Finite Group Databasebeta

← C101×#20300 #38802451

Subgroups — C101×#20300 #38802451

Order 25856.

578 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3374C211yesmaximal, characteristic, complemented
2C101×#3372C211yesmaximal, characteristic, complemented
3C101×#3368C211yesmaximal, characteristic
4C101×#3333C211yesmaximal, characteristic
5C101×#1711C211yesmaximal, characteristic, complemented
6C101×#1704C211yesmaximal, characteristic, complemented
7C101×#1702C211yesmaximal, characteristic, complemented
8C101×#1699C211yesmaximal, characteristic, complemented
9C101×#1698C211yesmaximal, characteristic, complemented
10C101×#1644C211yesmaximal, characteristic, complemented
11C101×#1642C211yesmaximal, characteristic
12C101×#1636C211yesmaximal, characteristic, complemented
13C101×#1626C211yesmaximal, characteristic, complemented
14C101×#1591C211yesmaximal, characteristic, complemented
15C101×#1590C211yesmaximal, characteristic, complemented
16#557×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#550×C101C2211yescharacteristic
20#491×C101—21no—
21#491×C101—21no—
22#490×C101—21no—
23#487×C101C2211yescharacteristic
24#487×C101C2211yescharacteristic
25#487×C101C2211yescharacteristic
26#486×C101C2211yescharacteristic
27#486×C101C2211yescharacteristic
28#486×C101C2211yescharacteristic
29#480×C101—21no—
30#479×C101—21no—
31#479×C101—21no—
32#478×C101—21no—
33#477×C101C2211yescharacteristic
34#477×C101C2211yescharacteristic
35#475×C101C2211yescharacteristic
36#474×C101C2211yescharacteristic
37#468×C101—21no—
38#462×C101—21no—
39#462×C101C2211yescharacteristic
40#461×C101—21no—
41#461×C101C2211yescharacteristic
42#460×C101—21no—
43#460×C101C2211yescharacteristic
44#460×C101C2211yescharacteristic
45#452×C101—21no—
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#441×C101—21no—
50#440×C101—21no—
51#440×C101—21no—
52C4×Q16×C101C2211yescharacteristic
53C4×SD16×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#331×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101D411yescharacteristic
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101—21no—
73C2×SD16×C101D411yescharacteristic
74C2×M16×C101—21no—
75C4⋊Q8×C101—21no—
76C4⋊Q8×C101—21no—
77C4⋊Q8×C101C2311yescharacteristic
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80#127×C101—21no—
81#127×C101C2311yescharacteristic
82#125×C101—21no—
83#125×C101—21no—
84#125×C101—21no—
85#125×C101—41no—
86#125×C101—41no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—41no—
89#121×C101—21no—
90#121×C101—41no—
91C4×Q8×C101—21no—
92C4×Q8×C101—21no—
93C4×Q8×C101—21no—
94C4×Q8×C101—21no—
95C4×Q8×C101C2311yescharacteristic
96C4×Q8×C101C2311yescharacteristic
97C4×Q8×C101C2311yescharacteristic
98C4×D4×C101—21no—
99C4×D4×C101—21no—
100C4×D4×C101C2311yescharacteristic
101C2×C4⋊C4×C101—21no—
102#107×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#107×C101D411yescharacteristic
106#106×C101—21no—
107#106×C101D411yescharacteristic
108C4⋊C8×C101—21no—
109C4⋊C8×C101—21no—
110C4⋊C8×C101—21no—
111C4⋊C8×C101C2311yescharacteristic
112C4⋊C8×C101C2311yescharacteristic
113C4⋊C8×C101C2311yescharacteristic
114C4⋊C8×C101C2311yescharacteristic
115#103×C101—21no—
116#103×C101—21no—
117#103×C101—21no—
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×C101—41no—
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—41no—
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138#97×C101—21no—
139#97×C101—21no—
140#97×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—42no—
145#41×C101—81no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×D4×C101—21no—
153C2×D4×C101—21no—
154C2×D4×C101—21no—
155C2×D4×C101—41no—
156C2×D4×C101—41no—
157C2×D4×C101C2×D411yescharacteristic
158C22×C4×C101—21no—
159C22×C4×C101—41no—
160C22×C4×C101—41no—
161Q16×C101—41no—
162Q16×C101—42no—
163SD16×C101—41no—
164SD16×C101—42no—
165SD16×C101—42no—
166SD16×C101—81no—
167M16×C101—81no—
168C2×C8×C101—21no—
169C2×C8×C101—21no—
170C2×C8×C101—21no—
171C2×C8×C101—21no—
172C2×C8×C101—21no—
173C2×C8×C101C2×D411yescharacteristic
174C2×C8×C101C2×D411yescharacteristic
175C2×C8×C101C2×D411yescharacteristic
176C2×C8×C101C2×D411yescharacteristic
177C4⋊C4×C101—21no—
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×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—41no—
200C22⋊C4×C101—41no—
201C42×C101—21no—
202C42×C101—21no—
203C42×C101—21no—
204C42×C101—41no—
205C42×C101—41no—
206C42×C101C2411yescharacteristic
207C23×C101—21no—
208C23×C101—41no—
209Q8×C101—21no—
210Q8×C101—21no—
211Q8×C101—21no—
212Q8×C101—21no—
213Q8×C101—21no—
214Q8×C101—21no—
215Q8×C101—41no—
216Q8×C101—41no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—81no—
220D4×C101—21no—
221D4×C101—21no—
222D4×C101—41no—
223D4×C101—41no—
224D4×C101—41no—
225D4×C101—41no—
226D4×C101—81no—
227D4×C101—82no—
228D4×C101—161no—
229C2×C4×C101—21no—
230C2×C4×C101—21no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—41no—
240C2×C4×C101—41no—
241C2×C4×C101—82no—
242C2×C4×C101—161no—
243C2×C4×C101C22×D411yescharacteristic
244C2×C4×C101C22×D411yescharacteristic
245C2×C4×C101H(5,𝔽2)11yescharacteristic
246C8×C101—21no—
247C8×C101—21no—
248C8×C101—21no—
249C8×C101—21no—
250C8×C101—41no—
251C8×C101—41no—
252C8×C101—41no—
253C8×C101—41no—
254C8×C101—41no—
255C22×C101—41no—
256C22×C101—41no—
257C22×C101—41no—
258C22×C101—81no—
259C22×C101—81no—
260C22×C101—81no—
261C22×C101D4211yescharacteristic
262C4×C101—21no—
263C4×C101—41no—
264C4×C101—41no—
265C4×C101—41no—
266C4×C101—41no—
267C4×C101—41no—
268C4×C101—41no—
269C4×C101—41no—
270C4×C101—81no—
271C4×C101—81no—
272C4×C101—81no—
273C4×C101#57511yescharacteristic
274C4×C101#57511yescharacteristic
275C4×C101#57711yescharacteristic
276C4×C101#57811yescharacteristic
277#20300C10111yesmaximal, characteristic, direct product factor, Sylow
278C2×C101—81no—
279C2×C101—161no—
280C2×C101#327511yescharacteristic
281C2×C101#327711yescharacteristic
282C2×C101#329011yescharacteristic
283#3374C2×C10111yescharacteristic, complemented
284#3372C2×C10111yescharacteristic, complemented
285#3368C2×C10111yescharacteristic
286#3333C2×C10111yescharacteristic
287#1711C2×C10111yescharacteristic, complemented
288#1704C2×C10111yescharacteristic, complemented
289#1702C2×C10111yescharacteristic, complemented
290#1699C2×C10111yescharacteristic, complemented
291#1698C2×C10111yescharacteristic, complemented
292#1644C2×C10111yescharacteristic, complemented
293#1642C2×C10111yescharacteristic
294#1636C2×C10111yescharacteristic, complemented
295#1626C2×C10111yescharacteristic, complemented
296#1591C2×C10111yescharacteristic, complemented
297#1590C2×C10111yescharacteristic, complemented
298C101#2030011yescharacteristic, direct product factor, Sylow
299#557C22×C10111yescharacteristic
300#557C22×C10111yescharacteristic
301#554C22×C10111yescharacteristic
302#550C22×C10111yescharacteristic
303#491—21no—
304#491—21no—
305#490—21no—
306#487C22×C10111yescharacteristic
307#487C22×C10111yescharacteristic
308#487C22×C10111yescharacteristic
309#486C22×C10111yescharacteristic
310#486C22×C10111yescharacteristic
311#486C22×C10111yescharacteristic
312#480—21no—
313#479—21no—
314#479—21no—
315#478—21no—
316#477C22×C10111yescharacteristic
317#477C22×C10111yescharacteristic
318#475C22×C10111yescharacteristic
319#474C22×C10111yescharacteristic
320#468—21no—
321#462—21no—
322#462C22×C10111yescharacteristic
323#461—21no—
324#461C22×C10111yescharacteristic
325#460—21no—
326#460C22×C10111yescharacteristic
327#460C22×C10111yescharacteristic
328#452—21no—
329#446C22×C10111yescharacteristic
330#446C22×C10111yescharacteristic
331#446C22×C10111yescharacteristic
332#441—21no—
333#440—21no—
334#440—21no—
335C4×Q16C22×C10111yescharacteristic
336C4×SD16C22×C10111yescharacteristic
337#436C22×C10111yescharacteristic
338#417—21no—
339#335C22×C10111yescharacteristic
340#334C22×C10111yescharacteristic
341#333C22×C10111yescharacteristic
342#332C22×C10111yescharacteristic
343#332C22×C10111yescharacteristic
344#331C22×C10111yescharacteristic
345Q8⋊C8C22×C10111yescharacteristic
346Q8⋊C8C22×C10111yescharacteristic
347Q8⋊C8C22×C10111yescharacteristic
348D4⋊C8C22×C10111yescharacteristic
349C82C22×C10111yescharacteristic
350C2×#41—21no—
351C2×Q16—21no—
352C2×Q16D4×C10111yescharacteristic
353C2×SD16—21no—
354C2×SD16—21no—
355C2×SD16—21no—
356C2×SD16D4×C10111yescharacteristic
357C2×M16—21no—
358C4⋊Q8—21no—
359C4⋊Q8—21no—
360C4⋊Q8C23×C10111yescharacteristic
361C4⋊Q8C23×C10111yescharacteristic
362C4⋊Q8C23×C10111yescharacteristic
363#127—21no—
364#127C23×C10111yescharacteristic
365#125—21no—
366#125—21no—
367#125—21no—
368#125—41no—
369#125—41no—
370C22⋊Q8—21no—
371C22⋊Q8—41no—
372#121—21no—
373#121—41no—
374C4×Q8—21no—
375C4×Q8—21no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C10111yescharacteristic
379C4×Q8C23×C10111yescharacteristic
380C4×Q8C23×C10111yescharacteristic
381C4×D4—21no—
382C4×D4—21no—
383C4×D4C23×C10111yescharacteristic
384C2×C4⋊C4—21no—
385#107—21no—
386#107—21no—
387#107—21no—
388#107D4×C10111yescharacteristic
389#106—21no—
390#106D4×C10111yescharacteristic
391C4⋊C8—21no—
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C10111yescharacteristic
395C4⋊C8C23×C10111yescharacteristic
396C4⋊C8C23×C10111yescharacteristic
397C4⋊C8C23×C10111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—41no—
408#103D4×C10111yescharacteristic
409#103D4×C10111yescharacteristic
410#103D4×C10111yescharacteristic
411#102—21no—
412#102—21no—
413#102—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—41no—
419#102D4×C10111yescharacteristic
420C22⋊C8—21no—
421#97—21no—
422#97—21no—
423#97—21no—
424C4×C8C23×C10111yescharacteristic
425C4×C8C23×C10111yescharacteristic
426C4×C8C23×C10111yescharacteristic
427#41—42no—
428#41—81no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8C2×D4×C10111yescharacteristic
433C2×Q8C2×D4×C10111yescharacteristic
434C2×Q8C2×D4×C10111yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C2×D4×C10111yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4—41no—
444Q16—41no—
445Q16—42no—
446SD16—41no—
447SD16—42no—
448SD16—42no—
449SD16—81no—
450M16—81no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8C2×D4×C10111yescharacteristic
457C2×C8C2×D4×C10111yescharacteristic
458C2×C8C2×D4×C10111yescharacteristic
459C2×C8C2×D4×C10111yescharacteristic
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—41no—
474C4⋊C4—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C10111yescharacteristic
478C4⋊C4C2×D4×C10111yescharacteristic
479C4⋊C4C2×D4×C10111yescharacteristic
480C4⋊C4C2×D4×C10111yescharacteristic
481C22⋊C4—21no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—41no—
488C42—41no—
489C42C24×C10111yescharacteristic
490C23—21no—
491C23—41no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—81no—
503D4—21no—
504D4—21no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—41no—
509D4—81no—
510D4—82no—
511D4—161no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4—161no—
526C2×C4C22×D4×C10111yescharacteristic
527C2×C4C22×D4×C10111yescharacteristic
528C2×C4H(5,𝔽2)×C10111yescharacteristic
529C8—21no—
530C8—21no—
531C8—21no—
532C8—21no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22D42×C10111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4#575×C10111yescharacteristic
557C4#575×C10111yescharacteristic
558C4#577×C10111yescharacteristic
559C4#578×C10111yescharacteristic
560C2—81no—
561C2—161no—
562C2C101×#327511yescharacteristic
563C2C101×#327711yescharacteristic
564C2C101×#329011yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radical#550×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
1. C101×#3374C2semidirect
2. C101×#3372C2semidirect
5. C101×#1711C2semidirect
6. C101×#1704C2semidirect
7. C101×#1702C2semidirect
8. C101×#1699C2semidirect
9. C101×#1698C2semidirect
10. C101×#1644C2semidirect
12. C101×#1636C2semidirect
13. C101×#1626C2semidirect
14. C101×#1591C2semidirect
15. C101×#1590C2semidirect
277. #20300C101direct (N × H)
283. #3374C2×C101semidirect
284. #3372C2×C101semidirect
287. #1711C2×C101semidirect
288. #1704C2×C101semidirect
289. #1702C2×C101semidirect
290. #1699C2×C101semidirect
291. #1698C2×C101semidirect
292. #1644C2×C101semidirect
294. #1636C2×C101semidirect
295. #1626C2×C101semidirect
296. #1591C2×C101semidirect
297. #1590C2×C101semidirect
298. C101#20300direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33742
C101×#33722
C101×#33682
C101×#33332
C101×#17112
C101×#17042
C101×#17022
C101×#16992
C101×#16982
C101×#16442
C101×#16422
C101×#16362
C101×#16262
C101×#15912
C101×#15902
#20300101