Finite Group Databasebeta

← C101×#20250 #38802401

Subgroups — C101×#20250 #38802401

Order 25856.

666 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3393C211yesmaximal, characteristic, complemented
2C101×#3353C211yesmaximal, characteristic, complemented
3C101×#3324C211yesmaximal, characteristic, complemented
4C101×#3272C211yesmaximal, characteristic
5C101×#1722C211yesmaximal, characteristic, complemented
6C101×#1701C211yesmaximal, characteristic, complemented
7C101×#1693C211yesmaximal, characteristic, complemented
8C101×#1689C211yesmaximal, characteristic, complemented
9C101×#1666C211yesmaximal, characteristic, complemented
10C101×#1650C211yesmaximal, characteristic, complemented
11C101×#1647C211yesmaximal, characteristic, complemented
12C101×#1639C211yesmaximal, characteristic, complemented
13C101×#1628C211yesmaximal, characteristic, complemented
14C101×#1594C211yesmaximal, characteristic, complemented
15C101×#1583C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C101—21no—
17#556×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic, complemented
19#547×C101C2211yescharacteristic
20D42×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic, complemented
22#500×C101C2211yescharacteristic, complemented
23#495×C101—21no—
24#494×C101C2211yescharacteristic, complemented
25#492×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#484×C101—21no—
29#482×C101—21no—
30#482×C101—21no—
31#475×C101C2211yescharacteristic, complemented
32#474×C101C2211yescharacteristic
33#474×C101C2211yescharacteristic
34#468×C101—21no—
35#468×C101—21no—
36#468×C101—21no—
37#464×C101—21no—
38#464×C101—21no—
39#461×C101C2211yescharacteristic
40#461×C101C2211yescharacteristic
41#461×C101C2211yescharacteristic, complemented
42#460×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#450×C101—21no—
45#450×C101—21no—
46#449×C101—21no—
47C8×Q8×C101C2211yescharacteristic, complemented
48C4×Q16×C101—21no—
49C4×SD16×C101C2211yescharacteristic
50C4×D8×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic, complemented
54#428×C101—21no—
55#418×C101—21no—
56#334×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#332×C101C2211yescharacteristic, complemented
59#332×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic, complemented
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic, complemented
66#322×C101C2211yescharacteristic, complemented
67C2×#41×C101—21no—
68C22×D4×C101—21no—
69C22×D4×C101—21no—
70AGL(1,ℤ/8)×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×C101—21no—
79C2×SD16×C101D411yescharacteristic
80C2×D8×C101—21no—
81C2×D8×C101D411yescharacteristic
82C2×M16×C101—21no—
83C2×M16×C101—21no—
84C2×M16×C101—21no—
85C4⋊Q8×C101C2311yescharacteristic
86C4⋊Q8×C101C2311yescharacteristic
87C4⋊Q8×C101C2311yescharacteristic
88#127×C101C2311yescharacteristic
89#126×C101—41no—
90#126×C101—41no—
91#124×C101—21no—
92#124×C101—21no—
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#120×C101—41no—
101C4×Q8×C101—21no—
102C4×Q8×C101—21no—
103C4×Q8×C101C2311yescharacteristic
104C4×D4×C101C2311yescharacteristic
105C4×D4×C101C2311yescharacteristic
106C4×D4×C101C2311yescharacteristic
107#117×C101—21no—
108#117×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—41no—
115#107×C101D411yescharacteristic
116#106×C101—21no—
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×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—41no—
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141C4×C8×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145C24×C101—41no—
146#41×C101—42no—
147#41×C101—81no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101C2×D411yescharacteristic
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—81no—
161C2×D4×C101—81no—
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—
169Q16×C101—42no—
170Q16×C101—81no—
171SD16×C101—41no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—81no—
175SD16×C101—81no—
176SD16×C101—81no—
177SD16×C101—81no—
178D8×C101—22no—
179D8×C101—42no—
180M16×C101—42no—
181M16×C101—42no—
182M16×C101—81no—
183C2×C8×C101—21no—
184C2×C8×C101—21no—
185C2×C8×C101—21no—
186C2×C8×C101—21no—
187C2×C8×C101—21no—
188C2×C8×C101C2×D411yescharacteristic
189C2×C8×C101C2×D411yescharacteristic
190C2×C8×C101C2×D411yescharacteristic
191C2×C8×C101C2×D411yescharacteristic
192C4⋊C4×C101—21no—
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—21no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C22⋊C4×C101—41no—
213C22⋊C4×C101—41no—
214C22⋊C4×C101—41no—
215C42×C101—21no—
216C42×C101—41no—
217C42×C101—41no—
218C42×C101C2411yescharacteristic
219C23×C101—21no—
220C23×C101—21no—
221C23×C101—21no—
222C23×C101—41no—
223C23×C101—82no—
224C23×C101—82no—
225C23×C101—161no—
226Q8×C101—21no—
227Q8×C101—21no—
228Q8×C101—41no—
229Q8×C101—41no—
230Q8×C101—41no—
231Q8×C101—41no—
232Q8×C101—41no—
233Q8×C101—41no—
234D4×C101—21no—
235D4×C101—21no—
236D4×C101—21no—
237D4×C101—21no—
238D4×C101—21no—
239D4×C101—21no—
240D4×C101—41no—
241D4×C101—41no—
242D4×C101—41no—
243D4×C101—41no—
244D4×C101—81no—
245D4×C101—82no—
246D4×C101—82no—
247D4×C101—82no—
248C2×C4×C101—21no—
249C2×C4×C101—21no—
250C2×C4×C101—21no—
251C2×C4×C101—21no—
252C2×C4×C101—21no—
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×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×C101AGL(1,ℤ/8)12yes—
275C22×C101—41no—
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×C101—164no—
288C22×C101D4211yescharacteristic
289C4×C101—21no—
290C4×C101—41no—
291C4×C101—41no—
292C4×C101—41no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—81no—
296C4×C101—81no—
297C4×C101—81no—
298C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
299C4×C101#57511yescharacteristic
300C4×C101#57611yescharacteristic
301C4×C101#57711yescharacteristic
302#20250C10111yesmaximal, characteristic, direct product factor, Sylow
303C2×C101—81no—
304C2×C101—81no—
305C2×C101—81no—
306C2×C101—161no—
307C2×C101#326711yescharacteristic
308C2×C101#327411yescharacteristic
309C2×C101#328911yescharacteristic
310#3393C2×C10111yescharacteristic, complemented
311#3353C2×C10111yescharacteristic, complemented
312#3324C2×C10111yescharacteristic, complemented
313#3272C2×C10111yescharacteristic
314#1722C2×C10111yescharacteristic, complemented
315#1701C2×C10111yescharacteristic, complemented
316#1693C2×C10111yescharacteristic, complemented
317#1689C2×C10111yescharacteristic, complemented
318#1666C2×C10111yescharacteristic, complemented
319#1650C2×C10111yescharacteristic, complemented
320#1647C2×C10111yescharacteristic, complemented
321#1639C2×C10111yescharacteristic, complemented
322#1628C2×C10111yescharacteristic, complemented
323#1594C2×C10111yescharacteristic, complemented
324#1583C2×C10111yescharacteristic, complemented
325C101#2025011yescharacteristic, direct product factor, Sylow
326C2×AGL(1,ℤ/8)—21no—
327#556C22×C10111yescharacteristic
328#556C22×C10111yescharacteristic, complemented
329#547C22×C10111yescharacteristic
330D42C22×C10111yescharacteristic
331#500C22×C10111yescharacteristic, complemented
332#500C22×C10111yescharacteristic, complemented
333#495—21no—
334#494C22×C10111yescharacteristic, complemented
335#492C22×C10111yescharacteristic
336#486C22×C10111yescharacteristic
337#486C22×C10111yescharacteristic
338#484—21no—
339#482—21no—
340#482—21no—
341#475C22×C10111yescharacteristic, complemented
342#474C22×C10111yescharacteristic
343#474C22×C10111yescharacteristic
344#468—21no—
345#468—21no—
346#468—21no—
347#464—21no—
348#464—21no—
349#461C22×C10111yescharacteristic
350#461C22×C10111yescharacteristic
351#461C22×C10111yescharacteristic, complemented
352#460C22×C10111yescharacteristic
353#459C22×C10111yescharacteristic
354#450—21no—
355#450—21no—
356#449—21no—
357C8×Q8C22×C10111yescharacteristic, complemented
358C4×Q16—21no—
359C4×SD16C22×C10111yescharacteristic
360C4×D8C22×C10111yescharacteristic
361#436C22×C10111yescharacteristic
362#436C22×C10111yescharacteristic
363#436C22×C10111yescharacteristic, complemented
364#428—21no—
365#418—21no—
366#334C22×C10111yescharacteristic, complemented
367#334C22×C10111yescharacteristic, complemented
368#332C22×C10111yescharacteristic, complemented
369#332C22×C10111yescharacteristic, complemented
370#332C22×C10111yescharacteristic, complemented
371#331C22×C10111yescharacteristic
372Q8⋊C8C22×C10111yescharacteristic, complemented
373D4⋊C8C22×C10111yescharacteristic
374D4⋊C8C22×C10111yescharacteristic
375D4⋊C8C22×C10111yescharacteristic, complemented
376#322C22×C10111yescharacteristic, complemented
377C2×#41—21no—
378C22×D4—21no—
379C22×D4—21no—
380AGL(1,ℤ/8)—44no—
381C2×Q16—21no—
382C2×Q16—21no—
383C2×SD16—21no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—21no—
388C2×SD16—21no—
389C2×SD16D4×C10111yescharacteristic
390C2×D8—21no—
391C2×D8D4×C10111yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C4⋊Q8C23×C10111yescharacteristic
396C4⋊Q8C23×C10111yescharacteristic
397C4⋊Q8C23×C10111yescharacteristic
398#127C23×C10111yescharacteristic
399#126—41no—
400#126—41no—
401#124—21no—
402#124—21no—
403#123—41no—
404C22⋊Q8—21no—
405C22⋊Q8—21no—
406C22⋊Q8—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#120—41no—
411C4×Q8—21no—
412C4×Q8—21no—
413C4×Q8C23×C10111yescharacteristic
414C4×D4C23×C10111yescharacteristic
415C4×D4C23×C10111yescharacteristic
416C4×D4C23×C10111yescharacteristic
417#117—21no—
418#117—21no—
419C2×C4⋊C4—21no—
420#107—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107—41no—
425#107D4×C10111yescharacteristic
426#106—21no—
427#106D4×C10111yescharacteristic
428C4⋊C8—21no—
429C4⋊C8C23×C10111yescharacteristic
430C4⋊C8C23×C10111yescharacteristic
431C4⋊C8C23×C10111yescharacteristic
432C4⋊C8C23×C10111yescharacteristic
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—21no—
444#102—41no—
445#102D4×C10111yescharacteristic
446#102D4×C10111yescharacteristic
447#102D4×C10111yescharacteristic
448C22⋊C8—21no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C4×C8—21no—
452C4×C8C23×C10111yescharacteristic
453C4×C8C23×C10111yescharacteristic
454C4×C8C23×C10111yescharacteristic
455C24—41no—
456#41—42no—
457#41—81no—
458C2×Q8—21no—
459C2×Q8—21no—
460C2×Q8—21no—
461C2×Q8C2×D4×C10111yescharacteristic
462C2×D4—21no—
463C2×D4—21no—
464C2×D4—21no—
465C2×D4—41no—
466C2×D4—41no—
467C2×D4—42no—
468C2×D4—42no—
469C2×D4—41no—
470C2×D4—81no—
471C2×D4—81no—
472C2×D4C2×D4×C10111yescharacteristic
473C2×D4C2×D4×C10111yescharacteristic
474C2×D4C2×D4×C10111yescharacteristic
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—41no—
479Q16—42no—
480Q16—81no—
481SD16—41no—
482SD16—42no—
483SD16—42no—
484SD16—81no—
485SD16—81no—
486SD16—81no—
487SD16—81no—
488D8—22no—
489D8—42no—
490M16—42no—
491M16—42no—
492M16—81no—
493C2×C8—21no—
494C2×C8—21no—
495C2×C8—21no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8C2×D4×C10111yescharacteristic
499C2×C8C2×D4×C10111yescharacteristic
500C2×C8C2×D4×C10111yescharacteristic
501C2×C8C2×D4×C10111yescharacteristic
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—41no—
510C4⋊C4—41no—
511C4⋊C4—41no—
512C4⋊C4C2×D4×C10111yescharacteristic
513C4⋊C4C2×D4×C10111yescharacteristic
514C4⋊C4C2×D4×C10111yescharacteristic
515C4⋊C4C2×D4×C10111yescharacteristic
516C22⋊C4—21no—
517C22⋊C4—21no—
518C22⋊C4—21no—
519C22⋊C4—41no—
520C22⋊C4—41no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C42—21no—
526C42—41no—
527C42—41no—
528C42C24×C10111yescharacteristic
529C23—21no—
530C23—21no—
531C23—21no—
532C23—41no—
533C23—82no—
534C23—82no—
535C23—161no—
536Q8—21no—
537Q8—21no—
538Q8—41no—
539Q8—41no—
540Q8—41no—
541Q8—41no—
542Q8—41no—
543Q8—41no—
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—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—41no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—82no—
573C2×C4C22×D4×C10111yescharacteristic
574C2×C4C22×D4×C10111yescharacteristic
575C2×C4H(5,𝔽2)×C10111yescharacteristic
576C8—21no—
577C8—21no—
578C8—21no—
579C8—41no—
580C8—41no—
581C8—41no—
582C8—41no—
583C8—41no—
584C8AGL(1,ℤ/8)×C10112yes—
585C22—41no—
586C22—41no—
587C22—41no—
588C22—41no—
589C22—41no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—81no—
595C22—81no—
596C22—81no—
597C22—164no—
598C22D42×C10111yescharacteristic
599C4—21no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—41no—
605C4—81no—
606C4—81no—
607C4—81no—
608C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
609C4#575×C10111yescharacteristic
610C4#576×C10111yescharacteristic
611C4#577×C10111yescharacteristic
612C2—81no—
613C2—81no—
614C2—81no—
615C2—161no—
616C2C101×#326711yescharacteristic
617C2C101×#327411yescharacteristic
618C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3272C2
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×#3393C2semidirect
2. C101×#3353C2semidirect
3. C101×#3324C2semidirect
5. C101×#1722C2semidirect
6. C101×#1701C2semidirect
7. C101×#1693C2semidirect
8. C101×#1689C2semidirect
9. C101×#1666C2semidirect
10. C101×#1650C2semidirect
11. C101×#1647C2semidirect
12. C101×#1639C2semidirect
13. C101×#1628C2semidirect
14. C101×#1594C2semidirect
15. C101×#1583C2semidirect
18. #556×C101C22semidirect
21. #500×C101C22semidirect
22. #500×C101C22semidirect
24. #494×C101C22semidirect
31. #475×C101C22semidirect
41. #461×C101C22semidirect
47. C8×Q8×C101C22semidirect
53. #436×C101C22semidirect
56. #334×C101C22semidirect
57. #334×C101C22semidirect
58. #332×C101C22semidirect
59. #332×C101C22semidirect
60. #332×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
65. D4⋊C8×C101C22semidirect
66. #322×C101C22semidirect
302. #20250C101direct (N × H)
310. #3393C2×C101semidirect
311. #3353C2×C101semidirect
312. #3324C2×C101semidirect
314. #1722C2×C101semidirect
315. #1701C2×C101semidirect
316. #1693C2×C101semidirect
317. #1689C2×C101semidirect
318. #1666C2×C101semidirect
319. #1650C2×C101semidirect
320. #1647C2×C101semidirect
321. #1639C2×C101semidirect
322. #1628C2×C101semidirect
323. #1594C2×C101semidirect
324. #1583C2×C101semidirect
325. C101#20250direct (N × H)
328. #556C22×C101semidirect
331. #500C22×C101semidirect
332. #500C22×C101semidirect
334. #494C22×C101semidirect
341. #475C22×C101semidirect
351. #461C22×C101semidirect
357. C8×Q8C22×C101semidirect
363. #436C22×C101semidirect
366. #334C22×C101semidirect
367. #334C22×C101semidirect
368. #332C22×C101semidirect
369. #332C22×C101semidirect
370. #332C22×C101semidirect
372. Q8⋊C8C22×C101semidirect
375. D4⋊C8C22×C101semidirect
376. #322C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33932
C101×#33532
C101×#33242
C101×#32722
C101×#17222
C101×#17012
C101×#16932
C101×#16892
C101×#16662
C101×#16502
C101×#16472
C101×#16392
C101×#16282
C101×#15942
C101×#15832
#20250101