Finite Group Databasebeta

← #16017398

Subgroups — #16017398

Order 3328.

738 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718854C211yesmaximal, characteristic, complemented
2C22×#88052C211yesmaximal, characteristic, complemented
3C2×#11718776C211yesmaximal, characteristic, complemented
4#13116951C212yesmaximal, complemented
5#13116937C212yesmaximal, complemented
6#13116934C212yesmaximal, complemented
7#13116920C212yesmaximal, complemented
8#13116625C211yesmaximal, characteristic, complemented
9#13116551C211yesmaximal, characteristic, complemented
10#13116548C211yesmaximal, characteristic, complemented
11C13×#3050C211yesmaximal, characteristic, complemented
12C2×C13×#135C2211yescharacteristic
13C23×C8×C13C2211yescharacteristic
14C13×#525—21no—
15C2×#88184—21no—
16C22×D104C2211yescharacteristic
17C13×#467C2211yescharacteristic, complemented
18C13×#467C2211yescharacteristic, complemented
19C13×#466C2211yescharacteristic, complemented
20C13×#466C2211yescharacteristic, complemented
21C13×#465—21no—
22C13×#465—21no—
23C13×#427C2211yescharacteristic
24C13×#416—21no—
25#11718854—24no—
26C2×#88068C2212yescomplemented
27C2×#88066C2212yescomplemented
28#11718776—21no—
29#11718776—21no—
30#11718776C2212yes—
31#11718776C2212yes—
32C2×#88061—21no—
33C2×#88058C2211yescharacteristic
34C2×#88052—24no—
35C2×#88052C2211yescharacteristic
36C2×#88052C2211yescharacteristic
37C2×#88052C2212yescomplemented
38C22×#6090C2212yescomplemented
39#11718156C2212yescomplemented
40#11718154C2212yescomplemented
41#11718083C2212yescomplemented
42#11718083C2212yescomplemented
43#11718082C2212yescomplemented
44#11718081C2212yescomplemented
45C2×C13×#41—21no—
46C23×C4×C13D411yescharacteristic
47C22×C22⋊D13—41no—
48C22×D52—21no—
49C13×#135—22no—
50C13×#135—22no—
51C2×C13×Q16C2311yescharacteristic
52C2×C13×SD16—21no—
53C2×C13×D8C2311yescharacteristic
54C22×C8×C13—22no—
55C22×C8×C13—22no—
56C22×C8×C13D411yescharacteristic
57C22×C8×C13D411yescharacteristic
58C22×C8×C13D411yescharacteristic
59C22×C8×C13C2311yescharacteristic
60C22×C8×C13C2311yescharacteristic
61C22×C8×C13C2311yescharacteristic
62C13×#123—41no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—21no—
65C13×#121—21no—
66C13×#121—21no—
67C13×#120—41no—
68C4×D4×C13—41no—
69C4×D4×C13—41no—
70C13×#117—21no—
71#88184—22no—
72#88184—22no—
73#88184—41no—
74#88184—41no—
75C2×#6103—41no—
76C2×C4⋊Dic13—21no—
77C2×D104—22no—
78C2×D104—22no—
79C2×D104—21no—
80C2×D104C2312yes—
81C13×#107C2311yescharacteristic
82C13×#107C2311yescharacteristic
83C13×#106—21no—
84C13×#103—21no—
85C13×#103—21no—
86C13×#102—21no—
87C13×#102—21no—
88#88068—24no—
89#88066—24no—
90#88061—22no—
91#88061—22no—
92#88058—21no—
93#88058C2312yes—
94#88052—22no—
95#88052—24no—
96#88052D414yescomplemented
97C2×#6090—24no—
98C2×#6090C2312yes—
99C2×#6090C2312yes—
100#33605—131nomaximal, Sylow
101C24×C13D811yescharacteristic
102C23×D13—41no—
103C13×#41—42no—
104C13×#41—42no—
105C2×Q8×C13—21no—
106C2×D4×C13—21no—
107C2×D4×C13—41no—
108C2×D4×C13—41no—
109C2×D4×C13—41no—
110C22×C4×C13—22no—
111C22×C4×C13—22no—
112C22×C4×C13—41no—
113C22×C4×C13D811yescharacteristic
114C22×C4×C13D811yescharacteristic
115C22×C4×C13D811yescharacteristic
116C22×C4×C13C2×D411yescharacteristic
117C22×C4×C13C2×D411yescharacteristic
118C22×C4×C13C2×D411yescharacteristic
119C2×C22⋊D13—42no—
120C2×C22⋊D13—42no—
121C2×C22⋊D13—84no—
122C22×Dic13—41no—
123C2×D52—22no—
124C2×D52—42no—
125C2×D52—42no—
126C2×D52—41no—
127C13×Q16—21no—
128C13×Q16—21no—
129C13×SD16—42no—
130C13×D8—21no—
131C13×D8—21no—
132C2×C8×C13—22no—
133C2×C8×C13—22no—
134C2×C8×C13—22no—
135C2×C8×C13—21no—
136C2×C8×C13—21no—
137C2×C8×C13—21no—
138C2×C8×C13—21no—
139C2×C8×C13C2×D411yescharacteristic
140C2×C8×C13C2×D411yescharacteristic
141C2×C8×C13C2×D411yescharacteristic
142C2×C8×C13C2×D412yes—
143C2×C8×C13#4112yes—
144C2×C8×C13C2411yescharacteristic
145C13×C4⋊C4—21no—
146C13×C4⋊C4—21no—
147C13×C4⋊C4—41no—
148C13×C4⋊C4—41no—
149C13×C22⋊C4—41no—
150C13×C22⋊C4—41no—
151C13×C22⋊C4—41no—
152C13×C22⋊C4—41no—
153C13×C22⋊C4—41no—
154C42×C13—41no—
155#6103—42no—
156#6103—42no—
157C4⋊Dic13—22no—
158C4⋊Dic13—41no—
159D104—22no—
160D104—22no—
161D104—42no—
162#6090—22no—
163#6090C2×D414yescomplemented
164C2×#509—131no—
165C22×M32—131no—
166#3050D1311yescharacteristic, complemented
167C2×#466—131no—
168#2220—132no—
169#2218—132no—
170#2217—132no—
171#2215—132no—
172#2159—131no—
173#2140—131no—
174#2139—131no—
175C23×C13—22no—
176C23×C13—22no—
177C23×C13—41no—
178C23×C13—41no—
179C23×C13C2×D811yescharacteristic
180C23×C13C2×D811yescharacteristic
181C23×C13C2×D811yescharacteristic
182C22×D13—42no—
183C22×D13—82no—
184C22×D13—82no—
185C22×D13—82no—
186Q8×C13—41no—
187Q8×C13—41no—
188D4×C13—41no—
189D4×C13—41no—
190D4×C13—82no—
191D4×C13—82no—
192D4×C13—82no—
193C2×C4×C13—22no—
194C2×C4×C13—21no—
195C2×C4×C13—21no—
196C2×C4×C13—21no—
197C2×C4×C13—21no—
198C2×C4×C13—22no—
199C2×C4×C13—22no—
200C2×C4×C13—41no—
201C2×C4×C13—41no—
202C2×C4×C13—41no—
203C2×C4×C13—82no—
204C2×C4×C13#12112yes—
205C2×C4×C13C2×D811yescharacteristic
206C2×C4×C13C2×D811yescharacteristic
207C2×C4×C13C2×D811yescharacteristic
208C2×C4×C13#13512yes—
209C2×C4×C13C22×D411yescharacteristic
210C22⋊D13—84no—
211C22⋊D13—84no—
212C2×Dic13—42no—
213C2×Dic13—82no—
214D52—42no—
215D52—42no—
216D52—82no—
217C8×C13—21no—
218C8×C13—21no—
219C8×C13#12112yes—
220C8×C13C22×D411yescharacteristic
221C8×C13C2×#4111yescharacteristic
222C2×#135C2×D1311yescharacteristic
223C22×D8—131no—
224C23×C8C2×D1311yescharacteristic
225#525—21no—
226C2×#121—261no—
227#509—264no—
228C2×SD32—132no—
229C2×D16—132no—
230C2×M32—131no—
231C2×M32—131no—
232C2×M32—132no—
233C2×M32—264no—
234C22×C16—132no—
235#467C2×D1311yescharacteristic, complemented
236#467C2×D1311yescharacteristic, complemented
237#466—132no—
238#466—132no—
239#466—261no—
240#466—261no—
241#466C2×D1311yescharacteristic, complemented
242#466C2×D1311yescharacteristic, complemented
243#465—21no—
244#465—21no—
245#427C2×D1311yescharacteristic
246C2×#107—131no—
247#416—21no—
248C2×#102—261no—
249#367—132no—
250#366—132no—
251#358—132no—
252#357—132no—
253#357—132no—
254#357—132no—
255C22×C13—21no—
256C22×C13—21no—
257C22×C13—21no—
258C22×C13—21no—
259C22×C13—21no—
260C22×C13—21no—
261C22×C13—21no—
262C22×C13—44no—
263C22×C13—81no—
264C22×C13—81no—
265C22×C13—81no—
266C22×C13#46612yes—
267C22×C13#50912yescomplemented
268C22×C13C22×D811yescharacteristic
269C2×D13—82no—
270C2×D13—82no—
271C2×D13—82no—
272C2×D13—164no—
273C4×C13—21no—
274C4×C13—21no—
275C4×C13—81no—
276C4×C13—81no—
277C4×C13—81no—
278C4×C13#46612yes—
279C4×C13C2×#12111yescharacteristic
280C4×C13C2×#13511yescharacteristic
281Dic13—82no—
282C2×#41—21no—
283C22×D4—261no—
284C22×D4—521no—
285C23×C4C22⋊D1311yescharacteristic
286#135—22no—
287#135—22no—
288C2×Q16C22×D1311yescharacteristic
289C2×SD16—21no—
290C2×D8—132no—
291C2×D8—262no—
292C2×D8—262no—
293C2×D8—261no—
294C2×D8C22×D1311yescharacteristic
295C22×C8—22no—
296C22×C8—22no—
297C22×C8C22⋊D1311yescharacteristic
298C22×C8C22⋊D1311yescharacteristic
299C22×C8C22⋊D1311yescharacteristic
300C22×C8C22×D1311yescharacteristic
301C22×C8C22×D1311yescharacteristic
302C22×C8C22×D1311yescharacteristic
303#123—41no—
304C22⋊Q8—21no—
305C22⋊Q8—21no—
306#121—21no—
307#121—21no—
308#121—262no—
309#121—262no—
310#121—521no—
311#121—521no—
312#120—41no—
313C4×D4—41no—
314C4×D4—41no—
315#117—21no—
316C2×C4⋊C4—261no—
317C2×C22⋊C4—521no—
318SD32—264no—
319D16—264no—
320M32—134no—
321M32—264no—
322M32—262no—
323C2×C16—132no—
324C2×C16—132no—
325C2×C16—264no—
326#107—132no—
327#107—261no—
328#107C22×D1311yescharacteristic
329#107C22×D1311yescharacteristic
330#106—21no—
331#103—21no—
332#103—21no—
333#102—21no—
334#102—21no—
335#102—262no—
336#102—262no—
337C2×C13—22no—
338C2×C13—22no—
339C2×C13—41no—
340C2×C13—161no—
341C2×C13C2×#46611yescharacteristic
342C2×C13C2×#50911yescharacteristic
343C2×C13#341411yescharacteristic
344D13—162no—
345C24—521no—
346C24#610411yescharacteristic
347#41—42no—
348#41—42no—
349C2×Q8—21no—
350C2×D4—21no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—41no—
354C2×D4—262no—
355C2×D4—522no—
356C2×D4—522no—
357C2×D4—521no—
358C2×D4—522no—
359C2×D4—522no—
360C2×D4—1044no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—41no—
364C22×C4—521no—
365C22×C4#610411yescharacteristic
366C22×C4#610411yescharacteristic
367C22×C4#610411yescharacteristic
368C22×C4C2×C22⋊D1311yescharacteristic
369C22×C4C2×C22⋊D1311yescharacteristic
370C22×C4C2×C22⋊D1311yescharacteristic
371Q16—21no—
372Q16—21no—
373SD16—42no—
374D8—21no—
375D8—21no—
376D8—262no—
377D8—262no—
378D8—522no—
379C2×C8—22no—
380C2×C8—22no—
381C2×C8—22no—
382C2×C8—21no—
383C2×C8—21no—
384C2×C8—21no—
385C2×C8—21no—
386C2×C8D4×D1312yes—
387C2×C8#612912yes—
388C2×C8C2×C22⋊D1311yescharacteristic
389C2×C8C2×C22⋊D1311yescharacteristic
390C2×C8C2×C22⋊D1311yescharacteristic
391C2×C8C23×D1311yescharacteristic
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—262no—
397C4⋊C4—521no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—41no—
402C22⋊C4—41no—
403C22⋊C4—522no—
404C22⋊C4—522no—
405C42—41no—
406C16—134no—
407C16—262no—
408C13#3360511yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—41no—
412C23—41no—
413C23—522no—
414C23—1042no—
415C23—1042no—
416C23—1042no—
417C23C2×#610411yescharacteristic
418C23C2×#610411yescharacteristic
419C23C2×#610411yescharacteristic
420Q8—41no—
421Q8—41no—
422D4—41no—
423D4—41no—
424D4—82no—
425D4—82no—
426D4—82no—
427D4—522no—
428D4—522no—
429D4—1044no—
430D4—1044no—
431D4—1042no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—82no—
443C2×C4—522no—
444C2×C4—1042no—
445C2×C4C2×#610411yescharacteristic
446C2×C4C2×#610411yescharacteristic
447C2×C4C2×#610411yescharacteristic
448C2×C4#8819312yes—
449C2×C4#8820412yes—
450C2×C4C22×C22⋊D1311yescharacteristic
451C8—21no—
452C8—21no—
453C8#8819312yes—
454C8C2×D4×D1311yescharacteristic
455C8C2×#612911yescharacteristic
456C22—21no—
457C22—21no—
458C22—21no—
459C22—21no—
460C22—21no—
461C22—21no—
462C22—21no—
463C22—44no—
464C22—81no—
465C22—81no—
466C22—81no—
467C22—1042no—
468C22—1042no—
469C22—1042no—
470C22—2084no—
471C22#1171869912yes—
472C22#1171885412yescomplemented
473C22C22×#610411yescharacteristic
474C4—21no—
475C4—21no—
476C4—81no—
477C4—81no—
478C4—81no—
479C4—1042no—
480C4#1171869912yes—
481C4C2×#8819311yescharacteristic
482C4C2×#8820411yescharacteristic
483C2—22no—
484C2—22no—
485C2—41no—
486C2—161no—
487C2—2082no—
488C2C2×#1171869911yescharacteristic
489C2C2×#1171885411yescharacteristic
490C2#1312797011yescharacteristic
subgroupG/H
centerC22C22×#6104
commutator, cosocleC2×C8×C13C24
FrattiniC2×C8C23×D13
FittingC13×#3050C2
socleC22×C13C22×D8
hypercenter#3050D13
hypocenterC13#33605
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. C2×#11718854C2semidirect
2. C22×#88052C2semidirect
3. C2×#11718776C2semidirect
4. #13116951C2semidirect
5. #13116937C2semidirect
6. #13116934C2semidirect
7. #13116920C2semidirect
8. #13116625C2semidirect
9. #13116551C2semidirect
10. #13116548C2semidirect
11. C13×#3050C2semidirect
17. C13×#467C22semidirect
18. C13×#467C22semidirect
19. C13×#466C22semidirect
20. C13×#466C22semidirect
26. C2×#88068C22semidirect
27. C2×#88066C22semidirect
37. C2×#88052C22semidirect
38. C22×#6090C22semidirect
39. #11718156C22semidirect
40. #11718154C22semidirect
41. #11718083C22semidirect
42. #11718083C22semidirect
43. #11718082C22semidirect
44. #11718081C22semidirect
96. #88052D4semidirect
163. #6090C2×D4semidirect
166. #3050D13semidirect
235. #467C2×D13semidirect
236. #467C2×D13semidirect
241. #466C2×D13semidirect
242. #466C2×D13semidirect
267. C22×C13#509semidirect
408. C13#33605semidirect
472. C22#11718854semidirect

Maximal subgroups

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

subgroupindex
C2×#117188542
C22×#880522
C2×#117187762
#131169512
#131169372
#131169342
#131169202
#131166252
#131165512
#131165482
C13×#30502
#3360513