Finite Group Databasebeta

← #15931111

Subgroups — #15931111

Order 3328.

798 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117872C211yesmaximal, characteristic
2#13116151C211yesmaximal, characteristic, complemented
3#13116018C211yesmaximal, characteristic
4#13115969C211yesmaximal, characteristic, complemented
5#13115837C211yesmaximal, characteristic
6#13115789C211yesmaximal, characteristic, complemented
7#13115515C211yesmaximal, characteristic, complemented
8#13115474C211yesmaximal, characteristic, complemented
9#13115444C211yesmaximal, characteristic, complemented
10#13115428C211yesmaximal, characteristic, complemented
11#13115173C211yesmaximal, characteristic, complemented
12#13115149C211yesmaximal, characteristic, complemented
13#13114928C211yesmaximal, characteristic, complemented
14C4×#88049C211yesmaximal, characteristic, complemented
15C13×#2492C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8C2211yescharacteristic
18C22×#6106C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C13×#400—21no—
23C13×#393—21no—
24C13×#391—21no—
25C13×#391C2211yescharacteristic
26C13×#391C2211yescharacteristic
27C13×#388—21no—
28C13×#380C2211yescharacteristic
29C4×C13×C4⋊C4C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88047C2211yescharacteristic
40#11718618—21no—
41#11718617—21no—
42#11718600C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44#11718589C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×C4×#1055C2211yescharacteristic
47#11718330—21no—
48#11718327—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13—21no—
60C22×Q8×C13C2311yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—41no—
67C13×C22⋊Q8—22no—
68C13×C22⋊Q8—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4D411yescharacteristic
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C42×C13—21no—
79C2×C42×C13C2311yescharacteristic
80C2×C42×C13C2311yescharacteristic
81C2×C22⋊Dic13—21no—
82C2×#6106—22no—
83C2×#6106—41no—
84C2×#6106—41no—
85#88184—22no—
86#88184—22no—
87C2×#6103—21no—
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91#88180—22no—
92#88180—41no—
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C4×D52—22no—
104C4×D52—41no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88075—22no—
114#88075—22no—
115#88075—41no—
116#88071—21no—
117#88071—21no—
118C22⋊#1055—41no—
119C22⋊#1055—41no—
120#88049—22no—
121#88049—22no—
122#88049—41no—
123#88047—22no—
124C4⋊#1055—41no—
125C4×#1055—41no—
126#26731—131nomaximal, Sylow
127C24×C13C2×D411yescharacteristic
128C23×D13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13—21no—
132C2×Q8×C13—21no—
133C2×Q8×C13—21no—
134C2×Q8×C13—21no—
135C2×Q8×C13—42no—
136C2×Q8×C13—42no—
137C2×Q8×C13—81no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2411yescharacteristic
154C2×C22⋊D13—24no—
155C2×C22⋊D13—81no—
156C2×C22⋊D13—81no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C2×D52—21no—
164C2×D52—21no—
165C2×D52#4112yes—
166C2×C4×D13—42no—
167C2×C4×D13—42no—
168C2×C4×D13—81no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4#4112yes—
177C13×C22⋊C4—22no—
178C13×C22⋊C4—22no—
179C13×C22⋊C4—42no—
180C13×C22⋊C4—81no—
181C42×C13—21no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—81no—
186C22⋊Dic13—42no—
187#6106—44no—
188#6103—24no—
189#6103—42no—
190#6103—42no—
191#6103—81no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13#4112yes—
197C4⋊Dic13#4112yes—
198#6101—81no—
199C4×Dic13—42no—
200C4×Dic13—81no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213#2492D1311yescharacteristic, complemented
214#2363—131no—
215#2055—131no—
216#2033—131no—
217#2023—131no—
218#2000—131no—
219#1988—131no—
220#1933—131no—
221#1928—131no—
222#1923—131no—
223#1921—131no—
224#1877—131no—
225#1873—131no—
226#1825—131no—
227C4×#102—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13—21no—
235C23×C13C22×D411yescharacteristic
236C22×D13—22no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243Q8×C13—41no—
244Q8×C13—41no—
245Q8×C13—41no—
246Q8×C13—41no—
247Q8×C13—84no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13#13512yes—
278C2×C4×C13#13712yes—
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13C2×#4111yescharacteristic
281C2×C4×C13C2×#4111yescharacteristic
282C2×C4×C13C2×#4111yescharacteristic
283C2×C4×C13H(5,𝔽2)11yescharacteristic
284C2×C4×C13H(5,𝔽2)11yescharacteristic
285C22⋊D13—84no—
286C2×Dic13—22no—
287C2×Dic13—22no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292C2×Dic13—41no—
293C2×Dic13—41no—
294C2×Dic13—41no—
295D52—22no—
296D52—22no—
297D52—41no—
298D52—41no—
299C4×D13—84no—
300#1055—41no—
301#1055—41no—
302#1055—41no—
303#1055—41no—
304C22×SD16—131no—
305C2×C4⋊Q8C2×D1311yescharacteristic
306C2×C22⋊Q8C2×D1311yescharacteristic
307C2×#121—131no—
308C2×C4×D4—131no—
309C2×#117—131no—
310C2×#107—131no—
311C2×C4⋊C8—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#102—131no—
316C2×#102—131no—
317C2×#102—131no—
318C2×C22⋊C8—131no—
319C2×C22⋊C8—131no—
320C2×C4×C8—131no—
321#400—21no—
322#393—21no—
323#391—21no—
324#391C2×D1311yescharacteristic
325#391C2×D1311yescharacteristic
326#390—131no—
327#390—261no—
328#389—131no—
329#388—21no—
330#388—261no—
331#386—261no—
332#380C2×D1311yescharacteristic
333C4×C4⋊C4—131no—
334C4×C4⋊C4C2×D1311yescharacteristic
335C4×C22⋊C4—261no—
336C4×C22⋊C4C2×D1311yescharacteristic
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#340—131no—
343#340—131no—
344#340—131no—
345#336—131no—
346#336—131no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—41no—
354C22×C13#52511yescharacteristic
355C22×C13#54611yescharacteristic
356C22×C13#54611yescharacteristic
357C22×C13C2×#13511yescharacteristic
358C22×C13C2×#13711yescharacteristic
359C22×C13#57611yescharacteristic
360C22×C13#57711yescharacteristic
361C2×D13—42no—
362C2×D13—42no—
363C2×D13—42no—
364C2×D13—81no—
365C2×D13—81no—
366C2×D13—81no—
367C2×D13—81no—
368C4×C13—22no—
369C4×C13—22no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—42no—
373C4×C13—41no—
374C4×C13—81no—
375C4×C13—81no—
376C4×C13—81no—
377C4×C13#52911yescharacteristic
378C4×C13#53811yescharacteristic
379C4×C13#55511yescharacteristic
380C4×C13#55911yescharacteristic
381Dic13—42no—
382Dic13—42no—
383Dic13—81no—
384C22×Q8—21no—
385C22×Q8C22×D1311yescharacteristic
386C22×D4—131no—
387C22×D4—261no—
388C23×C4—261no—
389C23×C4C22×D1311yescharacteristic
390C2×SD16—262no—
391C2×SD16—521no—
392C2×SD16—521no—
393C22×C8—131no—
394C22×C8—131no—
395C22×C8—131no—
396C22×C8—131no—
397C4⋊Q8—22no—
398C4⋊Q8—41no—
399C22⋊Q8—22no—
400C22⋊Q8—41no—
401#121—262no—
402#121—262no—
403C4×D4—262no—
404C4×D4—521no—
405#117—262no—
406#117—521no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—131no—
410C2×C4⋊C4—131no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—261no—
413C2×C4⋊C4C22×D1311yescharacteristic
414C2×C4⋊C4C22×D1311yescharacteristic
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C22⋊C4—21no—
417C2×C22⋊C4—21no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4C22⋊D1311yescharacteristic
424C2×C22⋊C4C22⋊D1311yescharacteristic
425C2×C42—21no—
426C2×C42—261no—
427C2×C42—261no—
428C2×C42C22×D1311yescharacteristic
429C2×C42C22×D1311yescharacteristic
430#107—262no—
431C4⋊C8—521no—
432#103—262no—
433#103—262no—
434#103—521no—
435#102—262no—
436#102—262no—
437#102—521no—
438C22⋊C8—521no—
439C22⋊C8—521no—
440C4×C8—521no—
441#95—21no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—21no—
446#95—21no—
447#95—261no—
448#95—261no—
449#95C22⋊D1311yescharacteristic
450#95C22⋊D1311yescharacteristic
451C2×C13—81no—
452C2×C13#245911yescharacteristic
453C2×C13#310711yescharacteristic
454C2×C13#311811yescharacteristic
455C2×C13#329711yescharacteristic
456C2×C13#330411yescharacteristic
457C2×C13#331411yescharacteristic
458C2×C13#332911yescharacteristic
459D13—82no—
460C24—261no—
461C24C2×C22⋊D1311yescharacteristic
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8—42no—
469C2×Q8—42no—
470C2×Q8—81no—
471C2×D4—132no—
472C2×D4—264no—
473C2×D4—261no—
474C2×D4—261no—
475C2×D4—261no—
476C2×D4—261no—
477C2×D4—261no—
478C2×D4—1041no—
479C2×D4—1041no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—261no—
491C22×C4—261no—
492C22×C4—261no—
493C22×C4—522no—
494C22×C4—522no—
495C22×C4—1041no—
496C22×C4C2×C22⋊D1311yescharacteristic
497C22×C4C2×C22⋊D1311yescharacteristic
498C22×C4C2×C22⋊D1311yescharacteristic
499C22×C4C2×C22⋊D1311yescharacteristic
500C22×C4C2×C22⋊D1311yescharacteristic
501C22×C4C23×D1311yescharacteristic
502SD16—524no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C2×C8—261no—
509C2×C8—261no—
510C2×C8—261no—
511C2×C8—261no—
512C2×C8—261no—
513C2×C8—261no—
514C2×C8—261no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—42no—
521C4⋊C4—42no—
522C4⋊C4—132no—
523C4⋊C4—132no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—261no—
528C4⋊C4—1041no—
529C4⋊C4#612912yes—
530C22⋊C4—22no—
531C22⋊C4—22no—
532C22⋊C4—42no—
533C22⋊C4—81no—
534C22⋊C4—264no—
535C22⋊C4—522no—
536C22⋊C4—522no—
537C22⋊C4—522no—
538C22⋊C4—1041no—
539C42—21no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—81no—
544C42—522no—
545C42—1041no—
546C13#2673111yescharacteristic, complemented, Sylow
547C23—21no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—21no—
552C23—21no—
553C23—21no—
554C23—262no—
555C23—521no—
556C23—521no—
557C23—521no—
558C23—521no—
559C23—521no—
560C23—521no—
561C23C22×C22⋊D1311yescharacteristic
562Q8—41no—
563Q8—41no—
564Q8—41no—
565Q8—41no—
566Q8—84no—
567D4—262no—
568D4—262no—
569D4—521no—
570D4—521no—
571D4—1044no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—262no—
602C2×C4—262no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4—521no—
606C2×C4—521no—
607C2×C4—521no—
608C2×C4—521no—
609C2×C4—521no—
610C2×C4—1044no—
611C2×C4#8819612yes—
612C2×C4#8820412yes—
613C2×C4C2×#612911yescharacteristic
614C2×C4#8825111yescharacteristic
615C2×C4#41×D1311yescharacteristic
616C2×C4#41×D1311yescharacteristic
617C2×C4#41×D1311yescharacteristic
618C2×C4#8825611yescharacteristic
619C8—521no—
620C8—521no—
621C8—521no—
622C8—521no—
623C22—41no—
624C22—41no—
625C22—41no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—522no—
631C22—522no—
632C22—522no—
633C22—1041no—
634C22—1041no—
635C22—1041no—
636C22—1041no—
637C22#1171951111yescharacteristic
638C22C2×#8819611yescharacteristic
639C22C2×#8820411yescharacteristic
640C22#1171953311yescharacteristic
641C22#1171953411yescharacteristic
642C22#1171954011yescharacteristic
643C22#1171954211yescharacteristic
644C4—22no—
645C4—22no—
646C4—42no—
647C4—41no—
648C4—41no—
649C4—41no—
650C4—81no—
651C4—81no—
652C4—81no—
653C4—522no—
654C4—522no—
655C4—1041no—
656C4#1171937511yescharacteristic
657C4#1171938311yescharacteristic
658C4#1171938511yescharacteristic
659C4#1171938611yescharacteristic
660C2—81no—
661C2—1042no—
662C2#1311876911yescharacteristic
663C2#1312490111yescharacteristic
664C2#1312501411yescharacteristic
665C2#1312668611yescharacteristic
666C2#1312676911yescharacteristic
667C2#1312691111yescharacteristic
668C2#1312713011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2492C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2492D13
hypocenterC13#26731
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2492

Complements

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

NH ≅ G/Ntype
2. #13116151C2semidirect
4. #13115969C2semidirect
6. #13115789C2semidirect
7. #13115515C2semidirect
8. #13115474C2semidirect
9. #13115444C2semidirect
10. #13115428C2semidirect
11. #13115173C2semidirect
12. #13115149C2semidirect
13. #13114928C2semidirect
14. C4×#88049C2semidirect
15. C13×#2492C2semidirect
213. #2492D13semidirect
546. C13#26731semidirect

Maximal subgroups

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

subgroupindex
#131178722
#131161512
#131160182
#131159692
#131158372
#131157892
#131155152
#131154742
#131154442
#131154282
#131151732
#131151492
#131149282
C4×#880492
C13×#24922
#2673113