Finite Group Databasebeta

← #15926764

Subgroups — #15926764

Order 3328.

756 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13118527C211yesmaximal, characteristic
2#13116404C211yesmaximal, characteristic, complemented
3#13116327C211yesmaximal, characteristic, complemented
4#13116231C211yesmaximal, characteristic, complemented
5#13115977C211yesmaximal, characteristic, complemented
6#13115788C211yesmaximal, characteristic, complemented
7#13115428C211yesmaximal, characteristic, complemented
8#13115270C211yesmaximal, characteristic
9#13115149C211yesmaximal, characteristic
10#13115090C211yesmaximal, characteristic, complemented
11#13115024C211yesmaximal, characteristic
12#13115021C211yesmaximal, characteristic
13#13114851C211yesmaximal, characteristic, complemented
14#13114555C211yesmaximal, characteristic
15C13×#2360C211yesmaximal, characteristic
16C2×C13×C22⋊Q8C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88180C2211yescharacteristic
20C22×#6099C2211yescharacteristic
21C2×#88123C2211yescharacteristic
22C13×#391C2211yescharacteristic
23C13×#389—21no—
24C13×#389C2211yescharacteristic
25C13×#387—21no—
26C13×#385—21no—
27C4×C13×C4⋊C4C2211yescharacteristic
28C4×C13×C22⋊C4—21no—
29C4×C13×C22⋊C4C2211yescharacteristic
30C2×#88075C2211yescharacteristic
31C2×#88075C2211yescharacteristic
32C2×#88075C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34#11718873C2211yescharacteristic
35C2×C22⋊#1055C2211yescharacteristic
36C2×#88047C2211yescharacteristic
37C2×#88047C2211yescharacteristic
38#11718609—21no—
39#11718608—21no—
40#11718597C2211yescharacteristic
41#11718589C2211yescharacteristic
42#11718589C2211yescharacteristic
43C2×C4⋊#1055C2211yescharacteristic
44C2×C4⋊#1055C2211yescharacteristic
45#11718316—21no—
46#11718307—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×C13C2311yescharacteristic
60C23×C4×C13—21no—
61C23×C4×C13C2311yescharacteristic
62C22×Dic26—21no—
63C13×C22⋊Q8—22no—
64C13×C22⋊Q8Q814yescomplemented
65C4×Q8×C13—22no—
66C4×Q8×C13—41no—
67C2×C13×C4⋊C4—21no—
68C2×C13×C4⋊C4—22no—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4—21no—
71C2×C13×C4⋊C4—21no—
72C2×C13×C4⋊C4—41no—
73C2×C13×C4⋊C4C2311yescharacteristic
74C2×C13×C4⋊C4C2311yescharacteristic
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C22⋊C4—21no—
77C2×C13×C22⋊C4D411yescharacteristic
78C2×C13×C22⋊C4D411yescharacteristic
79C2×C42×C13—21no—
80C2×C42×C13—21no—
81C2×C42×C13C2311yescharacteristic
82C2×C42×C13C2311yescharacteristic
83C2×C22⋊Dic13—21no—
84C2×C22⋊Dic13—21no—
85#88180—22no—
86#88180—41no—
87C2×C4⋊Dic13—21no—
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×#6101—21no—
94C2×C4×Dic13—21no—
95C2×#6099—22no—
96C2×#6099—41no—
97C2×#6099—41no—
98C22×#1055C2311yescharacteristic
99C22×#1055C2311yescharacteristic
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102#88123—22no—
103#88123—41no—
104C13×#95—21no—
105C13×#95—21no—
106C13×#95—21no—
107C13×#95—21no—
108C13×#95D411yescharacteristic
109C13×#95D411yescharacteristic
110#88075—22no—
111#88075—41no—
112#88075—41no—
113#88075—41no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119C22⋊#1055—22no—
120#88047—22no—
121#88047—41no—
122C4⋊#1055—41no—
123C4⋊#1055—41no—
124#26428—131nomaximal, Sylow
125C24×C13C2×D411yescharacteristic
126C2×Q8×C13—21no—
127C2×Q8×C13—21no—
128C2×Q8×C13—21no—
129C2×Q8×C13—21no—
130C2×Q8×C13—21no—
131C2×Q8×C13C2×Q812yes—
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—21no—
140C22×C4×C13—42no—
141C22×C4×C13—42no—
142C22×C4×C13—81no—
143C22×C4×C13C2×D411yescharacteristic
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2×D411yescharacteristic
147C22×C4×C13C2×D411yescharacteristic
148C22×C4×C13C2×Q812yes—
149C22×C4×C13#4112yes—
150C22×C4×C13C2411yescharacteristic
151C22×Dic13—21no—
152C22×Dic13—21no—
153C22×Dic13—21no—
154C22×Dic13—21no—
155C2×Dic26—42no—
156C2×Dic26—42no—
157C2×Dic26—81no—
158C13×C4⋊C4—24no—
159C13×C4⋊C4—21no—
160C13×C4⋊C4—21no—
161C13×C4⋊C4—21no—
162C13×C4⋊C4—21no—
163C13×C4⋊C4—42no—
164C13×C4⋊C4—42no—
165C13×C4⋊C4—81no—
166C13×C4⋊C4C2×Q812yes—
167C13×C4⋊C4#4112yes—
168C13×C22⋊C4—24no—
169C13×C22⋊C4—22no—
170C13×C22⋊C4—41no—
171C42×C13—21no—
172C42×C13—21no—
173C42×C13—21no—
174C42×C13—21no—
175C42×C13—42no—
176C42×C13—81no—
177C22⋊Dic13—42no—
178C22⋊Dic13—81no—
179C4⋊Dic13—21no—
180C4⋊Dic13—21no—
181C4⋊Dic13—21no—
182C4⋊Dic13—21no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13—21no—
186C4⋊Dic13—42no—
187C4⋊Dic13#4112yes—
188#6101—42no—
189#6101—81no—
190C4×Dic13—42no—
191#6099—44no—
192C2×#1055—21no—
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—
204#2439—131no—
205#2360D1311yescharacteristic
206#2101—131no—
207#2086—131no—
208#2068—131no—
209#2024—131no—
210#1988—131no—
211#1921—131no—
212#1894—131no—
213#1873—131no—
214#1863—131no—
215#1852—131no—
216#1851—131no—
217#1805—131no—
218#1736—131no—
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13C22⋊Q812yes—
226C23×C13C22×D411yescharacteristic
227Q8×C13—22no—
228Q8×C13—22no—
229Q8×C13—41no—
230Q8×C13—41no—
231C2×C4×C13—21no—
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—22no—
236C2×C4×C13—22no—
237C2×C4×C13—22no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—22no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—41no—
256C2×C4×C13—41no—
257C2×C4×C13—41no—
258C2×C4×C13—41no—
259C2×C4×C13—41no—
260C2×C4×C13—84no—
261C2×C4×C13C22⋊Q812yes—
262C2×C4×C13#13712yes—
263C2×C4×C13C22×Q811yescharacteristic
264C2×C4×C13C2×#4111yescharacteristic
265C2×C4×C13C2×#4111yescharacteristic
266C2×C4×C13C2×#4111yescharacteristic
267C2×C4×C13H(5,𝔽2)11yescharacteristic
268C2×C4×C13H(5,𝔽2)11yescharacteristic
269C2×Dic13—22no—
270C2×Dic13—41no—
271C2×Dic13—41no—
272C2×Dic13—41no—
273C2×Dic13—41no—
274C2×Dic13—41no—
275C2×Dic13—41no—
276C2×Dic13—41no—
277C2×Dic13—41no—
278C2×Dic13—41no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281Dic26—84no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285#1055—41no—
286C22×M16—131no—
287C2×C4⋊Q8—131no—
288C2×C22⋊Q8C2×D1311yescharacteristic
289C2×C4×Q8C2×D1311yescharacteristic
290C2×#117—131no—
291C22×C4⋊C4C2×D1311yescharacteristic
292C2×#107—131no—
293C2×#107—131no—
294C2×C4⋊C8—131no—
295C2×C4⋊C8—131no—
296C2×#103—131no—
297C2×#103—131no—
298C2×#103—131no—
299C2×#103—131no—
300C2×C22⋊C8—131no—
301#396—261no—
302#393—261no—
303#391—261no—
304#391C2×D1311yescharacteristic
305#389—21no—
306#389—131no—
307#389—131no—
308#389C2×D1311yescharacteristic
309#387—21no—
310#387—261no—
311#385—21no—
312#382—131no—
313#380—131no—
314C4×C4⋊C4C2×D1311yescharacteristic
315C4×C22⋊C4—21no—
316C4×C22⋊C4C2×D1311yescharacteristic
317#340—131no—
318#340—131no—
319#340—131no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#336—131no—
328#336—131no—
329C22×C13—22no—
330C22×C13—22no—
331C22×C13—22no—
332C22×C13—41no—
333C22×C13—41no—
334C22×C13—41no—
335C22×C13—41no—
336C22×C13C2×C22⋊Q811yescharacteristic
337C22×C13#54611yescharacteristic
338C22×C13#54611yescharacteristic
339C22×C13C2×#13711yescharacteristic
340C22×C13#57511yescharacteristic
341C22×C13#57611yescharacteristic
342C22×C13#57811yescharacteristic
343C4×C13—22no—
344C4×C13—22no—
345C4×C13—41no—
346C4×C13—42no—
347C4×C13—42no—
348C4×C13—41no—
349C4×C13—42no—
350C4×C13—41no—
351C4×C13—81no—
352C4×C13#52911yescharacteristic
353C4×C13#53811yescharacteristic
354C4×C13#55411yescharacteristic
355C4×C13#55411yescharacteristic
356Dic13—42no—
357Dic13—81no—
358Dic13—81no—
359Dic13—81no—
360C22×Q8—261no—
361C22×Q8C22×D1311yescharacteristic
362C23×C4—21no—
363C23×C4C22×D1311yescharacteristic
364C2×M16—262no—
365C2×M16—521no—
366C2×M16—521no—
367C22×C8—131no—
368C22×C8—131no—
369C22×C8—131no—
370C22×C8—131no—
371C4⋊Q8—262no—
372C4⋊Q8—521no—
373C22⋊Q8—22no—
374C22⋊Q8Dic2614yescomplemented
375C4×Q8—22no—
376C4×Q8—41no—
377#117—262no—
378#117—521no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—41no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—261no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4C22×D1311yescharacteristic
393C2×C4⋊C4C22×D1311yescharacteristic
394C2×C4⋊C4C22×D1311yescharacteristic
395C2×C22⋊C4—21no—
396C2×C22⋊C4—261no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4C22⋊D1311yescharacteristic
399C2×C22⋊C4C22⋊D1311yescharacteristic
400C2×C42—21no—
401C2×C42—21no—
402C2×C42—261no—
403C2×C42C22×D1311yescharacteristic
404C2×C42C22×D1311yescharacteristic
405#107—262no—
406#107—521no—
407C4⋊C8—521no—
408C4⋊C8—521no—
409#103—262no—
410#103—521no—
411#103—521no—
412#103—521no—
413C22⋊C8—262no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—261no—
419#95—261no—
420#95—261no—
421#95—261no—
422#95—261no—
423#95C22⋊D1311yescharacteristic
424#95C22⋊D1311yescharacteristic
425C2×C13—42no—
426C2×C13#245011yescharacteristic
427C2×C13#307811yescharacteristic
428C2×C13#308311yescharacteristic
429C2×C13#331411yescharacteristic
430C2×C13#331911yescharacteristic
431C2×C13#332711yescharacteristic
432C2×C13#332811yescharacteristic
433C24C2×C22⋊D1311yescharacteristic
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—522no—
440C2×Q8—522no—
441C2×Q8—1041no—
442C2×Q8C2×Dic2612yes—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—81no—
454C22×C4—261no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4C2×Dic2612yes—
459C22×C4#612712yes—
460C22×C4C2×C22⋊D1311yescharacteristic
461C22×C4C2×C22⋊D1311yescharacteristic
462C22×C4C2×C22⋊D1311yescharacteristic
463C22×C4C2×C22⋊D1311yescharacteristic
464C22×C4C2×C22⋊D1311yescharacteristic
465C22×C4C23×D1311yescharacteristic
466M16—524no—
467C2×C8—261no—
468C2×C8—261no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4—81no—
487C4⋊C4—132no—
488C4⋊C4—261no—
489C4⋊C4—261no—
490C4⋊C4—261no—
491C4⋊C4—261no—
492C4⋊C4—261no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—522no—
496C4⋊C4—522no—
497C4⋊C4—1041no—
498C4⋊C4C2×Dic2612yes—
499C4⋊C4#612912yes—
500C22⋊C4—24no—
501C22⋊C4—22no—
502C22⋊C4—41no—
503C22⋊C4—522no—
504C22⋊C4—1041no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—42no—
510C42—81no—
511C42—522no—
512C13#2642811yescharacteristic, complemented, Sylow
513C23—21no—
514C23—21no—
515C23—21no—
516C23—21no—
517C23—21no—
518C23—21no—
519C23#8817812yes—
520C23C22×C22⋊D1311yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—41no—
524Q8—41no—
525Q8—1044no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4—262no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4—521no—
562C2×C4—521no—
563C2×C4—521no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4#8817812yes—
569C2×C4#8819612yes—
570C2×C4C22×Dic2611yescharacteristic
571C2×C4C2×#612711yescharacteristic
572C2×C4C2×#612911yescharacteristic
573C2×C4#8825111yescharacteristic
574C2×C4#41×D1311yescharacteristic
575C2×C4#8825611yescharacteristic
576C8—521no—
577C8—521no—
578C8—521no—
579C8—521no—
580C22—22no—
581C22—22no—
582C22—22no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22C2×#8817811yescharacteristic
588C22#1171951111yescharacteristic
589C22C2×#8819611yescharacteristic
590C22#1171952711yescharacteristic
591C22#1171953411yescharacteristic
592C22#1171954011yescharacteristic
593C22#1171954311yescharacteristic
594C4—22no—
595C4—22no—
596C4—42no—
597C4—41no—
598C4—42no—
599C4—41no—
600C4—42no—
601C4—41no—
602C4—81no—
603C4—522no—
604C4—1041no—
605C4—1041no—
606C4—1041no—
607C4#1171924311yescharacteristic
608C4#1171924411yescharacteristic
609C4#1171924811yescharacteristic
610C4#1171926511yescharacteristic
611C2—42no—
612C2#1311865411yescharacteristic
613C2#1312464111yescharacteristic
614C2#1312468711yescharacteristic
615C2#1312691111yescharacteristic
616C2#1312699211yescharacteristic
617C2#1312709811yescharacteristic
618C2#1312711911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC13×#2360C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenter#2360D13
hypocenterC13#26428
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #2360

Complements

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

NH ≅ G/Ntype
2. #13116404C2semidirect
3. #13116327C2semidirect
4. #13116231C2semidirect
5. #13115977C2semidirect
6. #13115788C2semidirect
7. #13115428C2semidirect
10. #13115090C2semidirect
13. #13114851C2semidirect
64. C13×C22⋊Q8Q8semidirect
374. C22⋊Q8Dic26semidirect
512. C13#26428semidirect

Maximal subgroups

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

subgroupindex
#131185272
#131164042
#131163272
#131162312
#131159772
#131157882
#131154282
#131152702
#131151492
#131150902
#131150242
#131150212
#131148512
#131145552
C13×#23602
#2642813