Subgroups — #26109709

Order 12032.

514 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245793	C₂	1	1	yes	maximal, characteristic
2	#20243365	C₂	1	1	yes	maximal, characteristic
3	#20243365	C₂	1	1	yes	maximal, characteristic
4	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241271	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13093982	—	2	1	no	—
9	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
12	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
13	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
14	#15688993	C₂²	1	1	yes	characteristic
15	#15688988	—	2	1	no	—
16	#15688980	—	2	1	no	—
17	#15688980	C₄	1	2	yes	—
18	C₄⋊C₄×Dic₄₇	—	2	1	no	—
19	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
20	#15688877	—	2	1	no	—
21	#15688877	—	2	1	no	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#384	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
28	C₂²×C₄₇⋊C₈	—	2	1	no	—
29	C₂²×C₄₇⋊C₈	—	2	1	no	—
30	#13093982	—	4	2	no	—
31	#13093982	—	4	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	1	no	—
33	C₂×C₄⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
35	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
40	C₄²×D₄₇	—	2	1	no	—
41	C₄²×D₄₇	—	2	1	no	—
42	C₄²×D₄₇	—	2	1	no	—
43	C₄²×D₄₇	—	2	1	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
45	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
47	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
48	(C₂×D₄₇)⋊C₈	—	4	2	no	—
49	(C₂×D₄₇)⋊C₈	—	4	2	no	—
50	C₄₇⋊#95	—	2	2	no	—
51	C₄₇⋊#95	—	2	2	no	—
52	C₂²×C₈×C₄₇	—	2	1	no	—
53	C₂²×C₈×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
58	C₄⋊C₈×C₄₇	—	2	1	no	—
59	C₄⋊C₈×C₄₇	—	2	1	no	—
60	C₄⋊C₈×C₄₇	—	2	1	no	—
61	C₄⋊C₈×C₄₇	—	2	1	no	—
62	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
67	C₂²×Dic₄₇	—	2	2	no	—
68	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
71	C₂×C₄×D₄₇	—	2	1	no	—
72	C₂×C₄×D₄₇	—	2	1	no	—
73	C₂×C₄×D₄₇	—	2	1	no	—
74	C₂×C₄×D₄₇	—	2	1	no	—
75	C₂×C₄×D₄₇	—	2	1	no	—
76	C₂×C₄×D₄₇	—	2	1	no	—
77	C₂×C₄×D₄₇	—	2	1	no	—
78	C₂×C₄×D₄₇	—	2	1	no	—
79	C₂×C₄×D₄₇	—	2	1	no	—
80	C₂×C₄×D₄₇	—	2	1	no	—
81	C₂×C₄×D₄₇	—	2	1	no	—
82	C₂×C₄×D₄₇	—	2	1	no	—
83	C₂×C₄×D₄₇	—	4	1	no	—
84	C₂×C₄×D₄₇	—	4	1	no	—
85	C₂×C₄×D₄₇	SD₁₆	1	2	yes	—
86	C₂×C₄×D₄₇	Q₁₆	1	2	yes	—
87	C₂×C₈×C₄₇	—	4	1	no	—
88	C₂×C₈×C₄₇	—	4	1	no	—
89	C₂×C₈×C₄₇	—	4	1	no	—
90	C₂×C₈×C₄₇	—	4	1	no	—
91	C₂×C₈×C₄₇	—	4	1	no	—
92	C₂×C₈×C₄₇	—	4	1	no	—
93	C₄⋊C₄×C₄₇	—	4	2	no	—
94	C₄⋊C₄×C₄₇	—	4	1	no	—
95	C₄⋊C₄×C₄₇	—	4	1	no	—
96	C₄⋊C₄×C₄₇	—	4	1	no	—
97	C₄⋊C₄×C₄₇	—	4	1	no	—
98	C₄²×C₄₇	#41	1	1	yes	characteristic
99	C₄²×C₄₇	#41	1	1	yes	characteristic
100	C₄²×C₄₇	#41	1	1	yes	characteristic
101	C₄²×C₄₇	#41	1	1	yes	characteristic
102	(C₂×D₄₇)⋊C₄	—	4	4	no	—
103	C₄⋊Dic₄₇	—	4	1	no	—
104	C₄⋊Dic₄₇	—	4	1	no	—
105	C₄⋊Dic₄₇	—	4	1	no	—
106	C₄⋊Dic₄₇	—	4	1	no	—
107	C₄⋊Dic₄₇	—	4	2	no	—
108	C₄×Dic₄₇	—	2	1	no	—
109	C₄×Dic₄₇	—	2	1	no	—
110	C₄×Dic₄₇	—	2	1	no	—
111	C₄×Dic₄₇	—	2	1	no	—
112	C₄×Dic₄₇	—	2	1	no	—
113	C₄×Dic₄₇	—	2	1	no	—
114	C₄×Dic₄₇	—	4	4	no	—
115	C₂×C₄₇⋊C₈	—	4	1	no	—
116	C₂×C₄₇⋊C₈	—	4	1	no	—
117	C₂×C₄₇⋊C₈	—	4	1	no	—
118	C₂×C₄₇⋊C₈	—	4	1	no	—
119	C₂×C₄₇⋊C₈	—	4	1	no	—
120	C₂×C₄₇⋊C₈	—	4	1	no	—
121	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂²×D₄₇	—	2	1	no	—
123	C₂²×D₄₇	—	2	1	no	—
124	C₂²×D₄₇	—	2	1	no	—
125	C₂²×D₄₇	—	2	1	no	—
126	C₂²×D₄₇	—	2	1	no	—
127	C₂²×D₄₇	—	2	1	no	—
128	C₂²×D₄₇	#103	1	2	yes	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
135	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
137	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
138	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
144	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
148	C₂×Dic₄₇	—	2	1	no	—
149	C₂×Dic₄₇	—	2	1	no	—
150	C₂×Dic₄₇	—	2	1	no	—
151	C₂×Dic₄₇	—	2	1	no	—
152	C₂×Dic₄₇	—	2	1	no	—
153	C₂×Dic₄₇	—	2	1	no	—
154	C₂×Dic₄₇	—	2	1	no	—
155	C₂×Dic₄₇	—	2	1	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	#103	1	2	yes	—
160	C₄×D₄₇	—	2	2	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	4	2	no	—
165	C₄×D₄₇	—	4	2	no	—
166	C₄×D₄₇	—	4	1	no	—
167	C₄×D₄₇	—	4	1	no	—
168	C₄×D₄₇	—	4	1	no	—
169	C₄×D₄₇	—	4	1	no	—
170	C₈×C₄₇	—	8	1	no	—
171	C₈×C₄₇	—	8	1	no	—
172	C₄₇⋊C₈	—	8	1	no	—
173	C₄₇⋊C₈	—	8	1	no	—
174	#8727	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	#381	1	1	yes	characteristic
176	C₂²×C₄₇	#413	1	1	yes	characteristic
177	C₂²×C₄₇	#413	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
179	C₂²×C₄₇	#416	1	1	yes	characteristic
180	C₂²×C₄₇	#417	1	1	yes	characteristic
181	C₂²×C₄₇	#418	1	1	yes	characteristic
182	C₂×D₄₇	—	2	2	no	—
183	C₂×D₄₇	—	2	2	no	—
184	C₂×D₄₇	—	2	2	no	—
185	C₂×D₄₇	—	4	1	no	—
186	C₂×D₄₇	—	4	1	no	—
187	C₂×D₄₇	—	4	1	no	—
188	C₂×D₄₇	—	4	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	#481	1	1	yes	characteristic
193	C₄×C₄₇	#481	1	1	yes	characteristic
194	C₄×C₄₇	#482	1	1	yes	characteristic
195	C₄×C₄₇	#482	1	1	yes	characteristic
196	C₄×C₄₇	#484	1	1	yes	characteristic
197	C₄×C₄₇	#484	1	1	yes	characteristic
198	C₄×C₄₇	#485	1	1	yes	characteristic
199	C₄×C₄₇	#485	1	1	yes	characteristic
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	4	1	no	—
202	Dic₄₇	—	4	1	no	—
203	Dic₄₇	—	8	2	no	—
204	#2285	—	47	1	no	—
205	#1797	—	47	1	no	—
206	#1797	—	47	1	no	—
207	#1296	—	47	1	no	—
208	#1296	—	47	1	no	—
209	#1296	—	47	1	no	—
210	#1296	D₄₇	1	1	yes	characteristic, complemented
211	C₂×C₄₇	#1542	1	1	yes	characteristic
212	C₂×C₄₇	#1550	1	1	yes	characteristic
213	C₂×C₄₇	#1553	1	1	yes	characteristic
214	C₂×C₄₇	#1557	1	1	yes	characteristic
215	C₂×C₄₇	#1822	1	1	yes	characteristic
216	C₂×C₄₇	#1824	1	1	yes	characteristic
217	C₂×C₄₇	#1825	1	1	yes	characteristic
218	D₄₇	—	4	2	no	—
219	C₂×#117	—	94	1	no	—
220	C₂²×C₄²	—	47	1	no	—
221	C₂×C₄⋊C₈	—	47	1	no	—
222	C₂×C₄⋊C₈	—	47	1	no	—
223	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₂²⋊C₈	—	94	1	no	—
226	C₂×C₂²⋊C₈	—	94	1	no	—
227	#384	—	47	1	no	—
228	#384	C₂×D₄₇	1	1	yes	characteristic
229	#382	—	94	1	no	—
230	#380	—	47	2	no	—
231	#380	—	94	1	no	—
232	C₄×C₄⋊C₄	—	47	2	no	—
233	C₄×C₄⋊C₄	—	94	1	no	—
234	#336	—	94	1	no	—
235	#336	—	94	1	no	—
236	C₄₇	#8727	1	1	yes	characteristic, complemented, Sylow
237	C₂³×C₄	—	47	1	no	—
238	C₂³×C₄	—	47	1	no	—
239	C₂³×C₄	—	47	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	94	1	no	—
243	C₂²×C₈	—	94	1	no	—
244	#117	—	188	2	no	—
245	#117	—	188	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	47	2	no	—
249	C₂×C₄⋊C₄	—	94	1	no	—
250	C₂×C₄⋊C₄	—	94	1	no	—
251	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
252	C₂×C₂²⋊C₄	—	94	2	no	—
253	C₂×C₄²	—	47	1	no	—
254	C₂×C₄²	—	47	1	no	—
255	C₂×C₄²	—	47	1	no	—
256	C₂×C₄²	—	94	1	no	—
257	C₂×C₄²	—	94	1	no	—
258	C₂×C₄²	—	94	1	no	—
259	C₂×C₄²	—	94	1	no	—
260	C₂×C₄²	—	94	2	no	—
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	2	1	no	—
266	C₄⋊C₈	—	94	1	no	—
267	C₄⋊C₈	—	94	1	no	—
268	C₄⋊C₈	—	94	1	no	—
269	C₄⋊C₈	—	94	1	no	—
270	C₂²⋊C₈	—	188	2	no	—
271	C₂²⋊C₈	—	188	2	no	—
272	#95	—	94	2	no	—
273	#95	—	94	2	no	—
274	C₂⁴	—	47	1	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	47	1	no	—
277	C₂²×C₄	—	47	2	no	—
278	C₂²×C₄	—	47	2	no	—
279	C₂²×C₄	—	47	1	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	94	1	no	—
282	C₂²×C₄	—	94	1	no	—
283	C₂²×C₄	—	94	1	no	—
284	C₂²×C₄	—	94	1	no	—
285	C₂²×C₄	—	94	1	no	—
286	C₂²×C₄	—	94	1	no	—
287	C₂²×C₄	—	94	1	no	—
288	C₂²×C₄	—	94	1	no	—
289	C₂²×C₄	—	94	1	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	94	1	no	—
292	C₂²×C₄	—	94	1	no	—
293	C₂²×C₄	—	94	2	no	—
294	C₂²×C₄	—	188	1	no	—
295	C₂²×C₄	—	188	1	no	—
296	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	188	1	no	—
306	C₂×C₈	—	188	1	no	—
307	C₂×C₈	—	188	1	no	—
308	C₂×C₈	—	188	1	no	—
309	C₂×C₈	—	188	1	no	—
310	C₂×C₈	—	188	1	no	—
311	C₄⋊C₄	—	4	2	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	—	4	1	no	—
316	C₄⋊C₄	—	188	2	no	—
317	C₄⋊C₄	—	188	1	no	—
318	C₄⋊C₄	—	188	1	no	—
319	C₄⋊C₄	—	188	1	no	—
320	C₄⋊C₄	—	188	1	no	—
321	C₂²⋊C₄	—	188	4	no	—
322	C₄²	—	94	1	no	—
323	C₄²	—	94	1	no	—
324	C₄²	—	94	1	no	—
325	C₄²	—	94	1	no	—
326	C₄²	—	94	1	no	—
327	C₄²	—	94	1	no	—
328	C₄²	—	188	4	no	—
329	C₄²	#10625350	1	1	yes	characteristic
330	C₄²	#10625350	1	1	yes	characteristic
331	C₄²	#10625352	1	1	yes	characteristic
332	C₄²	#10625354	1	1	yes	characteristic
333	C₂³	—	47	2	no	—
334	C₂³	—	94	1	no	—
335	C₂³	—	94	1	no	—
336	C₂³	—	94	1	no	—
337	C₂³	—	94	1	no	—
338	C₂³	—	94	1	no	—
339	C₂³	—	94	1	no	—
340	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	94	1	no	—
348	C₂×C₄	—	94	1	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	1	no	—
354	C₂×C₄	—	94	1	no	—
355	C₂×C₄	—	94	1	no	—
356	C₂×C₄	—	94	1	no	—
357	C₂×C₄	—	94	1	no	—
358	C₂×C₄	—	94	1	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	1	no	—
365	C₂×C₄	—	188	1	no	—
366	C₂×C₄	—	188	1	no	—
367	C₂×C₄	—	188	1	no	—
368	C₂×C₄	#13093981	1	1	yes	characteristic
369	C₂×C₄	#13093982	1	1	yes	characteristic
370	C₂×C₄	#13094006	1	1	yes	characteristic
371	C₂×C₄	#13094006	1	1	yes	characteristic
372	C₂×C₄	#13094009	1	1	yes	characteristic
373	C₂×C₄	#13094009	1	1	yes	characteristic
374	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
375	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
376	C₂×C₄	#13094043	1	1	yes	characteristic
377	C₂×C₄	#13094045	1	1	yes	characteristic
378	C₂×C₄	#13094048	1	1	yes	characteristic
379	C₂×C₄	#13094051	1	1	yes	characteristic
380	C₂×C₄	#13094051	1	1	yes	characteristic
381	C₂×C₄	#13094056	1	1	yes	characteristic
382	C₈	—	8	1	no	—
383	C₈	—	8	1	no	—
384	C₈	—	376	1	no	—
385	C₈	—	376	1	no	—
386	C₂²	—	94	2	no	—
387	C₂²	—	94	2	no	—
388	C₂²	—	94	2	no	—
389	C₂²	—	188	1	no	—
390	C₂²	—	188	1	no	—
391	C₂²	—	188	1	no	—
392	C₂²	—	188	1	no	—
393	C₂²	#15688985	1	1	yes	characteristic
394	C₂²	#15689104	1	1	yes	characteristic
395	C₂²	#15689106	1	1	yes	characteristic
396	C₂²	#103×D₄₇	1	1	yes	characteristic
397	C₂²	#15689116	1	1	yes	characteristic
398	C₂²	#15689123	1	1	yes	characteristic
399	C₂²	#15689126	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	94	2	no	—
404	C₄	—	376	2	no	—
405	C₄	—	188	1	no	—
406	C₄	—	188	1	no	—
407	C₄	#15689440	1	1	yes	characteristic
408	C₄	#15689443	1	1	yes	characteristic
409	C₄	#15689445	1	1	yes	characteristic
410	C₄	#15689449	1	1	yes	characteristic
411	C₄	#15689457	1	1	yes	characteristic
412	C₄	#15689460	1	1	yes	characteristic
413	C₄	#15689462	1	1	yes	characteristic
414	C₄	#15689466	1	1	yes	characteristic
415	C₂	—	188	2	no	—
416	C₂	#20242044	1	1	yes	characteristic
417	C₂	#20242075	1	1	yes	characteristic
418	C₂	#20242090	1	1	yes	characteristic
419	C₂	#20242109	1	1	yes	characteristic
420	C₂	#20243470	1	1	yes	characteristic
421	C₂	#20243477	1	1	yes	characteristic
422	C₂	#20243481	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#8727
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
4. #20241272	C₂	semidirect
5. #20241272	C₂	semidirect
6. #20241271	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
210. #1296	D₄₇	semidirect
236. C₄₇	#8727	semidirect

Maximal subgroups

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

subgroup	index
#20245793	2
#20243365	2
#20241272	2
#20241271	2
C₄₇×#1296	2
#8727	47