Finite Group Databasebeta

← C101×#20316 #38802467

Subgroups — C101×#20316 #38802467

Order 25856.

628 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×#3367C211yesmaximal, characteristic, complemented
2C101×#3366C211yesmaximal, characteristic
3C101×#3356C211yesmaximal, characteristic, complemented
4C101×#3278C211yesmaximal, characteristic, complemented
5C101×#1708C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1698C211yesmaximal, characteristic, complemented
8C101×#1691C211yesmaximal, characteristic, complemented
9C101×#1685C211yesmaximal, characteristic, complemented
10C101×#1644C211yesmaximal, characteristic, complemented
11C101×#1642C211yesmaximal, characteristic, complemented
12C101×#1637C211yesmaximal, characteristic, complemented
13C101×#1628C211yesmaximal, characteristic, complemented
14C101×#1591C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16C2×#137×C101—21no—
17#556×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20D4×Q8×C101C2211yescharacteristic
21#498×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic
23#490×C101—21no—
24#489×C101—21no—
25#487×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#485×C101—21no—
30#483×C101—21no—
31#478×C101—21no—
32#477×C101—21no—
33#477×C101C2211yescharacteristic
34#476×C101C2211yescharacteristic
35#475×C101C2211yescharacteristic
36#474×C101C2211yescharacteristic
37#470×C101—21no—
38#468×C101—21no—
39#463×C101—21no—
40#462×C101C2211yescharacteristic
41#461×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#459×C101—21no—
44#459×C101C2211yescharacteristic
45#452×C101—21no—
46#448×C101—21no—
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#442×C101—21no—
50#440×C101—21no—
51C4×Q16×C101C2211yescharacteristic
52C4×D8×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#428×C101—21no—
56#335×C101C2211yescharacteristic
57#335×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C22×Q8×C101—21no—
69#137×C101—44no—
70C2×Q16×C101—21no—
71C2×Q16×C101D411yescharacteristic
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101D411yescharacteristic
78C2×M16×C101—21no—
79C2×M16×C101—21no—
80C4⋊Q8×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101—21no—
85#127×C101C2311yescharacteristic
86#126×C101—41no—
87#125×C101—21no—
88#124×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—41no—
93C22⋊Q8×C101—41no—
94#121×C101—21no—
95#121×C101—41no—
96C4×Q8×C101—21no—
97C4×Q8×C101C2311yescharacteristic
98C4×Q8×C101C2311yescharacteristic
99C4×D4×C101—21no—
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101C2311yescharacteristic
103C4×D4×C101C2311yescharacteristic
104#117×C101—21no—
105C2×C4⋊C4×C101—21no—
106#107×C101—21no—
107#107×C101—21no—
108#107×C101D411yescharacteristic
109#107×C101D411yescharacteristic
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114C4⋊C8×C101—21no—
115C4⋊C8×C101—21no—
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
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×C101—41no—
127#103×C101D411yescharacteristic
128#103×C101D411yescharacteristic
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
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×C101—21no—
141#97×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—81no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101—41no—
151C2×Q8×C101—42no—
152C2×Q8×C101—81no—
153C2×Q8×C101C2×D411yescharacteristic
154C2×Q8×C101C2×D411yescharacteristic
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101C2×D411yescharacteristic
161C2×D4×C101C2×D411yescharacteristic
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—41no—
165C22×C4×C101—41no—
166C22×C4×C101—41no—
167Q16×C101—22no—
168Q16×C101—42no—
169SD16×C101—42no—
170SD16×C101—42no—
171SD16×C101—42no—
172SD16×C101—81no—
173D8×C101—41no—
174D8×C101—42no—
175M16×C101—42no—
176M16×C101—42no—
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—21no—
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—21no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C42×C101—21no—
210C42×C101—21no—
211C42×C101—41no—
212C42×C101C2411yescharacteristic
213C23×C101—21no—
214C23×C101—21no—
215C23×C101—41no—
216Q8×C101—21no—
217Q8×C101—21no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—81no—
225Q8×C101—82no—
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—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—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—41no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101AGL(1,ℤ/8)12yes—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
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—81no—
283C4×C101—81no—
284C4×C101—81no—
285C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
286C4×C101#57511yescharacteristic
287C4×C101#57711yescharacteristic
288C4×C101#57811yescharacteristic
289#20316C10111yesmaximal, characteristic, direct product factor, Sylow
290C2×C101—81no—
291C2×C101—81no—
292C2×C101—161no—
293C2×C101#327211yescharacteristic
294C2×C101#327711yescharacteristic
295C2×C101#329011yescharacteristic
296#3367C2×C10111yescharacteristic, complemented
297#3366C2×C10111yescharacteristic
298#3356C2×C10111yescharacteristic, complemented
299#3278C2×C10111yescharacteristic, complemented
300#1708C2×C10111yescharacteristic, complemented
301#1700C2×C10111yescharacteristic, complemented
302#1698C2×C10111yescharacteristic, complemented
303#1691C2×C10111yescharacteristic, complemented
304#1685C2×C10111yescharacteristic, complemented
305#1644C2×C10111yescharacteristic, complemented
306#1642C2×C10111yescharacteristic, complemented
307#1637C2×C10111yescharacteristic, complemented
308#1628C2×C10111yescharacteristic, complemented
309#1591C2×C10111yescharacteristic, complemented
310#1589C2×C10111yescharacteristic, complemented
311C101#2031611yescharacteristic, direct product factor, Sylow
312C2×#137—21no—
313#556C22×C10111yescharacteristic
314#554C22×C10111yescharacteristic
315#550C22×C10111yescharacteristic
316D4×Q8C22×C10111yescharacteristic
317#498C22×C10111yescharacteristic
318#492C22×C10111yescharacteristic
319#490—21no—
320#489—21no—
321#487C22×C10111yescharacteristic
322#487C22×C10111yescharacteristic
323#486C22×C10111yescharacteristic
324#486C22×C10111yescharacteristic
325#485—21no—
326#483—21no—
327#478—21no—
328#477—21no—
329#477C22×C10111yescharacteristic
330#476C22×C10111yescharacteristic
331#475C22×C10111yescharacteristic
332#474C22×C10111yescharacteristic
333#470—21no—
334#468—21no—
335#463—21no—
336#462C22×C10111yescharacteristic
337#461C22×C10111yescharacteristic
338#460C22×C10111yescharacteristic
339#459—21no—
340#459C22×C10111yescharacteristic
341#452—21no—
342#448—21no—
343#446C22×C10111yescharacteristic
344#446C22×C10111yescharacteristic
345#442—21no—
346#440—21no—
347C4×Q16C22×C10111yescharacteristic
348C4×D8C22×C10111yescharacteristic
349#436C22×C10111yescharacteristic
350#436C22×C10111yescharacteristic
351#428—21no—
352#335C22×C10111yescharacteristic
353#335C22×C10111yescharacteristic
354#333C22×C10111yescharacteristic
355#332C22×C10111yescharacteristic
356#332C22×C10111yescharacteristic
357#331C22×C10111yescharacteristic
358Q8⋊C8C22×C10111yescharacteristic
359Q8⋊C8C22×C10111yescharacteristic
360D4⋊C8C22×C10111yescharacteristic
361D4⋊C8C22×C10111yescharacteristic
362C82C22×C10111yescharacteristic
363C2×#41—21no—
364C22×Q8—21no—
365#137—44no—
366C2×Q16—21no—
367C2×Q16D4×C10111yescharacteristic
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×D8—21no—
373C2×D8D4×C10111yescharacteristic
374C2×M16—21no—
375C2×M16—21no—
376C4⋊Q8—21no—
377C4⋊Q8C23×C10111yescharacteristic
378C4⋊Q8C23×C10111yescharacteristic
379C4⋊Q8C23×C10111yescharacteristic
380#127—21no—
381#127C23×C10111yescharacteristic
382#126—41no—
383#125—21no—
384#124—21no—
385C22⋊Q8—21no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389C22⋊Q8—41no—
390#121—21no—
391#121—41no—
392C4×Q8—21no—
393C4×Q8C23×C10111yescharacteristic
394C4×Q8C23×C10111yescharacteristic
395C4×D4—21no—
396C4×D4—21no—
397C4×D4—21no—
398C4×D4C23×C10111yescharacteristic
399C4×D4C23×C10111yescharacteristic
400#117—21no—
401C2×C4⋊C4—21no—
402#107—21no—
403#107—21no—
404#107D4×C10111yescharacteristic
405#107D4×C10111yescharacteristic
406#106—21no—
407#106—21no—
408#106—21no—
409#106—21no—
410C4⋊C8—21no—
411C4⋊C8—21no—
412C4⋊C8C23×C10111yescharacteristic
413C4⋊C8C23×C10111yescharacteristic
414C4⋊C8C23×C10111yescharacteristic
415C4⋊C8C23×C10111yescharacteristic
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103—41no—
423#103D4×C10111yescharacteristic
424#103D4×C10111yescharacteristic
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—41no—
432#102D4×C10111yescharacteristic
433#102D4×C10111yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437#97—21no—
438C4×C8C23×C10111yescharacteristic
439C4×C8C23×C10111yescharacteristic
440C4×C8C23×C10111yescharacteristic
441#41—42no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8—41no—
447C2×Q8—42no—
448C2×Q8—81no—
449C2×Q8C2×D4×C10111yescharacteristic
450C2×Q8C2×D4×C10111yescharacteristic
451C2×D4—21no—
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—41no—
455C2×D4—41no—
456C2×D4C2×D4×C10111yescharacteristic
457C2×D4C2×D4×C10111yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—41no—
461C22×C4—41no—
462C22×C4—41no—
463Q16—22no—
464Q16—42no—
465SD16—42no—
466SD16—42no—
467SD16—42no—
468SD16—81no—
469D8—41no—
470D8—42no—
471M16—42no—
472M16—42no—
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—21no—
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—21no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C42—21no—
506C42—21no—
507C42—41no—
508C42C24×C10111yescharacteristic
509C23—21no—
510C23—21no—
511C23—41no—
512Q8—21no—
513Q8—21no—
514Q8—21no—
515Q8—21no—
516Q8—41no—
517Q8—41no—
518Q8—41no—
519Q8—41no—
520Q8—81no—
521Q8—82no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—81no—
531D4—82no—
532D4—161no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—82no—
547C2×C4—82no—
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—
560C8AGL(1,ℤ/8)×C10112yes—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—81no—
568C22—81no—
569C22—81no—
570C22D42×C10111yescharacteristic
571C4—21no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
582C4#575×C10111yescharacteristic
583C4#577×C10111yescharacteristic
584C4#578×C10111yescharacteristic
585C2—81no—
586C2—81no—
587C2—161no—
588C2C101×#327211yescharacteristic
589C2C101×#327711yescharacteristic
590C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3366C2
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×#3367C2semidirect
3. C101×#3356C2semidirect
4. C101×#3278C2semidirect
5. C101×#1708C2semidirect
6. C101×#1700C2semidirect
7. C101×#1698C2semidirect
8. C101×#1691C2semidirect
9. C101×#1685C2semidirect
10. C101×#1644C2semidirect
11. C101×#1642C2semidirect
12. C101×#1637C2semidirect
13. C101×#1628C2semidirect
14. C101×#1591C2semidirect
15. C101×#1589C2semidirect
289. #20316C101direct (N × H)
296. #3367C2×C101semidirect
298. #3356C2×C101semidirect
299. #3278C2×C101semidirect
300. #1708C2×C101semidirect
301. #1700C2×C101semidirect
302. #1698C2×C101semidirect
303. #1691C2×C101semidirect
304. #1685C2×C101semidirect
305. #1644C2×C101semidirect
306. #1642C2×C101semidirect
307. #1637C2×C101semidirect
308. #1628C2×C101semidirect
309. #1591C2×C101semidirect
310. #1589C2×C101semidirect
311. C101#20316direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33672
C101×#33662
C101×#33562
C101×#32782
C101×#17082
C101×#17002
C101×#16982
C101×#16912
C101×#16852
C101×#16442
C101×#16422
C101×#16372
C101×#16282
C101×#15912
C101×#15892
#20316101