Finite Group Databasebeta

← C101×#19725 #38801876

Subgroups — C101×#19725 #38801876

Order 25856.

764 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3230C211yesmaximal, characteristic, complemented
2C101×#3228C211yesmaximal, characteristic, complemented
3C101×#3227C211yesmaximal, characteristic, complemented
4C101×#3207C211yesmaximal, characteristic
5C101×#3182C211yesmaximal, characteristic, complemented
6C101×#3152C211yesmaximal, characteristic, complemented
7C101×#1723C211yesmaximal, characteristic, complemented
8C101×#1722C211yesmaximal, characteristic, complemented
9C101×#1720C211yesmaximal, characteristic, complemented
10C101×#1717C211yesmaximal, characteristic, complemented
11C101×#1714C211yesmaximal, characteristic, complemented
12C101×#1714C211yesmaximal, characteristic, complemented
13C101×#1707C211yesmaximal, characteristic, complemented
14C101×#1706C211yesmaximal, characteristic, complemented
15C101×#1453C211yesmaximal, characteristic, complemented
16C2×#137×C101—22no—
17#533×C101C2211yescharacteristic
18#532×C101C2211yescharacteristic
19#532×C101C2211yescharacteristic
20C2×C4⋊Q8×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#500×C101C2211yescharacteristic
23#500×C101C2211yescharacteristic
24#500×C101C2211yescharacteristic
25#498×C101C2211yescharacteristic
26#498×C101C2211yescharacteristic
27#498×C101C2211yescharacteristic
28#497×C101—22no—
29#494×C101C2211yescharacteristic
30#494×C101C2211yescharacteristic
31#493×C101C2211yescharacteristic
32#492×C101C2211yescharacteristic
33#492×C101C2211yescharacteristic
34#492×C101C2211yescharacteristic
35#492×C101C2211yescharacteristic
36#487×C101C2211yescharacteristic
37#487×C101C2211yescharacteristic
38#487×C101C2211yescharacteristic
39#487×C101C2211yescharacteristic
40#486×C101C2211yescharacteristic
41#486×C101C2211yescharacteristic
42#486×C101C2211yescharacteristic
43#486×C101C2211yescharacteristic
44#486×C101C2211yescharacteristic
45#486×C101C2211yescharacteristic
46#484×C101—22no—
47#482×C101—22no—
48#481×C101—22no—
49#478×C101—22no—
50#477×C101—22no—
51#476×C101—22no—
52#468×C101—22no—
53#463×C101—22no—
54#449×C101—22no—
55#440×C101—22no—
56#431×C101C2211yescharacteristic
57#431×C101C2211yescharacteristic
58C4×M16×C101C2211yescharacteristic
59#322×C101C2211yescharacteristic
60#322×C101C2211yescharacteristic
61#322×C101C2211yescharacteristic
62C82×C101C2211yescharacteristic
63C2×#41×C101—21no—
64C2×#41×C101—21no—
65C22×Q8×C101—21no—
66#137×C101—48no—
67C2×Q16×C101—22no—
68C2×Q16×C101—22no—
69C2×SD16×C101—22no—
70C2×SD16×C101—22no—
71C2×SD16×C101—22no—
72C2×SD16×C101—22no—
73C2×D8×C101—22no—
74C2×M16×C101D412yes—
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
83C4⋊Q8×C101C2311yescharacteristic
84#127×C101C2311yescharacteristic
85#127×C101C2311yescharacteristic
86#125×C101—21no—
87#124×C101—21no—
88#124×C101—21no—
89C22⋊Q8×C101—21no—
90C22⋊Q8×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—
101#117×C101—21no—
102C2×C4⋊C4×C101—21no—
103C2×C4⋊C4×C101—21no—
104C2×C42×C101C2311yescharacteristic
105#107×C101—22no—
106#107×C101—22no—
107#107×C101—22no—
108#107×C101—22no—
109#106×C101—22no—
110#106×C101—22no—
111#106×C101—22no—
112C4⋊C8×C101D412yes—
113C4⋊C8×C101D412yes—
114#103×C101—22no—
115#103×C101—22no—
116#103×C101—22no—
117#103×C101—22no—
118#102×C101—22no—
119#102×C101—22no—
120#102×C101—22no—
121#102×C101—22no—
122#102×C101—22no—
123#102×C101—22no—
124C22⋊C8×C101D412yes—
125C22⋊C8×C101D412yes—
126#97×C101D412yes—
127C4×C8×C101C2311yescharacteristic
128C4×C8×C101C2311yescharacteristic
129C4×C8×C101C2311yescharacteristic
130C4×C8×C101C2311yescharacteristic
131C4×C8×C101C2311yescharacteristic
132C4×C8×C101C2311yescharacteristic
133#41×C101—44no—
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—21no—
141C2×Q8×C101—44no—
142C2×Q8×C101—41no—
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—
151C22×C4×C101—41no—
152C22×C4×C101—41no—
153C22×C4×C101—41no—
154C22×C4×C101C2×D411yescharacteristic
155C22×C4×C101C2×D411yescharacteristic
156C22×C4×C101C2×D411yescharacteristic
157Q16×C101—44no—
158Q16×C101—44no—
159SD16×C101—44no—
160SD16×C101—44no—
161SD16×C101—44no—
162SD16×C101—82no—
163D8×C101—82no—
164M16×C101—24no—
165C2×C8×C101C2×D412yes—
166C2×C8×C101C2×D412yes—
167C2×C8×C101C2×D412yes—
168C2×C8×C101C2×D412yes—
169C2×C8×C101C2×D412yes—
170C2×C8×C101C2×D412yes—
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—21no—
183C4⋊C4×C101—41no—
184C4⋊C4×C101—41no—
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—
192C42×C101—41no—
193C42×C101C2×D411yescharacteristic
194C42×C101C2×D411yescharacteristic
195C42×C101C2×D411yescharacteristic
196C42×C101C2411yescharacteristic
197C23×C101—41no—
198C23×C101—41no—
199C23×C101#12711yescharacteristic
200Q8×C101—42no—
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—82no—
214D4×C101—82no—
215C2×C4×C101—22no—
216C2×C4×C101—22no—
217C2×C4×C101—22no—
218C2×C4×C101—41no—
219C2×C4×C101—41no—
220C2×C4×C101—41no—
221C2×C4×C101—41no—
222C2×C4×C101—41no—
223C2×C4×C101—41no—
224C2×C4×C101—82no—
225C2×C4×C101—82no—
226C2×C4×C101—82no—
227C2×C4×C101#12711yescharacteristic
228C2×C4×C101#12711yescharacteristic
229C2×C4×C101#12711yescharacteristic
230C2×C4×C101C22×D411yescharacteristic
231C2×C4×C101C22×D411yescharacteristic
232C2×C4×C101C22×D411yescharacteristic
233C8×C101—22no—
234C8×C101—22no—
235C8×C101—22no—
236C8×C101—22no—
237C8×C101—22no—
238C8×C101AGL(1,ℤ/8)14yes—
239C22×C101—21no—
240C22×C101—21no—
241C22×C101—21no—
242C22×C101—81no—
243C22×C101—81no—
244C22×C101—81no—
245C22×C101—81no—
246C22×C101—81no—
247C22×C101—81no—
248C22×C101C2×#12711yescharacteristic
249C4×C101—21no—
250C4×C101—21no—
251C4×C101—21no—
252C4×C101—81no—
253C4×C101—81no—
254C4×C101—81no—
255C4×C101—81no—
256C4×C101—81no—
257C4×C101—81no—
258C4×C101C2×AGL(1,ℤ/8)12yes—
259C4×C101#57712yes—
260C4×C101#57812yes—
261#19725C10111yesmaximal, characteristic, direct product factor, Sylow
262C2×C101—41no—
263C2×C101—161no—
264C2×C101—161no—
265C2×C101#315111yescharacteristic
266C2×C101#315411yescharacteristic
267C2×C101#315611yescharacteristic
268#3230C2×C10111yescharacteristic, complemented
269#3228C2×C10111yescharacteristic, complemented
270#3227C2×C10111yescharacteristic, complemented
271#3207C2×C10111yescharacteristic
272#3182C2×C10111yescharacteristic, complemented
273#3152C2×C10111yescharacteristic, complemented
274#1723C2×C10111yescharacteristic, complemented
275#1722C2×C10111yescharacteristic, complemented
276#1720C2×C10111yescharacteristic, complemented
277#1717C2×C10111yescharacteristic, complemented
278#1714C2×C10111yescharacteristic, complemented
279#1714C2×C10111yescharacteristic, complemented
280#1707C2×C10111yescharacteristic, complemented
281#1706C2×C10111yescharacteristic, complemented
282#1453C2×C10111yescharacteristic, complemented
283C101#1972511yescharacteristic, direct product factor, Sylow
284C2×#137—22no—
285#533C22×C10111yescharacteristic
286#532C22×C10111yescharacteristic
287#532C22×C10111yescharacteristic
288C2×C4⋊Q8C22×C10111yescharacteristic
289#500C22×C10111yescharacteristic
290#500C22×C10111yescharacteristic
291#500C22×C10111yescharacteristic
292#500C22×C10111yescharacteristic
293#498C22×C10111yescharacteristic
294#498C22×C10111yescharacteristic
295#498C22×C10111yescharacteristic
296#497—22no—
297#494C22×C10111yescharacteristic
298#494C22×C10111yescharacteristic
299#493C22×C10111yescharacteristic
300#492C22×C10111yescharacteristic
301#492C22×C10111yescharacteristic
302#492C22×C10111yescharacteristic
303#492C22×C10111yescharacteristic
304#487C22×C10111yescharacteristic
305#487C22×C10111yescharacteristic
306#487C22×C10111yescharacteristic
307#487C22×C10111yescharacteristic
308#486C22×C10111yescharacteristic
309#486C22×C10111yescharacteristic
310#486C22×C10111yescharacteristic
311#486C22×C10111yescharacteristic
312#486C22×C10111yescharacteristic
313#486C22×C10111yescharacteristic
314#484—22no—
315#482—22no—
316#481—22no—
317#478—22no—
318#477—22no—
319#476—22no—
320#468—22no—
321#463—22no—
322#449—22no—
323#440—22no—
324#431C22×C10111yescharacteristic
325#431C22×C10111yescharacteristic
326C4×M16C22×C10111yescharacteristic
327#322C22×C10111yescharacteristic
328#322C22×C10111yescharacteristic
329#322C22×C10111yescharacteristic
330C82C22×C10111yescharacteristic
331C2×#41—21no—
332C2×#41—21no—
333C22×Q8—21no—
334#137—48no—
335C2×Q16—22no—
336C2×Q16—22no—
337C2×SD16—22no—
338C2×SD16—22no—
339C2×SD16—22no—
340C2×SD16—22no—
341C2×D8—22no—
342C2×M16D4×C10112yes—
343C4⋊Q8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8C23×C10111yescharacteristic
347C4⋊Q8C23×C10111yescharacteristic
348C4⋊Q8C23×C10111yescharacteristic
349C4⋊Q8C23×C10111yescharacteristic
350C4⋊Q8C23×C10111yescharacteristic
351C4⋊Q8C23×C10111yescharacteristic
352#127C23×C10111yescharacteristic
353#127C23×C10111yescharacteristic
354#125—21no—
355#124—21no—
356#124—21no—
357C22⋊Q8—21no—
358C22⋊Q8—21no—
359#121—21no—
360#121—21no—
361#121—21no—
362#121—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×D4—21no—
366C4×D4—21no—
367C4×D4—21no—
368C4×D4—21no—
369#117—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C42C23×C10111yescharacteristic
373#107—22no—
374#107—22no—
375#107—22no—
376#107—22no—
377#106—22no—
378#106—22no—
379#106—22no—
380C4⋊C8D4×C10112yes—
381C4⋊C8D4×C10112yes—
382#103—22no—
383#103—22no—
384#103—22no—
385#103—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#102—22no—
391#102—22no—
392C22⋊C8D4×C10112yes—
393C22⋊C8D4×C10112yes—
394#97D4×C10112yes—
395C4×C8C23×C10111yescharacteristic
396C4×C8C23×C10111yescharacteristic
397C4×C8C23×C10111yescharacteristic
398C4×C8C23×C10111yescharacteristic
399C4×C8C23×C10111yescharacteristic
400C4×C8C23×C10111yescharacteristic
401#41—44no—
402#41—82no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—44no—
410C2×Q8—41no—
411C2×D4—21no—
412C2×D4—21no—
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—41no—
418C2×D4—41no—
419C22×C4—41no—
420C22×C4—41no—
421C22×C4—41no—
422C22×C4C2×D4×C10111yescharacteristic
423C22×C4C2×D4×C10111yescharacteristic
424C22×C4C2×D4×C10111yescharacteristic
425Q16—44no—
426Q16—44no—
427SD16—44no—
428SD16—44no—
429SD16—44no—
430SD16—82no—
431D8—82no—
432M16—24no—
433C2×C8C2×D4×C10112yes—
434C2×C8C2×D4×C10112yes—
435C2×C8C2×D4×C10112yes—
436C2×C8C2×D4×C10112yes—
437C2×C8C2×D4×C10112yes—
438C2×C8C2×D4×C10112yes—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
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—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C42—41no—
461C42C2×D4×C10111yescharacteristic
462C42C2×D4×C10111yescharacteristic
463C42C2×D4×C10111yescharacteristic
464C42C24×C10111yescharacteristic
465C23—41no—
466C23—41no—
467C23#127×C10111yescharacteristic
468Q8—42no—
469Q8—42no—
470Q8—42no—
471Q8—42no—
472Q8—42no—
473Q8—42no—
474Q8—82no—
475D4—42no—
476D4—42no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—82no—
482D4—82no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—82no—
493C2×C4—82no—
494C2×C4—82no—
495C2×C4#127×C10111yescharacteristic
496C2×C4#127×C10111yescharacteristic
497C2×C4#127×C10111yescharacteristic
498C2×C4C22×D4×C10111yescharacteristic
499C2×C4C22×D4×C10111yescharacteristic
500C2×C4C22×D4×C10111yescharacteristic
501C8—22no—
502C8—22no—
503C8—22no—
504C8—22no—
505C8—22no—
506C8AGL(1,ℤ/8)×C10114yes—
507C22—21no—
508C22—21no—
509C22—21no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22—81no—
514C22—81no—
515C22—81no—
516C22C2×#127×C10111yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4—81no—
526C4C2×AGL(1,ℤ/8)×C10112yes—
527C4#577×C10112yes—
528C4#578×C10112yes—
529C2—41no—
530C2—161no—
531C2—161no—
532C2C101×#315111yescharacteristic
533C2C101×#315411yescharacteristic
534C2C101×#315611yescharacteristic
subgroupG/H
center, socleC22×C101C2×#127
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3207C2
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×#3230C2semidirect
2. C101×#3228C2semidirect
3. C101×#3227C2semidirect
5. C101×#3182C2semidirect
6. C101×#3152C2semidirect
7. C101×#1723C2semidirect
8. C101×#1722C2semidirect
9. C101×#1720C2semidirect
10. C101×#1717C2semidirect
11. C101×#1714C2semidirect
12. C101×#1714C2semidirect
13. C101×#1707C2semidirect
14. C101×#1706C2semidirect
15. C101×#1453C2semidirect
261. #19725C101direct (N × H)
268. #3230C2×C101semidirect
269. #3228C2×C101semidirect
270. #3227C2×C101semidirect
272. #3182C2×C101semidirect
273. #3152C2×C101semidirect
274. #1723C2×C101semidirect
275. #1722C2×C101semidirect
276. #1720C2×C101semidirect
277. #1717C2×C101semidirect
278. #1714C2×C101semidirect
279. #1714C2×C101semidirect
280. #1707C2×C101semidirect
281. #1706C2×C101semidirect
282. #1453C2×C101semidirect
283. C101#19725direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32302
C101×#32282
C101×#32272
C101×#32072
C101×#31822
C101×#31522
C101×#17232
C101×#17222
C101×#17202
C101×#17172
C101×#17142
C101×#17072
C101×#17062
C101×#14532
#19725101