Finite Group Databasebeta

← C101×#19855 #38802006

Subgroups — C101×#19855 #38802006

Order 25856.

622 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3399C211yesmaximal, characteristic, complemented
2C101×#3394C211yesmaximal, characteristic, complemented
3C101×#3340C211yesmaximal, characteristic, complemented
4C101×#3305C211yesmaximal, characteristic, complemented
5C101×#1715C211yesmaximal, characteristic, complemented
6C101×#1692C211yesmaximal, characteristic, complemented
7C101×#1678C211yesmaximal, characteristic, complemented
8C101×#1667C211yesmaximal, characteristic, complemented
9C101×#1665C211yesmaximal, characteristic, complemented
10C101×#1641C211yesmaximal, characteristic, complemented
11C101×#1630C211yesmaximal, characteristic, complemented
12C101×#1628C211yesmaximal, characteristic, complemented
13C101×#1624C211yesmaximal, characteristic, complemented
14C101×#1582C211yesmaximal, characteristic, complemented
15C101×SD16⋊C8C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#556×C101C2211yescharacteristic
18#555×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#498×C101C2211yescharacteristic
21#496×C101—21no—
22#495×C101—21no—
23#493×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#485×C101—21no—
29#482×C101—21no—
30#482×C101—21no—
31#477×C101C2211yescharacteristic
32#477×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#466×C101—21no—
35#465×C101—21no—
36#464×C101—21no—
37#463×C101—21no—
38#463×C101—21no—
39#462×C101C2211yescharacteristic
40#460×C101C2211yescharacteristic
41#459×C101—21no—
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#459×C101C2211yescharacteristic
45#449×C101—21no—
46#446×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48#442×C101—21no—
49C4×SD16×C101—21no—
50C4×SD16×C101C2211yescharacteristic
51C4×SD16×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54#427×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—
68C2×Q16×C101—21no—
69C2×SD16×C101—21no—
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—41no—
73C2×SD16×C101D411yescharacteristic
74C2×SD16×C101D411yescharacteristic
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101—21no—
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C22×C8×C101—21no—
81C22×C8×C101—21no—
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101—21no—
85#127×C101C2311yescharacteristic
86#127×C101C2311yescharacteristic
87#126×C101—41no—
88#124×C101—21no—
89#124×C101—21no—
90#124×C101—21no—
91#124×C101—41no—
92#123×C101—41no—
93C22⋊Q8×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—41no—
98C4×Q8×C101—21no—
99C4×Q8×C101C2311yescharacteristic
100C4×Q8×C101C2311yescharacteristic
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101C2311yescharacteristic
105C4×D4×C101C2311yescharacteristic
106#117×C101—21no—
107#117×C101—21no—
108#117×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101D411yescharacteristic
115#106×C101D411yescharacteristic
116C4⋊C8×C101—21no—
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×C101D411yescharacteristic
126#103×C101D411yescharacteristic
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—81no—
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—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—41no—
157C2×D4×C101—41no—
158C2×D4×C101—41no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C22×C4×C101—21no—
162C22×C4×C101—21no—
163C22×C4×C101—41no—
164C22×C4×C101—41no—
165Q16×C101—81no—
166SD16×C101—22no—
167SD16×C101—41no—
168SD16×C101—42no—
169SD16×C101—81no—
170SD16×C101—81no—
171SD16×C101—82no—
172D8×C101—42no—
173D8×C101—81no—
174D8×C101—81no—
175D8×C101—81no—
176D8×C101—81no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—42no—
183C2×C8×C101—81no—
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—41no—
195C4⋊C4×C101C2×D411yescharacteristic
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C22⋊C4×C101—21no—
200C22⋊C4×C101—21no—
201C22⋊C4×C101—41no—
202C22⋊C4×C101—41no—
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—21no—
211C42×C101—41no—
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—
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—161no—
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—161no—
256C2×C4×C101C22×D411yescharacteristic
257C2×C4×C101C22×D411yescharacteristic
258C2×C4×C101H(5,𝔽2)11yescharacteristic
259C8×C101—21no—
260C8×C101—21no—
261C8×C101—21no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101—41no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101#13512yes—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—81no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101—81no—
280C22×C101D4211yescharacteristic
281C4×C101—21no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—41no—
288C4×C101—81no—
289C4×C101—81no—
290C4×C101C2×#13511yescharacteristic
291C4×C101#57511yescharacteristic
292C4×C101#57611yescharacteristic
293C4×C101#57711yescharacteristic
294#19855C10111yesmaximal, characteristic, direct product factor, Sylow
295C2×C101—81no—
296C2×C101—81no—
297C2×C101—161no—
298C2×C101—161no—
299C2×C101#326811yescharacteristic
300C2×C101#328411yescharacteristic
301C2×C101#328811yescharacteristic
302#3399C2×C10111yescharacteristic, complemented
303#3394C2×C10111yescharacteristic, complemented
304#3340C2×C10111yescharacteristic, complemented
305#3305C2×C10111yescharacteristic, complemented
306#1715C2×C10111yescharacteristic, complemented
307#1692C2×C10111yescharacteristic, complemented
308#1678C2×C10111yescharacteristic, complemented
309#1667C2×C10111yescharacteristic, complemented
310#1665C2×C10111yescharacteristic, complemented
311#1641C2×C10111yescharacteristic, complemented
312#1630C2×C10111yescharacteristic, complemented
313#1628C2×C10111yescharacteristic, complemented
314#1624C2×C10111yescharacteristic, complemented
315#1582C2×C10111yescharacteristic, complemented
316SD16⋊C8C2×C10111yescharacteristic, complemented
317C101#1985511yescharacteristic, direct product factor, Sylow
318#559C22×C10111yescharacteristic
319#556C22×C10111yescharacteristic
320#555C22×C10111yescharacteristic
321#550C22×C10111yescharacteristic
322#498C22×C10111yescharacteristic
323#496—21no—
324#495—21no—
325#493C22×C10111yescharacteristic
326#492C22×C10111yescharacteristic
327#492C22×C10111yescharacteristic
328#486C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#485—21no—
331#482—21no—
332#482—21no—
333#477C22×C10111yescharacteristic
334#477C22×C10111yescharacteristic
335#474C22×C10111yescharacteristic
336#466—21no—
337#465—21no—
338#464—21no—
339#463—21no—
340#463—21no—
341#462C22×C10111yescharacteristic
342#460C22×C10111yescharacteristic
343#459—21no—
344#459C22×C10111yescharacteristic
345#459C22×C10111yescharacteristic
346#459C22×C10111yescharacteristic
347#449—21no—
348#446C22×C10111yescharacteristic
349C8×Q8C22×C10111yescharacteristic
350#442—21no—
351C4×SD16—21no—
352C4×SD16C22×C10111yescharacteristic
353C4×SD16C22×C10111yescharacteristic
354C8×D4C22×C10111yescharacteristic
355C8×D4C22×C10111yescharacteristic
356#427—21no—
357#416—21no—
358#335C22×C10111yescharacteristic
359#334C22×C10111yescharacteristic
360#333C22×C10111yescharacteristic
361#332C22×C10111yescharacteristic
362#331C22×C10111yescharacteristic
363#331C22×C10111yescharacteristic
364Q8⋊C8C22×C10111yescharacteristic
365Q8⋊C8C22×C10111yescharacteristic
366D4⋊C8C22×C10111yescharacteristic
367D4⋊C8C22×C10111yescharacteristic
368#322C22×C10111yescharacteristic
369C2×#41—21no—
370C2×Q16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×SD16—41no—
375C2×SD16D4×C10111yescharacteristic
376C2×SD16D4×C10111yescharacteristic
377C2×D8—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—21no—
382C22×C8—21no—
383C22×C8—21no—
384C4⋊Q8C23×C10111yescharacteristic
385C4⋊Q8C23×C10111yescharacteristic
386#127—21no—
387#127C23×C10111yescharacteristic
388#127C23×C10111yescharacteristic
389#126—41no—
390#124—21no—
391#124—21no—
392#124—21no—
393#124—41no—
394#123—41no—
395C22⋊Q8—21no—
396#121—21no—
397#121—21no—
398#121—21no—
399#121—41no—
400C4×Q8—21no—
401C4×Q8C23×C10111yescharacteristic
402C4×Q8C23×C10111yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4—21no—
406C4×D4C23×C10111yescharacteristic
407C4×D4C23×C10111yescharacteristic
408#117—21no—
409#117—21no—
410#117—21no—
411#107—21no—
412#107—21no—
413#107—21no—
414#106—21no—
415#106—21no—
416#106D4×C10111yescharacteristic
417#106D4×C10111yescharacteristic
418C4⋊C8—21no—
419C4⋊C8—21no—
420C4⋊C8C23×C10111yescharacteristic
421C4⋊C8C23×C10111yescharacteristic
422C4⋊C8C23×C10111yescharacteristic
423C4⋊C8C23×C10111yescharacteristic
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—41no—
437#102D4×C10111yescharacteristic
438#102D4×C10111yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C10111yescharacteristic
444C4×C8C23×C10111yescharacteristic
445C4×C8C23×C10111yescharacteristic
446#41—42no—
447#41—81no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8C2×D4×C10111yescharacteristic
451C2×Q8C2×D4×C10111yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—41no—
459C2×D4—41no—
460C2×D4—41no—
461C2×D4C2×D4×C10111yescharacteristic
462C2×D4C2×D4×C10111yescharacteristic
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466C22×C4—41no—
467Q16—81no—
468SD16—22no—
469SD16—41no—
470SD16—42no—
471SD16—81no—
472SD16—81no—
473SD16—82no—
474D8—42no—
475D8—81no—
476D8—81no—
477D8—81no—
478D8—81no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—42no—
485C2×C8—81no—
486C2×C8C2×D4×C10111yescharacteristic
487C2×C8C2×D4×C10111yescharacteristic
488C2×C8C2×D4×C10111yescharacteristic
489C2×C8C2×D4×C10111yescharacteristic
490C4⋊C4—21no—
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—41no—
497C4⋊C4C2×D4×C10111yescharacteristic
498C4⋊C4C2×D4×C10111yescharacteristic
499C4⋊C4C2×D4×C10111yescharacteristic
500C4⋊C4C2×D4×C10111yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C22⋊C4—41no—
508C22⋊C4—41no—
509C22⋊C4—41no—
510C22⋊C4—41no—
511C42—21no—
512C42—21no—
513C42—41no—
514C42—41no—
515C42C24×C10111yescharacteristic
516C23—21no—
517C23—21no—
518C23—41no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—21no—
524Q8—41no—
525Q8—41no—
526Q8—81no—
527D4—21no—
528D4—21no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—161no—
543D4—161no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—161no—
558C2×C4C22×D4×C10111yescharacteristic
559C2×C4C22×D4×C10111yescharacteristic
560C2×C4H(5,𝔽2)×C10111yescharacteristic
561C8—21no—
562C8—21no—
563C8—21no—
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8#135×C10112yes—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22D42×C10111yescharacteristic
583C4—21no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—41no—
589C4—41no—
590C4—81no—
591C4—81no—
592C4C2×#135×C10111yescharacteristic
593C4#575×C10111yescharacteristic
594C4#576×C10111yescharacteristic
595C4#577×C10111yescharacteristic
596C2—81no—
597C2—81no—
598C2—161no—
599C2—161no—
600C2C101×#326811yescharacteristic
601C2C101×#328411yescharacteristic
602C2C101×#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×#3394C2semidirect
3. C101×#3340C2semidirect
4. C101×#3305C2semidirect
5. C101×#1715C2semidirect
6. C101×#1692C2semidirect
7. C101×#1678C2semidirect
8. C101×#1667C2semidirect
9. C101×#1665C2semidirect
10. C101×#1641C2semidirect
11. C101×#1630C2semidirect
12. C101×#1628C2semidirect
13. C101×#1624C2semidirect
14. C101×#1582C2semidirect
15. C101×SD16⋊C8C2semidirect
294. #19855C101direct (N × H)
302. #3399C2×C101semidirect
303. #3394C2×C101semidirect
304. #3340C2×C101semidirect
305. #3305C2×C101semidirect
306. #1715C2×C101semidirect
307. #1692C2×C101semidirect
308. #1678C2×C101semidirect
309. #1667C2×C101semidirect
310. #1665C2×C101semidirect
311. #1641C2×C101semidirect
312. #1630C2×C101semidirect
313. #1628C2×C101semidirect
314. #1624C2×C101semidirect
315. #1582C2×C101semidirect
316. SD16⋊C8C2×C101semidirect
317. C101#19855direct (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×#33942
C101×#33402
C101×#33052
C101×#17152
C101×#16922
C101×#16782
C101×#16672
C101×#16652
C101×#16412
C101×#16302
C101×#16282
C101×#16242
C101×#15822
C101×SD16⋊C82
#19855101