Subgroups — #26230212

Order 12032.

820 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253869	C₂	1	1	yes	maximal, characteristic
2	#20252304	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252240	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244286	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243918	C₂	1	2	yes	maximal, complemented
6	#20243912	C₂	1	2	yes	maximal, complemented
7	#20243873	C₂	1	2	yes	maximal, complemented
8	#20243871	C₂	1	2	yes	maximal, complemented
9	#20243513	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243143	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1978	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094050	C₂²	1	2	yes	—
13	C₂×#13094046	C₂²	1	1	yes	characteristic
14	#15689889	C₂²	1	2	yes	—
15	#15689690	C₂²	1	2	yes	—
16	#15689598	C₂²	1	2	yes	—
17	#15689511	C₄	1	4	yes	complemented
18	#15689506	C₄	1	2	yes	complemented
19	#15689498	C₄	1	2	yes	complemented
20	#15689244	—	2	2	no	—
21	#15689239	—	2	2	no	—
22	#15689235	—	2	2	no	—
23	D₈×Dic₄₇	—	2	2	no	—
24	#15689161	C₂²	1	1	yes	characteristic
25	#15689139	C₂²	1	2	yes	—
26	#15689139	C₂²	1	2	yes	—
27	#15689128	C₂²	1	2	yes	—
28	#15689096	C₂²	1	2	yes	—
29	#15689078	C₂²	1	1	yes	characteristic
30	#15689078	C₂²	1	1	yes	characteristic
31	#15688895	C₂²	1	2	yes	—
32	C₄₇⋊#338	C₂²	1	1	yes	characteristic
33	#15688880	C₂²	1	2	yes	—
34	#15688880	C₂²	1	1	yes	characteristic
35	#15688879	C₂²	1	1	yes	characteristic
36	#15688879	C₂²	1	1	yes	characteristic
37	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#418	C₂²	1	2	yes	—
40	C₂×#100×C₄₇	C₂²	1	2	yes	—
41	C₄₇×#405	C₂²	1	1	yes	characteristic
42	C₂×#10625350	C₂³	1	2	yes	—
43	#13094050	—	4	2	no	—
44	#13094050	—	4	2	no	—
45	#13094046	—	2	1	no	—
46	#13094046	—	2	1	no	—
47	#13094046	—	2	1	no	—
48	#13094046	—	2	1	no	—
49	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
50	C₂×#10625325	C₂×C₄	1	2	yes	complemented
51	C₂×#10625335	C₂×C₄	1	4	yes	complemented
52	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
53	C₂×#10625334	C₂×C₄	1	4	yes	complemented
54	#13094032	—	2	4	no	—
55	#13094030	—	4	2	no	—
56	C₂×#10625329	C₂³	1	1	yes	characteristic
57	C₂×#10625329	C₂³	1	1	yes	characteristic
58	M₁₆×D₄₇	—	4	2	no	—
59	#13094020	C₂×C₄	1	4	yes	complemented
60	#13094011	C₂×C₄	1	4	yes	complemented
61	#13093995	—	4	2	no	—
62	#13093993	—	4	2	no	—
63	D₄×Dic₄₇	—	2	4	no	—
64	D₄×Dic₄₇	—	4	2	no	—
65	#13093983	C₂³	1	2	yes	—
66	#13093983	C₂³	1	1	yes	characteristic
67	#13093983	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊Dic₄₇	—	4	2	no	—
69	#13093958	—	2	1	no	—
70	#13093956	—	2	1	no	—
71	#13093950	—	2	4	no	—
72	#13093950	—	4	2	no	—
73	#13093945	—	2	4	no	—
74	#13093938	—	4	2	no	—
75	#13093934	C₂×C₄	1	2	yes	complemented
76	#13093934	D₄	1	2	yes	complemented
77	C₈×Dic₄₇	C₂×C₄	1	2	yes	complemented
78	C₈×Dic₄₇	D₄	1	2	yes	complemented
79	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
80	C₂×D₈×C₄₇	—	2	1	no	—
81	C₂×D₈×C₄₇	—	2	1	no	—
82	C₂×D₈×C₄₇	—	2	1	no	—
83	C₂×D₈×C₄₇	—	2	1	no	—
84	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
85	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
86	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
87	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	#117×C₄₇	C₂³	1	1	yes	characteristic
90	#108×C₄₇	—	2	1	no	—
91	#108×C₄₇	—	2	1	no	—
92	#102×C₄₇	—	4	2	no	—
93	#100×C₄₇	—	4	2	no	—
94	#97×C₄₇	—	2	1	no	—
95	C₄×C₈×C₄₇	—	2	1	no	—
96	C₂⁴×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	—	2	2	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₇	—	2	2	no	—
105	C₂×C₂²⋊D₄₇	—	4	4	no	—
106	C₂²×Dic₄₇	—	4	4	no	—
107	#10625350	—	2	2	no	—
108	#10625350	—	2	2	no	—
109	#10625350	—	2	2	no	—
110	#10625350	—	2	2	no	—
111	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
114	D₈×C₄₇	—	2	2	no	—
115	D₈×C₄₇	—	2	2	no	—
116	D₈×C₄₇	—	2	2	no	—
117	D₈×C₄₇	—	2	2	no	—
118	M₁₆×C₄₇	—	2	2	no	—
119	M₁₆×C₄₇	—	2	1	no	—
120	M₁₆×C₄₇	—	2	2	no	—
121	M₁₆×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
129	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
130	C₄⋊C₄×C₄₇	—	2	1	no	—
131	C₂²⋊C₄×C₄₇	—	2	1	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₂²⋊Dic₄₇	—	2	1	no	—
134	C₂²⋊Dic₄₇	—	2	1	no	—
135	C₂²⋊Dic₄₇	—	2	2	no	—
136	C₂²⋊Dic₄₇	—	4	4	no	—
137	C₂²⋊Dic₄₇	—	4	4	no	—
138	#10625335	—	4	4	no	—
139	#10625334	—	4	4	no	—
140	C₄⋊Dic₄₇	—	2	1	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
145	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
146	#10625329	—	2	1	no	—
147	#10625329	—	2	1	no	—
148	#10625329	—	2	1	no	—
149	#10625329	—	2	1	no	—
150	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	Dic₁₈₈	—	2	1	no	—
153	Dic₁₈₈	—	2	1	no	—
154	D₃₇₆	—	2	1	no	—
155	D₃₇₆	—	2	1	no	—
156	#10625325	—	2	2	no	—
157	#10625325	—	2	2	no	—
158	#10625324	—	4	4	no	—
159	C₈×D₄₇	—	4	4	no	—
160	C₂³×C₄₇	—	2	4	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	16	2	no	—
164	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
165	C₂²×D₄₇	—	2	2	no	—
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	1	no	—
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	1	yes	characteristic
174	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
175	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
176	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂²⋊D₄₇	—	4	2	no	—
178	C₂²⋊D₄₇	—	4	2	no	—
179	C₂²⋊D₄₇	—	16	4	no	—
180	C₂×Dic₄₇	—	2	2	no	—
181	C₂×Dic₄₇	—	2	2	no	—
182	C₂×Dic₄₇	—	2	2	no	—
183	C₂×Dic₄₇	—	4	2	no	—
184	C₂×Dic₄₇	—	16	4	no	—
185	D₁₈₈	—	2	2	no	—
186	D₁₈₈	—	2	2	no	—
187	C₄×D₄₇	—	4	2	no	—
188	C₄×D₄₇	—	4	2	no	—
189	Dic₉₄	—	2	2	no	—
190	Dic₉₄	—	2	2	no	—
191	C₈×C₄₇	—	4	2	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
194	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
195	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
196	C₈×C₄₇	C₄×D₄	1	1	yes	characteristic
197	C₄₇⋊C₈	—	2	2	no	—
198	C₄₇⋊C₈	—	2	2	no	—
199	#22286	—	47	1	no	maximal, Sylow
200	C₂²×C₄₇	—	4	1	no	—
201	C₂²×C₄₇	—	4	4	no	—
202	C₂²×C₄₇	—	8	4	no	—
203	C₂²×C₄₇	—	8	4	no	—
204	C₂²×C₄₇	—	16	2	no	—
205	C₂²×C₄₇	#518	1	1	yes	characteristic
206	C₂²×C₄₇	#535	1	1	yes	characteristic
207	C₂²×C₄₇	#540	1	1	yes	characteristic
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	—	8	2	no	—
210	C₄×C₄₇	—	8	1	no	—
211	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₄×C₄₇	#518	1	1	yes	characteristic
213	C₄×C₄₇	#535	1	1	yes	characteristic
214	C₄×C₄₇	#540	1	1	yes	characteristic
215	Dic₄₇	—	4	2	no	—
216	Dic₄₇	—	4	2	no	—
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	8	2	no	—
219	#3155	—	47	1	no	—
220	#2957	—	47	1	no	—
221	#2948	—	47	1	no	—
222	#1978	D₄₇	1	1	yes	characteristic, complemented
223	#1976	—	47	1	no	—
224	#1911	—	47	2	no	—
225	#1910	—	47	2	no	—
226	#1904	—	47	2	no	—
227	#1903	—	47	2	no	—
228	#1833	—	47	1	no	—
229	#1747	—	47	1	no	—
230	C₂×C₄₇	—	2	1	no	—
231	C₂×C₄₇	—	2	1	no	—
232	C₂×C₄₇	—	2	1	no	—
233	C₂×C₄₇	—	8	4	no	—
234	C₂×C₄₇	#2328	1	1	yes	characteristic
235	D₄₇	—	8	2	no	—
236	C₂×AGL(1,ℤ/8)	—	47	2	no	—
237	C₂×#135	—	47	1	no	—
238	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
239	#568	—	47	2	no	—
240	#535	—	47	2	no	—
241	#518	—	47	2	no	—
242	#496	—	47	4	no	—
243	#495	—	47	2	no	—
244	#493	—	47	2	no	—
245	#444	—	94	2	no	—
246	#443	—	94	2	no	—
247	#442	—	94	2	no	—
248	C₄×D₈	—	94	2	no	—
249	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
250	#427	—	47	1	no	—
251	#421	—	47	2	no	—
252	#421	—	47	2	no	—
253	#418	—	47	2	no	—
254	#418	C₂×D₄₇	1	2	yes	—
255	C₂×#100	C₂×D₄₇	1	2	yes	—
256	#410	—	47	2	no	—
257	#405	—	47	1	no	—
258	#405	—	47	1	no	—
259	#405	C₂×D₄₇	1	1	yes	characteristic
260	#344	—	47	2	no	—
261	#338	—	47	1	no	—
262	H(3,ℤ/4)	—	47	2	no	—
263	H(3,ℤ/4)	—	47	1	no	—
264	H(3,ℤ/4)	—	47	1	no	—
265	H(3,ℤ/4)	—	47	1	no	—
266	C₄₇	#22286	1	1	yes	characteristic, complemented, Sylow
267	C₂×#41	—	47	2	no	—
268	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
269	AGL(1,ℤ/8)	—	188	2	no	—
270	AGL(1,ℤ/8)	—	188	2	no	—
271	#135	—	94	1	no	—
272	#135	—	94	1	no	—
273	#135	—	94	1	no	—
274	#135	—	94	1	no	—
275	C₂×Q₁₆	—	47	1	no	—
276	C₂×SD₁₆	—	47	4	no	—
277	C₂×SD₁₆	—	47	2	no	—
278	C₂×D₈	—	2	1	no	—
279	C₂×D₈	—	2	1	no	—
280	C₂×D₈	—	2	1	no	—
281	C₂×D₈	—	2	1	no	—
282	C₂×D₈	—	47	4	no	—
283	C₂×D₈	—	47	1	no	—
284	C₂×D₈	C₄×D₄₇	1	2	yes	—
285	C₂×D₈	C₄×D₄₇	1	2	yes	—
286	#131	—	94	4	no	—
287	#131	—	188	2	no	—
288	C₂×M₁₆	—	47	1	no	—
289	C₂×M₁₆	—	47	1	no	—
290	C₂×M₁₆	—	188	2	no	—
291	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
292	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
293	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
294	#127	—	47	4	no	—
295	#124	—	47	4	no	—
296	#121	—	188	2	no	—
297	#120	—	188	2	no	—
298	C₄×D₄	—	94	4	no	—
299	C₄×D₄	—	188	2	no	—
300	#117	—	47	1	no	—
301	#117	—	47	1	no	—
302	#117	—	47	2	no	—
303	#117	C₂²×D₄₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	—	188	2	no	—
305	#108	—	2	1	no	—
306	#108	—	2	1	no	—
307	#107	—	94	1	no	—
308	#106	—	94	1	no	—
309	#104	—	94	4	no	—
310	#104	—	188	2	no	—
311	#102	—	4	2	no	—
312	#102	—	94	4	no	—
313	#100	—	4	2	no	—
314	#99	—	188	2	no	—
315	#97	—	2	1	no	—
316	#97	—	47	2	no	—
317	#97	—	47	2	no	—
318	C₄×C₈	—	2	1	no	—
319	C₄×C₈	—	47	2	no	—
320	C₄×C₈	—	47	2	no	—
321	C₂⁴	—	2	2	no	—
322	#41	—	94	2	no	—
323	#41	—	94	2	no	—
324	#41	—	94	2	no	—
325	#41	—	94	2	no	—
326	C₂×Q₈	—	47	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	47	2	no	—
333	C₂×D₄	—	94	2	no	—
334	C₂×D₄	—	188	4	no	—
335	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
336	C₂²×C₄	—	94	2	no	—
337	C₂²×C₄	—	188	4	no	—
338	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
339	Q₁₆	—	94	1	no	—
340	Q₁₆	—	94	1	no	—
341	SD₁₆	—	94	2	no	—
342	SD₁₆	—	94	2	no	—
343	SD₁₆	—	188	4	no	—
344	D₈	—	2	2	no	—
345	D₈	—	2	2	no	—
346	D₈	—	2	2	no	—
347	D₈	—	2	2	no	—
348	D₈	—	94	1	no	—
349	D₈	—	94	1	no	—
350	D₈	—	188	4	no	—
351	M₁₆	—	2	2	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	2	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	94	1	no	—
356	M₁₆	—	94	1	no	—
357	M₁₆	—	94	1	no	—
358	M₁₆	—	94	1	no	—
359	M₁₆	—	188	4	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	47	2	no	—
363	C₂×C₈	—	47	2	no	—
364	C₂×C₈	—	188	4	no	—
365	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
368	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
369	C₂×C₈	#10625352	1	1	yes	characteristic
370	C₂×C₈	#10625352	1	1	yes	characteristic
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	94	1	no	—
373	C₄⋊C₄	—	94	1	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₂²⋊C₄	—	2	1	no	—
376	C₂²⋊C₄	—	94	1	no	—
377	C₂²⋊C₄	—	94	1	no	—
378	C₂²⋊C₄	—	94	2	no	—
379	C₂²⋊C₄	—	188	4	no	—
380	C₂²⋊C₄	—	188	4	no	—
381	C₄²	—	2	1	no	—
382	C₄²	—	47	2	no	—
383	C₄²	—	47	2	no	—
384	C₄²	—	94	2	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	16	2	no	—
389	C₂³	—	94	2	no	—
390	C₂³	#13094070	1	1	yes	characteristic
391	Q₈	—	94	2	no	—
392	Q₈	—	94	2	no	—
393	D₄	—	2	4	no	—
394	D₄	—	2	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	4	2	no	—
397	D₄	—	94	2	no	—
398	D₄	—	94	2	no	—
399	D₄	—	188	2	no	—
400	D₄	—	188	2	no	—
401	D₄	—	752	4	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	94	2	no	—
404	C₂×C₄	—	94	2	no	—
405	C₂×C₄	—	94	2	no	—
406	C₂×C₄	—	188	2	no	—
407	C₂×C₄	—	188	2	no	—
408	C₂×C₄	—	188	2	no	—
409	C₂×C₄	—	752	4	no	—
410	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
413	C₂×C₄	#13094069	1	1	yes	characteristic
414	C₂×C₄	#13094069	1	1	yes	characteristic
415	C₂×C₄	#13094070	1	1	yes	characteristic
416	C₈	—	4	2	no	—
417	C₈	—	4	1	no	—
418	C₈	—	94	2	no	—
419	C₈	—	94	2	no	—
420	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
421	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
422	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
423	C₈	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
424	C₂²	—	4	1	no	—
425	C₂²	—	4	4	no	—
426	C₂²	—	8	4	no	—
427	C₂²	—	8	4	no	—
428	C₂²	—	16	2	no	—
429	C₂²	—	376	2	no	—
430	C₂²	—	188	2	no	—
431	C₂²	#15689595	1	1	yes	characteristic
432	C₂²	#15689691	1	1	yes	characteristic
433	C₂²	#15689726	1	1	yes	characteristic
434	C₄	—	8	1	no	—
435	C₄	—	376	2	no	—
436	C₄	—	188	2	no	—
437	C₄	—	188	2	no	—
438	C₄	—	188	2	no	—
439	C₄	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
440	C₄	#15689595	1	1	yes	characteristic
441	C₄	#15689686	1	1	yes	characteristic
442	C₄	#15689726	1	1	yes	characteristic
443	C₂	—	2	1	no	—
444	C₂	—	2	1	no	—
445	C₂	—	2	1	no	—
446	C₂	—	8	4	no	—
447	C₂	—	376	2	no	—
448	C₂	#20246112	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#20246112
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1978	C₂
socle	C₂×C₄₇	#2328
prime radical	#20253869	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1978	D₄₇
hypocenter	C₄₇	#22286
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1978

Complements

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

N	H ≅ G/N	type
2. #20252304	C₂	semidirect
3. #20252240	C₂	semidirect
4. #20244286	C₂	semidirect
5. #20243918	C₂	semidirect
6. #20243912	C₂	semidirect
7. #20243873	C₂	semidirect
8. #20243871	C₂	semidirect
9. #20243513	C₂	semidirect
10. #20243143	C₂	semidirect
11. C₄₇×#1978	C₂	semidirect
17. #15689511	C₄	semidirect
18. #15689506	C₄	semidirect
19. #15689498	C₄	semidirect
49. C₂×Dic₁₈₈	C₂×C₄	semidirect
50. C₂×#10625325	C₂×C₄	semidirect
51. C₂×#10625335	C₂×C₄	semidirect
52. C₂×D₃₇₆	C₂×C₄	semidirect
53. C₂×#10625334	C₂×C₄	semidirect
59. #13094020	C₂×C₄	semidirect
60. #13094011	C₂×C₄	semidirect
75. #13093934	C₂×C₄	semidirect
76. #13093934	D₄	semidirect
77. C₈×Dic₄₇	C₂×C₄	semidirect
78. C₈×Dic₄₇	D₄	semidirect
222. #1978	D₄₇	semidirect
266. C₄₇	#22286	semidirect

Maximal subgroups

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

subgroup	index
#20253869	2
#20252304	2
#20252240	2
#20244286	2
#20243918	2
#20243912	2
#20243873	2
#20243871	2
#20243513	2
#20243143	2
C₄₇×#1978	2
#22286	47