Finite Group Databasebeta

← C101×#20298 #38802449

Subgroups — C101×#20298 #38802449

Order 25856.

662 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3399C211yesmaximal, characteristic, complemented
2C101×#3373C211yesmaximal, characteristic, complemented
3C101×#3332C211yesmaximal, characteristic, complemented
4C101×#3276C211yesmaximal, characteristic, complemented
5C101×#1709C211yesmaximal, characteristic, complemented
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1701C211yesmaximal, characteristic, complemented
8C101×#1690C211yesmaximal, characteristic, complemented
9C101×#1687C211yesmaximal, characteristic, complemented
10C101×#1642C211yesmaximal, characteristic, complemented
11C101×#1640C211yesmaximal, characteristic, complemented
12C101×#1627C211yesmaximal, characteristic, complemented
13C101×#1625C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1590C211yesmaximal, characteristic, complemented
16C2×#137×C101—21no—
17#559×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#496×C101—21no—
22#494×C101C2211yescharacteristic
23#493×C101C2211yescharacteristic
24#489×C101—21no—
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#481×C101—21no—
30#476×C101—21no—
31#475×C101C2211yescharacteristic
32#475×C101C2211yescharacteristic
33#470×C101—21no—
34#469×C101—21no—
35#463×C101—21no—
36#463×C101—21no—
37#462×C101C2211yescharacteristic
38#461×C101C2211yescharacteristic
39#460×C101C2211yescharacteristic
40#459×C101—21no—
41#459×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#452×C101—21no—
45#451×C101—21no—
46#449×C101—21no—
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#442×C101—21no—
50#442×C101—21no—
51C4×SD16×C101C2211yescharacteristic
52C4×SD16×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#417×C101—21no—
56#334×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C22×Q8×C101—21no—
70#137×C101—44no—
71C2×Q16×C101—21no—
72C2×Q16×C101—21no—
73C2×Q16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101D411yescharacteristic
77C2×SD16×C101D411yescharacteristic
78C2×D8×C101—21no—
79C2×D8×C101—21no—
80C2×D8×C101—21no—
81C2×D8×C101—21no—
82C2×D8×C101—21no—
83C2×M16×C101—21no—
84C2×M16×C101—21no—
85C4⋊Q8×C101—21no—
86C4⋊Q8×C101C2311yescharacteristic
87C4⋊Q8×C101C2311yescharacteristic
88#127×C101—21no—
89#127×C101C2311yescharacteristic
90#127×C101C2311yescharacteristic
91#124×C101—21no—
92#124×C101—21no—
93#123×C101—41no—
94#123×C101—41no—
95C22⋊Q8×C101—21no—
96C22⋊Q8×C101—21no—
97C22⋊Q8×C101—41no—
98#121×C101—21no—
99#121×C101—21no—
100#121×C101—41no—
101C4×Q8×C101C2311yescharacteristic
102C4×Q8×C101C2311yescharacteristic
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105C4×D4×C101—21no—
106C4×D4×C101—21no—
107C4×D4×C101C2311yescharacteristic
108C4×D4×C101C2311yescharacteristic
109C2×C4⋊C4×C101—21no—
110#106×C101—21no—
111#106×C101—21no—
112#106×C101D411yescharacteristic
113#106×C101D411yescharacteristic
114C4⋊C8×C101—21no—
115C4⋊C8×C101—21no—
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120#103×C101—21no—
121#103×C101—21no—
122#103×C101—21no—
123#103×C101—21no—
124#103×C101D411yescharacteristic
125#103×C101D411yescharacteristic
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×C101—41no—
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×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—81no—
148#41×C101—81no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—41no—
152C2×Q8×C101—42no—
153C2×Q8×C101—81no—
154C2×Q8×C101C2×D411yescharacteristic
155C2×Q8×C101C2×D411yescharacteristic
156C2×D4×C101—21no—
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—21no—
161C2×D4×C101—21no—
162C2×D4×C101—41no—
163C2×D4×C101—41no—
164C2×D4×C101—41no—
165C2×D4×C101C2×D411yescharacteristic
166C2×D4×C101C2×D411yescharacteristic
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—41no—
170C22×C4×C101—41no—
171C22×C4×C101—41no—
172C22×C4×C101—41no—
173Q16×C101—42no—
174Q16×C101—42no—
175Q16×C101—81no—
176SD16×C101—22no—
177SD16×C101—41no—
178SD16×C101—42no—
179SD16×C101—81no—
180D8×C101—42no—
181D8×C101—42no—
182D8×C101—81no—
183D8×C101—81no—
184D8×C101—81no—
185M16×C101—42no—
186M16×C101—81no—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101—21no—
191C2×C8×C101—21no—
192C2×C8×C101C2×D411yescharacteristic
193C2×C8×C101C2×D411yescharacteristic
194C2×C8×C101C2×D411yescharacteristic
195C2×C8×C101C2×D411yescharacteristic
196C4⋊C4×C101—21no—
197C4⋊C4×C101—21no—
198C4⋊C4×C101—21no—
199C4⋊C4×C101—21no—
200C4⋊C4×C101—21no—
201C4⋊C4×C101—21no—
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—41no—
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—21no—
218C42×C101C2411yescharacteristic
219C23×C101—21no—
220C23×C101—21no—
221C23×C101—41no—
222C23×C101—41no—
223Q8×C101—21no—
224Q8×C101—21no—
225Q8×C101—21no—
226Q8×C101—21no—
227Q8×C101—41no—
228Q8×C101—41no—
229Q8×C101—41no—
230Q8×C101—41no—
231Q8×C101—82no—
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—41no—
241D4×C101—41no—
242D4×C101—41no—
243D4×C101—41no—
244D4×C101—81no—
245D4×C101—81no—
246D4×C101—82no—
247D4×C101—82no—
248D4×C101—161no—
249C2×C4×C101—21no—
250C2×C4×C101—21no—
251C2×C4×C101—21no—
252C2×C4×C101—21no—
253C2×C4×C101—21no—
254C2×C4×C101—21no—
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—82no—
262C2×C4×C101—82no—
263C2×C4×C101—82no—
264C2×C4×C101—161no—
265C2×C4×C101C22×D411yescharacteristic
266C2×C4×C101C22×D411yescharacteristic
267C2×C4×C101H(5,𝔽2)11yescharacteristic
268C8×C101—21no—
269C8×C101—21no—
270C8×C101—21no—
271C8×C101—41no—
272C8×C101—41no—
273C8×C101—41no—
274C8×C101—41no—
275C8×C101—41no—
276C8×C101AGL(1,ℤ/8)12yes—
277C22×C101—41no—
278C22×C101—41no—
279C22×C101—41no—
280C22×C101—41no—
281C22×C101—41no—
282C22×C101—41no—
283C22×C101—81no—
284C22×C101—81no—
285C22×C101—81no—
286C22×C101—81no—
287C22×C101—81no—
288C22×C101—81no—
289C22×C101D4211yescharacteristic
290C4×C101—21no—
291C4×C101—41no—
292C4×C101—41no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—41no—
296C4×C101—41no—
297C4×C101—81no—
298C4×C101—81no—
299C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
300C4×C101#57511yescharacteristic
301C4×C101#57611yescharacteristic
302C4×C101#57711yescharacteristic
303#20298C10111yesmaximal, characteristic, direct product factor, Sylow
304C2×C101—81no—
305C2×C101—81no—
306C2×C101—161no—
307C2×C101—161no—
308C2×C101#327411yescharacteristic
309C2×C101#327511yescharacteristic
310C2×C101#329011yescharacteristic
311#3399C2×C10111yescharacteristic, complemented
312#3373C2×C10111yescharacteristic, complemented
313#3332C2×C10111yescharacteristic, complemented
314#3276C2×C10111yescharacteristic, complemented
315#1709C2×C10111yescharacteristic, complemented
316#1702C2×C10111yescharacteristic, complemented
317#1701C2×C10111yescharacteristic, complemented
318#1690C2×C10111yescharacteristic, complemented
319#1687C2×C10111yescharacteristic, complemented
320#1642C2×C10111yescharacteristic, complemented
321#1640C2×C10111yescharacteristic, complemented
322#1627C2×C10111yescharacteristic, complemented
323#1625C2×C10111yescharacteristic, complemented
324#1590C2×C10111yescharacteristic, complemented
325#1590C2×C10111yescharacteristic, complemented
326C101#2029811yescharacteristic, direct product factor, Sylow
327C2×#137—21no—
328#559C22×C10111yescharacteristic
329#550C22×C10111yescharacteristic
330D4×Q8C22×C10111yescharacteristic
331#547C22×C10111yescharacteristic
332#496—21no—
333#494C22×C10111yescharacteristic
334#493C22×C10111yescharacteristic
335#489—21no—
336#486C22×C10111yescharacteristic
337#486C22×C10111yescharacteristic
338#486C22×C10111yescharacteristic
339#486C22×C10111yescharacteristic
340#481—21no—
341#476—21no—
342#475C22×C10111yescharacteristic
343#475C22×C10111yescharacteristic
344#470—21no—
345#469—21no—
346#463—21no—
347#463—21no—
348#462C22×C10111yescharacteristic
349#461C22×C10111yescharacteristic
350#460C22×C10111yescharacteristic
351#459—21no—
352#459C22×C10111yescharacteristic
353#459C22×C10111yescharacteristic
354#459C22×C10111yescharacteristic
355#452—21no—
356#451—21no—
357#449—21no—
358#446C22×C10111yescharacteristic
359#446C22×C10111yescharacteristic
360#442—21no—
361#442—21no—
362C4×SD16C22×C10111yescharacteristic
363C4×SD16C22×C10111yescharacteristic
364#436C22×C10111yescharacteristic
365#436C22×C10111yescharacteristic
366#417—21no—
367#334C22×C10111yescharacteristic
368#334C22×C10111yescharacteristic
369#332C22×C10111yescharacteristic
370#332C22×C10111yescharacteristic
371#331C22×C10111yescharacteristic
372#331C22×C10111yescharacteristic
373Q8⋊C8C22×C10111yescharacteristic
374Q8⋊C8C22×C10111yescharacteristic
375D4⋊C8C22×C10111yescharacteristic
376D4⋊C8C22×C10111yescharacteristic
377C82C22×C10111yescharacteristic
378C2×#41—21no—
379C2×#41—21no—
380C22×Q8—21no—
381#137—44no—
382C2×Q16—21no—
383C2×Q16—21no—
384C2×Q16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16D4×C10111yescharacteristic
388C2×SD16D4×C10111yescharacteristic
389C2×D8—21no—
390C2×D8—21no—
391C2×D8—21no—
392C2×D8—21no—
393C2×D8—21no—
394C2×M16—21no—
395C2×M16—21no—
396C4⋊Q8—21no—
397C4⋊Q8C23×C10111yescharacteristic
398C4⋊Q8C23×C10111yescharacteristic
399#127—21no—
400#127C23×C10111yescharacteristic
401#127C23×C10111yescharacteristic
402#124—21no—
403#124—21no—
404#123—41no—
405#123—41no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—41no—
409#121—21no—
410#121—21no—
411#121—41no—
412C4×Q8C23×C10111yescharacteristic
413C4×Q8C23×C10111yescharacteristic
414C4×D4—21no—
415C4×D4—21no—
416C4×D4—21no—
417C4×D4—21no—
418C4×D4C23×C10111yescharacteristic
419C4×D4C23×C10111yescharacteristic
420C2×C4⋊C4—21no—
421#106—21no—
422#106—21no—
423#106D4×C10111yescharacteristic
424#106D4×C10111yescharacteristic
425C4⋊C8—21no—
426C4⋊C8—21no—
427C4⋊C8C23×C10111yescharacteristic
428C4⋊C8C23×C10111yescharacteristic
429C4⋊C8C23×C10111yescharacteristic
430C4⋊C8C23×C10111yescharacteristic
431#103—21no—
432#103—21no—
433#103—21no—
434#103—21no—
435#103D4×C10111yescharacteristic
436#103D4×C10111yescharacteristic
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—41no—
446#102—41no—
447#102D4×C10111yescharacteristic
448#102D4×C10111yescharacteristic
449C22⋊C8—21no—
450C22⋊C8—21no—
451#97—21no—
452#97—21no—
453C4×C8C23×C10111yescharacteristic
454C4×C8C23×C10111yescharacteristic
455C4×C8C23×C10111yescharacteristic
456#41—42no—
457#41—42no—
458#41—81no—
459#41—81no—
460C2×Q8—21no—
461C2×Q8—21no—
462C2×Q8—41no—
463C2×Q8—42no—
464C2×Q8—81no—
465C2×Q8C2×D4×C10111yescharacteristic
466C2×Q8C2×D4×C10111yescharacteristic
467C2×D4—21no—
468C2×D4—21no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4—21no—
472C2×D4—21no—
473C2×D4—41no—
474C2×D4—41no—
475C2×D4—41no—
476C2×D4C2×D4×C10111yescharacteristic
477C2×D4C2×D4×C10111yescharacteristic
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4—41no—
482C22×C4—41no—
483C22×C4—41no—
484Q16—42no—
485Q16—42no—
486Q16—81no—
487SD16—22no—
488SD16—41no—
489SD16—42no—
490SD16—81no—
491D8—42no—
492D8—42no—
493D8—81no—
494D8—81no—
495D8—81no—
496M16—42no—
497M16—81no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
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—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—21no—
528C42—21no—
529C42C24×C10111yescharacteristic
530C23—21no—
531C23—21no—
532C23—41no—
533C23—41no—
534Q8—21no—
535Q8—21no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—82no—
543D4—21no—
544D4—21no—
545D4—21no—
546D4—21no—
547D4—41no—
548D4—41no—
549D4—41no—
550D4—41no—
551D4—41no—
552D4—41no—
553D4—41no—
554D4—41no—
555D4—81no—
556D4—81no—
557D4—82no—
558D4—82no—
559D4—161no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4—82no—
574C2×C4—82no—
575C2×C4—161no—
576C2×C4C22×D4×C10111yescharacteristic
577C2×C4C22×D4×C10111yescharacteristic
578C2×C4H(5,𝔽2)×C10111yescharacteristic
579C8—21no—
580C8—21no—
581C8—21no—
582C8—41no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8AGL(1,ℤ/8)×C10112yes—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22D42×C10111yescharacteristic
601C4—21no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—41no—
608C4—81no—
609C4—81no—
610C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
611C4#575×C10111yescharacteristic
612C4#576×C10111yescharacteristic
613C4#577×C10111yescharacteristic
614C2—81no—
615C2—81no—
616C2—161no—
617C2—161no—
618C2C101×#327411yescharacteristic
619C2C101×#327511yescharacteristic
620C2C101×#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×#3399C2semidirect
2. C101×#3373C2semidirect
3. C101×#3332C2semidirect
4. C101×#3276C2semidirect
5. C101×#1709C2semidirect
6. C101×#1702C2semidirect
7. C101×#1701C2semidirect
8. C101×#1690C2semidirect
9. C101×#1687C2semidirect
10. C101×#1642C2semidirect
11. C101×#1640C2semidirect
12. C101×#1627C2semidirect
13. C101×#1625C2semidirect
14. C101×#1590C2semidirect
15. C101×#1590C2semidirect
303. #20298C101direct (N × H)
311. #3399C2×C101semidirect
312. #3373C2×C101semidirect
313. #3332C2×C101semidirect
314. #3276C2×C101semidirect
315. #1709C2×C101semidirect
316. #1702C2×C101semidirect
317. #1701C2×C101semidirect
318. #1690C2×C101semidirect
319. #1687C2×C101semidirect
320. #1642C2×C101semidirect
321. #1640C2×C101semidirect
322. #1627C2×C101semidirect
323. #1625C2×C101semidirect
324. #1590C2×C101semidirect
325. #1590C2×C101semidirect
326. C101#20298direct (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×#33732
C101×#33322
C101×#32762
C101×#17092
C101×#17022
C101×#17012
C101×#16902
C101×#16872
C101×#16422
C101×#16402
C101×#16272
C101×#16252
C101×#15902
#20298101