Finite Group Databasebeta

← C101×#20229 #38802380

Subgroups — C101×#20229 #38802380

Order 25856.

564 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3385C211yesmaximal, characteristic, complemented
2C101×#3369C211yesmaximal, characteristic, complemented
3C101×#3357C211yesmaximal, characteristic
4C101×#3340C211yesmaximal, characteristic
5C101×#1723C211yesmaximal, characteristic, complemented
6C101×#1703C211yesmaximal, characteristic, complemented
7C101×#1696C211yesmaximal, characteristic, complemented
8C101×#1692C211yesmaximal, characteristic, complemented
9C101×#1675C211yesmaximal, characteristic, complemented
10C101×#1644C211yesmaximal, characteristic, complemented
11C101×#1638C211yesmaximal, characteristic, complemented
12C101×#1634C211yesmaximal, characteristic
13C101×#1633C211yesmaximal, characteristic, complemented
14C101×#1592C211yesmaximal, characteristic, complemented
15C101×#1582C211yesmaximal, characteristic, complemented
16Q82×C101C2211yescharacteristic
17#556×C101C2211yescharacteristic
18#555×C101C2211yescharacteristic
19#554×C101C2211yescharacteristic
20#501×C101—21no—
21#500×C101C2211yescharacteristic
22#500×C101C2211yescharacteristic
23#498×C101C2211yescharacteristic
24#494×C101C2211yescharacteristic
25#489×C101—21no—
26#487×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#485×C101—21no—
29#485×C101—21no—
30#482×C101—21no—
31#480×C101—21no—
32#479×C101—21no—
33#477×C101C2211yescharacteristic
34#477×C101C2211yescharacteristic
35#477×C101C2211yescharacteristic
36#476×C101C2211yescharacteristic
37#476×C101C2211yescharacteristic
38#476×C101C2211yescharacteristic
39#475×C101—21no—
40#474×C101—21no—
41#474×C101C2211yescharacteristic
42#468×C101—21no—
43#465×C101—21no—
44#464×C101—21no—
45#462×C101C2211yescharacteristic
46#446×C101C2211yescharacteristic
47#446×C101C2211yescharacteristic
48#441×C101—21no—
49#440×C101—21no—
50C4×SD16×C101C2211yescharacteristic
51C4×SD16×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54#428×C101—21no—
55#427×C101—21no—
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#333×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#333×C101C2211yescharacteristic
61#332×C101C2211yescharacteristic
62Q8⋊C8×C101C2211yescharacteristic
63Q8⋊C8×C101C2211yescharacteristic
64D4⋊C8×C101C2211yescharacteristic
65D4⋊C8×C101C2211yescharacteristic
66#322×C101C2211yescharacteristic
67C2×Q16×C101—21no—
68C2×Q16×C101—41no—
69C2×SD16×C101D411yescharacteristic
70C2×SD16×C101D411yescharacteristic
71C2×M16×C101—21no—
72C22×C8×C101—21no—
73C4⋊Q8×C101—21no—
74C4⋊Q8×C101—21no—
75C4⋊Q8×C101—41no—
76C4⋊Q8×C101C2311yescharacteristic
77C4⋊Q8×C101C2311yescharacteristic
78C4⋊Q8×C101C2311yescharacteristic
79C4⋊Q8×C101C2311yescharacteristic
80#126×C101—41no—
81#125×C101—21no—
82#124×C101—21no—
83#124×C101—41no—
84C22⋊Q8×C101—21no—
85C22⋊Q8×C101—21no—
86C22⋊Q8×C101—41no—
87#121×C101—21no—
88#121×C101—21no—
89C4×Q8×C101—21no—
90C4×Q8×C101—21no—
91C4×Q8×C101—21no—
92C4×Q8×C101C2311yescharacteristic
93C4×Q8×C101C2311yescharacteristic
94C4×D4×C101—21no—
95C4×D4×C101C2311yescharacteristic
96C4×D4×C101C2311yescharacteristic
97#117×C101—21no—
98#117×C101—21no—
99#117×C101—21no—
100C2×C4⋊C4×C101—21no—
101#107×C101—21no—
102#107×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#107×C101—21no—
106#107×C101—21no—
107#107×C101—21no—
108#107×C101—21no—
109#106×C101—21no—
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101D411yescharacteristic
115#106×C101D411yescharacteristic
116C4⋊C8×C101—21no—
117C4⋊C8×C101—21no—
118C4⋊C8×C101C2311yescharacteristic
119C4⋊C8×C101C2311yescharacteristic
120C4⋊C8×C101C2311yescharacteristic
121C4⋊C8×C101C2311yescharacteristic
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×C101—41no—
129#103×C101D411yescharacteristic
130#103×C101D411yescharacteristic
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134#102×C101—21no—
135#102×C101D411yescharacteristic
136#102×C101D411yescharacteristic
137C22⋊C8×C101—21no—
138C22⋊C8×C101—21no—
139#97×C101—21no—
140#97×C101—21no—
141C4×C8×C101C2311yescharacteristic
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144C2×Q8×C101—21no—
145C2×Q8×C101—21no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—41no—
149C2×Q8×C101C2×D411yescharacteristic
150C2×Q8×C101C2×D411yescharacteristic
151C2×D4×C101—41no—
152C2×D4×C101C2×D411yescharacteristic
153C2×D4×C101C2×D411yescharacteristic
154C22×C4×C101—21no—
155C22×C4×C101—21no—
156C22×C4×C101—41no—
157Q16×C101—42no—
158Q16×C101—82no—
159SD16×C101—22no—
160SD16×C101—41no—
161M16×C101—42no—
162C2×C8×C101—21no—
163C2×C8×C101—21no—
164C2×C8×C101—21no—
165C2×C8×C101—21no—
166C2×C8×C101—21no—
167C2×C8×C101—42no—
168C2×C8×C101C2×D411yescharacteristic
169C2×C8×C101C2×D411yescharacteristic
170C2×C8×C101C2×D411yescharacteristic
171C2×C8×C101C2×D411yescharacteristic
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—41no—
183C4⋊C4×C101—41no—
184C4⋊C4×C101—41no—
185C4⋊C4×C101—41no—
186C4⋊C4×C101—41no—
187C4⋊C4×C101C2×D411yescharacteristic
188C4⋊C4×C101C2×D411yescharacteristic
189C4⋊C4×C101C2×D411yescharacteristic
190C4⋊C4×C101C2×D411yescharacteristic
191C22⋊C4×C101—21no—
192C22⋊C4×C101—21no—
193C22⋊C4×C101—41no—
194C22⋊C4×C101—41no—
195C22⋊C4×C101—41no—
196C22⋊C4×C101—41no—
197C22⋊C4×C101—41no—
198C42×C101—21no—
199C42×C101—21no—
200C42×C101—41no—
201C42×C101—41no—
202C42×C101—41no—
203C42×C101C2411yescharacteristic
204C23×C101—21no—
205C23×C101—21no—
206Q8×C101—21no—
207Q8×C101—21no—
208Q8×C101—21no—
209Q8×C101—21no—
210Q8×C101—41no—
211Q8×C101—41no—
212Q8×C101—81no—
213Q8×C101—81no—
214Q8×C101—81no—
215Q8×C101—161no—
216D4×C101—21no—
217D4×C101—21no—
218D4×C101—21no—
219D4×C101—21no—
220D4×C101—161no—
221C2×C4×C101—21no—
222C2×C4×C101—21no—
223C2×C4×C101—21no—
224C2×C4×C101—21no—
225C2×C4×C101—21no—
226C2×C4×C101—21no—
227C2×C4×C101—41no—
228C2×C4×C101—41no—
229C2×C4×C101—41no—
230C2×C4×C101—41no—
231C2×C4×C101—41no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—161no—
236C2×C4×C101C22×D411yescharacteristic
237C2×C4×C101C22×D411yescharacteristic
238C2×C4×C101H(5,𝔽2)11yescharacteristic
239C8×C101—21no—
240C8×C101—21no—
241C8×C101—21no—
242C8×C101—41no—
243C8×C101—41no—
244C8×C101—41no—
245C8×C101—41no—
246C8×C101—41no—
247C8×C101#13712yes—
248C22×C101—41no—
249C22×C101—41no—
250C22×C101—41no—
251C22×C101—41no—
252C22×C101—41no—
253C22×C101—41no—
254C22×C101D4211yescharacteristic
255C4×C101—21no—
256C4×C101—41no—
257C4×C101—41no—
258C4×C101—41no—
259C4×C101—41no—
260C4×C101—41no—
261C4×C101—41no—
262C4×C101—81no—
263C4×C101—81no—
264C4×C101—81no—
265C4×C101—81no—
266C4×C101C2×#13711yescharacteristic
267C4×C101#57511yescharacteristic
268C4×C101#57811yescharacteristic
269C4×C101#57811yescharacteristic
270#20229C10111yesmaximal, characteristic, direct product factor, Sylow
271C2×C101—81no—
272C2×C101—81no—
273C2×C101#326911yescharacteristic
274C2×C101#327611yescharacteristic
275C2×C101#328811yescharacteristic
276#3385C2×C10111yescharacteristic, complemented
277#3369C2×C10111yescharacteristic, complemented
278#3357C2×C10111yescharacteristic
279#3340C2×C10111yescharacteristic
280#1723C2×C10111yescharacteristic, complemented
281#1703C2×C10111yescharacteristic, complemented
282#1696C2×C10111yescharacteristic, complemented
283#1692C2×C10111yescharacteristic, complemented
284#1675C2×C10111yescharacteristic, complemented
285#1644C2×C10111yescharacteristic, complemented
286#1638C2×C10111yescharacteristic, complemented
287#1634C2×C10111yescharacteristic
288#1633C2×C10111yescharacteristic, complemented
289#1592C2×C10111yescharacteristic, complemented
290#1582C2×C10111yescharacteristic, complemented
291C101#2022911yescharacteristic, direct product factor, Sylow
292Q82C22×C10111yescharacteristic
293#556C22×C10111yescharacteristic
294#555C22×C10111yescharacteristic
295#554C22×C10111yescharacteristic
296#501—21no—
297#500C22×C10111yescharacteristic
298#500C22×C10111yescharacteristic
299#498C22×C10111yescharacteristic
300#494C22×C10111yescharacteristic
301#489—21no—
302#487C22×C10111yescharacteristic
303#487C22×C10111yescharacteristic
304#485—21no—
305#485—21no—
306#482—21no—
307#480—21no—
308#479—21no—
309#477C22×C10111yescharacteristic
310#477C22×C10111yescharacteristic
311#477C22×C10111yescharacteristic
312#476C22×C10111yescharacteristic
313#476C22×C10111yescharacteristic
314#476C22×C10111yescharacteristic
315#475—21no—
316#474—21no—
317#474C22×C10111yescharacteristic
318#468—21no—
319#465—21no—
320#464—21no—
321#462C22×C10111yescharacteristic
322#446C22×C10111yescharacteristic
323#446C22×C10111yescharacteristic
324#441—21no—
325#440—21no—
326C4×SD16C22×C10111yescharacteristic
327C4×SD16C22×C10111yescharacteristic
328#436C22×C10111yescharacteristic
329C8×D4C22×C10111yescharacteristic
330#428—21no—
331#427—21no—
332#335C22×C10111yescharacteristic
333#334C22×C10111yescharacteristic
334#333C22×C10111yescharacteristic
335#333C22×C10111yescharacteristic
336#333C22×C10111yescharacteristic
337#332C22×C10111yescharacteristic
338Q8⋊C8C22×C10111yescharacteristic
339Q8⋊C8C22×C10111yescharacteristic
340D4⋊C8C22×C10111yescharacteristic
341D4⋊C8C22×C10111yescharacteristic
342#322C22×C10111yescharacteristic
343C2×Q16—21no—
344C2×Q16—41no—
345C2×SD16D4×C10111yescharacteristic
346C2×SD16D4×C10111yescharacteristic
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351C4⋊Q8—41no—
352C4⋊Q8C23×C10111yescharacteristic
353C4⋊Q8C23×C10111yescharacteristic
354C4⋊Q8C23×C10111yescharacteristic
355C4⋊Q8C23×C10111yescharacteristic
356#126—41no—
357#125—21no—
358#124—21no—
359#124—41no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363#121—21no—
364#121—21no—
365C4×Q8—21no—
366C4×Q8—21no—
367C4×Q8—21no—
368C4×Q8C23×C10111yescharacteristic
369C4×Q8C23×C10111yescharacteristic
370C4×D4—21no—
371C4×D4C23×C10111yescharacteristic
372C4×D4C23×C10111yescharacteristic
373#117—21no—
374#117—21no—
375#117—21no—
376C2×C4⋊C4—21no—
377#107—21no—
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#107—21no—
384#107—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106D4×C10111yescharacteristic
391#106D4×C10111yescharacteristic
392C4⋊C8—21no—
393C4⋊C8—21no—
394C4⋊C8C23×C10111yescharacteristic
395C4⋊C8C23×C10111yescharacteristic
396C4⋊C8C23×C10111yescharacteristic
397C4⋊C8C23×C10111yescharacteristic
398#103—21no—
399#103—21no—
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—41no—
405#103D4×C10111yescharacteristic
406#103D4×C10111yescharacteristic
407#102—21no—
408#102—21no—
409#102—21no—
410#102—21no—
411#102D4×C10111yescharacteristic
412#102D4×C10111yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—21no—
415#97—21no—
416#97—21no—
417C4×C8C23×C10111yescharacteristic
418C4×C8C23×C10111yescharacteristic
419C4×C8C23×C10111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8—41no—
425C2×Q8C2×D4×C10111yescharacteristic
426C2×Q8C2×D4×C10111yescharacteristic
427C2×D4—41no—
428C2×D4C2×D4×C10111yescharacteristic
429C2×D4C2×D4×C10111yescharacteristic
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—41no—
433Q16—42no—
434Q16—82no—
435SD16—22no—
436SD16—41no—
437M16—42no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—42no—
444C2×C8C2×D4×C10111yescharacteristic
445C2×C8C2×D4×C10111yescharacteristic
446C2×C8C2×D4×C10111yescharacteristic
447C2×C8C2×D4×C10111yescharacteristic
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—21no—
457C4⋊C4—21no—
458C4⋊C4—41no—
459C4⋊C4—41no—
460C4⋊C4—41no—
461C4⋊C4—41no—
462C4⋊C4—41no—
463C4⋊C4C2×D4×C10111yescharacteristic
464C4⋊C4C2×D4×C10111yescharacteristic
465C4⋊C4C2×D4×C10111yescharacteristic
466C4⋊C4C2×D4×C10111yescharacteristic
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—41no—
470C22⋊C4—41no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—41no—
477C42—41no—
478C42—41no—
479C42C24×C10111yescharacteristic
480C23—21no—
481C23—21no—
482Q8—21no—
483Q8—21no—
484Q8—21no—
485Q8—21no—
486Q8—41no—
487Q8—41no—
488Q8—81no—
489Q8—81no—
490Q8—81no—
491Q8—161no—
492D4—21no—
493D4—21no—
494D4—21no—
495D4—21no—
496D4—161no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—161no—
512C2×C4C22×D4×C10111yescharacteristic
513C2×C4C22×D4×C10111yescharacteristic
514C2×C4H(5,𝔽2)×C10111yescharacteristic
515C8—21no—
516C8—21no—
517C8—21no—
518C8—41no—
519C8—41no—
520C8—41no—
521C8—41no—
522C8—41no—
523C8#137×C10112yes—
524C22—41no—
525C22—41no—
526C22—41no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22D42×C10111yescharacteristic
531C4—21no—
532C4—41no—
533C4—41no—
534C4—41no—
535C4—41no—
536C4—41no—
537C4—41no—
538C4—81no—
539C4—81no—
540C4—81no—
541C4—81no—
542C4C2×#137×C10111yescharacteristic
543C4#575×C10111yescharacteristic
544C4#578×C10111yescharacteristic
545C4#578×C10111yescharacteristic
546C2—81no—
547C2—81no—
548C2C101×#326911yescharacteristic
549C2C101×#327611yescharacteristic
550C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radical#555×C101C22
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×#3385C2semidirect
2. C101×#3369C2semidirect
5. C101×#1723C2semidirect
6. C101×#1703C2semidirect
7. C101×#1696C2semidirect
8. C101×#1692C2semidirect
9. C101×#1675C2semidirect
10. C101×#1644C2semidirect
11. C101×#1638C2semidirect
13. C101×#1633C2semidirect
14. C101×#1592C2semidirect
15. C101×#1582C2semidirect
270. #20229C101direct (N × H)
276. #3385C2×C101semidirect
277. #3369C2×C101semidirect
280. #1723C2×C101semidirect
281. #1703C2×C101semidirect
282. #1696C2×C101semidirect
283. #1692C2×C101semidirect
284. #1675C2×C101semidirect
285. #1644C2×C101semidirect
286. #1638C2×C101semidirect
288. #1633C2×C101semidirect
289. #1592C2×C101semidirect
290. #1582C2×C101semidirect
291. C101#20229direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33852
C101×#33692
C101×#33572
C101×#33402
C101×#17232
C101×#17032
C101×#16962
C101×#16922
C101×#16752
C101×#16442
C101×#16382
C101×#16342
C101×#16332
C101×#15922
C101×#15822
#20229101