Subgroups — #26224781

Order 12032.

1126 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689224	C₂	1	2	yes	maximal, complemented
2	C₂×SD₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
3	#20246114	C₂	1	1	yes	maximal, characteristic
4	#20246108	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244271	C₂	1	2	yes	maximal, complemented
6	#20244244	C₂	1	2	yes	maximal, complemented
7	#20244213	C₂	1	1	yes	maximal, characteristic
8	#20244209	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243552	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243074	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#492	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
14	#15689224	—	2	8	no	—
15	SD₁₆×Dic₄₇	—	2	8	no	—
16	C₂×#13093958	C₂²	1	2	yes	—
17	C₂×#13093956	C₂²	1	2	yes	—
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093945	C₂²	1	2	yes	—
21	C₂×#13093945	C₂²	1	2	yes	—
22	C₂×#13093935	C₂²	1	1	yes	characteristic
23	C₂×#13093934	C₂²	1	1	yes	characteristic
24	C₂×#13093934	C₂²	1	1	yes	characteristic
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	#15689030	C₂²	1	2	yes	—
28	#15689026	C₂²	1	2	yes	—
29	#15689009	—	2	4	no	—
30	#15689003	—	2	4	no	—
31	#15688989	C₂²	1	1	yes	characteristic
32	#15688989	C₂²	1	1	yes	characteristic
33	#15688969	C₂²	1	1	yes	characteristic
34	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
35	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
36	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#492	C₄	1	8	yes	complemented
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂³×Dic₄₇	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	Q₈×Dic₄₇	—	2	4	no	—
44	Q₈×Dic₄₇	—	2	4	no	—
45	D₄×Dic₄₇	—	2	4	no	—
46	D₄×Dic₄₇	—	2	4	no	—
47	C₂×C₄⋊Dic₄₇	—	2	2	no	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
55	#13093958	—	2	4	no	—
56	#13093956	—	2	4	no	—
57	#13093948	—	2	4	no	—
58	#13093948	—	2	4	no	—
59	#13093945	—	2	4	no	—
60	#13093945	—	2	4	no	—
61	#13093935	—	2	2	no	—
62	#13093934	—	2	2	no	—
63	#13093934	D₄	1	4	yes	complemented
64	C₈×Dic₄₇	—	2	2	no	—
65	C₈×Dic₄₇	D₄	1	4	yes	complemented
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	4	no	—
69	C₄₇⋊#95	D₄	1	4	yes	—
70	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
71	C₂²×D₄×C₄₇	—	2	2	no	—
72	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
73	C₂×SD₁₆×C₄₇	—	2	4	no	—
74	C₂×SD₁₆×C₄₇	—	2	4	no	—
75	C₂×SD₁₆×C₄₇	—	2	4	no	—
76	C₂×SD₁₆×C₄₇	—	2	4	no	—
77	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
78	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₄₇	—	2	2	no	—
82	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
83	#127×C₄₇	—	2	2	no	—
84	#127×C₄₇	C₂×C₄	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
88	C₂⁴×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	2	no	—
94	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂×D₄×C₄₇	—	2	8	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	8	4	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	4	4	no	—
109	C₂²×Dic₄₇	—	8	4	no	—
110	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
111	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
112	SD₁₆×C₄₇	—	2	16	no	—
113	SD₁₆×C₄₇	—	2	16	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	#41	1	2	yes	—
119	C₂×C₈×C₄₇	#41	1	2	yes	—
120	C₄⋊C₄×C₄₇	—	2	8	no	—
121	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
122	C₄²×C₄₇	#41	1	2	yes	—
123	C₂²⋊Dic₄₇	—	4	4	no	—
124	C₂²⋊Dic₄₇	—	8	4	no	—
125	C₄⋊Dic₄₇	—	2	2	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	4	4	no	—
130	C₄×Dic₄₇	—	2	1	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	—	4	4	no	—
133	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
134	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
140	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
141	C₂³×C₄₇	—	2	4	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	4	no	—
145	C₂³×C₄₇	—	4	4	no	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₇	—	2	4	no	—
148	Q₈×C₄₇	—	2	4	no	—
149	Q₈×C₄₇	—	4	2	no	—
150	Q₈×C₄₇	—	4	2	no	—
151	D₄×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	8	8	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	4	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	4	4	no	—
174	C₂×Dic₄₇	—	8	8	no	—
175	C₂×Dic₄₇	#127	1	4	yes	—
176	C₈×C₄₇	C₄×D₄	1	4	yes	—
177	C₈×C₄₇	C₄×D₄	1	4	yes	—
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	#21695	—	47	1	no	maximal, Sylow
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	4	8	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	—	8	4	no	—
186	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
188	C₂²×C₄₇	#532	1	1	yes	characteristic
189	C₂²×C₄₇	#577	1	4	yes	—
190	C₄×C₄₇	—	2	4	no	—
191	C₄×C₄₇	—	4	4	no	—
192	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₄×C₄₇	#532	1	1	yes	characteristic
195	C₄×C₄₇	#532	1	1	yes	characteristic
196	Dic₄₇	—	2	4	no	—
197	Dic₄₇	—	4	2	no	—
198	Dic₄₇	—	8	2	no	—
199	Dic₄₇	—	8	2	no	—
200	C₂×#492	D₄₇	1	1	yes	characteristic
201	C₂×#440	—	47	2	no	—
202	C₂×C₄×SD₁₆	—	47	2	no	—
203	#2328	—	47	1	no	—
204	#2327	—	47	1	no	—
205	#1973	—	47	2	no	—
206	#1968	—	47	2	no	—
207	#1961	—	47	1	no	—
208	#1960	—	47	1	no	—
209	#1846	—	47	1	no	—
210	#1726	—	47	1	no	—
211	C₂×C₄₇	—	8	4	no	—
212	C₂×C₄₇	C₄×#127	1	1	yes	characteristic
213	C₂×C₄₇	#2949	1	2	yes	—
214	C₂×C₄₇	#3154	1	2	yes	—
215	C₂×C₄₇	#3174	1	2	yes	—
216	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
217	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
218	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
219	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄×Q₈	—	47	2	no	—
221	C₂×C₄×D₄	—	47	2	no	—
222	#492	Dic₄₇	1	8	yes	complemented
223	#440	—	94	8	no	—
224	C₄×SD₁₆	—	94	8	no	—
225	C₂×#107	—	47	2	no	—
226	C₂×#106	—	47	2	no	—
227	C₂×#103	—	47	2	no	—
228	C₂×#103	—	47	2	no	—
229	C₂×#102	—	47	2	no	—
230	C₂×#102	—	47	2	no	—
231	C₂×#97	—	47	1	no	—
232	C₂×#97	—	47	1	no	—
233	C₂×#97	—	47	1	no	—
234	C₂×C₄×C₈	—	47	1	no	—
235	C₂×C₄×C₈	—	47	1	no	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	#391	—	47	2	no	—
238	#390	—	47	2	no	—
239	#387	—	94	4	no	—
240	#386	—	94	4	no	—
241	#382	—	47	1	no	—
242	#382	—	47	1	no	—
243	#376	—	47	1	no	—
244	C₄₇	#21695	1	1	yes	characteristic, complemented, Sylow
245	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
246	C₂²×D₄	—	2	2	no	—
247	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
248	C₂³×C₄	—	94	2	no	—
249	C₂×SD₁₆	—	2	4	no	—
250	C₂×SD₁₆	—	2	4	no	—
251	C₂×SD₁₆	—	2	4	no	—
252	C₂×SD₁₆	—	2	4	no	—
253	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
254	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
258	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
259	C₄⋊Q₈	—	2	2	no	—
260	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	complemented
261	#127	—	2	2	no	—
262	#127	C₂×Dic₄₇	1	4	yes	—
263	C₄×Q₈	—	94	4	no	—
264	C₄×Q₈	—	94	4	no	—
265	C₄×D₄	—	94	4	no	—
266	C₄×D₄	—	94	4	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄⋊C₄	—	47	2	no	—
270	C₂×C₄⋊C₄	—	94	2	no	—
271	C₂×C₂²⋊C₄	—	94	4	no	—
272	C₂×C₂²⋊C₄	—	94	2	no	—
273	C₂×C₄²	—	47	1	no	—
274	C₂×C₄²	—	47	1	no	—
275	C₂×C₄²	—	94	2	no	—
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	#107	—	94	4	no	—
278	#106	—	94	4	no	—
279	#103	—	94	4	no	—
280	#103	—	94	4	no	—
281	#102	—	94	4	no	—
282	#102	—	94	4	no	—
283	#97	—	47	4	no	—
284	#97	—	94	2	no	—
285	#97	—	94	2	no	—
286	C₄×C₈	—	47	4	no	—
287	C₄×C₈	—	94	2	no	—
288	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
289	#95	—	47	4	no	—
290	#95	—	94	4	no	—
291	#95	—	94	2	no	—
292	#95	—	94	2	no	—
293	C₂⁴	—	2	2	no	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
300	C₂×D₄	—	2	8	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	8	4	no	—
307	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	47	2	no	—
310	C₂²×C₄	—	47	2	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	376	4	no	—
314	C₂²×C₄	—	188	4	no	—
315	C₂²×C₄	D₄×D₄₇	1	2	yes	—
316	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
317	SD₁₆	—	2	16	no	—
318	SD₁₆	—	2	16	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	47	2	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	D₄×D₄₇	1	2	yes	—
326	C₂×C₈	D₄×D₄₇	1	2	yes	—
327	C₂×C₈	#10625352	1	2	yes	—
328	C₂×C₈	#10625352	1	2	yes	—
329	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
330	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
331	C₄⋊C₄	—	2	8	no	—
332	C₄⋊C₄	—	94	2	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	94	2	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	—	188	4	no	—
337	C₂²⋊C₄	—	376	4	no	—
338	C₂²⋊C₄	—	188	4	no	—
339	C₄²	—	47	2	no	—
340	C₄²	—	47	2	no	—
341	C₄²	—	94	1	no	—
342	C₄²	—	94	1	no	—
343	C₄²	—	188	4	no	—
344	C₄²	#10625352	1	2	yes	—
345	C₄²	C₂²×Dic₄₇	1	2	yes	—
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	4	no	—
350	C₂³	—	4	4	no	—
351	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
352	Q₈	—	2	4	no	—
353	Q₈	—	2	4	no	—
354	Q₈	—	4	2	no	—
355	Q₈	—	4	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	2	4	no	—
358	D₄	—	4	2	no	—
359	D₄	—	4	2	no	—
360	D₄	—	8	8	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	47	4	no	—
366	C₂×C₄	—	94	4	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	4	no	—
369	C₂×C₄	—	376	8	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	4	no	—
373	C₂×C₄	—	188	4	no	—
374	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
375	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
379	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
381	C₈	—	94	2	no	—
382	C₈	—	94	2	no	—
383	C₈	D₄×Dic₄₇	1	4	yes	—
384	C₈	D₄×Dic₄₇	1	4	yes	—
385	C₂²	—	4	8	no	—
386	C₂²	—	4	4	no	—
387	C₂²	—	8	4	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
391	C₂²	#127×D₄₇	1	1	yes	characteristic
392	C₂²	#15689671	1	1	yes	characteristic
393	C₂²	#15689929	1	4	yes	—
394	C₄	—	2	4	no	—
395	C₄	—	4	4	no	—
396	C₄	—	94	4	no	—
397	C₄	—	376	2	no	—
398	C₄	—	376	2	no	—
399	C₄	—	188	2	no	—
400	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
401	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
402	C₄	#15689671	1	1	yes	characteristic
403	C₄	#15689671	1	1	yes	characteristic
404	C₂	—	8	4	no	—
405	C₂	#127×Dic₄₇	1	1	yes	characteristic
406	C₂	#20252248	1	2	yes	—
407	C₂	#20253857	1	2	yes	—
408	C₂	#20254013	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#492	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#492	D₄₇
hypocenter	C₄₇	#21695
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. C₂×#15689224	C₂	semidirect
2. C₂×SD₁₆×Dic₄₇	C₂	semidirect
4. #20246108	C₂	semidirect
5. #20244271	C₂	semidirect
6. #20244244	C₂	semidirect
8. #20244209	C₂	semidirect
9. #20243552	C₂	semidirect
10. #20243074	C₂	semidirect
38. C₄₇×#492	C₄	semidirect
63. #13093934	D₄	semidirect
65. C₈×Dic₄₇	D₄	semidirect
77. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
78. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
82. C₄⋊Q₈×C₄₇	C₂×C₄	semidirect
87. C₄×C₈×C₄₇	C₂×C₄	semidirect
222. #492	Dic₄₇	semidirect
244. C₄₇	#21695	semidirect
253. C₂×SD₁₆	C₂×Dic₄₇	semidirect
254. C₂×SD₁₆	C₂×Dic₄₇	semidirect
260. C₄⋊Q₈	C₂×Dic₄₇	semidirect
288. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689224	2
C₂×SD₁₆×Dic₄₇	2
#20246114	2
#20246108	2
#20244271	2
#20244244	2
#20244213	2
#20244209	2
#20243552	2
#20243074	2
C₂×C₄₇×#492	2
#21695	47