Subgroups — #26185621

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252517	C₂	1	1	yes	maximal, characteristic
2	#20252509	C₂	1	1	yes	maximal, characteristic
3	#20252354	C₂	1	1	yes	maximal, characteristic
4	#20242176	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242176	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242165	C₂	1	2	yes	maximal, complemented
7	#20242157	C₂	1	2	yes	maximal, complemented
8	#20242154	C₂	1	2	yes	maximal, complemented
9	#20242144	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242139	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1564	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689253	—	2	1	no	—
14	#15689253	C₄	1	1	yes	characteristic
15	#15689253	C₄	1	1	yes	characteristic
16	C₈×Dic₉₄	—	2	1	no	—
17	#15689202	—	2	1	no	—
18	#15689202	C₄	1	1	yes	characteristic
19	#15689202	C₄	1	1	yes	characteristic
20	#15689198	—	2	2	no	—
21	#15689197	—	2	2	no	—
22	#15689194	C₄	1	2	yes	—
23	#15689194	C₄	1	2	yes	—
24	C₈×D₁₈₈	—	2	1	no	—
25	#15689179	C₂²	1	2	yes	—
26	#15689176	C₂²	1	1	yes	characteristic
27	#15689175	C₂²	1	2	yes	—
28	#15689174	C₂²	1	2	yes	—
29	#15689147	C₂²	1	1	yes	characteristic
30	#15689147	C₂²	1	1	yes	characteristic
31	#15689145	C₂²	1	2	yes	—
32	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
33	C₄×#10625324	C₂²	1	2	yes	—
34	#15688875	C₂²	1	2	yes	—
35	#15688875	C₂²	1	2	yes	—
36	#15688874	C₂²	1	2	yes	—
37	#15688874	C₂²	1	2	yes	—
38	#15688873	C₂²	1	2	yes	—
39	#15688873	C₂²	1	2	yes	—
40	C₄₇×#431	C₂²	1	1	yes	characteristic
41	C₄₇×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#335	C₂²	1	1	yes	characteristic
44	C₄₇×#335	C₂²	1	1	yes	characteristic
45	C₄₇×#334	C₂²	1	1	yes	characteristic
46	C₄₇×#334	C₂²	1	1	yes	characteristic
47	C₂×#10625350	Q₈	1	1	yes	characteristic
48	C₂×#10625329	—	2	1	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625324	—	2	2	no	—
51	C₂×#10625324	C₂×C₄	1	2	yes	—
52	C₂×#10625324	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
55	C₄×Dic₉₄	D₄	1	1	yes	characteristic
56	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
57	C₄×D₁₈₈	D₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
59	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
60	#13093983	Q₈	1	1	yes	characteristic
61	#13093981	Q₈	1	2	yes	—
62	C₄²×D₄₇	C₂³	1	2	yes	—
63	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
64	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	Dic₄₇⋊C₈	—	2	2	no	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
72	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
73	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
78	#13093934	—	2	2	no	—
79	#13093934	C₂×C₄	1	2	yes	—
80	#13093934	C₂×C₄	1	2	yes	—
81	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
82	C₈×Dic₄₇	—	2	2	no	—
83	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²⋊C₈×C₄₇	—	2	1	no	—
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₄×C₈×C₄₇	—	2	1	no	—
93	C₄×C₈×C₄₇	—	2	1	no	—
94	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
95	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
96	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
101	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	2	yes	—
102	#10625350	—	4	2	no	—
103	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
107	C₂×Dic₉₄	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	4	1	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
121	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
122	C₂²⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
125	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
126	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
127	Dic₄₇⋊C₄	C₄⋊C₄	1	2	yes	—
128	Dic₄₇⋊C₄	C₄⋊C₄	1	2	yes	—
129	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
130	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
131	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
132	#10625329	—	8	1	no	—
133	#10625329	—	8	1	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
138	#10625324	—	2	4	no	—
139	#10625324	—	4	2	no	—
140	#10625324	—	8	2	no	—
141	C₈×D₄₇	—	8	2	no	—
142	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂²⋊D₄₇	—	4	2	no	—
156	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
159	D₁₈₈	—	2	2	no	—
160	C₄×D₄₇	—	2	2	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	4	2	no	—
165	Dic₉₄	—	2	2	no	—
166	C₈×C₄₇	—	2	1	no	—
167	C₈×C₄₇	—	2	1	no	—
168	C₈×C₄₇	—	2	1	no	—
169	C₈×C₄₇	—	4	1	no	—
170	C₈×C₄₇	—	4	1	no	—
171	C₈×C₄₇	—	4	1	no	—
172	C₈×C₄₇	—	4	1	no	—
173	C₈×C₄₇	#131	1	2	yes	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	#17841	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₂×D₄₇	—	2	2	no	—
184	C₂×D₄₇	—	2	2	no	—
185	C₂×D₄₇	—	2	2	no	—
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	#430	1	2	yes	—
190	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
191	C₄×C₄₇	#568	1	1	yes	characteristic
192	C₄×C₄₇	#577	1	1	yes	characteristic
193	C₄×C₄₇	#577	1	1	yes	characteristic
194	Dic₄₇	—	2	2	no	—
195	Dic₄₇	—	2	2	no	—
196	Dic₄₇	—	2	2	no	—
197	#2991	—	47	1	no	—
198	#2990	—	47	1	no	—
199	#2965	—	47	1	no	—
200	#1574	—	47	1	no	—
201	#1574	—	47	1	no	—
202	#1572	—	47	2	no	—
203	#1570	—	47	2	no	—
204	#1569	—	47	2	no	—
205	#1566	—	47	1	no	—
206	#1565	—	47	2	no	—
207	#1564	D₄₇	1	1	yes	characteristic, complemented
208	C₂×C₄₇	—	4	1	no	—
209	C₂×C₄₇	#2906	1	1	yes	characteristic
210	C₂×C₄₇	#2912	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#430	1	1	yes	characteristic
212	D₄₇	—	4	2	no	—
213	C₄×#41	—	47	1	no	—
214	#446	—	47	1	no	—
215	#446	—	47	1	no	—
216	#446	—	94	1	no	—
217	C₈×Q₈	—	94	1	no	—
218	#436	—	47	1	no	—
219	#436	—	47	1	no	—
220	#436	—	94	1	no	—
221	#436	—	94	2	no	—
222	#435	—	47	2	no	—
223	#435	—	47	2	no	—
224	#435	—	94	2	no	—
225	C₈×D₄	—	94	1	no	—
226	#432	—	47	2	no	—
227	#431	—	47	1	no	—
228	#431	—	47	2	no	—
229	#431	—	47	2	no	—
230	#431	C₂×D₄₇	1	1	yes	characteristic
231	#431	C₂×D₄₇	1	1	yes	characteristic
232	#423	—	47	1	no	—
233	#423	—	47	1	no	—
234	#423	—	47	2	no	—
235	C₂×C₄⋊C₈	—	47	2	no	—
236	C₄×M₁₆	—	47	2	no	—
237	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
238	#335	—	47	2	no	—
239	#335	—	47	2	no	—
240	#335	C₂×D₄₇	1	1	yes	characteristic
241	#335	C₂×D₄₇	1	1	yes	characteristic
242	#334	—	47	2	no	—
243	#334	—	47	2	no	—
244	#334	—	47	2	no	—
245	#334	—	47	2	no	—
246	#334	C₂×D₄₇	1	1	yes	characteristic
247	#334	C₂×D₄₇	1	1	yes	characteristic
248	C₄₇	#17841	1	1	yes	characteristic, complemented, Sylow
249	C₂×#41	—	47	1	no	—
250	C₂×M₁₆	—	47	2	no	—
251	C₂×M₁₆	—	47	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	1	no	—
254	C₂×M₁₆	—	94	1	no	—
255	C₂²×C₈	—	94	2	no	—
256	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
257	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
258	C₄×Q₈	—	47	1	no	—
259	C₄×Q₈	—	47	1	no	—
260	C₄×D₄	—	47	2	no	—
261	C₄×D₄	—	47	2	no	—
262	C₄×D₄	—	47	1	no	—
263	C₄×D₄	—	47	1	no	—
264	#117	—	47	1	no	—
265	#117	—	47	2	no	—
266	C₂×C₄²	—	47	2	no	—
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₄⋊C₈	—	47	2	no	—
269	C₄⋊C₈	—	47	2	no	—
270	C₄⋊C₈	—	47	1	no	—
271	C₄⋊C₈	—	47	1	no	—
272	C₄⋊C₈	—	47	2	no	—
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	94	2	no	—
275	C₄⋊C₈	—	94	2	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	—	94	1	no	—
278	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
279	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
280	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
281	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	47	2	no	—
285	C₂²⋊C₈	—	47	2	no	—
286	C₂²⋊C₈	—	47	2	no	—
287	C₂²⋊C₈	—	94	2	no	—
288	C₂²⋊C₈	—	94	2	no	—
289	#97	—	47	2	no	—
290	#97	—	47	2	no	—
291	#97	—	94	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	47	2	no	—
295	C₄×C₈	—	94	2	no	—
296	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
297	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
300	#41	—	188	2	no	—
301	C₂×Q₈	—	47	1	no	—
302	C₂×D₄	—	47	2	no	—
303	C₂×D₄	—	47	1	no	—
304	C₂²×C₄	—	47	2	no	—
305	C₂²×C₄	—	47	2	no	—
306	C₂²×C₄	—	47	2	no	—
307	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
310	M₁₆	—	94	4	no	—
311	M₁₆	—	376	2	no	—
312	M₁₆	—	376	1	no	—
313	M₁₆	—	376	1	no	—
314	M₁₆	—	188	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	47	2	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	376	2	no	—
326	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
329	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
330	C₄⋊C₄	—	47	2	no	—
331	C₄⋊C₄	—	47	2	no	—
332	C₄⋊C₄	—	47	1	no	—
333	C₄⋊C₄	—	47	1	no	—
334	C₂²⋊C₄	—	47	2	no	—
335	C₂²⋊C₄	—	47	2	no	—
336	C₂²⋊C₄	—	47	2	no	—
337	C₄²	—	47	2	no	—
338	C₄²	—	47	2	no	—
339	C₄²	—	47	2	no	—
340	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
341	C₄²	D₄×D₄₇	1	1	yes	characteristic
342	C₄²	Q₈×D₄₇	1	1	yes	characteristic
343	C₄²	C₂³×D₄₇	1	1	yes	characteristic
344	C₂³	—	47	2	no	—
345	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
346	Q₈	—	94	2	no	—
347	D₄	—	94	2	no	—
348	D₄	—	188	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	47	2	no	—
355	C₂×C₄	—	47	2	no	—
356	C₂×C₄	—	47	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
363	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
368	C₈	—	2	1	no	—
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	94	2	no	—
376	C₈	—	94	2	no	—
377	C₈	—	188	2	no	—
378	C₈	—	188	2	no	—
379	C₈	#13094030	1	2	yes	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	94	2	no	—
384	C₂²	—	94	2	no	—
385	C₂²	—	94	2	no	—
386	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	94	2	no	—
391	C₄	—	94	2	no	—
392	C₄	—	94	2	no	—
393	C₄	#15689170	1	2	yes	—
394	C₄	C₂×#13094030	1	1	yes	characteristic
395	C₄	#15689889	1	1	yes	characteristic
396	C₄	#15689930	1	1	yes	characteristic
397	C₄	#15689930	1	1	yes	characteristic
398	C₂	—	4	1	no	—
399	C₂	—	188	2	no	—
400	C₂	#20251953	1	1	yes	characteristic
401	C₂	#20251980	1	1	yes	characteristic
402	C₂	C₂×#15689170	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1564	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂×#10625350	Q₈
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1564	D₄₇
hypocenter	C₄₇	#17841
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1564

Complements

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

N	H ≅ G/N	type
4. #20242176	C₂	semidirect
5. #20242176	C₂	semidirect
6. #20242165	C₂	semidirect
7. #20242157	C₂	semidirect
8. #20242154	C₂	semidirect
9. #20242144	C₂	semidirect
10. #20242139	C₂	semidirect
11. C₄₇×#1564	C₂	semidirect
207. #1564	D₄₇	semidirect
248. C₄₇	#17841	semidirect

Maximal subgroups

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

subgroup	index
#20252517	2
#20252509	2
#20252354	2
#20242176	2
#20242165	2
#20242157	2
#20242154	2
#20242144	2
#20242139	2
C₄₇×#1564	2
#17841	47