	1	yes	characteristic
112	C₂⁴×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	2	2	no	—
118	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	—	4	2	no	—
122	C₂²×C₄×C₄₇	—	8	4	no	—
123	C₂²×C₄×C₄₇	#41	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₇	—	2	1	no	—
126	#10625350	—	2	1	no	—
127	#10625350	—	2	1	no	—
128	#10625350	C₂²×C₄	1	2	yes	—
129	#10625350	#41	1	2	yes	—
130	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×D₄₇	—	2	1	no	—
132	C₂×C₄×D₄₇	—	2	2	no	—
133	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
134	D₈×C₄₇	—	2	4	no	—
135	D₈×C₄₇	—	2	4	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
139	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₂×C₈×C₄₇	#41	1	2	yes	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₂²⋊C₄×C₄₇	—	4	2	no	—
147	C₂²⋊C₄×C₄₇	—	4	2	no	—
148	C₄²×C₄₇	C₂×D₄	1	2	yes	—
149	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂²⋊Dic₄₇	—	2	1	no	—
152	#10625335	—	2	8	no	—
153	#10625334	—	2	8	no	—
154	(C₂×D₄₇)⋊C₄	—	2	2	no	—
155	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
156	Dic₄₇⋊C₄	—	2	2	no	—
157	C₄×Dic₄₇	—	2	2	no	—
158	C₄×Dic₄₇	—	2	1	no	—
159	#10625329	—	2	1	no	—
160	#10625329	—	2	1	no	—
161	#10625329	—	2	2	no	—
162	#10625329	—	2	2	no	—
163	#10625329	—	2	2	no	—
164	#10625329	C₂²×C₄	1	2	yes	—
165	#10625329	C₂²×C₄	1	4	yes	—
166	#10625329	#41	1	2	yes	—
167	C₂×C₄₇⋊C₈	—	2	1	no	—
168	C₂×C₄₇⋊C₈	—	2	1	no	—
169	C₂×C₄₇⋊C₈	—	2	2	no	—
170	C₂×C₄₇⋊C₈	—	2	2	no	—
171	#10625324	—	2	4	no	—
172	#10625324	—	2	4	no	—
173	C₈×D₄₇	—	2	4	no	—
174	C₈×D₄₇	—	2	4	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	4	2	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	8	2	no	—
179	C₂³×C₄₇	—	8	2	no	—
180	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂²×D₄₇	—	2	1	no	—
182	D₄×C₄₇	—	2	4	no	—
183	D₄×C₄₇	—	2	4	no	—
184	D₄×C₄₇	—	4	2	no	—
185	D₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	8	4	no	—
189	C₂×C₄×C₄₇	—	8	4	no	—
190	C₂×C₄×C₄₇	—	8	2	no	—
191	C₂×C₄×C₄₇	#121	1	2	yes	—
192	C₂×C₄×C₄₇	#121	1	2	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂²⋊D₄₇	—	2	2	no	—
200	C₂²⋊D₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	2	no	—
203	D₁₈₈	—	2	1	no	—
204	D₁₈₈	C₄×D₄	1	2	yes	—
205	C₄×D₄₇	—	2	2	no	—
206	C₄×D₄₇	—	2	2	no	—
207	C₄×D₄₇	—	8	2	no	—
208	Dic₉₄	—	2	1	no	—
209	Dic₉₄	C₄×D₄	1	2	yes	—
210	C₈×C₄₇	—	2	1	no	—
211	C₈×C₄₇	—	2	1	no	—
212	C₈×C₄₇	C₄×D₄	1	2	yes	—
213	C₈×C₄₇	C₄×D₄	1	2	yes	—
214	C₄₇⋊C₈	—	2	2	no	—
215	C₄₇⋊C₈	—	2	4	no	—
216	C₄₇⋊C₈	—	2	2	no	—
217	C₄₇⋊C₈	—	4	2	no	—
218	#21555	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	4	4	no	—
221	C₂²×C₄₇	—	8	4	no	—
222	C₂²×C₄₇	—	8	4	no	—
223	C₂²×C₄₇	—	8	2	no	—
224	C₂²×C₄₇	—	8	2	no	—
225	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
227	C₂²×C₄₇	#529	1	1	yes	characteristic
228	C₂×D₄₇	—	2	2	no	—
229	C₂×D₄₇	—	4	2	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	8	2	no	—
233	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
234	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₄₇	#525	1	1	yes	characteristic
236	C₄×C₄₇	#532	1	1	yes	characteristic
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	4	2	no	—
239	C₂×#472	—	47	1	no	—
240	C₄×AGL(1,ℤ/8)	—	47	2	no	—
241	C₂×#442	D₄₇	1	1	yes	characteristic, complemented
242	#2875	—	47	1	no	—
243	#1978	—	47	1	no	—
244	#1951	—	47	1	no	—
245	#1931	—	47	2	no	—
246	#1907	—	47	2	no	—
247	#1815	—	47	1	no	—
248	#1778	—	47	1	no	—
249	C₄×#100	—	47	2	no	—
250	C₂×C₄₇	—	2	1	no	—
251	C₂×C₄₇	—	2	1	no	—
252	C₂×C₄₇	—	8	4	no	—
253	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
254	C₂×C₄₇	#3068	1	2	yes	—
255	D₄₇	—	4	2	no	—
256	C₂×AGL(1,ℤ/8)	—	47	2	no	—
257	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
258	C₂×#131	—	47	1	no	—
259	C₂×#131	—	47	1	no	—
260	C₄×#41	—	47	1	no	—
261	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
262	#472	—	47	8	no	—
263	#442	—	2	1	no	—
264	#442	—	2	1	no	—
265	#442	—	2	1	no	—
266	#442	—	2	1	no	—
267	#442	—	94	2	no	—
268	#440	—	94	2	no	—
269	C₄×SD₁₆	—	94	2	no	—
270	C₄×D₈	—	94	2	no	—
271	C₂×#108	—	47	1	no	—
272	C₂×#108	—	47	1	no	—
273	#428	—	47	2	no	—
274	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
275	#418	—	47	2	no	—
276	#417	—	47	2	no	—
277	C₂×#102	C₂×D₄₇	1	2	yes	—
278	C₂×#100	—	47	2	no	—
279	C₂×#100	—	47	2	no	—
280	#405	—	47	1	no	—
281	#405	—	47	1	no	—
282	#405	—	94	1	no	—
283	#405	—	94	1	no	—
284	C₄×M₁₆	—	47	1	no	—
285	C₄×M₁₆	—	47	2	no	—
286	C₄×M₁₆	—	94	1	no	—
287	C₂×#97	—	94	1	no	—
288	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
289	#343	—	47	2	no	—
290	#343	—	47	2	no	—
291	#341	—	47	2	no	—
292	C₄₇	#21555	1	1	yes	characteristic, complemented, Sylow
293	C₂×#41	—	47	1	no	—
294	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
295	C₂³×C₄	—	2	2	no	—
296	AGL(1,ℤ/8)	—	47	8	no	—
297	AGL(1,ℤ/8)	—	94	4	no	—
298	C₂×SD₁₆	—	94	2	no	—
299	C₂×D₈	—	2	2	no	—
300	C₂×D₈	—	2	1	no	—
301	C₂×D₈	—	2	1	no	—
302	C₂×D₈	—	94	2	no	—
303	C₂×D₈	C₄×D₄₇	1	4	yes	complemented
304	#131	—	47	4	no	—
305	#131	—	94	2	no	—
306	#131	—	94	2	no	—
307	#131	—	94	2	no	—
308	C₂×M₁₆	—	47	1	no	—
309	C₂×M₁₆	—	47	1	no	—
310	C₂×M₁₆	—	47	2	no	—
311	C₂×M₁₆	—	47	2	no	—
312	C₂×M₁₆	—	94	1	no	—
313	C₂×M₁₆	—	94	1	no	—
314	C₂²×C₈	—	94	1	no	—
315	C₂²×C₈	—	94	1	no	—
316	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	C₄×Q₈	—	47	2	no	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	47	2	no	—
324	C₄×D₄	—	94	2	no	—
325	#117	—	47	1	no	—
326	#117	—	94	1	no	—
327	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
328	C₂×C₂²⋊C₄	—	2	2	no	—
329	C₂×C₄²	—	94	1	no	—
330	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
331	#108	—	47	4	no	—
332	#108	—	94	2	no	—
333	#107	—	94	2	no	—
334	#106	—	2	1	no	—
335	#106	—	2	1	no	—
336	#106	—	94	2	no	—
337	#103	—	94	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	94	2	no	—
341	#102	—	94	2	no	—
342	#102	—	94	2	no	—
343	#100	—	47	8	no	—
344	#100	—	94	4	no	—
345	#97	—	94	1	no	—
346	#97	—	94	1	no	—
347	#97	—	94	2	no	—
348	#97	—	94	1	no	—
349	#97	C₂²⋊D₄₇	1	1	yes	characteristic
350	#97	C₂²⋊D₄₇	1	1	yes	characteristic
351	#97	C₂²⋊D₄₇	1	1	yes	characteristic
352	#97	C₂²⋊D₄₇	1	1	yes	characteristic
353	C₄×C₈	—	94	1	no	—
354	C₄×C₈	—	94	1	no	—
355	C₄×C₈	—	94	2	no	—
356	C₄×C₈	—	94	1	no	—
357	C₂⁴	—	2	2	no	—
358	#41	—	47	2	no	—
359	#41	—	47	2	no	—
360	#41	—	94	1	no	—
361	#41	—	94	1	no	—
362	C₂×Q₈	—	47	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	47	1	no	—
369	C₂×D₄	—	94	1	no	—
370	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	4	2	no	—
373	C₂²×C₄	—	4	2	no	—
374	C₂²×C₄	—	8	4	no	—
375	C₂²×C₄	—	94	1	no	—
376	C₂²×C₄	—	94	2	no	—
377	C₂²×C₄	#10625352	1	2	yes	—
378	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
379	SD₁₆	—	94	8	no	—
380	D₈	—	2	4	no	—
381	D₈	—	2	4	no	—
382	D₈	—	94	8	no	—
383	M₁₆	—	47	2	no	—
384	M₁₆	—	47	4	no	—
385	M₁₆	—	47	2	no	—
386	M₁₆	—	94	4	no	—
387	M₁₆	—	94	1	no	—
388	M₁₆	—	94	2	no	—
389	M₁₆	—	94	1	no	—
390	M₁₆	—	94	4	no	—
391	M₁₆	—	94	2	no	—
392	M₁₆	—	94	2	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	94	4	no	—
396	C₂×C₈	—	94	2	no	—
397	C₂×C₈	—	94	1	no	—
398	C₂×C₈	—	94	1	no	—
399	C₂×C₈	—	94	4	no	—
400	C₂×C₈	—	94	2	no	—
401	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
402	C₂×C₈	#10625350	1	2	yes	—
403	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
404	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	47	2	no	—
410	C₄⋊C₄	—	94	2	no	—
411	C₂²⋊C₄	—	4	2	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	94	1	no	—
414	C₂²⋊C₄	—	94	2	no	—
415	C₄²	—	94	2	no	—
416	C₄²	—	94	1	no	—
417	C₄²	D₄×D₄₇	1	2	yes	—
418	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
419	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
420	C₂³	—	2	4	no	—
421	C₂³	—	4	2	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	94	1	no	—
426	C₂³	C₂×#10625352	1	1	yes	characteristic
427	Q₈	—	47	2	no	—
428	Q₈	—	94	1	no	—
429	D₄	—	2	4	no	—
430	D₄	—	2	4	no	—
431	D₄	—	4	2	no	—
432	D₄	—	4	2	no	—
433	D₄	—	47	2	no	—
434	D₄	—	94	2	no	—
435	D₄	—	94	2	no	—
436	D₄	—	94	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	8	4	no	—
440	C₂×C₄	—	8	4	no	—
441	C₂×C₄	—	8	2	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	2	no	—
444	C₂×C₄	—	94	2	no	—
445	C₂×C₄	—	94	2	no	—
446	C₂×C₄	—	376	2	no	—
447	C₂×C₄	#13093995	1	2	yes	—
448	C₂×C₄	#13093995	1	2	yes	—
449	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
452	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
453	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
454	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	94	4	no	—
458	C₈	—	94	2	no	—
459	C₈	—	94	2	no	—
460	C₈	—	188	2	no	—
461	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
462	C₈	C₄×C₂²⋊D₄₇	1	2	yes	—
463	C₂²	—	2	2	no	—
464	C₂²	—	4	4	no	—
465	C₂²	—	8	4	no	—
466	C₂²	—	8	4	no	—
467	C₂²	—	8	2	no	—
468	C₂²	—	8	2	no	—
469	C₂²	—	94	2	no	—
470	C₂²	—	188	2	no	—
471	C₂²	C₄×#10625352	1	1	yes	characteristic
472	C₂²	C₂×#13093995	1	1	yes	characteristic
473	C₂²	#15689655	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	8	2	no	—
477	C₄	—	94	2	no	—
478	C₄	—	188	2	no	—
479	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
480	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
481	C₄	#15689630	1	1	yes	characteristic
482	C₄	#15689670	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	8	4	no	—
486	C₂	—	188	2	no	—
487	C₂	C₄×#13093995	1	1	yes	characteristic
488	C₂	#20253112	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#13093995
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#442	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#15689390	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#442	D₄₇
hypocenter	C₄₇	#21555
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×#442

Complements

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

N	H ≅ G/N	type
2. C₄×#13094050	C₂	semidirect
3. #20251813	C₂	semidirect
4. #20244299	C₂	semidirect
5. #20244166	C₂	semidirect
6. #20244047	C₂	semidirect
7. #20243899	C₂	semidirect
8. #20243448	C₂	semidirect
9. #20243294	C₂	semidirect
10. C₄×#13093941	C₂	semidirect
11. C₂×C₄₇×#442	C₂	semidirect
16. #15689390	C₄	semidirect
50. #13094050	C₂×C₄	semidirect
56. #13094030	C₂×C₄	semidirect
72. #13093960	C₂×C₄	semidirect
80. #13093941	C₂×C₄	semidirect
94. C₂×D₈×C₄₇	C₂×C₄	semidirect
241. C₂×#442	D₄₇	semidirect
292. C₄₇	#21555	semidirect
303. C₂×D₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689390	2
C₄×#13094050	2
#20251813	2
#20244299	2
#20244166	2
#20244047	2
#20243899	2
#20243448	2
#20243294	2
C₄×#13093941	2
C₂×C₄₇×#442	2
#21555	47