Subgroups — #26188034

Order 12032.

722 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	#20253963	C₂	1	1	yes	maximal, characteristic
2	#20252134	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242271	C₂	1	2	yes	maximal, complemented
4	#20242217	C₂	1	2	yes	maximal, complemented
5	#20242215	C₂	1	2	yes	maximal, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241787	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241786	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094032	—	2	1	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	#15689526	C₄	1	1	yes	characteristic
15	#15689499	C₄	1	1	yes	characteristic
16	#15689471	C₄	1	1	yes	characteristic
17	#15689469	C₄	1	1	yes	characteristic
18	#15689357	C₄	1	2	yes	—
19	#15689357	C₄	1	2	yes	—
20	C₄×#10625334	C₂²	1	2	yes	—
21	C₄×#10625334	C₂²	1	2	yes	—
22	#15689202	C₂²	1	2	yes	—
23	#15689196	—	2	2	no	—
24	C₈×D₁₈₈	C₂²	1	2	yes	—
25	#15689176	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	#15689091	—	2	1	no	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688875	C₂²	1	1	yes	characteristic
30	#15688875	C₂²	1	1	yes	characteristic
31	#15688875	C₂²	1	1	yes	characteristic
32	#15688875	C₂²	1	1	yes	characteristic
33	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
34	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	#15688850	C₂²	1	2	yes	—
36	#15688850	C₂²	1	2	yes	—
37	#15688844	C₂²	1	2	yes	—
38	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
39	C₂×#131×C₄₇	—	2	1	no	—
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₄₇×#436	C₂²	1	2	yes	—
42	C₄₇×#435	—	2	2	no	—
43	C₈×D₄×C₄₇	C₂²	1	2	yes	—
44	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#408	—	2	1	no	—
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625334	C₂×C₄	1	2	yes	—
49	C₂×#10625334	C₂×C₄	1	2	yes	—
50	#13094032	—	4	4	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₄₇	—	2	2	no	—
56	#13094024	C₂×C₄	1	1	yes	characteristic
57	#13094021	C₂×C₄	1	1	yes	characteristic
58	#13094012	—	2	1	no	—
59	#13093998	—	2	1	no	—
60	#13093998	C₂×C₄	1	2	yes	—
61	C₄×D₁₈₈	—	2	1	no	—
62	C₄×D₁₈₈	C₂³	1	2	yes	—
63	#13093957	C₂×C₄	1	2	yes	—
64	#13093957	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	#13093945	C₂×C₄	1	2	yes	—
70	#13093945	C₂×C₄	1	2	yes	—
71	#13093944	C₂×C₄	1	2	yes	—
72	#13093944	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×#41×C₄₇	—	2	1	no	—
82	#131×C₄₇	—	4	4	no	—
83	C₂×M₁₆×C₄₇	—	2	2	no	—
84	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
85	C₂×M₁₆×C₄₇	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	—	2	1	no	—
87	C₂²×C₈×C₄₇	—	2	2	no	—
88	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
90	#124×C₄₇	—	2	1	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	C₂³	1	2	yes	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₄₇	—	2	2	no	—
100	C₂²⋊C₈×C₄₇	—	2	2	no	—
101	#97×C₄₇	D₄	1	2	yes	—
102	C₄×C₈×C₄₇	C₂³	1	2	yes	—
103	#41×C₄₇	—	4	2	no	—
104	#41×C₄₇	—	4	2	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₇	—	2	2	no	—
115	#10625350	—	4	2	no	—
116	#10625350	—	4	2	no	—
117	C₂×D₁₈₈	—	2	1	no	—
118	C₂×D₁₈₈	—	2	1	no	—
119	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
120	C₂×C₄×D₄₇	—	2	2	no	—
121	C₂×Dic₉₄	—	2	1	no	—
122	M₁₆×C₄₇	—	2	2	no	—
123	M₁₆×C₄₇	—	4	4	no	—
124	M₁₆×C₄₇	D₈	1	4	yes	complemented
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	4	2	no	—
128	C₂×C₈×C₄₇	—	4	4	no	—
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂²⋊C₄×C₄₇	—	2	2	no	—
134	C₂²⋊C₄×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₇	#41	1	1	yes	characteristic
138	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
139	#10625334	—	2	4	no	—
140	#10625334	—	4	2	no	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	(C₂×D₄₇)⋊C₄	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₂×C₄₇⋊C₈	—	4	1	no	—
150	C₂×C₄₇⋊C₈	—	4	2	no	—
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	#10625324	—	4	4	no	—
156	C₈×D₄₇	—	4	4	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	2	no	—
160	Q₈×C₄₇	—	4	2	no	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	4	4	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	8	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
176	C₂×C₄×C₄₇	#135	1	2	yes	—
177	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	4	4	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	D₁₈₈	—	2	2	no	—
183	D₁₈₈	—	2	2	no	—
184	D₁₈₈	—	4	2	no	—
185	D₁₈₈	—	8	1	no	—
186	C₄×D₄₇	—	4	2	no	—
187	C₄×D₄₇	—	4	2	no	—
188	Dic₉₄	—	4	2	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₈×C₄₇	—	4	1	no	—
192	C₈×C₄₇	C₂×D₈	1	4	yes	—
193	C₄₇⋊C₈	—	2	1	no	—
194	C₄₇⋊C₈	—	2	1	no	—
195	C₄₇⋊C₈	—	2	1	no	—
196	C₄₇⋊C₈	—	4	2	no	—
197	C₄₇⋊C₈	—	4	1	no	—
198	C₄₇⋊C₈	—	4	1	no	—
199	C₄₇⋊C₈	#131	1	2	yes	complemented
200	#18066	—	47	1	no	maximal, Sylow
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	1	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	C₄×D₈	1	2	yes	—
207	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	—	4	2	no	—
210	C₂×D₄₇	—	4	2	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	2	1	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	C₄×D₈	1	2	yes	—
216	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
217	C₄×C₄₇	#568	1	1	yes	characteristic
218	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
219	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
220	Dic₄₇	—	4	2	no	—
221	#3169	—	47	1	no	—
222	#2935	—	47	1	no	—
223	#2935	D₄₇	1	1	yes	characteristic, complemented
224	#1589	—	47	2	no	—
225	#1581	—	47	2	no	—
226	#1581	—	47	2	no	—
227	C₈×D₈	—	47	2	no	—
228	C₂×#335	—	47	1	no	—
229	#1480	—	47	1	no	—
230	#1480	—	47	1	no	—
231	C₈×M₁₆	—	47	1	no	—
232	C₂×C₄₇	—	2	2	no	—
233	C₂×C₄₇	—	8	2	no	—
234	C₂×C₄₇	#2935	1	1	yes	characteristic
235	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
236	C₂×C₄₇	#2957	1	1	yes	characteristic
237	D₄₇	—	8	2	no	—
238	C₂×#131	—	2	1	no	—
239	C₂×#131	—	94	1	no	—
240	#532	—	47	1	no	—
241	#532	C₂×D₄₇	1	1	yes	characteristic
242	#500	—	47	1	no	—
243	#493	—	47	1	no	—
244	#486	—	47	1	no	—
245	#486	—	47	1	no	—
246	#466	—	47	2	no	—
247	#466	—	47	2	no	—
248	C₄×D₈	—	47	2	no	—
249	C₄×D₈	—	47	2	no	—
250	#436	—	47	2	no	—
251	#436	C₂×D₄₇	1	2	yes	—
252	#435	—	2	2	no	—
253	#435	—	94	2	no	—
254	C₈×D₄	—	47	2	no	—
255	C₈×D₄	C₂×D₄₇	1	2	yes	—
256	#431	—	47	1	no	—
257	C₂×C₄⋊C₈	—	47	1	no	—
258	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
259	#408	—	2	1	no	—
260	#408	—	94	1	no	—
261	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄×C₈	—	47	1	no	—
263	#335	—	47	1	no	—
264	#335	—	47	1	no	—
265	#335	—	47	1	no	—
266	#335	—	47	1	no	—
267	D₄⋊C₈	—	47	2	no	—
268	D₄⋊C₈	—	47	2	no	—
269	D₄⋊C₈	—	47	2	no	—
270	D₄⋊C₈	—	47	2	no	—
271	#322	—	47	2	no	—
272	C₈²	—	47	2	no	—
273	C₄₇	#18066	1	1	yes	characteristic, complemented, Sylow
274	C₂×#41	—	2	1	no	—
275	C₂×#41	—	94	1	no	—
276	C₂×D₈	—	47	2	no	—
277	C₂×D₈	—	47	2	no	—
278	#131	—	4	4	no	—
279	#131	—	188	4	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	—	94	2	no	—
282	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
283	C₂×M₁₆	C₂²⋊D₄₇	1	1	yes	characteristic
284	C₂²×C₈	—	2	1	no	—
285	C₂²×C₈	—	2	2	no	—
286	C₂²×C₈	—	47	1	no	—
287	C₂²×C₈	—	47	1	no	—
288	C₂²×C₈	—	94	1	no	—
289	C₂²×C₈	—	94	2	no	—
290	C₄⋊Q₈	—	47	1	no	—
291	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
292	#127	—	47	1	no	—
293	#127	C₄×D₄₇	1	1	yes	characteristic
294	#124	—	2	1	no	—
295	#124	—	94	1	no	—
296	#121	—	2	1	no	—
297	#121	—	47	2	no	—
298	#121	—	94	1	no	—
299	#121	C₄×D₄₇	1	2	yes	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	47	2	no	—
302	C₄×D₄	—	94	1	no	—
303	C₄×D₄	C₂²×D₄₇	1	2	yes	—
304	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
305	#107	—	47	2	no	—
306	#107	—	47	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	47	1	no	—
309	C₄⋊C₈	—	47	1	no	—
310	C₄⋊C₈	—	94	1	no	—
311	C₄⋊C₈	—	94	1	no	—
312	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
314	#102	—	47	2	no	—
315	#102	—	47	2	no	—
316	#102	—	47	2	no	—
317	#102	—	47	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	—	2	2	no	—
320	C₂²⋊C₈	—	94	1	no	—
321	C₂²⋊C₈	—	94	2	no	—
322	C₂²⋊C₈	—	94	2	no	—
323	#97	C₂²⋊D₄₇	1	2	yes	—
324	C₄×C₈	—	47	1	no	—
325	C₄×C₈	—	47	1	no	—
326	C₄×C₈	—	47	1	no	—
327	C₄×C₈	—	47	1	no	—
328	C₄×C₈	—	47	2	no	—
329	C₄×C₈	C₂²×D₄₇	1	2	yes	—
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	#41	—	188	2	no	—
333	#41	—	188	2	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	94	1	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	47	2	no	—
340	C₂×D₄	—	94	2	no	—
341	C₂×D₄	—	94	1	no	—
342	C₂×D₄	—	94	1	no	—
343	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	#10625350	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
349	D₈	—	94	4	no	—
350	D₈	—	188	2	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	4	4	no	—
353	M₁₆	—	188	4	no	—
354	M₁₆	#10625334	1	4	yes	complemented
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	4	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	—	47	1	no	—
360	C₂×C₈	—	47	1	no	—
361	C₂×C₈	—	47	1	no	—
362	C₂×C₈	—	47	1	no	—
363	C₂×C₈	—	94	2	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	—	94	2	no	—
367	C₂×C₈	—	188	1	no	—
368	C₂×C₈	—	188	2	no	—
369	C₂×C₈	—	188	4	no	—
370	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
371	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	47	2	no	—
374	C₄⋊C₄	—	94	1	no	—
375	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	94	2	no	—
380	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
381	C₄²	#10625350	1	1	yes	characteristic
382	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₄²	C₂³×D₄₇	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	94	2	no	—
386	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
387	Q₈	—	4	2	no	—
388	Q₈	—	188	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	4	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	94	2	no	—
395	D₄	—	94	2	no	—
396	D₄	—	376	1	no	—
397	D₄	—	188	4	no	—
398	D₄	—	188	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
410	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×#10625334	1	2	yes	—
412	C₂×C₄	#13094044	1	2	yes	—
413	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	47	2	no	—
420	C₈	—	94	1	no	—
421	C₈	—	94	1	no	—
422	C₈	—	94	1	no	—
423	C₈	—	188	2	no	—
424	C₈	—	188	1	no	—
425	C₈	—	188	1	no	—
426	C₈	C₂×#10625334	1	4	yes	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	188	2	no	—
433	C₂²	—	188	2	no	—
434	C₂²	—	188	2	no	—
435	C₂²	C₄×#10625334	1	2	yes	—
436	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	4	2	no	—
441	C₄	—	188	2	no	—
442	C₄	C₄×#10625334	1	2	yes	—
443	C₄	#131×D₄₇	1	1	yes	characteristic
444	C₄	#15689888	1	1	yes	characteristic
445	C₄	C₂²×#10625334	1	1	yes	characteristic
446	C₄	C₂×#13094044	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	8	2	no	—
449	C₂	—	376	2	no	—
450	C₂	#20252130	1	1	yes	characteristic
451	C₂	C₂×C₄×#10625334	1	1	yes	characteristic
452	C₂	#20252303	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2935	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253963	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2935	D₄₇
hypocenter	C₄₇	#18066
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2935

Complements

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

N	H ≅ G/N	type
2. #20252134	C₂	semidirect
3. #20242271	C₂	semidirect
4. #20242217	C₂	semidirect
5. #20242215	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. C₂×#15688875	C₂	semidirect
8. #20241787	C₂	semidirect
9. #20241786	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#2935	C₂	semidirect
124. M₁₆×C₄₇	D₈	semidirect
199. C₄₇⋊C₈	#131	semidirect
223. #2935	D₄₇	semidirect
273. C₄₇	#18066	semidirect
354. M₁₆	#10625334	semidirect

Maximal subgroups

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

subgroup	index
#20253963	2
#20252134	2
#20242271	2
#20242217	2
#20242215	2
C₈×#10625334	2
C₂×#15688875	2
#20241787	2
#20241786	2
M₁₆×C₄₇⋊C₈	2
C₄₇×#2935	2
#18066	47