Finite Group Databasebeta

← #15832979

Subgroups — #15832979

Order 3328.

648 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
1#13124883C211yesmaximal, characteristic
2#13123987C211yesmaximal, characteristic, complemented
3#13113700C211yesmaximal, characteristic, complemented
4#13113693C211yesmaximal, characteristic, complemented
5#13113672C211yesmaximal, characteristic, complemented
6#13113665C211yesmaximal, characteristic, complemented
7#13113658C211yesmaximal, characteristic, complemented
8#13113648C211yesmaximal, characteristic, complemented
9C8×#6105C211yesmaximal, characteristic, complemented
10C8×#6104C211yesmaximal, characteristic, complemented
11#13113624C211yesmaximal, characteristic, complemented
12#13113261C211yesmaximal, characteristic, complemented
13#13113242C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#2972C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17#11719184C2211yescharacteristic
18C8×D4×C13—21no—
19C8×D4×C13—21no—
20C8×D4×C13C2211yescharacteristic
21C8×D4×C13C2211yescharacteristic
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#431C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C2×C13×C22⋊C8—21no—
27C2×C13×C22⋊C8—21no—
28#11718879C411yescharacteristic
29#11718878C411yescharacteristic
30C4×#6105C2211yescharacteristic
31C4×#6105C2211yescharacteristic
32#11718677C411yescharacteristic
33#11718677C411yescharacteristic
34C4×#6104C2211yescharacteristic
35C4×#6104C2211yescharacteristic
36#11718670C411yescharacteristic
37#11718670C411yescharacteristic
38#11718631C411yescharacteristic
39#11718629C411yescharacteristic
40#11718586C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718585C2211yescharacteristic
43#11718501—21no—
44#11718500—21no—
45#11718390—21no—
46#11718389—21no—
47#11718349C2211yescharacteristic, complemented
48C8×D52C2211yescharacteristic, complemented
49#11718340C2211yescharacteristic, complemented
50C8×Dic26C2211yescharacteristic, complemented
51D4⋊#1055C2211yescharacteristic
52D4⋊#1055C2211yescharacteristic
53D4⋊#1055C2211yescharacteristic
54D4⋊#1055C2211yescharacteristic
55#11718076C2211yescharacteristic, complemented
56#11718076C2211yescharacteristic, complemented
57#11718075C2211yescharacteristic, complemented
58#11718075C2211yescharacteristic, complemented
59#11718072C2211yescharacteristic, complemented
60#11718072C2211yescharacteristic, complemented
61#11718071C2211yescharacteristic, complemented
62#11718071C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C22×C8×C13—21no—
70C22×C8×C13—21no—
71C22×C8×C13—21no—
72C22×C8×C13—21no—
73C4×D4×C13—21no—
74C4×D4×C13—21no—
75C4×D4×C13C2×C411yescharacteristic
76C4×D4×C13C2×C411yescharacteristic
77C4×D4×C13C2311yescharacteristic
78C4×D4×C13C2311yescharacteristic
79C2×C13×C4⋊C4C2×C411yescharacteristic
80C2×C13×C22⋊C4—21no—
81C2×C42×C13C2311yescharacteristic
82C2×#6105C2×C411yescharacteristic
83C2×#6105C2×C411yescharacteristic
84C2×#6104C2×C411yescharacteristic
85C2×#6104C2×C411yescharacteristic
86#88184C2×C411yescharacteristic
87#88183—21no—
88C4×C22⋊D13—21no—
89#88178C2×C411yescharacteristic
90C2×#6099—21no—
91C2×#6094—21no—
92C2×C8×D13—21no—
93#88130—21no—
94#88129C2×C411yescharacteristic
95C4×D52C2311yescharacteristic
96#88126—21no—
97#88124C2×C411yescharacteristic
98C4×Dic26C2311yescharacteristic
99C13×C4⋊C8D411yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8D411yescharacteristic
109C13×C22⋊C8D411yescharacteristic
110C4×C8×C13—21no—
111C4×C8×C13C2311yescharacteristic
112C4×C8×C13C2311yescharacteristic
113#88072C2×C411yescharacteristic
114#88072C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117C22⋊#1055—21no—
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055C2×C411yescharacteristic
120#88060—21no—
121#88060—21no—
122#88055—21no—
123#88054—21no—
124#88054—21no—
125C8×Dic13—21no—
126#88050C2×C411yescharacteristic
127#88050C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88049C2×C411yescharacteristic
130#88048C2×C411yescharacteristic
131#88048C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133#88047C2×C411yescharacteristic
134C4⋊#1055—21no—
135C4⋊#1055—21no—
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2×C411yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4⋊#1055C2311yescharacteristic
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#17918—131nomaximal, Sylow
145C24×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—22no—
148C2×D4×C13—21no—
149C2×D4×C13C22×C411yescharacteristic
150C2×D4×C13C22×C411yescharacteristic
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
154C22×C4×C13—21no—
155C22×C4×C13—21no—
156C22×C4×C13—81no—
157C22×C4×C13—81no—
158C22×C4×C13C22×C411yescharacteristic
159C22×C4×C13C2×D411yescharacteristic
160C22×C4×C13#4111yescharacteristic
161C2×C22⋊D13—21no—
162C2×D52C22×C411yescharacteristic
163C2×C4×D13—21no—
164C2×Dic26C22×C411yescharacteristic
165C2×C8×C13—21no—
166C2×C8×C13—21no—
167C2×C8×C13—81no—
168C2×C8×C13—81no—
169C2×C8×C13—81no—
170C2×C8×C13—81no—
171C2×C8×C13C2×D411yescharacteristic
172C2×C8×C13C2×D411yescharacteristic
173C2×C8×C13C2×D411yescharacteristic
174C2×C8×C13C2×D411yescharacteristic
175C13×C4⋊C4—21no—
176C13×C4⋊C4C22×C411yescharacteristic
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C22⋊C4—21no—
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C42×C13C22×C411yescharacteristic
183C42×C13C2×D411yescharacteristic
184C42×C13#4111yescharacteristic
185C42×C13C2411yescharacteristic
186C22⋊Dic13—21no—
187#6105—22no—
188#6105—22no—
189#6104—22no—
190#6104—22no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194#6103—21no—
195C4⋊Dic13C22×C411yescharacteristic
196C4⋊Dic13C22×C411yescharacteristic
197#6101—21no—
198#6101—21no—
199#6101—21no—
200#6101—21no—
201C4×Dic13—21no—
202#6099—81no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—21no—
207C2×#1055C22×C411yescharacteristic
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211#6094—81no—
212C8×D13—81no—
213#3105—131no—
214#2993—131no—
215#2972D1311yescharacteristic, complemented
216#1586—131no—
217#1585—131no—
218#1582—131no—
219#1581—131no—
220#1580—131no—
221SD16⋊C8—131no—
222C8×SD16—131no—
223C8×D8—131no—
224#1574—131no—
225#1486—131no—
226#1482—131no—
227#1454—131no—
228C23×C13—24no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—81no—
232C23×C13—81no—
233C23×C13C4×D411yescharacteristic
234C22×D13—21no—
235D4×C13—24no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13#13112yes—
239D4×C13#13112yes—
240C2×C4×C13—21no—
241C2×C4×C13—21no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—41no—
247C2×C4×C13—41no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—81no—
252C2×C4×C13—81no—
253C2×C4×C13—81no—
254C2×C4×C13C4×D411yescharacteristic
255C2×C4×C13C4×D411yescharacteristic
256C2×C4×C13C4×D411yescharacteristic
257C2×C4×C13C23×C411yescharacteristic
258C2×C4×C13C22×D411yescharacteristic
259C2×C4×C13C2×#4111yescharacteristic
260C22⋊D13—81no—
261C2×Dic13—21no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264D52—21no—
265D52—21no—
266C4×D13—41no—
267C4×D13—41no—
268Dic26—21no—
269Dic26—21no—
270C8×C13—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—41no—
275C8×C13—41no—
276#1055—21no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—41no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#529—131no—
285C2×C4×D4C2×D1311yescharacteristic
286#484—131no—
287#481—131no—
288#478—131no—
289#478—131no—
290#463—131no—
291#463—131no—
292#450—131no—
293#447—131no—
294#446—131no—
295C8×Q8—131no—
296C4×SD16—131no—
297C4×SD16—131no—
298C4×D8—131no—
299C4×D8—131no—
300#436—131no—
301#436—261no—
302#435—261no—
303C8×D4—21no—
304C8×D4—21no—
305C8×D4—131no—
306C8×D4C2×D1311yescharacteristic
307C8×D4C2×D1311yescharacteristic
308C8×D4C2×D1311yescharacteristic
309C8×D4C2×D1311yescharacteristic
310#433—261no—
311#431—131no—
312#431—131no—
313#431C2×D1311yescharacteristic
314#431C2×D1311yescharacteristic
315#424—261no—
316#423—131no—
317C2×C22⋊C8—21no—
318C2×C22⋊C8—21no—
319#335—131no—
320#335—131no—
321#334—131no—
322#334—131no—
323Q8⋊C8—131no—
324Q8⋊C8—131no—
325D4⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331#322—131no—
332#322—131no—
333#322—131no—
334C82—131no—
335C22×C13—21no—
336C22×C13—22no—
337C22×C13—22no—
338C22×C13—21no—
339C22×C13—21no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—84no—
345C22×C13C2×C4×D411yescharacteristic
346C2×D13—41no—
347C2×D13—41no—
348C2×D13—41no—
349C4×C13—21no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—41no—
354C4×C13—41no—
355C4×C13C2×#13111yescharacteristic
356C4×C13C2×#13111yescharacteristic
357C4×C13#57611yescharacteristic
358C4×C13#57711yescharacteristic
359Dic13—41no—
360Dic13—41no—
361Dic13—41no—
362C22×D4C4×D1311yescharacteristic
363C23×C4—21no—
364C2×SD16—131no—
365C2×SD16—131no—
366C2×D8—131no—
367C2×D8—131no—
368C2×M16—261no—
369C2×M16—261no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—261no—
375#126—261no—
376#125—131no—
377#124—131no—
378#123—261no—
379C22⋊Q8—131no—
380#121—131no—
381C4×Q8—131no—
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—131no—
385C4×D4—261no—
386C4×D4C4×D1311yescharacteristic
387C4×D4C4×D1311yescharacteristic
388C4×D4C22×D1311yescharacteristic
389C4×D4C22×D1311yescharacteristic
390#117—261no—
391C2×C4⋊C4C4×D1311yescharacteristic
392C2×C22⋊C4—21no—
393C2×C42C22×D1311yescharacteristic
394#107—131no—
395#107—131no—
396#106—131no—
397#106—131no—
398C4⋊C8—131no—
399C4⋊C8—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—261no—
403C4⋊C8—261no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8C22⋊D1311yescharacteristic
407C4⋊C8C22⋊D1311yescharacteristic
408C4⋊C8C22×D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410#103—131no—
411#103—131no—
412#102—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418C22⋊C8—21no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—131no—
424C22⋊C8—131no—
425C22⋊C8—261no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8C22⋊D1311yescharacteristic
429C22⋊C8C22⋊D1311yescharacteristic
430#97—261no—
431C4×C8—21no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8C22×D1311yescharacteristic
438C4×C8C22×D1311yescharacteristic
439C2×C13—41no—
440C2×C13—42no—
441C2×C13—42no—
442C2×C13#292911yescharacteristic
443C2×C13#294611yescharacteristic
444C2×C13#295711yescharacteristic
445D13—81no—
446C24—21no—
447C2×Q8—131no—
448C2×D4—22no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—131no—
452C2×D4—261no—
453C2×D4C2×C4×D1311yescharacteristic
454C2×D4C2×C4×D1311yescharacteristic
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—81no—
461C22×C4—81no—
462C22×C4—261no—
463C22×C4C2×C4×D1311yescharacteristic
464C22×C4#612711yescharacteristic
465C22×C4C2×C22⋊D1311yescharacteristic
466SD16—262no—
467SD16—262no—
468D8—262no—
469D8—262no—
470M16—1041no—
471M16—1041no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—131no—
479C2×C8—131no—
480C2×C8—131no—
481C2×C8—131no—
482C2×C8—261no—
483C2×C8—261no—
484C2×C8—261no—
485C2×C8—261no—
486C2×C8—1041no—
487C2×C8C2×C22⋊D1311yescharacteristic
488C2×C8C2×C22⋊D1311yescharacteristic
489C2×C8C2×C22⋊D1311yescharacteristic
490C2×C8C2×C22⋊D1311yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—131no—
493C4⋊C4—131no—
494C4⋊C4—261no—
495C4⋊C4—261no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4C2×C4×D1311yescharacteristic
499C4⋊C4C2×C4×D1311yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—261no—
505C22⋊C4—261no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C42—261no—
510C42C2×C4×D1311yescharacteristic
511C42#612711yescharacteristic
512C42C2×C22⋊D1311yescharacteristic
513C42C23×D1311yescharacteristic
514C13#1791811yescharacteristic, complemented, Sylow
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—261no—
521C23C4×C22⋊D1311yescharacteristic
522Q8—261no—
523Q8—261no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—261no—
528D4—261no—
529D4—1041no—
530D4#8815512yes—
531D4#8815512yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—261no—
547C2×C4—261no—
548C2×C4—261no—
549C2×C4—521no—
550C2×C4—521no—
551C2×C4C4×C22⋊D1311yescharacteristic
552C2×C4C4×C22⋊D1311yescharacteristic
553C2×C4C4×C22⋊D1311yescharacteristic
554C2×C4C22×C4×D1311yescharacteristic
555C2×C4C2×#612711yescharacteristic
556C2×C4C22×C22⋊D1311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—261no—
564C8—261no—
565C8—261no—
566C8—261no—
567C8—521no—
568C8—521no—
569C8—521no—
570C8—521no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—521no—
582C22—521no—
583C22—521no—
584C22C2×C4×C22⋊D1311yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—521no—
592C4—521no—
593C4—521no—
594C4C2×#8815511yescharacteristic
595C4C2×#8815511yescharacteristic
596C4#1171954011yescharacteristic
597C4#1171954111yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—1041no—
602C2#1312353011yescharacteristic
603C2#1312366811yescharacteristic
604C2#1312375111yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2972C2
socleC22×C13C2×C4×D4
prime radical#11718878C4
cosocleC42×C13C24
hypercenter#2972D13
hypocenterC13#17918
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #13123987C2semidirect
3. #13113700C2semidirect
4. #13113693C2semidirect
5. #13113672C2semidirect
6. #13113665C2semidirect
7. #13113658C2semidirect
8. #13113648C2semidirect
9. C8×#6105C2semidirect
10. C8×#6104C2semidirect
11. #13113624C2semidirect
12. #13113261C2semidirect
13. #13113242C2semidirect
14. #13113136C2semidirect
15. C13×#2972C2semidirect
47. #11718349C22semidirect
48. C8×D52C22semidirect
49. #11718340C22semidirect
50. C8×Dic26C22semidirect
55. #11718076C22semidirect
56. #11718076C22semidirect
57. #11718075C22semidirect
58. #11718075C22semidirect
59. #11718072C22semidirect
60. #11718072C22semidirect
61. #11718071C22semidirect
62. #11718071C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
215. #2972D13semidirect
514. C13#17918semidirect

Maximal subgroups

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

subgroupindex
#131248832
#131239872
#131137002
#131136932
#131136722
#131136652
#131136582
#131136482
C8×#61052
C8×#61042
#131136242
#131132612
#131132422
#131131362
C13×#29722
#1791813