Finite Group Databasebeta

← #15834217

Subgroups — #15834217

Order 3328.

656 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13124836C211yesmaximal, characteristic
2#13123902C211yesmaximal, characteristic, complemented
3#13123871C211yesmaximal, characteristic, complemented
4#13113747C211yesmaximal, characteristic, complemented
5#13113718C211yesmaximal, characteristic, complemented
6#13113703C211yesmaximal, characteristic, complemented
7#13113697C211yesmaximal, characteristic, complemented
8#13113668C211yesmaximal, characteristic, complemented
9#13113662C211yesmaximal, characteristic, complemented
10#13113657C211yesmaximal, characteristic, complemented
11#13113628C211yesmaximal, characteristic, complemented
12#13113614C211yesmaximal, characteristic, complemented
13#13113306C211yesmaximal, characteristic, complemented
14#13113136C211yesmaximal, characteristic, complemented
15C13×#1478C211yesmaximal, characteristic, complemented
16C2×C4×D4×C13C2211yescharacteristic
17#11719182C2211yescharacteristic
18C13×#431C2211yescharacteristic
19C13×#431C2211yescharacteristic
20#11718878C411yescharacteristic
21#11718878C411yescharacteristic
22#11718868—21no—
23C2×C22⋊#1055—21no—
24#11718676C411yescharacteristic
25#11718676C411yescharacteristic
26C4×#6104C2211yescharacteristic
27C4×#6104C2211yescharacteristic
28C4×#6104C2211yescharacteristic
29C4×#6104C2211yescharacteristic
30#11718673C2211yescharacteristic
31#11718673C2211yescharacteristic
32#11718672—21no—
33#11718672—21no—
34D4×#1055C2211yescharacteristic
35D4×#1055C2211yescharacteristic
36#11718668C411yescharacteristic
37#11718668C411yescharacteristic
38#11718628C411yescharacteristic
39#11718628C411yescharacteristic
40#11718587C2211yescharacteristic
41#11718586C2211yescharacteristic
42#11718586C2211yescharacteristic
43#11718499C2211yescharacteristic, complemented
44#11718499C2211yescharacteristic, complemented
45#11718495C2211yescharacteristic, complemented
46#11718495C2211yescharacteristic, complemented
47#11718388—21no—
48#11718388—21no—
49#11718349—21no—
50C8×D52—21no—
51C13×D4⋊C8C2211yescharacteristic
52C13×D4⋊C8C2211yescharacteristic
53C13×D4⋊C8C2211yescharacteristic
54C13×D4⋊C8C2211yescharacteristic
55#11718072C2211yescharacteristic, complemented
56#11718072C2211yescharacteristic, complemented
57#11718071C2211yescharacteristic, complemented
58#11718071C2211yescharacteristic, complemented
59#11718051C2211yescharacteristic, complemented
60#11718051C2211yescharacteristic, complemented
61#11718051C2211yescharacteristic, complemented
62#11718051C2211yescharacteristic, complemented
63#11718047C2211yescharacteristic, complemented
64#11718046C2211yescharacteristic, complemented
65#11718046C2211yescharacteristic, complemented
66C8×#1055C2211yescharacteristic, complemented
67C22×D4×C13C2×C411yescharacteristic
68C23×C4×C13—21no—
69C2×#6127—21no—
70C4×D4×C13—21no—
71C4×D4×C13—21no—
72C4×D4×C13C2×C411yescharacteristic
73C4×D4×C13C2×C411yescharacteristic
74C4×D4×C13C2311yescharacteristic
75C4×D4×C13C2311yescharacteristic
76C2×C13×C4⋊C4C2×C411yescharacteristic
77C2×C13×C22⋊C4—21no—
78C2×C42×C13C2311yescharacteristic
79C2×#6104C2×C411yescharacteristic
80C2×#6104C2×C411yescharacteristic
81C2×#6104C2×C411yescharacteristic
82C2×#6104C2×C411yescharacteristic
83#88184—21no—
84#88184C2×C411yescharacteristic
85#88184C2×C411yescharacteristic
86C2×#6099—21no—
87C2×#6099—21no—
88C22×#1055—21no—
89C22×#1055—21no—
90C2×#6094—21no—
91C2×#6094—21no—
92C2×C8×D13—21no—
93C2×C8×D13—21no—
94#88129—21no—
95#88128C2×C411yescharacteristic
96C4×D52—21no—
97C4×D52C2311yescharacteristic
98C4×D52C2311yescharacteristic
99#88123C2×C411yescharacteristic
100C13×C4⋊C8—21no—
101C13×C4⋊C8C2311yescharacteristic
102C13×C4⋊C8C2311yescharacteristic
103C13×C22⋊C8—21no—
104C13×C22⋊C8—21no—
105C4×C8×C13—21no—
106C4×C8×C13C2311yescharacteristic
107C4×C8×C13C2311yescharacteristic
108#88072C2×C411yescharacteristic
109#88072C2×C411yescharacteristic
110#88072C2×C411yescharacteristic
111#88072C2×C411yescharacteristic
112C22⋊#1055—21no—
113C22⋊#1055—21no—
114C22⋊#1055—21no—
115C22⋊#1055—21no—
116C22⋊#1055—21no—
117C22⋊#1055C2×C411yescharacteristic
118C22⋊#1055C2×C411yescharacteristic
119C22⋊#1055D411yescharacteristic
120C22⋊#1055D411yescharacteristic
121#88060—21no—
122#88060—21no—
123#88060—21no—
124#88060—21no—
125#88049C2×C411yescharacteristic
126#88049C2×C411yescharacteristic
127#88049C2×C411yescharacteristic
128#88049C2×C411yescharacteristic
129#88047C2×C411yescharacteristic
130#88047C2×C411yescharacteristic
131#88047C2×C411yescharacteristic
132#88047C2×C411yescharacteristic
133C4⋊#1055C2×C411yescharacteristic
134C4⋊#1055C2×C411yescharacteristic
135C4⋊#1055D411yescharacteristic
136C4⋊#1055D411yescharacteristic
137C4⋊#1055C2311yescharacteristic
138C4⋊#1055C2311yescharacteristic
139#88043—21no—
140C4×#1055C2311yescharacteristic
141C4×#1055C2311yescharacteristic
142C4×#1055C2311yescharacteristic
143C4×#1055C2311yescharacteristic
144#18026—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×C22⋊D13—21no—
163#6127—81no—
164#6127—81no—
165C2×D52—21no—
166C2×D52—21no—
167C2×D52C22×C411yescharacteristic
168C2×D52C22×C411yescharacteristic
169C2×C4×D13—21no—
170C2×C4×D13—21no—
171C2×Dic26—21no—
172C2×C8×C13—21no—
173C2×C8×C13—21no—
174C2×C8×C13—21no—
175C2×C8×C13—21no—
176C13×C4⋊C4—21no—
177C13×C4⋊C4C22×C411yescharacteristic
178C13×C4⋊C4C22×C411yescharacteristic
179C13×C22⋊C4—21no—
180C13×C22⋊C4—21no—
181C13×C22⋊C4—21no—
182C13×C22⋊C4—21no—
183C42×C13C22×C411yescharacteristic
184C42×C13C2×D411yescharacteristic
185C42×C13#4111yescharacteristic
186C42×C13C2411yescharacteristic
187#6104—22no—
188#6104—22no—
189#6104—41no—
190#6104—41no—
191#6103—21no—
192#6103—21no—
193#6103—21no—
194#6103—21no—
195C4⋊Dic13—21no—
196C4⋊Dic13C22×C411yescharacteristic
197C4⋊Dic13C22×C411yescharacteristic
198#6099—81no—
199#6099—81no—
200C2×#1055—21no—
201C2×#1055—21no—
202C2×#1055—81no—
203C2×#1055—81no—
204C2×#1055C22×C411yescharacteristic
205C2×#1055C22×C411yescharacteristic
206C2×#1055C22×C411yescharacteristic
207C2×#1055C22×C411yescharacteristic
208C2×#1055C2×D411yescharacteristic
209C2×#1055C2×D411yescharacteristic
210C2×#1055C2×D411yescharacteristic
211C2×#1055C2×D411yescharacteristic
212#6094—81no—
213#6094—81no—
214C8×D13—81no—
215C8×D13—81no—
216#3100—131no—
217#2979—131no—
218#2974—131no—
219#1594—131no—
220#1589—131no—
221#1586—131no—
222#1586—131no—
223#1581—131no—
224#1581—131no—
225#1580—131no—
226C8×D8—131no—
227#1572—131no—
228#1496—131no—
229#1478D1311yescharacteristic, complemented
230#1454—131no—
231C23×C13—21no—
232C23×C13—21no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—81no—
236C23×C13C4×D411yescharacteristic
237C22×D13—21no—
238C22×D13—21no—
239D4×C13—21no—
240D4×C13—21no—
241D4×C13—21no—
242D4×C13—42no—
243D4×C13#13112yes—
244C2×C4×C13—21no—
245C2×C4×C13—21no—
246C2×C4×C13—21no—
247C2×C4×C13—21no—
248C2×C4×C13—21no—
249C2×C4×C13—21no—
250C2×C4×C13—41no—
251C2×C4×C13—41no—
252C2×C4×C13—41no—
253C2×C4×C13—41no—
254C2×C4×C13—41no—
255C2×C4×C13—81no—
256C2×C4×C13—81no—
257C2×C4×C13—81no—
258C2×C4×C13C4×D411yescharacteristic
259C2×C4×C13C4×D411yescharacteristic
260C2×C4×C13C4×D411yescharacteristic
261C2×C4×C13C23×C411yescharacteristic
262C2×C4×C13C22×D411yescharacteristic
263C2×C4×C13C2×#4111yescharacteristic
264C22⋊D13—81no—
265C22⋊D13—81no—
266C2×Dic13—21no—
267C2×Dic13—21no—
268D52—21no—
269D52—21no—
270D52—21no—
271D52—21no—
272D52—42no—
273D52—81no—
274C4×D13—41no—
275C4×D13—41no—
276C4×D13—41no—
277C4×D13—41no—
278Dic26—81no—
279C8×C13—41no—
280C8×C13—41no—
281C8×C13—41no—
282C8×C13—41no—
283#1055—21no—
284#1055—21no—
285#1055—21no—
286#1055—21no—
287#1055—21no—
288#1055—21no—
289#1055—21no—
290#1055—21no—
291#1055—41no—
292#1055—41no—
293#532—131no—
294C2×C4×D4C2×D1311yescharacteristic
295#480—131no—
296#480—131no—
297#474—131no—
298#474—131no—
299#459—131no—
300#459—131no—
301#447—131no—
302#447—131no—
303C4×D8—131no—
304C4×D8—131no—
305C4×D8—131no—
306C4×D8—131no—
307#436—131no—
308#436—131no—
309#436—131no—
310#436—131no—
311#436—261no—
312#435—261no—
313#435—261no—
314C8×D4—131no—
315C8×D4—131no—
316C8×D4—131no—
317C8×D4—131no—
318C8×D4—261no—
319#432—131no—
320#431—131no—
321#431—131no—
322#431C2×D1311yescharacteristic
323#431C2×D1311yescharacteristic
324#408—261no—
325#408—261no—
326#407—261no—
327C2×C22⋊C8—261no—
328#335—131no—
329#335—131no—
330#334—131no—
331#334—131no—
332D4⋊C8—131no—
333D4⋊C8—131no—
334D4⋊C8—131no—
335D4⋊C8—131no—
336D4⋊C8C2×D1311yescharacteristic
337D4⋊C8C2×D1311yescharacteristic
338D4⋊C8C2×D1311yescharacteristic
339D4⋊C8C2×D1311yescharacteristic
340#322—131no—
341#322—131no—
342#322—131no—
343C82—131no—
344C22×C13—21no—
345C22×C13—22no—
346C22×C13—21no—
347C22×C13—21no—
348C22×C13—41no—
349C22×C13—41no—
350C22×C13—41no—
351C22×C13—41no—
352C22×C13—41no—
353C22×C13—84no—
354C22×C13C2×C4×D411yescharacteristic
355C2×D13—41no—
356C2×D13—41no—
357C2×D13—41no—
358C2×D13—41no—
359C2×D13—41no—
360C2×D13—41no—
361C4×C13—21no—
362C4×C13—21no—
363C4×C13—21no—
364C4×C13—21no—
365C4×C13—41no—
366C4×C13—41no—
367C4×C13C2×#13111yescharacteristic
368C4×C13#56811yescharacteristic
369C4×C13#57611yescharacteristic
370C4×C13#57611yescharacteristic
371Dic13—41no—
372Dic13—41no—
373C2×#41—261no—
374C22×D4C4×D1311yescharacteristic
375C23×C4—21no—
376C2×D8—131no—
377C2×D8—131no—
378C2×D8—131no—
379C2×D8—131no—
380C2×M16—261no—
381C2×M16—261no—
382C2×M16—261no—
383C2×M16—261no—
384C22×C8—261no—
385C22×C8—261no—
386C22×C8—261no—
387C22×C8—261no—
388C4⋊Q8—131no—
389#127—131no—
390#124—261no—
391#121—131no—
392#121—131no—
393#121—261no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—131no—
397C4×D4—131no—
398C4×D4—261no—
399C4×D4C4×D1311yescharacteristic
400C4×D4C4×D1311yescharacteristic
401C4×D4C22×D1311yescharacteristic
402C4×D4C22×D1311yescharacteristic
403C2×C4⋊C4C4×D1311yescharacteristic
404C2×C22⋊C4—21no—
405C2×C42C22×D1311yescharacteristic
406#107—131no—
407#107—131no—
408#107—131no—
409#107—131no—
410C4⋊C8—21no—
411C4⋊C8—131no—
412C4⋊C8—131no—
413C4⋊C8—131no—
414C4⋊C8—131no—
415C4⋊C8—131no—
416C4⋊C8—131no—
417C4⋊C8C22×D1311yescharacteristic
418C4⋊C8C22×D1311yescharacteristic
419#102—131no—
420#102—131no—
421#102—131no—
422#102—131no—
423#102—131no—
424#102—131no—
425#102—131no—
426#102—131no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—131no—
430C22⋊C8—131no—
431C22⋊C8—131no—
432C22⋊C8—131no—
433C22⋊C8—261no—
434C22⋊C8—261no—
435C22⋊C8—261no—
436C22⋊C8—261no—
437C22⋊C8—261no—
438C22⋊C8—261no—
439C22⋊C8—261no—
440C22⋊C8—261no—
441C22⋊C8—261no—
442#97—261no—
443C4×C8—21no—
444C4×C8—131no—
445C4×C8—131no—
446C4×C8—131no—
447C4×C8—131no—
448C4×C8C22×D1311yescharacteristic
449C4×C8C22×D1311yescharacteristic
450C2×C13—41no—
451C2×C13—42no—
452C2×C13—81no—
453C2×C13#293311yescharacteristic
454C2×C13#294811yescharacteristic
455C2×C13#295511yescharacteristic
456D13—81no—
457D13—81no—
458C24—21no—
459#41—1041no—
460#41—1041no—
461C2×Q8—261no—
462C2×D4—22no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—131no—
466C2×D4—131no—
467C2×D4—261no—
468C2×D4—261no—
469C2×D4—261no—
470C2×D4—261no—
471C2×D4C2×C4×D1311yescharacteristic
472C2×D4C2×C4×D1311yescharacteristic
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—81no—
479C22×C4—81no—
480C22×C4—261no—
481C22×C4—261no—
482C22×C4C2×C4×D1311yescharacteristic
483C22×C4D4×D1311yescharacteristic
484C22×C4#612911yescharacteristic
485D8—262no—
486D8—262no—
487D8—521no—
488D8—521no—
489M16—1041no—
490M16—1041no—
491M16—1041no—
492M16—1041no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—131no—
498C2×C8—131no—
499C2×C8—131no—
500C2×C8—131no—
501C2×C8—131no—
502C2×C8—131no—
503C2×C8—131no—
504C2×C8—131no—
505C2×C8—261no—
506C2×C8—261no—
507C2×C8—1041no—
508C2×C8—1041no—
509C2×C8—1041no—
510C2×C8—1041no—
511C4⋊C4—21no—
512C4⋊C4—131no—
513C4⋊C4—131no—
514C4⋊C4—261no—
515C4⋊C4C2×C4×D1311yescharacteristic
516C4⋊C4C2×C4×D1311yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—261no—
522C22⋊C4—261no—
523C22⋊C4—261no—
524C22⋊C4—261no—
525C42C2×C4×D1311yescharacteristic
526C42D4×D1311yescharacteristic
527C42#612911yescharacteristic
528C42C23×D1311yescharacteristic
529C13#1802611yescharacteristic, complemented, Sylow
530C23—21no—
531C23—21no—
532C23—42no—
533C23—42no—
534C23—81no—
535C23—261no—
536C23—261no—
537C23#8813511yescharacteristic
538Q8—1041no—
539D4—21no—
540D4—21no—
541D4—21no—
542D4—42no—
543D4—261no—
544D4—261no—
545D4—261no—
546D4—261no—
547D4—522no—
548D4—1041no—
549D4—1041no—
550D4—1041no—
551D4#8815512yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—261no—
567C2×C4—261no—
568C2×C4—521no—
569C2×C4—521no—
570C2×C4—521no—
571C2×C4—521no—
572C2×C4#8813511yescharacteristic
573C2×C4#8813511yescharacteristic
574C2×C4#8813511yescharacteristic
575C2×C4C22×C4×D1311yescharacteristic
576C2×C4C2×D4×D1311yescharacteristic
577C2×C4C2×#612911yescharacteristic
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—261no—
583C8—261no—
584C8—261no—
585C8—261no—
586C8—261no—
587C8—261no—
588C8—261no—
589C8—261no—
590C8—521no—
591C8—521no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—84no—
602C22—521no—
603C22—521no—
604C22—521no—
605C22—521no—
606C22—521no—
607C22—521no—
608C22C2×#8813511yescharacteristic
609C4—21no—
610C4—21no—
611C4—21no—
612C4—21no—
613C4—41no—
614C4—41no—
615C4—521no—
616C4—521no—
617C4C2×#8815511yescharacteristic
618C4#1171945011yescharacteristic
619C4#1171947911yescharacteristic
620C4#1171947911yescharacteristic
621C2—41no—
622C2—42no—
623C2—81no—
624C2—1041no—
625C2—1041no—
626C2#1312355711yescharacteristic
627C2#1312368411yescharacteristic
628C2#1312373511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D13
commutatorC2×C4×C13C23×C4
FrattiniC42C23×D13
FittingC13×#1478C2
socleC22×C13C2×C4×D4
prime radical#13124836C2
cosocleC42×C13C24
hypercenter#1478D13
hypocenterC13#18026
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1478

Complements

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

NH ≅ G/Ntype
2. #13123902C2semidirect
3. #13123871C2semidirect
4. #13113747C2semidirect
5. #13113718C2semidirect
6. #13113703C2semidirect
7. #13113697C2semidirect
8. #13113668C2semidirect
9. #13113662C2semidirect
10. #13113657C2semidirect
11. #13113628C2semidirect
12. #13113614C2semidirect
13. #13113306C2semidirect
14. #13113136C2semidirect
15. C13×#1478C2semidirect
43. #11718499C22semidirect
44. #11718499C22semidirect
45. #11718495C22semidirect
46. #11718495C22semidirect
55. #11718072C22semidirect
56. #11718072C22semidirect
57. #11718071C22semidirect
58. #11718071C22semidirect
59. #11718051C22semidirect
60. #11718051C22semidirect
61. #11718051C22semidirect
62. #11718051C22semidirect
63. #11718047C22semidirect
64. #11718046C22semidirect
65. #11718046C22semidirect
66. C8×#1055C22semidirect
229. #1478D13semidirect
529. C13#18026semidirect

Maximal subgroups

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

subgroupindex
#131248362
#131239022
#131238712
#131137472
#131137182
#131137032
#131136972
#131136682
#131136622
#131136572
#131136282
#131136142
#131133062
#131131362
C13×#14782
#1802613