Subgroups — #26219524

Order 12032.

780 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	#20252186	C₂	1	1	yes	maximal, characteristic
2	#20252037	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244036	C₂	1	2	yes	maximal, complemented
4	#20243987	C₂	1	2	yes	maximal, complemented
5	#20243715	C₂	1	2	yes	maximal
6	#20243663	C₂	1	2	yes	maximal, complemented
7	#20243295	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13093950	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13093951	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243136	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2875	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094044	C₂²	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689233	C₄	1	2	yes	complemented
15	#15689228	C₄	1	2	yes	complemented
16	#15689223	C₄	1	2	yes	complemented
17	#15689221	C₄	1	2	yes	complemented
18	#15689185	—	2	1	no	—
19	#15689185	—	2	1	no	—
20	#15689178	—	2	2	no	—
21	C₂×#13093959	C₂²	1	2	yes	—
22	#15689159	C₂²	1	1	yes	characteristic
23	#15689149	C₂²	1	2	yes	—
24	C₂×#13093951	C₂²	1	2	yes	—
25	C₂×#13093950	C₂²	1	2	yes	—
26	#15689119	C₂²	1	1	yes	characteristic
27	#15689117	C₂²	1	1	yes	characteristic
28	#15689089	C₂²	1	2	yes	—
29	C₄×#10625329	C₂²	1	1	yes	characteristic
30	C₂×#13093935	C₂²	1	1	yes	characteristic
31	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688887	C₂²	1	2	yes	—
33	#15688884	C₂²	1	2	yes	—
34	#15688882	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×#131×C₄₇	C₂²	1	2	yes	—
38	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#405	—	2	2	no	—
40	C₄₇×#405	C₂²	1	2	yes	—
41	C₄×M₁₆×C₄₇	—	2	1	no	—
42	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
43	C₂×#97×C₄₇	—	2	1	no	—
44	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625350	C₂³	1	1	yes	characteristic
46	#13094044	—	2	4	no	—
47	C₂×#10625337	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625335	C₂×C₄	1	1	yes	characteristic
49	C₂×#10625336	C₂×C₄	1	1	yes	characteristic
50	C₂×#10625334	C₂×C₄	1	1	yes	characteristic
51	C₂×#10625329	C₂³	1	2	yes	—
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
54	C₄×Dic₉₄	C₂×C₄	1	2	yes	—
55	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
56	C₄×C₂²⋊D₄₇	—	2	2	no	—
57	#13093983	C₂³	1	1	yes	characteristic
58	#13093981	—	2	1	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
61	C₄²×D₄₇	—	2	1	no	—
62	#13093959	—	2	4	no	—
63	#13093957	C₂×C₄	1	2	yes	—
64	#13093955	C₂×C₄	1	2	yes	—
65	Dic₄₇⋊C₈	—	2	2	no	—
66	Dic₄₇⋊C₈	—	2	2	no	—
67	#13093951	—	2	4	no	—
68	#13093950	—	2	4	no	—
69	#13093948	C₂×C₄	1	2	yes	—
70	#13093947	C₂×C₄	1	2	yes	—
71	#13093945	C₂×C₄	1	2	yes	—
72	#13093944	C₂×C₄	1	2	yes	—
73	(C₂×D₄₇)⋊C₈	—	2	2	no	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	#13093935	—	2	1	no	—
76	#13093935	C₂×C₄	1	2	yes	—
77	#13093935	C₂×C₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	—	2	1	no	—
79	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
80	#131×C₄₇	—	2	4	no	—
81	#131×C₄₇	—	2	4	no	—
82	C₂×M₁₆×C₄₇	—	2	2	no	—
83	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₇	—	2	2	no	—
85	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
86	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
87	C₄×D₄×C₄₇	—	2	2	no	—
88	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
89	#117×C₄₇	—	2	1	no	—
90	#117×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#97×C₄₇	—	2	2	no	—
94	#97×C₄₇	—	2	1	no	—
95	#97×C₄₇	D₄	1	1	yes	characteristic
96	#97×C₄₇	D₄	1	1	yes	characteristic
97	#97×C₄₇	D₄	1	2	yes	—
98	C₄×C₈×C₄₇	—	2	2	no	—
99	C₄×C₈×C₄₇	—	2	1	no	—
100	#41×C₄₇	—	2	2	no	—
101	#41×C₄₇	#41	1	4	yes	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	#41	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	#10625350	—	2	2	no	—
112	#10625350	—	2	2	no	—
113	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₄₇	—	2	1	no	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
117	M₁₆×C₄₇	—	2	8	no	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	#41	1	4	yes	—
120	C₂×C₈×C₄₇	—	2	8	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂²⋊C₄×C₄₇	—	2	1	no	—
129	C₂²⋊C₄×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²⋊Dic₄₇	—	2	1	no	—
136	#10625337	—	2	2	no	—
137	#10625336	—	2	2	no	—
138	#10625335	—	2	2	no	—
139	#10625334	—	2	2	no	—
140	(C₂×D₄₇)⋊C₄	—	2	2	no	—
141	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
142	Dic₄₇⋊C₄	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₄×Dic₄₇	—	4	4	no	—
148	#10625329	—	2	2	no	—
149	#10625329	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	1	no	—
159	Q₈×C₄₇	—	2	1	no	—
160	Q₈×C₄₇	#117	1	2	yes	—
161	D₄×C₄₇	—	2	4	no	—
162	D₄×C₄₇	—	2	1	no	—
163	D₄×C₄₇	#117	1	2	yes	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	8	2	no	—
169	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
170	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
171	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
175	C₂²⋊D₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	2	4	no	—
177	C₂×Dic₄₇	—	2	1	no	—
178	C₂×Dic₄₇	—	2	2	no	—
179	C₂×Dic₄₇	—	4	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	D₁₈₈	—	2	1	no	—
182	D₁₈₈	—	2	1	no	—
183	C₄×D₄₇	—	4	2	no	—
184	C₄×D₄₇	—	8	2	no	—
185	Dic₉₄	—	2	1	no	—
186	Dic₉₄	—	2	1	no	—
187	C₈×C₄₇	—	2	2	no	—
188	C₈×C₄₇	—	2	4	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₄₇⋊C₈	—	2	1	no	—
191	C₄₇⋊C₈	—	2	1	no	—
192	C₄₇⋊C₈	—	2	2	no	—
193	C₄₇⋊C₈	—	4	2	no	—
194	#21139	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
199	C₂²×C₄₇	#529	1	2	yes	—
200	C₂×D₄₇	—	4	2	no	—
201	C₂×D₄₇	—	4	1	no	—
202	C₄×C₄₇	—	2	2	no	—
203	C₄×C₄₇	—	2	2	no	—
204	C₄×C₄₇	—	2	2	no	—
205	C₄×C₄₇	—	4	2	no	—
206	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
207	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
208	C₄×C₄₇	#525	1	2	yes	—
209	Dic₄₇	—	4	4	no	—
210	Dic₄₇	—	4	2	no	—
211	Dic₄₇	—	4	1	no	—
212	#2943	—	47	1	no	—
213	#2923	—	47	1	no	—
214	#2875	D₄₇	1	1	yes	characteristic, complemented
215	#1929	—	47	2	no	—
216	#1922	—	47	2	no	—
217	#1876	—	47	2	no	—
218	#1866	—	47	2	no	—
219	#1778	—	47	1	no	—
220	C₄×#104	—	47	1	no	—
221	C₄×#104	—	47	1	no	—
222	#1745	—	47	1	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	—	4	2	no	—
225	C₂×C₄₇	#2290	1	1	yes	characteristic
226	C₂×C₄₇	#2956	1	2	yes	—
227	D₄₇	—	8	1	no	—
228	C₂×#135	—	47	1	no	—
229	C₂×#131	C₂×D₄₇	1	2	yes	—
230	C₄×#41	—	47	1	no	—
231	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
232	#442	—	47	2	no	—
233	#441	—	47	2	no	—
234	#440	—	47	2	no	—
235	#440	—	47	2	no	—
236	#433	—	94	1	no	—
237	#433	—	94	1	no	—
238	#432	—	94	2	no	—
239	C₂×#108	—	47	2	no	—
240	#427	—	47	1	no	—
241	#424	—	47	2	no	—
242	C₂×#104	—	47	2	no	—
243	C₂×#104	—	47	2	no	—
244	#416	—	47	1	no	—
245	#416	—	47	1	no	—
246	#408	—	47	2	no	—
247	#405	—	2	2	no	—
248	#405	C₂×D₄₇	1	2	yes	—
249	C₄×M₁₆	—	2	1	no	—
250	C₄×M₁₆	—	47	1	no	—
251	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
252	C₂×#97	—	2	1	no	—
253	C₂×#97	—	47	1	no	—
254	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
255	C₄³	—	47	1	no	—
256	#341	—	47	2	no	—
257	#339	—	47	2	no	—
258	#339	—	47	2	no	—
259	#336	—	47	2	no	—
260	#336	—	47	2	no	—
261	C₄₇	#21139	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	47	1	no	—
263	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
264	#135	—	94	4	no	—
265	C₂×Q₁₆	—	47	1	no	—
266	C₂×SD₁₆	—	47	1	no	—
267	C₂×SD₁₆	—	47	1	no	—
268	C₂×D₈	—	47	1	no	—
269	#131	—	2	4	no	—
270	#131	—	2	4	no	—
271	C₂×M₁₆	—	2	2	no	—
272	C₂×M₁₆	—	47	2	no	—
273	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
274	C₂²×C₈	—	2	2	no	—
275	C₂²×C₈	—	47	1	no	—
276	C₂²×C₈	—	47	1	no	—
277	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
278	C₄×Q₈	—	47	2	no	—
279	C₄×Q₈	C₄×D₄₇	1	2	yes	—
280	C₄×D₄	—	2	2	no	—
281	C₄×D₄	—	47	2	no	—
282	C₄×D₄	—	94	2	no	—
283	C₄×D₄	C₄×D₄₇	1	2	yes	—
284	#117	—	2	1	no	—
285	#117	—	47	1	no	—
286	#117	—	94	1	no	—
287	#117	C₂²×D₄₇	1	1	yes	characteristic
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	47	2	no	—
290	C₂×C₄²	—	94	1	no	—
291	C₂×C₄²	—	94	2	no	—
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	#108	—	94	4	no	—
294	#107	—	47	2	no	—
295	#106	—	47	2	no	—
296	C₄⋊C₈	—	94	2	no	—
297	C₄⋊C₈	—	94	2	no	—
298	#104	—	94	4	no	—
299	#104	—	94	4	no	—
300	#103	—	47	2	no	—
301	#103	—	47	2	no	—
302	#102	—	47	2	no	—
303	#102	—	47	2	no	—
304	C₂²⋊C₈	—	94	2	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	#97	—	2	2	no	—
307	#97	—	2	1	no	—
308	#97	—	47	2	no	—
309	#97	—	47	2	no	—
310	#97	—	94	1	no	—
311	#97	C₂²⋊D₄₇	1	1	yes	characteristic
312	#97	C₂²⋊D₄₇	1	1	yes	characteristic
313	#97	C₂²⋊D₄₇	1	2	yes	—
314	C₄×C₈	—	2	2	no	—
315	C₄×C₈	—	2	1	no	—
316	C₄×C₈	—	94	1	no	—
317	#41	—	2	2	no	—
318	#41	—	94	2	no	—
319	#41	—	94	2	no	—
320	#41	#10625350	1	4	yes	—
321	C₂×Q₈	—	47	1	no	—
322	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	47	1	no	—
325	C₂×D₄	—	94	1	no	—
326	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	94	2	no	—
330	C₂²×C₄	—	94	2	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	#10625350	1	2	yes	—
333	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
334	Q₁₆	—	94	2	no	—
335	SD₁₆	—	94	2	no	—
336	SD₁₆	—	94	2	no	—
337	D₈	—	94	2	no	—
338	M₁₆	—	2	8	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	94	2	no	—
341	M₁₆	—	94	2	no	—
342	M₁₆	#10625350	1	4	yes	—
343	C₂×C₈	—	2	8	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	47	2	no	—
348	C₂×C₈	—	47	1	no	—
349	C₂×C₈	—	47	1	no	—
350	C₂×C₈	—	94	2	no	—
351	C₂×C₈	—	94	2	no	—
352	C₂×C₈	—	94	2	no	—
353	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
354	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	47	2	no	—
357	C₄⋊C₄	—	94	2	no	—
358	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
359	C₂²⋊C₄	—	2	1	no	—
360	C₂²⋊C₄	—	2	2	no	—
361	C₂²⋊C₄	—	94	1	no	—
362	C₂²⋊C₄	—	94	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	1	no	—
365	C₄²	—	94	2	no	—
366	C₄²	—	94	1	no	—
367	C₄²	—	94	2	no	—
368	C₄²	—	94	2	no	—
369	C₄²	—	188	4	no	—
370	C₄²	C₂×C₄×D₄₇	1	2	yes	—
371	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
372	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
373	C₂³	—	2	1	no	—
374	C₂³	—	94	1	no	—
375	C₂³	C₂×#10625350	1	1	yes	characteristic
376	Q₈	—	2	1	no	—
377	Q₈	—	94	1	no	—
378	Q₈	—	94	1	no	—
379	Q₈	#13093981	1	2	yes	—
380	D₄	—	2	4	no	—
381	D₄	—	2	1	no	—
382	D₄	—	94	1	no	—
383	D₄	—	94	1	no	—
384	D₄	—	188	2	no	—
385	D₄	#13093981	1	2	yes	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	94	4	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	1	no	—
394	C₂×C₄	—	376	2	no	—
395	C₂×C₄	—	188	2	no	—
396	C₂×C₄	—	188	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
399	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
400	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
401	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
402	C₂×C₄	C₂×#10625350	1	2	yes	—
403	C₂×C₄	C₂×#10625350	1	2	yes	—
404	C₈	—	2	2	no	—
405	C₈	—	2	4	no	—
406	C₈	—	2	2	no	—
407	C₈	—	94	1	no	—
408	C₈	—	94	1	no	—
409	C₈	—	94	2	no	—
410	C₈	—	188	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	188	1	no	—
415	C₂²	—	188	2	no	—
416	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
417	C₂²	#15689657	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	2	no	—
422	C₄	—	188	4	no	—
423	C₄	—	188	1	no	—
424	C₄	—	188	2	no	—
425	C₄	C₂×#13093981	1	1	yes	characteristic
426	C₄	C₄×#10625350	1	1	yes	characteristic
427	C₄	#15689634	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	376	1	no	—
431	C₂	#20245831	1	1	yes	characteristic
432	C₂	#20252295	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2875	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094044	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2875	D₄₇
hypocenter	C₄₇	#21139
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #2875

Complements

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

N	H ≅ G/N	type
2. #20252037	C₂	semidirect
3. #20244036	C₂	semidirect
4. #20243987	C₂	semidirect
6. #20243663	C₂	semidirect
7. #20243295	C₂	semidirect
8. C₄×#13093950	C₂	semidirect
9. C₄×#13093951	C₂	semidirect
10. #20243136	C₂	semidirect
11. C₄₇×#2875	C₂	semidirect
14. #15689233	C₄	semidirect
15. #15689228	C₄	semidirect
16. #15689223	C₄	semidirect
17. #15689221	C₄	semidirect
214. #2875	D₄₇	semidirect
261. C₄₇	#21139	semidirect

Maximal subgroups

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

subgroup	index
#20252186	2
#20252037	2
#20244036	2
#20243987	2
#20243715	2
#20243663	2
#20243295	2
C₄×#13093950	2
C₄×#13093951	2
#20243136	2
C₄₇×#2875	2
#21139	47