Finite Group Databasebeta

← #15770376

Subgroups — #15770376

Order 3328.

852 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718785C211yesmaximal, characteristic, complemented
2C2×#11718666C211yesmaximal, characteristic
3#13123353C211yesmaximal, characteristic
4#13123280C211yesmaximal, characteristic
5C2×#11718125C211yesmaximal, characteristic, complemented
6C2×#11718125C211yesmaximal, characteristic, complemented
7C13×#1733C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C2×C13×#117C2211yescharacteristic
11C2×C13×#117C2211yescharacteristic
12C22×#6099C2211yescharacteristic
13C22×#6099C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718790—22no—
16#11718787—22no—
17#11718785—22no—
18#11718785—22no—
19C2×#88062—22no—
20#11718771—22no—
21#11718666—22no—
22#11718666—22no—
23#11718665C412yescomplemented
24#11718663—22no—
25#11718662C412yescomplemented
26#11718627—22no—
27C2×#88045—22no—
28C13×#339—22no—
29#11718125—22no—
30#11718125—22no—
31C23×C4×C13C2311yescharacteristic
32C22×C22⋊D13—21no—
33C2×#6127—21no—
34C2×#6127—21no—
35C2×#6127—21no—
36C2×#6127—21no—
37C2×#6127—21no—
38C2×#6127—21no—
39C2×#6127—21no—
40C2×#6127—21no—
41C2×#6127—21no—
42C2×#6127—21no—
43C2×#6127D412yes—
44C2×#6127Q812yes—
45C22×D52C2×C411yescharacteristic
46C22×C4×D13—21no—
47C22×Dic26C2×C411yescharacteristic
48C2×C13×M16—21no—
49C2×C13×M16—21no—
50C2×C13×M16—21no—
51C2×C13×M16—21no—
52C2×C13×M16—21no—
53C2×C13×M16D412yes—
54C22×C8×C13—21no—
55C13×#117—21no—
56C13×#117—21no—
57C13×#117—21no—
58C13×#117—21no—
59C13×#117—21no—
60C13×#117—21no—
61C13×#117C2×C412yes—
62C13×#117D412yes—
63C2×C13×C4⋊C4—21no—
64C2×C13×C4⋊C4—21no—
65C2×C13×C22⋊C4—21no—
66C2×C13×C22⋊C4—21no—
67C2×C42×C13—21no—
68C2×C42×C13—21no—
69C2×#6099—21no—
70C2×#6099—21no—
71C2×#6099—21no—
72C2×#6099—21no—
73C2×#6099—21no—
74C2×#6099—21no—
75C2×#6099—21no—
76C2×#6099—21no—
77C2×#6099—21no—
78C2×#6099—21no—
79C2×#6099—21no—
80C2×#6099—21no—
81C2×#6099—21no—
82C2×#6099—21no—
83C2×#6099C2×C412yes—
84C2×#6099D412yes—
85C2×#6099D412yes—
86C2×#6099D412yes—
87C22×#1055—21no—
88C22×#1055—21no—
89C22×#1055D412yes—
90#88062—28no—
91#88060—28no—
92#88050—24no—
93#88049—24no—
94#88045—28no—
95#11131—131nomaximal, Sylow
96C24×C13#4111yescharacteristic
97C23×D13—21no—
98C22×C4×C13—41no—
99C22×C4×C13—41no—
100C22×C4×C13C22×C411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13C2×D411yescharacteristic
105C22×C4×C13C2×D411yescharacteristic
106C22×C4×C13C2×D411yescharacteristic
107C22×C4×C13C2×D411yescharacteristic
108C22×C4×C13C2×Q811yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C22×C4×C13#4111yescharacteristic
114C2×C22⋊D13—22no—
115C2×C22⋊D13—22no—
116C2×C22⋊D13—41no—
117C2×C22⋊D13—41no—
118C2×C22⋊D13—41no—
119C2×C22⋊D13—41no—
120C22×Dic13—21no—
121#6127—22no—
122#6127—22no—
123#6127—22no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—22no—
129#6127—41no—
130#6127—41no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136#6127—41no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52C4⋊C412yes—
143C2×C4×D13—22no—
144C2×C4×D13—22no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13—41no—
148C2×C4×D13—41no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26C4⋊C412yes—
155C13×M16—22no—
156C13×M16—22no—
157C13×M16—41no—
158C13×M16—41no—
159C2×C8×C13—22no—
160C2×C8×C13—41no—
161C2×C8×C13—41no—
162C13×C4⋊C4—22no—
163C13×C4⋊C4—22no—
164C13×C4⋊C4—41no—
165C13×C4⋊C4—41no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—22no—
168C13×C22⋊C4—41no—
169C13×C22⋊C4—41no—
170C42×C13—22no—
171C42×C13—22no—
172C42×C13—41no—
173C42×C13—41no—
174#6099—22no—
175#6099—22no—
176#6099—22no—
177#6099—22no—
178#6099—22no—
179#6099—22no—
180#6099—22no—
181#6099—22no—
182#6099—41no—
183#6099—41no—
184#6099—41no—
185#6099—41no—
186C2×#1055—22no—
187C2×#1055—22no—
188C2×#1055—22no—
189C2×#1055—22no—
190C2×#1055—41no—
191C2×#1055—41no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#1055C22⋊C414yes—
195C2×#430—131no—
196C2×#421—131no—
197#2896—131no—
198#2879—131no—
199C2×#344—131no—
200C2×#344—131no—
201#1733D1311yescharacteristic, complemented
202C23×C13—81no—
203C23×C13C4×D411yescharacteristic
204C23×C13#12111yescharacteristic
205C23×C13C22⋊Q811yescharacteristic
206C23×C13#12311yescharacteristic
207C23×C13#12411yescharacteristic
208C23×C13#12411yescharacteristic
209C23×C13#12611yescharacteristic
210C22×D13—22no—
211C22×D13—41no—
212C22×D13—41no—
213C22×D13—82no—
214C2×C4×C13—42no—
215C2×C4×C13—42no—
216C2×C4×C13—82no—
217C2×C4×C13—82no—
218C2×C4×C13C2×C22⋊C411yescharacteristic
219C2×C4×C13C2×C4⋊C411yescharacteristic
220C2×C4×C13#11711yescharacteristic
221C2×C4×C13C4×D411yescharacteristic
222C2×C4×C13C4×D411yescharacteristic
223C2×C4×C13C4×D411yescharacteristic
224C2×C4×C13#12011yescharacteristic
225C2×C4×C13#12011yescharacteristic
226C2×C4×C13#12011yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13#12111yescharacteristic
230C2×C4×C13#12111yescharacteristic
231C2×C4×C13#12111yescharacteristic
232C2×C4×C13#12111yescharacteristic
233C2×C4×C13#12111yescharacteristic
234C2×C4×C13C22⋊Q811yescharacteristic
235C2×C4×C13C22⋊Q811yescharacteristic
236C2×C4×C13C22⋊Q811yescharacteristic
237C2×C4×C13C22⋊Q811yescharacteristic
238C2×C4×C13C22⋊Q811yescharacteristic
239C2×C4×C13#12311yescharacteristic
240C2×C4×C13#12311yescharacteristic
241C2×C4×C13#12311yescharacteristic
242C2×C4×C13#12311yescharacteristic
243C2×C4×C13#12411yescharacteristic
244C2×C4×C13#12611yescharacteristic
245C2×C4×C13#12711yescharacteristic
246C22⋊D13—42no—
247C22⋊D13—42no—
248C22⋊D13—42no—
249C22⋊D13—42no—
250C2×Dic13—22no—
251C2×Dic13—41no—
252C2×Dic13—41no—
253D52—22no—
254D52—22no—
255D52—41no—
256D52—41no—
257C4×D13—42no—
258C4×D13—42no—
259C4×D13—42no—
260C4×D13—42no—
261Dic26—22no—
262Dic26—22no—
263Dic26—41no—
264Dic26—41no—
265C8×C13—42no—
266#1055—24no—
267#1055—42no—
268#1055—42no—
269C22×#41—131no—
270C22×M16—131no—
271C22×M16—131no—
272C22×M16—131no—
273C22×M16C2×D1311yescharacteristic
274C2×#117C2×D1311yescharacteristic
275C2×#117C2×D1311yescharacteristic
276#430—262no—
277#430—262no—
278C2×#108—262no—
279#421—262no—
280#421—262no—
281C2×#104—262no—
282#419—132no—
283#418—132no—
284#417—262no—
285#416—262no—
286#408—262no—
287#408—262no—
288#407—262no—
289#344—262no—
290#344—262no—
291#339—22no—
292C22×C13—41no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13#38511yescharacteristic
300C22×C13#38811yescharacteristic
301C22×C13#39011yescharacteristic
302C22×C13#39311yescharacteristic
303C22×C13#39411yescharacteristic
304C22×C13#39611yescharacteristic
305C22×C13#39711yescharacteristic
306C2×D13—44no—
307C2×D13—42no—
308C2×D13—82no—
309C2×D13—82no—
310C4×C13—82no—
311C4×C13—82no—
312C4×C13#38011yescharacteristic
313C4×C13#38511yescharacteristic
314C4×C13#38611yescharacteristic
315C4×C13#38811yescharacteristic
316C4×C13#39211yescharacteristic
317C4×C13#39411yescharacteristic
318C4×C13#39611yescharacteristic
319C4×C13#39911yescharacteristic
320Dic13—42no—
321C2×#41—132no—
322C2×#41—132no—
323C2×#41—261no—
324C2×#41—261no—
325C2×#41—261no—
326C2×#41—261no—
327C2×#41—261no—
328C2×#41—261no—
329C2×#41—261no—
330C2×#41—261no—
331C2×#41—261no—
332C2×#41—261no—
333C22×Q8—131no—
334C22×D4—131no—
335C22×D4—261no—
336C23×C4—261no—
337C23×C4C22×D1311yescharacteristic
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—132no—
344C2×M16—132no—
345C2×M16—132no—
346C2×M16—132no—
347C2×M16—261no—
348C2×M16—261no—
349C2×M16—261no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16—261no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16—261no—
359C2×M16—261no—
360C2×M16—261no—
361C2×M16D5212yes—
362C22×C8—21no—
363C22×C8—132no—
364C22×C8—261no—
365C22×C8—261no—
366#117—21no—
367#117—21no—
368#117—21no—
369#117—21no—
370#117—21no—
371#117—21no—
372#117C4×D1312yes—
373#117C22⋊D1312yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C42—21no—
379C2×C42—21no—
380#108—268no—
381#104—268no—
382#103—264no—
383#102—264no—
384C22⋊C8—268no—
385C2×C13—21no—
386C2×C13—21no—
387C2×C13—21no—
388C2×C13—21no—
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—21no—
392C2×C13#143911yescharacteristic
393D13—82no—
394C24—261no—
395C24#612911yescharacteristic
396#41—262no—
397#41—262no—
398#41—262no—
399#41—262no—
400#41—262no—
401#41—262no—
402#41—262no—
403#41—262no—
404#41—521no—
405#41—521no—
406#41—521no—
407#41—521no—
408#41—521no—
409#41—521no—
410#41—521no—
411#41—521no—
412C2×Q8—132no—
413C2×Q8—261no—
414C2×Q8—261no—
415C2×Q8—261no—
416C2×Q8—261no—
417C2×Q8—261no—
418C2×D4—132no—
419C2×D4—262no—
420C2×D4—262no—
421C2×D4—261no—
422C2×D4—261no—
423C2×D4—261no—
424C2×D4—261no—
425C2×D4—261no—
426C2×D4—521no—
427C2×D4—521no—
428C2×D4—521no—
429C2×D4—521no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—261no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—521no—
436C22×C4—521no—
437C22×C4—521no—
438C22×C4—521no—
439C22×C4C2×C4×D1311yescharacteristic
440C22×C4C2×D5211yescharacteristic
441C22×C4#612711yescharacteristic
442C22×C4#612711yescharacteristic
443C22×C4#612711yescharacteristic
444C22×C4#612711yescharacteristic
445C22×C4D4×D1311yescharacteristic
446C22×C4D4×D1311yescharacteristic
447C22×C4D4×D1311yescharacteristic
448C22×C4D4×D1311yescharacteristic
449C22×C4D4×D1311yescharacteristic
450C22×C4Q8×D1311yescharacteristic
451C22×C4#613111yescharacteristic
452C22×C4C2×C22⋊D1311yescharacteristic
453M16—22no—
454M16—22no—
455M16—41no—
456M16—41no—
457M16—262no—
458M16—262no—
459M16—262no—
460M16—262no—
461M16—262no—
462M16—262no—
463M16—262no—
464M16—262no—
465M16—521no—
466M16—521no—
467M16—521no—
468M16—521no—
469C2×C8—22no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—134no—
473C2×C8—262no—
474C2×C8—262no—
475C2×C8—262no—
476C2×C8—262no—
477C2×C8—521no—
478C2×C8—521no—
479C2×C8—521no—
480C2×C8—521no—
481C4⋊C4—22no—
482C4⋊C4—22no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C22⋊C4—22no—
486C22⋊C4—22no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—22no—
490C42—22no—
491C42—41no—
492C42—41no—
493C13#1113111yescharacteristic, complemented, Sylow
494C23—81no—
495C23—262no—
496C23—521no—
497C23—521no—
498C23—1042no—
499C23#8813511yescharacteristic
500C23#8813711yescharacteristic
501C23#8813911yescharacteristic
502C23#8813911yescharacteristic
503C23#8815111yescharacteristic
504C23#8815211yescharacteristic
505C23#8819311yescharacteristic
506Q8—262no—
507Q8—262no—
508Q8—521no—
509Q8—521no—
510D4—262no—
511D4—262no—
512D4—522no—
513D4—522no—
514D4—522no—
515D4—522no—
516D4—521no—
517D4—521no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—82no—
521C2×C4—82no—
522C2×C4—262no—
523C2×C4—521no—
524C2×C4—521no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4#8812611yescharacteristic
530C2×C4C4×D5211yescharacteristic
531C2×C4#8812911yescharacteristic
532C2×C4#8813011yescharacteristic
533C2×C4C22⋊C4×D1311yescharacteristic
534C2×C4#8813611yescharacteristic
535C2×C4#8813611yescharacteristic
536C2×C4#8813811yescharacteristic
537C2×C4#8813811yescharacteristic
538C2×C4#8813811yescharacteristic
539C2×C4#8813811yescharacteristic
540C2×C4#8813811yescharacteristic
541C2×C4C4⋊C4×D1311yescharacteristic
542C2×C4#8814711yescharacteristic
543C2×C4#8814811yescharacteristic
544C2×C4#8814811yescharacteristic
545C2×C4#8814811yescharacteristic
546C2×C4#8814911yescharacteristic
547C2×C4#8815011yescharacteristic
548C2×C4#8815011yescharacteristic
549C2×C4#8815011yescharacteristic
550C2×C4#8815011yescharacteristic
551C2×C4C4×C22⋊D1311yescharacteristic
552C2×C4#8818311yescharacteristic
553C2×C4#8818411yescharacteristic
554C2×C4#8819111yescharacteristic
555C2×C4#8819411yescharacteristic
556C2×C4#8820011yescharacteristic
557C8—42no—
558C8—264no—
559C8—522no—
560C8—522no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—524no—
569C22—522no—
570C22—1042no—
571C22—1042no—
572C22#1171832911yescharacteristic
573C22#1171833011yescharacteristic
574C22#1171833411yescharacteristic
575C22#1171833611yescharacteristic
576C22#1171861811yescharacteristic
577C22#1171862011yescharacteristic
578C22#1171865511yescharacteristic
579C4—82no—
580C4—82no—
581C4—522no—
582C4#1171832611yescharacteristic
583C4#1171832811yescharacteristic
584C4#1171833311yescharacteristic
585C4#1171833711yescharacteristic
586C4#1171860111yescharacteristic
587C4#1171862111yescharacteristic
588C4#1171865011yescharacteristic
589C4#1171865311yescharacteristic
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—1042no—
598C2#1311308011yescharacteristic
subgroupG/H
centerC4#11718621
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1733C2
socleC2×C13#1439
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenter#1733D13
hypocenterC13#11131
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1733

Complements

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

NH ≅ G/Ntype
1. C2×#11718785C2semidirect
5. C2×#11718125C2semidirect
6. C2×#11718125C2semidirect
7. C13×#1733C2semidirect
23. #11718665C4semidirect
25. #11718662C4semidirect
201. #1733D13semidirect
493. C13#11131semidirect

Maximal subgroups

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

subgroupindex
C2×#117187852
C2×#117186662
#131233532
#131232802
C2×#117181252
C13×#17332
#1113113