Finite Group Databasebeta

← C101×#20268 #38802419

Subgroups — C101×#20268 #38802419

Order 25856.

590 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3400C211yesmaximal, characteristic, complemented
2C101×#3394C211yesmaximal, characteristic
3C101×#3386C211yesmaximal, characteristic, complemented
4C101×#3328C211yesmaximal, characteristic, complemented
5C101×#1714C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1686C211yesmaximal, characteristic, complemented
8C101×#1685C211yesmaximal, characteristic
9C101×#1674C211yesmaximal, characteristic, complemented
10C101×#1653C211yesmaximal, characteristic, complemented
11C101×#1652C211yesmaximal, characteristic, complemented
12C101×#1640C211yesmaximal, characteristic, complemented
13C101×#1627C211yesmaximal, characteristic
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1584C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#501×C101—21no—
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#497×C101—21no—
24#495×C101—21no—
25#492×C101C2211yescharacteristic
26#492×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#485×C101—21no—
30#478×C101—21no—
31#477×C101—21no—
32#475×C101C2211yescharacteristic
33#475×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#470×C101—21no—
36#464×C101—21no—
37#464×C101—21no—
38#463×C101—21no—
39#462×C101C2211yescharacteristic
40#462×C101C2211yescharacteristic
41#462×C101C2211yescharacteristic
42#461×C101—21no—
43#460×C101C2211yescharacteristic
44#459×C101C2211yescharacteristic
45#451×C101—21no—
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#440×C101—21no—
50#440×C101—21no—
51C4×Q16×C101C2211yescharacteristic
52C4×SD16×C101—21no—
53C4×SD16×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#419×C101—21no—
56#335×C101C2211yescharacteristic
57#335×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
67C22×Q8×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101—21no—
71C2×Q16×C101D411yescharacteristic
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101D411yescharacteristic
78C2×D8×C101—21no—
79C2×M16×C101—21no—
80C4⋊Q8×C101—21no—
81C4⋊Q8×C101—21no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85#127×C101C2311yescharacteristic
86#126×C101—41no—
87#125×C101—21no—
88#125×C101—41no—
89#124×C101—21no—
90#124×C101—21no—
91#124×C101—21no—
92#123×C101—41no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—21no—
95C22⋊Q8×C101—41no—
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×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101C2311yescharacteristic
106#117×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101D411yescharacteristic
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—41no—
114#106×C101D411yescharacteristic
115C4⋊C8×C101—21no—
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122#103×C101—21no—
123#103×C101—21no—
124#103×C101—21no—
125#103×C101—21no—
126#103×C101—21no—
127#103×C101—21no—
128#103×C101—21no—
129#103×C101D411yescharacteristic
130#103×C101D411yescharacteristic
131#103×C101D411yescharacteristic
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—
139#97×C101—21no—
140C4×C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C2×Q8×C101—21no—
145C2×Q8×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101—41no—
148C2×Q8×C101—42no—
149C2×Q8×C101—81no—
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×Q8×C101C2×D411yescharacteristic
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101C2×D411yescharacteristic
157C22×C4×C101—21no—
158C22×C4×C101—41no—
159C22×C4×C101—41no—
160Q16×C101—41no—
161Q16×C101—81no—
162Q16×C101—81no—
163Q16×C101—81no—
164SD16×C101—22no—
165SD16×C101—42no—
166SD16×C101—42no—
167SD16×C101—81no—
168SD16×C101—81no—
169SD16×C101—81no—
170D8×C101—81no—
171M16×C101—81no—
172C2×C8×C101—21no—
173C2×C8×C101—21no—
174C2×C8×C101—21no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101C2×D411yescharacteristic
178C2×C8×C101C2×D411yescharacteristic
179C2×C8×C101C2×D411yescharacteristic
180C2×C8×C101C2×D411yescharacteristic
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—21no—
189C4⋊C4×C101—21no—
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—
203C22⋊C4×C101—41no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C42×C101—21no—
207C42×C101—21no—
208C42×C101—21no—
209C42×C101—41no—
210C42×C101—41no—
211C42×C101C2411yescharacteristic
212C23×C101—21no—
213C23×C101—41no—
214Q8×C101—21no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—21no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—82no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—41no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—81no—
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—21no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—82no—
247C2×C4×C101—161no—
248C2×C4×C101C22×D411yescharacteristic
249C2×C4×C101C22×D411yescharacteristic
250C2×C4×C101H(5,𝔽2)11yescharacteristic
251C8×C101—21no—
252C8×C101—21no—
253C8×C101—21no—
254C8×C101—41no—
255C8×C101—41no—
256C8×C101—41no—
257C8×C101—41no—
258C8×C101—41no—
259C8×C101#13712yes—
260C22×C101—41no—
261C22×C101—41no—
262C22×C101—41no—
263C22×C101—81no—
264C22×C101—81no—
265C22×C101—81no—
266C22×C101D4211yescharacteristic
267C4×C101—21no—
268C4×C101—41no—
269C4×C101—41no—
270C4×C101—41no—
271C4×C101—41no—
272C4×C101—41no—
273C4×C101—41no—
274C4×C101—41no—
275C4×C101—81no—
276C4×C101—81no—
277C4×C101—81no—
278C4×C101C2×#13711yescharacteristic
279C4×C101#57511yescharacteristic
280C4×C101#57611yescharacteristic
281C4×C101#57711yescharacteristic
282#20268C10111yesmaximal, characteristic, direct product factor, Sylow
283C2×C101—81no—
284C2×C101—161no—
285C2×C101#326811yescharacteristic
286C2×C101#327811yescharacteristic
287C2×C101#328911yescharacteristic
288#3400C2×C10111yescharacteristic, complemented
289#3394C2×C10111yescharacteristic
290#3386C2×C10111yescharacteristic, complemented
291#3328C2×C10111yescharacteristic, complemented
292#1714C2×C10111yescharacteristic, complemented
293#1700C2×C10111yescharacteristic, complemented
294#1686C2×C10111yescharacteristic, complemented
295#1685C2×C10111yescharacteristic
296#1674C2×C10111yescharacteristic, complemented
297#1653C2×C10111yescharacteristic, complemented
298#1652C2×C10111yescharacteristic, complemented
299#1640C2×C10111yescharacteristic, complemented
300#1627C2×C10111yescharacteristic
301#1592C2×C10111yescharacteristic, complemented
302#1584C2×C10111yescharacteristic, complemented
303C101#2026811yescharacteristic, direct product factor, Sylow
304#559C22×C10111yescharacteristic
305#557C22×C10111yescharacteristic
306#556C22×C10111yescharacteristic
307D4×Q8C22×C10111yescharacteristic
308#501—21no—
309#500C22×C10111yescharacteristic
310#498C22×C10111yescharacteristic
311#497—21no—
312#495—21no—
313#492C22×C10111yescharacteristic
314#492C22×C10111yescharacteristic
315#487C22×C10111yescharacteristic
316#486C22×C10111yescharacteristic
317#485—21no—
318#478—21no—
319#477—21no—
320#475C22×C10111yescharacteristic
321#475C22×C10111yescharacteristic
322#474C22×C10111yescharacteristic
323#470—21no—
324#464—21no—
325#464—21no—
326#463—21no—
327#462C22×C10111yescharacteristic
328#462C22×C10111yescharacteristic
329#462C22×C10111yescharacteristic
330#461—21no—
331#460C22×C10111yescharacteristic
332#459C22×C10111yescharacteristic
333#451—21no—
334#446C22×C10111yescharacteristic
335#446C22×C10111yescharacteristic
336C8×Q8C22×C10111yescharacteristic
337#440—21no—
338#440—21no—
339C4×Q16C22×C10111yescharacteristic
340C4×SD16—21no—
341C4×SD16C22×C10111yescharacteristic
342#436C22×C10111yescharacteristic
343#419—21no—
344#335C22×C10111yescharacteristic
345#335C22×C10111yescharacteristic
346#332C22×C10111yescharacteristic
347#332C22×C10111yescharacteristic
348#332C22×C10111yescharacteristic
349#331C22×C10111yescharacteristic
350Q8⋊C8C22×C10111yescharacteristic
351Q8⋊C8C22×C10111yescharacteristic
352Q8⋊C8C22×C10111yescharacteristic
353D4⋊C8C22×C10111yescharacteristic
354#322C22×C10111yescharacteristic
355C22×Q8—21no—
356C2×Q16—21no—
357C2×Q16—21no—
358C2×Q16—21no—
359C2×Q16D4×C10111yescharacteristic
360C2×SD16—21no—
361C2×SD16—21no—
362C2×SD16—21no—
363C2×SD16—21no—
364C2×SD16—21no—
365C2×SD16D4×C10111yescharacteristic
366C2×D8—21no—
367C2×M16—21no—
368C4⋊Q8—21no—
369C4⋊Q8—21no—
370C4⋊Q8C23×C10111yescharacteristic
371C4⋊Q8C23×C10111yescharacteristic
372C4⋊Q8C23×C10111yescharacteristic
373#127C23×C10111yescharacteristic
374#126—41no—
375#125—21no—
376#125—41no—
377#124—21no—
378#124—21no—
379#124—21no—
380#123—41no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383C22⋊Q8—41no—
384C4×Q8—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8C23×C10111yescharacteristic
388C4×Q8C23×C10111yescharacteristic
389C4×Q8C23×C10111yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C23×C10111yescharacteristic
394#117—21no—
395#107—21no—
396#107—21no—
397#107—21no—
398#107D4×C10111yescharacteristic
399#106—21no—
400#106—21no—
401#106—41no—
402#106D4×C10111yescharacteristic
403C4⋊C8—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8C23×C10111yescharacteristic
407C4⋊C8C23×C10111yescharacteristic
408C4⋊C8C23×C10111yescharacteristic
409C4⋊C8C23×C10111yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103D4×C10111yescharacteristic
418#103D4×C10111yescharacteristic
419#103D4×C10111yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—41no—
424#102D4×C10111yescharacteristic
425C22⋊C8—21no—
426#97—21no—
427#97—21no—
428C4×C8—21no—
429C4×C8C23×C10111yescharacteristic
430C4×C8C23×C10111yescharacteristic
431C4×C8C23×C10111yescharacteristic
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—41no—
436C2×Q8—42no—
437C2×Q8—81no—
438C2×Q8C2×D4×C10111yescharacteristic
439C2×Q8C2×D4×C10111yescharacteristic
440C2×Q8C2×D4×C10111yescharacteristic
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4C2×D4×C10111yescharacteristic
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—41no—
449Q16—81no—
450Q16—81no—
451Q16—81no—
452SD16—22no—
453SD16—42no—
454SD16—42no—
455SD16—81no—
456SD16—81no—
457SD16—81no—
458D8—81no—
459M16—81no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8C2×D4×C10111yescharacteristic
466C2×C8C2×D4×C10111yescharacteristic
467C2×C8C2×D4×C10111yescharacteristic
468C2×C8C2×D4×C10111yescharacteristic
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4C2×D4×C10111yescharacteristic
484C4⋊C4C2×D4×C10111yescharacteristic
485C4⋊C4C2×D4×C10111yescharacteristic
486C4⋊C4C2×D4×C10111yescharacteristic
487C22⋊C4—21no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—41no—
499C42C24×C10111yescharacteristic
500C23—21no—
501C23—41no—
502Q8—21no—
503Q8—21no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8—21no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—82no—
515D4—21no—
516D4—21no—
517D4—41no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—81no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—161no—
536C2×C4C22×D4×C10111yescharacteristic
537C2×C4C22×D4×C10111yescharacteristic
538C2×C4H(5,𝔽2)×C10111yescharacteristic
539C8—21no—
540C8—21no—
541C8—21no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—41no—
546C8—41no—
547C8#137×C10112yes—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—81no—
552C22—81no—
553C22—81no—
554C22D42×C10111yescharacteristic
555C4—21no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—81no—
564C4—81no—
565C4—81no—
566C4C2×#137×C10111yescharacteristic
567C4#575×C10111yescharacteristic
568C4#576×C10111yescharacteristic
569C4#577×C10111yescharacteristic
570C2—81no—
571C2—161no—
572C2C101×#326811yescharacteristic
573C2C101×#327811yescharacteristic
574C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radical#459×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
1. C101×#3400C2semidirect
3. C101×#3386C2semidirect
4. C101×#3328C2semidirect
5. C101×#1714C2semidirect
6. C101×#1700C2semidirect
7. C101×#1686C2semidirect
9. C101×#1674C2semidirect
10. C101×#1653C2semidirect
11. C101×#1652C2semidirect
12. C101×#1640C2semidirect
14. C101×#1592C2semidirect
15. C101×#1584C2semidirect
282. #20268C101direct (N × H)
288. #3400C2×C101semidirect
290. #3386C2×C101semidirect
291. #3328C2×C101semidirect
292. #1714C2×C101semidirect
293. #1700C2×C101semidirect
294. #1686C2×C101semidirect
296. #1674C2×C101semidirect
297. #1653C2×C101semidirect
298. #1652C2×C101semidirect
299. #1640C2×C101semidirect
301. #1592C2×C101semidirect
302. #1584C2×C101semidirect
303. C101#20268direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#34002
C101×#33942
C101×#33862
C101×#33282
C101×#17142
C101×#17002
C101×#16862
C101×#16852
C101×#16742
C101×#16532
C101×#16522
C101×#16402
C101×#16272
C101×#15922
C101×#15842
#20268101