Finite Group Databasebeta

← C101×#19823 #38801974

Subgroups — C101×#19823 #38801974

Order 25856.

632 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3360C211yesmaximal, characteristic, complemented
2C101×#3340C211yesmaximal, characteristic, complemented
3C101×#3325C211yesmaximal, characteristic
4C101×#3295C211yesmaximal, characteristic, complemented
5C101×#1720C211yesmaximal, characteristic, complemented
6C101×#1703C211yesmaximal, characteristic, complemented
7C101×#1678C211yesmaximal, characteristic, complemented
8C101×#1677C211yesmaximal, characteristic, complemented
9C101×#1671C211yesmaximal, characteristic, complemented
10C101×#1639C211yesmaximal, characteristic, complemented
11C101×#1634C211yesmaximal, characteristic, complemented
12C101×#1632C211yesmaximal, characteristic, complemented
13C101×#1628C211yesmaximal, characteristic, complemented
14C101×#1583C211yesmaximal, characteristic, complemented
15C101×#1580C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic, complemented
17#555×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19D42×C101C2211yescharacteristic
20#498×C101C2211yescharacteristic, complemented
21#494×C101C2211yescharacteristic, complemented
22#488×C101—21no—
23#487×C101C2211yescharacteristic, complemented
24#486×C101C2211yescharacteristic
25#486×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#485×C101—21no—
28#482×C101—21no—
29#482×C101—21no—
30#481×C101—21no—
31#479×C101—21no—
32#477×C101C2211yescharacteristic, complemented
33#476×C101C2211yescharacteristic
34#476×C101C2211yescharacteristic
35#476×C101C2211yescharacteristic, complemented
36#474×C101C2211yescharacteristic
37#469×C101—21no—
38#465×C101—21no—
39#465×C101—21no—
40#463×C101—21no—
41#461×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#450×C101—21no—
45#447×C101—21no—
46C8×Q8×C101C2211yescharacteristic, complemented
47C4×SD16×C101—21no—
48C4×SD16×C101C2211yescharacteristic
49C4×D8×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51C8×D4×C101C2211yescharacteristic
52C8×D4×C101C2211yescharacteristic, complemented
53#427×C101—21no—
54#418×C101—21no—
55C2×#102×C101—21no—
56#334×C101C2211yescharacteristic, complemented
57#334×C101C2211yescharacteristic, complemented
58#333×C101C2211yescharacteristic, complemented
59#333×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
67C22×D4×C101—21no—
68C22×D4×C101—21no—
69C2×Q16×C101—41no—
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101D411yescharacteristic
73C2×D8×C101—21no—
74C2×D8×C101D411yescharacteristic
75C2×M16×C101—21no—
76C22×C8×C101—21no—
77C22×C8×C101—21no—
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81#127×C101C2311yescharacteristic
82#126×C101—41no—
83#125×C101—21no—
84#124×C101—21no—
85#124×C101—41no—
86C22⋊Q8×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—41no—
89#121×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#120×C101—41no—
94C4×Q8×C101—21no—
95C4×Q8×C101C2311yescharacteristic
96C4×D4×C101—21no—
97C4×D4×C101C2311yescharacteristic
98C4×D4×C101C2311yescharacteristic
99C4×D4×C101C2311yescharacteristic
100#117×C101—21no—
101#117×C101—21no—
102#117×C101—21no—
103C2×C4⋊C4×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101D411yescharacteristic
107#106×C101—21no—
108#106×C101—21no—
109#106×C101—21no—
110#106×C101—21no—
111#106×C101—21no—
112#106×C101D411yescharacteristic
113C4⋊C8×C101—21no—
114C4⋊C8×C101C2311yescharacteristic
115C4⋊C8×C101C2311yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118#103×C101—21no—
119#103×C101—21no—
120#103×C101—21no—
121#103×C101—21no—
122#103×C101D411yescharacteristic
123#102×C101—21no—
124#102×C101—21no—
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—41no—
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140C4×C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C24×C101—41no—
145C2×Q8×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101C2×D411yescharacteristic
149C2×D4×C101—21no—
150C2×D4×C101—21no—
151C2×D4×C101—21no—
152C2×D4×C101—41no—
153C2×D4×C101—41no—
154C2×D4×C101—42no—
155C2×D4×C101—42no—
156C2×D4×C101—41no—
157C2×D4×C101—81no—
158C2×D4×C101—81no—
159C2×D4×C101C2×D411yescharacteristic
160C2×D4×C101C2×D411yescharacteristic
161C2×D4×C101C2×D411yescharacteristic
162C22×C4×C101—21no—
163C22×C4×C101—21no—
164C22×C4×C101—21no—
165C22×C4×C101—41no—
166Q16×C101—82no—
167SD16×C101—41no—
168SD16×C101—42no—
169SD16×C101—81no—
170D8×C101—22no—
171D8×C101—81no—
172M16×C101—81no—
173C2×C8×C101—21no—
174C2×C8×C101—21no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101—42no—
179C2×C8×C101—81no—
180C2×C8×C101C2×D411yescharacteristic
181C2×C8×C101C2×D411yescharacteristic
182C2×C8×C101C2×D411yescharacteristic
183C2×C8×C101C2×D411yescharacteristic
184C4⋊C4×C101—21no—
185C4⋊C4×C101—21no—
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—21no—
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—41no—
192C4⋊C4×C101—41no—
193C4⋊C4×C101—41no—
194C4⋊C4×C101C2×D411yescharacteristic
195C4⋊C4×C101C2×D411yescharacteristic
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—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C42×C101—21no—
208C42×C101—41no—
209C42×C101—41no—
210C42×C101C2411yescharacteristic
211C23×C101—21no—
212C23×C101—21no—
213C23×C101—21no—
214C23×C101—41no—
215C23×C101—82no—
216C23×C101—82no—
217C23×C101—161no—
218Q8×C101—21no—
219Q8×C101—21no—
220Q8×C101—41no—
221Q8×C101—41no—
222Q8×C101—81no—
223Q8×C101—81no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—21no—
229D4×C101—41no—
230D4×C101—41no—
231D4×C101—41no—
232D4×C101—41no—
233D4×C101—81no—
234D4×C101—82no—
235D4×C101—82no—
236D4×C101—161no—
237D4×C101#13512yes—
238C2×C4×C101—21no—
239C2×C4×C101—21no—
240C2×C4×C101—21no—
241C2×C4×C101—21no—
242C2×C4×C101—21no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—41no—
252C2×C4×C101—161no—
253C2×C4×C101C22×D411yescharacteristic
254C2×C4×C101C22×D411yescharacteristic
255C2×C4×C101H(5,𝔽2)11yescharacteristic
256C8×C101—21no—
257C8×C101—21no—
258C8×C101—21no—
259C8×C101—21no—
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C8×C101—41no—
265C22×C101—22no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101—41no—
270C22×C101—41no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—81no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101—164no—
278C22×C101D4211yescharacteristic
279C4×C101—21no—
280C4×C101—41no—
281C4×C101—41no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—41no—
285C4×C101—81no—
286C4×C101—81no—
287C4×C101—81no—
288C4×C101C2×#13511yescharacteristic
289C4×C101#57511yescharacteristic
290C4×C101#57711yescharacteristic
291C4×C101#57711yescharacteristic
292#19823C10111yesmaximal, characteristic, direct product factor, Sylow
293C2×C101—42no—
294C2×C101—81no—
295C2×C101—81no—
296C2×C101—161no—
297C2×C101#326711yescharacteristic
298C2×C101#328211yescharacteristic
299C2×C101#328811yescharacteristic
300#3360C2×C10111yescharacteristic, complemented
301#3340C2×C10111yescharacteristic, complemented
302#3325C2×C10111yescharacteristic
303#3295C2×C10111yescharacteristic, complemented
304#1720C2×C10111yescharacteristic, complemented
305#1703C2×C10111yescharacteristic, complemented
306#1678C2×C10111yescharacteristic, complemented
307#1677C2×C10111yescharacteristic, complemented
308#1671C2×C10111yescharacteristic, complemented
309#1639C2×C10111yescharacteristic, complemented
310#1634C2×C10111yescharacteristic, complemented
311#1632C2×C10111yescharacteristic, complemented
312#1628C2×C10111yescharacteristic, complemented
313#1583C2×C10111yescharacteristic, complemented
314#1580C2×C10111yescharacteristic, complemented
315C101#1982311yescharacteristic, direct product factor, Sylow
316#556C22×C10111yescharacteristic, complemented
317#555C22×C10111yescharacteristic
318#554C22×C10111yescharacteristic
319D42C22×C10111yescharacteristic
320#498C22×C10111yescharacteristic, complemented
321#494C22×C10111yescharacteristic, complemented
322#488—21no—
323#487C22×C10111yescharacteristic, complemented
324#486C22×C10111yescharacteristic
325#486C22×C10111yescharacteristic
326#486C22×C10111yescharacteristic
327#485—21no—
328#482—21no—
329#482—21no—
330#481—21no—
331#479—21no—
332#477C22×C10111yescharacteristic, complemented
333#476C22×C10111yescharacteristic
334#476C22×C10111yescharacteristic
335#476C22×C10111yescharacteristic, complemented
336#474C22×C10111yescharacteristic
337#469—21no—
338#465—21no—
339#465—21no—
340#463—21no—
341#461C22×C10111yescharacteristic
342#460C22×C10111yescharacteristic
343#459C22×C10111yescharacteristic
344#450—21no—
345#447—21no—
346C8×Q8C22×C10111yescharacteristic, complemented
347C4×SD16—21no—
348C4×SD16C22×C10111yescharacteristic
349C4×D8C22×C10111yescharacteristic
350#436C22×C10111yescharacteristic
351C8×D4C22×C10111yescharacteristic
352C8×D4C22×C10111yescharacteristic, complemented
353#427—21no—
354#418—21no—
355C2×#102—21no—
356#334C22×C10111yescharacteristic, complemented
357#334C22×C10111yescharacteristic, complemented
358#333C22×C10111yescharacteristic, complemented
359#333C22×C10111yescharacteristic, complemented
360#332C22×C10111yescharacteristic, complemented
361#331C22×C10111yescharacteristic
362Q8⋊C8C22×C10111yescharacteristic, complemented
363D4⋊C8C22×C10111yescharacteristic
364D4⋊C8C22×C10111yescharacteristic
365D4⋊C8C22×C10111yescharacteristic, complemented
366#322C22×C10111yescharacteristic, complemented
367C22×D4—21no—
368C22×D4—21no—
369C2×Q16—41no—
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16D4×C10111yescharacteristic
373C2×D8—21no—
374C2×D8D4×C10111yescharacteristic
375C2×M16—21no—
376C22×C8—21no—
377C22×C8—21no—
378C4⋊Q8C23×C10111yescharacteristic
379C4⋊Q8C23×C10111yescharacteristic
380C4⋊Q8C23×C10111yescharacteristic
381#127C23×C10111yescharacteristic
382#126—41no—
383#125—21no—
384#124—21no—
385#124—41no—
386C22⋊Q8—21no—
387C22⋊Q8—21no—
388C22⋊Q8—41no—
389#121—21no—
390#121—21no—
391#121—21no—
392#121—21no—
393#120—41no—
394C4×Q8—21no—
395C4×Q8C23×C10111yescharacteristic
396C4×D4—21no—
397C4×D4C23×C10111yescharacteristic
398C4×D4C23×C10111yescharacteristic
399C4×D4C23×C10111yescharacteristic
400#117—21no—
401#117—21no—
402#117—21no—
403C2×C4⋊C4—21no—
404#107—21no—
405#107—21no—
406#107D4×C10111yescharacteristic
407#106—21no—
408#106—21no—
409#106—21no—
410#106—21no—
411#106—21no—
412#106D4×C10111yescharacteristic
413C4⋊C8—21no—
414C4⋊C8C23×C10111yescharacteristic
415C4⋊C8C23×C10111yescharacteristic
416C4⋊C8C23×C10111yescharacteristic
417C4⋊C8C23×C10111yescharacteristic
418#103—21no—
419#103—21no—
420#103—21no—
421#103—21no—
422#103D4×C10111yescharacteristic
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—41no—
434#102D4×C10111yescharacteristic
435#102D4×C10111yescharacteristic
436#102D4×C10111yescharacteristic
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440C4×C8—21no—
441C4×C8C23×C10111yescharacteristic
442C4×C8C23×C10111yescharacteristic
443C4×C8C23×C10111yescharacteristic
444C24—41no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8C2×D4×C10111yescharacteristic
449C2×D4—21no—
450C2×D4—21no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—42no—
455C2×D4—42no—
456C2×D4—41no—
457C2×D4—81no—
458C2×D4—81no—
459C2×D4C2×D4×C10111yescharacteristic
460C2×D4C2×D4×C10111yescharacteristic
461C2×D4C2×D4×C10111yescharacteristic
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—41no—
466Q16—82no—
467SD16—41no—
468SD16—42no—
469SD16—81no—
470D8—22no—
471D8—81no—
472M16—81no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—42no—
479C2×C8—81no—
480C2×C8C2×D4×C10111yescharacteristic
481C2×C8C2×D4×C10111yescharacteristic
482C2×C8C2×D4×C10111yescharacteristic
483C2×C8C2×D4×C10111yescharacteristic
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4—41no—
494C4⋊C4C2×D4×C10111yescharacteristic
495C4⋊C4C2×D4×C10111yescharacteristic
496C4⋊C4C2×D4×C10111yescharacteristic
497C4⋊C4C2×D4×C10111yescharacteristic
498C22⋊C4—21no—
499C22⋊C4—21no—
500C22⋊C4—21no—
501C22⋊C4—41no—
502C22⋊C4—41no—
503C22⋊C4—41no—
504C22⋊C4—41no—
505C22⋊C4—41no—
506C22⋊C4—41no—
507C42—21no—
508C42—41no—
509C42—41no—
510C42C24×C10111yescharacteristic
511C23—21no—
512C23—21no—
513C23—21no—
514C23—41no—
515C23—82no—
516C23—82no—
517C23—161no—
518Q8—21no—
519Q8—21no—
520Q8—41no—
521Q8—41no—
522Q8—81no—
523Q8—81no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—41no—
530D4—41no—
531D4—41no—
532D4—41no—
533D4—81no—
534D4—82no—
535D4—82no—
536D4—161no—
537D4#135×C10112yes—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—161no—
553C2×C4C22×D4×C10111yescharacteristic
554C2×C4C22×D4×C10111yescharacteristic
555C2×C4H(5,𝔽2)×C10111yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—41no—
564C8—41no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—164no—
578C22D42×C10111yescharacteristic
579C4—21no—
580C4—41no—
581C4—41no—
582C4—41no—
583C4—41no—
584C4—41no—
585C4—81no—
586C4—81no—
587C4—81no—
588C4C2×#135×C10111yescharacteristic
589C4#575×C10111yescharacteristic
590C4#577×C10111yescharacteristic
591C4#577×C10111yescharacteristic
592C2—42no—
593C2—81no—
594C2—81no—
595C2—161no—
596C2C101×#326711yescharacteristic
597C2C101×#328211yescharacteristic
598C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3325C2
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×#3360C2semidirect
2. C101×#3340C2semidirect
4. C101×#3295C2semidirect
5. C101×#1720C2semidirect
6. C101×#1703C2semidirect
7. C101×#1678C2semidirect
8. C101×#1677C2semidirect
9. C101×#1671C2semidirect
10. C101×#1639C2semidirect
11. C101×#1634C2semidirect
12. C101×#1632C2semidirect
13. C101×#1628C2semidirect
14. C101×#1583C2semidirect
15. C101×#1580C2semidirect
16. #556×C101C22semidirect
20. #498×C101C22semidirect
21. #494×C101C22semidirect
23. #487×C101C22semidirect
32. #477×C101C22semidirect
35. #476×C101C22semidirect
46. C8×Q8×C101C22semidirect
52. C8×D4×C101C22semidirect
56. #334×C101C22semidirect
57. #334×C101C22semidirect
58. #333×C101C22semidirect
59. #333×C101C22semidirect
60. #332×C101C22semidirect
62. Q8⋊C8×C101C22semidirect
65. D4⋊C8×C101C22semidirect
66. #322×C101C22semidirect
292. #19823C101direct (N × H)
300. #3360C2×C101semidirect
301. #3340C2×C101semidirect
303. #3295C2×C101semidirect
304. #1720C2×C101semidirect
305. #1703C2×C101semidirect
306. #1678C2×C101semidirect
307. #1677C2×C101semidirect
308. #1671C2×C101semidirect
309. #1639C2×C101semidirect
310. #1634C2×C101semidirect
311. #1632C2×C101semidirect
312. #1628C2×C101semidirect
313. #1583C2×C101semidirect
314. #1580C2×C101semidirect
315. C101#19823direct (N × H)
316. #556C22×C101semidirect
320. #498C22×C101semidirect
321. #494C22×C101semidirect
323. #487C22×C101semidirect
332. #477C22×C101semidirect
335. #476C22×C101semidirect
346. C8×Q8C22×C101semidirect
352. C8×D4C22×C101semidirect
356. #334C22×C101semidirect
357. #334C22×C101semidirect
358. #333C22×C101semidirect
359. #333C22×C101semidirect
360. #332C22×C101semidirect
362. Q8⋊C8C22×C101semidirect
365. D4⋊C8C22×C101semidirect
366. #322C22×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33602
C101×#33402
C101×#33252
C101×#32952
C101×#17202
C101×#17032
C101×#16782
C101×#16772
C101×#16712
C101×#16392
C101×#16342
C101×#16322
C101×#16282
C101×#15832
C101×#15802
#19823101