Finite Group Databasebeta

← C101×#19852 #38802003

Subgroups — C101×#19852 #38802003

Order 25856.

660 conjugacy classes of subgroups.

The subgroup lattice has 614 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×#3335C211yesmaximal, characteristic, complemented
4C101×#3284C211yesmaximal, characteristic, complemented
5C101×#1715C211yesmaximal, characteristic, complemented
6C101×#1692C211yesmaximal, characteristic, complemented
7C101×#1677C211yesmaximal, characteristic, complemented
8C101×#1667C211yesmaximal, characteristic, complemented
9C101×#1666C211yesmaximal, characteristic, complemented
10C101×#1640C211yesmaximal, characteristic, complemented
11C101×#1631C211yesmaximal, characteristic, complemented
12C101×#1625C211yesmaximal, characteristic, complemented
13C101×#1622C211yesmaximal, characteristic, complemented
14C101×#1582C211yesmaximal, characteristic, complemented
15C101×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#559×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#498×C101C2211yescharacteristic
22#496×C101—21no—
23#493×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#488×C101—21no—
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#483×C101—21no—
30#481×C101—21no—
31#478×C101—21no—
32#477×C101C2211yescharacteristic
33#476×C101C2211yescharacteristic
34#475×C101C2211yescharacteristic
35#465×C101—21no—
36#465×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#452×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#442×C101—21no—
50C4×SD16×C101C2211yescharacteristic
51C4×SD16×C101C2211yescharacteristic
52C4×D8×C101—21no—
53C8×D4×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55C2×#106×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—
69#135×C101—44no—
70C2×Q16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—41no—
75C2×SD16×C101D411yescharacteristic
76C2×SD16×C101D411yescharacteristic
77C2×D8×C101—21no—
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C2×D8×C101—21no—
81C2×D8×C101—21no—
82C22×C8×C101—21no—
83C22×C8×C101—21no—
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101—21no—
87#127×C101C2311yescharacteristic
88#127×C101C2311yescharacteristic
89#125×C101—21no—
90#124×C101—21no—
91#124×C101—21no—
92#123×C101—41no—
93#123×C101—41no—
94C22⋊Q8×C101—21no—
95C22⋊Q8×C101—21no—
96C22⋊Q8×C101—41no—
97#121×C101—21no—
98#121×C101—21no—
99#121×C101—41no—
100C4×Q8×C101C2311yescharacteristic
101C4×Q8×C101C2311yescharacteristic
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101—21no—
106C4×D4×C101C2311yescharacteristic
107C4×D4×C101C2311yescharacteristic
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110#107×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101—21no—
115#106×C101D411yescharacteristic
116#106×C101D411yescharacteristic
117C4⋊C8×C101—21no—
118C4⋊C8×C101—21no—
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123#103×C101—21no—
124#103×C101—21no—
125#103×C101—21no—
126#103×C101D411yescharacteristic
127#103×C101D411yescharacteristic
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—21no—
135#102×C101—41no—
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×C101—21no—
141C4×C8×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—81no—
148#41×C101—81no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
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—
169C22×C4×C101—41no—
170Q16×C101—42no—
171SD16×C101—22no—
172SD16×C101—22no—
173SD16×C101—42no—
174SD16×C101—81no—
175SD16×C101—81no—
176SD16×C101—82no—
177D8×C101—42no—
178D8×C101—42no—
179D8×C101—42no—
180D8×C101—81no—
181D8×C101—81no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—42no—
188C2×C8×C101—42no—
189C2×C8×C101C2×D411yescharacteristic
190C2×C8×C101C2×D411yescharacteristic
191C2×C8×C101C2×D411yescharacteristic
192C2×C8×C101C2×D411yescharacteristic
193C4⋊C4×C101—21no—
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C22⋊C4×C101—21no—
207C22⋊C4×C101—21no—
208C22⋊C4×C101—41no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C42×C101—21no—
215C42×C101—21no—
216C42×C101C2411yescharacteristic
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—41no—
220C23×C101—41no—
221Q8×C101—21no—
222Q8×C101—21no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—81no—
228D4×C101—21no—
229D4×C101—21no—
230D4×C101—21no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—81no—
240D4×C101—81no—
241D4×C101—82no—
242D4×C101—82no—
243D4×C101—161no—
244D4×C101AGL(1,ℤ/8)12yes—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
248C2×C4×C101—21no—
249C2×C4×C101—21no—
250C2×C4×C101—21no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101—41no—
257C2×C4×C101—82no—
258C2×C4×C101—82no—
259C2×C4×C101—161no—
260C2×C4×C101—161no—
261C2×C4×C101C22×D411yescharacteristic
262C2×C4×C101C22×D411yescharacteristic
263C2×C4×C101H(5,𝔽2)11yescharacteristic
264C8×C101—21no—
265C8×C101—21no—
266C8×C101—21no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C8×C101—41no—
271C8×C101—41no—
272C8×C101#13512yescomplemented
273C22×C101—22no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—81no—
280C22×C101—81no—
281C22×C101—81no—
282C22×C101—81no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101D4211yescharacteristic
286C4×C101—21no—
287C4×C101—41no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—41no—
291C4×C101—41no—
292C4×C101—41no—
293C4×C101—81no—
294C4×C101—81no—
295C4×C101C2×#13511yescharacteristic
296C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
297C4×C101#57711yescharacteristic
298C4×C101#57711yescharacteristic
299#19852C10111yesmaximal, characteristic, direct product factor, Sylow
300C2×C101—42no—
301C2×C101—81no—
302C2×C101—161no—
303C2×C101—161no—
304C2×C101#326511yescharacteristic
305C2×C101#328411yescharacteristic
306C2×C101#328811yescharacteristic
307#3399C2×C10111yescharacteristic, complemented
308#3361C2×C10111yescharacteristic, complemented
309#3335C2×C10111yescharacteristic, complemented
310#3284C2×C10111yescharacteristic, complemented
311#1715C2×C10111yescharacteristic, complemented
312#1692C2×C10111yescharacteristic, complemented
313#1677C2×C10111yescharacteristic, complemented
314#1667C2×C10111yescharacteristic, complemented
315#1666C2×C10111yescharacteristic, complemented
316#1640C2×C10111yescharacteristic, complemented
317#1631C2×C10111yescharacteristic, complemented
318#1625C2×C10111yescharacteristic, complemented
319#1622C2×C10111yescharacteristic, complemented
320#1582C2×C10111yescharacteristic, complemented
321SD16⋊C8C2×C10111yescharacteristic, complemented
322C101#1985211yescharacteristic, direct product factor, Sylow
323C2×#135—21no—
324#559C22×C10111yescharacteristic
325#554C22×C10111yescharacteristic
326#550C22×C10111yescharacteristic
327#547C22×C10111yescharacteristic
328#498C22×C10111yescharacteristic
329#496—21no—
330#493C22×C10111yescharacteristic
331#492C22×C10111yescharacteristic
332#492C22×C10111yescharacteristic
333#488—21no—
334#486C22×C10111yescharacteristic
335#486C22×C10111yescharacteristic
336#483—21no—
337#481—21no—
338#478—21no—
339#477C22×C10111yescharacteristic
340#476C22×C10111yescharacteristic
341#475C22×C10111yescharacteristic
342#465—21no—
343#465—21no—
344#463—21no—
345#463—21no—
346#462C22×C10111yescharacteristic
347#460C22×C10111yescharacteristic
348#459—21no—
349#459C22×C10111yescharacteristic
350#459C22×C10111yescharacteristic
351#459C22×C10111yescharacteristic
352#452—21no—
353#449—21no—
354#446C22×C10111yescharacteristic
355C8×Q8C22×C10111yescharacteristic
356#442—21no—
357C4×SD16C22×C10111yescharacteristic
358C4×SD16C22×C10111yescharacteristic
359C4×D8—21no—
360C8×D4C22×C10111yescharacteristic
361C8×D4C22×C10111yescharacteristic
362C2×#106—21no—
363#335C22×C10111yescharacteristic
364#334C22×C10111yescharacteristic
365#333C22×C10111yescharacteristic
366#332C22×C10111yescharacteristic
367#331C22×C10111yescharacteristic
368#331C22×C10111yescharacteristic
369Q8⋊C8C22×C10111yescharacteristic
370Q8⋊C8C22×C10111yescharacteristic
371D4⋊C8C22×C10111yescharacteristic
372D4⋊C8C22×C10111yescharacteristic
373#322C22×C10111yescharacteristic
374C2×#41—21no—
375C2×#41—21no—
376#135—44no—
377C2×Q16—21no—
378C2×SD16—21no—
379C2×SD16—21no—
380C2×SD16—21no—
381C2×SD16—41no—
382C2×SD16D4×C10111yescharacteristic
383C2×SD16D4×C10111yescharacteristic
384C2×D8—21no—
385C2×D8—21no—
386C2×D8—21no—
387C2×D8—21no—
388C2×D8—21no—
389C22×C8—21no—
390C22×C8—21no—
391C4⋊Q8C23×C10111yescharacteristic
392C4⋊Q8C23×C10111yescharacteristic
393#127—21no—
394#127C23×C10111yescharacteristic
395#127C23×C10111yescharacteristic
396#125—21no—
397#124—21no—
398#124—21no—
399#123—41no—
400#123—41no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—41no—
404#121—21no—
405#121—21no—
406#121—41no—
407C4×Q8C23×C10111yescharacteristic
408C4×Q8C23×C10111yescharacteristic
409C4×D4—21no—
410C4×D4—21no—
411C4×D4—21no—
412C4×D4—21no—
413C4×D4C23×C10111yescharacteristic
414C4×D4C23×C10111yescharacteristic
415C2×C4⋊C4—21no—
416C2×C4⋊C4—21no—
417#107—21no—
418#106—21no—
419#106—21no—
420#106—21no—
421#106—21no—
422#106D4×C10111yescharacteristic
423#106D4×C10111yescharacteristic
424C4⋊C8—21no—
425C4⋊C8—21no—
426C4⋊C8C23×C10111yescharacteristic
427C4⋊C8C23×C10111yescharacteristic
428C4⋊C8C23×C10111yescharacteristic
429C4⋊C8C23×C10111yescharacteristic
430#103—21no—
431#103—21no—
432#103—21no—
433#103D4×C10111yescharacteristic
434#103D4×C10111yescharacteristic
435#102—21no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—41no—
443#102D4×C10111yescharacteristic
444#102D4×C10111yescharacteristic
445C22⋊C8—21no—
446C22⋊C8—21no—
447#97—21no—
448C4×C8—21no—
449C4×C8C23×C10111yescharacteristic
450C4×C8C23×C10111yescharacteristic
451C4×C8C23×C10111yescharacteristic
452#41—42no—
453#41—42no—
454#41—81no—
455#41—81no—
456C2×Q8—21no—
457C2×Q8—21no—
458C2×Q8C2×D4×C10111yescharacteristic
459C2×Q8C2×D4×C10111yescharacteristic
460C2×D4—21no—
461C2×D4—21no—
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—41no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4C2×D4×C10111yescharacteristic
470C2×D4C2×D4×C10111yescharacteristic
471C22×C4—21no—
472C22×C4—21no—
473C22×C4—41no—
474C22×C4—41no—
475C22×C4—41no—
476C22×C4—41no—
477Q16—42no—
478SD16—22no—
479SD16—22no—
480SD16—42no—
481SD16—81no—
482SD16—81no—
483SD16—82no—
484D8—42no—
485D8—42no—
486D8—42no—
487D8—81no—
488D8—81no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—42no—
495C2×C8—42no—
496C2×C8C2×D4×C10111yescharacteristic
497C2×C8C2×D4×C10111yescharacteristic
498C2×C8C2×D4×C10111yescharacteristic
499C2×C8C2×D4×C10111yescharacteristic
500C4⋊C4—21no—
501C4⋊C4—21no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—41no—
507C4⋊C4—41no—
508C4⋊C4—41no—
509C4⋊C4C2×D4×C10111yescharacteristic
510C4⋊C4C2×D4×C10111yescharacteristic
511C4⋊C4C2×D4×C10111yescharacteristic
512C4⋊C4C2×D4×C10111yescharacteristic
513C22⋊C4—21no—
514C22⋊C4—21no—
515C22⋊C4—41no—
516C22⋊C4—41no—
517C22⋊C4—41no—
518C22⋊C4—41no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C42—21no—
522C42—21no—
523C42C24×C10111yescharacteristic
524C23—21no—
525C23—21no—
526C23—41no—
527C23—41no—
528Q8—21no—
529Q8—21no—
530Q8—21no—
531Q8—21no—
532Q8—41no—
533Q8—41no—
534Q8—81no—
535D4—21no—
536D4—21no—
537D4—21no—
538D4—41no—
539D4—41no—
540D4—41no—
541D4—41no—
542D4—41no—
543D4—41no—
544D4—41no—
545D4—41no—
546D4—81no—
547D4—81no—
548D4—82no—
549D4—82no—
550D4—161no—
551D4AGL(1,ℤ/8)×C10112yes—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—82no—
565C2×C4—82no—
566C2×C4—161no—
567C2×C4—161no—
568C2×C4C22×D4×C10111yescharacteristic
569C2×C4C22×D4×C10111yescharacteristic
570C2×C4H(5,𝔽2)×C10111yescharacteristic
571C8—21no—
572C8—21no—
573C8—21no—
574C8—41no—
575C8—41no—
576C8—41no—
577C8—41no—
578C8—41no—
579C8#135×C10112yescomplemented
580C22—22no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—81no—
587C22—81no—
588C22—81no—
589C22—81no—
590C22—81no—
591C22—81no—
592C22D42×C10111yescharacteristic
593C4—21no—
594C4—41no—
595C4—41no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4—41no—
600C4—81no—
601C4—81no—
602C4C2×#135×C10111yescharacteristic
603C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
604C4#577×C10111yescharacteristic
605C4#577×C10111yescharacteristic
606C2—42no—
607C2—81no—
608C2—161no—
609C2—161no—
610C2C101×#326511yescharacteristic
611C2C101×#328411yescharacteristic
612C2C101×#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×#3335C2semidirect
4. C101×#3284C2semidirect
5. C101×#1715C2semidirect
6. C101×#1692C2semidirect
7. C101×#1677C2semidirect
8. C101×#1667C2semidirect
9. C101×#1666C2semidirect
10. C101×#1640C2semidirect
11. C101×#1631C2semidirect
12. C101×#1625C2semidirect
13. C101×#1622C2semidirect
14. C101×#1582C2semidirect
15. C101×SD16⋊C8C2semidirect
272. C8×C101#135semidirect
299. #19852C101direct (N × H)
307. #3399C2×C101semidirect
308. #3361C2×C101semidirect
309. #3335C2×C101semidirect
310. #3284C2×C101semidirect
311. #1715C2×C101semidirect
312. #1692C2×C101semidirect
313. #1677C2×C101semidirect
314. #1667C2×C101semidirect
315. #1666C2×C101semidirect
316. #1640C2×C101semidirect
317. #1631C2×C101semidirect
318. #1625C2×C101semidirect
319. #1622C2×C101semidirect
320. #1582C2×C101semidirect
321. SD16⋊C8C2×C101semidirect
322. C101#19852direct (N × H)
579. C8#135×C101semidirect

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×#33352
C101×#32842
C101×#17152
C101×#16922
C101×#16772
C101×#16672
C101×#16662
C101×#16402
C101×#16312
C101×#16252
C101×#16222
C101×#15822
C101×SD16⋊C82
#19852101