Finite Group Databasebeta

← C101×#19487 #38801638

Subgroups — C101×#19487 #38801638

Order 25856.

576 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3231C211yesmaximal, characteristic, complemented
2C101×#3116C211yesmaximal, characteristic
3C101×#3076C211yesmaximal, characteristic
4C101×#2990C211yesmaximal, characteristic
5C101×#1704C211yesmaximal, characteristic, complemented
6C101×#1700C211yesmaximal, characteristic, complemented
7C101×#1696C211yesmaximal, characteristic, complemented
8C101×#1692C211yesmaximal, characteristic, complemented
9C101×#1683C211yesmaximal, characteristic, complemented
10C101×#1679C211yesmaximal, characteristic, complemented
11C101×#1675C211yesmaximal, characteristic, complemented
12C101×#1671C211yesmaximal, characteristic, complemented
13C101×#1573C211yesmaximal, characteristic, complemented
14C101×#1559C211yesmaximal, characteristic, complemented
15C101×#1550C211yesmaximal, characteristic, complemented
16#533×C101C2211yescharacteristic
17#533×C101C2211yescharacteristic
18C4×#41×C101C2211yescharacteristic
19#500×C101C2211yescharacteristic
20#498×C101C2211yescharacteristic
21#487×C101C2211yescharacteristic
22#487×C101C2211yescharacteristic
23#485×C101—21no—
24#485×C101—21no—
25#485×C101—21no—
26#479×C101—21no—
27#479×C101—21no—
28#479×C101—21no—
29#478×C101—21no—
30#477×C101C2211yescharacteristic
31#477×C101C2211yescharacteristic
32#476×C101C2211yescharacteristic
33#476×C101C2211yescharacteristic
34#475×C101C2211yescharacteristic
35#474×C101C2211yescharacteristic
36#462×C101C2211yescharacteristic
37#461×C101C2211yescharacteristic
38#452×C101—21no—
39#446×C101C2211yescharacteristic
40#446×C101C2211yescharacteristic
41#441×C101—21no—
42#440×C101—21no—
43#435×C101—21no—
44#435×C101—21no—
45C8×D4×C101C2211yescharacteristic
46C8×D4×C101C2211yescharacteristic
47#432×C101—21no—
48#432×C101C2211yescharacteristic
49#431×C101C2211yescharacteristic
50#427×C101—21no—
51#423×C101C2211yescharacteristic
52C2×C4⋊C8×C101—21no—
53C2×C4⋊C8×C101C2211yescharacteristic
54#416×C101—21no—
55#335×C101C2211yescharacteristic
56#335×C101C2211yescharacteristic
57#334×C101C2211yescharacteristic
58#334×C101C2211yescharacteristic
59#333×C101C2211yescharacteristic
60#333×C101C2211yescharacteristic
61#333×C101C2211yescharacteristic
62#333×C101C2211yescharacteristic
63#332×C101C2211yescharacteristic
64#332×C101C2211yescharacteristic
65#332×C101C2211yescharacteristic
66#332×C101C2211yescharacteristic
67C2×#41×C101D411yescharacteristic
68C2×Q16×C101—21no—
69C2×SD16×C101—21no—
70C2×M16×C101—21no—
71C22×C8×C101—21no—
72C22×C8×C101—21no—
73C22×C8×C101—21no—
74C4⋊Q8×C101C2311yescharacteristic
75C4⋊Q8×C101C2311yescharacteristic
76C4⋊Q8×C101C2311yescharacteristic
77C4⋊Q8×C101C2311yescharacteristic
78#125×C101—21no—
79#125×C101—21no—
80C22⋊Q8×C101—21no—
81C22⋊Q8×C101—21no—
82C22⋊Q8×C101—21no—
83C22⋊Q8×C101—21no—
84C4×Q8×C101—21no—
85C4×Q8×C101—21no—
86C4×Q8×C101—21no—
87C4×Q8×C101—21no—
88C4×Q8×C101D411yescharacteristic
89C4×Q8×C101C2311yescharacteristic
90C4×D4×C101—21no—
91C4×D4×C101—21no—
92C4×D4×C101D411yescharacteristic
93C4×D4×C101C2311yescharacteristic
94#117×C101—21no—
95#117×C101—21no—
96#117×C101—21no—
97#117×C101D411yescharacteristic
98C2×C42×C101—21no—
99C2×C42×C101C2311yescharacteristic
100#107×C101—21no—
101#107×C101—21no—
102#107×C101—21no—
103#107×C101—21no—
104#107×C101—21no—
105#106×C101—21no—
106#106×C101—21no—
107#106×C101—21no—
108#106×C101—21no—
109#106×C101—21no—
110C4⋊C8×C101—21no—
111C4⋊C8×C101—21no—
112C4⋊C8×C101—21no—
113C4⋊C8×C101—21no—
114C4⋊C8×C101D411yescharacteristic
115C4⋊C8×C101D411yescharacteristic
116C4⋊C8×C101C2311yescharacteristic
117C4⋊C8×C101C2311yescharacteristic
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—21no—
129#103×C101—21no—
130#103×C101—21no—
131#102×C101—21no—
132#102×C101—21no—
133#102×C101—21no—
134C22⋊C8×C101—21no—
135C22⋊C8×C101—21no—
136C22⋊C8×C101—21no—
137C22⋊C8×C101D411yescharacteristic
138C22⋊C8×C101D411yescharacteristic
139#97×C101—21no—
140#97×C101—21no—
141#97×C101—21no—
142C4×C8×C101C2311yescharacteristic
143C4×C8×C101C2311yescharacteristic
144#41×C101—22no—
145#41×C101—41no—
146C2×Q8×C101—21no—
147C2×Q8×C101—21no—
148C2×Q8×C101—21no—
149C2×Q8×C101—21no—
150C2×Q8×C101C2×D411yescharacteristic
151C2×D4×C101—21no—
152C2×D4×C101C2×D411yescharacteristic
153C22×C4×C101—21no—
154C22×C4×C101—21no—
155C22×C4×C101—21no—
156C22×C4×C101C2×D411yescharacteristic
157C22×C4×C101C2×D411yescharacteristic
158C22×C4×C101#4111yescharacteristic
159Q16×C101—42no—
160SD16×C101—42no—
161M16×C101—81no—
162C2×C8×C101—21no—
163C2×C8×C101—21no—
164C2×C8×C101—21no—
165C2×C8×C101—21no—
166C2×C8×C101—21no—
167C2×C8×C101—21no—
168C2×C8×C101—42no—
169C2×C8×C101—81no—
170C2×C8×C101—81no—
171C2×C8×C101C2×D411yescharacteristic
172C2×C8×C101C2×D411yescharacteristic
173C2×C8×C101C2×D411yescharacteristic
174C2×C8×C101C2×D411yescharacteristic
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—
187C4⋊C4×C101—41no—
188C4⋊C4×C101—41no—
189C4⋊C4×C101C2×D411yescharacteristic
190C4⋊C4×C101C2×D411yescharacteristic
191C22⋊C4×C101—21no—
192C22⋊C4×C101—21no—
193C22⋊C4×C101—21no—
194C22⋊C4×C101—41no—
195C22⋊C4×C101—41no—
196C42×C101—21no—
197C42×C101—21no—
198C42×C101—21no—
199C42×C101—41no—
200C42×C101—41no—
201C42×C101C2×D411yescharacteristic
202C42×C101C2×D411yescharacteristic
203C42×C101#4111yescharacteristic
204C42×C101C2411yescharacteristic
205C23×C101—21no—
206C23×C101#12111yescharacteristic
207Q8×C101—21no—
208Q8×C101—21no—
209Q8×C101—41no—
210Q8×C101—41no—
211Q8×C101—41no—
212Q8×C101—41no—
213Q8×C101—81no—
214Q8×C101—81no—
215D4×C101—21no—
216D4×C101—42no—
217D4×C101#13712yes—
218C2×C4×C101—21no—
219C2×C4×C101—21no—
220C2×C4×C101—21no—
221C2×C4×C101—21no—
222C2×C4×C101—21no—
223C2×C4×C101—21no—
224C2×C4×C101—21no—
225C2×C4×C101—41no—
226C2×C4×C101—42no—
227C2×C4×C101—42no—
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#12111yescharacteristic
235C2×C4×C101#12111yescharacteristic
236C2×C4×C101#12111yescharacteristic
237C2×C4×C101C22×D411yescharacteristic
238C2×C4×C101C22×D411yescharacteristic
239C2×C4×C101C2×#4111yescharacteristic
240C8×C101—21no—
241C8×C101—21no—
242C8×C101—21no—
243C8×C101—21no—
244C8×C101—41no—
245C8×C101—41no—
246C8×C101—41no—
247C8×C101—41no—
248C8×C101—41no—
249C8×C101—41no—
250C22×C101—21no—
251C22×C101—21no—
252C22×C101—22no—
253C22×C101—21no—
254C22×C101—41no—
255C22×C101—41no—
256C22×C101C2×#12111yescharacteristic
257C4×C101—21no—
258C4×C101—21no—
259C4×C101—21no—
260C4×C101—21no—
261C4×C101—41no—
262C4×C101—41no—
263C4×C101—41no—
264C4×C101—81no—
265C4×C101—81no—
266C4×C101—81no—
267C4×C101—81no—
268C4×C101C2×#13711yescharacteristic
269C4×C101#57511yescharacteristic
270C4×C101#57711yescharacteristic
271C4×C101#57811yescharacteristic
272#19487C10111yesmaximal, characteristic, direct product factor, Sylow
273C2×C101—41no—
274C2×C101—42no—
275C2×C101#304611yescharacteristic
276C2×C101#305611yescharacteristic
277C2×C101#306711yescharacteristic
278#3231C2×C10111yescharacteristic, complemented
279#3116C2×C10111yescharacteristic
280#3076C2×C10111yescharacteristic
281#2990C2×C10111yescharacteristic
282#1704C2×C10111yescharacteristic, complemented
283#1700C2×C10111yescharacteristic, complemented
284#1696C2×C10111yescharacteristic, complemented
285#1692C2×C10111yescharacteristic, complemented
286#1683C2×C10111yescharacteristic, complemented
287#1679C2×C10111yescharacteristic, complemented
288#1675C2×C10111yescharacteristic, complemented
289#1671C2×C10111yescharacteristic, complemented
290#1573C2×C10111yescharacteristic, complemented
291#1559C2×C10111yescharacteristic, complemented
292#1550C2×C10111yescharacteristic, complemented
293C101#1948711yescharacteristic, direct product factor, Sylow
294#533C22×C10111yescharacteristic
295#533C22×C10111yescharacteristic
296C4×#41C22×C10111yescharacteristic
297#500C22×C10111yescharacteristic
298#498C22×C10111yescharacteristic
299#487C22×C10111yescharacteristic
300#487C22×C10111yescharacteristic
301#485—21no—
302#485—21no—
303#485—21no—
304#479—21no—
305#479—21no—
306#479—21no—
307#478—21no—
308#477C22×C10111yescharacteristic
309#477C22×C10111yescharacteristic
310#476C22×C10111yescharacteristic
311#476C22×C10111yescharacteristic
312#475C22×C10111yescharacteristic
313#474C22×C10111yescharacteristic
314#462C22×C10111yescharacteristic
315#461C22×C10111yescharacteristic
316#452—21no—
317#446C22×C10111yescharacteristic
318#446C22×C10111yescharacteristic
319#441—21no—
320#440—21no—
321#435—21no—
322#435—21no—
323C8×D4C22×C10111yescharacteristic
324C8×D4C22×C10111yescharacteristic
325#432—21no—
326#432C22×C10111yescharacteristic
327#431C22×C10111yescharacteristic
328#427—21no—
329#423C22×C10111yescharacteristic
330C2×C4⋊C8—21no—
331C2×C4⋊C8C22×C10111yescharacteristic
332#416—21no—
333#335C22×C10111yescharacteristic
334#335C22×C10111yescharacteristic
335#334C22×C10111yescharacteristic
336#334C22×C10111yescharacteristic
337#333C22×C10111yescharacteristic
338#333C22×C10111yescharacteristic
339#333C22×C10111yescharacteristic
340#333C22×C10111yescharacteristic
341#332C22×C10111yescharacteristic
342#332C22×C10111yescharacteristic
343#332C22×C10111yescharacteristic
344#332C22×C10111yescharacteristic
345C2×#41D4×C10111yescharacteristic
346C2×Q16—21no—
347C2×SD16—21no—
348C2×M16—21no—
349C22×C8—21no—
350C22×C8—21no—
351C22×C8—21no—
352C4⋊Q8C23×C10111yescharacteristic
353C4⋊Q8C23×C10111yescharacteristic
354C4⋊Q8C23×C10111yescharacteristic
355C4⋊Q8C23×C10111yescharacteristic
356#125—21no—
357#125—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8D4×C10111yescharacteristic
367C4×Q8C23×C10111yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4D4×C10111yescharacteristic
371C4×D4C23×C10111yescharacteristic
372#117—21no—
373#117—21no—
374#117—21no—
375#117D4×C10111yescharacteristic
376C2×C42—21no—
377C2×C42C23×C10111yescharacteristic
378#107—21no—
379#107—21no—
380#107—21no—
381#107—21no—
382#107—21no—
383#106—21no—
384#106—21no—
385#106—21no—
386#106—21no—
387#106—21no—
388C4⋊C8—21no—
389C4⋊C8—21no—
390C4⋊C8—21no—
391C4⋊C8—21no—
392C4⋊C8D4×C10111yescharacteristic
393C4⋊C8D4×C10111yescharacteristic
394C4⋊C8C23×C10111yescharacteristic
395C4⋊C8C23×C10111yescharacteristic
396C4⋊C8C23×C10111yescharacteristic
397C4⋊C8C23×C10111yescharacteristic
398C4⋊C8C23×C10111yescharacteristic
399C4⋊C8C23×C10111yescharacteristic
400#103—21no—
401#103—21no—
402#103—21no—
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—21no—
408#103—21no—
409#102—21no—
410#102—21no—
411#102—21no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8D4×C10111yescharacteristic
416C22⋊C8D4×C10111yescharacteristic
417#97—21no—
418#97—21no—
419#97—21no—
420C4×C8C23×C10111yescharacteristic
421C4×C8C23×C10111yescharacteristic
422#41—22no—
423#41—41no—
424C2×Q8—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8C2×D4×C10111yescharacteristic
429C2×D4—21no—
430C2×D4C2×D4×C10111yescharacteristic
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4C2×D4×C10111yescharacteristic
435C22×C4C2×D4×C10111yescharacteristic
436C22×C4#41×C10111yescharacteristic
437Q16—42no—
438SD16—42no—
439M16—81no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—42no—
447C2×C8—81no—
448C2×C8—81no—
449C2×C8C2×D4×C10111yescharacteristic
450C2×C8C2×D4×C10111yescharacteristic
451C2×C8C2×D4×C10111yescharacteristic
452C2×C8C2×D4×C10111yescharacteristic
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4—41no—
466C4⋊C4—41no—
467C4⋊C4C2×D4×C10111yescharacteristic
468C4⋊C4C2×D4×C10111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—41no—
478C42—41no—
479C42C2×D4×C10111yescharacteristic
480C42C2×D4×C10111yescharacteristic
481C42#41×C10111yescharacteristic
482C42C24×C10111yescharacteristic
483C23—21no—
484C23#121×C10111yescharacteristic
485Q8—21no—
486Q8—21no—
487Q8—41no—
488Q8—41no—
489Q8—41no—
490Q8—41no—
491Q8—81no—
492Q8—81no—
493D4—21no—
494D4—42no—
495D4#137×C10112yes—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4#121×C10111yescharacteristic
513C2×C4#121×C10111yescharacteristic
514C2×C4#121×C10111yescharacteristic
515C2×C4C22×D4×C10111yescharacteristic
516C2×C4C22×D4×C10111yescharacteristic
517C2×C4C2×#41×C10111yescharacteristic
518C8—21no—
519C8—21no—
520C8—21no—
521C8—21no—
522C8—41no—
523C8—41no—
524C8—41no—
525C8—41no—
526C8—41no—
527C8—41no—
528C22—21no—
529C22—21no—
530C22—22no—
531C22—21no—
532C22—41no—
533C22—41no—
534C22C2×#121×C10111yescharacteristic
535C4—21no—
536C4—21no—
537C4—21no—
538C4—21no—
539C4—41no—
540C4—41no—
541C4—41no—
542C4—81no—
543C4—81no—
544C4—81no—
545C4—81no—
546C4C2×#137×C10111yescharacteristic
547C4#575×C10111yescharacteristic
548C4#577×C10111yescharacteristic
549C4#578×C10111yescharacteristic
550C2—41no—
551C2—42no—
552C2C101×#304611yescharacteristic
553C2C101×#305611yescharacteristic
554C2C101×#306711yescharacteristic
subgroupG/H
center, socleC22×C101C2×#121
commutator, Frattini, cosocleC42C24×C101
prime radicalC2×#41×C101D4
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×#3231C2semidirect
5. C101×#1704C2semidirect
6. C101×#1700C2semidirect
7. C101×#1696C2semidirect
8. C101×#1692C2semidirect
9. C101×#1683C2semidirect
10. C101×#1679C2semidirect
11. C101×#1675C2semidirect
12. C101×#1671C2semidirect
13. C101×#1573C2semidirect
14. C101×#1559C2semidirect
15. C101×#1550C2semidirect
272. #19487C101direct (N × H)
278. #3231C2×C101semidirect
282. #1704C2×C101semidirect
283. #1700C2×C101semidirect
284. #1696C2×C101semidirect
285. #1692C2×C101semidirect
286. #1683C2×C101semidirect
287. #1679C2×C101semidirect
288. #1675C2×C101semidirect
289. #1671C2×C101semidirect
290. #1573C2×C101semidirect
291. #1559C2×C101semidirect
292. #1550C2×C101semidirect
293. C101#19487direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#32312
C101×#31162
C101×#30762
C101×#29902
C101×#17042
C101×#17002
C101×#16962
C101×#16922
C101×#16832
C101×#16792
C101×#16752
C101×#16712
C101×#15732
C101×#15592
C101×#15502
#19487101