Finite Group Databasebeta

← C101×#20305 #38802456

Subgroups — C101×#20305 #38802456

Order 25856.

604 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3384C211yesmaximal, characteristic, complemented
2C101×#3354C211yesmaximal, characteristic
3C101×#3331C211yesmaximal, characteristic, complemented
4C101×#3329C211yesmaximal, characteristic, complemented
5C101×#1707C211yesmaximal, characteristic, complemented
6C101×#1703C211yesmaximal, characteristic, complemented
7C101×#1703C211yesmaximal, characteristic, complemented
8C101×#1692C211yesmaximal, characteristic, complemented
9C101×#1691C211yesmaximal, characteristic, complemented
10C101×#1649C211yesmaximal, characteristic, complemented
11C101×#1647C211yesmaximal, characteristic, complemented
12C101×#1634C211yesmaximal, characteristic, complemented
13C101×#1632C211yesmaximal, characteristic, complemented
14C101×#1590C211yesmaximal, characteristic, complemented
15C101×#1589C211yesmaximal, characteristic, complemented
16#555×C101C2211yescharacteristic
17#554×C101C2211yescharacteristic
18D4×Q8×C101C2211yescharacteristic
19#547×C101C2211yescharacteristic
20#501×C101—21no—
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#494×C101C2211yescharacteristic
25#487×C101C2211yescharacteristic
26#487×C101C2211yescharacteristic
27#485×C101—21no—
28#483×C101—21no—
29#482×C101—21no—
30#481×C101—21no—
31#478×C101—21no—
32#477×C101C2211yescharacteristic
33#476×C101—21no—
34#476×C101C2211yescharacteristic
35#476×C101C2211yescharacteristic
36#476×C101C2211yescharacteristic
37#474×C101C2211yescharacteristic
38#474×C101C2211yescharacteristic
39#470×C101—21no—
40#469×C101—21no—
41#468×C101—21no—
42#462×C101C2211yescharacteristic
43#461×C101C2211yescharacteristic
44#452×C101—21no—
45#448×C101—21no—
46#446×C101C2211yescharacteristic
47#442×C101—21no—
48C4×SD16×C101C2211yescharacteristic
49C4×D8×C101C2211yescharacteristic
50#436×C101C2211yescharacteristic
51#436×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53#428×C101—21no—
54#419×C101—21no—
55#417×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#332×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63D4⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66C82×C101C2211yescharacteristic
67C2×#41×C101—21no—
68C22×Q8×C101—21no—
69C2×Q16×C101—21no—
70C2×Q16×C101—41no—
71C2×SD16×C101—21no—
72C2×SD16×C101D411yescharacteristic
73C2×D8×C101D411yescharacteristic
74C2×M16×C101—21no—
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#125×C101—21no—
83#124×C101—41no—
84#123×C101—41no—
85C22⋊Q8×C101—21no—
86C22⋊Q8×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—41no—
89C22⋊Q8×C101—41no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93C4×Q8×C101C2311yescharacteristic
94C4×D4×C101—21no—
95C4×D4×C101—21no—
96C4×D4×C101C2311yescharacteristic
97C4×D4×C101C2311yescharacteristic
98C4×D4×C101C2311yescharacteristic
99#117×C101—21no—
100#117×C101—21no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101—41no—
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×C101C2311yescharacteristic
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
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×C101D411yescharacteristic
129#102×C101—21no—
130#102×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101D411yescharacteristic
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139C22⋊C8×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×C101—21no—
150C2×Q8×C101—41no—
151C2×Q8×C101—42no—
152C2×Q8×C101—81no—
153C2×Q8×C101C2×D411yescharacteristic
154C2×D4×C101—41no—
155C2×D4×C101—41no—
156C2×D4×C101C2×D411yescharacteristic
157C2×D4×C101C2×D411yescharacteristic
158C2×D4×C101C2×D411yescharacteristic
159C22×C4×C101—21no—
160C22×C4×C101—21no—
161C22×C4×C101—21no—
162C22×C4×C101—41no—
163C22×C4×C101—41no—
164C22×C4×C101—41no—
165Q16×C101—82no—
166Q16×C101—81no—
167SD16×C101—41no—
168SD16×C101—81no—
169D8×C101—22no—
170M16×C101—42no—
171M16×C101—81no—
172M16×C101—81no—
173C2×C8×C101—21no—
174C2×C8×C101—21no—
175C2×C8×C101—21no—
176C2×C8×C101—21no—
177C2×C8×C101—21no—
178C2×C8×C101C2×D411yescharacteristic
179C2×C8×C101C2×D411yescharacteristic
180C2×C8×C101C2×D411yescharacteristic
181C2×C8×C101C2×D411yescharacteristic
182C4⋊C4×C101—21no—
183C4⋊C4×C101—21no—
184C4⋊C4×C101—21no—
185C4⋊C4×C101—21no—
186C4⋊C4×C101—21no—
187C4⋊C4×C101—21no—
188C4⋊C4×C101—21no—
189C4⋊C4×C101—21no—
190C4⋊C4×C101—21no—
191C4⋊C4×C101—41no—
192C4⋊C4×C101—41no—
193C4⋊C4×C101—41no—
194C4⋊C4×C101—41no—
195C4⋊C4×C101C2×D411yescharacteristic
196C4⋊C4×C101C2×D411yescharacteristic
197C4⋊C4×C101C2×D411yescharacteristic
198C4⋊C4×C101C2×D411yescharacteristic
199C22⋊C4×C101—21no—
200C22⋊C4×C101—21no—
201C22⋊C4×C101—21no—
202C22⋊C4×C101—41no—
203C22⋊C4×C101—41no—
204C22⋊C4×C101—41no—
205C22⋊C4×C101—41no—
206C22⋊C4×C101—41no—
207C42×C101—21no—
208C42×C101—41no—
209C42×C101C2411yescharacteristic
210C23×C101—21no—
211C23×C101—21no—
212C23×C101—21no—
213Q8×C101—21no—
214Q8×C101—21no—
215Q8×C101—41no—
216Q8×C101—41no—
217Q8×C101—41no—
218Q8×C101—41no—
219Q8×C101—81no—
220Q8×C101—81no—
221Q8×C101—82no—
222D4×C101—21no—
223D4×C101—21no—
224D4×C101—21no—
225D4×C101—21no—
226D4×C101—21no—
227D4×C101—21no—
228D4×C101—82no—
229D4×C101—161no—
230C2×C4×C101—21no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
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—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—82no—
246C2×C4×C101—82no—
247C2×C4×C101—161no—
248C2×C4×C101C22×D411yescharacteristic
249C2×C4×C101C22×D411yescharacteristic
250C2×C4×C101H(5,𝔽2)11yescharacteristic
251C8×C101—22no—
252C8×C101—21no—
253C8×C101—21no—
254C8×C101—21no—
255C8×C101—41no—
256C8×C101—41no—
257C8×C101—41no—
258C8×C101—41no—
259C8×C101#13712yes—
260C22×C101—41no—
261C22×C101—41no—
262C22×C101—41no—
263C22×C101—41no—
264C22×C101—41no—
265C22×C101—41no—
266C22×C101—41no—
267C22×C101—41no—
268C22×C101—41no—
269C22×C101D4211yescharacteristic
270C4×C101—21no—
271C4×C101—41no—
272C4×C101—41no—
273C4×C101—41no—
274C4×C101—41no—
275C4×C101—41no—
276C4×C101—81no—
277C4×C101—81no—
278C4×C101—81no—
279C4×C101—81no—
280C4×C101C2×#13711yescharacteristic
281C4×C101#57511yescharacteristic
282C4×C101#57611yescharacteristic
283C4×C101#57811yescharacteristic
284#20305C10111yesmaximal, characteristic, direct product factor, Sylow
285C2×C101—81no—
286C2×C101—81no—
287C2×C101—81no—
288C2×C101#327311yescharacteristic
289C2×C101#327611yescharacteristic
290C2×C101#329111yescharacteristic
291#3384C2×C10111yescharacteristic, complemented
292#3354C2×C10111yescharacteristic
293#3331C2×C10111yescharacteristic, complemented
294#3329C2×C10111yescharacteristic, complemented
295#1707C2×C10111yescharacteristic, complemented
296#1703C2×C10111yescharacteristic, complemented
297#1703C2×C10111yescharacteristic, complemented
298#1692C2×C10111yescharacteristic, complemented
299#1691C2×C10111yescharacteristic, complemented
300#1649C2×C10111yescharacteristic, complemented
301#1647C2×C10111yescharacteristic, complemented
302#1634C2×C10111yescharacteristic, complemented
303#1632C2×C10111yescharacteristic, complemented
304#1590C2×C10111yescharacteristic, complemented
305#1589C2×C10111yescharacteristic, complemented
306C101#2030511yescharacteristic, direct product factor, Sylow
307#555C22×C10111yescharacteristic
308#554C22×C10111yescharacteristic
309D4×Q8C22×C10111yescharacteristic
310#547C22×C10111yescharacteristic
311#501—21no—
312#500C22×C10111yescharacteristic
313#498C22×C10111yescharacteristic
314#498C22×C10111yescharacteristic
315#494C22×C10111yescharacteristic
316#487C22×C10111yescharacteristic
317#487C22×C10111yescharacteristic
318#485—21no—
319#483—21no—
320#482—21no—
321#481—21no—
322#478—21no—
323#477C22×C10111yescharacteristic
324#476—21no—
325#476C22×C10111yescharacteristic
326#476C22×C10111yescharacteristic
327#476C22×C10111yescharacteristic
328#474C22×C10111yescharacteristic
329#474C22×C10111yescharacteristic
330#470—21no—
331#469—21no—
332#468—21no—
333#462C22×C10111yescharacteristic
334#461C22×C10111yescharacteristic
335#452—21no—
336#448—21no—
337#446C22×C10111yescharacteristic
338#442—21no—
339C4×SD16C22×C10111yescharacteristic
340C4×D8C22×C10111yescharacteristic
341#436C22×C10111yescharacteristic
342#436C22×C10111yescharacteristic
343#436C22×C10111yescharacteristic
344#428—21no—
345#419—21no—
346#417—21no—
347#335C22×C10111yescharacteristic
348#334C22×C10111yescharacteristic
349#333C22×C10111yescharacteristic
350#333C22×C10111yescharacteristic
351#332C22×C10111yescharacteristic
352#332C22×C10111yescharacteristic
353Q8⋊C8C22×C10111yescharacteristic
354D4⋊C8C22×C10111yescharacteristic
355D4⋊C8C22×C10111yescharacteristic
356D4⋊C8C22×C10111yescharacteristic
357C82C22×C10111yescharacteristic
358C2×#41—21no—
359C22×Q8—21no—
360C2×Q16—21no—
361C2×Q16—41no—
362C2×SD16—21no—
363C2×SD16D4×C10111yescharacteristic
364C2×D8D4×C10111yescharacteristic
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C4⋊Q8—21no—
369C4⋊Q8C23×C10111yescharacteristic
370C4⋊Q8C23×C10111yescharacteristic
371C4⋊Q8C23×C10111yescharacteristic
372C4⋊Q8C23×C10111yescharacteristic
373#125—21no—
374#124—41no—
375#123—41no—
376C22⋊Q8—21no—
377C22⋊Q8—21no—
378C22⋊Q8—21no—
379C22⋊Q8—41no—
380C22⋊Q8—41no—
381#121—21no—
382#121—21no—
383#121—21no—
384C4×Q8C23×C10111yescharacteristic
385C4×D4—21no—
386C4×D4—21no—
387C4×D4C23×C10111yescharacteristic
388C4×D4C23×C10111yescharacteristic
389C4×D4C23×C10111yescharacteristic
390#117—21no—
391#117—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394#107—21no—
395#107—21no—
396#107—21no—
397#107—41no—
398#107D4×C10111yescharacteristic
399#106—21no—
400#106—21no—
401#106—21no—
402#106—21no—
403#106—21no—
404#106—21no—
405#106—21no—
406#106D4×C10111yescharacteristic
407C4⋊C8—21no—
408C4⋊C8C23×C10111yescharacteristic
409C4⋊C8C23×C10111yescharacteristic
410C4⋊C8C23×C10111yescharacteristic
411C4⋊C8C23×C10111yescharacteristic
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#103—21no—
418#103—21no—
419#103D4×C10111yescharacteristic
420#102—21no—
421#102—21no—
422#102—21no—
423#102—21no—
424#102—21no—
425#102D4×C10111yescharacteristic
426#102D4×C10111yescharacteristic
427#102D4×C10111yescharacteristic
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431#97—21no—
432C4×C8C23×C10111yescharacteristic
433C4×C8C23×C10111yescharacteristic
434C4×C8C23×C10111yescharacteristic
435#41—42no—
436#41—81no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—41no—
442C2×Q8—42no—
443C2×Q8—81no—
444C2×Q8C2×D4×C10111yescharacteristic
445C2×D4—41no—
446C2×D4—41no—
447C2×D4C2×D4×C10111yescharacteristic
448C2×D4C2×D4×C10111yescharacteristic
449C2×D4C2×D4×C10111yescharacteristic
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—41no—
454C22×C4—41no—
455C22×C4—41no—
456Q16—82no—
457Q16—81no—
458SD16—41no—
459SD16—81no—
460D8—22no—
461M16—42no—
462M16—81no—
463M16—81no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8C2×D4×C10111yescharacteristic
470C2×C8C2×D4×C10111yescharacteristic
471C2×C8C2×D4×C10111yescharacteristic
472C2×C8C2×D4×C10111yescharacteristic
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—21no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4C2×D4×C10111yescharacteristic
487C4⋊C4C2×D4×C10111yescharacteristic
488C4⋊C4C2×D4×C10111yescharacteristic
489C4⋊C4C2×D4×C10111yescharacteristic
490C22⋊C4—21no—
491C22⋊C4—21no—
492C22⋊C4—21no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C42—21no—
499C42—41no—
500C42C24×C10111yescharacteristic
501C23—21no—
502C23—21no—
503C23—21no—
504Q8—21no—
505Q8—21no—
506Q8—41no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—81no—
511Q8—81no—
512Q8—82no—
513D4—21no—
514D4—21no—
515D4—21no—
516D4—21no—
517D4—21no—
518D4—21no—
519D4—82no—
520D4—161no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—82no—
537C2×C4—82no—
538C2×C4—161no—
539C2×C4C22×D4×C10111yescharacteristic
540C2×C4C22×D4×C10111yescharacteristic
541C2×C4H(5,𝔽2)×C10111yescharacteristic
542C8—22no—
543C8—21no—
544C8—21no—
545C8—21no—
546C8—41no—
547C8—41no—
548C8—41no—
549C8—41no—
550C8#137×C10112yes—
551C22—41no—
552C22—41no—
553C22—41no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—41no—
558C22—41no—
559C22—41no—
560C22D42×C10111yescharacteristic
561C4—21no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—41no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4C2×#137×C10111yescharacteristic
572C4#575×C10111yescharacteristic
573C4#576×C10111yescharacteristic
574C4#578×C10111yescharacteristic
575C2—81no—
576C2—81no—
577C2—81no—
578C2C101×#327311yescharacteristic
579C2C101×#327611yescharacteristic
580C2C101×#329111yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3354C2
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×#3384C2semidirect
3. C101×#3331C2semidirect
4. C101×#3329C2semidirect
5. C101×#1707C2semidirect
6. C101×#1703C2semidirect
7. C101×#1703C2semidirect
8. C101×#1692C2semidirect
9. C101×#1691C2semidirect
10. C101×#1649C2semidirect
11. C101×#1647C2semidirect
12. C101×#1634C2semidirect
13. C101×#1632C2semidirect
14. C101×#1590C2semidirect
15. C101×#1589C2semidirect
284. #20305C101direct (N × H)
291. #3384C2×C101semidirect
293. #3331C2×C101semidirect
294. #3329C2×C101semidirect
295. #1707C2×C101semidirect
296. #1703C2×C101semidirect
297. #1703C2×C101semidirect
298. #1692C2×C101semidirect
299. #1691C2×C101semidirect
300. #1649C2×C101semidirect
301. #1647C2×C101semidirect
302. #1634C2×C101semidirect
303. #1632C2×C101semidirect
304. #1590C2×C101semidirect
305. #1589C2×C101semidirect
306. C101#20305direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33842
C101×#33542
C101×#33312
C101×#33292
C101×#17072
C101×#17032
C101×#16922
C101×#16912
C101×#16492
C101×#16472
C101×#16342
C101×#16322
C101×#15902
C101×#15892
#20305101