Finite Group Databasebeta

← #15862612

Subgroups — #15862612

Order 3328.

1330 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719450C211yesmaximal, characteristic
2C2×#11718785C211yesmaximal, characteristic, complemented
3C2×#11718656C211yesmaximal, characteristic, complemented
4#13123353C211yesmaximal, characteristic
5C2×#11718794C211yesmaximal, characteristic
6#13114899C214yesmaximal, complemented
7#13114894C214yesmaximal, complemented
8C2×#11718146C211yesmaximal, 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#11719450—24no—
18#11719450C418yescomplemented
19C2×#88161C2214yes—
20C2×M16×D13—22no—
21C2×#88155—22no—
22#11718794—22no—
23#11718794C2214yes—
24#11718785—24no—
25C2×#88062C2214yescomplemented
26C2×#88061—21no—
27C2×#88056—21no—
28#11718665—21no—
29#11718663—22no—
30#11718662—21no—
31#11718656—22no—
32#11718656—22no—
33#11718627C2212yes—
34#11718627C2212yes—
35C2×#88048C2212yescomplemented
36C2×#88047C2212yescomplemented
37C13×#343C2212yescomplemented
38C13×#343C2212yescomplemented
39#11718146C2214yescomplemented
40C23×C4×C13C2311yescharacteristic
41C22×C22⋊D13—21no—
42C23×Dic13—21no—
43C2×#6127—21no—
44C2×#6127—22no—
45C2×#6127—21no—
46C2×#6127—22no—
47C2×#6127C2×C414yes—
48C2×#6127D412yes—
49C2×#6127Q814yes—
50C2×#6127C2312yes—
51C22×D52D411yescharacteristic
52C22×C4×D13—21no—
53C22×Dic26D411yescharacteristic
54C2×C13×M16—21no—
55C2×C13×M16—22no—
56C2×C13×M16—21no—
57C2×C13×M16—22no—
58C2×C13×M16—22no—
59C2×C13×M16C2×C414yes—
60C2×C13×M16C2312yes—
61C2×C13×M16C2312yes—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C13×#117—21no—
65C13×#117—21no—
66C13×#117—21no—
67C13×#117—21no—
68C2×C13×C4⋊C4C2311yescharacteristic
69C2×C13×C4⋊C4C2311yescharacteristic
70C2×C13×C22⋊C4—21no—
71C2×C42×C13—21no—
72C2×C4⋊Dic13—21no—
73C2×C4⋊Dic13—21no—
74C2×C4⋊Dic13—21no—
75C2×C4⋊Dic13—21no—
76C2×C4⋊Dic13—21no—
77C2×C4⋊Dic13C2312yes—
78C2×#6099—21no—
79C2×#6099—22no—
80C2×#6099—22no—
81C2×#6099C2×C414yes—
82C2×#6099D412yes—
83C2×#6099D412yes—
84C2×#6099D414yes—
85C2×#6099C2312yes—
86C22×#1055—21no—
87C22×#1055C2312yes—
88#88161—28no—
89#88161C2×C4116yescomplemented
90M16×D13—216no—
91#88155—216no—
92C2×#6094—24no—
93C2×C8×D13—24no—
94#88062—28no—
95#88061—24no—
96#88056—24no—
97#88050—22no—
98#88050—22no—
99#88049—22no—
100#88049—22no—
101#88048—24no—
102#88047—24no—
103#20679—131nomaximal, Sylow
104C24×C13#4111yescharacteristic
105C23×D13—21no—
106C22×C4×C13—21no—
107C22×C4×C13—21no—
108C22×C4×C13C22×C412yes—
109C22×C4×C13C2×D412yes—
110C22×C4×C13C2×D411yescharacteristic
111C22×C4×C13C2×D411yescharacteristic
112C22×C4×C13C2×D411yescharacteristic
113C22×C4×C13C2×D411yescharacteristic
114C22×C4×C13C2×Q812yes—
115C22×C4×C13#4111yescharacteristic
116C22×C4×C13#4112yes—
117C22×C4×C13C2411yescharacteristic
118C2×C22⋊D13—24no—
119C2×C22⋊D13—22no—
120C2×C22⋊D13—24no—
121C2×C22⋊D13—22no—
122C22×Dic13—21no—
123C22×Dic13—22no—
124C22×Dic13—41no—
125C22×Dic13—41no—
126C22×Dic13—82no—
127#6127—24no—
128#6127—24no—
129#6127—24no—
130#6127—24no—
131#6127—24no—
132#6127—22no—
133#6127—22no—
134#6127C4⋊C418yes—
135#6127C22×C414yes—
136#6127C2×Q814yes—
137C2×D52—22no—
138C2×D52—21no—
139C2×D52C4⋊C414yes—
140C2×D52C2×D412yes—
141C2×C4×D13—24no—
142C2×C4×D13—22no—
143C2×C4×D13—24no—
144C2×C4×D13—22no—
145C2×Dic26—22no—
146C2×Dic26—21no—
147C2×Dic26C4⋊C414yes—
148C2×Dic26C2×D412yes—
149C13×M16—24no—
150C13×M16—22no—
151C13×M16—22no—
152C13×M16—22no—
153C13×M16—42no—
154C13×M16C22×C414yes—
155C2×C8×C13—24no—
156C2×C8×C13—22no—
157C2×C8×C13—22no—
158C2×C8×C13—42no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C22⋊C4—41no—
164C13×C22⋊C4—41no—
165C42×C13—41no—
166C42×C13—41no—
167C4⋊Dic13—22no—
168C4⋊Dic13—22no—
169C4⋊Dic13—41no—
170C4⋊Dic13—41no—
171#6099—22no—
172#6099—22no—
173#6099—42no—
174#6099C22⋊C418yes—
175#6099C22⋊C418yes—
176C2×#1055—22no—
177C2×#1055—42no—
178C2×#1055C22×C414yes—
179C2×#1055C2×D414yes—
180C2×#1055C2×D414yes—
181#6094—216no—
182C8×D13—216no—
183C2×#568—131no—
184C2×#430—131no—
185C2×#428—131no—
186#2896—131no—
187C2×#417—131no—
188#1816—134no—
189#1815—134no—
190#1742D1311yescharacteristic, complemented
191C2×#343—131no—
192C23×C13—41no—
193C23×C13—41no—
194C23×C13#11712yes—
195C23×C13#12111yescharacteristic
196C23×C13#12111yescharacteristic
197C23×C13C22⋊Q812yes—
198C23×C13C2×#4111yescharacteristic
199C22×D13—22no—
200C22×D13—24no—
201C22×D13—81no—
202C22×D13—81no—
203C2×C4×C13—41no—
204C2×C4×C13—41no—
205C2×C4×C13—81no—
206C2×C4×C13—81no—
207C2×C4×C13C2×C22⋊C412yes—
208C2×C4×C13C2×C22⋊C412yes—
209C2×C4×C13C2×C4⋊C412yes—
210C2×C4×C13C2×C4⋊C412yes—
211C2×C4×C13#11712yes—
212C2×C4×C13#12112yes—
213C2×C4×C13#12112yes—
214C2×C4×C13#12111yescharacteristic
215C2×C4×C13#12111yescharacteristic
216C2×C4×C13C22⋊Q812yes—
217C2×C4×C13C22⋊Q812yes—
218C2×C4×C13C22⋊Q812yes—
219C2×C4×C13C23×C411yescharacteristic
220C2×C4×C13C22×D411yescharacteristic
221C2×C4×C13C22×D411yescharacteristic
222C2×C4×C13C22×D411yescharacteristic
223C2×C4×C13C22×Q811yescharacteristic
224C2×C4×C13C2×#4111yescharacteristic
225C22⋊D13—24no—
226C22⋊D13—24no—
227C22⋊D13—28no—
228C2×Dic13—22no—
229C2×Dic13—24no—
230C2×Dic13—42no—
231C2×Dic13—82no—
232C2×Dic13—82no—
233C2×Dic13—82no—
234D52—22no—
235D52—24no—
236D52C2×C4⋊C414yes—
237C4×D13—24no—
238C4×D13—24no—
239C4×D13—28no—
240Dic26—22no—
241Dic26—24no—
242Dic26C2×C4⋊C414yes—
243C8×C13—24no—
244C8×C13—42no—
245#1055—42no—
246#1055C2×C22⋊C418yes—
247C22×#41—131no—
248#568—138no—
249#568—264no—
250C2×#131—134no—
251C2×#131—262no—
252C22×M16—131no—
253C22×M16—131no—
254C22×M16—262no—
255C22×M16C2×D1311yescharacteristic
256C22×M16C2×D1311yescharacteristic
257C2×#117C2×D1311yescharacteristic
258C22×C4⋊C4—131no—
259#430—264no—
260C2×#108—134no—
261#428—262no—
262#428—262no—
263C2×#107—132no—
264C2×#106—132no—
265#419—261no—
266#418—261no—
267#417—134no—
268#417—132no—
269#417—132no—
270#417—262no—
271#416—262no—
272C2×#103—261no—
273C2×#102—261no—
274#343—134no—
275#343C2×D1312yescomplemented
276#343C2×D1312yescomplemented
277C22×C13—21no—
278C22×C13—21no—
279C22×C13—21no—
280C22×C13—21no—
281C22×C13—21no—
282C22×C13—21no—
283C22×C13—42no—
284C22×C13—42no—
285C22×C13#38012yes—
286C22×C13#38012yes—
287C22×C13C2×#11711yescharacteristic
288C22×C13C2×#12111yescharacteristic
289C22×C13C2×C22⋊Q811yescharacteristic
290C2×D13—24no—
291C2×D13—42no—
292C2×D13—42no—
293C2×D13—84no—
294C4×C13—81no—
295C4×C13—81no—
296C4×C13#38012yes—
297C4×C13#38012yes—
298C4×C13C22×C22⋊C411yescharacteristic
299C4×C13C22×C4⋊C411yescharacteristic
300C4×C13C2×#12111yescharacteristic
301C4×C13C2×C22⋊Q811yescharacteristic
302Dic13—24no—
303Dic13—82no—
304C2×#41—134no—
305C2×#41—132no—
306C2×#41—134no—
307C2×#41—132no—
308C2×#41—261no—
309C2×#41—262no—
310C2×#41—261no—
311C2×#41—262no—
312C22×Q8—131no—
313C22×D4—131no—
314C22×D4—261no—
315C23×C4—261no—
316C23×C4—261no—
317C23×C4C22×D1311yescharacteristic
318#131—1316no—
319#131—2616no—
320#131—268no—
321C2×M16—21no—
322C2×M16—22no—
323C2×M16—21no—
324C2×M16—22no—
325C2×M16—22no—
326C2×M16—134no—
327C2×M16—132no—
328C2×M16—132no—
329C2×M16—134no—
330C2×M16—132no—
331C2×M16—264no—
332C2×M16—2616no—
333C2×M16—261no—
334C2×M16—262no—
335C2×M16—262no—
336C2×M16C4×D1314yes—
337C2×M16C22×D1312yes—
338C2×M16C22×D1312yes—
339C22×C8—21no—
340C22×C8—21no—
341C22×C8—132no—
342C22×C8—264no—
343C22×C8—261no—
344#117—21no—
345#117—21no—
346#117—21no—
347#117—21no—
348C2×C4⋊C4—132no—
349C2×C4⋊C4—261no—
350C2×C4⋊C4—261no—
351C2×C4⋊C4—261no—
352C2×C4⋊C4—261no—
353C2×C4⋊C4—261no—
354C2×C4⋊C4C22×D1311yescharacteristic
355C2×C4⋊C4C22×D1311yescharacteristic
356C2×C22⋊C4—21no—
357C2×C42—21no—
358#108—268no—
359#107—264no—
360#106—264no—
361#103—262no—
362#103—262no—
363#103—264no—
364#102—262no—
365#102—262no—
366#102—264no—
367C2×C13—22no—
368C2×C13—21no—
369C2×C13—21no—
370C2×C13—22no—
371C2×C13C2×#38011yescharacteristic
372C2×C13#306811yescharacteristic
373C2×C13#306911yescharacteristic
374D13—44no—
375C24—261no—
376C24#612711yescharacteristic
377#41—138no—
378#41—134no—
379#41—134no—
380#41—264no—
381#41—264no—
382#41—264no—
383#41—264no—
384#41—264no—
385#41—262no—
386#41—262no—
387C2×Q8—134no—
388C2×Q8—132no—
389C2×Q8—261no—
390C2×Q8—262no—
391C2×D4—134no—
392C2×D4—132no—
393C2×D4—264no—
394C2×D4—262no—
395C2×D4—264no—
396C2×D4—262no—
397C2×D4—262no—
398C2×D4—261no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—261no—
402C22×C4—264no—
403C22×C4—262no—
404C22×C4—264no—
405C22×C4—262no—
406C22×C4—262no—
407C22×C4—521no—
408C22×C4—521no—
409C22×C4—1042no—
410C22×C4C2×C4×D1312yes—
411C22×C4#612711yescharacteristic
412C22×C4#612712yes—
413C22×C4D4×D1312yes—
414C22×C4D4×D1311yescharacteristic
415C22×C4D4×D1311yescharacteristic
416C22×C4D4×D1311yescharacteristic
417C22×C4D4×D1311yescharacteristic
418C22×C4Q8×D1312yes—
419C22×C4C23×D1311yescharacteristic
420M16—24no—
421M16—22no—
422M16—22no—
423M16—22no—
424M16—42no—
425M16—138no—
426M16—138no—
427M16—2616no—
428M16—262no—
429M16—262no—
430M16—522no—
431M16C2×C4×D1314yes—
432C2×C8—24no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—42no—
436C2×C8—134no—
437C2×C8—134no—
438C2×C8—134no—
439C2×C8—2616no—
440C2×C8—262no—
441C2×C8—522no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—262no—
447C4⋊C4—262no—
448C4⋊C4—521no—
449C4⋊C4—521no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C42—41no—
453C42—41no—
454C13#2067911yescharacteristic, complemented, Sylow
455C23—41no—
456C23—41no—
457C23—262no—
458C23—264no—
459C23—1041no—
460C23—1041no—
461C23#8812612yes—
462C23#8813811yescharacteristic
463C23#8813811yescharacteristic
464C23#8815012yes—
465C23C2×#612711yescharacteristic
466Q8—134no—
467Q8—262no—
468Q8—264no—
469D4—134no—
470D4—264no—
471D4—264no—
472D4—268no—
473D4—262no—
474D4—264no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—81no—
478C2×C4—81no—
479C2×C4—262no—
480C2×C4—264no—
481C2×C4—264no—
482C2×C4—264no—
483C2×C4—268no—
484C2×C4—522no—
485C2×C4—1042no—
486C2×C4—1042no—
487C2×C4—1042no—
488C2×C4#8812612yes—
489C2×C4C22⋊C4×D1312yes—
490C2×C4C22⋊C4×D1312yes—
491C2×C4#8813812yes—
492C2×C4#8813812yes—
493C2×C4#8813811yescharacteristic
494C2×C4#8813811yescharacteristic
495C2×C4C4⋊C4×D1312yes—
496C2×C4C4⋊C4×D1312yes—
497C2×C4#8815012yes—
498C2×C4#8815012yes—
499C2×C4#8815012yes—
500C2×C4C22×C4×D1311yescharacteristic
501C2×C4C2×#612711yescharacteristic
502C2×C4C2×D4×D1311yescharacteristic
503C2×C4C2×D4×D1311yescharacteristic
504C2×C4C2×D4×D1311yescharacteristic
505C2×C4C2×Q8×D1311yescharacteristic
506C8—24no—
507C8—42no—
508C8—138no—
509C8—522no—
510C22—21no—
511C22—21no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—42no—
517C22—42no—
518C22—264no—
519C22—522no—
520C22—522no—
521C22—1044no—
522C22#1171832812yes—
523C22#1171832812yes—
524C22C2×#8812611yescharacteristic
525C22C2×#8813811yescharacteristic
526C22C2×#8815011yescharacteristic
527C4—81no—
528C4—81no—
529C4—264no—
530C4—1042no—
531C4#1171832812yes—
532C4#1171832812yes—
533C4C2×C22⋊C4×D1311yescharacteristic
534C4C2×#8813811yescharacteristic
535C4C2×C4⋊C4×D1311yescharacteristic
536C4C2×#8815011yescharacteristic
537C2—22no—
538C2—21no—
539C2—21no—
540C2—22no—
541C2—524no—
542C2C2×#1171832811yescharacteristic
543C2#1312456711yescharacteristic
544C2#1312457611yescharacteristic
subgroupG/H
centerC22C2×#88138
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1742C2
socleC22×C13C2×#121
prime radicalC22×#6127C22
cosocleC22×C4×C13C24
hypercenter#1742D13
hypocenterC13#20679
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1742

Complements

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

NH ≅ G/Ntype
2. C2×#11718785C2semidirect
3. C2×#11718656C2semidirect
6. #13114899C2semidirect
7. #13114894C2semidirect
8. C2×#11718146C2semidirect
9. C13×#1742C2semidirect
18. #11719450C4semidirect
25. C2×#88062C22semidirect
35. C2×#88048C22semidirect
36. C2×#88047C22semidirect
37. C13×#343C22semidirect
38. C13×#343C22semidirect
39. #11718146C22semidirect
89. #88161C2×C4semidirect
190. #1742D13semidirect
275. #343C2×D13semidirect
276. #343C2×D13semidirect
454. C13#20679semidirect

Maximal subgroups

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

subgroupindex
C2×#117194502
C2×#117187852
C2×#117186562
#131233532
C2×#117187942
#131148992
#131148942
C2×#117181462
C13×#17422
#2067913