Finite Group Databasebeta

← C101×#20262 #38802413

Subgroups — C101×#20262 #38802413

Order 25856.

626 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3399C211yesmaximal, characteristic, complemented
2C101×#3361C211yesmaximal, characteristic, complemented
3C101×#3332C211yesmaximal, characteristic, complemented
4C101×#3331C211yesmaximal, characteristic, complemented
5C101×#1717C211yesmaximal, characteristic, complemented
6C101×#1704C211yesmaximal, characteristic, complemented
7C101×#1697C211yesmaximal, characteristic, complemented
8C101×#1687C211yesmaximal, characteristic, complemented
9C101×#1682C211yesmaximal, characteristic, complemented
10C101×#1640C211yesmaximal, characteristic, complemented
11C101×#1631C211yesmaximal, characteristic, complemented
12C101×#1625C211yesmaximal, characteristic, complemented
13C101×#1622C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1583C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#554×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#496×C101—21no—
21#493×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic
23#488×C101—21no—
24#487×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#483×C101—21no—
29#481×C101—21no—
30#478×C101—21no—
31#477×C101C2211yescharacteristic
32#476×C101C2211yescharacteristic
33#475×C101C2211yescharacteristic
34#470×C101—21no—
35#469×C101—21no—
36#463×C101—21no—
37#463×C101—21no—
38#462×C101C2211yescharacteristic
39#460×C101C2211yescharacteristic
40#459×C101—21no—
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#452×C101—21no—
45#449×C101—21no—
46#446×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48#442×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×SD16×C101C2211yescharacteristic
51C4×D8×C101—21no—
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#417×C101—21no—
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×Q16×C101—21no—
70C2×SD16×C101—21no—
71C2×SD16×C101—41no—
72C2×SD16×C101D411yescharacteristic
73C2×SD16×C101D411yescharacteristic
74C2×D8×C101—21no—
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×D8×C101—21no—
79C2×M16×C101—21no—
80C2×M16×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101—21no—
84#127×C101C2311yescharacteristic
85#127×C101C2311yescharacteristic
86#125×C101—21no—
87#124×C101—21no—
88#124×C101—21no—
89#123×C101—41no—
90#123×C101—41no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93C22⋊Q8×C101—41no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—41no—
97C4×Q8×C101C2311yescharacteristic
98C4×Q8×C101C2311yescharacteristic
99C4×D4×C101—21no—
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101C2311yescharacteristic
104C4×D4×C101C2311yescharacteristic
105C2×C4⋊C4×C101—21no—
106C2×C4⋊C4×C101—21no—
107#107×C101—21no—
108#106×C101—21no—
109#106×C101—21no—
110#106×C101D411yescharacteristic
111#106×C101D411yescharacteristic
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×C101D411yescharacteristic
124#103×C101D411yescharacteristic
125#102×C101—21no—
126#102×C101—21no—
127#102×C101—21no—
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—
140C4×C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—42no—
145#41×C101—42no—
146#41×C101—81no—
147#41×C101—81no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101—41no—
161C2×D4×C101C2×D411yescharacteristic
162C2×D4×C101C2×D411yescharacteristic
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—41no—
166C22×C4×C101—41no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169Q16×C101—81no—
170SD16×C101—41no—
171SD16×C101—41no—
172SD16×C101—81no—
173SD16×C101—82no—
174D8×C101—42no—
175D8×C101—42no—
176D8×C101—81no—
177D8×C101—81no—
178D8×C101—81no—
179M16×C101—81no—
180M16×C101—81no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101C2×D411yescharacteristic
187C2×C8×C101C2×D411yescharacteristic
188C2×C8×C101C2×D411yescharacteristic
189C2×C8×C101C2×D411yescharacteristic
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—41no—
197C4⋊C4×C101—41no—
198C4⋊C4×C101—41no—
199C4⋊C4×C101C2×D411yescharacteristic
200C4⋊C4×C101C2×D411yescharacteristic
201C4⋊C4×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C22⋊C4×C101—21no—
204C22⋊C4×C101—21no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C22⋊C4×C101—41no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C42×C101—21no—
212C42×C101—21no—
213C42×C101C2411yescharacteristic
214C23×C101—21no—
215C23×C101—21no—
216C23×C101—41no—
217C23×C101—41no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—81no—
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—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—81no—
238D4×C101—81no—
239D4×C101—82no—
240D4×C101—82no—
241D4×C101—161no—
242C2×C4×C101—21no—
243C2×C4×C101—21no—
244C2×C4×C101—21no—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—82no—
255C2×C4×C101—82no—
256C2×C4×C101—161no—
257C2×C4×C101—161no—
258C2×C4×C101C22×D411yescharacteristic
259C2×C4×C101C22×D411yescharacteristic
260C2×C4×C101H(5,𝔽2)11yescharacteristic
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—21no—
264C8×C101—21no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101—81no—
282C22×C101D4211yescharacteristic
283C4×C101—21no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—81no—
291C4×C101—81no—
292C4×C101#57511yescharacteristic
293C4×C101#57511yescharacteristic
294C4×C101#57611yescharacteristic
295C4×C101#57711yescharacteristic
296#20262C10111yesmaximal, characteristic, direct product factor, Sylow
297C2×C101—81no—
298C2×C101—81no—
299C2×C101—161no—
300C2×C101—161no—
301C2×C101#326811yescharacteristic
302C2×C101#327511yescharacteristic
303C2×C101#328811yescharacteristic
304#3399C2×C10111yescharacteristic, complemented
305#3361C2×C10111yescharacteristic, complemented
306#3332C2×C10111yescharacteristic, complemented
307#3331C2×C10111yescharacteristic, complemented
308#1717C2×C10111yescharacteristic, complemented
309#1704C2×C10111yescharacteristic, complemented
310#1697C2×C10111yescharacteristic, complemented
311#1687C2×C10111yescharacteristic, complemented
312#1682C2×C10111yescharacteristic, complemented
313#1640C2×C10111yescharacteristic, complemented
314#1631C2×C10111yescharacteristic, complemented
315#1625C2×C10111yescharacteristic, complemented
316#1622C2×C10111yescharacteristic, complemented
317#1592C2×C10111yescharacteristic, complemented
318#1583C2×C10111yescharacteristic, complemented
319C101#2026211yescharacteristic, direct product factor, Sylow
320#559C22×C10111yescharacteristic
321#554C22×C10111yescharacteristic
322#550C22×C10111yescharacteristic
323#547C22×C10111yescharacteristic
324#496—21no—
325#493C22×C10111yescharacteristic
326#492C22×C10111yescharacteristic
327#488—21no—
328#487C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#486C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic
332#483—21no—
333#481—21no—
334#478—21no—
335#477C22×C10111yescharacteristic
336#476C22×C10111yescharacteristic
337#475C22×C10111yescharacteristic
338#470—21no—
339#469—21no—
340#463—21no—
341#463—21no—
342#462C22×C10111yescharacteristic
343#460C22×C10111yescharacteristic
344#459—21no—
345#459C22×C10111yescharacteristic
346#459C22×C10111yescharacteristic
347#459C22×C10111yescharacteristic
348#452—21no—
349#449—21no—
350#446C22×C10111yescharacteristic
351C8×Q8C22×C10111yescharacteristic
352#442—21no—
353C4×SD16C22×C10111yescharacteristic
354C4×SD16C22×C10111yescharacteristic
355C4×D8—21no—
356#436C22×C10111yescharacteristic
357#436C22×C10111yescharacteristic
358#417—21no—
359#417—21no—
360#335C22×C10111yescharacteristic
361#334C22×C10111yescharacteristic
362#333C22×C10111yescharacteristic
363#332C22×C10111yescharacteristic
364#331C22×C10111yescharacteristic
365#331C22×C10111yescharacteristic
366Q8⋊C8C22×C10111yescharacteristic
367Q8⋊C8C22×C10111yescharacteristic
368D4⋊C8C22×C10111yescharacteristic
369D4⋊C8C22×C10111yescharacteristic
370#322C22×C10111yescharacteristic
371C2×#41—21no—
372C2×#41—21no—
373C2×Q16—21no—
374C2×SD16—21no—
375C2×SD16—41no—
376C2×SD16D4×C10111yescharacteristic
377C2×SD16D4×C10111yescharacteristic
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C2×D8—21no—
383C2×M16—21no—
384C2×M16—21no—
385C4⋊Q8C23×C10111yescharacteristic
386C4⋊Q8C23×C10111yescharacteristic
387#127—21no—
388#127C23×C10111yescharacteristic
389#127C23×C10111yescharacteristic
390#125—21no—
391#124—21no—
392#124—21no—
393#123—41no—
394#123—41no—
395C22⋊Q8—21no—
396C22⋊Q8—21no—
397C22⋊Q8—41no—
398#121—21no—
399#121—21no—
400#121—41no—
401C4×Q8C23×C10111yescharacteristic
402C4×Q8C23×C10111yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4—21no—
407C4×D4C23×C10111yescharacteristic
408C4×D4C23×C10111yescharacteristic
409C2×C4⋊C4—21no—
410C2×C4⋊C4—21no—
411#107—21no—
412#106—21no—
413#106—21no—
414#106D4×C10111yescharacteristic
415#106D4×C10111yescharacteristic
416C4⋊C8—21no—
417C4⋊C8—21no—
418C4⋊C8C23×C10111yescharacteristic
419C4⋊C8C23×C10111yescharacteristic
420C4⋊C8C23×C10111yescharacteristic
421C4⋊C8C23×C10111yescharacteristic
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103D4×C10111yescharacteristic
428#103D4×C10111yescharacteristic
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—21no—
437#102—21no—
438#102—41no—
439#102D4×C10111yescharacteristic
440#102D4×C10111yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443#97—21no—
444C4×C8—21no—
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447C4×C8C23×C10111yescharacteristic
448#41—42no—
449#41—42no—
450#41—81no—
451#41—81no—
452C2×Q8—21no—
453C2×Q8—21no—
454C2×Q8C2×D4×C10111yescharacteristic
455C2×Q8C2×D4×C10111yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4C2×D4×C10111yescharacteristic
466C2×D4C2×D4×C10111yescharacteristic
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—41no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473Q16—81no—
474SD16—41no—
475SD16—41no—
476SD16—81no—
477SD16—82no—
478D8—42no—
479D8—42no—
480D8—81no—
481D8—81no—
482D8—81no—
483M16—81no—
484M16—81no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—21no—
490C2×C8C2×D4×C10111yescharacteristic
491C2×C8C2×D4×C10111yescharacteristic
492C2×C8C2×D4×C10111yescharacteristic
493C2×C8C2×D4×C10111yescharacteristic
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C10111yescharacteristic
504C4⋊C4C2×D4×C10111yescharacteristic
505C4⋊C4C2×D4×C10111yescharacteristic
506C4⋊C4C2×D4×C10111yescharacteristic
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C22⋊C4—41no—
515C42—21no—
516C42—21no—
517C42C24×C10111yescharacteristic
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—81no—
542D4—81no—
543D4—82no—
544D4—82no—
545D4—161no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—82no—
559C2×C4—82no—
560C2×C4—161no—
561C2×C4—161no—
562C2×C4C22×D4×C10111yescharacteristic
563C2×C4C22×D4×C10111yescharacteristic
564C2×C4H(5,𝔽2)×C10111yescharacteristic
565C8—21no—
566C8—21no—
567C8—21no—
568C8—21no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C8—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22D42×C10111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#575×C10111yescharacteristic
597C4#575×C10111yescharacteristic
598C4#576×C10111yescharacteristic
599C4#577×C10111yescharacteristic
600C2—81no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C101×#326811yescharacteristic
605C2C101×#327511yescharacteristic
606C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
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×#3399C2semidirect
2. C101×#3361C2semidirect
3. C101×#3332C2semidirect
4. C101×#3331C2semidirect
5. C101×#1717C2semidirect
6. C101×#1704C2semidirect
7. C101×#1697C2semidirect
8. C101×#1687C2semidirect
9. C101×#1682C2semidirect
10. C101×#1640C2semidirect
11. C101×#1631C2semidirect
12. C101×#1625C2semidirect
13. C101×#1622C2semidirect
14. C101×#1592C2semidirect
15. C101×#1583C2semidirect
296. #20262C101direct (N × H)
304. #3399C2×C101semidirect
305. #3361C2×C101semidirect
306. #3332C2×C101semidirect
307. #3331C2×C101semidirect
308. #1717C2×C101semidirect
309. #1704C2×C101semidirect
310. #1697C2×C101semidirect
311. #1687C2×C101semidirect
312. #1682C2×C101semidirect
313. #1640C2×C101semidirect
314. #1631C2×C101semidirect
315. #1625C2×C101semidirect
316. #1622C2×C101semidirect
317. #1592C2×C101semidirect
318. #1583C2×C101semidirect
319. C101#20262direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33992
C101×#33612
C101×#33322
C101×#33312
C101×#17172
C101×#17042
C101×#16972
C101×#16872
C101×#16822
C101×#16402
C101×#16312
C101×#16252
C101×#16222
C101×#15922
C101×#15832
#20262101