Finite Group Databasebeta

← #15926661

Subgroups — #15926661

Order 3328.

794 conjugacy classes of subgroups.

The subgroup lattice has 650 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117872C211yesmaximal, characteristic
2#13116398C211yesmaximal, characteristic, complemented
3#13116337C211yesmaximal, characteristic, complemented
4#13116207C211yesmaximal, characteristic, complemented
5#13115979C211yesmaximal, characteristic, complemented
6#13115794C211yesmaximal, characteristic, complemented
7#13115404C211yesmaximal, characteristic, complemented
8#13115262C211yesmaximal, characteristic
9#13115158C211yesmaximal, characteristic
10#13115082C211yesmaximal, characteristic, complemented
11#13115033C211yesmaximal, characteristic, complemented
12#13115016C211yesmaximal, characteristic, complemented
13#13114833C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C13×#2441C211yesmaximal, characteristic, complemented
16C2×C13×#125C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C2×#88184C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×C4×D52C2211yescharacteristic
22C13×#399—21no—
23C13×#396—21no—
24C13×#389—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#387—21no—
28C13×#384C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C22⋊C4C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88049C2211yescharacteristic
33C2×#88049C2211yescharacteristic
34C2×#88049C2211yescharacteristic
35C2×#88049C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718618—21no—
39#11718617—21no—
40#11718600C2211yescharacteristic
41C4×C4⋊Dic13C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718330—21no—
46#11718327—21no—
47#11718121C2211yescharacteristic
48#11718121C2211yescharacteristic
49#11718121C2211yescharacteristic
50#11718121C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C22×D52C2311yescharacteristic
62C22×C4×D13—21no—
63C13×#125—22no—
64C13×#125—41no—
65C13×#117—22no—
66C13×#117—41no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—21no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85#88184—22no—
86#88184Q814yes—
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×#1055—22no—
100C22×#1055—41no—
101C22×#1055—41no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C4×D52—22no—
107C4×D52—41no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95D411yescharacteristic
112C13×#95D411yescharacteristic
113#88071—21no—
114#88071—21no—
115C22⋊#1055—22no—
116#88049—22no—
117#88049—41no—
118#88049—41no—
119#88049—41no—
120#88048—41no—
121#88047—22no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#26421—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C23×D13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13C2×D411yescharacteristic
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×Q812yes—
141C22×C4×C13#4112yes—
142C22×C4×C13C2411yescharacteristic
143C2×C22⋊D13—24no—
144C2×C22⋊D13—81no—
145C2×C22⋊D13—81no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C2×D52—21no—
150C2×D52—21no—
151C2×D52—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52C2×Q812yes—
155C2×C4×D13—42no—
156C2×C4×D13—42no—
157C2×C4×D13—81no—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—42no—
166C13×C4⋊C4—42no—
167C13×C4⋊C4—42no—
168C13×C4⋊C4—42no—
169C13×C4⋊C4—81no—
170C13×C4⋊C4—81no—
171C13×C4⋊C4#4112yes—
172C13×C22⋊C4—22no—
173C13×C22⋊C4—41no—
174C13×C22⋊C4—42no—
175C13×C22⋊C4—81no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—21no—
180C42×C13—42no—
181C22⋊Dic13—42no—
182#6103—24no—
183#6103—42no—
184#6103—42no—
185#6103—81no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13C2×Q812yes—
191C4⋊Dic13#4112yes—
192#6101—81no—
193C4×Dic13—42no—
194C4×Dic13—81no—
195C2×#1055—21no—
196C2×#1055—21no—
197C2×#1055—21no—
198C2×#1055—21no—
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—44no—
208#2441D1311yescharacteristic, complemented
209#2363—131no—
210#2100—131no—
211#2088—131no—
212#2065—131no—
213#2025—131no—
214#1989—131no—
215#1918—131no—
216#1893—131no—
217#1875—131no—
218#1862—131no—
219#1854—131no—
220#1850—131no—
221#1802—131no—
222#1735—131no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13C22⋊Q812yes—
230C23×C13C22×D411yescharacteristic
231C22×D13—22no—
232C22×D13—41no—
233C22×D13—41no—
234C22×D13—41no—
235C22×D13—41no—
236C22×D13—41no—
237C22×D13—41no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—22no—
245C2×C4×C13—22no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—22no—
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—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13C22⋊Q812yes—
268C2×C4×C13#13512yes—
269C2×C4×C13C22×Q811yescharacteristic
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13H(5,𝔽2)11yescharacteristic
274C2×C4×C13H(5,𝔽2)11yescharacteristic
275C22⋊D13—84no—
276C2×Dic13—22no—
277C2×Dic13—22no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285D52—22no—
286D52—22no—
287D52—41no—
288D52—41no—
289C4×D13—84no—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C23×C8—131no—
295C2×#125C2×D1311yescharacteristic
296C2×#121—131no—
297C2×C4×D4—131no—
298C2×#117—131no—
299C2×#117C2×D1311yescharacteristic
300C2×#107—131no—
301C2×#106—131no—
302C2×C4⋊C8—131no—
303C2×C4⋊C8—131no—
304C2×#102—131no—
305C2×#102—131no—
306C2×#102—131no—
307C2×#102—131no—
308C2×C22⋊C8—131no—
309#399—21no—
310#396—21no—
311#390—131no—
312#390—261no—
313#389—21no—
314#389—131no—
315#389C2×D1311yescharacteristic
316#389C2×D1311yescharacteristic
317#388—261no—
318#387—21no—
319#386—261no—
320#384C2×D1311yescharacteristic
321#380C2×D1311yescharacteristic
322C4×C4⋊C4—131no—
323C4×C22⋊C4—261no—
324C4×C22⋊C4C2×D1311yescharacteristic
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#336—131no—
336#336—131no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13C2×C22⋊Q811yescharacteristic
345C22×C13#54611yescharacteristic
346C22×C13#54611yescharacteristic
347C22×C13C2×#13511yescharacteristic
348C22×C13#57511yescharacteristic
349C22×C13#57611yescharacteristic
350C22×C13#57711yescharacteristic
351C2×D13—42no—
352C2×D13—42no—
353C2×D13—42no—
354C2×D13—81no—
355C2×D13—81no—
356C2×D13—81no—
357C2×D13—81no—
358C4×C13—22no—
359C4×C13—22no—
360C4×C13—41no—
361C4×C13—42no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—81no—
365C4×C13—81no—
366C4×C13—81no—
367C4×C13#52911yescharacteristic
368C4×C13#53811yescharacteristic
369C4×C13#55411yescharacteristic
370C4×C13#55411yescharacteristic
371Dic13—42no—
372Dic13—42no—
373Dic13—81no—
374C22×D4—131no—
375C22×D4—261no—
376C23×C4—261no—
377C23×C4C22×D1311yescharacteristic
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381C22×C8—131no—
382C22×C8—262no—
383C22×C8—521no—
384C22×C8—521no—
385#125—22no—
386#125—41no—
387#121—134no—
388#121—262no—
389C4×D4—262no—
390C4×D4—521no—
391#117—22no—
392#117—41no—
393#117—262no—
394#117—521no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—21no—
400C2×C4⋊C4—21no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—131no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—261no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42—21no—
419C2×C42—261no—
420C2×C42—261no—
421C2×C42C22×D1311yescharacteristic
422C2×C42C22×D1311yescharacteristic
423#107—262no—
424#106—521no—
425C4⋊C8—521no—
426C4⋊C8—521no—
427#102—262no—
428#102—521no—
429#102—521no—
430#102—521no—
431C22⋊C8—262no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—261no—
436#95—261no—
437#95C22⋊D1311yescharacteristic
438#95C22⋊D1311yescharacteristic
439C2×C13—42no—
440C2×C13#245011yescharacteristic
441C2×C13#307611yescharacteristic
442C2×C13#308111yescharacteristic
443C2×C13#329711yescharacteristic
444C2×C13#330311yescharacteristic
445C2×C13#330911yescharacteristic
446C2×C13#331711yescharacteristic
447D13—82no—
448C24—261no—
449C24C2×C22⋊D1311yescharacteristic
450C2×D4—132no—
451C2×D4—264no—
452C2×D4—261no—
453C2×D4—261no—
454C2×D4—261no—
455C2×D4—261no—
456C2×D4—261no—
457C2×D4—1041no—
458C2×D4—1041no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—522no—
471C22×C4—522no—
472C22×C4—1041no—
473C22×C4Q8×D1312yes—
474C22×C4#613112yes—
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C2×C22⋊D1311yescharacteristic
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C23×D1311yescharacteristic
481C2×C8—261no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—261no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—524no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—42no—
503C4⋊C4—42no—
504C4⋊C4—42no—
505C4⋊C4—81no—
506C4⋊C4—81no—
507C4⋊C4—132no—
508C4⋊C4—132no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—261no—
512C4⋊C4—261no—
513C4⋊C4—1041no—
514C4⋊C4#612912yes—
515C22⋊C4—22no—
516C22⋊C4—41no—
517C22⋊C4—42no—
518C22⋊C4—81no—
519C22⋊C4—264no—
520C22⋊C4—522no—
521C22⋊C4—522no—
522C22⋊C4—522no—
523C22⋊C4—1041no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—522no—
530C42—1041no—
531C13#2642111yescharacteristic, complemented, Sylow
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—262no—
539C23—521no—
540C23—521no—
541C23—521no—
542C23—521no—
543C23—521no—
544C23—521no—
545C23#8820012yes—
546C23C22×C22⋊D1311yescharacteristic
547D4—262no—
548D4—262no—
549D4—521no—
550D4—521no—
551D4—1044no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—262no—
582C2×C4—262no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—1044no—
591C2×C4#8820012yes—
592C2×C4#8820412yes—
593C2×C4C2×#612911yescharacteristic
594C2×C4#8825111yescharacteristic
595C2×C4C2×Q8×D1311yescharacteristic
596C2×C4C2×#613111yescharacteristic
597C2×C4#41×D1311yescharacteristic
598C2×C4#8825611yescharacteristic
599C8—521no—
600C8—521no—
601C8—521no—
602C8—521no—
603C22—22no—
604C22—22no—
605C22—22no—
606C22—41no—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—522no—
611C22—522no—
612C22—522no—
613C22—1041no—
614C22—1041no—
615C22—1041no—
616C22—1041no—
617C22#1171951111yescharacteristic
618C22C2×#8820011yescharacteristic
619C22C2×#8820411yescharacteristic
620C22#1171952711yescharacteristic
621C22#1171953411yescharacteristic
622C22#1171954011yescharacteristic
623C22#1171954211yescharacteristic
624C4—22no—
625C4—22no—
626C4—41no—
627C4—41no—
628C4—42no—
629C4—41no—
630C4—81no—
631C4—81no—
632C4—81no—
633C4—522no—
634C4—522no—
635C4—1041no—
636C4#1171932911yescharacteristic
637C4#1171934011yescharacteristic
638C4#1171934111yescharacteristic
639C4#1171934911yescharacteristic
640C2—42no—
641C2—1042no—
642C2#1311865611yescharacteristic
643C2#1312461811yescharacteristic
644C2#1312466111yescharacteristic
645C2#1312668011yescharacteristic
646C2#1312676411yescharacteristic
647C2#1312684211yescharacteristic
648C2#1312695611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2441C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2441D13
hypocenterC13#26421
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2441

Complements

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

NH ≅ G/Ntype
2. #13116398C2semidirect
3. #13116337C2semidirect
4. #13116207C2semidirect
5. #13115979C2semidirect
6. #13115794C2semidirect
7. #13115404C2semidirect
10. #13115082C2semidirect
11. #13115033C2semidirect
12. #13115016C2semidirect
13. #13114833C2semidirect
14. #13114552C2semidirect
15. C13×#2441C2semidirect
208. #2441D13semidirect
531. C13#26421semidirect

Maximal subgroups

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

subgroupindex
#131178722
#131163982
#131163372
#131162072
#131159792
#131157942
#131154042
#131152622
#131151582
#131150822
#131150332
#131150162
#131148332
#131145522
C13×#24412
#2642113