Finite Group Databasebeta

← C101×#20272 #38802423

Subgroups — C101×#20272 #38802423

Order 25856.

662 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3400C211yesmaximal, characteristic, complemented
2C101×#3399C211yesmaximal, characteristic, complemented
3C101×#3368C211yesmaximal, characteristic, complemented
4C101×#3287C211yesmaximal, characteristic, complemented
5C101×#1721C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1688C211yesmaximal, characteristic, complemented
8C101×#1688C211yesmaximal, characteristic, complemented
9C101×#1665C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1626C211yesmaximal, characteristic, complemented
12C101×#1621C211yesmaximal, characteristic, complemented
13C101×#1620C211yesmaximal, characteristic, complemented
14C101×#1593C211yesmaximal, characteristic, complemented
15C101×#1582C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#559×C101C2211yescharacteristic
18#557×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#550×C101C2211yescharacteristic
21#497×C101—21no—
22#496×C101—21no—
23#493×C101C2211yescharacteristic
24#493×C101C2211yescharacteristic
25#493×C101C2211yescharacteristic
26#492×C101C2211yescharacteristic
27#490×C101—21no—
28#486×C101C2211yescharacteristic
29#486×C101C2211yescharacteristic
30#478×C101—21no—
31#474×C101C2211yescharacteristic
32#466×C101—21no—
33#464×C101—21no—
34#463×C101—21no—
35#462×C101C2211yescharacteristic
36#461×C101—21no—
37#460×C101—21no—
38#460×C101C2211yescharacteristic
39#460×C101C2211yescharacteristic
40#460×C101C2211yescharacteristic
41#460×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#459×C101—21no—
44#459×C101C2211yescharacteristic
45#449×C101—21no—
46#449×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
55C8×D4×C101C2211yescharacteristic
56#334×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#331×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69#135×C101—44no—
70C2×Q16×C101—21no—
71C2×Q16×C101D411yescharacteristic
72C2×SD16×C101—21no—
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×C101D411yescharacteristic
80C2×D8×C101—21no—
81C2×D8×C101—21no—
82C2×D8×C101—21no—
83C2×D8×C101—21no—
84C2×D8×C101—21no—
85C2×D8×C101—41no—
86C22×C8×C101—21no—
87C4⋊Q8×C101—21no—
88C4⋊Q8×C101C2311yescharacteristic
89#127×C101—21no—
90#127×C101—21no—
91#127×C101C2311yescharacteristic
92#127×C101C2311yescharacteristic
93#127×C101C2311yescharacteristic
94#125×C101—21no—
95#125×C101—41no—
96#124×C101—21no—
97#124×C101—21no—
98#123×C101—41no—
99#121×C101—21no—
100#121×C101—21no—
101#121×C101—41no—
102#121×C101—41no—
103C4×Q8×C101—21no—
104C4×Q8×C101—21no—
105C4×Q8×C101C2311yescharacteristic
106C4×Q8×C101C2311yescharacteristic
107C4×Q8×C101C2311yescharacteristic
108C4×D4×C101—21no—
109C4×D4×C101—21no—
110C4×D4×C101—21no—
111C4×D4×C101—21no—
112C4×D4×C101C2311yescharacteristic
113#107×C101—21no—
114#107×C101D411yescharacteristic
115#106×C101D411yescharacteristic
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101—21no—
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123#103×C101—21no—
124#103×C101D411yescharacteristic
125#103×C101D411yescharacteristic
126#103×C101D411yescharacteristic
127#102×C101—21no—
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—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—42no—
147#41×C101—81no—
148#41×C101—81no—
149C2×Q8×C101—21no—
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×Q8×C101C2×D411yescharacteristic
153C2×D4×C101—21no—
154C2×D4×C101—21no—
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—21no—
162C2×D4×C101—41no—
163C2×D4×C101—41no—
164C2×D4×C101—41no—
165C2×D4×C101—41no—
166C2×D4×C101C2×D411yescharacteristic
167C22×C4×C101—21no—
168C22×C4×C101—41no—
169C22×C4×C101—41no—
170C22×C4×C101—41no—
171Q16×C101—22no—
172Q16×C101—81no—
173SD16×C101—41no—
174SD16×C101—42no—
175SD16×C101—42no—
176SD16×C101—42no—
177SD16×C101—42no—
178SD16×C101—81no—
179SD16×C101—81no—
180SD16×C101—81no—
181D8×C101—42no—
182D8×C101—42no—
183D8×C101—81no—
184D8×C101—81no—
185D8×C101—81no—
186D8×C101—82no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101—21no—
191C2×C8×C101—21no—
192C2×C8×C101—42no—
193C2×C8×C101C2×D411yescharacteristic
194C2×C8×C101C2×D411yescharacteristic
195C2×C8×C101C2×D411yescharacteristic
196C2×C8×C101C2×D411yescharacteristic
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—21no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101—41no—
204C4⋊C4×C101—41no—
205C4⋊C4×C101C2×D411yescharacteristic
206C4⋊C4×C101C2×D411yescharacteristic
207C4⋊C4×C101C2×D411yescharacteristic
208C4⋊C4×C101C2×D411yescharacteristic
209C22⋊C4×C101—21no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C22⋊C4×C101—41no—
215C42×C101—21no—
216C42×C101—21no—
217C42×C101—21no—
218C42×C101—41no—
219C42×C101C2411yescharacteristic
220C23×C101—21no—
221C23×C101—41no—
222C23×C101—41no—
223C23×C101—41no—
224Q8×C101—21no—
225Q8×C101—21no—
226Q8×C101—21no—
227Q8×C101—21no—
228Q8×C101—21no—
229Q8×C101—21no—
230Q8×C101—41no—
231Q8×C101—41no—
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—41no—
243D4×C101—41no—
244D4×C101—41no—
245D4×C101—41no—
246D4×C101—81no—
247D4×C101—81no—
248D4×C101—81no—
249D4×C101—82no—
250D4×C101—82no—
251D4×C101—161no—
252D4×C101—161no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
255C2×C4×C101—21no—
256C2×C4×C101—21no—
257C2×C4×C101—21no—
258C2×C4×C101—21no—
259C2×C4×C101—21no—
260C2×C4×C101—41no—
261C2×C4×C101—41no—
262C2×C4×C101—41no—
263C2×C4×C101—82no—
264C2×C4×C101—82no—
265C2×C4×C101—161no—
266C2×C4×C101C22×D411yescharacteristic
267C2×C4×C101C22×D411yescharacteristic
268C2×C4×C101H(5,𝔽2)11yescharacteristic
269C8×C101—21no—
270C8×C101—21no—
271C8×C101—21no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101—41no—
275C8×C101—41no—
276C8×C101—41no—
277C8×C101AGL(1,ℤ/8)12yes—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—81no—
282C22×C101—81no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101—81no—
286C22×C101—81no—
287C22×C101—81no—
288C22×C101—81no—
289C22×C101—81no—
290C22×C101D4211yescharacteristic
291C4×C101—21no—
292C4×C101—41no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—41no—
296C4×C101—41no—
297C4×C101—41no—
298C4×C101—41no—
299C4×C101—81no—
300C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C101#57511yescharacteristic
302C4×C101#57611yescharacteristic
303C4×C101#57711yescharacteristic
304#20272C10111yesmaximal, characteristic, direct product factor, Sylow
305C2×C101—81no—
306C2×C101—161no—
307C2×C101—161no—
308C2×C101—161no—
309C2×C101#327111yescharacteristic
310C2×C101#327411yescharacteristic
311C2×C101#328811yescharacteristic
312#3400C2×C10111yescharacteristic, complemented
313#3399C2×C10111yescharacteristic, complemented
314#3368C2×C10111yescharacteristic, complemented
315#3287C2×C10111yescharacteristic, complemented
316#1721C2×C10111yescharacteristic, complemented
317#1702C2×C10111yescharacteristic, complemented
318#1688C2×C10111yescharacteristic, complemented
319#1688C2×C10111yescharacteristic, complemented
320#1665C2×C10111yescharacteristic, complemented
321#1641C2×C10111yescharacteristic, complemented
322#1626C2×C10111yescharacteristic, complemented
323#1621C2×C10111yescharacteristic, complemented
324#1620C2×C10111yescharacteristic, complemented
325#1593C2×C10111yescharacteristic, complemented
326#1582C2×C10111yescharacteristic, complemented
327C101#2027211yescharacteristic, direct product factor, Sylow
328C2×#135—21no—
329#559C22×C10111yescharacteristic
330#557C22×C10111yescharacteristic
331#550C22×C10111yescharacteristic
332#550C22×C10111yescharacteristic
333#497—21no—
334#496—21no—
335#493C22×C10111yescharacteristic
336#493C22×C10111yescharacteristic
337#493C22×C10111yescharacteristic
338#492C22×C10111yescharacteristic
339#490—21no—
340#486C22×C10111yescharacteristic
341#486C22×C10111yescharacteristic
342#478—21no—
343#474C22×C10111yescharacteristic
344#466—21no—
345#464—21no—
346#463—21no—
347#462C22×C10111yescharacteristic
348#461—21no—
349#460—21no—
350#460C22×C10111yescharacteristic
351#460C22×C10111yescharacteristic
352#460C22×C10111yescharacteristic
353#460C22×C10111yescharacteristic
354#460C22×C10111yescharacteristic
355#459—21no—
356#459C22×C10111yescharacteristic
357#449—21no—
358#449—21no—
359#446C22×C10111yescharacteristic
360#446C22×C10111yescharacteristic
361#446C22×C10111yescharacteristic
362#442—21no—
363#440—21no—
364#440—21no—
365C4×Q16C22×C10111yescharacteristic
366C4×SD16C22×C10111yescharacteristic
367C8×D4C22×C10111yescharacteristic
368#334C22×C10111yescharacteristic
369#334C22×C10111yescharacteristic
370#332C22×C10111yescharacteristic
371#331C22×C10111yescharacteristic
372#331C22×C10111yescharacteristic
373#331C22×C10111yescharacteristic
374Q8⋊C8C22×C10111yescharacteristic
375Q8⋊C8C22×C10111yescharacteristic
376Q8⋊C8C22×C10111yescharacteristic
377D4⋊C8C22×C10111yescharacteristic
378#322C22×C10111yescharacteristic
379C2×#41—21no—
380C2×#41—21no—
381#135—44no—
382C2×Q16—21no—
383C2×Q16D4×C10111yescharacteristic
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16—21no—
391C2×SD16D4×C10111yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×D8—21no—
396C2×D8—21no—
397C2×D8—41no—
398C22×C8—21no—
399C4⋊Q8—21no—
400C4⋊Q8C23×C10111yescharacteristic
401#127—21no—
402#127—21no—
403#127C23×C10111yescharacteristic
404#127C23×C10111yescharacteristic
405#127C23×C10111yescharacteristic
406#125—21no—
407#125—41no—
408#124—21no—
409#124—21no—
410#123—41no—
411#121—21no—
412#121—21no—
413#121—41no—
414#121—41no—
415C4×Q8—21no—
416C4×Q8—21no—
417C4×Q8C23×C10111yescharacteristic
418C4×Q8C23×C10111yescharacteristic
419C4×Q8C23×C10111yescharacteristic
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4C23×C10111yescharacteristic
425#107—21no—
426#107D4×C10111yescharacteristic
427#106D4×C10111yescharacteristic
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8C23×C10111yescharacteristic
432C4⋊C8C23×C10111yescharacteristic
433C4⋊C8C23×C10111yescharacteristic
434C4⋊C8C23×C10111yescharacteristic
435#103—21no—
436#103D4×C10111yescharacteristic
437#103D4×C10111yescharacteristic
438#103D4×C10111yescharacteristic
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—41no—
449#102D4×C10111yescharacteristic
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453#97—21no—
454C4×C8C23×C10111yescharacteristic
455C4×C8C23×C10111yescharacteristic
456C4×C8C23×C10111yescharacteristic
457#41—42no—
458#41—42no—
459#41—81no—
460#41—81no—
461C2×Q8—21no—
462C2×Q8C2×D4×C10111yescharacteristic
463C2×Q8C2×D4×C10111yescharacteristic
464C2×Q8C2×D4×C10111yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—41no—
477C2×D4—41no—
478C2×D4C2×D4×C10111yescharacteristic
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483Q16—22no—
484Q16—81no—
485SD16—41no—
486SD16—42no—
487SD16—42no—
488SD16—42no—
489SD16—42no—
490SD16—81no—
491SD16—81no—
492SD16—81no—
493D8—42no—
494D8—42no—
495D8—81no—
496D8—81no—
497D8—81no—
498D8—82no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—42no—
505C2×C8C2×D4×C10111yescharacteristic
506C2×C8C2×D4×C10111yescharacteristic
507C2×C8C2×D4×C10111yescharacteristic
508C2×C8C2×D4×C10111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4—41no—
517C4⋊C4C2×D4×C10111yescharacteristic
518C4⋊C4C2×D4×C10111yescharacteristic
519C4⋊C4C2×D4×C10111yescharacteristic
520C4⋊C4C2×D4×C10111yescharacteristic
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42—21no—
530C42—41no—
531C42C24×C10111yescharacteristic
532C23—21no—
533C23—41no—
534C23—41no—
535C23—41no—
536Q8—21no—
537Q8—21no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544D4—21no—
545D4—21no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—81no—
559D4—81no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—161no—
564D4—161no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—21no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
576C2×C4—82no—
577C2×C4—161no—
578C2×C4C22×D4×C10111yescharacteristic
579C2×C4C22×D4×C10111yescharacteristic
580C2×C4H(5,𝔽2)×C10111yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8AGL(1,ℤ/8)×C10112yes—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22D42×C10111yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—81no—
612C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
613C4#575×C10111yescharacteristic
614C4#576×C10111yescharacteristic
615C4#577×C10111yescharacteristic
616C2—81no—
617C2—161no—
618C2—161no—
619C2—161no—
620C2C101×#327111yescharacteristic
621C2C101×#327411yescharacteristic
622C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
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×#3399C2semidirect
3. C101×#3368C2semidirect
4. C101×#3287C2semidirect
5. C101×#1721C2semidirect
6. C101×#1702C2semidirect
7. C101×#1688C2semidirect
8. C101×#1688C2semidirect
9. C101×#1665C2semidirect
10. C101×#1641C2semidirect
11. C101×#1626C2semidirect
12. C101×#1621C2semidirect
13. C101×#1620C2semidirect
14. C101×#1593C2semidirect
15. C101×#1582C2semidirect
304. #20272C101direct (N × H)
312. #3400C2×C101semidirect
313. #3399C2×C101semidirect
314. #3368C2×C101semidirect
315. #3287C2×C101semidirect
316. #1721C2×C101semidirect
317. #1702C2×C101semidirect
318. #1688C2×C101semidirect
319. #1688C2×C101semidirect
320. #1665C2×C101semidirect
321. #1641C2×C101semidirect
322. #1626C2×C101semidirect
323. #1621C2×C101semidirect
324. #1620C2×C101semidirect
325. #1593C2×C101semidirect
326. #1582C2×C101semidirect
327. C101#20272direct (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×#33992
C101×#33682
C101×#32872
C101×#17212
C101×#17022
C101×#16882
C101×#16652
C101×#16412
C101×#16262
C101×#16212
C101×#16202
C101×#15932
C101×#15822
#20272101