Finite Group Databasebeta

← C101×#20256 #38802407

Subgroups — C101×#20256 #38802407

Order 25856.

686 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3399C211yesmaximal, characteristic, complemented
2C101×#3399C211yesmaximal, characteristic, complemented
3C101×#3332C211yesmaximal, characteristic, complemented
4C101×#3284C211yesmaximal, characteristic, complemented
5C101×#1721C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1687C211yesmaximal, characteristic, complemented
8C101×#1686C211yesmaximal, characteristic, complemented
9C101×#1667C211yesmaximal, characteristic, complemented
10C101×#1640C211yesmaximal, characteristic, complemented
11C101×#1625C211yesmaximal, characteristic, complemented
12C101×#1621C211yesmaximal, characteristic, complemented
13C101×#1621C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1582C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#559×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#496×C101—21no—
22#496×C101—21no—
23#493×C101C2211yescharacteristic
24#493×C101C2211yescharacteristic
25#493×C101C2211yescharacteristic
26#492×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#481×C101—21no—
30#475×C101C2211yescharacteristic
31#469×C101—21no—
32#465×C101—21no—
33#463×C101—21no—
34#463×C101—21no—
35#462×C101C2211yescharacteristic
36#460×C101C2211yescharacteristic
37#460×C101C2211yescharacteristic
38#459×C101—21no—
39#459×C101—21no—
40#459×C101C2211yescharacteristic
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#452×C101—21no—
45#449×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#442×C101—21no—
50#442×C101—21no—
51C4×SD16×C101C2211yescharacteristic
52C4×SD16×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#331×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—21no—
70#135×C101—44no—
71C2×Q16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101D411yescharacteristic
77C2×SD16×C101D411yescharacteristic
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C2×D8×C101—21no—
81C2×D8×C101—21no—
82C2×D8×C101—21no—
83C2×D8×C101—21no—
84C2×D8×C101—21no—
85C2×D8×C101—21no—
86C2×D8×C101—41no—
87C2×M16×C101—21no—
88C22×C8×C101—21no—
89C4⋊Q8×C101C2311yescharacteristic
90#127×C101—21no—
91#127×C101—21no—
92#127×C101C2311yescharacteristic
93#127×C101C2311yescharacteristic
94#127×C101C2311yescharacteristic
95#124×C101—21no—
96#124×C101—21no—
97#123×C101—41no—
98#123×C101—41no—
99C22⋊Q8×C101—21no—
100#121×C101—21no—
101#121×C101—21no—
102#121×C101—21no—
103#121×C101—41no—
104#121×C101—41no—
105C4×Q8×C101C2311yescharacteristic
106C4×Q8×C101C2311yescharacteristic
107C4×D4×C101—21no—
108C4×D4×C101—21no—
109C4×D4×C101—21no—
110C4×D4×C101—21no—
111C4×D4×C101C2311yescharacteristic
112C4×D4×C101C2311yescharacteristic
113C2×C4⋊C4×C101—21no—
114#106×C101—21no—
115#106×C101D411yescharacteristic
116#106×C101D411yescharacteristic
117C4⋊C8×C101—21no—
118C4⋊C8×C101—21no—
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123#103×C101—21no—
124#103×C101—21no—
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—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—42no—
147#41×C101—42no—
148#41×C101—81no—
149#41×C101—81no—
150#41×C101—81no—
151C2×Q8×C101—21no—
152C2×Q8×C101C2×D411yescharacteristic
153C2×Q8×C101C2×D411yescharacteristic
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—21no—
163C2×D4×C101—41no—
164C2×D4×C101—41no—
165C2×D4×C101—41no—
166C2×D4×C101—41no—
167C2×D4×C101—41no—
168C2×D4×C101C2×D411yescharacteristic
169C2×D4×C101C2×D411yescharacteristic
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—41no—
173C22×C4×C101—41no—
174C22×C4×C101—41no—
175C22×C4×C101—41no—
176Q16×C101—42no—
177SD16×C101—22no—
178SD16×C101—41no—
179SD16×C101—42no—
180SD16×C101—81no—
181SD16×C101—81no—
182SD16×C101—81no—
183D8×C101—42no—
184D8×C101—42no—
185D8×C101—42no—
186D8×C101—81no—
187D8×C101—81no—
188D8×C101—81no—
189D8×C101—81no—
190D8×C101—81no—
191D8×C101—82no—
192M16×C101—81no—
193C2×C8×C101—21no—
194C2×C8×C101—21no—
195C2×C8×C101—21no—
196C2×C8×C101—21no—
197C2×C8×C101—21no—
198C2×C8×C101—42no—
199C2×C8×C101C2×D411yescharacteristic
200C2×C8×C101C2×D411yescharacteristic
201C2×C8×C101C2×D411yescharacteristic
202C2×C8×C101C2×D411yescharacteristic
203C4⋊C4×C101—21no—
204C4⋊C4×C101—21no—
205C4⋊C4×C101—21no—
206C4⋊C4×C101—21no—
207C4⋊C4×C101—41no—
208C4⋊C4×C101C2×D411yescharacteristic
209C4⋊C4×C101C2×D411yescharacteristic
210C4⋊C4×C101C2×D411yescharacteristic
211C4⋊C4×C101C2×D411yescharacteristic
212C22⋊C4×C101—21no—
213C22⋊C4×C101—21no—
214C22⋊C4×C101—41no—
215C22⋊C4×C101—41no—
216C22⋊C4×C101—41no—
217C22⋊C4×C101—41no—
218C22⋊C4×C101—41no—
219C22⋊C4×C101—41no—
220C42×C101—21no—
221C42×C101—21no—
222C42×C101C2411yescharacteristic
223C23×C101—21no—
224C23×C101—21no—
225C23×C101—41no—
226C23×C101—41no—
227C23×C101—41no—
228Q8×C101—21no—
229Q8×C101—21no—
230Q8×C101—21no—
231Q8×C101—21no—
232Q8×C101—41no—
233Q8×C101—41no—
234D4×C101—21no—
235D4×C101—21no—
236D4×C101—21no—
237D4×C101—21no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—41no—
241D4×C101—41no—
242D4×C101—41no—
243D4×C101—41no—
244D4×C101—41no—
245D4×C101—41no—
246D4×C101—41no—
247D4×C101—41no—
248D4×C101—41no—
249D4×C101—41no—
250D4×C101—81no—
251D4×C101—81no—
252D4×C101—81no—
253D4×C101—82no—
254D4×C101—82no—
255D4×C101—82no—
256D4×C101—161no—
257D4×C101—161no—
258C2×C4×C101—21no—
259C2×C4×C101—21no—
260C2×C4×C101—21no—
261C2×C4×C101—21no—
262C2×C4×C101—21no—
263C2×C4×C101—21no—
264C2×C4×C101—41no—
265C2×C4×C101—41no—
266C2×C4×C101—41no—
267C2×C4×C101—41no—
268C2×C4×C101—41no—
269C2×C4×C101—82no—
270C2×C4×C101—82no—
271C2×C4×C101—82no—
272C2×C4×C101—161no—
273C2×C4×C101C22×D411yescharacteristic
274C2×C4×C101C22×D411yescharacteristic
275C2×C4×C101H(5,𝔽2)11yescharacteristic
276C8×C101—21no—
277C8×C101—21no—
278C8×C101—21no—
279C8×C101—41no—
280C8×C101—41no—
281C8×C101—41no—
282C8×C101—41no—
283C8×C101—41no—
284C8×C101AGL(1,ℤ/8)12yes—
285C22×C101—41no—
286C22×C101—41no—
287C22×C101—41no—
288C22×C101—41no—
289C22×C101—41no—
290C22×C101—41no—
291C22×C101—81no—
292C22×C101—81no—
293C22×C101—81no—
294C22×C101—81no—
295C22×C101—81no—
296C22×C101—81no—
297C22×C101—81no—
298C22×C101—81no—
299C22×C101—81no—
300C22×C101D4211yescharacteristic
301C4×C101—21no—
302C4×C101—41no—
303C4×C101—41no—
304C4×C101—41no—
305C4×C101—41no—
306C4×C101—41no—
307C4×C101—41no—
308C4×C101—81no—
309C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
310C4×C101#57511yescharacteristic
311C4×C101#57611yescharacteristic
312C4×C101#57611yescharacteristic
313#20256C10111yesmaximal, characteristic, direct product factor, Sylow
314C2×C101—81no—
315C2×C101—81no—
316C2×C101—161no—
317C2×C101—161no—
318C2×C101—161no—
319C2×C101#326811yescharacteristic
320C2×C101#327411yescharacteristic
321C2×C101#328811yescharacteristic
322#3399C2×C10111yescharacteristic, complemented
323#3399C2×C10111yescharacteristic, complemented
324#3332C2×C10111yescharacteristic, complemented
325#3284C2×C10111yescharacteristic, complemented
326#1721C2×C10111yescharacteristic, complemented
327#1702C2×C10111yescharacteristic, complemented
328#1687C2×C10111yescharacteristic, complemented
329#1686C2×C10111yescharacteristic, complemented
330#1667C2×C10111yescharacteristic, complemented
331#1640C2×C10111yescharacteristic, complemented
332#1625C2×C10111yescharacteristic, complemented
333#1621C2×C10111yescharacteristic, complemented
334#1621C2×C10111yescharacteristic, complemented
335#1592C2×C10111yescharacteristic, complemented
336#1582C2×C10111yescharacteristic, complemented
337C101#2025611yescharacteristic, direct product factor, Sylow
338C2×#135—21no—
339#559C22×C10111yescharacteristic
340#550C22×C10111yescharacteristic
341#550C22×C10111yescharacteristic
342#547C22×C10111yescharacteristic
343#496—21no—
344#496—21no—
345#493C22×C10111yescharacteristic
346#493C22×C10111yescharacteristic
347#493C22×C10111yescharacteristic
348#492C22×C10111yescharacteristic
349#486C22×C10111yescharacteristic
350#486C22×C10111yescharacteristic
351#481—21no—
352#475C22×C10111yescharacteristic
353#469—21no—
354#465—21no—
355#463—21no—
356#463—21no—
357#462C22×C10111yescharacteristic
358#460C22×C10111yescharacteristic
359#460C22×C10111yescharacteristic
360#459—21no—
361#459—21no—
362#459C22×C10111yescharacteristic
363#459C22×C10111yescharacteristic
364#459C22×C10111yescharacteristic
365#459C22×C10111yescharacteristic
366#452—21no—
367#449—21no—
368#449—21no—
369#446C22×C10111yescharacteristic
370#446C22×C10111yescharacteristic
371#442—21no—
372#442—21no—
373C4×SD16C22×C10111yescharacteristic
374C4×SD16C22×C10111yescharacteristic
375#436C22×C10111yescharacteristic
376C8×D4C22×C10111yescharacteristic
377#417—21no—
378#335C22×C10111yescharacteristic
379#334C22×C10111yescharacteristic
380#332C22×C10111yescharacteristic
381#331C22×C10111yescharacteristic
382#331C22×C10111yescharacteristic
383#331C22×C10111yescharacteristic
384Q8⋊C8C22×C10111yescharacteristic
385Q8⋊C8C22×C10111yescharacteristic
386D4⋊C8C22×C10111yescharacteristic
387D4⋊C8C22×C10111yescharacteristic
388#322C22×C10111yescharacteristic
389C2×#41—21no—
390C2×#41—21no—
391C2×#41—21no—
392#135—44no—
393C2×Q16—21no—
394C2×SD16—21no—
395C2×SD16—21no—
396C2×SD16—21no—
397C2×SD16—21no—
398C2×SD16D4×C10111yescharacteristic
399C2×SD16D4×C10111yescharacteristic
400C2×D8—21no—
401C2×D8—21no—
402C2×D8—21no—
403C2×D8—21no—
404C2×D8—21no—
405C2×D8—21no—
406C2×D8—21no—
407C2×D8—21no—
408C2×D8—41no—
409C2×M16—21no—
410C22×C8—21no—
411C4⋊Q8C23×C10111yescharacteristic
412#127—21no—
413#127—21no—
414#127C23×C10111yescharacteristic
415#127C23×C10111yescharacteristic
416#127C23×C10111yescharacteristic
417#124—21no—
418#124—21no—
419#123—41no—
420#123—41no—
421C22⋊Q8—21no—
422#121—21no—
423#121—21no—
424#121—21no—
425#121—41no—
426#121—41no—
427C4×Q8C23×C10111yescharacteristic
428C4×Q8C23×C10111yescharacteristic
429C4×D4—21no—
430C4×D4—21no—
431C4×D4—21no—
432C4×D4—21no—
433C4×D4C23×C10111yescharacteristic
434C4×D4C23×C10111yescharacteristic
435C2×C4⋊C4—21no—
436#106—21no—
437#106D4×C10111yescharacteristic
438#106D4×C10111yescharacteristic
439C4⋊C8—21no—
440C4⋊C8—21no—
441C4⋊C8C23×C10111yescharacteristic
442C4⋊C8C23×C10111yescharacteristic
443C4⋊C8C23×C10111yescharacteristic
444C4⋊C8C23×C10111yescharacteristic
445#103—21no—
446#103—21no—
447#103D4×C10111yescharacteristic
448#103D4×C10111yescharacteristic
449#102—21no—
450#102—21no—
451#102—21no—
452#102—21no—
453#102—21no—
454#102—21no—
455#102—21no—
456#102—21no—
457#102—41no—
458#102D4×C10111yescharacteristic
459#102D4×C10111yescharacteristic
460C22⋊C8—21no—
461C22⋊C8—21no—
462#97—21no—
463#97—21no—
464C4×C8C23×C10111yescharacteristic
465C4×C8C23×C10111yescharacteristic
466C4×C8C23×C10111yescharacteristic
467#41—42no—
468#41—42no—
469#41—42no—
470#41—81no—
471#41—81no—
472#41—81no—
473C2×Q8—21no—
474C2×Q8C2×D4×C10111yescharacteristic
475C2×Q8C2×D4×C10111yescharacteristic
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—21no—
481C2×D4—21no—
482C2×D4—21no—
483C2×D4—21no—
484C2×D4—21no—
485C2×D4—41no—
486C2×D4—41no—
487C2×D4—41no—
488C2×D4—41no—
489C2×D4—41no—
490C2×D4C2×D4×C10111yescharacteristic
491C2×D4C2×D4×C10111yescharacteristic
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—41no—
495C22×C4—41no—
496C22×C4—41no—
497C22×C4—41no—
498Q16—42no—
499SD16—22no—
500SD16—41no—
501SD16—42no—
502SD16—81no—
503SD16—81no—
504SD16—81no—
505D8—42no—
506D8—42no—
507D8—42no—
508D8—81no—
509D8—81no—
510D8—81no—
511D8—81no—
512D8—81no—
513D8—82no—
514M16—81no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8—42no—
521C2×C8C2×D4×C10111yescharacteristic
522C2×C8C2×D4×C10111yescharacteristic
523C2×C8C2×D4×C10111yescharacteristic
524C2×C8C2×D4×C10111yescharacteristic
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—41no—
530C4⋊C4C2×D4×C10111yescharacteristic
531C4⋊C4C2×D4×C10111yescharacteristic
532C4⋊C4C2×D4×C10111yescharacteristic
533C4⋊C4C2×D4×C10111yescharacteristic
534C22⋊C4—21no—
535C22⋊C4—21no—
536C22⋊C4—41no—
537C22⋊C4—41no—
538C22⋊C4—41no—
539C22⋊C4—41no—
540C22⋊C4—41no—
541C22⋊C4—41no—
542C42—21no—
543C42—21no—
544C42C24×C10111yescharacteristic
545C23—21no—
546C23—21no—
547C23—41no—
548C23—41no—
549C23—41no—
550Q8—21no—
551Q8—21no—
552Q8—21no—
553Q8—21no—
554Q8—41no—
555Q8—41no—
556D4—21no—
557D4—21no—
558D4—21no—
559D4—21no—
560D4—41no—
561D4—41no—
562D4—41no—
563D4—41no—
564D4—41no—
565D4—41no—
566D4—41no—
567D4—41no—
568D4—41no—
569D4—41no—
570D4—41no—
571D4—41no—
572D4—81no—
573D4—81no—
574D4—81no—
575D4—82no—
576D4—82no—
577D4—82no—
578D4—161no—
579D4—161no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—41no—
589C2×C4—41no—
590C2×C4—41no—
591C2×C4—82no—
592C2×C4—82no—
593C2×C4—82no—
594C2×C4—161no—
595C2×C4C22×D4×C10111yescharacteristic
596C2×C4C22×D4×C10111yescharacteristic
597C2×C4H(5,𝔽2)×C10111yescharacteristic
598C8—21no—
599C8—21no—
600C8—21no—
601C8—41no—
602C8—41no—
603C8—41no—
604C8—41no—
605C8—41no—
606C8AGL(1,ℤ/8)×C10112yes—
607C22—41no—
608C22—41no—
609C22—41no—
610C22—41no—
611C22—41no—
612C22—41no—
613C22—81no—
614C22—81no—
615C22—81no—
616C22—81no—
617C22—81no—
618C22—81no—
619C22—81no—
620C22—81no—
621C22—81no—
622C22D42×C10111yescharacteristic
623C4—21no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—41no—
628C4—41no—
629C4—41no—
630C4—81no—
631C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
632C4#575×C10111yescharacteristic
633C4#576×C10111yescharacteristic
634C4#576×C10111yescharacteristic
635C2—81no—
636C2—81no—
637C2—161no—
638C2—161no—
639C2—161no—
640C2C101×#326811yescharacteristic
641C2C101×#327411yescharacteristic
642C2C101×#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×#3399C2semidirect
2. C101×#3399C2semidirect
3. C101×#3332C2semidirect
4. C101×#3284C2semidirect
5. C101×#1721C2semidirect
6. C101×#1702C2semidirect
7. C101×#1687C2semidirect
8. C101×#1686C2semidirect
9. C101×#1667C2semidirect
10. C101×#1640C2semidirect
11. C101×#1625C2semidirect
12. C101×#1621C2semidirect
13. C101×#1621C2semidirect
14. C101×#1592C2semidirect
15. C101×#1582C2semidirect
313. #20256C101direct (N × H)
322. #3399C2×C101semidirect
323. #3399C2×C101semidirect
324. #3332C2×C101semidirect
325. #3284C2×C101semidirect
326. #1721C2×C101semidirect
327. #1702C2×C101semidirect
328. #1687C2×C101semidirect
329. #1686C2×C101semidirect
330. #1667C2×C101semidirect
331. #1640C2×C101semidirect
332. #1625C2×C101semidirect
333. #1621C2×C101semidirect
334. #1621C2×C101semidirect
335. #1592C2×C101semidirect
336. #1582C2×C101semidirect
337. C101#20256direct (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×#33322
C101×#32842
C101×#17212
C101×#17022
C101×#16872
C101×#16862
C101×#16672
C101×#16402
C101×#16252
C101×#16212
C101×#15922
C101×#15822
#20256101