Subgroups — #20257817

Order 6016.

1050 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689872	C₂	1	2	yes	maximal, complemented
2	#15689863	C₂	1	2	yes	maximal, complemented
3	#15689839	C₂	1	2	yes	maximal, complemented
4	#15689817	C₂	1	2	yes	maximal, complemented
5	#15689807	C₂	1	2	yes	maximal, complemented
6	#15689801	C₂	1	2	yes	maximal, complemented
7	#15689784	C₂	1	2	yes	maximal, complemented
8	#15689764	C₂	1	2	yes	maximal, complemented
9	#15689725	C₂	1	4	yes	maximal, complemented
10	#15689707	C₂	1	4	yes	maximal, complemented
11	#15689703	C₂	1	2	yes	maximal, complemented
12	#15689687	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689669	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689659	C₂	1	2	yes	maximal, complemented
15	C₄₇×#536	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10625354	C₂²	1	2	yes	—
17	C₂×#10625350	C₂²	1	1	yes	characteristic, complemented
18	C₂²×D₁₈₈	C₂²	1	1	yes	characteristic
19	#13094022	C₂²	1	1	yes	characteristic, complemented
20	#13094020	C₂²	1	1	yes	characteristic
21	#13094020	C₂²	1	2	yes	—
22	#13094019	C₂²	1	4	yes	complemented
23	#13094018	C₂²	1	4	yes	complemented
24	#13094017	C₂²	1	4	yes	—
25	#13094015	C₂²	1	2	yes	complemented
26	#13094014	C₂²	1	4	yes	complemented
27	#13094013	C₂²	1	2	yes	—
28	#13094013	C₂²	1	2	yes	—
29	#13094013	C₂²	1	4	yes	complemented
30	#13094013	C₂²	1	1	yes	characteristic, complemented
31	#13094011	C₂²	1	1	yes	characteristic
32	#13094009	C₂²	1	4	yes	—
33	#13094008	C₂²	1	4	yes	complemented
34	#13094006	C₂²	1	4	yes	—
35	#13094006	C₂²	1	4	yes	complemented
36	#13094002	C₂²	1	4	yes	complemented
37	#13094000	C₂²	1	2	yes	complemented
38	#13094000	C₂²	1	4	yes	complemented
39	#13093999	C₂²	1	2	yes	—
40	#13093999	C₂²	1	4	yes	—
41	#13093999	C₂²	1	4	yes	complemented
42	#13093998	C₂²	1	2	yes	—
43	#13093998	C₂²	1	2	yes	—
44	#13093998	C₂²	1	4	yes	complemented
45	#13093997	C₂²	1	4	yes	complemented
46	#13093997	C₂²	1	4	yes	complemented
47	#13093997	C₂²	1	4	yes	complemented
48	#13093996	C₂²	1	2	yes	—
49	#13093996	C₂²	1	2	yes	complemented
50	#13093994	C₂²	1	4	yes	—
51	#13093992	C₂²	1	2	yes	—
52	#13093992	C₂²	1	2	yes	—
53	Q₈×Dic₄₇	C₂²	1	2	yes	complemented
54	C₄×D₁₈₈	C₂²	1	4	yes	complemented
55	#13093986	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
57	C₄×C₂²⋊D₄₇	C₂²	1	4	yes	complemented
58	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
59	(C₂²⋊D₄₇)⋊C₄	C₂²	1	4	yes	complemented
60	#13093983	C₂²	1	1	yes	characteristic
61	#13093982	C₂²	1	4	yes	complemented
62	#13093982	C₂²	1	4	yes	complemented
63	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
64	C₂²⋊C₄×D₄₇	C₂²	1	4	yes	—
65	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
66	C₂×#41×C₄₇	C₂²	1	1	yes	characteristic
67	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
68	C₄⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
69	#124×C₄₇	C₂²	1	2	yes	—
70	#123×C₄₇	C₂²	1	2	yes	—
71	#123×C₄₇	C₂²	1	2	yes	complemented
72	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
73	C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	complemented
74	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₂³×D₄₇	C₂³	1	2	yes	—
76	#41×C₄₇	—	4	2	no	—
77	C₂×Q₈×C₄₇	—	4	2	no	—
78	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
79	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
80	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₄₇	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
93	C₂²×Dic₄₇	C₂³	1	2	yes	—
94	#10625354	—	4	4	no	—
95	#10625350	—	4	2	no	—
96	C₂×D₁₈₈	—	4	2	no	—
97	C₂×D₁₈₈	C₂³	1	2	yes	—
98	C₂×D₁₈₈	C₂³	1	4	yes	—
99	C₂×D₁₈₈	C₂³	1	4	yes	—
100	C₂×D₁₈₈	C₂³	1	2	yes	—
101	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₂³	1	2	yes	—
103	C₂×C₄×D₄₇	C₂³	1	4	yes	—
104	C₂×C₄×D₄₇	C₂³	1	4	yes	—
105	C₂×C₄×D₄₇	C₂³	1	4	yes	—
106	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
107	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
110	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
112	C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
113	C₄²×C₄₇	C₂³	1	2	yes	—
114	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
115	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
116	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
117	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
118	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
120	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
124	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₄₇)⋊C₄	C₂³	1	4	yes	—
126	C₄⋊Dic₄₇	C₂³	1	2	yes	—
127	C₄⋊Dic₄₇	C₂³	1	4	yes	—
128	C₄⋊Dic₄₇	C₂³	1	4	yes	—
129	Dic₄₇⋊C₄	C₂³	1	4	yes	—
130	Dic₄₇⋊C₄	C₂³	1	4	yes	—
131	Dic₄₇⋊C₄	C₂³	1	2	yes	—
132	Dic₄₇⋊C₄	C₂³	1	2	yes	—
133	Dic₄₇⋊C₄	C₂³	1	4	yes	—
134	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
135	C₄×Dic₄₇	C₂³	1	2	yes	—
136	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
137	C₄×Dic₄₇	C₂³	1	2	yes	—
138	C₄×Dic₄₇	C₂³	1	4	yes	—
139	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
140	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
141	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂²×D₄₇	—	4	2	no	—
143	C₂²×D₄₇	—	4	4	no	—
144	C₂²×D₄₇	C₂⁴	1	4	yes	—
145	C₂²×D₄₇	C₂⁴	1	2	yes	—
146	Q₈×C₄₇	—	2	4	no	—
147	Q₈×C₄₇	—	4	2	no	—
148	Q₈×C₄₇	—	4	1	no	—
149	D₄×C₄₇	—	4	1	no	—
150	D₄×C₄₇	—	4	1	no	—
151	D₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
159	C₂×C₄×C₄₇	C₂⁴	1	4	yes	—
160	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
162	C₂²⋊D₄₇	—	4	2	no	—
163	C₂²⋊D₄₇	—	4	4	no	—
164	C₂²⋊D₄₇	—	4	4	no	—
165	C₂²⋊D₄₇	—	4	2	no	—
166	C₂²⋊D₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	C₂⁴	1	2	yes	—
169	C₂×Dic₄₇	C₂⁴	1	2	yes	—
170	C₂×Dic₄₇	C₂⁴	1	4	yes	—
171	C₂×Dic₄₇	C₂⁴	1	2	yes	—
172	D₁₈₈	—	2	4	no	—
173	D₁₈₈	—	4	2	no	—
174	D₁₈₈	—	4	4	no	—
175	D₁₈₈	—	4	1	no	—
176	D₁₈₈	—	4	4	no	—
177	C₄×D₄₇	—	2	4	no	—
178	C₄×D₄₇	—	4	4	no	—
179	C₄×D₄₇	—	4	4	no	—
180	C₄×D₄₇	—	4	4	no	—
181	Dic₉₄	—	4	1	no	—
182	C₂²×C₄₇	—	2	1	no	—
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
189	C₂×D₄₇	—	2	2	no	—
190	C₂×D₄₇	—	2	4	no	—
191	C₂×D₄₇	—	2	2	no	—
192	C₂×D₄₇	—	2	4	no	—
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	4	no	—
195	C₂×D₄₇	—	8	4	no	—
196	C₄×C₄₇	—	2	1	no	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	4	no	—
201	C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
202	Dic₄₇	—	2	2	no	—
203	Dic₄₇	—	2	2	no	—
204	Dic₄₇	—	2	4	no	—
205	Dic₄₇	—	2	2	no	—
206	#3551	—	47	1	no	maximal, Sylow
207	C₂×C₄₇	—	4	1	no	—
208	C₂×C₄₇	—	4	1	no	—
209	C₂×C₄₇	—	4	1	no	—
210	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
211	C₂×C₄₇	#585	1	2	yes	—
212	D₄₇	—	4	2	no	—
213	D₄₇	—	4	4	no	—
214	#563	—	47	2	no	—
215	#560	—	47	2	no	—
216	#555	—	47	2	no	—
217	#553	—	47	2	no	—
218	#552	—	47	2	no	—
219	#551	—	47	2	no	—
220	#548	—	47	2	no	—
221	#546	—	47	2	no	—
222	#540	—	47	4	no	—
223	#538	—	47	4	no	—
224	#537	—	47	2	no	—
225	#536	D₄₇	1	1	yes	characteristic, complemented
226	#535	—	47	1	no	—
227	#532	—	47	1	no	—
228	#529	—	47	2	no	—
229	C₄₇	#3551	1	1	yes	characteristic, complemented, Sylow
230	C₂×#41	—	47	2	no	—
231	C₂×#41	—	47	1	no	—
232	C₂×#41	C₂×D₄₇	1	1	yes	characteristic
233	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
234	C₂²×D₄	—	47	1	no	—
235	C₄⋊Q₈	—	47	1	no	—
236	C₄⋊Q₈	C₂×D₄₇	1	2	yes	complemented
237	#127	—	47	1	no	—
238	#127	—	47	2	no	—
239	#126	—	47	4	no	—
240	#126	—	47	4	no	—
241	#126	—	47	4	no	—
242	#125	—	47	2	no	—
243	#125	—	47	4	no	—
244	#124	—	47	2	no	—
245	#124	—	47	1	no	—
246	#124	—	47	2	no	—
247	#124	—	47	4	no	—
248	#124	—	47	1	no	—
249	#124	C₂×D₄₇	1	2	yes	—
250	#123	—	47	4	no	—
251	#123	—	47	4	no	—
252	#123	—	47	4	no	—
253	#123	—	47	4	no	—
254	#123	C₂×D₄₇	1	2	yes	—
255	#123	C₂×D₄₇	1	2	yes	complemented
256	C₂²⋊Q₈	—	47	2	no	—
257	C₂²⋊Q₈	—	47	4	no	—
258	C₂²⋊Q₈	—	47	4	no	—
259	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
260	C₂²⋊Q₈	C₂×D₄₇	1	2	yes	complemented
261	#121	—	47	2	no	—
262	#121	—	47	2	no	—
263	#121	—	47	2	no	—
264	#121	—	47	2	no	—
265	#121	—	47	4	no	—
266	#121	—	47	2	no	—
267	#121	—	47	4	no	—
268	#121	—	47	4	no	—
269	#121	—	47	4	no	—
270	#121	—	47	4	no	—
271	#121	—	47	4	no	—
272	#120	—	47	2	no	—
273	#120	—	47	2	no	—
274	#120	—	47	4	no	—
275	C₄×Q₈	—	47	2	no	—
276	C₄×D₄	—	47	2	no	—
277	C₄×D₄	—	47	2	no	—
278	C₄×D₄	—	47	4	no	—
279	C₄×D₄	—	47	2	no	—
280	C₄×D₄	—	47	4	no	—
281	C₄×D₄	—	47	4	no	—
282	#117	—	47	1	no	—
283	#117	—	47	4	no	—
284	#117	—	47	4	no	—
285	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
286	C₂×C₄⋊C₄	—	47	2	no	—
287	C₂×C₂²⋊C₄	—	47	4	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂⁴	—	47	2	no	—
290	#41	—	4	2	no	—
291	#41	—	188	2	no	—
292	#41	—	188	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	47	1	no	—
295	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
296	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
297	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₂×D₄	—	47	2	no	—
299	C₂×D₄	—	47	4	no	—
300	C₂×D₄	—	47	4	no	—
301	C₂×D₄	—	47	2	no	—
302	C₂×D₄	—	47	2	no	—
303	C₂×D₄	—	47	2	no	—
304	C₂×D₄	—	47	4	no	—
305	C₂×D₄	—	47	4	no	—
306	C₂×D₄	—	47	1	no	—
307	C₂×D₄	—	47	2	no	—
308	C₂×D₄	—	188	2	no	—
309	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
310	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
311	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	—	47	2	no	—
314	C₂²×C₄	—	47	4	no	—
315	C₂²×C₄	—	47	4	no	—
316	C₂²×C₄	—	47	4	no	—
317	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
321	C₄⋊C₄	—	47	4	no	—
322	C₄⋊C₄	—	47	4	no	—
323	C₄⋊C₄	—	47	2	no	—
324	C₄⋊C₄	—	47	2	no	—
325	C₄⋊C₄	—	47	4	no	—
326	C₄⋊C₄	—	47	2	no	—
327	C₄⋊C₄	—	47	4	no	—
328	C₄⋊C₄	—	47	4	no	—
329	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
330	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
331	C₄⋊C₄	C₂²×D₄₇	1	4	yes	—
332	C₂²⋊C₄	—	47	2	no	—
333	C₂²⋊C₄	—	47	2	no	—
334	C₂²⋊C₄	—	47	2	no	—
335	C₂²⋊C₄	—	47	4	no	—
336	C₂²⋊C₄	—	47	4	no	—
337	C₂²⋊C₄	—	47	2	no	—
338	C₂²⋊C₄	—	47	4	no	—
339	C₂²⋊C₄	—	47	4	no	—
340	C₂²⋊C₄	—	47	2	no	—
341	C₂²⋊C₄	—	47	4	no	—
342	C₂²⋊C₄	—	47	4	no	—
343	C₂²⋊C₄	—	47	4	no	—
344	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
345	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
346	C₂²⋊C₄	C₂²×D₄₇	1	4	yes	—
347	C₄²	—	47	1	no	—
348	C₄²	—	47	2	no	—
349	C₄²	—	47	1	no	—
350	C₄²	—	47	2	no	—
351	C₄²	—	47	4	no	—
352	C₄²	C₂²×D₄₇	1	2	yes	—
353	C₂³	—	47	4	no	—
354	C₂³	—	47	2	no	—
355	C₂³	—	188	2	no	—
356	C₂³	—	188	4	no	—
357	C₂³	C₂³×D₄₇	1	1	yes	characteristic
358	C₂³	C₂³×D₄₇	1	1	yes	characteristic
359	C₂³	C₂³×D₄₇	1	1	yes	characteristic
360	Q₈	—	2	4	no	—
361	Q₈	—	4	2	no	—
362	Q₈	—	4	1	no	—
363	Q₈	—	188	1	no	—
364	D₄	—	4	1	no	—
365	D₄	—	4	1	no	—
366	D₄	—	4	1	no	—
367	D₄	—	94	4	no	—
368	D₄	—	188	4	no	—
369	D₄	—	188	2	no	—
370	D₄	—	188	1	no	—
371	D₄	—	188	4	no	—
372	D₄	—	188	4	no	—
373	D₄	—	188	4	no	—
374	D₄	—	188	2	no	—
375	D₄	—	188	2	no	—
376	D₄	—	188	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	47	2	no	—
382	C₂×C₄	—	47	2	no	—
383	C₂×C₄	—	47	4	no	—
384	C₂×C₄	—	47	2	no	—
385	C₂×C₄	—	94	4	no	—
386	C₂×C₄	—	188	4	no	—
387	C₂×C₄	—	188	4	no	—
388	C₂×C₄	—	188	4	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₄₇	1	4	yes	—
393	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂³×D₄₇	1	4	yes	—
395	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	94	2	no	—
403	C₂²	—	94	4	no	—
404	C₂²	—	94	2	no	—
405	C₂²	—	94	4	no	—
406	C₂²	—	94	2	no	—
407	C₂²	—	94	4	no	—
408	C₂²	—	376	4	no	—
409	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	4	no	—
414	C₄	—	2	4	no	—
415	C₄	—	94	2	no	—
416	C₄	—	94	2	no	—
417	C₄	—	94	4	no	—
418	C₄	—	94	2	no	—
419	C₄	#13094069	1	2	yes	—
420	C₂	—	4	1	no	—
421	C₂	—	4	1	no	—
422	C₂	—	4	1	no	—
423	C₂	—	188	4	no	—
424	C₂	—	188	2	no	—
425	C₂	C₂×#13094069	1	1	yes	characteristic
426	C₂	#15689960	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#536	C₂
hypercenter	#536	D₄₇
hypocenter	C₄₇	#3551
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. #15689872	C₂	semidirect
2. #15689863	C₂	semidirect
3. #15689839	C₂	semidirect
4. #15689817	C₂	semidirect
5. #15689807	C₂	semidirect
6. #15689801	C₂	semidirect
7. #15689784	C₂	semidirect
8. #15689764	C₂	semidirect
9. #15689725	C₂	semidirect
10. #15689707	C₂	semidirect
11. #15689703	C₂	semidirect
12. #15689687	C₂	semidirect
13. #15689669	C₂	semidirect
14. #15689659	C₂	semidirect
15. C₄₇×#536	C₂	semidirect
17. C₂×#10625350	C₂²	semidirect
19. #13094022	C₂²	semidirect
22. #13094019	C₂²	semidirect
23. #13094018	C₂²	semidirect
25. #13094015	C₂²	semidirect
26. #13094014	C₂²	semidirect
29. #13094013	C₂²	semidirect
30. #13094013	C₂²	semidirect
33. #13094008	C₂²	semidirect
35. #13094006	C₂²	semidirect
36. #13094002	C₂²	semidirect
37. #13094000	C₂²	semidirect
38. #13094000	C₂²	semidirect
41. #13093999	C₂²	semidirect
44. #13093998	C₂²	semidirect
45. #13093997	C₂²	semidirect
46. #13093997	C₂²	semidirect
47. #13093997	C₂²	semidirect
49. #13093996	C₂²	semidirect
53. Q₈×Dic₄₇	C₂²	semidirect
54. C₄×D₁₈₈	C₂²	semidirect
57. C₄×C₂²⋊D₄₇	C₂²	semidirect
58. C₄×C₂²⋊D₄₇	C₂²	semidirect
59. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
61. #13093982	C₂²	semidirect
62. #13093982	C₂²	semidirect
63. C₄⋊C₄×D₄₇	C₂²	semidirect
65. C₂×C₄×Dic₄₇	C₂²	semidirect
67. C₂²×Q₈×C₄₇	C₂²	semidirect
68. C₄⋊Q₈×C₄₇	C₂²	semidirect
71. #123×C₄₇	C₂²	semidirect
73. C₂²⋊Q₈×C₄₇	C₂²	semidirect
74. #117×C₄₇	C₂²	semidirect
225. #536	D₄₇	semidirect
229. C₄₇	#3551	semidirect
233. C₂²×Q₈	C₂×D₄₇	semidirect
236. C₄⋊Q₈	C₂×D₄₇	semidirect
255. #123	C₂×D₄₇	semidirect
260. C₂²⋊Q₈	C₂×D₄₇	semidirect
285. #117	C₂×D₄₇	semidirect