Finite Group Databasebeta

← C101×#20288 #38802439

Subgroups — C101×#20288 #38802439

Order 25856.

670 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3398C211yesmaximal, characteristic, complemented
2C101×#3368C211yesmaximal, characteristic, complemented
3C101×#3324C211yesmaximal, characteristic, complemented
4C101×#3274C211yesmaximal, characteristic
5C101×#1709C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1701C211yesmaximal, characteristic, complemented
8C101×#1689C211yesmaximal, characteristic, complemented
9C101×#1688C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1639C211yesmaximal, characteristic, complemented
12C101×#1628C211yesmaximal, characteristic, complemented
13C101×#1626C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1590C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C101—21no—
17#557×C101C2211yescharacteristic, complemented
18#556×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20D42×C101C2211yescharacteristic
21#497×C101—21no—
22#494×C101C2211yescharacteristic, complemented
23#493×C101C2211yescharacteristic
24#490×C101—21no—
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic, complemented
28#486×C101C2211yescharacteristic, complemented
29#482×C101—21no—
30#478×C101—21no—
31#474×C101C2211yescharacteristic
32#474×C101C2211yescharacteristic
33#469×C101—21no—
34#468×C101—21no—
35#464×C101—21no—
36#462×C101—21no—
37#462×C101C2211yescharacteristic, complemented
38#461×C101C2211yescharacteristic
39#460×C101—21no—
40#460×C101C2211yescharacteristic
41#460×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic, complemented
43#459×C101C2211yescharacteristic
44#450×C101—21no—
45#449×C101—21no—
46#447×C101—21no—
47#446×C101C2211yescharacteristic, complemented
48#446×C101C2211yescharacteristic, complemented
49#441×C101—21no—
50#440×C101—21no—
51C4×SD16×C101C2211yescharacteristic
52C4×SD16×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#418×C101—21no—
56#334×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#332×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic, complemented
62Q8⋊C8×C101C2211yescharacteristic, complemented
63Q8⋊C8×C101C2211yescharacteristic, complemented
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic, complemented
67C2×#41×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70AGL(1,ℤ/8)×C101—44no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×Q16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101—21no—
78C2×SD16×C101D411yescharacteristic
79C2×SD16×C101D411yescharacteristic
80C2×D8×C101—21no—
81C2×D8×C101—21no—
82C2×D8×C101—21no—
83C2×M16×C101—21no—
84C2×M16×C101—21no—
85C4⋊Q8×C101—21no—
86C4⋊Q8×C101C2311yescharacteristic
87C4⋊Q8×C101C2311yescharacteristic
88#127×C101—21no—
89#127×C101C2311yescharacteristic
90#127×C101C2311yescharacteristic
91#126×C101—41no—
92#125×C101—21no—
93#125×C101—41no—
94#124×C101—21no—
95C22⋊Q8×C101—21no—
96#121×C101—21no—
97#121×C101—21no—
98#121×C101—21no—
99#121×C101—41no—
100#120×C101—41no—
101C4×Q8×C101—21no—
102C4×Q8×C101—21no—
103C4×Q8×C101—21no—
104C4×Q8×C101C2311yescharacteristic
105C4×Q8×C101C2311yescharacteristic
106C4×D4×C101—21no—
107C4×D4×C101C2311yescharacteristic
108C4×D4×C101C2311yescharacteristic
109#117×C101—21no—
110#107×C101—21no—
111#107×C101—21no—
112#106×C101D411yescharacteristic
113#106×C101D411yescharacteristic
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×C101D411yescharacteristic
123#103×C101D411yescharacteristic
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×C101—41no—
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
145C24×C101—41no—
146#41×C101—42no—
147#41×C101—81no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
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×C101—41no—
161C2×D4×C101—41no—
162C2×D4×C101—42no—
163C2×D4×C101—42no—
164C2×D4×C101—81no—
165C2×D4×C101—81no—
166C2×D4×C101C2×D411yescharacteristic
167C2×D4×C101C2×D411yescharacteristic
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—41no—
171Q16×C101—42no—
172Q16×C101—81no—
173Q16×C101—81no—
174SD16×C101—22no—
175SD16×C101—41no—
176SD16×C101—42no—
177SD16×C101—42no—
178SD16×C101—81no—
179SD16×C101—81no—
180D8×C101—42no—
181D8×C101—42no—
182D8×C101—81no—
183M16×C101—42no—
184M16×C101—81no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
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—21no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101—41no—
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C4⋊C4×C101C2×D411yescharacteristic
207C4⋊C4×C101C2×D411yescharacteristic
208C22⋊C4×C101—21no—
209C22⋊C4×C101—21no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C42×C101—21no—
215C42×C101—21no—
216C42×C101—41no—
217C42×C101—41no—
218C42×C101C2411yescharacteristic
219C23×C101—21no—
220C23×C101—21no—
221C23×C101—41no—
222C23×C101—41no—
223C23×C101—82no—
224C23×C101—82no—
225C23×C101—161no—
226Q8×C101—21no—
227Q8×C101—21no—
228Q8×C101—21no—
229Q8×C101—21no—
230Q8×C101—41no—
231Q8×C101—41no—
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—81no—
247D4×C101—81no—
248D4×C101—82no—
249D4×C101—82no—
250D4×C101—82no—
251D4×C101—161no—
252C2×C4×C101—21no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
255C2×C4×C101—21no—
256C2×C4×C101—21no—
257C2×C4×C101—21no—
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—41no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101—41no—
275C8×C101—41no—
276C8×C101AGL(1,ℤ/8)12yes—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—41no—
282C22×C101—41no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101—81no—
286C22×C101—81no—
287C22×C101—81no—
288C22×C101—81no—
289C22×C101—164no—
290C22×C101D4211yescharacteristic
291C4×C101—21no—
292C4×C101—41no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—41no—
296C4×C101—41no—
297C4×C101—41no—
298C4×C101—81no—
299C4×C101—81no—
300C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C101#57511yescharacteristic
302C4×C101#57611yescharacteristic
303C4×C101#57711yescharacteristic
304#20288C10111yesmaximal, characteristic, direct product factor, Sylow
305C2×C101—81no—
306C2×C101—81no—
307C2×C101—161no—
308C2×C101—161no—
309C2×C101#327411yescharacteristic
310C2×C101#327511yescharacteristic
311C2×C101#329011yescharacteristic
312#3398C2×C10111yescharacteristic, complemented
313#3368C2×C10111yescharacteristic, complemented
314#3324C2×C10111yescharacteristic, complemented
315#3274C2×C10111yescharacteristic
316#1709C2×C10111yescharacteristic, complemented
317#1702C2×C10111yescharacteristic, complemented
318#1701C2×C10111yescharacteristic, complemented
319#1689C2×C10111yescharacteristic, complemented
320#1688C2×C10111yescharacteristic, complemented
321#1641C2×C10111yescharacteristic, complemented
322#1639C2×C10111yescharacteristic, complemented
323#1628C2×C10111yescharacteristic, complemented
324#1626C2×C10111yescharacteristic, complemented
325#1590C2×C10111yescharacteristic, complemented
326#1590C2×C10111yescharacteristic, complemented
327C101#2028811yescharacteristic, direct product factor, Sylow
328C2×AGL(1,ℤ/8)—21no—
329#557C22×C10111yescharacteristic, complemented
330#556C22×C10111yescharacteristic
331#550C22×C10111yescharacteristic
332D42C22×C10111yescharacteristic
333#497—21no—
334#494C22×C10111yescharacteristic, complemented
335#493C22×C10111yescharacteristic
336#490—21no—
337#486C22×C10111yescharacteristic
338#486C22×C10111yescharacteristic
339#486C22×C10111yescharacteristic, complemented
340#486C22×C10111yescharacteristic, complemented
341#482—21no—
342#478—21no—
343#474C22×C10111yescharacteristic
344#474C22×C10111yescharacteristic
345#469—21no—
346#468—21no—
347#464—21no—
348#462—21no—
349#462C22×C10111yescharacteristic, complemented
350#461C22×C10111yescharacteristic
351#460—21no—
352#460C22×C10111yescharacteristic
353#460C22×C10111yescharacteristic
354#460C22×C10111yescharacteristic, complemented
355#459C22×C10111yescharacteristic
356#450—21no—
357#449—21no—
358#447—21no—
359#446C22×C10111yescharacteristic, complemented
360#446C22×C10111yescharacteristic, complemented
361#441—21no—
362#440—21no—
363C4×SD16C22×C10111yescharacteristic
364C4×SD16C22×C10111yescharacteristic
365#436C22×C10111yescharacteristic
366#436C22×C10111yescharacteristic
367#418—21no—
368#334C22×C10111yescharacteristic, complemented
369#334C22×C10111yescharacteristic, complemented
370#332C22×C10111yescharacteristic, complemented
371#332C22×C10111yescharacteristic, complemented
372#331C22×C10111yescharacteristic
373#331C22×C10111yescharacteristic, complemented
374Q8⋊C8C22×C10111yescharacteristic, complemented
375Q8⋊C8C22×C10111yescharacteristic, complemented
376D4⋊C8C22×C10111yescharacteristic
377D4⋊C8C22×C10111yescharacteristic
378C82C22×C10111yescharacteristic, complemented
379C2×#41—21no—
380C22×D4—21no—
381C22×D4—21no—
382AGL(1,ℤ/8)—44no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×Q16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16—21no—
390C2×SD16D4×C10111yescharacteristic
391C2×SD16D4×C10111yescharacteristic
392C2×D8—21no—
393C2×D8—21no—
394C2×D8—21no—
395C2×M16—21no—
396C2×M16—21no—
397C4⋊Q8—21no—
398C4⋊Q8C23×C10111yescharacteristic
399C4⋊Q8C23×C10111yescharacteristic
400#127—21no—
401#127C23×C10111yescharacteristic
402#127C23×C10111yescharacteristic
403#126—41no—
404#125—21no—
405#125—41no—
406#124—21no—
407C22⋊Q8—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#121—41no—
412#120—41no—
413C4×Q8—21no—
414C4×Q8—21no—
415C4×Q8—21no—
416C4×Q8C23×C10111yescharacteristic
417C4×Q8C23×C10111yescharacteristic
418C4×D4—21no—
419C4×D4C23×C10111yescharacteristic
420C4×D4C23×C10111yescharacteristic
421#117—21no—
422#107—21no—
423#107—21no—
424#106D4×C10111yescharacteristic
425#106D4×C10111yescharacteristic
426C4⋊C8—21no—
427C4⋊C8—21no—
428C4⋊C8C23×C10111yescharacteristic
429C4⋊C8C23×C10111yescharacteristic
430C4⋊C8C23×C10111yescharacteristic
431C4⋊C8C23×C10111yescharacteristic
432#103—21no—
433#103—21no—
434#103D4×C10111yescharacteristic
435#103D4×C10111yescharacteristic
436#102—21no—
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—41no—
447#102—41no—
448#102D4×C10111yescharacteristic
449#102D4×C10111yescharacteristic
450C22⋊C8—21no—
451C22⋊C8—21no—
452#97—21no—
453#97—21no—
454C4×C8C23×C10111yescharacteristic
455C4×C8C23×C10111yescharacteristic
456C4×C8C23×C10111yescharacteristic
457C24—41no—
458#41—42no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8C2×D4×C10111yescharacteristic
463C2×Q8C2×D4×C10111yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—41no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—42no—
475C2×D4—42no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C10111yescharacteristic
479C2×D4C2×D4×C10111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—41no—
483Q16—42no—
484Q16—81no—
485Q16—81no—
486SD16—22no—
487SD16—41no—
488SD16—42no—
489SD16—42no—
490SD16—81no—
491SD16—81no—
492D8—42no—
493D8—42no—
494D8—81no—
495M16—42no—
496M16—81no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8C2×D4×C10111yescharacteristic
503C2×C8C2×D4×C10111yescharacteristic
504C2×C8C2×D4×C10111yescharacteristic
505C2×C8C2×D4×C10111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—41no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4—41no—
516C4⋊C4C2×D4×C10111yescharacteristic
517C4⋊C4C2×D4×C10111yescharacteristic
518C4⋊C4C2×D4×C10111yescharacteristic
519C4⋊C4C2×D4×C10111yescharacteristic
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C42—21no—
527C42—21no—
528C42—41no—
529C42—41no—
530C42C24×C10111yescharacteristic
531C23—21no—
532C23—21no—
533C23—41no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—21no—
539Q8—21no—
540Q8—21no—
541Q8—21no—
542Q8—41no—
543Q8—41no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—41no—
556D4—41no—
557D4—41no—
558D4—81no—
559D4—81no—
560D4—82no—
561D4—82no—
562D4—82no—
563D4—161no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4C22×D4×C10111yescharacteristic
578C2×C4C22×D4×C10111yescharacteristic
579C2×C4H(5,𝔽2)×C10111yescharacteristic
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8AGL(1,ℤ/8)×C10112yes—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—164no—
602C22D42×C10111yescharacteristic
603C4—21no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
613C4#575×C10111yescharacteristic
614C4#576×C10111yescharacteristic
615C4#577×C10111yescharacteristic
616C2—81no—
617C2—81no—
618C2—161no—
619C2—161no—
620C2C101×#327411yescharacteristic
621C2C101×#327511yescharacteristic
622C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3274C2
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×#3398C2semidirect
2. C101×#3368C2semidirect
3. C101×#3324C2semidirect
5. C101×#1709C2semidirect
6. C101×#1702C2semidirect
7. C101×#1701C2semidirect
8. C101×#1689C2semidirect
9. C101×#1688C2semidirect
10. C101×#1641C2semidirect
11. C101×#1639C2semidirect
12. C101×#1628C2semidirect
13. C101×#1626C2semidirect
14. C101×#1590C2semidirect
15. C101×#1590C2semidirect
17. #557×C101C22semidirect
22. #494×C101C22semidirect
27. #486×C101C22semidirect
28. #486×C101C22semidirect
37. #462×C101C22semidirect
42. #460×C101C22semidirect
47. #446×C101C22semidirect
48. #446×C101C22semidirect
56. #334×C101C22semidirect
57. #334×C101C22semidirect
58. #332×C101C22semidirect
59. #332×C101C22semidirect
61. #331×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
66. C82×C101C22semidirect
304. #20288C101direct (N × H)
312. #3398C2×C101semidirect
313. #3368C2×C101semidirect
314. #3324C2×C101semidirect
316. #1709C2×C101semidirect
317. #1702C2×C101semidirect
318. #1701C2×C101semidirect
319. #1689C2×C101semidirect
320. #1688C2×C101semidirect
321. #1641C2×C101semidirect
322. #1639C2×C101semidirect
323. #1628C2×C101semidirect
324. #1626C2×C101semidirect
325. #1590C2×C101semidirect
326. #1590C2×C101semidirect
327. C101#20288direct (N × H)
329. #557C22×C101semidirect
334. #494C22×C101semidirect
339. #486C22×C101semidirect
340. #486C22×C101semidirect
349. #462C22×C101semidirect
354. #460C22×C101semidirect
359. #446C22×C101semidirect
360. #446C22×C101semidirect
368. #334C22×C101semidirect
369. #334C22×C101semidirect
370. #332C22×C101semidirect
371. #332C22×C101semidirect
373. #331C22×C101semidirect
374. Q8⋊C8C22×C101semidirect
375. Q8⋊C8C22×C101semidirect
378. C82C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33982
C101×#33682
C101×#33242
C101×#32742
C101×#17092
C101×#17022
C101×#17012
C101×#16892
C101×#16882
C101×#16412
C101×#16392
C101×#16282
C101×#16262
C101×#15902
#20288101