Subgroups — #26188049

Order 12032.

654 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253943	C₂	1	1	yes	maximal, characteristic
2	#20252331	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252132	C₂	1	1	yes	maximal, characteristic
4	#20242281	C₂	1	2	yes	maximal, complemented
5	#20242234	C₂	1	2	yes	maximal, complemented
6	#20242221	C₂	1	2	yes	maximal, complemented
7	#20242191	C₂	1	2	yes	maximal, complemented
8	C₂×#15688873	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241792	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1480	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	—	2	1	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	#15689519	C₄	1	1	yes	characteristic
15	#15689495	C₄	1	1	yes	characteristic
16	#15689475	C₄	1	1	yes	characteristic
17	#15689469	C₄	1	1	yes	characteristic
18	#15689350	C₄	1	2	yes	—
19	#15689350	C₄	1	2	yes	—
20	#15689252	—	2	2	no	—
21	#15689250	C₂²	1	2	yes	—
22	#15689247	C₂²	1	2	yes	—
23	C₄×#10625335	C₂²	1	2	yes	—
24	C₄×#10625335	C₂²	1	2	yes	—
25	#15689201	C₂²	1	2	yes	—
26	#15689195	—	2	2	no	—
27	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
28	#15689149	—	2	1	no	—
29	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	#15689090	—	2	1	no	—
31	#15689078	—	2	1	no	—
32	C₄×#10625329	C₂²	1	1	yes	characteristic
33	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	#15688873	C₂²	1	1	yes	characteristic
35	#15688873	C₂²	1	1	yes	characteristic
36	#15688873	C₂²	1	1	yes	characteristic
37	#15688873	C₂²	1	1	yes	characteristic
38	#15688855	C₂²	1	2	yes	—
39	#15688855	C₂²	1	2	yes	—
40	#15688845	C₂²	1	2	yes	—
41	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
42	C₄₇×#532	C₂²	1	1	yes	characteristic
43	C₄₇×#431	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
46	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
47	C₂×#10625335	C₂×C₄	1	2	yes	—
48	C₂×#10625335	C₂×C₄	1	2	yes	—
49	#13094031	—	4	4	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂×#10625329	D₄	1	1	yes	characteristic
52	C₂×#10625329	D₄	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	—	2	1	no	—
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
57	#13094024	C₂×C₄	1	1	yes	characteristic
58	#13094024	C₂×C₄	1	1	yes	characteristic
59	#13094016	—	2	1	no	—
60	#13094003	—	2	1	no	—
61	#13094003	C₂×C₄	1	2	yes	—
62	C₄×Dic₉₄	—	2	1	no	—
63	C₄×Dic₉₄	C₂³	1	2	yes	—
64	#13093983	—	2	1	no	—
65	#13093955	C₂×C₄	1	2	yes	—
66	#13093955	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
70	Dic₄₇⋊C₈	—	2	2	no	—
71	Dic₄₇⋊C₈	—	2	2	no	—
72	#13093947	C₂×C₄	1	2	yes	—
73	#13093947	C₂×C₄	1	2	yes	—
74	#13093945	C₂×C₄	1	2	yes	—
75	#13093945	C₂×C₄	1	2	yes	—
76	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
77	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
78	#13093935	D₄	1	2	yes	—
79	#13093934	—	2	2	no	—
80	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
82	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
83	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₈×Dic₄₇	—	2	2	no	—
86	C₂×#41×C₄₇	—	2	1	no	—
87	C₂²×C₈×C₄₇	—	2	1	no	—
88	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
90	#124×C₄₇	—	2	1	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	C₂×C₄	1	2	yes	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	C₂³	1	2	yes	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²⋊C₈×C₄₇	—	2	1	no	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	#41×C₄₇	—	4	2	no	—
103	#41×C₄₇	—	4	2	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	1	no	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
113	C₂×Dic₉₄	—	2	1	no	—
114	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	4	2	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²⋊C₄×C₄₇	—	2	2	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₄₇	#41	1	1	yes	characteristic
126	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂²⋊Dic₄₇	—	2	2	no	—
128	#10625335	—	2	4	no	—
129	#10625335	—	4	2	no	—
130	C₄⋊Dic₄₇	—	2	1	no	—
131	C₄⋊Dic₄₇	—	2	1	no	—
132	C₄⋊Dic₄₇	—	2	1	no	—
133	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
134	Dic₄₇⋊C₄	—	2	2	no	—
135	Dic₄₇⋊C₄	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	#10625329	—	2	2	no	—
138	#10625329	—	4	4	no	—
139	#10625329	SD₁₆	1	4	yes	complemented
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	4	1	no	—
144	C₂×C₄₇⋊C₈	—	4	2	no	—
145	C₂×C₄₇⋊C₈	—	4	4	no	—
146	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
154	Q₈×C₄₇	—	4	2	no	—
155	D₄×C₄₇	—	2	2	no	—
156	D₄×C₄₇	—	2	2	no	—
157	D₄×C₄₇	—	4	4	no	—
158	D₄×C₄₇	—	4	2	no	—
159	D₄×C₄₇	—	8	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	1	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
170	C₂×C₄×C₄₇	#135	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	1	yes	characteristic
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	Dic₉₄	—	2	2	no	—
177	Dic₉₄	—	2	2	no	—
178	Dic₉₄	—	8	1	no	—
179	C₈×C₄₇	—	4	2	no	—
180	C₈×C₄₇	—	4	1	no	—
181	C₈×C₄₇	—	4	1	no	—
182	C₄₇⋊C₈	—	2	1	no	—
183	C₄₇⋊C₈	—	2	1	no	—
184	C₄₇⋊C₈	—	2	1	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	4	1	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	C₄₇⋊C₈	#131	1	2	yes	complemented
189	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	—
190	#18067	—	47	1	no	maximal, Sylow
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	4	2	no	—
194	C₂²×C₄₇	—	4	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
197	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	C₄×SD₁₆	1	2	yes	—
203	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
204	C₄×C₄₇	#568	1	1	yes	characteristic
205	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
207	Dic₄₇	—	4	2	no	—
208	Dic₄₇	—	4	2	no	—
209	#3167	—	47	1	no	—
210	#2962	—	47	1	no	—
211	#2935	—	47	1	no	—
212	#1590	—	47	2	no	—
213	#1583	—	47	2	no	—
214	#1582	—	47	2	no	—
215	C₈×SD₁₆	—	47	2	no	—
216	C₂×#334	—	47	1	no	—
217	#1481	—	47	1	no	—
218	#1480	D₄₇	1	1	yes	characteristic
219	C₈×M₁₆	—	47	1	no	—
220	C₂×C₄₇	—	2	2	no	—
221	C₂×C₄₇	—	8	2	no	—
222	C₂×C₄₇	#2935	1	1	yes	characteristic
223	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
224	C₂×C₄₇	#2957	1	1	yes	characteristic
225	C₂×#131	—	94	1	no	—
226	#533	—	47	1	no	—
227	#532	C₂×D₄₇	1	1	yes	characteristic
228	#498	—	47	1	no	—
229	#492	—	47	1	no	—
230	#487	—	47	1	no	—
231	#486	—	47	1	no	—
232	#465	—	47	2	no	—
233	#465	—	47	2	no	—
234	#446	—	47	2	no	—
235	#446	—	94	2	no	—
236	C₈×Q₈	—	47	2	no	—
237	C₄×SD₁₆	—	47	2	no	—
238	C₄×SD₁₆	—	47	2	no	—
239	#436	—	47	2	no	—
240	#435	—	94	2	no	—
241	C₈×D₄	—	47	2	no	—
242	#431	C₂×D₄₇	1	1	yes	characteristic
243	#424	—	94	1	no	—
244	C₂×C₄⋊C₈	—	47	1	no	—
245	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
246	#408	—	94	1	no	—
247	#405	—	94	1	no	—
248	C₄×M₁₆	—	47	1	no	—
249	C₂×C₄×C₈	—	47	1	no	—
250	#334	—	47	1	no	—
251	#334	—	47	1	no	—
252	#334	—	47	1	no	—
253	#334	—	47	1	no	—
254	Q₈⋊C₈	—	47	2	no	—
255	Q₈⋊C₈	—	47	2	no	—
256	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
257	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
258	#322	—	47	2	no	—
259	C₈²	—	47	2	no	—
260	C₄₇	#18067	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	2	1	no	—
262	C₂×SD₁₆	—	47	2	no	—
263	C₂×SD₁₆	—	47	2	no	—
264	#131	—	188	4	no	—
265	C₂×M₁₆	—	47	1	no	—
266	C₂×M₁₆	—	47	1	no	—
267	C₂×M₁₆	—	94	2	no	—
268	C₂²×C₈	—	2	1	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	1	no	—
271	C₂²×C₈	—	94	2	no	—
272	C₂²×C₈	—	94	1	no	—
273	C₄⋊Q₈	—	47	1	no	—
274	C₄⋊Q₈	—	47	1	no	—
275	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
276	#127	C₄×D₄₇	1	1	yes	characteristic
277	#125	—	94	1	no	—
278	#124	—	2	1	no	—
279	C₂²⋊Q₈	—	47	2	no	—
280	C₂²⋊Q₈	—	94	1	no	—
281	#121	—	2	1	no	—
282	#121	C₄×D₄₇	1	2	yes	—
283	C₄×Q₈	—	47	2	no	—
284	C₄×Q₈	—	94	1	no	—
285	C₄×D₄	—	2	1	no	—
286	C₄×D₄	C₂²×D₄₇	1	2	yes	—
287	#117	—	94	1	no	—
288	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
289	#106	—	47	2	no	—
290	#106	—	47	2	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	47	1	no	—
294	C₄⋊C₈	—	47	1	no	—
295	C₄⋊C₈	—	94	2	no	—
296	C₄⋊C₈	—	94	2	no	—
297	C₄⋊C₈	—	94	1	no	—
298	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
300	#103	—	47	2	no	—
301	#103	—	47	2	no	—
302	#102	—	47	2	no	—
303	#102	—	47	2	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₂²⋊C₈	—	94	2	no	—
307	#97	—	47	2	no	—
308	#97	—	94	2	no	—
309	C₄×C₈	—	47	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	2	no	—
313	C₄×C₈	—	47	1	no	—
314	C₄×C₈	—	94	2	no	—
315	C₄×C₈	C₂²×D₄₇	1	2	yes	—
316	#41	—	4	2	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	47	2	no	—
320	C₂×Q₈	—	94	1	no	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	1	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	#10625352	1	1	yes	characteristic
329	SD₁₆	—	94	4	no	—
330	SD₁₆	—	188	2	no	—
331	M₁₆	—	47	4	no	—
332	M₁₆	—	94	2	no	—
333	M₁₆	—	188	4	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	47	1	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	47	1	no	—
341	C₂×C₈	—	47	1	no	—
342	C₂×C₈	—	47	1	no	—
343	C₂×C₈	—	47	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	1	no	—
346	C₂×C₈	—	94	1	no	—
347	C₂×C₈	—	188	4	no	—
348	C₂×C₈	—	188	1	no	—
349	C₂×C₈	—	188	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	47	2	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₄⋊C₄	—	94	1	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₄⋊C₄	—	94	2	no	—
357	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
358	C₂²⋊C₄	—	2	2	no	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	94	2	no	—
361	C₄²	—	94	2	no	—
362	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₄²	D₄×D₄₇	1	1	yes	characteristic
364	C₄²	#10625352	1	1	yes	characteristic
365	C₄²	C₂³×D₄₇	1	1	yes	characteristic
366	C₂³	—	2	2	no	—
367	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	94	2	no	—
370	Q₈	—	94	2	no	—
371	Q₈	—	376	1	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	2	no	—
374	D₄	—	4	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	8	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
386	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
389	C₂×C₄	#13094043	1	2	yes	—
390	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	4	1	no	—
395	C₈	—	4	1	no	—
396	C₈	—	47	2	no	—
397	C₈	—	47	4	no	—
398	C₈	—	94	1	no	—
399	C₈	—	94	1	no	—
400	C₈	—	94	1	no	—
401	C₈	—	94	2	no	—
402	C₈	—	188	1	no	—
403	C₈	—	188	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	4	2	no	—
407	C₂²	—	4	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	#15689214	1	2	yes	—
410	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	4	2	no	—
415	C₄	—	188	2	no	—
416	C₄	—	188	2	no	—
417	C₄	#15689214	1	2	yes	—
418	C₄	#131×D₄₇	1	1	yes	characteristic
419	C₄	#15689888	1	1	yes	characteristic
420	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
421	C₄	C₂×#13094043	1	1	yes	characteristic
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	#20252128	1	1	yes	characteristic
425	C₂	C₂×#15689214	1	1	yes	characteristic
426	C₂	#20252301	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1480	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₄₇×#532	C₂²
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1480	D₄₇
hypocenter	C₄₇	#18067
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1480

Complements

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

N	H ≅ G/N	type
2. #20252331	C₂	semidirect
4. #20242281	C₂	semidirect
5. #20242234	C₂	semidirect
6. #20242221	C₂	semidirect
7. #20242191	C₂	semidirect
8. C₂×#15688873	C₂	semidirect
9. #20241792	C₂	semidirect
10. #20241669	C₂	semidirect
139. #10625329	SD₁₆	semidirect
188. C₄₇⋊C₈	#131	semidirect
260. C₄₇	#18067	semidirect

Maximal subgroups

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

subgroup	index
#20253943	2
#20252331	2
#20252132	2
#20242281	2
#20242234	2
#20242221	2
#20242191	2
C₂×#15688873	2
#20241792	2
#20241669	2
C₄₇×#1480	2
#18067	47