Subgroups — #26223180

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×#15689393	C₂	1	1	yes	maximal, characteristic
2	C₄×#13094049	C₂	1	2	yes	maximal, complemented
3	C₂×#15689236	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244298	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244168	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244050	C₂	1	2	yes	maximal, complemented
7	#20243896	C₂	1	2	yes	maximal, complemented
8	#20243447	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243294	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13093940	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094049	C₂²	1	2	yes	—
13	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₁₈₈	C₂²	1	2	yes	—
15	#15689393	C₄	1	8	yes	complemented
16	#15689236	—	2	1	no	—
17	#15689236	—	2	1	no	—
18	#15689236	—	2	1	no	—
19	#15689236	—	2	1	no	—
20	#15689233	—	2	2	no	—
21	#15689221	—	2	2	no	—
22	C₄×#10625336	—	2	2	no	—
23	C₄×#10625334	—	2	2	no	—
24	C₂×#13093960	C₂²	1	1	yes	characteristic
25	C₂×#13093960	C₂²	1	1	yes	characteristic
26	#15689166	C₂²	1	2	yes	—
27	C₂×#13093956	C₂²	1	1	yes	characteristic
28	#15689127	C₂²	1	2	yes	—
29	#15689124	C₂²	1	2	yes	—
30	C₂×#13093946	C₂²	1	2	yes	—
31	C₂×#13093940	C₂²	1	2	yes	—
32	C₂×#13093940	C₂²	1	2	yes	—
33	C₄×#10625329	C₂²	1	2	yes	—
34	#15688891	C₂²	1	2	yes	—
35	#15688891	C₂²	1	2	yes	—
36	#15688888	C₂²	1	2	yes	—
37	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#405	—	2	1	no	—
41	C₄₇×#405	—	2	1	no	—
42	C₄₇×#405	C₂²	1	1	yes	characteristic
43	C₄₇×#405	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	—	2	1	no	—
45	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×#97×C₄₇	—	2	1	no	—
47	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
48	C₂²×D₁₈₈	C₂³	1	2	yes	—
49	C₂²×C₄×D₄₇	—	2	2	no	—
50	#13094049	—	2	4	no	—
51	#13094049	C₂×C₄	1	8	yes	complemented
52	C₂×#10625336	—	2	2	no	—
53	C₂×D₃₇₆	—	2	1	no	—
54	C₂×D₃₇₆	—	2	1	no	—
55	C₂×D₃₇₆	—	2	2	no	—
56	C₂×D₃₇₆	C₂×C₄	1	4	yes	complemented
57	C₂×#10625334	—	2	2	no	—
58	C₂×#10625329	C₂³	1	2	yes	—
59	C₂×#10625329	C₂³	1	2	yes	—
60	C₄×D₁₈₈	—	2	2	no	—
61	C₄×D₁₈₈	—	2	2	no	—
62	C₄×D₁₈₈	—	2	2	no	—
63	C₄×D₁₈₈	—	2	2	no	—
64	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
65	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
66	#13093960	—	2	2	no	—
67	#13093960	C₂×C₄	1	4	yes	complemented
68	#13093957	—	2	2	no	—
69	#13093956	—	2	1	no	—
70	#13093956	—	2	1	no	—
71	#13093955	—	2	2	no	—
72	#13093948	—	2	2	no	—
73	#13093946	—	2	2	no	—
74	#13093946	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	#13093944	—	2	2	no	—
77	#13093944	—	2	2	no	—
78	#13093940	—	2	4	no	—
79	#13093940	C₂×C₄	1	8	yes	complemented
80	#13093935	—	2	2	no	—
81	C₄×C₄₇⋊C₈	—	2	2	no	—
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	C₂×C₄	1	4	yes	complemented
87	C₂×M₁₆×C₄₇	—	2	1	no	—
88	C₂×M₁₆×C₄₇	—	2	1	no	—
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	—	2	1	no	—
93	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄×Q₈×C₄₇	D₄	1	2	yes	—
96	C₄×D₄×C₄₇	—	2	2	no	—
97	C₄×D₄×C₄₇	D₄	1	2	yes	—
98	#117×C₄₇	—	2	1	no	—
99	#117×C₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	#97×C₄₇	—	2	1	no	—
103	#97×C₄₇	—	2	1	no	—
104	#97×C₄₇	—	2	1	no	—
105	#97×C₄₇	D₄	1	1	yes	characteristic
106	#97×C₄₇	D₄	1	1	yes	characteristic
107	#97×C₄₇	D₄	1	1	yes	characteristic
108	#97×C₄₇	D₄	1	1	yes	characteristic
109	C₄×C₈×C₄₇	—	2	1	no	—
110	C₄×C₈×C₄₇	—	2	1	no	—
111	C₄×C₈×C₄₇	—	2	1	no	—
112	C₂³×D₄₇	—	2	2	no	—
113	#41×C₄₇	—	2	1	no	—
114	#41×C₄₇	—	2	1	no	—
115	#41×C₄₇	C₂²×C₄	1	2	yes	—
116	#41×C₄₇	#41	1	2	yes	—
117	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×D₄×C₄₇	—	2	1	no	—
119	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	#41	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂²×Dic₄₇	—	2	2	no	—
125	C₂×D₁₈₈	—	2	2	no	—
126	C₂×D₁₈₈	—	2	2	no	—
127	C₂×D₁₈₈	—	2	2	no	—
128	C₂×D₁₈₈	—	2	2	no	—
129	C₂×D₁₈₈	—	2	2	no	—
130	C₂×D₁₈₈	C₂²×C₄	1	4	yes	—
131	C₂×C₄×D₄₇	—	4	2	no	—
132	C₂×C₄×D₄₇	—	4	2	no	—
133	C₂×C₄×D₄₇	—	8	4	no	—
134	M₁₆×C₄₇	—	2	4	no	—
135	M₁₆×C₄₇	—	2	1	no	—
136	M₁₆×C₄₇	—	2	1	no	—
137	M₁₆×C₄₇	—	2	4	no	—
138	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
139	M₁₆×C₄₇	#41	1	2	yes	—
140	C₂×C₈×C₄₇	—	2	4	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	—	2	4	no	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂×C₈×C₄₇	#41	1	2	yes	—
152	C₄⋊C₄×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
154	C₂²⋊C₄×C₄₇	—	2	1	no	—
155	C₂²⋊C₄×C₄₇	—	2	2	no	—
156	C₄²×C₄₇	—	2	2	no	—
157	C₄²×C₄₇	—	2	1	no	—
158	C₄²×C₄₇	C₂×D₄	1	2	yes	—
159	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
161	#10625336	—	2	8	no	—
162	#10625334	—	2	8	no	—
163	(C₂×D₄₇)⋊C₄	—	4	2	no	—
164	(C₂×D₄₇)⋊C₄	—	4	2	no	—
165	C₄⋊Dic₄₇	—	2	2	no	—
166	C₄⋊Dic₄₇	—	2	2	no	—
167	#10625329	—	2	2	no	—
168	#10625329	—	2	2	no	—
169	#10625329	—	2	2	no	—
170	#10625329	C₂²×C₄	1	4	yes	—
171	C₂×C₄₇⋊C₈	—	2	2	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	D₃₇₆	—	2	4	no	—
174	D₃₇₆	—	2	4	no	—
175	C₂³×C₄₇	—	2	1	no	—
176	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂²×D₄₇	—	2	4	no	—
178	C₂²×D₄₇	—	4	2	no	—
179	C₂²×D₄₇	—	4	2	no	—
180	C₂²×D₄₇	—	8	2	no	—
181	C₂²×D₄₇	—	8	2	no	—
182	Q₈×C₄₇	—	2	1	no	—
183	Q₈×C₄₇	C₄×D₄	1	2	yes	—
184	D₄×C₄₇	—	2	2	no	—
185	D₄×C₄₇	—	2	2	no	—
186	D₄×C₄₇	—	2	1	no	—
187	D₄×C₄₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	8	2	no	—
194	C₂×C₄×C₄₇	#121	1	2	yes	—
195	C₂×C₄×C₄₇	#121	1	2	yes	—
196	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	8	2	no	—
204	D₁₈₈	—	2	4	no	—
205	D₁₈₈	—	2	4	no	—
206	D₁₈₈	—	4	2	no	—
207	D₁₈₈	—	4	2	no	—
208	C₄×D₄₇	—	8	4	no	—
209	C₄×D₄₇	—	8	4	no	—
210	C₈×C₄₇	—	2	2	no	—
211	C₈×C₄₇	—	2	1	no	—
212	C₈×C₄₇	—	2	2	no	—
213	C₈×C₄₇	—	2	1	no	—
214	C₈×C₄₇	C₄×D₄	1	2	yes	—
215	C₈×C₄₇	C₄×D₄	1	2	yes	—
216	C₄₇⋊C₈	—	2	4	no	—
217	C₄₇⋊C₈	—	4	2	no	—
218	#21555	—	47	1	no	maximal, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	4	2	no	—
222	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
224	C₂²×C₄₇	#529	1	1	yes	characteristic
225	C₂×D₄₇	—	4	4	no	—
226	C₂×D₄₇	—	8	4	no	—
227	C₂×D₄₇	—	8	2	no	—
228	C₂×D₄₇	—	8	2	no	—
229	C₂×D₄₇	—	8	4	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
235	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₄×C₄₇	#525	1	1	yes	characteristic
237	C₄×C₄₇	#532	1	1	yes	characteristic
238	Dic₄₇	—	8	2	no	—
239	C₂×#472	—	47	1	no	—
240	C₄×AGL(1,ℤ/8)	—	47	2	no	—
241	C₂×#442	—	47	1	no	—
242	#2875	D₄₇	1	1	yes	characteristic, complemented
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	—	4	2	no	—
253	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
254	C₂×C₄₇	#3068	1	2	yes	—
255	D₄₇	—	8	4	no	—
256	C₂×AGL(1,ℤ/8)	—	47	2	no	—
257	C₂²×D₈	—	47	1	no	—
258	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
259	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
260	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₄×D₄	—	47	2	no	—
262	#472	—	47	8	no	—
263	#442	—	94	2	no	—
264	#442	—	94	1	no	—
265	#442	—	94	1	no	—
266	#442	—	94	1	no	—
267	#442	—	94	1	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	—	47	1	no	—
275	#418	—	47	2	no	—
276	#417	—	47	2	no	—
277	C₂×#102	—	47	2	no	—
278	C₂×#100	—	47	2	no	—
279	C₂×#100	—	47	2	no	—
280	#405	—	2	1	no	—
281	#405	—	2	1	no	—
282	#405	C₂×D₄₇	1	1	yes	characteristic
283	#405	C₂×D₄₇	1	1	yes	characteristic
284	C₄×M₁₆	—	2	1	no	—
285	C₄×M₁₆	—	47	2	no	—
286	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
287	C₂×#97	—	2	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	C₂²×D₄₇	1	1	yes	characteristic
294	C₂²×D₄	—	47	2	no	—
295	C₂³×C₄	—	94	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	—	47	4	no	—
300	C₂×D₈	—	94	2	no	—
301	C₂×D₈	—	94	2	no	—
302	C₂×D₈	—	94	1	no	—
303	C₂×D₈	—	94	1	no	—
304	#131	—	2	2	no	—
305	#131	—	2	2	no	—
306	#131	—	2	2	no	—
307	#131	C₄×D₄₇	1	4	yes	complemented
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	47	2	no	—
311	C₂×M₁₆	—	47	2	no	—
312	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
313	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
314	C₂²×C₈	—	2	1	no	—
315	C₂²×C₈	—	2	1	no	—
316	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
318	C₄×Q₈	D₁₈₈	1	2	yes	—
319	C₄×D₄	—	2	2	no	—
320	C₄×D₄	—	94	2	no	—
321	C₄×D₄	—	94	2	no	—
322	C₄×D₄	—	94	2	no	—
323	C₄×D₄	—	94	2	no	—
324	C₄×D₄	D₁₈₈	1	2	yes	—
325	#117	—	2	1	no	—
326	#117	C₂²×D₄₇	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	47	2	no	—
328	C₂×C₂²⋊C₄	—	94	2	no	—
329	C₂×C₄²	—	2	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	—	94	1	no	—
335	#106	—	94	1	no	—
336	#106	—	94	2	no	—
337	#103	—	94	2	no	—
338	#102	—	94	2	no	—
339	#102	—	94	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	—	2	1	no	—
346	#97	—	2	1	no	—
347	#97	—	2	1	no	—
348	#97	—	94	2	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	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	—	2	1	no	—
356	C₄×C₈	—	94	2	no	—
357	C₂⁴	—	94	2	no	—
358	#41	—	2	1	no	—
359	#41	—	2	1	no	—
360	#41	C₂×C₄×D₄₇	1	2	yes	—
361	#41	#10625350	1	2	yes	—
362	C₂×Q₈	C₂×D₁₈₈	1	1	yes	characteristic
363	C₂×D₄	—	2	1	no	—
364	C₂×D₄	—	47	4	no	—
365	C₂×D₄	—	94	2	no	—
366	C₂×D₄	—	94	2	no	—
367	C₂×D₄	—	94	2	no	—
368	C₂×D₄	—	94	2	no	—
369	C₂×D₄	—	94	2	no	—
370	C₂×D₄	C₂×D₁₈₈	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	94	2	no	—
374	C₂²×C₄	—	376	4	no	—
375	C₂²×C₄	—	188	2	no	—
376	C₂²×C₄	—	188	2	no	—
377	C₂²×C₄	#10625350	1	2	yes	—
378	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
379	SD₁₆	—	94	8	no	—
380	D₈	—	94	8	no	—
381	D₈	—	94	4	no	—
382	D₈	—	94	4	no	—
383	M₁₆	—	2	4	no	—
384	M₁₆	—	2	1	no	—
385	M₁₆	—	2	1	no	—
386	M₁₆	—	2	4	no	—
387	M₁₆	—	47	4	no	—
388	M₁₆	—	94	2	no	—
389	M₁₆	—	94	2	no	—
390	M₁₆	—	94	2	no	—
391	M₁₆	C₂×C₄×D₄₇	1	2	yes	—
392	M₁₆	#10625350	1	2	yes	—
393	C₂×C₈	—	2	4	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	4	no	—
399	C₂×C₈	—	94	2	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	—	94	2	no	—
409	C₄⋊C₄	—	94	2	no	—
410	C₄⋊C₄	C₂×D₁₈₈	1	2	yes	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	188	2	no	—
414	C₂²⋊C₄	—	188	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	2	1	no	—
417	C₄²	C₂×D₁₈₈	1	2	yes	—
418	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
419	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
420	C₂³	—	2	1	no	—
421	C₂³	—	94	4	no	—
422	C₂³	—	376	2	no	—
423	C₂³	—	376	2	no	—
424	C₂³	—	188	2	no	—
425	C₂³	—	188	2	no	—
426	C₂³	C₂×#10625350	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	C₄×D₁₈₈	1	2	yes	—
429	D₄	—	2	2	no	—
430	D₄	—	2	2	no	—
431	D₄	—	2	1	no	—
432	D₄	—	94	4	no	—
433	D₄	—	94	4	no	—
434	D₄	—	188	2	no	—
435	D₄	—	188	2	no	—
436	D₄	C₄×D₁₈₈	1	2	yes	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	8	2	no	—
443	C₂×C₄	—	376	4	no	—
444	C₂×C₄	—	376	4	no	—
445	C₂×C₄	—	376	2	no	—
446	C₂×C₄	—	188	2	no	—
447	C₂×C₄	#13093998	1	2	yes	—
448	C₂×C₄	#13093998	1	2	yes	—
449	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
452	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
454	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	2	no	—
458	C₈	—	2	1	no	—
459	C₈	—	94	4	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	—	2	2	no	—
465	C₂²	—	4	2	no	—
466	C₂²	—	376	4	no	—
467	C₂²	—	376	4	no	—
468	C₂²	—	376	2	no	—
469	C₂²	—	376	2	no	—
470	C₂²	—	188	4	no	—
471	C₂²	C₄×#10625350	1	1	yes	characteristic
472	C₂²	C₂×#13093998	1	1	yes	characteristic
473	C₂²	#15689657	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	4	2	no	—
478	C₄	—	376	2	no	—
479	C₄	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
480	C₄	C₂×C₄×D₁₈₈	1	1	yes	characteristic
481	C₄	#15689634	1	1	yes	characteristic
482	C₄	#15689673	1	1	yes	characteristic
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	4	2	no	—
486	C₂	—	376	4	no	—
487	C₂	C₄×#13093998	1	1	yes	characteristic
488	C₂	#20253116	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×#13093998
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2875	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#15689393	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2875	D₄₇
hypocenter	C₄₇	#21555
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2875

Complements

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

N	H ≅ G/N	type
2. C₄×#13094049	C₂	semidirect
3. C₂×#15689236	C₂	semidirect
4. #20244298	C₂	semidirect
5. #20244168	C₂	semidirect
6. #20244050	C₂	semidirect
7. #20243896	C₂	semidirect
8. #20243447	C₂	semidirect
9. #20243294	C₂	semidirect
10. C₄×#13093940	C₂	semidirect
11. C₄₇×#2875	C₂	semidirect
15. #15689393	C₄	semidirect
51. #13094049	C₂×C₄	semidirect
56. C₂×D₃₇₆	C₂×C₄	semidirect
67. #13093960	C₂×C₄	semidirect
79. #13093940	C₂×C₄	semidirect
86. #131×C₄₇	C₂×C₄	semidirect
242. #2875	D₄₇	semidirect
292. C₄₇	#21555	semidirect
307. #131	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×#15689393	2
C₄×#13094049	2
C₂×#15689236	2
#20244298	2
#20244168	2
#20244050	2
#20243896	2
#20243447	2
#20243294	2
C₄×#13093940	2
C₄₇×#2875	2
#21555	47