Finite Group Databasebeta

← #15920081

Subgroups — #15920081

Order 3328.

946 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718683C211yesmaximal, characteristic, complemented
2C22×#88075C211yesmaximal, characteristic
3#13118560C211yesmaximal, characteristic
4#13116384C211yesmaximal, characteristic, complemented
5#13116231C211yesmaximal, characteristic, complemented
6#13116217C211yesmaximal, characteristic, complemented
7#13115987C211yesmaximal, characteristic, complemented
8#13115104C211yesmaximal, characteristic, complemented
9#13115090C211yesmaximal, characteristic, complemented
10#13115023C211yesmaximal, characteristic
11#13115016C211yesmaximal, characteristic
12#13114859C211yesmaximal, characteristic
13#13114851C211yesmaximal, characteristic, complemented
14#13114771C211yesmaximal, characteristic
15Q8×C13×C22⋊C4C211yesmaximal, characteristic
16C23×Q8×C13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×C4×Q8×C13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C13×#391—21no—
23C13×#391—21no—
24C13×#391C2211yescharacteristic
25C13×#391C2211yescharacteristic
26C13×#380—21no—
27C13×#380C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88075—24no—
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88075C2211yescharacteristic
36C2×#88075C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39#11718873C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41#11718683—24no—
42C2×#88048C2211yescharacteristic
43C2×#88048C2211yescharacteristic
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
61C22×Q8×C13—21no—
62C22×Q8×C13—22no—
63C22×Q8×C13—22no—
64C22×Q8×C13—22no—
65C22×Q8×C13—41no—
66C22×Q8×C13—41no—
67C22×Q8×C13Q814yes—
68C22×Q8×C13C2311yescharacteristic
69C22×Q8×C13C2311yescharacteristic
70C23×C4×C13—21no—
71C23×C4×C13C2311yescharacteristic
72C23×Dic13—21no—
73C4×Q8×C13—22no—
74C4×Q8×C13—22no—
75C4×Q8×C13—41no—
76C4×Q8×C13—41no—
77C2×C13×C4⋊C4—21no—
78C2×C13×C4⋊C4—21no—
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
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×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—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055—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—22no—
119#88075—22no—
120#88075—22no—
121#88075—41no—
122#88075—41no—
123#88075D414yes—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88071—21no—
129C22⋊#1055—22no—
130#88048—22no—
131#88048—41no—
132#88047—22no—
133#88047—41no—
134C4⋊#1055—22no—
135C4⋊#1055—41no—
136#25957—131nomaximal, Sylow
137C24×C13C2×D411yescharacteristic
138C2×Q8×C13—24no—
139C2×Q8×C13—21no—
140C2×Q8×C13—21no—
141C2×Q8×C13—21no—
142C2×Q8×C13—21no—
143C2×Q8×C13—28no—
144C2×Q8×C13—21no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—42no—
149C2×Q8×C13—42no—
150C2×Q8×C13—44no—
151C2×Q8×C13—44no—
152C2×Q8×C13—44no—
153C2×Q8×C13C2×D412yes—
154C2×Q8×C13C2×Q812yes—
155C2×Q8×C13C2×Q812yes—
156C2×Q8×C13#4112yes—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—24no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—42no—
167C22×C4×C13—42no—
168C22×C4×C13C2×D411yescharacteristic
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2×Q812yes—
174C22×C4×C13#4112yes—
175C22×C4×C13C2411yescharacteristic
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—42no—
181C22×Dic13—42no—
182C22×Dic13—81no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C4⋊C4—21no—
186C13×C4⋊C4—21no—
187C13×C4⋊C4—42no—
188C13×C4⋊C4—42no—
189C13×C22⋊C4—22no—
190C13×C22⋊C4—22no—
191C13×C22⋊C4—42no—
192C42×C13—21no—
193C42×C13—21no—
194C42×C13—21no—
195C42×C13—21no—
196C42×C13—42no—
197C42×C13—42no—
198C22⋊Dic13—42no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206C4⋊Dic13—42no—
207C4⋊Dic13C2×D412yes—
208#6101—42no—
209#6101—42no—
210#6101—81no—
211#6101—81no—
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—21no—
221C2×#1055—21no—
222C2×#1055—21no—
223C2×#1055—44no—
224C2×#1055C2×D412yes—
225C2×#479—131no—
226C22×#103—131no—
227#2442—131no—
228Q8×C22⋊C4D1311yescharacteristic
229#2097—131no—
230#2068—131no—
231#2066—131no—
232#2026—131no—
233#1865—131no—
234#1863—131no—
235#1852—131no—
236#1850—131no—
237#1807—131no—
238#1805—131no—
239#1787—131no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13C22⋊Q812yes—
245C23×C13#13512yes—
246C23×C13#13712yes—
247C23×C13C22×D411yescharacteristic
248Q8×C13—22no—
249Q8×C13—22no—
250Q8×C13—22no—
251Q8×C13—22no—
252Q8×C13—22no—
253Q8×C13—48no—
254Q8×C13—41no—
255Q8×C13—41no—
256Q8×C13C22⋊Q814yes—
257C2×C4×C13—22no—
258C2×C4×C13—21no—
259C2×C4×C13—22no—
260C2×C4×C13—22no—
261C2×C4×C13—21no—
262C2×C4×C13—22no—
263C2×C4×C13—22no—
264C2×C4×C13—22no—
265C2×C4×C13—22no—
266C2×C4×C13—22no—
267C2×C4×C13—21no—
268C2×C4×C13—21no—
269C2×C4×C13—21no—
270C2×C4×C13—21no—
271C2×C4×C13—21no—
272C2×C4×C13—21no—
273C2×C4×C13—21no—
274C2×C4×C13—21no—
275C2×C4×C13—21no—
276C2×C4×C13—21no—
277C2×C4×C13—21no—
278C2×C4×C13—21no—
279C2×C4×C13—48no—
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×C13C22⋊Q812yes—
289C2×C4×C13C22×D411yescharacteristic
290C2×C4×C13C22×Q811yescharacteristic
291C2×C4×C13C2×#4111yescharacteristic
292C2×C4×C13C2×#4111yescharacteristic
293C2×C4×C13H(5,𝔽2)11yescharacteristic
294C2×C4×C13H(5,𝔽2)11yescharacteristic
295C2×Dic13—22no—
296C2×Dic13—41no—
297C2×Dic13—41no—
298C2×Dic13—41no—
299C2×Dic13—41no—
300C2×Dic13—41no—
301C2×Dic13—41no—
302C2×Dic13—41no—
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
306C2×Dic13—41no—
307C2×Dic13—84no—
308#1055—22no—
309#1055—41no—
310#1055—41no—
311#1055—41no—
312C23×Q8C2×D1311yescharacteristic
313C23×C8—131no—
314C2×#125—131no—
315C2×C4×Q8C2×D1311yescharacteristic
316C2×C4×Q8C2×D1311yescharacteristic
317C22×C4⋊C4—131no—
318#479—264no—
319C2×#107—131no—
320C2×#107—131no—
321C2×#106—131no—
322C2×#106—131no—
323C2×C4⋊C8—131no—
324C2×C4⋊C8—131no—
325C2×#103—131no—
326C2×#103—131no—
327C2×#103—131no—
328C2×#103—131no—
329C2×#103—131no—
330C2×#103—131no—
331C2×#103—131no—
332C2×#103—131no—
333C2×#103—264no—
334C2×C22⋊C8—131no—
335#400—261no—
336#398—261no—
337#391—21no—
338#391—21no—
339#391C2×D1311yescharacteristic
340#391C2×D1311yescharacteristic
341#389—131no—
342#389—131no—
343#385—261no—
344#382—131no—
345#380—21no—
346#380—131no—
347#380—261no—
348#380C2×D1311yescharacteristic
349C4×C22⋊C4—21no—
350C4×C22⋊C4C2×D1311yescharacteristic
351#340—131no—
352#340—131no—
353#340—131no—
354#340—131no—
355#336—131no—
356#336—131no—
357C22×C13—22no—
358C22×C13—22no—
359C22×C13—22no—
360C22×C13—22no—
361C22×C13—22no—
362C22×C13—22no—
363C22×C13#47914yescomplemented
364C22×C13C2×C22⋊Q811yescharacteristic
365C22×C13D4211yescharacteristic
366C22×C13#54611yescharacteristic
367C22×C13C2×#13511yescharacteristic
368C22×C13C2×#13711yescharacteristic
369C22×C13#57711yescharacteristic
370C22×C13#57811yescharacteristic
371C4×C13—22no—
372C4×C13—24no—
373C4×C13—42no—
374C4×C13—41no—
375C4×C13—41no—
376C4×C13—41no—
377C4×C13—41no—
378C4×C13—81no—
379C4×C13—81no—
380C4×C13C2×C22⋊Q811yescharacteristic
381C4×C13#54311yescharacteristic
382C4×C13#54611yescharacteristic
383C4×C13#55111yescharacteristic
384Dic13—42no—
385Dic13—81no—
386Dic13—81no—
387Dic13—81no—
388C22×Q8—22no—
389C22×Q8—21no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—41no—
393C22×Q8—41no—
394C22×Q8Dic2614yes—
395C22×Q8C22×D1311yescharacteristic
396C22×Q8C22×D1311yescharacteristic
397C23×C4—21no—
398C23×C4—261no—
399C23×C4C22×D1311yescharacteristic
400C22×C8—131no—
401C22×C8—131no—
402C22×C8—131no—
403C22×C8—131no—
404C22×C8—262no—
405C22×C8—262no—
406C22×C8—521no—
407#125—262no—
408#125—521no—
409C4×Q8—22no—
410C4×Q8—22no—
411C4×Q8—41no—
412C4×Q8—41no—
413C2×C4⋊C4—21no—
414C2×C4⋊C4—21no—
415C2×C4⋊C4—131no—
416C2×C4⋊C4—131no—
417C2×C4⋊C4—131no—
418C2×C4⋊C4—131no—
419C2×C4⋊C4—262no—
420C2×C4⋊C4—261no—
421C2×C4⋊C4—261no—
422C2×C4⋊C4—261no—
423C2×C4⋊C4—261no—
424C2×C4⋊C4—261no—
425C2×C4⋊C4—521no—
426C2×C4⋊C4C22×D1311yescharacteristic
427C2×C4⋊C4C22×D1311yescharacteristic
428C2×C22⋊C4—21no—
429C2×C22⋊C4—261no—
430C2×C22⋊C4C22⋊D1311yescharacteristic
431C2×C22⋊C4C22⋊D1311yescharacteristic
432C2×C42—21no—
433C2×C42—21no—
434C2×C42C22×D1311yescharacteristic
435C2×C42C22×D1311yescharacteristic
436#107—262no—
437#107—521no—
438#106—262no—
439#106—521no—
440C4⋊C8—262no—
441C4⋊C8—521no—
442#103—134no—
443#103—262no—
444#103—262no—
445#103—262no—
446#103—262no—
447#103—262no—
448#103—521no—
449#103—521no—
450C22⋊C8—262no—
451#95—21no—
452#95—21no—
453#95—21no—
454#95—21no—
455#95—21no—
456#95—261no—
457#95—261no—
458#95—261no—
459#95—261no—
460#95—261no—
461#95C22⋊D1311yescharacteristic
462#95C22⋊D1311yescharacteristic
463C2×C13—24no—
464C2×C13#243711yescharacteristic
465C2×C13C2×#47911yescharacteristic
466C2×C13#308211yescharacteristic
467C2×C13#327011yescharacteristic
468C2×C13#328211yescharacteristic
469C2×C13#330011yescharacteristic
470C2×C13#332011yescharacteristic
471C24C2×C22⋊D1311yescharacteristic
472C2×Q8—24no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—28no—
478C2×Q8—21no—
479C2×Q8—21no—
480C2×Q8—21no—
481C2×Q8—21no—
482C2×Q8—42no—
483C2×Q8—42no—
484C2×Q8—44no—
485C2×Q8—44no—
486C2×Q8—44no—
487C2×Q8C2×Dic2612yes—
488C2×Q8C2×Dic2612yes—
489C2×Q8D4×D1312yes—
490C2×Q8#612912yes—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—24no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—42no—
501C22×C4—42no—
502C22×C4—261no—
503C22×C4—261no—
504C22×C4—261no—
505C22×C4—261no—
506C22×C4—522no—
507C22×C4—522no—
508C22×C4—1041no—
509C22×C4C2×Dic2612yes—
510C22×C4#612712yes—
511C22×C4C2×C22⋊D1311yescharacteristic
512C22×C4C2×C22⋊D1311yescharacteristic
513C22×C4C2×C22⋊D1311yescharacteristic
514C22×C4C2×C22⋊D1311yescharacteristic
515C22×C4C2×C22⋊D1311yescharacteristic
516C22×C4C23×D1311yescharacteristic
517C2×C8—132no—
518C2×C8—261no—
519C2×C8—261no—
520C2×C8—261no—
521C2×C8—261no—
522C2×C8—261no—
523C2×C8—261no—
524C2×C8—261no—
525C2×C8—261no—
526C2×C8—261no—
527C2×C8—261no—
528C2×C8—261no—
529C2×C8—524no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—132no—
537C4⋊C4—261no—
538C4⋊C4—261no—
539C4⋊C4—261no—
540C4⋊C4—261no—
541C4⋊C4—261no—
542C4⋊C4—261no—
543C4⋊C4—261no—
544C4⋊C4—522no—
545C4⋊C4—522no—
546C4⋊C4—522no—
547C4⋊C4—1041no—
548C4⋊C4—1041no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—42no—
552C22⋊C4—522no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—42no—
558C42—42no—
559C13#2595711yescharacteristic, complemented, Sylow
560C23—21no—
561C23—21no—
562C23—21no—
563C23—21no—
564C23#8817812yes—
565C23#8819612yes—
566C23#8820412yes—
567C23C22×C22⋊D1311yescharacteristic
568Q8—22no—
569Q8—22no—
570Q8—22no—
571Q8—22no—
572Q8—22no—
573Q8—48no—
574Q8—41no—
575Q8—41no—
576Q8#8813214yes—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—21no—
580C2×C4—22no—
581C2×C4—21no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—48no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—262no—
609C2×C4—521no—
610C2×C4—521no—
611C2×C4—521no—
612C2×C4—521no—
613C2×C4—521no—
614C2×C4—521no—
615C2×C4—521no—
616C2×C4—521no—
617C2×C4—521no—
618C2×C4—521no—
619C2×C4—521no—
620C2×C4—1044no—
621C2×C4#8817812yes—
622C2×C4C22×Dic2611yescharacteristic
623C2×C4C2×#612711yescharacteristic
624C2×C4C2×D4×D1311yescharacteristic
625C2×C4C2×#612911yescharacteristic
626C2×C4#8825111yescharacteristic
627C2×C4#8825111yescharacteristic
628C8—262no—
629C8—521no—
630C8—521no—
631C8—521no—
632C22—22no—
633C22—22no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—22no—
638C22#1171868314yescomplemented
639C22C2×#8817811yescharacteristic
640C22D4×C22⋊D1311yescharacteristic
641C22#1171951111yescharacteristic
642C22C2×#8819611yescharacteristic
643C22C2×#8820411yescharacteristic
644C22#1171954211yescharacteristic
645C22#1171954311yescharacteristic
646C4—22no—
647C4—24no—
648C4—41no—
649C4—42no—
650C4—41no—
651C4—41no—
652C4—41no—
653C4—81no—
654C4—81no—
655C4—522no—
656C4—1041no—
657C4—1041no—
658C4—1041no—
659C4C2×#8813211yescharacteristic
660C4#1171918811yescharacteristic
661C4#1171919511yescharacteristic
662C4#1171920011yescharacteristic
663C2—24no—
664C2#1311849711yescharacteristic
665C2C2×#1171868311yescharacteristic
666C2#1312467811yescharacteristic
667C2#1312640711yescharacteristic
668C2#1312654411yescharacteristic
669C2#1312672311yescharacteristic
670C2#1312700711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingQ8×C13×C22⋊C4C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterQ8×C22⋊C4D13
hypocenterC13#25957
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718683C2semidirect
4. #13116384C2semidirect
5. #13116231C2semidirect
6. #13116217C2semidirect
7. #13115987C2semidirect
8. #13115104C2semidirect
9. #13115090C2semidirect
13. #13114851C2semidirect
363. C22×C13#479semidirect
559. C13#25957semidirect
638. C22#11718683semidirect

Maximal subgroups

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

subgroupindex
C2×#117186832
C22×#880752
#131185602
#131163842
#131162312
#131162172
#131159872
#131151042
#131150902
#131150232
#131150162
#131148592
#131148512
#131147712
Q8×C13×C22⋊C42
#2595713