Subgroups — #26187461

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	#20253460	C₂	1	1	yes	maximal, characteristic
2	#20252509	C₂	1	1	yes	maximal, characteristic
3	#20252489	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242286	C₂	1	2	yes	maximal, complemented
5	#20242261	C₂	1	2	yes	maximal, complemented
6	#20242247	C₂	1	2	yes	maximal, complemented
7	C₈×#10625325	C₂	1	2	yes	maximal, complemented
8	#20242177	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241844	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241771	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689680	C₂²	1	1	yes	characteristic
13	C₄×#10625350	C₂²	1	1	yes	characteristic
14	#15689465	C₄	1	2	yes	—
15	#15689409	C₄	1	1	yes	characteristic
16	#15689404	C₄	1	1	yes	characteristic
17	#15689334	C₄	1	1	yes	characteristic
18	#15689329	C₄	1	1	yes	characteristic
19	#15689287	C₄	1	2	yes	—
20	#15689253	C₂²	1	2	yes	—
21	#15689253	C₂²	1	2	yes	—
22	#15689250	—	2	1	no	—
23	C₈×Dic₉₄	C₂²	1	2	yes	—
24	#15689247	—	2	1	no	—
25	C₄×Dic₁₈₈	C₂²	1	2	yes	—
26	C₄×#10625325	C₂²	1	2	yes	—
27	#15689197	—	2	2	no	—
28	C₈×D₁₈₈	C₂²	1	2	yes	—
29	#15689181	—	2	2	no	—
30	#15689179	—	2	1	no	—
31	#15689176	C₂²	1	1	yes	characteristic
32	#15689147	C₂²	1	1	yes	characteristic
33	C₄⋊C₈×D₄₇	—	2	1	no	—
34	#15688876	C₂²	1	2	yes	—
35	#15688874	C₂²	1	2	yes	—
36	#15688855	C₂²	1	2	yes	—
37	#15688855	C₂²	1	2	yes	—
38	#15688855	C₂²	1	1	yes	characteristic
39	#15688855	C₂²	1	1	yes	characteristic
40	#15688852	C₂²	1	1	yes	characteristic
41	#15688852	C₂²	1	1	yes	characteristic
42	C₄₇×#431	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×#322	C₂²	1	2	yes	—
46	C₈²×C₄₇	C₂²	1	2	yes	—
47	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
48	C₂×Dic₁₈₈	C₂×C₄	1	2	yes	—
49	C₂×#10625325	C₂×C₄	1	2	yes	—
50	C₂×#10625329	—	2	1	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	#13094024	C₂×C₄	1	1	yes	characteristic
53	#13094024	C₂×C₄	1	1	yes	characteristic
54	#13094016	—	2	1	no	—
55	#13094003	—	2	1	no	—
56	#13094003	C₂×C₄	1	2	yes	—
57	C₄×Dic₉₄	—	2	1	no	—
58	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
59	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
60	C₄×Dic₉₄	C₂³	1	2	yes	—
61	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
62	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
63	C₄×C₂²⋊D₄₇	—	2	1	no	—
64	C₄×C₂²⋊D₄₇	—	2	1	no	—
65	#13093983	—	2	1	no	—
66	#13093983	C₂×C₄	1	1	yes	characteristic
67	#13093981	—	2	1	no	—
68	C₄²×D₄₇	—	2	1	no	—
69	#13093958	C₂×C₄	1	2	yes	—
70	#13093956	C₂×C₄	1	2	yes	—
71	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
72	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
73	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
74	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
75	Dic₄₇⋊C₈	—	2	2	no	—
76	Dic₄₇⋊C₈	—	2	2	no	—
77	Dic₄₇⋊C₈	—	2	2	no	—
78	#13093949	C₂×C₄	1	2	yes	—
79	#13093949	C₂×C₄	1	2	yes	—
80	#13093949	C₂×C₄	1	2	yes	—
81	#13093946	C₂×C₄	1	2	yes	—
82	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
83	(C₂×D₄₇)⋊C₈	—	2	2	no	—
84	#13093934	—	2	2	no	—
85	#13093934	—	2	2	no	—
86	C₄×C₄₇⋊C₈	—	2	1	no	—
87	C₈×Dic₄₇	—	2	2	no	—
88	C₂²×C₈×C₄₇	—	2	1	no	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
93	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
94	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
95	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₇	C₂³	1	2	yes	—
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂×C₂²⋊D₄₇	—	2	1	no	—
105	#10625350	—	2	2	no	—
106	#10625350	—	4	1	no	—
107	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×Dic₉₄	—	2	1	no	—
112	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
113	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
114	C₂×C₈×C₄₇	—	2	4	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
121	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₄₇	#41	1	1	yes	characteristic
124	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²⋊Dic₄₇	—	2	2	no	—
126	C₂²⋊Dic₄₇	—	2	1	no	—
127	(C₂×D₄₇)⋊C₄	—	2	1	no	—
128	(C₂×D₄₇)⋊C₄	—	2	1	no	—
129	C₄⋊Dic₄₇	—	2	1	no	—
130	C₄⋊Dic₄₇	—	2	1	no	—
131	C₄⋊Dic₄₇	—	2	1	no	—
132	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
133	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
135	Dic₄₇⋊C₄	—	2	1	no	—
136	Dic₄₇⋊C₄	—	2	2	no	—
137	Dic₄₇⋊C₄	—	2	1	no	—
138	Dic₄₇⋊C₄	—	2	2	no	—
139	C₄×Dic₄₇	—	2	1	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	#10625329	—	8	1	no	—
144	C₂×C₄₇⋊C₈	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	Dic₁₈₈	—	4	2	no	—
148	#10625325	—	2	4	no	—
149	C₈×D₄₇	—	8	2	no	—
150	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂²×D₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₄₇	—	4	2	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	1	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	D₁₈₈	—	2	1	no	—
170	D₁₈₈	#131	1	2	yes	—
171	C₄×D₄₇	—	4	2	no	—
172	C₄×D₄₇	—	4	1	no	—
173	C₄×D₄₇	—	4	1	no	—
174	C₄×D₄₇	—	4	2	no	—
175	Dic₉₄	—	2	2	no	—
176	Dic₉₄	—	2	1	no	—
177	Dic₉₄	—	2	1	no	—
178	Dic₉₄	—	2	2	no	—
179	Dic₉₄	—	4	2	no	—
180	C₈×C₄₇	—	2	2	no	—
181	C₈×C₄₇	—	2	2	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₈×C₄₇	—	2	2	no	—
184	C₈×C₄₇	—	2	2	no	—
185	C₈×C₄₇	—	2	2	no	—
186	C₄₇⋊C₈	—	4	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	#443	1	2	yes	—
201	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
202	C₄×C₄₇	#568	1	1	yes	characteristic
203	C₄×C₄₇	#577	1	1	yes	characteristic
204	C₄×C₄₇	#578	1	1	yes	characteristic
205	Dic₄₇	—	4	1	no	—
206	Dic₄₇	—	4	2	no	—
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	4	2	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	—	47	1	no	—
219	#1476	—	47	1	no	—
220	#1450	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
247	#431	C₂×D₄₇	1	1	yes	characteristic
248	#423	—	47	1	no	—
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	2	no	—
254	Q₈⋊C₈	—	47	2	no	—
255	Q₈⋊C₈	—	47	1	no	—
256	Q₈⋊C₈	—	47	1	no	—
257	D₄⋊C₈	—	47	1	no	—
258	D₄⋊C₈	—	47	1	no	—
259	#322	C₂×D₄₇	1	2	yes	—
260	C₈²	C₂×D₄₇	1	2	yes	—
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	—	94	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	94	2	no	—
268	C₄⋊Q₈	—	47	1	no	—
269	C₄⋊Q₈	—	47	1	no	—
270	#125	—	94	1	no	—
271	C₂²⋊Q₈	—	47	2	no	—
272	C₂²⋊Q₈	—	94	1	no	—
273	C₄×Q₈	—	47	1	no	—
274	C₄×Q₈	—	47	1	no	—
275	C₄×Q₈	—	47	2	no	—
276	C₄×Q₈	—	94	1	no	—
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	—	47	1	no	—
282	#117	—	94	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	—	47	1	no	—
289	C₄⋊C₈	—	47	1	no	—
290	C₄⋊C₈	—	47	2	no	—
291	C₄⋊C₈	—	94	2	no	—
292	C₄⋊C₈	—	94	2	no	—
293	C₄⋊C₈	—	94	2	no	—
294	C₄⋊C₈	—	94	1	no	—
295	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
296	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
297	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
298	C₄⋊C₈	D₁₈₈	1	1	yes	characteristic
299	#103	—	47	2	no	—
300	#103	—	47	2	no	—
301	#103	—	47	2	no	—
302	#102	—	47	2	no	—
303	C₂²⋊C₈	—	94	1	no	—
304	C₂²⋊C₈	—	94	2	no	—
305	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
306	C₂²⋊C₈	D₁₈₈	1	2	yes	—
307	#97	—	94	2	no	—
308	#97	—	94	2	no	—
309	C₄×C₈	—	2	1	no	—
310	C₄×C₈	—	94	2	no	—
311	C₄×C₈	—	94	1	no	—
312	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
314	C₄×C₈	C₂²×D₄₇	1	2	yes	—
315	C₄×C₈	C₂²×D₄₇	1	2	yes	—
316	#41	—	94	2	no	—
317	#41	—	188	1	no	—
318	C₂×Q₈	—	47	1	no	—
319	C₂×Q₈	—	47	2	no	—
320	C₂×Q₈	—	94	1	no	—
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	C₂×D₁₈₈	1	1	yes	characteristic
328	C₂²×C₄	#10625350	1	1	yes	characteristic
329	Q₁₆	—	188	2	no	—
330	SD₁₆	—	94	4	no	—
331	M₁₆	—	376	1	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	94	1	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	376	2	no	—
339	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
340	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
341	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
342	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
343	C₄⋊C₄	—	47	2	no	—
344	C₄⋊C₄	—	47	1	no	—
345	C₄⋊C₄	—	47	1	no	—
346	C₄⋊C₄	—	94	1	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	94	1	no	—
350	C₄⋊C₄	—	94	1	no	—
351	C₄⋊C₄	—	94	1	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₂²⋊C₄	—	94	1	no	—
354	C₂²⋊C₄	—	94	2	no	—
355	C₂²⋊C₄	—	94	1	no	—
356	C₂²⋊C₄	—	94	1	no	—
357	C₄²	—	94	1	no	—
358	C₄²	—	94	1	no	—
359	C₄²	—	94	2	no	—
360	C₄²	—	94	1	no	—
361	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₄²	C₂×D₁₈₈	1	1	yes	characteristic
363	C₄²	#10625350	1	1	yes	characteristic
364	C₄²	C₂³×D₄₇	1	1	yes	characteristic
365	C₂³	—	94	1	no	—
366	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
367	Q₈	—	94	2	no	—
368	Q₈	—	94	1	no	—
369	Q₈	—	94	1	no	—
370	Q₈	—	94	2	no	—
371	Q₈	—	188	2	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	—	94	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	1	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	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	C₄×D₁₈₈	1	1	yes	characteristic
390	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
391	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
394	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
395	C₈	—	2	2	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	2	2	no	—
400	C₈	—	2	2	no	—
401	C₈	—	188	1	no	—
402	C₈	—	188	2	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×C₄×D₁₈₈	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	188	1	no	—
415	C₄	—	188	1	no	—
416	C₄	—	188	2	no	—
417	C₄	—	188	1	no	—
418	C₄	—	188	2	no	—
419	C₄	#15689241	1	2	yes	—
420	C₄	#131×D₄₇	1	1	yes	characteristic
421	C₄	#15689888	1	1	yes	characteristic
422	C₄	#15689935	1	1	yes	characteristic
423	C₄	#15689940	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	188	2	no	—
426	C₂	#20252116	1	1	yes	characteristic
427	C₂	#20252233	1	1	yes	characteristic
428	C₂	C₂×#15689241	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1450	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#10625350	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1450	D₄₇
hypocenter	C₄₇	#18016
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #431 ◁ #1450

Complements

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

N	H ≅ G/N	type
3. #20252489	C₂	semidirect
4. #20242286	C₂	semidirect
5. #20242261	C₂	semidirect
6. #20242247	C₂	semidirect
7. C₈×#10625325	C₂	semidirect
8. #20242177	C₂	semidirect
9. #20241844	C₂	semidirect
11. C₄₇×#1450	C₂	semidirect
220. #1450	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
#20253460	2
#20252509	2
#20252489	2
#20242286	2
#20242261	2
#20242247	2
C₈×#10625325	2
#20242177	2
#20241844	2
#20241771	2
C₄₇×#1450	2
#18016	47