Finite Group Databasebeta

← C101×#19899 #38802050

Subgroups — C101×#19899 #38802050

Order 25856.

666 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3330C211yesmaximal, characteristic, complemented
2C101×#3325C211yesmaximal, characteristic, complemented
3C101×#3303C211yesmaximal, characteristic, complemented
4C101×#3294C211yesmaximal, characteristic, complemented
5C101×#1711C211yesmaximal, characteristic, complemented
6C101×#1699C211yesmaximal, characteristic, complemented
7C101×#1697C211yesmaximal, characteristic, complemented
8C101×#1683C211yesmaximal, characteristic, complemented
9C101×#1681C211yesmaximal, characteristic, complemented
10C101×#1646C211yesmaximal, characteristic, complemented
11C101×#1639C211yesmaximal, characteristic, complemented
12C101×#1635C211yesmaximal, characteristic, complemented
13C101×#1625C211yesmaximal, characteristic, complemented
14C101×#1589C211yesmaximal, characteristic, complemented
15C8×D8×C101C211yesmaximal, characteristic, complemented
16#555×C101C2211yescharacteristic
17#547×C101C2211yescharacteristic
18#547×C101C2211yescharacteristic, complemented
19D42×C101C2211yescharacteristic
20#487×C101C2211yescharacteristic, complemented
21#487×C101C2211yescharacteristic, complemented
22#487×C101C2211yescharacteristic, complemented
23#486×C101C2211yescharacteristic
24#486×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#485×C101—21no—
27#484×C101—21no—
28#482×C101—21no—
29#480×C101—21no—
30#476×C101C2211yescharacteristic
31#476×C101C2211yescharacteristic, complemented
32#474×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#469×C101—21no—
35#468×C101—21no—
36#466×C101—21no—
37#465×C101—21no—
38#461×C101C2211yescharacteristic
39#461×C101C2211yescharacteristic, complemented
40#459×C101C2211yescharacteristic
41#459×C101C2211yescharacteristic
42#449×C101—21no—
43#449×C101—21no—
44#447×C101—21no—
45#447×C101—21no—
46C4×D8×C101C2211yescharacteristic
47C4×D8×C101C2211yescharacteristic
48#436×C101C2211yescharacteristic
49#436×C101C2211yescharacteristic, complemented
50C8×D4×C101C2211yescharacteristic
51C8×D4×C101C2211yescharacteristic, complemented
52#418×C101—21no—
53#417×C101—21no—
54#416×C101—21no—
55C2×#102×C101—21no—
56#335×C101C2211yescharacteristic, complemented
57#335×C101C2211yescharacteristic, complemented
58#333×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62D4⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic, complemented
65D4⋊C8×C101C2211yescharacteristic, complemented
66C82×C101C2211yescharacteristic, complemented
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C22×D4×C101—21no—
70C22×D4×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×D8×C101—21no—
74C2×D8×C101—21no—
75C2×D8×C101D411yescharacteristic
76C2×D8×C101D411yescharacteristic
77C2×M16×C101—21no—
78C2×M16×C101—21no—
79C22×C8×C101—21no—
80C22×C8×C101—21no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#124×C101—41no—
86#123×C101—41no—
87#123×C101—41no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#120×C101—41no—
97C4×D4×C101C2311yescharacteristic
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101#117×C101—21no—
102#117×C101—21no—
103C2×C4⋊C4×C101—21no—
104C2×C4⋊C4×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101D411yescharacteristic
108#107×C101D411yescharacteristic
109#106×C101—21no—
110#106×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—41no—
122#102×C101—21no—
123#102×C101—21no—
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—41no—
133#102×C101D411yescharacteristic
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C24×C101—41no—
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×C101—21no—
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—41no—
161C2×D4×C101—41no—
162C2×D4×C101—81no—
163C2×D4×C101—81no—
164C2×D4×C101C2×D411yescharacteristic
165C2×D4×C101C2×D411yescharacteristic
166C2×D4×C101C2×D411yescharacteristic
167C2×D4×C101C2×D411yescharacteristic
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—21no—
172C22×C4×C101—41no—
173C22×C4×C101—41no—
174SD16×C101—81no—
175SD16×C101—81no—
176D8×C101—22no—
177D8×C101—41no—
178D8×C101—81no—
179D8×C101—81no—
180M16×C101—81no—
181M16×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—81no—
188C2×C8×C101—81no—
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×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C22⋊C4×C101—21no—
206C22⋊C4×C101—21no—
207C22⋊C4×C101—21no—
208C22⋊C4×C101—21no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C42×C101—41no—
215C42×C101C2411yescharacteristic
216C23×C101—21no—
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—21no—
220C23×C101—41no—
221C23×C101—82no—
222C23×C101—82no—
223C23×C101—161no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—41no—
228Q8×C101—81no—
229D4×C101—21no—
230D4×C101—21no—
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—82no—
245D4×C101—161no—
246D4×C101#13512yes—
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—41no—
261C2×C4×C101—41no—
262C2×C4×C101—82no—
263C2×C4×C101—82no—
264C2×C4×C101C22×D411yescharacteristic
265C2×C4×C101C22×D411yescharacteristic
266C2×C4×C101H(5,𝔽2)11yescharacteristic
267C8×C101—21no—
268C8×C101—21no—
269C8×C101—21no—
270C8×C101—21no—
271C8×C101—41no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101—41no—
275C8×C101—41no—
276C22×C101—22no—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—41no—
282C22×C101—41no—
283C22×C101—41no—
284C22×C101—41no—
285C22×C101—41no—
286C22×C101—41no—
287C22×C101—41no—
288C22×C101—81no—
289C22×C101—81no—
290C22×C101—81no—
291C22×C101—164no—
292C22×C101D4211yescharacteristic
293C4×C101—21no—
294C4×C101—41no—
295C4×C101—41no—
296C4×C101—41no—
297C4×C101—41no—
298C4×C101—81no—
299C4×C101—81no—
300C4×C101—81no—
301C4×C101C2×#13511yescharacteristic
302C4×C101#57511yescharacteristic
303C4×C101#57611yescharacteristic
304C4×C101#57611yescharacteristic
305#19899C10111yesmaximal, characteristic, direct product factor, Sylow
306C2×C101—42no—
307C2×C101—81no—
308C2×C101—81no—
309C2×C101—81no—
310C2×C101—161no—
311C2×C101#327311yescharacteristic
312C2×C101#328011yescharacteristic
313C2×C101#329011yescharacteristic
314#3330C2×C10111yescharacteristic, complemented
315#3325C2×C10111yescharacteristic, complemented
316#3303C2×C10111yescharacteristic, complemented
317#3294C2×C10111yescharacteristic, complemented
318#1711C2×C10111yescharacteristic, complemented
319#1699C2×C10111yescharacteristic, complemented
320#1697C2×C10111yescharacteristic, complemented
321#1683C2×C10111yescharacteristic, complemented
322#1681C2×C10111yescharacteristic, complemented
323#1646C2×C10111yescharacteristic, complemented
324#1639C2×C10111yescharacteristic, complemented
325#1635C2×C10111yescharacteristic, complemented
326#1625C2×C10111yescharacteristic, complemented
327#1589C2×C10111yescharacteristic, complemented
328C8×D8C2×C10111yescharacteristic, complemented
329C101#1989911yescharacteristic, direct product factor, Sylow
330#555C22×C10111yescharacteristic
331#547C22×C10111yescharacteristic
332#547C22×C10111yescharacteristic, complemented
333D42C22×C10111yescharacteristic
334#487C22×C10111yescharacteristic, complemented
335#487C22×C10111yescharacteristic, complemented
336#487C22×C10111yescharacteristic, complemented
337#486C22×C10111yescharacteristic
338#486C22×C10111yescharacteristic
339#486C22×C10111yescharacteristic
340#485—21no—
341#484—21no—
342#482—21no—
343#480—21no—
344#476C22×C10111yescharacteristic
345#476C22×C10111yescharacteristic, complemented
346#474C22×C10111yescharacteristic
347#474C22×C10111yescharacteristic
348#469—21no—
349#468—21no—
350#466—21no—
351#465—21no—
352#461C22×C10111yescharacteristic
353#461C22×C10111yescharacteristic, complemented
354#459C22×C10111yescharacteristic
355#459C22×C10111yescharacteristic
356#449—21no—
357#449—21no—
358#447—21no—
359#447—21no—
360C4×D8C22×C10111yescharacteristic
361C4×D8C22×C10111yescharacteristic
362#436C22×C10111yescharacteristic
363#436C22×C10111yescharacteristic, complemented
364C8×D4C22×C10111yescharacteristic
365C8×D4C22×C10111yescharacteristic, complemented
366#418—21no—
367#417—21no—
368#416—21no—
369C2×#102—21no—
370#335C22×C10111yescharacteristic, complemented
371#335C22×C10111yescharacteristic, complemented
372#333C22×C10111yescharacteristic, complemented
373#332C22×C10111yescharacteristic, complemented
374#332C22×C10111yescharacteristic, complemented
375#331C22×C10111yescharacteristic
376D4⋊C8C22×C10111yescharacteristic
377D4⋊C8C22×C10111yescharacteristic
378D4⋊C8C22×C10111yescharacteristic, complemented
379D4⋊C8C22×C10111yescharacteristic, complemented
380C82C22×C10111yescharacteristic, complemented
381C2×#41—21no—
382C2×#41—21no—
383C22×D4—21no—
384C22×D4—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×D8—21no—
388C2×D8—21no—
389C2×D8D4×C10111yescharacteristic
390C2×D8D4×C10111yescharacteristic
391C2×M16—21no—
392C2×M16—21no—
393C22×C8—21no—
394C22×C8—21no—
395C4⋊Q8C23×C10111yescharacteristic
396C4⋊Q8C23×C10111yescharacteristic
397C4⋊Q8C23×C10111yescharacteristic
398#127C23×C10111yescharacteristic
399#124—41no—
400#123—41no—
401#123—41no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×D4C23×C10111yescharacteristic
412C4×D4C23×C10111yescharacteristic
413C4×D4C23×C10111yescharacteristic
414C4×D4C23×C10111yescharacteristic
415#117—21no—
416#117—21no—
417C2×C4⋊C4—21no—
418C2×C4⋊C4—21no—
419#107—21no—
420#107—21no—
421#107D4×C10111yescharacteristic
422#107D4×C10111yescharacteristic
423#106—21no—
424#106—21no—
425C4⋊C8C23×C10111yescharacteristic
426C4⋊C8C23×C10111yescharacteristic
427C4⋊C8C23×C10111yescharacteristic
428C4⋊C8C23×C10111yescharacteristic
429#103—21no—
430#103—21no—
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103—41no—
436#102—21no—
437#102—21no—
438#102—21no—
439#102—21no—
440#102—21no—
441#102—21no—
442#102—21no—
443#102—21no—
444#102—21no—
445#102—21no—
446#102—41no—
447#102D4×C10111yescharacteristic
448#102D4×C10111yescharacteristic
449#102D4×C10111yescharacteristic
450#102D4×C10111yescharacteristic
451C22⋊C8—21no—
452C22⋊C8—21no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455C4×C8C23×C10111yescharacteristic
456C4×C8C23×C10111yescharacteristic
457C4×C8C23×C10111yescharacteristic
458C24—41no—
459#41—42no—
460#41—42no—
461#41—81no—
462#41—81no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×D4—21no—
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—42no—
472C2×D4—42no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4—81no—
477C2×D4—81no—
478C2×D4C2×D4×C10111yescharacteristic
479C2×D4C2×D4×C10111yescharacteristic
480C2×D4C2×D4×C10111yescharacteristic
481C2×D4C2×D4×C10111yescharacteristic
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—41no—
487C22×C4—41no—
488SD16—81no—
489SD16—81no—
490D8—22no—
491D8—41no—
492D8—81no—
493D8—81no—
494M16—81no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—81no—
502C2×C8—81no—
503C2×C8C2×D4×C10111yescharacteristic
504C2×C8C2×D4×C10111yescharacteristic
505C2×C8C2×D4×C10111yescharacteristic
506C2×C8C2×D4×C10111yescharacteristic
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—41no—
514C4⋊C4—41no—
515C4⋊C4C2×D4×C10111yescharacteristic
516C4⋊C4C2×D4×C10111yescharacteristic
517C4⋊C4C2×D4×C10111yescharacteristic
518C4⋊C4C2×D4×C10111yescharacteristic
519C22⋊C4—21no—
520C22⋊C4—21no—
521C22⋊C4—21no—
522C22⋊C4—21no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C22⋊C4—41no—
528C42—41no—
529C42C24×C10111yescharacteristic
530C23—21no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—41no—
535C23—82no—
536C23—82no—
537C23—161no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—81no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—21no—
548D4—21no—
549D4—21no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—81no—
555D4—82no—
556D4—82no—
557D4—82no—
558D4—82no—
559D4—161no—
560D4#135×C10112yes—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—82no—
577C2×C4—82no—
578C2×C4C22×D4×C10111yescharacteristic
579C2×C4C22×D4×C10111yescharacteristic
580C2×C4H(5,𝔽2)×C10111yescharacteristic
581C8—21no—
582C8—21no—
583C8—21no—
584C8—21no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—41no—
589C8—41no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—41no—
601C22—41no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—164no—
606C22D42×C10111yescharacteristic
607C4—21no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—41no—
612C4—81no—
613C4—81no—
614C4—81no—
615C4C2×#135×C10111yescharacteristic
616C4#575×C10111yescharacteristic
617C4#576×C10111yescharacteristic
618C4#576×C10111yescharacteristic
619C2—42no—
620C2—81no—
621C2—81no—
622C2—81no—
623C2—161no—
624C2C101×#327311yescharacteristic
625C2C101×#328011yescharacteristic
626C2C101×#329011yescharacteristic
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×#3330C2semidirect
2. C101×#3325C2semidirect
3. C101×#3303C2semidirect
4. C101×#3294C2semidirect
5. C101×#1711C2semidirect
6. C101×#1699C2semidirect
7. C101×#1697C2semidirect
8. C101×#1683C2semidirect
9. C101×#1681C2semidirect
10. C101×#1646C2semidirect
11. C101×#1639C2semidirect
12. C101×#1635C2semidirect
13. C101×#1625C2semidirect
14. C101×#1589C2semidirect
15. C8×D8×C101C2semidirect
18. #547×C101C22semidirect
20. #487×C101C22semidirect
21. #487×C101C22semidirect
22. #487×C101C22semidirect
31. #476×C101C22semidirect
39. #461×C101C22semidirect
49. #436×C101C22semidirect
51. C8×D4×C101C22semidirect
56. #335×C101C22semidirect
57. #335×C101C22semidirect
58. #333×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
64. D4⋊C8×C101C22semidirect
65. D4⋊C8×C101C22semidirect
66. C82×C101C22semidirect
305. #19899C101direct (N × H)
314. #3330C2×C101semidirect
315. #3325C2×C101semidirect
316. #3303C2×C101semidirect
317. #3294C2×C101semidirect
318. #1711C2×C101semidirect
319. #1699C2×C101semidirect
320. #1697C2×C101semidirect
321. #1683C2×C101semidirect
322. #1681C2×C101semidirect
323. #1646C2×C101semidirect
324. #1639C2×C101semidirect
325. #1635C2×C101semidirect
326. #1625C2×C101semidirect
327. #1589C2×C101semidirect
328. C8×D8C2×C101semidirect
329. C101#19899direct (N × H)
332. #547C22×C101semidirect
334. #487C22×C101semidirect
335. #487C22×C101semidirect
336. #487C22×C101semidirect
345. #476C22×C101semidirect
353. #461C22×C101semidirect
363. #436C22×C101semidirect
365. C8×D4C22×C101semidirect
370. #335C22×C101semidirect
371. #335C22×C101semidirect
372. #333C22×C101semidirect
373. #332C22×C101semidirect
374. #332C22×C101semidirect
378. D4⋊C8C22×C101semidirect
379. D4⋊C8C22×C101semidirect
380. C82C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33302
C101×#33252
C101×#33032
C101×#32942
C101×#17112
C101×#16992
C101×#16972
C101×#16832
C101×#16812
C101×#16462
C101×#16392
C101×#16352
C101×#16252
C101×#15892
C8×D8×C1012
#19899101