Finite Group Databasebeta

← C101×#20270 #38802421

Subgroups — C101×#20270 #38802421

Order 25856.

652 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3397C211yesmaximal, characteristic, complemented
2C101×#3366C211yesmaximal, characteristic, complemented
3C101×#3356C211yesmaximal, characteristic, complemented
4C101×#3287C211yesmaximal, characteristic, complemented
5C101×#1715C211yesmaximal, characteristic, complemented
6C101×#1698C211yesmaximal, characteristic, complemented
7C101×#1687C211yesmaximal, characteristic, complemented
8C101×#1686C211yesmaximal, characteristic, complemented
9C101×#1671C211yesmaximal, characteristic, complemented
10C101×#1642C211yesmaximal, characteristic, complemented
11C101×#1631C211yesmaximal, characteristic, complemented
12C101×#1628C211yesmaximal, characteristic, complemented
13C101×#1622C211yesmaximal, characteristic, complemented
14C101×#1593C211yesmaximal, characteristic, complemented
15C101×#1581C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#556×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#550×C101C2211yescharacteristic
21#498×C101C2211yescharacteristic
22#496×C101—21no—
23#493×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#490×C101—21no—
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#485×C101—21no—
30#483×C101—21no—
31#478×C101—21no—
32#477×C101C2211yescharacteristic
33#476×C101C2211yescharacteristic
34#475×C101C2211yescharacteristic
35#470×C101—21no—
36#466×C101—21no—
37#463×C101—21no—
38#461×C101C2211yescharacteristic
39#460×C101—21no—
40#460×C101C2211yescharacteristic
41#460×C101C2211yescharacteristic
42#459×C101—21no—
43#459×C101C2211yescharacteristic
44#459×C101C2211yescharacteristic
45#449×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#442×C101—21no—
50#440×C101—21no—
51C4×Q16×C101C2211yescharacteristic
52C4×D8×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55#428×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69#135×C101—44no—
70C2×Q16×C101D411yescharacteristic
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—41no—
77C2×D8×C101—21no—
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C2×D8×C101—21no—
81C2×D8×C101D411yescharacteristic
82C2×M16×C101—21no—
83C22×C8×C101—21no—
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101—21no—
87#127×C101—21no—
88#127×C101C2311yescharacteristic
89#127×C101C2311yescharacteristic
90#126×C101—41no—
91#125×C101—21no—
92#124×C101—21no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—21no—
95C22⋊Q8×C101—41no—
96#121×C101—21no—
97#121×C101—21no—
98#121×C101—41no—
99#121×C101—41no—
100C4×Q8×C101—21no—
101C4×Q8×C101C2311yescharacteristic
102C4×Q8×C101C2311yescharacteristic
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101—21no—
106C4×D4×C101C2311yescharacteristic
107C4×D4×C101C2311yescharacteristic
108#117×C101—21no—
109C2×C4⋊C4×C101—21no—
110#107×C101—21no—
111#107×C101D411yescharacteristic
112#107×C101D411yescharacteristic
113#106×C101—21no—
114#106×C101—21no—
115#106×C101—21no—
116#106×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×C101—21no—
125#103×C101—21no—
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—41no—
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×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×C101—21no—
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—41no—
160C2×D4×C101—41no—
161C2×D4×C101—41no—
162C2×D4×C101—41no—
163C2×D4×C101C2×D411yescharacteristic
164C2×D4×C101C2×D411yescharacteristic
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169C22×C4×C101—41no—
170Q16×C101—22no—
171SD16×C101—42no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—81no—
175SD16×C101—81no—
176SD16×C101—82no—
177D8×C101—41no—
178D8×C101—42no—
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×C101—42no—
189C2×C8×C101C2×D411yescharacteristic
190C2×C8×C101C2×D411yescharacteristic
191C2×C8×C101C2×D411yescharacteristic
192C2×C8×C101C2×D411yescharacteristic
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×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C22⋊C4×C101—21no—
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—41no—
216C42×C101C2411yescharacteristic
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—41no—
220C23×C101—41no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—81no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—81no—
241D4×C101—81no—
242D4×C101—82no—
243D4×C101—82no—
244D4×C101—161no—
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—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101—41no—
257C2×C4×C101—41no—
258C2×C4×C101—82no—
259C2×C4×C101—82no—
260C2×C4×C101—161no—
261C2×C4×C101C22×D411yescharacteristic
262C2×C4×C101C22×D411yescharacteristic
263C2×C4×C101H(5,𝔽2)11yescharacteristic
264C8×C101—21no—
265C8×C101—21no—
266C8×C101—21no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C8×C101—41no—
271C8×C101—41no—
272C8×C101AGL(1,ℤ/8)12yes—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101—81no—
282C22×C101—81no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101D4211yescharacteristic
286C4×C101—21no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—41no—
291C4×C101—41no—
292C4×C101—41no—
293C4×C101—81no—
294C4×C101—81no—
295C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
296C4×C101#57511yescharacteristic
297C4×C101#57711yescharacteristic
298C4×C101#57711yescharacteristic
299#20270C10111yesmaximal, characteristic, direct product factor, Sylow
300C2×C101—81no—
301C2×C101—81no—
302C2×C101—161no—
303C2×C101—161no—
304C2×C101#327111yescharacteristic
305C2×C101#327211yescharacteristic
306C2×C101#328811yescharacteristic
307#3397C2×C10111yescharacteristic, complemented
308#3366C2×C10111yescharacteristic, complemented
309#3356C2×C10111yescharacteristic, complemented
310#3287C2×C10111yescharacteristic, complemented
311#1715C2×C10111yescharacteristic, complemented
312#1698C2×C10111yescharacteristic, complemented
313#1687C2×C10111yescharacteristic, complemented
314#1686C2×C10111yescharacteristic, complemented
315#1671C2×C10111yescharacteristic, complemented
316#1642C2×C10111yescharacteristic, complemented
317#1631C2×C10111yescharacteristic, complemented
318#1628C2×C10111yescharacteristic, complemented
319#1622C2×C10111yescharacteristic, complemented
320#1593C2×C10111yescharacteristic, complemented
321#1581C2×C10111yescharacteristic, complemented
322C101#2027011yescharacteristic, direct product factor, Sylow
323C2×#135—21no—
324#556C22×C10111yescharacteristic
325#554C22×C10111yescharacteristic
326#550C22×C10111yescharacteristic
327#550C22×C10111yescharacteristic
328#498C22×C10111yescharacteristic
329#496—21no—
330#493C22×C10111yescharacteristic
331#492C22×C10111yescharacteristic
332#492C22×C10111yescharacteristic
333#490—21no—
334#486C22×C10111yescharacteristic
335#486C22×C10111yescharacteristic
336#485—21no—
337#483—21no—
338#478—21no—
339#477C22×C10111yescharacteristic
340#476C22×C10111yescharacteristic
341#475C22×C10111yescharacteristic
342#470—21no—
343#466—21no—
344#463—21no—
345#461C22×C10111yescharacteristic
346#460—21no—
347#460C22×C10111yescharacteristic
348#460C22×C10111yescharacteristic
349#459—21no—
350#459C22×C10111yescharacteristic
351#459C22×C10111yescharacteristic
352#449—21no—
353#449—21no—
354#446C22×C10111yescharacteristic
355#446C22×C10111yescharacteristic
356#442—21no—
357#440—21no—
358C4×Q16C22×C10111yescharacteristic
359C4×D8C22×C10111yescharacteristic
360#436C22×C10111yescharacteristic
361C8×D4C22×C10111yescharacteristic
362#428—21no—
363#335C22×C10111yescharacteristic
364#334C22×C10111yescharacteristic
365#333C22×C10111yescharacteristic
366#332C22×C10111yescharacteristic
367#331C22×C10111yescharacteristic
368#331C22×C10111yescharacteristic
369Q8⋊C8C22×C10111yescharacteristic
370Q8⋊C8C22×C10111yescharacteristic
371D4⋊C8C22×C10111yescharacteristic
372D4⋊C8C22×C10111yescharacteristic
373#322C22×C10111yescharacteristic
374C2×#41—21no—
375C2×#41—21no—
376#135—44no—
377C2×Q16D4×C10111yescharacteristic
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—21no—
382C2×SD16—21no—
383C2×SD16—41no—
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8D4×C10111yescharacteristic
389C2×M16—21no—
390C22×C8—21no—
391C4⋊Q8C23×C10111yescharacteristic
392C4⋊Q8C23×C10111yescharacteristic
393#127—21no—
394#127—21no—
395#127C23×C10111yescharacteristic
396#127C23×C10111yescharacteristic
397#126—41no—
398#125—21no—
399#124—21no—
400C22⋊Q8—21no—
401C22⋊Q8—21no—
402C22⋊Q8—41no—
403#121—21no—
404#121—21no—
405#121—41no—
406#121—41no—
407C4×Q8—21no—
408C4×Q8C23×C10111yescharacteristic
409C4×Q8C23×C10111yescharacteristic
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C10111yescharacteristic
414C4×D4C23×C10111yescharacteristic
415#117—21no—
416C2×C4⋊C4—21no—
417#107—21no—
418#107D4×C10111yescharacteristic
419#107D4×C10111yescharacteristic
420#106—21no—
421#106—21no—
422#106—21no—
423#106—21no—
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8C23×C10111yescharacteristic
427C4⋊C8C23×C10111yescharacteristic
428C4⋊C8C23×C10111yescharacteristic
429C4⋊C8C23×C10111yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C10111yescharacteristic
434#103D4×C10111yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C10111yescharacteristic
444#102D4×C10111yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448#97—21no—
449C4×C8C23×C10111yescharacteristic
450C4×C8C23×C10111yescharacteristic
451C4×C8C23×C10111yescharacteristic
452#41—42no—
453#41—42no—
454#41—81no—
455#41—81no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×D4×C10111yescharacteristic
459C2×Q8C2×D4×C10111yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4C2×D4×C10111yescharacteristic
471C2×D4C2×D4×C10111yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477Q16—22no—
478SD16—42no—
479SD16—42no—
480SD16—42no—
481SD16—81no—
482SD16—81no—
483SD16—82no—
484D8—41no—
485D8—42no—
486D8—42no—
487D8—81no—
488D8—81no—
489M16—42no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—42no—
496C2×C8C2×D4×C10111yescharacteristic
497C2×C8C2×D4×C10111yescharacteristic
498C2×C8C2×D4×C10111yescharacteristic
499C2×C8C2×D4×C10111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×D4×C10111yescharacteristic
510C4⋊C4C2×D4×C10111yescharacteristic
511C4⋊C4C2×D4×C10111yescharacteristic
512C4⋊C4C2×D4×C10111yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C42—21no—
521C42—21no—
522C42—41no—
523C42C24×C10111yescharacteristic
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—41no—
547D4—81no—
548D4—81no—
549D4—82no—
550D4—82no—
551D4—161no—
552D4—161no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—82no—
566C2×C4—82no—
567C2×C4—161no—
568C2×C4C22×D4×C10111yescharacteristic
569C2×C4C22×D4×C10111yescharacteristic
570C2×C4H(5,𝔽2)×C10111yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8AGL(1,ℤ/8)×C10112yes—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C10111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
603C4#575×C10111yescharacteristic
604C4#577×C10111yescharacteristic
605C4#577×C10111yescharacteristic
606C2—81no—
607C2—81no—
608C2—161no—
609C2—161no—
610C2C101×#327111yescharacteristic
611C2C101×#327211yescharacteristic
612C2C101×#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×#3397C2semidirect
2. C101×#3366C2semidirect
3. C101×#3356C2semidirect
4. C101×#3287C2semidirect
5. C101×#1715C2semidirect
6. C101×#1698C2semidirect
7. C101×#1687C2semidirect
8. C101×#1686C2semidirect
9. C101×#1671C2semidirect
10. C101×#1642C2semidirect
11. C101×#1631C2semidirect
12. C101×#1628C2semidirect
13. C101×#1622C2semidirect
14. C101×#1593C2semidirect
15. C101×#1581C2semidirect
299. #20270C101direct (N × H)
307. #3397C2×C101semidirect
308. #3366C2×C101semidirect
309. #3356C2×C101semidirect
310. #3287C2×C101semidirect
311. #1715C2×C101semidirect
312. #1698C2×C101semidirect
313. #1687C2×C101semidirect
314. #1686C2×C101semidirect
315. #1671C2×C101semidirect
316. #1642C2×C101semidirect
317. #1631C2×C101semidirect
318. #1628C2×C101semidirect
319. #1622C2×C101semidirect
320. #1593C2×C101semidirect
321. #1581C2×C101semidirect
322. C101#20270direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33972
C101×#33662
C101×#33562
C101×#32872
C101×#17152
C101×#16982
C101×#16872
C101×#16862
C101×#16712
C101×#16422
C101×#16312
C101×#16282
C101×#16222
C101×#15932
C101×#15812
#20270101