Subgroups — #26186285

Order 12032.

632 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253460	C₂	1	1	yes	maximal, characteristic
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic
3	#20252322	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242261	C₂	1	2	yes	maximal, complemented
5	#20242247	C₂	1	2	yes	maximal, complemented
6	C₈×Dic₁₈₈	C₂	1	2	yes	maximal, complemented
7	C₈×#10625325	C₂	1	2	yes	maximal, complemented
8	#20242177	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241828	C₂	1	1	yes	maximal, characteristic
10	#20241810	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689680	C₂²	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689465	C₄	1	2	yes	—
15	#15689409	C₄	1	1	yes	characteristic
16	#15689404	C₄	1	1	yes	characteristic
17	#15689334	C₄	1	1	yes	characteristic
18	#15689329	C₄	1	1	yes	characteristic
19	#15689287	C₄	1	2	yes	—
20	#15689253	—	2	1	no	—
21	#15689253	C₂²	1	2	yes	—
22	C₈×Dic₉₄	—	2	1	no	—
23	C₈×Dic₉₄	C₂²	1	2	yes	—
24	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
25	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	C₄×Dic₁₈₈	C₂²	1	2	yes	—
27	C₄×#10625325	C₂²	1	2	yes	—
28	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
29	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₄₇	—	2	1	no	—
31	C₈×C₂²⋊D₄₇	—	2	1	no	—
32	#15689176	C₂²	1	1	yes	characteristic
33	#15689174	—	2	1	no	—
34	#15689149	—	2	1	no	—
35	#15689147	C₂²	1	1	yes	characteristic
36	#15689078	—	2	1	no	—
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688876	C₂²	1	2	yes	—
39	#15688874	C₂²	1	2	yes	—
40	#15688855	C₂²	1	2	yes	—
41	#15688855	C₂²	1	2	yes	—
42	#15688855	C₂²	1	2	yes	—
43	#15688852	C₂²	1	2	yes	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#322	C₂²	1	2	yes	—
48	C₈²×C₄₇	C₂²	1	2	yes	—
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
51	C₂×#10625325	C₂×C₄	1	2	yes	—
52	C₂×#10625329	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	1	no	—
54	C₂×C₈×D₄₇	—	2	1	no	—
55	#13094024	C₂×C₄	1	1	yes	characteristic
56	#13094024	C₂×C₄	1	1	yes	characteristic
57	#13094016	—	2	1	no	—
58	#13094003	—	2	1	no	—
59	#13094003	C₂×C₄	1	2	yes	—
60	C₄×Dic₉₄	—	2	1	no	—
61	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂³	1	2	yes	—
64	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
66	C₄×C₂²⋊D₄₇	—	2	1	no	—
67	C₄×C₂²⋊D₄₇	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093983	C₂×C₄	1	1	yes	characteristic
70	#13093981	—	2	1	no	—
71	C₄²×D₄₇	—	2	1	no	—
72	#13093958	C₂×C₄	1	2	yes	—
73	#13093956	C₂×C₄	1	2	yes	—
74	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
75	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
76	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
78	Dic₄₇⋊C₈	—	2	2	no	—
79	Dic₄₇⋊C₈	—	2	2	no	—
80	Dic₄₇⋊C₈	—	2	1	no	—
81	Dic₄₇⋊C₈	—	2	1	no	—
82	#13093949	C₂×C₄	1	2	yes	—
83	#13093949	C₂×C₄	1	2	yes	—
84	#13093949	C₂×C₄	1	2	yes	—
85	#13093946	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	1	no	—
88	(C₂×D₄₇)⋊C₈	—	2	1	no	—
89	#13093934	—	2	2	no	—
90	C₄×C₄₇⋊C₈	—	2	1	no	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₈×Dic₄₇	—	2	1	no	—
93	C₈×Dic₄₇	—	2	1	no	—
94	C₂×M₁₆×C₄₇	—	2	1	no	—
95	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
101	#97×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
103	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
104	C₄×C₈×C₄₇	C₂³	1	2	yes	—
105	C₄×C₈×C₄₇	C₂³	1	2	yes	—
106	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
111	C₂×C₂²⋊D₄₇	—	2	1	no	—
112	#10625350	—	2	2	no	—
113	#10625350	—	2	2	no	—
114	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₄₇	—	2	1	no	—
116	C₂×C₄×D₄₇	—	2	1	no	—
117	C₂×C₄×D₄₇	—	2	1	no	—
118	C₂×Dic₉₄	—	2	1	no	—
119	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
120	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
121	M₁₆×C₄₇	—	2	4	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	4	1	no	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₄₇	#41	1	1	yes	characteristic
134	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂²⋊Dic₄₇	—	2	2	no	—
136	C₂²⋊Dic₄₇	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	(C₂×D₄₇)⋊C₄	—	2	1	no	—
139	C₄⋊Dic₄₇	—	2	1	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
143	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	Dic₄₇⋊C₄	—	2	1	no	—
146	Dic₄₇⋊C₄	—	2	2	no	—
147	Dic₄₇⋊C₄	—	2	1	no	—
148	Dic₄₇⋊C₄	—	2	2	no	—
149	C₄×Dic₄₇	—	2	1	no	—
150	C₄×Dic₄₇	—	2	1	no	—
151	C₄×Dic₄₇	—	2	1	no	—
152	C₄×Dic₄₇	—	2	2	no	—
153	#10625329	—	4	2	no	—
154	C₂×C₄₇⋊C₈	—	2	1	no	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	Dic₁₈₈	—	2	4	no	—
158	#10625325	—	2	4	no	—
159	C₈×D₄₇	—	4	2	no	—
160	C₈×D₄₇	—	4	2	no	—
161	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂²×D₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
174	C₂²⋊D₄₇	—	2	4	no	—
175	C₂×Dic₄₇	—	2	1	no	—
176	C₂×Dic₄₇	—	2	1	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	2	2	no	—
180	D₁₈₈	—	2	1	no	—
181	D₁₈₈	#131	1	2	yes	—
182	C₄×D₄₇	—	2	4	no	—
183	C₄×D₄₇	—	4	1	no	—
184	C₄×D₄₇	—	4	1	no	—
185	C₄×D₄₇	—	4	2	no	—
186	Dic₉₄	—	2	1	no	—
187	Dic₉₄	—	2	2	no	—
188	Dic₉₄	—	2	2	no	—
189	Dic₉₄	—	4	2	no	—
190	Dic₉₄	#131	1	2	yes	—
191	C₈×C₄₇	—	2	4	no	—
192	C₈×C₄₇	—	2	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	2	1	no	—
195	C₈×C₄₇	—	2	1	no	—
196	C₈×C₄₇	—	2	1	no	—
197	C₈×C₄₇	#137	1	2	yes	—
198	C₄₇⋊C₈	—	4	1	no	—
199	C₄₇⋊C₈	—	4	1	no	—
200	C₄₇⋊C₈	—	4	2	no	—
201	#17913	—	47	1	no	maximal, Sylow
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂×D₄₇	—	2	2	no	—
207	C₂×D₄₇	—	4	1	no	—
208	C₂×D₄₇	—	4	1	no	—
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	#443	1	2	yes	—
213	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
214	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
215	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
216	C₄×C₄₇	#575	1	1	yes	characteristic
217	Dic₄₇	—	2	2	no	—
218	Dic₄₇	—	4	2	no	—
219	Dic₄₇	—	4	1	no	—
220	Dic₄₇	—	4	2	no	—
221	Dic₄₇	—	4	1	no	—
222	#3107	—	47	1	no	—
223	C₈×#41	—	47	1	no	—
224	#2960	—	47	1	no	—
225	#1587	—	47	2	no	—
226	#1585	—	47	2	no	—
227	C₈×Q₁₆	—	47	2	no	—
228	C₈×SD₁₆	—	47	2	no	—
229	#1574	—	47	1	no	—
230	#1489	—	47	1	no	—
231	#1485	—	47	1	no	—
232	C₈×M₁₆	D₄₇	1	1	yes	characteristic, complemented
233	C₂×C₄₇	—	4	1	no	—
234	C₂×C₄₇	#2929	1	1	yes	characteristic
235	C₂×C₄₇	C₄×#137	1	1	yes	characteristic
236	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
237	D₄₇	—	4	2	no	—
238	#533	—	47	1	no	—
239	C₄×#41	—	47	1	no	—
240	#485	—	47	2	no	—
241	#475	—	47	1	no	—
242	#474	—	47	1	no	—
243	#462	—	47	1	no	—
244	#461	—	47	1	no	—
245	#452	—	47	2	no	—
246	#446	—	47	2	no	—
247	#446	—	94	1	no	—
248	C₈×Q₈	—	47	2	no	—
249	C₈×Q₈	—	47	1	no	—
250	C₈×Q₈	—	47	1	no	—
251	C₈×Q₈	—	94	1	no	—
252	C₄×Q₁₆	—	47	2	no	—
253	C₄×SD₁₆	—	47	2	no	—
254	C₈×D₄	—	47	1	no	—
255	C₈×D₄	—	47	1	no	—
256	C₈×D₄	—	94	1	no	—
257	C₈×D₄	—	94	1	no	—
258	#431	—	47	1	no	—
259	#431	—	94	1	no	—
260	#431	C₂×D₄₇	1	1	yes	characteristic
261	#424	—	94	1	no	—
262	#423	—	47	1	no	—
263	#405	—	94	1	no	—
264	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	—	94	1	no	—
266	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
267	#335	—	47	2	no	—
268	#334	—	47	2	no	—
269	Q₈⋊C₈	—	47	2	no	—
270	Q₈⋊C₈	—	47	2	no	—
271	Q₈⋊C₈	—	47	2	no	—
272	D₄⋊C₈	—	47	2	no	—
273	#322	C₂×D₄₇	1	2	yes	—
274	C₈²	C₂×D₄₇	1	2	yes	—
275	C₄₇	#17913	1	1	yes	characteristic, complemented, Sylow
276	C₂×#41	—	47	1	no	—
277	C₂×Q₁₆	—	47	2	no	—
278	C₂×SD₁₆	—	47	2	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	94	1	no	—
281	C₂²×C₈	—	94	1	no	—
282	C₂²×C₈	—	94	1	no	—
283	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
284	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
285	C₄⋊Q₈	—	47	1	no	—
286	C₄⋊Q₈	—	47	1	no	—
287	#125	—	94	1	no	—
288	C₂²⋊Q₈	—	47	2	no	—
289	C₂²⋊Q₈	—	94	1	no	—
290	C₄×Q₈	—	47	1	no	—
291	C₄×Q₈	—	47	1	no	—
292	C₄×Q₈	—	47	2	no	—
293	C₄×Q₈	—	94	1	no	—
294	C₄×D₄	—	47	1	no	—
295	C₄×D₄	—	47	1	no	—
296	C₄×D₄	—	94	1	no	—
297	C₄×D₄	—	94	1	no	—
298	#117	—	47	1	no	—
299	#117	—	94	1	no	—
300	#117	—	94	1	no	—
301	C₂×C₄²	—	94	1	no	—
302	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
303	#107	—	47	2	no	—
304	#106	—	47	2	no	—
305	C₄⋊C₈	—	47	2	no	—
306	C₄⋊C₈	—	47	1	no	—
307	C₄⋊C₈	—	47	1	no	—
308	C₄⋊C₈	—	94	2	no	—
309	C₄⋊C₈	—	94	2	no	—
310	C₄⋊C₈	—	94	1	no	—
311	C₄⋊C₈	—	94	1	no	—
312	C₄⋊C₈	—	94	1	no	—
313	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
314	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
315	#103	—	47	2	no	—
316	#103	—	47	2	no	—
317	#103	—	47	2	no	—
318	#102	—	47	2	no	—
319	C₂²⋊C₈	—	94	1	no	—
320	C₂²⋊C₈	—	94	1	no	—
321	C₂²⋊C₈	—	94	1	no	—
322	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
323	#97	—	2	1	no	—
324	#97	—	94	2	no	—
325	C₄×C₈	—	94	1	no	—
326	C₄×C₈	—	94	1	no	—
327	C₄×C₈	—	94	2	no	—
328	C₄×C₈	—	94	1	no	—
329	C₄×C₈	D₁₈₈	1	1	yes	characteristic
330	C₄×C₈	D₁₈₈	1	1	yes	characteristic
331	C₄×C₈	C₂²×D₄₇	1	2	yes	—
332	C₄×C₈	C₂²×D₄₇	1	2	yes	—
333	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
334	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
335	#41	—	94	2	no	—
336	#41	—	94	2	no	—
337	C₂×Q₈	—	47	1	no	—
338	C₂×Q₈	—	47	2	no	—
339	C₂×Q₈	—	94	1	no	—
340	C₂×D₄	—	47	1	no	—
341	C₂×D₄	—	94	1	no	—
342	C₂²×C₄	—	94	1	no	—
343	C₂²×C₄	—	94	1	no	—
344	C₂²×C₄	—	94	1	no	—
345	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
347	C₂²×C₄	#10625350	1	1	yes	characteristic
348	Q₁₆	—	94	4	no	—
349	SD₁₆	—	94	4	no	—
350	M₁₆	—	2	4	no	—
351	M₁₆	—	188	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	4	1	no	—
355	C₂×C₈	—	94	1	no	—
356	C₂×C₈	—	94	1	no	—
357	C₂×C₈	—	94	2	no	—
358	C₂×C₈	—	188	2	no	—
359	C₂×C₈	—	188	2	no	—
360	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
361	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
362	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
363	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
364	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
365	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
366	C₄⋊C₄	—	47	2	no	—
367	C₄⋊C₄	—	47	1	no	—
368	C₄⋊C₄	—	47	1	no	—
369	C₄⋊C₄	—	94	1	no	—
370	C₄⋊C₄	—	94	2	no	—
371	C₄⋊C₄	—	94	1	no	—
372	C₄⋊C₄	—	94	1	no	—
373	C₄⋊C₄	—	94	1	no	—
374	C₄⋊C₄	—	94	1	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₂²⋊C₄	—	94	1	no	—
377	C₂²⋊C₄	—	94	2	no	—
378	C₂²⋊C₄	—	94	1	no	—
379	C₂²⋊C₄	—	94	1	no	—
380	C₄²	—	94	1	no	—
381	C₄²	—	94	1	no	—
382	C₄²	—	94	1	no	—
383	C₄²	—	94	2	no	—
384	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
386	C₄²	#10625350	1	1	yes	characteristic
387	C₄²	C₂³×D₄₇	1	1	yes	characteristic
388	C₂³	—	94	1	no	—
389	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
390	Q₈	—	47	2	no	—
391	Q₈	—	94	1	no	—
392	Q₈	—	94	2	no	—
393	Q₈	—	94	2	no	—
394	Q₈	—	188	2	no	—
395	D₄	—	47	2	no	—
396	D₄	—	94	4	no	—
397	D₄	—	94	1	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	94	4	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	94	1	no	—
407	C₂×C₄	—	94	2	no	—
408	C₂×C₄	—	94	2	no	—
409	C₂×C₄	—	188	2	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
413	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
414	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
415	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
417	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
418	C₈	—	2	4	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	1	no	—
422	C₈	—	2	1	no	—
423	C₈	—	2	1	no	—
424	C₈	—	188	1	no	—
425	C₈	—	188	1	no	—
426	C₈	—	188	2	no	—
427	C₈	#13094057	1	2	yes	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	94	2	no	—
432	C₂²	—	188	1	no	—
433	C₂²	—	188	1	no	—
434	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	94	2	no	—
439	C₄	—	188	1	no	—
440	C₄	—	188	1	no	—
441	C₄	—	188	2	no	—
442	C₄	—	188	2	no	—
443	C₄	#15689241	1	2	yes	—
444	C₄	#131×D₄₇	1	1	yes	characteristic
445	C₄	#131×D₄₇	1	1	yes	characteristic
446	C₄	C₂×#13094057	1	1	yes	characteristic
447	C₄	#15689923	1	1	yes	characteristic
448	C₂	—	4	1	no	—
449	C₂	—	188	2	no	—
450	C₂	#20252084	1	1	yes	characteristic
451	C₂	C₄×#13094057	1	1	yes	characteristic
452	C₂	C₂×#15689241	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×M₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×M₁₆	D₄₇
hypocenter	C₄₇	#17913
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
3. #20252322	C₂	semidirect
4. #20242261	C₂	semidirect
5. #20242247	C₂	semidirect
6. C₈×Dic₁₈₈	C₂	semidirect
7. C₈×#10625325	C₂	semidirect
8. #20242177	C₂	semidirect
10. #20241810	C₂	semidirect
11. C₈×M₁₆×C₄₇	C₂	semidirect
232. C₈×M₁₆	D₄₇	semidirect
275. C₄₇	#17913	semidirect

Maximal subgroups

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

subgroup	index
#20253460	2
C₈×#10625350	2
#20252322	2
#20242261	2
#20242247	2
C₈×Dic₁₈₈	2
C₈×#10625325	2
#20242177	2
#20241828	2
#20241810	2
C₈×M₁₆×C₄₇	2
#17913	47