Finite Group Databasebeta

← #15913078

Subgroups — #15913078

Order 3328.

914 conjugacy classes of subgroups.

The subgroup lattice has 714 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic, complemented
2C2×D4×#1055C211yesmaximal, characteristic, complemented
3#13120002C211yesmaximal, characteristic, complemented
4#13116273C211yesmaximal, characteristic, complemented
5#13116267C211yesmaximal, characteristic, complemented
6#13116022C211yesmaximal, characteristic, complemented
7#13116015C211yesmaximal, characteristic, complemented
8#13115800C211yesmaximal, characteristic, complemented
9#13115602C211yesmaximal, characteristic, complemented
10#13115265C211yesmaximal, characteristic, complemented
11#13115265C211yesmaximal, characteristic, complemented
12#13114863C211yesmaximal, characteristic, complemented
13#13114859C211yesmaximal, characteristic, complemented
14C4×#88072C211yesmaximal, characteristic, complemented
15C13×#2535C211yesmaximal, characteristic
16C2×C13×#121C2211yescharacteristic
17C2×C13×#121C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C2×C4×D4×C13C2211yescharacteristic
20C23×#1055C2211yescharacteristic
21C23×#1055C2211yescharacteristic
22C2×#88124C2211yescharacteristic
23C13×#397—21no—
24C13×#392—21no—
25C13×#386—21no—
26C13×#386—21no—
27C13×#382C2211yescharacteristic
28C13×#380C2211yescharacteristic
29C13×#380C2211yescharacteristic
30#11718883—21no—
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C2×#88072C2211yescharacteristic
34C2×#88072C2211yescharacteristic
35#11718873C2211yescharacteristic
36#11718873C2211yescharacteristic
37#11718873C2211yescharacteristic
38#11718873C2211yescharacteristic
39C2×C22⋊#1055C2211yescharacteristic
40C2×C22⋊#1055C2211yescharacteristic
41D4×#1055—24no—
42#11718670—24no—
43#11718643—21no—
44C2×#88048C2211yescharacteristic
45C2×#88048C2211yescharacteristic
46C2×#88047C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718606—21no—
49#11718606—21no—
50C4×C4⋊Dic13C2211yescharacteristic
51C2×C4⋊#1055C2211yescharacteristic
52C2×C4×#1055C2211yescharacteristic
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C22×D4×C13—21no—
62C22×D4×C13—21no—
63C22×D4×C13D411yescharacteristic
64C22×D4×C13C2311yescharacteristic
65C23×C4×C13—21no—
66C23×C4×C13C2311yescharacteristic
67C23×C4×C13C2311yescharacteristic
68C13×#121—22no—
69C13×#121—22no—
70C13×#121—41no—
71C13×#121—41no—
72C4×D4×C13—22no—
73C4×D4×C13—22no—
74C4×D4×C13—22no—
75C4×D4×C13—22no—
76C2×C13×C4⋊C4D411yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C13×C22⋊C4—21no—
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C13×C22⋊C4D411yescharacteristic
86C2×C13×C22⋊C4D411yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×C22⋊Dic13—21no—
89C2×C22⋊Dic13—21no—
90C2×C22⋊Dic13—21no—
91C2×C22⋊Dic13—21no—
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×#6101—21no—
97C2×#6101—21no—
98C2×C4×Dic13—21no—
99C22×#1055—22no—
100C22×#1055—22no—
101C22×#1055—22no—
102C22×#1055—22no—
103C22×#1055—41no—
104C22×#1055—41no—
105C22×#1055C2311yescharacteristic
106C22×#1055C2311yescharacteristic
107C22×#1055C2311yescharacteristic
108C22×#1055C2311yescharacteristic
109#88124—22no—
110#88124—22no—
111C13×#95—21no—
112C13×#95—21no—
113C13×#95—21no—
114C13×#95—21no—
115#88072—22no—
116#88072—22no—
117#88072—22no—
118#88072—22no—
119#88071—21no—
120#88071—21no—
121#88071—21no—
122#88071—21no—
123#88071—21no—
124C22⋊#1055—22no—
125C22⋊#1055—22no—
126#88048—22no—
127#88048—41no—
128#88047—22no—
129#88047—41no—
130C4⋊#1055D414yescomplemented
131C4×#1055—22no—
132#25342—131nomaximal, Sylow
133C24×C13—21no—
134C24×C13C2×D411yescharacteristic
135C24×C13C2×D411yescharacteristic
136C2×D4×C13—22no—
137C2×D4×C13—22no—
138C2×D4×C13—22no—
139C2×D4×C13—21no—
140C2×D4×C13—21no—
141C2×D4×C13—21no—
142C2×D4×C13—21no—
143C2×D4×C13—21no—
144C2×D4×C13—42no—
145C2×D4×C13—42no—
146C2×D4×C13—42no—
147C2×D4×C13—42no—
148C2×D4×C13—81no—
149C2×D4×C13—81no—
150C2×D4×C13#4112yes—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—21no—
157C22×C4×C13—21no—
158C22×C4×C13—21no—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13—21no—
164C22×C4×C13—21no—
165C22×C4×C13—21no—
166C22×C4×C13—42no—
167C22×C4×C13—81no—
168C22×C4×C13—81no—
169C22×C4×C13C2×D411yescharacteristic
170C22×C4×C13C2×D411yescharacteristic
171C22×C4×C13C2×D411yescharacteristic
172C22×C4×C13C2×D411yescharacteristic
173C22×C4×C13C2411yescharacteristic
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C13×C4⋊C4—22no—
179C13×C4⋊C4—21no—
180C13×C4⋊C4—21no—
181C13×C4⋊C4—21no—
182C13×C4⋊C4—21no—
183C13×C4⋊C4—21no—
184C13×C4⋊C4—21no—
185C13×C22⋊C4—22no—
186C13×C22⋊C4—22no—
187C13×C22⋊C4—42no—
188C13×C22⋊C4—42no—
189C13×C22⋊C4—42no—
190C13×C22⋊C4—81no—
191C13×C22⋊C4—81no—
192C42×C13C2×D412yes—
193C42×C13#4112yes—
194C22⋊Dic13—42no—
195C22⋊Dic13—42no—
196C22⋊Dic13—81no—
197C22⋊Dic13—81no—
198C4⋊Dic13—21no—
199C4⋊Dic13—21no—
200C4⋊Dic13—21no—
201C4⋊Dic13—21no—
202C4⋊Dic13—21no—
203C4⋊Dic13—21no—
204C4⋊Dic13—21no—
205C4⋊Dic13—21no—
206#6101—42no—
207#6101—42no—
208C4×Dic13—81no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#1055—21no—
214C2×#1055—21no—
215C2×#1055—21no—
216C2×#1055—21no—
217C2×#1055—21no—
218C2×#1055—44no—
219C2×#1055—44no—
220C2×#1055C2×D412yes—
221C2×#1055C2×D412yes—
222C2×#1055#4112yes—
223C2×#478—131no—
224C2×C8×D4—131no—
225#2562—131no—
226#2535D1311yescharacteristic
227#2077—131no—
228#2076—131no—
229#2034—131no—
230#2033—131no—
231#1991—131no—
232#1949—131no—
233#1893—131no—
234#1893—131no—
235#1808—131no—
236#1807—131no—
237C4×#102—131no—
238C23×C13—21no—
239C23×C13—21no—
240C23×C13—21no—
241C23×C13—21no—
242C23×C13—21no—
243C23×C13—21no—
244C23×C13—21no—
245C23×C13—21no—
246C23×C13—21no—
247C23×C13—21no—
248C23×C13—21no—
249C23×C13—21no—
250C23×C13—22no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13—41no—
257C23×C13#13512yes—
258C23×C13#13512yes—
259C23×C13C22×D411yescharacteristic
260D4×C13—28no—
261D4×C13—22no—
262D4×C13—22no—
263D4×C13—41no—
264D4×C13—41no—
265D4×C13—84no—
266D4×C13—84no—
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—41no—
278C2×C4×C13—41no—
279C2×C4×C13—41no—
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×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—84no—
295C2×C4×C13#12112yes—
296C2×C4×C13#12112yes—
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C2×#4111yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C2×C4×C13C2×#4111yescharacteristic
301C2×C4×C13H(5,𝔽2)11yescharacteristic
302C2×C4×C132−1+411yescharacteristic
303C2×Dic13—41no—
304C2×Dic13—41no—
305C2×Dic13—41no—
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—
315#1055—22no—
316#1055—22no—
317#1055—22no—
318#1055—41no—
319C23×C8—131no—
320C23×C8—131no—
321C2×#125—131no—
322C2×#121C2×D1311yescharacteristic
323C2×#121C2×D1311yescharacteristic
324C2×C4×D4C2×D1311yescharacteristic
325C2×C4×D4C2×D1311yescharacteristic
326#478—264no—
327C8×D4—264no—
328C2×#107—131no—
329C2×#107—131no—
330C2×#106—131no—
331C2×#106—131no—
332C2×C4⋊C8—131no—
333C2×#102—131no—
334C2×#102—131no—
335C2×#102—131no—
336C2×#102—131no—
337C2×C22⋊C8—131no—
338C2×C22⋊C8—131no—
339C2×C4×C8—131no—
340#400—261no—
341#397—21no—
342#394—261no—
343#392—21no—
344#388—261no—
345#388—261no—
346#386—21no—
347#386—21no—
348#382C2×D1311yescharacteristic
349#380—131no—
350#380—131no—
351#380—131no—
352#380—131no—
353#380C2×D1311yescharacteristic
354#380C2×D1311yescharacteristic
355C4×C4⋊C4—131no—
356#340—131no—
357#340—131no—
358#340—131no—
359#340—131no—
360#340—131no—
361#340—131no—
362#340—131no—
363#340—131no—
364C22×C13—22no—
365C22×C13—22no—
366C22×C13—22no—
367C22×C13—22no—
368C22×C13—22no—
369C22×C13—22no—
370C22×C13—41no—
371C22×C13—41no—
372C22×C13—41no—
373C22×C13—41no—
374C22×C13—41no—
375C22×C13—41no—
376C22×C13—41no—
377C22×C13—41no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—81no—
382C22×C13—81no—
383C22×C13—81no—
384C22×C13—81no—
385C22×C13C2×#12111yescharacteristic
386C22×C13#54611yescharacteristic
387C22×C13#54711yescharacteristic
388C22×C13C2×#13511yescharacteristic
389C22×C13C2×#13511yescharacteristic
390C22×C13#57611yescharacteristic
391C22×C13#57711yescharacteristic
392C4×C13—22no—
393C4×C13—22no—
394C4×C13—41no—
395C4×C13—41no—
396C4×C13—81no—
397C4×C13—81no—
398C4×C13—81no—
399C4×C13#52911yescharacteristic
400C4×C13#54211yescharacteristic
401C4×C13#54611yescharacteristic
402C4×C13#54811yescharacteristic
403Dic13—81no—
404Dic13—81no—
405Dic13—81no—
406Dic13—81no—
407C22×D4—21no—
408C22×D4—21no—
409C22×D4C22⋊D1311yescharacteristic
410C22×D4C22×D1311yescharacteristic
411C23×C4—21no—
412C23×C4C22×D1311yescharacteristic
413C23×C4C22×D1311yescharacteristic
414C22×C8—131no—
415C22×C8—131no—
416C22×C8—131no—
417C22×C8—131no—
418C22×C8—262no—
419C22×C8—262no—
420C22×C8—262no—
421C22×C8—262no—
422C22×C8—521no—
423C22×C8—521no—
424#125—262no—
425#125—262no—
426#121—22no—
427#121—22no—
428#121—41no—
429#121—41no—
430C4×D4—22no—
431C4×D4—22no—
432C4×D4—22no—
433C4×D4—22no—
434C2×C4⋊C4—131no—
435C2×C4⋊C4—131no—
436C2×C4⋊C4—131no—
437C2×C4⋊C4—131no—
438C2×C4⋊C4—261no—
439C2×C4⋊C4—261no—
440C2×C4⋊C4C22⋊D1311yescharacteristic
441C2×C4⋊C4C22×D1311yescharacteristic
442C2×C4⋊C4C22×D1311yescharacteristic
443C2×C4⋊C4C22×D1311yescharacteristic
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C22⋊C4—21no—
449C2×C22⋊C4—261no—
450C2×C22⋊C4—261no—
451C2×C22⋊C4—261no—
452C2×C22⋊C4—261no—
453C2×C22⋊C4C22⋊D1311yescharacteristic
454C2×C22⋊C4C22⋊D1311yescharacteristic
455C2×C42—261no—
456C2×C42C22×D1311yescharacteristic
457#107—262no—
458#107—521no—
459#106—262no—
460#106—521no—
461C4⋊C8—134no—
462#102—262no—
463#102—262no—
464#102—262no—
465#102—262no—
466C22⋊C8—262no—
467C22⋊C8—262no—
468C4×C8—262no—
469#95—21no—
470#95—21no—
471#95—21no—
472#95—21no—
473#95—261no—
474#95—261no—
475#95—261no—
476#95—261no—
477#95—261no—
478C2×C13—42no—
479C2×C13—42no—
480C2×C13—82no—
481C2×C13#242711yescharacteristic
482C2×C13#305011yescharacteristic
483C2×C13#306211yescharacteristic
484C2×C13#329611yescharacteristic
485C2×C13#329711yescharacteristic
486C2×C13#333711yescharacteristic
487C2×C13#333911yescharacteristic
488C24—21no—
489C24C2×C22⋊D1311yescharacteristic
490C24C2×C22⋊D1311yescharacteristic
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—22no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—21no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—81no—
504C2×D4—81no—
505C2×D4#612912yes—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—42no—
522C22×C4—81no—
523C22×C4—81no—
524C22×C4—261no—
525C22×C4—261no—
526C22×C4—261no—
527C22×C4—261no—
528C22×C4C2×C22⋊D1311yescharacteristic
529C22×C4C2×C22⋊D1311yescharacteristic
530C22×C4C2×C22⋊D1311yescharacteristic
531C22×C4C2×C22⋊D1311yescharacteristic
532C22×C4C23×D1311yescharacteristic
533C2×C8—132no—
534C2×C8—132no—
535C2×C8—132no—
536C2×C8—261no—
537C2×C8—261no—
538C2×C8—261no—
539C2×C8—261no—
540C2×C8—261no—
541C2×C8—261no—
542C2×C8—261no—
543C2×C8—261no—
544C2×C8—261no—
545C2×C8—524no—
546C2×C8—524no—
547C4⋊C4—22no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—261no—
555C4⋊C4—261no—
556C4⋊C4—261no—
557C4⋊C4—261no—
558C4⋊C4—261no—
559C4⋊C4—261no—
560C4⋊C4—261no—
561C4⋊C4—261no—
562C4⋊C4—522no—
563C4⋊C4—522no—
564C22⋊C4—22no—
565C22⋊C4—22no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—81no—
570C22⋊C4—81no—
571C22⋊C4—522no—
572C22⋊C4—522no—
573C22⋊C4—1041no—
574C22⋊C4—1041no—
575C42—1041no—
576C42D4×D1312yes—
577C42#612912yes—
578C13#2534211yescharacteristic, complemented, Sylow
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—21no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—22no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23—41no—
598C23#8820412yes—
599C23#8820412yes—
600C23C22×C22⋊D1311yescharacteristic
601D4—28no—
602D4—22no—
603D4—22no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—21no—
618C2×C4—41no—
619C2×C4—41no—
620C2×C4—41no—
621C2×C4—41no—
622C2×C4—41no—
623C2×C4—41no—
624C2×C4—41no—
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—41no—
634C2×C4—41no—
635C2×C4—84no—
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—521no—
648C2×C4#8819312yes—
649C2×C4#8819312yes—
650C2×C4C2×D4×D1311yescharacteristic
651C2×C4C2×#612911yescharacteristic
652C2×C4C2×#612911yescharacteristic
653C2×C4#8825111yescharacteristic
654C2×C4#41×D1311yescharacteristic
655C2×C4#8825711yescharacteristic
656C8—262no—
657C8—262no—
658C8—262no—
659C8—521no—
660C22—22no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—41no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—42no—
675C22—42no—
676C22—42no—
677C22—81no—
678C22—81no—
679C22—81no—
680C22—81no—
681C22C2×#8819311yescharacteristic
682C22#1171951111yescharacteristic
683C22C2×#8820411yescharacteristic
684C22C2×#8820411yescharacteristic
685C22#1171952911yescharacteristic
686C22#1171954011yescharacteristic
687C22#1171954111yescharacteristic
688C4—22no—
689C4—22no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—1041no—
696C4—1041no—
697C4—1041no—
698C4—1041no—
699C4#1171930311yescharacteristic
700C4#1171930511yescharacteristic
701C4#1171930811yescharacteristic
702C4#1171931711yescharacteristic
703C2—42no—
704C2—42no—
705C2—82no—
706C2#1311841511yescharacteristic
707C2#1312441411yescharacteristic
708C2#1312451211yescharacteristic
709C2#1312667111yescharacteristic
710C2#1312668611yescharacteristic
711C2#1312720911yescharacteristic
712C2#1312723211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC13×#2535C2
socleC23×C13C22×D4
hypercenter#2535D13
hypocenterC13#25342
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2535

Complements

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

NH ≅ G/Ntype
1. C2×#11718670C2semidirect
2. C2×D4×#1055C2semidirect
3. #13120002C2semidirect
4. #13116273C2semidirect
5. #13116267C2semidirect
6. #13116022C2semidirect
7. #13116015C2semidirect
8. #13115800C2semidirect
9. #13115602C2semidirect
10. #13115265C2semidirect
11. #13115265C2semidirect
12. #13114863C2semidirect
13. #13114859C2semidirect
14. C4×#88072C2semidirect
130. C4⋊#1055D4semidirect
578. C13#25342semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×D4×#10552
#131200022
#131162732
#131162672
#131160222
#131160152
#131158002
#131156022
#131152652
#131148632
#131148592
C4×#880722
C13×#25352
#2534213