Finite Group Databasebeta

← C101×#19742 #38801893

Subgroups — C101×#19742 #38801893

Order 25856.

738 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3227C211yesmaximal, characteristic, complemented
2C101×#3226C211yesmaximal, characteristic, complemented
3C101×#3207C211yesmaximal, characteristic, complemented
4C101×#3207C211yesmaximal, characteristic, complemented
5C101×#3207C211yesmaximal, characteristic, complemented
6C101×#3206C211yesmaximal, characteristic, complemented
7C101×#1721C211yesmaximal, characteristic, complemented
8C101×#1719C211yesmaximal, characteristic, complemented
9C101×#1718C211yesmaximal, characteristic, complemented
10C101×#1717C211yesmaximal, characteristic, complemented
11C101×#1715C211yesmaximal, characteristic, complemented
12C101×#1714C211yesmaximal, characteristic, complemented
13C101×#1708C211yesmaximal, characteristic, complemented
14C101×#1706C211yesmaximal, characteristic, complemented
15C101×#1454C211yesmaximal, characteristic, complemented
16#532×C101C2211yescharacteristic
17#532×C101C2211yescharacteristic
18#532×C101C2211yescharacteristic
19C2×C4⋊Q8×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#498×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#493×C101C2211yescharacteristic
25#493×C101C2211yescharacteristic
26#493×C101C2211yescharacteristic
27#492×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#487×C101C2211yescharacteristic
37#486×C101C2211yescharacteristic
38#486×C101C2211yescharacteristic
39#486×C101C2211yescharacteristic
40#486×C101C2211yescharacteristic
41#486×C101C2211yescharacteristic
42#486×C101C2211yescharacteristic
43#486×C101C2211yescharacteristic
44#481×C101—22no—
45#480×C101—22no—
46#476×C101—22no—
47#474×C101—22no—
48#463×C101—22no—
49#463×C101—22no—
50#463×C101—22no—
51#461×C101—22no—
52#449×C101—22no—
53#449×C101—22no—
54#449×C101—22no—
55#448×C101—22no—
56#431×C101C2211yescharacteristic
57#431×C101C2211yescharacteristic
58#431×C101C2211yescharacteristic
59#322×C101C2211yescharacteristic
60#322×C101C2211yescharacteristic
61#322×C101C2211yescharacteristic
62C82×C101C2211yescharacteristic
63C2×#41×C101—21no—
64C2×#41×C101—21no—
65C2×#41×C101—21no—
66C22×Q8×C101—21no—
67C2×SD16×C101—22no—
68C2×SD16×C101—22no—
69C2×SD16×C101—22no—
70C2×SD16×C101—22no—
71C2×SD16×C101—22no—
72C2×D8×C101—22no—
73C2×D8×C101—22no—
74C2×D8×C101—22no—
75C4⋊Q8×C101—21no—
76C4⋊Q8×C101—21no—
77C4⋊Q8×C101—21no—
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80C4⋊Q8×C101C2311yescharacteristic
81C4⋊Q8×C101C2311yescharacteristic
82C4⋊Q8×C101C2311yescharacteristic
83#127×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#127×C101C2311yescharacteristic
86#124×C101—21no—
87#124×C101—21no—
88#124×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×D4×C101—21no—
96C4×D4×C101—21no—
97C4×D4×C101—21no—
98C4×D4×C101—21no—
99C4×D4×C101—21no—
100C4×D4×C101—21no—
101C2×C4⋊C4×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C42×C101C2311yescharacteristic
104#107×C101—22no—
105#107×C101—22no—
106#106×C101—22no—
107#106×C101—22no—
108C4⋊C8×C101D412yes—
109C4⋊C8×C101D412yes—
110C4⋊C8×C101D412yes—
111#103×C101—22no—
112#103×C101—22no—
113#103×C101—22no—
114#103×C101—22no—
115#103×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—
125C22⋊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×Q8×C101—41no—
141C2×Q8×C101—82no—
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—21no—
150C2×D4×C101—21no—
151C2×D4×C101—41no—
152C2×D4×C101—41no—
153C2×D4×C101—41no—
154C22×C4×C101—41no—
155C22×C4×C101—41no—
156C22×C4×C101—41no—
157C22×C4×C101—41no—
158C22×C4×C101C2×D411yescharacteristic
159C22×C4×C101C2×D411yescharacteristic
160C22×C4×C101C2×D411yescharacteristic
161SD16×C101—82no—
162SD16×C101—82no—
163SD16×C101—82no—
164SD16×C101—82no—
165SD16×C101—82no—
166D8×C101—82no—
167D8×C101—82no—
168D8×C101—82no—
169C2×C8×C101C2×D412yes—
170C2×C8×C101C2×D412yes—
171C2×C8×C101C2×D412yes—
172C2×C8×C101C2×D412yes—
173C2×C8×C101C2×D412yes—
174C2×C8×C101C2×D412yes—
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—21no—
184C4⋊C4×C101—21no—
185C4⋊C4×C101—41no—
186C4⋊C4×C101—41no—
187C22⋊C4×C101—41no—
188C22⋊C4×C101—41no—
189C22⋊C4×C101—41no—
190C22⋊C4×C101—41no—
191C22⋊C4×C101—41no—
192C22⋊C4×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—
206Q8×C101—82no—
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—42no—
216D4×C101—82no—
217D4×C101—82no—
218D4×C101—82no—
219C2×C4×C101—22no—
220C2×C4×C101—22no—
221C2×C4×C101—22no—
222C2×C4×C101—41no—
223C2×C4×C101—41no—
224C2×C4×C101—41no—
225C2×C4×C101—41no—
226C2×C4×C101—41no—
227C2×C4×C101—82no—
228C2×C4×C101—82no—
229C2×C4×C101—82no—
230C2×C4×C101—82no—
231C2×C4×C101#12711yescharacteristic
232C2×C4×C101#12711yescharacteristic
233C2×C4×C101#12711yescharacteristic
234C2×C4×C101C22×D411yescharacteristic
235C2×C4×C101C22×D411yescharacteristic
236C2×C4×C101C22×D411yescharacteristic
237C8×C101—22no—
238C8×C101—22no—
239C8×C101—22no—
240C8×C101—22no—
241C8×C101—22no—
242C8×C101—22no—
243C22×C101—21no—
244C22×C101—21no—
245C22×C101—21no—
246C22×C101—81no—
247C22×C101—81no—
248C22×C101—81no—
249C22×C101—81no—
250C22×C101—81no—
251C22×C101—81no—
252C22×C101—81no—
253C22×C101—81no—
254C22×C101—81no—
255C22×C101C2×#12711yescharacteristic
256C4×C101—21no—
257C4×C101—21no—
258C4×C101—21no—
259C4×C101—81no—
260C4×C101—81no—
261C4×C101—81no—
262C4×C101—81no—
263C4×C101—81no—
264C4×C101#57612yes—
265C4×C101#57712yes—
266C4×C101#57712yes—
267#19742C10111yesmaximal, characteristic, direct product factor, Sylow
268C2×C101—41no—
269C2×C101—161no—
270C2×C101—161no—
271C2×C101—161no—
272C2×C101#315411yescharacteristic
273C2×C101#315411yescharacteristic
274C2×C101#315511yescharacteristic
275#3227C2×C10111yescharacteristic, complemented
276#3226C2×C10111yescharacteristic, complemented
277#3207C2×C10111yescharacteristic, complemented
278#3207C2×C10111yescharacteristic, complemented
279#3207C2×C10111yescharacteristic, complemented
280#3206C2×C10111yescharacteristic, complemented
281#1721C2×C10111yescharacteristic, complemented
282#1719C2×C10111yescharacteristic, complemented
283#1718C2×C10111yescharacteristic, complemented
284#1717C2×C10111yescharacteristic, complemented
285#1715C2×C10111yescharacteristic, complemented
286#1714C2×C10111yescharacteristic, complemented
287#1708C2×C10111yescharacteristic, complemented
288#1706C2×C10111yescharacteristic, complemented
289#1454C2×C10111yescharacteristic, complemented
290C101#1974211yescharacteristic, direct product factor, Sylow
291#532C22×C10111yescharacteristic
292#532C22×C10111yescharacteristic
293#532C22×C10111yescharacteristic
294C2×C4⋊Q8C22×C10111yescharacteristic
295#500C22×C10111yescharacteristic
296#500C22×C10111yescharacteristic
297#498C22×C10111yescharacteristic
298#498C22×C10111yescharacteristic
299#493C22×C10111yescharacteristic
300#493C22×C10111yescharacteristic
301#493C22×C10111yescharacteristic
302#492C22×C10111yescharacteristic
303#492C22×C10111yescharacteristic
304#492C22×C10111yescharacteristic
305#492C22×C10111yescharacteristic
306#492C22×C10111yescharacteristic
307#487C22×C10111yescharacteristic
308#487C22×C10111yescharacteristic
309#487C22×C10111yescharacteristic
310#487C22×C10111yescharacteristic
311#487C22×C10111yescharacteristic
312#486C22×C10111yescharacteristic
313#486C22×C10111yescharacteristic
314#486C22×C10111yescharacteristic
315#486C22×C10111yescharacteristic
316#486C22×C10111yescharacteristic
317#486C22×C10111yescharacteristic
318#486C22×C10111yescharacteristic
319#481—22no—
320#480—22no—
321#476—22no—
322#474—22no—
323#463—22no—
324#463—22no—
325#463—22no—
326#461—22no—
327#449—22no—
328#449—22no—
329#449—22no—
330#448—22no—
331#431C22×C10111yescharacteristic
332#431C22×C10111yescharacteristic
333#431C22×C10111yescharacteristic
334#322C22×C10111yescharacteristic
335#322C22×C10111yescharacteristic
336#322C22×C10111yescharacteristic
337C82C22×C10111yescharacteristic
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C22×Q8—21no—
342C2×SD16—22no—
343C2×SD16—22no—
344C2×SD16—22no—
345C2×SD16—22no—
346C2×SD16—22no—
347C2×D8—22no—
348C2×D8—22no—
349C2×D8—22no—
350C4⋊Q8—21no—
351C4⋊Q8—21no—
352C4⋊Q8—21no—
353C4⋊Q8C23×C10111yescharacteristic
354C4⋊Q8C23×C10111yescharacteristic
355C4⋊Q8C23×C10111yescharacteristic
356C4⋊Q8C23×C10111yescharacteristic
357C4⋊Q8C23×C10111yescharacteristic
358#127C23×C10111yescharacteristic
359#127C23×C10111yescharacteristic
360#127C23×C10111yescharacteristic
361#124—21no—
362#124—21no—
363#124—21no—
364#121—21no—
365#121—21no—
366#121—21no—
367#121—21no—
368#121—21no—
369#121—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4—21no—
374C4×D4—21no—
375C4×D4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C42C23×C10111yescharacteristic
379#107—22no—
380#107—22no—
381#106—22no—
382#106—22no—
383C4⋊C8D4×C10112yes—
384C4⋊C8D4×C10112yes—
385C4⋊C8D4×C10112yes—
386#103—22no—
387#103—22no—
388#103—22no—
389#103—22no—
390#103—22no—
391#102—22no—
392#102—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398C22⋊C8D4×C10112yes—
399C22⋊C8D4×C10112yes—
400C22⋊C8D4×C10112yes—
401C4×C8C23×C10111yescharacteristic
402C4×C8C23×C10111yescharacteristic
403C4×C8C23×C10111yescharacteristic
404C4×C8C23×C10111yescharacteristic
405C4×C8C23×C10111yescharacteristic
406C4×C8C23×C10111yescharacteristic
407#41—82no—
408#41—82no—
409#41—82no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—41no—
416C2×Q8—82no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433C22×C4C2×D4×C10111yescharacteristic
434C22×C4C2×D4×C10111yescharacteristic
435C22×C4C2×D4×C10111yescharacteristic
436SD16—82no—
437SD16—82no—
438SD16—82no—
439SD16—82no—
440SD16—82no—
441D8—82no—
442D8—82no—
443D8—82no—
444C2×C8C2×D4×C10112yes—
445C2×C8C2×D4×C10112yes—
446C2×C8C2×D4×C10112yes—
447C2×C8C2×D4×C10112yes—
448C2×C8C2×D4×C10112yes—
449C2×C8C2×D4×C10112yes—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C22⋊C4—41no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C22⋊C4—41no—
468C42C2×D4×C10111yescharacteristic
469C42C2×D4×C10111yescharacteristic
470C42C2×D4×C10111yescharacteristic
471C42C24×C10111yescharacteristic
472C23—41no—
473C23—41no—
474C23—41no—
475C23#127×C10111yescharacteristic
476Q8—42no—
477Q8—42no—
478Q8—42no—
479Q8—42no—
480Q8—42no—
481Q8—82no—
482D4—42no—
483D4—42no—
484D4—42no—
485D4—42no—
486D4—42no—
487D4—42no—
488D4—42no—
489D4—42no—
490D4—42no—
491D4—82no—
492D4—82no—
493D4—82no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—82no—
503C2×C4—82no—
504C2×C4—82no—
505C2×C4—82no—
506C2×C4#127×C10111yescharacteristic
507C2×C4#127×C10111yescharacteristic
508C2×C4#127×C10111yescharacteristic
509C2×C4C22×D4×C10111yescharacteristic
510C2×C4C22×D4×C10111yescharacteristic
511C2×C4C22×D4×C10111yescharacteristic
512C8—22no—
513C8—22no—
514C8—22no—
515C8—22no—
516C8—22no—
517C8—22no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—81no—
522C22—81no—
523C22—81no—
524C22—81no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22—81no—
529C22—81no—
530C22C2×#127×C10111yescharacteristic
531C4—21no—
532C4—21no—
533C4—21no—
534C4—81no—
535C4—81no—
536C4—81no—
537C4—81no—
538C4—81no—
539C4#576×C10112yes—
540C4#577×C10112yes—
541C4#577×C10112yes—
542C2—41no—
543C2—161no—
544C2—161no—
545C2—161no—
546C2C101×#315411yescharacteristic
547C2C101×#315411yescharacteristic
548C2C101×#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×#3227C2semidirect
2. C101×#3226C2semidirect
3. C101×#3207C2semidirect
4. C101×#3207C2semidirect
5. C101×#3207C2semidirect
6. C101×#3206C2semidirect
7. C101×#1721C2semidirect
8. C101×#1719C2semidirect
9. C101×#1718C2semidirect
10. C101×#1717C2semidirect
11. C101×#1715C2semidirect
12. C101×#1714C2semidirect
13. C101×#1708C2semidirect
14. C101×#1706C2semidirect
15. C101×#1454C2semidirect
267. #19742C101direct (N × H)
275. #3227C2×C101semidirect
276. #3226C2×C101semidirect
277. #3207C2×C101semidirect
278. #3207C2×C101semidirect
279. #3207C2×C101semidirect
280. #3206C2×C101semidirect
281. #1721C2×C101semidirect
282. #1719C2×C101semidirect
283. #1718C2×C101semidirect
284. #1717C2×C101semidirect
285. #1715C2×C101semidirect
286. #1714C2×C101semidirect
287. #1708C2×C101semidirect
288. #1706C2×C101semidirect
289. #1454C2×C101semidirect
290. C101#19742direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32272
C101×#32262
C101×#32072
C101×#32062
C101×#17212
C101×#17192
C101×#17182
C101×#17172
C101×#17152
C101×#17142
C101×#17082
C101×#17062
C101×#14542
#19742101