Finite Group Databasebeta

← C101×#20260 #38802411

Subgroups — C101×#20260 #38802411

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×#3373C211yesmaximal, characteristic, complemented
3C101×#3329C211yesmaximal, characteristic, complemented
4C101×#3305C211yesmaximal, characteristic, complemented
5C101×#1717C211yesmaximal, characteristic, complemented
6C101×#1704C211yesmaximal, characteristic, complemented
7C101×#1698C211yesmaximal, characteristic, complemented
8C101×#1687C211yesmaximal, characteristic, complemented
9C101×#1681C211yesmaximal, characteristic, complemented
10C101×#1642C211yesmaximal, characteristic, complemented
11C101×#1630C211yesmaximal, characteristic, complemented
12C101×#1627C211yesmaximal, characteristic, complemented
13C101×#1624C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1582C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#555×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#496×C101—21no—
21#493×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic
23#489×C101—21no—
24#487×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#485×C101—21no—
29#482×C101—21no—
30#477×C101C2211yescharacteristic
31#477×C101C2211yescharacteristic
32#476×C101—21no—
33#475×C101C2211yescharacteristic
34#468×C101—21no—
35#466×C101—21no—
36#463×C101—21no—
37#463×C101—21no—
38#461×C101C2211yescharacteristic
39#460×C101C2211yescharacteristic
40#459×C101—21no—
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#449×C101—21no—
45#448×C101—21no—
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#442×C101—21no—
49#442×C101—21no—
50C4×SD16×C101C2211yescharacteristic
51C4×SD16×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54#419×C101—21no—
55#416×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—
68C22×Q8×C101—21no—
69C2×SD16×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—
80C22×C8×C101—21no—
81C4⋊Q8×C101—21no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101—21no—
85#127×C101C2311yescharacteristic
86#127×C101C2311yescharacteristic
87#124×C101—21no—
88#124×C101—21no—
89#124×C101—41no—
90#123×C101—41no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—41no—
93#121×C101—21no—
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
105#117×C101—21no—
106#117×C101—21no—
107#107×C101—21no—
108#107×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×C101—21no—
124#103×C101D411yescharacteristic
125#103×C101D411yescharacteristic
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—
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—41no—
149C2×Q8×C101—42no—
150C2×Q8×C101—81no—
151C2×Q8×C101C2×D411yescharacteristic
152C2×Q8×C101C2×D411yescharacteristic
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—41no—
160C2×D4×C101—41no—
161C2×D4×C101—41no—
162C2×D4×C101C2×D411yescharacteristic
163C2×D4×C101C2×D411yescharacteristic
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—41no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169SD16×C101—41no—
170SD16×C101—41no—
171SD16×C101—81no—
172SD16×C101—81no—
173SD16×C101—82no—
174D8×C101—42no—
175D8×C101—42no—
176D8×C101—81no—
177D8×C101—81no—
178D8×C101—81no—
179M16×C101—81no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—81no—
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×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—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C42×C101—21no—
211C42×C101—21no—
212C42×C101—41no—
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—
225Q8×C101—82no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—81no—
239D4×C101—81no—
240D4×C101—82no—
241D4×C101—161no—
242D4×C101—161no—
243C2×C4×C101—21no—
244C2×C4×C101—21no—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
248C2×C4×C101—21no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—82no—
256C2×C4×C101—82no—
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#20260C10111yesmaximal, 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#3373C2×C10111yescharacteristic, complemented
306#3329C2×C10111yescharacteristic, complemented
307#3305C2×C10111yescharacteristic, complemented
308#1717C2×C10111yescharacteristic, complemented
309#1704C2×C10111yescharacteristic, complemented
310#1698C2×C10111yescharacteristic, complemented
311#1687C2×C10111yescharacteristic, complemented
312#1681C2×C10111yescharacteristic, complemented
313#1642C2×C10111yescharacteristic, complemented
314#1630C2×C10111yescharacteristic, complemented
315#1627C2×C10111yescharacteristic, complemented
316#1624C2×C10111yescharacteristic, complemented
317#1592C2×C10111yescharacteristic, complemented
318#1582C2×C10111yescharacteristic, complemented
319C101#2026011yescharacteristic, direct product factor, Sylow
320#559C22×C10111yescharacteristic
321#555C22×C10111yescharacteristic
322#550C22×C10111yescharacteristic
323D4×Q8C22×C10111yescharacteristic
324#496—21no—
325#493C22×C10111yescharacteristic
326#492C22×C10111yescharacteristic
327#489—21no—
328#487C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#486C22×C10111yescharacteristic
331#486C22×C10111yescharacteristic
332#485—21no—
333#482—21no—
334#477C22×C10111yescharacteristic
335#477C22×C10111yescharacteristic
336#476—21no—
337#475C22×C10111yescharacteristic
338#468—21no—
339#466—21no—
340#463—21no—
341#463—21no—
342#461C22×C10111yescharacteristic
343#460C22×C10111yescharacteristic
344#459—21no—
345#459C22×C10111yescharacteristic
346#459C22×C10111yescharacteristic
347#459C22×C10111yescharacteristic
348#449—21no—
349#448—21no—
350#446C22×C10111yescharacteristic
351#446C22×C10111yescharacteristic
352#442—21no—
353#442—21no—
354C4×SD16C22×C10111yescharacteristic
355C4×SD16C22×C10111yescharacteristic
356#436C22×C10111yescharacteristic
357C8×D4C22×C10111yescharacteristic
358#419—21no—
359#416—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—
372C22×Q8—21no—
373C2×SD16—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—
384C22×C8—21no—
385C4⋊Q8—21no—
386C4⋊Q8C23×C10111yescharacteristic
387C4⋊Q8C23×C10111yescharacteristic
388#127—21no—
389#127C23×C10111yescharacteristic
390#127C23×C10111yescharacteristic
391#124—21no—
392#124—21no—
393#124—41no—
394#123—41no—
395C22⋊Q8—21no—
396C22⋊Q8—41no—
397#121—21no—
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
409#117—21no—
410#117—21no—
411#107—21no—
412#107—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#103—21no—
428#103D4×C10111yescharacteristic
429#103D4×C10111yescharacteristic
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—
444#97—21no—
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447C4×C8C23×C10111yescharacteristic
448#41—42no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C10111yescharacteristic
456C2×Q8C2×D4×C10111yescharacteristic
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—41no—
464C2×D4—41no—
465C2×D4—41no—
466C2×D4C2×D4×C10111yescharacteristic
467C2×D4C2×D4×C10111yescharacteristic
468C22×C4—21no—
469C22×C4—21no—
470C22×C4—41no—
471C22×C4—41no—
472C22×C4—41no—
473SD16—41no—
474SD16—41no—
475SD16—81no—
476SD16—81no—
477SD16—82no—
478D8—42no—
479D8—42no—
480D8—81no—
481D8—81no—
482D8—81no—
483M16—81no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—21no—
489C2×C8—81no—
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⋊C4C2×D4×C10111yescharacteristic
502C4⋊C4C2×D4×C10111yescharacteristic
503C4⋊C4C2×D4×C10111yescharacteristic
504C4⋊C4C2×D4×C10111yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C22⋊C4—41no—
514C42—21no—
515C42—21no—
516C42—41no—
517C42C24×C10111yescharacteristic
518C23—21no—
519C23—21no—
520C23—41no—
521C23—41no—
522Q8—21no—
523Q8—21no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529Q8—82no—
530D4—21no—
531D4—21no—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—81no—
543D4—81no—
544D4—82no—
545D4—161no—
546D4—161no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—82no—
560C2×C4—82no—
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×#3373C2semidirect
3. C101×#3329C2semidirect
4. C101×#3305C2semidirect
5. C101×#1717C2semidirect
6. C101×#1704C2semidirect
7. C101×#1698C2semidirect
8. C101×#1687C2semidirect
9. C101×#1681C2semidirect
10. C101×#1642C2semidirect
11. C101×#1630C2semidirect
12. C101×#1627C2semidirect
13. C101×#1624C2semidirect
14. C101×#1592C2semidirect
15. C101×#1582C2semidirect
296. #20260C101direct (N × H)
304. #3399C2×C101semidirect
305. #3373C2×C101semidirect
306. #3329C2×C101semidirect
307. #3305C2×C101semidirect
308. #1717C2×C101semidirect
309. #1704C2×C101semidirect
310. #1698C2×C101semidirect
311. #1687C2×C101semidirect
312. #1681C2×C101semidirect
313. #1642C2×C101semidirect
314. #1630C2×C101semidirect
315. #1627C2×C101semidirect
316. #1624C2×C101semidirect
317. #1592C2×C101semidirect
318. #1582C2×C101semidirect
319. C101#20260direct (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×#33732
C101×#33292
C101×#33052
C101×#17172
C101×#17042
C101×#16982
C101×#16872
C101×#16812
C101×#16422
C101×#16302
C101×#16272
C101×#16242
C101×#15922
C101×#15822
#20260101