Subgroups — #26182334

Order 12032.

940 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252473	C₂	1	1	yes	maximal, characteristic, complemented
2	#20252469	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241757	C₂	1	4	yes	maximal, complemented
4	#20241740	C₂	1	4	yes	maximal, complemented
5	#20241709	C₂	1	2	yes	maximal, complemented
6	#20241702	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#542	C₂	1	1	yes	maximal, characteristic
8	#15689254	—	2	4	no	—
9	Q₈×C₄₇⋊C₈	—	2	4	no	—
10	#15689180	C₂²	1	4	yes	—
11	#15689176	C₂²	1	2	yes	—
12	#15689176	C₂²	1	2	yes	—
13	#15689176	C₂²	1	4	yes	—
14	#15688849	C₂²	1	4	yes	—
15	#15688847	C₂²	1	4	yes	—
16	#15688847	C₂²	1	8	yes	—
17	C₄₇×#542	—	2	4	no	—
18	C₄₇×#542	—	2	4	no	—
19	C₂×C₄⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
20	C₂×#126×C₄₇	C₂²	1	2	yes	—
21	C₂×#124×C₄₇	C₄	1	1	yes	characteristic
22	C₂×#124×C₄₇	C₂²	1	2	yes	—
23	C₂×#123×C₄₇	C₄	1	2	yes	—
24	C₂×C₂²⋊Q₈×C₄₇	C₄	1	2	yes	—
25	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
26	C₂×#121×C₄₇	C₄	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
31	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
32	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
33	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
34	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
35	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
36	#13093935	—	2	4	no	—
37	C₄×C₄₇⋊C₈	—	2	2	no	—
38	C₄×C₄₇⋊C₈	—	2	4	no	—
39	C₄×C₄₇⋊C₈	—	2	2	no	—
40	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
42	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
46	C₄⋊Q₈×C₄₇	—	2	4	no	—
47	#126×C₄₇	—	2	4	no	—
48	#126×C₄₇	—	2	4	no	—
49	#124×C₄₇	—	2	4	no	—
50	#124×C₄₇	—	2	4	no	—
51	#124×C₄₇	—	2	4	no	—
52	#123×C₄₇	—	2	8	no	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	8	no	—
55	#121×C₄₇	—	2	4	no	—
56	C₄×Q₈×C₄₇	D₄	1	4	yes	—
57	C₄×Q₈×C₄₇	D₄	1	4	yes	—
58	C₄×D₄×C₄₇	—	2	2	no	—
59	C₄×D₄×C₄₇	—	2	2	no	—
60	#117×C₄₇	—	2	2	no	—
61	#117×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
73	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
79	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
81	C₂×Q₈×C₄₇	—	2	4	no	—
82	C₂×Q₈×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	8	2	no	—
84	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	8	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	8	2	no	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	2	1	no	—
107	C₄⋊C₄×C₄₇	—	2	1	no	—
108	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
109	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
110	C₂²⋊C₄×C₄₇	—	2	2	no	—
111	C₂²⋊C₄×C₄₇	—	2	4	no	—
112	C₂²⋊C₄×C₄₇	—	2	4	no	—
113	C₂²⋊C₄×C₄₇	—	2	4	no	—
114	C₂²⋊C₄×C₄₇	—	2	4	no	—
115	C₂²⋊C₄×C₄₇	—	2	1	no	—
116	C₂²⋊C₄×C₄₇	—	2	1	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	C₂×D₄	1	2	yes	—
121	C₄²×C₄₇	C₂×D₄	1	2	yes	—
122	C₄²×C₄₇	C₂×D₄	1	4	yes	—
123	C₄²×C₄₇	C₂×D₄	1	4	yes	—
124	C₂×C₄₇⋊C₈	—	2	4	no	—
125	C₂×C₄₇⋊C₈	—	2	4	no	—
126	C₂³×C₄₇	—	2	1	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	4	1	no	—
132	C₂³×C₄₇	—	4	1	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	2	8	no	—
136	Q₈×C₄₇	—	8	4	no	—
137	D₄×C₄₇	—	4	4	no	—
138	D₄×C₄₇	—	8	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	8	4	no	—
153	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	#131	1	4	yes	—
158	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₄₇⋊C₈	—	4	4	no	—
161	C₄₇⋊C₈	—	4	4	no	—
162	#17390	—	47	1	no	maximal, Sylow
163	C₂²×C₄₇	—	2	1	no	—
164	C₂²×C₄₇	—	2	1	no	—
165	C₂²×C₄₇	—	4	1	no	—
166	C₂²×C₄₇	—	4	2	no	—
167	C₂²×C₄₇	—	4	1	no	—
168	C₂²×C₄₇	—	4	2	no	—
169	C₂²×C₄₇	—	4	2	no	—
170	C₂²×C₄₇	—	4	1	no	—
171	C₂²×C₄₇	—	8	2	no	—
172	C₂²×C₄₇	—	8	4	no	—
173	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×#131	1	2	yes	—
175	C₄×C₄₇	—	2	4	no	—
176	C₄×C₄₇	—	2	1	no	—
177	C₄×C₄₇	—	2	1	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	4	1	no	—
181	C₄×C₄₇	—	4	1	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	4	1	no	—
184	C₄×C₄₇	#408	1	4	yes	—
185	C₂×#542	D₄₇	1	1	yes	characteristic
186	#2983	—	47	1	no	—
187	#2982	—	47	1	no	—
188	#1473	—	47	4	no	—
189	#1469	—	47	4	no	—
190	#1460	—	47	2	no	—
191	#1458	—	47	2	no	—
192	C₂×C₄₇	—	2	2	no	—
193	C₂×C₄₇	—	8	1	no	—
194	C₂×C₄₇	—	8	2	no	—
195	C₂×C₄₇	C₂×#408	1	1	yes	characteristic
196	C₂×C₄₇	#2884	1	1	yes	characteristic
197	C₂×C₄₇	#2888	1	1	yes	characteristic
198	#542	—	2	4	no	—
199	#542	—	2	4	no	—
200	C₂×C₄⋊Q₈	Dic₄₇	1	1	yes	characteristic
201	C₂×#126	C₂×D₄₇	1	2	yes	—
202	C₂×#124	Dic₄₇	1	1	yes	characteristic
203	C₂×#124	C₂×D₄₇	1	2	yes	—
204	C₂×#123	Dic₄₇	1	2	yes	—
205	C₂×C₂²⋊Q₈	Dic₄₇	1	2	yes	—
206	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
207	C₂×#121	Dic₄₇	1	1	yes	characteristic
208	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
209	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
210	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
211	#446	—	94	4	no	—
212	C₈×Q₈	—	94	4	no	—
213	#432	—	47	4	no	—
214	#431	—	47	2	no	—
215	#431	—	47	4	no	—
216	#431	—	47	2	no	—
217	#324	—	47	4	no	—
218	#323	—	47	4	no	—
219	#323	—	47	8	no	—
220	C₄₇	#17390	1	1	yes	characteristic, complemented, Sylow
221	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
222	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
223	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
224	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
225	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
226	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
227	C₄⋊Q₈	—	2	4	no	—
228	#126	—	2	4	no	—
229	#126	—	2	4	no	—
230	#124	—	2	4	no	—
231	#124	—	2	4	no	—
232	#124	—	2	4	no	—
233	#123	—	2	8	no	—
234	C₂²⋊Q₈	—	2	4	no	—
235	C₂²⋊Q₈	—	2	8	no	—
236	#121	—	2	4	no	—
237	C₄×Q₈	C₂²⋊D₄₇	1	4	yes	—
238	C₄×Q₈	C₂²⋊D₄₇	1	4	yes	—
239	C₄×D₄	—	2	2	no	—
240	C₄×D₄	—	2	2	no	—
241	#117	—	2	2	no	—
242	#117	—	2	2	no	—
243	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
244	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
246	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
248	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
249	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
250	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
251	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
252	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
253	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
254	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
255	C₂×C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
256	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
257	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
260	C₄⋊C₈	—	94	2	no	—
261	C₄⋊C₈	—	94	4	no	—
262	C₄⋊C₈	—	94	2	no	—
263	C₄⋊C₈	—	94	4	no	—
264	C₂²⋊C₈	—	47	4	no	—
265	C₂²⋊C₈	—	47	4	no	—
266	#97	—	94	4	no	—
267	C₄×C₈	—	94	2	no	—
268	C₄×C₈	—	94	4	no	—
269	C₄×C₈	—	94	2	no	—
270	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
271	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
272	C₂×Q₈	—	2	4	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	8	2	no	—
275	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	8	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	2	4	no	—
283	C₂²×C₄	—	8	2	no	—
284	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
286	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
289	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
291	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
293	C₂×C₈	—	94	4	no	—
294	C₂×C₈	—	94	4	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	2	1	no	—
301	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
302	C₄⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
303	C₂²⋊C₄	—	2	2	no	—
304	C₂²⋊C₄	—	2	4	no	—
305	C₂²⋊C₄	—	2	4	no	—
306	C₂²⋊C₄	—	2	4	no	—
307	C₂²⋊C₄	—	2	4	no	—
308	C₂²⋊C₄	—	2	1	no	—
309	C₂²⋊C₄	—	2	1	no	—
310	C₂²⋊C₄	—	2	2	no	—
311	C₂²⋊C₄	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
314	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
315	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
316	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	—	2	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	1	no	—
323	C₂³	—	4	1	no	—
324	C₂³	—	4	2	no	—
325	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
326	Q₈	—	2	8	no	—
327	Q₈	—	8	4	no	—
328	D₄	—	4	4	no	—
329	D₄	—	8	4	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	8	4	no	—
344	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
345	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
346	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
347	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
348	C₂×C₄	#13094031	1	4	yes	—
349	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
350	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
351	C₈	—	188	4	no	—
352	C₈	—	188	4	no	—
353	C₂²	—	2	1	no	—
354	C₂²	—	2	1	no	—
355	C₂²	—	4	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	2	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	1	no	—
361	C₂²	—	8	2	no	—
362	C₂²	—	8	4	no	—
363	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
364	C₂²	C₂×#13094031	1	2	yes	—
365	C₄	—	2	4	no	—
366	C₄	—	2	1	no	—
367	C₄	—	2	1	no	—
368	C₄	—	2	2	no	—
369	C₄	—	2	4	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	1	no	—
374	C₄	#15689090	1	4	yes	—
375	C₂	—	2	2	no	—
376	C₂	—	8	1	no	—
377	C₂	—	8	2	no	—
378	C₂	C₂×#15689090	1	1	yes	characteristic
379	C₂	#20251852	1	1	yes	characteristic
380	C₂	#20251867	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂³×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#542	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
prime radical	C₂×#121×C₄₇	C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#542	D₄₇
hypocenter	C₄₇	#17390
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄×Q₈ ◁ C₂×#542

Complements

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

N	H ≅ G/N	type
1. #20252473	C₂	semidirect
2. #20252469	C₂	semidirect
3. #20241757	C₂	semidirect
4. #20241740	C₂	semidirect
5. #20241709	C₂	semidirect
6. #20241702	C₂	semidirect
220. C₄₇	#17390	semidirect

Maximal subgroups

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

subgroup	index
#20252473	2
#20252469	2
#20241757	2
#20241740	2
#20241709	2
#20241702	2
C₂×C₄₇×#542	2
#17390	47