Finite Group Databasebeta

← C101×#19708 #38801859

Subgroups — C101×#19708 #38801859

Order 25856.

738 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×#3228C211yesmaximal, characteristic, complemented
2C101×#3210C211yesmaximal, characteristic, complemented
3C101×#3207C211yesmaximal, characteristic, complemented
4C101×#3207C211yesmaximal, characteristic, complemented
5C101×#3169C211yesmaximal, characteristic, complemented
6C101×#3167C211yesmaximal, characteristic, complemented
7C101×#1722C211yesmaximal, characteristic, complemented
8C101×#1721C211yesmaximal, characteristic, complemented
9C101×#1720C211yesmaximal, characteristic, complemented
10C101×#1718C211yesmaximal, characteristic, complemented
11C101×#1717C211yesmaximal, characteristic, complemented
12C101×#1717C211yesmaximal, characteristic, complemented
13C101×#1715C211yesmaximal, characteristic, complemented
14C101×#1714C211yesmaximal, characteristic, complemented
15C101×#1452C211yesmaximal, characteristic, complemented
16#533×C101C2211yescharacteristic
17#532×C101C2211yescharacteristic
18#532×C101C2211yescharacteristic
19#532×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#494×C101C2211yescharacteristic
25#493×C101C2211yescharacteristic
26#493×C101C2211yescharacteristic
27#493×C101C2211yescharacteristic
28#492×C101C2211yescharacteristic
29#492×C101C2211yescharacteristic
30#492×C101C2211yescharacteristic
31#492×C101C2211yescharacteristic
32#487×C101C2211yescharacteristic
33#487×C101C2211yescharacteristic
34#487×C101C2211yescharacteristic
35#487×C101C2211yescharacteristic
36#486×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic
40#486×C101C2211yescharacteristic
41#486×C101C2211yescharacteristic
42#486×C101C2211yescharacteristic
43#486×C101C2211yescharacteristic
44#482×C101—22no—
45#478×C101—22no—
46#466×C101—22no—
47#465×C101—22no—
48#464×C101—22no—
49#463×C101—22no—
50#463×C101—22no—
51#452×C101—22no—
52#449×C101—22no—
53#449×C101—22no—
54C4×SD16×C101—22no—
55C4×D8×C101—22no—
56#431×C101C2211yescharacteristic
57#431×C101C2211yescharacteristic
58C2×C4×C8×C101C2211yescharacteristic
59#322×C101C2211yescharacteristic
60#322×C101C2211yescharacteristic
61#322×C101C2211yescharacteristic
62#322×C101C2211yescharacteristic
63C2×#41×C101—21no—
64C2×#41×C101—21no—
65C2×#41×C101—21no—
66C2×Q16×C101—22no—
67C2×SD16×C101—22no—
68C2×SD16×C101—22no—
69C2×SD16×C101—22no—
70C2×SD16×C101—22no—
71C2×D8×C101—22no—
72C2×D8×C101—22no—
73C2×D8×C101—22no—
74C22×C8×C101D412yes—
75C4⋊Q8×C101C2311yescharacteristic
76C4⋊Q8×C101C2311yescharacteristic
77C4⋊Q8×C101C2311yescharacteristic
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80#127×C101C2311yescharacteristic
81#127×C101C2311yescharacteristic
82#127×C101C2311yescharacteristic
83#125×C101—21no—
84#124×C101—21no—
85#124×C101—21no—
86#124×C101—21no—
87C22⋊Q8×C101—21no—
88C22⋊Q8×C101—21no—
89#121×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101—21no—
93#121×C101—21no—
94#121×C101—21no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×D4×C101—21no—
98C4×D4×C101—21no—
99C4×D4×C101—21no—
100C4×D4×C101—21no—
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103#117×C101—21no—
104C2×C42×C101C2311yescharacteristic
105#107×C101—22no—
106#107×C101—22no—
107#106×C101—22no—
108#106×C101—22no—
109C4⋊C8×C101D412yes—
110C4⋊C8×C101D412yes—
111#103×C101—22no—
112#103×C101—22no—
113#103×C101—22no—
114#103×C101—22no—
115#102×C101—22no—
116#102×C101—22no—
117#102×C101—22no—
118#102×C101—22no—
119#102×C101—22no—
120#102×C101—22no—
121#102×C101—22no—
122#102×C101—22no—
123C22⋊C8×C101D412yes—
124C22⋊C8×C101D412yes—
125C4×C8×C101D412yes—
126C4×C8×C101C2311yescharacteristic
127C4×C8×C101C2311yescharacteristic
128C4×C8×C101C2311yescharacteristic
129C4×C8×C101C2311yescharacteristic
130C4×C8×C101C2311yescharacteristic
131C4×C8×C101C2311yescharacteristic
132#41×C101—82no—
133#41×C101—82no—
134#41×C101—82no—
135C2×Q8×C101—21no—
136C2×Q8×C101—21no—
137C2×Q8×C101—21no—
138C2×Q8×C101—21no—
139C2×Q8×C101—21no—
140C2×D4×C101—21no—
141C2×D4×C101—21no—
142C2×D4×C101—21no—
143C2×D4×C101—21no—
144C2×D4×C101—21no—
145C2×D4×C101—21no—
146C2×D4×C101—21no—
147C2×D4×C101—21no—
148C2×D4×C101—21no—
149C2×D4×C101—41no—
150C2×D4×C101—41no—
151C2×D4×C101—41no—
152C22×C4×C101—41no—
153C22×C4×C101—41no—
154C22×C4×C101—41no—
155C22×C4×C101C2×D411yescharacteristic
156C22×C4×C101C2×D411yescharacteristic
157C22×C4×C101C2×D411yescharacteristic
158Q16×C101—82no—
159SD16×C101—44no—
160SD16×C101—82no—
161SD16×C101—82no—
162SD16×C101—82no—
163D8×C101—44no—
164D8×C101—82no—
165D8×C101—82no—
166C2×C8×C101—42no—
167C2×C8×C101C2×D412yes—
168C2×C8×C101C2×D412yes—
169C2×C8×C101C2×D412yes—
170C2×C8×C101C2×D412yes—
171C2×C8×C101C2×D412yes—
172C2×C8×C101C2×D412yes—
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—41no—
184C4⋊C4×C101—41no—
185C22⋊C4×C101—41no—
186C22⋊C4×C101—41no—
187C22⋊C4×C101—41no—
188C22⋊C4×C101—41no—
189C22⋊C4×C101—41no—
190C22⋊C4×C101—41no—
191C22⋊C4×C101—41no—
192C42×C101—41no—
193C42×C101C2×D411yescharacteristic
194C42×C101C2×D411yescharacteristic
195C42×C101C2×D411yescharacteristic
196C42×C101C2411yescharacteristic
197C23×C101—41no—
198C23×C101—41no—
199C23×C101—41no—
200C23×C101#12711yescharacteristic
201Q8×C101—42no—
202Q8×C101—42no—
203Q8×C101—42no—
204Q8×C101—42no—
205Q8×C101—42no—
206D4×C101—42no—
207D4×C101—42no—
208D4×C101—42no—
209D4×C101—42no—
210D4×C101—42no—
211D4×C101—42no—
212D4×C101—42no—
213D4×C101—42no—
214D4×C101—42no—
215D4×C101—82no—
216D4×C101—82no—
217D4×C101—82no—
218C2×C4×C101—22no—
219C2×C4×C101—22no—
220C2×C4×C101—22no—
221C2×C4×C101—41no—
222C2×C4×C101—41no—
223C2×C4×C101—41no—
224C2×C4×C101—41no—
225C2×C4×C101—41no—
226C2×C4×C101—82no—
227C2×C4×C101—82no—
228C2×C4×C101—82no—
229C2×C4×C101#12711yescharacteristic
230C2×C4×C101#12711yescharacteristic
231C2×C4×C101#12711yescharacteristic
232C2×C4×C101C22×D411yescharacteristic
233C2×C4×C101C22×D411yescharacteristic
234C2×C4×C101C22×D411yescharacteristic
235C8×C101—22no—
236C8×C101—22no—
237C8×C101—22no—
238C8×C101—22no—
239C8×C101—22no—
240C8×C101—22no—
241C22×C101—21no—
242C22×C101—21no—
243C22×C101—21no—
244C22×C101—81no—
245C22×C101—81no—
246C22×C101—81no—
247C22×C101—81no—
248C22×C101—81no—
249C22×C101—81no—
250C22×C101—81no—
251C22×C101—81no—
252C22×C101—81no—
253C22×C101C2×#12711yescharacteristic
254C4×C101—21no—
255C4×C101—21no—
256C4×C101—21no—
257C4×C101—81no—
258C4×C101—81no—
259C4×C101—81no—
260C4×C101—81no—
261C4×C101—81no—
262C4×C101#57512yes—
263C4×C101#57612yes—
264C4×C101#57712yes—
265#19708C10111yesmaximal, characteristic, direct product factor, Sylow
266C2×C101—41no—
267C2×C101—161no—
268C2×C101—161no—
269C2×C101—161no—
270C2×C101#315011yescharacteristic
271C2×C101#315411yescharacteristic
272C2×C101#315511yescharacteristic
273#3228C2×C10111yescharacteristic, complemented
274#3210C2×C10111yescharacteristic, complemented
275#3207C2×C10111yescharacteristic, complemented
276#3207C2×C10111yescharacteristic, complemented
277#3169C2×C10111yescharacteristic, complemented
278#3167C2×C10111yescharacteristic, complemented
279#1722C2×C10111yescharacteristic, complemented
280#1721C2×C10111yescharacteristic, complemented
281#1720C2×C10111yescharacteristic, complemented
282#1718C2×C10111yescharacteristic, complemented
283#1717C2×C10111yescharacteristic, complemented
284#1717C2×C10111yescharacteristic, complemented
285#1715C2×C10111yescharacteristic, complemented
286#1714C2×C10111yescharacteristic, complemented
287#1452C2×C10111yescharacteristic, complemented
288C101#1970811yescharacteristic, direct product factor, Sylow
289#533C22×C10111yescharacteristic
290#532C22×C10111yescharacteristic
291#532C22×C10111yescharacteristic
292#532C22×C10111yescharacteristic
293#500C22×C10111yescharacteristic
294#500C22×C10111yescharacteristic
295#498C22×C10111yescharacteristic
296#498C22×C10111yescharacteristic
297#494C22×C10111yescharacteristic
298#493C22×C10111yescharacteristic
299#493C22×C10111yescharacteristic
300#493C22×C10111yescharacteristic
301#492C22×C10111yescharacteristic
302#492C22×C10111yescharacteristic
303#492C22×C10111yescharacteristic
304#492C22×C10111yescharacteristic
305#487C22×C10111yescharacteristic
306#487C22×C10111yescharacteristic
307#487C22×C10111yescharacteristic
308#487C22×C10111yescharacteristic
309#486C22×C10111yescharacteristic
310#486C22×C10111yescharacteristic
311#486C22×C10111yescharacteristic
312#486C22×C10111yescharacteristic
313#486C22×C10111yescharacteristic
314#486C22×C10111yescharacteristic
315#486C22×C10111yescharacteristic
316#486C22×C10111yescharacteristic
317#482—22no—
318#478—22no—
319#466—22no—
320#465—22no—
321#464—22no—
322#463—22no—
323#463—22no—
324#452—22no—
325#449—22no—
326#449—22no—
327C4×SD16—22no—
328C4×D8—22no—
329#431C22×C10111yescharacteristic
330#431C22×C10111yescharacteristic
331C2×C4×C8C22×C10111yescharacteristic
332#322C22×C10111yescharacteristic
333#322C22×C10111yescharacteristic
334#322C22×C10111yescharacteristic
335#322C22×C10111yescharacteristic
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×Q16—22no—
340C2×SD16—22no—
341C2×SD16—22no—
342C2×SD16—22no—
343C2×SD16—22no—
344C2×D8—22no—
345C2×D8—22no—
346C2×D8—22no—
347C22×C8D4×C10112yes—
348C4⋊Q8C23×C10111yescharacteristic
349C4⋊Q8C23×C10111yescharacteristic
350C4⋊Q8C23×C10111yescharacteristic
351C4⋊Q8C23×C10111yescharacteristic
352C4⋊Q8C23×C10111yescharacteristic
353#127C23×C10111yescharacteristic
354#127C23×C10111yescharacteristic
355#127C23×C10111yescharacteristic
356#125—21no—
357#124—21no—
358#124—21no—
359#124—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368C4×Q8—21no—
369C4×Q8—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376#117—21no—
377C2×C42C23×C10111yescharacteristic
378#107—22no—
379#107—22no—
380#106—22no—
381#106—22no—
382C4⋊C8D4×C10112yes—
383C4⋊C8D4×C10112yes—
384#103—22no—
385#103—22no—
386#103—22no—
387#103—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396C22⋊C8D4×C10112yes—
397C22⋊C8D4×C10112yes—
398C4×C8D4×C10112yes—
399C4×C8C23×C10111yescharacteristic
400C4×C8C23×C10111yescharacteristic
401C4×C8C23×C10111yescharacteristic
402C4×C8C23×C10111yescharacteristic
403C4×C8C23×C10111yescharacteristic
404C4×C8C23×C10111yescharacteristic
405#41—82no—
406#41—82no—
407#41—82no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4C2×D4×C10111yescharacteristic
429C22×C4C2×D4×C10111yescharacteristic
430C22×C4C2×D4×C10111yescharacteristic
431Q16—82no—
432SD16—44no—
433SD16—82no—
434SD16—82no—
435SD16—82no—
436D8—44no—
437D8—82no—
438D8—82no—
439C2×C8—42no—
440C2×C8C2×D4×C10112yes—
441C2×C8C2×D4×C10112yes—
442C2×C8C2×D4×C10112yes—
443C2×C8C2×D4×C10112yes—
444C2×C8C2×D4×C10112yes—
445C2×C8C2×D4×C10112yes—
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—21no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C42—41no—
466C42C2×D4×C10111yescharacteristic
467C42C2×D4×C10111yescharacteristic
468C42C2×D4×C10111yescharacteristic
469C42C24×C10111yescharacteristic
470C23—41no—
471C23—41no—
472C23—41no—
473C23#127×C10111yescharacteristic
474Q8—42no—
475Q8—42no—
476Q8—42no—
477Q8—42no—
478Q8—42no—
479D4—42no—
480D4—42no—
481D4—42no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—82no—
489D4—82no—
490D4—82no—
491C2×C4—22no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—82no—
500C2×C4—82no—
501C2×C4—82no—
502C2×C4#127×C10111yescharacteristic
503C2×C4#127×C10111yescharacteristic
504C2×C4#127×C10111yescharacteristic
505C2×C4C22×D4×C10111yescharacteristic
506C2×C4C22×D4×C10111yescharacteristic
507C2×C4C22×D4×C10111yescharacteristic
508C8—22no—
509C8—22no—
510C8—22no—
511C8—22no—
512C8—22no—
513C8—22no—
514C22—21no—
515C22—21no—
516C22—21no—
517C22—81no—
518C22—81no—
519C22—81no—
520C22—81no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22C2×#127×C10111yescharacteristic
527C4—21no—
528C4—21no—
529C4—21no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4—81no—
534C4—81no—
535C4#575×C10112yes—
536C4#576×C10112yes—
537C4#577×C10112yes—
538C2—41no—
539C2—161no—
540C2—161no—
541C2—161no—
542C2C101×#315011yescharacteristic
543C2C101×#315411yescharacteristic
544C2C101×#315511yescharacteristic
subgroupG/H
center, socleC22×C101C2×#127
commutator, Frattini, cosocleC42C24×C101
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C2×C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#3228C2semidirect
2. C101×#3210C2semidirect
3. C101×#3207C2semidirect
4. C101×#3207C2semidirect
5. C101×#3169C2semidirect
6. C101×#3167C2semidirect
7. C101×#1722C2semidirect
8. C101×#1721C2semidirect
9. C101×#1720C2semidirect
10. C101×#1718C2semidirect
11. C101×#1717C2semidirect
12. C101×#1717C2semidirect
13. C101×#1715C2semidirect
14. C101×#1714C2semidirect
15. C101×#1452C2semidirect
265. #19708C101direct (N × H)
273. #3228C2×C101semidirect
274. #3210C2×C101semidirect
275. #3207C2×C101semidirect
276. #3207C2×C101semidirect
277. #3169C2×C101semidirect
278. #3167C2×C101semidirect
279. #1722C2×C101semidirect
280. #1721C2×C101semidirect
281. #1720C2×C101semidirect
282. #1718C2×C101semidirect
283. #1717C2×C101semidirect
284. #1717C2×C101semidirect
285. #1715C2×C101semidirect
286. #1714C2×C101semidirect
287. #1452C2×C101semidirect
288. C101#19708direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32282
C101×#32102
C101×#32072
C101×#31692
C101×#31672
C101×#17222
C101×#17212
C101×#17202
C101×#17182
C101×#17172
C101×#17152
C101×#17142
C101×#14522
#19708101