Finite Group Databasebeta

← C101×#19825 #38801976

Subgroups — C101×#19825 #38801976

Order 25856.

642 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3394C211yesmaximal, characteristic, complemented
2C101×#3361C211yesmaximal, characteristic, complemented
3C101×#3324C211yesmaximal, characteristic, complemented
4C101×#3295C211yesmaximal, characteristic, complemented
5C101×#1717C211yesmaximal, characteristic, complemented
6C101×#1697C211yesmaximal, characteristic, complemented
7C101×#1682C211yesmaximal, characteristic, complemented
8C101×#1678C211yesmaximal, characteristic, complemented
9C101×#1665C211yesmaximal, characteristic, complemented
10C101×#1644C211yesmaximal, characteristic, complemented
11C101×#1638C211yesmaximal, characteristic, complemented
12C101×#1620C211yesmaximal, characteristic, complemented
13C101×#1619C211yesmaximal, characteristic
14C101×#1583C211yesmaximal, characteristic, complemented
15C101×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic, complemented
17#556×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19D42×C101C2211yescharacteristic
20#495×C101—21no—
21#493×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic, complemented
23#488×C101—21no—
24#487×C101C2211yescharacteristic, complemented
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic, complemented
28#482×C101—21no—
29#481×C101—21no—
30#478×C101—21no—
31#477×C101C2211yescharacteristic, complemented
32#476×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#468×C101—21no—
35#465×C101—21no—
36#464×C101—21no—
37#463×C101—21no—
38#463×C101—21no—
39#462×C101C2211yescharacteristic, complemented
40#460×C101C2211yescharacteristic
41#460×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#450×C101—21no—
45#450×C101—21no—
46C8×Q8×C101C2211yescharacteristic, complemented
47C8×Q8×C101C2211yescharacteristic, complemented
48C4×SD16×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×SD16×C101C2211yescharacteristic
51C4×D8×C101—21no—
52#436×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54#418×C101—21no—
55C2×#102×C101—21no—
56#335×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#333×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
66#322×C101C2211yescharacteristic, complemented
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C2×Q16×C101—21no—
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101D411yescharacteristic
75C2×SD16×C101D411yescharacteristic
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×D8×C101—41no—
79C2×M16×C101—21no—
80C22×C8×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#126×C101—41no—
86#125×C101—21no—
87#124×C101—21no—
88#124×C101—21no—
89#124×C101—21no—
90#123×C101—41no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93C22⋊Q8×C101—41no—
94#121×C101—21no—
95#121×C101—21no—
96#120×C101—41no—
97C4×Q8×C101—21no—
98C4×Q8×C101C2311yescharacteristic
99C4×Q8×C101C2311yescharacteristic
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101C2311yescharacteristic
104C4×D4×C101C2311yescharacteristic
105#117×C101—21no—
106C2×C4⋊C4×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#106×C101—21no—
110#106×C101D411yescharacteristic
111#106×C101D411yescharacteristic
112C4⋊C8×C101—21no—
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#103×C101D411yescharacteristic
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×C101—21no—
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139C4×C8×C101—21no—
140C4×C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C24×C101—41no—
145C2×Q8×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101C2×D411yescharacteristic
148C2×Q8×C101C2×D411yescharacteristic
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101—42no—
158C2×D4×C101—42no—
159C2×D4×C101—81no—
160C2×D4×C101—81no—
161C2×D4×C101C2×D411yescharacteristic
162C2×D4×C101C2×D411yescharacteristic
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—41no—
166C22×C4×C101—41no—
167Q16×C101—81no—
168SD16×C101—22no—
169SD16×C101—41no—
170SD16×C101—42no—
171SD16×C101—81no—
172SD16×C101—81no—
173SD16×C101—81no—
174D8×C101—42no—
175D8×C101—81no—
176D8×C101—82no—
177M16×C101—81no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—81no—
184C2×C8×C101C2×D411yescharacteristic
185C2×C8×C101C2×D411yescharacteristic
186C2×C8×C101C2×D411yescharacteristic
187C2×C8×C101C2×D411yescharacteristic
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×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C4⋊C4×C101C2×D411yescharacteristic
200C4⋊C4×C101C2×D411yescharacteristic
201C22⋊C4×C101—21no—
202C22⋊C4×C101—21no—
203C22⋊C4×C101—41no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C42×C101—21no—
211C42×C101—21no—
212C42×C101—41no—
213C42×C101C2411yescharacteristic
214C23×C101—21no—
215C23×C101—21no—
216C23×C101—41no—
217C23×C101—41no—
218C23×C101—82no—
219C23×C101—82no—
220C23×C101—161no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—81no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—81no—
240D4×C101—81no—
241D4×C101—82no—
242D4×C101—82no—
243D4×C101#13512yes—
244C2×C4×C101—21no—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
248C2×C4×C101—21no—
249C2×C4×C101—21no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101—161no—
257C2×C4×C101—161no—
258C2×C4×C101C22×D411yescharacteristic
259C2×C4×C101C22×D411yescharacteristic
260C2×C4×C101H(5,𝔽2)11yescharacteristic
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—21no—
264C8×C101—21no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C22×C101—22no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101—81no—
282C22×C101—164no—
283C22×C101D4211yescharacteristic
284C4×C101—21no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—41no—
291C4×C101—81no—
292C4×C101—81no—
293C4×C101C2×#13511yescharacteristic
294C4×C101#57511yescharacteristic
295C4×C101#57611yescharacteristic
296C4×C101#57711yescharacteristic
297#19825C10111yesmaximal, characteristic, direct product factor, Sylow
298C2×C101—42no—
299C2×C101—81no—
300C2×C101—161no—
301C2×C101—161no—
302C2×C101#326811yescharacteristic
303C2×C101#328211yescharacteristic
304C2×C101#328811yescharacteristic
305#3394C2×C10111yescharacteristic, complemented
306#3361C2×C10111yescharacteristic, complemented
307#3324C2×C10111yescharacteristic, complemented
308#3295C2×C10111yescharacteristic, complemented
309#1717C2×C10111yescharacteristic, complemented
310#1697C2×C10111yescharacteristic, complemented
311#1682C2×C10111yescharacteristic, complemented
312#1678C2×C10111yescharacteristic, complemented
313#1665C2×C10111yescharacteristic, complemented
314#1644C2×C10111yescharacteristic, complemented
315#1638C2×C10111yescharacteristic, complemented
316#1620C2×C10111yescharacteristic, complemented
317#1619C2×C10111yescharacteristic
318#1583C2×C10111yescharacteristic, complemented
319SD16⋊C8C2×C10111yescharacteristic, complemented
320C101#1982511yescharacteristic, direct product factor, Sylow
321#559C22×C10111yescharacteristic, complemented
322#556C22×C10111yescharacteristic
323#554C22×C10111yescharacteristic
324D42C22×C10111yescharacteristic
325#495—21no—
326#493C22×C10111yescharacteristic
327#492C22×C10111yescharacteristic, complemented
328#488—21no—
329#487C22×C10111yescharacteristic, complemented
330#486C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic
332#486C22×C10111yescharacteristic, complemented
333#482—21no—
334#481—21no—
335#478—21no—
336#477C22×C10111yescharacteristic, complemented
337#476C22×C10111yescharacteristic
338#474C22×C10111yescharacteristic
339#468—21no—
340#465—21no—
341#464—21no—
342#463—21no—
343#463—21no—
344#462C22×C10111yescharacteristic, complemented
345#460C22×C10111yescharacteristic
346#460C22×C10111yescharacteristic
347#459C22×C10111yescharacteristic
348#459C22×C10111yescharacteristic
349#450—21no—
350#450—21no—
351C8×Q8C22×C10111yescharacteristic, complemented
352C8×Q8C22×C10111yescharacteristic, complemented
353C4×SD16—21no—
354C4×SD16C22×C10111yescharacteristic
355C4×SD16C22×C10111yescharacteristic
356C4×D8—21no—
357#436C22×C10111yescharacteristic
358C8×D4C22×C10111yescharacteristic
359#418—21no—
360C2×#102—21no—
361#335C22×C10111yescharacteristic, complemented
362#334C22×C10111yescharacteristic, complemented
363#333C22×C10111yescharacteristic, complemented
364#332C22×C10111yescharacteristic, complemented
365#331C22×C10111yescharacteristic
366#331C22×C10111yescharacteristic, complemented
367Q8⋊C8C22×C10111yescharacteristic, complemented
368Q8⋊C8C22×C10111yescharacteristic, complemented
369D4⋊C8C22×C10111yescharacteristic
370D4⋊C8C22×C10111yescharacteristic
371#322C22×C10111yescharacteristic, complemented
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16—21no—
379C2×SD16D4×C10111yescharacteristic
380C2×SD16D4×C10111yescharacteristic
381C2×D8—21no—
382C2×D8—21no—
383C2×D8—41no—
384C2×M16—21no—
385C22×C8—21no—
386C4⋊Q8C23×C10111yescharacteristic
387C4⋊Q8C23×C10111yescharacteristic
388#127C23×C10111yescharacteristic
389#127C23×C10111yescharacteristic
390#126—41no—
391#125—21no—
392#124—21no—
393#124—21no—
394#124—21no—
395#123—41no—
396C22⋊Q8—21no—
397C22⋊Q8—21no—
398C22⋊Q8—41no—
399#121—21no—
400#121—21no—
401#120—41no—
402C4×Q8—21no—
403C4×Q8C23×C10111yescharacteristic
404C4×Q8C23×C10111yescharacteristic
405C4×D4—21no—
406C4×D4—21no—
407C4×D4—21no—
408C4×D4C23×C10111yescharacteristic
409C4×D4C23×C10111yescharacteristic
410#117—21no—
411C2×C4⋊C4—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106D4×C10111yescharacteristic
416#106D4×C10111yescharacteristic
417C4⋊C8—21no—
418C4⋊C8—21no—
419C4⋊C8C23×C10111yescharacteristic
420C4⋊C8C23×C10111yescharacteristic
421C4⋊C8C23×C10111yescharacteristic
422C4⋊C8C23×C10111yescharacteristic
423#103—21no—
424#103—21no—
425#103—41no—
426#103D4×C10111yescharacteristic
427#103D4×C10111yescharacteristic
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102D4×C10111yescharacteristic
441#102D4×C10111yescharacteristic
442C22⋊C8—21no—
443C22⋊C8—21no—
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C10111yescharacteristic
447C4×C8C23×C10111yescharacteristic
448C4×C8C23×C10111yescharacteristic
449C24—41no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8C2×D4×C10111yescharacteristic
453C2×Q8C2×D4×C10111yescharacteristic
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—41no—
461C2×D4—41no—
462C2×D4—42no—
463C2×D4—42no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C10111yescharacteristic
467C2×D4C2×D4×C10111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472Q16—81no—
473SD16—22no—
474SD16—41no—
475SD16—42no—
476SD16—81no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480D8—81no—
481D8—82no—
482M16—81no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—81no—
489C2×C8C2×D4×C10111yescharacteristic
490C2×C8C2×D4×C10111yescharacteristic
491C2×C8C2×D4×C10111yescharacteristic
492C2×C8C2×D4×C10111yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4C2×D4×C10111yescharacteristic
503C4⋊C4C2×D4×C10111yescharacteristic
504C4⋊C4C2×D4×C10111yescharacteristic
505C4⋊C4C2×D4×C10111yescharacteristic
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42—41no—
518C42C24×C10111yescharacteristic
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—82no—
524C23—82no—
525C23—161no—
526Q8—21no—
527Q8—21no—
528Q8—21no—
529Q8—21no—
530Q8—41no—
531Q8—41no—
532Q8—81no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—81no—
545D4—81no—
546D4—82no—
547D4—82no—
548D4#135×C10112yes—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—161no—
562C2×C4—161no—
563C2×C4C22×D4×C10111yescharacteristic
564C2×C4C22×D4×C10111yescharacteristic
565C2×C4H(5,𝔽2)×C10111yescharacteristic
566C8—21no—
567C8—21no—
568C8—21no—
569C8—21no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C8—41no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22—164no—
588C22D42×C10111yescharacteristic
589C4—21no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—41no—
595C4—41no—
596C4—81no—
597C4—81no—
598C4C2×#135×C10111yescharacteristic
599C4#575×C10111yescharacteristic
600C4#576×C10111yescharacteristic
601C4#577×C10111yescharacteristic
602C2—42no—
603C2—81no—
604C2—161no—
605C2—161no—
606C2C101×#326811yescharacteristic
607C2C101×#328211yescharacteristic
608C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#1619C2
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×#3394C2semidirect
2. C101×#3361C2semidirect
3. C101×#3324C2semidirect
4. C101×#3295C2semidirect
5. C101×#1717C2semidirect
6. C101×#1697C2semidirect
7. C101×#1682C2semidirect
8. C101×#1678C2semidirect
9. C101×#1665C2semidirect
10. C101×#1644C2semidirect
11. C101×#1638C2semidirect
12. C101×#1620C2semidirect
14. C101×#1583C2semidirect
15. C101×SD16⋊C8C2semidirect
16. #559×C101C22semidirect
22. #492×C101C22semidirect
24. #487×C101C22semidirect
27. #486×C101C22semidirect
31. #477×C101C22semidirect
39. #462×C101C22semidirect
46. C8×Q8×C101C22semidirect
47. C8×Q8×C101C22semidirect
56. #335×C101C22semidirect
57. #334×C101C22semidirect
58. #333×C101C22semidirect
59. #332×C101C22semidirect
61. #331×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
66. #322×C101C22semidirect
297. #19825C101direct (N × H)
305. #3394C2×C101semidirect
306. #3361C2×C101semidirect
307. #3324C2×C101semidirect
308. #3295C2×C101semidirect
309. #1717C2×C101semidirect
310. #1697C2×C101semidirect
311. #1682C2×C101semidirect
312. #1678C2×C101semidirect
313. #1665C2×C101semidirect
314. #1644C2×C101semidirect
315. #1638C2×C101semidirect
316. #1620C2×C101semidirect
318. #1583C2×C101semidirect
319. SD16⋊C8C2×C101semidirect
320. C101#19825direct (N × H)
321. #559C22×C101semidirect
327. #492C22×C101semidirect
329. #487C22×C101semidirect
332. #486C22×C101semidirect
336. #477C22×C101semidirect
344. #462C22×C101semidirect
351. C8×Q8C22×C101semidirect
352. C8×Q8C22×C101semidirect
361. #335C22×C101semidirect
362. #334C22×C101semidirect
363. #333C22×C101semidirect
364. #332C22×C101semidirect
366. #331C22×C101semidirect
367. Q8⋊C8C22×C101semidirect
368. Q8⋊C8C22×C101semidirect
371. #322C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33942
C101×#33612
C101×#33242
C101×#32952
C101×#17172
C101×#16972
C101×#16822
C101×#16782
C101×#16652
C101×#16442
C101×#16382
C101×#16202
C101×#16192
C101×#15832
C101×SD16⋊C82
#19825101