Subgroups — #26188295

Order 12032.

604 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253948	C₂	1	1	yes	maximal, characteristic
2	#20252454	C₂	1	1	yes	maximal, characteristic
3	#20242288	C₂	1	2	yes	maximal, complemented
4	#20242231	C₂	1	2	yes	maximal, complemented
5	#20242222	C₂	1	2	yes	maximal, complemented
6	#20242198	C₂	1	2	yes	maximal, complemented
7	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241809	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241804	C₂	1	1	yes	maximal, characteristic
10	#20241678	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689519	C₄	1	1	yes	characteristic
14	#15689497	C₄	1	1	yes	characteristic
15	#15689473	C₄	1	1	yes	characteristic
16	#15689471	C₄	1	1	yes	characteristic
17	#15689354	C₄	1	2	yes	—
18	#15689354	C₄	1	2	yes	—
19	C₄×#10625336	C₂²	1	2	yes	—
20	C₄×#10625336	C₂²	1	2	yes	—
21	#15689202	C₂²	1	2	yes	—
22	#15689200	—	2	1	no	—
23	C₈×D₁₈₈	C₂²	1	2	yes	—
24	#15689188	—	2	1	no	—
25	#15689176	C₂²	1	1	yes	characteristic
26	#15689088	—	2	2	no	—
27	C₄×#10625329	C₂²	1	1	yes	characteristic
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	#15688873	C₂²	1	1	yes	characteristic
32	#15688873	C₂²	1	1	yes	characteristic
33	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
34	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	#15688850	C₂²	1	2	yes	—
36	#15688850	C₂²	1	2	yes	—
37	#15688845	C₂²	1	2	yes	—
38	#15688844	C₂²	1	2	yes	—
39	C₄₇×#533	C₂²	1	1	yes	characteristic
40	C₄₇×#446	—	2	1	no	—
41	C₄₇×#446	C₂²	1	2	yes	—
42	C₈×Q₈×C₄₇	—	2	1	no	—
43	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
44	C₄₇×#433	—	2	2	no	—
45	C₄₇×#431	C₂²	1	1	yes	characteristic
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂×#10625336	C₂×C₄	1	2	yes	—
49	C₂×#10625336	C₂×C₄	1	2	yes	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₄₇	—	2	2	no	—
55	#13094024	C₂×C₄	1	1	yes	characteristic
56	#13094021	C₂×C₄	1	1	yes	characteristic
57	#13094012	—	2	1	no	—
58	#13093998	—	2	1	no	—
59	#13093998	C₂×C₄	1	2	yes	—
60	C₄×D₁₈₈	—	2	1	no	—
61	C₄×D₁₈₈	C₂³	1	2	yes	—
62	#13093955	C₂×C₄	1	2	yes	—
63	#13093955	C₂×C₄	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
66	#13093948	C₂×C₄	1	2	yes	—
67	#13093948	C₂×C₄	1	2	yes	—
68	#13093944	C₂×C₄	1	2	yes	—
69	#13093944	C₂×C₄	1	2	yes	—
70	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
71	(C₂×D₄₇)⋊C₈	—	2	2	no	—
72	(C₂×D₄₇)⋊C₈	—	2	2	no	—
73	#13093935	—	2	1	no	—
74	C₄×C₄₇⋊C₈	—	2	1	no	—
75	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
76	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
82	#125×C₄₇	—	2	1	no	—
83	C₂²⋊Q₈×C₄₇	—	2	1	no	—
84	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₄×Q₈×C₄₇	—	2	1	no	—
86	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
87	#117×C₄₇	—	2	1	no	—
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	—	2	2	no	—
90	C₄⋊C₈×C₄₇	—	2	2	no	—
91	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₂²⋊C₈×C₄₇	—	2	1	no	—
96	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
97	#97×C₄₇	—	2	2	no	—
98	C₄×C₈×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	2	no	—
107	#10625350	—	8	1	no	—
108	#10625350	—	8	1	no	—
109	C₂×D₁₈₈	—	2	1	no	—
110	C₂×D₁₈₈	—	2	1	no	—
111	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×Dic₉₄	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂²⋊C₄×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	#41	1	1	yes	characteristic
129	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
130	#10625336	—	2	4	no	—
131	#10625336	—	4	2	no	—
132	(C₂×D₄₇)⋊C₄	—	2	2	no	—
133	(C₂×D₄₇)⋊C₄	—	2	2	no	—
134	C₄⋊Dic₄₇	—	2	1	no	—
135	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
136	#10625329	—	4	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	4	1	no	—
142	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
146	#10625324	—	8	2	no	—
147	C₈×D₄₇	—	8	2	no	—
148	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	2	no	—
150	Q₈×C₄₇	—	2	2	no	—
151	Q₈×C₄₇	—	2	2	no	—
152	Q₈×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂²⋊D₄₇	—	8	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	D₁₈₈	—	2	2	no	—
169	D₁₈₈	—	2	2	no	—
170	D₁₈₈	—	4	2	no	—
171	D₁₈₈	—	8	1	no	—
172	C₄×D₄₇	—	4	2	no	—
173	C₄×D₄₇	—	4	2	no	—
174	Dic₉₄	—	8	1	no	—
175	C₈×C₄₇	—	2	2	no	—
176	C₈×C₄₇	—	2	2	no	—
177	C₈×C₄₇	—	4	1	no	—
178	C₈×C₄₇	—	4	1	no	—
179	C₄₇⋊C₈	—	2	1	no	—
180	C₄₇⋊C₈	—	2	1	no	—
181	C₄₇⋊C₈	—	2	1	no	—
182	C₄₇⋊C₈	—	4	2	no	—
183	C₄₇⋊C₈	—	4	1	no	—
184	C₄₇⋊C₈	—	4	1	no	—
185	C₄₇⋊C₈	#131	1	2	yes	—
186	#18089	—	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	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂×D₄₇	—	4	2	no	—
192	C₂×D₄₇	—	4	2	no	—
193	C₂×D₄₇	—	4	2	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	4	2	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	#444	1	2	yes	—
200	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
201	C₄×C₄₇	#568	1	1	yes	characteristic
202	C₄×C₄₇	#577	1	1	yes	characteristic
203	C₄×C₄₇	#577	1	1	yes	characteristic
204	Dic₄₇	—	4	2	no	—
205	#3167	—	47	1	no	—
206	#2986	D₄₇	1	1	yes	characteristic, complemented
207	#2979	—	47	1	no	—
208	#1592	—	47	2	no	—
209	#1583	—	47	2	no	—
210	#1582	—	47	2	no	—
211	SD₁₆⋊C₈	—	47	2	no	—
212	#1564	—	47	1	no	—
213	#1485	—	47	1	no	—
214	#1484	—	47	1	no	—
215	#1451	—	47	1	no	—
216	C₂×C₄₇	—	4	1	no	—
217	C₂×C₄₇	#2935	1	1	yes	characteristic
218	C₂×C₄₇	#2949	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
220	D₄₇	—	8	2	no	—
221	#533	C₂×D₄₇	1	1	yes	characteristic
222	#532	—	47	1	no	—
223	#498	—	47	1	no	—
224	#492	—	47	1	no	—
225	#487	—	47	1	no	—
226	#486	—	47	1	no	—
227	#465	—	47	2	no	—
228	#465	—	47	2	no	—
229	#446	—	2	1	no	—
230	#446	C₂×D₄₇	1	2	yes	—
231	C₈×Q₈	—	2	1	no	—
232	C₈×Q₈	C₂×D₄₇	1	2	yes	—
233	C₄×SD₁₆	—	47	2	no	—
234	C₄×SD₁₆	—	47	2	no	—
235	#436	—	47	2	no	—
236	#436	—	94	1	no	—
237	C₈×D₄	—	47	2	no	—
238	C₈×D₄	—	94	1	no	—
239	#433	—	2	2	no	—
240	#431	—	47	1	no	—
241	#431	C₂×D₄₇	1	1	yes	characteristic
242	#431	C₂×D₄₇	1	1	yes	characteristic
243	#408	—	94	2	no	—
244	C₄×M₁₆	—	47	1	no	—
245	C₂×C₄×C₈	—	47	1	no	—
246	#335	—	47	1	no	—
247	#335	—	47	1	no	—
248	#334	—	47	1	no	—
249	#334	—	47	1	no	—
250	Q₈⋊C₈	—	47	2	no	—
251	Q₈⋊C₈	—	47	2	no	—
252	D₄⋊C₈	—	47	2	no	—
253	D₄⋊C₈	—	47	2	no	—
254	#322	—	47	2	no	—
255	#322	—	47	2	no	—
256	C₄₇	#18089	1	1	yes	characteristic, complemented, Sylow
257	C₂×#41	—	94	1	no	—
258	C₂×SD₁₆	—	47	2	no	—
259	C₂×SD₁₆	—	47	2	no	—
260	C₂×M₁₆	—	94	1	no	—
261	C₂×M₁₆	—	94	2	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₂²×C₈	—	94	2	no	—
265	C₄⋊Q₈	—	47	1	no	—
266	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
267	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
268	#127	—	47	1	no	—
269	#125	—	2	1	no	—
270	#124	—	94	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
273	#121	—	47	2	no	—
274	#121	—	94	1	no	—
275	C₄×Q₈	—	2	1	no	—
276	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
277	C₄×D₄	—	47	2	no	—
278	C₄×D₄	—	94	1	no	—
279	#117	—	2	1	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#106	—	47	2	no	—
282	#106	—	47	2	no	—
283	C₄⋊C₈	—	2	2	no	—
284	C₄⋊C₈	—	2	2	no	—
285	C₄⋊C₈	—	47	1	no	—
286	C₄⋊C₈	—	47	1	no	—
287	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
288	C₄⋊C₈	C₂²⋊D₄₇	1	1	yes	characteristic
289	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
291	#103	—	47	2	no	—
292	#103	—	47	2	no	—
293	#102	—	47	2	no	—
294	#102	—	47	2	no	—
295	C₂²⋊C₈	—	2	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	2	no	—
301	#97	—	94	1	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	2	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	—	47	2	no	—
309	C₄×C₈	—	94	1	no	—
310	C₄×C₈	C₂²×D₄₇	1	2	yes	—
311	#41	—	376	1	no	—
312	#41	—	376	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	94	1	no	—
315	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
316	C₂×D₄	—	47	2	no	—
317	C₂×D₄	—	94	2	no	—
318	C₂×D₄	—	94	1	no	—
319	C₂×D₄	—	94	1	no	—
320	C₂²×C₄	—	94	2	no	—
321	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	#10625350	1	1	yes	characteristic
323	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	SD₁₆	—	94	4	no	—
325	SD₁₆	—	188	2	no	—
326	M₁₆	—	376	2	no	—
327	M₁₆	—	188	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	47	1	no	—
331	C₂×C₈	—	47	1	no	—
332	C₂×C₈	—	47	1	no	—
333	C₂×C₈	—	47	1	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	376	2	no	—
339	C₂×C₈	—	188	1	no	—
340	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
341	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	47	2	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₄²	—	2	2	no	—
354	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
355	C₄²	#10625350	1	1	yes	characteristic
356	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₄²	C₂³×D₄₇	1	1	yes	characteristic
358	C₂³	—	94	2	no	—
359	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
360	Q₈	—	2	2	no	—
361	Q₈	—	2	2	no	—
362	Q₈	—	4	2	no	—
363	Q₈	—	376	1	no	—
364	D₄	—	94	2	no	—
365	D₄	—	94	2	no	—
366	D₄	—	376	1	no	—
367	D₄	—	376	2	no	—
368	D₄	—	188	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	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	—	94	2	no	—
377	C₂×C₄	—	188	2	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
385	C₈	—	2	2	no	—
386	C₈	—	2	2	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	1	no	—
389	C₈	—	47	2	no	—
390	C₈	—	94	1	no	—
391	C₈	—	94	1	no	—
392	C₈	—	94	1	no	—
393	C₈	—	188	2	no	—
394	C₈	—	188	1	no	—
395	C₈	—	188	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	188	2	no	—
400	C₂²	—	188	2	no	—
401	C₂²	—	188	2	no	—
402	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	—	2	1	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	188	2	no	—
409	C₄	#15689243	1	2	yes	—
410	C₄	#131×D₄₇	1	1	yes	characteristic
411	C₄	#15689888	1	1	yes	characteristic
412	C₄	#15689931	1	1	yes	characteristic
413	C₄	#15689931	1	1	yes	characteristic
414	C₂	—	4	1	no	—
415	C₂	—	376	2	no	—
416	C₂	#20252130	1	1	yes	characteristic
417	C₂	#20252247	1	1	yes	characteristic
418	C₂	C₂×#15689243	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×#2986	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689673	C₂²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2986	D₄₇
hypocenter	C₄₇	#18089
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #2986

Complements

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

N	H ≅ G/N	type
3. #20242288	C₂	semidirect
4. #20242231	C₂	semidirect
5. #20242222	C₂	semidirect
6. #20242198	C₂	semidirect
7. #20242134	C₂	semidirect
8. #20241809	C₂	semidirect
10. #20241678	C₂	semidirect
11. C₄₇×#2986	C₂	semidirect
206. #2986	D₄₇	semidirect
256. C₄₇	#18089	semidirect

Maximal subgroups

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

subgroup	index
#20253948	2
#20252454	2
#20242288	2
#20242231	2
#20242222	2
#20242198	2
#20242134	2
#20241809	2
#20241804	2
#20241678	2
C₄₇×#2986	2
#18089	47