Subgroups — #26187463

Order 12032.

600 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	#20253453	C₂	1	1	yes	maximal, characteristic
2	#20252514	C₂	1	1	yes	maximal, characteristic
3	#20252490	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242282	C₂	1	2	yes	maximal, complemented
5	#20242256	C₂	1	2	yes	maximal, complemented
6	#20242248	C₂	1	2	yes	maximal, complemented
7	#20242185	C₂	1	2	yes	maximal, complemented
8	#20242179	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241771	C₂	1	1	yes	maximal, characteristic
10	#20241671	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689461	C₄	1	2	yes	—
14	#15689405	C₄	1	1	yes	characteristic
15	#15689400	C₄	1	1	yes	characteristic
16	#15689330	C₄	1	1	yes	characteristic
17	#15689325	C₄	1	1	yes	characteristic
18	#15689283	C₄	1	2	yes	—
19	#15689254	—	2	1	no	—
20	#15689254	C₂²	1	2	yes	—
21	#15689250	C₂²	1	2	yes	—
22	Q₈×C₄₇⋊C₈	—	2	1	no	—
23	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
24	C₄×#10625337	C₂²	1	2	yes	—
25	C₄×#10625336	C₂²	1	2	yes	—
26	#15689192	—	2	2	no	—
27	#15689188	C₂²	1	2	yes	—
28	#15689184	—	2	2	no	—
29	#15689179	—	2	1	no	—
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689176	C₂²	1	1	yes	characteristic
32	#15689176	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₄₇	—	2	1	no	—
34	#15688875	C₂²	1	2	yes	—
35	#15688873	C₂²	1	2	yes	—
36	#15688855	C₂²	1	1	yes	characteristic
37	#15688855	C₂²	1	1	yes	characteristic
38	#15688852	C₂²	1	1	yes	characteristic
39	#15688852	C₂²	1	1	yes	characteristic
40	#15688844	C₂²	1	2	yes	—
41	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
42	C₄₇×#533	C₂²	1	1	yes	characteristic
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
47	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625337	C₂×C₄	1	2	yes	—
49	C₂×#10625336	C₂×C₄	1	2	yes	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
52	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
53	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
54	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₄₇	—	2	1	no	—
56	C₄×C₂²⋊D₄₇	—	2	1	no	—
57	#13093983	C₂×C₄	1	1	yes	characteristic
58	#13093981	—	2	1	no	—
59	C₄²×D₄₇	—	2	1	no	—
60	#13093957	C₂×C₄	1	2	yes	—
61	#13093955	C₂×C₄	1	2	yes	—
62	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
63	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
64	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
67	C₄⋊(C₄₇⋊C₈)	D₄	1	1	yes	characteristic
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	#13093948	C₂×C₄	1	2	yes	—
72	#13093948	C₂×C₄	1	2	yes	—
73	#13093947	C₂×C₄	1	2	yes	—
74	#13093944	C₂×C₄	1	2	yes	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
76	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
77	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
78	(C₂×D₄₇)⋊C₈	—	2	2	no	—
79	#13093935	—	2	2	no	—
80	#13093934	—	2	2	no	—
81	C₄×C₄₇⋊C₈	—	2	1	no	—
82	C₄×C₄₇⋊C₈	—	2	2	no	—
83	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
84	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
85	C₂×M₁₆×C₄₇	—	2	1	no	—
86	C₂²×C₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	#125×C₄₇	—	2	1	no	—
90	C₂²⋊Q₈×C₄₇	—	2	1	no	—
91	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
94	#117×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
98	C₄×C₈×C₄₇	—	2	1	no	—
99	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	1	no	—
107	#10625350	—	2	2	no	—
108	#10625350	—	4	1	no	—
109	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
114	M₁₆×C₄₇	—	8	1	no	—
115	C₂×C₈×C₄₇	—	2	4	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	—	2	1	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	#41	1	1	yes	characteristic
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²⋊Dic₄₇	—	2	1	no	—
132	#10625337	—	4	2	no	—
133	#10625336	—	2	4	no	—
134	(C₂×D₄₇)⋊C₄	—	2	1	no	—
135	(C₂×D₄₇)⋊C₄	—	2	1	no	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
138	Dic₄₇⋊C₄	—	2	1	no	—
139	Dic₄₇⋊C₄	—	2	1	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₂×C₄₇⋊C₈	—	2	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
146	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
147	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
148	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
149	C₈×D₄₇	—	8	2	no	—
150	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₄₇	—	2	1	no	—
152	Q₈×C₄₇	—	2	2	no	—
153	Q₈×C₄₇	—	2	2	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂²⋊D₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	D₁₈₈	—	2	1	no	—
173	D₁₈₈	#131	1	2	yes	—
174	C₄×D₄₇	—	4	2	no	—
175	C₄×D₄₇	—	4	1	no	—
176	C₄×D₄₇	—	4	1	no	—
177	C₄×D₄₇	—	4	2	no	—
178	Dic₉₄	—	2	1	no	—
179	Dic₉₄	—	2	1	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	2	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₄₇⋊C₈	—	2	2	no	—
184	C₄₇⋊C₈	—	2	2	no	—
185	C₄₇⋊C₈	—	2	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	C₄₇⋊C₈	—	4	1	no	—
189	#18016	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	4	1	no	—
196	C₂×D₄₇	—	4	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	4	2	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	#443	1	2	yes	—
203	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
204	C₄×C₄₇	#568	1	1	yes	characteristic
205	C₄×C₄₇	#577	1	1	yes	characteristic
206	C₄×C₄₇	#578	1	1	yes	characteristic
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	4	1	no	—
209	Dic₄₇	—	4	1	no	—
210	#3107	—	47	1	no	—
211	#2990	—	47	1	no	—
212	#2986	—	47	1	no	—
213	#1591	—	47	2	no	—
214	#1587	—	47	2	no	—
215	#1585	—	47	2	no	—
216	C₈×SD₁₆	—	47	2	no	—
217	#1574	—	47	1	no	—
218	#1493	D₄₇	1	1	yes	characteristic, complemented
219	#1476	—	47	1	no	—
220	#1450	—	47	1	no	—
221	C₂×C₄₇	—	4	1	no	—
222	C₂×C₄₇	#2933	1	1	yes	characteristic
223	C₂×C₄₇	#2947	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
225	D₄₇	—	4	2	no	—
226	#533	C₂×D₄₇	1	1	yes	characteristic
227	C₄×#41	—	47	1	no	—
228	#485	—	47	2	no	—
229	#475	—	47	1	no	—
230	#474	—	47	1	no	—
231	#462	—	47	1	no	—
232	#461	—	47	1	no	—
233	#452	—	47	2	no	—
234	#446	—	47	2	no	—
235	#446	—	47	2	no	—
236	#446	—	94	1	no	—
237	C₈×Q₈	—	47	2	no	—
238	C₈×Q₈	—	94	1	no	—
239	C₄×Q₁₆	—	47	2	no	—
240	C₄×SD₁₆	—	47	2	no	—
241	#435	—	94	2	no	—
242	C₈×D₄	—	47	2	no	—
243	#433	—	94	2	no	—
244	#432	—	94	1	no	—
245	#431	—	47	1	no	—
246	#431	—	47	1	no	—
247	#431	—	47	1	no	—
248	#423	C₂×D₄₇	1	1	yes	characteristic
249	C₂×C₄⋊C₈	—	94	1	no	—
250	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
251	#335	—	47	2	no	—
252	#334	—	47	2	no	—
253	Q₈⋊C₈	—	47	1	no	—
254	Q₈⋊C₈	—	47	1	no	—
255	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
256	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
257	D₄⋊C₈	—	47	1	no	—
258	D₄⋊C₈	—	47	1	no	—
259	#322	—	47	2	no	—
260	C₈²	—	47	2	no	—
261	C₄₇	#18016	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	47	1	no	—
263	C₂×Q₁₆	—	47	2	no	—
264	C₂×SD₁₆	—	47	2	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	94	2	no	—
268	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
269	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
270	#125	—	2	1	no	—
271	C₂²⋊Q₈	—	2	1	no	—
272	C₂²⋊Q₈	C₄×D₄₇	1	2	yes	—
273	C₄×Q₈	—	2	1	no	—
274	C₄×Q₈	—	47	1	no	—
275	C₄×Q₈	—	47	1	no	—
276	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
277	C₄×D₄	—	47	1	no	—
278	C₄×D₄	—	47	1	no	—
279	C₄×D₄	—	94	1	no	—
280	C₄×D₄	—	94	1	no	—
281	#117	—	2	1	no	—
282	#117	—	47	1	no	—
283	#117	—	94	1	no	—
284	C₂×C₄²	—	94	1	no	—
285	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
286	#107	—	47	2	no	—
287	#106	—	47	2	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	47	1	no	—
290	C₄⋊C₈	—	47	1	no	—
291	C₄⋊C₈	—	47	1	no	—
292	C₄⋊C₈	—	47	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	2	no	—
298	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
299	#103	—	47	2	no	—
300	#103	—	47	2	no	—
301	#103	—	47	2	no	—
302	#102	—	47	2	no	—
303	C₂²⋊C₈	—	47	2	no	—
304	C₂²⋊C₈	—	47	2	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₂²⋊C₈	—	94	1	no	—
307	#97	—	94	2	no	—
308	#97	—	94	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	47	2	no	—
311	C₄×C₈	—	47	2	no	—
312	C₄×C₈	—	94	2	no	—
313	C₄×C₈	—	94	1	no	—
314	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
316	#41	—	94	2	no	—
317	#41	—	188	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	47	1	no	—
320	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
321	C₂×D₄	—	47	1	no	—
322	C₂×D₄	—	94	1	no	—
323	C₂²×C₄	—	94	1	no	—
324	C₂²×C₄	—	94	1	no	—
325	C₂²×C₄	—	94	1	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	Q₁₆	—	188	2	no	—
330	SD₁₆	—	94	4	no	—
331	M₁₆	—	8	1	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	47	2	no	—
338	C₂×C₈	—	47	2	no	—
339	C₂×C₈	—	47	2	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	—	94	1	no	—
342	C₂×C₈	—	376	2	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	47	1	no	—
349	C₄⋊C₄	—	47	1	no	—
350	C₄⋊C₄	—	94	1	no	—
351	C₄⋊C₄	—	94	1	no	—
352	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
353	C₂²⋊C₄	—	2	2	no	—
354	C₂²⋊C₄	—	94	1	no	—
355	C₂²⋊C₄	—	94	1	no	—
356	C₂²⋊C₄	—	94	1	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	94	1	no	—
359	C₄²	—	94	1	no	—
360	C₄²	—	94	1	no	—
361	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₄²	D₄×D₄₇	1	1	yes	characteristic
363	C₄²	#10625352	1	1	yes	characteristic
364	C₄²	C₂³×D₄₇	1	1	yes	characteristic
365	C₂³	—	94	1	no	—
366	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
367	Q₈	—	2	2	no	—
368	Q₈	—	2	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	94	1	no	—
371	Q₈	—	94	1	no	—
372	D₄	—	47	2	no	—
373	D₄	—	94	1	no	—
374	D₄	—	188	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	94	1	no	—
383	C₂×C₄	—	94	1	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	188	2	no	—
386	C₂×C₄	—	188	2	no	—
387	C₂×C₄	—	188	1	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
390	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
391	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	4	2	no	—
398	C₈	—	94	2	no	—
399	C₈	—	94	2	no	—
400	C₈	—	94	2	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	—	2	1	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	188	1	no	—
409	C₂²	—	188	1	no	—
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	—	4	2	no	—
416	C₄	—	188	1	no	—
417	C₄	—	188	1	no	—
418	C₄	—	188	1	no	—
419	C₄	#15689237	1	2	yes	—
420	C₄	#131×D₄₇	1	1	yes	characteristic
421	C₄	#15689888	1	1	yes	characteristic
422	C₄	#15689929	1	1	yes	characteristic
423	C₄	#15689936	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	188	2	no	—
426	C₂	#20252118	1	1	yes	characteristic
427	C₂	#20252225	1	1	yes	characteristic
428	C₂	C₂×#15689237	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×#1493	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1493	D₄₇
hypocenter	C₄₇	#18016
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1493

Complements

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

N	H ≅ G/N	type
3. #20252490	C₂	semidirect
4. #20242282	C₂	semidirect
5. #20242256	C₂	semidirect
6. #20242248	C₂	semidirect
7. #20242185	C₂	semidirect
8. #20242179	C₂	semidirect
10. #20241671	C₂	semidirect
11. C₄₇×#1493	C₂	semidirect
218. #1493	D₄₇	semidirect
261. C₄₇	#18016	semidirect

Maximal subgroups

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

subgroup	index
#20253453	2
#20252514	2
#20252490	2
#20242282	2
#20242256	2
#20242248	2
#20242185	2
#20242179	2
#20241771	2
#20241671	2
C₄₇×#1493	2
#18016	47