Finite Group Databasebeta

← C101×#20307 #38802458

Subgroups — C101×#20307 #38802458

Order 25856.

608 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3397C211yesmaximal, characteristic
2C101×#3384C211yesmaximal, characteristic, complemented
3C101×#3333C211yesmaximal, characteristic, complemented
4C101×#3328C211yesmaximal, characteristic, complemented
5C101×#1708C211yesmaximal, characteristic, complemented
6C101×#1699C211yesmaximal, characteristic, complemented
7C101×#1697C211yesmaximal, characteristic, complemented
8C101×#1692C211yesmaximal, characteristic, complemented
9C101×#1686C211yesmaximal, characteristic, complemented
10C101×#1643C211yesmaximal, characteristic, complemented
11C101×#1641C211yesmaximal, characteristic, complemented
12C101×#1638C211yesmaximal, characteristic, complemented
13C101×#1627C211yesmaximal, characteristic, complemented
14C101×#1591C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic
17#554×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#501×C101—21no—
21#498×C101C2211yescharacteristic
22#496×C101—21no—
23#492×C101C2211yescharacteristic
24#487×C101C2211yescharacteristic
25#487×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#485×C101—21no—
29#480×C101—21no—
30#478×C101—21no—
31#477×C101C2211yescharacteristic
32#476×C101—21no—
33#476×C101C2211yescharacteristic
34#475×C101C2211yescharacteristic
35#474×C101C2211yescharacteristic
36#470×C101—21no—
37#468×C101—21no—
38#463×C101—21no—
39#462×C101C2211yescharacteristic
40#461×C101C2211yescharacteristic
41#460×C101—21no—
42#460×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#452×C101—21no—
45#451×C101—21no—
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#442×C101—21no—
49#440×C101—21no—
50C4×Q16×C101C2211yescharacteristic
51C4×D8×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#419×C101—21no—
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#335×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C22×Q8×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×D8×C101—21no—
76C2×D8×C101D411yescharacteristic
77C2×M16×C101—21no—
78C2×M16×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#124×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—41no—
92C22⋊Q8×C101—41no—
93#121×C101—21no—
94#121×C101—41no—
95C4×Q8×C101—21no—
96C4×Q8×C101C2311yescharacteristic
97C4×Q8×C101C2311yescharacteristic
98C4×D4×C101—21no—
99C4×D4×C101—21no—
100C4×D4×C101—21no—
101C4×D4×C101C2311yescharacteristic
102C4×D4×C101C2311yescharacteristic
103#117×C101—21no—
104C2×C4⋊C4×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101D411yescharacteristic
108#107×C101D411yescharacteristic
109#106×C101—21no—
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113C4⋊C8×C101—21no—
114C4⋊C8×C101—21no—
115C4⋊C8×C101C2311yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
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—41no—
126#103×C101D411yescharacteristic
127#103×C101D411yescharacteristic
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×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139#97×C101—21no—
140#97×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×C101—41no—
150C2×Q8×C101—42no—
151C2×Q8×C101—81no—
152C2×Q8×C101C2×D411yescharacteristic
153C2×Q8×C101C2×D411yescharacteristic
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—41no—
164C22×C4×C101—41no—
165C22×C4×C101—41no—
166Q16×C101—41no—
167Q16×C101—81no—
168SD16×C101—42no—
169SD16×C101—81no—
170SD16×C101—81no—
171SD16×C101—81no—
172D8×C101—22no—
173D8×C101—81no—
174M16×C101—81no—
175M16×C101—81no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101C2×D411yescharacteristic
182C2×C8×C101C2×D411yescharacteristic
183C2×C8×C101C2×D411yescharacteristic
184C2×C8×C101C2×D411yescharacteristic
185C4⋊C4×C101—21no—
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—21no—
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—41no—
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—
208C42×C101—21no—
209C42×C101—21no—
210C42×C101—41no—
211C42×C101C2411yescharacteristic
212C23×C101—21no—
213C23×C101—21no—
214C23×C101—41no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—21no—
218Q8×C101—21no—
219Q8×C101—41no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—81no—
224Q8×C101—82no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—41no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—81no—
234D4×C101—82no—
235D4×C101—161no—
236C2×C4×C101—21no—
237C2×C4×C101—21no—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—82no—
250C2×C4×C101—82no—
251C2×C4×C101—161no—
252C2×C4×C101C22×D411yescharacteristic
253C2×C4×C101C22×D411yescharacteristic
254C2×C4×C101H(5,𝔽2)11yescharacteristic
255C8×C101—21no—
256C8×C101—21no—
257C8×C101—21no—
258C8×C101—41no—
259C8×C101—41no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101#13712yes—
264C22×C101—41no—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—81no—
271C22×C101—81no—
272C22×C101—81no—
273C22×C101D4211yescharacteristic
274C4×C101—21no—
275C4×C101—41no—
276C4×C101—41no—
277C4×C101—41no—
278C4×C101—41no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—81no—
282C4×C101—81no—
283C4×C101—81no—
284C4×C101C2×#13711yescharacteristic
285C4×C101#57511yescharacteristic
286C4×C101#57611yescharacteristic
287C4×C101#57711yescharacteristic
288#20307C10111yesmaximal, characteristic, direct product factor, Sylow
289C2×C101—81no—
290C2×C101—81no—
291C2×C101—161no—
292C2×C101#327311yescharacteristic
293C2×C101#327811yescharacteristic
294C2×C101#329011yescharacteristic
295#3397C2×C10111yescharacteristic
296#3384C2×C10111yescharacteristic, complemented
297#3333C2×C10111yescharacteristic, complemented
298#3328C2×C10111yescharacteristic, complemented
299#1708C2×C10111yescharacteristic, complemented
300#1699C2×C10111yescharacteristic, complemented
301#1697C2×C10111yescharacteristic, complemented
302#1692C2×C10111yescharacteristic, complemented
303#1686C2×C10111yescharacteristic, complemented
304#1643C2×C10111yescharacteristic, complemented
305#1641C2×C10111yescharacteristic, complemented
306#1638C2×C10111yescharacteristic, complemented
307#1627C2×C10111yescharacteristic, complemented
308#1591C2×C10111yescharacteristic, complemented
309#1589C2×C10111yescharacteristic, complemented
310C101#2030711yescharacteristic, direct product factor, Sylow
311#556C22×C10111yescharacteristic
312#554C22×C10111yescharacteristic
313#550C22×C10111yescharacteristic
314D4×Q8C22×C10111yescharacteristic
315#501—21no—
316#498C22×C10111yescharacteristic
317#496—21no—
318#492C22×C10111yescharacteristic
319#487C22×C10111yescharacteristic
320#487C22×C10111yescharacteristic
321#486C22×C10111yescharacteristic
322#486C22×C10111yescharacteristic
323#485—21no—
324#480—21no—
325#478—21no—
326#477C22×C10111yescharacteristic
327#476—21no—
328#476C22×C10111yescharacteristic
329#475C22×C10111yescharacteristic
330#474C22×C10111yescharacteristic
331#470—21no—
332#468—21no—
333#463—21no—
334#462C22×C10111yescharacteristic
335#461C22×C10111yescharacteristic
336#460—21no—
337#460C22×C10111yescharacteristic
338#459C22×C10111yescharacteristic
339#452—21no—
340#451—21no—
341#446C22×C10111yescharacteristic
342#446C22×C10111yescharacteristic
343#442—21no—
344#440—21no—
345C4×Q16C22×C10111yescharacteristic
346C4×D8C22×C10111yescharacteristic
347#436C22×C10111yescharacteristic
348#436C22×C10111yescharacteristic
349#419—21no—
350#417—21no—
351#335C22×C10111yescharacteristic
352#335C22×C10111yescharacteristic
353#333C22×C10111yescharacteristic
354#332C22×C10111yescharacteristic
355#332C22×C10111yescharacteristic
356#331C22×C10111yescharacteristic
357Q8⋊C8C22×C10111yescharacteristic
358Q8⋊C8C22×C10111yescharacteristic
359D4⋊C8C22×C10111yescharacteristic
360D4⋊C8C22×C10111yescharacteristic
361C82C22×C10111yescharacteristic
362C2×#41—21no—
363C22×Q8—21no—
364C2×Q16—21no—
365C2×Q16D4×C10111yescharacteristic
366C2×SD16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×D8—21no—
371C2×D8D4×C10111yescharacteristic
372C2×M16—21no—
373C2×M16—21no—
374C4⋊Q8—21no—
375C4⋊Q8C23×C10111yescharacteristic
376C4⋊Q8C23×C10111yescharacteristic
377C4⋊Q8C23×C10111yescharacteristic
378#127—21no—
379#127C23×C10111yescharacteristic
380#126—41no—
381#125—21no—
382#124—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—21no—
386C22⋊Q8—41no—
387C22⋊Q8—41no—
388#121—21no—
389#121—41no—
390C4×Q8—21no—
391C4×Q8C23×C10111yescharacteristic
392C4×Q8C23×C10111yescharacteristic
393C4×D4—21no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4C23×C10111yescharacteristic
397C4×D4C23×C10111yescharacteristic
398#117—21no—
399C2×C4⋊C4—21no—
400#107—21no—
401#107—21no—
402#107D4×C10111yescharacteristic
403#107D4×C10111yescharacteristic
404#106—21no—
405#106—21no—
406#106—21no—
407#106—21no—
408C4⋊C8—21no—
409C4⋊C8—21no—
410C4⋊C8C23×C10111yescharacteristic
411C4⋊C8C23×C10111yescharacteristic
412C4⋊C8C23×C10111yescharacteristic
413C4⋊C8C23×C10111yescharacteristic
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—41no—
421#103D4×C10111yescharacteristic
422#103D4×C10111yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—41no—
430#102D4×C10111yescharacteristic
431#102D4×C10111yescharacteristic
432C22⋊C8—21no—
433C22⋊C8—21no—
434#97—21no—
435#97—21no—
436C4×C8C23×C10111yescharacteristic
437C4×C8C23×C10111yescharacteristic
438C4×C8C23×C10111yescharacteristic
439#41—42no—
440#41—81no—
441C2×Q8—21no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—41no—
445C2×Q8—42no—
446C2×Q8—81no—
447C2×Q8C2×D4×C10111yescharacteristic
448C2×Q8C2×D4×C10111yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4C2×D4×C10111yescharacteristic
455C2×D4C2×D4×C10111yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461Q16—41no—
462Q16—81no—
463SD16—42no—
464SD16—81no—
465SD16—81no—
466SD16—81no—
467D8—22no—
468D8—81no—
469M16—81no—
470M16—81no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×D4×C10111yescharacteristic
477C2×C8C2×D4×C10111yescharacteristic
478C2×C8C2×D4×C10111yescharacteristic
479C2×C8C2×D4×C10111yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—41no—
492C4⋊C4C2×D4×C10111yescharacteristic
493C4⋊C4C2×D4×C10111yescharacteristic
494C4⋊C4C2×D4×C10111yescharacteristic
495C4⋊C4C2×D4×C10111yescharacteristic
496C22⋊C4—21no—
497C22⋊C4—21no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C42—21no—
504C42—21no—
505C42—41no—
506C42C24×C10111yescharacteristic
507C23—21no—
508C23—21no—
509C23—41no—
510Q8—21no—
511Q8—21no—
512Q8—21no—
513Q8—21no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8—41no—
518Q8—81no—
519Q8—82no—
520D4—21no—
521D4—21no—
522D4—21no—
523D4—21no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—81no—
529D4—82no—
530D4—161no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—82no—
545C2×C4—82no—
546C2×C4—161no—
547C2×C4C22×D4×C10111yescharacteristic
548C2×C4C22×D4×C10111yescharacteristic
549C2×C4H(5,𝔽2)×C10111yescharacteristic
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8#137×C10112yes—
559C22—41no—
560C22—41no—
561C22—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22D42×C10111yescharacteristic
569C4—21no—
570C4—41no—
571C4—41no—
572C4—41no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#137×C10111yescharacteristic
580C4#575×C10111yescharacteristic
581C4#576×C10111yescharacteristic
582C4#577×C10111yescharacteristic
583C2—81no—
584C2—81no—
585C2—161no—
586C2C101×#327311yescharacteristic
587C2C101×#327811yescharacteristic
588C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3397C2
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×#3384C2semidirect
3. C101×#3333C2semidirect
4. C101×#3328C2semidirect
5. C101×#1708C2semidirect
6. C101×#1699C2semidirect
7. C101×#1697C2semidirect
8. C101×#1692C2semidirect
9. C101×#1686C2semidirect
10. C101×#1643C2semidirect
11. C101×#1641C2semidirect
12. C101×#1638C2semidirect
13. C101×#1627C2semidirect
14. C101×#1591C2semidirect
15. C101×#1589C2semidirect
288. #20307C101direct (N × H)
296. #3384C2×C101semidirect
297. #3333C2×C101semidirect
298. #3328C2×C101semidirect
299. #1708C2×C101semidirect
300. #1699C2×C101semidirect
301. #1697C2×C101semidirect
302. #1692C2×C101semidirect
303. #1686C2×C101semidirect
304. #1643C2×C101semidirect
305. #1641C2×C101semidirect
306. #1638C2×C101semidirect
307. #1627C2×C101semidirect
308. #1591C2×C101semidirect
309. #1589C2×C101semidirect
310. C101#20307direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33972
C101×#33842
C101×#33332
C101×#33282
C101×#17082
C101×#16992
C101×#16972
C101×#16922
C101×#16862
C101×#16432
C101×#16412
C101×#16382
C101×#16272
C101×#15912
C101×#15892
#20307101