Finite Group Databasebeta

← C101×#20255 #38802406

Subgroups — C101×#20255 #38802406

Order 25856.

632 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3397C211yesmaximal, characteristic, complemented
2C101×#3332C211yesmaximal, characteristic, complemented
3C101×#3330C211yesmaximal, characteristic, complemented
4C101×#3302C211yesmaximal, characteristic, complemented
5C101×#1719C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1699C211yesmaximal, characteristic, complemented
8C101×#1685C211yesmaximal, characteristic, complemented
9C101×#1681C211yesmaximal, characteristic, complemented
10C101×#1650C211yesmaximal, characteristic, complemented
11C101×#1647C211yesmaximal, characteristic, complemented
12C101×#1641C211yesmaximal, characteristic, complemented
13C101×#1625C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1581C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic
17#550×C101C2211yescharacteristic
18#547×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#496×C101—21no—
22#492×C101C2211yescharacteristic
23#487×C101C2211yescharacteristic
24#487×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#485×C101—21no—
28#484×C101—21no—
29#481×C101—21no—
30#475×C101C2211yescharacteristic
31#474×C101C2211yescharacteristic
32#474×C101C2211yescharacteristic
33#469×C101—21no—
34#468×C101—21no—
35#467×C101—21no—
36#463×C101—21no—
37#462×C101C2211yescharacteristic
38#461×C101C2211yescharacteristic
39#461×C101C2211yescharacteristic
40#460×C101—21no—
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#452×C101—21no—
44#449×C101—21no—
45#449×C101—21no—
46#446×C101C2211yescharacteristic
47#440×C101—21no—
48C4×SD16×C101C2211yescharacteristic
49C4×D8×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic
53#417×C101—21no—
54#417×C101—21no—
55#416×C101—21no—
56#335×C101C2211yescharacteristic
57#335×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—21no—
70C2×Q16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101D411yescharacteristic
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×D8×C101D411yescharacteristic
79C2×M16×C101—21no—
80C2×M16×C101—21no—
81C22×C8×C101—21no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85#127×C101—21no—
86#127×C101C2311yescharacteristic
87#126×C101—41no—
88#124×C101—21no—
89#123×C101—41no—
90#123×C101—41no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93C22⋊Q8×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—41no—
98C4×Q8×C101—21no—
99C4×Q8×C101C2311yescharacteristic
100C4×D4×C101—21no—
101C4×D4×C101C2311yescharacteristic
102C4×D4×C101C2311yescharacteristic
103C4×D4×C101C2311yescharacteristic
104#117×C101—21no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#107×C101—41no—
110#107×C101D411yescharacteristic
111#106×C101—21no—
112#106×C101D411yescharacteristic
113C4⋊C8×C101—21no—
114C4⋊C8×C101C2311yescharacteristic
115C4⋊C8×C101C2311yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118#103×C101—21no—
119#103×C101—21no—
120#103×C101—21no—
121#103×C101—21no—
122#103×C101—21no—
123#103×C101—21no—
124#103×C101—21no—
125#103×C101—21no—
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—41no—
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—42no—
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—81no—
148#41×C101—81no—
149#41×C101—81no—
150C2×Q8×C101—21no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101C2×D411yescharacteristic
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101—41no—
161C2×D4×C101C2×D411yescharacteristic
162C2×D4×C101C2×D411yescharacteristic
163C2×D4×C101C2×D411yescharacteristic
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169C22×C4×C101—41no—
170Q16×C101—81no—
171SD16×C101—41no—
172SD16×C101—42no—
173SD16×C101—81no—
174SD16×C101—81no—
175SD16×C101—81no—
176D8×C101—41no—
177D8×C101—81no—
178D8×C101—81no—
179M16×C101—81no—
180M16×C101—81no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—81no—
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×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C22⋊C4×C101—21no—
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—41no—
215C42×C101C2411yescharacteristic
216C23×C101—21no—
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—41no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—41no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—81no—
239D4×C101—82no—
240D4×C101—82no—
241D4×C101—82no—
242D4×C101—161no—
243C2×C4×C101—21no—
244C2×C4×C101—21no—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
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—82no—
260C2×C4×C101C22×D411yescharacteristic
261C2×C4×C101C22×D411yescharacteristic
262C2×C4×C101H(5,𝔽2)11yescharacteristic
263C8×C101—21no—
264C8×C101—21no—
265C8×C101—21no—
266C8×C101—21no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C8×C101—41no—
271C8×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—81no—
282C22×C101—81no—
283C22×C101—81no—
284C22×C101D4211yescharacteristic
285C4×C101—21no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—41no—
291C4×C101—81no—
292C4×C101—81no—
293C4×C101—81no—
294C4×C101#57511yescharacteristic
295C4×C101#57511yescharacteristic
296C4×C101#57611yescharacteristic
297C4×C101#57611yescharacteristic
298#20255C10111yesmaximal, characteristic, direct product factor, Sylow
299C2×C101—81no—
300C2×C101—81no—
301C2×C101—81no—
302C2×C101—161no—
303C2×C101#326811yescharacteristic
304C2×C101#327311yescharacteristic
305C2×C101#328911yescharacteristic
306#3397C2×C10111yescharacteristic, complemented
307#3332C2×C10111yescharacteristic, complemented
308#3330C2×C10111yescharacteristic, complemented
309#3302C2×C10111yescharacteristic, complemented
310#1719C2×C10111yescharacteristic, complemented
311#1700C2×C10111yescharacteristic, complemented
312#1699C2×C10111yescharacteristic, complemented
313#1685C2×C10111yescharacteristic, complemented
314#1681C2×C10111yescharacteristic, complemented
315#1650C2×C10111yescharacteristic, complemented
316#1647C2×C10111yescharacteristic, complemented
317#1641C2×C10111yescharacteristic, complemented
318#1625C2×C10111yescharacteristic, complemented
319#1592C2×C10111yescharacteristic, complemented
320#1581C2×C10111yescharacteristic, complemented
321C101#2025511yescharacteristic, direct product factor, Sylow
322#556C22×C10111yescharacteristic
323#550C22×C10111yescharacteristic
324#547C22×C10111yescharacteristic
325#547C22×C10111yescharacteristic
326#500C22×C10111yescharacteristic
327#496—21no—
328#492C22×C10111yescharacteristic
329#487C22×C10111yescharacteristic
330#487C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic
332#486C22×C10111yescharacteristic
333#485—21no—
334#484—21no—
335#481—21no—
336#475C22×C10111yescharacteristic
337#474C22×C10111yescharacteristic
338#474C22×C10111yescharacteristic
339#469—21no—
340#468—21no—
341#467—21no—
342#463—21no—
343#462C22×C10111yescharacteristic
344#461C22×C10111yescharacteristic
345#461C22×C10111yescharacteristic
346#460—21no—
347#459C22×C10111yescharacteristic
348#459C22×C10111yescharacteristic
349#452—21no—
350#449—21no—
351#449—21no—
352#446C22×C10111yescharacteristic
353#440—21no—
354C4×SD16C22×C10111yescharacteristic
355C4×D8C22×C10111yescharacteristic
356#436C22×C10111yescharacteristic
357#436C22×C10111yescharacteristic
358C8×D4C22×C10111yescharacteristic
359#417—21no—
360#417—21no—
361#416—21no—
362#335C22×C10111yescharacteristic
363#335C22×C10111yescharacteristic
364#332C22×C10111yescharacteristic
365#332C22×C10111yescharacteristic
366#332C22×C10111yescharacteristic
367#331C22×C10111yescharacteristic
368Q8⋊C8C22×C10111yescharacteristic
369D4⋊C8C22×C10111yescharacteristic
370D4⋊C8C22×C10111yescharacteristic
371D4⋊C8C22×C10111yescharacteristic
372#322C22×C10111yescharacteristic
373C2×#41—21no—
374C2×#41—21no—
375C2×#41—21no—
376C2×Q16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16D4×C10111yescharacteristic
382C2×D8—21no—
383C2×D8—21no—
384C2×D8D4×C10111yescharacteristic
385C2×M16—21no—
386C2×M16—21no—
387C22×C8—21no—
388C4⋊Q8C23×C10111yescharacteristic
389C4⋊Q8C23×C10111yescharacteristic
390C4⋊Q8C23×C10111yescharacteristic
391#127—21no—
392#127C23×C10111yescharacteristic
393#126—41no—
394#124—21no—
395#123—41no—
396#123—41no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8—21no—
400#121—21no—
401#121—21no—
402#121—21no—
403#121—41no—
404C4×Q8—21no—
405C4×Q8C23×C10111yescharacteristic
406C4×D4—21no—
407C4×D4C23×C10111yescharacteristic
408C4×D4C23×C10111yescharacteristic
409C4×D4C23×C10111yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412C2×C4⋊C4—21no—
413#107—21no—
414#107—21no—
415#107—41no—
416#107D4×C10111yescharacteristic
417#106—21no—
418#106D4×C10111yescharacteristic
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#103—21no—
428#103—21no—
429#103—21no—
430#103—21no—
431#103—21no—
432#103D4×C10111yescharacteristic
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—41no—
440#102D4×C10111yescharacteristic
441#102D4×C10111yescharacteristic
442#102D4×C10111yescharacteristic
443C22⋊C8—21no—
444C22⋊C8—21no—
445C22⋊C8—21no—
446#97—21no—
447C4×C8C23×C10111yescharacteristic
448C4×C8C23×C10111yescharacteristic
449C4×C8C23×C10111yescharacteristic
450#41—42no—
451#41—42no—
452#41—42no—
453#41—81no—
454#41—81no—
455#41—81no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8—21no—
459C2×Q8C2×D4×C10111yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4C2×D4×C10111yescharacteristic
468C2×D4C2×D4×C10111yescharacteristic
469C2×D4C2×D4×C10111yescharacteristic
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476Q16—81no—
477SD16—41no—
478SD16—42no—
479SD16—81no—
480SD16—81no—
481SD16—81no—
482D8—41no—
483D8—81no—
484D8—81no—
485M16—81no—
486M16—81no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—81no—
493C2×C8C2×D4×C10111yescharacteristic
494C2×C8C2×D4×C10111yescharacteristic
495C2×C8C2×D4×C10111yescharacteristic
496C2×C8C2×D4×C10111yescharacteristic
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—41no—
505C4⋊C4—41no—
506C4⋊C4—41no—
507C4⋊C4C2×D4×C10111yescharacteristic
508C4⋊C4C2×D4×C10111yescharacteristic
509C4⋊C4C2×D4×C10111yescharacteristic
510C4⋊C4C2×D4×C10111yescharacteristic
511C22⋊C4—21no—
512C22⋊C4—21no—
513C22⋊C4—21no—
514C22⋊C4—41no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C42—21no—
520C42—41no—
521C42C24×C10111yescharacteristic
522C23—21no—
523C23—21no—
524C23—21no—
525C23—41no—
526Q8—21no—
527Q8—21no—
528Q8—41no—
529Q8—41no—
530Q8—41no—
531Q8—41no—
532Q8—41no—
533Q8—41no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—21no—
539D4—21no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—82no—
546D4—82no—
547D4—82no—
548D4—161no—
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—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—82no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4C22×D4×C10111yescharacteristic
567C2×C4C22×D4×C10111yescharacteristic
568C2×C4H(5,𝔽2)×C10111yescharacteristic
569C8—21no—
570C8—21no—
571C8—21no—
572C8—21no—
573C8—41no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—41no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22D42×C10111yescharacteristic
591C4—21no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—81no—
598C4—81no—
599C4—81no—
600C4#575×C10111yescharacteristic
601C4#575×C10111yescharacteristic
602C4#576×C10111yescharacteristic
603C4#576×C10111yescharacteristic
604C2—81no—
605C2—81no—
606C2—81no—
607C2—161no—
608C2C101×#326811yescharacteristic
609C2C101×#327311yescharacteristic
610C2C101×#328911yescharacteristic
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×#3332C2semidirect
3. C101×#3330C2semidirect
4. C101×#3302C2semidirect
5. C101×#1719C2semidirect
6. C101×#1700C2semidirect
7. C101×#1699C2semidirect
8. C101×#1685C2semidirect
9. C101×#1681C2semidirect
10. C101×#1650C2semidirect
11. C101×#1647C2semidirect
12. C101×#1641C2semidirect
13. C101×#1625C2semidirect
14. C101×#1592C2semidirect
15. C101×#1581C2semidirect
298. #20255C101direct (N × H)
306. #3397C2×C101semidirect
307. #3332C2×C101semidirect
308. #3330C2×C101semidirect
309. #3302C2×C101semidirect
310. #1719C2×C101semidirect
311. #1700C2×C101semidirect
312. #1699C2×C101semidirect
313. #1685C2×C101semidirect
314. #1681C2×C101semidirect
315. #1650C2×C101semidirect
316. #1647C2×C101semidirect
317. #1641C2×C101semidirect
318. #1625C2×C101semidirect
319. #1592C2×C101semidirect
320. #1581C2×C101semidirect
321. C101#20255direct (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×#33322
C101×#33302
C101×#33022
C101×#17192
C101×#17002
C101×#16992
C101×#16852
C101×#16812
C101×#16502
C101×#16472
C101×#16412
C101×#16252
C101×#15922
C101×#15812
#20255101