Finite Group Databasebeta

← C101×#20322 #38802473

Subgroups — C101×#20322 #38802473

Order 25856.

556 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3398C211yesmaximal, characteristic
2C101×#3387C211yesmaximal, characteristic, complemented
3C101×#3385C211yesmaximal, characteristic
4C101×#3356C211yesmaximal, characteristic
5C101×#1707C211yesmaximal, characteristic, complemented
6C101×#1696C211yesmaximal, characteristic, complemented
7C101×#1692C211yesmaximal, characteristic, complemented
8C101×#1691C211yesmaximal, characteristic
9C101×#1690C211yesmaximal, characteristic, complemented
10C101×#1645C211yesmaximal, characteristic, complemented
11C101×#1643C211yesmaximal, characteristic
12C101×#1638C211yesmaximal, characteristic
13C101×#1636C211yesmaximal, characteristic, complemented
14C101×#1591C211yesmaximal, characteristic, complemented
15C101×#1590C211yesmaximal, characteristic
16Q82×C101C2211yescharacteristic
17#557×C101C2211yescharacteristic
18#556×C101C2211yescharacteristic
19#554×C101C2211yescharacteristic
20#501×C101—21no—
21#501×C101—21no—
22#500×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#498×C101C2211yescharacteristic
25#497×C101—21no—
26#494×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#487×C101C2211yescharacteristic
29#485×C101—21no—
30#483×C101—21no—
31#479×C101—21no—
32#479×C101—21no—
33#477×C101C2211yescharacteristic
34#477×C101C2211yescharacteristic
35#477×C101C2211yescharacteristic
36#476×C101C2211yescharacteristic
37#475×C101—21no—
38#475×C101C2211yescharacteristic
39#475×C101C2211yescharacteristic
40#474×C101—21no—
41#470×C101—21no—
42#464×C101—21no—
43#462×C101—21no—
44#462×C101C2211yescharacteristic
45#461×C101C2211yescharacteristic
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#446×C101C2211yescharacteristic
49#441×C101—21no—
50#441×C101—21no—
51#440×C101—21no—
52C4×Q16×C101C2211yescharacteristic
53C4×SD16×C101C2211yescharacteristic
54#436×C101C2211yescharacteristic
55#428×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64Q8⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×Q16×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101D411yescharacteristic
71C2×SD16×C101—21no—
72C2×SD16×C101D411yescharacteristic
73C2×M16×C101—21no—
74C4⋊Q8×C101—21no—
75C4⋊Q8×C101—21no—
76C4⋊Q8×C101—21no—
77C4⋊Q8×C101—41no—
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82#126×C101—41no—
83#125×C101—21no—
84#125×C101—21no—
85#125×C101—41no—
86#124×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—41no—
90C4×Q8×C101—21no—
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×C101C2311yescharacteristic
100#117×C101—21no—
101C2×C4⋊C4×C101—21no—
102#107×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101D411yescharacteristic
108#106×C101—21no—
109#106×C101—21no—
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101—21no—
115#106×C101D411yescharacteristic
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101—21no—
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
122C4⋊C8×C101C2311yescharacteristic
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—41no—
131#103×C101—41no—
132#103×C101D411yescharacteristic
133#103×C101D411yescharacteristic
134#103×C101D411yescharacteristic
135#102×C101—21no—
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
144C2×Q8×C101—21no—
145C2×Q8×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—41no—
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×Q8×C101C2×D411yescharacteristic
152C2×D4×C101C2×D411yescharacteristic
153C22×C4×C101—21no—
154C22×C4×C101—41no—
155Q16×C101—22no—
156Q16×C101—42no—
157Q16×C101—81no—
158Q16×C101—81no—
159SD16×C101—22no—
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×C101C2×D411yescharacteristic
191C4⋊C4×C101C2×D411yescharacteristic
192C4⋊C4×C101C2×D411yescharacteristic
193C4⋊C4×C101C2×D411yescharacteristic
194C22⋊C4×C101—21no—
195C22⋊C4×C101—41no—
196C22⋊C4×C101—41no—
197C22⋊C4×C101—41no—
198C42×C101—21no—
199C42×C101—21no—
200C42×C101—21no—
201C42×C101—41no—
202C42×C101—41no—
203C42×C101—41no—
204C42×C101C2411yescharacteristic
205C23×C101—21no—
206Q8×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—81no—
217Q8×C101—81no—
218Q8×C101—161no—
219D4×C101—21no—
220D4×C101—21no—
221C2×C4×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—41no—
229C2×C4×C101—41no—
230C2×C4×C101—41no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—161no—
235C2×C4×C101C22×D411yescharacteristic
236C2×C4×C101C22×D411yescharacteristic
237C2×C4×C101H(5,𝔽2)11yescharacteristic
238C8×C101—21no—
239C8×C101—21no—
240C8×C101—41no—
241C8×C101—41no—
242C8×C101—41no—
243C8×C101—41no—
244C8×C101—41no—
245C8×C101#13712yes—
246C8×C101#13712yes—
247C22×C101—41no—
248C22×C101—41no—
249C22×C101—41no—
250C22×C101D4211yescharacteristic
251C4×C101—21no—
252C4×C101—41no—
253C4×C101—41no—
254C4×C101—41no—
255C4×C101—41no—
256C4×C101—41no—
257C4×C101—41no—
258C4×C101—41no—
259C4×C101—81no—
260C4×C101—81no—
261C4×C101—81no—
262C4×C101—81no—
263C4×C101C2×#13711yescharacteristic
264C4×C101C2×#13711yescharacteristic
265C4×C101#57711yescharacteristic
266C4×C101#57811yescharacteristic
267#20322C10111yesmaximal, characteristic, direct product factor, Sylow
268C2×C101—81no—
269C2×C101#327611yescharacteristic
270C2×C101#327811yescharacteristic
271C2×C101#329011yescharacteristic
272#3398C2×C10111yescharacteristic
273#3387C2×C10111yescharacteristic, complemented
274#3385C2×C10111yescharacteristic
275#3356C2×C10111yescharacteristic
276#1707C2×C10111yescharacteristic, complemented
277#1696C2×C10111yescharacteristic, complemented
278#1692C2×C10111yescharacteristic, complemented
279#1691C2×C10111yescharacteristic
280#1690C2×C10111yescharacteristic, complemented
281#1645C2×C10111yescharacteristic, complemented
282#1643C2×C10111yescharacteristic
283#1638C2×C10111yescharacteristic
284#1636C2×C10111yescharacteristic, complemented
285#1591C2×C10111yescharacteristic, complemented
286#1590C2×C10111yescharacteristic
287C101#2032211yescharacteristic, direct product factor, Sylow
288Q82C22×C10111yescharacteristic
289#557C22×C10111yescharacteristic
290#556C22×C10111yescharacteristic
291#554C22×C10111yescharacteristic
292#501—21no—
293#501—21no—
294#500C22×C10111yescharacteristic
295#498C22×C10111yescharacteristic
296#498C22×C10111yescharacteristic
297#497—21no—
298#494C22×C10111yescharacteristic
299#487C22×C10111yescharacteristic
300#487C22×C10111yescharacteristic
301#485—21no—
302#483—21no—
303#479—21no—
304#479—21no—
305#477C22×C10111yescharacteristic
306#477C22×C10111yescharacteristic
307#477C22×C10111yescharacteristic
308#476C22×C10111yescharacteristic
309#475—21no—
310#475C22×C10111yescharacteristic
311#475C22×C10111yescharacteristic
312#474—21no—
313#470—21no—
314#464—21no—
315#462—21no—
316#462C22×C10111yescharacteristic
317#461C22×C10111yescharacteristic
318#446C22×C10111yescharacteristic
319#446C22×C10111yescharacteristic
320#446C22×C10111yescharacteristic
321#441—21no—
322#441—21no—
323#440—21no—
324C4×Q16C22×C10111yescharacteristic
325C4×SD16C22×C10111yescharacteristic
326#436C22×C10111yescharacteristic
327#428—21no—
328#335C22×C10111yescharacteristic
329#334C22×C10111yescharacteristic
330#333C22×C10111yescharacteristic
331#333C22×C10111yescharacteristic
332#332C22×C10111yescharacteristic
333#332C22×C10111yescharacteristic
334Q8⋊C8C22×C10111yescharacteristic
335Q8⋊C8C22×C10111yescharacteristic
336Q8⋊C8C22×C10111yescharacteristic
337D4⋊C8C22×C10111yescharacteristic
338C82C22×C10111yescharacteristic
339C2×Q16—21no—
340C2×Q16—21no—
341C2×Q16—21no—
342C2×Q16D4×C10111yescharacteristic
343C2×SD16—21no—
344C2×SD16D4×C10111yescharacteristic
345C2×M16—21no—
346C4⋊Q8—21no—
347C4⋊Q8—21no—
348C4⋊Q8—21no—
349C4⋊Q8—41no—
350C4⋊Q8C23×C10111yescharacteristic
351C4⋊Q8C23×C10111yescharacteristic
352C4⋊Q8C23×C10111yescharacteristic
353C4⋊Q8C23×C10111yescharacteristic
354#126—41no—
355#125—21no—
356#125—21no—
357#125—41no—
358#124—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—41no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8C23×C10111yescharacteristic
368C4×Q8C23×C10111yescharacteristic
369C4×Q8C23×C10111yescharacteristic
370C4×D4—21no—
371C4×D4C23×C10111yescharacteristic
372#117—21no—
373C2×C4⋊C4—21no—
374#107—21no—
375#107—21no—
376#107—21no—
377#107—21no—
378#107—21no—
379#107D4×C10111yescharacteristic
380#106—21no—
381#106—21no—
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—41no—
403#103—41no—
404#103D4×C10111yescharacteristic
405#103D4×C10111yescharacteristic
406#103D4×C10111yescharacteristic
407#102—21no—
408#102D4×C10111yescharacteristic
409C22⋊C8—21no—
410#97—21no—
411#97—21no—
412#97—21no—
413C4×C8C23×C10111yescharacteristic
414C4×C8C23×C10111yescharacteristic
415C4×C8C23×C10111yescharacteristic
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—41no—
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—22no—
432SD16—81no—
433M16—42no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8C2×D4×C10111yescharacteristic
440C2×C8C2×D4×C10111yescharacteristic
441C2×C8C2×D4×C10111yescharacteristic
442C2×C8C2×D4×C10111yescharacteristic
443C4⋊C4—21no—
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—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4C2×D4×C10111yescharacteristic
463C4⋊C4C2×D4×C10111yescharacteristic
464C4⋊C4C2×D4×C10111yescharacteristic
465C4⋊C4C2×D4×C10111yescharacteristic
466C22⋊C4—21no—
467C22⋊C4—41no—
468C22⋊C4—41no—
469C22⋊C4—41no—
470C42—21no—
471C42—21no—
472C42—21no—
473C42—41no—
474C42—41no—
475C42—41no—
476C42C24×C10111yescharacteristic
477C23—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—21no—
482Q8—21no—
483Q8—21no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—161no—
491D4—21no—
492D4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—161no—
507C2×C4C22×D4×C10111yescharacteristic
508C2×C4C22×D4×C10111yescharacteristic
509C2×C4H(5,𝔽2)×C10111yescharacteristic
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8#137×C10112yes—
518C8#137×C10112yes—
519C22—41no—
520C22—41no—
521C22—41no—
522C22D42×C10111yescharacteristic
523C4—21no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—41no—
530C4—41no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4C2×#137×C10111yescharacteristic
536C4C2×#137×C10111yescharacteristic
537C4#577×C10111yescharacteristic
538C4#578×C10111yescharacteristic
539C2—81no—
540C2C101×#327611yescharacteristic
541C2C101×#327811yescharacteristic
542C2C101×#329011yescharacteristic
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×#3387C2semidirect
5. C101×#1707C2semidirect
6. C101×#1696C2semidirect
7. C101×#1692C2semidirect
9. C101×#1690C2semidirect
10. C101×#1645C2semidirect
13. C101×#1636C2semidirect
14. C101×#1591C2semidirect
267. #20322C101direct (N × H)
273. #3387C2×C101semidirect
276. #1707C2×C101semidirect
277. #1696C2×C101semidirect
278. #1692C2×C101semidirect
280. #1690C2×C101semidirect
281. #1645C2×C101semidirect
284. #1636C2×C101semidirect
285. #1591C2×C101semidirect
287. C101#20322direct (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×#33872
C101×#33852
C101×#33562
C101×#17072
C101×#16962
C101×#16922
C101×#16912
C101×#16902
C101×#16452
C101×#16432
C101×#16382
C101×#16362
C101×#15912
C101×#15902
#20322101