Finite Group Databasebeta

← #15892955

Subgroups — #15892955

Order 3328.

836 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#88184C211yesmaximal, characteristic
2#13117234C211yesmaximal, characteristic, complemented
3#13116405C211yesmaximal, characteristic, complemented
4#13116356C211yesmaximal, characteristic, complemented
5#13116319C211yesmaximal, characteristic, complemented
6#13116269C211yesmaximal, characteristic, complemented
7#13116264C211yesmaximal, characteristic, complemented
8#13116251C211yesmaximal, characteristic, complemented
9#13116026C211yesmaximal, characteristic
10#13116019C211yesmaximal, characteristic
11C4×#88058C211yesmaximal, characteristic, complemented
12C4×#88057C211yesmaximal, characteristic, complemented
13C4×#88061C211yesmaximal, characteristic, complemented
14C4×#88061C211yesmaximal, characteristic, complemented
15C4×C13×C22⋊C8C211yesmaximal, characteristic, complemented
16C22×C42×C13C2211yescharacteristic
17C2×#88184C2211yescharacteristic
18C2×C4×C22⋊D13—21no—
19C2×C4×D52C2211yescharacteristic
20C2×C13×C22⋊C8C2211yescharacteristic
21C2×C13×C22⋊C8C2211yescharacteristic
22C2×C4×C8×C13C2211yescharacteristic
23C2×C4×C8×C13C2211yescharacteristic
24#11718874—21no—
25#11718873C2211yescharacteristic
26#11718873C2211yescharacteristic
27#11718873C2211yescharacteristic
28#11718872—21no—
29C4×C22⋊Dic13—21no—
30C2×#88061C2211yescharacteristic
31C2×#88061C2211yescharacteristic
32C2×#88061C2211yescharacteristic
33C2×#88061C2211yescharacteristic
34C2×#88058C2211yescharacteristic
35C2×#88058C2211yescharacteristic
36C2×#88057C2211yescharacteristic
37C2×#88057C2211yescharacteristic
38#11718601—21no—
39#11718600C2211yescharacteristic
40C4×#6103—21no—
41#11718598—21no—
42#11718597C2211yescharacteristic
43#11718597C2211yescharacteristic
44C4×C4⋊Dic13C2211yescharacteristic
45C4×C4⋊Dic13C2211yescharacteristic
46C4×C4⋊Dic13C2211yescharacteristic
47#11718593—21no—
48#11718589C2211yescharacteristic
49C13×#336C2211yescharacteristic
50C13×#336C2211yescharacteristic
51#11718143C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718143C2211yescharacteristic
57#11718143C2211yescharacteristic
58#11718143C2211yescharacteristic
59C23×C4×C13D411yescharacteristic
60C23×C4×C13D411yescharacteristic
61C23×C4×C13C2311yescharacteristic
62C22×C22⋊D13—21no—
63C22×D52C2311yescharacteristic
64C22×C4×D13—21no—
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C22×C8×C13C2311yescharacteristic
68C22×C8×C13C2311yescharacteristic
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13D411yescharacteristic
72C2×C42×C13D411yescharacteristic
73C2×C42×C13C2311yescharacteristic
74C2×C42×C13C2311yescharacteristic
75C2×C22⋊Dic13—21no—
76C2×C22⋊Dic13—21no—
77C2×C22⋊Dic13—21no—
78#88184—22no—
79#88184—22no—
80C4×C22⋊D13—44no—
81C2×#6103—21no—
82C2×#6103—21no—
83C2×#6103—21no—
84C2×#6103—21no—
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89C2×C4⋊Dic13C2311yescharacteristic
90C2×C4⋊Dic13C2311yescharacteristic
91C2×C4⋊Dic13C2311yescharacteristic
92C2×#6101—21no—
93C2×C4×Dic13—21no—
94C2×C4×Dic13—21no—
95C2×C4×Dic13—21no—
96C4×D52—22no—
97C4×D52—22no—
98C13×C22⋊C8—22no—
99C13×C22⋊C8—22no—
100C4×C8×C13—22no—
101C4×C8×C13—22no—
102#88071—21no—
103#88071—21no—
104#88071—21no—
105#88071—21no—
106#88071—21no—
107#88071—21no—
108#88071—21no—
109#88071—21no—
110#88071—21no—
111#88071—21no—
112#88071—21no—
113#88061—22no—
114#88061—22no—
115#88061—22no—
116#88061—22no—
117#88058—22no—
118#88058—22no—
119#88057—22no—
120#88057—22no—
121#23758—131nomaximal, Sylow
122C24×C13C2×D411yescharacteristic
123C23×D13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—41no—
136C22×C4×C13C2×D411yescharacteristic
137C22×C4×C13C2×D411yescharacteristic
138C22×C4×C13C2×D411yescharacteristic
139C22×C4×C13C2×D411yescharacteristic
140C22×C4×C13C2×D411yescharacteristic
141C22×C4×C13C2411yescharacteristic
142C2×C22⋊D13—24no—
143C2×C22⋊D13—42no—
144C2×C22⋊D13—42no—
145C22×Dic13—21no—
146C22×Dic13—21no—
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C2×D52—21no—
153C2×D52—21no—
154C2×D52—21no—
155C2×D52—21no—
156C2×D52—21no—
157C2×D52#4112yes—
158C2×C4×D13—42no—
159C2×C4×D13—42no—
160C2×C4×D13—42no—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13—21no—
171C2×C8×C13#4112yes—
172C2×C8×C13#4112yes—
173C42×C13—22no—
174C42×C13—22no—
175C42×C13—21no—
176C42×C13—21no—
177C42×C13#4112yes—
178C42×C13#4112yes—
179C22⋊Dic13—42no—
180C22⋊Dic13—42no—
181C22⋊Dic13—42no—
182#6103—24no—
183#6103—42no—
184#6103—42no—
185#6103—42no—
186C4⋊Dic13—21no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13—21no—
197C4⋊Dic13—21no—
198C4⋊Dic13—21no—
199C4⋊Dic13#4112yes—
200#6101—42no—
201C4×Dic13—42no—
202C4×Dic13—42no—
203C4×Dic13—42no—
204C4×#121—131no—
205#2283—131no—
206#2101—131no—
207#2092—131no—
208#2085—131no—
209#2077—131no—
210#2076—131no—
211#2073—131no—
212#2034—131no—
213#2033—131no—
214C4×#107—131no—
215C4×#106—131no—
216C4×#102—131no—
217C4×#102—131no—
218C4×C22⋊C8D1311yescharacteristic, complemented
219C23×C13—21no—
220C23×C13—21no—
221C23×C13—21no—
222C23×C13—21no—
223C23×C13—21no—
224C23×C13—21no—
225C23×C13#13512yes—
226C23×C13C22×D411yescharacteristic
227C22×D13—22no—
228C22×D13—41no—
229C22×D13—41no—
230C22×D13—41no—
231C22×D13—41no—
232C22×D13—41no—
233C22×D13—41no—
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—44no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—44no—
251C2×C4×C13#12312yes—
252C2×C4×C13#12312yes—
253C2×C4×C13#13512yes—
254C2×C4×C13AGL(1,ℤ/8)12yes—
255C2×C4×C13C2×#4111yescharacteristic
256C2×C4×C13C2×#4111yescharacteristic
257C2×C4×C13C2×#4111yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C22⋊D13—48no—
262C2×Dic13—22no—
263C2×Dic13—41no—
264C2×Dic13—41no—
265C2×Dic13—41no—
266C2×Dic13—41no—
267C2×Dic13—41no—
268C2×Dic13—41no—
269C2×Dic13—41no—
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—
281C2×Dic13—41no—
282C2×Dic13—41no—
283D52—22no—
284D52—22no—
285D52—41no—
286D52—41no—
287C4×D13—84no—
288C8×C13—22no—
289C8×C13—22no—
290C8×C13—41no—
291C8×C13—41no—
292C2×#121—131no—
293C2×C4×D4—131no—
294C2×C4×D4—261no—
295C22×C42C2×D1311yescharacteristic
296C2×#107—131no—
297C2×#107—131no—
298C2×#106—131no—
299C2×#106—131no—
300C2×#102—131no—
301C2×#102—131no—
302C2×#102—131no—
303C2×#102—131no—
304C2×C22⋊C8C2×D1311yescharacteristic
305C2×C22⋊C8C2×D1311yescharacteristic
306C2×C4×C8C2×D1311yescharacteristic
307C2×C4×C8C2×D1311yescharacteristic
308#390—131no—
309#389—131no—
310#388—261no—
311#386—261no—
312#383—261no—
313#382—131no—
314#382—131no—
315#381—261no—
316#380—131no—
317#380—131no—
318#380—131no—
319C4×C4⋊C4—131no—
320C4×C4⋊C4—131no—
321C4×C4⋊C4—131no—
322C4×C22⋊C4—261no—
323C4×C22⋊C4—261no—
324#376—261no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340—131no—
331#340—131no—
332#340—131no—
333#336C2×D1311yescharacteristic
334#336C2×D1311yescharacteristic
335C22×C13—22no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—41no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13C2×#12311yescharacteristic
343C22×C13#52511yescharacteristic
344C22×C13#53211yescharacteristic
345C22×C13C2×#13511yescharacteristic
346C22×C13C2×#13511yescharacteristic
347C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
348C22×C13#57511yescharacteristic
349C2×D13—42no—
350C2×D13—42no—
351C2×D13—42no—
352C2×D13—81no—
353C2×D13—81no—
354C2×D13—81no—
355C2×D13—81no—
356C4×C13—22no—
357C4×C13—41no—
358C4×C13—41no—
359C4×C13—41no—
360C4×C13#48214yes—
361C4×C13#52911yescharacteristic
362C4×C13#52911yescharacteristic
363C4×C13#52911yescharacteristic
364C4×C13#52911yescharacteristic
365Dic13—42no—
366Dic13—81no—
367Dic13—81no—
368Dic13—81no—
369Dic13—81no—
370Dic13—81no—
371Dic13—81no—
372C22×D4—131no—
373C22×D4—261no—
374C23×C4—261no—
375C23×C4D5211yescharacteristic
376C23×C4D5211yescharacteristic
377C23×C4C22×D1311yescharacteristic
378C22×C8C22×D1311yescharacteristic
379C22×C8C22×D1311yescharacteristic
380C22×C8C22×D1311yescharacteristic
381C22×C8C22×D1311yescharacteristic
382#121—262no—
383#121—262no—
384C4×D4—262no—
385C4×D4—262no—
386C4×D4—524no—
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⋊C4—261no—
395C2×C22⋊C4—261no—
396C2×C22⋊C4—261no—
397C2×C22⋊C4—261no—
398C2×C22⋊C4—261no—
399C2×C22⋊C4—261no—
400C2×C22⋊C4—261no—
401C2×C22⋊C4—261no—
402C2×C42—22no—
403C2×C42—22no—
404C2×C42—261no—
405C2×C42—261no—
406C2×C42—261no—
407C2×C42D5211yescharacteristic
408C2×C42D5211yescharacteristic
409C2×C42C22×D1311yescharacteristic
410C2×C42C22×D1311yescharacteristic
411#107—262no—
412#107—262no—
413#106—262no—
414#106—262no—
415#102—262no—
416#102—262no—
417#102—262no—
418#102—262no—
419C22⋊C8—22no—
420C22⋊C8—22no—
421C4×C8—22no—
422C4×C8—22no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428#95—261no—
429#95—261no—
430#95—261no—
431#95—261no—
432#95—261no—
433#95—261no—
434C2×C13—42no—
435C2×C13#239511yescharacteristic
436C2×C13C2×#48211yescharacteristic
437C2×C13#309111yescharacteristic
438C2×C13#310211yescharacteristic
439C2×C13#310511yescharacteristic
440C2×C13#316811yescharacteristic
441C2×C13#317111yescharacteristic
442D13—82no—
443C24—261no—
444C24C2×D5211yescharacteristic
445C2×D4—132no—
446C2×D4—264no—
447C2×D4—261no—
448C2×D4—261no—
449C2×D4—261no—
450C2×D4—261no—
451C2×D4—261no—
452C2×D4—522no—
453C2×D4—522no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—261no—
467C22×C4—261no—
468C22×C4—261no—
469C22×C4—261no—
470C22×C4—261no—
471C22×C4—261no—
472C22×C4—261no—
473C22×C4—522no—
474C22×C4—522no—
475C22×C4—522no—
476C22×C4C2×D5211yescharacteristic
477C22×C4C2×D5211yescharacteristic
478C22×C4C2×D5211yescharacteristic
479C22×C4C2×D5211yescharacteristic
480C22×C4C2×D5211yescharacteristic
481C22×C4C23×D1311yescharacteristic
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8#612712yes—
493C2×C8#612712yes—
494C4⋊C4—132no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4—261no—
501C4⋊C4—261no—
502C4⋊C4—261no—
503C4⋊C4—261no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—522no—
509C22⋊C4—264no—
510C22⋊C4—522no—
511C22⋊C4—522no—
512C22⋊C4—522no—
513C22⋊C4—522no—
514C22⋊C4—522no—
515C22⋊C4—522no—
516C42—22no—
517C42—22no—
518C42—21no—
519C42—21no—
520C42—522no—
521C42—522no—
522C42—522no—
523C42#612912yes—
524C42#612912yes—
525C13#2375811yescharacteristic, complemented, Sylow
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23—21no—
531C23—21no—
532C23—262no—
533C23—521no—
534C23—521no—
535C23—521no—
536C23—521no—
537C23—521no—
538C23—521no—
539C23#8815812yes—
540C23C22×D5211yescharacteristic
541D4—262no—
542D4—262no—
543D4—528no—
544D4—521no—
545D4—521no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—44no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—44no—
563C2×C4—262no—
564C2×C4—521no—
565C2×C4—521no—
566C2×C4—521no—
567C2×C4—521no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4—521no—
573C2×C4—521no—
574C2×C4—521no—
575C2×C4—521no—
576C2×C4—521no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—1044no—
585C2×C4#8814012yes—
586C2×C4#8814012yes—
587C2×C4#8815812yes—
588C2×C4#8816212yes—
589C2×C4C2×#612711yescharacteristic
590C2×C4C2×#612711yescharacteristic
591C2×C4C2×#612911yescharacteristic
592C2×C4C2×#612911yescharacteristic
593C2×C4#41×D1311yescharacteristic
594C2×C4#41×D1311yescharacteristic
595C8—22no—
596C8—22no—
597C8—41no—
598C8—41no—
599C22—22no—
600C22—22no—
601C22—22no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22—41no—
606C22—522no—
607C22—522no—
608C22—522no—
609C22—1041no—
610C22—1041no—
611C22—1041no—
612C22—1041no—
613C22#1171918211yescharacteristic
614C22C2×#8814011yescharacteristic
615C22#1171922911yescharacteristic
616C22C2×#8815811yescharacteristic
617C22C2×#8815811yescharacteristic
618C22C2×#8816211yescharacteristic
619C22#1171945311yescharacteristic
620C4—22no—
621C4—41no—
622C4—41no—
623C4—41no—
624C4—522no—
625C4—1041no—
626C4—1041no—
627C4—1041no—
628C4—1041no—
629C4—1041no—
630C4—1041no—
631C4#1171839814yes—
632C4#1171924311yescharacteristic
633C4#1171924311yescharacteristic
634C4#1171926211yescharacteristic
635C4#1171926211yescharacteristic
636C2—42no—
637C2—1042no—
638C2#1311809611yescharacteristic
639C2C2×#1171839811yescharacteristic
640C2#1312475111yescharacteristic
641C2#1312485611yescharacteristic
642C2#1312488511yescharacteristic
643C2#1312540611yescharacteristic
644C2#1312543111yescharacteristic
subgroupG/H
centerC22×C4C2×D52
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC4×C13×C22⋊C8C2
socleC23×C13C22×D4
prime radicalC2×#88184C22
hypercenterC4×C22⋊C8D13
hypocenterC13#23758
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #13117234C2semidirect
3. #13116405C2semidirect
4. #13116356C2semidirect
5. #13116319C2semidirect
6. #13116269C2semidirect
7. #13116264C2semidirect
8. #13116251C2semidirect
11. C4×#88058C2semidirect
12. C4×#88057C2semidirect
13. C4×#88061C2semidirect
14. C4×#88061C2semidirect
15. C4×C13×C22⋊C8C2semidirect
218. C4×C22⋊C8D13semidirect
525. C13#23758semidirect

Maximal subgroups

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

subgroupindex
C4×#881842
#131172342
#131164052
#131163562
#131163192
#131162692
#131162642
#131162512
#131160262
#131160192
C4×#880582
C4×#880572
C4×#880612
C4×C13×C22⋊C82
#2375813