Finite Group Databasebeta

← C101×#19838 #38801989

Subgroups — C101×#19838 #38801989

Order 25856.

574 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3383C211yesmaximal, characteristic, complemented
2C101×#3372C211yesmaximal, characteristic
3C101×#3359C211yesmaximal, characteristic
4C101×#3299C211yesmaximal, characteristic
5C101×#1718C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1684C211yesmaximal, characteristic, complemented
8C101×#1684C211yesmaximal, characteristic, complemented
9C101×#1673C211yesmaximal, characteristic
10C101×#1653C211yesmaximal, characteristic, complemented
11C101×#1651C211yesmaximal, characteristic
12C101×#1643C211yesmaximal, characteristic
13C101×#1636C211yesmaximal, characteristic, complemented
14C101×#1584C211yesmaximal, characteristic, complemented
15C101×SD16⋊C8C211yesmaximal, characteristic
16#557×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#499×C101—21no—
22#498×C101C2211yescharacteristic
23#491×C101—21no—
24#487×C101—21no—
25#487×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#487×C101C2211yescharacteristic
29#484×C101—21no—
30#479×C101—21no—
31#479×C101—21no—
32#479×C101—21no—
33#477×C101C2211yescharacteristic
34#477×C101C2211yescharacteristic
35#475×C101—21no—
36#475×C101C2211yescharacteristic
37#475×C101C2211yescharacteristic
38#475×C101C2211yescharacteristic
39#467×C101—21no—
40#462×C101C2211yescharacteristic
41#461×C101—21no—
42#461×C101—21no—
43#461×C101C2211yescharacteristic
44#461×C101C2211yescharacteristic
45#451×C101—21no—
46#446×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#440×C101—21no—
50C4×Q16×C101—21no—
51C4×Q16×C101C2211yescharacteristic
52C4×SD16×C101—21no—
53C4×SD16×C101C2211yescharacteristic
54C8×D4×C101C2211yescharacteristic
55C2×#103×C101—21no—
56#335×C101C2211yescharacteristic
57#335×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C22×Q8×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101D411yescharacteristic
70C2×SD16×C101—21no—
71C2×SD16×C101—21no—
72C2×SD16×C101D411yescharacteristic
73C22×C8×C101—21no—
74C4⋊Q8×C101—21no—
75C4⋊Q8×C101—21no—
76C4⋊Q8×C101—21no—
77C4⋊Q8×C101C2311yescharacteristic
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81#125×C101—21no—
82#125×C101—21no—
83#125×C101—21no—
84#125×C101—41no—
85#125×C101—41no—
86C22⋊Q8×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—41no—
89C22⋊Q8×C101—41no—
90C4×Q8×C101—21no—
91C4×Q8×C101—21no—
92C4×Q8×C101—21no—
93C4×Q8×C101—21no—
94C4×Q8×C101C2311yescharacteristic
95C4×Q8×C101C2311yescharacteristic
96C4×Q8×C101C2311yescharacteristic
97C4×D4×C101—21no—
98C4×D4×C101—21no—
99C4×D4×C101C2311yescharacteristic
100C2×C4⋊C4×C101—21no—
101#107×C101—21no—
102#107×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#107×C101D411yescharacteristic
106#106×C101—21no—
107#106×C101—21no—
108#106×C101—21no—
109#106×C101—41no—
110#106×C101D411yescharacteristic
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×C101—21no—
125#103×C101—21no—
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—41no—
133#103×C101D411yescharacteristic
134#103×C101D411yescharacteristic
135#103×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138#97×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—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—41no—
149C2×Q8×C101—42no—
150C2×Q8×C101—81no—
151C2×Q8×C101C2×D411yescharacteristic
152C2×Q8×C101C2×D411yescharacteristic
153C2×Q8×C101C2×D411yescharacteristic
154C2×D4×C101C2×D411yescharacteristic
155C22×C4×C101—21no—
156C22×C4×C101—41no—
157C22×C4×C101—41no—
158Q16×C101—22no—
159Q16×C101—81no—
160SD16×C101—22no—
161SD16×C101—42no—
162SD16×C101—42no—
163C2×C8×C101—21no—
164C2×C8×C101—21no—
165C2×C8×C101—21no—
166C2×C8×C101—21no—
167C2×C8×C101—21no—
168C2×C8×C101—81no—
169C2×C8×C101C2×D411yescharacteristic
170C2×C8×C101C2×D411yescharacteristic
171C2×C8×C101C2×D411yescharacteristic
172C2×C8×C101C2×D411yescharacteristic
173C4⋊C4×C101—21no—
174C4⋊C4×C101—21no—
175C4⋊C4×C101—21no—
176C4⋊C4×C101—21no—
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—41no—
185C4⋊C4×C101—41no—
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×C101C2×D411yescharacteristic
194C4⋊C4×C101C2×D411yescharacteristic
195C4⋊C4×C101C2×D411yescharacteristic
196C4⋊C4×C101C2×D411yescharacteristic
197C22⋊C4×C101—21no—
198C22⋊C4×C101—41no—
199C22⋊C4×C101—41no—
200C42×C101—21no—
201C42×C101—21no—
202C42×C101—21no—
203C42×C101—41no—
204C42×C101—41no—
205C42×C101C2411yescharacteristic
206C23×C101—21no—
207Q8×C101—21no—
208Q8×C101—21no—
209Q8×C101—21no—
210Q8×C101—21no—
211Q8×C101—21no—
212Q8×C101—41no—
213Q8×C101—41no—
214Q8×C101—41no—
215Q8×C101—41no—
216Q8×C101—41no—
217Q8×C101—41no—
218Q8×C101—82no—
219Q8×C101—81no—
220Q8×C101#13712yes—
221D4×C101—21no—
222D4×C101#13512yes—
223C2×C4×C101—21no—
224C2×C4×C101—21no—
225C2×C4×C101—21no—
226C2×C4×C101—21no—
227C2×C4×C101—21no—
228C2×C4×C101—21no—
229C2×C4×C101—21no—
230C2×C4×C101—41no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
236C2×C4×C101—82no—
237C2×C4×C101—161no—
238C2×C4×C101C22×D411yescharacteristic
239C2×C4×C101C22×D411yescharacteristic
240C2×C4×C101H(5,𝔽2)11yescharacteristic
241C8×C101—21no—
242C8×C101—21no—
243C8×C101—21no—
244C8×C101—21no—
245C8×C101—41no—
246C8×C101—41no—
247C8×C101—41no—
248C8×C101—41no—
249C8×C101—41no—
250C22×C101—22no—
251C22×C101—41no—
252C22×C101—41no—
253C22×C101D4211yescharacteristic
254C4×C101—22no—
255C4×C101—21no—
256C4×C101—41no—
257C4×C101—41no—
258C4×C101—41no—
259C4×C101—41no—
260C4×C101—41no—
261C4×C101—41no—
262C4×C101—81no—
263C4×C101—81no—
264C4×C101—81no—
265C4×C101—81no—
266C4×C101C2×#13511yescharacteristic
267C4×C101C2×#13711yescharacteristic
268C4×C101#57711yescharacteristic
269C4×C101#57811yescharacteristic
270#19838C10111yesmaximal, characteristic, direct product factor, Sylow
271C2×C101—42no—
272C2×C101#326611yescharacteristic
273C2×C101#328511yescharacteristic
274C2×C101#328911yescharacteristic
275#3383C2×C10111yescharacteristic, complemented
276#3372C2×C10111yescharacteristic
277#3359C2×C10111yescharacteristic
278#3299C2×C10111yescharacteristic
279#1718C2×C10111yescharacteristic, complemented
280#1700C2×C10111yescharacteristic, complemented
281#1684C2×C10111yescharacteristic, complemented
282#1684C2×C10111yescharacteristic, complemented
283#1673C2×C10111yescharacteristic
284#1653C2×C10111yescharacteristic, complemented
285#1651C2×C10111yescharacteristic
286#1643C2×C10111yescharacteristic
287#1636C2×C10111yescharacteristic, complemented
288#1584C2×C10111yescharacteristic, complemented
289SD16⋊C8C2×C10111yescharacteristic
290C101#1983811yescharacteristic, direct product factor, Sylow
291#557C22×C10111yescharacteristic
292#557C22×C10111yescharacteristic
293#554C22×C10111yescharacteristic
294D4×Q8C22×C10111yescharacteristic
295#500C22×C10111yescharacteristic
296#499—21no—
297#498C22×C10111yescharacteristic
298#491—21no—
299#487—21no—
300#487C22×C10111yescharacteristic
301#487C22×C10111yescharacteristic
302#487C22×C10111yescharacteristic
303#487C22×C10111yescharacteristic
304#484—21no—
305#479—21no—
306#479—21no—
307#479—21no—
308#477C22×C10111yescharacteristic
309#477C22×C10111yescharacteristic
310#475—21no—
311#475C22×C10111yescharacteristic
312#475C22×C10111yescharacteristic
313#475C22×C10111yescharacteristic
314#467—21no—
315#462C22×C10111yescharacteristic
316#461—21no—
317#461—21no—
318#461C22×C10111yescharacteristic
319#461C22×C10111yescharacteristic
320#451—21no—
321#446C22×C10111yescharacteristic
322C8×Q8C22×C10111yescharacteristic
323C8×Q8C22×C10111yescharacteristic
324#440—21no—
325C4×Q16—21no—
326C4×Q16C22×C10111yescharacteristic
327C4×SD16—21no—
328C4×SD16C22×C10111yescharacteristic
329C8×D4C22×C10111yescharacteristic
330C2×#103—21no—
331#335C22×C10111yescharacteristic
332#335C22×C10111yescharacteristic
333#333C22×C10111yescharacteristic
334#332C22×C10111yescharacteristic
335#332C22×C10111yescharacteristic
336#332C22×C10111yescharacteristic
337Q8⋊C8C22×C10111yescharacteristic
338Q8⋊C8C22×C10111yescharacteristic
339Q8⋊C8C22×C10111yescharacteristic
340D4⋊C8C22×C10111yescharacteristic
341#322C22×C10111yescharacteristic
342C22×Q8—21no—
343C2×Q16—21no—
344C2×Q16D4×C10111yescharacteristic
345C2×SD16—21no—
346C2×SD16—21no—
347C2×SD16D4×C10111yescharacteristic
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8C23×C10111yescharacteristic
353C4⋊Q8C23×C10111yescharacteristic
354C4⋊Q8C23×C10111yescharacteristic
355C4⋊Q8C23×C10111yescharacteristic
356#125—21no—
357#125—21no—
358#125—21no—
359#125—41no—
360#125—41no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C22⋊Q8—41no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8—21no—
369C4×Q8C23×C10111yescharacteristic
370C4×Q8C23×C10111yescharacteristic
371C4×Q8C23×C10111yescharacteristic
372C4×D4—21no—
373C4×D4—21no—
374C4×D4C23×C10111yescharacteristic
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107D4×C10111yescharacteristic
381#106—21no—
382#106—21no—
383#106—21no—
384#106—41no—
385#106D4×C10111yescharacteristic
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C23×C10111yescharacteristic
390C4⋊C8C23×C10111yescharacteristic
391C4⋊C8C23×C10111yescharacteristic
392C4⋊C8C23×C10111yescharacteristic
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
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#102D4×C10111yescharacteristic
412C22⋊C8—21no—
413#97—21no—
414C4×C8—21no—
415C4×C8—21no—
416C4×C8C23×C10111yescharacteristic
417C4×C8C23×C10111yescharacteristic
418C4×C8C23×C10111yescharacteristic
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—41no—
424C2×Q8—42no—
425C2×Q8—81no—
426C2×Q8C2×D4×C10111yescharacteristic
427C2×Q8C2×D4×C10111yescharacteristic
428C2×Q8C2×D4×C10111yescharacteristic
429C2×D4C2×D4×C10111yescharacteristic
430C22×C4—21no—
431C22×C4—41no—
432C22×C4—41no—
433Q16—22no—
434Q16—81no—
435SD16—22no—
436SD16—42no—
437SD16—42no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—81no—
444C2×C8C2×D4×C10111yescharacteristic
445C2×C8C2×D4×C10111yescharacteristic
446C2×C8C2×D4×C10111yescharacteristic
447C2×C8C2×D4×C10111yescharacteristic
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4—41no—
468C4⋊C4C2×D4×C10111yescharacteristic
469C4⋊C4C2×D4×C10111yescharacteristic
470C4⋊C4C2×D4×C10111yescharacteristic
471C4⋊C4C2×D4×C10111yescharacteristic
472C22⋊C4—21no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—41no—
479C42—41no—
480C42C24×C10111yescharacteristic
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—41no—
493Q8—82no—
494Q8—81no—
495Q8#137×C10112yes—
496D4—21no—
497D4#135×C10112yes—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—82no—
512C2×C4—161no—
513C2×C4C22×D4×C10111yescharacteristic
514C2×C4C22×D4×C10111yescharacteristic
515C2×C4H(5,𝔽2)×C10111yescharacteristic
516C8—21no—
517C8—21no—
518C8—21no—
519C8—21no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8—41no—
524C8—41no—
525C22—22no—
526C22—41no—
527C22—41no—
528C22D42×C10111yescharacteristic
529C4—22no—
530C4—21no—
531C4—41no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—81no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4C2×#135×C10111yescharacteristic
542C4C2×#137×C10111yescharacteristic
543C4#577×C10111yescharacteristic
544C4#578×C10111yescharacteristic
545C2—42no—
546C2C101×#326611yescharacteristic
547C2C101×#328511yescharacteristic
548C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC2×D4×C101C2×D4
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×#3383C2semidirect
5. C101×#1718C2semidirect
6. C101×#1700C2semidirect
7. C101×#1684C2semidirect
8. C101×#1684C2semidirect
10. C101×#1653C2semidirect
13. C101×#1636C2semidirect
14. C101×#1584C2semidirect
270. #19838C101direct (N × H)
275. #3383C2×C101semidirect
279. #1718C2×C101semidirect
280. #1700C2×C101semidirect
281. #1684C2×C101semidirect
282. #1684C2×C101semidirect
284. #1653C2×C101semidirect
287. #1636C2×C101semidirect
288. #1584C2×C101semidirect
290. C101#19838direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33832
C101×#33722
C101×#33592
C101×#32992
C101×#17182
C101×#17002
C101×#16842
C101×#16732
C101×#16532
C101×#16512
C101×#16432
C101×#16362
C101×#15842
C101×SD16⋊C82
#19838101