Finite Group Databasebeta

← C101×#20287 #38802438

Subgroups — C101×#20287 #38802438

Order 25856.

634 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×#3367C211yesmaximal, characteristic, complemented
2C101×#3329C211yesmaximal, characteristic, complemented
3C101×#3325C211yesmaximal, characteristic
4C101×#3324C211yesmaximal, characteristic, complemented
5C101×#1711C211yesmaximal, characteristic, complemented
6C101×#1703C211yesmaximal, characteristic, complemented
7C101×#1701C211yesmaximal, characteristic, complemented
8C101×#1699C211yesmaximal, characteristic, complemented
9C101×#1698C211yesmaximal, characteristic, complemented
10C101×#1646C211yesmaximal, characteristic, complemented
11C101×#1639C211yesmaximal, characteristic, complemented
12C101×#1638C211yesmaximal, characteristic, complemented
13C101×#1627C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic
17#555×C101C2211yescharacteristic
18D4×Q8×C101C2211yescharacteristic, complemented
19D42×C101C2211yescharacteristic
20#489×C101—21no—
21#487×C101C2211yescharacteristic, complemented
22#487×C101C2211yescharacteristic, complemented
23#487×C101C2211yescharacteristic, complemented
24#486×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#485×C101—21no—
28#482×C101—21no—
29#482×C101—21no—
30#477×C101—21no—
31#477×C101C2211yescharacteristic, complemented
32#476×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#469×C101—21no—
36#468×C101—21no—
37#468×C101—21no—
38#463×C101—21no—
39#461×C101C2211yescharacteristic
40#461×C101C2211yescharacteristic, complemented
41#460×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#450×C101—21no—
44#448×C101—21no—
45#447×C101—21no—
46#446×C101C2211yescharacteristic, complemented
47#440×C101—21no—
48C4×SD16×C101C2211yescharacteristic
49C4×D8×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic, complemented
53#419×C101—21no—
54#418×C101—21no—
55#418×C101—21no—
56#335×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#333×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic, complemented
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic, complemented
66C82×C101C2211yescharacteristic, complemented
67C22×Q8×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101D411yescharacteristic
74C2×D8×C101—21no—
75C2×D8×C101D411yescharacteristic
76C2×M16×C101—21no—
77C2×M16×C101—21no—
78C2×M16×C101—21no—
79C4⋊Q8×C101—21no—
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101C2311yescharacteristic
84#126×C101—41no—
85#124×C101—21no—
86#124×C101—41no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—41no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#120×C101—41no—
95C4×Q8×C101—21no—
96C4×Q8×C101C2311yescharacteristic
97C4×D4×C101—21no—
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101#117×C101—21no—
102#117×C101—21no—
103#117×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101D411yescharacteristic
108#106×C101—21no—
109#106×C101D411yescharacteristic
110C4⋊C8×C101—21no—
111C4⋊C8×C101C2311yescharacteristic
112C4⋊C8×C101C2311yescharacteristic
113C4⋊C8×C101C2311yescharacteristic
114C4⋊C8×C101C2311yescharacteristic
115#103×C101—21no—
116#103×C101—21no—
117#103×C101—21no—
118#103×C101—21no—
119#103×C101—21no—
120#103×C101—21no—
121#103×C101—21no—
122#103×C101—41no—
123#103×C101D411yescharacteristic
124#102×C101—21no—
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—41no—
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C24×C101—41no—
145C2×Q8×C101—21no—
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×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101—42no—
158C2×D4×C101—42no—
159C2×D4×C101—41no—
160C2×D4×C101—81no—
161C2×D4×C101—81no—
162C2×D4×C101C2×D411yescharacteristic
163C2×D4×C101C2×D411yescharacteristic
164C2×D4×C101C2×D411yescharacteristic
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—21no—
168C22×C4×C101—41no—
169SD16×C101—41no—
170SD16×C101—42no—
171SD16×C101—81no—
172SD16×C101—81no—
173D8×C101—41no—
174D8×C101—81no—
175M16×C101—81no—
176M16×C101—81no—
177M16×C101—81no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101C2×D411yescharacteristic
184C2×C8×C101C2×D411yescharacteristic
185C2×C8×C101C2×D411yescharacteristic
186C2×C8×C101C2×D411yescharacteristic
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—21no—
194C4⋊C4×C101—41no—
195C4⋊C4×C101—41no—
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C4⋊C4×C101C2×D411yescharacteristic
200C22⋊C4×C101—21no—
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—
209C42×C101—21no—
210C42×C101—41no—
211C42×C101—41no—
212C42×C101C2411yescharacteristic
213C23×C101—21no—
214C23×C101—21no—
215C23×C101—21no—
216C23×C101—41no—
217C23×C101—82no—
218C23×C101—82no—
219C23×C101—161no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—81no—
227Q8×C101—82no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
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—41no—
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—41no—
255C2×C4×C101—41no—
256C2×C4×C101—82no—
257C2×C4×C101C22×D411yescharacteristic
258C2×C4×C101C22×D411yescharacteristic
259C2×C4×C101H(5,𝔽2)11yescharacteristic
260C8×C101—21no—
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—21no—
264C8×C101—41no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×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×C101—41no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101—164no—
282C22×C101D4211yescharacteristic
283C4×C101—21no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—81no—
290C4×C101—81no—
291C4×C101—81no—
292C4×C101#57511yescharacteristic
293C4×C101#57511yescharacteristic
294C4×C101#57611yescharacteristic
295C4×C101#57711yescharacteristic
296#20287C10111yesmaximal, characteristic, direct product factor, Sylow
297C2×C101—81no—
298C2×C101—81no—
299C2×C101—81no—
300C2×C101—161no—
301C2×C101#327311yescharacteristic
302C2×C101#327511yescharacteristic
303C2×C101#329011yescharacteristic
304#3367C2×C10111yescharacteristic, complemented
305#3329C2×C10111yescharacteristic, complemented
306#3325C2×C10111yescharacteristic
307#3324C2×C10111yescharacteristic, complemented
308#1711C2×C10111yescharacteristic, complemented
309#1703C2×C10111yescharacteristic, complemented
310#1701C2×C10111yescharacteristic, complemented
311#1699C2×C10111yescharacteristic, complemented
312#1698C2×C10111yescharacteristic, complemented
313#1646C2×C10111yescharacteristic, complemented
314#1639C2×C10111yescharacteristic, complemented
315#1638C2×C10111yescharacteristic, complemented
316#1627C2×C10111yescharacteristic, complemented
317#1590C2×C10111yescharacteristic, complemented
318#1589C2×C10111yescharacteristic, complemented
319C101#2028711yescharacteristic, direct product factor, Sylow
320#556C22×C10111yescharacteristic
321#555C22×C10111yescharacteristic
322D4×Q8C22×C10111yescharacteristic, complemented
323D42C22×C10111yescharacteristic
324#489—21no—
325#487C22×C10111yescharacteristic, complemented
326#487C22×C10111yescharacteristic, complemented
327#487C22×C10111yescharacteristic, complemented
328#486C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#486C22×C10111yescharacteristic
331#485—21no—
332#482—21no—
333#482—21no—
334#477—21no—
335#477C22×C10111yescharacteristic, complemented
336#476C22×C10111yescharacteristic
337#474C22×C10111yescharacteristic
338#474C22×C10111yescharacteristic
339#469—21no—
340#468—21no—
341#468—21no—
342#463—21no—
343#461C22×C10111yescharacteristic
344#461C22×C10111yescharacteristic, complemented
345#460C22×C10111yescharacteristic
346#459C22×C10111yescharacteristic
347#450—21no—
348#448—21no—
349#447—21no—
350#446C22×C10111yescharacteristic, complemented
351#440—21no—
352C4×SD16C22×C10111yescharacteristic
353C4×D8C22×C10111yescharacteristic
354#436C22×C10111yescharacteristic
355#436C22×C10111yescharacteristic
356#436C22×C10111yescharacteristic, complemented
357#419—21no—
358#418—21no—
359#418—21no—
360#335C22×C10111yescharacteristic, complemented
361#334C22×C10111yescharacteristic, complemented
362#333C22×C10111yescharacteristic, complemented
363#332C22×C10111yescharacteristic, complemented
364#332C22×C10111yescharacteristic, complemented
365#331C22×C10111yescharacteristic
366Q8⋊C8C22×C10111yescharacteristic, complemented
367D4⋊C8C22×C10111yescharacteristic
368D4⋊C8C22×C10111yescharacteristic
369D4⋊C8C22×C10111yescharacteristic, complemented
370C82C22×C10111yescharacteristic, complemented
371C22×Q8—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16D4×C10111yescharacteristic
378C2×D8—21no—
379C2×D8D4×C10111yescharacteristic
380C2×M16—21no—
381C2×M16—21no—
382C2×M16—21no—
383C4⋊Q8—21no—
384C4⋊Q8C23×C10111yescharacteristic
385C4⋊Q8C23×C10111yescharacteristic
386C4⋊Q8C23×C10111yescharacteristic
387#127C23×C10111yescharacteristic
388#126—41no—
389#124—21no—
390#124—41no—
391C22⋊Q8—21no—
392C22⋊Q8—21no—
393C22⋊Q8—41no—
394#121—21no—
395#121—21no—
396#121—21no—
397#121—21no—
398#120—41no—
399C4×Q8—21no—
400C4×Q8C23×C10111yescharacteristic
401C4×D4—21no—
402C4×D4C23×C10111yescharacteristic
403C4×D4C23×C10111yescharacteristic
404C4×D4C23×C10111yescharacteristic
405#117—21no—
406#117—21no—
407#117—21no—
408#107—21no—
409#107—21no—
410#107—21no—
411#107D4×C10111yescharacteristic
412#106—21no—
413#106D4×C10111yescharacteristic
414C4⋊C8—21no—
415C4⋊C8C23×C10111yescharacteristic
416C4⋊C8C23×C10111yescharacteristic
417C4⋊C8C23×C10111yescharacteristic
418C4⋊C8C23×C10111yescharacteristic
419#103—21no—
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—41no—
427#103D4×C10111yescharacteristic
428#102—21no—
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—41no—
438#102D4×C10111yescharacteristic
439#102D4×C10111yescharacteristic
440#102D4×C10111yescharacteristic
441C22⋊C8—21no—
442C22⋊C8—21no—
443C22⋊C8—21no—
444#97—21no—
445C4×C8C23×C10111yescharacteristic
446C4×C8C23×C10111yescharacteristic
447C4×C8C23×C10111yescharacteristic
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—41no—
453C2×Q8—42no—
454C2×Q8—81no—
455C2×Q8C2×D4×C10111yescharacteristic
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4—42no—
462C2×D4—42no—
463C2×D4—41no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4C2×D4×C10111yescharacteristic
467C2×D4C2×D4×C10111yescharacteristic
468C2×D4C2×D4×C10111yescharacteristic
469C22×C4—21no—
470C22×C4—21no—
471C22×C4—21no—
472C22×C4—41no—
473SD16—41no—
474SD16—42no—
475SD16—81no—
476SD16—81no—
477D8—41no—
478D8—81no—
479M16—81no—
480M16—81no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8C2×D4×C10111yescharacteristic
488C2×C8C2×D4×C10111yescharacteristic
489C2×C8C2×D4×C10111yescharacteristic
490C2×C8C2×D4×C10111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
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—
512C22⋊C4—41no—
513C42—21no—
514C42—41no—
515C42—41no—
516C42C24×C10111yescharacteristic
517C23—21no—
518C23—21no—
519C23—21no—
520C23—41no—
521C23—82no—
522C23—82no—
523C23—161no—
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—41no—
530Q8—81no—
531Q8—82no—
532D4—21no—
533D4—21no—
534D4—21no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
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—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—82no—
561C2×C4C22×D4×C10111yescharacteristic
562C2×C4C22×D4×C10111yescharacteristic
563C2×C4H(5,𝔽2)×C10111yescharacteristic
564C8—21no—
565C8—21no—
566C8—21no—
567C8—21no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22D42×C10111yescharacteristic
587C4—21no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4—41no—
593C4—81no—
594C4—81no—
595C4—81no—
596C4#575×C10111yescharacteristic
597C4#575×C10111yescharacteristic
598C4#576×C10111yescharacteristic
599C4#577×C10111yescharacteristic
600C2—81no—
601C2—81no—
602C2—81no—
603C2—161no—
604C2C101×#327311yescharacteristic
605C2C101×#327511yescharacteristic
606C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3325C2
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×#3329C2semidirect
4. C101×#3324C2semidirect
5. C101×#1711C2semidirect
6. C101×#1703C2semidirect
7. C101×#1701C2semidirect
8. C101×#1699C2semidirect
9. C101×#1698C2semidirect
10. C101×#1646C2semidirect
11. C101×#1639C2semidirect
12. C101×#1638C2semidirect
13. C101×#1627C2semidirect
14. C101×#1590C2semidirect
15. C101×#1589C2semidirect
18. D4×Q8×C101C22semidirect
21. #487×C101C22semidirect
22. #487×C101C22semidirect
23. #487×C101C22semidirect
31. #477×C101C22semidirect
40. #461×C101C22semidirect
46. #446×C101C22semidirect
52. #436×C101C22semidirect
56. #335×C101C22semidirect
57. #334×C101C22semidirect
58. #333×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
65. D4⋊C8×C101C22semidirect
66. C82×C101C22semidirect
296. #20287C101direct (N × H)
304. #3367C2×C101semidirect
305. #3329C2×C101semidirect
307. #3324C2×C101semidirect
308. #1711C2×C101semidirect
309. #1703C2×C101semidirect
310. #1701C2×C101semidirect
311. #1699C2×C101semidirect
312. #1698C2×C101semidirect
313. #1646C2×C101semidirect
314. #1639C2×C101semidirect
315. #1638C2×C101semidirect
316. #1627C2×C101semidirect
317. #1590C2×C101semidirect
318. #1589C2×C101semidirect
319. C101#20287direct (N × H)
322. D4×Q8C22×C101semidirect
325. #487C22×C101semidirect
326. #487C22×C101semidirect
327. #487C22×C101semidirect
335. #477C22×C101semidirect
344. #461C22×C101semidirect
350. #446C22×C101semidirect
356. #436C22×C101semidirect
360. #335C22×C101semidirect
361. #334C22×C101semidirect
362. #333C22×C101semidirect
363. #332C22×C101semidirect
364. #332C22×C101semidirect
366. Q8⋊C8C22×C101semidirect
369. D4⋊C8C22×C101semidirect
370. C82C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33672
C101×#33292
C101×#33252
C101×#33242
C101×#17112
C101×#17032
C101×#17012
C101×#16992
C101×#16982
C101×#16462
C101×#16392
C101×#16382
C101×#16272
C101×#15902
C101×#15892
#20287101