Finite Group Databasebeta

← C101×#20290 #38802441

Subgroups — C101×#20290 #38802441

Order 25856.

626 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×#3366C211yesmaximal, characteristic, complemented
2C101×#3332C211yesmaximal, characteristic, complemented
3C101×#3331C211yesmaximal, characteristic, complemented
4C101×#3330C211yesmaximal, characteristic, complemented
5C101×#1711C211yesmaximal, characteristic, complemented
6C101×#1703C211yesmaximal, characteristic, complemented
7C101×#1701C211yesmaximal, characteristic, complemented
8C101×#1700C211yesmaximal, characteristic, complemented
9C101×#1697C211yesmaximal, characteristic, complemented
10C101×#1643C211yesmaximal, characteristic, complemented
11C101×#1641C211yesmaximal, characteristic, complemented
12C101×#1635C211yesmaximal, characteristic, complemented
13C101×#1625C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16#554×C101C2211yescharacteristic
17#550×C101C2211yescharacteristic
18#547×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#490×C101—21no—
21#487×C101C2211yescharacteristic
22#487×C101C2211yescharacteristic
23#487×C101C2211yescharacteristic
24#486×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#484×C101—21no—
28#483×C101—21no—
29#481×C101—21no—
30#478×C101—21no—
31#476×C101C2211yescharacteristic
32#476×C101C2211yescharacteristic
33#475×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#470×C101—21no—
36#469×C101—21no—
37#468×C101—21no—
38#462×C101C2211yescharacteristic
39#461×C101C2211yescharacteristic
40#459×C101—21no—
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#452×C101—21no—
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
52#436×C101C2211yescharacteristic
53#417×C101—21no—
54#417×C101—21no—
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—21no—
70C2×Q16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101D411yescharacteristic
73C2×D8×C101—21no—
74C2×D8×C101—21no—
75C2×D8×C101D411yescharacteristic
76C2×M16×C101—21no—
77C2×M16×C101—21no—
78C2×M16×C101—21no—
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82#127×C101—21no—
83#127×C101C2311yescharacteristic
84#125×C101—21no—
85#123×C101—41no—
86#123×C101—41no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—41no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—41no—
95C4×Q8×C101C2311yescharacteristic
96C4×D4×C101—21no—
97C4×D4×C101—21no—
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101—21no—
104#107×C101—21no—
105#107×C101D411yescharacteristic
106#106×C101—21no—
107#106×C101—21no—
108#106×C101—21no—
109#106×C101D411yescharacteristic
110C4⋊C8×C101—21no—
111C4⋊C8×C101C2311yescharacteristic
112C4⋊C8×C101C2311yescharacteristic
113C4⋊C8×C101C2311yescharacteristic
114C4⋊C8×C101C2311yescharacteristic
115#103×C101—21no—
116#103×C101—21no—
117#103×C101—21no—
118#103×C101—21no—
119#103×C101—21no—
120#103×C101—21no—
121#103×C101—21no—
122#103×C101—41no—
123#103×C101D411yescharacteristic
124#102×C101—21no—
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—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—
170C22×C4×C101—41no—
171Q16×C101—81no—
172SD16×C101—41no—
173SD16×C101—81no—
174D8×C101—41no—
175D8×C101—42no—
176D8×C101—81no—
177M16×C101—81no—
178M16×C101—81no—
179M16×C101—81no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101C2×D411yescharacteristic
186C2×C8×C101C2×D411yescharacteristic
187C2×C8×C101C2×D411yescharacteristic
188C2×C8×C101C2×D411yescharacteristic
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—21no—
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—41no—
197C4⋊C4×C101—41no—
198C4⋊C4×C101—41no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101C2×D411yescharacteristic
201C4⋊C4×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C22⋊C4×C101—21no—
205C22⋊C4×C101—21no—
206C22⋊C4×C101—21no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C42×C101—21no—
212C42×C101C2411yescharacteristic
213C23×C101—21no—
214C23×C101—21no—
215C23×C101—21no—
216C23×C101—41no—
217Q8×C101—21no—
218Q8×C101—21no—
219Q8×C101—41no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—81no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—81no—
235D4×C101—82no—
236D4×C101—82no—
237D4×C101—82no—
238D4×C101—161no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
243C2×C4×C101—21no—
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—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—82no—
254C2×C4×C101—82no—
255C2×C4×C101—82no—
256C2×C4×C101—161no—
257C2×C4×C101C22×D411yescharacteristic
258C2×C4×C101C22×D411yescharacteristic
259C2×C4×C101H(5,𝔽2)11yescharacteristic
260C8×C101—21no—
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—21no—
264C8×C101—41no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101—41no—
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—81no—
289C4×C101—81no—
290C4×C101—81no—
291C4×C101#57511yescharacteristic
292C4×C101#57511yescharacteristic
293C4×C101#57611yescharacteristic
294C4×C101#57711yescharacteristic
295#20290C10111yesmaximal, characteristic, direct product factor, Sylow
296C2×C101—81no—
297C2×C101—81no—
298C2×C101—81no—
299C2×C101—161no—
300C2×C101#327311yescharacteristic
301C2×C101#327511yescharacteristic
302C2×C101#329011yescharacteristic
303#3366C2×C10111yescharacteristic, complemented
304#3332C2×C10111yescharacteristic, complemented
305#3331C2×C10111yescharacteristic, complemented
306#3330C2×C10111yescharacteristic, complemented
307#1711C2×C10111yescharacteristic, complemented
308#1703C2×C10111yescharacteristic, complemented
309#1701C2×C10111yescharacteristic, complemented
310#1700C2×C10111yescharacteristic, complemented
311#1697C2×C10111yescharacteristic, complemented
312#1643C2×C10111yescharacteristic, complemented
313#1641C2×C10111yescharacteristic, complemented
314#1635C2×C10111yescharacteristic, complemented
315#1625C2×C10111yescharacteristic, complemented
316#1590C2×C10111yescharacteristic, complemented
317#1589C2×C10111yescharacteristic, complemented
318C101#2029011yescharacteristic, direct product factor, Sylow
319#554C22×C10111yescharacteristic
320#550C22×C10111yescharacteristic
321#547C22×C10111yescharacteristic
322#547C22×C10111yescharacteristic
323#490—21no—
324#487C22×C10111yescharacteristic
325#487C22×C10111yescharacteristic
326#487C22×C10111yescharacteristic
327#486C22×C10111yescharacteristic
328#486C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#484—21no—
331#483—21no—
332#481—21no—
333#478—21no—
334#476C22×C10111yescharacteristic
335#476C22×C10111yescharacteristic
336#475C22×C10111yescharacteristic
337#474C22×C10111yescharacteristic
338#470—21no—
339#469—21no—
340#468—21no—
341#462C22×C10111yescharacteristic
342#461C22×C10111yescharacteristic
343#459—21no—
344#459C22×C10111yescharacteristic
345#459C22×C10111yescharacteristic
346#452—21no—
347#449—21no—
348#449—21no—
349#446C22×C10111yescharacteristic
350#442—21no—
351C4×SD16C22×C10111yescharacteristic
352C4×D8C22×C10111yescharacteristic
353#436C22×C10111yescharacteristic
354#436C22×C10111yescharacteristic
355#436C22×C10111yescharacteristic
356#417—21no—
357#417—21no—
358#417—21no—
359#335C22×C10111yescharacteristic
360#334C22×C10111yescharacteristic
361#333C22×C10111yescharacteristic
362#332C22×C10111yescharacteristic
363#332C22×C10111yescharacteristic
364#331C22×C10111yescharacteristic
365Q8⋊C8C22×C10111yescharacteristic
366D4⋊C8C22×C10111yescharacteristic
367D4⋊C8C22×C10111yescharacteristic
368D4⋊C8C22×C10111yescharacteristic
369C82C22×C10111yescharacteristic
370C2×#41—21no—
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16D4×C10111yescharacteristic
376C2×D8—21no—
377C2×D8—21no—
378C2×D8D4×C10111yescharacteristic
379C2×M16—21no—
380C2×M16—21no—
381C2×M16—21no—
382C4⋊Q8C23×C10111yescharacteristic
383C4⋊Q8C23×C10111yescharacteristic
384C4⋊Q8C23×C10111yescharacteristic
385#127—21no—
386#127C23×C10111yescharacteristic
387#125—21no—
388#123—41no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—41no—
398C4×Q8C23×C10111yescharacteristic
399C4×D4—21no—
400C4×D4—21no—
401C4×D4C23×C10111yescharacteristic
402C4×D4C23×C10111yescharacteristic
403C4×D4C23×C10111yescharacteristic
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406C2×C4⋊C4—21no—
407#107—21no—
408#107D4×C10111yescharacteristic
409#106—21no—
410#106—21no—
411#106—21no—
412#106D4×C10111yescharacteristic
413C4⋊C8—21no—
414C4⋊C8C23×C10111yescharacteristic
415C4⋊C8C23×C10111yescharacteristic
416C4⋊C8C23×C10111yescharacteristic
417C4⋊C8C23×C10111yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C10111yescharacteristic
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—41no—
437#102D4×C10111yescharacteristic
438#102D4×C10111yescharacteristic
439#102D4×C10111yescharacteristic
440C22⋊C8—21no—
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444C4×C8C23×C10111yescharacteristic
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447#41—42no—
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452#41—81no—
453C2×Q8—21no—
454C2×Q8—21no—
455C2×Q8—21no—
456C2×Q8C2×D4×C10111yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C10111yescharacteristic
465C2×D4C2×D4×C10111yescharacteristic
466C2×D4C2×D4×C10111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473C22×C4—41no—
474Q16—81no—
475SD16—41no—
476SD16—81no—
477D8—41no—
478D8—42no—
479D8—81no—
480M16—81no—
481M16—81no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8C2×D4×C10111yescharacteristic
489C2×C8C2×D4×C10111yescharacteristic
490C2×C8C2×D4×C10111yescharacteristic
491C2×C8C2×D4×C10111yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C10111yescharacteristic
504C4⋊C4C2×D4×C10111yescharacteristic
505C4⋊C4C2×D4×C10111yescharacteristic
506C4⋊C4C2×D4×C10111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42C24×C10111yescharacteristic
516C23—21no—
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—81no—
538D4—82no—
539D4—82no—
540D4—82no—
541D4—161no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4—161no—
560C2×C4C22×D4×C10111yescharacteristic
561C2×C4C22×D4×C10111yescharacteristic
562C2×C4H(5,𝔽2)×C10111yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22D42×C10111yescharacteristic
585C4—21no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4#575×C10111yescharacteristic
595C4#575×C10111yescharacteristic
596C4#576×C10111yescharacteristic
597C4#577×C10111yescharacteristic
598C2—81no—
599C2—81no—
600C2—81no—
601C2—161no—
602C2C101×#327311yescharacteristic
603C2C101×#327511yescharacteristic
604C2C101×#329011yescharacteristic
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×#3332C2semidirect
3. C101×#3331C2semidirect
4. C101×#3330C2semidirect
5. C101×#1711C2semidirect
6. C101×#1703C2semidirect
7. C101×#1701C2semidirect
8. C101×#1700C2semidirect
9. C101×#1697C2semidirect
10. C101×#1643C2semidirect
11. C101×#1641C2semidirect
12. C101×#1635C2semidirect
13. C101×#1625C2semidirect
14. C101×#1590C2semidirect
15. C101×#1589C2semidirect
295. #20290C101direct (N × H)
303. #3366C2×C101semidirect
304. #3332C2×C101semidirect
305. #3331C2×C101semidirect
306. #3330C2×C101semidirect
307. #1711C2×C101semidirect
308. #1703C2×C101semidirect
309. #1701C2×C101semidirect
310. #1700C2×C101semidirect
311. #1697C2×C101semidirect
312. #1643C2×C101semidirect
313. #1641C2×C101semidirect
314. #1635C2×C101semidirect
315. #1625C2×C101semidirect
316. #1590C2×C101semidirect
317. #1589C2×C101semidirect
318. C101#20290direct (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×#33322
C101×#33312
C101×#33302
C101×#17112
C101×#17032
C101×#17012
C101×#17002
C101×#16972
C101×#16432
C101×#16412
C101×#16352
C101×#16252
C101×#15902
C101×#15892
#20290101