Finite Group Databasebeta

← #15926479

Subgroups — #15926479

Order 3328.

802 conjugacy classes of subgroups.

The subgroup lattice has 652 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118527C211yesmaximal, characteristic, complemented
2#13116404C211yesmaximal, characteristic, complemented
3#13116337C211yesmaximal, characteristic, complemented
4#13116210C211yesmaximal, characteristic, complemented
5#13115972C211yesmaximal, characteristic, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115428C211yesmaximal, characteristic, complemented
8#13115265C211yesmaximal, characteristic
9#13115159C211yesmaximal, characteristic
10#13115083C211yesmaximal, characteristic, complemented
11#13115035C211yesmaximal, characteristic, complemented
12#13115016C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C13×#2363C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C13×#390—21no—
23C13×#390C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#388—21no—
26C13×#386—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88048C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718609—21no—
39#11718608—21no—
40#11718597C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718316—21no—
46#11718307—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
59C22×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C22×Dic26—21no—
64C13×#121—22no—
65C13×#121Q814yescomplemented
66C4×D4×C13—22no—
67C4×D4×C13—41no—
68C13×#117—22no—
69C13×#117—41no—
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⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4—21no—
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C13×C22⋊C4D411yescharacteristic
81C2×C42×C13—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86C2×C22⋊Dic13—21no—
87#88180—22no—
88#88180—41no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×C4×Dic13—21no—
97C22×#1055—22no—
98C22×#1055—41no—
99C22×#1055—41no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88123—22no—
105#88123—41no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110#88072—22no—
111#88072—41no—
112#88072—41no—
113#88072—41no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—22no—
120#88048—41no—
121#88047—22no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#26409—131nomaximal, Sylow
125C24×C13—21no—
126C24×C13C2×D411yescharacteristic
127C2×D4×C13—24no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—81no—
134C2×D4×C13—81no—
135C2×D4×C13C2×Q812yes—
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—42no—
144C22×C4×C13—42no—
145C22×C4×C13—81no—
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×Q812yes—
152C22×C4×C13#4112yes—
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C2×Dic26—42no—
159C2×Dic26—42no—
160C2×Dic26—81no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4C2×Q812yes—
167C13×C4⋊C4#4112yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—41no—
171C13×C22⋊C4—42no—
172C13×C22⋊C4—42no—
173C13×C22⋊C4—42no—
174C13×C22⋊C4—81no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—21no—
178C42×C13—21no—
179C42×C13—42no—
180C42×C13—81no—
181C22⋊Dic13—42no—
182C22⋊Dic13—81no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—42no—
191C4⋊Dic13#4112yes—
192#6101—42no—
193#6101—81no—
194C4×Dic13—42no—
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#2439—131no—
209#2363D1311yescharacteristic
210#2101—131no—
211#2088—131no—
212#2065—131no—
213#2023—131no—
214#1988—131no—
215#1921—131no—
216#1893—131no—
217#1875—131no—
218#1862—131no—
219#1854—131no—
220#1850—131no—
221#1804—131no—
222#1735—131no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13—21no—
229C23×C13—22no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13C22⋊Q812yes—
237C23×C13C22×D411yescharacteristic
238D4×C13—22no—
239D4×C13—22no—
240D4×C13—41no—
241D4×C13—41no—
242D4×C13—84no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—22no—
248C2×C4×C13—22no—
249C2×C4×C13—22no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—22no—
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—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—84no—
270C2×C4×C13C22⋊Q812yes—
271C2×C4×C13#13512yes—
272C2×C4×C13C22×Q811yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13C2×#4111yescharacteristic
276C2×C4×C13H(5,𝔽2)11yescharacteristic
277C2×C4×C13H(5,𝔽2)11yescharacteristic
278C2×Dic13—22no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290Dic26—84no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294#1055—41no—
295C23×C8—131no—
296C2×C4⋊Q8—131no—
297C2×#121C2×D1311yescharacteristic
298C2×C4×D4C2×D1311yescharacteristic
299C2×#117—131no—
300C2×#117C2×D1311yescharacteristic
301C2×#107—131no—
302C2×#106—131no—
303C2×C4⋊C8—131no—
304C2×C4⋊C8—131no—
305C2×#102—131no—
306C2×#102—131no—
307C2×#102—131no—
308C2×#102—131no—
309C2×C22⋊C8—131no—
310#396—261no—
311#393—261no—
312#391—261no—
313#390—21no—
314#390C2×D1311yescharacteristic
315#389—131no—
316#389—131no—
317#389C2×D1311yescharacteristic
318#388—21no—
319#387—261no—
320#386—21no—
321#382—131no—
322#380—131no—
323C4×C4⋊C4C2×D1311yescharacteristic
324C4×C22⋊C4—21no—
325C4×C22⋊C4C2×D1311yescharacteristic
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#340—131no—
336#336—131no—
337#336—131no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—81no—
349C22×C13—81no—
350C22×C13—81no—
351C22×C13—81no—
352C22×C13C2×C22⋊Q811yescharacteristic
353C22×C13#54611yescharacteristic
354C22×C13#54611yescharacteristic
355C22×C13C2×#13511yescharacteristic
356C22×C13#57511yescharacteristic
357C22×C13#57611yescharacteristic
358C22×C13#57711yescharacteristic
359C4×C13—22no—
360C4×C13—22no—
361C4×C13—42no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—42no—
365C4×C13—41no—
366C4×C13—81no—
367C4×C13#52911yescharacteristic
368C4×C13#53811yescharacteristic
369C4×C13#55411yescharacteristic
370C4×C13#55411yescharacteristic
371Dic13—42no—
372Dic13—81no—
373Dic13—81no—
374Dic13—81no—
375C22×Q8—261no—
376C22×D4—21no—
377C22×D4C22×D1311yescharacteristic
378C23×C4—21no—
379C23×C4C22×D1311yescharacteristic
380C22×C8—131no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—262no—
385C22×C8—521no—
386C22×C8—521no—
387C4⋊Q8—262no—
388C4⋊Q8—521no—
389#121—22no—
390#121Dic2614yescomplemented
391C4×D4—22no—
392C4×D4—41no—
393#117—22no—
394#117—41no—
395#117—262no—
396#117—521no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C22⋊C4—21no—
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—261no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4C22⋊D1311yescharacteristic
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C42—21no—
418C2×C42—21no—
419C2×C42—261no—
420C2×C42C22×D1311yescharacteristic
421C2×C42C22×D1311yescharacteristic
422#107—262no—
423#106—521no—
424C4⋊C8—521no—
425C4⋊C8—521no—
426#102—262no—
427#102—521no—
428#102—521no—
429#102—521no—
430C22⋊C8—262no—
431#95—21no—
432#95—21no—
433#95—261no—
434#95—261no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95C22⋊D1311yescharacteristic
439#95C22⋊D1311yescharacteristic
440C2×C13—42no—
441C2×C13—82no—
442C2×C13#245011yescharacteristic
443C2×C13#307611yescharacteristic
444C2×C13#308111yescharacteristic
445C2×C13#329711yescharacteristic
446C2×C13#330411yescharacteristic
447C2×C13#331911yescharacteristic
448C2×C13#332111yescharacteristic
449C24—21no—
450C24C2×C22⋊D1311yescharacteristic
451C2×Q8—522no—
452C2×Q8—522no—
453C2×Q8—1041no—
454C2×D4—24no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—81no—
461C2×D4—81no—
462C2×D4C2×Dic2612yes—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—81no—
473C22×C4—261no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4C2×Dic2612yes—
478C22×C4#612712yes—
479C22×C4C2×C22⋊D1311yescharacteristic
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C23×D1311yescharacteristic
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—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—524no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—81no—
503C4⋊C4—132no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—261no—
510C4⋊C4—261no—
511C4⋊C4—522no—
512C4⋊C4—522no—
513C4⋊C4—1041no—
514C4⋊C4C2×Dic2612yes—
515C4⋊C4#612912yes—
516C22⋊C4—24no—
517C22⋊C4—22no—
518C22⋊C4—41no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—42no—
522C22⋊C4—81no—
523C22⋊C4—522no—
524C22⋊C4—1041no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—42no—
530C42—81no—
531C42—522no—
532C13#2640911yescharacteristic, complemented, Sylow
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—22no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23—41no—
546C23#8817812yes—
547C23C22×C22⋊D1311yescharacteristic
548Q8—1044no—
549D4—22no—
550D4—22no—
551D4—41no—
552D4—41no—
553D4—84no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—21no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—84no—
581C2×C4—262no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4—521no—
591C2×C4—521no—
592C2×C4—521no—
593C2×C4#8817812yes—
594C2×C4#8820412yes—
595C2×C4C22×Dic2611yescharacteristic
596C2×C4C2×#612711yescharacteristic
597C2×C4C2×#612911yescharacteristic
598C2×C4#8825111yescharacteristic
599C2×C4#41×D1311yescharacteristic
600C2×C4#8825611yescharacteristic
601C8—521no—
602C8—521no—
603C8—521no—
604C8—521no—
605C22—22no—
606C22—22no—
607C22—22no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—42no—
613C22—42no—
614C22—42no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22C2×#8817811yescharacteristic
620C22#1171951111yescharacteristic
621C22C2×#8820411yescharacteristic
622C22#1171952711yescharacteristic
623C22#1171953411yescharacteristic
624C22#1171954011yescharacteristic
625C22#1171954111yescharacteristic
626C4—22no—
627C4—22no—
628C4—42no—
629C4—41no—
630C4—42no—
631C4—41no—
632C4—41no—
633C4—81no—
634C4—522no—
635C4—1041no—
636C4—1041no—
637C4—1041no—
638C4#1171924311yescharacteristic
639C4#1171924411yescharacteristic
640C4#1171924811yescharacteristic
641C4#1171926511yescharacteristic
642C2—42no—
643C2—82no—
644C2#1311865411yescharacteristic
645C2#1312462411yescharacteristic
646C2#1312466711yescharacteristic
647C2#1312668011yescharacteristic
648C2#1312677511yescharacteristic
649C2#1312699211yescharacteristic
650C2#1312701611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2363C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2363D13
hypocenterC13#26409
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2363

Complements

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

NH ≅ G/Ntype
1. #13118527C2semidirect
2. #13116404C2semidirect
3. #13116337C2semidirect
4. #13116210C2semidirect
5. #13115972C2semidirect
6. #13115788C2semidirect
7. #13115428C2semidirect
10. #13115083C2semidirect
11. #13115035C2semidirect
12. #13115016C2semidirect
13. #13114846C2semidirect
14. #13114552C2semidirect
65. C13×#121Q8semidirect
390. #121Dic26semidirect
532. C13#26409semidirect

Maximal subgroups

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

subgroupindex
#131185272
#131164042
#131163372
#131162102
#131159722
#131157882
#131154282
#131152652
#131151592
#131150832
#131150352
#131150162
#131148462
#131145522
C13×#23632
#2640913