Finite Group Databasebeta

← C101×#20281 #38802432

Subgroups — C101×#20281 #38802432

Order 25856.

566 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3400C211yesmaximal, characteristic
2C101×#3400C211yesmaximal, characteristic
3C101×#3383C211yesmaximal, characteristic, complemented
4C101×#3374C211yesmaximal, characteristic, complemented
5C101×#1714C211yesmaximal, characteristic
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1694C211yesmaximal, characteristic, complemented
8C101×#1686C211yesmaximal, characteristic
9C101×#1666C211yesmaximal, characteristic
10C101×#1653C211yesmaximal, characteristic, complemented
11C101×#1653C211yesmaximal, characteristic, complemented
12C101×#1640C211yesmaximal, characteristic
13C101×#1626C211yesmaximal, characteristic
14C101×#1593C211yesmaximal, characteristic, complemented
15C101×#1584C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#557×C101C2211yescharacteristic
19#557×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#499×C101—21no—
22#498×C101C2211yescharacteristic
23#497×C101—21no—
24#497×C101—21no—
25#492×C101C2211yescharacteristic
26#492×C101C2211yescharacteristic
27#491×C101—21no—
28#487×C101C2211yescharacteristic
29#486×C101C2211yescharacteristic
30#479×C101—21no—
31#479×C101—21no—
32#479×C101—21no—
33#475×C101C2211yescharacteristic
34#475×C101C2211yescharacteristic
35#475×C101C2211yescharacteristic
36#464×C101—21no—
37#464×C101—21no—
38#462×C101—21no—
39#462×C101C2211yescharacteristic
40#462×C101C2211yescharacteristic
41#462×C101C2211yescharacteristic
42#461×C101—21no—
43#461×C101—21no—
44#460×C101C2211yescharacteristic
45#460×C101C2211yescharacteristic
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49C8×Q8×C101C2211yescharacteristic
50#441×C101—21no—
51#440×C101—21no—
52#440×C101—21no—
53C4×Q16×C101—21no—
54C4×Q16×C101C2211yescharacteristic
55C4×Q16×C101C2211yescharacteristic
56#335×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
65Q8⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×Q16×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101D411yescharacteristic
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×C101—21no—
78C4⋊Q8×C101—21no—
79C4⋊Q8×C101—21no—
80C4⋊Q8×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#125×C101—21no—
86#125×C101—21no—
87#125×C101—21no—
88#125×C101—41no—
89#125×C101—41no—
90#125×C101—41no—
91#124×C101—21no—
92#124×C101—21no—
93#123×C101—41no—
94C4×Q8×C101—21no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×Q8×C101—21no—
98C4×Q8×C101—21no—
99C4×Q8×C101—21no—
100C4×Q8×C101C2311yescharacteristic
101C4×Q8×C101C2311yescharacteristic
102C4×Q8×C101C2311yescharacteristic
103C4×Q8×C101C2311yescharacteristic
104C4×D4×C101—21no—
105C4×D4×C101—21no—
106#107×C101—21no—
107#107×C101—21no—
108#107×C101D411yescharacteristic
109#107×C101D411yescharacteristic
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—41no—
114C4⋊C8×C101—21no—
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×C101—21no—
130#103×C101D411yescharacteristic
131#103×C101D411yescharacteristic
132#103×C101D411yescharacteristic
133#103×C101D411yescharacteristic
134#102×C101—21no—
135#102×C101—21no—
136#102×C101—41no—
137#97×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×C101C2×D411yescharacteristic
148C2×Q8×C101C2×D411yescharacteristic
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C22×C4×C101—41no—
155Q16×C101—22no—
156Q16×C101—41no—
157Q16×C101—42no—
158Q16×C101—81no—
159Q16×C101—81no—
160SD16×C101—42no—
161SD16×C101—42no—
162SD16×C101—81no—
163SD16×C101—81no—
164SD16×C101—81no—
165SD16×C101—81no—
166C2×C8×C101—21no—
167C2×C8×C101—21no—
168C2×C8×C101—21no—
169C2×C8×C101—21no—
170C2×C8×C101—21no—
171C2×C8×C101C2×D411yescharacteristic
172C2×C8×C101C2×D411yescharacteristic
173C2×C8×C101C2×D411yescharacteristic
174C2×C8×C101C2×D411yescharacteristic
175C4⋊C4×C101—21no—
176C4⋊C4×C101—21no—
177C4⋊C4×C101—21no—
178C4⋊C4×C101—21no—
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—41no—
186C4⋊C4×C101—41no—
187C4⋊C4×C101—41no—
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×C101C2×D411yescharacteristic
195C4⋊C4×C101C2×D411yescharacteristic
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C22⋊C4×C101—41no—
199C22⋊C4×C101—41no—
200C22⋊C4×C101—41no—
201C42×C101—21no—
202C42×C101—21no—
203C42×C101—21no—
204C42×C101—21no—
205C42×C101—41no—
206C42×C101—41no—
207C42×C101—41no—
208C42×C101C2411yescharacteristic
209C23×C101—41no—
210Q8×C101—21no—
211Q8×C101—21no—
212Q8×C101—21no—
213Q8×C101—21no—
214Q8×C101—21no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—21no—
218Q8×C101—41no—
219Q8×C101—41no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—41no—
224D4×C101—41no—
225D4×C101—41no—
226D4×C101—41no—
227D4×C101—41no—
228D4×C101—81no—
229C2×C4×C101—21no—
230C2×C4×C101—21no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—21no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—41no—
240C2×C4×C101—161no—
241C2×C4×C101C22×D411yescharacteristic
242C2×C4×C101C22×D411yescharacteristic
243C2×C4×C101H(5,𝔽2)11yescharacteristic
244C8×C101—21no—
245C8×C101—21no—
246C8×C101—21no—
247C8×C101—41no—
248C8×C101—41no—
249C8×C101—41no—
250C8×C101—41no—
251C8×C101—41no—
252C8×C101#13712yes—
253C22×C101—81no—
254C22×C101—81no—
255C22×C101—81no—
256C22×C101D4211yescharacteristic
257C4×C101—21no—
258C4×C101—41no—
259C4×C101—41no—
260C4×C101—41no—
261C4×C101—41no—
262C4×C101—41no—
263C4×C101—41no—
264C4×C101—41no—
265C4×C101—41no—
266C4×C101—81no—
267C4×C101—81no—
268C4×C101—81no—
269C4×C101C2×#13711yescharacteristic
270C4×C101#57511yescharacteristic
271C4×C101#57711yescharacteristic
272C4×C101#57711yescharacteristic
273#20281C10111yesmaximal, characteristic, direct product factor, Sylow
274C2×C101—161no—
275C2×C101#327111yescharacteristic
276C2×C101#327811yescharacteristic
277C2×C101#328911yescharacteristic
278#3400C2×C10111yescharacteristic
279#3400C2×C10111yescharacteristic
280#3383C2×C10111yescharacteristic, complemented
281#3374C2×C10111yescharacteristic, complemented
282#1714C2×C10111yescharacteristic
283#1700C2×C10111yescharacteristic, complemented
284#1694C2×C10111yescharacteristic, complemented
285#1686C2×C10111yescharacteristic
286#1666C2×C10111yescharacteristic
287#1653C2×C10111yescharacteristic, complemented
288#1653C2×C10111yescharacteristic, complemented
289#1640C2×C10111yescharacteristic
290#1626C2×C10111yescharacteristic
291#1593C2×C10111yescharacteristic, complemented
292#1584C2×C10111yescharacteristic, complemented
293C101#2028111yescharacteristic, direct product factor, Sylow
294#559C22×C10111yescharacteristic
295#557C22×C10111yescharacteristic
296#557C22×C10111yescharacteristic
297#557C22×C10111yescharacteristic
298#500C22×C10111yescharacteristic
299#499—21no—
300#498C22×C10111yescharacteristic
301#497—21no—
302#497—21no—
303#492C22×C10111yescharacteristic
304#492C22×C10111yescharacteristic
305#491—21no—
306#487C22×C10111yescharacteristic
307#486C22×C10111yescharacteristic
308#479—21no—
309#479—21no—
310#479—21no—
311#475C22×C10111yescharacteristic
312#475C22×C10111yescharacteristic
313#475C22×C10111yescharacteristic
314#464—21no—
315#464—21no—
316#462—21no—
317#462C22×C10111yescharacteristic
318#462C22×C10111yescharacteristic
319#462C22×C10111yescharacteristic
320#461—21no—
321#461—21no—
322#460C22×C10111yescharacteristic
323#460C22×C10111yescharacteristic
324#446C22×C10111yescharacteristic
325#446C22×C10111yescharacteristic
326#446C22×C10111yescharacteristic
327C8×Q8C22×C10111yescharacteristic
328#441—21no—
329#440—21no—
330#440—21no—
331C4×Q16—21no—
332C4×Q16C22×C10111yescharacteristic
333C4×Q16C22×C10111yescharacteristic
334#335C22×C10111yescharacteristic
335#334C22×C10111yescharacteristic
336#332C22×C10111yescharacteristic
337#332C22×C10111yescharacteristic
338#332C22×C10111yescharacteristic
339#331C22×C10111yescharacteristic
340Q8⋊C8C22×C10111yescharacteristic
341Q8⋊C8C22×C10111yescharacteristic
342Q8⋊C8C22×C10111yescharacteristic
343Q8⋊C8C22×C10111yescharacteristic
344#322C22×C10111yescharacteristic
345C2×Q16—21no—
346C2×Q16—21no—
347C2×Q16—21no—
348C2×Q16D4×C10111yescharacteristic
349C2×Q16D4×C10111yescharacteristic
350C2×SD16—21no—
351C2×SD16—21no—
352C2×SD16—21no—
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C4⋊Q8—21no—
357C4⋊Q8—21no—
358C4⋊Q8—21no—
359C4⋊Q8C23×C10111yescharacteristic
360C4⋊Q8C23×C10111yescharacteristic
361C4⋊Q8C23×C10111yescharacteristic
362#127C23×C10111yescharacteristic
363#125—21no—
364#125—21no—
365#125—21no—
366#125—41no—
367#125—41no—
368#125—41no—
369#124—21no—
370#124—21no—
371#123—41no—
372C4×Q8—21no—
373C4×Q8—21no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C10111yescharacteristic
379C4×Q8C23×C10111yescharacteristic
380C4×Q8C23×C10111yescharacteristic
381C4×Q8C23×C10111yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384#107—21no—
385#107—21no—
386#107D4×C10111yescharacteristic
387#107D4×C10111yescharacteristic
388#106—21no—
389#106—21no—
390#106—21no—
391#106—41no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8C23×C10111yescharacteristic
397C4⋊C8C23×C10111yescharacteristic
398C4⋊C8C23×C10111yescharacteristic
399C4⋊C8C23×C10111yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103D4×C10111yescharacteristic
409#103D4×C10111yescharacteristic
410#103D4×C10111yescharacteristic
411#103D4×C10111yescharacteristic
412#102—21no—
413#102—21no—
414#102—41no—
415#97—21no—
416#97—21no—
417#97—21no—
418C4×C8—21no—
419C4×C8C23×C10111yescharacteristic
420C4×C8C23×C10111yescharacteristic
421C4×C8C23×C10111yescharacteristic
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—21no—
425C2×Q8C2×D4×C10111yescharacteristic
426C2×Q8C2×D4×C10111yescharacteristic
427C2×Q8C2×D4×C10111yescharacteristic
428C2×Q8C2×D4×C10111yescharacteristic
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C22×C4—41no—
433Q16—22no—
434Q16—41no—
435Q16—42no—
436Q16—81no—
437Q16—81no—
438SD16—42no—
439SD16—42no—
440SD16—81no—
441SD16—81no—
442SD16—81no—
443SD16—81no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8C2×D4×C10111yescharacteristic
450C2×C8C2×D4×C10111yescharacteristic
451C2×C8C2×D4×C10111yescharacteristic
452C2×C8C2×D4×C10111yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4—41no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4C2×D4×C10111yescharacteristic
473C4⋊C4C2×D4×C10111yescharacteristic
474C4⋊C4C2×D4×C10111yescharacteristic
475C4⋊C4C2×D4×C10111yescharacteristic
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—41no—
484C42—41no—
485C42—41no—
486C42C24×C10111yescharacteristic
487C23—41no—
488Q8—21no—
489Q8—21no—
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—41no—
497Q8—41no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505D4—41no—
506D4—81no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—161no—
519C2×C4C22×D4×C10111yescharacteristic
520C2×C4C22×D4×C10111yescharacteristic
521C2×C4H(5,𝔽2)×C10111yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—41no—
526C8—41no—
527C8—41no—
528C8—41no—
529C8—41no—
530C8#137×C10112yes—
531C22—81no—
532C22—81no—
533C22—81no—
534C22D42×C10111yescharacteristic
535C4—21no—
536C4—41no—
537C4—41no—
538C4—41no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—81no—
545C4—81no—
546C4—81no—
547C4C2×#137×C10111yescharacteristic
548C4#575×C10111yescharacteristic
549C4#577×C10111yescharacteristic
550C4#577×C10111yescharacteristic
551C2—161no—
552C2C101×#327111yescharacteristic
553C2C101×#327811yescharacteristic
554C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radical#127×C101C23
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#3383C2semidirect
4. C101×#3374C2semidirect
6. C101×#1700C2semidirect
7. C101×#1694C2semidirect
10. C101×#1653C2semidirect
11. C101×#1653C2semidirect
14. C101×#1593C2semidirect
15. C101×#1584C2semidirect
273. #20281C101direct (N × H)
280. #3383C2×C101semidirect
281. #3374C2×C101semidirect
283. #1700C2×C101semidirect
284. #1694C2×C101semidirect
287. #1653C2×C101semidirect
288. #1653C2×C101semidirect
291. #1593C2×C101semidirect
292. #1584C2×C101semidirect
293. C101#20281direct (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×#33832
C101×#33742
C101×#17142
C101×#17002
C101×#16942
C101×#16862
C101×#16662
C101×#16532
C101×#16402
C101×#16262
C101×#15932
C101×#15842
#20281101