Finite Group Databasebeta

← C101×#19801 #38801952

Subgroups — C101×#19801 #38801952

Order 25856.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3392C211yesmaximal, characteristic
2C101×#3374C211yesmaximal, characteristic, complemented
3C101×#3364C211yesmaximal, characteristic, complemented
4C101×#3304C211yesmaximal, characteristic
5C101×#1719C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1680C211yesmaximal, characteristic, complemented
8C101×#1679C211yesmaximal, characteristic, complemented
9C101×#1666C211yesmaximal, characteristic, complemented
10C101×#1650C211yesmaximal, characteristic, complemented
11C101×#1648C211yesmaximal, characteristic, complemented
12C101×#1641C211yesmaximal, characteristic
13C101×#1626C211yesmaximal, characteristic, complemented
14C101×#1582C211yesmaximal, characteristic, complemented
15C101×#1579C211yesmaximal, characteristic, complemented
16#557×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#492×C101—21no—
22#492×C101C2211yescharacteristic
23#491×C101—21no—
24#488×C101—21no—
25#487×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#482×C101—21no—
30#479×C101—21no—
31#479×C101—21no—
32#475×C101C2211yescharacteristic
33#475×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#465×C101—21no—
36#464×C101—21no—
37#462×C101—21no—
38#462×C101C2211yescharacteristic
39#462×C101C2211yescharacteristic
40#461×C101—21no—
41#461×C101C2211yescharacteristic
42#460×C101—21no—
43#460×C101C2211yescharacteristic
44#460×C101C2211yescharacteristic
45#452×C101—21no—
46#446×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#441×C101—21no—
50C4×Q16×C101—21no—
51C4×Q16×C101C2211yescharacteristic
52C4×SD16×C101—21no—
53C4×SD16×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55#416×C101—21no—
56#334×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101D411yescharacteristic
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101D411yescharacteristic
77C22×C8×C101—21no—
78C4⋊Q8×C101—21no—
79C4⋊Q8×C101—21no—
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101—21no—
84#127×C101C2311yescharacteristic
85#126×C101—41no—
86#125×C101—21no—
87#125×C101—21no—
88#125×C101—41no—
89#125×C101—41no—
90#124×C101—21no—
91C22⋊Q8×C101—21no—
92#121×C101—21no—
93#121×C101—41no—
94C4×Q8×C101—21no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×Q8×C101—21no—
98C4×Q8×C101—21no—
99C4×Q8×C101C2311yescharacteristic
100C4×Q8×C101C2311yescharacteristic
101C4×Q8×C101C2311yescharacteristic
102C4×D4×C101—21no—
103C4×D4×C101C2311yescharacteristic
104#117×C101—21no—
105#107×C101—21no—
106#107×C101—41no—
107#107×C101D411yescharacteristic
108#106×C101—21no—
109#106×C101—21no—
110#106×C101D411yescharacteristic
111C4⋊C8×C101—21no—
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—21no—
121#103×C101—21no—
122#103×C101—21no—
123#103×C101—21no—
124#103×C101—21no—
125#103×C101—21no—
126#103×C101—21no—
127#103×C101D411yescharacteristic
128#103×C101D411yescharacteristic
129#103×C101D411yescharacteristic
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
137C22⋊C8×C101—21no—
138#97×C101—21no—
139C4×C8×C101—21no—
140C4×C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—42no—
145#41×C101—81no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101C2×D411yescharacteristic
158C22×C4×C101—21no—
159C22×C4×C101—41no—
160Q16×C101—22no—
161Q16×C101—42no—
162Q16×C101—42no—
163SD16×C101—41no—
164SD16×C101—42no—
165SD16×C101—81no—
166SD16×C101—81no—
167SD16×C101—81no—
168SD16×C101—81no—
169C2×C8×C101—21no—
170C2×C8×C101—21no—
171C2×C8×C101—21no—
172C2×C8×C101—21no—
173C2×C8×C101—21no—
174C2×C8×C101—81no—
175C2×C8×C101C2×D411yescharacteristic
176C2×C8×C101C2×D411yescharacteristic
177C2×C8×C101C2×D411yescharacteristic
178C2×C8×C101C2×D411yescharacteristic
179C4⋊C4×C101—21no—
180C4⋊C4×C101—21no—
181C4⋊C4×C101—21no—
182C4⋊C4×C101—21no—
183C4⋊C4×C101—21no—
184C4⋊C4×C101—21no—
185C4⋊C4×C101—21no—
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—41no—
189C4⋊C4×C101—41no—
190C4⋊C4×C101—41no—
191C4⋊C4×C101—41no—
192C4⋊C4×C101—41no—
193C4⋊C4×C101—41no—
194C4⋊C4×C101—41no—
195C4⋊C4×C101C2×D411yescharacteristic
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C22⋊C4×C101—21no—
200C22⋊C4×C101—41no—
201C22⋊C4×C101—41no—
202C22⋊C4×C101—41no—
203C42×C101—21no—
204C42×C101—21no—
205C42×C101—21no—
206C42×C101—41no—
207C42×C101—41no—
208C42×C101—41no—
209C42×C101C2411yescharacteristic
210C23×C101—21no—
211C23×C101—41no—
212Q8×C101—21no—
213Q8×C101—21no—
214Q8×C101—21no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—41no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101#13512yes—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—41no—
227D4×C101—41no—
228D4×C101—41no—
229D4×C101—41no—
230D4×C101—82no—
231D4×C101—81no—
232D4×C101—161no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—21no—
237C2×C4×C101—21no—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—82no—
246C2×C4×C101C22×D411yescharacteristic
247C2×C4×C101C22×D411yescharacteristic
248C2×C4×C101H(5,𝔽2)11yescharacteristic
249C8×C101—21no—
250C8×C101—21no—
251C8×C101—21no—
252C8×C101—21no—
253C8×C101—41no—
254C8×C101—41no—
255C8×C101—41no—
256C8×C101—41no—
257C8×C101—41no—
258C22×C101—41no—
259C22×C101—41no—
260C22×C101—41no—
261C22×C101—81no—
262C22×C101—81no—
263C22×C101—81no—
264C22×C101D4211yescharacteristic
265C4×C101—22no—
266C4×C101—21no—
267C4×C101—41no—
268C4×C101—41no—
269C4×C101—41no—
270C4×C101—41no—
271C4×C101—41no—
272C4×C101—41no—
273C4×C101—81no—
274C4×C101—81no—
275C4×C101—81no—
276C4×C101C2×#13511yescharacteristic
277C4×C101#57511yescharacteristic
278C4×C101#57711yescharacteristic
279C4×C101#57711yescharacteristic
280#19801C10111yesmaximal, characteristic, direct product factor, Sylow
281C2×C101—81no—
282C2×C101—161no—
283C2×C101#327111yescharacteristic
284C2×C101#328211yescharacteristic
285C2×C101#328911yescharacteristic
286#3392C2×C10111yescharacteristic
287#3374C2×C10111yescharacteristic, complemented
288#3364C2×C10111yescharacteristic, complemented
289#3304C2×C10111yescharacteristic
290#1719C2×C10111yescharacteristic, complemented
291#1702C2×C10111yescharacteristic, complemented
292#1680C2×C10111yescharacteristic, complemented
293#1679C2×C10111yescharacteristic, complemented
294#1666C2×C10111yescharacteristic, complemented
295#1650C2×C10111yescharacteristic, complemented
296#1648C2×C10111yescharacteristic, complemented
297#1641C2×C10111yescharacteristic
298#1626C2×C10111yescharacteristic, complemented
299#1582C2×C10111yescharacteristic, complemented
300#1579C2×C10111yescharacteristic, complemented
301C101#1980111yescharacteristic, direct product factor, Sylow
302#557C22×C10111yescharacteristic
303#557C22×C10111yescharacteristic
304#556C22×C10111yescharacteristic
305#550C22×C10111yescharacteristic
306#500C22×C10111yescharacteristic
307#492—21no—
308#492C22×C10111yescharacteristic
309#491—21no—
310#488—21no—
311#487C22×C10111yescharacteristic
312#487C22×C10111yescharacteristic
313#486C22×C10111yescharacteristic
314#486C22×C10111yescharacteristic
315#482—21no—
316#479—21no—
317#479—21no—
318#475C22×C10111yescharacteristic
319#475C22×C10111yescharacteristic
320#474C22×C10111yescharacteristic
321#465—21no—
322#464—21no—
323#462—21no—
324#462C22×C10111yescharacteristic
325#462C22×C10111yescharacteristic
326#461—21no—
327#461C22×C10111yescharacteristic
328#460—21no—
329#460C22×C10111yescharacteristic
330#460C22×C10111yescharacteristic
331#452—21no—
332#446C22×C10111yescharacteristic
333C8×Q8C22×C10111yescharacteristic
334C8×Q8C22×C10111yescharacteristic
335#441—21no—
336C4×Q16—21no—
337C4×Q16C22×C10111yescharacteristic
338C4×SD16—21no—
339C4×SD16C22×C10111yescharacteristic
340C8×D4C22×C10111yescharacteristic
341#416—21no—
342#334C22×C10111yescharacteristic
343#334C22×C10111yescharacteristic
344#332C22×C10111yescharacteristic
345#332C22×C10111yescharacteristic
346#332C22×C10111yescharacteristic
347#331C22×C10111yescharacteristic
348Q8⋊C8C22×C10111yescharacteristic
349Q8⋊C8C22×C10111yescharacteristic
350Q8⋊C8C22×C10111yescharacteristic
351D4⋊C8C22×C10111yescharacteristic
352#322C22×C10111yescharacteristic
353C2×#41—21no—
354C2×Q16—21no—
355C2×Q16—21no—
356C2×Q16D4×C10111yescharacteristic
357C2×SD16—21no—
358C2×SD16—21no—
359C2×SD16—21no—
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16D4×C10111yescharacteristic
363C22×C8—21no—
364C4⋊Q8—21no—
365C4⋊Q8—21no—
366C4⋊Q8C23×C10111yescharacteristic
367C4⋊Q8C23×C10111yescharacteristic
368C4⋊Q8C23×C10111yescharacteristic
369#127—21no—
370#127C23×C10111yescharacteristic
371#126—41no—
372#125—21no—
373#125—21no—
374#125—41no—
375#125—41no—
376#124—21no—
377C22⋊Q8—21no—
378#121—21no—
379#121—41no—
380C4×Q8—21no—
381C4×Q8—21no—
382C4×Q8—21no—
383C4×Q8—21no—
384C4×Q8—21no—
385C4×Q8C23×C10111yescharacteristic
386C4×Q8C23×C10111yescharacteristic
387C4×Q8C23×C10111yescharacteristic
388C4×D4—21no—
389C4×D4C23×C10111yescharacteristic
390#117—21no—
391#107—21no—
392#107—41no—
393#107D4×C10111yescharacteristic
394#106—21no—
395#106—21no—
396#106D4×C10111yescharacteristic
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8C23×C10111yescharacteristic
401C4⋊C8C23×C10111yescharacteristic
402C4⋊C8C23×C10111yescharacteristic
403C4⋊C8C23×C10111yescharacteristic
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103D4×C10111yescharacteristic
414#103D4×C10111yescharacteristic
415#103D4×C10111yescharacteristic
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—41no—
422#102D4×C10111yescharacteristic
423C22⋊C8—21no—
424#97—21no—
425C4×C8—21no—
426C4×C8—21no—
427C4×C8C23×C10111yescharacteristic
428C4×C8C23×C10111yescharacteristic
429C4×C8C23×C10111yescharacteristic
430#41—42no—
431#41—81no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8C2×D4×C10111yescharacteristic
436C2×Q8C2×D4×C10111yescharacteristic
437C2×Q8C2×D4×C10111yescharacteristic
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4C2×D4×C10111yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446Q16—22no—
447Q16—42no—
448Q16—42no—
449SD16—41no—
450SD16—42no—
451SD16—81no—
452SD16—81no—
453SD16—81no—
454SD16—81no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—81no—
461C2×C8C2×D4×C10111yescharacteristic
462C2×C8C2×D4×C10111yescharacteristic
463C2×C8C2×D4×C10111yescharacteristic
464C2×C8C2×D4×C10111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4C2×D4×C10111yescharacteristic
482C4⋊C4C2×D4×C10111yescharacteristic
483C4⋊C4C2×D4×C10111yescharacteristic
484C4⋊C4C2×D4×C10111yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C42—21no—
490C42—21no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42—41no—
495C42C24×C10111yescharacteristic
496C23—21no—
497C23—41no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—21no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8#135×C10112yes—
510D4—21no—
511D4—21no—
512D4—41no—
513D4—41no—
514D4—41no—
515D4—41no—
516D4—82no—
517D4—81no—
518D4—161no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—82no—
532C2×C4C22×D4×C10111yescharacteristic
533C2×C4C22×D4×C10111yescharacteristic
534C2×C4H(5,𝔽2)×C10111yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—21no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—41no—
543C8—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22D42×C10111yescharacteristic
551C4—22no—
552C4—21no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4C2×#135×C10111yescharacteristic
563C4#575×C10111yescharacteristic
564C4#577×C10111yescharacteristic
565C4#577×C10111yescharacteristic
566C2—81no—
567C2—161no—
568C2C101×#327111yescharacteristic
569C2C101×#328211yescharacteristic
570C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radical#550×C101C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C101×#3374C2semidirect
3. C101×#3364C2semidirect
5. C101×#1719C2semidirect
6. C101×#1702C2semidirect
7. C101×#1680C2semidirect
8. C101×#1679C2semidirect
9. C101×#1666C2semidirect
10. C101×#1650C2semidirect
11. C101×#1648C2semidirect
13. C101×#1626C2semidirect
14. C101×#1582C2semidirect
15. C101×#1579C2semidirect
280. #19801C101direct (N × H)
287. #3374C2×C101semidirect
288. #3364C2×C101semidirect
290. #1719C2×C101semidirect
291. #1702C2×C101semidirect
292. #1680C2×C101semidirect
293. #1679C2×C101semidirect
294. #1666C2×C101semidirect
295. #1650C2×C101semidirect
296. #1648C2×C101semidirect
298. #1626C2×C101semidirect
299. #1582C2×C101semidirect
300. #1579C2×C101semidirect
301. C101#19801direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33922
C101×#33742
C101×#33642
C101×#33042
C101×#17192
C101×#17022
C101×#16802
C101×#16792
C101×#16662
C101×#16502
C101×#16482
C101×#16412
C101×#16262
C101×#15822
C101×#15792
#19801101