Finite Group Databasebeta

← #15926689

Subgroups — #15926689

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#13118549C211yesmaximal, characteristic, complemented
2#13116394C211yesmaximal, characteristic, complemented
3#13116332C211yesmaximal, characteristic, complemented
4#13116224C211yesmaximal, characteristic, complemented
5#13115982C211yesmaximal, characteristic, complemented
6#13115793C211yesmaximal, characteristic, complemented
7#13115421C211yesmaximal, characteristic, complemented
8#13115265C211yesmaximal, characteristic
9#13115159C211yesmaximal, characteristic
10#13115097C211yesmaximal, characteristic, complemented
11#13115035C211yesmaximal, characteristic, complemented
12#13115016C211yesmaximal, characteristic, complemented
13#13114836C211yesmaximal, characteristic, complemented
14#13114552C211yesmaximal, characteristic, complemented
15C13×#2363C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C13×#117C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88124C2211yescharacteristic
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#11718610—21no—
39#11718609—21no—
40#11718596C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718315—21no—
46#11718308—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
63C13×#121—22no—
64C13×#121Q814yes—
65C4×D4×C13—22no—
66C4×D4×C13—41no—
67C13×#117—22no—
68C13×#117—41no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C13×C22⋊C4—21no—
74C2×C13×C22⋊C4—21no—
75C2×C13×C22⋊C4—21no—
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4—21no—
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C13×C22⋊C4D411yescharacteristic
80C2×C42×C13—21no—
81C2×C42×C13—21no—
82C2×C42×C13C2311yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C22⋊Dic13—21no—
85C2×C22⋊Dic13—21no—
86#88180—22no—
87#88180—41no—
88C2×C4⋊Dic13—21no—
89C2×C4⋊Dic13—21no—
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C22×#1055—22no—
100C22×#1055—41no—
101C22×#1055—41no—
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106#88124—22no—
107#88124—41no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88072—22no—
113#88072—41no—
114#88072—41no—
115#88072—41no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—22no—
120#88048—22no—
121#88047—41no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#26423—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—
158C13×C4⋊C4—21no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—81no—
163C13×C4⋊C4C2×Q812yes—
164C13×C4⋊C4#4112yes—
165C13×C22⋊C4—24no—
166C13×C22⋊C4—22no—
167C13×C22⋊C4—41no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—42no—
170C13×C22⋊C4—42no—
171C13×C22⋊C4—81no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—42no—
177C42×C13—81no—
178C22⋊Dic13—42no—
179C22⋊Dic13—81no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—21no—
187C4⋊Dic13—42no—
188C4⋊Dic13—81no—
189C4⋊Dic13#4112yes—
190#6101—42no—
191#6101—42no—
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#2441—131no—
209#2363D1311yescharacteristic
210#2099—131no—
211#2087—131no—
212#2067—131no—
213#2025—131no—
214#1989—131no—
215#1920—131no—
216#1893—131no—
217#1875—131no—
218#1864—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×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—
290#1055—41no—
291#1055—41no—
292#1055—41no—
293#1055—41no—
294C23×C8—131no—
295C2×#125—131no—
296C2×#121C2×D1311yescharacteristic
297C2×C4×D4C2×D1311yescharacteristic
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—261no—
310#396—261no—
311#390—21no—
312#390C2×D1311yescharacteristic
313#389—131no—
314#389—131no—
315#389—261no—
316#389C2×D1311yescharacteristic
317#388—21no—
318#387—261no—
319#386—21no—
320#384—131no—
321#380—131no—
322C4×C4⋊C4C2×D1311yescharacteristic
323C4×C22⋊C4—21no—
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×C13—42no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13—81no—
350C22×C13—81no—
351C22×C13C2×C22⋊Q811yescharacteristic
352C22×C13#54611yescharacteristic
353C22×C13#54611yescharacteristic
354C22×C13C2×#13511yescharacteristic
355C22×C13#57511yescharacteristic
356C22×C13#57611yescharacteristic
357C22×C13#57711yescharacteristic
358C4×C13—22no—
359C4×C13—22no—
360C4×C13—42no—
361C4×C13—42no—
362C4×C13—41no—
363C4×C13—41no—
364C4×C13—41no—
365C4×C13—81no—
366C4×C13#52911yescharacteristic
367C4×C13#53811yescharacteristic
368C4×C13#55411yescharacteristic
369C4×C13#55411yescharacteristic
370Dic13—42no—
371Dic13—81no—
372Dic13—81no—
373Dic13—81no—
374C22×D4—21no—
375C22×D4C22×D1311yescharacteristic
376C23×C4—21no—
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—262no—
386#125—521no—
387#121—22no—
388#121Dic2614yes—
389C4×D4—22no—
390C4×D4—41no—
391#117—22no—
392#117—41no—
393#117—262no—
394#117—521no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—131no—
398C2×C4⋊C4—131no—
399C2×C4⋊C4—131no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—21no—
411C2×C22⋊C4—21no—
412C2×C22⋊C4—21no—
413C2×C22⋊C4—21no—
414C2×C22⋊C4—261no—
415C2×C22⋊C4—261no—
416C2×C22⋊C4C22⋊D1311yescharacteristic
417C2×C22⋊C4C22⋊D1311yescharacteristic
418C2×C42—21no—
419C2×C42—21no—
420C2×C42—261no—
421C2×C42C22×D1311yescharacteristic
422C2×C42C22×D1311yescharacteristic
423#107—521no—
424#106—262no—
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—261no—
435#95—261no—
436#95—261no—
437#95C22⋊D1311yescharacteristic
438#95C22⋊D1311yescharacteristic
439C2×C13—42no—
440C2×C13—82no—
441C2×C13#245011yescharacteristic
442C2×C13#307611yescharacteristic
443C2×C13#308111yescharacteristic
444C2×C13#329611yescharacteristic
445C2×C13#330511yescharacteristic
446C2×C13#330711yescharacteristic
447C2×C13#330911yescharacteristic
448C24—21no—
449C24C2×C22⋊D1311yescharacteristic
450C2×D4—24no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—81no—
457C2×D4—81no—
458C2×D4C2×Dic2612yes—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—42no—
467C22×C4—42no—
468C22×C4—81no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4C2×Dic2612yes—
474C22×C4#612712yes—
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—81no—
499C4⋊C4—132no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—522no—
508C4⋊C4—522no—
509C4⋊C4—522no—
510C4⋊C4—522no—
511C4⋊C4—1041no—
512C4⋊C4—1041no—
513C4⋊C4C2×Dic2612yes—
514C4⋊C4#612912yes—
515C22⋊C4—24no—
516C22⋊C4—22no—
517C22⋊C4—41no—
518C22⋊C4—42no—
519C22⋊C4—42no—
520C22⋊C4—42no—
521C22⋊C4—81no—
522C22⋊C4—522no—
523C22⋊C4—1041no—
524C42—21no—
525C42—21no—
526C42—21no—
527C42—21no—
528C42—42no—
529C42—81no—
530C42—522no—
531C13#2642311yescharacteristic, complemented, Sylow
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23—21no—
538C23—22no—
539C23—41no—
540C23—41no—
541C23—41no—
542C23—41no—
543C23—41no—
544C23—41no—
545C23#8817812yes—
546C23C22×C22⋊D1311yescharacteristic
547D4—22no—
548D4—22no—
549D4—41no—
550D4—41no—
551D4—84no—
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—22no—
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—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—84no—
579C2×C4—262no—
580C2×C4—521no—
581C2×C4—521no—
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#8817812yes—
592C2×C4#8820412yes—
593C2×C4C22×Dic2611yescharacteristic
594C2×C4C2×#612711yescharacteristic
595C2×C4C2×#612911yescharacteristic
596C2×C4#8825111yescharacteristic
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—42no—
611C22—42no—
612C22—42no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22C2×#8817811yescharacteristic
618C22#1171951111yescharacteristic
619C22C2×#8820411yescharacteristic
620C22#1171952711yescharacteristic
621C22#1171953411yescharacteristic
622C22#1171954011yescharacteristic
623C22#1171954111yescharacteristic
624C4—22no—
625C4—22no—
626C4—42no—
627C4—42no—
628C4—41no—
629C4—41no—
630C4—41no—
631C4—81no—
632C4—522no—
633C4—1041no—
634C4—1041no—
635C4—1041no—
636C4#1171924311yescharacteristic
637C4#1171924411yescharacteristic
638C4#1171924811yescharacteristic
639C4#1171926511yescharacteristic
640C2—42no—
641C2—82no—
642C2#1311865411yescharacteristic
643C2#1312462411yescharacteristic
644C2#1312466711yescharacteristic
645C2#1312667111yescharacteristic
646C2#1312678011yescharacteristic
647C2#1312680611yescharacteristic
648C2#1312684211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2363C2
socleC23×C13C22×D4
prime radicalC2×C13×#121C22
hypercenter#2363D13
hypocenterC13#26423
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. #13118549C2semidirect
2. #13116394C2semidirect
3. #13116332C2semidirect
4. #13116224C2semidirect
5. #13115982C2semidirect
6. #13115793C2semidirect
7. #13115421C2semidirect
10. #13115097C2semidirect
11. #13115035C2semidirect
12. #13115016C2semidirect
13. #13114836C2semidirect
14. #13114552C2semidirect
531. C13#26423semidirect

Maximal subgroups

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

subgroupindex
#131185492
#131163942
#131163322
#131162242
#131159822
#131157932
#131154212
#131152652
#131151592
#131150972
#131150352
#131150162
#131148362
#131145522
C13×#23632
#2642313