Finite Group Databasebeta

← C101×#19413 #38801564

Subgroups — C101×#19413 #38801564

Order 25856.

628 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3210C211yesmaximal, characteristic, complemented
2C101×#3115C211yesmaximal, characteristic
3C101×#3107C211yesmaximal, characteristic, complemented
4C101×#2988C211yesmaximal, characteristic, complemented
5C101×#1682C211yesmaximal, characteristic, complemented
6C101×#1681C211yesmaximal, characteristic, complemented
7C101×#1680C211yesmaximal, characteristic, complemented
8C101×#1679C211yesmaximal, characteristic, complemented
9C101×#1670C211yesmaximal, characteristic, complemented
10C101×#1669C211yesmaximal, characteristic, complemented
11C101×#1666C211yesmaximal, characteristic, complemented
12C101×#1665C211yesmaximal, characteristic, complemented
13C101×#1572C211yesmaximal, characteristic, complemented
14C101×#1552C211yesmaximal, characteristic, complemented
15C101×#1540C211yesmaximal, characteristic, complemented
16#533×C101C2211yescharacteristic
17#532×C101C2211yescharacteristic
18C4×#41×C101C2211yescharacteristic
19#494×C101C2211yescharacteristic
20#492×C101C2211yescharacteristic
21#487×C101C2211yescharacteristic
22#486×C101C2211yescharacteristic
23#485×C101—21no—
24#482×C101—21no—
25#475×C101C2211yescharacteristic
26#475×C101C2211yescharacteristic
27#474×C101C2211yescharacteristic
28#474×C101C2211yescharacteristic
29#464×C101—21no—
30#464×C101—21no—
31#462×C101C2211yescharacteristic
32#461×C101C2211yescharacteristic
33#460×C101C2211yescharacteristic
34#459×C101C2211yescharacteristic
35#452×C101—21no—
36#452×C101—21no—
37#452×C101—21no—
38#449×C101—21no—
39C8×Q8×C101C2211yescharacteristic
40C8×Q8×C101C2211yescharacteristic
41#442×C101—21no—
42#440×C101—21no—
43C4×Q16×C101—21no—
44C4×SD16×C101—21no—
45C8×D4×C101—21no—
46C8×D4×C101—21no—
47C8×D4×C101C2211yescharacteristic
48C8×D4×C101C2211yescharacteristic
49#432×C101C2211yescharacteristic
50#431×C101—21no—
51#431×C101C2211yescharacteristic
52#431×C101C2211yescharacteristic
53C2×C4⋊C8×C101—21no—
54C2×C4⋊C8×C101C2211yescharacteristic
55#335×C101C2211yescharacteristic
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#334×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62#332×C101C2211yescharacteristic
63#332×C101C2211yescharacteristic
64#332×C101C2211yescharacteristic
65#331×C101C2211yescharacteristic
66#331×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101D411yescharacteristic
69C2×Q16×C101—21no—
70C2×Q16×C101—21no—
71C2×Q16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×D8×C101—21no—
77C22×C8×C101—21no—
78C22×C8×C101—21no—
79C22×C8×C101—21no—
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101C2311yescharacteristic
84#125×C101—21no—
85#124×C101—21no—
86C22⋊Q8×C101—21no—
87C22⋊Q8×C101—21no—
88#121×C101—21no—
89#121×C101—21no—
90C4×Q8×C101—21no—
91C4×Q8×C101—21no—
92C4×Q8×C101D411yescharacteristic
93C4×Q8×C101C2311yescharacteristic
94C4×D4×C101—21no—
95C4×D4×C101—21no—
96C4×D4×C101—21no—
97C4×D4×C101—21no—
98C4×D4×C101D411yescharacteristic
99C4×D4×C101C2311yescharacteristic
100#117×C101—21no—
101#117×C101—21no—
102#117×C101D411yescharacteristic
103C2×C42×C101—21no—
104C2×C42×C101C2311yescharacteristic
105#107×C101—21no—
106#107×C101—21no—
107#106×C101—21no—
108#106×C101—21no—
109C4⋊C8×C101—21no—
110C4⋊C8×C101—21no—
111C4⋊C8×C101—21no—
112C4⋊C8×C101D411yescharacteristic
113C4⋊C8×C101D411yescharacteristic
114C4⋊C8×C101C2311yescharacteristic
115C4⋊C8×C101C2311yescharacteristic
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×C101—21no—
125#103×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—
132C22⋊C8×C101—21no—
133C22⋊C8×C101—21no—
134C22⋊C8×C101—21no—
135C22⋊C8×C101—21no—
136C22⋊C8×C101D411yescharacteristic
137C22⋊C8×C101D411yescharacteristic
138#97×C101—21no—
139C4×C8×C101—21no—
140C4×C8×C101—21no—
141C4×C8×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—22no—
145#41×C101—22no—
146#41×C101—81no—
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—21no—
156C2×D4×C101—41no—
157C2×D4×C101C2×D411yescharacteristic
158C22×C4×C101—21no—
159C22×C4×C101—21no—
160C22×C4×C101—21no—
161C22×C4×C101—41no—
162C22×C4×C101C2×D411yescharacteristic
163C22×C4×C101C2×D411yescharacteristic
164C22×C4×C101#4111yescharacteristic
165Q16×C101—42no—
166Q16×C101—81no—
167Q16×C101—81no—
168SD16×C101—42no—
169SD16×C101—42no—
170SD16×C101—81no—
171SD16×C101—81no—
172D8×C101—42no—
173C2×C8×C101—21no—
174C2×C8×C101—21no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—21no—
179C2×C8×C101—81no—
180C2×C8×C101—81no—
181C2×C8×C101—81no—
182C2×C8×C101C2×D411yescharacteristic
183C2×C8×C101C2×D411yescharacteristic
184C2×C8×C101C2×D411yescharacteristic
185C2×C8×C101C2×D411yescharacteristic
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—21no—
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—21no—
192C4⋊C4×C101—21no—
193C4⋊C4×C101—21no—
194C4⋊C4×C101—41no—
195C4⋊C4×C101—41no—
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C22⋊C4×C101—21no—
199C22⋊C4×C101—21no—
200C22⋊C4×C101—21no—
201C22⋊C4×C101—41no—
202C22⋊C4×C101—41no—
203C22⋊C4×C101—41no—
204C42×C101—21no—
205C42×C101—21no—
206C42×C101—21no—
207C42×C101—41no—
208C42×C101C2×D411yescharacteristic
209C42×C101C2×D411yescharacteristic
210C42×C101#4111yescharacteristic
211C42×C101C2411yescharacteristic
212C23×C101—21no—
213C23×C101—41no—
214C23×C101#12111yescharacteristic
215Q8×C101—21no—
216Q8×C101—41no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—41no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101#13512yes—
223D4×C101—24no—
224D4×C101—21no—
225D4×C101—41no—
226D4×C101—41no—
227D4×C101—41no—
228D4×C101—41no—
229D4×C101—81no—
230D4×C101—82no—
231D4×C101#13512yes—
232C2×C4×C101—24no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—21no—
237C2×C4×C101—21no—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—81no—
247C2×C4×C101—82no—
248C2×C4×C101#12111yescharacteristic
249C2×C4×C101#12111yescharacteristic
250C2×C4×C101#12111yescharacteristic
251C2×C4×C101C22×D411yescharacteristic
252C2×C4×C101C22×D411yescharacteristic
253C2×C4×C101C2×#4111yescharacteristic
254C8×C101—21no—
255C8×C101—21no—
256C8×C101—21no—
257C8×C101—21no—
258C8×C101—41no—
259C8×C101—41no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C22×C101—21no—
265C22×C101—21no—
266C22×C101—22no—
267C22×C101—21no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—81no—
271C22×C101—81no—
272C22×C101—81no—
273C22×C101C2×#12111yescharacteristic
274C4×C101—21no—
275C4×C101—21no—
276C4×C101—22no—
277C4×C101—21no—
278C4×C101—21no—
279C4×C101—41no—
280C4×C101—41no—
281C4×C101—81no—
282C4×C101—81no—
283C4×C101—81no—
284C4×C101C2×#13511yescharacteristic
285C4×C101C2×#13511yescharacteristic
286C4×C101#57611yescharacteristic
287C4×C101#57711yescharacteristic
288#19413C10111yesmaximal, characteristic, direct product factor, Sylow
289C2×C101—41no—
290C2×C101—42no—
291C2×C101—161no—
292C2×C101#304511yescharacteristic
293C2×C101#305011yescharacteristic
294C2×C101#306911yescharacteristic
295#3210C2×C10111yescharacteristic, complemented
296#3115C2×C10111yescharacteristic
297#3107C2×C10111yescharacteristic, complemented
298#2988C2×C10111yescharacteristic, complemented
299#1682C2×C10111yescharacteristic, complemented
300#1681C2×C10111yescharacteristic, complemented
301#1680C2×C10111yescharacteristic, complemented
302#1679C2×C10111yescharacteristic, complemented
303#1670C2×C10111yescharacteristic, complemented
304#1669C2×C10111yescharacteristic, complemented
305#1666C2×C10111yescharacteristic, complemented
306#1665C2×C10111yescharacteristic, complemented
307#1572C2×C10111yescharacteristic, complemented
308#1552C2×C10111yescharacteristic, complemented
309#1540C2×C10111yescharacteristic, complemented
310C101#1941311yescharacteristic, direct product factor, Sylow
311#533C22×C10111yescharacteristic
312#532C22×C10111yescharacteristic
313C4×#41C22×C10111yescharacteristic
314#494C22×C10111yescharacteristic
315#492C22×C10111yescharacteristic
316#487C22×C10111yescharacteristic
317#486C22×C10111yescharacteristic
318#485—21no—
319#482—21no—
320#475C22×C10111yescharacteristic
321#475C22×C10111yescharacteristic
322#474C22×C10111yescharacteristic
323#474C22×C10111yescharacteristic
324#464—21no—
325#464—21no—
326#462C22×C10111yescharacteristic
327#461C22×C10111yescharacteristic
328#460C22×C10111yescharacteristic
329#459C22×C10111yescharacteristic
330#452—21no—
331#452—21no—
332#452—21no—
333#449—21no—
334C8×Q8C22×C10111yescharacteristic
335C8×Q8C22×C10111yescharacteristic
336#442—21no—
337#440—21no—
338C4×Q16—21no—
339C4×SD16—21no—
340C8×D4—21no—
341C8×D4—21no—
342C8×D4C22×C10111yescharacteristic
343C8×D4C22×C10111yescharacteristic
344#432C22×C10111yescharacteristic
345#431—21no—
346#431C22×C10111yescharacteristic
347#431C22×C10111yescharacteristic
348C2×C4⋊C8—21no—
349C2×C4⋊C8C22×C10111yescharacteristic
350#335C22×C10111yescharacteristic
351#335C22×C10111yescharacteristic
352#334C22×C10111yescharacteristic
353#334C22×C10111yescharacteristic
354#332C22×C10111yescharacteristic
355#332C22×C10111yescharacteristic
356#332C22×C10111yescharacteristic
357#332C22×C10111yescharacteristic
358#332C22×C10111yescharacteristic
359#332C22×C10111yescharacteristic
360#331C22×C10111yescharacteristic
361#331C22×C10111yescharacteristic
362C2×#41—21no—
363C2×#41D4×C10111yescharacteristic
364C2×Q16—21no—
365C2×Q16—21no—
366C2×Q16—21no—
367C2×SD16—21no—
368C2×SD16—21no—
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C4⋊Q8C23×C10111yescharacteristic
376C4⋊Q8C23×C10111yescharacteristic
377C4⋊Q8C23×C10111yescharacteristic
378#127C23×C10111yescharacteristic
379#125—21no—
380#124—21no—
381C22⋊Q8—21no—
382C22⋊Q8—21no—
383#121—21no—
384#121—21no—
385C4×Q8—21no—
386C4×Q8—21no—
387C4×Q8D4×C10111yescharacteristic
388C4×Q8C23×C10111yescharacteristic
389C4×D4—21no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4D4×C10111yescharacteristic
394C4×D4C23×C10111yescharacteristic
395#117—21no—
396#117—21no—
397#117D4×C10111yescharacteristic
398C2×C42—21no—
399C2×C42C23×C10111yescharacteristic
400#107—21no—
401#107—21no—
402#106—21no—
403#106—21no—
404C4⋊C8—21no—
405C4⋊C8—21no—
406C4⋊C8—21no—
407C4⋊C8D4×C10111yescharacteristic
408C4⋊C8D4×C10111yescharacteristic
409C4⋊C8C23×C10111yescharacteristic
410C4⋊C8C23×C10111yescharacteristic
411C4⋊C8C23×C10111yescharacteristic
412C4⋊C8C23×C10111yescharacteristic
413C4⋊C8C23×C10111yescharacteristic
414C4⋊C8C23×C10111yescharacteristic
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103—21no—
420#103—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8D4×C10111yescharacteristic
432C22⋊C8D4×C10111yescharacteristic
433#97—21no—
434C4×C8—21no—
435C4×C8—21no—
436C4×C8—21no—
437C4×C8C23×C10111yescharacteristic
438C4×C8C23×C10111yescharacteristic
439#41—22no—
440#41—22no—
441#41—81no—
442#41—81no—
443C2×Q8—21no—
444C2×Q8—21no—
445C2×Q8—21no—
446C2×Q8C2×D4×C10111yescharacteristic
447C2×D4—21no—
448C2×D4—21no—
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—41no—
452C2×D4C2×D4×C10111yescharacteristic
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—41no—
457C22×C4C2×D4×C10111yescharacteristic
458C22×C4C2×D4×C10111yescharacteristic
459C22×C4#41×C10111yescharacteristic
460Q16—42no—
461Q16—81no—
462Q16—81no—
463SD16—42no—
464SD16—42no—
465SD16—81no—
466SD16—81no—
467D8—42no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—81no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8C2×D4×C10111yescharacteristic
478C2×C8C2×D4×C10111yescharacteristic
479C2×C8C2×D4×C10111yescharacteristic
480C2×C8C2×D4×C10111yescharacteristic
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4C2×D4×C10111yescharacteristic
492C4⋊C4C2×D4×C10111yescharacteristic
493C22⋊C4—21no—
494C22⋊C4—21no—
495C22⋊C4—21no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C42—21no—
500C42—21no—
501C42—21no—
502C42—41no—
503C42C2×D4×C10111yescharacteristic
504C42C2×D4×C10111yescharacteristic
505C42#41×C10111yescharacteristic
506C42C24×C10111yescharacteristic
507C23—21no—
508C23—41no—
509C23#121×C10111yescharacteristic
510Q8—21no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517Q8#135×C10112yes—
518D4—24no—
519D4—21no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—81no—
525D4—82no—
526D4#135×C10112yes—
527C2×C4—24no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—81no—
542C2×C4—82no—
543C2×C4#121×C10111yescharacteristic
544C2×C4#121×C10111yescharacteristic
545C2×C4#121×C10111yescharacteristic
546C2×C4C22×D4×C10111yescharacteristic
547C2×C4C22×D4×C10111yescharacteristic
548C2×C4C2×#41×C10111yescharacteristic
549C8—21no—
550C8—21no—
551C8—21no—
552C8—21no—
553C8—41no—
554C8—41no—
555C8—41no—
556C8—41no—
557C8—41no—
558C8—41no—
559C22—21no—
560C22—21no—
561C22—22no—
562C22—21no—
563C22—41no—
564C22—41no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22C2×#121×C10111yescharacteristic
569C4—21no—
570C4—21no—
571C4—22no—
572C4—21no—
573C4—21no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4C2×#135×C10111yescharacteristic
580C4C2×#135×C10111yescharacteristic
581C4#576×C10111yescharacteristic
582C4#577×C10111yescharacteristic
583C2—41no—
584C2—42no—
585C2—161no—
586C2C101×#304511yescharacteristic
587C2C101×#305011yescharacteristic
588C2C101×#306911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3115C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C101×#3210C2semidirect
3. C101×#3107C2semidirect
4. C101×#2988C2semidirect
5. C101×#1682C2semidirect
6. C101×#1681C2semidirect
7. C101×#1680C2semidirect
8. C101×#1679C2semidirect
9. C101×#1670C2semidirect
10. C101×#1669C2semidirect
11. C101×#1666C2semidirect
12. C101×#1665C2semidirect
13. C101×#1572C2semidirect
14. C101×#1552C2semidirect
15. C101×#1540C2semidirect
288. #19413C101direct (N × H)
295. #3210C2×C101semidirect
297. #3107C2×C101semidirect
298. #2988C2×C101semidirect
299. #1682C2×C101semidirect
300. #1681C2×C101semidirect
301. #1680C2×C101semidirect
302. #1679C2×C101semidirect
303. #1670C2×C101semidirect
304. #1669C2×C101semidirect
305. #1666C2×C101semidirect
306. #1665C2×C101semidirect
307. #1572C2×C101semidirect
308. #1552C2×C101semidirect
309. #1540C2×C101semidirect
310. C101#19413direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32102
C101×#31152
C101×#31072
C101×#29882
C101×#16822
C101×#16812
C101×#16802
C101×#16792
C101×#16702
C101×#16692
C101×#16662
C101×#16652
C101×#15722
C101×#15522
C101×#15402
#19413101