Subgroups — #26201470

Order 12032.

662 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253483	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253384	C₂	1	1	yes	maximal, characteristic
3	#20252411	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242822	C₂	1	2	yes	maximal, complemented
5	#20242808	C₂	1	2	yes	maximal, complemented
6	#20242750	C₂	1	2	yes	maximal, complemented
7	#20242726	C₂	1	2	yes	maximal, complemented
8	#20242168	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242093	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242053	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
13	#15689456	—	2	1	no	—
14	#15689434	—	2	1	no	—
15	#15689400	C₂²	1	2	yes	—
16	#15689400	C₂²	1	2	yes	—
17	#15689325	C₂²	1	2	yes	—
18	#15689315	C₂²	1	2	yes	—
19	#15689273	—	2	1	no	—
20	#15689256	—	2	1	no	—
21	#15689221	—	2	2	no	—
22	C₄×#10625334	—	2	2	no	—
23	C₈×D₁₈₈	C₂²	1	2	yes	—
24	C₈×D₁₈₈	C₂²	1	2	yes	—
25	#15689188	—	2	2	no	—
26	#15689180	C₂²	1	1	yes	characteristic
27	#15689176	C₂²	1	1	yes	characteristic
28	#15689176	C₂²	1	1	yes	characteristic
29	C₂²⋊C₈×D₄₇	—	2	2	no	—
30	#15688876	C₂²	1	2	yes	complemented
31	#15688874	C₂²	1	2	yes	complemented
32	#15688869	C₂²	1	2	yes	complemented
33	#15688869	C₂²	1	2	yes	complemented
34	#15688869	C₂²	1	2	yes	complemented
35	#15688867	C₂²	1	2	yes	complemented
36	C₄₇×#533	C₂²	1	1	yes	characteristic
37	C₄₇×#532	C₂²	1	1	yes	characteristic
38	C₄₇×#494	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#492	C₂²	1	1	yes	characteristic, complemented
40	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
41	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
42	C₄₇×#464	—	2	2	no	—
43	C₄₇×#452	—	2	2	no	—
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	—	2	1	no	—
47	C₂×#10625336	—	2	2	no	—
48	C₂×#10625334	—	2	2	no	—
49	C₂×C₈×D₄₇	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₄×D₁₈₈	—	2	1	no	—
52	C₄×D₁₈₈	—	2	1	no	—
53	C₄×D₁₈₈	D₄	1	2	yes	—
54	C₄×D₁₈₈	C₂³	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
57	#13093957	—	2	2	no	—
58	#13093957	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
62	#13093948	—	2	2	no	—
63	#13093945	—	2	2	no	—
64	#13093944	—	2	2	no	—
65	#13093944	—	2	2	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
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	—	2	1	no	—
73	C₄×C₄₇⋊C₈	—	2	1	no	—
74	C₂×#41×C₄₇	—	2	1	no	—
75	C₂×Q₁₆×C₄₇	—	2	2	no	—
76	C₂×SD₁₆×C₄₇	—	2	2	no	—
77	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
80	#127×C₄₇	C₂³	1	1	yes	characteristic
81	#125×C₄₇	—	2	1	no	—
82	#124×C₄₇	—	2	1	no	—
83	C₂²⋊Q₈×C₄₇	—	2	1	no	—
84	C₂²⋊Q₈×C₄₇	—	2	1	no	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	1	no	—
87	C₄×Q₈×C₄₇	—	2	1	no	—
88	C₄×Q₈×C₄₇	—	2	1	no	—
89	C₄×D₄×C₄₇	—	2	1	no	—
90	C₄×D₄×C₄₇	—	2	1	no	—
91	#117×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
94	#103×C₄₇	—	2	2	no	—
95	#102×C₄₇	—	2	2	no	—
96	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₂³×D₄₇	—	2	1	no	—
100	#41×C₄₇	—	8	2	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	2	1	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	—	4	1	no	—
108	C₂²×C₄×C₄₇	—	4	1	no	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
112	C₂²×Dic₄₇	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	—	2	4	no	—
115	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
116	C₂×C₄×D₄₇	—	2	2	no	—
117	C₂×C₄×D₄₇	—	2	2	no	—
118	C₂×C₄×D₄₇	—	8	2	no	—
119	Q₁₆×C₄₇	—	8	2	no	—
120	SD₁₆×C₄₇	—	8	2	no	—
121	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	1	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	4	1	no	—
130	C₄⋊C₄×C₄₇	—	4	1	no	—
131	C₂²⋊C₄×C₄₇	—	4	1	no	—
132	C₂²⋊C₄×C₄₇	—	4	1	no	—
133	C₂²⋊C₄×C₄₇	—	4	1	no	—
134	C₄²×C₄₇	—	4	1	no	—
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄²×C₄₇	#41	1	1	yes	characteristic
138	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
139	#10625336	—	4	4	no	—
140	#10625334	—	4	4	no	—
141	(C₂×D₄₇)⋊C₄	—	2	2	no	—
142	(C₂×D₄₇)⋊C₄	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	1	no	—
144	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₈×D₄₇	—	8	2	no	—
149	C₈×D₄₇	—	8	2	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	#121	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	2	no	—
153	C₂²×D₄₇	—	2	4	no	—
154	C₂²×D₄₇	—	8	1	no	—
155	C₂²×D₄₇	—	8	1	no	—
156	Q₈×C₄₇	—	4	2	no	—
157	Q₈×C₄₇	—	4	2	no	—
158	Q₈×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	4	2	no	—
160	D₄×C₄₇	—	4	2	no	—
161	D₄×C₄₇	—	8	1	no	—
162	D₄×C₄₇	—	8	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	—	4	1	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	8	2	no	—
170	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
172	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	8	1	no	—
178	D₁₈₈	—	2	4	no	—
179	D₁₈₈	—	2	2	no	—
180	D₁₈₈	#135	1	4	yes	—
181	C₄×D₄₇	—	4	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	C₄×D₄₇	—	8	2	no	—
184	C₈×C₄₇	—	2	2	no	—
185	C₈×C₄₇	—	2	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	C₄₇⋊C₈	—	4	2	no	—
188	C₄₇⋊C₈	—	4	2	no	—
189	#19388	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	8	1	no	—
194	C₂²×C₄₇	—	8	1	no	—
195	C₂²×C₄₇	—	8	1	no	—
196	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
197	C₂×D₄₇	—	2	4	no	—
198	C₂×D₄₇	—	4	2	no	—
199	C₂×D₄₇	—	4	2	no	—
200	C₂×D₄₇	—	8	4	no	—
201	C₄×C₄₇	—	2	1	no	—
202	C₄×C₄₇	—	2	1	no	—
203	C₄×C₄₇	—	2	1	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	8	1	no	—
206	C₄×C₄₇	—	8	1	no	—
207	C₄×C₄₇	—	8	1	no	—
208	C₄×C₄₇	C₂×#135	1	2	yes	—
209	C₄×C₄₇	#576	1	2	yes	—
210	Dic₄₇	—	4	2	no	—
211	#3210	D₄₇	1	1	yes	characteristic, complemented
212	#3110	—	47	1	no	—
213	#3100	—	47	1	no	—
214	#2972	—	47	1	no	—
215	#1681	—	47	2	no	—
216	#1679	—	47	2	no	—
217	#1669	—	47	2	no	—
218	#1665	—	47	2	no	—
219	#1572	—	47	1	no	—
220	#1553	—	47	1	no	—
221	#1544	—	47	1	no	—
222	C₂×C₄₇	—	4	1	no	—
223	C₂×C₄₇	—	16	1	no	—
224	C₂×C₄₇	#3041	1	1	yes	characteristic
225	C₂×C₄₇	#3050	1	1	yes	characteristic
226	C₂×C₄₇	#3069	1	1	yes	characteristic
227	D₄₇	—	4	4	no	—
228	#533	C₂×D₄₇	1	1	yes	characteristic
229	#532	C₂×D₄₇	1	1	yes	characteristic
230	C₂×C₄×D₄	—	47	1	no	—
231	#494	C₂×D₄₇	1	1	yes	characteristic, complemented
232	#492	C₂×D₄₇	1	1	yes	characteristic, complemented
233	#487	C₂×D₄₇	1	1	yes	characteristic, complemented
234	#486	C₂×D₄₇	1	1	yes	characteristic, complemented
235	#484	—	94	1	no	—
236	#480	—	94	1	no	—
237	#474	—	47	2	no	—
238	#474	—	47	2	no	—
239	#464	—	2	2	no	—
240	#461	—	47	2	no	—
241	#459	—	47	2	no	—
242	#452	—	2	2	no	—
243	#450	—	94	1	no	—
244	#447	—	94	1	no	—
245	#440	—	94	2	no	—
246	C₄×D₈	—	94	2	no	—
247	C₈×D₄	—	47	2	no	—
248	C₈×D₄	—	47	2	no	—
249	C₈×D₄	—	94	2	no	—
250	#432	—	47	1	no	—
251	#431	—	47	1	no	—
252	#431	—	47	1	no	—
253	#431	C₂×D₄₇	1	1	yes	characteristic
254	C₂×C₂²⋊C₈	—	94	2	no	—
255	#335	—	47	2	no	—
256	#334	—	47	2	no	—
257	#332	—	47	2	no	—
258	#332	—	47	2	no	—
259	#332	—	47	2	no	—
260	#331	—	47	2	no	—
261	C₄₇	#19388	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	2	1	no	—
263	C₂²×D₄	—	47	1	no	—
264	C₂³×C₄	—	94	1	no	—
265	C₂×Q₁₆	—	2	2	no	—
266	C₂×SD₁₆	—	2	2	no	—
267	C₂×SD₁₆	—	94	2	no	—
268	C₂×D₈	—	94	2	no	—
269	C₂²×C₈	—	94	2	no	—
270	C₂²×C₈	—	94	2	no	—
271	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
272	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
273	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
274	#127	C₂²×D₄₇	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	#124	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	2	1	no	—
279	#121	—	2	1	no	—
280	#121	—	2	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	2	1	no	—
283	C₄×D₄	—	2	1	no	—
284	C₄×D₄	—	2	1	no	—
285	C₄×D₄	—	47	2	no	—
286	C₄×D₄	—	47	2	no	—
287	C₄×D₄	—	94	1	no	—
288	C₄×D₄	—	94	1	no	—
289	#117	—	2	1	no	—
290	C₂×C₄⋊C₄	—	47	1	no	—
291	C₂×C₂²⋊C₄	—	94	1	no	—
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	#107	—	94	2	no	—
294	#107	—	94	2	no	—
295	C₄⋊C₈	—	47	2	no	—
296	C₄⋊C₈	—	47	2	no	—
297	C₄⋊C₈	—	47	2	no	—
298	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
299	#103	—	2	2	no	—
300	#103	—	94	2	no	—
301	#102	—	2	2	no	—
302	#102	—	94	2	no	—
303	#102	—	94	2	no	—
304	#102	—	94	2	no	—
305	C₂²⋊C₈	—	94	1	no	—
306	C₂²⋊C₈	—	94	1	no	—
307	C₂²⋊C₈	—	94	1	no	—
308	C₂²⋊C₈	—	94	2	no	—
309	C₂²⋊C₈	—	94	2	no	—
310	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
311	#97	—	94	1	no	—
312	C₄×C₈	—	94	1	no	—
313	C₄×C₈	—	94	1	no	—
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
316	C₂⁴	—	94	1	no	—
317	#41	—	8	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	2	1	no	—
321	C₂×D₄	—	2	1	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	4	1	no	—
325	C₂×D₄	—	47	2	no	—
326	C₂×D₄	—	94	4	no	—
327	C₂×D₄	—	94	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	94	1	no	—
330	C₂²×C₄	—	94	2	no	—
331	C₂²×C₄	—	94	2	no	—
332	C₂²×C₄	—	376	2	no	—
333	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
334	C₂²×C₄	#10625352	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
336	Q₁₆	—	8	2	no	—
337	SD₁₆	—	8	2	no	—
338	SD₁₆	—	188	4	no	—
339	D₈	—	188	4	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	376	2	no	—
344	C₂×C₈	—	376	2	no	—
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
346	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	47	2	no	—
356	C₄⋊C₄	—	94	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	94	2	no	—
361	C₂²⋊C₄	—	94	2	no	—
362	C₄²	—	4	1	no	—
363	C₄²	D₄×D₄₇	1	1	yes	characteristic
364	C₄²	#10625352	1	1	yes	characteristic
365	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₄²	C₂³×D₄₇	1	1	yes	characteristic
367	C₂³	—	4	1	no	—
368	C₂³	—	94	4	no	—
369	C₂³	—	94	2	no	—
370	C₂³	—	376	1	no	—
371	C₂³	—	376	1	no	—
372	C₂³	#13093995	1	1	yes	characteristic
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	2	no	—
378	D₄	—	8	1	no	—
379	D₄	—	8	2	no	—
380	D₄	—	47	4	no	—
381	D₄	—	94	4	no	—
382	D₄	—	94	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	376	2	no	—
392	C₂×C₄	—	376	1	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	—	188	2	no	—
395	C₂×C₄	#13093995	1	1	yes	characteristic
396	C₂×C₄	#13093995	1	1	yes	characteristic
397	C₂×C₄	#13093995	1	1	yes	characteristic
398	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
400	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
401	C₈	—	2	2	no	—
402	C₈	—	2	2	no	—
403	C₈	—	188	2	no	—
404	C₈	—	188	2	no	—
405	C₈	—	188	2	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	1	no	—
412	C₂²	—	94	4	no	—
413	C₂²	—	376	4	no	—
414	C₂²	—	188	2	no	—
415	C₂²	—	188	2	no	—
416	C₂²	C₂×#13093995	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	2	1	no	—
421	C₄	—	8	1	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	188	2	no	—
425	C₄	#135×D₄₇	1	2	yes	—
426	C₄	#15689926	1	2	yes	—
427	C₂	—	4	1	no	—
428	C₂	—	16	1	no	—
429	C₂	—	188	4	no	—
430	C₂	#20252887	1	1	yes	characteristic
431	C₂	#20252965	1	1	yes	characteristic
432	C₂	#20253121	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3210	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#20253384	C₂
hypercenter	#3210	D₄₇
hypocenter	C₄₇	#19388
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3210

Complements

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

N	H ≅ G/N	type
1. #20253483	C₂	semidirect
3. #20252411	C₂	semidirect
4. #20242822	C₂	semidirect
5. #20242808	C₂	semidirect
6. #20242750	C₂	semidirect
7. #20242726	C₂	semidirect
8. #20242168	C₂	semidirect
9. #20242093	C₂	semidirect
10. #20242053	C₂	semidirect
11. C₄₇×#3210	C₂	semidirect
30. #15688876	C₂²	semidirect
31. #15688874	C₂²	semidirect
32. #15688869	C₂²	semidirect
33. #15688869	C₂²	semidirect
34. #15688869	C₂²	semidirect
35. #15688867	C₂²	semidirect
38. C₄₇×#494	C₂²	semidirect
39. C₄₇×#492	C₂²	semidirect
40. C₄₇×#487	C₂²	semidirect
41. C₄₇×#486	C₂²	semidirect
211. #3210	D₄₇	semidirect
231. #494	C₂×D₄₇	semidirect
232. #492	C₂×D₄₇	semidirect
233. #487	C₂×D₄₇	semidirect
234. #486	C₂×D₄₇	semidirect
261. C₄₇	#19388	semidirect

Maximal subgroups

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

subgroup	index
#20253483	2
#20253384	2
#20252411	2
#20242822	2
#20242808	2
#20242750	2
#20242726	2
#20242168	2
#20242093	2
#20242053	2
C₄₇×#3210	2
#19388	47