Finite Group Databasebeta

← C101×#19865 #38802016

Subgroups — C101×#19865 #38802016

Order 25856.

572 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×#3380C211yesmaximal, characteristic
2C101×#3360C211yesmaximal, characteristic
3C101×#3356C211yesmaximal, characteristic, complemented
4C101×#3338C211yesmaximal, characteristic, complemented
5C101×#1723C211yesmaximal, characteristic, complemented
6C101×#1695C211yesmaximal, characteristic, complemented
7C101×#1684C211yesmaximal, characteristic, complemented
8C101×#1676C211yesmaximal, characteristic, complemented
9C101×#1671C211yesmaximal, characteristic, complemented
10C101×#1643C211yesmaximal, characteristic, complemented
11C101×#1638C211yesmaximal, characteristic, complemented
12C101×#1632C211yesmaximal, characteristic, complemented
13C101×#1632C211yesmaximal, characteristic, complemented
14C101×#1581C211yesmaximal, characteristic
15C101×#1579C211yesmaximal, characteristic, complemented
16#556×C101C2211yescharacteristic
17#554×C101C2211yescharacteristic
18#554×C101C2211yescharacteristic
19#554×C101C2211yescharacteristic
20#500×C101C2211yescharacteristic
21#500×C101C2211yescharacteristic
22#499×C101—21no—
23#498×C101C2211yescharacteristic
24#494×C101C2211yescharacteristic
25#488×C101—21no—
26#487×C101C2211yescharacteristic
27#487×C101C2211yescharacteristic
28#485×C101—21no—
29#484×C101—21no—
30#484×C101—21no—
31#483×C101—21no—
32#479×C101—21no—
33#478×C101—21no—
34#478×C101—21no—
35#477×C101C2211yescharacteristic
36#477×C101C2211yescharacteristic
37#477×C101C2211yescharacteristic
38#476×C101C2211yescharacteristic
39#476×C101C2211yescharacteristic
40#476×C101C2211yescharacteristic
41#475×C101C2211yescharacteristic
42#470×C101—21no—
43#467×C101—21no—
44#463×C101—21no—
45#461×C101C2211yescharacteristic
46C8×Q8×C101C2211yescharacteristic
47C8×Q8×C101C2211yescharacteristic
48C4×Q16×C101C2211yescharacteristic
49C4×SD16×C101—21no—
50C4×D8×C101—21no—
51C4×D8×C101C2211yescharacteristic
52#436×C101C2211yescharacteristic
53C8×D4×C101C2211yescharacteristic
54#428×C101—21no—
55C2×#107×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—41no—
68C2×Q16×C101D411yescharacteristic
69C2×SD16×C101—21no—
70C2×D8×C101D411yescharacteristic
71C2×M16×C101—21no—
72C22×C8×C101—21no—
73C4⋊Q8×C101C2311yescharacteristic
74C4⋊Q8×C101C2311yescharacteristic
75C4⋊Q8×C101C2311yescharacteristic
76C4⋊Q8×C101C2311yescharacteristic
77#126×C101—41no—
78#125×C101—21no—
79#125×C101—21no—
80#125×C101—21no—
81#124×C101—21no—
82C22⋊Q8×C101—21no—
83C22⋊Q8×C101—21no—
84C22⋊Q8×C101—21no—
85C22⋊Q8×C101—21no—
86C22⋊Q8×C101—41no—
87C22⋊Q8×C101—41no—
88C22⋊Q8×C101—41no—
89C4×Q8×C101—21no—
90C4×Q8×C101C2311yescharacteristic
91C4×Q8×C101C2311yescharacteristic
92C4×D4×C101—21no—
93C4×D4×C101—21no—
94C4×D4×C101—21no—
95C4×D4×C101C2311yescharacteristic
96C4×D4×C101C2311yescharacteristic
97#117×C101—21no—
98C2×C4⋊C4×C101—21no—
99C2×C4⋊C4×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×C101D411yescharacteristic
109#107×C101D411yescharacteristic
110#106×C101—21no—
111#106×C101—21no—
112#106×C101—21no—
113#106×C101—21no—
114#106×C101—21no—
115#106×C101—21no—
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—21no—
129#103×C101—41no—
130#103×C101D411yescharacteristic
131#103×C101D411yescharacteristic
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—
139C4×C8×C101—21no—
140C4×C8×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×C101C2×D411yescharacteristic
149C2×Q8×C101C2×D411yescharacteristic
150C2×D4×C101C2×D411yescharacteristic
151C2×D4×C101C2×D411yescharacteristic
152C22×C4×C101—21no—
153C22×C4×C101—21no—
154C22×C4×C101—41no—
155C22×C4×C101—41no—
156C22×C4×C101—41no—
157Q16×C101—22no—
158Q16×C101—82no—
159SD16×C101—42no—
160D8×C101—22no—
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×C101—41no—
188C4⋊C4×C101—41no—
189C4⋊C4×C101C2×D411yescharacteristic
190C4⋊C4×C101C2×D411yescharacteristic
191C4⋊C4×C101C2×D411yescharacteristic
192C4⋊C4×C101C2×D411yescharacteristic
193C22⋊C4×C101—21no—
194C22⋊C4×C101—21no—
195C22⋊C4×C101—41no—
196C22⋊C4×C101—41no—
197C22⋊C4×C101—41no—
198C22⋊C4×C101—41no—
199C22⋊C4×C101—41no—
200C42×C101—21no—
201C42×C101—21no—
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—
215D4×C101—21no—
216D4×C101—21no—
217D4×C101—21no—
218D4×C101#13712yes—
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—41no—
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—161no—
234C2×C4×C101—161no—
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#13512yes—
248C22×C101—22no—
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×#13511yescharacteristic
267C4×C101C2×#13711yescharacteristic
268C4×C101#57811yescharacteristic
269C4×C101#57811yescharacteristic
270#19865C10111yesmaximal, characteristic, direct product factor, Sylow
271C2×C101—42no—
272C2×C101—81no—
273C2×C101#327011yescharacteristic
274C2×C101#328311yescharacteristic
275C2×C101#328811yescharacteristic
276#3380C2×C10111yescharacteristic
277#3360C2×C10111yescharacteristic
278#3356C2×C10111yescharacteristic, complemented
279#3338C2×C10111yescharacteristic, complemented
280#1723C2×C10111yescharacteristic, complemented
281#1695C2×C10111yescharacteristic, complemented
282#1684C2×C10111yescharacteristic, complemented
283#1676C2×C10111yescharacteristic, complemented
284#1671C2×C10111yescharacteristic, complemented
285#1643C2×C10111yescharacteristic, complemented
286#1638C2×C10111yescharacteristic, complemented
287#1632C2×C10111yescharacteristic, complemented
288#1632C2×C10111yescharacteristic, complemented
289#1581C2×C10111yescharacteristic
290#1579C2×C10111yescharacteristic, complemented
291C101#1986511yescharacteristic, direct product factor, Sylow
292#556C22×C10111yescharacteristic
293#554C22×C10111yescharacteristic
294#554C22×C10111yescharacteristic
295#554C22×C10111yescharacteristic
296#500C22×C10111yescharacteristic
297#500C22×C10111yescharacteristic
298#499—21no—
299#498C22×C10111yescharacteristic
300#494C22×C10111yescharacteristic
301#488—21no—
302#487C22×C10111yescharacteristic
303#487C22×C10111yescharacteristic
304#485—21no—
305#484—21no—
306#484—21no—
307#483—21no—
308#479—21no—
309#478—21no—
310#478—21no—
311#477C22×C10111yescharacteristic
312#477C22×C10111yescharacteristic
313#477C22×C10111yescharacteristic
314#476C22×C10111yescharacteristic
315#476C22×C10111yescharacteristic
316#476C22×C10111yescharacteristic
317#475C22×C10111yescharacteristic
318#470—21no—
319#467—21no—
320#463—21no—
321#461C22×C10111yescharacteristic
322C8×Q8C22×C10111yescharacteristic
323C8×Q8C22×C10111yescharacteristic
324C4×Q16C22×C10111yescharacteristic
325C4×SD16—21no—
326C4×D8—21no—
327C4×D8C22×C10111yescharacteristic
328#436C22×C10111yescharacteristic
329C8×D4C22×C10111yescharacteristic
330#428—21no—
331C2×#107—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—41no—
344C2×Q16D4×C10111yescharacteristic
345C2×SD16—21no—
346C2×D8D4×C10111yescharacteristic
347C2×M16—21no—
348C22×C8—21no—
349C4⋊Q8C23×C10111yescharacteristic
350C4⋊Q8C23×C10111yescharacteristic
351C4⋊Q8C23×C10111yescharacteristic
352C4⋊Q8C23×C10111yescharacteristic
353#126—41no—
354#125—21no—
355#125—21no—
356#125—21no—
357#124—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—21no—
362C22⋊Q8—41no—
363C22⋊Q8—41no—
364C22⋊Q8—41no—
365C4×Q8—21no—
366C4×Q8C23×C10111yescharacteristic
367C4×Q8C23×C10111yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4C23×C10111yescharacteristic
372C4×D4C23×C10111yescharacteristic
373#117—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—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#107D4×C10111yescharacteristic
385#107D4×C10111yescharacteristic
386#106—21no—
387#106—21no—
388#106—21no—
389#106—21no—
390#106—21no—
391#106—21no—
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—21no—
405#103—41no—
406#103D4×C10111yescharacteristic
407#103D4×C10111yescharacteristic
408#102—21no—
409#102—21no—
410#102—21no—
411#102D4×C10111yescharacteristic
412#102D4×C10111yescharacteristic
413C22⋊C8—21no—
414C22⋊C8—21no—
415C4×C8—21no—
416C4×C8—21no—
417C4×C8C23×C10111yescharacteristic
418C4×C8C23×C10111yescharacteristic
419C4×C8C23×C10111yescharacteristic
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×D4×C10111yescharacteristic
425C2×Q8C2×D4×C10111yescharacteristic
426C2×D4C2×D4×C10111yescharacteristic
427C2×D4C2×D4×C10111yescharacteristic
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—41no—
431C22×C4—41no—
432C22×C4—41no—
433Q16—22no—
434Q16—82no—
435SD16—42no—
436D8—22no—
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⋊C4—41no—
464C4⋊C4—41no—
465C4⋊C4C2×D4×C10111yescharacteristic
466C4⋊C4C2×D4×C10111yescharacteristic
467C4⋊C4C2×D4×C10111yescharacteristic
468C4⋊C4C2×D4×C10111yescharacteristic
469C22⋊C4—21no—
470C22⋊C4—21no—
471C22⋊C4—41no—
472C22⋊C4—41no—
473C22⋊C4—41no—
474C22⋊C4—41no—
475C22⋊C4—41no—
476C42—21no—
477C42—21no—
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—
491D4—21no—
492D4—21no—
493D4—21no—
494D4#137×C10112yes—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—161no—
510C2×C4—161no—
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#135×C10112yes—
524C22—22no—
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×#135×C10111yescharacteristic
543C4C2×#137×C10111yescharacteristic
544C4#578×C10111yescharacteristic
545C4#578×C10111yescharacteristic
546C2—42no—
547C2—81no—
548C2C101×#327011yescharacteristic
549C2C101×#328311yescharacteristic
550C2C101×#328811yescharacteristic
subgroupG/H
center, socleC22×C101D42
commutator, Frattini, cosocleC42C24×C101
prime radicalC2×D8×C101D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C42×C101 ◁ G

Complements

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

NH ≅ G/Ntype
3. C101×#3356C2semidirect
4. C101×#3338C2semidirect
5. C101×#1723C2semidirect
6. C101×#1695C2semidirect
7. C101×#1684C2semidirect
8. C101×#1676C2semidirect
9. C101×#1671C2semidirect
10. C101×#1643C2semidirect
11. C101×#1638C2semidirect
12. C101×#1632C2semidirect
13. C101×#1632C2semidirect
15. C101×#1579C2semidirect
270. #19865C101direct (N × H)
278. #3356C2×C101semidirect
279. #3338C2×C101semidirect
280. #1723C2×C101semidirect
281. #1695C2×C101semidirect
282. #1684C2×C101semidirect
283. #1676C2×C101semidirect
284. #1671C2×C101semidirect
285. #1643C2×C101semidirect
286. #1638C2×C101semidirect
287. #1632C2×C101semidirect
288. #1632C2×C101semidirect
290. #1579C2×C101semidirect
291. C101#19865direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#33802
C101×#33602
C101×#33562
C101×#33382
C101×#17232
C101×#16952
C101×#16842
C101×#16762
C101×#16712
C101×#16432
C101×#16382
C101×#16322
C101×#15812
C101×#15792
#19865101