Finite Group Databasebeta

← C101×#26271 #38808422

Subgroups — C101×#26271 #38808422

Order 25856.

752 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3156C211yesmaximal, characteristic
2C101×#3097C212yesmaximal, complemented
3C101×#2951C211yesmaximal, characteristic
4C101×#2052C212yesmaximal, complemented
5C101×#2038C212yesmaximal, complemented
6C101×#1979C211yesmaximal, characteristic, complemented
7C101×#1974C211yesmaximal, characteristic
8C101×#1969C211yesmaximal, characteristic, complemented
9C101×#1952C211yesmaximal, characteristic, complemented
10C101×#1882C212yesmaximal, complemented
11C101×#1772C211yesmaximal, characteristic, complemented
12C2×#137×C101C2212yes—
13C2×#135×C101C2211yescharacteristic
14C22×Q16×C101C2211yescharacteristic
15#536×C101C2212yes—
16#520×C101C2212yes—
17#497×C101—22no—
18#495×C101—21no—
19#494×C101—21no—
20#485×C101—22no—
21#485×C101—22no—
22#484×C101—22no—
23#483×C101—22no—
24#440×C101—22no—
25C4×Q16×C101—21no—
26C4×D8×C101—21no—
27C2×#108×C101C2211yescharacteristic
28C2×#108×C101C2211yescharacteristic
29#428×C101C2212yes—
30#427×C101C2211yescharacteristic
31C2×#107×C101C2211yescharacteristic
32C2×#104×C101C2212yes—
33#419×C101C2212yes—
34#417×C101C2212yes—
35C2×#103×C101C2212yes—
36C2×#101×C101C2212yes—
37#408×C101C2212yes—
38#405×C101C2211yescharacteristic
39#405×C101C2211yescharacteristic
40C2×C4×C8×C101C2211yescharacteristic
41#391×C101C2212yes—
42#343×C101C2212yes—
43#339×C101C2211yescharacteristic
44#339×C101C2211yescharacteristic
45C2×#41×C101C2312yes—
46C22×Q8×C101C2312yes—
47#137×C101—24no—
48#137×C101—42no—
49#135×C101—22no—
50#135×C101—22no—
51C2×Q16×C101—22no—
52C2×Q16×C101—21no—
53C2×Q16×C101—21no—
54C2×Q16×C101—22no—
55C2×Q16×C101—22no—
56C2×Q16×C101D411yescharacteristic
57C2×SD16×C101—22no—
58C2×SD16×C101D412yes—
59C2×D8×C101D411yescharacteristic
60C2×M16×C101C2311yescharacteristic
61C2×M16×C101C2312yes—
62C2×M16×C101C2311yescharacteristic
63C22×C8×C101C2311yescharacteristic
64C22×C8×C101C2311yescharacteristic
65C4⋊Q8×C101—22no—
66#124×C101—22no—
67#123×C101—42no—
68C22⋊Q8×C101—22no—
69C22⋊Q8×C101—22no—
70C4×Q8×C101—22no—
71C4×D4×C101—22no—
72C4×D4×C101—42no—
73#117×C101—22no—
74#117×C101C2311yescharacteristic
75#117×C101C2311yescharacteristic
76C2×C4⋊C4×C101—22no—
77C2×C4⋊C4×C101C2312yes—
78C2×C42×C101C2311yescharacteristic
79#108×C101—22no—
80#108×C101—22no—
81#107×C101—21no—
82#107×C101—21no—
83#107×C101—22no—
84#107×C101D411yescharacteristic
85#107×C101D411yescharacteristic
86#106×C101—22no—
87#106×C101D411yescharacteristic
88#106×C101D411yescharacteristic
89#104×C101—42no—
90#103×C101—22no—
91#103×C101—22no—
92#103×C101—22no—
93#103×C101—22no—
94#103×C101—22no—
95#102×C101—22no—
96#101×C101—42no—
97C22⋊C8×C101—22no—
98C22⋊C8×C101—22no—
99#97×C101—21no—
100#97×C101—21no—
101C4×C8×C101—21no—
102C4×C8×C101—21no—
103C4×C8×C101—22no—
104#95×C101—42no—
105#41×C101—22no—
106#41×C101—22no—
107#41×C101—22no—
108#41×C101—22no—
109C2×Q8×C101—22no—
110C2×Q8×C101—22no—
111C2×Q8×C101—22no—
112C2×Q8×C101—22no—
113C2×Q8×C101—22no—
114C2×Q8×C101—22no—
115C2×Q8×C101C2×D412yes—
116C2×D4×C101—22no—
117C2×D4×C101C2×D412yes—
118C22×C4×C101—21no—
119C22×C4×C101—22no—
120C22×C4×C101—22no—
121C22×C4×C101—22no—
122C22×C4×C101—42no—
123C22×C4×C101C2411yescharacteristic
124Q16×C101—22no—
125Q16×C101—44no—
126Q16×C101—42no—
127Q16×C101—42no—
128SD16×C101—24no—
129SD16×C101—44no—
130D8×C101—22no—
131M16×C101—21no—
132M16×C101—21no—
133M16×C101—22no—
134M16×C101—21no—
135M16×C101—22no—
136M16×C101#4112yes—
137C2×C8×C101—21no—
138C2×C8×C101—21no—
139C2×C8×C101—21no—
140C2×C8×C101—21no—
141C2×C8×C101—22no—
142C2×C8×C101C2×D411yescharacteristic
143C2×C8×C101C2×D411yescharacteristic
144C2×C8×C101C2×D411yescharacteristic
145C2×C8×C101C2×D411yescharacteristic
146C2×C8×C101#4112yes—
147C2×C8×C101#4112yes—
148C4⋊C4×C101—22no—
149C4⋊C4×C101—22no—
150C4⋊C4×C101—42no—
151C4⋊C4×C101—42no—
152C4⋊C4×C101—42no—
153C4⋊C4×C101C2×D411yescharacteristic
154C4⋊C4×C101C2×D411yescharacteristic
155C4⋊C4×C101C2×D411yescharacteristic
156C4⋊C4×C101C2×D411yescharacteristic
157C22⋊C4×C101—21no—
158C22⋊C4×C101—21no—
159C22⋊C4×C101—42no—
160C22⋊C4×C101—42no—
161C22⋊C4×C101—42no—
162C42×C101—21no—
163C42×C101—21no—
164C42×C101—21no—
165C42×C101—21no—
166C42×C101—42no—
167C23×C101—22no—
168C23×C101H(5,𝔽2)11yescharacteristic
169Q8×C101—22no—
170Q8×C101—22no—
171Q8×C101—42no—
172Q8×C101—42no—
173Q8×C101—42no—
174Q8×C101—42no—
175D4×C101—22no—
176D4×C101—22no—
177D4×C101—42no—
178D4×C101—42no—
179C2×C4×C101—22no—
180C2×C4×C101—21no—
181C2×C4×C101—21no—
182C2×C4×C101—21no—
183C2×C4×C101—21no—
184C2×C4×C101—22no—
185C2×C4×C101—41no—
186C2×C4×C101—41no—
187C2×C4×C101—42no—
188C2×C4×C101—42no—
189C2×C4×C101—42no—
190C2×C4×C101—42no—
191C2×C4×C101—42no—
192C2×C4×C101—42no—
193C2×C4×C101—82no—
194C2×C4×C101—162no—
195C2×C4×C101C22×D411yescharacteristic
196C2×C4×C101C22×D411yescharacteristic
197C2×C4×C101C2×#4111yescharacteristic
198C2×C4×C101C2×#4111yescharacteristic
199C2×C4×C101C2×#4111yescharacteristic
200C2×C4×C101H(5,𝔽2)11yescharacteristic
201C8×C101—21no—
202C8×C101—21no—
203C8×C101—22no—
204C8×C101—41no—
205C8×C101—42no—
206C8×C101#12312yes—
207C8×C101#12312yes—
208C22×C101—21no—
209C22×C101—21no—
210C22×C101—42no—
211C22×C101—42no—
212C22×C101—42no—
213C22×C101#54011yescharacteristic
214C22×C101D4211yescharacteristic
215C22×C101#55911yescharacteristic
216C4×C101—42no—
217C4×C101—42no—
218C4×C101—41no—
219C4×C101—41no—
220C4×C101—41no—
221C4×C101—41no—
222C4×C101—82no—
223C4×C101—82no—
224C4×C101C2×#12311yescharacteristic
225C4×C101#53211yescharacteristic
226C4×C101#54611yescharacteristic
227C4×C101#55011yescharacteristic
228#26271C10111yesmaximal, characteristic, direct product factor, Sylow
229C2×C101—21no—
230C2×C101—21no—
231C2×C101—82no—
232C2×C101#244511yescharacteristic
233C2×C101#329011yescharacteristic
234C2×C101#329311yescharacteristic
235#3156C2×C10111yescharacteristic
236#3097C2×C10112yescomplemented
237#2951C2×C10111yescharacteristic
238#2052C2×C10112yescomplemented
239#2038C2×C10112yescomplemented
240#1979C2×C10111yescharacteristic, complemented
241#1974C2×C10111yescharacteristic
242#1969C2×C10111yescharacteristic, complemented
243#1952C2×C10111yescharacteristic, complemented
244#1882C2×C10112yescomplemented
245#1772C2×C10111yescharacteristic, complemented
246C101#2627111yescharacteristic, direct product factor, Sylow
247C2×#137C22×C10112yes—
248C2×#135C22×C10111yescharacteristic
249C22×Q16C22×C10111yescharacteristic
250#536C22×C10112yes—
251#520C22×C10112yes—
252#497—22no—
253#495—21no—
254#494—21no—
255#485—22no—
256#485—22no—
257#484—22no—
258#483—22no—
259#440—22no—
260C4×Q16—21no—
261C4×D8—21no—
262C2×#108C22×C10111yescharacteristic
263C2×#108C22×C10111yescharacteristic
264#428C22×C10112yes—
265#427C22×C10111yescharacteristic
266C2×#107C22×C10111yescharacteristic
267C2×#104C22×C10112yes—
268#419C22×C10112yes—
269#417C22×C10112yes—
270C2×#103C22×C10112yes—
271C2×#101C22×C10112yes—
272#408C22×C10112yes—
273#405C22×C10111yescharacteristic
274#405C22×C10111yescharacteristic
275C2×C4×C8C22×C10111yescharacteristic
276#391C22×C10112yes—
277#343C22×C10112yes—
278#339C22×C10111yescharacteristic
279#339C22×C10111yescharacteristic
280C2×#41C23×C10112yes—
281C22×Q8C23×C10112yes—
282#137—24no—
283#137—42no—
284#135—22no—
285#135—22no—
286C2×Q16—22no—
287C2×Q16—21no—
288C2×Q16—21no—
289C2×Q16—22no—
290C2×Q16—22no—
291C2×Q16D4×C10111yescharacteristic
292C2×SD16—22no—
293C2×SD16D4×C10112yes—
294C2×D8D4×C10111yescharacteristic
295C2×M16C23×C10111yescharacteristic
296C2×M16C23×C10112yes—
297C2×M16C23×C10111yescharacteristic
298C22×C8C23×C10111yescharacteristic
299C22×C8C23×C10111yescharacteristic
300C4⋊Q8—22no—
301#124—22no—
302#123—42no—
303C22⋊Q8—22no—
304C22⋊Q8—22no—
305C4×Q8—22no—
306C4×D4—22no—
307C4×D4—42no—
308#117—22no—
309#117C23×C10111yescharacteristic
310#117C23×C10111yescharacteristic
311C2×C4⋊C4—22no—
312C2×C4⋊C4C23×C10112yes—
313C2×C42C23×C10111yescharacteristic
314#108—22no—
315#108—22no—
316#107—21no—
317#107—21no—
318#107—22no—
319#107D4×C10111yescharacteristic
320#107D4×C10111yescharacteristic
321#106—22no—
322#106D4×C10111yescharacteristic
323#106D4×C10111yescharacteristic
324#104—42no—
325#103—22no—
326#103—22no—
327#103—22no—
328#103—22no—
329#103—22no—
330#102—22no—
331#101—42no—
332C22⋊C8—22no—
333C22⋊C8—22no—
334#97—21no—
335#97—21no—
336C4×C8—21no—
337C4×C8—21no—
338C4×C8—22no—
339#95—42no—
340#41—22no—
341#41—22no—
342#41—22no—
343#41—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8—22no—
347C2×Q8—22no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8C2×D4×C10112yes—
351C2×D4—22no—
352C2×D4C2×D4×C10112yes—
353C22×C4—21no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
357C22×C4—42no—
358C22×C4C24×C10111yescharacteristic
359Q16—22no—
360Q16—44no—
361Q16—42no—
362Q16—42no—
363SD16—24no—
364SD16—44no—
365D8—22no—
366M16—21no—
367M16—21no—
368M16—22no—
369M16—21no—
370M16—22no—
371M16#41×C10112yes—
372C2×C8—21no—
373C2×C8—21no—
374C2×C8—21no—
375C2×C8—21no—
376C2×C8—22no—
377C2×C8C2×D4×C10111yescharacteristic
378C2×C8C2×D4×C10111yescharacteristic
379C2×C8C2×D4×C10111yescharacteristic
380C2×C8C2×D4×C10111yescharacteristic
381C2×C8#41×C10112yes—
382C2×C8#41×C10112yes—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—42no—
386C4⋊C4—42no—
387C4⋊C4—42no—
388C4⋊C4C2×D4×C10111yescharacteristic
389C4⋊C4C2×D4×C10111yescharacteristic
390C4⋊C4C2×D4×C10111yescharacteristic
391C4⋊C4C2×D4×C10111yescharacteristic
392C22⋊C4—21no—
393C22⋊C4—21no—
394C22⋊C4—42no—
395C22⋊C4—42no—
396C22⋊C4—42no—
397C42—21no—
398C42—21no—
399C42—21no—
400C42—21no—
401C42—42no—
402C23—22no—
403C23H(5,𝔽2)×C10111yescharacteristic
404Q8—22no—
405Q8—22no—
406Q8—42no—
407Q8—42no—
408Q8—42no—
409Q8—42no—
410D4—22no—
411D4—22no—
412D4—42no—
413D4—42no—
414C2×C4—22no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—22no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—82no—
429C2×C4—162no—
430C2×C4C22×D4×C10111yescharacteristic
431C2×C4C22×D4×C10111yescharacteristic
432C2×C4C2×#41×C10111yescharacteristic
433C2×C4C2×#41×C10111yescharacteristic
434C2×C4C2×#41×C10111yescharacteristic
435C2×C4H(5,𝔽2)×C10111yescharacteristic
436C8—21no—
437C8—21no—
438C8—22no—
439C8—41no—
440C8—42no—
441C8#123×C10112yes—
442C8#123×C10112yes—
443C22—21no—
444C22—21no—
445C22—42no—
446C22—42no—
447C22—42no—
448C22#540×C10111yescharacteristic
449C22D42×C10111yescharacteristic
450C22#559×C10111yescharacteristic
451C4—42no—
452C4—42no—
453C4—41no—
454C4—41no—
455C4—41no—
456C4—41no—
457C4—82no—
458C4—82no—
459C4C2×#123×C10111yescharacteristic
460C4#532×C10111yescharacteristic
461C4#546×C10111yescharacteristic
462C4#550×C10111yescharacteristic
463C2—21no—
464C2—21no—
465C2—82no—
466C2C101×#244511yescharacteristic
467C2C101×#329011yescharacteristic
468C2C101×#329311yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#135×C101C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C22×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#3097C2semidirect
4. C101×#2052C2semidirect
5. C101×#2038C2semidirect
6. C101×#1979C2semidirect
8. C101×#1969C2semidirect
9. C101×#1952C2semidirect
10. C101×#1882C2semidirect
11. C101×#1772C2semidirect
228. #26271C101direct (N × H)
236. #3097C2×C101semidirect
238. #2052C2×C101semidirect
239. #2038C2×C101semidirect
240. #1979C2×C101semidirect
242. #1969C2×C101semidirect
243. #1952C2×C101semidirect
244. #1882C2×C101semidirect
245. #1772C2×C101semidirect
246. C101#26271direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#31562
C101×#30972
C101×#29512
C101×#20522
C101×#20382
C101×#19792
C101×#19742
C101×#19692
C101×#19522
C101×#18822
C101×#17722
#26271101