Finite Group Databasebeta

← #15879609

Subgroups — #15879609

Order 3328.

990 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719274C211yesmaximal, characteristic
2C2×#11718492C211yesmaximal, characteristic
3#13117788C211yesmaximal, characteristic
4#13115807C211yesmaximal, characteristic
5#13115803C211yesmaximal, characteristic
6#13115800C211yesmaximal, characteristic
7#13115791C211yesmaximal, characteristic
8#13115790C211yesmaximal, characteristic
9#13115782C211yesmaximal, characteristic
10#13114849C211yesmaximal, characteristic
11#13114839C211yesmaximal, characteristic
12#13114668C211yesmaximal, characteristic
13#13114668C211yesmaximal, characteristic
14C4×#88075C211yesmaximal, characteristic
15C13×#1805C211yesmaximal, characteristic
16C2×C4×Q8×C13C2211yescharacteristic
17C2×Q8×Dic13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19#11719274—24no—
20#11719274C418yescomplemented
21C2×#88144—21no—
22C2×#88144C2211yescharacteristic
23C2×#88142—21no—
24C2×#88142C2211yescharacteristic
25C2×#88124—21no—
26C2×#88124C2211yescharacteristic
27C2×C4×Dic26—21no—
28C2×C4×Dic26C2211yescharacteristic
29C2×C13×C4⋊C8C2211yescharacteristic
30C2×C13×#103C2211yescharacteristic
31C2×C13×#103C2211yescharacteristic
32C13×#382C2211yescharacteristic
33C2×#88075C2211yescharacteristic
34C2×#88075C2211yescharacteristic
35C2×#88055C2211yescharacteristic
36C2×#88055C2211yescharacteristic
37C2×#88054C2211yescharacteristic
38C2×#88054C2211yescharacteristic
39#11718638C2211yescharacteristic
40#11718637C2211yescharacteristic
41C4⋊C4×Dic13C2211yescharacteristic
42C4⋊C4×Dic13C2211yescharacteristic
43C4×C4⋊Dic13C2211yescharacteristic
44C2×C4×#1055C2211yescharacteristic
45#11718492—24no—
46#11718314—21no—
47#11718313—21no—
48#11718310—21no—
49#11718307—21no—
50C13×#340C2211yescharacteristic
51C13×#340C2211yescharacteristic
52#11718143C2211yescharacteristic
53#11718143C2211yescharacteristic
54#11718143C2211yescharacteristic
55#11718143C2211yescharacteristic
56#11718121C2211yescharacteristic
57#11718121C2211yescharacteristic
58#11718121C2211yescharacteristic
59#11718121C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62C22×Q8×C13C2311yescharacteristic
63C22×Dic26—21no—
64C22×Dic26D411yescharacteristic
65C22×C8×C13C2311yescharacteristic
66C22×C8×C13C2311yescharacteristic
67C4×Q8×C13—22no—
68C4×Q8×C13C2×C414yes—
69C2×C13×C4⋊C4—21no—
70C2×C13×C4⋊C4C2311yescharacteristic
71C2×C13×C4⋊C4C2311yescharacteristic
72C2×C13×C4⋊C4C2311yescharacteristic
73C2×C42×C13—21no—
74C2×C42×C13C2311yescharacteristic
75Q8×Dic13—22no—
76Q8×Dic13—22no—
77Q8×Dic13C2×C414yes—
78Q8×Dic13C2×C414yes—
79C2×C4⋊Dic13—21no—
80C2×C4⋊Dic13—21no—
81C2×C4⋊Dic13—21no—
82C2×C4⋊Dic13D411yescharacteristic
83C2×C4⋊Dic13C2311yescharacteristic
84C2×C4⋊Dic13C2311yescharacteristic
85C2×C4⋊Dic13C2311yescharacteristic
86C2×C4⋊Dic13C2311yescharacteristic
87C2×#6101—21no—
88C2×#6101—21no—
89C2×#6101—21no—
90C2×#6101—21no—
91C2×#6101—21no—
92C2×#6101—21no—
93C2×#6101D411yescharacteristic
94C2×#6101D411yescharacteristic
95C2×C4×Dic13—21no—
96C2×C4×Dic13—21no—
97C2×C4×Dic13—21no—
98C2×C4×Dic13—21no—
99C2×C4×Dic13—21no—
100C2×C4×Dic13C2311yescharacteristic
101C2×C4×Dic13C2311yescharacteristic
102C22×#1055C2311yescharacteristic
103C22×#1055C2311yescharacteristic
104#88144—28no—
105#88144—22no—
106#88144C2×C414yes—
107#88142—28no—
108#88142—22no—
109#88142C2×C414yes—
110#88124—22no—
111#88124—28no—
112#88124C2×C414yes—
113C4×Dic26—28no—
114C4×Dic26C2×C414yes—
115C4×Dic26D414yes—
116C13×C4⋊C8—22no—
117C13×#103—22no—
118C13×#103—22no—
119C13×#95—21no—
120C13×#95—21no—
121#88075—22no—
122#88075Q814yescomplemented
123#88071—21no—
124#88071—21no—
125#88071—21no—
126#88071—21no—
127#88071—21no—
128#88055—22no—
129#88055—22no—
130#88054—22no—
131#88054—22no—
132C4×#1055—22no—
133#22527—131nomaximal, Sylow
134C2×Q8×C13—21no—
135C2×Q8×C13—21no—
136C2×Q8×C13—21no—
137C2×Q8×C13C22×C412yes—
138C2×Q8×C13C2×Q812yes—
139C2×Q8×C13#4112yes—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13C2×D411yescharacteristic
145C22×C4×C13C2×D411yescharacteristic
146C22×C4×C13C2411yescharacteristic
147C22×Dic13—21no—
148C22×Dic13—21no—
149C22×Dic13—21no—
150C22×Dic13—21no—
151C22×Dic13C2×D411yescharacteristic
152C22×Dic13C2×D411yescharacteristic
153C22×Dic13C2×D411yescharacteristic
154C22×Dic13C2×D411yescharacteristic
155C2×Dic26—24no—
156C2×Dic26—41no—
157C2×Dic26—41no—
158C2×Dic26—42no—
159C2×Dic26—42no—
160C2×Dic26C22⋊C414yes—
161C2×C8×C13—21no—
162C2×C8×C13—21no—
163C2×C8×C13—21no—
164C2×C8×C13—21no—
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C13×C4⋊C4—24no—
168C13×C4⋊C4—21no—
169C13×C4⋊C4—21no—
170C13×C4⋊C4—21no—
171C13×C4⋊C4—21no—
172C13×C4⋊C4—21no—
173C13×C4⋊C4C22×C412yes—
174C42×C13—24no—
175C42×C13C22×C412yes—
176C42×C13C2×D412yes—
177C4⋊Dic13—21no—
178C4⋊Dic13—21no—
179C4⋊Dic13—21no—
180C4⋊Dic13—24no—
181C4⋊Dic13—24no—
182C4⋊Dic13—24no—
183C4⋊Dic13—21no—
184C4⋊Dic13—21no—
185C4⋊Dic13C22⋊C414yes—
186C4⋊Dic13C22×C412yes—
187C4⋊Dic13C22×C412yes—
188C4⋊Dic13C2×Q812yes—
189#6101—24no—
190#6101—24no—
191#6101—24no—
192#6101—24no—
193#6101—42no—
194#6101—81no—
195#6101C22⋊C414yes—
196#6101C22⋊C414yes—
197C4×Dic13—24no—
198C4×Dic13—24no—
199C4×Dic13—42no—
200C4×Dic13—81no—
201C4×Dic13—81no—
202C4×Dic13C22×C412yes—
203C4×Dic13C22×C412yes—
204C4×Dic13C2×D412yes—
205C4×Dic13C2×D412yes—
206C2×#1055—21no—
207C2×#1055—21no—
208C2×#1055—21no—
209C2×#1055—21no—
210C2×#1055—21no—
211C2×#1055C2×Q812yes—
212C2×#557—131no—
213C2×#446—131no—
214#2355—131no—
215#1993—131no—
216#1992—131no—
217#1991—131no—
218#1989—131no—
219#1989—131no—
220#1987—131no—
221#1805—131no—
222#1805D1311yescharacteristic
223#1803—131no—
224#1763—131no—
225#1763—131no—
226C4×#103—131no—
227C23×C13C22×D411yescharacteristic
228Q8×C13—22no—
229Q8×C13—22no—
230Q8×C13—22no—
231Q8×C13C4×Q814yes—
232C2×C4×C13—22no—
233C2×C4×C13—22no—
234C2×C4×C13—22no—
235C2×C4×C13—21no—
236C2×C4×C13—21no—
237C2×C4×C13—21no—
238C2×C4×C13—21no—
239C2×C4×C13—22no—
240C2×C4×C13—41no—
241C2×C4×C13—41no—
242C2×C4×C13—41no—
243C2×C4×C13—41no—
244C2×C4×C13—41no—
245C2×C4×C13—41no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13C2×C22⋊C412yes—
249C2×C4×C13C2×C22⋊C412yes—
250C2×C4×C13C23×C411yescharacteristic
251C2×C4×C13C22×D411yescharacteristic
252C2×C4×C13C22×Q811yescharacteristic
253C2×C4×C13C2×#4111yescharacteristic
254C2×C4×C132−1+411yescharacteristic
255C2×C4×C132−1+411yescharacteristic
256C2×Dic13—21no—
257C2×Dic13—21no—
258C2×Dic13—21no—
259C2×Dic13—21no—
260C2×Dic13—21no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—22no—
265C2×Dic13—22no—
266C2×Dic13—22no—
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×Dic13C2×C22⋊C412yes—
277C2×Dic13C2×C22⋊C412yes—
278C2×Dic13C2×C22⋊C412yes—
279C2×Dic13C2×C22⋊C412yes—
280Dic26—44no—
281Dic26—48no—
282C8×C13—41no—
283C8×C13—41no—
284#1055—22no—
285#1055—41no—
286#557—138no—
287#557—264no—
288C2×C4⋊Q8—131no—
289C2×C4⋊Q8—261no—
290C2×#125—131no—
291C2×#125—131no—
292C2×#125—261no—
293C2×#125—261no—
294C2×C4×Q8—131no—
295C2×C4×Q8—131no—
296C2×C4×Q8—131no—
297C2×C4×Q8—261no—
298C2×C4×Q8C2×D1311yescharacteristic
299#446—264no—
300C2×C4⋊C8—131no—
301C2×C4⋊C8—131no—
302C2×C4⋊C8C2×D1311yescharacteristic
303C2×#103—131no—
304C2×#103—131no—
305C2×#103C2×D1311yescharacteristic
306C2×#103C2×D1311yescharacteristic
307C2×#97—131no—
308C2×#97—131no—
309C2×C4×C8—131no—
310#391—261no—
311#387—261no—
312#387—261no—
313#384—131no—
314#382—131no—
315#382C2×D1311yescharacteristic
316C4×C4⋊C4—131no—
317C4×C4⋊C4—131no—
318C4×C4⋊C4—131no—
319C4×C4⋊C4—261no—
320#340—131no—
321#340—131no—
322#340—131no—
323#340—131no—
324#340—131no—
325#340—131no—
326#340—131no—
327#340—131no—
328#340—131no—
329#340—131no—
330#340C2×D1311yescharacteristic
331#340C2×D1311yescharacteristic
332C22×C13C22×C22⋊C411yescharacteristic
333C22×C13#54811yescharacteristic
334C22×C13D4×Q811yescharacteristic
335C22×C13#57511yescharacteristic
336C22×C13#57511yescharacteristic
337C22×C13#57711yescharacteristic
338C22×C13#57811yescharacteristic
339C4×C13—24no—
340C4×C13—22no—
341C4×C13—22no—
342C4×C13—42no—
343C4×C13—81no—
344C4×C13—81no—
345C4×C13C2×C4×Q811yescharacteristic
346C4×C13#51911yescharacteristic
347C4×C13#54811yescharacteristic
348C4×C13D4×Q811yescharacteristic
349Dic13—22no—
350Dic13—22no—
351Dic13—22no—
352Dic13—22no—
353Dic13—42no—
354Dic13—42no—
355Dic13—42no—
356Dic13—81no—
357C22×Q8—131no—
358C22×Q8—261no—
359C22×Q8C22×D1311yescharacteristic
360C22×C8—131no—
361C22×C8—131no—
362C22×C8C22×D1311yescharacteristic
363C22×C8C22×D1311yescharacteristic
364C4⋊Q8—134no—
365C4⋊Q8—262no—
366C4⋊Q8—268no—
367#125—134no—
368#125—134no—
369#125—268no—
370#125—262no—
371#125—268no—
372#125—262no—
373C4×Q8—22no—
374C4×Q8—134no—
375C4×Q8—134no—
376C4×Q8—134no—
377C4×Q8—134no—
378C4×Q8—268no—
379C4×Q8—262no—
380C4×Q8—262no—
381C4×Q8C4×D1314yes—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—131no—
384C2×C4⋊C4—131no—
385C2×C4⋊C4—131no—
386C2×C4⋊C4—131no—
387C2×C4⋊C4—131no—
388C2×C4⋊C4—131no—
389C2×C4⋊C4—131no—
390C2×C4⋊C4—261no—
391C2×C4⋊C4—261no—
392C2×C4⋊C4—261no—
393C2×C4⋊C4—261no—
394C2×C4⋊C4—261no—
395C2×C4⋊C4—261no—
396C2×C4⋊C4—261no—
397C2×C4⋊C4—261no—
398C2×C4⋊C4—261no—
399C2×C4⋊C4C22×D1311yescharacteristic
400C2×C4⋊C4C22×D1311yescharacteristic
401C2×C4⋊C4C22×D1311yescharacteristic
402C2×C42—21no—
403C2×C42—131no—
404C2×C42—131no—
405C2×C42—261no—
406C2×C42—261no—
407C2×C42—261no—
408C2×C42—261no—
409C2×C42—261no—
410C2×C42C22×D1311yescharacteristic
411C4⋊C8—22no—
412C4⋊C8—262no—
413C4⋊C8—262no—
414#103—22no—
415#103—22no—
416#103—134no—
417#103—262no—
418#97—262no—
419#97—262no—
420C4×C8—262no—
421#95—21no—
422#95—21no—
423#95—261no—
424#95—261no—
425#95—261no—
426#95—261no—
427#95—261no—
428C2×C13Q8×C22⋊C411yescharacteristic
429C2×C13#289611yescharacteristic
430C2×C13#289811yescharacteristic
431C2×C13#337111yescharacteristic
432C2×C13#337711yescharacteristic
433C2×C13#338811yescharacteristic
434C2×C13#339011yescharacteristic
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8—21no—
438C2×Q8—134no—
439C2×Q8—264no—
440C2×Q8—521no—
441C2×Q8—521no—
442C2×Q8—522no—
443C2×Q8—522no—
444C2×Q8C2×C4×D1312yes—
445C2×Q8#612912yes—
446C2×Q8Q8×D1312yes—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—131no—
452C22×C4—131no—
453C22×C4—131no—
454C22×C4—131no—
455C22×C4—261no—
456C22×C4—261no—
457C22×C4—261no—
458C22×C4—261no—
459C22×C4D4×D1311yescharacteristic
460C22×C4D4×D1311yescharacteristic
461C22×C4C23×D1311yescharacteristic
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—132no—
469C2×C8—261no—
470C2×C8—261no—
471C2×C8—261no—
472C2×C8—261no—
473C2×C8—261no—
474C4⋊C4—24no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—134no—
481C4⋊C4—134no—
482C4⋊C4—134no—
483C4⋊C4—132no—
484C4⋊C4—132no—
485C4⋊C4—132no—
486C4⋊C4—264no—
487C4⋊C4—264no—
488C4⋊C4—264no—
489C4⋊C4—264no—
490C4⋊C4—264no—
491C4⋊C4—264no—
492C4⋊C4—264no—
493C4⋊C4—261no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—522no—
499C4⋊C4—1041no—
500C4⋊C4C2×C4×D1312yes—
501C42—24no—
502C42—132no—
503C42—132no—
504C42—132no—
505C42—132no—
506C42—264no—
507C42—264no—
508C42—522no—
509C42—1041no—
510C42—1041no—
511C42C2×C4×D1312yes—
512C42D4×D1312yes—
513C13#2252711yescharacteristic, complemented, Sylow
514C23C2×D4×D1311yescharacteristic
515Q8—22no—
516Q8—22no—
517Q8—22no—
518Q8—524no—
519Q8—528no—
520Q8#8814114yes—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—132no—
538C2×C4—132no—
539C2×C4—132no—
540C2×C4—132no—
541C2×C4—261no—
542C2×C4—261no—
543C2×C4—261no—
544C2×C4—261no—
545C2×C4—261no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—262no—
550C2×C4—262no—
551C2×C4—262no—
552C2×C4—521no—
553C2×C4—521no—
554C2×C4—521no—
555C2×C4—521no—
556C2×C4—521no—
557C2×C4—521no—
558C2×C4—521no—
559C2×C4—521no—
560C2×C4—521no—
561C2×C4C22⋊C4×D1312yes—
562C2×C4C22⋊C4×D1312yes—
563C2×C4C22×C4×D1311yescharacteristic
564C2×C4C2×D4×D1311yescharacteristic
565C2×C4C2×#612911yescharacteristic
566C2×C4C2×Q8×D1311yescharacteristic
567C2×C4#8825711yescharacteristic
568C2×C4#8825711yescharacteristic
569C8—41no—
570C8—41no—
571C8—262no—
572C8—521no—
573C22C2×C22⋊C4×D1311yescharacteristic
574C22#1171930311yescharacteristic
575C22#1171933711yescharacteristic
576C22#1171947311yescharacteristic
577C22#1171947311yescharacteristic
578C22#1171948311yescharacteristic
579C22#1171948411yescharacteristic
580C4—22no—
581C4—22no—
582C4—24no—
583C4—42no—
584C4—81no—
585C4—81no—
586C4—262no—
587C4—262no—
588C4—262no—
589C4—262no—
590C4—522no—
591C4—522no—
592C4—522no—
593C4—1041no—
594C4C2×#8814111yescharacteristic
595C4#1171922111yescharacteristic
596C4#1171930311yescharacteristic
597C4#1171933711yescharacteristic
598C2#1311766811yescharacteristic
599C2#1312335111yescharacteristic
600C2#1312336811yescharacteristic
601C2#1312760811yescharacteristic
602C2#1312768211yescharacteristic
603C2#1312777911yescharacteristic
604C2#1312780311yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC13×#1805C2
socle, prime radicalC23×C13C22×D4
cosocleC22×C4×C13C24
hypercenter#1805D13
hypocenterC13#22527
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1805

Complements

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

NH ≅ G/Ntype
20. #11719274C4semidirect
122. #88075Q8semidirect
513. C13#22527semidirect

Maximal subgroups

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

subgroupindex
C2×#117192742
C2×#117184922
#131177882
#131158072
#131158032
#131158002
#131157912
#131157902
#131157822
#131148492
#131148392
#131146682
C4×#880752
C13×#18052
#2252713