Finite Group Databasebeta

← #15891835

Subgroups — #15891835

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718656C211yesmaximal, characteristic, complemented
2#13123353C211yesmaximal, characteristic
3C2×#11718794C211yesmaximal, characteristic
4#13123280C211yesmaximal, characteristic
5#13116285C214yesmaximal, complemented
6#13116280C214yesmaximal, complemented
7C2×#11718146C211yesmaximal, characteristic, complemented
8#13114562C211yesmaximal, characteristic, complemented
9C13×#1742C211yesmaximal, characteristic, complemented
10C22×#6127C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C22×C13×M16C2211yescharacteristic
13C2×C13×#117C2211yescharacteristic
14C22×C4⋊Dic13C2211yescharacteristic
15C22×#6099C2211yescharacteristic
16C22×#6099C2211yescharacteristic
17#11718794—22no—
18#11718794C2214yes—
19#11718790C2214yes—
20#11718787—22no—
21C2×#88061—21no—
22#11718771—22no—
23C2×#88056—21no—
24#11718665—21no—
25#11718663—22no—
26#11718662—21no—
27#11718656—22no—
28#11718656—22no—
29#11718627C2212yes—
30#11718627C2212yes—
31C2×#88048C2212yescomplemented
32C2×#88047C2212yescomplemented
33C13×#343C2212yescomplemented
34C13×#343C2212yescomplemented
35#11718150C2214yescomplemented
36#11718146C2214yescomplemented
37C23×C4×C13C2311yescharacteristic
38C22×C22⋊D13—21no—
39C23×Dic13—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—22no—
43C2×#6127—22no—
44C2×#6127—22no—
45C2×#6127—22no—
46C2×#6127D412yes—
47C2×#6127C2312yes—
48C22×D52D411yescharacteristic
49C22×C4×D13—21no—
50C22×Dic26D411yescharacteristic
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16—22no—
54C2×C13×M16—22no—
55C2×C13×M16—22no—
56C2×C13×M16—22no—
57C2×C13×M16C2312yes—
58C2×C13×M16C2312yes—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C13×#117—21no—
62C13×#117—21no—
63C13×#117—21no—
64C13×#117—21no—
65C2×C13×C4⋊C4C2311yescharacteristic
66C2×C13×C4⋊C4C2311yescharacteristic
67C2×C13×C22⋊C4—21no—
68C2×C42×C13—21no—
69C2×C4⋊Dic13—21no—
70C2×C4⋊Dic13—21no—
71C2×C4⋊Dic13—21no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13C2312yes—
75C2×#6099—22no—
76C2×#6099—22no—
77C2×#6099—21no—
78C2×#6099—22no—
79C2×#6099—22no—
80C2×#6099D412yes—
81C2×#6099D412yes—
82C2×#6099C2312yes—
83C22×#1055—21no—
84C22×#1055C2312yes—
85#88061—24no—
86#88060—28no—
87#88056—24no—
88#88050—22no—
89#88050—22no—
90#88049—22no—
91#88049—22no—
92#88048—24no—
93#88047—24no—
94#23647—131nomaximal, Sylow
95C24×C13#4111yescharacteristic
96C23×D13—21no—
97C22×C4×C13—21no—
98C22×C4×C13—21no—
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13#4111yescharacteristic
104C22×C4×C13#4112yes—
105C22×C4×C13#4112yes—
106C22×C4×C13#4112yes—
107C22×C4×C13#4112yes—
108C22×C4×C13C2411yescharacteristic
109C2×C22⋊D13—22no—
110C2×C22⋊D13—22no—
111C2×C22⋊D13—42no—
112C2×C22⋊D13—42no—
113C22×Dic13—21no—
114C22×Dic13—22no—
115C22×Dic13—41no—
116C22×Dic13—41no—
117C22×Dic13—82no—
118#6127—24no—
119#6127—24no—
120#6127—22no—
121#6127—22no—
122#6127—22no—
123#6127—22no—
124#6127—42no—
125#6127—42no—
126#6127—42no—
127#6127—42no—
128C2×D52—22no—
129C2×D52—22no—
130C2×D52—21no—
131C2×D52C2×D412yes—
132C2×C4×D13—22no—
133C2×C4×D13—22no—
134C2×C4×D13—42no—
135C2×C4×D13—42no—
136C2×Dic26—22no—
137C2×Dic26—22no—
138C2×Dic26—21no—
139C2×Dic26C2×D412yes—
140C13×M16—22no—
141C13×M16—22no—
142C13×M16—22no—
143C13×M16—22no—
144C13×M16—42no—
145C13×M16—42no—
146C2×C8×C13—22no—
147C2×C8×C13—22no—
148C2×C8×C13—42no—
149C2×C8×C13—42no—
150C13×C4⋊C4—21no—
151C13×C4⋊C4—21no—
152C13×C4⋊C4—21no—
153C13×C4⋊C4—21no—
154C13×C22⋊C4—41no—
155C13×C22⋊C4—41no—
156C42×C13—41no—
157C42×C13—41no—
158C4⋊Dic13—22no—
159C4⋊Dic13—22no—
160C4⋊Dic13—41no—
161C4⋊Dic13—41no—
162#6099—24no—
163#6099—24no—
164#6099—22no—
165#6099—22no—
166#6099—42no—
167C2×#1055—22no—
168C2×#1055—22no—
169C2×#1055—22no—
170C2×#1055—42no—
171C2×#1055C2×D414yes—
172C2×#428—131no—
173#2896—131no—
174C2×#417—131no—
175#2879—131no—
176#2079—134no—
177#2078—134no—
178#1742D1311yescharacteristic, complemented
179C2×#343—131no—
180#1738—131no—
181C23×C13—41no—
182C23×C13—41no—
183C23×C13#12111yescharacteristic
184C23×C13#12111yescharacteristic
185C23×C13#12612yes—
186C23×C13#12612yes—
187C23×C13C2×#4111yescharacteristic
188C22×D13—22no—
189C22×D13—42no—
190C22×D13—81no—
191C22×D13—81no—
192C2×C4×C13—41no—
193C2×C4×C13—41no—
194C2×C4×C13—81no—
195C2×C4×C13—81no—
196C2×C4×C13#12111yescharacteristic
197C2×C4×C13#12111yescharacteristic
198C2×C4×C13#12312yes—
199C2×C4×C13#12312yes—
200C2×C4×C13#12312yes—
201C2×C4×C13#12312yes—
202C2×C4×C13#12312yes—
203C2×C4×C13#12312yes—
204C2×C4×C13#12412yes—
205C2×C4×C13#12412yes—
206C2×C4×C13#12612yes—
207C2×C4×C13#12612yes—
208C2×C4×C13C22×D411yescharacteristic
209C2×C4×C13C22×D411yescharacteristic
210C2×C4×C13C2×#4111yescharacteristic
211C2×C4×C13C2×#4111yescharacteristic
212C2×C4×C13C2×#4111yescharacteristic
213C2×C4×C13C2×#4111yescharacteristic
214C22⋊D13—42no—
215C22⋊D13—42no—
216C22⋊D13—44no—
217C2×Dic13—22no—
218C2×Dic13—42no—
219C2×Dic13—42no—
220C2×Dic13—82no—
221C2×Dic13—82no—
222C2×Dic13—82no—
223D52—22no—
224D52—22no—
225D52—42no—
226C4×D13—42no—
227C4×D13—42no—
228C4×D13—44no—
229Dic26—22no—
230Dic26—22no—
231Dic26—42no—
232C8×C13—42no—
233C8×C13—42no—
234#1055—24no—
235#1055—42no—
236C22×#41—131no—
237C22×M16—131no—
238C22×M16—131no—
239C22×M16C2×D1311yescharacteristic
240C22×M16C2×D1311yescharacteristic
241C2×#117C2×D1311yescharacteristic
242C22×C4⋊C4—131no—
243#428—262no—
244#428—262no—
245C2×#107—132no—
246C2×#106—132no—
247#419—261no—
248#418—261no—
249#417—134no—
250#417—132no—
251#417—132no—
252#417—262no—
253#416—262no—
254C2×#103—261no—
255C2×#102—261no—
256#408—134no—
257#408—262no—
258#407—262no—
259#343—134no—
260#343C2×D1312yescomplemented
261#343C2×D1312yescomplemented
262#341—134no—
263C22×C13—21no—
264C22×C13—21no—
265C22×C13—21no—
266C22×C13—21no—
267C22×C13—21no—
268C22×C13—21no—
269C22×C13—42no—
270C22×C13—42no—
271C22×C13#39712yes—
272C22×C13#39712yes—
273C22×C13C2×#12111yescharacteristic
274C22×C13C2×#12611yescharacteristic
275C22×C13C2×#12611yescharacteristic
276C2×D13—42no—
277C2×D13—42no—
278C2×D13—42no—
279C2×D13—84no—
280C4×C13—81no—
281C4×C13—81no—
282C4×C13#39712yes—
283C4×C13#39712yes—
284C4×C13C2×#12311yescharacteristic
285C4×C13C2×#12311yescharacteristic
286C4×C13C2×#12311yescharacteristic
287C4×C13C2×#12411yescharacteristic
288Dic13—42no—
289Dic13—82no—
290C2×#41—132no—
291C2×#41—132no—
292C2×#41—261no—
293C2×#41—261no—
294C2×#41—262no—
295C2×#41—262no—
296C2×#41—262no—
297C2×#41—262no—
298C22×Q8—131no—
299C22×D4—131no—
300C22×D4—261no—
301C23×C4—261no—
302C23×C4—261no—
303C23×C4C22×D1311yescharacteristic
304C2×M16—21no—
305C2×M16—21no—
306C2×M16—22no—
307C2×M16—22no—
308C2×M16—22no—
309C2×M16—22no—
310C2×M16—132no—
311C2×M16—132no—
312C2×M16—132no—
313C2×M16—262no—
314C2×M16—262no—
315C2×M16—261no—
316C2×M16—262no—
317C2×M16—262no—
318C2×M16C22×D1312yes—
319C2×M16C22×D1312yes—
320C22×C8—21no—
321C22×C8—21no—
322C22×C8—132no—
323C22×C8—261no—
324#117—21no—
325#117—21no—
326#117—21no—
327#117—21no—
328C2×C4⋊C4—132no—
329C2×C4⋊C4—261no—
330C2×C4⋊C4—261no—
331C2×C4⋊C4—261no—
332C2×C4⋊C4—261no—
333C2×C4⋊C4—261no—
334C2×C4⋊C4C22×D1311yescharacteristic
335C2×C4⋊C4C22×D1311yescharacteristic
336C2×C22⋊C4—21no—
337C2×C42—21no—
338#107—264no—
339#106—264no—
340#103—262no—
341#103—262no—
342#103—264no—
343#102—262no—
344#102—262no—
345#102—264no—
346C22⋊C8—268no—
347C2×C13—22no—
348C2×C13—21no—
349C2×C13—21no—
350C2×C13—22no—
351C2×C13C2×#39711yescharacteristic
352C2×C13#306811yescharacteristic
353C2×C13#306911yescharacteristic
354D13—82no—
355C24—261no—
356C24#612711yescharacteristic
357#41—264no—
358#41—264no—
359#41—262no—
360#41—262no—
361#41—262no—
362#41—262no—
363#41—522no—
364#41—522no—
365#41—522no—
366#41—522no—
367C2×Q8—132no—
368C2×Q8—261no—
369C2×Q8—262no—
370C2×Q8—262no—
371C2×D4—132no—
372C2×D4—262no—
373C2×D4—262no—
374C2×D4—262no—
375C2×D4—261no—
376C2×D4—262no—
377C2×D4—522no—
378C2×D4—522no—
379C22×C4—21no—
380C22×C4—21no—
381C22×C4—261no—
382C22×C4—262no—
383C22×C4—262no—
384C22×C4—262no—
385C22×C4—522no—
386C22×C4—522no—
387C22×C4—521no—
388C22×C4—521no—
389C22×C4—1042no—
390C22×C4#612711yescharacteristic
391C22×C4#612712yes—
392C22×C4#612712yes—
393C22×C4D4×D1311yescharacteristic
394C22×C4D4×D1311yescharacteristic
395C22×C4D4×D1311yescharacteristic
396C22×C4D4×D1311yescharacteristic
397C22×C4#612912yes—
398C22×C4#613112yes—
399C22×C4C23×D1311yescharacteristic
400M16—22no—
401M16—22no—
402M16—22no—
403M16—22no—
404M16—42no—
405M16—42no—
406M16—264no—
407M16—264no—
408M16—262no—
409M16—262no—
410M16—522no—
411C2×C8—22no—
412C2×C8—22no—
413C2×C8—42no—
414C2×C8—42no—
415C2×C8—134no—
416C2×C8—262no—
417C2×C8—262no—
418C2×C8—262no—
419C2×C8—522no—
420C4⋊C4—21no—
421C4⋊C4—21no—
422C4⋊C4—21no—
423C4⋊C4—21no—
424C4⋊C4—262no—
425C4⋊C4—262no—
426C4⋊C4—521no—
427C4⋊C4—521no—
428C22⋊C4—41no—
429C22⋊C4—41no—
430C42—41no—
431C42—41no—
432C13#2364711yescharacteristic, complemented, Sylow
433C23—41no—
434C23—41no—
435C23—262no—
436C23—522no—
437C23—1041no—
438C23—1041no—
439C23#8813012yes—
440C23#8813811yescharacteristic
441C23#8813811yescharacteristic
442C23#8815212yes—
443C23C2×#612711yescharacteristic
444Q8—262no—
445Q8—262no—
446Q8—522no—
447D4—262no—
448D4—262no—
449D4—522no—
450D4—522no—
451D4—524no—
452D4—522no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—81no—
456C2×C4—81no—
457C2×C4—262no—
458C2×C4—522no—
459C2×C4—522no—
460C2×C4—522no—
461C2×C4—524no—
462C2×C4—522no—
463C2×C4—1042no—
464C2×C4—1042no—
465C2×C4—1042no—
466C2×C4#8813012yes—
467C2×C4#8813712yes—
468C2×C4#8813712yes—
469C2×C4#8813811yescharacteristic
470C2×C4#8813811yescharacteristic
471C2×C4#8813912yes—
472C2×C4#8813912yes—
473C2×C4#8814812yes—
474C2×C4#8814812yes—
475C2×C4#8814812yes—
476C2×C4#8814812yes—
477C2×C4#8815212yes—
478C2×C4C2×#612711yescharacteristic
479C2×C4C2×#612711yescharacteristic
480C2×C4C2×D4×D1311yescharacteristic
481C2×C4C2×D4×D1311yescharacteristic
482C2×C4C2×#612911yescharacteristic
483C2×C4C2×#613111yescharacteristic
484C8—42no—
485C8—42no—
486C8—264no—
487C8—522no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—42no—
495C22—42no—
496C22—522no—
497C22—522no—
498C22—522no—
499C22—1044no—
500C22#1171833612yes—
501C22#1171833612yes—
502C22C2×#8813011yescharacteristic
503C22C2×#8813811yescharacteristic
504C22C2×#8815211yescharacteristic
505C4—81no—
506C4—81no—
507C4—522no—
508C4—1042no—
509C4#1171833612yes—
510C4#1171833612yes—
511C4C2×#8813711yescharacteristic
512C4C2×#8813911yescharacteristic
513C4C2×#8814811yescharacteristic
514C4C2×#8814811yescharacteristic
515C2—22no—
516C2—21no—
517C2—21no—
518C2—22no—
519C2—1042no—
520C2C2×#1171833611yescharacteristic
521C2#1312456711yescharacteristic
522C2#1312457611yescharacteristic
subgroupG/H
centerC22C2×#88138
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#1742C2
socleC22×C13C2×#121
prime radicalC22×#6127C22
hypercenter#1742D13
hypocenterC13#23647
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
1. C2×#11718656C2semidirect
5. #13116285C2semidirect
6. #13116280C2semidirect
7. C2×#11718146C2semidirect
8. #13114562C2semidirect
9. C13×#1742C2semidirect
31. C2×#88048C22semidirect
32. C2×#88047C22semidirect
33. C13×#343C22semidirect
34. C13×#343C22semidirect
35. #11718150C22semidirect
36. #11718146C22semidirect
178. #1742D13semidirect
260. #343C2×D13semidirect
261. #343C2×D13semidirect
432. C13#23647semidirect

Maximal subgroups

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

subgroupindex
C2×#117186562
#131233532
C2×#117187942
#131232802
#131162852
#131162802
C2×#117181462
#131145622
C13×#17422
#2364713