Finite Group Databasebeta

← C101×#19795 #38801946

Subgroups — C101×#19795 #38801946

Order 25856.

652 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3368C211yesmaximal, characteristic, complemented
2C101×#3359C211yesmaximal, characteristic, complemented
3C101×#3298C211yesmaximal, characteristic, complemented
4C101×#3284C211yesmaximal, characteristic
5C101×#1719C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1681C211yesmaximal, characteristic, complemented
8C101×#1679C211yesmaximal, characteristic, complemented
9C101×#1666C211yesmaximal, characteristic, complemented
10C101×#1648C211yesmaximal, characteristic, complemented
11C101×#1647C211yesmaximal, characteristic, complemented
12C101×#1642C211yesmaximal, characteristic, complemented
13C101×#1627C211yesmaximal, characteristic, complemented
14C101×#1582C211yesmaximal, characteristic, complemented
15C101×SD16⋊C8C211yesmaximal, characteristic, complemented
16C2×#135×C101—21no—
17#557×C101C2211yescharacteristic
18#550×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#547×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic
23#490×C101—21no—
24#487×C101—21no—
25#487×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#483×C101—21no—
30#478×C101—21no—
31#475×C101—21no—
32#475×C101C2211yescharacteristic
33#475×C101C2211yescharacteristic
34#474×C101C2211yescharacteristic
35#465×C101—21no—
36#465×C101—21no—
37#462×C101C2211yescharacteristic
38#461×C101—21no—
39#461×C101C2211yescharacteristic
40#461×C101C2211yescharacteristic
41#460×C101—21no—
42#460×C101C2211yescharacteristic
43#459×C101C2211yescharacteristic
44#452×C101—21no—
45#449×C101—21no—
46#448×C101—21no—
47#446×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#440×C101—21no—
50C4×SD16×C101—21no—
51C4×SD16×C101C2211yescharacteristic
52C4×SD16×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55C2×#103×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#332×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×#41×C101—21no—
69C22×Q8×C101—21no—
70#135×C101—44no—
71C2×Q16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—21no—
75C2×SD16×C101—21no—
76C2×SD16×C101—21no—
77C2×SD16×C101D411yescharacteristic
78C2×SD16×C101D411yescharacteristic
79C2×D8×C101—21no—
80C22×C8×C101—21no—
81C22×C8×C101—21no—
82C4⋊Q8×C101—21no—
83C4⋊Q8×C101—21no—
84C4⋊Q8×C101C2311yescharacteristic
85C4⋊Q8×C101C2311yescharacteristic
86C4⋊Q8×C101C2311yescharacteristic
87#127×C101—21no—
88#127×C101C2311yescharacteristic
89#125×C101—21no—
90#125×C101—41no—
91#123×C101—41no—
92C22⋊Q8×C101—21no—
93C22⋊Q8×C101—21no—
94C22⋊Q8×C101—41no—
95#121×C101—21no—
96#121×C101—21no—
97#121×C101—41no—
98C4×Q8×C101—21no—
99C4×Q8×C101—21no—
100C4×Q8×C101C2311yescharacteristic
101C4×Q8×C101C2311yescharacteristic
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101C2311yescharacteristic
105C4×D4×C101C2311yescharacteristic
106C2×C4⋊C4×C101—21no—
107#107×C101—21no—
108#107×C101—41no—
109#106×C101—21no—
110#106×C101—21no—
111#106×C101D411yescharacteristic
112#106×C101D411yescharacteristic
113C4⋊C8×C101—21no—
114C4⋊C8×C101—21no—
115C4⋊C8×C101C2311yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
119#103×C101—21no—
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#103×C101—21no—
127#103×C101—21no—
128#103×C101D411yescharacteristic
129#103×C101D411yescharacteristic
130#102×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101—21no—
135#102×C101—41no—
136#102×C101D411yescharacteristic
137#102×C101D411yescharacteristic
138C22⋊C8×C101—21no—
139C22⋊C8×C101—21no—
140#97×C101—21no—
141C4×C8×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C4×C8×C101C2311yescharacteristic
145#41×C101—42no—
146#41×C101—42no—
147#41×C101—81no—
148#41×C101—81no—
149C2×Q8×C101—21no—
150C2×Q8×C101—21no—
151C2×Q8×C101—21no—
152C2×Q8×C101—41no—
153C2×Q8×C101—42no—
154C2×Q8×C101—81no—
155C2×Q8×C101C2×D411yescharacteristic
156C2×Q8×C101C2×D411yescharacteristic
157C2×D4×C101—21no—
158C2×D4×C101—21no—
159C2×D4×C101—21no—
160C2×D4×C101—41no—
161C2×D4×C101—41no—
162C2×D4×C101—41no—
163C2×D4×C101C2×D411yescharacteristic
164C2×D4×C101C2×D411yescharacteristic
165C22×C4×C101—21no—
166C22×C4×C101—21no—
167C22×C4×C101—41no—
168C22×C4×C101—41no—
169C22×C4×C101—41no—
170Q16×C101—42no—
171SD16×C101—22no—
172SD16×C101—22no—
173SD16×C101—42no—
174SD16×C101—42no—
175SD16×C101—42no—
176SD16×C101—81no—
177SD16×C101—81no—
178D8×C101—42no—
179C2×C8×C101—21no—
180C2×C8×C101—21no—
181C2×C8×C101—21no—
182C2×C8×C101—21no—
183C2×C8×C101—21no—
184C2×C8×C101—42no—
185C2×C8×C101—81no—
186C2×C8×C101C2×D411yescharacteristic
187C2×C8×C101C2×D411yescharacteristic
188C2×C8×C101C2×D411yescharacteristic
189C2×C8×C101C2×D411yescharacteristic
190C4⋊C4×C101—21no—
191C4⋊C4×C101—21no—
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—41no—
199C4⋊C4×C101—41no—
200C4⋊C4×C101—41no—
201C4⋊C4×C101—41no—
202C4⋊C4×C101—41no—
203C4⋊C4×C101C2×D411yescharacteristic
204C4⋊C4×C101C2×D411yescharacteristic
205C4⋊C4×C101C2×D411yescharacteristic
206C4⋊C4×C101C2×D411yescharacteristic
207C22⋊C4×C101—21no—
208C22⋊C4×C101—21no—
209C22⋊C4×C101—41no—
210C22⋊C4×C101—41no—
211C22⋊C4×C101—41no—
212C42×C101—21no—
213C42×C101—21no—
214C42×C101—41no—
215C42×C101C2411yescharacteristic
216C23×C101—21no—
217C23×C101—21no—
218C23×C101—41no—
219Q8×C101—21no—
220Q8×C101—21no—
221Q8×C101—21no—
222Q8×C101—41no—
223Q8×C101—41no—
224Q8×C101—41no—
225Q8×C101—41no—
226Q8×C101—41no—
227Q8×C101—41no—
228Q8×C101—82no—
229Q8×C101#13512yescomplemented
230D4×C101—21no—
231D4×C101—21no—
232D4×C101—21no—
233D4×C101—41no—
234D4×C101—41no—
235D4×C101—41no—
236D4×C101—41no—
237D4×C101—81no—
238D4×C101—82no—
239D4×C101—82no—
240D4×C101—161no—
241D4×C101AGL(1,ℤ/8)12yes—
242C2×C4×C101—21no—
243C2×C4×C101—21no—
244C2×C4×C101—21no—
245C2×C4×C101—21no—
246C2×C4×C101—21no—
247C2×C4×C101—21no—
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—82no—
256C2×C4×C101—82no—
257C2×C4×C101—82no—
258C2×C4×C101C22×D411yescharacteristic
259C2×C4×C101C22×D411yescharacteristic
260C2×C4×C101H(5,𝔽2)11yescharacteristic
261C8×C101—21no—
262C8×C101—21no—
263C8×C101—21no—
264C8×C101—21no—
265C8×C101—41no—
266C8×C101—41no—
267C8×C101—41no—
268C8×C101—41no—
269C8×C101—41no—
270C22×C101—22no—
271C22×C101—41no—
272C22×C101—41no—
273C22×C101—41no—
274C22×C101—41no—
275C22×C101—41no—
276C22×C101—81no—
277C22×C101—81no—
278C22×C101—81no—
279C22×C101D4211yescharacteristic
280C4×C101—22no—
281C4×C101—21no—
282C4×C101—41no—
283C4×C101—41no—
284C4×C101—41no—
285C4×C101—41no—
286C4×C101—41no—
287C4×C101—81no—
288C4×C101—81no—
289C4×C101—81no—
290C4×C101C2×#13511yescharacteristic
291C4×C101C2×AGL(1,ℤ/8)11yescharacteristic
292C4×C101#57711yescharacteristic
293C4×C101#57711yescharacteristic
294#19795C10111yesmaximal, characteristic, direct product factor, Sylow
295C2×C101—42no—
296C2×C101—81no—
297C2×C101—161no—
298C2×C101#326511yescharacteristic
299C2×C101#328211yescharacteristic
300C2×C101#328911yescharacteristic
301#3368C2×C10111yescharacteristic, complemented
302#3359C2×C10111yescharacteristic, complemented
303#3298C2×C10111yescharacteristic, complemented
304#3284C2×C10111yescharacteristic
305#1719C2×C10111yescharacteristic, complemented
306#1700C2×C10111yescharacteristic, complemented
307#1681C2×C10111yescharacteristic, complemented
308#1679C2×C10111yescharacteristic, complemented
309#1666C2×C10111yescharacteristic, complemented
310#1648C2×C10111yescharacteristic, complemented
311#1647C2×C10111yescharacteristic, complemented
312#1642C2×C10111yescharacteristic, complemented
313#1627C2×C10111yescharacteristic, complemented
314#1582C2×C10111yescharacteristic, complemented
315SD16⋊C8C2×C10111yescharacteristic, complemented
316C101#1979511yescharacteristic, direct product factor, Sylow
317C2×#135—21no—
318#557C22×C10111yescharacteristic
319#550C22×C10111yescharacteristic
320D4×Q8C22×C10111yescharacteristic
321#547C22×C10111yescharacteristic
322#500C22×C10111yescharacteristic
323#492C22×C10111yescharacteristic
324#490—21no—
325#487—21no—
326#487C22×C10111yescharacteristic
327#487C22×C10111yescharacteristic
328#486C22×C10111yescharacteristic
329#486C22×C10111yescharacteristic
330#483—21no—
331#478—21no—
332#475—21no—
333#475C22×C10111yescharacteristic
334#475C22×C10111yescharacteristic
335#474C22×C10111yescharacteristic
336#465—21no—
337#465—21no—
338#462C22×C10111yescharacteristic
339#461—21no—
340#461C22×C10111yescharacteristic
341#461C22×C10111yescharacteristic
342#460—21no—
343#460C22×C10111yescharacteristic
344#459C22×C10111yescharacteristic
345#452—21no—
346#449—21no—
347#448—21no—
348#446C22×C10111yescharacteristic
349C8×Q8C22×C10111yescharacteristic
350#440—21no—
351C4×SD16—21no—
352C4×SD16C22×C10111yescharacteristic
353C4×SD16C22×C10111yescharacteristic
354C8×D4C22×C10111yescharacteristic
355C8×D4C22×C10111yescharacteristic
356C2×#103—21no—
357#335C22×C10111yescharacteristic
358#334C22×C10111yescharacteristic
359#332C22×C10111yescharacteristic
360#332C22×C10111yescharacteristic
361#332C22×C10111yescharacteristic
362#331C22×C10111yescharacteristic
363Q8⋊C8C22×C10111yescharacteristic
364Q8⋊C8C22×C10111yescharacteristic
365D4⋊C8C22×C10111yescharacteristic
366D4⋊C8C22×C10111yescharacteristic
367#322C22×C10111yescharacteristic
368C2×#41—21no—
369C2×#41—21no—
370C22×Q8—21no—
371#135—44no—
372C2×Q16—21no—
373C2×SD16—21no—
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×SD16D4×C10111yescharacteristic
379C2×SD16D4×C10111yescharacteristic
380C2×D8—21no—
381C22×C8—21no—
382C22×C8—21no—
383C4⋊Q8—21no—
384C4⋊Q8—21no—
385C4⋊Q8C23×C10111yescharacteristic
386C4⋊Q8C23×C10111yescharacteristic
387C4⋊Q8C23×C10111yescharacteristic
388#127—21no—
389#127C23×C10111yescharacteristic
390#125—21no—
391#125—41no—
392#123—41no—
393C22⋊Q8—21no—
394C22⋊Q8—21no—
395C22⋊Q8—41no—
396#121—21no—
397#121—21no—
398#121—41no—
399C4×Q8—21no—
400C4×Q8—21no—
401C4×Q8C23×C10111yescharacteristic
402C4×Q8C23×C10111yescharacteristic
403C4×D4—21no—
404C4×D4—21no—
405C4×D4C23×C10111yescharacteristic
406C4×D4C23×C10111yescharacteristic
407C2×C4⋊C4—21no—
408#107—21no—
409#107—41no—
410#106—21no—
411#106—21no—
412#106D4×C10111yescharacteristic
413#106D4×C10111yescharacteristic
414C4⋊C8—21no—
415C4⋊C8—21no—
416C4⋊C8C23×C10111yescharacteristic
417C4⋊C8C23×C10111yescharacteristic
418C4⋊C8C23×C10111yescharacteristic
419C4⋊C8C23×C10111yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#103—21no—
424#103—21no—
425#103—21no—
426#103—21no—
427#103—21no—
428#103—21no—
429#103D4×C10111yescharacteristic
430#103D4×C10111yescharacteristic
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436#102—41no—
437#102D4×C10111yescharacteristic
438#102D4×C10111yescharacteristic
439C22⋊C8—21no—
440C22⋊C8—21no—
441#97—21no—
442C4×C8—21no—
443C4×C8C23×C10111yescharacteristic
444C4×C8C23×C10111yescharacteristic
445C4×C8C23×C10111yescharacteristic
446#41—42no—
447#41—42no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8—21no—
452C2×Q8—21no—
453C2×Q8—41no—
454C2×Q8—42no—
455C2×Q8—81no—
456C2×Q8C2×D4×C10111yescharacteristic
457C2×Q8C2×D4×C10111yescharacteristic
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—21no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4C2×D4×C10111yescharacteristic
465C2×D4C2×D4×C10111yescharacteristic
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—41no—
469C22×C4—41no—
470C22×C4—41no—
471Q16—42no—
472SD16—22no—
473SD16—22no—
474SD16—42no—
475SD16—42no—
476SD16—42no—
477SD16—81no—
478SD16—81no—
479D8—42no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—42no—
486C2×C8—81no—
487C2×C8C2×D4×C10111yescharacteristic
488C2×C8C2×D4×C10111yescharacteristic
489C2×C8C2×D4×C10111yescharacteristic
490C2×C8C2×D4×C10111yescharacteristic
491C4⋊C4—21no—
492C4⋊C4—21no—
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—41no—
500C4⋊C4—41no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4—41no—
504C4⋊C4C2×D4×C10111yescharacteristic
505C4⋊C4C2×D4×C10111yescharacteristic
506C4⋊C4C2×D4×C10111yescharacteristic
507C4⋊C4C2×D4×C10111yescharacteristic
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C22⋊C4—41no—
512C22⋊C4—41no—
513C42—21no—
514C42—21no—
515C42—41no—
516C42C24×C10111yescharacteristic
517C23—21no—
518C23—21no—
519C23—41no—
520Q8—21no—
521Q8—21no—
522Q8—21no—
523Q8—41no—
524Q8—41no—
525Q8—41no—
526Q8—41no—
527Q8—41no—
528Q8—41no—
529Q8—82no—
530Q8#135×C10112yescomplemented
531D4—21no—
532D4—21no—
533D4—21no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—161no—
542D4AGL(1,ℤ/8)×C10112yes—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4C22×D4×C10111yescharacteristic
560C2×C4C22×D4×C10111yescharacteristic
561C2×C4H(5,𝔽2)×C10111yescharacteristic
562C8—21no—
563C8—21no—
564C8—21no—
565C8—21no—
566C8—41no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C22—22no—
572C22—41no—
573C22—41no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22D42×C10111yescharacteristic
581C4—22no—
582C4—21no—
583C4—41no—
584C4—41no—
585C4—41no—
586C4—41no—
587C4—41no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4C2×#135×C10111yescharacteristic
592C4C2×AGL(1,ℤ/8)×C10111yescharacteristic
593C4#577×C10111yescharacteristic
594C4#577×C10111yescharacteristic
595C2—42no—
596C2—81no—
597C2—161no—
598C2C101×#326511yescharacteristic
599C2C101×#328211yescharacteristic
600C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3284C2
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×#3368C2semidirect
2. C101×#3359C2semidirect
3. C101×#3298C2semidirect
5. C101×#1719C2semidirect
6. C101×#1700C2semidirect
7. C101×#1681C2semidirect
8. C101×#1679C2semidirect
9. C101×#1666C2semidirect
10. C101×#1648C2semidirect
11. C101×#1647C2semidirect
12. C101×#1642C2semidirect
13. C101×#1627C2semidirect
14. C101×#1582C2semidirect
15. C101×SD16⋊C8C2semidirect
229. Q8×C101#135semidirect
294. #19795C101direct (N × H)
301. #3368C2×C101semidirect
302. #3359C2×C101semidirect
303. #3298C2×C101semidirect
305. #1719C2×C101semidirect
306. #1700C2×C101semidirect
307. #1681C2×C101semidirect
308. #1679C2×C101semidirect
309. #1666C2×C101semidirect
310. #1648C2×C101semidirect
311. #1647C2×C101semidirect
312. #1642C2×C101semidirect
313. #1627C2×C101semidirect
314. #1582C2×C101semidirect
315. SD16⋊C8C2×C101semidirect
316. C101#19795direct (N × H)
530. Q8#135×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#33682
C101×#33592
C101×#32982
C101×#32842
C101×#17192
C101×#17002
C101×#16812
C101×#16792
C101×#16662
C101×#16482
C101×#16472
C101×#16422
C101×#16272
C101×#15822
C101×SD16⋊C82
#19795101