Subgroups — #26110439

Order 12032.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246288	C₂	1	1	yes	maximal, characteristic
2	#20244147	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243547	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243389	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688850	C₂	1	1	yes	maximal, characteristic
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
9	C₂×#13093986	—	2	1	no	—
10	C₂×C₄⋊C₄×D₄₇	—	2	1	no	—
11	C₂×#13093958	—	2	1	no	—
12	C₂×#13093957	—	2	2	no	—
13	C₂×#13093946	—	2	1	no	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15689019	—	2	1	no	—
16	#15688994	—	2	2	no	—
17	#15688993	C₂²	1	1	yes	characteristic
18	#15688980	—	2	1	no	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	#15688886	—	2	1	no	—
21	#15688886	—	2	1	no	—
22	#15688850	C₄	1	4	yes	complemented
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#384	C₂²	1	1	yes	characteristic
26	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₄₇	—	2	1	no	—
28	C₂²×C₄×D₄₇	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	1	no	—
30	C₄×D₁₈₈	—	2	1	no	—
31	C₄×D₁₈₈	—	2	1	no	—
32	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
33	C₄×D₁₈₈	Q₈	1	2	yes	—
34	#13093986	—	4	2	no	—
35	#13093986	—	4	2	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	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
41	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
42	C₂×Dic₄₇⋊C₄	—	2	2	no	—
43	C₄⋊C₄×D₄₇	—	4	2	no	—
44	C₄⋊C₄×D₄₇	—	4	2	no	—
45	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
46	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
47	C₂×C₄×Dic₄₇	—	2	1	no	—
48	#13093958	—	4	2	no	—
49	#13093957	—	4	4	no	—
50	#13093946	—	4	2	no	—
51	C₄×C₄₇⋊C₈	—	2	1	no	—
52	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	complemented
53	C₄₇⋊#95	—	2	2	no	—
54	C₄₇⋊#95	—	2	1	no	—
55	C₂²×C₈×C₄₇	—	2	1	no	—
56	C₂²×C₈×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₄₇	—	2	1	no	—
62	C₄⋊C₈×C₄₇	—	2	1	no	—
63	C₄⋊C₈×C₄₇	—	2	1	no	—
64	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	complemented
65	C₂³×D₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×Dic₄₇	—	2	1	no	—
71	C₂²×Dic₄₇	—	2	1	no	—
72	C₂²×Dic₄₇	—	2	1	no	—
73	C₂²×Dic₄₇	—	4	1	no	—
74	C₂×D₁₈₈	—	2	1	no	—
75	C₂×D₁₈₈	—	2	1	no	—
76	C₂×D₁₈₈	—	2	1	no	—
77	C₂×D₁₈₈	C₄⋊C₄	1	2	yes	—
78	C₂×D₁₈₈	D₈	1	2	yes	—
79	C₂×D₁₈₈	Q₁₆	1	2	yes	—
80	C₂×C₄×D₄₇	—	2	2	no	—
81	C₂×C₄×D₄₇	—	2	2	no	—
82	C₂×C₄×D₄₇	—	4	1	no	—
83	C₂×C₄×D₄₇	—	4	1	no	—
84	C₂×C₄×D₄₇	—	4	1	no	—
85	C₂×C₄×D₄₇	—	4	1	no	—
86	C₂×C₄×D₄₇	—	4	4	no	—
87	C₂×C₄×D₄₇	—	4	4	no	—
88	C₂×C₄×D₄₇	—	8	2	no	—
89	C₂×C₈×C₄₇	—	2	2	no	—
90	C₂×C₈×C₄₇	—	4	1	no	—
91	C₂×C₈×C₄₇	—	4	1	no	—
92	C₂×C₈×C₄₇	—	4	1	no	—
93	C₂×C₈×C₄₇	—	4	1	no	—
94	C₂×C₈×C₄₇	—	4	1	no	—
95	C₄⋊C₄×C₄₇	—	4	2	no	—
96	C₄⋊C₄×C₄₇	—	4	1	no	—
97	C₄⋊C₄×C₄₇	—	4	1	no	—
98	C₄⋊C₄×C₄₇	—	4	1	no	—
99	C₄⋊C₄×C₄₇	—	4	1	no	—
100	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
102	C₄²×C₄₇	#41	1	1	yes	characteristic
103	C₄²×C₄₇	#41	1	1	yes	characteristic
104	(C₂×D₄₇)⋊C₄	—	2	2	no	—
105	(C₂×D₄₇)⋊C₄	—	2	2	no	—
106	(C₂×D₄₇)⋊C₄	—	4	4	no	—
107	C₄⋊Dic₄₇	—	2	1	no	—
108	C₄⋊Dic₄₇	—	2	1	no	—
109	C₄⋊Dic₄₇	—	2	1	no	—
110	C₄⋊Dic₄₇	—	2	1	no	—
111	C₄⋊Dic₄₇	—	4	2	no	—
112	C₄⋊Dic₄₇	—	4	1	no	—
113	C₄⋊Dic₄₇	—	4	1	no	—
114	C₄⋊Dic₄₇	—	4	1	no	—
115	C₄⋊Dic₄₇	—	4	1	no	—
116	C₄⋊Dic₄₇	C₄⋊C₄	1	2	yes	—
117	C₄⋊Dic₄₇	D₈	1	2	yes	—
118	Dic₄₇⋊C₄	—	4	4	no	—
119	C₄×Dic₄₇	—	4	1	no	—
120	C₄×Dic₄₇	—	4	1	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂³×C₄₇	#120	1	1	yes	characteristic
125	C₂²×D₄₇	—	2	2	no	—
126	C₂²×D₄₇	—	2	2	no	—
127	C₂²×D₄₇	—	2	2	no	—
128	C₂²×D₄₇	—	4	1	no	—
129	C₂²×D₄₇	—	4	1	no	—
130	C₂²×D₄₇	—	4	1	no	—
131	C₂²×D₄₇	—	4	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
147	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
150	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	4	1	no	—
154	C₂×Dic₄₇	—	4	1	no	—
155	C₂×Dic₄₇	—	4	1	no	—
156	C₂×Dic₄₇	—	4	1	no	—
157	C₂×Dic₄₇	—	4	1	no	—
158	C₂×Dic₄₇	—	4	1	no	—
159	C₂×Dic₄₇	—	4	1	no	—
160	C₂×Dic₄₇	—	8	1	no	—
161	C₂×Dic₄₇	—	8	1	no	—
162	C₂×Dic₄₇	—	8	1	no	—
163	D₁₈₈	—	2	2	no	—
164	D₁₈₈	—	2	2	no	—
165	D₁₈₈	—	2	2	no	—
166	D₁₈₈	#107	1	4	yes	complemented
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	C₄×D₄₇	—	4	2	no	—
170	C₄×D₄₇	—	4	2	no	—
171	C₄×D₄₇	—	8	8	no	—
172	C₈×C₄₇	—	4	2	no	—
173	C₈×C₄₇	—	8	1	no	—
174	C₄₇⋊C₈	—	2	4	no	—
175	#8882	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	#385	1	1	yes	characteristic
177	C₂²×C₄₇	#447	1	1	yes	characteristic
178	C₂²×C₄₇	#447	1	1	yes	characteristic
179	C₂²×C₄₇	#451	1	1	yes	characteristic
180	C₂²×C₄₇	#452	1	1	yes	characteristic
181	C₂²×C₄₇	#453	1	1	yes	characteristic
182	C₂²×C₄₇	#456	1	1	yes	characteristic
183	C₂×D₄₇	—	2	4	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₂×D₄₇	—	4	2	no	—
186	C₂×D₄₇	—	4	2	no	—
187	C₂×D₄₇	—	4	2	no	—
188	C₂×D₄₇	—	4	2	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	8	2	no	—
193	C₄×C₄₇	C₂×#107	1	1	yes	characteristic
194	C₄×C₄₇	#428	1	1	yes	characteristic
195	C₄×C₄₇	C₄×D₈	1	1	yes	characteristic
196	C₄×C₄₇	#440	1	1	yes	characteristic
197	C₄×C₄₇	#474	1	1	yes	characteristic
198	C₄×C₄₇	#478	1	1	yes	characteristic
199	C₄×C₄₇	#480	1	1	yes	characteristic
200	C₄×C₄₇	#484	1	1	yes	characteristic
201	Dic₄₇	—	4	2	no	—
202	Dic₄₇	—	4	2	no	—
203	Dic₄₇	—	8	1	no	—
204	Dic₄₇	—	16	1	no	—
205	D₄×C₄⋊C₄	—	47	1	no	—
206	#1947	—	47	1	no	—
207	#1845	—	47	1	no	—
208	#1802	—	47	1	no	—
209	C₂×D₄⋊C₈	—	47	1	no	—
210	#1296	D₄₇	1	1	yes	characteristic, complemented
211	#1279	—	47	1	no	—
212	C₂×C₄₇	#1619	1	1	yes	characteristic
213	C₂×C₄₇	#1632	1	1	yes	characteristic
214	C₂×C₄₇	#1647	1	1	yes	characteristic
215	C₂×C₄₇	#1649	1	1	yes	characteristic
216	C₂×C₄₇	#1852	1	1	yes	characteristic
217	C₂×C₄₇	#1859	1	1	yes	characteristic
218	C₂×C₄₇	#1862	1	1	yes	characteristic
219	D₄₇	—	4	4	no	—
220	C₂×C₄×D₄	—	47	1	no	—
221	C₂×C₄×D₄	—	94	1	no	—
222	C₂²×C₄⋊C₄	—	94	1	no	—
223	C₂×#107	—	94	1	no	—
224	C₂×#107	—	94	2	no	—
225	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
227	C₂×#102	—	94	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	#389	—	94	1	no	—
230	#385	—	94	2	no	—
231	#384	—	47	1	no	—
232	#384	C₂×D₄₇	1	1	yes	characteristic
233	#380	—	94	1	no	—
234	C₄×C₄⋊C₄	—	47	1	no	—
235	#340	—	94	1	no	—
236	#340	—	94	1	no	—
237	D₄⋊C₈	—	47	4	no	—
238	C₄₇	#8882	1	1	yes	characteristic, complemented, Sylow
239	C₂²×D₄	—	47	1	no	—
240	C₂³×C₄	—	94	2	no	—
241	C₂³×C₄	—	94	1	no	—
242	C₂²×C₈	—	2	1	no	—
243	C₂²×C₈	—	2	1	no	—
244	C₂²×C₈	—	94	1	no	—
245	C₄×D₄	—	47	2	no	—
246	C₄×D₄	—	47	2	no	—
247	C₄×D₄	—	94	1	no	—
248	C₄×D₄	—	94	1	no	—
249	C₄×D₄	—	188	2	no	—
250	C₄×D₄	—	188	2	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	47	1	no	—
254	C₂×C₄⋊C₄	—	47	1	no	—
255	C₂×C₄⋊C₄	—	47	1	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	—	94	1	no	—
258	C₂×C₄⋊C₄	—	94	1	no	—
259	C₂×C₄⋊C₄	—	94	1	no	—
260	C₂×C₄⋊C₄	—	188	2	no	—
261	C₂×C₄⋊C₄	—	188	2	no	—
262	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
263	C₂×C₂²⋊C₄	—	94	1	no	—
264	C₂×C₂²⋊C₄	—	94	2	no	—
265	C₂×C₄²	—	94	1	no	—
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	#107	—	188	4	no	—
268	#107	—	188	2	no	—
269	C₄⋊C₈	—	2	1	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	C₄×D₄₇	1	2	yes	complemented
273	#102	—	188	2	no	—
274	C₄×C₈	—	47	2	no	—
275	C₄×C₈	—	94	1	no	—
276	#95	—	94	2	no	—
277	#95	—	94	1	no	—
278	C₂⁴	—	94	1	no	—
279	C₂×D₄	—	47	2	no	—
280	C₂×D₄	—	47	2	no	—
281	C₂×D₄	—	47	2	no	—
282	C₂×D₄	—	94	1	no	—
283	C₂×D₄	—	94	1	no	—
284	C₂×D₄	—	94	1	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	94	1	no	—
287	C₂²×C₄	—	94	1	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	376	2	no	—
292	C₂²×C₄	—	188	4	no	—
293	C₂²×C₄	—	188	4	no	—
294	C₂²×C₄	—	188	1	no	—
295	C₂²×C₄	—	188	1	no	—
296	C₂²×C₄	—	188	1	no	—
297	C₂²×C₄	—	188	1	no	—
298	C₂²×C₄	—	188	1	no	—
299	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
300	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	1	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	2	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	—	47	2	no	—
317	C₄⋊C₄	—	47	2	no	—
318	C₄⋊C₄	—	94	1	no	—
319	C₄⋊C₄	—	94	1	no	—
320	C₄⋊C₄	—	94	1	no	—
321	C₄⋊C₄	—	94	1	no	—
322	C₄⋊C₄	—	188	2	no	—
323	C₄⋊C₄	—	188	4	no	—
324	C₄⋊C₄	—	188	1	no	—
325	C₄⋊C₄	—	188	1	no	—
326	C₄⋊C₄	—	188	1	no	—
327	C₄⋊C₄	—	188	1	no	—
328	C₂²⋊C₄	—	94	2	no	—
329	C₂²⋊C₄	—	94	2	no	—
330	C₂²⋊C₄	—	188	4	no	—
331	C₄²	—	188	1	no	—
332	C₄²	—	188	1	no	—
333	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₄²	#10625350	1	1	yes	characteristic
335	C₄²	#10625352	1	1	yes	characteristic
336	C₄²	Q₈×D₄₇	1	1	yes	characteristic
337	C₂³	—	94	2	no	—
338	C₂³	—	94	2	no	—
339	C₂³	—	94	2	no	—
340	C₂³	—	188	1	no	—
341	C₂³	—	188	1	no	—
342	C₂³	—	188	1	no	—
343	C₂³	—	188	1	no	—
344	C₂³	#13093994	1	1	yes	characteristic
345	D₄	—	47	4	no	—
346	D₄	—	94	2	no	—
347	D₄	—	94	2	no	—
348	D₄	—	94	2	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	376	8	no	—
357	C₂×C₄	—	376	1	no	—
358	C₂×C₄	—	376	1	no	—
359	C₂×C₄	—	376	1	no	—
360	C₂×C₄	—	188	1	no	—
361	C₂×C₄	—	188	1	no	—
362	C₂×C₄	—	188	1	no	—
363	C₂×C₄	—	188	1	no	—
364	C₂×C₄	—	188	1	no	—
365	C₂×C₄	—	188	1	no	—
366	C₂×C₄	—	188	1	no	—
367	C₂×C₄	—	188	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
373	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
374	C₂×C₄	#13094002	1	1	yes	characteristic
375	C₂×C₄	#13094004	1	1	yes	characteristic
376	C₂×C₄	#13094006	1	1	yes	characteristic
377	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
378	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
379	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
380	C₂×C₄	#13094045	1	1	yes	characteristic
381	C₂×C₄	#13094051	1	1	yes	characteristic
382	C₂×C₄	#13094051	1	1	yes	characteristic
383	C₂×C₄	#13094053	1	1	yes	characteristic
384	C₂×C₄	#13094056	1	1	yes	characteristic
385	C₈	—	4	2	no	—
386	C₈	—	8	1	no	—
387	C₈	—	94	4	no	—
388	C₂²	—	94	4	no	—
389	C₂²	—	188	2	no	—
390	C₂²	—	188	2	no	—
391	C₂²	—	188	2	no	—
392	C₂²	—	188	2	no	—
393	C₂²	—	188	2	no	—
394	C₂²	—	188	2	no	—
395	C₂²	#15688997	1	1	yes	characteristic
396	C₂²	#15689258	1	1	yes	characteristic
397	C₂²	#15689258	1	1	yes	characteristic
398	C₂²	#15689280	1	1	yes	characteristic
399	C₂²	#15689288	1	1	yes	characteristic
400	C₂²	#15689293	1	1	yes	characteristic
401	C₂²	#15689308	1	1	yes	characteristic
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	8	2	no	—
405	C₄	—	376	1	no	—
406	C₄	—	188	2	no	—
407	C₄	—	188	2	no	—
408	C₄	—	752	1	no	—
409	C₄	#107×D₄₇	1	1	yes	characteristic
410	C₄	#15689162	1	1	yes	characteristic
411	C₄	#15689203	1	1	yes	characteristic
412	C₄	#15689226	1	1	yes	characteristic
413	C₄	#15689402	1	1	yes	characteristic
414	C₄	#15689422	1	1	yes	characteristic
415	C₄	#15689435	1	1	yes	characteristic
416	C₄	#15689457	1	1	yes	characteristic
417	C₂	—	188	4	no	—
418	C₂	#20242443	1	1	yes	characteristic
419	C₂	#20242523	1	1	yes	characteristic
420	C₂	#20242624	1	1	yes	characteristic
421	C₂	#20242638	1	1	yes	characteristic
422	C₂	#20243577	1	1	yes	characteristic
423	C₂	#20243617	1	1	yes	characteristic
424	C₂	#20243636	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093994
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1296	C₂
socle	C₂³×C₄₇	#120
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1296	D₄₇
hypocenter	C₄₇	#8882
LCS	G ▷ C₄²×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
2. #20244147	C₂	semidirect
3. #20243547	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
22. #15688850	C₄	semidirect
52. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
64. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
166. D₁₈₈	#107	semidirect
210. #1296	D₄₇	semidirect
238. C₄₇	#8882	semidirect
272. C₄⋊C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246288	2
#20244147	2
#20243547	2
#20243389	2
C₂×#15688850	2
#20241227	2
C₄₇×#1296	2
#8882	47