Finite Group Databasebeta

← #16802259

Subgroups — #16802259

Order 3328.

814 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131007C211yesmaximal, characteristic, complemented
2#13131006C211yesmaximal, characteristic, complemented
3#13130935C211yesmaximal, characteristic, complemented
4#13130934C211yesmaximal, characteristic, complemented
5#13130892C211yesmaximal, characteristic, complemented
6#13130891C211yesmaximal, characteristic, complemented
7#13130891C211yesmaximal, characteristic, complemented
8#13130890C211yesmaximal, characteristic, complemented
9#13130780C211yesmaximal, characteristic
10#13130779C211yesmaximal, characteristic
11#13130692C211yesmaximal, characteristic
12C22⋊C4×#1057C211yesmaximal, characteristic
13C22⋊C4×#1057C211yesmaximal, characteristic
14C2×#11718290C211yesmaximal, characteristic
15#13117368C211yesmaximal, characteristic
16C23×#1057C2211yescharacteristic
17C23×#1057C2211yescharacteristic
18C22×C4×Dic13C2211yescharacteristic
19C2×#88141C2211yescharacteristic
20C2×#88132C411yescharacteristic
21C2×C22⋊#1057C2211yescharacteristic
22C2×C22⋊#1057C2211yescharacteristic
23C2×#88112C2211yescharacteristic
24C2×#88112C2211yescharacteristic
25C2×#88112C2211yescharacteristic
26C2×#88112C2211yescharacteristic
27C2×C4⋊#1057C2211yescharacteristic
28C2×C4⋊#1057C2211yescharacteristic
29C2×C4×#1057C2211yescharacteristic
30C2×C4×#1057C2211yescharacteristic
31C2×C4×#1057C2211yescharacteristic
32C2×C4×#1057C2211yescharacteristic
33C13×#385C411yescharacteristic
34#11718871C411yescharacteristic
35#11718639C411yescharacteristic
36C4⋊C4×Dic13C2211yescharacteristic
37#11718633C411yescharacteristic
38#11718603C411yescharacteristic
39C22⋊C4×Dic13C2211yescharacteristic
40C22⋊C4×Dic13C2211yescharacteristic
41#11718314C411yescharacteristic
42#11718310C2211yescharacteristic
43#11718310C2211yescharacteristic
44#11718307C411yescharacteristic
45#11718290C2211yescharacteristic
46#11718290C2211yescharacteristic
47#11718290C2211yescharacteristic
48#11718290C2211yescharacteristic
49#11718290C2211yescharacteristic
50#11718290C2211yescharacteristic
51#11718290C2211yescharacteristic
52#11718290C2211yescharacteristic
53#11718290C2211yescharacteristic
54#11718290C2211yescharacteristic
55#11718290C2211yescharacteristic
56#11718290C2211yescharacteristic
57#11718290C2211yescharacteristic
58#11718290C2211yescharacteristic
59C23×C4×C13C2×C411yescharacteristic
60C23×Dic13C2×C411yescharacteristic
61C23×Dic13C2311yescharacteristic
62C22×Dic26C2×C411yescharacteristic
63C22×#1057—22no—
64C22×#1057—41no—
65C22×#1057—41no—
66C22×#1057—41no—
67C22×#1057—41no—
68C22×#1057Q814yescomplemented
69C22×#1057C2311yescharacteristic
70C22×#1057C2311yescharacteristic
71C22×#1057C2311yescharacteristic
72C22×#1057C2311yescharacteristic
73C22×#1057C2311yescharacteristic
74C22×#1057C2311yescharacteristic
75C22×#1057C2311yescharacteristic
76C22×#1057C2311yescharacteristic
77C2×C13×C4⋊C4C2×C411yescharacteristic
78C2×C13×C4⋊C4C2×C411yescharacteristic
79C2×C13×C22⋊C4C2×C411yescharacteristic
80C2×C13×C22⋊C4C2×C411yescharacteristic
81C2×C22⋊Dic13C2×C411yescharacteristic
82C2×C22⋊Dic13C2×C411yescharacteristic
83C2×C4⋊Dic13C2×C411yescharacteristic
84C2×#6101C2×C411yescharacteristic
85C2×#6101C2×C411yescharacteristic
86C2×#6101C2×C411yescharacteristic
87C2×#6101C2×C411yescharacteristic
88C2×#6101C2×C411yescharacteristic
89C2×#6101C2×C411yescharacteristic
90C2×C4×Dic13—41no—
91C2×C4×Dic13—41no—
92C2×C4×Dic13C2×C411yescharacteristic
93C2×C4×Dic13C2×C411yescharacteristic
94C2×C4×Dic13C2311yescharacteristic
95C2×C4×Dic13C2311yescharacteristic
96C2×C4×Dic13C2311yescharacteristic
97C2×C4×Dic13C2311yescharacteristic
98C2×C4×Dic13C2311yescharacteristic
99C2×C4×Dic13C2311yescharacteristic
100#88141—41no—
101#88141—41no—
102#88132C818yescomplemented
103C22⋊#1057—22no—
104C22⋊#1057—22no—
105#88112—41no—
106#88112—41no—
107#88112—41no—
108#88112—41no—
109C4⋊#1057—41no—
110C4⋊#1057—41no—
111C4×#1057—41no—
112C4×#1057—41no—
113C4×#1057—41no—
114C4×#1057—41no—
115C13×#95C2×C411yescharacteristic
116C13×#95C2×C411yescharacteristic
117#88071C2×C411yescharacteristic
118#88071C2×C411yescharacteristic
119#88071C2×C411yescharacteristic
120#88071C2×C411yescharacteristic
121#88071C2×C411yescharacteristic
122#88071C2×C411yescharacteristic
123#88071C2×C411yescharacteristic
124#88071C2×C411yescharacteristic
125#22287—131nomaximal, Sylow
126C24×C13C22×C411yescharacteristic
127C22×C4×C13—22no—
128C22×C4×C13—41no—
129C22×C4×C13—41no—
130C22×C4×C13C22×C411yescharacteristic
131C22×C4×C13C22×C411yescharacteristic
132C22×C4×C13C22×C411yescharacteristic
133C22×C4×C13C22×C411yescharacteristic
134C22×C4×C13C22×C411yescharacteristic
135C22×C4×C13C22×C411yescharacteristic
136C22×Dic13—21no—
137C22×Dic13—21no—
138C22×Dic13—21no—
139C22×Dic13—21no—
140C22×Dic13—41no—
141C22×Dic13—41no—
142C22×Dic13C2×C814yes—
143C22×Dic13C22×C411yescharacteristic
144C22×Dic13C22×C411yescharacteristic
145C22×Dic13C22×C411yescharacteristic
146C22×Dic13C22×C411yescharacteristic
147C22×Dic13C22×C411yescharacteristic
148C22×Dic13C22×C411yescharacteristic
149C22×Dic13C22×C411yescharacteristic
150C22×Dic13C2×Q812yes—
151C22×Dic13#4112yes—
152C22×Dic13C2411yescharacteristic
153C2×Dic26—41no—
154C2×Dic26—41no—
155C2×Dic26C2×C814yescomplemented
156C2×#1057—21no—
157C2×#1057—21no—
158C2×#1057—21no—
159C2×#1057—21no—
160C2×#1057—21no—
161C2×#1057—21no—
162C2×#1057—21no—
163C2×#1057—21no—
164C2×#1057—21no—
165C2×#1057—21no—
166C2×#1057—21no—
167C2×#1057—21no—
168C2×#1057—21no—
169C2×#1057—21no—
170C2×#1057—21no—
171C2×#1057—21no—
172C2×#1057—21no—
173C2×#1057—21no—
174C2×#1057—21no—
175C2×#1057—21no—
176C2×#1057—21no—
177C2×#1057—21no—
178C2×#1057—44no—
179C2×#1057—44no—
180C2×#1057C2×Q812yes—
181C2×#1057C2×Q812yes—
182C13×C4⋊C4—41no—
183C13×C4⋊C4—41no—
184C13×C22⋊C4—22no—
185C13×C22⋊C4C2×C814yes—
186C22⋊Dic13—22no—
187C22⋊Dic13C2×C814yes—
188C4⋊Dic13C2×C814yescomplemented
189#6101—41no—
190#6101—41no—
191#6101—41no—
192#6101—41no—
193#6101C2×C814yescomplemented
194#6101C2×C814yescomplemented
195C4×Dic13—21no—
196C4×Dic13—21no—
197C4×Dic13—21no—
198C4×Dic13—21no—
199C4×Dic13—21no—
200C4×Dic13—21no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—21no—
206C4×Dic13—21no—
207C4×Dic13—41no—
208C4×Dic13—41no—
209C4×C22⋊Q8—131no—
210#1984—131no—
211#1984—131no—
212#1939—131no—
213#1939—131no—
214#1916—131no—
215#1916—131no—
216#1916—131no—
217#1916—131no—
218#1850—131no—
219#1850—131no—
220#1797—131no—
221C8×C22⋊C4—131no—
222C8×C22⋊C4—131no—
223C2×#336—131no—
224C23×C13—21no—
225C23×C13—21no—
226C23×C13—21no—
227C23×C13—21no—
228C23×C13C4×Q812yes—
229C23×C13C22×C812yes—
230C23×C13#13112yes—
231C23×C13C23×C411yescharacteristic
232C2×C4×C13—21no—
233C2×C4×C13—21no—
234C2×C4×C13—21no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—21no—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—44no—
249C2×C4×C13C22×C812yes—
250C2×C4×C13C22×C812yes—
251C2×Dic13—21no—
252C2×Dic13—21no—
253C2×Dic13—21no—
254C2×Dic13—21no—
255C2×Dic13—21no—
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—22no—
262C2×Dic13—22no—
263C2×Dic13—22no—
264C2×Dic13—22no—
265C2×Dic13—21no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—44no—
272C2×Dic13C4×Q812yes—
273C2×Dic13C22×C812yes—
274C2×Dic13C22×C812yes—
275C2×Dic13C22×C812yes—
276C2×Dic13C22×C812yes—
277C2×Dic13C22×Q811yescharacteristic
278C2×Dic13C2×#4111yescharacteristic
279C2×Dic13H(5,𝔽2)11yescharacteristic
280C2×Dic13H(5,𝔽2)11yescharacteristic
281C2×Dic13H(5,𝔽2)11yescharacteristic
282C2×Dic132−1+411yescharacteristic
283Dic26—44no—
284#1057—22no—
285#1057—22no—
286#1057—41no—
287#1057—41no—
288#1057—41no—
289#1057—41no—
290#1057—41no—
291#1057—41no—
292C23×C8—131no—
293C23×C8—131no—
294C2×C22⋊Q8—131no—
295C2×C4×Q8—131no—
296C22×C42—131no—
297C2×C4⋊C8—131no—
298C2×C4⋊C8—131no—
299C2×C4⋊C8—131no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8—131no—
302C2×C4⋊C8—131no—
303C2×C22⋊C8—131no—
304C2×C22⋊C8—131no—
305C2×C4×C8—131no—
306C2×C4×C8—131no—
307C2×C4×C8—131no—
308C2×C4×C8—131no—
309#391—131no—
310#389—131no—
311#387—131no—
312#387—131no—
313#385—131no—
314#385#26111yescharacteristic
315#380—131no—
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C22⋊C4—131no—
320C4×C22⋊C4—131no—
321#336—131no—
322#336—131no—
323#336—131no—
324#336—131no—
325#336—131no—
326#336—131no—
327#336—131no—
328#336—131no—
329#336—131no—
330#336—131no—
331#336—131no—
332#336—131no—
333#336—131no—
334#336—131no—
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—22no—
339C22×C13—22no—
340C22×C13—22no—
341C22×C13C8×Q814yes—
342C22×C13C2×C4×Q811yescharacteristic
343C22×C13#51811yescharacteristic
344C22×C13#52011yescharacteristic
345C22×C13C23×C811yescharacteristic
346C22×C13C2×#13111yescharacteristic
347C22×C13#56811yescharacteristic
348C22×C13#56811yescharacteristic
349C4×C13—22no—
350C4×C13—22no—
351C4×C13—41no—
352C4×C13—41no—
353C4×C13—41no—
354C4×C13—41no—
355Dic13—22no—
356Dic13—22no—
357Dic13—22no—
358Dic13—22no—
359Dic13—22no—
360Dic13—41no—
361Dic13—41no—
362Dic13#53811yescharacteristic
363Dic13#53911yescharacteristic
364Dic13#54311yescharacteristic
365Dic13#54411yescharacteristic
366C22×Q8—131no—
367C23×C4—131no—
368C23×C4—131no—
369C23×C4C2×#26111yescharacteristic
370C22×C8—131no—
371C22×C8—131no—
372C22×C8—134no—
373C22×C8—131no—
374C22×C8—131no—
375C22×C8—131no—
376C22×C8—131no—
377C22×C8—131no—
378C22×C8—131no—
379C22×C8—262no—
380C22×C8—521no—
381C22×C8—521no—
382C22×C8—521no—
383C22×C8—521no—
384C22⋊Q8—138no—
385C4×Q8—521no—
386C4×Q8—521no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—131no—
391C2×C4⋊C4—131no—
392C2×C4⋊C4—131no—
393C2×C4⋊C4—131no—
394C2×C4⋊C4C2×#26111yescharacteristic
395C2×C4⋊C4C2×#26111yescharacteristic
396C2×C22⋊C4—131no—
397C2×C22⋊C4—131no—
398C2×C22⋊C4C2×#26111yescharacteristic
399C2×C22⋊C4C2×#26111yescharacteristic
400C2×C42—131no—
401C2×C42—131no—
402C2×C42—131no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—131no—
406C2×C42—131no—
407C2×C42—131no—
408C2×C42—521no—
409C2×C42—521no—
410C4⋊C8—521no—
411C4⋊C8—521no—
412C4⋊C8—521no—
413C4⋊C8—521no—
414C4⋊C8—521no—
415C4⋊C8—521no—
416C22⋊C8—262no—
417C22⋊C8—262no—
418C4×C8—521no—
419C4×C8—521no—
420C4×C8—521no—
421C4×C8—521no—
422#95—131no—
423#95—131no—
424#95—131no—
425#95—131no—
426#95—131no—
427#95—131no—
428#95—131no—
429#95—131no—
430#95C2×#26111yescharacteristic
431#95C2×#26111yescharacteristic
432C2×C13—24no—
433C2×C13#232911yescharacteristic
434C2×C13C2×C8×Q811yescharacteristic
435C2×C13#296111yescharacteristic
436C2×C13#297211yescharacteristic
437C2×C13#297611yescharacteristic
438C2×C13#298811yescharacteristic
439C2×C13#299211yescharacteristic
440C24C22×#26111yescharacteristic
441C2×Q8—134no—
442C2×Q8—521no—
443C2×Q8—521no—
444C22×C4—22no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—131no—
448C22×C4—132no—
449C22×C4—132no—
450C22×C4—131no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—134no—
456C22×C4—131no—
457C22×C4—131no—
458C22×C4—261no—
459C22×C4—261no—
460C22×C4—261no—
461C22×C4—261no—
462C22×C4—521no—
463C22×C4—521no—
464C22×C4C22×#26111yescharacteristic
465C22×C4C22×#26111yescharacteristic
466C22×C4C22×#26111yescharacteristic
467C22×C4C22×#26111yescharacteristic
468C22×C4C22×#26111yescharacteristic
469C22×C4C22×#26111yescharacteristic
470C2×C8—132no—
471C2×C8—132no—
472C2×C8—261no—
473C2×C8—261no—
474C2×C8—261no—
475C2×C8—261no—
476C2×C8—261no—
477C2×C8—261no—
478C2×C8—261no—
479C2×C8—261no—
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—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—524no—
495C2×C8—524no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—134no—
499C4⋊C4—134no—
500C4⋊C4—134no—
501C4⋊C4—521no—
502C4⋊C4—521no—
503C4⋊C4—521no—
504C4⋊C4—521no—
505C22⋊C4—22no—
506C22⋊C4—134no—
507C22⋊C4—262no—
508C22⋊C4D13⋊C814yes—
509C42—261no—
510C42—261no—
511C42—261no—
512C42—261no—
513C42—261no—
514C42—261no—
515C42—261no—
516C42—261no—
517C42—261no—
518C42—261no—
519C42—261no—
520C42—261no—
521C42—521no—
522C42—521no—
523C13#2228711yescharacteristic, complemented, Sylow
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23C2×D13⋊C812yes—
529C23#8823812yes—
530C23Q8×#26112yes—
531C23C23×#26111yescharacteristic
532Q8—524no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—44no—
550C2×C4—131no—
551C2×C4—131no—
552C2×C4—131no—
553C2×C4—131no—
554C2×C4—131no—
555C2×C4—131no—
556C2×C4—132no—
557C2×C4—132no—
558C2×C4—132no—
559C2×C4—132no—
560C2×C4—132no—
561C2×C4—262no—
562C2×C4—262no—
563C2×C4—262no—
564C2×C4—262no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—261no—
571C2×C4—261no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—261no—
578C2×C4—261no—
579C2×C4—261no—
580C2×C4—261no—
581C2×C4—524no—
582C2×C4C2×D13⋊C812yes—
583C2×C4C2×D13⋊C812yes—
584C8—262no—
585C8—262no—
586C8—521no—
587C8—521no—
588C8—521no—
589C8—521no—
590C8—521no—
591C8—521no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22#1171907414yes—
599C22C22×D13⋊C811yescharacteristic
600C22C2×#8823811yescharacteristic
601C22#1171962111yescharacteristic
602C22#1171962311yescharacteristic
603C22C2×Q8×#26111yescharacteristic
604C22#1171962911yescharacteristic
605C22#1171963111yescharacteristic
606C4—22no—
607C4—22no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—131no—
613C4—131no—
614C4—131no—
615C4—131no—
616C4—262no—
617C4—262no—
618C4—262no—
619C4—262no—
620C4—262no—
621C4—521no—
622C4—521no—
623C2—24no—
624C2#1313132911yescharacteristic
625C2C2×#1171907411yescharacteristic
626C2#1313162711yescharacteristic
627C2#1313168411yescharacteristic
628C2#1313170211yescharacteristic
629C2#1313175211yescharacteristic
630C2#1313177111yescharacteristic
subgroupG/H
center, FrattiniC23C23×#261
commutatorC22×C13C23×C8
FittingC13×#385C4
socleC23×C13C23×C4
prime radicalC24×C13C22×C4
cosocleC22×Dic13C24
hypercenter#385#261
hypocenterC13#22287
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
1. #13131007C2semidirect
2. #13131006C2semidirect
3. #13130935C2semidirect
4. #13130934C2semidirect
5. #13130892C2semidirect
6. #13130891C2semidirect
7. #13130891C2semidirect
8. #13130890C2semidirect
68. C22×#1057Q8semidirect
102. #88132C8semidirect
155. C2×Dic26C2×C8semidirect
188. C4⋊Dic13C2×C8semidirect
193. #6101C2×C8semidirect
194. #6101C2×C8semidirect
523. C13#22287semidirect

Maximal subgroups

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

subgroupindex
#131310072
#131310062
#131309352
#131309342
#131308922
#131308912
#131308902
#131307802
#131307792
#131306922
C22⋊C4×#10572
C2×#117182902
#131173682
#2228713