Finite Group Databasebeta

← #15926751

Subgroups — #15926751

Order 3328.

840 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13117872C211yesmaximal, characteristic
2#13116393C211yesmaximal, characteristic, complemented
3#13116337C211yesmaximal, characteristic, complemented
4#13116207C211yesmaximal, characteristic, complemented
5#13115969C211yesmaximal, characteristic, complemented
6#13115785C211yesmaximal, characteristic, complemented
7#13115425C211yesmaximal, characteristic, complemented
8#13115272C211yesmaximal, characteristic
9#13115153C211yesmaximal, characteristic
10#13115082C211yesmaximal, characteristic, complemented
11#13115033C211yesmaximal, characteristic, complemented
12#13115021C211yesmaximal, characteristic, complemented
13#13114833C211yesmaximal, characteristic, complemented
14#13114555C211yesmaximal, characteristic, complemented
15C13×#2440C211yesmaximal, characteristic, complemented
16C2×C13×C4⋊Q8C2211yescharacteristic
17C2×C13×C22⋊Q8—21no—
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88184C2211yescharacteristic
20C2×#88180C2211yescharacteristic
21C22×#6099C2211yescharacteristic
22C2×C4×D52C2211yescharacteristic
23C13×#398—21no—
24C13×#395—21no—
25C13×#389C2211yescharacteristic
26C13×#389C2211yescharacteristic
27C13×#385—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
59C22×Q8×C13—21no—
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C13×C4⋊Q8—22no—
66C13×C4⋊Q8—41no—
67C13×C22⋊Q8—44no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—41no—
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4D411yescharacteristic
82C2×C13×C22⋊C4D411yescharacteristic
83C2×C42×C13C2311yescharacteristic
84C2×C42×C13C2311yescharacteristic
85C2×C22⋊Dic13—21no—
86#88184—22no—
87#88184Q814yescomplemented
88C2×#6103—21no—
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103—21no—
92#88180—22no—
93#88180—41no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×#6099—22no—
101C2×#6099—41no—
102C2×#6099—41no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C4×D52—22no—
108C4×D52—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95D411yescharacteristic
113C13×#95D411yescharacteristic
114#88071—21no—
115#88071—21no—
116C22⋊#1055—22no—
117#88049—22no—
118#88049—41no—
119#88049—41no—
120#88049—41no—
121#88048—41no—
122#88047—22no—
123C4⋊#1055—41no—
124C4⋊#1055—41no—
125#26427—131nomaximal, Sylow
126C24×C13C2×D411yescharacteristic
127C23×D13—21no—
128C2×Q8×C13—42no—
129C2×Q8×C13—42no—
130C2×Q8×C13—81no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—42no—
140C22×C4×C13—42no—
141C22×C4×C13—81no—
142C22×C4×C13C2×D411yescharacteristic
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×Q812yes—
148C22×C4×C13#4112yes—
149C22×C4×C13C2411yescharacteristic
150C2×C22⋊D13—24no—
151C2×C22⋊D13—81no—
152C2×C22⋊D13—81no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C2×D52—21no—
157C2×D52—21no—
158C2×D52—21no—
159C2×D52—21no—
160C2×D52—21no—
161C2×D52C2×Q812yes—
162C2×C4×D13—42no—
163C2×C4×D13—42no—
164C2×C4×D13—81no—
165C13×C4⋊C4—21no—
166C13×C4⋊C4—21no—
167C13×C4⋊C4—21no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—42no—
173C13×C4⋊C4—42no—
174C13×C4⋊C4—42no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—81no—
178C13×C4⋊C4#4112yes—
179C13×C22⋊C4—22no—
180C13×C22⋊C4—22no—
181C13×C22⋊C4—42no—
182C42×C13—21no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C22⋊Dic13—42no—
187#6103—24no—
188#6103—42no—
189#6103—42no—
190#6103—81no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C2×Q812yes—
196C4⋊Dic13#4112yes—
197#6101—81no—
198C4×Dic13—42no—
199C4×Dic13—81no—
200#6099—44no—
201C2×#1055—21no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213#2440D1311yescharacteristic, complemented
214#2363—131no—
215#2099—131no—
216#2088—131no—
217#2065—131no—
218#2023—131no—
219#1987—131no—
220#1921—131no—
221#1895—131no—
222#1874—131no—
223#1862—131no—
224#1854—131no—
225#1851—131no—
226#1802—131no—
227#1736—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C22⋊Q812yes—
235C23×C13C22×D411yescharacteristic
236C22×D13—22no—
237C22×D13—41no—
238C22×D13—41no—
239C22×D13—41no—
240C22×D13—41no—
241C22×D13—41no—
242C22×D13—41no—
243Q8×C13—84no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—22no—
251C2×C4×C13—22no—
252C2×C4×C13—22no—
253C2×C4×C13—22no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—22no—
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—41no—
268C2×C4×C13—41no—
269C2×C4×C13—41no—
270C2×C4×C13—41no—
271C2×C4×C13—41no—
272C2×C4×C13—84no—
273C2×C4×C13C22⋊Q812yes—
274C2×C4×C13AGL(1,ℤ/8)12yes—
275C2×C4×C13#13712yes—
276C2×C4×C13C22×Q811yescharacteristic
277C2×C4×C13C2×#4111yescharacteristic
278C2×C4×C13C2×#4111yescharacteristic
279C2×C4×C13C2×#4111yescharacteristic
280C2×C4×C13H(5,𝔽2)11yescharacteristic
281C2×C4×C13H(5,𝔽2)11yescharacteristic
282C22⋊D13—84no—
283C2×Dic13—22no—
284C2×Dic13—22no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289C2×Dic13—41no—
290C2×Dic13—41no—
291C2×Dic13—41no—
292D52—22no—
293D52—22no—
294D52—41no—
295D52—41no—
296C4×D13—84no—
297#1055—41no—
298#1055—41no—
299#1055—41no—
300#1055—41no—
301C22×M16—131no—
302C2×C4⋊Q8C2×D1311yescharacteristic
303C2×C22⋊Q8—21no—
304C2×#121—131no—
305C2×C4×D4—131no—
306C2×#117—131no—
307C22×C4⋊C4C2×D1311yescharacteristic
308C2×#107—131no—
309C2×#106—131no—
310C2×C4⋊C8—131no—
311C2×C4⋊C8—131no—
312C2×#102—131no—
313C2×#102—131no—
314C2×#102—131no—
315C2×#102—131no—
316C2×C22⋊C8—131no—
317#398—21no—
318#395—21no—
319#390—131no—
320#390—261no—
321#389—131no—
322#389C2×D1311yescharacteristic
323#389C2×D1311yescharacteristic
324#388—261no—
325#386—261no—
326#385—21no—
327#384C2×D1311yescharacteristic
328#380C2×D1311yescharacteristic
329C4×C4⋊C4—131no—
330C4×C22⋊C4—261no—
331C4×C22⋊C4C2×D1311yescharacteristic
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#340—131no—
339#340—131no—
340#340—131no—
341#340—131no—
342#336—131no—
343#336—131no—
344C22×C13—22no—
345C22×C13—22no—
346C22×C13—22no—
347C22×C13—41no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13C2×C22⋊Q811yescharacteristic
352C22×C13#54611yescharacteristic
353C22×C13#54611yescharacteristic
354C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
355C22×C13C2×#13711yescharacteristic
356C22×C13#57611yescharacteristic
357C22×C13#57711yescharacteristic
358C2×D13—42no—
359C2×D13—42no—
360C2×D13—42no—
361C2×D13—81no—
362C2×D13—81no—
363C2×D13—81no—
364C2×D13—81no—
365C4×C13—22no—
366C4×C13—22no—
367C4×C13—22no—
368C4×C13—41no—
369C4×C13—41no—
370C4×C13—42no—
371C4×C13—81no—
372C4×C13—81no—
373C4×C13—81no—
374C4×C13#52911yescharacteristic
375C4×C13#53811yescharacteristic
376C4×C13#55411yescharacteristic
377C4×C13#55411yescharacteristic
378Dic13—42no—
379Dic13—42no—
380Dic13—81no—
381C22×Q8—21no—
382C22×D4—131no—
383C22×D4—261no—
384C23×C4—21no—
385C23×C4—261no—
386C23×C4C22×D1311yescharacteristic
387C2×M16—262no—
388C2×M16—521no—
389C2×M16—521no—
390C22×C8—131no—
391C22×C8—131no—
392C22×C8—131no—
393C22×C8—131no—
394C4⋊Q8—22no—
395C4⋊Q8—41no—
396C22⋊Q8—44no—
397#121—134no—
398#121—262no—
399C4×D4—262no—
400C4×D4—521no—
401#117—262no—
402#117—521no—
403C2×C4⋊C4—22no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—131no—
412C2×C4⋊C4—131no—
413C2×C4⋊C4—131no—
414C2×C4⋊C4—261no—
415C2×C4⋊C4C22×D1311yescharacteristic
416C2×C4⋊C4C22×D1311yescharacteristic
417C2×C4⋊C4C22×D1311yescharacteristic
418C2×C4⋊C4C22×D1311yescharacteristic
419C2×C22⋊C4—21no—
420C2×C22⋊C4—261no—
421C2×C22⋊C4—261no—
422C2×C22⋊C4—261no—
423C2×C22⋊C4—261no—
424C2×C22⋊C4—261no—
425C2×C22⋊C4C22⋊D1311yescharacteristic
426C2×C22⋊C4C22⋊D1311yescharacteristic
427C2×C42—261no—
428C2×C42—261no—
429C2×C42C22×D1311yescharacteristic
430C2×C42C22×D1311yescharacteristic
431#107—262no—
432#106—521no—
433C4⋊C8—521no—
434C4⋊C8—521no—
435#102—262no—
436#102—521no—
437#102—521no—
438#102—521no—
439C22⋊C8—262no—
440#95—21no—
441#95—21no—
442#95—21no—
443#95—261no—
444#95—261no—
445#95C22⋊D1311yescharacteristic
446#95C22⋊D1311yescharacteristic
447C2×C13—42no—
448C2×C13#245011yescharacteristic
449C2×C13#307911yescharacteristic
450C2×C13#308111yescharacteristic
451C2×C13#330611yescharacteristic
452C2×C13#332011yescharacteristic
453C2×C13#332511yescharacteristic
454C2×C13#333311yescharacteristic
455D13—82no—
456C24—261no—
457C24C2×C22⋊D1311yescharacteristic
458C2×Q8—42no—
459C2×Q8—42no—
460C2×Q8—81no—
461C2×D4—132no—
462C2×D4—264no—
463C2×D4—261no—
464C2×D4—261no—
465C2×D4—261no—
466C2×D4—261no—
467C2×D4—261no—
468C2×D4—1041no—
469C2×D4—1041no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—42no—
479C22×C4—42no—
480C22×C4—81no—
481C22×C4—261no—
482C22×C4—261no—
483C22×C4—261no—
484C22×C4—522no—
485C22×C4—522no—
486C22×C4—1041no—
487C22×C4Q8×D1312yes—
488C22×C4#613112yes—
489C22×C4C2×C22⋊D1311yescharacteristic
490C22×C4C2×C22⋊D1311yescharacteristic
491C22×C4C2×C22⋊D1311yescharacteristic
492C22×C4C2×C22⋊D1311yescharacteristic
493C22×C4C2×C22⋊D1311yescharacteristic
494C22×C4C23×D1311yescharacteristic
495M16—524no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C2×C8—261no—
501C2×C8—261no—
502C2×C8—261no—
503C2×C8—261no—
504C2×C8—261no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—261no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—42no—
516C4⋊C4—42no—
517C4⋊C4—42no—
518C4⋊C4—42no—
519C4⋊C4—42no—
520C4⋊C4—81no—
521C4⋊C4—132no—
522C4⋊C4—132no—
523C4⋊C4—261no—
524C4⋊C4—261no—
525C4⋊C4—261no—
526C4⋊C4—261no—
527C4⋊C4—1041no—
528C4⋊C4#612912yes—
529C22⋊C4—22no—
530C22⋊C4—22no—
531C22⋊C4—42no—
532C22⋊C4—264no—
533C22⋊C4—522no—
534C22⋊C4—522no—
535C22⋊C4—522no—
536C22⋊C4—1041no—
537C42—21no—
538C42—21no—
539C42—21no—
540C42—21no—
541C42—522no—
542C42—1041no—
543C13#2642711yescharacteristic, complemented, Sylow
544C23—21no—
545C23—21no—
546C23—21no—
547C23—21no—
548C23—21no—
549C23—21no—
550C23—262no—
551C23—521no—
552C23—521no—
553C23—521no—
554C23—521no—
555C23—521no—
556C23—521no—
557C23#8820012yes—
558C23C22×C22⋊D1311yescharacteristic
559Q8—84no—
560D4—262no—
561D4—262no—
562D4—521no—
563D4—521no—
564D4—1044no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—22no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—41no—
592C2×C4—41no—
593C2×C4—84no—
594C2×C4—262no—
595C2×C4—262no—
596C2×C4—521no—
597C2×C4—521no—
598C2×C4—521no—
599C2×C4—521no—
600C2×C4—521no—
601C2×C4—521no—
602C2×C4—521no—
603C2×C4—1044no—
604C2×C4#8818612yes—
605C2×C4#8819612yes—
606C2×C4#8820012yes—
607C2×C4C2×#612911yescharacteristic
608C2×C4#8825111yescharacteristic
609C2×C4C2×Q8×D1311yescharacteristic
610C2×C4C2×#613111yescharacteristic
611C2×C4#41×D1311yescharacteristic
612C2×C4#8825611yescharacteristic
613C8—521no—
614C8—521no—
615C8—521no—
616C8—521no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—41no—
621C22—41no—
622C22—41no—
623C22—41no—
624C22—522no—
625C22—522no—
626C22—522no—
627C22—1041no—
628C22—1041no—
629C22—1041no—
630C22—1041no—
631C22C2×#8818611yescharacteristic
632C22#1171951111yescharacteristic
633C22C2×#8819611yescharacteristic
634C22C2×#8820011yescharacteristic
635C22#1171953411yescharacteristic
636C22#1171954011yescharacteristic
637C22#1171954211yescharacteristic
638C4—22no—
639C4—22no—
640C4—22no—
641C4—41no—
642C4—41no—
643C4—42no—
644C4—81no—
645C4—81no—
646C4—81no—
647C4—522no—
648C4—522no—
649C4—1041no—
650C4#1171932911yescharacteristic
651C4#1171934011yescharacteristic
652C4#1171934111yescharacteristic
653C4#1171934911yescharacteristic
654C2—42no—
655C2—1042no—
656C2#1311865611yescharacteristic
657C2#1312464511yescharacteristic
658C2#1312466111yescharacteristic
659C2#1312679111yescharacteristic
660C2#1312700711yescharacteristic
661C2#1312707811yescharacteristic
662C2#1312716811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2440C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenter#2440D13
hypocenterC13#26427
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2440

Complements

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

NH ≅ G/Ntype
2. #13116393C2semidirect
3. #13116337C2semidirect
4. #13116207C2semidirect
5. #13115969C2semidirect
6. #13115785C2semidirect
7. #13115425C2semidirect
10. #13115082C2semidirect
11. #13115033C2semidirect
12. #13115021C2semidirect
13. #13114833C2semidirect
14. #13114555C2semidirect
15. C13×#2440C2semidirect
87. #88184Q8semidirect
213. #2440D13semidirect
543. C13#26427semidirect

Maximal subgroups

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

subgroupindex
#131178722
#131163932
#131163372
#131162072
#131159692
#131157852
#131154252
#131152722
#131151532
#131150822
#131150332
#131150212
#131148332
#131145552
C13×#24402
#2642713