Finite Group Databasebeta

← C101×#19850 #38802001

Subgroups — C101×#19850 #38802001

Order 25856.

584 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3396C211yesmaximal, characteristic
2C101×#3375C211yesmaximal, characteristic, complemented
3C101×#3365C211yesmaximal, characteristic, complemented
4C101×#3363C211yesmaximal, characteristic, complemented
5C101×#1717C211yesmaximal, characteristic
6C101×#1702C211yesmaximal, characteristic, complemented
7C101×#1684C211yesmaximal, characteristic, complemented
8C101×#1678C211yesmaximal, characteristic, complemented
9C101×#1668C211yesmaximal, characteristic
10C101×#1640C211yesmaximal, characteristic, complemented
11C101×#1630C211yesmaximal, characteristic, complemented
12C101×#1626C211yesmaximal, characteristic, complemented
13C101×#1623C211yesmaximal, characteristic, complemented
14C101×#1584C211yesmaximal, characteristic, complemented
15C101×#1579C211yesmaximal, characteristic, complemented
16#559×C101C2211yescharacteristic
17#559×C101C2211yescharacteristic
18Q82×C101C2211yescharacteristic
19#557×C101C2211yescharacteristic
20#495×C101—21no—
21#493×C101C2211yescharacteristic
22#492×C101C2211yescharacteristic
23#489×C101—21no—
24#488×C101—21no—
25#487×C101—21no—
26#487×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#486×C101C2211yescharacteristic
30#478×C101—21no—
31#477×C101—21no—
32#477×C101C2211yescharacteristic
33#477×C101C2211yescharacteristic
34#475×C101C2211yescharacteristic
35#474×C101—21no—
36#464×C101—21no—
37#464×C101—21no—
38#463×C101—21no—
39#463×C101—21no—
40#462×C101—21no—
41#462×C101C2211yescharacteristic
42#460×C101C2211yescharacteristic
43#460×C101C2211yescharacteristic
44#460×C101C2211yescharacteristic
45#460×C101C2211yescharacteristic
46#446×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49C8×Q8×C101C2211yescharacteristic
50#440×C101—21no—
51C4×Q16×C101—21no—
52C4×Q16×C101C2211yescharacteristic
53C4×Q16×C101C2211yescharacteristic
54C4×SD16×C101—21no—
55C4×D8×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#331×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65Q8⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×Q16×C101—21no—
68C2×Q16×C101D411yescharacteristic
69C2×Q16×C101D411yescharacteristic
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×SD16×C101—41no—
75C2×D8×C101—21no—
76C2×D8×C101—21no—
77C4⋊Q8×C101—21no—
78C4⋊Q8×C101—21no—
79C4⋊Q8×C101—21no—
80C4⋊Q8×C101—41no—
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#125×C101—21no—
86#125×C101—41no—
87#124×C101—21no—
88#124×C101—21no—
89#124×C101—21no—
90#124×C101—21no—
91#123×C101—41no—
92#123×C101—41no—
93C4×Q8×C101—21no—
94C4×Q8×C101—21no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×Q8×C101C2311yescharacteristic
98C4×Q8×C101C2311yescharacteristic
99C4×Q8×C101C2311yescharacteristic
100C4×Q8×C101C2311yescharacteristic
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101D411yescharacteristic
108#107×C101D411yescharacteristic
109#106×C101—21no—
110C4⋊C8×C101—21no—
111C4⋊C8×C101—21no—
112C4⋊C8×C101—21no—
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×C101—21no—
123#103×C101—21no—
124#103×C101D411yescharacteristic
125#103×C101D411yescharacteristic
126#103×C101D411yescharacteristic
127#103×C101D411yescharacteristic
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×C101—21no—
135#102×C101—21no—
136#102×C101—41no—
137#97×C101—21no—
138C4×C8×C101—21no—
139C4×C8×C101—21no—
140C4×C8×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C2×Q8×C101—21no—
145C2×Q8×C101—21no—
146C2×Q8×C101—41no—
147C2×Q8×C101C2×D411yescharacteristic
148C2×Q8×C101C2×D411yescharacteristic
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×D4×C101—21no—
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—21no—
156C2×D4×C101—21no—
157C22×C4×C101—41no—
158C22×C4×C101—41no—
159Q16×C101—22no—
160Q16×C101—41no—
161Q16×C101—42no—
162SD16×C101—42no—
163SD16×C101—42no—
164SD16×C101—81no—
165SD16×C101—81no—
166SD16×C101—82no—
167D8×C101—42no—
168D8×C101—81no—
169C2×C8×C101—21no—
170C2×C8×C101—21no—
171C2×C8×C101—21no—
172C2×C8×C101—21no—
173C2×C8×C101—21no—
174C2×C8×C101C2×D411yescharacteristic
175C2×C8×C101C2×D411yescharacteristic
176C2×C8×C101C2×D411yescharacteristic
177C2×C8×C101C2×D411yescharacteristic
178C4⋊C4×C101—21no—
179C4⋊C4×C101—21no—
180C4⋊C4×C101—21no—
181C4⋊C4×C101—21no—
182C4⋊C4×C101—21no—
183C4⋊C4×C101—21no—
184C4⋊C4×C101—21no—
185C4⋊C4×C101—21no—
186C4⋊C4×C101—41no—
187C4⋊C4×C101—41no—
188C4⋊C4×C101—41no—
189C4⋊C4×C101—41no—
190C4⋊C4×C101—41no—
191C4⋊C4×C101C2×D411yescharacteristic
192C4⋊C4×C101C2×D411yescharacteristic
193C4⋊C4×C101C2×D411yescharacteristic
194C4⋊C4×C101C2×D411yescharacteristic
195C22⋊C4×C101—41no—
196C22⋊C4×C101—41no—
197C22⋊C4×C101—41no—
198C22⋊C4×C101—41no—
199C22⋊C4×C101—41no—
200C22⋊C4×C101—41no—
201C42×C101—21no—
202C42×C101—21no—
203C42×C101—21no—
204C42×C101—21no—
205C42×C101—41no—
206C42×C101—41no—
207C42×C101C2411yescharacteristic
208C23×C101—41no—
209C23×C101—41no—
210Q8×C101—21no—
211Q8×C101—21no—
212Q8×C101—21no—
213Q8×C101—21no—
214Q8×C101—21no—
215Q8×C101—21no—
216Q8×C101—21no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—81no—
220Q8×C101—161no—
221Q8×C101#13512yes—
222D4×C101—41no—
223D4×C101—41no—
224D4×C101—41no—
225D4×C101—41no—
226D4×C101—41no—
227D4×C101—41no—
228D4×C101—41no—
229D4×C101—41no—
230D4×C101—81no—
231D4×C101—81no—
232C2×C4×C101—21no—
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—161no—
243C2×C4×C101—161no—
244C2×C4×C101C22×D411yescharacteristic
245C2×C4×C101C22×D411yescharacteristic
246C2×C4×C101H(5,𝔽2)11yescharacteristic
247C8×C101—21no—
248C8×C101—21no—
249C8×C101—21no—
250C8×C101—21no—
251C8×C101—41no—
252C8×C101—41no—
253C8×C101—41no—
254C8×C101—41no—
255C8×C101—41no—
256C22×C101—81no—
257C22×C101—81no—
258C22×C101—81no—
259C22×C101—81no—
260C22×C101—81no—
261C22×C101—81no—
262C22×C101D4211yescharacteristic
263C4×C101—22no—
264C4×C101—21no—
265C4×C101—41no—
266C4×C101—41no—
267C4×C101—41no—
268C4×C101—41no—
269C4×C101—41no—
270C4×C101—41no—
271C4×C101—41no—
272C4×C101—81no—
273C4×C101—81no—
274C4×C101C2×#13511yescharacteristic
275C4×C101#57511yescharacteristic
276C4×C101#57711yescharacteristic
277C4×C101#57811yescharacteristic
278#19850C10111yesmaximal, characteristic, direct product factor, Sylow
279C2×C101—161no—
280C2×C101—161no—
281C2×C101#327111yescharacteristic
282C2×C101#328511yescharacteristic
283C2×C101#328811yescharacteristic
284#3396C2×C10111yescharacteristic
285#3375C2×C10111yescharacteristic, complemented
286#3365C2×C10111yescharacteristic, complemented
287#3363C2×C10111yescharacteristic, complemented
288#1717C2×C10111yescharacteristic
289#1702C2×C10111yescharacteristic, complemented
290#1684C2×C10111yescharacteristic, complemented
291#1678C2×C10111yescharacteristic, complemented
292#1668C2×C10111yescharacteristic
293#1640C2×C10111yescharacteristic, complemented
294#1630C2×C10111yescharacteristic, complemented
295#1626C2×C10111yescharacteristic, complemented
296#1623C2×C10111yescharacteristic, complemented
297#1584C2×C10111yescharacteristic, complemented
298#1579C2×C10111yescharacteristic, complemented
299C101#1985011yescharacteristic, direct product factor, Sylow
300#559C22×C10111yescharacteristic
301#559C22×C10111yescharacteristic
302Q82C22×C10111yescharacteristic
303#557C22×C10111yescharacteristic
304#495—21no—
305#493C22×C10111yescharacteristic
306#492C22×C10111yescharacteristic
307#489—21no—
308#488—21no—
309#487—21no—
310#487C22×C10111yescharacteristic
311#486C22×C10111yescharacteristic
312#486C22×C10111yescharacteristic
313#486C22×C10111yescharacteristic
314#478—21no—
315#477—21no—
316#477C22×C10111yescharacteristic
317#477C22×C10111yescharacteristic
318#475C22×C10111yescharacteristic
319#474—21no—
320#464—21no—
321#464—21no—
322#463—21no—
323#463—21no—
324#462—21no—
325#462C22×C10111yescharacteristic
326#460C22×C10111yescharacteristic
327#460C22×C10111yescharacteristic
328#460C22×C10111yescharacteristic
329#460C22×C10111yescharacteristic
330#446C22×C10111yescharacteristic
331C8×Q8C22×C10111yescharacteristic
332C8×Q8C22×C10111yescharacteristic
333C8×Q8C22×C10111yescharacteristic
334#440—21no—
335C4×Q16—21no—
336C4×Q16C22×C10111yescharacteristic
337C4×Q16C22×C10111yescharacteristic
338C4×SD16—21no—
339C4×D8—21no—
340#335C22×C10111yescharacteristic
341#334C22×C10111yescharacteristic
342#333C22×C10111yescharacteristic
343#332C22×C10111yescharacteristic
344#331C22×C10111yescharacteristic
345#331C22×C10111yescharacteristic
346Q8⋊C8C22×C10111yescharacteristic
347Q8⋊C8C22×C10111yescharacteristic
348Q8⋊C8C22×C10111yescharacteristic
349Q8⋊C8C22×C10111yescharacteristic
350#322C22×C10111yescharacteristic
351C2×Q16—21no—
352C2×Q16D4×C10111yescharacteristic
353C2×Q16D4×C10111yescharacteristic
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16—41no—
359C2×D8—21no—
360C2×D8—21no—
361C4⋊Q8—21no—
362C4⋊Q8—21no—
363C4⋊Q8—21no—
364C4⋊Q8—41no—
365C4⋊Q8C23×C10111yescharacteristic
366C4⋊Q8C23×C10111yescharacteristic
367#127C23×C10111yescharacteristic
368#127C23×C10111yescharacteristic
369#125—21no—
370#125—41no—
371#124—21no—
372#124—21no—
373#124—21no—
374#124—21no—
375#123—41no—
376#123—41no—
377C4×Q8—21no—
378C4×Q8—21no—
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C10111yescharacteristic
382C4×Q8C23×C10111yescharacteristic
383C4×Q8C23×C10111yescharacteristic
384C4×Q8C23×C10111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4—21no—
388C4×D4—21no—
389#107—21no—
390#107—21no—
391#107D4×C10111yescharacteristic
392#107D4×C10111yescharacteristic
393#106—21no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—21no—
398C4⋊C8C23×C10111yescharacteristic
399C4⋊C8C23×C10111yescharacteristic
400C4⋊C8C23×C10111yescharacteristic
401C4⋊C8C23×C10111yescharacteristic
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103D4×C10111yescharacteristic
409#103D4×C10111yescharacteristic
410#103D4×C10111yescharacteristic
411#103D4×C10111yescharacteristic
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—41no—
421#97—21no—
422C4×C8—21no—
423C4×C8—21no—
424C4×C8—21no—
425C4×C8C23×C10111yescharacteristic
426C4×C8C23×C10111yescharacteristic
427C4×C8C23×C10111yescharacteristic
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—41no—
431C2×Q8C2×D4×C10111yescharacteristic
432C2×Q8C2×D4×C10111yescharacteristic
433C2×Q8C2×D4×C10111yescharacteristic
434C2×Q8C2×D4×C10111yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—21no—
440C2×D4—21no—
441C22×C4—41no—
442C22×C4—41no—
443Q16—22no—
444Q16—41no—
445Q16—42no—
446SD16—42no—
447SD16—42no—
448SD16—81no—
449SD16—81no—
450SD16—82no—
451D8—42no—
452D8—81no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8C2×D4×C10111yescharacteristic
459C2×C8C2×D4×C10111yescharacteristic
460C2×C8C2×D4×C10111yescharacteristic
461C2×C8C2×D4×C10111yescharacteristic
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4C2×D4×C10111yescharacteristic
476C4⋊C4C2×D4×C10111yescharacteristic
477C4⋊C4C2×D4×C10111yescharacteristic
478C4⋊C4C2×D4×C10111yescharacteristic
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—41no—
491C42C24×C10111yescharacteristic
492C23—41no—
493C23—41no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—41no—
502Q8—41no—
503Q8—81no—
504Q8—161no—
505Q8#135×C10112yes—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—41no—
510D4—41no—
511D4—41no—
512D4—41no—
513D4—41no—
514D4—81no—
515D4—81no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—161no—
527C2×C4—161no—
528C2×C4C22×D4×C10111yescharacteristic
529C2×C4C22×D4×C10111yescharacteristic
530C2×C4H(5,𝔽2)×C10111yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C22—81no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22—81no—
546C22D42×C10111yescharacteristic
547C4—22no—
548C4—21no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—81no—
557C4—81no—
558C4C2×#135×C10111yescharacteristic
559C4#575×C10111yescharacteristic
560C4#577×C10111yescharacteristic
561C4#578×C10111yescharacteristic
562C2—161no—
563C2—161no—
564C2C101×#327111yescharacteristic
565C2C101×#328511yescharacteristic
566C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radical#493×C101C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3375C2semidirect
3. C101×#3365C2semidirect
4. C101×#3363C2semidirect
6. C101×#1702C2semidirect
7. C101×#1684C2semidirect
8. C101×#1678C2semidirect
10. C101×#1640C2semidirect
11. C101×#1630C2semidirect
12. C101×#1626C2semidirect
13. C101×#1623C2semidirect
14. C101×#1584C2semidirect
15. C101×#1579C2semidirect
278. #19850C101direct (N × H)
285. #3375C2×C101semidirect
286. #3365C2×C101semidirect
287. #3363C2×C101semidirect
289. #1702C2×C101semidirect
290. #1684C2×C101semidirect
291. #1678C2×C101semidirect
293. #1640C2×C101semidirect
294. #1630C2×C101semidirect
295. #1626C2×C101semidirect
296. #1623C2×C101semidirect
297. #1584C2×C101semidirect
298. #1579C2×C101semidirect
299. C101#19850direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33962
C101×#33752
C101×#33652
C101×#33632
C101×#17172
C101×#17022
C101×#16842
C101×#16782
C101×#16682
C101×#16402
C101×#16302
C101×#16262
C101×#16232
C101×#15842
C101×#15792
#19850101