Finite Group Databasebeta

← #15920426

Subgroups — #15920426

Order 3328.

988 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic
3#13118560C211yesmaximal, characteristic, complemented
4#13116384C211yesmaximal, characteristic, complemented
5#13116231C211yesmaximal, characteristic, complemented
6#13116231C211yesmaximal, characteristic, complemented
7#13115987C211yesmaximal, characteristic, complemented
8#13115083C211yesmaximal, characteristic, complemented
9#13115083C211yesmaximal, characteristic, complemented
10#13115023C211yesmaximal, characteristic, complemented
11#13115021C211yesmaximal, characteristic, complemented
12#13114867C211yesmaximal, characteristic, complemented
13#13114846C211yesmaximal, characteristic, complemented
14#13114776C211yesmaximal, characteristic
15C13×#2339C211yesmaximal, characteristic
16C22×C13×#41C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#391C2211yescharacteristic
24C13×#386—21no—
25C13×#386—21no—
26C13×#381—21no—
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4C2211yescharacteristic
29C2×C13×#95—21no—
30#11718893—24no—
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88072C2211yescharacteristic
36C2×#88072C2211yescharacteristic
37C2×#88072C2211yescharacteristic
38C2×#88072C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718670—24no—
42C2×#88048C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45C2×#88047C2211yescharacteristic
46#11718607—21no—
47#11718603—21no—
48#11718597C2211yescharacteristic
49#11718589C2211yescharacteristic
50#11718589C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4⋊#1055C2211yescharacteristic
53#11718321—21no—
54#11718318—21no—
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C2×C13×#41—22no—
62C2×C13×#41—22no—
63C2×C13×#41—22no—
64C2×C13×#41—41no—
65C2×C13×#41—41no—
66C2×C13×#41Q814yes—
67C22×Q8×C13C2311yescharacteristic
68C22×D4×C13—21no—
69C22×D4×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13—21no—
72C23×C4×C13—21no—
73C23×C4×C13C2311yescharacteristic
74C23×Dic13—21no—
75C4×D4×C13—22no—
76C4×D4×C13—22no—
77C4×D4×C13—41no—
78C4×D4×C13—41no—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4D411yescharacteristic
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—21no—
91C2×C4⋊Dic13—41no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6099—22no—
101C2×#6099—22no—
102C2×#6099—41no—
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107#88124—22no—
108#88124—41no—
109C13×#95—21no—
110C13×#95—21no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95D411yescharacteristic
115C13×#95D411yescharacteristic
116#88075—22no—
117#88075—22no—
118#88075—41no—
119#88075—41no—
120#88072—22no—
121#88072—22no—
122#88072—22no—
123#88072D414yes—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129C22⋊#1055—22no—
130#88048—22no—
131#88047—22no—
132#88047—41no—
133#88047—41no—
134C4⋊#1055—22no—
135C4⋊#1055—41no—
136#25980—131nomaximal, Sylow
137C24×C13—21no—
138C24×C13C2×D411yescharacteristic
139C13×#41—28no—
140C13×#41—44no—
141C13×#41—44no—
142C13×#41—44no—
143C2×Q8×C13—21no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13C2×Q812yes—
149C2×D4×C13—24no—
150C2×D4×C13—21no—
151C2×D4×C13—21no—
152C2×D4×C13—21no—
153C2×D4×C13—42no—
154C2×D4×C13—42no—
155C2×D4×C13C2×D412yes—
156C2×D4×C13C2×Q812yes—
157C2×D4×C13#4112yes—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—24no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—42no—
167C22×C4×C13—42no—
168C22×C4×C13—42no—
169C22×C4×C13—42no—
170C22×C4×C13—42no—
171C22×C4×C13—42no—
172C22×C4×C13—81no—
173C22×C4×C13—81no—
174C22×C4×C13C2×D411yescharacteristic
175C22×C4×C13C2×D411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×Q812yes—
180C22×C4×C13#4112yes—
181C22×C4×C13C2411yescharacteristic
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—42no—
187C22×Dic13—42no—
188C22×Dic13—81no—
189C13×C4⋊C4—21no—
190C13×C4⋊C4—21no—
191C13×C4⋊C4—21no—
192C13×C4⋊C4—21no—
193C13×C22⋊C4—41no—
194C13×C22⋊C4—41no—
195C13×C22⋊C4—42no—
196C13×C22⋊C4—42no—
197C13×C22⋊C4—81no—
198C42×C13—21no—
199C42×C13—21no—
200C42×C13—21no—
201C42×C13—21no—
202C22⋊Dic13—42no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—21no—
207C4⋊Dic13—21no—
208C4⋊Dic13—21no—
209C4⋊Dic13—21no—
210C4⋊Dic13—42no—
211C4⋊Dic13C2×D412yes—
212#6101—42no—
213#6101—42no—
214#6101—81no—
215#6101—81no—
216#6099—44no—
217C2×#1055—21no—
218C2×#1055—21no—
219C2×#1055—21no—
220C2×#1055—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—21no—
224C2×#1055—21no—
225C2×#1055—21no—
226C2×#1055—21no—
227C2×#1055—21no—
228C2×#1055C2×D412yes—
229C2×#478—131no—
230C2×#417—131no—
231#2442—131no—
232#2339D1311yescharacteristic
233#2097—131no—
234#2068—131no—
235#2068—131no—
236#2026—131no—
237#1862—131no—
238#1862—131no—
239#1852—131no—
240#1851—131no—
241#1809—131no—
242#1804—131no—
243#1788—131no—
244C23×C13—22no—
245C23×C13—22no—
246C23×C13—21no—
247C23×C13—22no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—21no—
251C23×C13—21no—
252C23×C13—21no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13C22⋊Q812yes—
258C23×C13C22×D411yescharacteristic
259Q8×C13—22no—
260Q8×C13—22no—
261Q8×C13—41no—
262Q8×C13—41no—
263D4×C13—22no—
264D4×C13—22no—
265D4×C13—22no—
266D4×C13—48no—
267D4×C13C22⋊Q814yes—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—22no—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—21no—
284C2×C4×C13—21no—
285C2×C4×C13—21no—
286C2×C4×C13—21no—
287C2×C4×C13—48no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—84no—
297C2×C4×C13—84no—
298C2×C4×C13C22⋊Q812yes—
299C2×C4×C13C22×D411yescharacteristic
300C2×C4×C13C22×Q811yescharacteristic
301C2×C4×C13C2×#4111yescharacteristic
302C2×C4×C13C2×#4111yescharacteristic
303C2×C4×C13H(5,𝔽2)11yescharacteristic
304C2×C4×C13H(5,𝔽2)11yescharacteristic
305C2×Dic13—22no—
306C2×Dic13—41no—
307C2×Dic13—41no—
308C2×Dic13—41no—
309C2×Dic13—41no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—84no—
318#1055—22no—
319#1055—41no—
320#1055—41no—
321#1055—41no—
322C22×#41C2×D1311yescharacteristic
323C22×M16—131no—
324C2×#125—131no—
325C2×C4×D4C2×D1311yescharacteristic
326C2×C4×D4C2×D1311yescharacteristic
327C22×C4⋊C4—131no—
328#478—264no—
329C2×#107—131no—
330C2×#107—131no—
331C2×#107—131no—
332C2×#106—131no—
333C2×C4⋊C8—131no—
334C2×C4⋊C8—131no—
335#417—264no—
336C2×#103—131no—
337C2×#103—131no—
338C2×#103—131no—
339C2×#103—131no—
340C2×#102—131no—
341C2×#102—131no—
342C2×#102—131no—
343C2×#102—131no—
344C2×C22⋊C8—131no—
345#400—261no—
346#398—261no—
347#391C2×D1311yescharacteristic
348#391C2×D1311yescharacteristic
349#389—131no—
350#389—131no—
351#386—21no—
352#386—21no—
353#385—261no—
354#382—131no—
355#381—21no—
356#380—131no—
357#380—261no—
358#380C2×D1311yescharacteristic
359C4×C22⋊C4C2×D1311yescharacteristic
360C2×#95—21no—
361#340—131no—
362#340—131no—
363#340—131no—
364#340—131no—
365#336—131no—
366#336—131no—
367C22×C13—22no—
368C22×C13—22no—
369C22×C13—22no—
370C22×C13—24no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—41no—
374C22×C13—42no—
375C22×C13—41no—
376C22×C13—42no—
377C22×C13—41no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—41no—
381C22×C13C2×C22⋊Q811yescharacteristic
382C22×C13D4211yescharacteristic
383C22×C13#54611yescharacteristic
384C22×C13#57511yescharacteristic
385C22×C13#57511yescharacteristic
386C22×C13#57611yescharacteristic
387C22×C13#57811yescharacteristic
388C4×C13—22no—
389C4×C13—42no—
390C4×C13—41no—
391C4×C13—41no—
392C4×C13—41no—
393C4×C13—41no—
394C4×C13—81no—
395C4×C13—81no—
396C4×C13C2×C22⋊Q811yescharacteristic
397C4×C13#54311yescharacteristic
398C4×C13#54611yescharacteristic
399C4×C13#55111yescharacteristic
400Dic13—42no—
401Dic13—81no—
402Dic13—81no—
403Dic13—81no—
404C2×#41—22no—
405C2×#41—22no—
406C2×#41—22no—
407C2×#41—41no—
408C2×#41—41no—
409C2×#41Dic2614yes—
410C22×Q8C22×D1311yescharacteristic
411C22×D4—21no—
412C22×D4C22×D1311yescharacteristic
413C23×C4—21no—
414C23×C4—21no—
415C23×C4—21no—
416C23×C4—261no—
417C23×C4C22×D1311yescharacteristic
418C2×M16—262no—
419C2×M16—262no—
420C2×M16—521no—
421C22×C8—131no—
422C22×C8—131no—
423C22×C8—131no—
424C22×C8—131no—
425#125—262no—
426#125—521no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—41no—
430C4×D4—41no—
431C2×C4⋊C4—131no—
432C2×C4⋊C4—131no—
433C2×C4⋊C4—131no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—262no—
436C2×C4⋊C4—261no—
437C2×C4⋊C4—261no—
438C2×C4⋊C4—261no—
439C2×C4⋊C4—261no—
440C2×C4⋊C4—261no—
441C2×C4⋊C4—521no—
442C2×C4⋊C4C22×D1311yescharacteristic
443C2×C4⋊C4C22×D1311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—261no—
448C2×C22⋊C4C22⋊D1311yescharacteristic
449C2×C22⋊C4C22⋊D1311yescharacteristic
450C2×C42C22×D1311yescharacteristic
451C2×C42C22×D1311yescharacteristic
452#107—262no—
453#107—521no—
454#107—521no—
455#106—262no—
456C4⋊C8—262no—
457C4⋊C8—521no—
458#103—262no—
459#103—262no—
460#103—521no—
461#103—521no—
462#102—134no—
463#102—262no—
464#102—262no—
465#102—262no—
466C22⋊C8—262no—
467#95—21no—
468#95—21no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—261no—
473#95—261no—
474#95—261no—
475#95—261no—
476#95—261no—
477#95C22⋊D1311yescharacteristic
478#95C22⋊D1311yescharacteristic
479C2×C13—42no—
480C2×C13—44no—
481C2×C13#243711yescharacteristic
482C2×C13#308011yescharacteristic
483C2×C13#308311yescharacteristic
484C2×C13#326911yescharacteristic
485C2×C13#327311yescharacteristic
486C2×C13#331511yescharacteristic
487C2×C13#332211yescharacteristic
488C24—21no—
489C24C2×C22⋊D1311yescharacteristic
490#41—28no—
491#41—44no—
492#41—44no—
493#41—44no—
494C2×Q8—21no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8C2×Dic2612yes—
500C2×D4—24no—
501C2×D4—21no—
502C2×D4—21no—
503C2×D4—21no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4C2×Dic2612yes—
507C2×D4D4×D1312yes—
508C2×D4#612912yes—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—24no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—42no—
518C22×C4—42no—
519C22×C4—42no—
520C22×C4—42no—
521C22×C4—42no—
522C22×C4—42no—
523C22×C4—81no—
524C22×C4—81no—
525C22×C4—261no—
526C22×C4—261no—
527C22×C4—261no—
528C22×C4—261no—
529C22×C4—522no—
530C22×C4—522no—
531C22×C4—1041no—
532C22×C4C2×Dic2612yes—
533C22×C4#612712yes—
534C22×C4C2×C22⋊D1311yescharacteristic
535C22×C4C2×C22⋊D1311yescharacteristic
536C22×C4C2×C22⋊D1311yescharacteristic
537C22×C4C2×C22⋊D1311yescharacteristic
538C22×C4C2×C22⋊D1311yescharacteristic
539C22×C4C23×D1311yescharacteristic
540M16—524no—
541C2×C8—132no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—261no—
546C2×C8—261no—
547C2×C8—261no—
548C2×C8—261no—
549C2×C8—261no—
550C2×C8—261no—
551C2×C8—261no—
552C2×C8—261no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—132no—
558C4⋊C4—261no—
559C4⋊C4—261no—
560C4⋊C4—261no—
561C4⋊C4—261no—
562C4⋊C4—261no—
563C4⋊C4—261no—
564C4⋊C4—261no—
565C4⋊C4—522no—
566C4⋊C4—522no—
567C4⋊C4—522no—
568C4⋊C4—1041no—
569C4⋊C4—1041no—
570C22⋊C4—41no—
571C22⋊C4—41no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—522no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C13#2598011yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—21no—
584C23—22no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23#8817812yes—
595C23C22×C22⋊D1311yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600D4—22no—
601D4—22no—
602D4—22no—
603D4—48no—
604D4#8813214yes—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—48no—
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—84no—
634C2×C4—84no—
635C2×C4—262no—
636C2×C4—521no—
637C2×C4—521no—
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—521no—
647C2×C4—1044no—
648C2×C4#8817812yes—
649C2×C4C22×Dic2611yescharacteristic
650C2×C4C2×#612711yescharacteristic
651C2×C4C2×D4×D1311yescharacteristic
652C2×C4C2×#612911yescharacteristic
653C2×C4#8825111yescharacteristic
654C2×C4#8825111yescharacteristic
655C8—262no—
656C8—521no—
657C8—521no—
658C8—521no—
659C22—22no—
660C22—24no—
661C22—22no—
662C22—22no—
663C22—41no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—42no—
670C22—41no—
671C22—41no—
672C22—42no—
673C22C2×#8817811yescharacteristic
674C22D4×C22⋊D1311yescharacteristic
675C22#1171951111yescharacteristic
676C22#1171952711yescharacteristic
677C22#1171952711yescharacteristic
678C22#1171954011yescharacteristic
679C22#1171954311yescharacteristic
680C4—22no—
681C4—41no—
682C4—42no—
683C4—41no—
684C4—41no—
685C4—41no—
686C4—81no—
687C4—81no—
688C4—522no—
689C4—1041no—
690C4—1041no—
691C4—1041no—
692C4C2×#8813211yescharacteristic
693C4#1171918811yescharacteristic
694C4#1171919511yescharacteristic
695C4#1171920011yescharacteristic
696C2—42no—
697C2—44no—
698C2#1311849711yescharacteristic
699C2#1312465811yescharacteristic
700C2#1312468711yescharacteristic
701C2#1312638711yescharacteristic
702C2#1312644311yescharacteristic
703C2#1312693211yescharacteristic
704C2#1312703711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2339C2
socleC23×C13C22×D4
prime radicalC22×C13×#41C22
hypercenter#2339D13
hypocenterC13#25980
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2339

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
3. #13118560C2semidirect
4. #13116384C2semidirect
5. #13116231C2semidirect
6. #13116231C2semidirect
7. #13115987C2semidirect
8. #13115083C2semidirect
9. #13115083C2semidirect
10. #13115023C2semidirect
11. #13115021C2semidirect
12. #13114867C2semidirect
13. #13114846C2semidirect
580. C13#25980semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×#117188932
#131185602
#131163842
#131162312
#131159872
#131150832
#131150232
#131150212
#131148672
#131148462
#131147762
C13×#23392
#2598013