Finite Group Databasebeta

← C101×#20312 #38802463

Subgroups — C101×#20312 #38802463

Order 25856.

644 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3400C211yesmaximal, characteristic, complemented
2C101×#3373C211yesmaximal, characteristic, complemented
3C101×#3368C211yesmaximal, characteristic, complemented
4C101×#3278C211yesmaximal, characteristic, complemented
5C101×#1706C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1702C211yesmaximal, characteristic, complemented
8C101×#1686C211yesmaximal, characteristic, complemented
9C101×#1685C211yesmaximal, characteristic, complemented
10C101×#1649C211yesmaximal, characteristic, complemented
11C101×#1648C211yesmaximal, characteristic, complemented
12C101×#1621C211yesmaximal, characteristic
13C101×#1620C211yesmaximal, characteristic, complemented
14C101×#1591C211yesmaximal, characteristic, complemented
15C101×#1590C211yesmaximal, characteristic, complemented
16C2×#137×C101—21no—
17#559×C101C2211yescharacteristic
18#557×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20D4×Q8×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#497×C101—21no—
23#493×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#490×C101—21no—
27#489×C101—21no—
28#486×C101C2211yescharacteristic
29#486×C101C2211yescharacteristic
30#478×C101—21no—
31#476×C101—21no—
32#475×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#468×C101—21no—
35#464×C101—21no—
36#463×C101—21no—
37#462×C101C2211yescharacteristic
38#462×C101C2211yescharacteristic
39#461×C101—21no—
40#460×C101—21no—
41#460×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#460×C101C2211yescharacteristic
44#459×C101C2211yescharacteristic
45#452×C101—21no—
46#448×C101—21no—
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#446×C101C2211yescharacteristic
50#442×C101—21no—
51#440×C101—21no—
52#440×C101—21no—
53C4×Q16×C101C2211yescharacteristic
54C4×SD16×C101C2211yescharacteristic
55#436×C101C2211yescharacteristic
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C22×Q8×C101—21no—
69#137×C101—44no—
70C2×Q16×C101—21no—
71C2×Q16×C101—21no—
72C2×Q16×C101D411yescharacteristic
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101—21no—
78C2×SD16×C101—21no—
79C2×SD16×C101—21no—
80C2×SD16×C101D411yescharacteristic
81C2×D8×C101—21no—
82C2×D8×C101—41no—
83C2×M16×C101—21no—
84C4⋊Q8×C101—21no—
85C4⋊Q8×C101—21no—
86C4⋊Q8×C101C2311yescharacteristic
87C4⋊Q8×C101C2311yescharacteristic
88#127×C101—21no—
89#127×C101C2311yescharacteristic
90#127×C101C2311yescharacteristic
91#125×C101—21no—
92#125×C101—41no—
93#124×C101—21no—
94#124×C101—21no—
95#123×C101—41no—
96C22⋊Q8×C101—21no—
97C22⋊Q8×C101—41no—
98#121×C101—21no—
99#121×C101—41no—
100C4×Q8×C101—21no—
101C4×Q8×C101—21no—
102C4×Q8×C101C2311yescharacteristic
103C4×Q8×C101C2311yescharacteristic
104C4×Q8×C101C2311yescharacteristic
105C4×D4×C101—21no—
106C4×D4×C101—21no—
107C4×D4×C101—21no—
108C4×D4×C101—21no—
109C4×D4×C101C2311yescharacteristic
110#107×C101—21no—
111#107×C101—41no—
112#107×C101D411yescharacteristic
113#106×C101—21no—
114#106×C101D411yescharacteristic
115C4⋊C8×C101—21no—
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122#103×C101—21no—
123#103×C101—21no—
124#103×C101—21no—
125#103×C101D411yescharacteristic
126#103×C101D411yescharacteristic
127#103×C101D411yescharacteristic
128#102×C101—21no—
129#102×C101—21no—
130#102×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101—21no—
135#102×C101—21no—
136#102×C101—21no—
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139#97×C101—21no—
140#97×C101—21no—
141#97×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—81no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101—41no—
150C2×Q8×C101—42no—
151C2×Q8×C101—81no—
152C2×Q8×C101C2×D411yescharacteristic
153C2×Q8×C101C2×D411yescharacteristic
154C2×Q8×C101C2×D411yescharacteristic
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—41no—
162C2×D4×C101—41no—
163C2×D4×C101C2×D411yescharacteristic
164C22×C4×C101—21no—
165C22×C4×C101—41no—
166C22×C4×C101—41no—
167C22×C4×C101—41no—
168Q16×C101—22no—
169Q16×C101—42no—
170Q16×C101—81no—
171SD16×C101—41no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—42no—
175SD16×C101—42no—
176SD16×C101—81no—
177SD16×C101—81no—
178SD16×C101—81no—
179D8×C101—42no—
180D8×C101—82no—
181M16×C101—42no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101C2×D411yescharacteristic
188C2×C8×C101C2×D411yescharacteristic
189C2×C8×C101C2×D411yescharacteristic
190C2×C8×C101C2×D411yescharacteristic
191C4⋊C4×C101—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—21no—
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—41no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C22⋊C4×C101—21no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C42×C101—21no—
213C42×C101—21no—
214C42×C101—21no—
215C42×C101—41no—
216C42×C101C2411yescharacteristic
217C23×C101—21no—
218C23×C101—41no—
219C23×C101—41no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—21no—
226Q8×C101—41no—
227Q8×C101—41no—
228Q8×C101—41no—
229Q8×C101—41no—
230Q8×C101—82no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—41no—
241D4×C101—81no—
242D4×C101—81no—
243D4×C101—82no—
244D4×C101—161no—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
248C2×C4×C101—21no—
249C2×C4×C101—21no—
250C2×C4×C101—21no—
251C2×C4×C101—21no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101—82no—
257C2×C4×C101—82no—
258C2×C4×C101—161no—
259C2×C4×C101C22×D411yescharacteristic
260C2×C4×C101C22×D411yescharacteristic
261C2×C4×C101H(5,𝔽2)11yescharacteristic
262C8×C101—22no—
263C8×C101—21no—
264C8×C101—21no—
265C8×C101—21no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C8×C101AGL(1,ℤ/8)12yes—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—81no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101D4211yescharacteristic
281C4×C101—21no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—81no—
290C4×C101—81no—
291C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C101#57511yescharacteristic
293C4×C101#57611yescharacteristic
294C4×C101#57811yescharacteristic
295#20312C10111yesmaximal, characteristic, direct product factor, Sylow
296C2×C101—81no—
297C2×C101—161no—
298C2×C101—161no—
299C2×C101#327411yescharacteristic
300C2×C101#327711yescharacteristic
301C2×C101#329111yescharacteristic
302#3400C2×C10111yescharacteristic, complemented
303#3373C2×C10111yescharacteristic, complemented
304#3368C2×C10111yescharacteristic, complemented
305#3278C2×C10111yescharacteristic, complemented
306#1706C2×C10111yescharacteristic, complemented
307#1702C2×C10111yescharacteristic, complemented
308#1702C2×C10111yescharacteristic, complemented
309#1686C2×C10111yescharacteristic, complemented
310#1685C2×C10111yescharacteristic, complemented
311#1649C2×C10111yescharacteristic, complemented
312#1648C2×C10111yescharacteristic, complemented
313#1621C2×C10111yescharacteristic
314#1620C2×C10111yescharacteristic, complemented
315#1591C2×C10111yescharacteristic, complemented
316#1590C2×C10111yescharacteristic, complemented
317C101#2031211yescharacteristic, direct product factor, Sylow
318C2×#137—21no—
319#559C22×C10111yescharacteristic
320#557C22×C10111yescharacteristic
321#550C22×C10111yescharacteristic
322D4×Q8C22×C10111yescharacteristic
323#500C22×C10111yescharacteristic
324#497—21no—
325#493C22×C10111yescharacteristic
326#492C22×C10111yescharacteristic
327#492C22×C10111yescharacteristic
328#490—21no—
329#489—21no—
330#486C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic
332#478—21no—
333#476—21no—
334#475C22×C10111yescharacteristic
335#474C22×C10111yescharacteristic
336#468—21no—
337#464—21no—
338#463—21no—
339#462C22×C10111yescharacteristic
340#462C22×C10111yescharacteristic
341#461—21no—
342#460—21no—
343#460C22×C10111yescharacteristic
344#460C22×C10111yescharacteristic
345#460C22×C10111yescharacteristic
346#459C22×C10111yescharacteristic
347#452—21no—
348#448—21no—
349#446C22×C10111yescharacteristic
350#446C22×C10111yescharacteristic
351#446C22×C10111yescharacteristic
352#442—21no—
353#440—21no—
354#440—21no—
355C4×Q16C22×C10111yescharacteristic
356C4×SD16C22×C10111yescharacteristic
357#436C22×C10111yescharacteristic
358#335C22×C10111yescharacteristic
359#334C22×C10111yescharacteristic
360#332C22×C10111yescharacteristic
361#332C22×C10111yescharacteristic
362#331C22×C10111yescharacteristic
363#331C22×C10111yescharacteristic
364Q8⋊C8C22×C10111yescharacteristic
365Q8⋊C8C22×C10111yescharacteristic
366Q8⋊C8C22×C10111yescharacteristic
367D4⋊C8C22×C10111yescharacteristic
368C82C22×C10111yescharacteristic
369C2×#41—21no—
370C22×Q8—21no—
371#137—44no—
372C2×Q16—21no—
373C2×Q16—21no—
374C2×Q16D4×C10111yescharacteristic
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16D4×C10111yescharacteristic
383C2×D8—21no—
384C2×D8—41no—
385C2×M16—21no—
386C4⋊Q8—21no—
387C4⋊Q8—21no—
388C4⋊Q8C23×C10111yescharacteristic
389C4⋊Q8C23×C10111yescharacteristic
390#127—21no—
391#127C23×C10111yescharacteristic
392#127C23×C10111yescharacteristic
393#125—21no—
394#125—41no—
395#124—21no—
396#124—21no—
397#123—41no—
398C22⋊Q8—21no—
399C22⋊Q8—41no—
400#121—21no—
401#121—41no—
402C4×Q8—21no—
403C4×Q8—21no—
404C4×Q8C23×C10111yescharacteristic
405C4×Q8C23×C10111yescharacteristic
406C4×Q8C23×C10111yescharacteristic
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—21no—
410C4×D4—21no—
411C4×D4C23×C10111yescharacteristic
412#107—21no—
413#107—41no—
414#107D4×C10111yescharacteristic
415#106—21no—
416#106D4×C10111yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8C23×C10111yescharacteristic
421C4⋊C8C23×C10111yescharacteristic
422C4⋊C8C23×C10111yescharacteristic
423C4⋊C8C23×C10111yescharacteristic
424#103—21no—
425#103—21no—
426#103—21no—
427#103D4×C10111yescharacteristic
428#103D4×C10111yescharacteristic
429#103D4×C10111yescharacteristic
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102D4×C10111yescharacteristic
440C22⋊C8—21no—
441#97—21no—
442#97—21no—
443#97—21no—
444C4×C8C23×C10111yescharacteristic
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447#41—42no—
448#41—81no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—41no—
452C2×Q8—42no—
453C2×Q8—81no—
454C2×Q8C2×D4×C10111yescharacteristic
455C2×Q8C2×D4×C10111yescharacteristic
456C2×Q8C2×D4×C10111yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C2×D4×C10111yescharacteristic
466C22×C4—21no—
467C22×C4—41no—
468C22×C4—41no—
469C22×C4—41no—
470Q16—22no—
471Q16—42no—
472Q16—81no—
473SD16—41no—
474SD16—42no—
475SD16—42no—
476SD16—42no—
477SD16—42no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481D8—42no—
482D8—82no—
483M16—42no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8C2×D4×C10111yescharacteristic
490C2×C8C2×D4×C10111yescharacteristic
491C2×C8C2×D4×C10111yescharacteristic
492C2×C8C2×D4×C10111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C10111yescharacteristic
505C4⋊C4C2×D4×C10111yescharacteristic
506C4⋊C4C2×D4×C10111yescharacteristic
507C4⋊C4C2×D4×C10111yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C10111yescharacteristic
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—82no—
533D4—21no—
534D4—21no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—81no—
544D4—81no—
545D4—82no—
546D4—161no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—161no—
561C2×C4C22×D4×C10111yescharacteristic
562C2×C4C22×D4×C10111yescharacteristic
563C2×C4H(5,𝔽2)×C10111yescharacteristic
564C8—22no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8AGL(1,ℤ/8)×C10112yes—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22D42×C10111yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
594C4#575×C10111yescharacteristic
595C4#576×C10111yescharacteristic
596C4#578×C10111yescharacteristic
597C2—81no—
598C2—161no—
599C2—161no—
600C2C101×#327411yescharacteristic
601C2C101×#327711yescharacteristic
602C2C101×#329111yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#1621C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3400C2semidirect
2. C101×#3373C2semidirect
3. C101×#3368C2semidirect
4. C101×#3278C2semidirect
5. C101×#1706C2semidirect
6. C101×#1702C2semidirect
7. C101×#1702C2semidirect
8. C101×#1686C2semidirect
9. C101×#1685C2semidirect
10. C101×#1649C2semidirect
11. C101×#1648C2semidirect
13. C101×#1620C2semidirect
14. C101×#1591C2semidirect
15. C101×#1590C2semidirect
295. #20312C101direct (N × H)
302. #3400C2×C101semidirect
303. #3373C2×C101semidirect
304. #3368C2×C101semidirect
305. #3278C2×C101semidirect
306. #1706C2×C101semidirect
307. #1702C2×C101semidirect
308. #1702C2×C101semidirect
309. #1686C2×C101semidirect
310. #1685C2×C101semidirect
311. #1649C2×C101semidirect
312. #1648C2×C101semidirect
314. #1620C2×C101semidirect
315. #1591C2×C101semidirect
316. #1590C2×C101semidirect
317. C101#20312direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#34002
C101×#33732
C101×#33682
C101×#32782
C101×#17062
C101×#17022
C101×#16862
C101×#16852
C101×#16492
C101×#16482
C101×#16212
C101×#16202
C101×#15912
C101×#15902
#20312101