Finite Group Databasebeta

← C101×#20313 #38802464

Subgroups — C101×#20313 #38802464

Order 25856.

644 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
1C101×#3400C211yesmaximal, characteristic, complemented
2C101×#3399C211yesmaximal, characteristic
3C101×#3386C211yesmaximal, characteristic, complemented
4C101×#3278C211yesmaximal, characteristic, complemented
5C101×#1706C211yesmaximal, characteristic, complemented
6C101×#1694C211yesmaximal, characteristic, complemented
7C101×#1688C211yesmaximal, characteristic, complemented
8C101×#1686C211yesmaximal, characteristic, complemented
9C101×#1685C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1640C211yesmaximal, characteristic, complemented
12C101×#1627C211yesmaximal, characteristic, complemented
13C101×#1626C211yesmaximal, 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#501×C101—21no—
22#500×C101C2211yescharacteristic
23#497×C101—21no—
24#496×C101—21no—
25#493×C101C2211yescharacteristic
26#492×C101C2211yescharacteristic
27#492×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#486×C101C2211yescharacteristic
30#478×C101—21no—
31#477×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×C101C2211yescharacteristic
41#460×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#459×C101—21no—
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—21no—
83C2×D8×C101—21no—
84C2×M16×C101—21no—
85C4⋊Q8×C101—21no—
86C4⋊Q8×C101—21no—
87C4⋊Q8×C101C2311yescharacteristic
88C4⋊Q8×C101C2311yescharacteristic
89#127×C101—21no—
90#127×C101C2311yescharacteristic
91#127×C101C2311yescharacteristic
92#125×C101—21no—
93#125×C101—41no—
94#124×C101—21no—
95#124×C101—21no—
96#123×C101—41no—
97C22⋊Q8×C101—21no—
98C22⋊Q8×C101—41no—
99#121×C101—21no—
100#121×C101—41no—
101C4×Q8×C101—21no—
102C4×Q8×C101—21no—
103C4×Q8×C101C2311yescharacteristic
104C4×Q8×C101C2311yescharacteristic
105C4×Q8×C101C2311yescharacteristic
106C4×D4×C101—21no—
107C4×D4×C101—21no—
108C4×D4×C101—21no—
109C4×D4×C101—21no—
110C4×D4×C101C2311yescharacteristic
111#107×C101—21no—
112#107×C101—21no—
113#107×C101—21no—
114#107×C101D411yescharacteristic
115#106×C101—21no—
116#106×C101D411yescharacteristic
117C4⋊C8×C101—21no—
118C4⋊C8×C101—21no—
119C4⋊C8×C101—21no—
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123C4⋊C8×C101C2311yescharacteristic
124#103×C101—21no—
125#103×C101—21no—
126#103×C101—21no—
127#103×C101D411yescharacteristic
128#103×C101D411yescharacteristic
129#103×C101D411yescharacteristic
130#102×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101—21no—
135#102×C101—41no—
136#102×C101—41no—
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—22no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—42no—
175SD16×C101—81no—
176SD16×C101—81no—
177SD16×C101—81no—
178SD16×C101—81no—
179D8×C101—42no—
180D8×C101—81no—
181D8×C101—81no—
182M16×C101—42no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101C2×D411yescharacteristic
189C2×C8×C101C2×D411yescharacteristic
190C2×C8×C101C2×D411yescharacteristic
191C2×C8×C101C2×D411yescharacteristic
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—21no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C4⋊C4×C101C2×D411yescharacteristic
207C22⋊C4×C101—21no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C42×C101—21no—
214C42×C101—21no—
215C42×C101—21no—
216C42×C101—41no—
217C42×C101C2411yescharacteristic
218C23×C101—21no—
219C23×C101—41no—
220C23×C101—41no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—21no—
226Q8×C101—21no—
227Q8×C101—41no—
228Q8×C101—41no—
229Q8×C101—41no—
230Q8×C101—41no—
231Q8×C101—82no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—41no—
241D4×C101—41no—
242D4×C101—81no—
243D4×C101—81no—
244D4×C101—82no—
245D4×C101—161no—
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—21no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101—41no—
257C2×C4×C101—82no—
258C2×C4×C101—82no—
259C2×C4×C101—161no—
260C2×C4×C101C22×D411yescharacteristic
261C2×C4×C101C22×D411yescharacteristic
262C2×C4×C101H(5,𝔽2)11yescharacteristic
263C8×C101—21no—
264C8×C101—21no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C8×C101AGL(1,ℤ/8)12yes—
271C8×C101#13712yescomplemented
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101D4211yescharacteristic
282C4×C101—21no—
283C4×C101—41no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—81no—
291C4×C101—81no—
292C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
293C4×C101C2×#13711yescharacteristic
294C4×C101#57611yescharacteristic
295C4×C101#57711yescharacteristic
296#20313C10111yesmaximal, characteristic, direct product factor, Sylow
297C2×C101—81no—
298C2×C101—161no—
299C2×C101—161no—
300C2×C101#327411yescharacteristic
301C2×C101#327811yescharacteristic
302C2×C101#329011yescharacteristic
303#3400C2×C10111yescharacteristic, complemented
304#3399C2×C10111yescharacteristic
305#3386C2×C10111yescharacteristic, complemented
306#3278C2×C10111yescharacteristic, complemented
307#1706C2×C10111yescharacteristic, complemented
308#1694C2×C10111yescharacteristic, complemented
309#1688C2×C10111yescharacteristic, complemented
310#1686C2×C10111yescharacteristic, complemented
311#1685C2×C10111yescharacteristic, complemented
312#1641C2×C10111yescharacteristic, complemented
313#1640C2×C10111yescharacteristic, complemented
314#1627C2×C10111yescharacteristic, complemented
315#1626C2×C10111yescharacteristic, complemented
316#1591C2×C10111yescharacteristic, complemented
317#1590C2×C10111yescharacteristic, complemented
318C101#2031311yescharacteristic, direct product factor, Sylow
319C2×#137—21no—
320#559C22×C10111yescharacteristic
321#557C22×C10111yescharacteristic
322#550C22×C10111yescharacteristic
323D4×Q8C22×C10111yescharacteristic
324#501—21no—
325#500C22×C10111yescharacteristic
326#497—21no—
327#496—21no—
328#493C22×C10111yescharacteristic
329#492C22×C10111yescharacteristic
330#492C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic
332#486C22×C10111yescharacteristic
333#478—21no—
334#477—21no—
335#475C22×C10111yescharacteristic
336#474C22×C10111yescharacteristic
337#468—21no—
338#464—21no—
339#463—21no—
340#462C22×C10111yescharacteristic
341#462C22×C10111yescharacteristic
342#461—21no—
343#460C22×C10111yescharacteristic
344#460C22×C10111yescharacteristic
345#460C22×C10111yescharacteristic
346#459—21no—
347#459C22×C10111yescharacteristic
348#452—21no—
349#448—21no—
350#446C22×C10111yescharacteristic
351#446C22×C10111yescharacteristic
352#446C22×C10111yescharacteristic
353#442—21no—
354#440—21no—
355#440—21no—
356C4×Q16C22×C10111yescharacteristic
357C4×SD16C22×C10111yescharacteristic
358#436C22×C10111yescharacteristic
359#335C22×C10111yescharacteristic
360#334C22×C10111yescharacteristic
361#332C22×C10111yescharacteristic
362#332C22×C10111yescharacteristic
363#331C22×C10111yescharacteristic
364#331C22×C10111yescharacteristic
365Q8⋊C8C22×C10111yescharacteristic
366Q8⋊C8C22×C10111yescharacteristic
367Q8⋊C8C22×C10111yescharacteristic
368D4⋊C8C22×C10111yescharacteristic
369C82C22×C10111yescharacteristic
370C2×#41—21no—
371C22×Q8—21no—
372#137—44no—
373C2×Q16—21no—
374C2×Q16—21no—
375C2×Q16D4×C10111yescharacteristic
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16D4×C10111yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×M16—21no—
388C4⋊Q8—21no—
389C4⋊Q8—21no—
390C4⋊Q8C23×C10111yescharacteristic
391C4⋊Q8C23×C10111yescharacteristic
392#127—21no—
393#127C23×C10111yescharacteristic
394#127C23×C10111yescharacteristic
395#125—21no—
396#125—41no—
397#124—21no—
398#124—21no—
399#123—41no—
400C22⋊Q8—21no—
401C22⋊Q8—41no—
402#121—21no—
403#121—41no—
404C4×Q8—21no—
405C4×Q8—21no—
406C4×Q8C23×C10111yescharacteristic
407C4×Q8C23×C10111yescharacteristic
408C4×Q8C23×C10111yescharacteristic
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C10111yescharacteristic
414#107—21no—
415#107—21no—
416#107—21no—
417#107D4×C10111yescharacteristic
418#106—21no—
419#106D4×C10111yescharacteristic
420C4⋊C8—21no—
421C4⋊C8—21no—
422C4⋊C8—21no—
423C4⋊C8C23×C10111yescharacteristic
424C4⋊C8C23×C10111yescharacteristic
425C4⋊C8C23×C10111yescharacteristic
426C4⋊C8C23×C10111yescharacteristic
427#103—21no—
428#103—21no—
429#103—21no—
430#103D4×C10111yescharacteristic
431#103D4×C10111yescharacteristic
432#103D4×C10111yescharacteristic
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—41no—
439#102—41no—
440#102D4×C10111yescharacteristic
441C22⋊C8—21no—
442#97—21no—
443#97—21no—
444#97—21no—
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447C4×C8C23×C10111yescharacteristic
448#41—42no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C10111yescharacteristic
456C2×Q8C2×D4×C10111yescharacteristic
457C2×Q8C2×D4×C10111yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C10111yescharacteristic
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—22no—
472Q16—42no—
473Q16—81no—
474SD16—22no—
475SD16—42no—
476SD16—42no—
477SD16—42no—
478SD16—81no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—42no—
483D8—81no—
484D8—81no—
485M16—42no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8C2×D4×C10111yescharacteristic
492C2×C8C2×D4×C10111yescharacteristic
493C2×C8C2×D4×C10111yescharacteristic
494C2×C8C2×D4×C10111yescharacteristic
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4C2×D4×C10111yescharacteristic
507C4⋊C4C2×D4×C10111yescharacteristic
508C4⋊C4C2×D4×C10111yescharacteristic
509C4⋊C4C2×D4×C10111yescharacteristic
510C22⋊C4—21no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C42—21no—
517C42—21no—
518C42—21no—
519C42—41no—
520C42C24×C10111yescharacteristic
521C23—21no—
522C23—41no—
523C23—41no—
524Q8—21no—
525Q8—21no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534Q8—82no—
535D4—21no—
536D4—21no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—81no—
546D4—81no—
547D4—82no—
548D4—161no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4—82no—
562C2×C4—161no—
563C2×C4C22×D4×C10111yescharacteristic
564C2×C4C22×D4×C10111yescharacteristic
565C2×C4H(5,𝔽2)×C10111yescharacteristic
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8AGL(1,ℤ/8)×C10112yes—
574C8#137×C10112yescomplemented
575C22—41no—
576C22—41no—
577C22—41no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22D42×C10111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
596C4C2×#137×C10111yescharacteristic
597C4#576×C10111yescharacteristic
598C4#577×C10111yescharacteristic
599C2—81no—
600C2—161no—
601C2—161no—
602C2C101×#327411yescharacteristic
603C2C101×#327811yescharacteristic
604C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3399C2
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
3. C101×#3386C2semidirect
4. C101×#3278C2semidirect
5. C101×#1706C2semidirect
6. C101×#1694C2semidirect
7. C101×#1688C2semidirect
8. C101×#1686C2semidirect
9. C101×#1685C2semidirect
10. C101×#1641C2semidirect
11. C101×#1640C2semidirect
12. C101×#1627C2semidirect
13. C101×#1626C2semidirect
14. C101×#1591C2semidirect
15. C101×#1590C2semidirect
271. C8×C101#137semidirect
296. #20313C101direct (N × H)
303. #3400C2×C101semidirect
305. #3386C2×C101semidirect
306. #3278C2×C101semidirect
307. #1706C2×C101semidirect
308. #1694C2×C101semidirect
309. #1688C2×C101semidirect
310. #1686C2×C101semidirect
311. #1685C2×C101semidirect
312. #1641C2×C101semidirect
313. #1640C2×C101semidirect
314. #1627C2×C101semidirect
315. #1626C2×C101semidirect
316. #1591C2×C101semidirect
317. #1590C2×C101semidirect
318. C101#20313direct (N × H)
574. C8#137×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34002
C101×#33992
C101×#33862
C101×#32782
C101×#17062
C101×#16942
C101×#16882
C101×#16862
C101×#16852
C101×#16412
C101×#16402
C101×#16272
C101×#16262
C101×#15912
C101×#15902
#20313101