Finite Group Databasebeta

← #15923640

Subgroups — #15923640

Order 3328.

886 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118276C211yesmaximal, characteristic
2#13116403C211yesmaximal, characteristic, complemented
3#13116267C211yesmaximal, characteristic, complemented
4#13116250C211yesmaximal, characteristic, complemented
5#13116018C211yesmaximal, characteristic, complemented
6#13115456C211yesmaximal, characteristic, complemented
7#13115428C211yesmaximal, characteristic, complemented
8#13115262C211yesmaximal, characteristic, complemented
9#13115158C211yesmaximal, characteristic, complemented
10#13115153C211yesmaximal, characteristic, complemented
11#13115129C211yesmaximal, characteristic, complemented
12#13115023C211yesmaximal, characteristic, complemented
13#13114931C211yesmaximal, characteristic, complemented
14C2×#11718121C211yesmaximal, characteristic, complemented
15C13×#2352C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88193—21no—
20C2×#88184C2211yescharacteristic
21C2×#88184C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C23×#1055C2211yescharacteristic
24C13×#388—21no—
25C13×#387—21no—
26C13×#386—21no—
27C13×#382C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30C4×C13×C4⋊C4C2211yescharacteristic
31C4×C13×C22⋊C4—21no—
32#11718873C2211yescharacteristic
33C2×C22⋊#1055C2211yescharacteristic
34C2×C22⋊#1055C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36#11718655—21no—
37C2×#88049C2211yescharacteristic
38C2×#88049C2211yescharacteristic
39C2×#88049C2211yescharacteristic
40C2×#88049C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718622—21no—
44#11718619—21no—
45#11718600C2211yescharacteristic
46#11718589C2211yescharacteristic
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×C13D411yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C23×C4×C13C2311yescharacteristic
63C22×C22⋊D13—21no—
64C22×C22⋊D13—21no—
65C23×Dic13—21no—
66C22×D52C2311yescharacteristic
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C13×#117—22no—
70C13×#117—41no—
71C2×C13×C4⋊C4—22no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—41no—
74C2×C13×C4⋊C4D411yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C13×C22⋊C4D411yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87C2×C22⋊Dic13—21no—
88#88193—44no—
89#88184—22no—
90#88184—22no—
91#88184—22no—
92#88184—41no—
93C2×#6103—21no—
94C2×#6103—21no—
95C2×#6103—21no—
96C2×#6103—21no—
97C2×C4⋊Dic13—22no—
98C2×C4⋊Dic13—21no—
99C2×C4⋊Dic13—41no—
100C2×C4⋊Dic13C2311yescharacteristic
101C2×C4⋊Dic13C2311yescharacteristic
102C2×C4⋊Dic13C2311yescharacteristic
103C2×#6101—21no—
104C22×#1055—22no—
105C22×#1055—41no—
106C22×#1055—41no—
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109C22×#1055C2311yescharacteristic
110C22×#1055C2311yescharacteristic
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115C13×#95—21no—
116#88071—21no—
117#88071—21no—
118C22⋊#1055—22no—
119C22⋊#1055—41no—
120C22⋊#1055—41no—
121#88049—22no—
122#88049—41no—
123#88049—41no—
124#88049—41no—
125#88047—22no—
126#88047—41no—
127#26208—131nomaximal, Sylow
128C24×C13C2×D411yescharacteristic
129C24×C13C2×D411yescharacteristic
130C23×D13—21no—
131C2×D4×C13—22no—
132C2×D4×C13—22no—
133C2×D4×C13—22no—
134C22×C4×C13—21no—
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×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13—21no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—81no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13C2411yescharacteristic
158C2×C22⋊D13—42no—
159C2×C22⋊D13—42no—
160C2×C22⋊D13—42no—
161C2×C22⋊D13—42no—
162C2×C22⋊D13—42no—
163C2×C22⋊D13—81no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—42no—
168C22×Dic13—42no—
169C22×Dic13—81no—
170C2×D52—21no—
171C2×D52—21no—
172C2×D52—21no—
173C2×D52—21no—
174C2×D52—21no—
175C2×D52—21no—
176C13×C4⋊C4—22no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—21no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—42no—
185C13×C4⋊C4#4112yes—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—22no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—81no—
191C42×C13—21no—
192C42×C13—21no—
193C42×C13—42no—
194C42×C13—81no—
195C22⋊Dic13—42no—
196#6103—42no—
197#6103—42no—
198#6103—42no—
199#6103—81no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—42no—
206C4⋊Dic13#4112yes—
207#6101—42no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—44no—
221#2416—131no—
222#2352D1311yescharacteristic, complemented
223#2101—131no—
224#2076—131no—
225#2073—131no—
226#2033—131no—
227#1925—131no—
228#1921—131no—
229#1893—131no—
230#1875—131no—
231#1874—131no—
232#1869—131no—
233#1852—131no—
234#1825—131no—
235C2×#340—131no—
236C23×C13—21no—
237C23×C13—21no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13#12312yes—
248C23×C13#13512yes—
249C23×C13AGL(1,ℤ/8)12yes—
250C23×C13C22×D411yescharacteristic
251C22×D13—41no—
252C22×D13—41no—
253C22×D13—41no—
254C22×D13—41no—
255C22×D13—41no—
256C22×D13—41no—
257C22×D13—41no—
258D4×C13—44no—
259C2×C4×C13—21no—
260C2×C4×C13—21no—
261C2×C4×C13—22no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—21no—
266C2×C4×C13—21no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—22no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—41no—
276C2×C4×C13—41no—
277C2×C4×C13—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
280C2×C4×C13—41no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—84no—
291C2×C4×C13#12312yes—
292C2×C4×C13C2×#4111yescharacteristic
293C2×C4×C13C2×#4111yescharacteristic
294C2×C4×C13C2×#4111yescharacteristic
295C2×C4×C13C2×#4111yescharacteristic
296C2×C4×C13H(5,𝔽2)11yescharacteristic
297C2×C4×C13H(5,𝔽2)11yescharacteristic
298C22⋊D13—84no—
299C22⋊D13—84no—
300C2×Dic13—22no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—84no—
310D52—41no—
311D52—41no—
312D52—41no—
313D52—41no—
314#1055—41no—
315#1055—41no—
316#1055—41no—
317#1055—41no—
318C23×C8—131no—
319C2×#121—131no—
320C2×#121—131no—
321C2×#121—261no—
322C2×C4×D4C2×D1311yescharacteristic
323C2×#117C2×D1311yescharacteristic
324C22×C4⋊C4—131no—
325C22×C4⋊C4C2×D1311yescharacteristic
326C2×#107—131no—
327C2×#107—131no—
328C2×#102—131no—
329C2×#102—131no—
330C2×#102—131no—
331C2×#102—131no—
332C2×C22⋊C8—131no—
333C2×C22⋊C8—131no—
334C2×C22⋊C8—131no—
335#396—261no—
336#394—261no—
337#390—131no—
338#389—131no—
339#388—21no—
340#387—21no—
341#386—21no—
342#386—261no—
343#382C2×D1311yescharacteristic
344#380—131no—
345#380C2×D1311yescharacteristic
346#380C2×D1311yescharacteristic
347C4×C4⋊C4C2×D1311yescharacteristic
348C4×C22⋊C4—21no—
349#340—131no—
350#340—131no—
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#340—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#336—131no—
360#336—131no—
361C22×C13—22no—
362C22×C13—22no—
363C22×C13—22no—
364C22×C13—22no—
365C22×C13—22no—
366C22×C13—22no—
367C22×C13—41no—
368C22×C13—41no—
369C22×C13—41no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—41no—
374C22×C13#48214yes—
375C22×C13C2×#12311yescharacteristic
376C22×C13#54611yescharacteristic
377C22×C13#54611yescharacteristic
378C22×C13C2×#13511yescharacteristic
379C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
380C22×C13#57611yescharacteristic
381C22×C13#57811yescharacteristic
382C2×D13—81no—
383C2×D13—81no—
384C2×D13—81no—
385C2×D13—81no—
386C2×D13—81no—
387C2×D13—81no—
388C2×D13—81no—
389C4×C13—22no—
390C4×C13—41no—
391C4×C13—41no—
392C4×C13—41no—
393C4×C13—42no—
394C4×C13—81no—
395C4×C13—81no—
396C4×C13—81no—
397C4×C13#52911yescharacteristic
398C4×C13#53811yescharacteristic
399C4×C13#55311yescharacteristic
400C4×C13#55311yescharacteristic
401Dic13—42no—
402Dic13—81no—
403Dic13—81no—
404C22×D4—131no—
405C22×D4—261no—
406C22×D4—261no—
407C22×D4C22⋊D1311yescharacteristic
408C23×C4—21no—
409C23×C4—261no—
410C23×C4C22×D1311yescharacteristic
411C23×C4C22×D1311yescharacteristic
412C22×C8—131no—
413C22×C8—131no—
414C22×C8—131no—
415C22×C8—131no—
416C22×C8—262no—
417C22×C8—521no—
418C22×C8—521no—
419#121—262no—
420#121—262no—
421#121—262no—
422#121—521no—
423#121—524no—
424C4×D4—22no—
425C4×D4—22no—
426#117—22no—
427#117—41no—
428C2×C4⋊C4—22no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—41no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—262no—
435C2×C4⋊C4—261no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4—521no—
438C2×C4⋊C4C22⋊D1311yescharacteristic
439C2×C4⋊C4C22×D1311yescharacteristic
440C2×C4⋊C4C22×D1311yescharacteristic
441C2×C4⋊C4C22×D1311yescharacteristic
442C2×C4⋊C4C22×D1311yescharacteristic
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—261no—
447C2×C22⋊C4—261no—
448C2×C22⋊C4—261no—
449C2×C22⋊C4—261no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4C22⋊D1311yescharacteristic
452C2×C22⋊C4C22⋊D1311yescharacteristic
453C2×C42—21no—
454C2×C42—21no—
455C2×C42C22×D1311yescharacteristic
456#107—262no—
457#107—521no—
458#102—262no—
459#102—521no—
460#102—521no—
461#102—521no—
462C22⋊C8—262no—
463C22⋊C8—521no—
464C22⋊C8—521no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—261no—
471#95—261no—
472C2×C13—24no—
473C2×C13—81no—
474C2×C13#244411yescharacteristic
475C2×C13C2×#48211yescharacteristic
476C2×C13#309811yescharacteristic
477C2×C13#329711yescharacteristic
478C2×C13#330011yescharacteristic
479C2×C13#330811yescharacteristic
480C2×C13#331811yescharacteristic
481D13—161no—
482C24—261no—
483C24C2×C22⋊D1311yescharacteristic
484C24C2×C22⋊D1311yescharacteristic
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—261no—
489C2×D4—261no—
490C2×D4—261no—
491C2×D4—261no—
492C2×D4—261no—
493C2×D4—261no—
494C2×D4—522no—
495C2×D4—522no—
496C2×D4—522no—
497C2×D4—522no—
498C2×D4—522no—
499C2×D4—1041no—
500C22×C4—21no—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—42no—
515C22×C4—42no—
516C22×C4—81no—
517C22×C4—261no—
518C22×C4—261no—
519C22×C4—261no—
520C22×C4—522no—
521C22×C4—522no—
522C22×C4—1041no—
523C22×C4#612712yes—
524C22×C4#612712yes—
525C22×C4C2×C22⋊D1311yescharacteristic
526C22×C4C2×C22⋊D1311yescharacteristic
527C22×C4C2×C22⋊D1311yescharacteristic
528C22×C4C2×C22⋊D1311yescharacteristic
529C22×C4C23×D1311yescharacteristic
530C2×C8—261no—
531C2×C8—261no—
532C2×C8—261no—
533C2×C8—261no—
534C2×C8—261no—
535C2×C8—261no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—524no—
543C4⋊C4—22no—
544C4⋊C4—21no—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—42no—
552C4⋊C4—132no—
553C4⋊C4—261no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—522no—
559C4⋊C4—522no—
560C4⋊C4#612912yes—
561C22⋊C4—22no—
562C22⋊C4—22no—
563C22⋊C4—42no—
564C22⋊C4—42no—
565C22⋊C4—81no—
566C22⋊C4—522no—
567C22⋊C4—522no—
568C22⋊C4—522no—
569C22⋊C4—522no—
570C22⋊C4—1041no—
571C42—21no—
572C42—21no—
573C42—42no—
574C42—81no—
575C13#2620811yescharacteristic, complemented, Sylow
576C23—21no—
577C23—21no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—521no—
588C23—521no—
589C23—521no—
590C23—521no—
591C23—521no—
592C23—521no—
593C23—521no—
594C23#8818312yes—
595C23#8820312yes—
596C23#8820412yes—
597C23C22×C22⋊D1311yescharacteristic
598D4—44no—
599D4—521no—
600D4—521no—
601D4—521no—
602D4—521no—
603D4—1044no—
604D4—1044no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—84no—
637C2×C4—262no—
638C2×C4—521no—
639C2×C4—521no—
640C2×C4—521no—
641C2×C4—521no—
642C2×C4—521no—
643C2×C4—521no—
644C2×C4—521no—
645C2×C4—521no—
646C2×C4—1044no—
647C2×C4#8818312yes—
648C2×C4C2×#612711yescharacteristic
649C2×C4C2×#612711yescharacteristic
650C2×C4C2×#612911yescharacteristic
651C2×C4#8825111yescharacteristic
652C2×C4#41×D1311yescharacteristic
653C2×C4#8825611yescharacteristic
654C8—521no—
655C8—521no—
656C8—521no—
657C8—521no—
658C22—22no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—41no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—1041no—
672C22—1041no—
673C22—1041no—
674C22—1041no—
675C22—1041no—
676C22—1041no—
677C22—1041no—
678C22#1171866414yes—
679C22C2×#8818311yescharacteristic
680C22#1171951111yescharacteristic
681C22C2×#8820311yescharacteristic
682C22C2×#8820411yescharacteristic
683C22#1171953411yescharacteristic
684C22#1171954011yescharacteristic
685C22#1171954311yescharacteristic
686C4—22no—
687C4—42no—
688C4—41no—
689C4—41no—
690C4—41no—
691C4—81no—
692C4—81no—
693C4—81no—
694C4—522no—
695C4—1041no—
696C4—1041no—
697C4#1171924311yescharacteristic
698C4#1171924511yescharacteristic
699C4#1171926511yescharacteristic
700C4#1171927011yescharacteristic
701C2—24no—
702C2—81no—
703C2—2081no—
704C2#1311858011yescharacteristic
705C2C2×#1171866411yescharacteristic
706C2#1312481411yescharacteristic
707C2#1312668611yescharacteristic
708C2#1312671711yescharacteristic
709C2#1312682711yescharacteristic
710C2#1312697111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2352C2
socleC23×C13C22×D4
prime radical#13118276C2
hypercenter#2352D13
hypocenterC13#26208
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. #13116403C2semidirect
3. #13116267C2semidirect
4. #13116250C2semidirect
5. #13116018C2semidirect
6. #13115456C2semidirect
7. #13115428C2semidirect
8. #13115262C2semidirect
9. #13115158C2semidirect
10. #13115153C2semidirect
11. #13115129C2semidirect
12. #13115023C2semidirect
13. #13114931C2semidirect
14. C2×#11718121C2semidirect
15. C13×#2352C2semidirect
222. #2352D13semidirect
575. C13#26208semidirect

Maximal subgroups

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

subgroupindex
#131182762
#131164032
#131162672
#131162502
#131160182
#131154562
#131154282
#131152622
#131151582
#131151532
#131151292
#131150232
#131149312
C2×#117181212
C13×#23522
#2620813