Subgroups — #26111068

Order 12032.

664 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689404	C₂	1	1	yes	maximal, characteristic
2	#20246288	C₂	1	1	yes	maximal, characteristic
3	#20244348	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244310	C₂	1	1	yes	maximal, characteristic, complemented
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×#13094024	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×#13093986	—	2	1	no	—
11	C₂×C₄⋊C₄×D₄₇	—	2	1	no	—
12	#15689404	—	2	2	no	—
13	#15689404	C₄	1	4	yes	complemented
14	C₂×#13093958	—	2	1	no	—
15	C₂×#13093949	—	2	1	no	—
16	C₂×#13093949	—	2	1	no	—
17	C₂×#13093946	—	2	1	no	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	#15689019	—	2	1	no	—
20	#15688994	—	2	2	no	—
21	#15688980	—	2	1	no	—
22	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
23	#15688885	—	2	2	no	—
24	#15688850	—	2	2	no	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#384	C₂²	1	1	yes	characteristic
28	C₂²×Dic₉₄	—	2	1	no	—
29	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	—	2	1	no	—
31	C₂²×C₄×D₄₇	—	2	2	no	—
32	C₂²×C₄₇⋊C₈	—	2	1	no	—
33	#13094024	—	2	1	no	—
34	#13094024	—	2	1	no	—
35	#13094024	—	2	1	no	—
36	#13094024	C₂×C₄	1	2	yes	complemented
37	C₄×D₁₈₈	—	2	1	no	—
38	C₄×D₁₈₈	—	2	1	no	—
39	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
40	C₄×D₁₈₈	D₄	1	2	yes	—
41	#13093986	—	4	2	no	—
42	#13093986	—	4	2	no	—
43	C₂×C₄⋊Dic₄₇	—	2	1	no	—
44	C₂×C₄⋊Dic₄₇	—	2	1	no	—
45	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
48	C₂×Dic₄₇⋊C₄	—	2	2	no	—
49	C₄⋊C₄×D₄₇	—	4	2	no	—
50	C₄⋊C₄×D₄₇	—	4	2	no	—
51	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
52	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	1	no	—
54	#13093958	—	2	4	no	—
55	#13093949	—	4	2	no	—
56	#13093949	—	4	2	no	—
57	#13093946	—	2	4	no	—
58	C₄×C₄₇⋊C₈	—	2	1	no	—
59	C₄×C₄₇⋊C₈	—	2	1	no	—
60	C₄₇⋊#95	—	2	2	no	—
61	C₄₇⋊#95	—	2	1	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂²×C₈×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	1	no	—
69	C₄⋊C₈×C₄₇	—	2	1	no	—
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	complemented
72	C₂³×D₄₇	—	2	1	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×Dic₄₇	—	2	1	no	—
78	C₂²×Dic₄₇	—	2	1	no	—
79	C₂²×Dic₄₇	—	2	1	no	—
80	C₂²×Dic₄₇	—	4	1	no	—
81	C₂×D₁₈₈	—	2	1	no	—
82	C₂×D₁₈₈	—	2	1	no	—
83	C₂×D₁₈₈	—	2	1	no	—
84	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
85	C₂×D₁₈₈	SD₁₆	1	2	yes	—
86	C₂×D₁₈₈	Q₁₆	1	2	yes	—
87	C₂×C₄×D₄₇	—	2	2	no	—
88	C₂×C₄×D₄₇	—	2	2	no	—
89	C₂×C₄×D₄₇	—	4	1	no	—
90	C₂×C₄×D₄₇	—	4	1	no	—
91	C₂×C₄×D₄₇	—	4	1	no	—
92	C₂×C₄×D₄₇	—	4	1	no	—
93	C₂×C₄×D₄₇	—	4	4	no	—
94	C₂×C₄×D₄₇	—	4	4	no	—
95	C₂×C₄×D₄₇	—	8	2	no	—
96	C₂×Dic₉₄	—	2	2	no	—
97	C₂×Dic₉₄	—	4	1	no	—
98	C₂×Dic₉₄	—	4	1	no	—
99	C₂×Dic₉₄	—	4	1	no	—
100	C₂×Dic₉₄	—	4	1	no	—
101	C₂×Dic₉₄	—	4	1	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	4	1	no	—
104	C₂×C₈×C₄₇	—	4	1	no	—
105	C₂×C₈×C₄₇	—	4	1	no	—
106	C₂×C₈×C₄₇	—	4	1	no	—
107	C₂×C₈×C₄₇	—	4	1	no	—
108	C₄⋊C₄×C₄₇	—	4	2	no	—
109	C₄⋊C₄×C₄₇	—	4	1	no	—
110	C₄⋊C₄×C₄₇	—	4	1	no	—
111	C₄⋊C₄×C₄₇	—	4	1	no	—
112	C₄⋊C₄×C₄₇	—	4	1	no	—
113	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₄₇	#41	1	1	yes	characteristic
116	C₄²×C₄₇	#41	1	1	yes	characteristic
117	(C₂×D₄₇)⋊C₄	—	2	2	no	—
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	(C₂×D₄₇)⋊C₄	—	4	4	no	—
120	C₄⋊Dic₄₇	—	2	1	no	—
121	C₄⋊Dic₄₇	—	2	1	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	1	no	—
125	C₄⋊Dic₄₇	—	2	1	no	—
126	C₄⋊Dic₄₇	—	4	1	no	—
127	C₄⋊Dic₄₇	—	4	1	no	—
128	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
129	C₄⋊Dic₄₇	D₈	1	2	yes	—
130	Dic₄₇⋊C₄	—	4	4	no	—
131	C₄×Dic₄₇	—	4	1	no	—
132	C₄×Dic₄₇	—	4	1	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	4	1	no	—
135	C₂×C₄₇⋊C₈	—	4	1	no	—
136	C₂³×C₄₇	#120	1	1	yes	characteristic
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	—	2	2	no	—
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	4	1	no	—
141	C₂²×D₄₇	—	4	1	no	—
142	C₂²×D₄₇	—	4	1	no	—
143	C₂²×D₄₇	—	4	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
159	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	4	1	no	—
167	C₂×Dic₄₇	—	4	1	no	—
168	C₂×Dic₄₇	—	4	1	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	1	no	—
171	C₂×Dic₄₇	—	4	1	no	—
172	C₂×Dic₄₇	—	4	1	no	—
173	C₂×Dic₄₇	—	8	1	no	—
174	C₂×Dic₄₇	—	8	1	no	—
175	D₁₈₈	—	2	2	no	—
176	D₁₈₈	—	2	2	no	—
177	D₁₈₈	—	2	2	no	—
178	D₁₈₈	#103	1	4	yes	complemented
179	C₄×D₄₇	—	4	2	no	—
180	C₄×D₄₇	—	4	2	no	—
181	C₄×D₄₇	—	4	2	no	—
182	C₄×D₄₇	—	4	2	no	—
183	C₄×D₄₇	—	8	8	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	Dic₉₄	—	8	1	no	—
187	Dic₉₄	—	8	1	no	—
188	C₈×C₄₇	—	4	2	no	—
189	C₈×C₄₇	—	8	1	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	#8981	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	#386	1	1	yes	characteristic
193	C₂²×C₄₇	#447	1	1	yes	characteristic
194	C₂²×C₄₇	#449	1	1	yes	characteristic
195	C₂²×C₄₇	#450	1	1	yes	characteristic
196	C₂²×C₄₇	#451	1	1	yes	characteristic
197	C₂²×C₄₇	#455	1	1	yes	characteristic
198	C₂²×C₄₇	#456	1	1	yes	characteristic
199	C₂×D₄₇	—	2	4	no	—
200	C₂×D₄₇	—	4	2	no	—
201	C₂×D₄₇	—	4	2	no	—
202	C₂×D₄₇	—	4	2	no	—
203	C₂×D₄₇	—	4	2	no	—
204	C₂×D₄₇	—	4	2	no	—
205	C₂×D₄₇	—	4	2	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	8	2	no	—
209	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
210	C₄×C₄₇	#417	1	1	yes	characteristic
211	C₄×C₄₇	C₄×D₈	1	1	yes	characteristic
212	C₄×C₄₇	#442	1	1	yes	characteristic
213	C₄×C₄₇	#459	1	1	yes	characteristic
214	C₄×C₄₇	#463	1	1	yes	characteristic
215	C₄×C₄₇	#483	1	1	yes	characteristic
216	C₄×C₄₇	#484	1	1	yes	characteristic
217	Dic₄₇	—	4	2	no	—
218	Dic₄₇	—	4	2	no	—
219	Dic₄₇	—	8	2	no	—
220	Dic₄₇	—	8	1	no	—
221	C₂×#474	—	47	1	no	—
222	D₄×C₄⋊C₄	—	47	1	no	—
223	#1990	—	47	1	no	—
224	#1981	—	47	1	no	—
225	C₂×D₄⋊C₈	—	47	1	no	—
226	#1296	D₄₇	1	1	yes	characteristic, complemented
227	#1279	—	47	1	no	—
228	C₂×C₄₇	#1639	1	1	yes	characteristic
229	C₂×C₄₇	#1644	1	1	yes	characteristic
230	C₂×C₄₇	#1649	1	1	yes	characteristic
231	C₂×C₄₇	#1654	1	1	yes	characteristic
232	C₂×C₄₇	#1872	1	1	yes	characteristic
233	C₂×C₄₇	#1879	1	1	yes	characteristic
234	C₂×C₄₇	#1882	1	1	yes	characteristic
235	D₄₇	—	4	4	no	—
236	C₂×C₄⋊Q₈	—	47	1	no	—
237	C₂×C₄×D₄	—	47	1	no	—
238	C₂×C₄×D₄	—	94	1	no	—
239	C₂²×C₄⋊C₄	—	94	1	no	—
240	#474	—	47	4	no	—
241	#474	—	94	2	no	—
242	C₂×#107	—	94	1	no	—
243	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
244	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
245	C₂×#103	—	94	1	no	—
246	C₂×#103	—	94	1	no	—
247	C₂×#102	—	94	1	no	—
248	C₂×C₄×C₈	—	47	1	no	—
249	#389	—	94	1	no	—
250	#385	—	94	2	no	—
251	#384	C₂×D₄₇	1	1	yes	characteristic
252	#380	—	94	1	no	—
253	C₄×C₄⋊C₄	—	47	1	no	—
254	#340	—	94	2	no	—
255	D₄⋊C₈	—	94	2	no	—
256	C₄₇	#8981	1	1	yes	characteristic, complemented, Sylow
257	C₂²×Q₈	—	94	1	no	—
258	C₂²×D₄	—	47	1	no	—
259	C₂³×C₄	—	94	2	no	—
260	C₂³×C₄	—	94	1	no	—
261	C₂²×C₈	—	2	1	no	—
262	C₂²×C₈	—	2	1	no	—
263	C₂²×C₈	—	94	1	no	—
264	C₄⋊Q₈	—	47	2	no	—
265	C₄⋊Q₈	—	94	1	no	—
266	C₄⋊Q₈	—	94	1	no	—
267	C₄⋊Q₈	—	94	1	no	—
268	C₄×D₄	—	47	2	no	—
269	C₄×D₄	—	47	2	no	—
270	C₄×D₄	—	94	1	no	—
271	C₄×D₄	—	94	1	no	—
272	C₄×D₄	—	188	2	no	—
273	C₄×D₄	—	188	2	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	47	1	no	—
277	C₂×C₄⋊C₄	—	47	1	no	—
278	C₂×C₄⋊C₄	—	47	1	no	—
279	C₂×C₄⋊C₄	—	94	1	no	—
280	C₂×C₄⋊C₄	—	94	1	no	—
281	C₂×C₄⋊C₄	—	94	2	no	—
282	C₂×C₄⋊C₄	—	188	2	no	—
283	C₂×C₄⋊C₄	—	188	2	no	—
284	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
285	C₂×C₂²⋊C₄	—	94	1	no	—
286	C₂×C₂²⋊C₄	—	94	2	no	—
287	C₂×C₄²	—	94	1	no	—
288	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
289	#107	—	94	4	no	—
290	C₄⋊C₈	—	2	1	no	—
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	C₄×D₄₇	1	2	yes	complemented
294	#103	—	188	2	no	—
295	#103	—	188	2	no	—
296	#102	—	94	4	no	—
297	C₄×C₈	—	94	1	no	—
298	C₄×C₈	—	94	1	no	—
299	#95	—	94	2	no	—
300	#95	—	94	1	no	—
301	C₂⁴	—	94	1	no	—
302	C₂×Q₈	—	94	2	no	—
303	C₂×Q₈	—	188	1	no	—
304	C₂×Q₈	—	188	1	no	—
305	C₂×Q₈	—	188	1	no	—
306	C₂×Q₈	—	188	1	no	—
307	C₂×Q₈	—	188	1	no	—
308	C₂×D₄	—	47	2	no	—
309	C₂×D₄	—	47	2	no	—
310	C₂×D₄	—	47	2	no	—
311	C₂×D₄	—	94	1	no	—
312	C₂×D₄	—	94	1	no	—
313	C₂×D₄	—	94	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	94	1	no	—
316	C₂²×C₄	—	94	1	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	—	94	2	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	376	2	no	—
321	C₂²×C₄	—	188	4	no	—
322	C₂²×C₄	—	188	4	no	—
323	C₂²×C₄	—	188	1	no	—
324	C₂²×C₄	—	188	1	no	—
325	C₂²×C₄	—	188	1	no	—
326	C₂²×C₄	—	188	1	no	—
327	C₂²×C₄	—	188	1	no	—
328	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	188	1	no	—
339	C₂×C₈	—	188	1	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₄⋊C₄	—	4	1	no	—
344	C₄⋊C₄	—	4	1	no	—
345	C₄⋊C₄	—	47	2	no	—
346	C₄⋊C₄	—	47	2	no	—
347	C₄⋊C₄	—	94	1	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	94	1	no	—
352	C₄⋊C₄	—	94	1	no	—
353	C₄⋊C₄	—	188	4	no	—
354	C₄⋊C₄	—	188	1	no	—
355	C₄⋊C₄	—	188	1	no	—
356	C₂²⋊C₄	—	94	2	no	—
357	C₂²⋊C₄	—	94	2	no	—
358	C₂²⋊C₄	—	188	4	no	—
359	C₄²	—	188	1	no	—
360	C₄²	—	188	1	no	—
361	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₄²	#10625350	1	1	yes	characteristic
363	C₄²	D₄×D₄₇	1	1	yes	characteristic
364	C₄²	#10625354	1	1	yes	characteristic
365	C₂³	—	94	2	no	—
366	C₂³	—	94	2	no	—
367	C₂³	—	94	2	no	—
368	C₂³	—	188	1	no	—
369	C₂³	—	188	1	no	—
370	C₂³	—	188	1	no	—
371	C₂³	—	188	1	no	—
372	C₂³	#13093994	1	1	yes	characteristic
373	Q₈	—	376	1	no	—
374	Q₈	—	376	1	no	—
375	Q₈	—	188	2	no	—
376	Q₈	—	188	2	no	—
377	D₄	—	47	4	no	—
378	D₄	—	94	2	no	—
379	D₄	—	94	2	no	—
380	D₄	—	94	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	376	8	no	—
389	C₂×C₄	—	376	1	no	—
390	C₂×C₄	—	376	1	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	1	no	—
393	C₂×C₄	—	188	1	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	1	no	—
397	C₂×C₄	—	188	1	no	—
398	C₂×C₄	—	188	1	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	—	188	2	no	—
403	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄	#13093986	1	1	yes	characteristic
405	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
406	C₂×C₄	#13093997	1	1	yes	characteristic
407	C₂×C₄	#13093999	1	1	yes	characteristic
408	C₂×C₄	#13094009	1	1	yes	characteristic
409	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
410	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
411	C₂×C₄	Q₁₆×D₄₇	1	1	yes	characteristic
412	C₂×C₄	#13094047	1	1	yes	characteristic
413	C₂×C₄	#13094048	1	1	yes	characteristic
414	C₂×C₄	#13094051	1	1	yes	characteristic
415	C₂×C₄	#13094051	1	1	yes	characteristic
416	C₂×C₄	#13094053	1	1	yes	characteristic
417	C₈	—	4	2	no	—
418	C₈	—	8	1	no	—
419	C₈	—	188	2	no	—
420	C₂²	—	94	4	no	—
421	C₂²	—	188	2	no	—
422	C₂²	—	188	2	no	—
423	C₂²	—	188	2	no	—
424	C₂²	—	188	2	no	—
425	C₂²	—	188	2	no	—
426	C₂²	—	188	2	no	—
427	C₂²	#15689001	1	1	yes	characteristic
428	C₂²	#15689258	1	1	yes	characteristic
429	C₂²	#15689271	1	1	yes	characteristic
430	C₂²	#15689275	1	1	yes	characteristic
431	C₂²	#15689280	1	1	yes	characteristic
432	C₂²	#15689303	1	1	yes	characteristic
433	C₂²	#15689308	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	2	no	—
437	C₄	—	376	2	no	—
438	C₄	—	376	1	no	—
439	C₄	—	188	2	no	—
440	C₄	—	188	2	no	—
441	C₄	#103×D₄₇	1	1	yes	characteristic
442	C₄	#15689121	1	1	yes	characteristic
443	C₄	#15689205	1	1	yes	characteristic
444	C₄	#15689234	1	1	yes	characteristic
445	C₄	#15689317	1	1	yes	characteristic
446	C₄	#15689341	1	1	yes	characteristic
447	C₄	#15689455	1	1	yes	characteristic
448	C₄	#15689460	1	1	yes	characteristic
449	C₂	—	188	4	no	—
450	C₂	#20242568	1	1	yes	characteristic
451	C₂	#20242603	1	1	yes	characteristic
452	C₂	#20242638	1	1	yes	characteristic
453	C₂	#20242673	1	1	yes	characteristic
454	C₂	#20243694	1	1	yes	characteristic
455	C₂	#20243737	1	1	yes	characteristic
456	C₂	#20243756	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	#8981
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
3. #20244348	C₂	semidirect
4. #20244310	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1296	C₂	semidirect
13. #15689404	C₄	semidirect
36. #13094024	C₂×C₄	semidirect
71. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
178. D₁₈₈	#103	semidirect
226. #1296	D₄₇	semidirect
256. C₄₇	#8981	semidirect
293. 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
C₂×#15689404	2
#20246288	2
#20244348	2
#20244310	2
C₂×#15688850	2
#20241227	2
C₄₇×#1296	2
#8981	47