Finite Group Databasebeta

← C101×#20265 #38802416

Subgroups — C101×#20265 #38802416

Order 25856.

608 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3400C211yesmaximal, characteristic, complemented
2C101×#3399C211yesmaximal, characteristic
3C101×#3381C211yesmaximal, characteristic, complemented
4C101×#3333C211yesmaximal, characteristic, complemented
5C101×#1715C211yesmaximal, characteristic, complemented
6C101×#1698C211yesmaximal, characteristic, complemented
7C101×#1692C211yesmaximal, characteristic, complemented
8C101×#1685C211yesmaximal, characteristic, complemented
9C101×#1668C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1630C211yesmaximal, characteristic, complemented
12C101×#1626C211yesmaximal, characteristic, complemented
13C101×#1622C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1584C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#499×C101—21no—
21#498×C101C2211yescharacteristic
22#497×C101—21no—
23#496×C101—21no—
24#493×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#492×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#480×C101—21no—
30#479×C101—21no—
31#478×C101—21no—
32#477×C101C2211yescharacteristic
33#477×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#468×C101—21no—
36#464×C101—21no—
37#463×C101—21no—
38#462×C101C2211yescharacteristic
39#461×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
48C8×Q8×C101C2211yescharacteristic
49#442×C101—21no—
50#440×C101—21no—
51C4×Q16×C101C2211yescharacteristic
52C4×SD16×C101—21no—
53C4×SD16×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#335×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101D411yescharacteristic
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—41no—
76C2×SD16×C101D411yescharacteristic
77C2×D8×C101—21no—
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C2×M16×C101—21no—
81C4⋊Q8×C101—21no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101—21no—
85#127×C101C2311yescharacteristic
86#127×C101C2311yescharacteristic
87#125×C101—21no—
88#125×C101—21no—
89#125×C101—41no—
90#124×C101—21no—
91#124×C101—21no—
92#123×C101—41no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—41no—
95#121×C101—21no—
96#121×C101—41no—
97C4×Q8×C101—21no—
98C4×Q8×C101—21no—
99C4×Q8×C101C2311yescharacteristic
100C4×Q8×C101C2311yescharacteristic
101C4×Q8×C101C2311yescharacteristic
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101—21no—
106C4×D4×C101C2311yescharacteristic
107C2×C4⋊C4×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101D411yescharacteristic
112#106×C101—21no—
113#106×C101—21no—
114#106×C101D411yescharacteristic
115C4⋊C8×C101—21no—
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122#103×C101—21no—
123#103×C101—21no—
124#103×C101—21no—
125#103×C101D411yescharacteristic
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
137C22⋊C8×C101—21no—
138#97×C101—21no—
139#97×C101—21no—
140C4×C8×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×C101C2×D411yescharacteristic
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101C2×D411yescharacteristic
160C22×C4×C101—21no—
161C22×C4×C101—41no—
162C22×C4×C101—41no—
163C22×C4×C101—41no—
164Q16×C101—41no—
165Q16×C101—81no—
166SD16×C101—22no—
167SD16×C101—42no—
168SD16×C101—81no—
169SD16×C101—81no—
170SD16×C101—81no—
171SD16×C101—81no—
172SD16×C101—82no—
173D8×C101—42no—
174D8×C101—81no—
175D8×C101—81no—
176M16×C101—81no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
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×C101—41no—
197C4⋊C4×C101—41no—
198C4⋊C4×C101C2×D411yescharacteristic
199C4⋊C4×C101C2×D411yescharacteristic
200C4⋊C4×C101C2×D411yescharacteristic
201C4⋊C4×C101C2×D411yescharacteristic
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—21no—
210C42×C101—21no—
211C42×C101—41no—
212C42×C101C2411yescharacteristic
213C23×C101—21no—
214C23×C101—41no—
215C23×C101—41no—
216Q8×C101—21no—
217Q8×C101—21no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—81no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—41no—
228D4×C101—41no—
229D4×C101—41no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—81no—
236D4×C101—81no—
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—21no—
245C2×C4×C101—21no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—82no—
251C2×C4×C101—161no—
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—41no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101#13712yes—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—81no—
269C22×C101—81no—
270C22×C101—81no—
271C22×C101—81no—
272C22×C101—81no—
273C22×C101—81no—
274C22×C101D4211yescharacteristic
275C4×C101—21no—
276C4×C101—41no—
277C4×C101—41no—
278C4×C101—41no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—41no—
282C4×C101—41no—
283C4×C101—81no—
284C4×C101—81no—
285C4×C101C2×#13711yescharacteristic
286C4×C101#57511yescharacteristic
287C4×C101#57611yescharacteristic
288C4×C101#57711yescharacteristic
289#20265C10111yesmaximal, characteristic, direct product factor, Sylow
290C2×C101—81no—
291C2×C101—161no—
292C2×C101—161no—
293C2×C101#326811yescharacteristic
294C2×C101#327811yescharacteristic
295C2×C101#328811yescharacteristic
296#3400C2×C10111yescharacteristic, complemented
297#3399C2×C10111yescharacteristic
298#3381C2×C10111yescharacteristic, complemented
299#3333C2×C10111yescharacteristic, complemented
300#1715C2×C10111yescharacteristic, complemented
301#1698C2×C10111yescharacteristic, complemented
302#1692C2×C10111yescharacteristic, complemented
303#1685C2×C10111yescharacteristic, complemented
304#1668C2×C10111yescharacteristic, complemented
305#1641C2×C10111yescharacteristic, complemented
306#1630C2×C10111yescharacteristic, complemented
307#1626C2×C10111yescharacteristic, complemented
308#1622C2×C10111yescharacteristic, complemented
309#1592C2×C10111yescharacteristic, complemented
310#1584C2×C10111yescharacteristic, complemented
311C101#2026511yescharacteristic, direct product factor, Sylow
312#559C22×C10111yescharacteristic
313#557C22×C10111yescharacteristic
314#554C22×C10111yescharacteristic
315#550C22×C10111yescharacteristic
316#499—21no—
317#498C22×C10111yescharacteristic
318#497—21no—
319#496—21no—
320#493C22×C10111yescharacteristic
321#492C22×C10111yescharacteristic
322#492C22×C10111yescharacteristic
323#486C22×C10111yescharacteristic
324#486C22×C10111yescharacteristic
325#480—21no—
326#479—21no—
327#478—21no—
328#477C22×C10111yescharacteristic
329#477C22×C10111yescharacteristic
330#474C22×C10111yescharacteristic
331#468—21no—
332#464—21no—
333#463—21no—
334#462C22×C10111yescharacteristic
335#461—21no—
336#460C22×C10111yescharacteristic
337#460C22×C10111yescharacteristic
338#460C22×C10111yescharacteristic
339#459—21no—
340#459C22×C10111yescharacteristic
341#452—21no—
342#446C22×C10111yescharacteristic
343#446C22×C10111yescharacteristic
344C8×Q8C22×C10111yescharacteristic
345#442—21no—
346#440—21no—
347C4×Q16C22×C10111yescharacteristic
348C4×SD16—21no—
349C4×SD16C22×C10111yescharacteristic
350#436C22×C10111yescharacteristic
351#417—21no—
352#335C22×C10111yescharacteristic
353#335C22×C10111yescharacteristic
354#333C22×C10111yescharacteristic
355#332C22×C10111yescharacteristic
356#331C22×C10111yescharacteristic
357#331C22×C10111yescharacteristic
358Q8⋊C8C22×C10111yescharacteristic
359Q8⋊C8C22×C10111yescharacteristic
360Q8⋊C8C22×C10111yescharacteristic
361D4⋊C8C22×C10111yescharacteristic
362#322C22×C10111yescharacteristic
363C2×#41—21no—
364C2×Q16—21no—
365C2×Q16D4×C10111yescharacteristic
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—41no—
372C2×SD16D4×C10111yescharacteristic
373C2×D8—21no—
374C2×D8—21no—
375C2×D8—21no—
376C2×M16—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C10111yescharacteristic
379C4⋊Q8C23×C10111yescharacteristic
380#127—21no—
381#127C23×C10111yescharacteristic
382#127C23×C10111yescharacteristic
383#125—21no—
384#125—21no—
385#125—41no—
386#124—21no—
387#124—21no—
388#123—41no—
389C22⋊Q8—21no—
390C22⋊Q8—41no—
391#121—21no—
392#121—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8C23×C10111yescharacteristic
396C4×Q8C23×C10111yescharacteristic
397C4×Q8C23×C10111yescharacteristic
398C4×D4—21no—
399C4×D4—21no—
400C4×D4—21no—
401C4×D4—21no—
402C4×D4C23×C10111yescharacteristic
403C2×C4⋊C4—21no—
404#107—21no—
405#107—21no—
406#107—21no—
407#107D4×C10111yescharacteristic
408#106—21no—
409#106—21no—
410#106D4×C10111yescharacteristic
411C4⋊C8—21no—
412C4⋊C8—21no—
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#103D4×C10111yescharacteristic
422#103D4×C10111yescharacteristic
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—41no—
432#102D4×C10111yescharacteristic
433C22⋊C8—21no—
434#97—21no—
435#97—21no—
436C4×C8—21no—
437C4×C8C23×C10111yescharacteristic
438C4×C8C23×C10111yescharacteristic
439C4×C8C23×C10111yescharacteristic
440#41—42no—
441#41—81no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8C2×D4×C10111yescharacteristic
445C2×Q8C2×D4×C10111yescharacteristic
446C2×Q8C2×D4×C10111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4C2×D4×C10111yescharacteristic
456C22×C4—21no—
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460Q16—41no—
461Q16—81no—
462SD16—22no—
463SD16—42no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467SD16—81no—
468SD16—82no—
469D8—42no—
470D8—81no—
471D8—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8C2×D4×C10111yescharacteristic
479C2×C8C2×D4×C10111yescharacteristic
480C2×C8C2×D4×C10111yescharacteristic
481C2×C8C2×D4×C10111yescharacteristic
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C10111yescharacteristic
495C4⋊C4C2×D4×C10111yescharacteristic
496C4⋊C4C2×D4×C10111yescharacteristic
497C4⋊C4C2×D4×C10111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C24×C10111yescharacteristic
509C23—21no—
510C23—41no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—21no—
517Q8—21no—
518Q8—41no—
519Q8—41no—
520Q8—81no—
521D4—21no—
522D4—21no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—81no—
532D4—81no—
533D4—82no—
534D4—161no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—161no—
548C2×C4—161no—
549C2×C4C22×D4×C10111yescharacteristic
550C2×C4C22×D4×C10111yescharacteristic
551C2×C4H(5,𝔽2)×C10111yescharacteristic
552C8—21no—
553C8—21no—
554C8—21no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8#137×C10112yes—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C10111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—81no—
580C4—81no—
581C4C2×#137×C10111yescharacteristic
582C4#575×C10111yescharacteristic
583C4#576×C10111yescharacteristic
584C4#577×C10111yescharacteristic
585C2—81no—
586C2—161no—
587C2—161no—
588C2C101×#326811yescharacteristic
589C2C101×#327811yescharacteristic
590C2C101×#328811yescharacteristic
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
1. C101×#3400C2semidirect
3. C101×#3381C2semidirect
4. C101×#3333C2semidirect
5. C101×#1715C2semidirect
6. C101×#1698C2semidirect
7. C101×#1692C2semidirect
8. C101×#1685C2semidirect
9. C101×#1668C2semidirect
10. C101×#1641C2semidirect
11. C101×#1630C2semidirect
12. C101×#1626C2semidirect
13. C101×#1622C2semidirect
14. C101×#1592C2semidirect
15. C101×#1584C2semidirect
289. #20265C101direct (N × H)
296. #3400C2×C101semidirect
298. #3381C2×C101semidirect
299. #3333C2×C101semidirect
300. #1715C2×C101semidirect
301. #1698C2×C101semidirect
302. #1692C2×C101semidirect
303. #1685C2×C101semidirect
304. #1668C2×C101semidirect
305. #1641C2×C101semidirect
306. #1630C2×C101semidirect
307. #1626C2×C101semidirect
308. #1622C2×C101semidirect
309. #1592C2×C101semidirect
310. #1584C2×C101semidirect
311. C101#20265direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#34002
C101×#33992
C101×#33812
C101×#33332
C101×#17152
C101×#16982
C101×#16922
C101×#16852
C101×#16682
C101×#16412
C101×#16302
C101×#16262
C101×#16222
C101×#15922
C101×#15842
#20265101