Finite Group Databasebeta

← #15925356

Subgroups — #15925356

Order 3328.

752 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117793C211yesmaximal, characteristic, complemented
2#13116369C211yesmaximal, characteristic, complemented
3#13116357C211yesmaximal, characteristic, complemented
4#13116249C211yesmaximal, characteristic, complemented
5#13116239C211yesmaximal, characteristic, complemented
6#13115777C211yesmaximal, characteristic, complemented
7#13115764C211yesmaximal, characteristic
8#13115661C211yesmaximal, characteristic
9#13115604C211yesmaximal, characteristic, complemented
10#13115460C211yesmaximal, characteristic, complemented
11#13115453C211yesmaximal, characteristic, complemented
12#13115453C211yesmaximal, characteristic, complemented
13#13115453C211yesmaximal, characteristic, complemented
14#13114734C211yesmaximal, characteristic, complemented
15C13×#2548C211yesmaximal, characteristic
16C2×C13×#127C2211yescharacteristic
17C2×C13×#124—21no—
18C2×C4×Q8×C13C2211yescharacteristic
19C13×#394—21no—
20C13×#394—21no—
21C13×#390—21no—
22C13×#390C2211yescharacteristic
23C13×#390C2211yescharacteristic
24C13×#390C2211yescharacteristic
25C13×#390C2211yescharacteristic
26C4×C13×C4⋊C4C2211yescharacteristic
27#11718891—21no—
28C2×#88072C2211yescharacteristic
29C2×#88072C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36#11718642—21no—
37#11718642—21no—
38C4⋊C4×Dic13—21no—
39C2×#88048C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88047C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43#11718597C2211yescharacteristic
44#11718597C2211yescharacteristic
45#11718596C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47C4×C4⋊Dic13C2211yescharacteristic
48C4×C4⋊Dic13C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×#88043C2211yescharacteristic
51#11718121C2211yescharacteristic
52#11718121C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718116C2211yescharacteristic
56#11718116C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59C22×Q8×C13D411yescharacteristic
60C22×D4×C13—21no—
61C22×D4×C13—21no—
62C22×D4×C13C2311yescharacteristic
63C22×D4×C13C2311yescharacteristic
64C13×#127—22no—
65C13×#127—22no—
66C13×#124—44no—
67C4×Q8×C13—22no—
68C4×Q8×C13—22no—
69C2×C13×C4⋊C4D411yescharacteristic
70C2×C13×C4⋊C4D411yescharacteristic
71C2×C13×C4⋊C4D411yescharacteristic
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⋊C4—21no—
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C42×C13—21no—
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C42×C13C2311yescharacteristic
86C2×C4⋊Dic13—21no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4×Dic13—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C22×#1055C2311yescharacteristic
96C22×#1055C2311yescharacteristic
97C22×#1055C2311yescharacteristic
98C22×#1055C2311yescharacteristic
99C13×#95—21no—
100#88072—22no—
101#88072—22no—
102#88072—22no—
103#88072—22no—
104#88072—41no—
105#88072—41no—
106#88072—41no—
107#88072—41no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88071—21no—
114#88071—21no—
115#88048—22no—
116#88048—41no—
117#88047—22no—
118#88047—41no—
119C4⋊#1055—22no—
120#88043—22no—
121#26334—131nomaximal, Sylow
122C24×C13—21no—
123C24×C13—21no—
124C2×Q8×C13—22no—
125C2×Q8×C13—22no—
126C2×Q8×C13—41no—
127C2×D4×C13—21no—
128C2×D4×C13—21no—
129C2×D4×C13—21no—
130C2×D4×C13—21no—
131C2×D4×C13—21no—
132C2×D4×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13—21no—
137C2×D4×C13—21no—
138C2×D4×C13—21no—
139C2×D4×C13—42no—
140C2×D4×C13—42no—
141C2×D4×C13—42no—
142C2×D4×C13—42no—
143C2×D4×C13—81no—
144C2×D4×C13—81no—
145C22×C4×C13—21no—
146C22×C4×C13—21no—
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×D411yescharacteristic
149C22×C4×C13C2×D411yescharacteristic
150C22×C4×C13C2×D411yescharacteristic
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2411yescharacteristic
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C13×C4⋊C4—22no—
159C13×C4⋊C4—22no—
160C13×C4⋊C4—22no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—21no—
164C13×C4⋊C4—21no—
165C13×C22⋊C4—42no—
166C13×C22⋊C4—42no—
167C13×C22⋊C4—42no—
168C13×C22⋊C4—42no—
169C13×C22⋊C4—81no—
170C13×C22⋊C4—81no—
171C13×C22⋊C4—81no—
172C13×C22⋊C4—81no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13—42no—
178C42×C13#4112yes—
179C42×C13#4112yes—
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—
190C4×Dic13—42no—
191C4×Dic13—81no—
192C4×Dic13—81no—
193C2×#1055—21no—
194C2×#1055—21no—
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#4112yes—
205#2548D1311yescharacteristic
206#2355—131no—
207#2094—131no—
208#2092—131no—
209#2073—131no—
210#2071—131no—
211#1985—131no—
212#1982—131no—
213#1961—131no—
214#1949—131no—
215#1926—131no—
216#1925—131no—
217#1925—131no—
218#1925—131no—
219#1776—131no—
220C23×C13—41no—
221C23×C13—41no—
222C23×C13—41no—
223C23×C13—41no—
224C23×C13—41no—
225C23×C13—41no—
226C23×C13—41no—
227C23×C13—41no—
228C23×C13—41no—
229C23×C13—41no—
230C23×C13—41no—
231C23×C13—41no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13C22×D411yescharacteristic
235Q8×C13—44no—
236D4×C13—41no—
237D4×C13—41no—
238D4×C13—41no—
239D4×C13—41no—
240D4×C13—41no—
241D4×C13—41no—
242D4×C13—41no—
243D4×C13—41no—
244D4×C13—84no—
245D4×C13—84no—
246C2×C4×C13—21no—
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—21no—
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—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13#12312yes—
268C2×C4×C13#12312yes—
269C2×C4×C13AGL(1,ℤ/8)12yes—
270C2×C4×C13C2×#4111yescharacteristic
271C2×C4×C13C2×#4111yescharacteristic
272C2×C4×C13C2×#4111yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13H(5,𝔽2)11yescharacteristic
275C2×C4×C132−1+411yescharacteristic
276C2×Dic13—22no—
277C2×Dic13—41no—
278C2×Dic13—41no—
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—
288#1055—22no—
289#1055—41no—
290#1055—41no—
291#1055—41no—
292C2×#127C2×D1311yescharacteristic
293C2×#124—21no—
294C2×C4×Q8C2×D1311yescharacteristic
295C2×#107—131no—
296C2×#107—131no—
297C2×#106—131no—
298C2×#106—131no—
299C2×C4⋊C8—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×#102—131no—
305C2×#102—131no—
306C2×#102—131no—
307C2×#102—131no—
308C2×#97—131no—
309#394—21no—
310#394—21no—
311#391—261no—
312#390—21no—
313#390C2×D1311yescharacteristic
314#390C2×D1311yescharacteristic
315#390C2×D1311yescharacteristic
316#390C2×D1311yescharacteristic
317#387—261no—
318#387—261no—
319#384—131no—
320#382—131no—
321#382—131no—
322C4×C4⋊C4—131no—
323C4×C4⋊C4—131no—
324C4×C4⋊C4—131no—
325C4×C4⋊C4—261no—
326C4×C4⋊C4C2×D1311yescharacteristic
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#336—131no—
332#336—131no—
333#336—131no—
334#336—131no—
335C22×C13—81no—
336C22×C13—81no—
337C22×C13—81no—
338C22×C13—81no—
339C22×C13—81no—
340C22×C13—81no—
341C22×C13—81no—
342C22×C13—81no—
343C22×C13—81no—
344C22×C13—81no—
345C22×C13—81no—
346C22×C13—81no—
347C22×C13—81no—
348C22×C13—81no—
349C22×C13C2×#12311yescharacteristic
350C22×C13#54811yescharacteristic
351C22×C13#55011yescharacteristic
352C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
353C22×C13#57511yescharacteristic
354C22×C13#57611yescharacteristic
355C22×C13#57711yescharacteristic
356C4×C13—22no—
357C4×C13—22no—
358C4×C13—22no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—81no—
363C4×C13—81no—
364C4×C13#52911yescharacteristic
365C4×C13#54211yescharacteristic
366C4×C13#55611yescharacteristic
367C4×C13#55911yescharacteristic
368Dic13—42no—
369Dic13—81no—
370Dic13—81no—
371Dic13—81no—
372C22×Q8C22⋊D1311yescharacteristic
373C22×D4—21no—
374C22×D4—21no—
375C22×D4C22×D1311yescharacteristic
376C22×D4C22×D1311yescharacteristic
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8—131no—
381#127—22no—
382#127—22no—
383#124—44no—
384C4×Q8—22no—
385C4×Q8—22no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4C22⋊D1311yescharacteristic
393C2×C4⋊C4C22⋊D1311yescharacteristic
394C2×C4⋊C4C22⋊D1311yescharacteristic
395C2×C4⋊C4C22×D1311yescharacteristic
396C2×C4⋊C4C22×D1311yescharacteristic
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—21no—
402C2×C22⋊C4—21no—
403C2×C22⋊C4—21no—
404C2×C22⋊C4—21no—
405C2×C42—21no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C2×C42C22×D1311yescharacteristic
410C2×C42C22×D1311yescharacteristic
411C2×C42C22×D1311yescharacteristic
412#107—262no—
413#107—521no—
414#106—262no—
415#106—521no—
416C4⋊C8—262no—
417#102—262no—
418#102—262no—
419#102—262no—
420#102—262no—
421#102—521no—
422#102—521no—
423#102—521no—
424#102—521no—
425#97—262no—
426#95—21no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434C2×C13—161no—
435C2×C13—161no—
436C2×C13#244811yescharacteristic
437C2×C13#309411yescharacteristic
438C2×C13#309611yescharacteristic
439C2×C13#336611yescharacteristic
440C2×C13#337111yescharacteristic
441C2×C13#339711yescharacteristic
442C2×C13#340311yescharacteristic
443C24—21no—
444C24—21no—
445C2×Q8—22no—
446C2×Q8—22no—
447C2×Q8—41no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—42no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4C2×C22⋊D1311yescharacteristic
473C22×C4C2×C22⋊D1311yescharacteristic
474C22×C4C2×C22⋊D1311yescharacteristic
475C22×C4C2×C22⋊D1311yescharacteristic
476C22×C4C2×C22⋊D1311yescharacteristic
477C22×C4C2×C22⋊D1311yescharacteristic
478C22×C4C23×D1311yescharacteristic
479C2×C8—132no—
480C2×C8—261no—
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—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—132no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—522no—
507C4⋊C4—1041no—
508C22⋊C4—42no—
509C22⋊C4—42no—
510C22⋊C4—42no—
511C22⋊C4—42no—
512C22⋊C4—81no—
513C22⋊C4—81no—
514C22⋊C4—81no—
515C22⋊C4—81no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—21no—
520C42—42no—
521C42—522no—
522C42—1041no—
523C42—1041no—
524C42#612912yes—
525C42#612912yes—
526C13#2633411yescharacteristic, complemented, Sylow
527C23—41no—
528C23—41no—
529C23—41no—
530C23—41no—
531C23—41no—
532C23—41no—
533C23—41no—
534C23—41no—
535C23—41no—
536C23—41no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×C22⋊D1311yescharacteristic
542Q8—44no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—84no—
552D4—84no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—262no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4#8818612yes—
587C2×C4#8818912yes—
588C2×C4#8818912yes—
589C2×C4C2×#612911yescharacteristic
590C2×C4C2×#612911yescharacteristic
591C2×C4#41×D1311yescharacteristic
592C2×C4#41×D1311yescharacteristic
593C2×C4#8825611yescharacteristic
594C2×C4#8825711yescharacteristic
595C8—262no—
596C8—521no—
597C8—521no—
598C8—521no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—81no—
608C22—81no—
609C22—81no—
610C22—81no—
611C22—81no—
612C22—81no—
613C22C2×#8818611yescharacteristic
614C22C2×#8818911yescharacteristic
615C22#1171952711yescharacteristic
616C22#1171953611yescharacteristic
617C22#1171953911yescharacteristic
618C22#1171954011yescharacteristic
619C22#1171954111yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—41no—
624C4—41no—
625C4—41no—
626C4—81no—
627C4—81no—
628C4—522no—
629C4—1041no—
630C4—1041no—
631C4—1041no—
632C4#1171937611yescharacteristic
633C4#1171938511yescharacteristic
634C4#1171938611yescharacteristic
635C4#1171938711yescharacteristic
636C2—161no—
637C2—161no—
638C2#1311863011yescharacteristic
639C2#1312477211yescharacteristic
640C2#1312478811yescharacteristic
641C2#1312753911yescharacteristic
642C2#1312759811yescharacteristic
643C2#1312785211yescharacteristic
644C2#1312792011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2548C2
socleC23×C13C22×D4
prime radicalC2×C13×#127C22
hypercenter#2548D13
hypocenterC13#26334
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2548

Complements

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

NH ≅ G/Ntype
1. #13117793C2semidirect
2. #13116369C2semidirect
3. #13116357C2semidirect
4. #13116249C2semidirect
5. #13116239C2semidirect
6. #13115777C2semidirect
9. #13115604C2semidirect
10. #13115460C2semidirect
11. #13115453C2semidirect
12. #13115453C2semidirect
13. #13115453C2semidirect
14. #13114734C2semidirect
526. C13#26334semidirect

Maximal subgroups

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

subgroupindex
#131177932
#131163692
#131163572
#131162492
#131162392
#131157772
#131157642
#131156612
#131156042
#131154602
#131154532
#131147342
C13×#25482
#2633413