Finite Group Databasebeta

← #15834149

Subgroups — #15834149

Order 3328.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124883C211yesmaximal, characteristic
2#13123998C211yesmaximal, characteristic, complemented
3#13113748C211yesmaximal, characteristic, complemented
4#13113738C211yesmaximal, characteristic, complemented
5#13113677C211yesmaximal, characteristic, complemented
6#13113672C211yesmaximal, characteristic, complemented
7#13113665C211yesmaximal, characteristic, complemented
8#13113663C211yesmaximal, characteristic, complemented
9#13113658C211yesmaximal, characteristic, complemented
10#13113648C211yesmaximal, characteristic, complemented
11#13113622C211yesmaximal, characteristic, complemented
12#13113294C211yesmaximal, characteristic, complemented
13C2×D4⋊#1055C211yesmaximal, characteristic, complemented
14#13113129C211yesmaximal, characteristic, complemented
15C13×#2974C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17#11719184C2211yescharacteristic
18C13×#436C2211yescharacteristic
19C13×#436C2211yescharacteristic
20C13×#435—21no—
21C13×#435—21no—
22C8×D4×C13C2211yescharacteristic
23C8×D4×C13C2211yescharacteristic
24C13×#432C2211yescharacteristic
25C13×#431C2211yescharacteristic
26C13×#407—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
41C2×C4⋊#1055C2211yescharacteristic
42C2×C4×#1055C2211yescharacteristic
43#11718501—21no—
44#11718500—21no—
45#11718391—21no—
46#11718386—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#11718047C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66#11718046C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C2×C13×M16—21no—
70C2×C13×M16—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
90C22×#1055—21no—
91C22×#1055—21no—
92C2×#6094—21no—
93C2×C8×D13—21no—
94#88130—21no—
95#88129C2×C411yescharacteristic
96C4×D52C2311yescharacteristic
97#88126—21no—
98#88124C2×C411yescharacteristic
99C4×Dic26C2311yescharacteristic
100C13×C4⋊C8D411yescharacteristic
101C13×C4⋊C8D411yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C4⋊C8C2311yescharacteristic
104C13×C22⋊C8—21no—
105C13×C22⋊C8—21no—
106C13×C22⋊C8—21no—
107C13×C22⋊C8—21no—
108C13×C22⋊C8—21no—
109C13×C22⋊C8D411yescharacteristic
110C13×C22⋊C8D411yescharacteristic
111C13×#97—21no—
112C4×C8×C13C2311yescharacteristic
113C4×C8×C13C2311yescharacteristic
114#88072C2×C411yescharacteristic
115#88072C2×C411yescharacteristic
116#88072C2×C411yescharacteristic
117#88072C2×C411yescharacteristic
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⋊#1055C2×C411yescharacteristic
136C4⋊#1055C2×C411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139C4×#1055—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18020—131nomaximal, Sylow
145C24×C13—21no—
146C2×D4×C13—22no—
147C2×D4×C13—21no—
148C2×D4×C13—41no—
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
165C13×M16—81no—
166C13×M16—81no—
167C2×C8×C13—21no—
168C2×C8×C13—21no—
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—41no—
189#6104—22no—
190#6104—41no—
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—
202C2×#1055—21no—
203C2×#1055—21no—
204C2×#1055—21no—
205C2×#1055—21no—
206C2×#1055—42no—
207C2×#1055—81no—
208C2×#1055C22×C411yescharacteristic
209C2×#1055C22×C411yescharacteristic
210C2×#1055C22×C411yescharacteristic
211C2×#1055C22×C411yescharacteristic
212#6094—81no—
213C8×D13—81no—
214#3105—131no—
215#2994—131no—
216#2974D1311yescharacteristic, complemented
217#1594—131no—
218#1592—131no—
219#1583—131no—
220#1582—131no—
221#1581—131no—
222#1581—131no—
223#1580—131no—
224SD16⋊C8—131no—
225#1573—131no—
226#1494—131no—
227C2×D4⋊C8—131no—
228#1452—131no—
229C23×C13—21no—
230C23×C13—21no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13—81no—
234C23×C13C4×D411yescharacteristic
235C22×D13—21no—
236D4×C13—21no—
237D4×C13—21no—
238D4×C13—21no—
239D4×C13—42no—
240D4×C13#13112yes—
241C2×C4×C13—22no—
242C2×C4×C13—21no—
243C2×C4×C13—21no—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—41no—
249C2×C4×C13—41no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—81no—
253C2×C4×C13—81no—
254C2×C4×C13—81no—
255C2×C4×C13C4×D411yescharacteristic
256C2×C4×C13C4×D411yescharacteristic
257C2×C4×C13C4×D411yescharacteristic
258C2×C4×C13C23×C411yescharacteristic
259C2×C4×C13C22×D411yescharacteristic
260C2×C4×C13C2×#4111yescharacteristic
261C22⋊D13—42no—
262C2×Dic13—21no—
263C2×Dic13—21no—
264C2×Dic13—21no—
265D52—21no—
266D52—21no—
267C4×D13—41no—
268C4×D13—41no—
269Dic26—21no—
270Dic26—21no—
271C8×C13—21no—
272C8×C13—21no—
273C8×C13—21no—
274C8×C13—21no—
275C8×C13—41no—
276C8×C13—41no—
277#1055—21no—
278#1055—21no—
279#1055—21no—
280#1055—21no—
281#1055—41no—
282#1055—41no—
283#1055—41no—
284#1055—41no—
285#529—131no—
286C2×C4×D4C2×D1311yescharacteristic
287#484—131no—
288#481—131no—
289#478—131no—
290#478—131no—
291#463—131no—
292#463—131no—
293#450—131no—
294#447—131no—
295#446—131no—
296C8×Q8—131no—
297C4×SD16—131no—
298C4×SD16—131no—
299C4×D8—131no—
300C4×D8—131no—
301#436—131no—
302#436C2×D1311yescharacteristic
303#436C2×D1311yescharacteristic
304#435—21no—
305#435—21no—
306#435—261no—
307C8×D4—131no—
308C8×D4—261no—
309C8×D4C2×D1311yescharacteristic
310C8×D4C2×D1311yescharacteristic
311#433—261no—
312#432C2×D1311yescharacteristic
313#431—131no—
314#431C2×D1311yescharacteristic
315#424—261no—
316C2×C4⋊C8—131no—
317#407—21no—
318C2×C22⋊C8—21no—
319C2×C4×C8—131no—
320#335—131no—
321#335—131no—
322#334—131no—
323#334—131no—
324Q8⋊C8—131no—
325Q8⋊C8—131no—
326D4⋊C8—131no—
327D4⋊C8—131no—
328D4⋊C8—131no—
329D4⋊C8—131no—
330D4⋊C8—131no—
331D4⋊C8—131no—
332#322—131no—
333#322—131no—
334#322—131no—
335#322—131no—
336C22×C13—21no—
337C22×C13—21no—
338C22×C13—22no—
339C22×C13—41no—
340C22×C13—41no—
341C22×C13—41no—
342C22×C13—41no—
343C22×C13—41no—
344C22×C13—84no—
345C22×C13#44412yes—
346C22×C13C2×C4×D411yescharacteristic
347C2×D13—41no—
348C2×D13—41no—
349C2×D13—41no—
350C4×C13—21no—
351C4×C13—21no—
352C4×C13—21no—
353C4×C13—21no—
354C4×C13—41no—
355C4×C13—41no—
356C4×C13C2×#13111yescharacteristic
357C4×C13#56811yescharacteristic
358C4×C13#57611yescharacteristic
359C4×C13#57711yescharacteristic
360Dic13—41no—
361Dic13—41no—
362Dic13—41no—
363C22×D4C4×D1311yescharacteristic
364C23×C4—21no—
365C2×SD16—131no—
366C2×SD16—131no—
367C2×D8—131no—
368C2×D8—131no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—261no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—261no—
375C22×C8—261no—
376C22×C8—261no—
377#126—261no—
378#125—131no—
379#124—131no—
380#123—261no—
381C22⋊Q8—131no—
382#121—131no—
383C4×Q8—131no—
384C4×D4—21no—
385C4×D4—21no—
386C4×D4—131no—
387C4×D4—261no—
388C4×D4C4×D1311yescharacteristic
389C4×D4C4×D1311yescharacteristic
390C4×D4C22×D1311yescharacteristic
391C4×D4C22×D1311yescharacteristic
392#117—261no—
393C2×C4⋊C4C4×D1311yescharacteristic
394C2×C22⋊C4—21no—
395C2×C42C22×D1311yescharacteristic
396#107—131no—
397#107—131no—
398#106—131no—
399#106—131no—
400C4⋊C8—131no—
401C4⋊C8—131no—
402C4⋊C8—131no—
403C4⋊C8—131no—
404C4⋊C8—261no—
405C4⋊C8—261no—
406C4⋊C8—261no—
407C4⋊C8C22⋊D1311yescharacteristic
408C4⋊C8C22⋊D1311yescharacteristic
409C4⋊C8C22×D1311yescharacteristic
410C4⋊C8C22×D1311yescharacteristic
411#103—131no—
412#103—131no—
413#102—131no—
414#102—131no—
415#102—131no—
416#102—131no—
417#102—131no—
418#102—131no—
419C22⋊C8—21no—
420C22⋊C8—21no—
421C22⋊C8—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8—131no—
425C22⋊C8—131no—
426C22⋊C8—261no—
427C22⋊C8—261no—
428C22⋊C8C22⋊D1311yescharacteristic
429C22⋊C8C22⋊D1311yescharacteristic
430#97—21no—
431#97—261no—
432C4×C8—131no—
433C4×C8—131no—
434C4×C8—131no—
435C4×C8—131no—
436C4×C8—261no—
437C4×C8—261no—
438C4×C8C22×D1311yescharacteristic
439C4×C8C22×D1311yescharacteristic
440C2×C13—22no—
441C2×C13—42no—
442C2×C13—81no—
443C2×C13#293311yescharacteristic
444C2×C13#294611yescharacteristic
445C2×C13C2×#44411yescharacteristic
446D13—81no—
447C24—21no—
448C2×Q8—131no—
449C2×D4—22no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4—131no—
453C2×D4—261no—
454C2×D4C2×C4×D1311yescharacteristic
455C2×D4C2×C4×D1311yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—261no—
464C22×C4C2×C4×D1311yescharacteristic
465C22×C4#612711yescharacteristic
466C22×C4C2×C22⋊D1311yescharacteristic
467SD16—262no—
468SD16—521no—
469D8—262no—
470D8—521no—
471M16—81no—
472M16—81no—
473M16—1041no—
474C2×C8—21no—
475C2×C8—21no—
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—522no—
487C2×C8—1041no—
488C2×C8—1041no—
489C2×C8C2×C22⋊D1311yescharacteristic
490C2×C8C2×C22⋊D1311yescharacteristic
491C2×C8C2×C22⋊D1311yescharacteristic
492C2×C8C2×C22⋊D1311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—131no—
495C4⋊C4—131no—
496C4⋊C4—261no—
497C4⋊C4—261no—
498C4⋊C4—261no—
499C4⋊C4—261no—
500C4⋊C4C2×C4×D1311yescharacteristic
501C4⋊C4C2×C4×D1311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—261no—
507C22⋊C4—261no—
508C22⋊C4—261no—
509C22⋊C4—261no—
510C22⋊C4—261no—
511C42—261no—
512C42C2×C4×D1311yescharacteristic
513C42#612711yescharacteristic
514C42C2×C22⋊D1311yescharacteristic
515C42C23×D1311yescharacteristic
516C13#1802011yescharacteristic, complemented, Sylow
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—261no—
523C23C4×C22⋊D1311yescharacteristic
524Q8—261no—
525Q8—261no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—261no—
531D4—261no—
532D4—522no—
533D4#8816112yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—261no—
549C2×C4—261no—
550C2×C4—261no—
551C2×C4—521no—
552C2×C4—521no—
553C2×C4C4×C22⋊D1311yescharacteristic
554C2×C4C4×C22⋊D1311yescharacteristic
555C2×C4C4×C22⋊D1311yescharacteristic
556C2×C4C22×C4×D1311yescharacteristic
557C2×C4C2×#612711yescharacteristic
558C2×C4C22×C22⋊D1311yescharacteristic
559C8—21no—
560C8—21no—
561C8—21no—
562C8—21no—
563C8—41no—
564C8—41no—
565C8—261no—
566C8—261no—
567C8—261no—
568C8—261no—
569C8—521no—
570C8—521no—
571C8—521no—
572C8—521no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—521no—
583C22—521no—
584C22—521no—
585C22#1171880612yes—
586C22C2×C4×C22⋊D1311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—521no—
594C4—521no—
595C4—521no—
596C4C2×#8816111yescharacteristic
597C4#1171945011yescharacteristic
598C4#1171954011yescharacteristic
599C4#1171954111yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—1041no—
604C2#1312356111yescharacteristic
605C2#1312366811yescharacteristic
606C2C2×#1171880611yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#2974C2
socleC22×C13C2×C4×D4
prime radical#11718878C4
cosocleC42×C13C24
hypercenter#2974D13
hypocenterC13#18020
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2974

Complements

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

NH ≅ G/Ntype
2. #13123998C2semidirect
3. #13113748C2semidirect
4. #13113738C2semidirect
5. #13113677C2semidirect
6. #13113672C2semidirect
7. #13113665C2semidirect
8. #13113663C2semidirect
9. #13113658C2semidirect
10. #13113648C2semidirect
11. #13113622C2semidirect
12. #13113294C2semidirect
13. C2×D4⋊#1055C2semidirect
14. #13113129C2semidirect
15. C13×#2974C2semidirect
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. #11718047C22semidirect
65. #11718046C22semidirect
66. #11718046C22semidirect
216. #2974D13semidirect
516. C13#18020semidirect

Maximal subgroups

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

subgroupindex
#131248832
#131239982
#131137482
#131137382
#131136772
#131136722
#131136652
#131136632
#131136582
#131136482
#131136222
#131132942
C2×D4⋊#10552
#131131292
C13×#29742
#1802013