Finite Group Databasebeta

← #15770504

Subgroups — #15770504

Order 3328.

818 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718800C211yesmaximal, characteristic
2C2×#11718774C211yesmaximal, characteristic
3C2×#11718793C211yesmaximal, characteristic
4C2×#11718148C211yesmaximal, characteristic, complemented
5C2×#11718149C211yesmaximal, characteristic, complemented
6#13114532C211yesmaximal, characteristic, complemented
7C2×C13×#341C211yesmaximal, characteristic, complemented
8C22×#6127C2211yescharacteristic
9C22×C13×M16C2211yescharacteristic
10C22×C13×M16C2211yescharacteristic
11C23×C8×C13C2211yescharacteristic
12C2×#88180C2211yescharacteristic
13C2×#88180C2211yescharacteristic
14C22×#6099C2211yescharacteristic
15#11718800—22no—
16#11718800—22no—
17C2×#88065—22no—
18C2×#88064—21no—
19#11718793—22no—
20#11718793C414yescomplemented
21C2×#88063—21no—
22#11718774—22no—
23#11718774—22no—
24C2×#88061—21no—
25C2×#88056—21no—
26C13×#341—22no—
27#11718149—22no—
28#11718148—22no—
29#11718142—22no—
30C23×C4×C13C2311yescharacteristic
31C22×C22⋊D13—21no—
32C2×#6127—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×#6127C2×C412yes—
43C2×#6127D412yes—
44C22×D52D411yescharacteristic
45C22×C4×D13—21no—
46C22×Dic26D411yescharacteristic
47C2×C13×M16—21no—
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×M16C2×C412yes—
58C2×C13×M16D412yes—
59C22×C8×C13—21no—
60C22×C8×C13—21no—
61C22×C8×C13—21no—
62C22×C8×C13—21no—
63C22×C8×C13—21no—
64C22×C8×C13—21no—
65C22×C8×C13—21no—
66C22×C8×C13—21no—
67C22×C8×C13D412yes—
68C2×C22⋊Dic13—21no—
69C2×C22⋊Dic13—21no—
70#88180—21no—
71#88180—21no—
72#88180—21no—
73#88180—21no—
74#88180—21no—
75#88180—21no—
76#88180—21no—
77#88180D412yes—
78C2×C4⋊Dic13—21no—
79C2×C4⋊Dic13—21no—
80C2×C4×Dic13—21no—
81C2×C4×Dic13D412yes—
82C2×#6099—21no—
83C2×#6099—21no—
84C2×#6099—21no—
85C2×#6099—21no—
86C2×#6099—21no—
87C2×#6099C2×C412yes—
88C22×#1055—21no—
89#88065—28no—
90#88064—24no—
91#88063—24no—
92#88061—24no—
93#88056—24no—
94#11150—131nomaximal, Sylow
95C24×C13#4111yescharacteristic
96C23×D13—21no—
97C22×C4×C13C22×C411yescharacteristic
98C22×C4×C13C2×D411yescharacteristic
99C22×C4×C13C2×D411yescharacteristic
100C22×C4×C13C2×D411yescharacteristic
101C22×C4×C13C2×D411yescharacteristic
102C22×C4×C13C2×D411yescharacteristic
103C22×C4×C13C2×D411yescharacteristic
104C22×C4×C13#4111yescharacteristic
105C22×C4×C13#4111yescharacteristic
106C22×C4×C13#4111yescharacteristic
107C22×C4×C13#4111yescharacteristic
108C22×C4×C13#4111yescharacteristic
109C22×C4×C13#4111yescharacteristic
110C22×C4×C13#4111yescharacteristic
111C2×C22⋊D13—22no—
112C2×C22⋊D13—22no—
113C2×C22⋊D13—41no—
114C2×C22⋊D13—41no—
115C2×C22⋊D13—41no—
116C2×C22⋊D13—41no—
117C22×Dic13—21no—
118C22×Dic13—22no—
119C22×Dic13—41no—
120#6127—22no—
121#6127—22no—
122#6127—22no—
123#6127—22no—
124#6127—22no—
125#6127—22no—
126#6127—22no—
127#6127—22no—
128#6127—41no—
129#6127—41no—
130#6127—41no—
131#6127—41no—
132#6127—41no—
133#6127—41no—
134#6127—41no—
135#6127—41no—
136C2×D52—21no—
137C2×D52—21no—
138C2×D52—21no—
139C2×D52—21no—
140C2×D52—21no—
141C2×D52C22⋊C412yes—
142C2×C4×D13—22no—
143C2×C4×D13—22no—
144C2×C4×D13—41no—
145C2×C4×D13—41no—
146C2×C4×D13—41no—
147C2×C4×D13—41no—
148C2×Dic26—21no—
149C2×Dic26—21no—
150C2×Dic26—21no—
151C2×Dic26—21no—
152C2×Dic26—21no—
153C2×Dic26C22⋊C412yes—
154C13×M16—22no—
155C13×M16—22no—
156C13×M16—22no—
157C13×M16—22no—
158C13×M16—41no—
159C13×M16—41no—
160C13×M16—41no—
161C13×M16—41no—
162C2×C8×C13—22no—
163C2×C8×C13—22no—
164C2×C8×C13—22no—
165C2×C8×C13—22no—
166C2×C8×C13—22no—
167C2×C8×C13—41no—
168C2×C8×C13—41no—
169C2×C8×C13—41no—
170C2×C8×C13—41no—
171C2×C8×C13—41no—
172C2×C8×C13—41no—
173C2×C8×C13—41no—
174C2×C8×C13—41no—
175C22⋊Dic13—22no—
176C22⋊Dic13—41no—
177C22⋊Dic13—41no—
178C22⋊Dic13—41no—
179C4⋊Dic13—22no—
180C4⋊Dic13—41no—
181C4⋊Dic13—41no—
182C4⋊Dic13—41no—
183C4×Dic13—22no—
184C4×Dic13—22no—
185C4×Dic13—22no—
186C4×Dic13—41no—
187#6099—22no—
188#6099—22no—
189#6099—41no—
190#6099—41no—
191C2×#1055—22no—
192C2×#1055—41no—
193C2×#1055—41no—
194C2×#421—131no—
195C2×#416—131no—
196C2×#413—131no—
197C2×#344—131no—
198C2×#341D1311yescharacteristic, complemented
199C2×H(3,ℤ/4)—131no—
200#1729—131no—
201C23×C13—42no—
202C23×C13#11711yescharacteristic
203C23×C13#12111yescharacteristic
204C23×C13#12311yescharacteristic
205C23×C13#12311yescharacteristic
206C23×C13#12311yescharacteristic
207C23×C13#12411yescharacteristic
208C23×C13#12611yescharacteristic
209C22×D13—22no—
210C22×D13—41no—
211C22×D13—41no—
212C22×D13—82no—
213C2×C4×C13C2×C22⋊C411yescharacteristic
214C2×C4×C13#11711yescharacteristic
215C2×C4×C13C4×D411yescharacteristic
216C2×C4×C13C4×D411yescharacteristic
217C2×C4×C13C4×D411yescharacteristic
218C2×C4×C13C4×D411yescharacteristic
219C2×C4×C13#12011yescharacteristic
220C2×C4×C13#12011yescharacteristic
221C2×C4×C13#12111yescharacteristic
222C2×C4×C13#12111yescharacteristic
223C2×C4×C13#12111yescharacteristic
224C2×C4×C13#12111yescharacteristic
225C2×C4×C13#12111yescharacteristic
226C2×C4×C13#12111yescharacteristic
227C2×C4×C13#12111yescharacteristic
228C2×C4×C13#12311yescharacteristic
229C2×C4×C13#12311yescharacteristic
230C2×C4×C13#12311yescharacteristic
231C2×C4×C13#12311yescharacteristic
232C2×C4×C13#12311yescharacteristic
233C2×C4×C13#12311yescharacteristic
234C2×C4×C13#12311yescharacteristic
235C2×C4×C13#12411yescharacteristic
236C2×C4×C13#12411yescharacteristic
237C2×C4×C13#12411yescharacteristic
238C2×C4×C13#12611yescharacteristic
239C2×C4×C13#12611yescharacteristic
240C2×C4×C13#12611yescharacteristic
241C22⋊D13—42no—
242C22⋊D13—42no—
243C22⋊D13—42no—
244C22⋊D13—42no—
245C2×Dic13—22no—
246C2×Dic13—41no—
247C2×Dic13—41no—
248C2×Dic13—44no—
249C2×Dic13—42no—
250C2×Dic13—42no—
251C2×Dic13—82no—
252D52—22no—
253D52—22no—
254D52—41no—
255D52—41no—
256C4×D13—42no—
257C4×D13—42no—
258C4×D13—42no—
259C4×D13—42no—
260Dic26—22no—
261Dic26—22no—
262Dic26—41no—
263Dic26—41no—
264C8×C13—42no—
265C8×C13—42no—
266C8×C13—42no—
267#1055—42no—
268C22×#41—131no—
269C22×M16—131no—
270C22×M16C2×D1311yescharacteristic
271C22×M16C2×D1311yescharacteristic
272C23×C8C2×D1311yescharacteristic
273C2×#117—131no—
274C2×#117—131no—
275#421—262no—
276#421—262no—
277C2×#104—262no—
278#416—262no—
279#416—262no—
280C2×#103—261no—
281C2×#102—261no—
282#413—134no—
283#413—262no—
284C2×#101—261no—
285C2×#100—261no—
286#344—262no—
287#341—22no—
288H(3,ℤ/4)—262no—
289#336—262no—
290C22×C13—22no—
291C22×C13—22no—
292C22×C13—22no—
293C22×C13—41no—
294C22×C13—41no—
295C22×C13—41no—
296C22×C13—41no—
297C22×C13#38111yescharacteristic
298C22×C13#38811yescharacteristic
299C22×C13#38811yescharacteristic
300C22×C13#39411yescharacteristic
301C22×C13#39411yescharacteristic
302C22×C13#39711yescharacteristic
303C22×C13#39711yescharacteristic
304C2×D13—42no—
305C2×D13—82no—
306C2×D13—82no—
307C2×D13—82no—
308C4×C13#38611yescharacteristic
309C4×C13#38611yescharacteristic
310C4×C13#38811yescharacteristic
311C4×C13#38811yescharacteristic
312C4×C13#39411yescharacteristic
313C4×C13#39411yescharacteristic
314C4×C13#39711yescharacteristic
315C4×C13#39711yescharacteristic
316Dic13—42no—
317Dic13—82no—
318Dic13—82no—
319C2×#41—132no—
320C2×#41—132no—
321C2×#41—261no—
322C2×#41—261no—
323C2×#41—261no—
324C2×#41—261no—
325C2×#41—261no—
326C2×#41—261no—
327C2×#41—261no—
328C2×#41—261no—
329C2×#41—261no—
330C2×#41—261no—
331C22×Q8—131no—
332C22×D4—131no—
333C22×D4—261no—
334C23×C4—261no—
335C23×C4C22×D1311yescharacteristic
336C2×M16—21no—
337C2×M16—21no—
338C2×M16—21no—
339C2×M16—21no—
340C2×M16—21no—
341C2×M16—21no—
342C2×M16—21no—
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—132no—
347C2×M16—261no—
348C2×M16—261no—
349C2×M16—261no—
350C2×M16—261no—
351C2×M16—261no—
352C2×M16C4×D1312yes—
353C2×M16D5212yes—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C22×C8—21no—
358C22×C8—21no—
359C22×C8—21no—
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—261no—
363C22×C8C22⋊D1312yes—
364#117—132no—
365#117—261no—
366#117—261no—
367#117—261no—
368#117—261no—
369#117—261no—
370#117—261no—
371#117—261no—
372C2×C4⋊C4—261no—
373C2×C4⋊C4—261no—
374C2×C22⋊C4—261no—
375C2×C22⋊C4—261no—
376C2×C42—132no—
377C2×C42—261no—
378#104—268no—
379#103—264no—
380#102—264no—
381#101—264no—
382#100—264no—
383C2×C13—21no—
384C2×C13—21no—
385C2×C13—21no—
386C2×C13—21no—
387C2×C13—21no—
388C2×C13—21no—
389C2×C13#144011yescharacteristic
390C2×C13#208012yes—
391D13—82no—
392C24—261no—
393C24#613111yescharacteristic
394#41—262no—
395#41—262no—
396#41—262no—
397#41—262no—
398#41—262no—
399#41—262no—
400#41—262no—
401#41—262no—
402#41—521no—
403#41—521no—
404#41—521no—
405#41—521no—
406#41—521no—
407#41—521no—
408#41—521no—
409#41—521no—
410C2×Q8—132no—
411C2×Q8—261no—
412C2×Q8—261no—
413C2×Q8—261no—
414C2×Q8—261no—
415C2×Q8—261no—
416C2×D4—132no—
417C2×D4—262no—
418C2×D4—262no—
419C2×D4—261no—
420C2×D4—261no—
421C2×D4—261no—
422C2×D4—261no—
423C2×D4—261no—
424C2×D4—521no—
425C2×D4—521no—
426C2×D4—521no—
427C2×D4—521no—
428C22×C4—261no—
429C22×C4—262no—
430C22×C4—262no—
431C22×C4—262no—
432C22×C4—521no—
433C22×C4—521no—
434C22×C4—521no—
435C22×C4—521no—
436C22×C4—521no—
437C22×C4C2×C4×D1311yescharacteristic
438C22×C4C2×D5211yescharacteristic
439C22×C4#612711yescharacteristic
440C22×C4#612711yescharacteristic
441C22×C4#612711yescharacteristic
442C22×C4#612711yescharacteristic
443C22×C4D4×D1311yescharacteristic
444C22×C4D4×D1311yescharacteristic
445C22×C4D4×D1311yescharacteristic
446C22×C4D4×D1311yescharacteristic
447C22×C4#612911yescharacteristic
448C22×C4#612911yescharacteristic
449C22×C4#613111yescharacteristic
450C22×C4C2×C22⋊D1311yescharacteristic
451M16—22no—
452M16—22no—
453M16—22no—
454M16—22no—
455M16—41no—
456M16—41no—
457M16—41no—
458M16—41no—
459M16—262no—
460M16—262no—
461M16—521no—
462M16—521no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8—22no—
467C2×C8—22no—
468C2×C8—41no—
469C2×C8—41no—
470C2×C8—41no—
471C2×C8—41no—
472C2×C8—41no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—41no—
476C2×C8—262no—
477C2×C8—521no—
478C2×C8—521no—
479C4⋊C4—262no—
480C4⋊C4—521no—
481C4⋊C4—521no—
482C4⋊C4—521no—
483C22⋊C4—262no—
484C22⋊C4—521no—
485C22⋊C4—521no—
486C22⋊C4—521no—
487C42—262no—
488C42—262no—
489C42—262no—
490C42—521no—
491C13#1115011yescharacteristic, complemented, Sylow
492C23—42no—
493C23—262no—
494C23—521no—
495C23—521no—
496C23—1042no—
497C23#8814611yescharacteristic
498C23#8814811yescharacteristic
499C23#8814811yescharacteristic
500C23#8814811yescharacteristic
501C23#8814911yescharacteristic
502C23#8815211yescharacteristic
503C23#8820111yescharacteristic
504Q8—262no—
505Q8—262no—
506Q8—521no—
507Q8—521no—
508D4—262no—
509D4—262no—
510D4—522no—
511D4—522no—
512D4—522no—
513D4—522no—
514D4—521no—
515D4—521no—
516C2×C4—262no—
517C2×C4—521no—
518C2×C4—521no—
519C2×C4—522no—
520C2×C4—522no—
521C2×C4—522no—
522C2×C4—522no—
523C2×C4—524no—
524C2×C4—522no—
525C2×C4—522no—
526C2×C4—1042no—
527C2×C4#8812611yescharacteristic
528C2×C4C4×D5211yescharacteristic
529C2×C4#8812911yescharacteristic
530C2×C4#8813011yescharacteristic
531C2×C4C22⋊C4×D1311yescharacteristic
532C2×C4#8813511yescharacteristic
533C2×C4#8813611yescharacteristic
534C2×C4#8813711yescharacteristic
535C2×C4#8813711yescharacteristic
536C2×C4#8813711yescharacteristic
537C2×C4#8813811yescharacteristic
538C2×C4#8813811yescharacteristic
539C2×C4#8813811yescharacteristic
540C2×C4#8813911yescharacteristic
541C2×C4#8813911yescharacteristic
542C2×C4#8814011yescharacteristic
543C2×C4#8814711yescharacteristic
544C2×C4#8814811yescharacteristic
545C2×C4#8814811yescharacteristic
546C2×C4#8814911yescharacteristic
547C2×C4#8815211yescharacteristic
548C2×C4#8815211yescharacteristic
549C2×C4C4×C22⋊D1311yescharacteristic
550C2×C4#8818311yescharacteristic
551C2×C4#8818411yescharacteristic
552C2×C4#8819111yescharacteristic
553C2×C4#8819211yescharacteristic
554C2×C4#8819311yescharacteristic
555C8—42no—
556C8—42no—
557C8—42no—
558C8—522no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—522no—
567C22—1042no—
568C22—1042no—
569C22—1042no—
570C22#1171832511yescharacteristic
571C22#1171833111yescharacteristic
572C22#1171833311yescharacteristic
573C22#1171833611yescharacteristic
574C22#1171865111yescharacteristic
575C22#1171865211yescharacteristic
576C22#1171865411yescharacteristic
577C4—522no—
578C4—1042no—
579C4—1042no—
580C4#1171832611yescharacteristic
581C4#1171833011yescharacteristic
582C4#1171833511yescharacteristic
583C4#1171833611yescharacteristic
584C4#1171860111yescharacteristic
585C4#1171861711yescharacteristic
586C4#1171862011yescharacteristic
587C4#1171862211yescharacteristic
588C2—21no—
589C2—21no—
590C2—21no—
591C2—21no—
592C2—21no—
593C2—21no—
594C2—1042no—
595C2#1311308411yescharacteristic
596C2#1311629212yes—
subgroupG/H
centerC2×C4#88139
commutatorC22×C4×C13C22×C4
FrattiniC23×C4C22×D13
FittingC2×C13×#341C2
socleC22×C13#397
prime radicalC22×#6127C22
cosocleC23×C4×C13C23
hypercenterC2×#341D13
hypocenterC13#11150
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
4. C2×#11718148C2semidirect
5. C2×#11718149C2semidirect
6. #13114532C2semidirect
7. C2×C13×#341C2semidirect
20. #11718793C4semidirect
198. C2×#341D13semidirect
491. C13#11150semidirect

Maximal subgroups

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

subgroupindex
C2×#117188002
C2×#117187742
C2×#117187932
C2×#117181482
C2×#117181492
#131145322
C2×C13×#3412
#1115013