Subgroups — #26187119

Order 12032.

624 conjugacy classes of subgroups.

The subgroup lattice has 424 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	#20252463	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242252	C₂	1	2	yes	maximal, complemented
4	#20242250	C₂	1	2	yes	maximal, complemented
5	#20242217	C₂	1	2	yes	maximal, complemented
6	#20242215	C₂	1	2	yes	maximal, complemented
7	#20242149	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241857	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241856	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241681	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2981	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689526	C₄	1	1	yes	characteristic
14	#15689499	C₄	1	1	yes	characteristic
15	#15689471	C₄	1	1	yes	characteristic
16	#15689469	C₄	1	1	yes	characteristic
17	#15689357	C₄	1	2	yes	—
18	#15689357	C₄	1	2	yes	—
19	C₄×#10625334	C₂²	1	2	yes	—
20	C₄×#10625334	C₂²	1	2	yes	—
21	#15689202	C₂²	1	2	yes	—
22	#15689193	—	2	2	no	—
23	C₈×D₁₈₈	C₂²	1	2	yes	—
24	#15689180	C₂²	1	1	yes	characteristic
25	#15689176	C₂²	1	1	yes	characteristic
26	#15689088	—	2	2	no	—
27	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	#15688875	C₂²	1	2	yes	—
29	#15688873	C₂²	1	2	yes	—
30	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
31	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
32	#15688850	C₂²	1	2	yes	—
33	#15688850	C₂²	1	2	yes	—
34	#15688845	C₂²	1	1	yes	characteristic
35	#15688845	C₂²	1	1	yes	characteristic
36	#15688844	C₂²	1	1	yes	characteristic
37	#15688844	C₂²	1	1	yes	characteristic
38	C₄₇×#532	C₂²	1	1	yes	characteristic
39	C₄₇×#436	C₂²	1	2	yes	—
40	C₄₇×#435	—	2	2	no	—
41	C₈×D₄×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#432	C₂²	1	1	yes	characteristic
43	C₄₇×#431	C₂²	1	1	yes	characteristic
44	C₄₇×#408	—	2	2	no	—
45	C₂×#10625350	—	2	1	no	—
46	C₂×#10625334	C₂×C₄	1	2	yes	—
47	C₂×#10625334	C₂×C₄	1	2	yes	—
48	C₂×#10625324	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₄₇	—	2	2	no	—
52	#13094024	C₂×C₄	1	1	yes	characteristic
53	#13094021	C₂×C₄	1	1	yes	characteristic
54	#13094012	—	2	1	no	—
55	#13093998	—	2	1	no	—
56	#13093998	C₂×C₄	1	2	yes	—
57	C₄×D₁₈₈	—	2	1	no	—
58	C₄×D₁₈₈	C₂³	1	2	yes	—
59	#13093957	C₂×C₄	1	2	yes	—
60	#13093957	C₂×C₄	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
63	#13093945	C₂×C₄	1	2	yes	—
64	#13093945	C₂×C₄	1	2	yes	—
65	#13093944	C₂×C₄	1	2	yes	—
66	#13093944	C₂×C₄	1	2	yes	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
69	(C₂×D₄₇)⋊C₈	—	2	2	no	—
70	(C₂×D₄₇)⋊C₈	—	2	2	no	—
71	#13093935	—	2	1	no	—
72	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂×#41×C₄₇	—	2	1	no	—
79	C₂×M₁₆×C₄₇	—	2	2	no	—
80	C₂²×C₈×C₄₇	—	2	2	no	—
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
83	#124×C₄₇	—	2	1	no	—
84	#121×C₄₇	—	2	1	no	—
85	#121×C₄₇	C₂×C₄	1	2	yes	—
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₄×D₄×C₄₇	C₂³	1	2	yes	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
90	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
91	C₂²⋊C₈×C₄₇	—	2	1	no	—
92	C₂²⋊C₈×C₄₇	—	2	2	no	—
93	C₂²⋊C₈×C₄₇	—	2	2	no	—
94	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
95	#97×C₄₇	—	2	1	no	—
96	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	#41×C₄₇	—	8	2	no	—
99	C₂×Q₈×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	1	no	—
103	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂×C₂²⋊D₄₇	—	2	2	no	—
109	#10625350	—	8	2	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	—	2	1	no	—
112	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×Dic₉₄	—	2	1	no	—
115	M₁₆×C₄₇	—	8	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	8	2	no	—
118	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₂²⋊C₄×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₄²×C₄₇	#41	1	1	yes	characteristic
127	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
128	#10625334	—	4	2	no	—
129	#10625334	—	4	2	no	—
130	(C₂×D₄₇)⋊C₄	—	2	2	no	—
131	(C₂×D₄₇)⋊C₄	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	1	no	—
133	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	4	1	no	—
138	C₂×C₄₇⋊C₈	—	4	1	no	—
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	#10625324	—	8	2	no	—
144	C₈×D₄₇	—	8	2	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
147	C₂²×D₄₇	—	2	2	no	—
148	Q₈×C₄₇	—	8	1	no	—
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	—	2	2	no	—
151	D₄×C₄₇	—	8	1	no	—
152	D₄×C₄₇	—	8	1	no	—
153	D₄×C₄₇	—	8	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂²⋊D₄₇	—	8	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	D₁₈₈	—	2	2	no	—
170	D₁₈₈	—	2	2	no	—
171	D₁₈₈	—	8	1	no	—
172	D₁₈₈	—	8	1	no	—
173	C₄×D₄₇	—	4	2	no	—
174	C₄×D₄₇	—	4	2	no	—
175	Dic₉₄	—	8	1	no	—
176	C₈×C₄₇	—	2	2	no	—
177	C₈×C₄₇	—	2	2	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₄₇⋊C₈	—	2	1	no	—
180	C₄₇⋊C₈	—	2	1	no	—
181	C₄₇⋊C₈	—	2	1	no	—
182	C₄₇⋊C₈	—	2	1	no	—
183	C₄₇⋊C₈	—	4	1	no	—
184	C₄₇⋊C₈	—	4	1	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	#17989	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	—	4	2	no	—
193	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₄₇	—	4	2	no	—
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	—	4	2	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	#568	1	1	yes	characteristic
203	C₄×C₄₇	#568	1	1	yes	characteristic
204	C₄×C₄₇	#576	1	2	yes	—
205	Dic₄₇	—	4	2	no	—
206	#3169	—	47	1	no	—
207	#2981	—	47	1	no	—
208	#2981	D₄₇	1	1	yes	characteristic, complemented
209	#1586	—	47	2	no	—
210	#1586	—	47	2	no	—
211	#1581	—	47	2	no	—
212	#1581	—	47	2	no	—
213	#1568	—	47	1	no	—
214	#1496	—	47	1	no	—
215	#1496	—	47	1	no	—
216	#1452	—	47	1	no	—
217	C₂×C₄₇	—	4	1	no	—
218	C₂×C₄₇	—	8	2	no	—
219	C₂×C₄₇	#2932	1	1	yes	characteristic
220	C₂×C₄₇	#2948	1	1	yes	characteristic
221	C₂×C₄₇	#2957	1	1	yes	characteristic
222	D₄₇	—	8	2	no	—
223	#532	—	47	1	no	—
224	#532	C₂×D₄₇	1	1	yes	characteristic
225	#500	—	47	1	no	—
226	#493	—	47	1	no	—
227	#486	—	47	1	no	—
228	#486	—	47	1	no	—
229	#466	—	47	2	no	—
230	#466	—	47	2	no	—
231	C₄×D₈	—	47	2	no	—
232	C₄×D₈	—	47	2	no	—
233	#436	—	47	2	no	—
234	#436	C₂×D₄₇	1	2	yes	—
235	#435	—	2	2	no	—
236	#435	—	94	2	no	—
237	C₈×D₄	—	47	2	no	—
238	C₈×D₄	C₂×D₄₇	1	2	yes	—
239	#432	—	47	1	no	—
240	#432	C₂×D₄₇	1	1	yes	characteristic
241	#431	—	47	1	no	—
242	#431	C₂×D₄₇	1	1	yes	characteristic
243	#408	—	2	2	no	—
244	#408	—	94	2	no	—
245	C₂×C₄×C₈	—	47	1	no	—
246	#335	—	47	2	no	—
247	#334	—	47	2	no	—
248	D₄⋊C₈	—	47	2	no	—
249	D₄⋊C₈	—	47	2	no	—
250	D₄⋊C₈	—	47	2	no	—
251	D₄⋊C₈	—	47	2	no	—
252	#322	—	47	1	no	—
253	#322	—	47	1	no	—
254	#322	—	47	1	no	—
255	#322	—	47	1	no	—
256	C₄₇	#17989	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	94	1	no	—
259	C₂×D₈	—	47	2	no	—
260	C₂×D₈	—	47	2	no	—
261	C₂×M₁₆	—	2	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	—	47	1	no	—
265	C₂²×C₈	—	47	1	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₄⋊Q₈	—	47	1	no	—
268	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
269	#127	—	47	1	no	—
270	#127	C₄×D₄₇	1	1	yes	characteristic
271	#124	—	2	1	no	—
272	#124	—	94	1	no	—
273	#121	—	2	1	no	—
274	#121	—	47	2	no	—
275	#121	—	94	1	no	—
276	#121	C₄×D₄₇	1	2	yes	—
277	C₄×D₄	—	2	1	no	—
278	C₄×D₄	—	47	2	no	—
279	C₄×D₄	—	94	1	no	—
280	C₄×D₄	C₂²×D₄₇	1	2	yes	—
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	#107	—	47	2	no	—
283	#107	—	47	2	no	—
284	C₄⋊C₈	—	47	2	no	—
285	C₄⋊C₈	—	94	1	no	—
286	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
287	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
288	#102	—	47	2	no	—
289	#102	—	47	2	no	—
290	#102	—	47	2	no	—
291	#102	—	47	2	no	—
292	C₂²⋊C₈	—	2	1	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	94	1	no	—
296	C₂²⋊C₈	—	94	1	no	—
297	C₂²⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
300	#97	—	2	1	no	—
301	#97	—	94	1	no	—
302	C₄×C₈	—	47	1	no	—
303	C₄×C₈	—	47	1	no	—
304	C₄×C₈	—	47	1	no	—
305	C₄×C₈	—	47	1	no	—
306	C₄×C₈	—	47	1	no	—
307	C₄×C₈	—	47	1	no	—
308	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
310	#41	—	8	2	no	—
311	#41	—	376	2	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	94	1	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	—	2	1	no	—
317	C₂×D₄	—	47	2	no	—
318	C₂×D₄	—	94	2	no	—
319	C₂×D₄	—	94	1	no	—
320	C₂×D₄	—	94	1	no	—
321	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₂²×C₄	#10625350	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
327	D₈	—	188	2	no	—
328	D₈	—	188	2	no	—
329	M₁₆	—	8	2	no	—
330	M₁₆	—	376	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	8	2	no	—
333	C₂×C₈	—	47	1	no	—
334	C₂×C₈	—	47	1	no	—
335	C₂×C₈	—	47	1	no	—
336	C₂×C₈	—	47	1	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	376	2	no	—
341	C₂×C₈	—	188	1	no	—
342	C₂×C₈	—	188	1	no	—
343	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
344	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	47	2	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
349	C₂²⋊C₄	—	2	2	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
354	C₄²	#10625350	1	1	yes	characteristic
355	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
356	C₄²	C₂³×D₄₇	1	1	yes	characteristic
357	C₂³	—	2	2	no	—
358	C₂³	—	94	2	no	—
359	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
360	Q₈	—	8	1	no	—
361	Q₈	—	376	1	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	2	no	—
367	D₄	—	94	2	no	—
368	D₄	—	94	2	no	—
369	D₄	—	376	1	no	—
370	D₄	—	376	1	no	—
371	D₄	—	376	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
388	C₈	—	2	2	no	—
389	C₈	—	2	2	no	—
390	C₈	—	4	2	no	—
391	C₈	—	94	1	no	—
392	C₈	—	94	1	no	—
393	C₈	—	94	1	no	—
394	C₈	—	94	1	no	—
395	C₈	—	188	1	no	—
396	C₈	—	188	1	no	—
397	C₈	—	188	2	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	188	2	no	—
405	C₂²	—	188	2	no	—
406	C₂²	—	188	2	no	—
407	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	188	2	no	—
414	C₄	#15689888	1	1	yes	characteristic
415	C₄	#15689888	1	1	yes	characteristic
416	C₄	#15689926	1	2	yes	—
417	C₂	—	4	1	no	—
418	C₂	—	8	2	no	—
419	C₂	—	376	2	no	—
420	C₂	#20252104	1	1	yes	characteristic
421	C₂	#20252238	1	1	yes	characteristic
422	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×#2981	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253963	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2981	D₄₇
hypocenter	C₄₇	#17989
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2981

Complements

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

N	H ≅ G/N	type
2. #20252463	C₂	semidirect
3. #20242252	C₂	semidirect
4. #20242250	C₂	semidirect
5. #20242217	C₂	semidirect
6. #20242215	C₂	semidirect
7. #20242149	C₂	semidirect
8. #20241857	C₂	semidirect
9. #20241856	C₂	semidirect
10. #20241681	C₂	semidirect
11. C₄₇×#2981	C₂	semidirect
208. #2981	D₄₇	semidirect
256. C₄₇	#17989	semidirect

Maximal subgroups

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

subgroup	index
#20253963	2
#20252463	2
#20242252	2
#20242250	2
#20242217	2
#20242215	2
#20242149	2
#20241857	2
#20241856	2
#20241681	2
C₄₇×#2981	2
#17989	47