Finite Group Databasebeta

← C101×#20258 #38802409

Subgroups — C101×#20258 #38802409

Order 25856.

658 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3397C211yesmaximal, characteristic, complemented
2C101×#3325C211yesmaximal, characteristic, complemented
3C101×#3324C211yesmaximal, characteristic, complemented
4C101×#3305C211yesmaximal, characteristic, complemented
5C101×#1717C211yesmaximal, characteristic, complemented
6C101×#1698C211yesmaximal, characteristic, complemented
7C101×#1697C211yesmaximal, characteristic, complemented
8C101×#1685C211yesmaximal, characteristic, complemented
9C101×#1681C211yesmaximal, characteristic, complemented
10C101×#1646C211yesmaximal, characteristic, complemented
11C101×#1638C211yesmaximal, characteristic, complemented
12C101×#1621C211yesmaximal, characteristic, complemented
13C101×#1619C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1581C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic
17#555×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic, complemented
19D42×C101C2211yescharacteristic
20#496×C101—21no—
21#493×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic, complemented
23#487×C101C2211yescharacteristic, complemented
24#486×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic, complemented
27#482×C101—21no—
28#482×C101—21no—
29#482×C101—21no—
30#477×C101C2211yescharacteristic, complemented
31#476×C101C2211yescharacteristic
32#474×C101C2211yescharacteristic
33#469×C101—21no—
34#468×C101—21no—
35#466×C101—21no—
36#463×C101—21no—
37#461×C101C2211yescharacteristic, complemented
38#460×C101—21no—
39#460×C101C2211yescharacteristic
40#459×C101C2211yescharacteristic
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#450×C101—21no—
44#449×C101—21no—
45#447×C101—21no—
46#446×C101C2211yescharacteristic, complemented
47#440×C101—21no—
48C4×SD16×C101C2211yescharacteristic
49C4×D8×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic, complemented
53#418×C101—21no—
54#418×C101—21no—
55#416×C101—21no—
56#335×C101C2211yescharacteristic, complemented
57#335×C101C2211yescharacteristic, complemented
58#333×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic, complemented
62Q8⋊C8×C101C2211yescharacteristic, complemented
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic, complemented
66#322×C101C2211yescharacteristic, complemented
67C2×#41×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101D411yescharacteristic
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×D8×C101—41no—
79C2×D8×C101D411yescharacteristic
80C2×M16×C101—21no—
81C2×M16×C101—21no—
82C22×C8×C101—21no—
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85#127×C101—21no—
86#127×C101C2311yescharacteristic
87#127×C101C2311yescharacteristic
88#126×C101—41no—
89#124×C101—21no—
90#124×C101—41no—
91C22⋊Q8×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—41no—
98#120×C101—41no—
99C4×Q8×C101—21no—
100C4×Q8×C101C2311yescharacteristic
101C4×D4×C101—21no—
102C4×D4×C101C2311yescharacteristic
103C4×D4×C101C2311yescharacteristic
104C4×D4×C101C2311yescharacteristic
105#117×C101—21no—
106#117×C101—21no—
107#117×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101D411yescharacteristic
111#106×C101—21no—
112#106×C101D411yescharacteristic
113C4⋊C8×C101—21no—
114C4⋊C8×C101C2311yescharacteristic
115C4⋊C8×C101C2311yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118#103×C101—21no—
119#103×C101—21no—
120#103×C101—41no—
121#103×C101D411yescharacteristic
122#102×C101—21no—
123#102×C101—21no—
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—21no—
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
144C24×C101—41no—
145#41×C101—42no—
146#41×C101—81no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101C2×D411yescharacteristic
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—41no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101—42no—
161C2×D4×C101—42no—
162C2×D4×C101—41no—
163C2×D4×C101—81no—
164C2×D4×C101—81no—
165C2×D4×C101C2×D411yescharacteristic
166C2×D4×C101C2×D411yescharacteristic
167C2×D4×C101C2×D411yescharacteristic
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—41no—
172SD16×C101—41no—
173SD16×C101—42no—
174SD16×C101—81no—
175SD16×C101—81no—
176SD16×C101—81no—
177D8×C101—41no—
178D8×C101—81no—
179D8×C101—81no—
180D8×C101—81no—
181D8×C101—82no—
182M16×C101—81no—
183M16×C101—81no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—81no—
190C2×C8×C101C2×D411yescharacteristic
191C2×C8×C101C2×D411yescharacteristic
192C2×C8×C101C2×D411yescharacteristic
193C2×C8×C101C2×D411yescharacteristic
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
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—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C42×C101—21no—
214C42×C101—41no—
215C42×C101—41no—
216C42×C101C2411yescharacteristic
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—21no—
220C23×C101—41no—
221C23×C101—41no—
222C23×C101—82no—
223C23×C101—82no—
224C23×C101—161no—
225Q8×C101—21no—
226Q8×C101—21no—
227Q8×C101—41no—
228Q8×C101—41no—
229Q8×C101—81no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—21no—
235D4×C101—21no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—41no—
241D4×C101—41no—
242D4×C101—41no—
243D4×C101—41no—
244D4×C101—81no—
245D4×C101—81no—
246D4×C101—82no—
247D4×C101—82no—
248D4×C101—82no—
249D4×C101—161no—
250D4×C101—161no—
251C2×C4×C101—21no—
252C2×C4×C101—21no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
255C2×C4×C101—21no—
256C2×C4×C101—41no—
257C2×C4×C101—41no—
258C2×C4×C101—41no—
259C2×C4×C101—41no—
260C2×C4×C101—41no—
261C2×C4×C101—41no—
262C2×C4×C101—41no—
263C2×C4×C101—41no—
264C2×C4×C101—82no—
265C2×C4×C101C22×D411yescharacteristic
266C2×C4×C101C22×D411yescharacteristic
267C2×C4×C101H(5,𝔽2)11yescharacteristic
268C8×C101—21no—
269C8×C101—21no—
270C8×C101—21no—
271C8×C101—21no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101—41no—
275C8×C101—41no—
276C8×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—41no—
282C22×C101—41no—
283C22×C101—41no—
284C22×C101—41no—
285C22×C101—41no—
286C22×C101—81no—
287C22×C101—81no—
288C22×C101—81no—
289C22×C101—81no—
290C22×C101—81no—
291C22×C101—81no—
292C22×C101—164no—
293C22×C101D4211yescharacteristic
294C4×C101—21no—
295C4×C101—41no—
296C4×C101—41no—
297C4×C101—41no—
298C4×C101—41no—
299C4×C101—41no—
300C4×C101—81no—
301C4×C101—81no—
302C4×C101#57511yescharacteristic
303C4×C101#57511yescharacteristic
304C4×C101#57611yescharacteristic
305C4×C101#57611yescharacteristic
306#20258C10111yesmaximal, characteristic, direct product factor, Sylow
307C2×C101—81no—
308C2×C101—81no—
309C2×C101—81no—
310C2×C101—161no—
311C2×C101—161no—
312C2×C101#326811yescharacteristic
313C2×C101#327311yescharacteristic
314C2×C101#328811yescharacteristic
315#3397C2×C10111yescharacteristic, complemented
316#3325C2×C10111yescharacteristic, complemented
317#3324C2×C10111yescharacteristic, complemented
318#3305C2×C10111yescharacteristic, complemented
319#1717C2×C10111yescharacteristic, complemented
320#1698C2×C10111yescharacteristic, complemented
321#1697C2×C10111yescharacteristic, complemented
322#1685C2×C10111yescharacteristic, complemented
323#1681C2×C10111yescharacteristic, complemented
324#1646C2×C10111yescharacteristic, complemented
325#1638C2×C10111yescharacteristic, complemented
326#1621C2×C10111yescharacteristic, complemented
327#1619C2×C10111yescharacteristic, complemented
328#1592C2×C10111yescharacteristic, complemented
329#1581C2×C10111yescharacteristic, complemented
330C101#2025811yescharacteristic, direct product factor, Sylow
331#556C22×C10111yescharacteristic
332#555C22×C10111yescharacteristic
333#550C22×C10111yescharacteristic, complemented
334D42C22×C10111yescharacteristic
335#496—21no—
336#493C22×C10111yescharacteristic
337#492C22×C10111yescharacteristic, complemented
338#487C22×C10111yescharacteristic, complemented
339#486C22×C10111yescharacteristic
340#486C22×C10111yescharacteristic
341#486C22×C10111yescharacteristic, complemented
342#482—21no—
343#482—21no—
344#482—21no—
345#477C22×C10111yescharacteristic, complemented
346#476C22×C10111yescharacteristic
347#474C22×C10111yescharacteristic
348#469—21no—
349#468—21no—
350#466—21no—
351#463—21no—
352#461C22×C10111yescharacteristic, complemented
353#460—21no—
354#460C22×C10111yescharacteristic
355#459C22×C10111yescharacteristic
356#459C22×C10111yescharacteristic
357#459C22×C10111yescharacteristic
358#450—21no—
359#449—21no—
360#447—21no—
361#446C22×C10111yescharacteristic, complemented
362#440—21no—
363C4×SD16C22×C10111yescharacteristic
364C4×D8C22×C10111yescharacteristic
365#436C22×C10111yescharacteristic
366#436C22×C10111yescharacteristic
367C8×D4C22×C10111yescharacteristic, complemented
368#418—21no—
369#418—21no—
370#416—21no—
371#335C22×C10111yescharacteristic, complemented
372#335C22×C10111yescharacteristic, complemented
373#333C22×C10111yescharacteristic, complemented
374#332C22×C10111yescharacteristic, complemented
375#331C22×C10111yescharacteristic
376#331C22×C10111yescharacteristic, complemented
377Q8⋊C8C22×C10111yescharacteristic, complemented
378D4⋊C8C22×C10111yescharacteristic
379D4⋊C8C22×C10111yescharacteristic
380D4⋊C8C22×C10111yescharacteristic, complemented
381#322C22×C10111yescharacteristic, complemented
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16D4×C10111yescharacteristic
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—41no—
394C2×D8D4×C10111yescharacteristic
395C2×M16—21no—
396C2×M16—21no—
397C22×C8—21no—
398C4⋊Q8C23×C10111yescharacteristic
399C4⋊Q8C23×C10111yescharacteristic
400#127—21no—
401#127C23×C10111yescharacteristic
402#127C23×C10111yescharacteristic
403#126—41no—
404#124—21no—
405#124—41no—
406C22⋊Q8—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—21no—
412#121—41no—
413#120—41no—
414C4×Q8—21no—
415C4×Q8C23×C10111yescharacteristic
416C4×D4—21no—
417C4×D4C23×C10111yescharacteristic
418C4×D4C23×C10111yescharacteristic
419C4×D4C23×C10111yescharacteristic
420#117—21no—
421#117—21no—
422#117—21no—
423#107—21no—
424#107—21no—
425#107D4×C10111yescharacteristic
426#106—21no—
427#106D4×C10111yescharacteristic
428C4⋊C8—21no—
429C4⋊C8C23×C10111yescharacteristic
430C4⋊C8C23×C10111yescharacteristic
431C4⋊C8C23×C10111yescharacteristic
432C4⋊C8C23×C10111yescharacteristic
433#103—21no—
434#103—21no—
435#103—41no—
436#103D4×C10111yescharacteristic
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#102—21no—
448#102—21no—
449#102D4×C10111yescharacteristic
450#102D4×C10111yescharacteristic
451#102D4×C10111yescharacteristic
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455#97—21no—
456C4×C8C23×C10111yescharacteristic
457C4×C8C23×C10111yescharacteristic
458C4×C8C23×C10111yescharacteristic
459C24—41no—
460#41—42no—
461#41—81no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×Q8C2×D4×C10111yescharacteristic
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—42no—
476C2×D4—42no—
477C2×D4—41no—
478C2×D4—81no—
479C2×D4—81no—
480C2×D4C2×D4×C10111yescharacteristic
481C2×D4C2×D4×C10111yescharacteristic
482C2×D4C2×D4×C10111yescharacteristic
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487SD16—41no—
488SD16—42no—
489SD16—81no—
490SD16—81no—
491SD16—81no—
492D8—41no—
493D8—81no—
494D8—81no—
495D8—81no—
496D8—82no—
497M16—81no—
498M16—81no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—81no—
505C2×C8C2×D4×C10111yescharacteristic
506C2×C8C2×D4×C10111yescharacteristic
507C2×C8C2×D4×C10111yescharacteristic
508C2×C8C2×D4×C10111yescharacteristic
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C10111yescharacteristic
516C4⋊C4C2×D4×C10111yescharacteristic
517C4⋊C4C2×D4×C10111yescharacteristic
518C4⋊C4C2×D4×C10111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—21no—
529C42—41no—
530C42—41no—
531C42C24×C10111yescharacteristic
532C23—21no—
533C23—21no—
534C23—21no—
535C23—41no—
536C23—41no—
537C23—82no—
538C23—82no—
539C23—161no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—81no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—21no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—41no—
559D4—81no—
560D4—81no—
561D4—82no—
562D4—82no—
563D4—82no—
564D4—161no—
565D4—161no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—82no—
580C2×C4C22×D4×C10111yescharacteristic
581C2×C4C22×D4×C10111yescharacteristic
582C2×C4H(5,𝔽2)×C10111yescharacteristic
583C8—21no—
584C8—21no—
585C8—21no—
586C8—21no—
587C8—41no—
588C8—41no—
589C8—41no—
590C8—41no—
591C8—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22—164no—
608C22D42×C10111yescharacteristic
609C4—21no—
610C4—41no—
611C4—41no—
612C4—41no—
613C4—41no—
614C4—41no—
615C4—81no—
616C4—81no—
617C4#575×C10111yescharacteristic
618C4#575×C10111yescharacteristic
619C4#576×C10111yescharacteristic
620C4#576×C10111yescharacteristic
621C2—81no—
622C2—81no—
623C2—81no—
624C2—161no—
625C2—161no—
626C2C101×#326811yescharacteristic
627C2C101×#327311yescharacteristic
628C2C101×#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×#3397C2semidirect
2. C101×#3325C2semidirect
3. C101×#3324C2semidirect
4. C101×#3305C2semidirect
5. C101×#1717C2semidirect
6. C101×#1698C2semidirect
7. C101×#1697C2semidirect
8. C101×#1685C2semidirect
9. C101×#1681C2semidirect
10. C101×#1646C2semidirect
11. C101×#1638C2semidirect
12. C101×#1621C2semidirect
13. C101×#1619C2semidirect
14. C101×#1592C2semidirect
15. C101×#1581C2semidirect
18. #550×C101C22semidirect
22. #492×C101C22semidirect
23. #487×C101C22semidirect
26. #486×C101C22semidirect
30. #477×C101C22semidirect
37. #461×C101C22semidirect
46. #446×C101C22semidirect
52. C8×D4×C101C22semidirect
56. #335×C101C22semidirect
57. #335×C101C22semidirect
58. #333×C101C22semidirect
59. #332×C101C22semidirect
61. #331×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
65. D4⋊C8×C101C22semidirect
66. #322×C101C22semidirect
306. #20258C101direct (N × H)
315. #3397C2×C101semidirect
316. #3325C2×C101semidirect
317. #3324C2×C101semidirect
318. #3305C2×C101semidirect
319. #1717C2×C101semidirect
320. #1698C2×C101semidirect
321. #1697C2×C101semidirect
322. #1685C2×C101semidirect
323. #1681C2×C101semidirect
324. #1646C2×C101semidirect
325. #1638C2×C101semidirect
326. #1621C2×C101semidirect
327. #1619C2×C101semidirect
328. #1592C2×C101semidirect
329. #1581C2×C101semidirect
330. C101#20258direct (N × H)
333. #550C22×C101semidirect
337. #492C22×C101semidirect
338. #487C22×C101semidirect
341. #486C22×C101semidirect
345. #477C22×C101semidirect
352. #461C22×C101semidirect
361. #446C22×C101semidirect
367. C8×D4C22×C101semidirect
371. #335C22×C101semidirect
372. #335C22×C101semidirect
373. #333C22×C101semidirect
374. #332C22×C101semidirect
376. #331C22×C101semidirect
377. Q8⋊C8C22×C101semidirect
380. D4⋊C8C22×C101semidirect
381. #322C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33972
C101×#33252
C101×#33242
C101×#33052
C101×#17172
C101×#16982
C101×#16972
C101×#16852
C101×#16812
C101×#16462
C101×#16382
C101×#16212
C101×#16192
C101×#15922
C101×#15812
#20258101