Finite Group Databasebeta

← C101×#20243 #38802394

Subgroups — C101×#20243 #38802394

Order 25856.

674 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3354C211yesmaximal, characteristic, complemented
2C101×#3341C211yesmaximal, characteristic, complemented
3C101×#3325C211yesmaximal, characteristic, complemented
4C101×#3272C211yesmaximal, characteristic, complemented
5C101×#1714C211yesmaximal, characteristic, complemented
6C101×#1697C211yesmaximal, characteristic, complemented
7C101×#1695C211yesmaximal, characteristic, complemented
8C101×#1691C211yesmaximal, characteristic, complemented
9C101×#1665C211yesmaximal, characteristic, complemented
10C101×#1646C211yesmaximal, characteristic, complemented
11C101×#1635C211yesmaximal, characteristic, complemented
12C101×#1629C211yesmaximal, characteristic, complemented
13C101×#1624C211yesmaximal, characteristic, complemented
14C101×#1594C211yesmaximal, characteristic, complemented
15C101×#1581C211yesmaximal, characteristic, complemented
16C2×AGL(1,ℤ/8)×C101—21no—
17#555×C101C2211yescharacteristic
18#555×C101C2211yescharacteristic, complemented
19#547×C101C2211yescharacteristic
20D42×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic, complemented
22#498×C101C2211yescharacteristic, complemented
23#492×C101C2211yescharacteristic
24#492×C101C2211yescharacteristic
25#487×C101C2211yescharacteristic, complemented
26#486×C101C2211yescharacteristic
27#482×C101—21no—
28#482×C101—21no—
29#482×C101—21no—
30#482×C101—21no—
31#481×C101—21no—
32#476×C101C2211yescharacteristic
33#476×C101C2211yescharacteristic
34#476×C101C2211yescharacteristic
35#476×C101C2211yescharacteristic, complemented
36#474×C101C2211yescharacteristic, complemented
37#469×C101—21no—
38#469×C101—21no—
39#468×C101—21no—
40#466×C101—21no—
41#461×C101C2211yescharacteristic
42#459×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#450×C101—21no—
45#449×C101—21no—
46#447×C101—21no—
47C4×D8×C101C2211yescharacteristic
48C4×D8×C101C2211yescharacteristic
49#436×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic, complemented
52C8×D4×C101C2211yescharacteristic, complemented
53#428×C101—21no—
54#427×C101—21no—
55#418×C101—21no—
56#335×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#333×C101C2211yescharacteristic, complemented
59#333×C101C2211yescharacteristic, complemented
60#332×C101C2211yescharacteristic, complemented
61#331×C101C2211yescharacteristic
62D4⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic, complemented
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×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—41no—
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C2×D8×C101D411yescharacteristic
78C2×D8×C101D411yescharacteristic
79C2×M16×C101—21no—
80C2×M16×C101—21no—
81C2×M16×C101—21no—
82C22×C8×C101—21no—
83C4⋊Q8×C101C2311yescharacteristic
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86#127×C101C2311yescharacteristic
87#124×C101—41no—
88#124×C101—41no—
89#123×C101—41no—
90C22⋊Q8×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—21no—
98#120×C101—41no—
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101C4×D4×C101C2311yescharacteristic
102C4×D4×C101C2311yescharacteristic
103#117×C101—21no—
104#117×C101—21no—
105#117×C101—21no—
106#117×C101—21no—
107C2×C4⋊C4×C101—21no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101D411yescharacteristic
112#107×C101D411yescharacteristic
113#106×C101—21no—
114#106×C101—21no—
115#106×C101—21no—
116#106×C101—21no—
117#106×C101—21no—
118#106×C101—21no—
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
123#103×C101—21no—
124#103×C101—41no—
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—21no—
133#102×C101—21no—
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C22⋊C8×C101—21no—
141C22⋊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×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—41no—
155C2×D4×C101—41no—
156C2×D4×C101—42no—
157C2×D4×C101—42no—
158C2×D4×C101—41no—
159C2×D4×C101—41no—
160C2×D4×C101—41no—
161C2×D4×C101—81no—
162C2×D4×C101—81no—
163C2×D4×C101C2×D411yescharacteristic
164C2×D4×C101C2×D411yescharacteristic
165C2×D4×C101C2×D411yescharacteristic
166C2×D4×C101C2×D411yescharacteristic
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101—21no—
171C22×C4×C101—41no—
172SD16×C101—42no—
173SD16×C101—42no—
174SD16×C101—81no—
175SD16×C101—82no—
176D8×C101—22no—
177D8×C101—41no—
178D8×C101—42no—
179D8×C101—81no—
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×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×C101C2×D411yescharacteristic
201C4⋊C4×C101C2×D411yescharacteristic
202C4⋊C4×C101C2×D411yescharacteristic
203C4⋊C4×C101C2×D411yescharacteristic
204C22⋊C4×C101—21no—
205C22⋊C4×C101—21no—
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—41no—
215C42×C101—41no—
216C42×C101C2411yescharacteristic
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—21no—
220C23×C101—21no—
221C23×C101—41no—
222C23×C101—82no—
223C23×C101—82no—
224C23×C101—161no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—81no—
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—21no—
237D4×C101—41no—
238D4×C101—41no—
239D4×C101—41no—
240D4×C101—41no—
241D4×C101—81no—
242D4×C101—82no—
243D4×C101—82no—
244D4×C101—82no—
245D4×C101—161no—
246D4×C101—161no—
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×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—41no—
285C22×C101—41no—
286C22×C101—41no—
287C22×C101—81no—
288C22×C101—81no—
289C22×C101—81no—
290C22×C101—164no—
291C22×C101D4211yescharacteristic
292C4×C101—21no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—41no—
296C4×C101—41no—
297C4×C101—81no—
298C4×C101—81no—
299C4×C101—81no—
300C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
301C4×C101#57511yescharacteristic
302C4×C101#57711yescharacteristic
303C4×C101#57711yescharacteristic
304#20243C10111yesmaximal, characteristic, direct product factor, Sylow
305C2×C101—81no—
306C2×C101—81no—
307C2×C101—81no—
308C2×C101—81no—
309C2×C101—161no—
310C2×C101#326711yescharacteristic
311C2×C101#327211yescharacteristic
312C2×C101#328811yescharacteristic
313#3354C2×C10111yescharacteristic, complemented
314#3341C2×C10111yescharacteristic, complemented
315#3325C2×C10111yescharacteristic, complemented
316#3272C2×C10111yescharacteristic, complemented
317#1714C2×C10111yescharacteristic, complemented
318#1697C2×C10111yescharacteristic, complemented
319#1695C2×C10111yescharacteristic, complemented
320#1691C2×C10111yescharacteristic, complemented
321#1665C2×C10111yescharacteristic, complemented
322#1646C2×C10111yescharacteristic, complemented
323#1635C2×C10111yescharacteristic, complemented
324#1629C2×C10111yescharacteristic, complemented
325#1624C2×C10111yescharacteristic, complemented
326#1594C2×C10111yescharacteristic, complemented
327#1581C2×C10111yescharacteristic, complemented
328C101#2024311yescharacteristic, direct product factor, Sylow
329C2×AGL(1,ℤ/8)—21no—
330#555C22×C10111yescharacteristic
331#555C22×C10111yescharacteristic, complemented
332#547C22×C10111yescharacteristic
333D42C22×C10111yescharacteristic
334#500C22×C10111yescharacteristic, complemented
335#498C22×C10111yescharacteristic, complemented
336#492C22×C10111yescharacteristic
337#492C22×C10111yescharacteristic
338#487C22×C10111yescharacteristic, complemented
339#486C22×C10111yescharacteristic
340#482—21no—
341#482—21no—
342#482—21no—
343#482—21no—
344#481—21no—
345#476C22×C10111yescharacteristic
346#476C22×C10111yescharacteristic
347#476C22×C10111yescharacteristic
348#476C22×C10111yescharacteristic, complemented
349#474C22×C10111yescharacteristic, complemented
350#469—21no—
351#469—21no—
352#468—21no—
353#466—21no—
354#461C22×C10111yescharacteristic
355#459C22×C10111yescharacteristic
356#459C22×C10111yescharacteristic
357#450—21no—
358#449—21no—
359#447—21no—
360C4×D8C22×C10111yescharacteristic
361C4×D8C22×C10111yescharacteristic
362#436C22×C10111yescharacteristic
363#436C22×C10111yescharacteristic
364#436C22×C10111yescharacteristic, complemented
365C8×D4C22×C10111yescharacteristic, complemented
366#428—21no—
367#427—21no—
368#418—21no—
369#335C22×C10111yescharacteristic, complemented
370#334C22×C10111yescharacteristic, complemented
371#333C22×C10111yescharacteristic, complemented
372#333C22×C10111yescharacteristic, complemented
373#332C22×C10111yescharacteristic, complemented
374#331C22×C10111yescharacteristic
375D4⋊C8C22×C10111yescharacteristic
376D4⋊C8C22×C10111yescharacteristic
377D4⋊C8C22×C10111yescharacteristic, complemented
378D4⋊C8C22×C10111yescharacteristic, complemented
379#322C22×C10111yescharacteristic, complemented
380C2×#41—21no—
381C22×D4—21no—
382C22×D4—21no—
383AGL(1,ℤ/8)—44no—
384C2×SD16—21no—
385C2×SD16—21no—
386C2×SD16—21no—
387C2×SD16—41no—
388C2×D8—21no—
389C2×D8—21no—
390C2×D8D4×C10111yescharacteristic
391C2×D8D4×C10111yescharacteristic
392C2×M16—21no—
393C2×M16—21no—
394C2×M16—21no—
395C22×C8—21no—
396C4⋊Q8C23×C10111yescharacteristic
397C4⋊Q8C23×C10111yescharacteristic
398C4⋊Q8C23×C10111yescharacteristic
399#127C23×C10111yescharacteristic
400#124—41no—
401#124—41no—
402#123—41no—
403C22⋊Q8—21no—
404#121—21no—
405#121—21no—
406#121—21no—
407#121—21no—
408#121—21no—
409#121—21no—
410#121—21no—
411#120—41no—
412C4×D4C23×C10111yescharacteristic
413C4×D4C23×C10111yescharacteristic
414C4×D4C23×C10111yescharacteristic
415C4×D4C23×C10111yescharacteristic
416#117—21no—
417#117—21no—
418#117—21no—
419#117—21no—
420C2×C4⋊C4—21no—
421#107—21no—
422#107—21no—
423#107—21no—
424#107D4×C10111yescharacteristic
425#107D4×C10111yescharacteristic
426#106—21no—
427#106—21no—
428#106—21no—
429#106—21no—
430#106—21no—
431#106—21no—
432C4⋊C8C23×C10111yescharacteristic
433C4⋊C8C23×C10111yescharacteristic
434C4⋊C8C23×C10111yescharacteristic
435C4⋊C8C23×C10111yescharacteristic
436#103—21no—
437#103—41no—
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—21no—
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—81no—
461C2×Q8—21no—
462C2×Q8—21no—
463C2×Q8—21no—
464C2×D4—21no—
465C2×D4—21no—
466C2×D4—21no—
467C2×D4—41no—
468C2×D4—41no—
469C2×D4—42no—
470C2×D4—42no—
471C2×D4—41no—
472C2×D4—41no—
473C2×D4—41no—
474C2×D4—81no—
475C2×D4—81no—
476C2×D4C2×D4×C10111yescharacteristic
477C2×D4C2×D4×C10111yescharacteristic
478C2×D4C2×D4×C10111yescharacteristic
479C2×D4C2×D4×C10111yescharacteristic
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—41no—
485SD16—42no—
486SD16—42no—
487SD16—81no—
488SD16—82no—
489D8—22no—
490D8—41no—
491D8—42no—
492D8—81no—
493M16—42no—
494M16—42no—
495M16—81no—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—42no—
502C2×C8C2×D4×C10111yescharacteristic
503C2×C8C2×D4×C10111yescharacteristic
504C2×C8C2×D4×C10111yescharacteristic
505C2×C8C2×D4×C10111yescharacteristic
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—21no—
511C4⋊C4—21no—
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—21no—
521C22⋊C4—41no—
522C22⋊C4—41no—
523C22⋊C4—41no—
524C22⋊C4—41no—
525C22⋊C4—41no—
526C22⋊C4—41no—
527C42—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—81no—
541Q8—81no—
542D4—21no—
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—161no—
559D4—161no—
560C2×C4—21no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
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—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—82no—
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—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22—41no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—164no—
604C22D42×C10111yescharacteristic
605C4—21no—
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—81no—
611C4—81no—
612C4—81no—
613C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
614C4#575×C10111yescharacteristic
615C4#577×C10111yescharacteristic
616C4#577×C10111yescharacteristic
617C2—81no—
618C2—81no—
619C2—81no—
620C2—81no—
621C2—161no—
622C2C101×#326711yescharacteristic
623C2C101×#327211yescharacteristic
624C2C101×#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×#3354C2semidirect
2. C101×#3341C2semidirect
3. C101×#3325C2semidirect
4. C101×#3272C2semidirect
5. C101×#1714C2semidirect
6. C101×#1697C2semidirect
7. C101×#1695C2semidirect
8. C101×#1691C2semidirect
9. C101×#1665C2semidirect
10. C101×#1646C2semidirect
11. C101×#1635C2semidirect
12. C101×#1629C2semidirect
13. C101×#1624C2semidirect
14. C101×#1594C2semidirect
15. C101×#1581C2semidirect
18. #555×C101C22semidirect
21. #500×C101C22semidirect
22. #498×C101C22semidirect
25. #487×C101C22semidirect
35. #476×C101C22semidirect
36. #474×C101C22semidirect
51. #436×C101C22semidirect
52. C8×D4×C101C22semidirect
56. #335×C101C22semidirect
57. #334×C101C22semidirect
58. #333×C101C22semidirect
59. #333×C101C22semidirect
60. #332×C101C22semidirect
64. D4⋊C8×C101C22semidirect
65. D4⋊C8×C101C22semidirect
66. #322×C101C22semidirect
304. #20243C101direct (N × H)
313. #3354C2×C101semidirect
314. #3341C2×C101semidirect
315. #3325C2×C101semidirect
316. #3272C2×C101semidirect
317. #1714C2×C101semidirect
318. #1697C2×C101semidirect
319. #1695C2×C101semidirect
320. #1691C2×C101semidirect
321. #1665C2×C101semidirect
322. #1646C2×C101semidirect
323. #1635C2×C101semidirect
324. #1629C2×C101semidirect
325. #1624C2×C101semidirect
326. #1594C2×C101semidirect
327. #1581C2×C101semidirect
328. C101#20243direct (N × H)
331. #555C22×C101semidirect
334. #500C22×C101semidirect
335. #498C22×C101semidirect
338. #487C22×C101semidirect
348. #476C22×C101semidirect
349. #474C22×C101semidirect
364. #436C22×C101semidirect
365. C8×D4C22×C101semidirect
369. #335C22×C101semidirect
370. #334C22×C101semidirect
371. #333C22×C101semidirect
372. #333C22×C101semidirect
373. #332C22×C101semidirect
377. D4⋊C8C22×C101semidirect
378. D4⋊C8C22×C101semidirect
379. #322C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33542
C101×#33412
C101×#33252
C101×#32722
C101×#17142
C101×#16972
C101×#16952
C101×#16912
C101×#16652
C101×#16462
C101×#16352
C101×#16292
C101×#16242
C101×#15942
C101×#15812
#20243101