Finite Group Databasebeta

← C101×#20291 #38802442

Subgroups — C101×#20291 #38802442

Order 25856.

640 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3367C211yesmaximal, characteristic, complemented
2C101×#3353C211yesmaximal, characteristic, complemented
3C101×#3330C211yesmaximal, characteristic
4C101×#3276C211yesmaximal, characteristic, complemented
5C101×#1707C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1699C211yesmaximal, characteristic, complemented
8C101×#1693C211yesmaximal, characteristic, complemented
9C101×#1689C211yesmaximal, characteristic, complemented
10C101×#1654C211yesmaximal, characteristic, complemented
11C101×#1654C211yesmaximal, characteristic, complemented
12C101×#1652C211yesmaximal, characteristic, complemented
13C101×#1651C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16C2×#137×C101—21no—
17#556×C101C2211yescharacteristic
18D4×Q8×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#494×C101C2211yescharacteristic
25#489×C101—21no—
26#487×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#484×C101—21no—
29#484×C101—21no—
30#482×C101—21no—
31#477×C101—21no—
32#475×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#474×C101C2211yescharacteristic
36#470×C101—21no—
37#468×C101—21no—
38#468×C101—21no—
39#463×C101—21no—
40#462×C101C2211yescharacteristic
41#461×C101C2211yescharacteristic
42#461×C101C2211yescharacteristic
43#461×C101C2211yescharacteristic
44#452×C101—21no—
45#451×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48#440×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×D8×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#428×C101—21no—
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C22×Q8×C101—21no—
70#137×C101—44no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×Q16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101D411yescharacteristic
78C2×D8×C101D411yescharacteristic
79C2×M16×C101—21no—
80C2×M16×C101—21no—
81C2×M16×C101—21no—
82C4⋊Q8×C101—21no—
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86C4⋊Q8×C101C2311yescharacteristic
87#126×C101—41no—
88#124×C101—21no—
89#123×C101—41no—
90#123×C101—41no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—21no—
95C22⋊Q8×C101—41no—
96#121×C101—21no—
97#121×C101—21no—
98C4×Q8×C101—21no—
99C4×Q8×C101C2311yescharacteristic
100C4×D4×C101—21no—
101C4×D4×C101C2311yescharacteristic
102C4×D4×C101C2311yescharacteristic
103C4×D4×C101C2311yescharacteristic
104#117×C101—21no—
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101—21no—
112#107×C101D411yescharacteristic
113#106×C101—21no—
114#106×C101—41no—
115#106×C101—41no—
116#106×C101D411yescharacteristic
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×C101—21no—
131#103×C101D411yescharacteristic
132#102×C101—21no—
133#102×C101—21no—
134#102×C101—21no—
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141#97×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—81no—
148#41×C101—81no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101—41no—
154C2×Q8×C101—42no—
155C2×Q8×C101—81no—
156C2×Q8×C101C2×D411yescharacteristic
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C2×D4×C101C2×D411yescharacteristic
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—41no—
166C22×C4×C101—41no—
167C22×C4×C101—41no—
168Q16×C101—42no—
169Q16×C101—42no—
170Q16×C101—81no—
171SD16×C101—22no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—81no—
175D8×C101—41no—
176M16×C101—42no—
177M16×C101—42no—
178M16×C101—81no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
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—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—41no—
198C4⋊C4×C101—41no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C22⋊C4×C101—21no—
206C22⋊C4×C101—21no—
207C22⋊C4×C101—21no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C42×C101—21no—
214C42×C101—41no—
215C42×C101C2411yescharacteristic
216C23×C101—21no—
217C23×C101—21no—
218C23×C101—21no—
219Q8×C101—21no—
220Q8×C101—21no—
221Q8×C101—41no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—41no—
228Q8×C101—41no—
229Q8×C101—82no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—21no—
235D4×C101—21no—
236D4×C101—82no—
237D4×C101—82no—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
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—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—82no—
254C2×C4×C101—82no—
255C2×C4×C101—82no—
256C2×C4×C101C22×D411yescharacteristic
257C2×C4×C101C22×D411yescharacteristic
258C2×C4×C101H(5,𝔽2)11yescharacteristic
259C8×C101—22no—
260C8×C101—21no—
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—41no—
264C8×C101—41no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101AGL(1,ℤ/8)12yes—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101D4211yescharacteristic
278C4×C101—21no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—41no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—81no—
285C4×C101—81no—
286C4×C101—81no—
287C4×C101—81no—
288C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
289C4×C101#57511yescharacteristic
290C4×C101#57711yescharacteristic
291C4×C101#57711yescharacteristic
292#20291C10111yesmaximal, characteristic, direct product factor, Sylow
293C2×C101—81no—
294C2×C101—81no—
295C2×C101—81no—
296C2×C101#327211yescharacteristic
297C2×C101#327511yescharacteristic
298C2×C101#329311yescharacteristic
299#3367C2×C10111yescharacteristic, complemented
300#3353C2×C10111yescharacteristic, complemented
301#3330C2×C10111yescharacteristic
302#3276C2×C10111yescharacteristic, complemented
303#1707C2×C10111yescharacteristic, complemented
304#1700C2×C10111yescharacteristic, complemented
305#1699C2×C10111yescharacteristic, complemented
306#1693C2×C10111yescharacteristic, complemented
307#1689C2×C10111yescharacteristic, complemented
308#1654C2×C10111yescharacteristic, complemented
309#1654C2×C10111yescharacteristic, complemented
310#1652C2×C10111yescharacteristic, complemented
311#1651C2×C10111yescharacteristic, complemented
312#1590C2×C10111yescharacteristic, complemented
313#1589C2×C10111yescharacteristic, complemented
314C101#2029111yescharacteristic, direct product factor, Sylow
315C2×#137—21no—
316#556C22×C10111yescharacteristic
317D4×Q8C22×C10111yescharacteristic
318#547C22×C10111yescharacteristic
319#547C22×C10111yescharacteristic
320#500C22×C10111yescharacteristic
321#498C22×C10111yescharacteristic
322#498C22×C10111yescharacteristic
323#494C22×C10111yescharacteristic
324#489—21no—
325#487C22×C10111yescharacteristic
326#487C22×C10111yescharacteristic
327#484—21no—
328#484—21no—
329#482—21no—
330#477—21no—
331#475C22×C10111yescharacteristic
332#474C22×C10111yescharacteristic
333#474C22×C10111yescharacteristic
334#474C22×C10111yescharacteristic
335#470—21no—
336#468—21no—
337#468—21no—
338#463—21no—
339#462C22×C10111yescharacteristic
340#461C22×C10111yescharacteristic
341#461C22×C10111yescharacteristic
342#461C22×C10111yescharacteristic
343#452—21no—
344#451—21no—
345#449—21no—
346#446C22×C10111yescharacteristic
347#440—21no—
348C4×SD16C22×C10111yescharacteristic
349C4×D8C22×C10111yescharacteristic
350#436C22×C10111yescharacteristic
351#436C22×C10111yescharacteristic
352#436C22×C10111yescharacteristic
353#428—21no—
354#417—21no—
355#335C22×C10111yescharacteristic
356#334C22×C10111yescharacteristic
357#332C22×C10111yescharacteristic
358#332C22×C10111yescharacteristic
359#332C22×C10111yescharacteristic
360#332C22×C10111yescharacteristic
361Q8⋊C8C22×C10111yescharacteristic
362D4⋊C8C22×C10111yescharacteristic
363D4⋊C8C22×C10111yescharacteristic
364D4⋊C8C22×C10111yescharacteristic
365C82C22×C10111yescharacteristic
366C2×#41—21no—
367C2×#41—21no—
368C22×Q8—21no—
369#137—44no—
370C2×Q16—21no—
371C2×Q16—21no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16D4×C10111yescharacteristic
377C2×D8D4×C10111yescharacteristic
378C2×M16—21no—
379C2×M16—21no—
380C2×M16—21no—
381C4⋊Q8—21no—
382C4⋊Q8C23×C10111yescharacteristic
383C4⋊Q8C23×C10111yescharacteristic
384C4⋊Q8C23×C10111yescharacteristic
385C4⋊Q8C23×C10111yescharacteristic
386#126—41no—
387#124—21no—
388#123—41no—
389#123—41no—
390C22⋊Q8—21no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—21no—
394C22⋊Q8—41no—
395#121—21no—
396#121—21no—
397C4×Q8—21no—
398C4×Q8C23×C10111yescharacteristic
399C4×D4—21no—
400C4×D4C23×C10111yescharacteristic
401C4×D4C23×C10111yescharacteristic
402C4×D4C23×C10111yescharacteristic
403#117—21no—
404C2×C4⋊C4—21no—
405C2×C4⋊C4—21no—
406#107—21no—
407#107—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107D4×C10111yescharacteristic
412#106—21no—
413#106—41no—
414#106—41no—
415#106D4×C10111yescharacteristic
416C4⋊C8—21no—
417C4⋊C8C23×C10111yescharacteristic
418C4⋊C8C23×C10111yescharacteristic
419C4⋊C8C23×C10111yescharacteristic
420C4⋊C8C23×C10111yescharacteristic
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103—21no—
430#103D4×C10111yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102D4×C10111yescharacteristic
435#102D4×C10111yescharacteristic
436#102D4×C10111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440#97—21no—
441C4×C8C23×C10111yescharacteristic
442C4×C8C23×C10111yescharacteristic
443C4×C8C23×C10111yescharacteristic
444#41—42no—
445#41—42no—
446#41—81no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C10111yescharacteristic
456C2×D4—41no—
457C2×D4—41no—
458C2×D4C2×D4×C10111yescharacteristic
459C2×D4C2×D4×C10111yescharacteristic
460C2×D4C2×D4×C10111yescharacteristic
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—41no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—42no—
468Q16—42no—
469Q16—81no—
470SD16—22no—
471SD16—42no—
472SD16—42no—
473SD16—81no—
474D8—41no—
475M16—42no—
476M16—42no—
477M16—81no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8C2×D4×C10111yescharacteristic
484C2×C8C2×D4×C10111yescharacteristic
485C2×C8C2×D4×C10111yescharacteristic
486C2×C8C2×D4×C10111yescharacteristic
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4—41no—
498C4⋊C4—41no—
499C4⋊C4—41no—
500C4⋊C4C2×D4×C10111yescharacteristic
501C4⋊C4C2×D4×C10111yescharacteristic
502C4⋊C4C2×D4×C10111yescharacteristic
503C4⋊C4C2×D4×C10111yescharacteristic
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C42—21no—
513C42—41no—
514C42C24×C10111yescharacteristic
515C23—21no—
516C23—21no—
517C23—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—82no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—82no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—82no—
553C2×C4—82no—
554C2×C4—82no—
555C2×C4C22×D4×C10111yescharacteristic
556C2×C4C22×D4×C10111yescharacteristic
557C2×C4H(5,𝔽2)×C10111yescharacteristic
558C8—22no—
559C8—21no—
560C8—21no—
561C8—21no—
562C8—41no—
563C8—41no—
564C8—41no—
565C8—41no—
566C8AGL(1,ℤ/8)×C10112yes—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22D42×C10111yescharacteristic
577C4—21no—
578C4—41no—
579C4—41no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—81no—
584C4—81no—
585C4—81no—
586C4—81no—
587C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
588C4#575×C10111yescharacteristic
589C4#577×C10111yescharacteristic
590C4#577×C10111yescharacteristic
591C2—81no—
592C2—81no—
593C2—81no—
594C2C101×#327211yescharacteristic
595C2C101×#327511yescharacteristic
596C2C101×#329311yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3330C2
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×#3367C2semidirect
2. C101×#3353C2semidirect
4. C101×#3276C2semidirect
5. C101×#1707C2semidirect
6. C101×#1700C2semidirect
7. C101×#1699C2semidirect
8. C101×#1693C2semidirect
9. C101×#1689C2semidirect
10. C101×#1654C2semidirect
11. C101×#1654C2semidirect
12. C101×#1652C2semidirect
13. C101×#1651C2semidirect
14. C101×#1590C2semidirect
15. C101×#1589C2semidirect
292. #20291C101direct (N × H)
299. #3367C2×C101semidirect
300. #3353C2×C101semidirect
302. #3276C2×C101semidirect
303. #1707C2×C101semidirect
304. #1700C2×C101semidirect
305. #1699C2×C101semidirect
306. #1693C2×C101semidirect
307. #1689C2×C101semidirect
308. #1654C2×C101semidirect
309. #1654C2×C101semidirect
310. #1652C2×C101semidirect
311. #1651C2×C101semidirect
312. #1590C2×C101semidirect
313. #1589C2×C101semidirect
314. C101#20291direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33672
C101×#33532
C101×#33302
C101×#32762
C101×#17072
C101×#17002
C101×#16992
C101×#16932
C101×#16892
C101×#16542
C101×#16522
C101×#16512
C101×#15902
C101×#15892
#20291101