Finite Group Databasebeta

← #15925960

Subgroups — #15925960

Order 3328.

884 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718670C211yesmaximal, characteristic
2C2×C4×#6105C211yesmaximal, characteristic
3#13118697C211yesmaximal, characteristic, complemented
4#13116375C211yesmaximal, characteristic, complemented
5#13116313C211yesmaximal, characteristic, complemented
6#13116228C211yesmaximal, characteristic, complemented
7#13116174C211yesmaximal, characteristic, complemented
8#13115566C211yesmaximal, characteristic, complemented
9#13115395C211yesmaximal, characteristic, complemented
10#13115170C211yesmaximal, characteristic
11#13115170C211yesmaximal, characteristic
12#13115103C211yesmaximal, characteristic, complemented
13#13115083C211yesmaximal, characteristic
14#13115083C211yesmaximal, characteristic
15D4×C13×C4⋊C4C211yesmaximal, characteristic
16C2×C4×D4×C13C2211yescharacteristic
17C2×C4×D4×C13C2211yescharacteristic
18C2×C4×D4×C13C2211yescharacteristic
19C22×C13×C4⋊C4—21no—
20C22×#6105C2211yescharacteristic
21C2×#88124C2211yescharacteristic
22C2×C4×Dic26C2211yescharacteristic
23C13×#389C2211yescharacteristic
24C13×#389C2211yescharacteristic
25C13×#385—21no—
26C13×#385—21no—
27C13×#384C2211yescharacteristic
28C13×#380—21no—
29C4×C13×C4⋊C4C2211yescharacteristic
30C2×#88072C2211yescharacteristic
31C2×#88072C2211yescharacteristic
32C2×#88072C2211yescharacteristic
33C4×#6105—24no—
34#11718670—24no—
35#11718641—21no—
36#11718633—21no—
37C2×#88050C2211yescharacteristic
38C2×#88050C2211yescharacteristic
39C2×#88050C2211yescharacteristic
40C2×#88048C2211yescharacteristic
41C2×#88048C2211yescharacteristic
42C2×#88047C2211yescharacteristic
43C2×#88047C2211yescharacteristic
44C2×#88047C2211yescharacteristic
45#11718590C2211yescharacteristic
46#11718590C2211yescharacteristic
47#11718589C2211yescharacteristic
48#11718589C2211yescharacteristic
49C2×C4⋊#1055C2211yescharacteristic
50C2×C4×#1055C2211yescharacteristic
51#11718319—21no—
52#11718313—21no—
53#11718121C2211yescharacteristic
54#11718121C2211yescharacteristic
55#11718121C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718116C2211yescharacteristic
58#11718116C2211yescharacteristic
59#11718116C2211yescharacteristic
60#11718116C2211yescharacteristic
61C22×D4×C13C2311yescharacteristic
62C23×C4×C13—21no—
63C23×C4×C13—21no—
64C23×C4×C13—21no—
65C22×Dic26C2311yescharacteristic
66C4×D4×C13—22no—
67C4×D4×C13—22no—
68C4×D4×C13—22no—
69C4×D4×C13—22no—
70C4×D4×C13—41no—
71C4×D4×C13—41no—
72C2×C13×C4⋊C4—21no—
73C2×C13×C4⋊C4—21no—
74C2×C13×C4⋊C4—21no—
75C2×C13×C4⋊C4—21no—
76C2×C13×C4⋊C4—44no—
77C2×C13×C4⋊C4D411yescharacteristic
78C2×C13×C4⋊C4D411yescharacteristic
79C2×C13×C4⋊C4C2311yescharacteristic
80C2×C13×C4⋊C4C2311yescharacteristic
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C22⋊C4—21no—
83C2×C13×C22⋊C4—21no—
84C2×C13×C22⋊C4—21no—
85C2×C42×C13C2311yescharacteristic
86C2×C42×C13C2311yescharacteristic
87C2×C42×C13C2311yescharacteristic
88C2×#6105—22no—
89C2×#6105—22no—
90C2×#6105Q814yes—
91C2×C4⋊Dic13C2311yescharacteristic
92C2×C4⋊Dic13C2311yescharacteristic
93C2×C4⋊Dic13C2311yescharacteristic
94C2×#6101—21no—
95C2×#6101—21no—
96C2×#6101—21no—
97C2×#6101—21no—
98C2×#6101—21no—
99C2×C4×Dic13—21no—
100C22×#1055C2311yescharacteristic
101C22×#1055C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88124—22no—
105#88124—41no—
106C4×Dic26—22no—
107C4×Dic26—41no—
108C13×#95—21no—
109C13×#95—21no—
110C13×#95D411yescharacteristic
111C13×#95D411yescharacteristic
112#88072—22no—
113#88072—22no—
114#88072D414yes—
115#88071—21no—
116#88071—21no—
117#88071—21no—
118#88071—21no—
119#88071—21no—
120#88071—21no—
121#88050—22no—
122#88050—22no—
123#88050—41no—
124#88048—22no—
125#88048—22no—
126#88047—22no—
127#88047—22no—
128#88047—41no—
129C4⋊#1055—22no—
130C4×#1055—22no—
131#26374—131nomaximal, Sylow
132C24×C13—21no—
133C2×D4×C13—21no—
134C2×D4×C13—21no—
135C2×D4×C13—21no—
136C2×D4×C13C2×D412yes—
137C2×D4×C13C2×Q812yes—
138C2×D4×C13#4112yes—
139C22×C4×C13—24no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—42no—
144C22×C4×C13—42no—
145C22×C4×C13—42no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—81no—
150C22×C4×C13—81no—
151C22×C4×C13C2×D411yescharacteristic
152C22×C4×C13C2×D411yescharacteristic
153C22×C4×C13C2×D411yescharacteristic
154C22×C4×C13C2×D411yescharacteristic
155C22×C4×C13C2×D411yescharacteristic
156C22×C4×C13C2×D411yescharacteristic
157C22×C4×C13C2411yescharacteristic
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C2×Dic26—21no—
163C2×Dic26—21no—
164C2×Dic26—21no—
165C2×Dic26—21no—
166C2×Dic26—21no—
167C2×Dic26C2×Q812yes—
168C13×C4⋊C4—22no—
169C13×C4⋊C4—22no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4—21no—
174C13×C4⋊C4—21no—
175C13×C4⋊C4—42no—
176C13×C4⋊C4—42no—
177C13×C4⋊C4—42no—
178C13×C4⋊C4—81no—
179C13×C4⋊C4#4112yes—
180C13×C22⋊C4—24no—
181C13×C22⋊C4—42no—
182C13×C22⋊C4—42no—
183C42×C13—21no—
184C42×C13—21no—
185C42×C13—21no—
186C42×C13—21no—
187C42×C13—21no—
188C42×C13—21no—
189#6105—28no—
190C4⋊Dic13—21no—
191C4⋊Dic13—21no—
192C4⋊Dic13—21no—
193C4⋊Dic13—21no—
194C4⋊Dic13—21no—
195C4⋊Dic13C2×D412yes—
196#6101—42no—
197#6101—42no—
198#6101—42no—
199#6101—42no—
200#6101—42no—
201C4×Dic13—42no—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055—21no—
212C2×#1055C2×D412yes—
213C2×#1055C2×Q812yes—
214C2×#478—131no—
215C2×C4×SD16—131no—
216#2453—131no—
217D4×C4⋊C4D1311yescharacteristic
218#2095—131no—
219#2084—131no—
220#2068—131no—
221#2059—131no—
222#1942—131no—
223#1916—131no—
224#1877—131no—
225#1877—131no—
226#1865—131no—
227#1862—131no—
228#1862—131no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—41no—
233C23×C13—41no—
234C23×C13—41no—
235C23×C13—41no—
236C23×C13C22×D411yescharacteristic
237D4×C13—22no—
238D4×C13—22no—
239D4×C13—22no—
240D4×C13C22⋊Q814yes—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—22no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—21no—
251C2×C4×C13—21no—
252C2×C4×C13—21no—
253C2×C4×C13—21no—
254C2×C4×C13—21no—
255C2×C4×C13—21no—
256C2×C4×C13—21no—
257C2×C4×C13—21no—
258C2×C4×C13—48no—
259C2×C4×C13—41no—
260C2×C4×C13—41no—
261C2×C4×C13—41no—
262C2×C4×C13—41no—
263C2×C4×C13—41no—
264C2×C4×C13—41no—
265C2×C4×C13—41no—
266C2×C4×C13—41no—
267C2×C4×C13—84no—
268C2×C4×C13—84no—
269C2×C4×C13#13512yes—
270C2×C4×C13AGL(1,ℤ/8)12yes—
271C2×C4×C13C22×D411yescharacteristic
272C2×C4×C13C22×Q811yescharacteristic
273C2×C4×C13C2×#4111yescharacteristic
274C2×C4×C13C2×#4111yescharacteristic
275C2×C4×C13H(5,𝔽2)11yescharacteristic
276C2×C4×C132−1+411yescharacteristic
277C2×Dic13—22no—
278C2×Dic13—22no—
279C2×Dic13—41no—
280C2×Dic13—41no—
281C2×Dic13—41no—
282C2×Dic13—41no—
283C2×Dic13—41no—
284C2×Dic13—41no—
285C2×Dic13—41no—
286C2×Dic13—41no—
287C2×Dic13—41no—
288C2×Dic13—41no—
289Dic26—22no—
290Dic26—22no—
291Dic26—41no—
292Dic26—41no—
293#1055—22no—
294#1055—22no—
295#1055—41no—
296#1055—41no—
297C22×SD16—131no—
298C2×#125—131no—
299C2×C4×Q8—131no—
300C2×C4×D4C2×D1311yescharacteristic
301C2×C4×D4C2×D1311yescharacteristic
302C2×C4×D4C2×D1311yescharacteristic
303C22×C4⋊C4—21no—
304#478—264no—
305C4×SD16—264no—
306C2×#107—131no—
307C2×#107—131no—
308C2×#107—131no—
309C2×#106—131no—
310C2×#106—131no—
311C2×C4⋊C8—131no—
312C2×#103—131no—
313C2×#103—131no—
314C2×#103—131no—
315C2×#102—131no—
316C2×#102—131no—
317C2×#102—131no—
318C2×C4×C8—131no—
319#400—261no—
320#398—261no—
321#391—131no—
322#391—131no—
323#389—131no—
324#389—131no—
325#389—261no—
326#389C2×D1311yescharacteristic
327#389C2×D1311yescharacteristic
328#387—261no—
329#385—21no—
330#385—21no—
331#384C2×D1311yescharacteristic
332#380—21no—
333C4×C4⋊C4C2×D1311yescharacteristic
334#340—131no—
335#340—131no—
336#340—131no—
337#340—131no—
338#336—131no—
339#336—131no—
340#336—131no—
341#336—131no—
342C22×C13—24no—
343C22×C13—42no—
344C22×C13—42no—
345C22×C13—42no—
346C22×C13—42no—
347C22×C13—42no—
348C22×C13—42no—
349C22×C13#52511yescharacteristic
350C22×C13D4211yescharacteristic
351C22×C13D4×Q811yescharacteristic
352C22×C13C2×#13511yescharacteristic
353C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
354C22×C13#57711yescharacteristic
355C22×C13#57811yescharacteristic
356C4×C13—22no—
357C4×C13—22no—
358C4×C13—42no—
359C4×C13—41no—
360C4×C13—41no—
361C4×C13—41no—
362C4×C13—41no—
363C4×C13—81no—
364C4×C13—81no—
365C4×C13C2×C22⋊Q811yescharacteristic
366C4×C13#53911yescharacteristic
367C4×C13#54711yescharacteristic
368C4×C13#55411yescharacteristic
369Dic13—42no—
370Dic13—42no—
371Dic13—81no—
372Dic13—81no—
373C22×Q8—131no—
374C22×D4C22×D1311yescharacteristic
375C23×C4—21no—
376C23×C4—21no—
377C23×C4—21no—
378C2×SD16—134no—
379C2×SD16—262no—
380C2×SD16—262no—
381C22×C8—131no—
382C22×C8—131no—
383C22×C8—131no—
384C22×C8—131no—
385#125—262no—
386#125—521no—
387C4×Q8—262no—
388C4×Q8—521no—
389C4×D4—22no—
390C4×D4—22no—
391C4×D4—22no—
392C4×D4—22no—
393C4×D4—41no—
394C4×D4—41no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—21no—
398C2×C4⋊C4—21no—
399C2×C4⋊C4—44no—
400C2×C4⋊C4—131no—
401C2×C4⋊C4—131no—
402C2×C4⋊C4—131no—
403C2×C4⋊C4—261no—
404C2×C4⋊C4—261no—
405C2×C4⋊C4—261no—
406C2×C4⋊C4—261no—
407C2×C4⋊C4—261no—
408C2×C4⋊C4C22⋊D1311yescharacteristic
409C2×C4⋊C4C22⋊D1311yescharacteristic
410C2×C4⋊C4C22×D1311yescharacteristic
411C2×C4⋊C4C22×D1311yescharacteristic
412C2×C4⋊C4C22×D1311yescharacteristic
413C2×C22⋊C4—21no—
414C2×C22⋊C4—21no—
415C2×C22⋊C4—21no—
416C2×C42—261no—
417C2×C42C22×D1311yescharacteristic
418C2×C42C22×D1311yescharacteristic
419C2×C42C22×D1311yescharacteristic
420#107—262no—
421#107—262no—
422#107—521no—
423#106—262no—
424#106—262no—
425C4⋊C8—262no—
426#103—262no—
427#103—262no—
428#103—521no—
429#102—134no—
430#102—262no—
431#102—262no—
432C4×C8—262no—
433#95—21no—
434#95—21no—
435#95—261no—
436#95—261no—
437#95—261no—
438#95—261no—
439#95—261no—
440#95—261no—
441#95C22⋊D1311yescharacteristic
442#95C22⋊D1311yescharacteristic
443C2×C13—44no—
444C2×C13#244911yescharacteristic
445C2×C13#310511yescharacteristic
446C2×C13#312011yescharacteristic
447C2×C13#326511yescharacteristic
448C2×C13#328311yescharacteristic
449C2×C13#338111yescharacteristic
450C2×C13#338611yescharacteristic
451C24—21no—
452C2×Q8—132no—
453C2×Q8—261no—
454C2×Q8—261no—
455C2×Q8—261no—
456C2×Q8—261no—
457C2×Q8—261no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4#612712yes—
462C2×D4D4×D1312yes—
463C2×D4Q8×D1312yes—
464C22×C4—24no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—42no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—42no—
474C22×C4—81no—
475C22×C4—81no—
476C22×C4—261no—
477C22×C4—261no—
478C22×C4—261no—
479C22×C4—261no—
480C22×C4C2×C22⋊D1311yescharacteristic
481C22×C4C2×C22⋊D1311yescharacteristic
482C22×C4C2×C22⋊D1311yescharacteristic
483C22×C4C2×C22⋊D1311yescharacteristic
484C22×C4C2×C22⋊D1311yescharacteristic
485C22×C4C2×C22⋊D1311yescharacteristic
486C22×C4C23×D1311yescharacteristic
487SD16—268no—
488C2×C8—132no—
489C2×C8—132no—
490C2×C8—261no—
491C2×C8—261no—
492C2×C8—261no—
493C2×C8—261no—
494C2×C8—261no—
495C2×C8—261no—
496C2×C8—261no—
497C2×C8—261no—
498C2×C8—261no—
499C2×C8—261no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—42no—
508C4⋊C4—42no—
509C4⋊C4—42no—
510C4⋊C4—81no—
511C4⋊C4—132no—
512C4⋊C4—261no—
513C4⋊C4—261no—
514C4⋊C4—261no—
515C4⋊C4—261no—
516C4⋊C4—261no—
517C4⋊C4—522no—
518C4⋊C4—522no—
519C4⋊C4—522no—
520C4⋊C4—522no—
521C4⋊C4—522no—
522C4⋊C4#612712yes—
523C22⋊C4—24no—
524C22⋊C4—42no—
525C22⋊C4—42no—
526C42—21no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—522no—
533C13#2637411yescharacteristic, complemented, Sylow
534C23—22no—
535C23—22no—
536C23—22no—
537C23—41no—
538C23—41no—
539C23—41no—
540C23—41no—
541C23C22×C22⋊D1311yescharacteristic
542Q8—262no—
543Q8—262no—
544Q8—521no—
545Q8—521no—
546D4—22no—
547D4—22no—
548D4—22no—
549D4#8815014yes—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—48no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—84no—
577C2×C4—84no—
578C2×C4—262no—
579C2×C4—262no—
580C2×C4—521no—
581C2×C4—521no—
582C2×C4—521no—
583C2×C4—521no—
584C2×C4—521no—
585C2×C4—521no—
586C2×C4—521no—
587C2×C4—521no—
588C2×C4—521no—
589C2×C4—521no—
590C2×C4#8818612yes—
591C2×C4#8820412yes—
592C2×C4C2×#612711yescharacteristic
593C2×C4C2×#612711yescharacteristic
594C2×C4C2×D4×D1311yescharacteristic
595C2×C4#8825111yescharacteristic
596C2×C4C2×Q8×D1311yescharacteristic
597C2×C4#8825411yescharacteristic
598C8—262no—
599C8—262no—
600C8—521no—
601C8—521no—
602C22—24no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—42no—
609C22#1171949611yescharacteristic
610C22C2×#8818611yescharacteristic
611C22D4×C22⋊D1311yescharacteristic
612C22Q8×C22⋊D1311yescharacteristic
613C22C2×#8820411yescharacteristic
614C22#1171954111yescharacteristic
615C22#1171954311yescharacteristic
616C4—22no—
617C4—22no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—81no—
625C4—522no—
626C4—522no—
627C4—1041no—
628C4—1041no—
629C4#1171921211yescharacteristic
630C4C2×#8815011yescharacteristic
631C4#1171921611yescharacteristic
632C4#1171922011yescharacteristic
633C2—44no—
634C2#1311864511yescharacteristic
635C2#1312488311yescharacteristic
636C2#1312505011yescharacteristic
637C2#1312632711yescharacteristic
638C2#1312655411yescharacteristic
639C2#1312771111yescharacteristic
640C2#1312775711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
FittingD4×C13×C4⋊C4C2
socleC23×C13C22×D4
prime radicalC22×D4×C13C23
hypercenterD4×C4⋊C4D13
hypocenterC13#26374
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #13118697C2semidirect
4. #13116375C2semidirect
5. #13116313C2semidirect
6. #13116228C2semidirect
7. #13116174C2semidirect
8. #13115566C2semidirect
9. #13115395C2semidirect
12. #13115103C2semidirect
533. C13#26374semidirect

Maximal subgroups

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

subgroupindex
C2×#117186702
C2×C4×#61052
#131186972
#131163752
#131163132
#131162282
#131161742
#131155662
#131153952
#131151702
#131151032
#131150832
D4×C13×C4⋊C42
#2637413