Subgroups — #26233894

Order 12032.

686 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252045	C₂	1	2	yes	maximal
2	#20251976	C₂	1	1	yes	maximal, characteristic
3	#20244137	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243990	C₂	1	2	yes	maximal, complemented
5	#20243984	C₂	1	2	yes	maximal, complemented
6	#20243486	C₂	1	2	yes	maximal
7	#20243427	C₂	1	1	yes	maximal, characteristic
8	#20243272	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243173	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1946	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	#117×D₄₇	C₂²	1	2	yes	—
14	#15689183	—	2	2	no	—
15	#15689183	—	2	2	no	—
16	#15689179	—	2	2	no	—
17	#15689175	—	2	2	no	—
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	#15689164	C₄	1	2	yes	complemented
20	#15689164	C₄	1	2	yes	complemented
21	#15689162	C₄	1	2	yes	complemented
22	#15689162	C₄	1	2	yes	complemented
23	#15689161	C₂²	1	1	yes	characteristic
24	#15689159	C₂²	1	2	yes	—
25	#15689150	C₂²	1	2	yes	—
26	#15689086	C₂²	1	2	yes	—
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	#15689081	C₂²	1	2	yes	—
29	#15689078	C₂²	1	2	yes	—
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
32	#15688887	C₂²	1	2	yes	—
33	#15688884	C₂²	1	2	yes	—
34	#15688883	C₂²	1	2	yes	—
35	#15688882	C₂²	1	2	yes	—
36	#15688878	C₂²	1	1	yes	characteristic
37	#15688877	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#427	C₂²	1	1	yes	characteristic
40	C₄₇×#424	C₂²	1	2	yes	—
41	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#339	C₂²	1	2	yes	—
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625329	C₂³	1	2	yes	—
45	C₂×#10625324	—	2	2	no	—
46	C₂×#10625324	—	2	2	no	—
47	C₂×#10625324	C₂×C₄	1	2	yes	—
48	C₂×#10625324	C₂×C₄	1	2	yes	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	#13093983	C₂³	1	2	yes	—
52	#13093982	C₂×C₄	1	2	yes	—
53	#13093982	C₂×C₄	1	2	yes	—
54	#13093981	—	2	2	no	—
55	#13093980	—	2	2	no	—
56	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
57	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
59	C₂²⋊C₄×D₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	C₄²×D₄₇	—	2	2	no	—
62	#13093960	—	2	2	no	—
63	#13093958	C₂×C₄	1	1	yes	characteristic
64	#13093958	C₂×C₄	1	1	yes	characteristic
65	#13093957	C₂×C₄	1	2	yes	—
66	#13093957	C₂×C₄	1	2	yes	—
67	#13093956	C₂×C₄	1	2	yes	—
68	#13093955	C₂×C₄	1	2	yes	—
69	#13093955	C₂×C₄	1	2	yes	—
70	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
71	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
72	(C₂×D₄₇)⋊C₈	—	2	2	no	—
73	(C₂×D₄₇)⋊C₈	—	2	2	no	—
74	(C₂×D₄₇)⋊C₈	D₄	1	2	yes	—
75	(C₂×D₄₇)⋊C₈	D₄	1	2	yes	—
76	#13093934	—	2	2	no	—
77	#13093934	—	2	2	no	—
78	C₈×Dic₄₇	—	2	2	no	—
79	C₈×Dic₄₇	—	2	2	no	—
80	C₈×Dic₄₇	—	2	2	no	—
81	C₄₇⋊#95	—	2	1	no	—
82	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	#117×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	#108×C₄₇	—	2	2	no	—
88	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
90	#106×C₄₇	C₂×C₄	1	2	yes	—
91	C₄⋊C₈×C₄₇	—	2	2	no	—
92	C₄⋊C₈×C₄₇	—	2	2	no	—
93	#97×C₄₇	—	2	2	no	—
94	C₂³×D₄₇	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	1	no	—
98	C₂²×Dic₄₇	#41	1	1	yes	characteristic
99	C₂×C₄×D₄₇	—	2	1	no	—
100	C₂×C₄×D₄₇	—	2	1	no	—
101	C₂×C₄×D₄₇	—	2	1	no	—
102	C₂×C₄×D₄₇	—	2	1	no	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
107	M₁₆×C₄₇	—	2	2	no	—
108	M₁₆×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₄₇	#41	1	2	yes	—
116	C₂×C₈×C₄₇	#41	1	2	yes	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	1	no	—
122	C₄²×C₄₇	—	2	1	no	—
123	C₂²⋊Dic₄₇	—	2	2	no	—
124	(C₂×D₄₇)⋊C₄	—	2	2	no	—
125	(C₂×D₄₇)⋊C₄	—	2	2	no	—
126	(C₂×D₄₇)⋊C₄	—	4	2	no	—
127	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
128	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
129	Dic₄₇⋊C₄	—	2	2	no	—
130	Dic₄₇⋊C₄	—	2	2	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	2	1	no	—
136	#10625329	—	2	2	no	—
137	#10625329	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
146	#10625324	—	2	4	no	—
147	#10625324	—	2	4	no	—
148	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	1	no	—
150	C₂²×D₄₇	—	2	1	no	—
151	C₂²×D₄₇	—	4	1	no	—
152	C₂²×D₄₇	—	4	1	no	—
153	C₂²×D₄₇	C₄×D₄	1	2	yes	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	1	no	—
159	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	1	no	—
172	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
173	C₄×D₄₇	—	2	2	no	—
174	C₄×D₄₇	—	2	2	no	—
175	C₄×D₄₇	—	2	2	no	—
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	4	4	no	—
178	C₄×D₄₇	—	8	2	no	—
179	C₈×C₄₇	—	2	2	no	—
180	C₈×C₄₇	—	4	2	no	—
181	C₈×C₄₇	#117	1	2	yes	—
182	C₈×C₄₇	#117	1	2	yes	—
183	C₄₇⋊C₈	—	2	2	no	—
184	C₄₇⋊C₈	—	2	1	no	—
185	C₄₇⋊C₈	—	2	1	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	#22608	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂²×C₄₇	#552	1	1	yes	characteristic
192	C₂²×C₄₇	#552	1	1	yes	characteristic
193	C₂×D₄₇	—	2	2	no	—
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	8	1	no	—
197	C₂×D₄₇	—	8	1	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	8	1	no	—
201	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
202	C₄×C₄₇	#519	1	1	yes	characteristic
203	C₄×C₄₇	#547	1	1	yes	characteristic
204	C₄×C₄₇	#547	1	1	yes	characteristic
205	Dic₄₇	—	2	2	no	—
206	Dic₄₇	—	4	2	no	—
207	Dic₄₇	—	4	2	no	—
208	Dic₄₇	—	4	2	no	—
209	#2924	—	47	2	no	—
210	#2911	—	47	1	no	—
211	#1946	D₄₇	1	1	yes	characteristic, complemented
212	#1945	—	47	1	no	—
213	#1922	—	47	2	no	—
214	#1922	—	47	2	no	—
215	#1826	—	47	2	no	—
216	#1811	—	47	1	no	—
217	#1773	—	47	1	no	—
218	#1772	—	47	1	no	—
219	#1753	—	47	1	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	2	1	no	—
222	C₂×C₄₇	#2344	1	1	yes	characteristic
223	C₂×C₄₇	#2955	1	1	yes	characteristic
224	C₂×C₄₇	#2956	1	1	yes	characteristic
225	D₄₇	—	4	2	no	—
226	C₂²×M₁₆	—	47	1	no	—
227	C₂×#117	—	47	2	no	—
228	#433	—	94	2	no	—
229	#433	—	94	2	no	—
230	#432	—	94	2	no	—
231	#431	—	94	2	no	—
232	C₂×#108	—	47	1	no	—
233	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
234	#428	—	47	2	no	—
235	#428	—	47	2	no	—
236	#428	—	47	2	no	—
237	#428	—	47	2	no	—
238	#427	—	47	1	no	—
239	#427	—	47	2	no	—
240	#427	C₂×D₄₇	1	1	yes	characteristic
241	#424	—	47	2	no	—
242	#424	C₂×D₄₇	1	2	yes	—
243	#407	—	47	2	no	—
244	C₂×C₂²⋊C₈	—	47	1	no	—
245	#405	—	47	2	no	—
246	#405	—	47	2	no	—
247	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×C₈	—	47	1	no	—
249	C₄×C₂²⋊C₄	—	47	1	no	—
250	#341	—	47	2	no	—
251	#339	—	47	2	no	—
252	#339	—	47	2	no	—
253	#339	—	47	2	no	—
254	#339	C₂×D₄₇	1	2	yes	—
255	#336	—	47	1	no	—
256	#336	—	47	1	no	—
257	C₄₇	#22608	1	1	yes	characteristic, complemented, Sylow
258	C₂³×C₄	—	47	1	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂×M₁₆	—	47	2	no	—
261	C₂×M₁₆	—	47	2	no	—
262	C₂×M₁₆	—	94	2	no	—
263	C₂×M₁₆	—	94	2	no	—
264	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
265	C₂²×C₈	—	47	1	no	—
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	#117	—	47	2	no	—
270	#117	—	47	2	no	—
271	#117	—	47	2	no	—
272	#117	—	94	2	no	—
273	#117	—	94	2	no	—
274	#117	C₂²×D₄₇	1	2	yes	—
275	C₂×C₄⋊C₄	—	47	2	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₂²⋊C₄	—	94	2	no	—
278	C₂×C₂²⋊C₄	—	94	1	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	—	94	2	no	—
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	#108	—	2	2	no	—
283	#108	—	94	2	no	—
284	#107	—	47	1	no	—
285	#107	—	47	1	no	—
286	#107	—	47	2	no	—
287	#107	—	47	2	no	—
288	#107	C₄×D₄₇	1	1	yes	characteristic
289	#107	C₄×D₄₇	1	1	yes	characteristic
290	#106	—	47	2	no	—
291	#106	—	47	2	no	—
292	#106	—	47	2	no	—
293	#106	C₄×D₄₇	1	2	yes	—
294	C₄⋊C₈	—	2	2	no	—
295	C₄⋊C₈	—	2	2	no	—
296	C₄⋊C₈	—	94	2	no	—
297	C₄⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	47	2	no	—
299	C₂²⋊C₈	—	47	2	no	—
300	C₂²⋊C₈	—	94	2	no	—
301	C₂²⋊C₈	—	94	2	no	—
302	#97	—	2	2	no	—
303	#97	—	94	2	no	—
304	#97	—	94	2	no	—
305	C₄×C₈	—	94	2	no	—
306	C₄×C₈	—	94	2	no	—
307	C₄×C₈	—	94	2	no	—
308	#95	—	94	1	no	—
309	C₂⁴	—	47	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	2	no	—
313	C₂²×C₄	—	47	2	no	—
314	C₂²×C₄	—	94	2	no	—
315	C₂²×C₄	—	94	2	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	1	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	94	1	no	—
321	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
322	M₁₆	—	2	2	no	—
323	M₁₆	—	2	2	no	—
324	M₁₆	—	94	4	no	—
325	M₁₆	—	94	4	no	—
326	M₁₆	—	94	2	no	—
327	M₁₆	—	94	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	47	2	no	—
332	C₂×C₈	—	47	1	no	—
333	C₂×C₈	—	47	1	no	—
334	C₂×C₈	—	94	1	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₈	D₄×D₄₇	1	2	yes	—
342	C₂×C₈	#10625352	1	2	yes	—
343	C₂×C₈	#10625354	1	2	yes	—
344	C₄⋊C₄	—	47	2	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
349	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₂²⋊C₄	—	94	2	no	—
354	C₂²⋊C₄	—	188	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	94	2	no	—
359	C₄²	—	94	2	no	—
360	C₄²	—	94	2	no	—
361	C₄²	—	94	1	no	—
362	C₄²	—	94	1	no	—
363	C₂³	—	47	2	no	—
364	C₂³	—	94	1	no	—
365	C₂³	—	94	1	no	—
366	C₂³	—	188	1	no	—
367	C₂³	—	188	1	no	—
368	C₂³	#41×D₄₇	1	1	yes	characteristic
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	47	2	no	—
375	C₂×C₄	—	94	1	no	—
376	C₂×C₄	—	94	1	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	94	2	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	376	2	no	—
385	C₂×C₄	—	188	4	no	—
386	C₂×C₄	—	188	1	no	—
387	C₂×C₄	—	188	1	no	—
388	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
392	C₂×C₄	#13094071	1	1	yes	characteristic
393	C₂×C₄	#13094072	1	1	yes	characteristic
394	C₈	—	2	2	no	—
395	C₈	—	4	2	no	—
396	C₈	—	94	1	no	—
397	C₈	—	94	1	no	—
398	C₈	—	94	2	no	—
399	C₈	—	188	2	no	—
400	C₈	#13093982	1	2	yes	—
401	C₈	#13093982	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	94	2	no	—
405	C₂²	—	94	2	no	—
406	C₂²	—	94	2	no	—
407	C₂²	—	376	1	no	—
408	C₂²	—	376	1	no	—
409	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
410	C₂²	#15689807	1	1	yes	characteristic
411	C₂²	#15689811	1	1	yes	characteristic
412	C₄	—	4	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	94	2	no	—
416	C₄	—	188	2	no	—
417	C₄	—	188	2	no	—
418	C₄	—	188	2	no	—
419	C₄	C₂×#13093982	1	1	yes	characteristic
420	C₄	#15689599	1	1	yes	characteristic
421	C₄	#15689773	1	1	yes	characteristic
422	C₄	#15689776	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	188	2	no	—
426	C₂	#20246256	1	1	yes	characteristic
427	C₂	#20252288	1	1	yes	characteristic
428	C₂	#20252296	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1946	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂³×D₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1946	D₄₇
hypocenter	C₄₇	#22608
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1946

Complements

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

N	H ≅ G/N	type
3. #20244137	C₂	semidirect
4. #20243990	C₂	semidirect
5. #20243984	C₂	semidirect
8. #20243272	C₂	semidirect
9. #20243270	C₂	semidirect
11. C₄₇×#1946	C₂	semidirect
19. #15689164	C₄	semidirect
20. #15689164	C₄	semidirect
21. #15689162	C₄	semidirect
22. #15689162	C₄	semidirect
211. #1946	D₄₇	semidirect
257. C₄₇	#22608	semidirect

Maximal subgroups

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

subgroup	index
#20252045	2
#20251976	2
#20244137	2
#20243990	2
#20243984	2
#20243486	2
#20243427	2
#20243272	2
#20243270	2
#20243173	2
C₄₇×#1946	2
#22608	47