Finite Group Databasebeta

← C101×#20252 #38802403

Subgroups — C101×#20252 #38802403

Order 25856.

580 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×#3393C211yesmaximal, characteristic
2C101×#3384C211yesmaximal, characteristic
3C101×#3356C211yesmaximal, characteristic, complemented
4C101×#3328C211yesmaximal, characteristic, complemented
5C101×#1716C211yesmaximal, characteristic, complemented
6C101×#1699C211yesmaximal, characteristic, complemented
7C101×#1691C211yesmaximal, characteristic, complemented
8C101×#1690C211yesmaximal, characteristic, complemented
9C101×#1672C211yesmaximal, characteristic, complemented
10C101×#1652C211yesmaximal, characteristic, complemented
11C101×#1651C211yesmaximal, characteristic, complemented
12C101×#1643C211yesmaximal, characteristic, complemented
13C101×#1638C211yesmaximal, characteristic, complemented
14C101×#1594C211yesmaximal, characteristic
15C101×#1584C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic
17#556×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19D4×Q8×C101C2211yescharacteristic
20#501×C101—21no—
21#498×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#495×C101—21no—
25#494×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#485×C101—21no—
29#485×C101—21no—
30#483×C101—21no—
31#478×C101—21no—
32#477×C101C2211yescharacteristic
33#476×C101—21no—
34#476×C101C2211yescharacteristic
35#475×C101C2211yescharacteristic
36#475×C101C2211yescharacteristic
37#474×C101C2211yescharacteristic
38#470×C101—21no—
39#470×C101—21no—
40#464×C101—21no—
41#464×C101—21no—
42#462×C101C2211yescharacteristic
43#461×C101C2211yescharacteristic
44#461×C101C2211yescharacteristic
45#451×C101—21no—
46#446×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48#442×C101—21no—
49C4×Q16×C101—21no—
50C4×Q16×C101C2211yescharacteristic
51C4×D8×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#436×C101C2211yescharacteristic
54#428×C101—21no—
55#419×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#332×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C22×Q8×C101—21no—
68C2×Q16×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101—21no—
71C2×Q16×C101D411yescharacteristic
72C2×SD16×C101—21no—
73C2×SD16×C101—21no—
74C2×D8×C101D411yescharacteristic
75C2×M16×C101—21no—
76C2×M16×C101—21no—
77C4⋊Q8×C101—21no—
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82#126×C101—41no—
83#126×C101—41no—
84#125×C101—21no—
85#124×C101—21no—
86#124×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×C101—21no—
91C22⋊Q8×C101—41no—
92C22⋊Q8×C101—41no—
93C4×Q8×C101—21no—
94C4×Q8×C101—21no—
95C4×Q8×C101C2311yescharacteristic
96C4×Q8×C101C2311yescharacteristic
97C4×D4×C101—21no—
98C4×D4×C101—21no—
99C4×D4×C101C2311yescharacteristic
100C4×D4×C101C2311yescharacteristic
101#117×C101—21no—
102#117×C101—21no—
103C2×C4⋊C4×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101D411yescharacteristic
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×C101—41no—
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—41no—
131#103×C101D411yescharacteristic
132#103×C101D411yescharacteristic
133#102×C101—21no—
134#102×C101—21no—
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×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×C101—41no—
149C2×Q8×C101—42no—
150C2×Q8×C101—81no—
151C2×Q8×C101C2×D411yescharacteristic
152C2×Q8×C101C2×D411yescharacteristic
153C2×D4×C101C2×D411yescharacteristic
154C2×D4×C101C2×D411yescharacteristic
155C22×C4×C101—21no—
156C22×C4×C101—21no—
157C22×C4×C101—41no—
158C22×C4×C101—41no—
159Q16×C101—41no—
160Q16×C101—42no—
161Q16×C101—81no—
162Q16×C101—81no—
163SD16×C101—81no—
164SD16×C101—81no—
165D8×C101—22no—
166M16×C101—42no—
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—21no—
187C4⋊C4×C101—41no—
188C4⋊C4×C101—41no—
189C4⋊C4×C101—41no—
190C4⋊C4×C101—41no—
191C4⋊C4×C101—41no—
192C4⋊C4×C101C2×D411yescharacteristic
193C4⋊C4×C101C2×D411yescharacteristic
194C4⋊C4×C101C2×D411yescharacteristic
195C4⋊C4×C101C2×D411yescharacteristic
196C22⋊C4×C101—21no—
197C22⋊C4×C101—21no—
198C22⋊C4×C101—41no—
199C22⋊C4×C101—41no—
200C22⋊C4×C101—41no—
201C22⋊C4×C101—41no—
202C22⋊C4×C101—41no—
203C22⋊C4×C101—41no—
204C42×C101—21no—
205C42×C101—21no—
206C42×C101—41no—
207C42×C101—41no—
208C42×C101C2411yescharacteristic
209C23×C101—21no—
210C23×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—41no—
220Q8×C101—41no—
221Q8×C101—81no—
222Q8×C101—82no—
223D4×C101—21no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227C2×C4×C101—21no—
228C2×C4×C101—21no—
229C2×C4×C101—21no—
230C2×C4×C101—21no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
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—41no—
250C8×C101—41no—
251C8×C101—41no—
252C8×C101—41no—
253C8×C101—41no—
254C8×C101#13712yes—
255C22×C101—41no—
256C22×C101—41no—
257C22×C101—41no—
258C22×C101—41no—
259C22×C101—41no—
260C22×C101—41no—
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—81no—
270C4×C101—81no—
271C4×C101—81no—
272C4×C101—81no—
273C4×C101C2×#13711yescharacteristic
274C4×C101#57511yescharacteristic
275C4×C101#57711yescharacteristic
276C4×C101#57711yescharacteristic
277#20252C10111yesmaximal, characteristic, direct product factor, Sylow
278C2×C101—81no—
279C2×C101—81no—
280C2×C101#326711yescharacteristic
281C2×C101#327811yescharacteristic
282C2×C101#328911yescharacteristic
283#3393C2×C10111yescharacteristic
284#3384C2×C10111yescharacteristic
285#3356C2×C10111yescharacteristic, complemented
286#3328C2×C10111yescharacteristic, complemented
287#1716C2×C10111yescharacteristic, complemented
288#1699C2×C10111yescharacteristic, complemented
289#1691C2×C10111yescharacteristic, complemented
290#1690C2×C10111yescharacteristic, complemented
291#1672C2×C10111yescharacteristic, complemented
292#1652C2×C10111yescharacteristic, complemented
293#1651C2×C10111yescharacteristic, complemented
294#1643C2×C10111yescharacteristic, complemented
295#1638C2×C10111yescharacteristic, complemented
296#1594C2×C10111yescharacteristic
297#1584C2×C10111yescharacteristic, complemented
298C101#2025211yescharacteristic, direct product factor, Sylow
299#556C22×C10111yescharacteristic
300#556C22×C10111yescharacteristic
301#554C22×C10111yescharacteristic
302D4×Q8C22×C10111yescharacteristic
303#501—21no—
304#498C22×C10111yescharacteristic
305#498C22×C10111yescharacteristic
306#498C22×C10111yescharacteristic
307#495—21no—
308#494C22×C10111yescharacteristic
309#487C22×C10111yescharacteristic
310#487C22×C10111yescharacteristic
311#485—21no—
312#485—21no—
313#483—21no—
314#478—21no—
315#477C22×C10111yescharacteristic
316#476—21no—
317#476C22×C10111yescharacteristic
318#475C22×C10111yescharacteristic
319#475C22×C10111yescharacteristic
320#474C22×C10111yescharacteristic
321#470—21no—
322#470—21no—
323#464—21no—
324#464—21no—
325#462C22×C10111yescharacteristic
326#461C22×C10111yescharacteristic
327#461C22×C10111yescharacteristic
328#451—21no—
329#446C22×C10111yescharacteristic
330C8×Q8C22×C10111yescharacteristic
331#442—21no—
332C4×Q16—21no—
333C4×Q16C22×C10111yescharacteristic
334C4×D8C22×C10111yescharacteristic
335#436C22×C10111yescharacteristic
336#436C22×C10111yescharacteristic
337#428—21no—
338#419—21no—
339#335C22×C10111yescharacteristic
340#334C22×C10111yescharacteristic
341#333C22×C10111yescharacteristic
342#332C22×C10111yescharacteristic
343#332C22×C10111yescharacteristic
344#332C22×C10111yescharacteristic
345Q8⋊C8C22×C10111yescharacteristic
346Q8⋊C8C22×C10111yescharacteristic
347D4⋊C8C22×C10111yescharacteristic
348D4⋊C8C22×C10111yescharacteristic
349#322C22×C10111yescharacteristic
350C22×Q8—21no—
351C2×Q16—21no—
352C2×Q16—21no—
353C2×Q16—21no—
354C2×Q16D4×C10111yescharacteristic
355C2×SD16—21no—
356C2×SD16—21no—
357C2×D8D4×C10111yescharacteristic
358C2×M16—21no—
359C2×M16—21no—
360C4⋊Q8—21no—
361C4⋊Q8C23×C10111yescharacteristic
362C4⋊Q8C23×C10111yescharacteristic
363C4⋊Q8C23×C10111yescharacteristic
364C4⋊Q8C23×C10111yescharacteristic
365#126—41no—
366#126—41no—
367#125—21no—
368#124—21no—
369#124—21no—
370C22⋊Q8—21no—
371C22⋊Q8—21no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—41no—
375C22⋊Q8—41no—
376C4×Q8—21no—
377C4×Q8—21no—
378C4×Q8C23×C10111yescharacteristic
379C4×Q8C23×C10111yescharacteristic
380C4×D4—21no—
381C4×D4—21no—
382C4×D4C23×C10111yescharacteristic
383C4×D4C23×C10111yescharacteristic
384#117—21no—
385#117—21no—
386C2×C4⋊C4—21no—
387#107—21no—
388#107—21no—
389#107D4×C10111yescharacteristic
390#107D4×C10111yescharacteristic
391#106—21no—
392#106—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—41no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8C23×C10111yescharacteristic
402C4⋊C8C23×C10111yescharacteristic
403C4⋊C8C23×C10111yescharacteristic
404C4⋊C8C23×C10111yescharacteristic
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—41no—
414#103D4×C10111yescharacteristic
415#103D4×C10111yescharacteristic
416#102—21no—
417#102—21no—
418#102D4×C10111yescharacteristic
419#102D4×C10111yescharacteristic
420C22⋊C8—21no—
421C22⋊C8—21no—
422#97—21no—
423C4×C8—21no—
424C4×C8C23×C10111yescharacteristic
425C4×C8C23×C10111yescharacteristic
426C4×C8C23×C10111yescharacteristic
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8—41no—
432C2×Q8—42no—
433C2×Q8—81no—
434C2×Q8C2×D4×C10111yescharacteristic
435C2×Q8C2×D4×C10111yescharacteristic
436C2×D4C2×D4×C10111yescharacteristic
437C2×D4C2×D4×C10111yescharacteristic
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—41no—
441C22×C4—41no—
442Q16—41no—
443Q16—42no—
444Q16—81no—
445Q16—81no—
446SD16—81no—
447SD16—81no—
448D8—22no—
449M16—42no—
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—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—21no—
480C22⋊C4—21no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—21no—
489C42—41no—
490C42—41no—
491C42C24×C10111yescharacteristic
492C23—21no—
493C23—21no—
494Q8—21no—
495Q8—21no—
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—82no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
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—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C8—41no—
537C8#137×C10112yes—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22D42×C10111yescharacteristic
545C4—21no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—81no—
553C4—81no—
554C4—81no—
555C4—81no—
556C4C2×#137×C10111yescharacteristic
557C4#575×C10111yescharacteristic
558C4#577×C10111yescharacteristic
559C4#577×C10111yescharacteristic
560C2—81no—
561C2—81no—
562C2C101×#326711yescharacteristic
563C2C101×#327811yescharacteristic
564C2C101×#328911yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC2×D8×C101D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#3356C2semidirect
4. C101×#3328C2semidirect
5. C101×#1716C2semidirect
6. C101×#1699C2semidirect
7. C101×#1691C2semidirect
8. C101×#1690C2semidirect
9. C101×#1672C2semidirect
10. C101×#1652C2semidirect
11. C101×#1651C2semidirect
12. C101×#1643C2semidirect
13. C101×#1638C2semidirect
15. C101×#1584C2semidirect
277. #20252C101direct (N × H)
285. #3356C2×C101semidirect
286. #3328C2×C101semidirect
287. #1716C2×C101semidirect
288. #1699C2×C101semidirect
289. #1691C2×C101semidirect
290. #1690C2×C101semidirect
291. #1672C2×C101semidirect
292. #1652C2×C101semidirect
293. #1651C2×C101semidirect
294. #1643C2×C101semidirect
295. #1638C2×C101semidirect
297. #1584C2×C101semidirect
298. C101#20252direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33932
C101×#33842
C101×#33562
C101×#33282
C101×#17162
C101×#16992
C101×#16912
C101×#16902
C101×#16722
C101×#16522
C101×#16512
C101×#16432
C101×#16382
C101×#15942
C101×#15842
#20252101