Finite Group Databasebeta

← #2418×C263 #46779387

Subgroups — #2418×C263 #46779387

Order 33664.

800 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#123×C263C211yesmaximal, characteristic, complemented
2C2×#120×C263C211yesmaximal, characteristic
3C2×C4×D4×C263C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×C263C211yesmaximal, characteristic, complemented
5#399×C263C211yesmaximal, characteristic, complemented
6#397×C263C211yesmaximal, characteristic, complemented
7#394×C263C211yesmaximal, characteristic, complemented
8#394×C263C211yesmaximal, characteristic, complemented
9#388×C263C211yesmaximal, characteristic, complemented
10#388×C263C211yesmaximal, characteristic, complemented
11#386×C263C211yesmaximal, characteristic, complemented
12#386×C263C211yesmaximal, characteristic, complemented
13#385×C263C211yesmaximal, characteristic, complemented
14#380×C263C211yesmaximal, characteristic, complemented
15#379×C263C211yesmaximal, characteristic, complemented
16C25×C263C2211yescharacteristic
17C22×D4×C263C2211yescharacteristic
18C22×D4×C263C2211yescharacteristic
19C22×D4×C263C2211yescharacteristic
20C23×C4×C263C2211yescharacteristic
21C23×C4×C263C2211yescharacteristic
22C23×C4×C263C2211yescharacteristic, complemented
23#123×C263—24no—
24#120×C263—24no—
25C4×D4×C263—24no—
26C2×C4⋊C4×C263C2211yescharacteristic, complemented
27C2×C4⋊C4×C263C2211yescharacteristic, complemented
28C2×C4⋊C4×C263C2211yescharacteristic, complemented
29C2×C4⋊C4×C263C2211yescharacteristic, complemented
30C2×C4⋊C4×C263C2211yescharacteristic, complemented
31C2×C22⋊C4×C263—24no—
32C2×C22⋊C4×C263C2211yescharacteristic
33C2×C22⋊C4×C263C2211yescharacteristic
34C2×C22⋊C4×C263C2211yescharacteristic
35C2×C22⋊C4×C263C2211yescharacteristic
36C2×C22⋊C4×C263C2211yescharacteristic
37C2×C22⋊C4×C263C2211yescharacteristic
38C2×C22⋊C4×C263C2211yescharacteristic
39C2×C22⋊C4×C263C2211yescharacteristic
40C2×C22⋊C4×C263C2211yescharacteristic
41C2×C22⋊C4×C263C2211yescharacteristic
42C2×C22⋊C4×C263C2211yescharacteristic
43C2×C22⋊C4×C263C2211yescharacteristic
44C2×C22⋊C4×C263C2211yescharacteristic
45C2×C22⋊C4×C263C2211yescharacteristic, complemented
46C2×C22⋊C4×C263C2211yescharacteristic, complemented
47C2×C22⋊C4×C263C2211yescharacteristic, complemented
48C2×C42×C263C2211yescharacteristic, complemented
49#95×C263C2211yescharacteristic, complemented
50#95×C263C2211yescharacteristic, complemented
51#95×C263C2211yescharacteristic, complemented
52#95×C263C2211yescharacteristic, complemented
53#95×C263C2211yescharacteristic, complemented
54#95×C263C2211yescharacteristic, complemented
55C24×C263—22no—
56C24×C263—22no—
57C24×C263—22no—
58C24×C263—22no—
59C24×C263—22no—
60C24×C263—41no—
61C24×C263—41no—
62C24×C263C2311yescharacteristic
63C24×C263C2311yescharacteristic
64C24×C263C2311yescharacteristic
65C24×C263C2311yescharacteristic
66C2×D4×C263—22no—
67C2×D4×C263—22no—
68C2×D4×C263—22no—
69C2×D4×C263—22no—
70C2×D4×C263—22no—
71C2×D4×C263—22no—
72C2×D4×C263—41no—
73C2×D4×C263—41no—
74C2×D4×C263D414yes—
75C22×C4×C263—22no—
76C22×C4×C263—22no—
77C22×C4×C263—22no—
78C22×C4×C263—22no—
79C22×C4×C263—22no—
80C22×C4×C263—22no—
81C22×C4×C263—41no—
82C22×C4×C263—41no—
83C22×C4×C263—41no—
84C22×C4×C263C2311yescharacteristic
85C22×C4×C263C2311yescharacteristic
86C22×C4×C263C2311yescharacteristic
87C22×C4×C263C2311yescharacteristic
88C22×C4×C263C2311yescharacteristic
89C22×C4×C263C2311yescharacteristic
90C22×C4×C263C2311yescharacteristic
91C22×C4×C263C2311yescharacteristic
92C22×C4×C263C2311yescharacteristic
93C22×C4×C263C2311yescharacteristic
94C22×C4×C263C2311yescharacteristic
95C4⋊C4×C263—22no—
96C4⋊C4×C263—22no—
97C4⋊C4×C263—22no—
98C4⋊C4×C263—41no—
99C4⋊C4×C263—41no—
100C22⋊C4×C263—22no—
101C22⋊C4×C263—22no—
102C22⋊C4×C263—22no—
103C22⋊C4×C263—22no—
104C22⋊C4×C263—22no—
105C22⋊C4×C263—22no—
106C22⋊C4×C263—22no—
107C22⋊C4×C263—22no—
108C22⋊C4×C263—22no—
109C22⋊C4×C263—22no—
110C22⋊C4×C263—22no—
111C22⋊C4×C263—22no—
112C22⋊C4×C263—41no—
113C22⋊C4×C263—41no—
114C22⋊C4×C263—41no—
115C22⋊C4×C263D414yescomplemented
116C42×C263—22no—
117C23×C263—21no—
118C23×C263—21no—
119C23×C263—21no—
120C23×C263—21no—
121C23×C263—28no—
122C23×C263—21no—
123C23×C263—21no—
124C23×C263—21no—
125C23×C263—21no—
126C23×C263—21no—
127C23×C263—21no—
128C23×C263—21no—
129C23×C263—21no—
130C23×C263—21no—
131C23×C263—21no—
132C23×C263—21no—
133C23×C263—21no—
134C23×C263—21no—
135C23×C263—21no—
136C23×C263—21no—
137C23×C263—21no—
138C23×C263—21no—
139C23×C263—21no—
140C23×C263—44no—
141C23×C263—44no—
142C23×C263—44no—
143C23×C263—44no—
144C23×C263—44no—
145C23×C263—44no—
146C23×C263C2×D412yes—
147C23×C263C2×D412yes—
148C23×C263C2×D412yes—
149C23×C263#4112yes—
150C23×C263#4112yes—
151C23×C263#4112yes—
152C23×C263C2411yescharacteristic
153D4×C263—28no—
154D4×C263—44no—
155D4×C263—44no—
156C2×C4×C263—21no—
157C2×C4×C263—21no—
158C2×C4×C263—21no—
159C2×C4×C263—21no—
160C2×C4×C263—21no—
161C2×C4×C263—21no—
162C2×C4×C263—21no—
163C2×C4×C263—21no—
164C2×C4×C263—21no—
165C2×C4×C263—21no—
166C2×C4×C263—21no—
167C2×C4×C263—21no—
168C2×C4×C263—21no—
169C2×C4×C263—21no—
170C2×C4×C263—21no—
171C2×C4×C263—21no—
172C2×C4×C263—21no—
173C2×C4×C263—21no—
174C2×C4×C263—21no—
175C2×C4×C263—21no—
176C2×C4×C263—21no—
177C2×C4×C263—21no—
178C2×C4×C263—21no—
179C2×C4×C263—21no—
180C2×C4×C263—21no—
181C2×C4×C263—21no—
182C2×C4×C263—21no—
183C2×C4×C263—21no—
184C2×C4×C263—21no—
185C2×C4×C263—21no—
186C2×C4×C263—44no—
187C2×C4×C263—44no—
188C2×C4×C263—44no—
189C2×C4×C263C2×D412yes—
190C2×C4×C263C2×D412yes—
191C2×C4×C263C2×D412yes—
192C22×C263—22no—
193C22×C263—22no—
194C22×C263—22no—
195C22×C263—22no—
196C22×C263—22no—
197C22×C263—22no—
198C22×C263—22no—
199C22×C263—22no—
200C22×C263—22no—
201C22×C263—22no—
202C22×C263—22no—
203C22×C263—22no—
204C22×C263—22no—
205C22×C263—22no—
206C22×C263—22no—
207C22×C263—416no—
208C22×C263—41no—
209C22×C263—41no—
210C22×C263—41no—
211C22×C263—41no—
212C22×C263—41no—
213C22×C263—41no—
214C22×C263—41no—
215C22×C263—41no—
216C22×C263—41no—
217C22×C263—41no—
218C22×C263—41no—
219C22×C263—41no—
220C22×C263#12314yescomplemented
221C22×C263C22×D411yescharacteristic
222C22×C263C22×D411yescharacteristic
223C22×C263C2×#4111yescharacteristic
224C22×C263C2×#4111yescharacteristic
225C22×C263C2×#4111yescharacteristic
226C22×C263H(5,𝔽2)11yescharacteristic
227C22×C263H(5,𝔽2)11yescharacteristic
228C4×C263—22no—
229C4×C263—22no—
230C4×C263—22no—
231C4×C263—41no—
232C4×C263—41no—
233C4×C263—41no—
234C4×C263—41no—
235C4×C263—41no—
236C4×C263—41no—
237C4×C263—41no—
238C4×C263—41no—
239C2×C263—24no—
240C2×C263—42no—
241C2×C263—42no—
242C2×C263—42no—
243C2×C263C2×#12311yescharacteristic
244C2×C263#52511yescharacteristic
245C2×C263#53811yescharacteristic
246C2×C263D4211yescharacteristic
247C2×C263#54611yescharacteristic
248C2×C263#54611yescharacteristic
249C2×C263#55111yescharacteristic
250C263#241811yescharacteristic, direct product factor, Sylow
251#2418C26311yesmaximal, characteristic, direct product factor, Sylow
252C2×#123C2×C26311yescharacteristic, complemented
253C2×#120C2×C26311yescharacteristic
254C2×C4×D4C2×C26311yescharacteristic, complemented
255C22×C22⋊C4C2×C26311yescharacteristic, complemented
256#399C2×C26311yescharacteristic, complemented
257#397C2×C26311yescharacteristic, complemented
258#394C2×C26311yescharacteristic, complemented
259#394C2×C26311yescharacteristic, complemented
260#388C2×C26311yescharacteristic, complemented
261#388C2×C26311yescharacteristic, complemented
262#386C2×C26311yescharacteristic, complemented
263#386C2×C26311yescharacteristic, complemented
264#385C2×C26311yescharacteristic, complemented
265#380C2×C26311yescharacteristic, complemented
266#379C2×C26311yescharacteristic, complemented
267C25C22×C26311yescharacteristic
268C22×D4C22×C26311yescharacteristic
269C22×D4C22×C26311yescharacteristic
270C22×D4C22×C26311yescharacteristic
271C23×C4C22×C26311yescharacteristic
272C23×C4C22×C26311yescharacteristic
273C23×C4C22×C26311yescharacteristic, complemented
274#123—24no—
275#120—24no—
276C4×D4—24no—
277C2×C4⋊C4C22×C26311yescharacteristic, complemented
278C2×C4⋊C4C22×C26311yescharacteristic, complemented
279C2×C4⋊C4C22×C26311yescharacteristic, complemented
280C2×C4⋊C4C22×C26311yescharacteristic, complemented
281C2×C4⋊C4C22×C26311yescharacteristic, complemented
282C2×C22⋊C4—24no—
283C2×C22⋊C4C22×C26311yescharacteristic
284C2×C22⋊C4C22×C26311yescharacteristic
285C2×C22⋊C4C22×C26311yescharacteristic
286C2×C22⋊C4C22×C26311yescharacteristic
287C2×C22⋊C4C22×C26311yescharacteristic
288C2×C22⋊C4C22×C26311yescharacteristic
289C2×C22⋊C4C22×C26311yescharacteristic
290C2×C22⋊C4C22×C26311yescharacteristic
291C2×C22⋊C4C22×C26311yescharacteristic
292C2×C22⋊C4C22×C26311yescharacteristic
293C2×C22⋊C4C22×C26311yescharacteristic
294C2×C22⋊C4C22×C26311yescharacteristic
295C2×C22⋊C4C22×C26311yescharacteristic
296C2×C22⋊C4C22×C26311yescharacteristic, complemented
297C2×C22⋊C4C22×C26311yescharacteristic, complemented
298C2×C22⋊C4C22×C26311yescharacteristic, complemented
299C2×C42C22×C26311yescharacteristic, complemented
300#95C22×C26311yescharacteristic, complemented
301#95C22×C26311yescharacteristic, complemented
302#95C22×C26311yescharacteristic, complemented
303#95C22×C26311yescharacteristic, complemented
304#95C22×C26311yescharacteristic, complemented
305#95C22×C26311yescharacteristic, complemented
306C24—22no—
307C24—22no—
308C24—22no—
309C24—22no—
310C24—22no—
311C24—41no—
312C24—41no—
313C24C23×C26311yescharacteristic
314C24C23×C26311yescharacteristic
315C24C23×C26311yescharacteristic
316C24C23×C26311yescharacteristic
317C2×D4—22no—
318C2×D4—22no—
319C2×D4—22no—
320C2×D4—22no—
321C2×D4—22no—
322C2×D4—22no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4D4×C26314yes—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—41no—
335C22×C4C23×C26311yescharacteristic
336C22×C4C23×C26311yescharacteristic
337C22×C4C23×C26311yescharacteristic
338C22×C4C23×C26311yescharacteristic
339C22×C4C23×C26311yescharacteristic
340C22×C4C23×C26311yescharacteristic
341C22×C4C23×C26311yescharacteristic
342C22×C4C23×C26311yescharacteristic
343C22×C4C23×C26311yescharacteristic
344C22×C4C23×C26311yescharacteristic
345C22×C4C23×C26311yescharacteristic
346C4⋊C4—22no—
347C4⋊C4—22no—
348C4⋊C4—22no—
349C4⋊C4—41no—
350C4⋊C4—41no—
351C22⋊C4—22no—
352C22⋊C4—22no—
353C22⋊C4—22no—
354C22⋊C4—22no—
355C22⋊C4—22no—
356C22⋊C4—22no—
357C22⋊C4—22no—
358C22⋊C4—22no—
359C22⋊C4—22no—
360C22⋊C4—22no—
361C22⋊C4—22no—
362C22⋊C4—22no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4D4×C26314yescomplemented
367C42—22no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—28no—
373C23—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—21no—
379C23—21no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—44no—
392C23—44no—
393C23—44no—
394C23—44no—
395C23—44no—
396C23—44no—
397C23C2×D4×C26312yes—
398C23C2×D4×C26312yes—
399C23C2×D4×C26312yes—
400C23#41×C26312yes—
401C23#41×C26312yes—
402C23#41×C26312yes—
403C23C24×C26311yescharacteristic
404D4—28no—
405D4—44no—
406D4—44no—
407C2×C4—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—44no—
438C2×C4—44no—
439C2×C4—44no—
440C2×C4C2×D4×C26312yes—
441C2×C4C2×D4×C26312yes—
442C2×C4C2×D4×C26312yes—
443C22—22no—
444C22—22no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—22no—
452C22—22no—
453C22—22no—
454C22—22no—
455C22—22no—
456C22—22no—
457C22—22no—
458C22—416no—
459C22—41no—
460C22—41no—
461C22—41no—
462C22—41no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22#123×C26314yescomplemented
472C22C22×D4×C26311yescharacteristic
473C22C22×D4×C26311yescharacteristic
474C22C2×#41×C26311yescharacteristic
475C22C2×#41×C26311yescharacteristic
476C22C2×#41×C26311yescharacteristic
477C22H(5,𝔽2)×C26311yescharacteristic
478C22H(5,𝔽2)×C26311yescharacteristic
479C4—22no—
480C4—22no—
481C4—22no—
482C4—41no—
483C4—41no—
484C4—41no—
485C4—41no—
486C4—41no—
487C4—41no—
488C4—41no—
489C4—41no—
490C2—24no—
491C2—42no—
492C2—42no—
493C2—42no—
494C2C2×#123×C26311yescharacteristic
495C2#525×C26311yescharacteristic
496C2#538×C26311yescharacteristic
497C2D42×C26311yescharacteristic
498C2#546×C26311yescharacteristic
499C2#546×C26311yescharacteristic
500C2#551×C26311yescharacteristic
subgroupG/H
center, socleC23×C263C24
commutator, Frattini, cosocleC23C24×C263
prime radicalC2×#120×C263C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C263 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#123×C263C2semidirect
3. C2×C4×D4×C263C2semidirect
4. C22×C22⋊C4×C263C2semidirect
5. #399×C263C2semidirect
6. #397×C263C2semidirect
7. #394×C263C2semidirect
8. #394×C263C2semidirect
9. #388×C263C2semidirect
10. #388×C263C2semidirect
11. #386×C263C2semidirect
12. #386×C263C2semidirect
13. #385×C263C2semidirect
14. #380×C263C2semidirect
15. #379×C263C2semidirect
22. C23×C4×C263C22semidirect
26. C2×C4⋊C4×C263C22semidirect
27. C2×C4⋊C4×C263C22semidirect
28. C2×C4⋊C4×C263C22semidirect
29. C2×C4⋊C4×C263C22semidirect
30. C2×C4⋊C4×C263C22semidirect
45. C2×C22⋊C4×C263C22semidirect
46. C2×C22⋊C4×C263C22semidirect
47. C2×C22⋊C4×C263C22semidirect
48. C2×C42×C263C22semidirect
49. #95×C263C22semidirect
50. #95×C263C22semidirect
51. #95×C263C22semidirect
52. #95×C263C22semidirect
53. #95×C263C22semidirect
54. #95×C263C22semidirect
115. C22⋊C4×C263D4semidirect
220. C22×C263#123semidirect
250. C263#2418direct (N × H)
251. #2418C263direct (N × H)
252. C2×#123C2×C263semidirect
254. C2×C4×D4C2×C263semidirect
255. C22×C22⋊C4C2×C263semidirect
256. #399C2×C263semidirect
257. #397C2×C263semidirect
258. #394C2×C263semidirect
259. #394C2×C263semidirect
260. #388C2×C263semidirect
261. #388C2×C263semidirect
262. #386C2×C263semidirect
263. #386C2×C263semidirect
264. #385C2×C263semidirect
265. #380C2×C263semidirect
266. #379C2×C263semidirect
273. C23×C4C22×C263semidirect
277. C2×C4⋊C4C22×C263semidirect
278. C2×C4⋊C4C22×C263semidirect
279. C2×C4⋊C4C22×C263semidirect
280. C2×C4⋊C4C22×C263semidirect
281. C2×C4⋊C4C22×C263semidirect
296. C2×C22⋊C4C22×C263semidirect
297. C2×C22⋊C4C22×C263semidirect
298. C2×C22⋊C4C22×C263semidirect
299. C2×C42C22×C263semidirect
300. #95C22×C263semidirect
301. #95C22×C263semidirect
302. #95C22×C263semidirect
303. #95C22×C263semidirect
304. #95C22×C263semidirect
305. #95C22×C263semidirect
366. C22⋊C4D4×C263semidirect
471. C22#123×C263semidirect

Maximal subgroups

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

subgroupindex
C2×#123×C2632
C2×#120×C2632
C2×C4×D4×C2632
C22×C22⋊C4×C2632
#399×C2632
#397×C2632
#394×C2632
#388×C2632
#386×C2632
#385×C2632
#380×C2632
#379×C2632
#2418263