Finite Group Databasebeta

← C101×#20244 #38802395

Subgroups — C101×#20244 #38802395

Order 25856.

616 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3366C211yesmaximal, characteristic, complemented
2C101×#3357C211yesmaximal, characteristic, complemented
3C101×#3332C211yesmaximal, characteristic, complemented
4C101×#3303C211yesmaximal, characteristic, complemented
5C101×#1719C211yesmaximal, characteristic, complemented
6C101×#1704C211yesmaximal, characteristic, complemented
7C101×#1701C211yesmaximal, characteristic, complemented
8C101×#1695C211yesmaximal, characteristic, complemented
9C101×#1677C211yesmaximal, characteristic, complemented
10C101×#1643C211yesmaximal, characteristic, complemented
11C101×#1635C211yesmaximal, characteristic, complemented
12C101×#1631C211yesmaximal, characteristic, complemented
13C101×#1624C211yesmaximal, characteristic, complemented
14C101×#1594C211yesmaximal, characteristic, complemented
15C101×#1582C211yesmaximal, characteristic, complemented
16#555×C101C2211yescharacteristic
17#554×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#492×C101C2211yescharacteristic
22#490×C101—21no—
23#487×C101C2211yescharacteristic
24#487×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#485×C101—21no—
28#485×C101—21no—
29#481×C101—21no—
30#480×C101—21no—
31#478×C101—21no—
32#477×C101C2211yescharacteristic
33#476×C101C2211yescharacteristic
34#476×C101C2211yescharacteristic
35#476×C101C2211yescharacteristic
36#475×C101C2211yescharacteristic
37#469×C101—21no—
38#468×C101—21no—
39#465×C101—21no—
40#461×C101C2211yescharacteristic
41#459×C101—21no—
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#449×C101—21no—
45#449×C101—21no—
46#446×C101C2211yescharacteristic
47#442×C101—21no—
48C4×SD16×C101C2211yescharacteristic
49C4×D8×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic
53#428×C101—21no—
54#417×C101—21no—
55#416×C101—21no—
56#334×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×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×SD16×C101—21no—
70C2×SD16×C101—41no—
71C2×SD16×C101D411yescharacteristic
72C2×D8×C101—21no—
73C2×D8×C101—21no—
74C2×D8×C101D411yescharacteristic
75C2×M16×C101—21no—
76C2×M16×C101—21no—
77C22×C8×C101—21no—
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81#127×C101—21no—
82#127×C101C2311yescharacteristic
83#125×C101—21no—
84#124×C101—41no—
85#123×C101—41no—
86C22⋊Q8×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—41no—
89#121×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—41no—
94C4×Q8×C101C2311yescharacteristic
95C4×D4×C101—21no—
96C4×D4×C101—21no—
97C4×D4×C101C2311yescharacteristic
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100#117×C101—21no—
101#117×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101D411yescharacteristic
108#106×C101—21no—
109#106×C101—21no—
110#106×C101—21no—
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—41no—
124#103×C101D411yescharacteristic
125#102×C101—21no—
126#102×C101—21no—
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×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—81no—
147#41×C101—81no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101C2×D411yescharacteristic
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C2×D4×C101C2×D411yescharacteristic
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—41no—
166C22×C4×C101—41no—
167C22×C4×C101—41no—
168SD16×C101—41no—
169SD16×C101—81no—
170SD16×C101—82no—
171D8×C101—41no—
172D8×C101—42no—
173D8×C101—81no—
174M16×C101—42no—
175M16×C101—81no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—81no—
182C2×C8×C101C2×D411yescharacteristic
183C2×C8×C101C2×D411yescharacteristic
184C2×C8×C101C2×D411yescharacteristic
185C2×C8×C101C2×D411yescharacteristic
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—21no—
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—41no—
194C4⋊C4×C101—41no—
195C4⋊C4×C101—41no—
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C4⋊C4×C101C2×D411yescharacteristic
200C22⋊C4×C101—21no—
201C22⋊C4×C101—21no—
202C22⋊C4×C101—21no—
203C22⋊C4×C101—41no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C22⋊C4×C101—41no—
208C42×C101—21no—
209C42×C101—41no—
210C42×C101C2411yescharacteristic
211C23×C101—21no—
212C23×C101—21no—
213C23×C101—21no—
214C23×C101—41no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—81no—
220Q8×C101—81no—
221D4×C101—21no—
222D4×C101—21no—
223D4×C101—21no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—41no—
228D4×C101—41no—
229D4×C101—41no—
230D4×C101—41no—
231D4×C101—81no—
232D4×C101—82no—
233D4×C101—82no—
234D4×C101—161no—
235D4×C101—161no—
236C2×C4×C101—21no—
237C2×C4×C101—21no—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—82no—
251C2×C4×C101—82no—
252C2×C4×C101—161no—
253C2×C4×C101C22×D411yescharacteristic
254C2×C4×C101C22×D411yescharacteristic
255C2×C4×C101H(5,𝔽2)11yescharacteristic
256C8×C101—21no—
257C8×C101—21no—
258C8×C101—21no—
259C8×C101—21no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101—41no—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—81no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101D4211yescharacteristic
278C4×C101—21no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—41no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—81no—
285C4×C101—81no—
286C4×C101—81no—
287C4×C101#57511yescharacteristic
288C4×C101#57511yescharacteristic
289C4×C101#57711yescharacteristic
290C4×C101#57711yescharacteristic
291#20244C10111yesmaximal, characteristic, direct product factor, Sylow
292C2×C101—81no—
293C2×C101—81no—
294C2×C101—81no—
295C2×C101—161no—
296C2×C101#326711yescharacteristic
297C2×C101#327511yescharacteristic
298C2×C101#328811yescharacteristic
299#3366C2×C10111yescharacteristic, complemented
300#3357C2×C10111yescharacteristic, complemented
301#3332C2×C10111yescharacteristic, complemented
302#3303C2×C10111yescharacteristic, complemented
303#1719C2×C10111yescharacteristic, complemented
304#1704C2×C10111yescharacteristic, complemented
305#1701C2×C10111yescharacteristic, complemented
306#1695C2×C10111yescharacteristic, complemented
307#1677C2×C10111yescharacteristic, complemented
308#1643C2×C10111yescharacteristic, complemented
309#1635C2×C10111yescharacteristic, complemented
310#1631C2×C10111yescharacteristic, complemented
311#1624C2×C10111yescharacteristic, complemented
312#1594C2×C10111yescharacteristic, complemented
313#1582C2×C10111yescharacteristic, complemented
314C101#2024411yescharacteristic, direct product factor, Sylow
315#555C22×C10111yescharacteristic
316#554C22×C10111yescharacteristic
317#550C22×C10111yescharacteristic
318#547C22×C10111yescharacteristic
319#500C22×C10111yescharacteristic
320#492C22×C10111yescharacteristic
321#490—21no—
322#487C22×C10111yescharacteristic
323#487C22×C10111yescharacteristic
324#486C22×C10111yescharacteristic
325#486C22×C10111yescharacteristic
326#485—21no—
327#485—21no—
328#481—21no—
329#480—21no—
330#478—21no—
331#477C22×C10111yescharacteristic
332#476C22×C10111yescharacteristic
333#476C22×C10111yescharacteristic
334#476C22×C10111yescharacteristic
335#475C22×C10111yescharacteristic
336#469—21no—
337#468—21no—
338#465—21no—
339#461C22×C10111yescharacteristic
340#459—21no—
341#459C22×C10111yescharacteristic
342#459C22×C10111yescharacteristic
343#449—21no—
344#449—21no—
345#446C22×C10111yescharacteristic
346#442—21no—
347C4×SD16C22×C10111yescharacteristic
348C4×D8C22×C10111yescharacteristic
349#436C22×C10111yescharacteristic
350#436C22×C10111yescharacteristic
351C8×D4C22×C10111yescharacteristic
352#428—21no—
353#417—21no—
354#416—21no—
355#334C22×C10111yescharacteristic
356#334C22×C10111yescharacteristic
357#333C22×C10111yescharacteristic
358#333C22×C10111yescharacteristic
359#332C22×C10111yescharacteristic
360#331C22×C10111yescharacteristic
361Q8⋊C8C22×C10111yescharacteristic
362D4⋊C8C22×C10111yescharacteristic
363D4⋊C8C22×C10111yescharacteristic
364D4⋊C8C22×C10111yescharacteristic
365#322C22×C10111yescharacteristic
366C2×#41—21no—
367C2×#41—21no—
368C2×SD16—21no—
369C2×SD16—41no—
370C2×SD16D4×C10111yescharacteristic
371C2×D8—21no—
372C2×D8—21no—
373C2×D8D4×C10111yescharacteristic
374C2×M16—21no—
375C2×M16—21no—
376C22×C8—21no—
377C4⋊Q8C23×C10111yescharacteristic
378C4⋊Q8C23×C10111yescharacteristic
379C4⋊Q8C23×C10111yescharacteristic
380#127—21no—
381#127C23×C10111yescharacteristic
382#125—21no—
383#124—41no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—41no—
388#121—21no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—41no—
393C4×Q8C23×C10111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C10111yescharacteristic
397C4×D4C23×C10111yescharacteristic
398C4×D4C23×C10111yescharacteristic
399#117—21no—
400#117—21no—
401C2×C4⋊C4—21no—
402C2×C4⋊C4—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#107D4×C10111yescharacteristic
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106D4×C10111yescharacteristic
412C4⋊C8—21no—
413C4⋊C8C23×C10111yescharacteristic
414C4⋊C8C23×C10111yescharacteristic
415C4⋊C8C23×C10111yescharacteristic
416C4⋊C8C23×C10111yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C10111yescharacteristic
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102D4×C10111yescharacteristic
434#102D4×C10111yescharacteristic
435#102D4×C10111yescharacteristic
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439#97—21no—
440C4×C8C23×C10111yescharacteristic
441C4×C8C23×C10111yescharacteristic
442C4×C8C23×C10111yescharacteristic
443#41—42no—
444#41—42no—
445#41—81no—
446#41—81no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C10111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C2×D4×C10111yescharacteristic
459C2×D4C2×D4×C10111yescharacteristic
460C2×D4C2×D4×C10111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467SD16—41no—
468SD16—81no—
469SD16—82no—
470D8—41no—
471D8—42no—
472D8—81no—
473M16—42no—
474M16—81no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—81no—
481C2×C8C2×D4×C10111yescharacteristic
482C2×C8C2×D4×C10111yescharacteristic
483C2×C8C2×D4×C10111yescharacteristic
484C2×C8C2×D4×C10111yescharacteristic
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4—41no—
495C4⋊C4C2×D4×C10111yescharacteristic
496C4⋊C4C2×D4×C10111yescharacteristic
497C4⋊C4C2×D4×C10111yescharacteristic
498C4⋊C4C2×D4×C10111yescharacteristic
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—41no—
509C42C24×C10111yescharacteristic
510C23—21no—
511C23—21no—
512C23—21no—
513C23—41no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—81no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4—82no—
533D4—161no—
534D4—161no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—161no—
552C2×C4C22×D4×C10111yescharacteristic
553C2×C4C22×D4×C10111yescharacteristic
554C2×C4H(5,𝔽2)×C10111yescharacteristic
555C8—21no—
556C8—21no—
557C8—21no—
558C8—21no—
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22D42×C10111yescharacteristic
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4#575×C10111yescharacteristic
587C4#575×C10111yescharacteristic
588C4#577×C10111yescharacteristic
589C4#577×C10111yescharacteristic
590C2—81no—
591C2—81no—
592C2—81no—
593C2—161no—
594C2C101×#326711yescharacteristic
595C2C101×#327511yescharacteristic
596C2C101×#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×#3366C2semidirect
2. C101×#3357C2semidirect
3. C101×#3332C2semidirect
4. C101×#3303C2semidirect
5. C101×#1719C2semidirect
6. C101×#1704C2semidirect
7. C101×#1701C2semidirect
8. C101×#1695C2semidirect
9. C101×#1677C2semidirect
10. C101×#1643C2semidirect
11. C101×#1635C2semidirect
12. C101×#1631C2semidirect
13. C101×#1624C2semidirect
14. C101×#1594C2semidirect
15. C101×#1582C2semidirect
291. #20244C101direct (N × H)
299. #3366C2×C101semidirect
300. #3357C2×C101semidirect
301. #3332C2×C101semidirect
302. #3303C2×C101semidirect
303. #1719C2×C101semidirect
304. #1704C2×C101semidirect
305. #1701C2×C101semidirect
306. #1695C2×C101semidirect
307. #1677C2×C101semidirect
308. #1643C2×C101semidirect
309. #1635C2×C101semidirect
310. #1631C2×C101semidirect
311. #1624C2×C101semidirect
312. #1594C2×C101semidirect
313. #1582C2×C101semidirect
314. C101#20244direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33662
C101×#33572
C101×#33322
C101×#33032
C101×#17192
C101×#17042
C101×#17012
C101×#16952
C101×#16772
C101×#16432
C101×#16352
C101×#16312
C101×#16242
C101×#15942
C101×#15822
#20244101