Finite Group Databasebeta

← C101×#24725 #38806876

Subgroups — C101×#24725 #38806876

Order 25856.

658 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3080C211yesmaximal, characteristic
2C2×#479×C101C211yesmaximal, characteristic, complemented
3C4×#137×C101C211yesmaximal, characteristic
4C101×#2925C211yesmaximal, characteristic
5C101×#2079C211yesmaximal, characteristic
6C101×#2078C211yesmaximal, characteristic
7C101×#2052C211yesmaximal, characteristic
8C101×#2052C211yesmaximal, characteristic
9C101×#1998C211yesmaximal, characteristic, complemented
10C101×#1952C211yesmaximal, characteristic, complemented
11C101×#1951C211yesmaximal, characteristic, complemented
12C101×#1950C211yesmaximal, characteristic, complemented
13C101×#1930C211yesmaximal, characteristic, complemented
14C101×#1930C211yesmaximal, characteristic, complemented
15C101×#1801C211yesmaximal, characteristic, complemented
16C2×#137×C101C2211yescharacteristic
17C2×#125×C101C2211yescharacteristic
18C4×#41×C101C2211yescharacteristic
19C2×C4×Q8×C101C2211yescharacteristic
20#479×C101—21no—
21#479×C101—21no—
22#479×C101—21no—
23#479×C101—21no—
24#479×C101—21no—
25#479×C101—21no—
26#478×C101—21no—
27#478×C101—21no—
28#441×C101—21no—
29#440×C101—21no—
30C4×Q16×C101—21no—
31C4×SD16×C101—21no—
32#433×C101—21no—
33#433×C101—21no—
34#432×C101—21no—
35#431×C101—21no—
36C2×#108×C101C2211yescharacteristic
37C2×#108×C101C2211yescharacteristic
38#428×C101C2211yescharacteristic
39#428×C101C2211yescharacteristic
40#428×C101C2211yescharacteristic
41C2×#107×C101C2211yescharacteristic
42C2×#106×C101C2211yescharacteristic
43#423×C101C2211yescharacteristic
44#423×C101C2211yescharacteristic
45C2×C4⋊C8×C101C2211yescharacteristic
46#419×C101C2211yescharacteristic
47#417×C101C2211yescharacteristic
48#417×C101C2211yescharacteristic
49#417×C101C2211yescharacteristic
50C2×#103×C101C2211yescharacteristic
51C2×#103×C101C2211yescharacteristic
52C2×#101×C101C2211yescharacteristic
53C2×#101×C101C2211yescharacteristic
54#408×C101C2211yescharacteristic
55#408×C101C2211yescharacteristic
56#405×C101C2211yescharacteristic
57#405×C101C2211yescharacteristic
58C4×M16×C101C2211yescharacteristic
59#343×C101C2211yescharacteristic
60#343×C101C2211yescharacteristic
61#343×C101C2211yescharacteristic
62#343×C101C2211yescharacteristic
63#343×C101C2211yescharacteristic
64#343×C101C2211yescharacteristic
65#341×C101C2211yescharacteristic
66#341×C101C2211yescharacteristic
67C2×#41×C101C2311yescharacteristic
68C22×Q8×C101C2311yescharacteristic
69#137×C101—22no—
70#137×C101—22no—
71C2×Q16×C101—21no—
72C2×SD16×C101—21no—
73C2×M16×C101C2311yescharacteristic
74C2×M16×C101C2311yescharacteristic
75C2×M16×C101C2311yescharacteristic
76C2×M16×C101C2311yescharacteristic
77C2×M16×C101C2311yescharacteristic
78C2×M16×C101C2311yescharacteristic
79C22×C8×C101C2311yescharacteristic
80C22×C8×C101C2311yescharacteristic
81#125×C101—21no—
82#125×C101—21no—
83#125×C101—21no—
84#125×C101—21no—
85C4×Q8×C101—21no—
86C4×Q8×C101—21no—
87C4×Q8×C101—21no—
88C4×Q8×C101—21no—
89C4×Q8×C101D411yescharacteristic
90C4×Q8×C101D411yescharacteristic
91C4×D4×C101—21no—
92C4×D4×C101—21no—
93C4×D4×C101D411yescharacteristic
94C4×D4×C101D411yescharacteristic
95#117×C101—21no—
96#117×C101C2311yescharacteristic
97C2×C4⋊C4×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×C101—21no—
100C2×C4⋊C4×C101C2311yescharacteristic
101C2×C4⋊C4×C101C2311yescharacteristic
102C2×C4⋊C4×C101C2311yescharacteristic
103C2×C42×C101—21no—
104C2×C42×C101—21no—
105C2×C42×C101C2311yescharacteristic
106#108×C101—22no—
107#108×C101—22no—
108#107×C101—21no—
109#107×C101—21no—
110#107×C101—21no—
111#107×C101—21no—
112#107×C101—21no—
113#106×C101—21no—
114#106×C101—21no—
115#106×C101—21no—
116#106×C101—21no—
117#106×C101—21no—
118C4⋊C8×C101—21no—
119C4⋊C8×C101—21no—
120C4⋊C8×C101—21no—
121C4⋊C8×C101—21no—
122C4⋊C8×C101D411yescharacteristic
123C4⋊C8×C101D411yescharacteristic
124C4⋊C8×C101D411yescharacteristic
125C4⋊C8×C101D411yescharacteristic
126#103×C101—21no—
127#103×C101—21no—
128#103×C101—21no—
129#103×C101—21no—
130#103×C101—21no—
131#103×C101—21no—
132#103×C101—21no—
133#103×C101—21no—
134#103×C101—21no—
135#102×C101—21no—
136#102×C101—21no—
137#102×C101—21no—
138#101×C101—22no—
139#101×C101—22no—
140C22⋊C8×C101—21no—
141C22⋊C8×C101—21no—
142C22⋊C8×C101—21no—
143C22⋊C8×C101—21no—
144#97×C101—21no—
145#97×C101—21no—
146#97×C101—21no—
147C4×C8×C101—21no—
148C4×C8×C101—21no—
149C4×C8×C101—21no—
150#41×C101—21no—
151#41×C101—21no—
152#41×C101—21no—
153#41×C101—21no—
154C2×Q8×C101—21no—
155C2×Q8×C101—21no—
156C2×Q8×C101—21no—
157C2×Q8×C101—21no—
158C2×Q8×C101—21no—
159C2×Q8×C101C2×D411yescharacteristic
160C2×Q8×C101#4112yes—
161C2×D4×C101—21no—
162C2×D4×C101C2×D411yescharacteristic
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—21no—
168C22×C4×C101—21no—
169C22×C4×C101—21no—
170C22×C4×C101#4111yescharacteristic
171C22×C4×C101#4111yescharacteristic
172C22×C4×C101C2411yescharacteristic
173Q16×C101—24no—
174SD16×C101—24no—
175M16×C101—21no—
176M16×C101—21no—
177M16×C101—21no—
178M16×C101—21no—
179M16×C101—21no—
180M16×C101—21no—
181M16×C101—21no—
182M16×C101—21no—
183M16×C101—21no—
184M16×C101—21no—
185M16×C101—21no—
186M16×C101#4112yes—
187C2×C8×C101—21no—
188C2×C8×C101—21no—
189C2×C8×C101—21no—
190C2×C8×C101—21no—
191C2×C8×C101—21no—
192C2×C8×C101—21no—
193C2×C8×C101—21no—
194C2×C8×C101—21no—
195C2×C8×C101—21no—
196C2×C8×C101—21no—
197C2×C8×C101C2×D411yescharacteristic
198C2×C8×C101C2×D411yescharacteristic
199C2×C8×C101C2×D411yescharacteristic
200C2×C8×C101C2×D411yescharacteristic
201C4⋊C4×C101—21no—
202C4⋊C4×C101—21no—
203C4⋊C4×C101—21no—
204C4⋊C4×C101—21no—
205C4⋊C4×C101—21no—
206C4⋊C4×C101—21no—
207C4⋊C4×C101—21no—
208C4⋊C4×C101—21no—
209C4⋊C4×C101—41no—
210C4⋊C4×C101—41no—
211C4⋊C4×C101—41no—
212C4⋊C4×C101—41no—
213C4⋊C4×C101—41no—
214C4⋊C4×C101—41no—
215C4⋊C4×C101C2×D411yescharacteristic
216C4⋊C4×C101C2×D411yescharacteristic
217C22⋊C4×C101—21no—
218C22⋊C4×C101—21no—
219C22⋊C4×C101—21no—
220C42×C101—21no—
221C42×C101—21no—
222C42×C101—21no—
223C42×C101—41no—
224C42×C101—41no—
225C42×C101C2×D411yescharacteristic
226C42×C101C2×D411yescharacteristic
227C42×C101C2×D411yescharacteristic
228C42×C101C2×D411yescharacteristic
229C23×C101—21no—
230C23×C101C2×#4111yescharacteristic
231Q8×C101—22no—
232Q8×C101—21no—
233Q8×C101—21no—
234Q8×C101—22no—
235Q8×C101—41no—
236Q8×C101—41no—
237D4×C101—21no—
238D4×C101—21no—
239D4×C101—41no—
240D4×C101—41no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
243C2×C4×C101—21no—
244C2×C4×C101—22no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—42no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—81no—
256C2×C4×C101—81no—
257C2×C4×C101—81no—
258C2×C4×C101—81no—
259C2×C4×C101#12111yescharacteristic
260C2×C4×C101#12111yescharacteristic
261C2×C4×C101#12111yescharacteristic
262C2×C4×C101#12111yescharacteristic
263C2×C4×C101C22×D411yescharacteristic
264C2×C4×C101C22×D411yescharacteristic
265C2×C4×C101C2×#4111yescharacteristic
266C2×C4×C101C2×#4111yescharacteristic
267C2×C4×C1012−1+411yescharacteristic
268C2×C4×C1012−1+411yescharacteristic
269C8×C101—22no—
270C8×C101—21no—
271C8×C101—21no—
272C8×C101—21no—
273C8×C101—21no—
274C8×C101—41no—
275C8×C101—41no—
276C8×C101—41no—
277C8×C101—41no—
278C8×C101—41no—
279C22×C101—21no—
280C22×C101—21no—
281C22×C101—41no—
282C22×C101—41no—
283C22×C101—41no—
284C22×C101C2×#12111yescharacteristic
285C22×C101#55211yescharacteristic
286C22×C101#55611yescharacteristic
287C4×C101—21no—
288C4×C101—21no—
289C4×C101—21no—
290C4×C101—21no—
291C4×C101—41no—
292C4×C101—42no—
293C4×C101—41no—
294C4×C101—41no—
295C4×C101—81no—
296C4×C101—81no—
297C4×C101—81no—
298C4×C101#52511yescharacteristic
299C4×C101#53611yescharacteristic
300C4×C101#54711yescharacteristic
301C4×C101#54811yescharacteristic
302#24725C10111yesmaximal, characteristic, direct product factor, Sylow
303C2×C101—21no—
304C2×C101—21no—
305C2×C101—81no—
306C2×C101#241511yescharacteristic
307C2×C101#306711yescharacteristic
308C2×C101#306911yescharacteristic
309#3080C2×C10111yescharacteristic
310C2×#479C2×C10111yescharacteristic, complemented
311C4×#137C2×C10111yescharacteristic
312#2925C2×C10111yescharacteristic
313#2079C2×C10111yescharacteristic
314#2078C2×C10111yescharacteristic
315#2052C2×C10111yescharacteristic
316#2052C2×C10111yescharacteristic
317#1998C2×C10111yescharacteristic, complemented
318#1952C2×C10111yescharacteristic, complemented
319#1951C2×C10111yescharacteristic, complemented
320#1950C2×C10111yescharacteristic, complemented
321#1930C2×C10111yescharacteristic, complemented
322#1930C2×C10111yescharacteristic, complemented
323#1801C2×C10111yescharacteristic, complemented
324C101#2472511yescharacteristic, direct product factor, Sylow
325C2×#137C22×C10111yescharacteristic
326C2×#125C22×C10111yescharacteristic
327C4×#41C22×C10111yescharacteristic
328C2×C4×Q8C22×C10111yescharacteristic
329#479—21no—
330#479—21no—
331#479—21no—
332#479—21no—
333#479—21no—
334#479—21no—
335#478—21no—
336#478—21no—
337#441—21no—
338#440—21no—
339C4×Q16—21no—
340C4×SD16—21no—
341#433—21no—
342#433—21no—
343#432—21no—
344#431—21no—
345C2×#108C22×C10111yescharacteristic
346C2×#108C22×C10111yescharacteristic
347#428C22×C10111yescharacteristic
348#428C22×C10111yescharacteristic
349#428C22×C10111yescharacteristic
350C2×#107C22×C10111yescharacteristic
351C2×#106C22×C10111yescharacteristic
352#423C22×C10111yescharacteristic
353#423C22×C10111yescharacteristic
354C2×C4⋊C8C22×C10111yescharacteristic
355#419C22×C10111yescharacteristic
356#417C22×C10111yescharacteristic
357#417C22×C10111yescharacteristic
358#417C22×C10111yescharacteristic
359C2×#103C22×C10111yescharacteristic
360C2×#103C22×C10111yescharacteristic
361C2×#101C22×C10111yescharacteristic
362C2×#101C22×C10111yescharacteristic
363#408C22×C10111yescharacteristic
364#408C22×C10111yescharacteristic
365#405C22×C10111yescharacteristic
366#405C22×C10111yescharacteristic
367C4×M16C22×C10111yescharacteristic
368#343C22×C10111yescharacteristic
369#343C22×C10111yescharacteristic
370#343C22×C10111yescharacteristic
371#343C22×C10111yescharacteristic
372#343C22×C10111yescharacteristic
373#343C22×C10111yescharacteristic
374#341C22×C10111yescharacteristic
375#341C22×C10111yescharacteristic
376C2×#41C23×C10111yescharacteristic
377C22×Q8C23×C10111yescharacteristic
378#137—22no—
379#137—22no—
380C2×Q16—21no—
381C2×SD16—21no—
382C2×M16C23×C10111yescharacteristic
383C2×M16C23×C10111yescharacteristic
384C2×M16C23×C10111yescharacteristic
385C2×M16C23×C10111yescharacteristic
386C2×M16C23×C10111yescharacteristic
387C2×M16C23×C10111yescharacteristic
388C22×C8C23×C10111yescharacteristic
389C22×C8C23×C10111yescharacteristic
390#125—21no—
391#125—21no—
392#125—21no—
393#125—21no—
394C4×Q8—21no—
395C4×Q8—21no—
396C4×Q8—21no—
397C4×Q8—21no—
398C4×Q8D4×C10111yescharacteristic
399C4×Q8D4×C10111yescharacteristic
400C4×D4—21no—
401C4×D4—21no—
402C4×D4D4×C10111yescharacteristic
403C4×D4D4×C10111yescharacteristic
404#117—21no—
405#117C23×C10111yescharacteristic
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4C23×C10111yescharacteristic
410C2×C4⋊C4C23×C10111yescharacteristic
411C2×C4⋊C4C23×C10111yescharacteristic
412C2×C42—21no—
413C2×C42—21no—
414C2×C42C23×C10111yescharacteristic
415#108—22no—
416#108—22no—
417#107—21no—
418#107—21no—
419#107—21no—
420#107—21no—
421#107—21no—
422#106—21no—
423#106—21no—
424#106—21no—
425#106—21no—
426#106—21no—
427C4⋊C8—21no—
428C4⋊C8—21no—
429C4⋊C8—21no—
430C4⋊C8—21no—
431C4⋊C8D4×C10111yescharacteristic
432C4⋊C8D4×C10111yescharacteristic
433C4⋊C8D4×C10111yescharacteristic
434C4⋊C8D4×C10111yescharacteristic
435#103—21no—
436#103—21no—
437#103—21no—
438#103—21no—
439#103—21no—
440#103—21no—
441#103—21no—
442#103—21no—
443#103—21no—
444#102—21no—
445#102—21no—
446#102—21no—
447#101—22no—
448#101—22no—
449C22⋊C8—21no—
450C22⋊C8—21no—
451C22⋊C8—21no—
452C22⋊C8—21no—
453#97—21no—
454#97—21no—
455#97—21no—
456C4×C8—21no—
457C4×C8—21no—
458C4×C8—21no—
459#41—21no—
460#41—21no—
461#41—21no—
462#41—21no—
463C2×Q8—21no—
464C2×Q8—21no—
465C2×Q8—21no—
466C2×Q8—21no—
467C2×Q8—21no—
468C2×Q8C2×D4×C10111yescharacteristic
469C2×Q8#41×C10112yes—
470C2×D4—21no—
471C2×D4C2×D4×C10111yescharacteristic
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4#41×C10111yescharacteristic
480C22×C4#41×C10111yescharacteristic
481C22×C4C24×C10111yescharacteristic
482Q16—24no—
483SD16—24no—
484M16—21no—
485M16—21no—
486M16—21no—
487M16—21no—
488M16—21no—
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16#41×C10112yes—
496C2×C8—21no—
497C2×C8—21no—
498C2×C8—21no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8C2×D4×C10111yescharacteristic
507C2×C8C2×D4×C10111yescharacteristic
508C2×C8C2×D4×C10111yescharacteristic
509C2×C8C2×D4×C10111yescharacteristic
510C4⋊C4—21no—
511C4⋊C4—21no—
512C4⋊C4—21no—
513C4⋊C4—21no—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—41no—
519C4⋊C4—41no—
520C4⋊C4—41no—
521C4⋊C4—41no—
522C4⋊C4—41no—
523C4⋊C4—41no—
524C4⋊C4C2×D4×C10111yescharacteristic
525C4⋊C4C2×D4×C10111yescharacteristic
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C42—21no—
530C42—21no—
531C42—21no—
532C42—41no—
533C42—41no—
534C42C2×D4×C10111yescharacteristic
535C42C2×D4×C10111yescharacteristic
536C42C2×D4×C10111yescharacteristic
537C42C2×D4×C10111yescharacteristic
538C23—21no—
539C23C2×#41×C10111yescharacteristic
540Q8—22no—
541Q8—21no—
542Q8—21no—
543Q8—22no—
544Q8—41no—
545Q8—41no—
546D4—21no—
547D4—21no—
548D4—41no—
549D4—41no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—21no—
553C2×C4—22no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—42no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4#121×C10111yescharacteristic
569C2×C4#121×C10111yescharacteristic
570C2×C4#121×C10111yescharacteristic
571C2×C4#121×C10111yescharacteristic
572C2×C4C22×D4×C10111yescharacteristic
573C2×C4C22×D4×C10111yescharacteristic
574C2×C4C2×#41×C10111yescharacteristic
575C2×C4C2×#41×C10111yescharacteristic
576C2×C42−1+4×C10111yescharacteristic
577C2×C42−1+4×C10111yescharacteristic
578C8—22no—
579C8—21no—
580C8—21no—
581C8—21no—
582C8—21no—
583C8—41no—
584C8—41no—
585C8—41no—
586C8—41no—
587C8—41no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22C2×#121×C10111yescharacteristic
594C22#552×C10111yescharacteristic
595C22#556×C10111yescharacteristic
596C4—21no—
597C4—21no—
598C4—21no—
599C4—21no—
600C4—41no—
601C4—42no—
602C4—41no—
603C4—41no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4#525×C10111yescharacteristic
608C4#536×C10111yescharacteristic
609C4#547×C10111yescharacteristic
610C4#548×C10111yescharacteristic
611C2—21no—
612C2—21no—
613C2—81no—
614C2C101×#241511yescharacteristic
615C2C101×#306711yescharacteristic
616C2C101×#306911yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#41×C101C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#479×C101C2semidirect
9. C101×#1998C2semidirect
10. C101×#1952C2semidirect
11. C101×#1951C2semidirect
12. C101×#1950C2semidirect
13. C101×#1930C2semidirect
14. C101×#1930C2semidirect
15. C101×#1801C2semidirect
302. #24725C101direct (N × H)
310. C2×#479C2×C101semidirect
317. #1998C2×C101semidirect
318. #1952C2×C101semidirect
319. #1951C2×C101semidirect
320. #1950C2×C101semidirect
321. #1930C2×C101semidirect
322. #1930C2×C101semidirect
323. #1801C2×C101semidirect
324. C101#24725direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#30802
C2×#479×C1012
C4×#137×C1012
C101×#29252
C101×#20792
C101×#20782
C101×#20522
C101×#19982
C101×#19522
C101×#19512
C101×#19502
C101×#19302
C101×#18012
#24725101