Subgroups — #26200080

Order 12032.

716 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253943	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×D₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242841	C₂	1	2	yes	maximal, complemented
5	#20242823	C₂	1	2	yes	maximal, complemented
6	#20242765	C₂	1	2	yes	maximal, complemented
7	#20242727	C₂	1	2	yes	maximal, complemented
8	#20242149	C₂	1	1	yes	maximal, characteristic, complemented
9	#20242089	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242083	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3109	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₇⋊C₈	—	2	1	no	—
13	#15689680	C₂²	1	1	yes	characteristic
14	#15689519	C₂²	1	1	yes	characteristic, complemented
15	#15689495	C₂²	1	1	yes	characteristic, complemented
16	#15689475	C₂²	1	1	yes	characteristic, complemented
17	#15689469	C₂²	1	1	yes	characteristic, complemented
18	#15689458	—	2	1	no	—
19	#15689403	C₂²	1	2	yes	—
20	#15689350	—	2	1	no	—
21	#15689350	—	2	1	no	—
22	#15689328	C₂²	1	2	yes	—
23	#15689274	—	2	1	no	—
24	#15689223	—	2	2	no	—
25	C₄×#10625335	—	2	1	no	—
26	C₄×#10625335	—	2	1	no	—
27	D₄×C₄₇⋊C₈	—	2	1	no	—
28	D₄×C₄₇⋊C₈	—	2	1	no	—
29	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
30	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
31	#15689180	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
34	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	#15688875	C₂²	1	2	yes	complemented
36	#15688873	C₂²	1	2	yes	complemented
37	#15688872	C₂²	1	2	yes	complemented
38	#15688870	C₂²	1	2	yes	complemented
39	#15688868	C₂²	1	2	yes	complemented
40	#15688867	C₂²	1	2	yes	complemented
41	C₄₇×#532	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#481	—	2	1	no	—
44	C₄₇×#476	C₂²	1	2	yes	—
45	C₄₇×#459	C₂²	1	2	yes	—
46	C₄₇×#447	—	2	1	no	—
47	C₄₇×#442	—	2	2	no	—
48	C₄₇×#432	C₂²	1	1	yes	characteristic
49	C₂×#10625335	—	2	2	no	—
50	C₂×#10625335	—	2	1	no	—
51	C₂×#10625335	—	2	1	no	—
52	C₂²×C₄₇⋊C₈	—	2	1	no	—
53	C₂²×C₄₇⋊C₈	—	2	2	no	—
54	C₂²×C₄₇⋊C₈	—	2	2	no	—
55	C₂²×C₄₇⋊C₈	—	4	4	no	—
56	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
58	#13094024	C₂³	1	1	yes	characteristic
59	#13094024	C₂³	1	1	yes	characteristic
60	#13094016	—	2	1	no	—
61	#13094003	—	2	1	no	—
62	#13094003	—	2	1	no	—
63	C₄×Dic₉₄	—	2	1	no	—
64	C₄×Dic₉₄	—	2	1	no	—
65	#13093983	—	2	1	no	—
66	#13093957	—	2	2	no	—
67	#13093955	—	2	1	no	—
68	#13093955	—	2	1	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
70	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
71	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
72	#13093947	—	2	2	no	—
73	#13093947	—	2	1	no	—
74	#13093947	—	2	1	no	—
75	#13093945	—	2	2	no	—
76	#13093945	—	2	1	no	—
77	#13093945	—	2	1	no	—
78	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
81	#13093935	—	2	1	no	—
82	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
83	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
84	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
85	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
86	C₂×#41×C₄₇	—	2	1	no	—
87	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
88	C₂³×C₄×C₄₇	—	2	1	no	—
89	C₂×D₈×C₄₇	—	2	2	no	—
90	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
91	#127×C₄₇	C₂³	1	1	yes	characteristic
92	#124×C₄₇	—	2	1	no	—
93	#121×C₄₇	—	2	1	no	—
94	#121×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	D₄	1	2	yes	—
100	C₄×D₄×C₄₇	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	#106×C₄₇	—	2	2	no	—
105	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	C₂²⋊C₈×C₄₇	—	2	1	no	—
109	#97×C₄₇	—	2	1	no	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	#41×C₄₇	—	8	2	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂×D₄×C₄₇	—	2	4	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	2	1	no	—
116	C₂×D₄×C₄₇	—	2	1	no	—
117	C₂×D₄×C₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	—	4	1	no	—
119	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	4	2	no	—
124	C₂²×C₄×C₄₇	—	4	2	no	—
125	C₂²×C₄×C₄₇	—	4	1	no	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
129	C₂×Dic₉₄	—	2	1	no	—
130	C₂×Dic₉₄	—	2	1	no	—
131	D₈×C₄₇	—	4	4	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	1	no	—
136	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
137	C₂²⋊C₄×C₄₇	—	2	2	no	—
138	C₂²⋊C₄×C₄₇	—	2	2	no	—
139	C₂²⋊C₄×C₄₇	—	4	1	no	—
140	C₂²⋊C₄×C₄₇	—	4	1	no	—
141	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
142	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
143	C₄²×C₄₇	#41	1	1	yes	characteristic
144	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
145	C₂²⋊Dic₄₇	—	4	1	no	—
146	#10625335	—	4	2	no	—
147	#10625335	—	4	4	no	—
148	#10625335	—	4	2	no	—
149	C₄⋊Dic₄₇	—	2	1	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	—	2	1	no	—
153	Dic₄₇⋊C₄	—	4	1	no	—
154	Dic₄₇⋊C₄	—	4	1	no	—
155	C₄×Dic₄₇	—	4	1	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	4	1	no	—
160	C₂×C₄₇⋊C₈	—	4	4	no	—
161	C₂×C₄₇⋊C₈	—	4	2	no	—
162	C₂×C₄₇⋊C₈	—	4	4	no	—
163	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
164	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
167	C₂³×C₄₇	—	2	4	no	—
168	C₂³×C₄₇	—	2	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	—	4	2	no	—
171	C₂³×C₄₇	—	4	1	no	—
172	C₂³×C₄₇	#121	1	1	yes	characteristic
173	Q₈×C₄₇	—	8	1	no	—
174	D₄×C₄₇	—	2	4	no	—
175	D₄×C₄₇	—	2	2	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	4	1	no	—
178	D₄×C₄₇	—	4	1	no	—
179	D₄×C₄₇	—	8	1	no	—
180	D₄×C₄₇	—	8	2	no	—
181	D₄×C₄₇	#135	1	4	yes	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	4	4	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	1	no	—
192	C₂×C₄×C₄₇	—	8	2	no	—
193	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
194	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
195	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	Dic₉₄	—	4	2	no	—
202	Dic₉₄	—	4	1	no	—
203	Dic₉₄	—	4	1	no	—
204	C₈×C₄₇	—	4	2	no	—
205	C₄₇⋊C₈	—	2	1	no	—
206	C₄₇⋊C₈	—	2	1	no	—
207	C₄₇⋊C₈	—	2	1	no	—
208	C₄₇⋊C₈	—	4	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	—
211	#19257	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	4	no	—
215	C₂²×C₄₇	—	4	8	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	—	8	1	no	—
219	C₂²×C₄₇	—	8	1	no	—
220	C₂²×C₄₇	—	8	1	no	—
221	C₂²×C₄₇	#471	1	2	yes	—
222	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
223	C₄×C₄₇	—	2	1	no	—
224	C₄×C₄₇	—	2	1	no	—
225	C₄×C₄₇	—	2	1	no	—
226	C₄×C₄₇	—	2	1	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	8	1	no	—
229	C₄×C₄₇	C₂×#135	1	2	yes	—
230	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
231	C₄×C₄₇	#575	1	1	yes	characteristic
232	Dic₄₇	—	8	1	no	—
233	Dic₄₇	—	8	1	no	—
234	#3167	—	47	1	no	—
235	#3110	—	47	1	no	—
236	#3109	D₄₇	1	1	yes	characteristic
237	C₂×C₈×D₄	—	47	1	no	—
238	#1683	—	47	2	no	—
239	#1681	—	47	2	no	—
240	#1671	—	47	2	no	—
241	#1665	—	47	2	no	—
242	#1568	—	47	1	no	—
243	#1552	—	47	1	no	—
244	#1551	—	47	1	no	—
245	C₂×C₄₇	—	2	2	no	—
246	C₂×C₄₇	—	4	4	no	—
247	C₂×C₄₇	—	16	1	no	—
248	C₂×C₄₇	#3036	1	1	yes	characteristic
249	C₂×C₄₇	#3050	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
251	C₂³×C₈	—	94	1	no	—
252	#533	—	47	1	no	—
253	#532	C₂×D₄₇	1	1	yes	characteristic
254	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
255	#498	—	47	1	no	—
256	#492	—	47	1	no	—
257	#487	—	47	1	no	—
258	#486	—	47	1	no	—
259	#484	—	94	1	no	—
260	#481	—	2	1	no	—
261	#476	C₂×D₄₇	1	2	yes	—
262	#474	—	47	2	no	—
263	#465	—	94	1	no	—
264	#465	—	94	1	no	—
265	#461	—	47	2	no	—
266	#459	C₂×D₄₇	1	2	yes	—
267	#450	—	94	1	no	—
268	#447	—	2	1	no	—
269	#442	—	2	2	no	—
270	#440	—	94	2	no	—
271	C₄×SD₁₆	—	94	1	no	—
272	C₄×SD₁₆	—	94	1	no	—
273	C₈×D₄	—	47	2	no	—
274	C₈×D₄	—	47	2	no	—
275	C₈×D₄	—	94	1	no	—
276	C₈×D₄	—	94	1	no	—
277	#432	—	47	1	no	—
278	#432	C₂×D₄₇	1	1	yes	characteristic
279	C₂×C₄⋊C₈	—	47	1	no	—
280	C₂×C₂²⋊C₈	—	94	1	no	—
281	C₂×C₄×C₈	—	47	1	no	—
282	#335	—	47	2	no	—
283	#334	—	47	2	no	—
284	#333	—	47	2	no	—
285	#332	—	47	2	no	—
286	#332	—	47	2	no	—
287	#331	—	47	2	no	—
288	C₄₇	#19257	1	1	yes	characteristic, complemented, Sylow
289	C₂×#41	—	2	1	no	—
290	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂×SD₁₆	—	94	1	no	—
293	C₂×SD₁₆	—	94	1	no	—
294	C₂×SD₁₆	—	94	2	no	—
295	C₂×D₈	—	2	2	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	47	1	no	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	—	94	2	no	—
300	C₂²×C₈	—	94	1	no	—
301	C₂²×C₈	—	188	4	no	—
302	C₄⋊Q₈	—	47	1	no	—
303	C₄⋊Q₈	—	47	1	no	—
304	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
305	#127	C₂²×D₄₇	1	1	yes	characteristic
306	#125	—	94	1	no	—
307	#124	—	2	1	no	—
308	C₂²⋊Q₈	—	94	1	no	—
309	C₂²⋊Q₈	—	94	1	no	—
310	#121	—	2	1	no	—
311	#121	—	2	1	no	—
312	C₄×Q₈	—	94	1	no	—
313	C₄×Q₈	—	94	1	no	—
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	2	1	no	—
317	C₄×D₄	—	2	1	no	—
318	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
319	C₄×D₄	C₂²×D₄₇	1	2	yes	—
320	#117	—	94	1	no	—
321	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
324	#107	—	94	2	no	—
325	#106	—	2	2	no	—
326	#106	—	94	1	no	—
327	#106	—	94	1	no	—
328	C₄⋊C₈	—	47	2	no	—
329	C₄⋊C₈	—	47	2	no	—
330	C₄⋊C₈	—	94	1	no	—
331	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
332	#103	—	94	1	no	—
333	#103	—	94	1	no	—
334	#103	—	94	2	no	—
335	#102	—	2	2	no	—
336	#102	—	2	2	no	—
337	#102	—	94	1	no	—
338	#102	—	94	1	no	—
339	#102	—	94	2	no	—
340	C₂²⋊C₈	—	2	1	no	—
341	C₂²⋊C₈	—	94	2	no	—
342	C₂²⋊C₈	—	94	2	no	—
343	C₂²⋊C₈	—	94	1	no	—
344	#97	—	2	1	no	—
345	#97	—	94	1	no	—
346	C₄×C₈	—	47	1	no	—
347	C₄×C₈	—	47	1	no	—
348	C₄×C₈	—	47	1	no	—
349	C₄×C₈	—	47	1	no	—
350	C₂⁴	—	2	1	no	—
351	#41	—	8	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	94	1	no	—
354	C₂×Q₈	—	94	1	no	—
355	C₂×D₄	—	2	4	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	4	1	no	—
361	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	1	no	—
368	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	#10625352	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	SD₁₆	—	188	2	no	—
372	SD₁₆	—	188	2	no	—
373	SD₁₆	—	188	4	no	—
374	D₈	—	4	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	47	1	no	—
377	C₂×C₈	—	47	1	no	—
378	C₂×C₈	—	47	1	no	—
379	C₂×C₈	—	47	1	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	188	4	no	—
384	C₂×C₈	—	188	1	no	—
385	C₂×C₈	—	188	4	no	—
386	C₂×C₈	—	188	2	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	94	1	no	—
391	C₄⋊C₄	—	94	1	no	—
392	C₄⋊C₄	—	94	1	no	—
393	C₄⋊C₄	—	94	1	no	—
394	C₄⋊C₄	—	188	1	no	—
395	C₄⋊C₄	—	188	1	no	—
396	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
397	C₂²⋊C₄	—	2	2	no	—
398	C₂²⋊C₄	—	2	2	no	—
399	C₂²⋊C₄	—	4	1	no	—
400	C₂²⋊C₄	—	4	1	no	—
401	C₂²⋊C₄	—	188	1	no	—
402	C₄²	—	188	1	no	—
403	C₄²	D₄×D₄₇	1	1	yes	characteristic
404	C₄²	#10625352	1	1	yes	characteristic
405	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
406	C₄²	C₂³×D₄₇	1	1	yes	characteristic
407	C₂³	—	2	4	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	#13093996	1	1	yes	characteristic
413	Q₈	—	8	1	no	—
414	Q₈	—	188	2	no	—
415	Q₈	—	188	1	no	—
416	Q₈	—	188	1	no	—
417	D₄	—	2	4	no	—
418	D₄	—	2	2	no	—
419	D₄	—	4	2	no	—
420	D₄	—	4	1	no	—
421	D₄	—	4	1	no	—
422	D₄	—	8	1	no	—
423	D₄	—	8	2	no	—
424	D₄	#13094044	1	4	yes	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	4	4	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	8	2	no	—
436	C₂×C₄	—	188	1	no	—
437	C₂×C₄	—	188	1	no	—
438	C₂×C₄	#13093996	1	1	yes	characteristic
439	C₂×C₄	#13093996	1	1	yes	characteristic
440	C₂×C₄	#13093996	1	1	yes	characteristic
441	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
442	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
443	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
444	C₈	—	4	2	no	—
445	C₈	—	47	2	no	—
446	C₈	—	94	1	no	—
447	C₈	—	94	1	no	—
448	C₈	—	94	1	no	—
449	C₈	—	188	2	no	—
450	C₈	—	188	2	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	1	no	—
453	C₂²	—	2	4	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	4	2	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	1	no	—
460	C₂²	#15689384	1	2	yes	—
461	C₂²	C₂×#13093996	1	1	yes	characteristic
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	2	1	no	—
466	C₄	—	4	2	no	—
467	C₄	—	8	1	no	—
468	C₄	—	376	1	no	—
469	C₄	—	376	1	no	—
470	C₄	C₂×#13094044	1	2	yes	—
471	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
472	C₄	#15689919	1	1	yes	characteristic
473	C₂	—	2	2	no	—
474	C₂	—	4	4	no	—
475	C₂	—	16	1	no	—
476	C₂	#20252849	1	1	yes	characteristic
477	C₂	#20252966	1	1	yes	characteristic
478	C₂	C₂×#15689384	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3109	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3109	D₄₇
hypocenter	C₄₇	#19257
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3109

Complements

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

N	H ≅ G/N	type
1. #20253943	C₂	semidirect
2. #20253487	C₂	semidirect
3. C₂×D₄×C₄₇⋊C₈	C₂	semidirect
4. #20242841	C₂	semidirect
5. #20242823	C₂	semidirect
6. #20242765	C₂	semidirect
7. #20242727	C₂	semidirect
8. #20242149	C₂	semidirect
9. #20242089	C₂	semidirect
10. #20242083	C₂	semidirect
14. #15689519	C₂²	semidirect
15. #15689495	C₂²	semidirect
16. #15689475	C₂²	semidirect
17. #15689469	C₂²	semidirect
35. #15688875	C₂²	semidirect
36. #15688873	C₂²	semidirect
37. #15688872	C₂²	semidirect
38. #15688870	C₂²	semidirect
39. #15688868	C₂²	semidirect
40. #15688867	C₂²	semidirect
288. C₄₇	#19257	semidirect

Maximal subgroups

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

subgroup	index
#20253943	2
#20253487	2
C₂×D₄×C₄₇⋊C₈	2
#20242841	2
#20242823	2
#20242765	2
#20242727	2
#20242149	2
#20242089	2
#20242083	2
C₄₇×#3109	2
#19257	47