Finite Group Databasebeta

← #16797436

Subgroups — #16797436

Order 3328.

1014 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719108C211yesmaximal, characteristic
2C2×#11719107C211yesmaximal, characteristic
3#13131408C211yesmaximal, characteristic, complemented
4#13131407C211yesmaximal, characteristic, complemented
5#13130656C211yesmaximal, characteristic, complemented
6#13130643C211yesmaximal, characteristic, complemented
7#13130640C211yesmaximal, characteristic, complemented
8#13130617C211yesmaximal, characteristic, complemented
9#13130615C211yesmaximal, characteristic, complemented
10#13130613C211yesmaximal, characteristic, complemented
11#13130611C211yesmaximal, characteristic, complemented
12C4×#88118C211yesmaximal, characteristic, complemented
13C4×#88116C211yesmaximal, characteristic, complemented
14#97×#261C211yesmaximal, characteristic, complemented
15#13123631C211yesmaximal, characteristic
16C2×#88240C2211yescharacteristic
17C2×#88240C2211yescharacteristic
18C2×#88238C2211yescharacteristic
19C2×#88238C2211yescharacteristic
20C2×#88170C2211yescharacteristic
21C4×#6131C2211yescharacteristic
22C4×#6129C2211yescharacteristic
23C2×#88118C2211yescharacteristic
24C2×#88118C2211yescharacteristic
25C2×#88116C2211yescharacteristic
26C2×#88116C2211yescharacteristic
27C4×#6122—21no—
28C2×#88110—21no—
29#11719108C418yescomplemented
30#11719107C418yescomplemented
31C2×#88104C2211yescharacteristic
32C2×#88103C2211yescharacteristic
33C2×#88100C2211yescharacteristic
34C2×#88100C2211yescharacteristic
35C2×C8×#261C2211yescharacteristic
36C2×C8×#261C2211yescharacteristic
37#11719072—21no—
38#11719072—21no—
39#11719072C2211yescharacteristic
40#11719072C2211yescharacteristic
41#11719072C2211yescharacteristic
42#11719072C2211yescharacteristic
43#11719062—21no—
44#11719062—21no—
45C42×#261C2211yescharacteristic
46C4×#6118—21no—
47C4×#6118C2211yescharacteristic
48C4×#6118C2211yescharacteristic
49#11719047—21no—
50#11719047C2211yescharacteristic
51C13×#440C411yescharacteristic, complemented
52#11718825C411yescharacteristic, complemented
53#11718691C411yescharacteristic, complemented
54#11718675C411yescharacteristic, complemented
55#11718550C411yescharacteristic, complemented
56#11718541C2211yescharacteristic
57#11718465C2211yescharacteristic
58#11718450C411yescharacteristic, complemented
59#11718446C411yescharacteristic, complemented
60#11718433C2211yescharacteristic
61#11718371C411yescharacteristic, complemented
62D13×#97C2211yescharacteristic
63#11718268C2211yescharacteristic
64#11718268C2211yescharacteristic
65#11718247C2211yescharacteristic
66#11718247C2211yescharacteristic
67#11718247C2211yescharacteristic
68#11718247C2211yescharacteristic
69C2×#6131C2311yescharacteristic
70C2×#6129C2311yescharacteristic
71C2×#6122—21no—
72C2×#6122—21no—
73C22×#1057—21no—
74C22×#1057—21no—
75#88240—22no—
76#88240—22no—
77#88240C2×C414yescomplemented
78#88240C2×C414yescomplemented
79#88238—22no—
80#88238—22no—
81#88238C2×C414yescomplemented
82#88238C2×C414yescomplemented
83C2×C4×#261—21no—
84C2×C4×#261—21no—
85C2×C4×#261C2311yescharacteristic
86C2×C4×#261C2311yescharacteristic
87C2×#6118—21no—
88C2×#6118—21no—
89C2×#6118C2311yescharacteristic
90C2×#6118C2311yescharacteristic
91C2×#6118C2311yescharacteristic
92C2×#6118C2311yescharacteristic
93C2×D13⋊C8—21no—
94C2×D13⋊C8—21no—
95C2×D13⋊C8C2311yescharacteristic
96C2×D13⋊C8C2311yescharacteristic
97C2×C13×SD16C2×C411yescharacteristic
98C4×Q8×C13C2×C411yescharacteristic
99C4×D4×C13C2×C411yescharacteristic
100Q8×Dic13C2×C411yescharacteristic
101C2×#6107C2×C411yescharacteristic
102D4×Dic13C2×C411yescharacteristic
103C2×#6104C2×C411yescharacteristic
104C4×C22⋊D13—21no—
105C2×C4×Dic13—21no—
106#88170C2×C414yes—
107#88170C2×C414yes—
108C2×#6095C2×C411yescharacteristic
109C2×C8×D13C2311yescharacteristic
110C2×C8×D13C2311yescharacteristic
111#88147—21no—
112#88147C2×C411yescharacteristic
113#88146—21no—
114#88146C2311yescharacteristic
115#88146C2311yescharacteristic
116#88141C2×C411yescharacteristic
117#88135—21no—
118#88131—21no—
119C4×D52—21no—
120C4×D52C2×C411yescharacteristic
121C42×D13—21no—
122C42×D13C2311yescharacteristic
123C4×Dic26C2×C411yescharacteristic
124#88118C2×C414yescomplemented
125#88118C2×C414yescomplemented
126#88116C2×C414yescomplemented
127#88116C2×C414yescomplemented
128#88110—21no—
129#88110—21no—
130#88110—21no—
131#88110—21no—
132#88110—21no—
133#88110—21no—
134#88110D411yescharacteristic
135#88110D411yescharacteristic
136#88110D411yescharacteristic
137#88110D411yescharacteristic
138C4×#1057—21no—
139C4×#1057—21no—
140C4×#1057—21no—
141C4×#1057—21no—
142C4×#1057—21no—
143C4×#1057—21no—
144#88104C2×C414yescomplemented
145#88103C2×C414yescomplemented
146#88100—22no—
147#88100C2×C414yescomplemented
148C8×#261—22no—
149C8×#261C2×C414yescomplemented
150C13×#107C2×C411yescharacteristic
151C13×#103C2×C411yescharacteristic
152C13×#102C2×C411yescharacteristic
153C13×#97C2×C411yescharacteristic
154#88075C2×C411yescharacteristic
155#88072C2×C411yescharacteristic
156#88061C2×C411yescharacteristic
157#88058C2×C411yescharacteristic
158#88056C2×C411yescharacteristic
159#88055C2×C411yescharacteristic
160#88055C2×C411yescharacteristic
161#88050C2×C411yescharacteristic
162#88049C2×C411yescharacteristic
163#88048C2×C411yescharacteristic
164#88048C2×C411yescharacteristic
165#88043C2×C411yescharacteristic
166#20512—131nomaximal, Sylow
167C22×#261—21no—
168C22×#261—21no—
169C2×Q8×C13C22×C411yescharacteristic
170C2×D4×C13C22×C411yescharacteristic
171C22×C4×C13—21no—
172C2×C22⋊D13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175#6131—21no—
176#6131—21no—
177#6131C22×C412yes—
178#6131C22×C412yes—
179#6129—21no—
180#6129—21no—
181#6129C22×C412yes—
182#6129C22×C412yes—
183C2×D52—21no—
184C2×D52C22×C411yescharacteristic
185C2×C4×D13—21no—
186C2×C4×D13—21no—
187C2×C4×D13—21no—
188C2×C4×D13#4111yescharacteristic
189C2×C4×D13#4111yescharacteristic
190C2×C4×D13C2411yescharacteristic
191C2×Dic26C22×C411yescharacteristic
192#6122—24no—
193#6122—24no—
194C2×#1057—21no—
195C2×#1057—21no—
196C2×#1057—21no—
197C2×#1057—21no—
198C2×#1057—24no—
199C2×#1057—24no—
200C2×#1057C2×D411yescharacteristic
201C2×#1057C2×D411yescharacteristic
202C2×#1057C2×D411yescharacteristic
203C2×#1057C2×D411yescharacteristic
204C4×#261—21no—
205C4×#261—21no—
206C4×#261—42no—
207C4×#261—42no—
208C4×#261C22×C412yes—
209C4×#261C22×C412yes—
210#6118—21no—
211#6118—21no—
212#6118—21no—
213#6118—21no—
214#6118—24no—
215#6118—24no—
216#6118C22×C412yes—
217#6118C22×C412yes—
218#6118C22×C412yes—
219#6118C22×C412yes—
220D13⋊C8—24no—
221D13⋊C8—24no—
222D13⋊C8C22×C412yes—
223D13⋊C8C22×C412yes—
224D13⋊C8#4112yes—
225D13⋊C8#4112yes—
226C13×SD16C4214yescomplemented
227C2×C8×C13C22×C411yescharacteristic
228C2×C8×C13C22×C411yescharacteristic
229C13×C4⋊C4—21no—
230C13×C4⋊C4C22×C411yescharacteristic
231C13×C4⋊C4C22×C411yescharacteristic
232C13×C22⋊C4—21no—
233C42×C13—21no—
234C42×C13C22×C411yescharacteristic
235C22⋊Dic13—21no—
236#6107C4214yescomplemented
237#6104C4214yescomplemented
238#6103—21no—
239#6103—21no—
240#6103—21no—
241#6103—21no—
242C4⋊Dic13—21no—
243C4⋊Dic13C22×C411yescharacteristic
244C4⋊Dic13C22×C411yescharacteristic
245#6101—21no—
246#6101—21no—
247C4×Dic13—21no—
248C4×Dic13—21no—
249C4×Dic13—21no—
250C4×Dic13—21no—
251C4×Dic13—21no—
252C4×Dic13C22×C411yescharacteristic
253C4×Dic13C2×D411yescharacteristic
254C4×Dic13C2×D411yescharacteristic
255C2×#1055C22×C411yescharacteristic
256C2×#1055C22×C411yescharacteristic
257#6095C4214yescomplemented
258C8×D13—21no—
259C8×D13—21no—
260C8×D13C22×C412yes—
261C8×D13C22×C412yes—
262C2×#444—131no—
263C2×#443—131no—
264#2943—131no—
265#2875—131no—
266#2875—131no—
267#1778—131no—
268#1773—131no—
269#1772—131no—
270#1765—131no—
271#1765—131no—
272#1764—131no—
273#1764—131no—
274C4×#104—131no—
275C4×#104—131no—
276C4×#97—131no—
277C23×C13—21no—
278C22×D13—21no—
279C22×D13C2×#4111yescharacteristic
280C2×#261—22no—
281C2×#261—22no—
282C2×#261—22no—
283C2×#261—22no—
284C2×#261—41no—
285C2×#261—41no—
286Q8×C13—21no—
287Q8×C13C2×C4212yes—
288D4×C13—21no—
289D4×C13C2×C4212yes—
290C2×C4×C13—21no—
291C2×C4×C13—21no—
292C2×C4×C13—21no—
293C2×C4×C13—81no—
294C2×C4×C13C4×D411yescharacteristic
295C2×C4×C13C4×D411yescharacteristic
296C2×C4×C13C23×C411yescharacteristic
297C22⋊D13—22no—
298C22⋊D13—22no—
299C2×Dic13—21no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—21no—
303C2×Dic13—21no—
304C2×Dic13—81no—
305C2×Dic13C4×D411yescharacteristic
306C2×Dic13C4×D411yescharacteristic
307C2×Dic13C22×D411yescharacteristic
308D52—22no—
309D52—22no—
310D52—21no—
311D52C2×C4212yes—
312C4×D13—22no—
313C4×D13—22no—
314C4×D13—41no—
315C4×D13—41no—
316C4×D13—81no—
317C4×D13—81no—
318C4×D13C23×C411yescharacteristic
319C4×D13C23×C411yescharacteristic
320C4×D13C2×#4111yescharacteristic
321C4×D13C2×#4111yescharacteristic
322Dic26—21no—
323Dic26C2×C4212yes—
324#1057—22no—
325#1057—22no—
326#1057—22no—
327#1057—22no—
328#1057C4×D412yes—
329#1057C4×D412yes—
330#1057C4×D412yes—
331#1057C4×D412yes—
332C8×C13—21no—
333C8×C13C2×C4212yes—
334#1055—21no—
335#1055C2×C4212yes—
336C2×#135—131no—
337C2×#131—131no—
338C2×#131—131no—
339C2×#131—131no—
340C2×#131—131no—
341C4×#41—131no—
342C4×#41—131no—
343#444—138no—
344#443—138no—
345#442—131no—
346#442—131no—
347#441—131no—
348#441—131no—
349#440—131no—
350#440—131no—
351#440—131no—
352#440#26111yescharacteristic, complemented
353C2×#108—131no—
354C2×#108—131no—
355#427—131no—
356C2×#104—131no—
357C2×#104—131no—
358C2×#104—131no—
359C2×#104—131no—
360#416—131no—
361#416—131no—
362#405—131no—
363#405—131no—
364#405—131no—
365#405—131no—
366#405—261no—
367#405—261no—
368#405—261no—
369#405—261no—
370C4×M16—131no—
371C4×M16—131no—
372C4×M16—261no—
373C4×M16—261no—
374C2×#97—131no—
375C2×#97—131no—
376C2×#97—131no—
377C2×#97—131no—
378C2×#97—261no—
379C2×#97—261no—
380C2×C4×C8—131no—
381C2×C4×C8—131no—
382C43—131no—
383#341—131no—
384#341—131no—
385#339—131no—
386#339—131no—
387#339—131no—
388#339—131no—
389C22×C13—22no—
390C22×C13—41no—
391C22×C13—41no—
392C22×C13C2×C4×D411yescharacteristic
393C2×D13—21no—
394C2×D13—21no—
395C2×D13—22no—
396C2×D13—41no—
397C2×D13—41no—
398C2×D13C4×#4111yescharacteristic
399C2×D13C4×#4111yescharacteristic
400#261—24no—
401#261—42no—
402C4×C13—21no—
403C4×C13—21no—
404C4×C13—22no—
405C4×C13—41no—
406C4×C13—41no—
407C4×C13C22×C4211yescharacteristic
408C4×C13C4×#4111yescharacteristic
409Dic13—21no—
410Dic13—21no—
411Dic13—22no—
412Dic13—41no—
413Dic13—41no—
414Dic13C2×C4×D411yescharacteristic
415Dic13C2×C4×D411yescharacteristic
416C2×#41—131no—
417C2×#41—131no—
418#135—134no—
419#135—134no—
420C2×Q16—131no—
421C2×SD16—131no—
422C2×SD16C2×#26111yescharacteristic
423C2×D8—131no—
424#131—134no—
425#131—134no—
426#131—134no—
427#131—134no—
428#131—262no—
429#131—262no—
430#131—262no—
431#131—262no—
432C2×M16—131no—
433C2×M16—131no—
434C2×M16—131no—
435C2×M16—131no—
436C2×M16—261no—
437C2×M16—261no—
438C2×M16—261no—
439C2×M16—261no—
440C22×C8—131no—
441C22×C8—131no—
442C22×C8—131no—
443C22×C8—131no—
444C22×C8—261no—
445C22×C8—261no—
446C22×C8—261no—
447C22×C8—261no—
448C4×Q8—131no—
449C4×Q8—131no—
450C4×Q8—131no—
451C4×Q8C2×#26111yescharacteristic
452C4×D4—131no—
453C4×D4—131no—
454C4×D4—131no—
455C4×D4—261no—
456C4×D4—261no—
457C4×D4—261no—
458C4×D4—261no—
459C4×D4C2×#26111yescharacteristic
460#117—131no—
461#117—131no—
462#117—261no—
463#117—261no—
464C2×C42—131no—
465C2×C42—131no—
466C2×C42—131no—
467C2×C42—261no—
468C2×C42—261no—
469C2×C42—261no—
470C2×C42—261no—
471#108—134no—
472#108—134no—
473#107—131no—
474#107C2×#26111yescharacteristic
475#106—131no—
476#106—131no—
477#104—134no—
478#104—134no—
479#104—134no—
480#104—134no—
481#103—131no—
482#103—131no—
483#103—131no—
484#103C2×#26111yescharacteristic
485#102—131no—
486#102—131no—
487#102—131no—
488#102C2×#26111yescharacteristic
489#97—134no—
490#97—131no—
491#97—131no—
492#97—131no—
493#97—131no—
494#97—131no—
495#97—131no—
496#97—131no—
497#97—261no—
498#97—261no—
499#97—262no—
500#97—261no—
501#97—261no—
502#97—261no—
503#97—261no—
504#97C2×#26111yescharacteristic
505C4×C8—134no—
506C4×C8—261no—
507C4×C8—261no—
508C4×C8—262no—
509C4×C8—261no—
510C4×C8—261no—
511C4×C8—261no—
512C4×C8—261no—
513C2×C13—42no—
514C2×C13C42×D411yescharacteristic
515C2×C13#295611yescharacteristic
516C2×C13#295611yescharacteristic
517D13—21no—
518D13—21no—
519D13—42no—
520#41—132no—
521#41—132no—
522#41—132no—
523#41—132no—
524#41—261no—
525#41—261no—
526#41—261no—
527#41—261no—
528C2×Q8—131no—
529C2×Q8C22×#26111yescharacteristic
530C2×D4—131no—
531C2×D4—261no—
532C2×D4—261no—
533C2×D4C22×#26111yescharacteristic
534C22×C4—21no—
535C22×C4—131no—
536C22×C4—131no—
537C22×C4—131no—
538C22×C4—261no—
539C22×C4—261no—
540C22×C4—261no—
541C22×C4—261no—
542C22×C4—261no—
543C22×C4—261no—
544C22×C4—261no—
545Q16—134no—
546SD16—134no—
547SD16C4×#26114yescomplemented
548D8—134no—
549M16—132no—
550M16—132no—
551M16—132no—
552M16—132no—
553M16—264no—
554M16—264no—
555M16—264no—
556M16—264no—
557M16—261no—
558M16—261no—
559M16—261no—
560M16—261no—
561C2×C8—132no—
562C2×C8—131no—
563C2×C8—131no—
564C2×C8—131no—
565C2×C8—132no—
566C2×C8—131no—
567C2×C8—132no—
568C2×C8—132no—
569C2×C8—131no—
570C2×C8—132no—
571C2×C8—132no—
572C2×C8—131no—
573C2×C8—261no—
574C2×C8—261no—
575C2×C8—264no—
576C2×C8—264no—
577C2×C8—264no—
578C2×C8—264no—
579C2×C8—261no—
580C2×C8—261no—
581C2×C8—261no—
582C2×C8—261no—
583C2×C8C22×#26111yescharacteristic
584C2×C8C22×#26111yescharacteristic
585C4⋊C4—21no—
586C4⋊C4—131no—
587C4⋊C4—131no—
588C4⋊C4—261no—
589C4⋊C4—261no—
590C4⋊C4—261no—
591C4⋊C4C22×#26111yescharacteristic
592C4⋊C4C22×#26111yescharacteristic
593C22⋊C4—21no—
594C22⋊C4—261no—
595C22⋊C4—261no—
596C22⋊C4—261no—
597C22⋊C4—261no—
598C22⋊C4—261no—
599C42—21no—
600C42—131no—
601C42—131no—
602C42—131no—
603C42—132no—
604C42—132no—
605C42—261no—
606C42—261no—
607C42—261no—
608C42—261no—
609C42—261no—
610C42—261no—
611C42—261no—
612C42—522no—
613C42—522no—
614C42C22×#26111yescharacteristic
615C13#2051211yescharacteristic, complemented, Sylow
616C23—21no—
617C23—131no—
618C23—261no—
619Q8—21no—
620Q8—132no—
621Q8—261no—
622Q8C2×C4×#26112yes—
623D4—21no—
624D4—132no—
625D4—262no—
626D4—262no—
627D4—262no—
628D4—262no—
629D4—261no—
630D4C2×C4×#26112yes—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—81no—
635C2×C4—131no—
636C2×C4—131no—
637C2×C4—131no—
638C2×C4—131no—
639C2×C4—131no—
640C2×C4—131no—
641C2×C4—131no—
642C2×C4—262no—
643C2×C4—262no—
644C2×C4—262no—
645C2×C4—262no—
646C2×C4—262no—
647C2×C4—262no—
648C2×C4—262no—
649C2×C4—261no—
650C2×C4—262no—
651C2×C4—261no—
652C2×C4—261no—
653C2×C4—521no—
654C2×C4—521no—
655C2×C4—521no—
656C2×C4—521no—
657C2×C4—1041no—
658C2×C4—1041no—
659C2×C4—1041no—
660C2×C4D4×#26111yescharacteristic
661C2×C4D4×#26111yescharacteristic
662C2×C4C23×#26111yescharacteristic
663C8—21no—
664C8—132no—
665C8—132no—
666C8—132no—
667C8—132no—
668C8—132no—
669C8—262no—
670C8—262no—
671C8—262no—
672C8—262no—
673C8—261no—
674C8C2×C4×#26112yes—
675C22—22no—
676C22—41no—
677C22—41no—
678C22—131no—
679C22—131no—
680C22—261no—
681C22—261no—
682C22—262no—
683C22—521no—
684C22—521no—
685C22C2×D4×#26111yescharacteristic
686C4—22no—
687C4—21no—
688C4—21no—
689C4—41no—
690C4—41no—
691C4—131no—
692C4—131no—
693C4—264no—
694C4—262no—
695C4—261no—
696C4—261no—
697C4—522no—
698C4—521no—
699C4—521no—
700C4C22×C4×#26111yescharacteristic
701C4#41×#26111yescharacteristic
702C2—42no—
703C2—261no—
704C2—261no—
705C2—522no—
706C2C4×D4×#26111yescharacteristic
707C2#1313161011yescharacteristic
708C2#1313161111yescharacteristic
subgroupG/H
centerC22C2×D4×#261
commutatorC4×C13C22×C42
FrattiniC2×C4C23×#261
FittingC13×#440C4
socleC22×C13C2×C4×D4
prime radicalC2×#88170C22
cosocleC2×C4×D13C24
hypercenter#440#261
hypocenterC13#20512
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
3. #13131408C2semidirect
4. #13131407C2semidirect
5. #13130656C2semidirect
6. #13130643C2semidirect
7. #13130640C2semidirect
8. #13130617C2semidirect
9. #13130615C2semidirect
10. #13130613C2semidirect
11. #13130611C2semidirect
12. C4×#88118C2semidirect
13. C4×#88116C2semidirect
14. #97×#261C2semidirect
29. #11719108C4semidirect
30. #11719107C4semidirect
51. C13×#440C4semidirect
52. #11718825C4semidirect
53. #11718691C4semidirect
54. #11718675C4semidirect
55. #11718550C4semidirect
58. #11718450C4semidirect
59. #11718446C4semidirect
61. #11718371C4semidirect
77. #88240C2×C4semidirect
78. #88240C2×C4semidirect
81. #88238C2×C4semidirect
82. #88238C2×C4semidirect
124. #88118C2×C4semidirect
125. #88118C2×C4semidirect
126. #88116C2×C4semidirect
127. #88116C2×C4semidirect
144. #88104C2×C4semidirect
145. #88103C2×C4semidirect
147. #88100C2×C4semidirect
149. C8×#261C2×C4semidirect
226. C13×SD16C42semidirect
236. #6107C42semidirect
237. #6104C42semidirect
257. #6095C42semidirect
352. #440#261semidirect
547. SD16C4×#261semidirect
615. C13#20512semidirect

Maximal subgroups

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

subgroupindex
C2×#117191082
C2×#117191072
#131314082
#131314072
#131306562
#131306432
#131306402
#131306172
#131306152
#131306132
#131306112
C4×#881182
C4×#881162
#97×#2612
#131236312
#2051213