Finite Group Databasebeta

← #15931409

Subgroups — #15931409

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13119188C211yesmaximal, characteristic
2#13116151C211yesmaximal, characteristic, complemented
3#13116029C211yesmaximal, characteristic, complemented
4#13115987C211yesmaximal, characteristic, complemented
5#13115837C211yesmaximal, characteristic
6#13115793C211yesmaximal, characteristic, complemented
7#13115532C211yesmaximal, characteristic, complemented
8#13115463C211yesmaximal, characteristic, complemented
9#13115451C211yesmaximal, characteristic, complemented
10#13115418C211yesmaximal, characteristic, complemented
11#13115191C211yesmaximal, characteristic, complemented
12#13115158C211yesmaximal, characteristic
13#13114931C211yesmaximal, characteristic, complemented
14#13114666C211yesmaximal, characteristic, complemented
15C13×#2362C211yesmaximal, characteristic, complemented
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C22×#6106C2211yescharacteristic
20C2×#88184C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#388—21no—
25C13×#388—21no—
26C13×#387—21no—
27C4×C13×C4⋊C4—21no—
28C4×C13×C4⋊C4C2211yescharacteristic
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33#11718873C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88049C2211yescharacteristic
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88048C2211yescharacteristic
40#11718620—21no—
41#11718618—21no—
42#11718600C2211yescharacteristic
43#11718600C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45C2×C4⋊#1055C2211yescharacteristic
46C2×#88043C2211yescharacteristic
47#11718336—21no—
48#11718330—21no—
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13C2311yescharacteristic
60C23×C4×C13C2311yescharacteristic
61C22×C22⋊D13—21no—
62C22×D52C2311yescharacteristic
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8—22no—
65C4×Q8×C13—22no—
66C4×Q8×C13—41no—
67C13×#117—22no—
68C13×#117—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×#6106—22no—
86C2×#6106—41no—
87C2×#6106—41no—
88#88184—22no—
89#88184—41no—
90C2×#6103—21no—
91C2×#6103—21no—
92C2×#6103—21no—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×C4⋊Dic13C2311yescharacteristic
98C2×#6101—21no—
99C2×#6101—21no—
100C2×C4×Dic13—21no—
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105#88124—22no—
106#88124—41no—
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#88048—22no—
124C4⋊#1055—41no—
125#88043—41no—
126#26751—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#4112yes—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
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×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2411yescharacteristic
151C2×C22⋊D13—42no—
152C2×C22⋊D13—42no—
153C2×C22⋊D13—81no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52—21no—
162C2×D52—21no—
163C13×C4⋊C4—24no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4—42no—
170C13×C4⋊C4#4112yes—
171C13×C4⋊C4#4112yes—
172C13×C22⋊C4—24no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—41no—
175C13×C22⋊C4—42no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—42no—
181C42×C13—42no—
182C42×C13—42no—
183C22⋊Dic13—81no—
184#6106—44no—
185#6103—42no—
186#6103—42no—
187#6103—81no—
188#6103—81no—
189#6103—81no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13#4112yes—
196#6101—42no—
197#6101—42no—
198C4×Dic13—81no—
199C2×#1055—21no—
200C2×#1055—21no—
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—
211#2490—131no—
212#2362D1311yescharacteristic, complemented
213#2055—131no—
214#2035—131no—
215#2026—131no—
216#2000—131no—
217#1989—131no—
218#1936—131no—
219#1926—131no—
220#1924—131no—
221#1920—131no—
222#1880—131no—
223#1875—131no—
224#1825—131no—
225#1763—131no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13C22×D411yescharacteristic
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240C22×D13—41no—
241Q8×C13—22no—
242Q8×C13—22no—
243Q8×C13—41no—
244Q8×C13—41no—
245C2×C4×C13—22no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—22no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—21no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—21no—
262C2×C4×C13—21no—
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×C13C2×#4111yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13H(5,𝔽2)11yescharacteristic
281C2×C4×C13H(5,𝔽2)11yescharacteristic
282C22⋊D13—84no—
283C2×Dic13—22no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292D52—41no—
293D52—41no—
294D52—41no—
295D52—41no—
296#1055—41no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300C22×SD16—131no—
301C2×#125—131no—
302C2×C22⋊Q8C2×D1311yescharacteristic
303C2×#121—131no—
304C2×C4×Q8C2×D1311yescharacteristic
305C2×#117C2×D1311yescharacteristic
306C2×#106—131no—
307C2×C4⋊C8—131no—
308C2×#103—131no—
309C2×#103—131no—
310C2×#103—131no—
311C2×#102—131no—
312C2×#102—131no—
313C2×#102—131no—
314C2×C22⋊C8—131no—
315C2×C22⋊C8—131no—
316C2×#97—131no—
317#397—261no—
318#394—261no—
319#391C2×D1311yescharacteristic
320#390—131no—
321#390—131no—
322#390—261no—
323#389C2×D1311yescharacteristic
324#388—21no—
325#388—21no—
326#388—261no—
327#387—21no—
328#380—131no—
329C4×C4⋊C4—21no—
330C4×C4⋊C4—131no—
331C4×C4⋊C4C2×D1311yescharacteristic
332C4×C22⋊C4C2×D1311yescharacteristic
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#336—131no—
342#336—131no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13#52511yescharacteristic
351C22×C13#54611yescharacteristic
352C22×C13#54611yescharacteristic
353C22×C13#57511yescharacteristic
354C22×C13#57511yescharacteristic
355C22×C13#57711yescharacteristic
356C22×C13#57711yescharacteristic
357C2×D13—81no—
358C2×D13—81no—
359C2×D13—81no—
360C2×D13—81no—
361C2×D13—81no—
362C2×D13—81no—
363C2×D13—81no—
364C4×C13—42no—
365C4×C13—41no—
366C4×C13—42no—
367C4×C13—41no—
368C4×C13—42no—
369C4×C13—41no—
370C4×C13—41no—
371C4×C13—41no—
372C4×C13—81no—
373C4×C13#52911yescharacteristic
374C4×C13#53811yescharacteristic
375C4×C13#55511yescharacteristic
376C4×C13#55911yescharacteristic
377Dic13—42no—
378Dic13—81no—
379Dic13—81no—
380C22×Q8C22×D1311yescharacteristic
381C22×D4—131no—
382C22×D4—261no—
383C23×C4C22×D1311yescharacteristic
384C2×SD16—262no—
385C2×SD16—521no—
386C2×SD16—521no—
387C22×C8—131no—
388C22×C8—131no—
389C22×C8—131no—
390C22×C8—131no—
391#125—262no—
392#125—521no—
393C22⋊Q8—22no—
394C22⋊Q8—22no—
395#121—262no—
396#121—521no—
397C4×Q8—22no—
398C4×Q8—41no—
399#117—22no—
400#117—41no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403C2×C4⋊C4—21no—
404C2×C4⋊C4—131no—
405C2×C4⋊C4—131no—
406C2×C4⋊C4—131no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4—261no—
409C2×C4⋊C4C22×D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4—261no—
417C2×C22⋊C4—261no—
418C2×C22⋊C4—261no—
419C2×C22⋊C4—261no—
420C2×C22⋊C4C22⋊D1311yescharacteristic
421C2×C22⋊C4C22⋊D1311yescharacteristic
422C2×C42—21no—
423C2×C42—21no—
424C2×C42—21no—
425C2×C42—261no—
426C2×C42C22×D1311yescharacteristic
427C2×C42C22×D1311yescharacteristic
428#106—262no—
429C4⋊C8—521no—
430#103—262no—
431#103—262no—
432#103—521no—
433#102—262no—
434#102—262no—
435#102—521no—
436C22⋊C8—521no—
437C22⋊C8—521no—
438#97—521no—
439#95—21no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—261no—
444#95—261no—
445#95C22⋊D1311yescharacteristic
446#95C22⋊D1311yescharacteristic
447C2×C13—81no—
448C2×C13#245911yescharacteristic
449C2×C13#311111yescharacteristic
450C2×C13#312611yescharacteristic
451C2×C13#330711yescharacteristic
452C2×C13#331111yescharacteristic
453C2×C13#331711yescharacteristic
454C2×C13#332611yescharacteristic
455D13—161no—
456C24—261no—
457C24C2×C22⋊D1311yescharacteristic
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8#612712yes—
464C2×D4—261no—
465C2×D4—261no—
466C2×D4—261no—
467C2×D4—261no—
468C2×D4—261no—
469C2×D4—261no—
470C2×D4—522no—
471C2×D4—522no—
472C2×D4—1041no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—261no—
484C22×C4—261no—
485C22×C4—261no—
486C22×C4C2×C22⋊D1311yescharacteristic
487C22×C4C2×C22⋊D1311yescharacteristic
488C22×C4C2×C22⋊D1311yescharacteristic
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C23×D1311yescharacteristic
492SD16—524no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C4⋊C4—24no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—132no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—261no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4#612712yes—
521C4⋊C4#612912yes—
522C22⋊C4—24no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—42no—
526C22⋊C4—522no—
527C22⋊C4—522no—
528C22⋊C4—1041no—
529C22⋊C4—1041no—
530C22⋊C4—1041no—
531C22⋊C4—1041no—
532C42—21no—
533C42—21no—
534C42—21no—
535C42—21no—
536C42—42no—
537C42—42no—
538C42—42no—
539C42—1041no—
540C13#2675111yescharacteristic, complemented, Sylow
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—521no—
549C23—521no—
550C23—521no—
551C23—521no—
552C23—521no—
553C23—521no—
554C23—521no—
555C23C22×C22⋊D1311yescharacteristic
556Q8—22no—
557Q8—22no—
558Q8—41no—
559Q8—41no—
560D4—521no—
561D4—521no—
562D4—521no—
563D4—521no—
564D4—1044no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—22no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—21no—
574C2×C4—21no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
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—262no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—521no—
604C2×C4—521no—
605C2×C4C2×#612711yescharacteristic
606C2×C4C2×#612711yescharacteristic
607C2×C4C2×#612911yescharacteristic
608C2×C4#8825111yescharacteristic
609C2×C4#41×D1311yescharacteristic
610C2×C4#8825611yescharacteristic
611C8—521no—
612C8—521no—
613C8—521no—
614C8—521no—
615C22—41no—
616C22—41no—
617C22—41no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22—1041no—
623C22—1041no—
624C22—1041no—
625C22—1041no—
626C22—1041no—
627C22—1041no—
628C22—1041no—
629C22#1171949611yescharacteristic
630C22#1171951111yescharacteristic
631C22#1171952711yescharacteristic
632C22#1171952711yescharacteristic
633C22#1171953411yescharacteristic
634C22#1171954211yescharacteristic
635C22#1171954211yescharacteristic
636C4—41no—
637C4—41no—
638C4—42no—
639C4—42no—
640C4—41no—
641C4—42no—
642C4—41no—
643C4—41no—
644C4—81no—
645C4—522no—
646C4—1041no—
647C4—1041no—
648C4#1171924311yescharacteristic
649C4#1171926411yescharacteristic
650C4#1171926511yescharacteristic
651C4#1171926811yescharacteristic
652C2—81no—
653C2—2081no—
654C2#1311876711yescharacteristic
655C2#1312494511yescharacteristic
656C2#1312512711yescharacteristic
657C2#1312681211yescharacteristic
658C2#1312686611yescharacteristic
659C2#1312695611yescharacteristic
660C2#1312708911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2362C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2362D13
hypocenterC13#26751
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2362

Complements

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

NH ≅ G/Ntype
2. #13116151C2semidirect
3. #13116029C2semidirect
4. #13115987C2semidirect
6. #13115793C2semidirect
7. #13115532C2semidirect
8. #13115463C2semidirect
9. #13115451C2semidirect
10. #13115418C2semidirect
11. #13115191C2semidirect
13. #13114931C2semidirect
14. #13114666C2semidirect
15. C13×#2362C2semidirect
212. #2362D13semidirect
540. C13#26751semidirect

Maximal subgroups

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

subgroupindex
#131191882
#131161512
#131160292
#131159872
#131158372
#131157932
#131155322
#131154632
#131154512
#131154182
#131151912
#131151582
#131149312
#131146662
C13×#23622
#2675113