Subgroups — #26233887

Order 12032.

686 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	#20252042	C₂	1	2	yes	maximal
2	#20251978	C₂	1	1	yes	maximal, characteristic
3	#20244141	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244136	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243988	C₂	1	2	yes	maximal, complemented
6	#20243988	C₂	1	2	yes	maximal, complemented
7	#20243488	C₂	1	2	yes	maximal
8	#20243430	C₂	1	1	yes	maximal, characteristic
9	#20243272	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	C₂²	1	2	yes	—
13	#15689181	—	2	2	no	—
14	#15689181	—	2	2	no	—
15	#15689177	—	2	2	no	—
16	#15689173	—	2	2	no	—
17	C₂×#13093960	C₂²	1	1	yes	characteristic
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	#15689165	C₄	1	2	yes	complemented
20	#15689165	C₄	1	2	yes	complemented
21	#15689165	C₄	1	2	yes	complemented
22	#15689165	C₄	1	2	yes	complemented
23	#15689161	C₂²	1	2	yes	—
24	#15689161	C₂²	1	1	yes	characteristic
25	#15689161	C₂²	1	1	yes	characteristic
26	#15689149	C₂²	1	2	yes	—
27	#15689149	C₂²	1	2	yes	—
28	#15689087	C₂²	1	2	yes	—
29	#15689078	C₂²	1	2	yes	—
30	#15689078	C₂²	1	2	yes	—
31	#15688888	C₂²	1	2	yes	—
32	#15688883	C₂²	1	2	yes	—
33	#15688883	C₂²	1	2	yes	—
34	#15688883	C₂²	1	2	yes	—
35	#15688883	C₂²	1	2	yes	—
36	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₂×#10625329	C₂³	1	2	yes	—
44	C₂×#10625329	C₂³	1	2	yes	—
45	#13093983	—	2	2	no	—
46	#13093983	—	2	2	no	—
47	#13093983	C₂×C₄	1	2	yes	—
48	#13093983	C₂×C₄	1	2	yes	—
49	#13093983	C₂³	1	2	yes	—
50	#13093983	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	#13093960	—	2	2	no	—
56	#13093960	—	2	2	no	—
57	#13093958	C₂×C₄	1	2	yes	—
58	#13093958	C₂×C₄	1	2	yes	—
59	#13093958	C₂×C₄	1	1	yes	characteristic
60	#13093958	C₂×C₄	1	1	yes	characteristic
61	#13093958	C₂×C₄	1	1	yes	characteristic
62	#13093958	C₂×C₄	1	1	yes	characteristic
63	#13093956	C₂×C₄	1	2	yes	—
64	#13093956	C₂×C₄	1	2	yes	—
65	#13093956	C₂×C₄	1	2	yes	—
66	#13093956	C₂×C₄	1	2	yes	—
67	Dic₄₇⋊C₈	—	2	2	no	—
68	Dic₄₇⋊C₈	—	2	2	no	—
69	Dic₄₇⋊C₈	—	2	2	no	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
73	#13093934	—	2	2	no	—
74	#13093934	—	2	2	no	—
75	C₈×Dic₄₇	—	2	2	no	—
76	C₈×Dic₄₇	—	2	2	no	—
77	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×M₁₆×C₄₇	—	2	2	no	—
79	C₂×M₁₆×C₄₇	—	2	2	no	—
80	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
81	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
90	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
91	#97×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	1	no	—
94	C₂⁴×C₄₇	#41	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	2	no	—
107	M₁₆×C₄₇	—	2	4	no	—
108	M₁₆×C₄₇	—	2	4	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	#41	1	2	yes	—
122	C₂×C₈×C₄₇	#41	1	2	yes	—
123	C₂²⋊C₄×C₄₇	—	4	2	no	—
124	C₄²×C₄₇	—	2	1	no	—
125	C₄²×C₄₇	—	2	1	no	—
126	C₄²×C₄₇	—	2	1	no	—
127	C₄²×C₄₇	—	2	1	no	—
128	C₂²⋊Dic₄₇	—	2	2	no	—
129	C₂²⋊Dic₄₇	—	2	2	no	—
130	C₂²⋊Dic₄₇	—	2	2	no	—
131	C₂²⋊Dic₄₇	—	2	2	no	—
132	C₄⋊Dic₄₇	—	2	2	no	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
135	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
136	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
137	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	#10625329	—	2	2	no	—
143	#10625329	—	2	2	no	—
144	#10625329	—	2	2	no	—
145	#10625329	—	2	2	no	—
146	C₂×C₄₇⋊C₈	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂³×C₄₇	—	2	1	no	—
149	C₂³×C₄₇	—	2	1	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	C₄×D₄	1	2	yes	—
153	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
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	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂²×D₄	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	2₋¹⁺⁴	1	1	yes	characteristic
172	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	2	2	no	—
175	C₂×Dic₄₇	—	2	2	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	4	4	no	—
178	C₂×Dic₄₇	—	8	2	no	—
179	C₈×C₄₇	—	2	2	no	—
180	C₈×C₄₇	—	2	1	no	—
181	C₈×C₄₇	—	2	1	no	—
182	C₈×C₄₇	—	2	2	no	—
183	C₈×C₄₇	#117	1	2	yes	—
184	C₈×C₄₇	#117	1	2	yes	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	#22608	—	47	1	no	maximal, Sylow
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	2	no	—
191	C₂²×C₄₇	—	2	2	no	—
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	8	1	no	—
194	C₂²×C₄₇	—	8	1	no	—
195	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
196	C₂²×C₄₇	#552	1	1	yes	characteristic
197	C₂²×C₄₇	#552	1	1	yes	characteristic
198	C₄×C₄₇	—	2	2	no	—
199	C₄×C₄₇	—	4	2	no	—
200	C₄×C₄₇	—	8	1	no	—
201	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
202	C₄×C₄₇	#519	1	1	yes	characteristic
203	C₄×C₄₇	#547	1	1	yes	characteristic
204	C₄×C₄₇	#547	1	1	yes	characteristic
205	Dic₄₇	—	4	2	no	—
206	Dic₄₇	—	4	2	no	—
207	Dic₄₇	—	4	2	no	—
208	Dic₄₇	—	4	2	no	—
209	#2924	—	47	2	no	—
210	#2911	—	47	1	no	—
211	#1946	—	47	1	no	—
212	#1945	—	47	1	no	—
213	#1922	—	47	2	no	—
214	#1922	—	47	2	no	—
215	#1826	—	47	2	no	—
216	#1811	—	47	1	no	—
217	#1773	—	47	1	no	—
218	#1772	—	47	1	no	—
219	#1753	D₄₇	1	1	yes	characteristic
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	2	1	no	—
222	C₂×C₄₇	—	4	2	no	—
223	C₂×C₄₇	#2344	1	1	yes	characteristic
224	C₂×C₄₇	#2955	1	1	yes	characteristic
225	C₂×C₄₇	#2956	1	1	yes	characteristic
226	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#117	—	47	2	no	—
228	#433	—	94	2	no	—
229	#433	—	94	2	no	—
230	#432	—	94	2	no	—
231	#431	—	94	2	no	—
232	C₂×#108	—	47	1	no	—
233	C₂×#108	—	47	1	no	—
234	#428	—	47	2	no	—
235	#428	—	47	2	no	—
236	#428	—	47	2	no	—
237	#428	—	47	2	no	—
238	#427	—	47	2	no	—
239	#427	—	47	1	no	—
240	#427	—	47	1	no	—
241	#424	—	47	2	no	—
242	#424	—	47	2	no	—
243	#407	—	47	2	no	—
244	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
245	#405	—	47	2	no	—
246	#405	—	47	2	no	—
247	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
249	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
250	#341	—	47	2	no	—
251	#339	—	47	2	no	—
252	#339	—	47	2	no	—
253	#339	—	47	2	no	—
254	#339	—	47	2	no	—
255	#336	C₂×D₄₇	1	1	yes	characteristic
256	#336	C₂×D₄₇	1	1	yes	characteristic
257	C₄₇	#22608	1	1	yes	characteristic, complemented, Sylow
258	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
259	C₂×M₁₆	—	2	2	no	—
260	C₂×M₁₆	—	2	2	no	—
261	C₂×M₁₆	—	47	2	no	—
262	C₂×M₁₆	—	47	2	no	—
263	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
264	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
265	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
266	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	#117	—	47	2	no	—
270	#117	—	47	2	no	—
271	#117	—	47	2	no	—
272	#117	—	47	2	no	—
273	#117	—	94	2	no	—
274	#117	—	94	2	no	—
275	C₂×C₄⋊C₄	—	47	2	no	—
276	C₂×C₄⋊C₄	—	47	2	no	—
277	C₂×C₂²⋊C₄	—	2	1	no	—
278	C₂×C₂²⋊C₄	—	94	2	no	—
279	C₂×C₄²	—	94	2	no	—
280	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
281	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
282	#108	—	94	2	no	—
283	#108	—	94	2	no	—
284	#107	—	47	2	no	—
285	#107	—	47	2	no	—
286	#107	—	47	1	no	—
287	#107	—	47	1	no	—
288	#107	—	47	1	no	—
289	#107	—	47	1	no	—
290	#106	—	47	2	no	—
291	#106	—	47	2	no	—
292	#106	—	47	2	no	—
293	#106	—	47	2	no	—
294	C₄⋊C₈	—	94	2	no	—
295	C₄⋊C₈	—	94	2	no	—
296	C₄⋊C₈	—	94	2	no	—
297	C₄⋊C₈	—	94	2	no	—
298	C₂²⋊C₈	—	94	2	no	—
299	C₂²⋊C₈	—	94	2	no	—
300	C₂²⋊C₈	D₁₈₈	1	2	yes	—
301	C₂²⋊C₈	D₁₈₈	1	2	yes	—
302	#97	—	2	2	no	—
303	#97	—	94	2	no	—
304	#97	—	94	2	no	—
305	C₄×C₈	—	2	2	no	—
306	C₄×C₈	—	94	2	no	—
307	C₄×C₈	—	94	2	no	—
308	#95	—	2	1	no	—
309	C₂⁴	#10625350	1	1	yes	characteristic
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	1	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
319	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
320	C₂²×C₄	#10625350	1	1	yes	characteristic
321	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
322	M₁₆	—	2	4	no	—
323	M₁₆	—	2	4	no	—
324	M₁₆	—	94	2	no	—
325	M₁₆	—	94	2	no	—
326	M₁₆	—	94	2	no	—
327	M₁₆	—	94	2	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	no	—
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
337	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
340	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
341	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
342	C₂×C₈	#10625352	1	2	yes	—
343	C₂×C₈	#10625352	1	2	yes	—
344	C₄⋊C₄	—	47	2	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	47	2	no	—
347	C₄⋊C₄	—	47	2	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₂²⋊C₄	—	94	2	no	—
354	C₂²⋊C₄	—	94	2	no	—
355	C₄²	—	2	1	no	—
356	C₄²	—	2	1	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	94	2	no	—
360	C₄²	—	94	2	no	—
361	C₄²	—	94	2	no	—
362	C₄²	—	94	2	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	C₄×D₁₈₈	1	2	yes	—
368	C₂³	C₂×#10625350	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	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	—	2	2	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	376	2	no	—
386	C₂×C₄	—	188	4	no	—
387	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
388	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
390	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
391	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
392	C₂×C₄	#13094071	1	1	yes	characteristic
393	C₂×C₄	#13094071	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	188	2	no	—
399	C₈	—	188	2	no	—
400	C₈	#13093980	1	2	yes	—
401	C₈	#13093980	1	2	yes	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	8	1	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
410	C₂²	#15689813	1	1	yes	characteristic
411	C₂²	#15689813	1	1	yes	characteristic
412	C₄	—	2	2	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	188	2	no	—
416	C₄	—	188	2	no	—
417	C₄	—	188	2	no	—
418	C₄	—	188	2	no	—
419	C₄	C₂×#13093980	1	1	yes	characteristic
420	C₄	#15689600	1	1	yes	characteristic
421	C₄	#15689777	1	1	yes	characteristic
422	C₄	#15689777	1	1	yes	characteristic
423	C₂	—	2	1	no	—
424	C₂	—	2	1	no	—
425	C₂	—	4	2	no	—
426	C₂	#20246255	1	1	yes	characteristic
427	C₂	#20252292	1	1	yes	characteristic
428	C₂	#20252299	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1753	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1753	D₄₇
hypocenter	C₄₇	#22608
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₂²⋊C₈ ◁ #1753

Complements

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

N	H ≅ G/N	type
3. #20244141	C₂	semidirect
4. #20244136	C₂	semidirect
5. #20243988	C₂	semidirect
6. #20243988	C₂	semidirect
9. #20243272	C₂	semidirect
10. #20243267	C₂	semidirect
19. #15689165	C₄	semidirect
20. #15689165	C₄	semidirect
21. #15689165	C₄	semidirect
22. #15689165	C₄	semidirect
257. C₄₇	#22608	semidirect

Maximal subgroups

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

subgroup	index
#20252042	2
#20251978	2
#20244141	2
#20244136	2
#20243988	2
#20243488	2
#20243430	2
#20243272	2
#20243267	2
C₄₇×#1753	2
#22608	47