Subgroups — #26224289

Order 12032.

890 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	C₂×#15689469	C₂	1	1	yes	maximal, characteristic
2	#20246136	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244360	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244213	C₂	1	1	yes	maximal, characteristic
5	#20244088	C₂	1	2	yes	maximal, complemented
6	#20244074	C₂	1	2	yes	maximal, complemented
7	#20243518	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243213	C₂	1	2	yes	maximal, complemented
9	C₄×#13093945	C₂	1	2	yes	maximal, complemented
10	#20243075	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2328	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094024	C₂²	1	1	yes	characteristic
13	#15689469	C₄	1	8	yes	complemented
14	C₂×#13093945	C₂²	1	2	yes	—
15	C₂×#13093945	C₂²	1	2	yes	—
16	C₂×#13093945	C₂²	1	2	yes	—
17	C₂×#13093945	C₂²	1	2	yes	—
18	C₂×#13093935	C₂²	1	1	yes	characteristic
19	C₂×#13093935	C₂²	1	1	yes	characteristic
20	C₂×#13093935	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	#15689027	—	2	2	no	—
25	#15689021	C₂²	1	2	yes	—
26	#15689006	—	2	2	no	—
27	#15688989	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	#15688885	C₂²	1	2	yes	—
30	#15688885	C₂²	1	2	yes	—
31	#15688885	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
35	C₄₇×#390	C₂²	1	2	yes	—
36	C₄₇×#386	—	2	2	no	—
37	C₄₇×#386	—	2	2	no	—
38	C₄₇×#382	C₂²	1	1	yes	characteristic
39	C₄₇×#376	C₂²	1	1	yes	characteristic
40	C₂²×Dic₉₄	—	2	1	no	—
41	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	#13094024	—	2	2	no	—
46	#13094024	C₂×C₄	1	4	yes	complemented
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
50	C₂×Dic₄₇⋊C₄	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	2	2	no	—
52	#13093945	—	2	4	no	—
53	#13093945	—	2	4	no	—
54	#13093945	C₂×C₄	1	8	yes	complemented
55	#13093945	C₂×C₄	1	8	yes	complemented
56	#13093935	—	2	2	no	—
57	#13093935	—	2	2	no	—
58	#13093935	—	2	2	no	—
59	C₄×C₄₇⋊C₈	—	2	2	no	—
60	C₄×C₄₇⋊C₈	—	2	2	no	—
61	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
62	C₄₇⋊#95	—	2	2	no	—
63	C₄₇⋊#95	—	2	1	no	—
64	C₄₇⋊#95	—	2	1	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₂²×D₄×C₄₇	—	2	1	no	—
67	C₂²×D₄×C₄₇	—	2	1	no	—
68	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₇	—	2	2	no	—
70	#127×C₄₇	—	2	2	no	—
71	#127×C₄₇	C₂×C₄	1	4	yes	—
72	C₄×D₄×C₄₇	—	2	4	no	—
73	C₄×D₄×C₄₇	—	2	4	no	—
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	#95×C₄₇	—	2	1	no	—
82	#95×C₄₇	—	2	1	no	—
83	#95×C₄₇	D₄	1	2	yes	—
84	#95×C₄₇	D₄	1	2	yes	—
85	C₂⁴×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	8	2	no	—
94	C₂×D₄×C₄₇	—	8	2	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	4	4	no	—
98	C₂²×C₄×C₄₇	—	8	2	no	—
99	C₂²×C₄×C₄₇	—	8	2	no	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂×Dic₉₄	—	2	4	no	—
108	C₂×Dic₉₄	—	8	2	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₂²⋊C₄×C₄₇	—	4	4	no	—
112	C₂²⋊C₄×C₄₇	—	8	2	no	—
113	C₂²⋊C₄×C₄₇	—	8	2	no	—
114	C₄²×C₄₇	—	2	1	no	—
115	C₄²×C₄₇	—	2	1	no	—
116	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₇	#41	1	2	yes	—
118	C₄²×C₄₇	#41	1	2	yes	—
119	C₄²×C₄₇	#41	1	2	yes	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
125	Dic₄₇⋊C₄	—	8	2	no	—
126	C₄×Dic₄₇	—	8	2	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
137	C₂×C₄₇⋊C₈	#41	1	2	yes	—
138	C₂×C₄₇⋊C₈	#41	1	2	yes	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	—	4	2	no	—
144	C₂³×C₄₇	—	4	2	no	—
145	C₂³×C₄₇	—	4	2	no	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	D₄×C₄₇	—	2	4	no	—
148	D₄×C₄₇	—	2	4	no	—
149	D₄×C₄₇	—	4	2	no	—
150	D₄×C₄₇	—	4	2	no	—
151	D₄×C₄₇	—	8	4	no	—
152	D₄×C₄₇	—	8	4	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	8	8	no	—
164	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₇	#124	1	4	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
171	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
172	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
173	C₂×Dic₄₇	—	2	4	no	—
174	C₂×Dic₄₇	—	4	2	no	—
175	C₂×Dic₄₇	—	4	2	no	—
176	C₂×Dic₄₇	—	4	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	4	2	no	—
179	Dic₉₄	—	8	4	no	—
180	C₄₇⋊C₈	—	2	2	no	—
181	C₄₇⋊C₈	—	2	2	no	—
182	C₄₇⋊C₈	—	2	2	no	—
183	C₄₇⋊C₈	—	2	2	no	—
184	#21644	—	47	1	no	maximal, Sylow
185	C₂²×C₄₇	—	4	4	no	—
186	C₂²×C₄₇	—	4	4	no	—
187	C₂²×C₄₇	—	4	4	no	—
188	C₂²×C₄₇	—	8	2	no	—
189	C₂²×C₄₇	—	8	2	no	—
190	C₂²×C₄₇	—	8	2	no	—
191	C₂²×C₄₇	—	8	2	no	—
192	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
194	C₂²×C₄₇	#532	1	1	yes	characteristic
195	C₂²×C₄₇	#576	1	2	yes	—
196	C₂²×C₄₇	#577	1	2	yes	—
197	C₄×C₄₇	—	2	4	no	—
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	2	2	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
203	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
204	C₄×C₄₇	#529	1	1	yes	characteristic
205	C₄×C₄₇	#529	1	1	yes	characteristic
206	Dic₄₇	—	4	4	no	—
207	Dic₄₇	—	8	2	no	—
208	C₂×#486	—	47	1	no	—
209	#2331	—	47	1	no	—
210	#2328	D₄₇	1	1	yes	characteristic
211	#1993	—	47	1	no	—
212	#1961	—	47	1	no	—
213	#1936	—	47	2	no	—
214	#1934	—	47	2	no	—
215	#1835	—	47	1	no	—
216	#1762	—	47	2	no	—
217	C₄×#102	—	47	2	no	—
218	#1726	—	47	1	no	—
219	C₂×C₄₇	—	8	4	no	—
220	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
221	C₂×C₄₇	#2948	1	1	yes	characteristic
222	C₂×C₄₇	#2949	1	1	yes	characteristic
223	C₂×C₄₇	#3136	1	2	yes	—
224	C₂×C₄₇	#3179	1	2	yes	—
225	C₂×C₄⋊Q₈	—	47	1	no	—
226	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
227	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
228	#486	—	47	8	no	—
229	C₂×#102	—	47	2	no	—
230	C₂×#102	—	47	2	no	—
231	C₂×#102	—	47	2	no	—
232	C₂×#102	—	47	2	no	—
233	C₂×#97	—	47	1	no	—
234	C₂×#97	—	47	1	no	—
235	C₂×#97	—	47	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	C₂×C₄×C₈	—	47	1	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	#391	—	94	2	no	—
240	#390	C₂×D₄₇	1	2	yes	—
241	#389	—	47	2	no	—
242	#387	—	94	2	no	—
243	#386	—	2	2	no	—
244	#386	—	2	2	no	—
245	#382	—	47	1	no	—
246	#382	C₂×D₄₇	1	1	yes	characteristic
247	C₄×C₄⋊C₄	—	47	2	no	—
248	#376	C₂×D₄₇	1	1	yes	characteristic
249	#340	—	47	2	no	—
250	#340	—	47	2	no	—
251	#340	—	47	2	no	—
252	#340	—	47	2	no	—
253	C₄₇	#21644	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	—	94	1	no	—
255	C₂²×D₄	—	2	1	no	—
256	C₂²×D₄	—	2	1	no	—
257	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
258	C₂³×C₄	—	2	2	no	—
259	C₂²×C₈	—	47	1	no	—
260	C₂²×C₈	—	47	1	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₄⋊Q₈	—	47	4	no	—
264	C₄⋊Q₈	—	94	2	no	—
265	#127	—	2	2	no	—
266	#127	C₄×D₄₇	1	4	yes	—
267	C₄×D₄	—	2	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	47	2	no	—
270	C₂×C₄⋊C₄	—	47	2	no	—
271	C₂×C₄⋊C₄	—	94	1	no	—
272	C₂×C₄⋊C₄	—	94	2	no	—
273	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	—	94	2	no	—
278	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
279	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	#102	—	47	8	no	—
282	#102	—	47	8	no	—
283	#102	—	94	4	no	—
284	#102	—	94	4	no	—
285	#97	—	94	2	no	—
286	#97	—	94	2	no	—
287	#97	—	94	2	no	—
288	C₄×C₈	—	47	4	no	—
289	C₄×C₈	—	94	2	no	—
290	C₄×C₈	—	94	2	no	—
291	#95	—	2	1	no	—
292	#95	—	2	1	no	—
293	#95	—	94	2	no	—
294	#95	—	94	1	no	—
295	#95	—	94	1	no	—
296	#95	—	94	2	no	—
297	#95	C₂²⋊D₄₇	1	2	yes	—
298	#95	C₂²⋊D₄₇	1	2	yes	—
299	C₂⁴	—	2	2	no	—
300	C₂×Q₈	—	94	4	no	—
301	C₂×Q₈	—	376	2	no	—
302	C₂×D₄	—	2	4	no	—
303	C₂×D₄	—	2	4	no	—
304	C₂×D₄	—	2	2	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	8	2	no	—
310	C₂×D₄	—	8	2	no	—
311	C₂×D₄	C₂×C₄×D₄₇	1	4	yes	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	8	2	no	—
315	C₂²×C₄	—	8	2	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
319	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
322	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
323	C₂×C₈	—	47	2	no	—
324	C₂×C₈	—	47	2	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	47	2	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	1	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	—	94	1	no	—
332	C₂×C₈	—	94	1	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	94	1	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	47	4	no	—
338	C₄⋊C₄	—	94	4	no	—
339	C₄⋊C₄	—	94	2	no	—
340	C₄⋊C₄	—	94	2	no	—
341	C₄⋊C₄	—	94	2	no	—
342	C₄⋊C₄	—	376	2	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₂²⋊C₄	—	8	2	no	—
345	C₂²⋊C₄	—	8	2	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	376	2	no	—
349	C₄²	C₂×C₄×D₄₇	1	2	yes	—
350	C₄²	#10625350	1	2	yes	—
351	C₄²	#10625352	1	2	yes	—
352	C₄²	#10625352	1	2	yes	—
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
361	Q₈	—	376	4	no	—
362	D₄	—	2	4	no	—
363	D₄	—	2	4	no	—
364	D₄	—	4	2	no	—
365	D₄	—	4	2	no	—
366	D₄	—	8	4	no	—
367	D₄	—	8	4	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	8	no	—
379	C₂×C₄	—	94	4	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	—	188	2	no	—
385	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
386	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
387	C₂×C₄	#13094011	1	4	yes	—
388	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
390	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
392	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
393	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
394	C₈	—	94	2	no	—
395	C₈	—	94	2	no	—
396	C₈	—	94	2	no	—
397	C₈	—	94	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	8	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	8	2	no	—
404	C₂²	—	8	2	no	—
405	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₂²	C₂×#13094011	1	1	yes	characteristic
407	C₂²	#15689669	1	1	yes	characteristic
408	C₂²	#15689926	1	2	yes	—
409	C₂²	#15689934	1	2	yes	—
410	C₄	—	2	4	no	—
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	2	no	—
415	C₄	—	376	2	no	—
416	C₄	—	188	4	no	—
417	C₄	C₄×#10625352	1	1	yes	characteristic
418	C₄	C₄×#10625352	1	1	yes	characteristic
419	C₄	#15689655	1	1	yes	characteristic
420	C₄	#15689655	1	1	yes	characteristic
421	C₂	—	8	4	no	—
422	C₂	C₄×#13094011	1	1	yes	characteristic
423	C₂	#20252238	1	1	yes	characteristic
424	C₂	#20252245	1	1	yes	characteristic
425	C₂	#20253742	1	2	yes	—
426	C₂	#20254073	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2328	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2328	D₄₇
hypocenter	C₄₇	#21644
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ #376 ◁ #2328

Complements

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

N	H ≅ G/N	type
2. #20246136	C₂	semidirect
3. #20244360	C₂	semidirect
5. #20244088	C₂	semidirect
6. #20244074	C₂	semidirect
7. #20243518	C₂	semidirect
8. #20243213	C₂	semidirect
9. C₄×#13093945	C₂	semidirect
10. #20243075	C₂	semidirect
13. #15689469	C₄	semidirect
46. #13094024	C₂×C₄	semidirect
54. #13093945	C₂×C₄	semidirect
55. #13093945	C₂×C₄	semidirect
61. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
253. C₄₇	#21644	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689469	2
#20246136	2
#20244360	2
#20244213	2
#20244088	2
#20244074	2
#20243518	2
#20243213	2
C₄×#13093945	2
#20243075	2
C₄₇×#2328	2
#21644	47