Finite Group Databasebeta

← #15925645

Subgroups — #15925645

Order 3328.

848 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718515C211yesmaximal, characteristic, complemented
2#13118532C211yesmaximal, characteristic
3#13117863C211yesmaximal, characteristic
4#13116371C211yesmaximal, characteristic, complemented
5#13116325C211yesmaximal, characteristic, complemented
6#13116226C211yesmaximal, characteristic, complemented
7#13116162C211yesmaximal, characteristic, complemented
8#13115596C211yesmaximal, characteristic, complemented
9#13115423C211yesmaximal, characteristic, complemented
10#13115269C211yesmaximal, characteristic
11#13115143C211yesmaximal, characteristic
12#13115101C211yesmaximal, characteristic, complemented
13#13115035C211yesmaximal, characteristic
14#13115019C211yesmaximal, characteristic
15C2×C13×#428C211yesmaximal, characteristic
16C22×C13×M16C2211yescharacteristic
17C2×C13×#117C2211yescharacteristic
18C22×C13×C4⋊C4C2211yescharacteristic
19C2×#88178—21no—
20C2×#88178C2211yescharacteristic
21C2×#88142C2211yescharacteristic
22C2×#88141C2211yescharacteristic
23C13×#428—24no—
24C2×C13×#107C2211yescharacteristic
25C2×C13×#107C2211yescharacteristic
26C2×C13×#106C2211yescharacteristic
27C2×C13×#106C2211yescharacteristic
28#11718873C2211yescharacteristic
29#11718871—21no—
30C4×C22⋊Dic13C2211yescharacteristic
31C2×C22⋊#1055C2211yescharacteristic
32C2×#88056C2211yescharacteristic
33C2×#88056C2211yescharacteristic
34C2×#88054C2211yescharacteristic
35C2×#88054C2211yescharacteristic
36#11718646C2211yescharacteristic
37#11718645—21no—
38#11718640—21no—
39#11718637C2211yescharacteristic
40C4⋊C4×Dic13C2211yescharacteristic
41#11718635C2211yescharacteristic
42#11718634C2211yescharacteristic
43#11718634C2211yescharacteristic
44C2×#88050C2211yescharacteristic
45C2×#88050C2211yescharacteristic
46C2×#88048C2211yescharacteristic
47C2×#88047C2211yescharacteristic
48#11718606—21no—
49#11718605—21no—
50#11718594—21no—
51C4×#6101—21no—
52#11718515—24no—
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718142C2211yescharacteristic
56#11718142C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13C2311yescharacteristic
63C22×Dic26—21no—
64C22×Dic26C2311yescharacteristic
65C2×C13×M16—22no—
66C2×C13×M16—22no—
67C2×C13×M16—22no—
68C22×C8×C13C2311yescharacteristic
69C22×C8×C13C2311yescharacteristic
70C13×#117—22no—
71C13×#117—41no—
72C2×C13×C4⋊C4—22no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—41no—
75C2×C13×C4⋊C4C2311yescharacteristic
76C2×C13×C4⋊C4C2311yescharacteristic
77C2×C13×C4⋊C4C2311yescharacteristic
78C2×C13×C4⋊C4C2311yescharacteristic
79C2×C13×C22⋊C4—21no—
80C2×C42×C13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13D411yescharacteristic
84C2×C22⋊Dic13D411yescharacteristic
85C2×C4⋊Dic13—21no—
86C2×C4⋊Dic13C2311yescharacteristic
87C2×C4⋊Dic13C2311yescharacteristic
88C2×C4⋊Dic13C2311yescharacteristic
89#88178—22no—
90#88178—44no—
91#88178Q814yescomplemented
92C2×#6101—21no—
93C2×#6101—21no—
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13—21no—
101C2×C4×Dic13C2311yescharacteristic
102C2×C4×Dic13C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104C22×#1055C2311yescharacteristic
105#88142—22no—
106#88142—41no—
107#88141—22no—
108#88141—41no—
109C13×#107—22no—
110C13×#107—22no—
111C13×#106—22no—
112C13×#106D414yes—
113#88071—21no—
114#88071—21no—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071D411yescharacteristic
121#88071D411yescharacteristic
122C22⋊#1055—22no—
123#88056—22no—
124#88056—22no—
125#88054—22no—
126#88054—22no—
127#88050—22no—
128#88050—41no—
129#88048—22no—
130#88047—41no—
131#26353—131nomaximal, Sylow
132C24×C13C2×D411yescharacteristic
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—21no—
141C22×C4×C13—42no—
142C22×C4×C13—42no—
143C22×C4×C13—81no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×Q812yes—
146C22×C4×C13#4112yes—
147C22×C4×C13C2411yescharacteristic
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13—21no—
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C22×Dic13C2×D411yescharacteristic
156C2×Dic26—21no—
157C2×Dic26—21no—
158C2×Dic26—21no—
159C2×Dic26—21no—
160C2×Dic26—21no—
161C2×Dic26—42no—
162C2×Dic26—42no—
163C2×Dic26—81no—
164C2×Dic26C2×Q812yes—
165C13×M16—28no—
166C2×C8×C13—21no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
169C2×C8×C13—21no—
170C2×C8×C13C2×D412yes—
171C2×C8×C13#4112yes—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4—21no—
178C13×C4⋊C4—42no—
179C13×C4⋊C4C2×D412yes—
180C13×C4⋊C4C2×D412yes—
181C13×C22⋊C4—42no—
182C42×C13—42no—
183C22⋊Dic13—24no—
184C22⋊Dic13—22no—
185C22⋊Dic13—22no—
186C22⋊Dic13—42no—
187C4⋊Dic13—21no—
188C4⋊Dic13—21no—
189C4⋊Dic13—21no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—42no—
193C4⋊Dic13C2×Q812yes—
194#6101—24no—
195#6101—42no—
196#6101—42no—
197#6101—42no—
198#6101—42no—
199#6101—42no—
200#6101—81no—
201C4×Dic13—21no—
202C4×Dic13—21no—
203C4×Dic13—21no—
204C4×Dic13—21no—
205C4×Dic13—42no—
206C4×Dic13—42no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055—21no—
213C2×#475—131no—
214C2×#428D1311yescharacteristic
215#2440—131no—
216#2362—131no—
217#2095—131no—
218#2086—131no—
219#2068—131no—
220#2057—131no—
221#1948—131no—
222#1920—131no—
223#1894—131no—
224#1872—131no—
225#1865—131no—
226#1854—131no—
227#1851—131no—
228C23×C13—21no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—21no—
234C23×C13C22⋊Q812yes—
235C23×C13C22×D411yescharacteristic
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—22no—
239C2×C4×C13—22no—
240C2×C4×C13—22no—
241C2×C4×C13—22no—
242C2×C4×C13—22no—
243C2×C4×C13—22no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—84no—
255C2×C4×C13C22⋊Q812yes—
256C2×C4×C13C22×D411yescharacteristic
257C2×C4×C13C22×Q811yescharacteristic
258C2×C4×C13C2×#4111yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C2×C4×C13H(5,𝔽2)11yescharacteristic
261C2×C4×C132−1+411yescharacteristic
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265C2×Dic13—21no—
266C2×Dic13—22no—
267C2×Dic13—22no—
268C2×Dic13—21no—
269C2×Dic13—21no—
270C2×Dic13—21no—
271C2×Dic13—21no—
272C2×Dic13—21no—
273C2×Dic13—21no—
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—
283C2×Dic13—41no—
284C2×Dic13AGL(1,ℤ/8)12yes—
285C2×Dic13#13712yes—
286Dic26—22no—
287Dic26—22no—
288Dic26—41no—
289Dic26—41no—
290Dic26—84no—
291C8×C13—22no—
292C8×C13—22no—
293#1055—41no—
294#1055—41no—
295C22×M16C2×D1311yescharacteristic
296C2×C4⋊Q8—131no—
297C2×C22⋊Q8—131no—
298C2×C22⋊Q8—261no—
299C2×C4×Q8—131no—
300C2×#117C2×D1311yescharacteristic
301C22×C4⋊C4C2×D1311yescharacteristic
302#475—264no—
303#428—24no—
304C2×#107—131no—
305C2×#107C2×D1311yescharacteristic
306C2×#107C2×D1311yescharacteristic
307C2×#106—131no—
308C2×#106C2×D1311yescharacteristic
309C2×#106C2×D1311yescharacteristic
310C2×C4⋊C8—131no—
311C2×C4⋊C8—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#103—131no—
316C2×C22⋊C8—131no—
317#398—261no—
318#395—261no—
319#391—131no—
320#389—131no—
321#389—131no—
322#389—131no—
323#388—261no—
324#388—261no—
325#387—261no—
326#385—261no—
327#384—131no—
328#380—131no—
329C4×C4⋊C4—131no—
330C4×C4⋊C4—261no—
331C4×C22⋊C4—131no—
332#340—131no—
333#340—131no—
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#336—131no—
339#336—131no—
340C22×C13—22no—
341C22×C13—22no—
342C22×C13—22no—
343C22×C13—41no—
344C22×C13—41no—
345C22×C13—41no—
346C22×C13—41no—
347C22×C13C2×C22⋊Q811yescharacteristic
348C22×C13D4211yescharacteristic
349C22×C13#54711yescharacteristic
350C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
351C22×C13C2×#13711yescharacteristic
352C22×C13#57711yescharacteristic
353C22×C13#57811yescharacteristic
354C4×C13—22no—
355C4×C13—42no—
356C4×C13—42no—
357C4×C13—81no—
358C4×C13—81no—
359C4×C13#52511yescharacteristic
360C4×C13#53911yescharacteristic
361C4×C13D4×Q811yescharacteristic
362C4×C13#55411yescharacteristic
363Dic13—22no—
364Dic13—22no—
365Dic13—42no—
366Dic13—41no—
367Dic13—42no—
368Dic13—41no—
369Dic13—81no—
370Dic13—81no—
371C22×Q8—131no—
372C22×Q8—261no—
373C23×C4—21no—
374C23×C4C22×D1311yescharacteristic
375C2×M16—22no—
376C2×M16—22no—
377C2×M16—22no—
378C22×C8—131no—
379C22×C8—131no—
380C22×C8C22×D1311yescharacteristic
381C22×C8C22×D1311yescharacteristic
382C4⋊Q8—262no—
383C4⋊Q8—521no—
384C22⋊Q8—134no—
385C22⋊Q8—262no—
386C22⋊Q8—524no—
387C4×Q8—262no—
388C4×Q8—521no—
389#117—22no—
390#117—41no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—41no—
394C2×C4⋊C4—131no—
395C2×C4⋊C4—131no—
396C2×C4⋊C4—131no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4—261no—
400C2×C4⋊C4—261no—
401C2×C4⋊C4—261no—
402C2×C4⋊C4—261no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4C22×D1311yescharacteristic
406C2×C4⋊C4C22×D1311yescharacteristic
407C2×C4⋊C4C22×D1311yescharacteristic
408C2×C4⋊C4C22×D1311yescharacteristic
409C2×C22⋊C4—21no—
410C2×C22⋊C4—131no—
411C2×C22⋊C4—131no—
412C2×C22⋊C4—261no—
413C2×C22⋊C4—261no—
414C2×C42—21no—
415C2×C42—131no—
416C2×C42—131no—
417C2×C42—261no—
418C2×C42—261no—
419#107—22no—
420#107—22no—
421#107—521no—
422#106—22no—
423#106—262no—
424#106C22⋊D1314yes—
425C4⋊C8—262no—
426C4⋊C8—262no—
427#103—262no—
428#103—262no—
429#103—262no—
430#103—521no—
431C22⋊C8—262no—
432#95—131no—
433#95—131no—
434#95—261no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440#95—261no—
441C2×C13—42no—
442C2×C13#244911yescharacteristic
443C2×C13#307911yescharacteristic
444C2×C13#308211yescharacteristic
445C2×C13#326511yescharacteristic
446C2×C13#327611yescharacteristic
447C2×C13#334411yescharacteristic
448C2×C13#335311yescharacteristic
449C24D4×D1311yescharacteristic
450C2×Q8—132no—
451C2×Q8—261no—
452C2×Q8—261no—
453C2×Q8—261no—
454C2×Q8—261no—
455C2×Q8—261no—
456C2×Q8—522no—
457C2×Q8—522no—
458C2×Q8—1041no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—42no—
468C22×C4—42no—
469C22×C4—81no—
470C22×C4—131no—
471C22×C4—131no—
472C22×C4—131no—
473C22×C4—131no—
474C22×C4—261no—
475C22×C4—261no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4#612712yes—
479C22×C4D4×D1311yescharacteristic
480C22×C4Q8×D1312yes—
481C22×C4C23×D1311yescharacteristic
482M16—28no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—261no—
488C2×C8—261no—
489C2×C8—261no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8#612712yes—
494C2×C8C2×C22⋊D1312yes—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—42no—
502C4⋊C4—132no—
503C4⋊C4—264no—
504C4⋊C4—261no—
505C4⋊C4—261no—
506C4⋊C4—261no—
507C4⋊C4—261no—
508C4⋊C4—261no—
509C4⋊C4—522no—
510C4⋊C4—522no—
511C4⋊C4—522no—
512C4⋊C4—522no—
513C4⋊C4—522no—
514C4⋊C4—522no—
515C4⋊C4—1041no—
516C4⋊C4C2×C22⋊D1312yes—
517C4⋊C4C2×C22⋊D1312yes—
518C22⋊C4—42no—
519C22⋊C4—262no—
520C22⋊C4—262no—
521C22⋊C4—264no—
522C22⋊C4—522no—
523C42—42no—
524C42—261no—
525C42—261no—
526C42—261no—
527C42—261no—
528C42—522no—
529C42—522no—
530C13#2635311yescharacteristic, complemented, Sylow
531C23—21no—
532C23—21no—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—21no—
537C23#8815012yes—
538C23C2×D4×D1311yescharacteristic
539Q8—262no—
540Q8—262no—
541Q8—521no—
542Q8—521no—
543Q8—1044no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—84no—
563C2×C4—132no—
564C2×C4—132no—
565C2×C4—261no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—261no—
569C2×C4—261no—
570C2×C4—262no—
571C2×C4—262no—
572C2×C4—261no—
573C2×C4—261no—
574C2×C4—261no—
575C2×C4—261no—
576C2×C4—261no—
577C2×C4—521no—
578C2×C4—521no—
579C2×C4—521no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4#8815012yes—
588C2×C4C2×#612711yescharacteristic
589C2×C4C2×#612711yescharacteristic
590C2×C4#8825111yescharacteristic
591C2×C4C2×Q8×D1311yescharacteristic
592C2×C4#8825411yescharacteristic
593C2×C4C22×C22⋊D1311yescharacteristic
594C8—22no—
595C8—22no—
596C8—521no—
597C8—521no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—41no—
602C22—41no—
603C22—41no—
604C22—41no—
605C22#1171921211yescharacteristic
606C22C2×#8815011yescharacteristic
607C22D13×AGL(1,ℤ/8)11yescharacteristic
608C22#1171948011yescharacteristic
609C22D13×#13711yescharacteristic
610C22#1171948411yescharacteristic
611C22D4×C22⋊D1311yescharacteristic
612C4—22no—
613C4—42no—
614C4—42no—
615C4—81no—
616C4—81no—
617C4—262no—
618C4—262no—
619C4—522no—
620C4—521no—
621C4—522no—
622C4—521no—
623C4—1041no—
624C4—1041no—
625C4#1171921611yescharacteristic
626C4#1171922011yescharacteristic
627C4#1171949611yescharacteristic
628C4Q8×C22⋊D1311yescharacteristic
629C2—42no—
630C2#1311864511yescharacteristic
631C2#1312464911yescharacteristic
632C2#1312467611yescharacteristic
633C2#1312632511yescharacteristic
634C2#1312647611yescharacteristic
635C2#1312729211yescharacteristic
636C2#1312741611yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingC2×C13×#428C2
socleC23×C13C22×D4
prime radicalC24×C13C2×D4
hypercenterC2×#428D13
hypocenterC13#26353
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C2×#11718515C2semidirect
4. #13116371C2semidirect
5. #13116325C2semidirect
6. #13116226C2semidirect
7. #13116162C2semidirect
8. #13115596C2semidirect
9. #13115423C2semidirect
12. #13115101C2semidirect
91. #88178Q8semidirect
530. C13#26353semidirect

Maximal subgroups

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

subgroupindex
C2×#117185152
#131185322
#131178632
#131163712
#131163252
#131162262
#131161622
#131155962
#131154232
#131152692
#131151432
#131151012
#131150352
#131150192
C2×C13×#4282
#2635313