Subgroups — #26316012

Order 12032.

878 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251751	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244950	C₂	1	2	yes	maximal, complemented
3	#20244619	C₂	1	2	yes	maximal
4	#20244088	C₂	1	4	yes	maximal, complemented
5	#20243388	C₂	1	2	yes	maximal, complemented
6	#20243388	C₂	1	2	yes	maximal, complemented
7	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#13094016	—	2	1	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×#13093945	C₂²	1	4	yes	—
12	C₂×#13093945	C₂²	1	4	yes	—
13	C₂×#13093935	C₂²	1	2	yes	—
14	#15689021	—	2	1	no	—
15	#15689021	—	2	1	no	—
16	#15689021	C₂²	1	2	yes	—
17	#15689021	C₂²	1	2	yes	—
18	#15688993	C₂²	1	1	yes	characteristic
19	#15688993	C₂²	1	1	yes	characteristic
20	#15688989	—	2	1	no	—
21	#15688885	C₂²	1	4	yes	—
22	#15688885	C₂²	1	4	yes	—
23	#15688878	C₂²	1	2	yes	—
24	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₇	—	2	1	no	—
26	C₂×C₄×D₄×C₄₇	—	2	1	no	—
27	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
28	C₄₇×#390	—	2	1	no	—
29	C₄₇×#390	—	2	1	no	—
30	C₄₇×#390	C₂²	1	2	yes	—
31	C₄₇×#384	C₂²	1	1	yes	characteristic
32	C₄³×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
34	#13094016	—	4	4	no	—
35	C₂×C₄⋊Dic₄₇	—	2	1	no	—
36	C₂×C₄⋊Dic₄₇	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	—	2	1	no	—
38	C₂×C₄⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
40	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
41	C₂×Dic₄₇⋊C₄	—	2	2	no	—
42	C₂×Dic₄₇⋊C₄	—	2	2	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
44	#13093945	—	2	8	no	—
45	#13093945	—	4	4	no	—
46	#13093935	—	4	2	no	—
47	C₄₇⋊#95	—	2	2	no	—
48	C₄₇⋊#95	—	2	2	no	—
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₇	—	2	2	no	—
53	#127×C₄₇	—	2	4	no	—
54	C₄×D₄×C₄₇	—	2	4	no	—
55	C₄×D₄×C₄₇	—	2	4	no	—
56	C₄×D₄×C₄₇	—	4	4	no	—
57	C₄×D₄×C₄₇	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₂⁴×C₄₇	—	2	2	no	—
72	C₂×D₄×C₄₇	—	2	4	no	—
73	C₂×D₄×C₄₇	—	2	4	no	—
74	C₂×D₄×C₄₇	—	2	2	no	—
75	C₂×D₄×C₄₇	—	2	2	no	—
76	C₂×D₄×C₄₇	—	2	2	no	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	4	2	no	—
80	C₂×D₄×C₄₇	—	4	2	no	—
81	C₂×D₄×C₄₇	—	4	2	no	—
82	C₂×D₄×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	#41	1	4	yes	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	4	4	no	—
86	C₂²×C₄×C₄₇	—	4	4	no	—
87	C₂²×C₄×C₄₇	—	4	4	no	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	—	2	2	no	—
99	C₄⋊C₄×C₄₇	—	4	2	no	—
100	C₄⋊C₄×C₄₇	—	4	2	no	—
101	C₂²⋊C₄×C₄₇	—	4	4	no	—
102	C₂²⋊C₄×C₄₇	—	4	4	no	—
103	C₂²⋊C₄×C₄₇	—	4	4	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	#41	1	4	yes	—
112	C₄⋊Dic₄₇	—	2	4	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	4	2	no	—
116	C₄⋊Dic₄₇	—	4	2	no	—
117	C₄⋊Dic₄₇	—	4	2	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	Dic₄₇⋊C₄	—	4	4	no	—
120	Dic₄₇⋊C₄	—	4	4	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	2	4	no	—
124	C₂³×C₄₇	—	2	4	no	—
125	C₂³×C₄₇	—	4	2	no	—
126	C₂³×C₄₇	—	4	2	no	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
132	D₄×C₄₇	—	2	4	no	—
133	D₄×C₄₇	—	2	4	no	—
134	D₄×C₄₇	—	4	8	no	—
135	D₄×C₄₇	—	4	8	no	—
136	D₄×C₄₇	—	4	2	no	—
137	D₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	8	8	no	—
154	C₂×C₄×C₄₇	#124	1	2	yes	—
155	C₂×C₄×C₄₇	#124	1	2	yes	—
156	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
157	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₄₇	#137	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
162	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₄₇⋊C₈	—	4	4	no	—
171	#29130	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	—	4	4	no	—
173	C₂²×C₄₇	—	4	4	no	—
174	C₂²×C₄₇	—	4	4	no	—
175	C₂²×C₄₇	—	8	2	no	—
176	C₂²×C₄₇	—	8	2	no	—
177	C₂²×C₄₇	—	8	2	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	#525	1	1	yes	characteristic
180	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
181	C₂²×C₄₇	#537	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	4	1	no	—
190	C₄×C₄₇	—	4	1	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	#490	1	4	yes	—
193	C₄×C₄₇	#552	1	2	yes	—
194	C₄×C₄₇	#553	1	2	yes	—
195	Dic₄₇	—	8	2	no	—
196	Dic₄₇	—	8	2	no	—
197	#2859	—	47	1	no	—
198	C₄×#127	D₄₇	1	1	yes	characteristic
199	#2100	—	47	2	no	—
200	#2041	—	47	2	no	—
201	#1936	—	47	4	no	—
202	#1802	—	47	2	no	—
203	#1802	—	47	2	no	—
204	#1767	—	47	1	no	—
205	C₂×C₄₇	—	8	4	no	—
206	C₂×C₄₇	#2562	1	1	yes	characteristic
207	C₂×C₄₇	#3109	1	1	yes	characteristic
208	C₂×C₄₇	#3110	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#490	1	1	yes	characteristic
210	C₂×C₄₇	#3141	1	1	yes	characteristic
211	C₂×C₄₇	#3253	1	1	yes	characteristic
212	C₂×C₄₇	#3254	1	1	yes	characteristic
213	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
214	C₂×#125	—	94	1	no	—
215	C₂×C₄×D₄	—	2	1	no	—
216	C₂×C₄×D₄	—	2	1	no	—
217	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×#102	—	47	4	no	—
220	C₂×#102	—	47	4	no	—
221	C₂×#97	—	47	2	no	—
222	#390	—	2	1	no	—
223	#390	—	2	1	no	—
224	#390	C₂×D₄₇	1	2	yes	—
225	#389	—	47	2	no	—
226	#389	—	47	2	no	—
227	#389	—	94	1	no	—
228	#389	—	94	1	no	—
229	#384	—	47	1	no	—
230	#384	—	47	1	no	—
231	#384	C₂×D₄₇	1	1	yes	characteristic
232	#382	—	94	1	no	—
233	C₄³	C₂×D₄₇	1	1	yes	characteristic
234	#340	—	47	4	no	—
235	#340	—	47	4	no	—
236	#336	—	47	2	no	—
237	C₄₇	#29130	1	1	yes	characteristic, complemented, Sylow
238	C₂²×D₄	—	2	1	no	—
239	C₂²×D₄	—	2	1	no	—
240	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
241	C₂³×C₄	—	2	2	no	—
242	C₂²×C₈	—	47	4	no	—
243	#127	—	2	4	no	—
244	#125	—	188	4	no	—
245	C₄×D₄	—	2	4	no	—
246	C₄×D₄	—	2	4	no	—
247	C₄×D₄	—	4	4	no	—
248	C₄×D₄	—	4	4	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	47	2	no	—
252	C₂×C₄⋊C₄	—	47	2	no	—
253	C₂×C₄⋊C₄	—	94	2	no	—
254	C₂×C₄⋊C₄	—	94	2	no	—
255	C₂×C₄⋊C₄	—	94	1	no	—
256	C₂×C₄⋊C₄	—	94	1	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	C₄⋊C₈	—	94	4	no	—
271	#102	—	94	8	no	—
272	#102	—	188	4	no	—
273	#97	—	188	2	no	—
274	#95	—	94	2	no	—
275	#95	—	94	2	no	—
276	C₂⁴	—	2	2	no	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	4	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	4	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	#10625350	1	4	yes	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	4	4	no	—
291	C₂²×C₄	—	4	4	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
302	C₂×C₈	—	94	4	no	—
303	C₂×C₈	—	94	4	no	—
304	C₂×C₈	—	94	4	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	4	2	no	—
308	C₄⋊C₄	—	4	2	no	—
309	C₄⋊C₄	—	94	4	no	—
310	C₄⋊C₄	—	94	2	no	—
311	C₄⋊C₄	—	94	2	no	—
312	C₄⋊C₄	—	188	4	no	—
313	C₄⋊C₄	—	188	2	no	—
314	C₄⋊C₄	—	188	2	no	—
315	C₄⋊C₄	—	188	4	no	—
316	C₄⋊C₄	—	188	2	no	—
317	C₄⋊C₄	—	188	2	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₄²	—	2	2	no	—
322	C₄²	—	2	2	no	—
323	C₄²	—	2	2	no	—
324	C₄²	—	2	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	2	1	no	—
328	C₄²	#10625352	1	4	yes	—
329	C₂³	—	2	4	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
337	D₄	—	2	4	no	—
338	D₄	—	2	4	no	—
339	D₄	—	4	8	no	—
340	D₄	—	4	8	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	8	no	—
359	C₂×C₄	—	188	2	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	—	188	2	no	—
365	C₂×C₄	#13094011	1	2	yes	—
366	C₂×C₄	#13094011	1	2	yes	—
367	C₂×C₄	#13094049	1	2	yes	—
368	C₂×C₄	#13094050	1	2	yes	—
369	C₂×C₄	#13094050	1	2	yes	—
370	C₂×C₄	#13094054	1	2	yes	—
371	C₂×C₄	C₂×#10625352	1	2	yes	—
372	C₂×C₄	C₂×#10625350	1	2	yes	—
373	C₂×C₄	#13094070	1	1	yes	characteristic
374	C₂×C₄	#13094071	1	1	yes	characteristic
375	C₈	—	188	4	no	—
376	C₂²	—	4	4	no	—
377	C₂²	—	4	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	—	8	2	no	—
383	C₂²	#15689634	1	1	yes	characteristic
384	C₂²	C₂×#13094011	1	1	yes	characteristic
385	C₂²	#15689701	1	1	yes	characteristic
386	C₂²	C₂×#13094049	1	1	yes	characteristic
387	C₂²	C₂×#13094050	1	1	yes	characteristic
388	C₂²	C₂×#13094050	1	1	yes	characteristic
389	C₂²	C₂×#13094054	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	376	2	no	—
397	C₄	—	376	2	no	—
398	C₄	#15689487	1	4	yes	—
399	C₄	#15689813	1	2	yes	—
400	C₄	#15689819	1	2	yes	—
401	C₂	—	8	4	no	—
402	C₂	#20248554	1	1	yes	characteristic
403	C₂	#20253479	1	1	yes	characteristic
404	C₂	#20253487	1	1	yes	characteristic
405	C₂	C₂×#15689487	1	1	yes	characteristic
406	C₂	#20253781	1	1	yes	characteristic
407	C₂	#20254766	1	1	yes	characteristic
408	C₂	#20254775	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄×#127×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
hypercenter	C₄×#127	D₄₇
hypocenter	C₄₇	#29130
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×#127

Complements

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

N	H ≅ G/N	type
1. #20251751	C₂	semidirect
2. #20244950	C₂	semidirect
4. #20244088	C₂	semidirect
5. #20243388	C₂	semidirect
6. #20243388	C₂	semidirect
7. #20243241	C₂	semidirect
237. C₄₇	#29130	semidirect

Maximal subgroups

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

subgroup	index
#20251751	2
#20244950	2
#20244619	2
#20244088	2
#20243388	2
#20243241	2
C₄×#127×C₄₇	2
#29130	47