Finite Group Databasebeta

← C101×#20299 #38802450

Subgroups — C101×#20299 #38802450

Order 25856.

608 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3399C211yesmaximal, characteristic
2C101×#3385C211yesmaximal, characteristic, complemented
3C101×#3375C211yesmaximal, characteristic, complemented
4C101×#3333C211yesmaximal, characteristic, complemented
5C101×#1706C211yesmaximal, characteristic, complemented
6C101×#1698C211yesmaximal, characteristic, complemented
7C101×#1697C211yesmaximal, characteristic, complemented
8C101×#1696C211yesmaximal, characteristic, complemented
9C101×#1688C211yesmaximal, characteristic, complemented
10C101×#1631C211yesmaximal, characteristic, complemented
11C101×#1630C211yesmaximal, characteristic, complemented
12C101×#1623C211yesmaximal, characteristic, complemented
13C101×#1622C211yesmaximal, characteristic, complemented
14C101×#1591C211yesmaximal, characteristic, complemented
15C101×#1590C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17Q82×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#501×C101—21no—
21#500×C101C2211yescharacteristic
22#496×C101—21no—
23#493×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#489×C101—21no—
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#480×C101—21no—
30#479×C101—21no—
31#477×C101C2211yescharacteristic
32#477×C101C2211yescharacteristic
33#477×C101C2211yescharacteristic
34#476×C101C2211yescharacteristic
35#474×C101—21no—
36#474×C101—21no—
37#468×C101—21no—
38#464×C101—21no—
39#463×C101—21no—
40#460×C101C2211yescharacteristic
41#460×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#459×C101—21no—
44#459×C101C2211yescharacteristic
45#452×C101—21no—
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#442×C101—21no—
50#440×C101—21no—
51#440×C101—21no—
52C4×Q16×C101C2211yescharacteristic
53C4×SD16×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×Q16×C101D411yescharacteristic
69C2×SD16×C101—21no—
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—41no—
73C2×SD16×C101—41no—
74C2×SD16×C101D411yescharacteristic
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×M16×C101—21no—
79C4⋊Q8×C101—21no—
80C4⋊Q8×C101—21no—
81C4⋊Q8×C101—41no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101—21no—
85#127×C101C2311yescharacteristic
86#127×C101C2311yescharacteristic
87#125×C101—21no—
88#124×C101—21no—
89#124×C101—21no—
90#123×C101—41no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—41no—
93#121×C101—21no—
94#121×C101—41no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×Q8×C101C2311yescharacteristic
98C4×Q8×C101C2311yescharacteristic
99C4×Q8×C101C2311yescharacteristic
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101C2311yescharacteristic
105C2×C4⋊C4×C101—21no—
106#107×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101D411yescharacteristic
112#106×C101—21no—
113#106×C101D411yescharacteristic
114C4⋊C8×C101—21no—
115C4⋊C8×C101—21no—
116C4⋊C8×C101—21no—
117C4⋊C8×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121#103×C101—21no—
122#103×C101—21no—
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×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138#97×C101—21no—
139#97×C101—21no—
140#97×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—42no—
145#41×C101—81no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—41no—
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101C2×D411yescharacteristic
161C22×C4×C101—21no—
162C22×C4×C101—41no—
163C22×C4×C101—41no—
164C22×C4×C101—41no—
165Q16×C101—41no—
166SD16×C101—22no—
167SD16×C101—42no—
168SD16×C101—82no—
169SD16×C101—82no—
170SD16×C101—81no—
171SD16×C101—81no—
172D8×C101—42no—
173D8×C101—81no—
174D8×C101—81no—
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×C101C2×D411yescharacteristic
182C2×C8×C101C2×D411yescharacteristic
183C2×C8×C101C2×D411yescharacteristic
184C2×C8×C101C2×D411yescharacteristic
185C4⋊C4×C101—21no—
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—41no—
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—41no—
202C22⋊C4×C101—41no—
203C22⋊C4×C101—41no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C42×C101—21no—
207C42×C101—21no—
208C42×C101—21no—
209C42×C101—41no—
210C42×C101C2411yescharacteristic
211C23×C101—21no—
212C23×C101—41no—
213C23×C101—41no—
214Q8×C101—21no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—21no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—81no—
221Q8×C101—81no—
222Q8×C101—161no—
223D4×C101—21no—
224D4×C101—21no—
225D4×C101—41no—
226D4×C101—41no—
227D4×C101—41no—
228D4×C101—41no—
229D4×C101—41no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—81no—
234D4×C101—81no—
235D4×C101—82no—
236D4×C101—161no—
237C2×C4×C101—21no—
238C2×C4×C101—21no—
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—82no—
249C2×C4×C101—161no—
250C2×C4×C101—161no—
251C2×C4×C101C22×D411yescharacteristic
252C2×C4×C101C22×D411yescharacteristic
253C2×C4×C101H(5,𝔽2)11yescharacteristic
254C8×C101—22no—
255C8×C101—21no—
256C8×C101—21no—
257C8×C101—21no—
258C8×C101—41no—
259C8×C101—41no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101#13712yes—
263C22×C101—41no—
264C22×C101—41no—
265C22×C101—41no—
266C22×C101—81no—
267C22×C101—81no—
268C22×C101—81no—
269C22×C101—81no—
270C22×C101—81no—
271C22×C101—81no—
272C22×C101D4211yescharacteristic
273C4×C101—21no—
274C4×C101—41no—
275C4×C101—41no—
276C4×C101—41no—
277C4×C101—41no—
278C4×C101—41no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—81no—
282C4×C101—81no—
283C4×C101C2×#13711yescharacteristic
284C4×C101#57511yescharacteristic
285C4×C101#57711yescharacteristic
286C4×C101#57711yescharacteristic
287#20299C10111yesmaximal, characteristic, direct product factor, Sylow
288C2×C101—81no—
289C2×C101—161no—
290C2×C101—161no—
291C2×C101#327511yescharacteristic
292C2×C101#327811yescharacteristic
293C2×C101#329211yescharacteristic
294#3399C2×C10111yescharacteristic
295#3385C2×C10111yescharacteristic, complemented
296#3375C2×C10111yescharacteristic, complemented
297#3333C2×C10111yescharacteristic, complemented
298#1706C2×C10111yescharacteristic, complemented
299#1698C2×C10111yescharacteristic, complemented
300#1697C2×C10111yescharacteristic, complemented
301#1696C2×C10111yescharacteristic, complemented
302#1688C2×C10111yescharacteristic, complemented
303#1631C2×C10111yescharacteristic, complemented
304#1630C2×C10111yescharacteristic, complemented
305#1623C2×C10111yescharacteristic, complemented
306#1622C2×C10111yescharacteristic, complemented
307#1591C2×C10111yescharacteristic, complemented
308#1590C2×C10111yescharacteristic, complemented
309C101#2029911yescharacteristic, direct product factor, Sylow
310#559C22×C10111yescharacteristic
311Q82C22×C10111yescharacteristic
312#554C22×C10111yescharacteristic
313#550C22×C10111yescharacteristic
314#501—21no—
315#500C22×C10111yescharacteristic
316#496—21no—
317#493C22×C10111yescharacteristic
318#492C22×C10111yescharacteristic
319#492C22×C10111yescharacteristic
320#489—21no—
321#486C22×C10111yescharacteristic
322#486C22×C10111yescharacteristic
323#480—21no—
324#479—21no—
325#477C22×C10111yescharacteristic
326#477C22×C10111yescharacteristic
327#477C22×C10111yescharacteristic
328#476C22×C10111yescharacteristic
329#474—21no—
330#474—21no—
331#468—21no—
332#464—21no—
333#463—21no—
334#460C22×C10111yescharacteristic
335#460C22×C10111yescharacteristic
336#460C22×C10111yescharacteristic
337#459—21no—
338#459C22×C10111yescharacteristic
339#452—21no—
340#446C22×C10111yescharacteristic
341#446C22×C10111yescharacteristic
342#446C22×C10111yescharacteristic
343#442—21no—
344#440—21no—
345#440—21no—
346C4×Q16C22×C10111yescharacteristic
347C4×SD16C22×C10111yescharacteristic
348#436C22×C10111yescharacteristic
349#417—21no—
350#335C22×C10111yescharacteristic
351#334C22×C10111yescharacteristic
352#333C22×C10111yescharacteristic
353#333C22×C10111yescharacteristic
354#331C22×C10111yescharacteristic
355#331C22×C10111yescharacteristic
356Q8⋊C8C22×C10111yescharacteristic
357Q8⋊C8C22×C10111yescharacteristic
358Q8⋊C8C22×C10111yescharacteristic
359D4⋊C8C22×C10111yescharacteristic
360C82C22×C10111yescharacteristic
361C2×#41—21no—
362C2×Q16D4×C10111yescharacteristic
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16—21no—
366C2×SD16—41no—
367C2×SD16—41no—
368C2×SD16D4×C10111yescharacteristic
369C2×D8—21no—
370C2×D8—21no—
371C2×D8—21no—
372C2×M16—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—41no—
376C4⋊Q8C23×C10111yescharacteristic
377C4⋊Q8C23×C10111yescharacteristic
378#127—21no—
379#127C23×C10111yescharacteristic
380#127C23×C10111yescharacteristic
381#125—21no—
382#124—21no—
383#124—21no—
384#123—41no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387#121—21no—
388#121—41no—
389C4×Q8—21no—
390C4×Q8—21no—
391C4×Q8C23×C10111yescharacteristic
392C4×Q8C23×C10111yescharacteristic
393C4×Q8C23×C10111yescharacteristic
394C4×D4—21no—
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C10111yescharacteristic
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107—21no—
403#107—21no—
404#107—21no—
405#107D4×C10111yescharacteristic
406#106—21no—
407#106D4×C10111yescharacteristic
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C10111yescharacteristic
412C4⋊C8C23×C10111yescharacteristic
413C4⋊C8C23×C10111yescharacteristic
414C4⋊C8C23×C10111yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103D4×C10111yescharacteristic
419#103D4×C10111yescharacteristic
420#103D4×C10111yescharacteristic
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102D4×C10111yescharacteristic
431C22⋊C8—21no—
432#97—21no—
433#97—21no—
434#97—21no—
435C4×C8C23×C10111yescharacteristic
436C4×C8C23×C10111yescharacteristic
437C4×C8C23×C10111yescharacteristic
438#41—42no—
439#41—81no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8—41no—
443C2×Q8C2×D4×C10111yescharacteristic
444C2×Q8C2×D4×C10111yescharacteristic
445C2×Q8C2×D4×C10111yescharacteristic
446C2×D4—21no—
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C10111yescharacteristic
455C22×C4—21no—
456C22×C4—41no—
457C22×C4—41no—
458C22×C4—41no—
459Q16—41no—
460SD16—22no—
461SD16—42no—
462SD16—82no—
463SD16—82no—
464SD16—81no—
465SD16—81no—
466D8—42no—
467D8—81no—
468D8—81no—
469M16—81no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8C2×D4×C10111yescharacteristic
476C2×C8C2×D4×C10111yescharacteristic
477C2×C8C2×D4×C10111yescharacteristic
478C2×C8C2×D4×C10111yescharacteristic
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—41no—
487C4⋊C4—41no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4C2×D4×C10111yescharacteristic
491C4⋊C4C2×D4×C10111yescharacteristic
492C4⋊C4C2×D4×C10111yescharacteristic
493C4⋊C4C2×D4×C10111yescharacteristic
494C22⋊C4—21no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C42—21no—
501C42—21no—
502C42—21no—
503C42—41no—
504C42C24×C10111yescharacteristic
505C23—21no—
506C23—41no—
507C23—41no—
508Q8—21no—
509Q8—21no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—81no—
515Q8—81no—
516Q8—161no—
517D4—21no—
518D4—21no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—81no—
528D4—81no—
529D4—82no—
530D4—161no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—82no—
543C2×C4—161no—
544C2×C4—161no—
545C2×C4C22×D4×C10111yescharacteristic
546C2×C4C22×D4×C10111yescharacteristic
547C2×C4H(5,𝔽2)×C10111yescharacteristic
548C8—22no—
549C8—21no—
550C8—21no—
551C8—21no—
552C8—41no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8#137×C10112yes—
557C22—41no—
558C22—41no—
559C22—41no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22D42×C10111yescharacteristic
567C4—21no—
568C4—41no—
569C4—41no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—81no—
576C4—81no—
577C4C2×#137×C10111yescharacteristic
578C4#575×C10111yescharacteristic
579C4#577×C10111yescharacteristic
580C4#577×C10111yescharacteristic
581C2—81no—
582C2—161no—
583C2—161no—
584C2C101×#327511yescharacteristic
585C2C101×#327811yescharacteristic
586C2C101×#329211yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3399C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C101×#3385C2semidirect
3. C101×#3375C2semidirect
4. C101×#3333C2semidirect
5. C101×#1706C2semidirect
6. C101×#1698C2semidirect
7. C101×#1697C2semidirect
8. C101×#1696C2semidirect
9. C101×#1688C2semidirect
10. C101×#1631C2semidirect
11. C101×#1630C2semidirect
12. C101×#1623C2semidirect
13. C101×#1622C2semidirect
14. C101×#1591C2semidirect
15. C101×#1590C2semidirect
287. #20299C101direct (N × H)
295. #3385C2×C101semidirect
296. #3375C2×C101semidirect
297. #3333C2×C101semidirect
298. #1706C2×C101semidirect
299. #1698C2×C101semidirect
300. #1697C2×C101semidirect
301. #1696C2×C101semidirect
302. #1688C2×C101semidirect
303. #1631C2×C101semidirect
304. #1630C2×C101semidirect
305. #1623C2×C101semidirect
306. #1622C2×C101semidirect
307. #1591C2×C101semidirect
308. #1590C2×C101semidirect
309. C101#20299direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33992
C101×#33852
C101×#33752
C101×#33332
C101×#17062
C101×#16982
C101×#16972
C101×#16962
C101×#16882
C101×#16312
C101×#16302
C101×#16232
C101×#16222
C101×#15912
C101×#15902
#20299101