Finite Group Databasebeta

← C101×#20279 #38802430

Subgroups — C101×#20279 #38802430

Order 25856.

556 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3398C211yesmaximal, characteristic
2C101×#3383C211yesmaximal, characteristic, complemented
3C101×#3372C211yesmaximal, characteristic
4C101×#3356C211yesmaximal, characteristic
5C101×#1723C211yesmaximal, characteristic, complemented
6C101×#1704C211yesmaximal, characteristic, complemented
7C101×#1693C211yesmaximal, characteristic
8C101×#1690C211yesmaximal, characteristic, complemented
9C101×#1672C211yesmaximal, characteristic, complemented
10C101×#1650C211yesmaximal, characteristic
11C101×#1648C211yesmaximal, characteristic, complemented
12C101×#1643C211yesmaximal, characteristic
13C101×#1636C211yesmaximal, characteristic, complemented
14C101×#1593C211yesmaximal, characteristic, complemented
15C101×#1583C211yesmaximal, characteristic
16#557×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic
19#554×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#499×C101—21no—
23#498×C101C2211yescharacteristic
24#497×C101—21no—
25#494×C101C2211yescharacteristic
26#491×C101—21no—
27#487×C101C2211yescharacteristic
28#487×C101C2211yescharacteristic
29#485×C101—21no—
30#483×C101—21no—
31#479×C101—21no—
32#479×C101—21no—
33#479×C101—21no—
34#477×C101C2211yescharacteristic
35#477×C101C2211yescharacteristic
36#475×C101C2211yescharacteristic
37#475×C101C2211yescharacteristic
38#475×C101C2211yescharacteristic
39#470×C101—21no—
40#464×C101—21no—
41#462×C101—21no—
42#462×C101C2211yescharacteristic
43#461×C101—21no—
44#461×C101C2211yescharacteristic
45#461×C101C2211yescharacteristic
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48C8×Q8×C101C2211yescharacteristic
49#441×C101—21no—
50#440×C101—21no—
51C4×Q16×C101—21no—
52C4×Q16×C101C2211yescharacteristic
53C4×SD16×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#428×C101—21no—
56#334×C101C2211yescharacteristic
57#334×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
67C2×Q16×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101D411yescharacteristic
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
80C4⋊Q8×C101C2311yescharacteristic
81#126×C101—41no—
82#125×C101—21no—
83#125×C101—21no—
84#125×C101—21no—
85#125×C101—41no—
86#125×C101—41no—
87#124×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—41no—
91C4×Q8×C101—21no—
92C4×Q8×C101—21no—
93C4×Q8×C101—21no—
94C4×Q8×C101—21no—
95C4×Q8×C101—21no—
96C4×Q8×C101C2311yescharacteristic
97C4×Q8×C101C2311yescharacteristic
98C4×Q8×C101C2311yescharacteristic
99C4×D4×C101—21no—
100C4×D4×C101C2311yescharacteristic
101#117×C101—21no—
102C2×C4⋊C4×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101—41no—
108#107×C101D411yescharacteristic
109#106×C101—21no—
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101D411yescharacteristic
115C4⋊C8×C101—21no—
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
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—
139#97×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×C101C2×D411yescharacteristic
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×D4×C101C2×D411yescharacteristic
152C22×C4×C101—21no—
153C22×C4×C101—41no—
154Q16×C101—22no—
155Q16×C101—42no—
156Q16×C101—81no—
157Q16×C101—81no—
158SD16×C101—41no—
159SD16×C101—42no—
160SD16×C101—81no—
161M16×C101—42no—
162C2×C8×C101—21no—
163C2×C8×C101—21no—
164C2×C8×C101—21no—
165C2×C8×C101—21no—
166C2×C8×C101—21no—
167C2×C8×C101C2×D411yescharacteristic
168C2×C8×C101C2×D411yescharacteristic
169C2×C8×C101C2×D411yescharacteristic
170C2×C8×C101C2×D411yescharacteristic
171C4⋊C4×C101—21no—
172C4⋊C4×C101—21no—
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—41no—
183C4⋊C4×C101—41no—
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×C101C2×D411yescharacteristic
192C4⋊C4×C101C2×D411yescharacteristic
193C4⋊C4×C101C2×D411yescharacteristic
194C4⋊C4×C101C2×D411yescharacteristic
195C22⋊C4×C101—21no—
196C22⋊C4×C101—41no—
197C22⋊C4×C101—41no—
198C22⋊C4×C101—41no—
199C42×C101—21no—
200C42×C101—21no—
201C42×C101—21no—
202C42×C101—41no—
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—21no—
213Q8×C101—41no—
214Q8×C101—41no—
215Q8×C101—41no—
216Q8×C101—41no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—81no—
220D4×C101—21no—
221D4×C101—21no—
222C2×C4×C101—21no—
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—41no—
230C2×C4×C101—41no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—161no—
236C2×C4×C101C22×D411yescharacteristic
237C2×C4×C101C22×D411yescharacteristic
238C2×C4×C101H(5,𝔽2)11yescharacteristic
239C8×C101—21no—
240C8×C101—21no—
241C8×C101—21no—
242C8×C101—41no—
243C8×C101—41no—
244C8×C101—41no—
245C8×C101—41no—
246C8×C101—41no—
247C8×C101#13712yes—
248C22×C101—41no—
249C22×C101—41no—
250C22×C101—41no—
251C22×C101D4211yescharacteristic
252C4×C101—21no—
253C4×C101—41no—
254C4×C101—41no—
255C4×C101—41no—
256C4×C101—41no—
257C4×C101—41no—
258C4×C101—41no—
259C4×C101—41no—
260C4×C101—81no—
261C4×C101—81no—
262C4×C101—81no—
263C4×C101—81no—
264C4×C101C2×#13711yescharacteristic
265C4×C101#57511yescharacteristic
266C4×C101#57711yescharacteristic
267C4×C101#57811yescharacteristic
268#20279C10111yesmaximal, characteristic, direct product factor, Sylow
269C2×C101—81no—
270C2×C101#327111yescharacteristic
271C2×C101#327611yescharacteristic
272C2×C101#328911yescharacteristic
273#3398C2×C10111yescharacteristic
274#3383C2×C10111yescharacteristic, complemented
275#3372C2×C10111yescharacteristic
276#3356C2×C10111yescharacteristic
277#1723C2×C10111yescharacteristic, complemented
278#1704C2×C10111yescharacteristic, complemented
279#1693C2×C10111yescharacteristic
280#1690C2×C10111yescharacteristic, complemented
281#1672C2×C10111yescharacteristic, complemented
282#1650C2×C10111yescharacteristic
283#1648C2×C10111yescharacteristic, complemented
284#1643C2×C10111yescharacteristic
285#1636C2×C10111yescharacteristic, complemented
286#1593C2×C10111yescharacteristic, complemented
287#1583C2×C10111yescharacteristic
288C101#2027911yescharacteristic, direct product factor, Sylow
289#557C22×C10111yescharacteristic
290#557C22×C10111yescharacteristic
291#556C22×C10111yescharacteristic
292#554C22×C10111yescharacteristic
293#500C22×C10111yescharacteristic
294#500C22×C10111yescharacteristic
295#499—21no—
296#498C22×C10111yescharacteristic
297#497—21no—
298#494C22×C10111yescharacteristic
299#491—21no—
300#487C22×C10111yescharacteristic
301#487C22×C10111yescharacteristic
302#485—21no—
303#483—21no—
304#479—21no—
305#479—21no—
306#479—21no—
307#477C22×C10111yescharacteristic
308#477C22×C10111yescharacteristic
309#475C22×C10111yescharacteristic
310#475C22×C10111yescharacteristic
311#475C22×C10111yescharacteristic
312#470—21no—
313#464—21no—
314#462—21no—
315#462C22×C10111yescharacteristic
316#461—21no—
317#461C22×C10111yescharacteristic
318#461C22×C10111yescharacteristic
319#446C22×C10111yescharacteristic
320#446C22×C10111yescharacteristic
321C8×Q8C22×C10111yescharacteristic
322#441—21no—
323#440—21no—
324C4×Q16—21no—
325C4×Q16C22×C10111yescharacteristic
326C4×SD16C22×C10111yescharacteristic
327#436C22×C10111yescharacteristic
328#428—21no—
329#334C22×C10111yescharacteristic
330#334C22×C10111yescharacteristic
331#333C22×C10111yescharacteristic
332#332C22×C10111yescharacteristic
333#332C22×C10111yescharacteristic
334#332C22×C10111yescharacteristic
335Q8⋊C8C22×C10111yescharacteristic
336Q8⋊C8C22×C10111yescharacteristic
337Q8⋊C8C22×C10111yescharacteristic
338D4⋊C8C22×C10111yescharacteristic
339#322C22×C10111yescharacteristic
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16—21no—
343C2×Q16D4×C10111yescharacteristic
344C2×SD16—21no—
345C2×SD16—21no—
346C2×SD16D4×C10111yescharacteristic
347C2×M16—21no—
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8C23×C10111yescharacteristic
351C4⋊Q8C23×C10111yescharacteristic
352C4⋊Q8C23×C10111yescharacteristic
353C4⋊Q8C23×C10111yescharacteristic
354#126—41no—
355#125—21no—
356#125—21no—
357#125—21no—
358#125—41no—
359#125—41no—
360#124—21no—
361C22⋊Q8—21no—
362C22⋊Q8—21no—
363C22⋊Q8—41no—
364C4×Q8—21no—
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×D4C23×C10111yescharacteristic
374#117—21no—
375C2×C4⋊C4—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—41no—
381#107D4×C10111yescharacteristic
382#106—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106D4×C10111yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8C23×C10111yescharacteristic
392C4⋊C8C23×C10111yescharacteristic
393C4⋊C8C23×C10111yescharacteristic
394C4⋊C8C23×C10111yescharacteristic
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—41no—
406#103D4×C10111yescharacteristic
407#103D4×C10111yescharacteristic
408#103D4×C10111yescharacteristic
409#102D4×C10111yescharacteristic
410C22⋊C8—21no—
411#97—21no—
412#97—21no—
413C4×C8—21no—
414C4×C8C23×C10111yescharacteristic
415C4×C8C23×C10111yescharacteristic
416C4×C8C23×C10111yescharacteristic
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8C2×D4×C10111yescharacteristic
422C2×Q8C2×D4×C10111yescharacteristic
423C2×Q8C2×D4×C10111yescharacteristic
424C2×D4C2×D4×C10111yescharacteristic
425C22×C4—21no—
426C22×C4—41no—
427Q16—22no—
428Q16—42no—
429Q16—81no—
430Q16—81no—
431SD16—41no—
432SD16—42no—
433SD16—81no—
434M16—42no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8C2×D4×C10111yescharacteristic
441C2×C8C2×D4×C10111yescharacteristic
442C2×C8C2×D4×C10111yescharacteristic
443C2×C8C2×D4×C10111yescharacteristic
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4—41no—
464C4⋊C4C2×D4×C10111yescharacteristic
465C4⋊C4C2×D4×C10111yescharacteristic
466C4⋊C4C2×D4×C10111yescharacteristic
467C4⋊C4C2×D4×C10111yescharacteristic
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C42—21no—
473C42—21no—
474C42—21no—
475C42—41no—
476C42—41no—
477C42—41no—
478C42C24×C10111yescharacteristic
479C23—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—41no—
492Q8—81no—
493D4—21no—
494D4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—161no—
509C2×C4C22×D4×C10111yescharacteristic
510C2×C4C22×D4×C10111yescharacteristic
511C2×C4H(5,𝔽2)×C10111yescharacteristic
512C8—21no—
513C8—21no—
514C8—21no—
515C8—41no—
516C8—41no—
517C8—41no—
518C8—41no—
519C8—41no—
520C8#137×C10112yes—
521C22—41no—
522C22—41no—
523C22—41no—
524C22D42×C10111yescharacteristic
525C4—21no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—41no—
532C4—41no—
533C4—81no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4C2×#137×C10111yescharacteristic
538C4#575×C10111yescharacteristic
539C4#577×C10111yescharacteristic
540C4#578×C10111yescharacteristic
541C2—81no—
542C2C101×#327111yescharacteristic
543C2C101×#327611yescharacteristic
544C2C101×#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
2. C101×#3383C2semidirect
5. C101×#1723C2semidirect
6. C101×#1704C2semidirect
8. C101×#1690C2semidirect
9. C101×#1672C2semidirect
11. C101×#1648C2semidirect
13. C101×#1636C2semidirect
14. C101×#1593C2semidirect
268. #20279C101direct (N × H)
274. #3383C2×C101semidirect
277. #1723C2×C101semidirect
278. #1704C2×C101semidirect
280. #1690C2×C101semidirect
281. #1672C2×C101semidirect
283. #1648C2×C101semidirect
285. #1636C2×C101semidirect
286. #1593C2×C101semidirect
288. C101#20279direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33982
C101×#33832
C101×#33722
C101×#33562
C101×#17232
C101×#17042
C101×#16932
C101×#16902
C101×#16722
C101×#16502
C101×#16482
C101×#16432
C101×#16362
C101×#15932
C101×#15832
#20279101