Finite Group Databasebeta

← C101×#19851 #38802002

Subgroups — C101×#19851 #38802002

Order 25856.

666 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3397C211yesmaximal, characteristic, complemented
2C101×#3334C211yesmaximal, characteristic, complemented
3C101×#3302C211yesmaximal, characteristic, complemented
4C101×#3284C211yesmaximal, characteristic, complemented
5C101×#1714C211yesmaximal, characteristic, complemented
6C101×#1694C211yesmaximal, characteristic, complemented
7C101×#1679C211yesmaximal, characteristic, complemented
8C101×#1665C211yesmaximal, characteristic, complemented
9C101×#1665C211yesmaximal, characteristic, complemented
10C101×#1654C211yesmaximal, characteristic, complemented
11C101×#1652C211yesmaximal, characteristic, complemented
12C101×#1641C211yesmaximal, characteristic, complemented
13C101×#1625C211yesmaximal, characteristic, complemented
14C101×#1582C211yesmaximal, characteristic, complemented
15C101×#1580C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#556×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#496×C101—21no—
24#492×C101C2211yescharacteristic
25#492×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#485×C101—21no—
29#480×C101—21no—
30#480×C101—21no—
31#474×C101C2211yescharacteristic
32#474×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#467×C101—21no—
35#466×C101—21no—
36#465×C101—21no—
37#463×C101—21no—
38#462×C101C2211yescharacteristic
39#462×C101C2211yescharacteristic
40#461×C101C2211yescharacteristic
41#460×C101—21no—
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#452×C101—21no—
45#452×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48#440×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×D8×C101C2211yescharacteristic
51C8×D4×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54C2×#107×C101—21no—
55#416×C101—21no—
56#334×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C2×#41×C101—21no—
70#135×C101—44no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101—21no—
78C2×SD16×C101D411yescharacteristic
79C2×D8×C101—21no—
80C2×D8×C101—21no—
81C2×D8×C101D411yescharacteristic
82C22×C8×C101—21no—
83C22×C8×C101—21no—
84C22×C8×C101—21no—
85C4⋊Q8×C101C2311yescharacteristic
86C4⋊Q8×C101C2311yescharacteristic
87C4⋊Q8×C101C2311yescharacteristic
88#127×C101—21no—
89#127×C101C2311yescharacteristic
90#126×C101—41no—
91#124×C101—21no—
92#123×C101—41no—
93#123×C101—41no—
94C22⋊Q8×C101—21no—
95C22⋊Q8×C101—21no—
96C22⋊Q8×C101—21no—
97#121×C101—21no—
98#121×C101—21no—
99#121×C101—21no—
100#121×C101—41no—
101C4×Q8×C101—21no—
102C4×Q8×C101C2311yescharacteristic
103C4×D4×C101—21no—
104C4×D4×C101C2311yescharacteristic
105C4×D4×C101C2311yescharacteristic
106C4×D4×C101C2311yescharacteristic
107#117×C101—21no—
108C2×C4⋊C4×C101—21no—
109C2×C4⋊C4×C101—21no—
110#107×C101—21no—
111#107×C101—21no—
112#107×C101—21no—
113#107×C101—21no—
114#107×C101—21no—
115#107×C101D411yescharacteristic
116#106×C101—41no—
117#106×C101D411yescharacteristic
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×C101—21no—
127#103×C101—21no—
128#103×C101D411yescharacteristic
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
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141#97×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—42no—
148#41×C101—81no—
149#41×C101—81no—
150#41×C101—81no—
151C2×Q8×C101—21no—
152C2×Q8×C101—21no—
153C2×Q8×C101—21no—
154C2×Q8×C101C2×D411yescharacteristic
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101—41no—
161C2×D4×C101—41no—
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—
169C22×C4×C101—41no—
170C22×C4×C101—41no—
171Q16×C101—42no—
172Q16×C101—81no—
173SD16×C101—22no—
174SD16×C101—42no—
175SD16×C101—42no—
176SD16×C101—81no—
177SD16×C101—81no—
178SD16×C101—81no—
179D8×C101—22no—
180D8×C101—42no—
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×C101—81no—
190C2×C8×C101C2×D411yescharacteristic
191C2×C8×C101C2×D411yescharacteristic
192C2×C8×C101C2×D411yescharacteristic
193C2×C8×C101C2×D411yescharacteristic
194C4⋊C4×C101—21no—
195C4⋊C4×C101—21no—
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101—41no—
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C4⋊C4×C101C2×D411yescharacteristic
207C4⋊C4×C101C2×D411yescharacteristic
208C22⋊C4×C101—21no—
209C22⋊C4×C101—21no—
210C22⋊C4×C101—21no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C22⋊C4×C101—41no—
215C22⋊C4×C101—41no—
216C42×C101—21no—
217C42×C101—41no—
218C42×C101C2411yescharacteristic
219C23×C101—21no—
220C23×C101—21no—
221C23×C101—21no—
222C23×C101—41no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—41no—
228Q8×C101—41no—
229Q8×C101—41no—
230Q8×C101—41no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—21no—
234D4×C101—21no—
235D4×C101—21no—
236D4×C101—41no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—81no—
241D4×C101—82no—
242D4×C101—82no—
243D4×C101—82no—
244D4×C101—161no—
245D4×C101AGL(1,ℤ/8)12yes—
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—41no—
258C2×C4×C101—41no—
259C2×C4×C101—41no—
260C2×C4×C101—82no—
261C2×C4×C101—82no—
262C2×C4×C101—82no—
263C2×C4×C101C22×D411yescharacteristic
264C2×C4×C101C22×D411yescharacteristic
265C2×C4×C101H(5,𝔽2)11yescharacteristic
266C8×C101—21no—
267C8×C101—21no—
268C8×C101—21no—
269C8×C101—41no—
270C8×C101—41no—
271C8×C101—41no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101#13512yescomplemented
275C22×C101—22no—
276C22×C101—41no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—41no—
282C22×C101—41no—
283C22×C101—41no—
284C22×C101—81no—
285C22×C101—81no—
286C22×C101—81no—
287C22×C101D4211yescharacteristic
288C4×C101—21no—
289C4×C101—41no—
290C4×C101—41no—
291C4×C101—41no—
292C4×C101—41no—
293C4×C101—41no—
294C4×C101—81no—
295C4×C101—81no—
296C4×C101—81no—
297C4×C101C2×#13511yescharacteristic
298C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C101#57611yescharacteristic
300C4×C101#57711yescharacteristic
301#19851C10111yesmaximal, characteristic, direct product factor, Sylow
302C2×C101—42no—
303C2×C101—81no—
304C2×C101—81no—
305C2×C101—161no—
306C2×C101#326411yescharacteristic
307C2×C101#328411yescharacteristic
308C2×C101#328911yescharacteristic
309#3397C2×C10111yescharacteristic, complemented
310#3334C2×C10111yescharacteristic, complemented
311#3302C2×C10111yescharacteristic, complemented
312#3284C2×C10111yescharacteristic, complemented
313#1714C2×C10111yescharacteristic, complemented
314#1694C2×C10111yescharacteristic, complemented
315#1679C2×C10111yescharacteristic, complemented
316#1665C2×C10111yescharacteristic, complemented
317#1665C2×C10111yescharacteristic, complemented
318#1654C2×C10111yescharacteristic, complemented
319#1652C2×C10111yescharacteristic, complemented
320#1641C2×C10111yescharacteristic, complemented
321#1625C2×C10111yescharacteristic, complemented
322#1582C2×C10111yescharacteristic, complemented
323#1580C2×C10111yescharacteristic, complemented
324C101#1985111yescharacteristic, direct product factor, Sylow
325C2×#135—21no—
326#556C22×C10111yescharacteristic
327#550C22×C10111yescharacteristic
328#547C22×C10111yescharacteristic
329#547C22×C10111yescharacteristic
330#500C22×C10111yescharacteristic
331#498C22×C10111yescharacteristic
332#496—21no—
333#492C22×C10111yescharacteristic
334#492C22×C10111yescharacteristic
335#487C22×C10111yescharacteristic
336#486C22×C10111yescharacteristic
337#485—21no—
338#480—21no—
339#480—21no—
340#474C22×C10111yescharacteristic
341#474C22×C10111yescharacteristic
342#474C22×C10111yescharacteristic
343#467—21no—
344#466—21no—
345#465—21no—
346#463—21no—
347#462C22×C10111yescharacteristic
348#462C22×C10111yescharacteristic
349#461C22×C10111yescharacteristic
350#460—21no—
351#459C22×C10111yescharacteristic
352#459C22×C10111yescharacteristic
353#452—21no—
354#452—21no—
355#449—21no—
356#446C22×C10111yescharacteristic
357#440—21no—
358C4×SD16C22×C10111yescharacteristic
359C4×D8C22×C10111yescharacteristic
360C8×D4C22×C10111yescharacteristic
361C8×D4C22×C10111yescharacteristic
362C8×D4C22×C10111yescharacteristic
363C2×#107—21no—
364#416—21no—
365#334C22×C10111yescharacteristic
366#334C22×C10111yescharacteristic
367#332C22×C10111yescharacteristic
368#332C22×C10111yescharacteristic
369#332C22×C10111yescharacteristic
370#331C22×C10111yescharacteristic
371Q8⋊C8C22×C10111yescharacteristic
372D4⋊C8C22×C10111yescharacteristic
373D4⋊C8C22×C10111yescharacteristic
374D4⋊C8C22×C10111yescharacteristic
375#322C22×C10111yescharacteristic
376C2×#41—21no—
377C2×#41—21no—
378C2×#41—21no—
379#135—44no—
380C2×Q16—21no—
381C2×Q16—21no—
382C2×SD16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16D4×C10111yescharacteristic
388C2×D8—21no—
389C2×D8—21no—
390C2×D8D4×C10111yescharacteristic
391C22×C8—21no—
392C22×C8—21no—
393C22×C8—21no—
394C4⋊Q8C23×C10111yescharacteristic
395C4⋊Q8C23×C10111yescharacteristic
396C4⋊Q8C23×C10111yescharacteristic
397#127—21no—
398#127C23×C10111yescharacteristic
399#126—41no—
400#124—21no—
401#123—41no—
402#123—41no—
403C22⋊Q8—21no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—41no—
410C4×Q8—21no—
411C4×Q8C23×C10111yescharacteristic
412C4×D4—21no—
413C4×D4C23×C10111yescharacteristic
414C4×D4C23×C10111yescharacteristic
415C4×D4C23×C10111yescharacteristic
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107D4×C10111yescharacteristic
425#106—41no—
426#106D4×C10111yescharacteristic
427C4⋊C8—21no—
428C4⋊C8C23×C10111yescharacteristic
429C4⋊C8C23×C10111yescharacteristic
430C4⋊C8C23×C10111yescharacteristic
431C4⋊C8C23×C10111yescharacteristic
432#103—21no—
433#103—21no—
434#103—21no—
435#103—21no—
436#103—21no—
437#103D4×C10111yescharacteristic
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—41no—
444#102D4×C10111yescharacteristic
445#102D4×C10111yescharacteristic
446#102D4×C10111yescharacteristic
447C22⋊C8—21no—
448C22⋊C8—21no—
449C22⋊C8—21no—
450#97—21no—
451C4×C8C23×C10111yescharacteristic
452C4×C8C23×C10111yescharacteristic
453C4×C8C23×C10111yescharacteristic
454#41—42no—
455#41—42no—
456#41—42no—
457#41—81no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8C2×D4×C10111yescharacteristic
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4C2×D4×C10111yescharacteristic
472C2×D4C2×D4×C10111yescharacteristic
473C2×D4C2×D4×C10111yescharacteristic
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—41no—
478C22×C4—41no—
479C22×C4—41no—
480Q16—42no—
481Q16—81no—
482SD16—22no—
483SD16—42no—
484SD16—42no—
485SD16—81no—
486SD16—81no—
487SD16—81no—
488D8—22no—
489D8—42no—
490D8—81no—
491C2×C8—21no—
492C2×C8—21no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—42no—
497C2×C8—42no—
498C2×C8—81no—
499C2×C8C2×D4×C10111yescharacteristic
500C2×C8C2×D4×C10111yescharacteristic
501C2×C8C2×D4×C10111yescharacteristic
502C2×C8C2×D4×C10111yescharacteristic
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C10111yescharacteristic
514C4⋊C4C2×D4×C10111yescharacteristic
515C4⋊C4C2×D4×C10111yescharacteristic
516C4⋊C4C2×D4×C10111yescharacteristic
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—21no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42C24×C10111yescharacteristic
528C23—21no—
529C23—21no—
530C23—21no—
531C23—41no—
532Q8—21no—
533Q8—21no—
534Q8—41no—
535Q8—41no—
536Q8—41no—
537Q8—41no—
538Q8—41no—
539Q8—41no—
540D4—21no—
541D4—21no—
542D4—21no—
543D4—21no—
544D4—21no—
545D4—41no—
546D4—41no—
547D4—41no—
548D4—41no—
549D4—81no—
550D4—82no—
551D4—82no—
552D4—82no—
553D4—161no—
554D4AGL(1,ℤ/8)×C10112yes—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—82no—
570C2×C4—82no—
571C2×C4—82no—
572C2×C4C22×D4×C10111yescharacteristic
573C2×C4C22×D4×C10111yescharacteristic
574C2×C4H(5,𝔽2)×C10111yescharacteristic
575C8—21no—
576C8—21no—
577C8—21no—
578C8—41no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8#135×C10112yescomplemented
584C22—22no—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—81no—
594C22—81no—
595C22—81no—
596C22D42×C10111yescharacteristic
597C4—21no—
598C4—41no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4C2×#135×C10111yescharacteristic
607C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
608C4#576×C10111yescharacteristic
609C4#577×C10111yescharacteristic
610C2—42no—
611C2—81no—
612C2—81no—
613C2—161no—
614C2C101×#326411yescharacteristic
615C2C101×#328411yescharacteristic
616C2C101×#328911yescharacteristic
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×#3397C2semidirect
2. C101×#3334C2semidirect
3. C101×#3302C2semidirect
4. C101×#3284C2semidirect
5. C101×#1714C2semidirect
6. C101×#1694C2semidirect
7. C101×#1679C2semidirect
8. C101×#1665C2semidirect
9. C101×#1665C2semidirect
10. C101×#1654C2semidirect
11. C101×#1652C2semidirect
12. C101×#1641C2semidirect
13. C101×#1625C2semidirect
14. C101×#1582C2semidirect
15. C101×#1580C2semidirect
274. C8×C101#135semidirect
301. #19851C101direct (N × H)
309. #3397C2×C101semidirect
310. #3334C2×C101semidirect
311. #3302C2×C101semidirect
312. #3284C2×C101semidirect
313. #1714C2×C101semidirect
314. #1694C2×C101semidirect
315. #1679C2×C101semidirect
316. #1665C2×C101semidirect
317. #1665C2×C101semidirect
318. #1654C2×C101semidirect
319. #1652C2×C101semidirect
320. #1641C2×C101semidirect
321. #1625C2×C101semidirect
322. #1582C2×C101semidirect
323. #1580C2×C101semidirect
324. C101#19851direct (N × H)
583. C8#135×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33972
C101×#33342
C101×#33022
C101×#32842
C101×#17142
C101×#16942
C101×#16792
C101×#16652
C101×#16542
C101×#16522
C101×#16412
C101×#16252
C101×#15822
C101×#15802
#19851101