Subgroups — #26185403

Order 12032.

602 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252501	C₂	1	1	yes	maximal, characteristic
2	#20252497	C₂	1	1	yes	maximal, characteristic
3	#20252033	C₂	1	1	yes	maximal, characteristic
4	#20242175	C₂	1	2	yes	maximal, complemented
5	#20242172	C₂	1	2	yes	maximal, complemented
6	#20242167	C₂	1	2	yes	maximal, complemented
7	#20242157	C₂	1	2	yes	maximal, complemented
8	#20242140	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689253	—	2	1	no	—
14	#15689247	—	2	1	no	—
15	#15689202	—	2	1	no	—
16	#15689191	—	2	2	no	—
17	#15689188	—	2	1	no	—
18	C₈×C₂²⋊D₄₇	—	2	2	no	—
19	#15689185	C₄	1	2	yes	—
20	#15689185	C₄	1	2	yes	—
21	#15689179	C₂²	1	2	yes	—
22	#15689176	C₂²	1	1	yes	characteristic
23	#15689175	C₂²	1	2	yes	—
24	#15689174	C₂²	1	2	yes	—
25	#15689174	C₂²	1	2	yes	—
26	#15689151	C₄	1	1	yes	characteristic
27	#15689151	C₄	1	1	yes	characteristic
28	#15689145	C₂²	1	2	yes	—
29	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
31	#15689091	C₄	1	1	yes	characteristic
32	#15689091	C₄	1	1	yes	characteristic
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688876	C₂²	1	2	yes	—
35	#15688875	C₂²	1	1	yes	characteristic
36	#15688875	C₂²	1	1	yes	characteristic
37	#15688874	C₂²	1	2	yes	—
38	#15688873	C₂²	1	2	yes	—
39	#15688873	C₂²	1	2	yes	—
40	#15688873	C₂²	1	1	yes	characteristic
41	#15688873	C₂²	1	1	yes	characteristic
42	C₄₇×#431	C₂²	1	1	yes	characteristic
43	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#335	C₂²	1	2	yes	—
46	C₄₇×#334	C₂²	1	2	yes	—
47	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625324	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	—	2	1	no	—
50	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₄₇	—	2	2	no	—
53	C₄×Dic₉₄	D₄	1	1	yes	characteristic
54	C₄×Dic₉₄	Q₈	1	1	yes	characteristic
55	C₄×D₁₈₈	D₄	1	1	yes	characteristic
56	C₄×D₁₈₈	Q₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
58	C₄×C₂²⋊D₄₇	Q₈	1	2	yes	—
59	#13093983	C₂×C₄	1	1	yes	characteristic
60	#13093981	C₂×C₄	1	2	yes	—
61	C₄²×D₄₇	C₂³	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
64	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
66	Dic₄₇⋊C₈	—	2	2	no	—
67	Dic₄₇⋊C₈	—	2	2	no	—
68	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
69	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
71	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
72	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
73	(C₂×D₄₇)⋊C₈	—	2	2	no	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
76	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
77	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
78	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
79	#13093934	—	2	2	no	—
80	C₄×C₄₇⋊C₈	—	2	1	no	—
81	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
83	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₈×Dic₄₇	—	2	2	no	—
86	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	1	no	—
91	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
93	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₇	—	2	1	no	—
95	#97×C₄₇	C₂×C₄	1	2	yes	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	C₂³	1	2	yes	—
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	—	2	2	no	—
103	#10625350	—	2	2	no	—
104	C₂×D₁₈₈	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
107	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
108	C₂×Dic₉₄	C₄⋊C₄	1	1	yes	characteristic
109	M₁₆×C₄₇	—	2	2	no	—
110	M₁₆×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	8	1	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
120	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂²⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
122	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
123	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	2	yes	—
124	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
125	C₄⋊Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
126	Dic₄₇⋊C₄	C₄⋊C₄	1	2	yes	—
127	Dic₄₇⋊C₄	C₄⋊C₄	1	2	yes	—
128	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
129	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
130	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	8	1	no	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
141	#10625324	—	8	2	no	—
142	C₈×D₄₇	—	8	2	no	—
143	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
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	#131	1	2	yes	—
152	C₂×C₄×C₄₇	#131	1	2	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂²⋊D₄₇	—	2	4	no	—
157	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
159	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
160	D₁₈₈	—	2	2	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	4	2	no	—
166	Dic₉₄	—	2	2	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₈×C₄₇	—	4	2	no	—
170	C₈×C₄₇	—	4	1	no	—
171	C₈×C₄₇	—	4	1	no	—
172	C₄₇⋊C₈	—	2	1	no	—
173	C₄₇⋊C₈	—	2	1	no	—
174	C₄₇⋊C₈	—	2	1	no	—
175	C₄₇⋊C₈	—	2	1	no	—
176	C₄₇⋊C₈	—	4	1	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	—	4	1	no	—
179	#17811	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	#424	1	2	yes	—
183	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂×D₄₇	—	2	2	no	—
185	C₂×D₄₇	—	2	2	no	—
186	C₂×D₄₇	—	2	2	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	#424	1	2	yes	—
191	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
192	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
193	C₄×C₄₇	#577	1	1	yes	characteristic
194	C₄×C₄₇	#577	1	1	yes	characteristic
195	Dic₄₇	—	2	2	no	—
196	Dic₄₇	—	2	2	no	—
197	Dic₄₇	—	2	2	no	—
198	#2989	—	47	1	no	—
199	#2988	—	47	1	no	—
200	#2922	—	47	1	no	—
201	#1574	—	47	2	no	—
202	#1573	—	47	2	no	—
203	#1572	—	47	2	no	—
204	#1570	—	47	2	no	—
205	#1565	—	47	1	no	—
206	#1565	D₄₇	1	1	yes	characteristic, complemented
207	#1564	—	47	1	no	—
208	C₂×#334	—	47	1	no	—
209	C₂×C₄₇	—	2	2	no	—
210	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
211	C₂×C₄₇	#2912	1	1	yes	characteristic
212	C₂×C₄₇	#2916	1	1	yes	characteristic
213	D₄₇	—	4	2	no	—
214	C₄×#41	—	47	1	no	—
215	#446	—	94	1	no	—
216	C₈×Q₈	—	94	1	no	—
217	#436	—	94	1	no	—
218	#435	—	94	2	no	—
219	C₈×D₄	—	94	1	no	—
220	C₈×D₄	—	94	2	no	—
221	#433	—	47	2	no	—
222	#433	—	47	2	no	—
223	#432	—	47	2	no	—
224	#431	—	47	2	no	—
225	#431	—	47	2	no	—
226	#431	—	47	1	no	—
227	#431	—	47	2	no	—
228	#431	C₂×D₄₇	1	1	yes	characteristic
229	#424	—	47	1	no	—
230	#424	—	47	1	no	—
231	#423	—	47	2	no	—
232	C₂×C₄⋊C₈	—	47	1	no	—
233	C₂×C₄⋊C₈	—	47	2	no	—
234	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
235	#408	—	47	1	no	—
236	#408	—	47	1	no	—
237	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
238	C₂×C₄×C₈	—	47	1	no	—
239	#335	—	47	1	no	—
240	#335	—	47	1	no	—
241	#335	—	47	2	no	—
242	#335	C₂×D₄₇	1	2	yes	—
243	#334	—	47	2	no	—
244	#334	—	47	2	no	—
245	#334	—	47	1	no	—
246	#334	—	47	1	no	—
247	#334	—	47	2	no	—
248	#334	C₂×D₄₇	1	2	yes	—
249	C₄₇	#17811	1	1	yes	characteristic, complemented, Sylow
250	C₂×#41	—	47	1	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
253	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
254	C₂²×C₈	—	2	1	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₂²×C₈	—	94	1	no	—
259	C₄×Q₈	—	47	1	no	—
260	C₄×Q₈	—	47	1	no	—
261	C₄×D₄	—	47	2	no	—
262	C₄×D₄	—	47	2	no	—
263	C₄×D₄	—	47	1	no	—
264	C₄×D₄	—	47	1	no	—
265	#117	—	47	1	no	—
266	#117	—	47	2	no	—
267	C₂×C₄²	—	47	2	no	—
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	47	2	no	—
271	C₄⋊C₈	—	47	2	no	—
272	C₄⋊C₈	—	47	2	no	—
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	47	1	no	—
275	C₄⋊C₈	—	47	2	no	—
276	C₄⋊C₈	—	47	1	no	—
277	C₄⋊C₈	—	94	2	no	—
278	C₄⋊C₈	—	94	2	no	—
279	C₄⋊C₈	—	94	1	no	—
280	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
281	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
282	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
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	—	47	2	no	—
288	C₂²⋊C₈	—	94	2	no	—
289	C₂²⋊C₈	—	94	2	no	—
290	C₂²⋊C₈	—	94	1	no	—
291	#97	—	94	2	no	—
292	#97	C₄×D₄₇	1	2	yes	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	47	1	no	—
295	C₄×C₈	—	47	1	no	—
296	C₄×C₈	—	47	1	no	—
297	C₄×C₈	—	47	1	no	—
298	C₄×C₈	—	94	2	no	—
299	C₄×C₈	—	94	1	no	—
300	C₄×C₈	C₂²×D₄₇	1	2	yes	—
301	#41	—	94	2	no	—
302	#41	—	94	2	no	—
303	C₂×Q₈	—	47	1	no	—
304	C₂×D₄	—	47	2	no	—
305	C₂×D₄	—	47	1	no	—
306	C₂²×C₄	—	47	2	no	—
307	C₂²×C₄	—	47	2	no	—
308	C₂²×C₄	—	47	2	no	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
312	M₁₆	—	2	2	no	—
313	M₁₆	—	2	2	no	—
314	M₁₆	—	376	2	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	8	1	no	—
319	C₂×C₈	—	47	1	no	—
320	C₂×C₈	—	47	1	no	—
321	C₂×C₈	—	47	1	no	—
322	C₂×C₈	—	47	1	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	94	1	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	376	2	no	—
329	C₂×C₈	—	376	1	no	—
330	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
331	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
332	C₄⋊C₄	—	47	2	no	—
333	C₄⋊C₄	—	47	2	no	—
334	C₄⋊C₄	—	47	1	no	—
335	C₄⋊C₄	—	47	1	no	—
336	C₂²⋊C₄	—	47	2	no	—
337	C₂²⋊C₄	—	47	2	no	—
338	C₂²⋊C₄	—	47	2	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	47	2	no	—
342	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
343	C₄²	D₄×D₄₇	1	1	yes	characteristic
344	C₄²	Q₈×D₄₇	1	1	yes	characteristic
345	C₄²	C₂³×D₄₇	1	1	yes	characteristic
346	C₂³	—	47	2	no	—
347	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
348	Q₈	—	94	2	no	—
349	D₄	—	94	4	no	—
350	D₄	—	94	2	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	4	1	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	#13094030	1	2	yes	—
366	C₂×C₄	#13094032	1	2	yes	—
367	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	2	no	—
375	C₈	—	94	1	no	—
376	C₈	—	94	1	no	—
377	C₈	—	94	1	no	—
378	C₈	—	94	1	no	—
379	C₈	—	188	1	no	—
380	C₈	—	188	2	no	—
381	C₈	—	188	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	94	2	no	—
385	C₂²	—	94	2	no	—
386	C₂²	—	94	2	no	—
387	C₂²	#15689148	1	2	yes	—
388	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	94	2	no	—
393	C₄	—	94	2	no	—
394	C₄	—	94	2	no	—
395	C₄	#15689148	1	2	yes	—
396	C₄	C₂×#13094030	1	1	yes	characteristic
397	C₄	C₂×#13094032	1	1	yes	characteristic
398	C₄	#15689932	1	1	yes	characteristic
399	C₄	#15689933	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	188	2	no	—
402	C₂	C₂×#15689148	1	1	yes	characteristic
403	C₂	#20251982	1	1	yes	characteristic
404	C₂	#20251998	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×#1565	C₂
socle	C₂²×C₄₇	C₂²×C₄⋊C₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1565	D₄₇
hypocenter	C₄₇	#17811
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
4. #20242175	C₂	semidirect
5. #20242172	C₂	semidirect
6. #20242167	C₂	semidirect
7. #20242157	C₂	semidirect
8. #20242140	C₂	semidirect
9. #20242134	C₂	semidirect
10. C₂×#15688873	C₂	semidirect
11. C₄₇×#1565	C₂	semidirect
206. #1565	D₄₇	semidirect
249. C₄₇	#17811	semidirect

Maximal subgroups

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

subgroup	index
#20252501	2
#20252497	2
#20252033	2
#20242175	2
#20242172	2
#20242167	2
#20242157	2
#20242140	2
#20242134	2
C₂×#15688873	2
C₄₇×#1565	2
#17811	47