Finite Group Databasebeta

← #15836791

Subgroups — #15836791

Order 3328.

972 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13125608C211yesmaximal, characteristic, complemented
2#13125593C211yesmaximal, characteristic
3#13120649C211yesmaximal, characteristic, complemented
4#13113867C214yesmaximal, complemented
5#13113799C214yesmaximal, complemented
6#13113408C211yesmaximal, characteristic, complemented
7#13113404C211yesmaximal, characteristic
8C2×#11718120C211yesmaximal, characteristic, complemented
9C2×C13×#539C211yesmaximal, characteristic
10C13×#539—22no—
11C13×#539—22no—
12C13×#539—22no—
13C13×#539C2214yes—
14C2×C13×#126—21no—
15C2×C13×#125—21no—
16C2×C13×#123—21no—
17C2×C13×#123—21no—
18C2×C13×C22⋊Q8—21no—
19C2×C13×C22⋊Q8C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×C4×D4×C13—21no—
22C22×C13×C4⋊C4C2211yescharacteristic
23C2×#88178C2211yescharacteristic
24#11718889—21no—
25#11718879—21no—
26#11718873C2211yescharacteristic
27#11718872—21no—
28#11718871—21no—
29C2×C22⋊#1055C2211yescharacteristic
30C2×C22⋊#1055C2211yescharacteristic
31#11718712—22no—
32#11718711C2212yescomplemented
33#11718705C2212yescomplemented
34#11718702—22no—
35#11718701C2212yes—
36#11718695C2212yes—
37#11718647C2212yescomplemented
38#11718645—22no—
39#11718640C2212yescomplemented
40#11718632—21no—
41#11718631—21no—
42#11718130C2214yescomplemented
43#11718129C2214yes—
44#11718120C2214yescomplemented
45C22×Q8×C13D411yescharacteristic
46C22×D4×C13—21no—
47C22×D4×C13D411yescharacteristic
48C23×C4×C13—21no—
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C22×Dic26C2311yescharacteristic
53C13×#126—24no—
54C13×#126—24no—
55C13×#125—24no—
56C13×#125—24no—
57C13×#123—24no—
58C13×#123—24no—
59C13×#123—24no—
60C13×#123—24no—
61C13×C22⋊Q8—24no—
62C13×C22⋊Q8—24no—
63C13×C22⋊Q8—21no—
64C13×C22⋊Q8—21no—
65C13×C22⋊Q8D412yes—
66C13×C22⋊Q8C2312yes—
67C13×#121—21no—
68C13×#121—21no—
69C13×#121D412yes—
70C13×#121C2312yes—
71C4×D4×C13—24no—
72C4×D4×C13—24no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—21no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4—21no—
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4D412yes—
82C2×C13×C4⋊C4D411yescharacteristic
83C2×C13×C4⋊C4D411yescharacteristic
84C2×C13×C4⋊C4C2312yes—
85C2×C13×C22⋊C4—21no—
86C2×C13×C22⋊C4—21no—
87C2×C13×C22⋊C4—21no—
88C2×C13×C22⋊C4—21no—
89C2×C13×C22⋊C4—21no—
90C2×C42×C13—21no—
91C2×C22⋊Dic13—21no—
92C2×C22⋊Dic13—21no—
93C2×#6107—22no—
94C2×#6105—22no—
95C2×C4⋊Dic13—21no—
96C2×C4⋊Dic13C2311yescharacteristic
97#88178—21no—
98#88178—21no—
99#88178—21no—
100#88178—21no—
101C2×#6101—21no—
102C2×#6101—22no—
103C22×#1055—21no—
104C22×#1055—21no—
105#88075—22no—
106#88072—22no—
107#88071—22no—
108#88071—22no—
109#88071—22no—
110#88071C2312yes—
111C22⋊#1055—21no—
112C22⋊#1055—21no—
113C22⋊#1055C2312yes—
114C22⋊#1055C2312yes—
115#88050—22no—
116#88050—22no—
117#88048—22no—
118#88047—22no—
119#18289—131nomaximal, Sylow
120C24×C13—21no—
121C24×C13C2×D411yescharacteristic
122C2×Q8×C13—21no—
123C2×Q8×C13—81no—
124C2×Q8×C13C2×D412yes—
125C2×D4×C13—22no—
126C2×D4×C13—22no—
127C2×D4×C13—21no—
128C2×D4×C13—42no—
129C2×D4×C13—42no—
130C2×D4×C13—81no—
131C2×D4×C13C2×D412yes—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—24no—
141C22×C4×C13—21no—
142C22×C4×C13—81no—
143C22×C4×C13—81no—
144C22×C4×C13—82no—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2411yescharacteristic
153C22×Dic13—21no—
154C22×Dic13—22no—
155C22×Dic13—21no—
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—81no—
159C13×C4⋊C4—24no—
160C13×C4⋊C4—24no—
161C13×C4⋊C4—24no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—22no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—22no—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4C2×D412yes—
171C13×C4⋊C4C2×D412yes—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—24no—
174C13×C22⋊C4—24no—
175C13×C22⋊C4—22no—
176C13×C22⋊C4—22no—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C42×C13—24no—
180C22⋊Dic13—41no—
181C22⋊Dic13—41no—
182C22⋊Dic13—42no—
183#6107—82no—
184#6105—82no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—81no—
188#6101—41no—
189#6101—41no—
190#6101—82no—
191C2×#1055—22no—
192C2×#1055—22no—
193C2×#1055—81no—
194C2×#1055—81no—
195C2×#539D1311yescharacteristic
196#3189—131no—
197#3187—131no—
198#2627—131no—
199#1615—134no—
200#1603—134no—
201#1520—131no—
202#1519—131no—
203C2×#324—131no—
204C23×C13—22no—
205C23×C13—41no—
206C23×C13—41no—
207C23×C13—42no—
208C23×C13—42no—
209C23×C13—42no—
210C23×C13#12011yescharacteristic
211C23×C13#12011yescharacteristic
212C23×C13#13512yes—
213C23×C13#13712yes—
214C23×C13C22×D411yescharacteristic
215Q8×C13—42no—
216Q8×C13—81no—
217D4×C13—42no—
218D4×C13—42no—
219D4×C13—42no—
220D4×C13—44no—
221D4×C13—81no—
222C2×C4×C13—22no—
223C2×C4×C13—22no—
224C2×C4×C13—22no—
225C2×C4×C13—22no—
226C2×C4×C13—22no—
227C2×C4×C13—22no—
228C2×C4×C13—22no—
229C2×C4×C13—41no—
230C2×C4×C13—41no—
231C2×C4×C13—41no—
232C2×C4×C13—41no—
233C2×C4×C13—41no—
234C2×C4×C13—41no—
235C2×C4×C13—42no—
236C2×C4×C13—42no—
237C2×C4×C13—42no—
238C2×C4×C13—42no—
239C2×C4×C13—42no—
240C2×C4×C13—42no—
241C2×C4×C13—42no—
242C2×C4×C13—81no—
243C2×C4×C13—84no—
244C2×C4×C13#12011yescharacteristic
245C2×C4×C13#12011yescharacteristic
246C2×C4×C13C22×D411yescharacteristic
247C2×C4×C13C22×D411yescharacteristic
248C2×Dic13—42no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—41no—
253C2×Dic13—41no—
254C2×Dic13—42no—
255Dic26—42no—
256Dic26—42no—
257#1055—42no—
258#1055—42no—
259#539—22no—
260#539—22no—
261#539—22no—
262#539C2×D1314yes—
263C2×#126—21no—
264C2×#125—21no—
265C2×#123—21no—
266C2×#123—21no—
267C2×C22⋊Q8—21no—
268C2×C22⋊Q8—131no—
269C2×C22⋊Q8C2×D1311yescharacteristic
270C2×#121C2×D1311yescharacteristic
271C2×C4×D4—21no—
272C22×C4⋊C4C2×D1311yescharacteristic
273#484—132no—
274#484—261no—
275#483—261no—
276#481—132no—
277#467—262no—
278#465—262no—
279#451—132no—
280#451—261no—
281#450—261no—
282#448—132no—
283C2×C22⋊C8—131no—
284C2×C22⋊C8—131no—
285#400—132no—
286#398—262no—
287#395—132no—
288#385—261no—
289#381—261no—
290#380—131no—
291#328—134no—
292#327—134no—
293#324—134no—
294C22×C13—21no—
295C22×C13—21no—
296C22×C13—21no—
297C22×C13—21no—
298C22×C13—21no—
299C22×C13—21no—
300C22×C13—42no—
301C22×C13—42no—
302C22×C13—42no—
303C22×C13—42no—
304C22×C13—42no—
305C22×C13—84no—
306C22×C13#45212yes—
307C22×C13#45212yes—
308C22×C13C2×#12011yescharacteristic
309C22×C13C2×#13511yescharacteristic
310C22×C13C2×#13711yescharacteristic
311C4×C13—21no—
312C4×C13—21no—
313C4×C13—21no—
314C4×C13—21no—
315C4×C13—42no—
316C4×C13—42no—
317C4×C13—42no—
318C4×C13—42no—
319C4×C13—42no—
320Dic13—82no—
321Dic13—81no—
322Dic13—81no—
323C22×Q8—131no—
324C22×Q8C22⋊D1311yescharacteristic
325C22×D4—21no—
326C22×D4C22⋊D1311yescharacteristic
327C23×C4—21no—
328C23×C4C22⋊D1311yescharacteristic
329C23×C4C22⋊D1311yescharacteristic
330C23×C4C22×D1311yescharacteristic
331C2×Q16—262no—
332C2×SD16—262no—
333C22×C8—261no—
334C22×C8—261no—
335#126—24no—
336#126—24no—
337#125—24no—
338#125—24no—
339#123—24no—
340#123—24no—
341#123—24no—
342#123—24no—
343C22⋊Q8—24no—
344C22⋊Q8—24no—
345C22⋊Q8—21no—
346C22⋊Q8—21no—
347C22⋊Q8—261no—
348C22⋊Q8—261no—
349C22⋊Q8—261no—
350C22⋊Q8—261no—
351C22⋊Q8C22⋊D1312yes—
352C22⋊Q8C22×D1312yes—
353#121—21no—
354#121—21no—
355#121C22⋊D1312yes—
356#121C22×D1312yes—
357C4×D4—24no—
358C4×D4—24no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—131no—
368C2×C4⋊C4—261no—
369C2×C4⋊C4—262no—
370C2×C4⋊C4—261no—
371C2×C4⋊C4C22⋊D1312yes—
372C2×C4⋊C4C22⋊D1311yescharacteristic
373C2×C4⋊C4C22⋊D1311yescharacteristic
374C2×C4⋊C4C22×D1312yes—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—261no—
381C2×C22⋊C4—261no—
382C2×C42—21no—
383#107—262no—
384#106—262no—
385#103—262no—
386#103—262no—
387#103—262no—
388#102—262no—
389C22⋊C8—132no—
390C22⋊C8—132no—
391C22⋊C8—261no—
392C22⋊C8—261no—
393#95—132no—
394#95—262no—
395#95—262no—
396#95—262no—
397C2×C13—21no—
398C2×C13—22no—
399C2×C13—21no—
400C2×C13—22no—
401C2×C13—82no—
402C2×C13C2×#45211yescharacteristic
403C2×C13#302011yescharacteristic
404C2×C13#302611yescharacteristic
405C24—21no—
406C24C2×C22⋊D1311yescharacteristic
407C2×Q8—21no—
408C2×Q8—81no—
409C2×Q8—261no—
410C2×Q8—261no—
411C2×Q8—1041no—
412C2×Q8C2×C22⋊D1312yes—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—42no—
417C2×D4—42no—
418C2×D4—81no—
419C2×D4C2×C22⋊D1312yes—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—21no—
430C22×C4—81no—
431C22×C4—81no—
432C22×C4—82no—
433C22×C4—262no—
434C22×C4—261no—
435C22×C4—261no—
436C22×C4C2×C22⋊D1312yes—
437C22×C4C2×C22⋊D1312yes—
438C22×C4C2×C22⋊D1311yescharacteristic
439C22×C4C2×C22⋊D1311yescharacteristic
440C22×C4C2×C22⋊D1311yescharacteristic
441C22×C4C2×C22⋊D1311yescharacteristic
442C22×C4C2×C22⋊D1311yescharacteristic
443C22×C4C23×D1311yescharacteristic
444Q16—1042no—
445SD16—1042no—
446C2×C8—262no—
447C2×C8—262no—
448C2×C8—1041no—
449C2×C8—1041no—
450C4⋊C4—24no—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—22no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—22no—
460C4⋊C4—22no—
461C4⋊C4—261no—
462C4⋊C4—261no—
463C4⋊C4—521no—
464C4⋊C4—521no—
465C4⋊C4—1042no—
466C4⋊C4—1041no—
467C4⋊C4C2×C22⋊D1312yes—
468C4⋊C4C2×C22⋊D1312yes—
469C22⋊C4—24no—
470C22⋊C4—24no—
471C22⋊C4—24no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—522no—
477C22⋊C4—521no—
478C22⋊C4—521no—
479C42—24no—
480C13#1828911yescharacteristic, complemented, Sylow
481C23—22no—
482C23—41no—
483C23—41no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23#8820412yes—
488C23#8820512yes—
489C23#8820711yescharacteristic
490C23#8820711yescharacteristic
491C23C22×C22⋊D1311yescharacteristic
492Q8—42no—
493Q8—81no—
494Q8—522no—
495Q8—522no—
496D4—42no—
497D4—42no—
498D4—42no—
499D4—44no—
500D4—81no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—81no—
522C2×C4—84no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—521no—
529C2×C4—521no—
530C2×C4#8820711yescharacteristic
531C2×C4#8820711yescharacteristic
532C2×C4C22×C22⋊D1311yescharacteristic
533C2×C4C22×C22⋊D1311yescharacteristic
534C8—522no—
535C8—522no—
536C22—21no—
537C22—21no—
538C22—21no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—42no—
543C22—42no—
544C22—42no—
545C22—42no—
546C22—42no—
547C22—84no—
548C22#1171890012yes—
549C22#1171890012yes—
550C22C2×#8820411yescharacteristic
551C22C2×#8820511yescharacteristic
552C22C2×#8820711yescharacteristic
553C4—21no—
554C4—21no—
555C4—21no—
556C4—21no—
557C4—42no—
558C4—42no—
559C4—42no—
560C4—42no—
561C4—42no—
562C4—1042no—
563C4—1041no—
564C4—1041no—
565C2—21no—
566C2—22no—
567C2—21no—
568C2—22no—
569C2—82no—
570C2C2×#1171890011yescharacteristic
571C2#1312420011yescharacteristic
572C2#1312423311yescharacteristic
subgroupG/H
centerC22C2×#88207
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#539C2
socleC22×C13C2×#120
prime radicalC2×C13×#121C22
hypercenterC2×#539D13
hypocenterC13#18289
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #13125608C2semidirect
3. #13120649C2semidirect
4. #13113867C2semidirect
5. #13113799C2semidirect
6. #13113408C2semidirect
8. C2×#11718120C2semidirect
32. #11718711C22semidirect
33. #11718705C22semidirect
37. #11718647C22semidirect
39. #11718640C22semidirect
42. #11718130C22semidirect
44. #11718120C22semidirect
480. C13#18289semidirect

Maximal subgroups

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

subgroupindex
#131256082
#131255932
#131206492
#131138672
#131137992
#131134082
#131134042
C2×#117181202
C2×C13×#5392
#1828913