Finite Group Databasebeta

← C101×#20267 #38802418

Subgroups — C101×#20267 #38802418

Order 25856.

616 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3398C211yesmaximal, characteristic, complemented
2C101×#3364C211yesmaximal, characteristic, complemented
3C101×#3324C211yesmaximal, characteristic
4C101×#3324C211yesmaximal, characteristic
5C101×#1720C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1699C211yesmaximal, characteristic, complemented
8C101×#1689C211yesmaximal, characteristic, complemented
9C101×#1682C211yesmaximal, characteristic, complemented
10C101×#1652C211yesmaximal, characteristic, complemented
11C101×#1652C211yesmaximal, characteristic, complemented
12C101×#1639C211yesmaximal, characteristic
13C101×#1626C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1583C211yesmaximal, characteristic, complemented
16#557×C101C2211yescharacteristic, complemented
17#556×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic
19D42×C101C2211yescharacteristic
20#498×C101C2211yescharacteristic, complemented
21#497×C101—21no—
22#494×C101C2211yescharacteristic, complemented
23#488×C101—21no—
24#487×C101C2211yescharacteristic, complemented
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#482×C101—21no—
29#482×C101—21no—
30#479×C101—21no—
31#474×C101C2211yescharacteristic
32#474×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#468×C101—21no—
35#468×C101—21no—
36#464×C101—21no—
37#464×C101—21no—
38#462×C101—21no—
39#462×C101C2211yescharacteristic, complemented
40#462×C101C2211yescharacteristic, complemented
41#461×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#460×C101C2211yescharacteristic
44#450×C101—21no—
45#450×C101—21no—
46#446×C101C2211yescharacteristic, complemented
47C8×Q8×C101C2211yescharacteristic, complemented
48#441×C101—21no—
49C4×Q16×C101—21no—
50C4×SD16×C101C2211yescharacteristic
51C4×SD16×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#418×C101—21no—
55#418×C101—21no—
56#335×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#332×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic, complemented
63Q8⋊C8×C101C2211yescharacteristic, complemented
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic, complemented
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101—21no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101D411yescharacteristic
77C2×SD16×C101D411yescharacteristic
78C2×M16×C101—21no—
79C2×M16×C101—21no—
80C4⋊Q8×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#126×C101—41no—
86#126×C101—41no—
87#125×C101—21no—
88#125×C101—41no—
89#124×C101—21no—
90#124×C101—21no—
91C22⋊Q8×C101—21no—
92C22⋊Q8×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#120×C101—41no—
96C4×Q8×C101—21no—
97C4×Q8×C101—21no—
98C4×Q8×C101—21no—
99C4×Q8×C101—21no—
100C4×Q8×C101C2311yescharacteristic
101C4×Q8×C101C2311yescharacteristic
102C4×D4×C101C2311yescharacteristic
103C4×D4×C101C2311yescharacteristic
104#117×C101—21no—
105#117×C101—21no—
106#107×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#106×C101—41no—
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
144C24×C101—41no—
145C2×Q8×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101C2×D411yescharacteristic
149C2×Q8×C101C2×D411yescharacteristic
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—41no—
154C2×D4×C101—41no—
155C2×D4×C101—42no—
156C2×D4×C101—42no—
157C2×D4×C101—81no—
158C2×D4×C101—81no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163Q16×C101—42no—
164Q16×C101—42no—
165Q16×C101—81no—
166Q16×C101—81no—
167SD16×C101—41no—
168SD16×C101—41no—
169SD16×C101—81no—
170SD16×C101—81no—
171SD16×C101—81no—
172M16×C101—81no—
173M16×C101—81no—
174C2×C8×C101—21no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101C2×D411yescharacteristic
180C2×C8×C101C2×D411yescharacteristic
181C2×C8×C101C2×D411yescharacteristic
182C2×C8×C101C2×D411yescharacteristic
183C4⋊C4×C101—21no—
184C4⋊C4×C101—21no—
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—41no—
192C4⋊C4×C101—41no—
193C4⋊C4×C101—41no—
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—41no—
203C22⋊C4×C101—41no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C42×C101—21no—
208C42×C101—21no—
209C42×C101—41no—
210C42×C101—41no—
211C42×C101—41no—
212C42×C101C2411yescharacteristic
213C23×C101—21no—
214C23×C101—21no—
215C23×C101—41no—
216C23×C101—82no—
217C23×C101—82no—
218C23×C101—161no—
219Q8×C101—21no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—41no—
228Q8×C101—41no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—81no—
238D4×C101—82no—
239D4×C101—82no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
243C2×C4×C101—21no—
244C2×C4×C101—21no—
245C2×C4×C101—21no—
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×C101C22×D411yescharacteristic
254C2×C4×C101C22×D411yescharacteristic
255C2×C4×C101H(5,𝔽2)11yescharacteristic
256C8×C101—21no—
257C8×C101—21no—
258C8×C101—21no—
259C8×C101—21no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101—41no—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—81no—
272C22×C101—81no—
273C22×C101—81no—
274C22×C101—164no—
275C22×C101D4211yescharacteristic
276C4×C101—21no—
277C4×C101—41no—
278C4×C101—41no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—41no—
282C4×C101—41no—
283C4×C101—81no—
284C4×C101—81no—
285C4×C101—81no—
286C4×C101#57511yescharacteristic
287C4×C101#57511yescharacteristic
288C4×C101#57611yescharacteristic
289C4×C101#57711yescharacteristic
290#20267C10111yesmaximal, characteristic, direct product factor, Sylow
291C2×C101—81no—
292C2×C101—81no—
293C2×C101—161no—
294C2×C101#326811yescharacteristic
295C2×C101#327511yescharacteristic
296C2×C101#328911yescharacteristic
297#3398C2×C10111yescharacteristic, complemented
298#3364C2×C10111yescharacteristic, complemented
299#3324C2×C10111yescharacteristic
300#3324C2×C10111yescharacteristic
301#1720C2×C10111yescharacteristic, complemented
302#1702C2×C10111yescharacteristic, complemented
303#1699C2×C10111yescharacteristic, complemented
304#1689C2×C10111yescharacteristic, complemented
305#1682C2×C10111yescharacteristic, complemented
306#1652C2×C10111yescharacteristic, complemented
307#1652C2×C10111yescharacteristic, complemented
308#1639C2×C10111yescharacteristic
309#1626C2×C10111yescharacteristic, complemented
310#1592C2×C10111yescharacteristic, complemented
311#1583C2×C10111yescharacteristic, complemented
312C101#2026711yescharacteristic, direct product factor, Sylow
313#557C22×C10111yescharacteristic, complemented
314#556C22×C10111yescharacteristic
315#556C22×C10111yescharacteristic
316D42C22×C10111yescharacteristic
317#498C22×C10111yescharacteristic, complemented
318#497—21no—
319#494C22×C10111yescharacteristic, complemented
320#488—21no—
321#487C22×C10111yescharacteristic, complemented
322#486C22×C10111yescharacteristic
323#486C22×C10111yescharacteristic
324#486C22×C10111yescharacteristic
325#482—21no—
326#482—21no—
327#479—21no—
328#474C22×C10111yescharacteristic
329#474C22×C10111yescharacteristic
330#474C22×C10111yescharacteristic
331#468—21no—
332#468—21no—
333#464—21no—
334#464—21no—
335#462—21no—
336#462C22×C10111yescharacteristic, complemented
337#462C22×C10111yescharacteristic, complemented
338#461C22×C10111yescharacteristic
339#460C22×C10111yescharacteristic
340#460C22×C10111yescharacteristic
341#450—21no—
342#450—21no—
343#446C22×C10111yescharacteristic, complemented
344C8×Q8C22×C10111yescharacteristic, complemented
345#441—21no—
346C4×Q16—21no—
347C4×SD16C22×C10111yescharacteristic
348C4×SD16C22×C10111yescharacteristic
349#436C22×C10111yescharacteristic
350#436C22×C10111yescharacteristic
351#418—21no—
352#418—21no—
353#335C22×C10111yescharacteristic, complemented
354#334C22×C10111yescharacteristic, complemented
355#332C22×C10111yescharacteristic, complemented
356#332C22×C10111yescharacteristic, complemented
357#332C22×C10111yescharacteristic, complemented
358#331C22×C10111yescharacteristic
359Q8⋊C8C22×C10111yescharacteristic, complemented
360Q8⋊C8C22×C10111yescharacteristic, complemented
361D4⋊C8C22×C10111yescharacteristic
362D4⋊C8C22×C10111yescharacteristic
363#322C22×C10111yescharacteristic, complemented
364C22×D4—21no—
365C22×D4—21no—
366C2×Q16—21no—
367C2×Q16—21no—
368C2×Q16—21no—
369C2×Q16—21no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16D4×C10111yescharacteristic
374C2×SD16D4×C10111yescharacteristic
375C2×M16—21no—
376C2×M16—21no—
377C4⋊Q8—21no—
378C4⋊Q8C23×C10111yescharacteristic
379C4⋊Q8C23×C10111yescharacteristic
380C4⋊Q8C23×C10111yescharacteristic
381#127C23×C10111yescharacteristic
382#126—41no—
383#126—41no—
384#125—21no—
385#125—41no—
386#124—21no—
387#124—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390#121—21no—
391#121—21no—
392#120—41no—
393C4×Q8—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8C23×C10111yescharacteristic
398C4×Q8C23×C10111yescharacteristic
399C4×D4C23×C10111yescharacteristic
400C4×D4C23×C10111yescharacteristic
401#117—21no—
402#117—21no—
403#107—21no—
404#107—21no—
405#107—21no—
406#106—41no—
407#106D4×C10111yescharacteristic
408#106D4×C10111yescharacteristic
409C4⋊C8—21no—
410C4⋊C8—21no—
411C4⋊C8C23×C10111yescharacteristic
412C4⋊C8C23×C10111yescharacteristic
413C4⋊C8C23×C10111yescharacteristic
414C4⋊C8C23×C10111yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103D4×C10111yescharacteristic
421#103D4×C10111yescharacteristic
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—41no—
432#102D4×C10111yescharacteristic
433#102D4×C10111yescharacteristic
434C22⋊C8—21no—
435C22⋊C8—21no—
436#97—21no—
437C4×C8—21no—
438C4×C8C23×C10111yescharacteristic
439C4×C8C23×C10111yescharacteristic
440C4×C8C23×C10111yescharacteristic
441C24—41no—
442C2×Q8—21no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8C2×D4×C10111yescharacteristic
446C2×Q8C2×D4×C10111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—42no—
453C2×D4—42no—
454C2×D4—81no—
455C2×D4—81no—
456C2×D4C2×D4×C10111yescharacteristic
457C2×D4C2×D4×C10111yescharacteristic
458C22×C4—21no—
459C22×C4—21no—
460Q16—42no—
461Q16—42no—
462Q16—81no—
463Q16—81no—
464SD16—41no—
465SD16—41no—
466SD16—81no—
467SD16—81no—
468SD16—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⋊C4—41no—
493C4⋊C4C2×D4×C10111yescharacteristic
494C4⋊C4C2×D4×C10111yescharacteristic
495C4⋊C4C2×D4×C10111yescharacteristic
496C4⋊C4C2×D4×C10111yescharacteristic
497C22⋊C4—21no—
498C22⋊C4—21no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C42—21no—
505C42—21no—
506C42—41no—
507C42—41no—
508C42—41no—
509C42C24×C10111yescharacteristic
510C23—21no—
511C23—21no—
512C23—41no—
513C23—82no—
514C23—82no—
515C23—161no—
516Q8—21no—
517Q8—21no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—41no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—81no—
535D4—82no—
536D4—82no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4C22×D4×C10111yescharacteristic
551C2×C4C22×D4×C10111yescharacteristic
552C2×C4H(5,𝔽2)×C10111yescharacteristic
553C8—21no—
554C8—21no—
555C8—21no—
556C8—21no—
557C8—41no—
558C8—41no—
559C8—41no—
560C8—41no—
561C8—41no—
562C22—41no—
563C22—41no—
564C22—41no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—81no—
569C22—81no—
570C22—81no—
571C22—164no—
572C22D42×C10111yescharacteristic
573C4—21no—
574C4—41no—
575C4—41no—
576C4—41no—
577C4—41no—
578C4—41no—
579C4—41no—
580C4—81no—
581C4—81no—
582C4—81no—
583C4#575×C10111yescharacteristic
584C4#575×C10111yescharacteristic
585C4#576×C10111yescharacteristic
586C4#577×C10111yescharacteristic
587C2—81no—
588C2—81no—
589C2—161no—
590C2C101×#326811yescharacteristic
591C2C101×#327511yescharacteristic
592C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalD42×C101C22
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×#3398C2semidirect
2. C101×#3364C2semidirect
5. C101×#1720C2semidirect
6. C101×#1702C2semidirect
7. C101×#1699C2semidirect
8. C101×#1689C2semidirect
9. C101×#1682C2semidirect
10. C101×#1652C2semidirect
11. C101×#1652C2semidirect
13. C101×#1626C2semidirect
14. C101×#1592C2semidirect
15. C101×#1583C2semidirect
16. #557×C101C22semidirect
20. #498×C101C22semidirect
22. #494×C101C22semidirect
24. #487×C101C22semidirect
39. #462×C101C22semidirect
40. #462×C101C22semidirect
46. #446×C101C22semidirect
47. C8×Q8×C101C22semidirect
56. #335×C101C22semidirect
57. #334×C101C22semidirect
58. #332×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
63. Q8⋊C8×C101C22semidirect
66. #322×C101C22semidirect
290. #20267C101direct (N × H)
297. #3398C2×C101semidirect
298. #3364C2×C101semidirect
301. #1720C2×C101semidirect
302. #1702C2×C101semidirect
303. #1699C2×C101semidirect
304. #1689C2×C101semidirect
305. #1682C2×C101semidirect
306. #1652C2×C101semidirect
307. #1652C2×C101semidirect
309. #1626C2×C101semidirect
310. #1592C2×C101semidirect
311. #1583C2×C101semidirect
312. C101#20267direct (N × H)
313. #557C22×C101semidirect
317. #498C22×C101semidirect
319. #494C22×C101semidirect
321. #487C22×C101semidirect
336. #462C22×C101semidirect
337. #462C22×C101semidirect
343. #446C22×C101semidirect
344. C8×Q8C22×C101semidirect
353. #335C22×C101semidirect
354. #334C22×C101semidirect
355. #332C22×C101semidirect
356. #332C22×C101semidirect
357. #332C22×C101semidirect
359. Q8⋊C8C22×C101semidirect
360. Q8⋊C8C22×C101semidirect
363. #322C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33982
C101×#33642
C101×#33242
C101×#17202
C101×#17022
C101×#16992
C101×#16892
C101×#16822
C101×#16522
C101×#16392
C101×#16262
C101×#15922
C101×#15832
#20267101