Finite Group Databasebeta

← #15770448

Subgroups — #15770448

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13123426C211yesmaximal, characteristic, complemented
2C2×#11718800C211yesmaximal, characteristic
3C2×#11718800C211yesmaximal, characteristic
4C2×#11718793C211yesmaximal, characteristic
5C2×#11718151C211yesmaximal, characteristic, complemented
6C2×#11718148C211yesmaximal, characteristic, complemented
7C13×#1738C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C22×C13×M16C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718800—22no—
16#11718800—22no—
17#11718800—22no—
18#11718800—22no—
19C2×#88065—22no—
20C2×#88065—22no—
21C2×#88064C412yescomplemented
22#11718793—22no—
23#11718793—22no—
24C2×#88063C412yescomplemented
25#11718782—22no—
26#11718782—22no—
27#11718767—22no—
28C13×#341—22no—
29#11718151—22no—
30#11718148—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×M16—21no—
54C2×C13×M16—21no—
55C2×C13×M16—21no—
56C2×C13×M16—21no—
57C2×C13×M16—21no—
58C2×C13×M16—21no—
59C2×C13×M16—21no—
60C2×C13×M16—21no—
61C2×C13×M16C2×C412yes—
62C2×C13×M16D412yes—
63C2×C13×M16D412yes—
64C2×C13×M16D412yes—
65C2×C13×M16D412yes—
66C22×C8×C13—21no—
67C22×C8×C13—21no—
68C22×C8×C13—21no—
69C2×C22⋊Dic13—21no—
70C2×C22⋊Dic13—21no—
71#88180—21no—
72#88180—21no—
73#88180—21no—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77#88180D412yes—
78#88180D412yes—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4×Dic13—21no—
82C2×C4×Dic13—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099—21no—
88C2×#6099C2×C412yes—
89C22×#1055—21no—
90#88065—28no—
91#88065—28no—
92#88064—24no—
93#88063—24no—
94#88058—24no—
95#88057—24no—
96#11141—131nomaximal, Sylow
97C24×C13#4111yescharacteristic
98C23×D13—21no—
99C22×C4×C13C22×C411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
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×Q811yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C22×C4×C13#4111yescharacteristic
112C22×C4×C13#4111yescharacteristic
113C2×C22⋊D13—22no—
114C2×C22⋊D13—22no—
115C2×C22⋊D13—41no—
116C2×C22⋊D13—41no—
117C2×C22⋊D13—41no—
118C2×C22⋊D13—41no—
119C22×Dic13—21no—
120C22×Dic13—41no—
121C22×Dic13—41no—
122#6127—22no—
123#6127—22no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—22no—
129#6127—22no—
130#6127—41no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136#6127—41no—
137#6127—41no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52—21no—
142C2×D52—21no—
143C2×D52C4⋊C412yes—
144C2×C4×D13—22no—
145C2×C4×D13—22no—
146C2×C4×D13—41no—
147C2×C4×D13—41no—
148C2×C4×D13—41no—
149C2×C4×D13—41no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26—21no—
154C2×Dic26—21no—
155C2×Dic26C4⋊C412yes—
156C13×M16—22no—
157C13×M16—22no—
158C13×M16—22no—
159C13×M16—22no—
160C13×M16—22no—
161C13×M16—22no—
162C13×M16—22no—
163C13×M16—41no—
164C13×M16—41no—
165C13×M16—41no—
166C13×M16—41no—
167C13×M16C22⋊C414yes—
168C2×C8×C13—22no—
169C2×C8×C13—22no—
170C2×C8×C13—22no—
171C2×C8×C13—22no—
172C2×C8×C13—22no—
173C2×C8×C13—41no—
174C2×C8×C13—41no—
175C2×C8×C13—41no—
176C2×C8×C13—41no—
177C22⋊Dic13—22no—
178C22⋊Dic13—22no—
179C22⋊Dic13—41no—
180C22⋊Dic13—41no—
181C4⋊Dic13—22no—
182C4⋊Dic13—22no—
183C4⋊Dic13—41no—
184C4⋊Dic13—41no—
185C4×Dic13—22no—
186C4×Dic13—22no—
187C4×Dic13—41no—
188C4×Dic13—41no—
189#6099—22no—
190#6099—22no—
191#6099—41no—
192#6099—41no—
193C2×#1055—22no—
194C2×#1055—41no—
195C2×#1055—41no—
196#2911—131no—
197C2×#421—131no—
198C2×#421—131no—
199C2×#413—131no—
200C2×#344—131no—
201C2×#344—131no—
202#1738D1311yescharacteristic, complemented
203C23×C13—81no—
204C23×C13#11711yescharacteristic
205C23×C13#12111yescharacteristic
206C23×C13#12111yescharacteristic
207C23×C13#12111yescharacteristic
208C23×C13C22⋊Q811yescharacteristic
209C23×C13#12611yescharacteristic
210C23×C13#12611yescharacteristic
211C22×D13—22no—
212C22×D13—41no—
213C22×D13—41no—
214C22×D13—82no—
215C2×C4×C13C2×C22⋊C411yescharacteristic
216C2×C4×C13C2×C4⋊C411yescharacteristic
217C2×C4×C13C4×D411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13C4×D411yescharacteristic
220C2×C4×C13C4×D411yescharacteristic
221C2×C4×C13#12011yescharacteristic
222C2×C4×C13#12011yescharacteristic
223C2×C4×C13#12011yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12111yescharacteristic
229C2×C4×C13C22⋊Q811yescharacteristic
230C2×C4×C13C22⋊Q811yescharacteristic
231C2×C4×C13C22⋊Q811yescharacteristic
232C2×C4×C13C22⋊Q811yescharacteristic
233C2×C4×C13C22⋊Q811yescharacteristic
234C2×C4×C13#12311yescharacteristic
235C2×C4×C13#12311yescharacteristic
236C2×C4×C13#12311yescharacteristic
237C2×C4×C13#12311yescharacteristic
238C2×C4×C13#12311yescharacteristic
239C2×C4×C13#12411yescharacteristic
240C2×C4×C13#12411yescharacteristic
241C2×C4×C13#12411yescharacteristic
242C2×C4×C13#12711yescharacteristic
243C22⋊D13—42no—
244C22⋊D13—42no—
245C22⋊D13—42no—
246C22⋊D13—42no—
247C2×Dic13—22no—
248C2×Dic13—41no—
249C2×Dic13—41no—
250C2×Dic13—42no—
251C2×Dic13—42no—
252C2×Dic13—82no—
253C2×Dic13—82no—
254D52—22no—
255D52—22no—
256D52—41no—
257D52—41no—
258C4×D13—42no—
259C4×D13—42no—
260C4×D13—42no—
261C4×D13—42no—
262Dic26—22no—
263Dic26—22no—
264Dic26—41no—
265Dic26—41no—
266C8×C13—24no—
267C8×C13—42no—
268C8×C13—42no—
269#1055—42no—
270C22×#41—131no—
271C22×M16—131no—
272C22×M16C2×D1311yescharacteristic
273C22×M16C2×D1311yescharacteristic
274C22×M16C2×D1311yescharacteristic
275C2×#117—131no—
276C2×#117—131no—
277#428—262no—
278#428—262no—
279#427—262no—
280#421—262no—
281#421—262no—
282#421—262no—
283#421—262no—
284C2×#104—262no—
285C2×#104—262no—
286#413—262no—
287#413—262no—
288C2×#101—132no—
289C2×#100—132no—
290#344—262no—
291#344—262no—
292#341—22no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13—41no—
298C22×C13—41no—
299C22×C13—41no—
300C22×C13#38011yescharacteristic
301C22×C13#38811yescharacteristic
302C22×C13#38811yescharacteristic
303C22×C13#39211yescharacteristic
304C22×C13#39611yescharacteristic
305C22×C13#39611yescharacteristic
306C22×C13#39711yescharacteristic
307C2×D13—42no—
308C2×D13—82no—
309C2×D13—82no—
310C2×D13—82no—
311C4×C13#38511yescharacteristic
312C4×C13#38511yescharacteristic
313C4×C13#38611yescharacteristic
314C4×C13#39011yescharacteristic
315C4×C13#39311yescharacteristic
316C4×C13#39411yescharacteristic
317C4×C13#39411yescharacteristic
318C4×C13#39911yescharacteristic
319Dic13—42no—
320Dic13—82no—
321Dic13—82no—
322C2×#41—132no—
323C2×#41—132no—
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—
333C2×#41—261no—
334C22×Q8—131no—
335C22×D4—131no—
336C22×D4—261no—
337C23×C4—261no—
338C23×C4C22×D1311yescharacteristic
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—132no—
353C2×M16—261no—
354C2×M16—261no—
355C2×M16—261no—
356C2×M16—261no—
357C2×M16—261no—
358C2×M16C4×D1312yes—
359C2×M16D5212yes—
360C2×M16D5212yes—
361C2×M16D5212yes—
362C2×M16C22⋊D1312yes—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—261no—
367#117—132no—
368#117—132no—
369#117—261no—
370#117—261no—
371#117—261no—
372#117—261no—
373#117—261no—
374#117—261no—
375C2×C4⋊C4—261no—
376C2×C4⋊C4—261no—
377C2×C22⋊C4—261no—
378C2×C22⋊C4—261no—
379C2×C42—261no—
380C2×C42—261no—
381#107—264no—
382#106—264no—
383#104—268no—
384#104—268no—
385#101—264no—
386#100—264no—
387C2×C13—21no—
388C2×C13—21no—
389C2×C13—21no—
390C2×C13—21no—
391C2×C13—21no—
392C2×C13—21no—
393C2×C13—21no—
394C2×C13#143911yescharacteristic
395D13—82no—
396C24—261no—
397C24#613111yescharacteristic
398#41—262no—
399#41—262no—
400#41—262no—
401#41—262no—
402#41—262no—
403#41—262no—
404#41—262no—
405#41—262no—
406#41—521no—
407#41—521no—
408#41—521no—
409#41—521no—
410#41—521no—
411#41—521no—
412#41—521no—
413#41—521no—
414C2×Q8—132no—
415C2×Q8—261no—
416C2×Q8—261no—
417C2×Q8—261no—
418C2×Q8—261no—
419C2×Q8—261no—
420C2×D4—132no—
421C2×D4—262no—
422C2×D4—262no—
423C2×D4—261no—
424C2×D4—261no—
425C2×D4—261no—
426C2×D4—261no—
427C2×D4—261no—
428C2×D4—521no—
429C2×D4—521no—
430C2×D4—521no—
431C2×D4—521no—
432C22×C4—261no—
433C22×C4—262no—
434C22×C4—262no—
435C22×C4—521no—
436C22×C4—521no—
437C22×C4—521no—
438C22×C4—521no—
439C22×C4—521no—
440C22×C4—521no—
441C22×C4C2×C4×D1311yescharacteristic
442C22×C4C2×D5211yescharacteristic
443C22×C4C2×D5211yescharacteristic
444C22×C4C2×D5211yescharacteristic
445C22×C4#612711yescharacteristic
446C22×C4#612711yescharacteristic
447C22×C4D4×D1311yescharacteristic
448C22×C4D4×D1311yescharacteristic
449C22×C4D4×D1311yescharacteristic
450C22×C4#612911yescharacteristic
451C22×C4#612911yescharacteristic
452C22×C4#612911yescharacteristic
453C22×C4Q8×D1311yescharacteristic
454C22×C4C2×C22⋊D1311yescharacteristic
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—262no—
467M16—262no—
468M16—521no—
469M16—521no—
470M16#610314yes—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—262no—
481C2×C8—521no—
482C2×C8—521no—
483C4⋊C4—262no—
484C4⋊C4—262no—
485C4⋊C4—521no—
486C4⋊C4—521no—
487C22⋊C4—262no—
488C22⋊C4—262no—
489C22⋊C4—521no—
490C22⋊C4—521no—
491C42—262no—
492C42—262no—
493C42—521no—
494C42—521no—
495C13#1114111yescharacteristic, complemented, Sylow
496C23—81no—
497C23—262no—
498C23—521no—
499C23—521no—
500C23—1042no—
501C23#8814611yescharacteristic
502C23#8814911yescharacteristic
503C23#8814911yescharacteristic
504C23#8814911yescharacteristic
505C23#8815211yescharacteristic
506C23#8815211yescharacteristic
507C23#8820011yescharacteristic
508Q8—262no—
509Q8—262no—
510Q8—521no—
511Q8—521no—
512D4—262no—
513D4—262no—
514D4—522no—
515D4—522no—
516D4—522no—
517D4—522no—
518D4—521no—
519D4—521no—
520C2×C4—262no—
521C2×C4—521no—
522C2×C4—521no—
523C2×C4—522no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—522no—
527C2×C4—522no—
528C2×C4—522no—
529C2×C4—1042no—
530C2×C4—1042no—
531C2×C4C4×D5211yescharacteristic
532C2×C4C4×D5211yescharacteristic
533C2×C4#8812811yescharacteristic
534C2×C4#8812911yescharacteristic
535C2×C4#8813511yescharacteristic
536C2×C4#8813511yescharacteristic
537C2×C4#8813611yescharacteristic
538C2×C4#8813611yescharacteristic
539C2×C4#8813611yescharacteristic
540C2×C4#8813711yescharacteristic
541C2×C4#8813711yescharacteristic
542C2×C4#8813911yescharacteristic
543C2×C4#8813911yescharacteristic
544C2×C4#8814011yescharacteristic
545C2×C4#8814011yescharacteristic
546C2×C4#8814011yescharacteristic
547C2×C4C4⋊C4×D1311yescharacteristic
548C2×C4#8815011yescharacteristic
549C2×C4#8815011yescharacteristic
550C2×C4#8815111yescharacteristic
551C2×C4#8815111yescharacteristic
552C2×C4#8815111yescharacteristic
553C2×C4C2×#610311yescharacteristic
554C2×C4#8818411yescharacteristic
555C2×C4#8818411yescharacteristic
556C2×C4#8819211yescharacteristic
557C2×C4#8819311yescharacteristic
558C2×C4#8819311yescharacteristic
559C8—24no—
560C8—42no—
561C8—42no—
562C8—522no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—522no—
571C22—1042no—
572C22—1042no—
573C22—1042no—
574C22#1171833111yescharacteristic
575C22#1171833111yescharacteristic
576C22#1171833211yescharacteristic
577C22#1171833511yescharacteristic
578C22#1171864811yescharacteristic
579C22#1171865511yescharacteristic
580C22#1171865511yescharacteristic
581C4—522no—
582C4—1042no—
583C4—1042no—
584C4#1171832911yescharacteristic
585C4#1171832911yescharacteristic
586C4#1171833411yescharacteristic
587C4#1171833811yescharacteristic
588C4#1171860011yescharacteristic
589C4#1171861911yescharacteristic
590C4#1171862211yescharacteristic
591C4#1171862211yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—21no—
599C2—1042no—
600C2#1311308211yescharacteristic
subgroupG/H
centerC4#11718622
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC13×#1738C2
socleC2×C13#1439
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenter#1738D13
hypocenterC13#11141
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ #1738

Complements

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

NH ≅ G/Ntype
1. #13123426C2semidirect
5. C2×#11718151C2semidirect
6. C2×#11718148C2semidirect
7. C13×#1738C2semidirect
21. C2×#88064C4semidirect
24. C2×#88063C4semidirect
202. #1738D13semidirect
495. C13#11141semidirect

Maximal subgroups

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

subgroupindex
#131234262
C2×#117188002
C2×#117187932
C2×#117181512
C2×#117181482
C13×#17382
#1114113