Subgroups — #26222240

Order 12032.

1290 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252737	C₂	1	1	yes	maximal, characteristic
2	#20252289	C₂	1	2	yes	maximal, complemented
3	#20252098	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243771	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243750	C₂	1	2	yes	maximal, complemented
6	#20243628	C₂	1	2	yes	maximal, complemented
7	#20243608	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243352	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243223	C₂	1	2	yes	maximal, complemented
10	#20243188	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3573	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689921	C₂²	1	2	yes	—
13	C₂×#13094030	C₂²	1	1	yes	characteristic, complemented
14	#15689669	C₂²	1	1	yes	characteristic
15	#15689306	C₄	1	2	yes	complemented
16	#15689301	C₄	1	2	yes	complemented
17	#15689296	C₄	1	2	yes	complemented
18	#15689291	C₄	1	2	yes	complemented
19	#15689243	—	2	4	no	—
20	#15689238	—	2	4	no	—
21	#15689199	—	2	2	no	—
22	C₈×C₂²⋊D₄₇	—	2	2	no	—
23	#15689171	C₂²	1	2	yes	complemented
24	#15689146	C₂²	1	1	yes	characteristic, complemented
25	#15689140	C₂²	1	2	yes	—
26	#15689139	C₂²	1	2	yes	complemented
27	C₂×#13093951	C₂²	1	2	yes	—
28	#15689119	C₂²	1	2	yes	—
29	#15689107	C₂²	1	1	yes	characteristic
30	#15689097	C₂²	1	1	yes	characteristic
31	#15689091	C₂²	1	1	yes	characteristic, complemented
32	#15689090	C₂²	1	1	yes	characteristic
33	#15689078	C₂²	1	2	yes	complemented
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
35	#15688894	C₂²	1	2	yes	complemented
36	#15688887	C₂²	1	2	yes	complemented
37	#15688884	C₂²	1	2	yes	complemented
38	C₄₇×#585	C₂²	1	1	yes	characteristic
39	C₄₇×#568	—	2	4	no	—
40	C₄₇×#568	—	2	2	no	—
41	C₄₇×#568	C₂²	1	2	yes	—
42	C₄₇×#568	C₂²	1	1	yes	characteristic
43	C₂×#131×C₄₇	—	2	4	no	—
44	C₂×#131×C₄₇	—	2	2	no	—
45	C₂×#131×C₄₇	C₂²	1	2	yes	—
46	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	C₂³	1	1	yes	characteristic
48	#13094055	—	2	2	no	—
49	#13094054	C₂×C₄	1	4	yes	—
50	#13094050	—	2	2	no	—
51	#13094049	C₂×C₄	1	4	yes	—
52	#13094044	—	2	4	no	—
53	#13094030	—	2	2	no	—
54	#13094030	—	2	2	no	—
55	C₂×#10625329	C₂³	1	1	yes	characteristic
56	C₂×#10625329	C₂³	1	2	yes	—
57	C₂×#10625324	—	2	1	no	—
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₄₇	—	2	1	no	—
60	#13094022	C₂×C₄	1	1	yes	characteristic
61	#13094020	C₂×C₄	1	1	yes	characteristic
62	#13094013	C₂×C₄	1	1	yes	characteristic
63	#13094011	C₂×C₄	1	1	yes	characteristic
64	#13093996	—	2	2	no	—
65	C₄×C₂²⋊D₄₇	—	2	2	no	—
66	#13093983	C₂³	1	2	yes	—
67	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
68	#13093959	—	2	4	no	—
69	Dic₄₇⋊C₈	—	2	2	no	—
70	#13093951	—	2	4	no	—
71	#13093951	C₂×C₄	1	4	yes	—
72	#13093951	C₂×C₄	1	4	yes	—
73	#13093950	—	2	4	no	—
74	#13093948	—	2	2	no	—
75	#13093945	—	2	2	no	—
76	#13093943	C₂×C₄	1	2	yes	—
77	#13093941	C₂×C₄	1	2	yes	—
78	#13093939	—	2	2	no	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
80	(C₂×D₄₇)⋊C₈	—	2	2	no	—
81	#13093934	—	2	2	no	—
82	C₈×Dic₄₇	—	2	2	no	—
83	C₈×Dic₄₇	—	2	1	no	—
84	C₈×Dic₄₇	—	2	1	no	—
85	2₋¹⁺⁴×C₄₇	—	2	2	no	—
86	2₋¹⁺⁴×C₄₇	C₂×C₄	1	2	yes	—
87	H(5,𝔽₂)×C₄₇	—	2	2	no	—
88	H(5,𝔽₂)×C₄₇	—	2	2	no	—
89	H(5,𝔽₂)×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×#41×C₄₇	—	2	4	no	—
91	C₂×#41×C₄₇	—	2	2	no	—
92	C₂×#41×C₄₇	C₂³	1	2	yes	—
93	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
94	#131×C₄₇	—	2	4	no	—
95	#131×C₄₇	—	2	8	no	—
96	#131×C₄₇	—	2	4	no	—
97	#131×C₄₇	—	2	4	no	—
98	#131×C₄₇	—	2	4	no	—
99	#131×C₄₇	—	2	2	no	—
100	#131×C₄₇	—	2	2	no	—
101	#131×C₄₇	—	2	4	no	—
102	#131×C₄₇	—	2	2	no	—
103	#131×C₄₇	—	2	2	no	—
104	#131×C₄₇	D₄	1	4	yes	complemented
105	#131×C₄₇	D₄	1	4	yes	complemented
106	C₂×M₁₆×C₄₇	—	2	8	no	—
107	C₂×M₁₆×C₄₇	—	2	4	no	—
108	C₂×M₁₆×C₄₇	—	2	2	no	—
109	C₂×M₁₆×C₄₇	—	2	4	no	—
110	C₂×M₁₆×C₄₇	—	2	2	no	—
111	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
112	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
113	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	—	2	4	no	—
115	C₂²×C₈×C₄₇	—	2	2	no	—
116	C₂²×C₈×C₄₇	D₄	1	2	yes	—
117	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
118	#41×C₄₇	—	2	4	no	—
119	#41×C₄₇	—	2	8	no	—
120	#41×C₄₇	—	2	4	no	—
121	#41×C₄₇	—	2	4	no	—
122	#41×C₄₇	—	2	4	no	—
123	#41×C₄₇	—	2	4	no	—
124	#41×C₄₇	—	2	2	no	—
125	#41×C₄₇	—	2	2	no	—
126	#41×C₄₇	—	2	2	no	—
127	#41×C₄₇	—	2	2	no	—
128	#41×C₄₇	C₂²×C₄	1	4	yes	—
129	#41×C₄₇	C₂×D₄	1	4	yes	—
130	C₂×Q₈×C₄₇	—	2	2	no	—
131	C₂×Q₈×C₄₇	—	2	4	no	—
132	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×Q₈×C₄₇	#41	1	2	yes	—
134	C₂×D₄×C₄₇	—	2	8	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	—	2	4	no	—
137	C₂×D₄×C₄₇	—	2	2	no	—
138	C₂×D₄×C₄₇	—	2	4	no	—
139	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂×D₄×C₄₇	#41	1	2	yes	—
141	C₂×D₄×C₄₇	#41	1	2	yes	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	2	2	no	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
146	C₂×C₂²⋊D₄₇	—	2	2	no	—
147	C₂×C₂²⋊D₄₇	—	2	1	no	—
148	C₂²×Dic₄₇	—	2	1	no	—
149	#10625350	—	2	2	no	—
150	#10625350	—	2	2	no	—
151	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₄×D₄₇	—	2	1	no	—
153	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
154	M₁₆×C₄₇	—	2	4	no	—
155	M₁₆×C₄₇	—	2	8	no	—
156	M₁₆×C₄₇	—	2	2	no	—
157	M₁₆×C₄₇	—	2	2	no	—
158	M₁₆×C₄₇	—	2	4	no	—
159	M₁₆×C₄₇	—	2	4	no	—
160	M₁₆×C₄₇	—	2	4	no	—
161	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
162	C₂×C₈×C₄₇	—	2	4	no	—
163	C₂×C₈×C₄₇	—	2	8	no	—
164	C₂×C₈×C₄₇	—	2	2	no	—
165	C₂×C₈×C₄₇	—	2	4	no	—
166	C₂×C₈×C₄₇	—	2	2	no	—
167	C₂×C₈×C₄₇	—	2	4	no	—
168	C₂×C₈×C₄₇	—	2	2	no	—
169	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
170	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
171	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₂²⋊Dic₄₇	—	2	2	no	—
175	C₂²⋊Dic₄₇	—	2	2	no	—
176	#10625337	—	2	4	no	—
177	#10625336	—	2	4	no	—
178	#10625335	—	2	4	no	—
179	#10625334	—	2	4	no	—
180	(C₂×D₄₇)⋊C₄	—	2	2	no	—
181	C₄⋊Dic₄₇	—	2	2	no	—
182	Dic₄₇⋊C₄	—	2	2	no	—
183	C₄×Dic₄₇	—	2	1	no	—
184	C₄×Dic₄₇	—	2	2	no	—
185	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
187	#10625329	—	2	2	no	—
188	#10625329	—	2	2	no	—
189	#10625329	C₂²×C₄	1	4	yes	—
190	C₂×C₄₇⋊C₈	—	2	2	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	2	no	—
194	#10625324	—	4	2	no	—
195	C₈×D₄₇	—	4	1	no	—
196	C₈×D₄₇	—	4	1	no	—
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	C₄×D₄	1	2	yes	—
200	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
201	C₂²×D₄₇	—	2	1	no	—
202	Q₈×C₄₇	—	2	4	no	—
203	Q₈×C₄₇	—	2	2	no	—
204	Q₈×C₄₇	—	2	2	no	—
205	Q₈×C₄₇	C₄×D₄	1	4	yes	—
206	D₄×C₄₇	—	2	8	no	—
207	D₄×C₄₇	—	2	4	no	—
208	D₄×C₄₇	—	2	4	no	—
209	D₄×C₄₇	—	2	4	no	—
210	D₄×C₄₇	—	2	4	no	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	2	2	no	—
213	D₄×C₄₇	C₄×D₄	1	4	yes	—
214	C₂×C₄×C₄₇	—	2	4	no	—
215	C₂×C₄×C₄₇	—	2	8	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	4	no	—
218	C₂×C₄×C₄₇	—	2	4	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
222	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
226	C₂²⋊D₄₇	—	4	4	no	—
227	C₂²⋊D₄₇	—	4	2	no	—
228	C₂×Dic₄₇	—	2	1	no	—
229	C₂×Dic₄₇	—	2	1	no	—
230	C₂×Dic₄₇	—	2	1	no	—
231	C₂×Dic₄₇	—	4	2	no	—
232	C₂×Dic₄₇	—	4	2	no	—
233	D₁₈₈	—	2	2	no	—
234	C₄×D₄₇	—	4	1	no	—
235	C₄×D₄₇	—	4	1	no	—
236	Dic₉₄	—	2	2	no	—
237	C₈×C₄₇	—	2	4	no	—
238	C₈×C₄₇	—	2	2	no	—
239	C₈×C₄₇	#120	1	1	yes	characteristic
240	C₈×C₄₇	#120	1	2	yes	—
241	C₈×C₄₇	#120	1	1	yes	characteristic
242	C₄₇⋊C₈	—	2	4	no	—
243	C₄₇⋊C₈	—	4	1	no	—
244	C₄₇⋊C₈	—	4	1	no	—
245	#21477	—	47	1	no	maximal, Sylow
246	C₂²×C₄₇	—	2	2	no	—
247	C₂²×C₄₇	—	2	4	no	—
248	C₂²×C₄₇	—	4	1	no	—
249	C₂²×C₄₇	—	4	2	no	—
250	C₂²×C₄₇	—	8	2	no	—
251	C₂²×C₄₇	—	8	4	no	—
252	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
253	C₂²×C₄₇	#525	1	2	yes	—
254	C₂×D₄₇	—	4	2	no	—
255	C₂×D₄₇	—	4	1	no	—
256	C₄×C₄₇	—	2	4	no	—
257	C₄×C₄₇	—	2	2	no	—
258	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
259	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
260	C₄×C₄₇	#525	1	1	yes	characteristic
261	Dic₄₇	—	2	2	no	—
262	Dic₄₇	—	4	1	no	—
263	Dic₄₇	—	4	1	no	—
264	Dic₄₇	—	8	2	no	—
265	#3573	D₄₇	1	1	yes	characteristic, complemented
266	#3018	—	47	1	no	—
267	#2955	—	47	2	no	—
268	#2931	—	47	1	no	—
269	#1884	—	47	1	no	—
270	#1881	—	47	2	no	—
271	#1861	—	47	2	no	—
272	#1858	—	47	1	no	—
273	#1794	—	47	1	no	—
274	#1764	—	47	2	no	—
275	#1757	—	47	1	no	—
276	C₂×C₄₇	—	2	1	no	—
277	C₂×C₄₇	—	2	2	no	—
278	C₂×C₄₇	—	4	2	no	—
279	C₂×C₄₇	—	4	4	no	—
280	C₂×C₄₇	C₄×#120	1	1	yes	characteristic
281	D₄₇	—	8	1	no	—
282	#585	C₂×D₄₇	1	1	yes	characteristic
283	#575	—	47	2	no	—
284	#568	—	2	4	no	—
285	#568	—	2	2	no	—
286	#568	C₂×D₄₇	1	1	yes	characteristic
287	#568	C₂×D₄₇	1	2	yes	—
288	C₂×#131	—	2	4	no	—
289	C₂×#131	—	2	2	no	—
290	C₂×#131	—	47	1	no	—
291	C₂×#131	C₂×D₄₇	1	2	yes	—
292	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
293	#532	—	47	1	no	—
294	#456	—	47	2	no	—
295	#455	—	47	2	no	—
296	#454	—	47	2	no	—
297	#453	—	47	2	no	—
298	#444	—	94	4	no	—
299	#443	—	94	4	no	—
300	#436	—	94	2	no	—
301	C₈×D₄	—	94	2	no	—
302	#430	—	47	2	no	—
303	#423	—	47	1	no	—
304	#421	—	47	2	no	—
305	#421	—	47	2	no	—
306	C₂×#104	—	47	2	no	—
307	#416	—	47	2	no	—
308	#413	—	47	1	no	—
309	#410	—	47	1	no	—
310	#408	—	47	1	no	—
311	#408	—	47	1	no	—
312	#405	—	47	2	no	—
313	C₂×C₄×C₈	—	47	1	no	—
314	#344	—	47	2	no	—
315	#341	—	47	2	no	—
316	#339	—	47	2	no	—
317	C₄₇	#21477	1	1	yes	characteristic, complemented, Sylow
318	2₋¹⁺⁴	—	2	2	no	—
319	2₋¹⁺⁴	C₄×D₄₇	1	2	yes	—
320	H(5,𝔽₂)	—	2	2	no	—
321	H(5,𝔽₂)	—	2	2	no	—
322	H(5,𝔽₂)	C₄×D₄₇	1	2	yes	—
323	C₂×#41	—	2	4	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	47	1	no	—
326	C₂×#41	C₂²×D₄₇	1	2	yes	—
327	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
328	#137	—	47	4	no	—
329	#137	—	94	2	no	—
330	AGL(1,ℤ/8)	—	47	4	no	—
331	AGL(1,ℤ/8)	—	94	2	no	—
332	#135	—	94	4	no	—
333	#131	—	2	4	no	—
334	#131	—	2	8	no	—
335	#131	—	2	4	no	—
336	#131	—	2	4	no	—
337	#131	—	2	4	no	—
338	#131	—	2	2	no	—
339	#131	—	2	2	no	—
340	#131	—	2	4	no	—
341	#131	—	2	2	no	—
342	#131	—	2	2	no	—
343	#131	—	94	2	no	—
344	#131	—	94	2	no	—
345	#131	C₂²⋊D₄₇	1	4	yes	complemented
346	#131	C₂²⋊D₄₇	1	4	yes	complemented
347	C₂×M₁₆	—	2	8	no	—
348	C₂×M₁₆	—	2	4	no	—
349	C₂×M₁₆	—	2	2	no	—
350	C₂×M₁₆	—	2	4	no	—
351	C₂×M₁₆	—	2	2	no	—
352	C₂×M₁₆	—	47	2	no	—
353	C₂×M₁₆	—	47	1	no	—
354	C₂×M₁₆	—	94	1	no	—
355	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
356	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
357	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
358	C₂²×C₈	—	2	4	no	—
359	C₂²×C₈	—	2	2	no	—
360	C₂²×C₈	—	47	1	no	—
361	C₂²×C₈	—	94	1	no	—
362	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
363	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
364	C₄⋊Q₈	—	47	1	no	—
365	#127	—	47	1	no	—
366	#124	—	47	1	no	—
367	#124	—	47	1	no	—
368	#121	—	94	2	no	—
369	C₄×D₄	—	94	2	no	—
370	#117	—	47	2	no	—
371	C₂×C₄²	—	47	1	no	—
372	#108	—	94	4	no	—
373	C₄⋊C₈	—	94	2	no	—
374	#104	—	47	4	no	—
375	#104	—	47	4	no	—
376	#104	—	94	4	no	—
377	#104	—	94	4	no	—
378	#103	—	94	2	no	—
379	#102	—	94	2	no	—
380	#101	—	47	2	no	—
381	#100	—	47	2	no	—
382	#99	—	94	2	no	—
383	C₂²⋊C₈	—	94	2	no	—
384	C₂²⋊C₈	—	94	2	no	—
385	#97	—	94	2	no	—
386	C₄×C₈	—	94	1	no	—
387	C₄×C₈	—	94	1	no	—
388	C₄×C₈	—	94	2	no	—
389	#41	—	2	4	no	—
390	#41	—	2	8	no	—
391	#41	—	2	4	no	—
392	#41	—	2	4	no	—
393	#41	—	2	4	no	—
394	#41	—	2	4	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	94	2	no	—
400	#41	—	94	2	no	—
401	#41	C₂×C₄×D₄₇	1	4	yes	—
402	#41	C₂×C₂²⋊D₄₇	1	4	yes	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	47	1	no	—
406	C₂×Q₈	C₂×C₄×D₄₇	1	1	yes	characteristic
407	C₂×Q₈	#10625350	1	2	yes	—
408	C₂×D₄	—	2	8	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	47	1	no	—
414	C₂×D₄	—	94	2	no	—
415	C₂×D₄	—	94	1	no	—
416	C₂×D₄	C₂×C₄×D₄₇	1	1	yes	characteristic
417	C₂×D₄	#10625350	1	2	yes	—
418	C₂×D₄	#10625350	1	2	yes	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	94	1	no	—
422	C₂²×C₄	—	94	1	no	—
423	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
424	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
425	Q₁₆	—	94	4	no	—
426	SD₁₆	—	94	4	no	—
427	SD₁₆	—	94	4	no	—
428	D₈	—	94	4	no	—
429	M₁₆	—	2	4	no	—
430	M₁₆	—	2	8	no	—
431	M₁₆	—	2	2	no	—
432	M₁₆	—	2	2	no	—
433	M₁₆	—	2	4	no	—
434	M₁₆	—	2	4	no	—
435	M₁₆	—	2	4	no	—
436	M₁₆	—	47	4	no	—
437	M₁₆	—	94	2	no	—
438	M₁₆	—	94	2	no	—
439	M₁₆	—	188	2	no	—
440	M₁₆	C₂×C₂²⋊D₄₇	1	4	yes	—
441	C₂×C₈	—	2	4	no	—
442	C₂×C₈	—	2	8	no	—
443	C₂×C₈	—	2	2	no	—
444	C₂×C₈	—	2	4	no	—
445	C₂×C₈	—	2	2	no	—
446	C₂×C₈	—	2	4	no	—
447	C₂×C₈	—	2	2	no	—
448	C₂×C₈	—	94	2	no	—
449	C₂×C₈	—	94	1	no	—
450	C₂×C₈	—	94	1	no	—
451	C₂×C₈	—	94	2	no	—
452	C₂×C₈	—	188	1	no	—
453	C₂×C₈	—	188	1	no	—
454	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
455	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
456	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
457	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
458	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
459	C₄⋊C₄	—	94	2	no	—
460	C₄⋊C₄	—	94	2	no	—
461	C₂²⋊C₄	—	94	2	no	—
462	C₂²⋊C₄	—	94	2	no	—
463	C₂²⋊C₄	—	94	2	no	—
464	C₄²	—	47	1	no	—
465	C₄²	—	47	1	no	—
466	C₄²	—	94	1	no	—
467	C₄²	—	94	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	94	1	no	—
471	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
472	C₂³	C₂×#10625350	1	1	yes	characteristic
473	Q₈	—	2	4	no	—
474	Q₈	—	2	2	no	—
475	Q₈	—	2	2	no	—
476	Q₈	—	94	2	no	—
477	Q₈	C₄×C₂²⋊D₄₇	1	4	yes	—
478	D₄	—	2	8	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	4	no	—
482	D₄	—	2	4	no	—
483	D₄	—	2	2	no	—
484	D₄	—	2	2	no	—
485	D₄	—	94	2	no	—
486	D₄	—	188	4	no	—
487	D₄	—	188	2	no	—
488	D₄	C₄×C₂²⋊D₄₇	1	4	yes	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	94	1	no	—
497	C₂×C₄	—	94	1	no	—
498	C₂×C₄	—	94	1	no	—
499	C₂×C₄	—	188	2	no	—
500	C₂×C₄	—	188	2	no	—
501	C₂×C₄	—	188	1	no	—
502	C₂×C₄	—	188	1	no	—
503	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
504	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
505	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
506	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
507	C₂×C₄	C₂×#10625350	1	2	yes	—
508	C₈	—	2	4	no	—
509	C₈	—	2	2	no	—
510	C₈	—	94	4	no	—
511	C₈	—	188	1	no	—
512	C₈	—	188	1	no	—
513	C₈	#13093993	1	1	yes	characteristic
514	C₈	#13093993	1	2	yes	—
515	C₈	#13093993	1	1	yes	characteristic
516	C₂²	—	2	2	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	4	1	no	—
519	C₂²	—	4	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	—	8	4	no	—
522	C₂²	—	188	2	no	—
523	C₂²	—	188	1	no	—
524	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
525	C₂²	#15689634	1	2	yes	—
526	C₄	—	2	4	no	—
527	C₄	—	2	2	no	—
528	C₄	—	94	2	no	—
529	C₄	—	376	2	no	—
530	C₄	—	188	1	no	—
531	C₄	—	188	1	no	—
532	C₄	C₂×C₄×C₂²⋊D₄₇	1	2	yes	—
533	C₄	C₂×#13093993	1	1	yes	characteristic
534	C₄	#15689634	1	1	yes	characteristic
535	C₂	—	2	1	no	—
536	C₂	—	2	2	no	—
537	C₂	—	4	2	no	—
538	C₂	—	4	4	no	—
539	C₂	—	376	1	no	—
540	C₂	C₄×#13093993	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13093993
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#3573	C₂
socle	C₂×C₄₇	C₄×#120
prime radical	#20252737	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3573	D₄₇
hypocenter	C₄₇	#21477
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #3573

Complements

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

N	H ≅ G/N	type
2. #20252289	C₂	semidirect
3. #20252098	C₂	semidirect
4. #20243771	C₂	semidirect
5. #20243750	C₂	semidirect
6. #20243628	C₂	semidirect
7. #20243608	C₂	semidirect
8. #20243352	C₂	semidirect
9. #20243223	C₂	semidirect
10. #20243188	C₂	semidirect
11. C₄₇×#3573	C₂	semidirect
13. C₂×#13094030	C₂²	semidirect
15. #15689306	C₄	semidirect
16. #15689301	C₄	semidirect
17. #15689296	C₄	semidirect
18. #15689291	C₄	semidirect
23. #15689171	C₂²	semidirect
24. #15689146	C₂²	semidirect
26. #15689139	C₂²	semidirect
31. #15689091	C₂²	semidirect
33. #15689078	C₂²	semidirect
34. C₂×C₈×Dic₄₇	C₂²	semidirect
35. #15688894	C₂²	semidirect
36. #15688887	C₂²	semidirect
37. #15688884	C₂²	semidirect
104. #131×C₄₇	D₄	semidirect
105. #131×C₄₇	D₄	semidirect
265. #3573	D₄₇	semidirect
317. C₄₇	#21477	semidirect
345. #131	C₂²⋊D₄₇	semidirect
346. #131	C₂²⋊D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252737	2
#20252289	2
#20252098	2
#20243771	2
#20243750	2
#20243628	2
#20243608	2
#20243352	2
#20243223	2
#20243188	2
C₄₇×#3573	2
#21477	47