Finite Group Databasebeta

← C101×#18697 #38800848

Subgroups — C101×#18697 #38800848

Order 25856.

890 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3550C211yesmaximal, characteristic, complemented
2C101×#3254C211yesmaximal, characteristic, complemented
3C101×#3253C211yesmaximal, characteristic
4C101×#3131C211yesmaximal, characteristic, complemented
5C101×#1638C212yesmaximal, complemented
6C101×#1637C212yesmaximal, complemented
7C101×#1628C212yesmaximal, complemented
8C101×#1627C212yesmaximal, complemented
9C101×#1561C211yesmaximal, characteristic, complemented
10C101×#1493C211yesmaximal, characteristic, complemented
11C101×#1492C211yesmaximal, characteristic, complemented
12#563×C101—22no—
13#559×C101—21no—
14Q82×C101—21no—
15#556×C101—21no—
16#556×C101C2212yes—
17D4×Q8×C101—21no—
18D4×Q8×C101C2212yes—
19#542×C101—22no—
20#542×C101—22no—
21#536×C101—22no—
22#533×C101C2211yescharacteristic
23#533×C101C2211yescharacteristic
24#532×C101C2211yescharacteristic
25#532×C101C2211yescharacteristic
26#488×C101—22no—
27#487×C101C2211yescharacteristic
28#487×C101C2211yescharacteristic
29#486×C101C2211yescharacteristic
30#486×C101C2211yescharacteristic
31#477×C101C2212yes—
32#476×C101—21no—
33#476×C101C2212yes—
34#474×C101—21no—
35#469×C101—22no—
36#468×C101—22no—
37#461×C101—21no—
38#460×C101C2212yes—
39#459×C101—21no—
40#459×C101C2212yes—
41#423×C101C2211yescharacteristic
42#423×C101C2211yescharacteristic
43#416×C101—22no—
44C2×C4×C8×C101C2211yescharacteristic
45#332×C101C2212yes—
46#332×C101C2212yes—
47Q8⋊C8×C101C2212yes—
48Q8⋊C8×C101C2212yes—
49D4⋊C8×C101C2212yes—
50D4⋊C8×C101C2212yes—
51C2×#41×C101—21no—
52C2×#41×C101—21no—
53C22×Q8×C101—22no—
54C2×SD16×C101—22no—
55C2×D8×C101—22no—
56C2×M16×C101—21no—
57C2×M16×C101—21no—
58C22×C8×C101—21no—
59C4⋊Q8×C101—24no—
60C4⋊Q8×C101—22no—
61C4⋊Q8×C101—22no—
62C4⋊Q8×C101D411yescharacteristic
63C4⋊Q8×C101D411yescharacteristic
64C4⋊Q8×C101D411yescharacteristic
65C4⋊Q8×C101C2311yescharacteristic
66C4⋊Q8×C101C2311yescharacteristic
67C4⋊Q8×C101C2311yescharacteristic
68#127×C101D411yescharacteristic
69#127×C101C2311yescharacteristic
70#126×C101—24no—
71#126×C101—24no—
72#125×C101—21no—
73#125×C101D412yes—
74#124×C101—24no—
75#124×C101—22no—
76#124×C101—22no—
77#124×C101—21no—
78#124×C101—21no—
79#123×C101—24no—
80#123×C101—24no—
81C22⋊Q8×C101—24no—
82C22⋊Q8×C101—22no—
83C22⋊Q8×C101—21no—
84C22⋊Q8×C101—21no—
85C22⋊Q8×C101—21no—
86C22⋊Q8×C101—22no—
87C22⋊Q8×C101—24no—
88C22⋊Q8×C101D412yes—
89#121×C101—21no—
90#121×C101—21no—
91#121×C101—21no—
92#121×C101D412yes—
93C4×Q8×C101—22no—
94C4×Q8×C101—22no—
95C4×Q8×C101—21no—
96C4×Q8×C101—21no—
97C4×Q8×C101—21no—
98C4×Q8×C101C2312yes—
99C4×D4×C101—22no—
100C4×D4×C101—22no—
101C4×D4×C101—21no—
102C4×D4×C101—21no—
103C4×D4×C101—21no—
104C4×D4×C101C2312yes—
105#117×C101—21no—
106#117×C101—22no—
107#117×C101D412yes—
108C2×C42×C101C2311yescharacteristic
109#107×C101—22no—
110#106×C101—22no—
111C4⋊C8×C101—21no—
112C4⋊C8×C101—21no—
113C4⋊C8×C101C2312yes—
114C4⋊C8×C101C2312yes—
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—
123C4×C8×C101—21no—
124C4×C8×C101C2311yescharacteristic
125C4×C8×C101C2311yescharacteristic
126#41×C101—44no—
127#41×C101—81no—
128#41×C101—81no—
129C2×Q8×C101—24no—
130C2×Q8×C101—21no—
131C2×Q8×C101—21no—
132C2×Q8×C101—21no—
133C2×Q8×C101—21no—
134C2×Q8×C101—21no—
135C2×Q8×C101—82no—
136C2×Q8×C101—82no—
137C2×Q8×C101C2×D412yes—
138C2×D4×C101—22no—
139C2×D4×C101—21no—
140C2×D4×C101—21no—
141C2×D4×C101—21no—
142C2×D4×C101—21no—
143C2×D4×C101—21no—
144C2×D4×C101—41no—
145C2×D4×C101C2×D412yes—
146C22×C4×C101—24no—
147C22×C4×C101—22no—
148C22×C4×C101—41no—
149C22×C4×C101C2×D411yescharacteristic
150C22×C4×C101C2×D411yescharacteristic
151C22×C4×C101C2×D411yescharacteristic
152SD16×C101—82no—
153D8×C101—82no—
154M16×C101—81no—
155M16×C101—81no—
156C2×C8×C101—21no—
157C2×C8×C101—21no—
158C2×C8×C101—22no—
159C2×C8×C101—22no—
160C2×C8×C101—42no—
161C4⋊C4×C101—24no—
162C4⋊C4×C101—24no—
163C4⋊C4×C101—21no—
164C4⋊C4×C101—21no—
165C4⋊C4×C101—21no—
166C4⋊C4×C101—21no—
167C4⋊C4×C101—22no—
168C4⋊C4×C101—22no—
169C4⋊C4×C101—22no—
170C4⋊C4×C101—21no—
171C4⋊C4×C101—21no—
172C4⋊C4×C101—22no—
173C4⋊C4×C101—21no—
174C4⋊C4×C101—21no—
175C4⋊C4×C101C2×D412yes—
176C4⋊C4×C101C2×D412yes—
177C4⋊C4×C101C2×D412yes—
178C4⋊C4×C101C2×D412yes—
179C22⋊C4×C101—24no—
180C22⋊C4×C101—24no—
181C22⋊C4×C101—24no—
182C22⋊C4×C101—22no—
183C22⋊C4×C101—22no—
184C22⋊C4×C101—22no—
185C22⋊C4×C101—22no—
186C22⋊C4×C101—41no—
187C22⋊C4×C101—41no—
188C42×C101—24no—
189C42×C101—22no—
190C42×C101—22no—
191C42×C101C2×D411yescharacteristic
192C42×C101C2×D411yescharacteristic
193C42×C101C2×D411yescharacteristic
194C42×C101C2411yescharacteristic
195C23×C101—22no—
196C23×C101—41no—
197C23×C101#12011yescharacteristic
198Q8×C101—22no—
199Q8×C101—22no—
200Q8×C101—42no—
201Q8×C101—41no—
202Q8×C101—41no—
203Q8×C101—41no—
204Q8×C101—41no—
205Q8×C101—42no—
206Q8×C101—81no—
207Q8×C101—84no—
208D4×C101—22no—
209D4×C101—22no—
210D4×C101—42no—
211D4×C101—41no—
212D4×C101—41no—
213D4×C101—41no—
214D4×C101—41no—
215D4×C101—42no—
216D4×C101—81no—
217D4×C101—82no—
218D4×C101—82no—
219C2×C4×C101—21no—
220C2×C4×C101—21no—
221C2×C4×C101—21no—
222C2×C4×C101—21no—
223C2×C4×C101—22no—
224C2×C4×C101—22no—
225C2×C4×C101—22no—
226C2×C4×C101—22no—
227C2×C4×C101—22no—
228C2×C4×C101—22no—
229C2×C4×C101—42no—
230C2×C4×C101—42no—
231C2×C4×C101—41no—
232C2×C4×C101—84no—
233C2×C4×C101—82no—
234C2×C4×C101#12011yescharacteristic
235C2×C4×C101#12011yescharacteristic
236C2×C4×C101#12011yescharacteristic
237C2×C4×C101C22×D411yescharacteristic
238C2×C4×C101C22×D411yescharacteristic
239C2×C4×C101C22×D411yescharacteristic
240C8×C101—41no—
241C8×C101—41no—
242C8×C101—42no—
243C8×C101—42no—
244C22×C101—21no—
245C22×C101—21no—
246C22×C101—21no—
247C22×C101—42no—
248C22×C101—42no—
249C22×C101—42no—
250C22×C101—81no—
251C22×C101—81no—
252C22×C101—81no—
253C22×C101C2×#12011yescharacteristic
254C4×C101—21no—
255C4×C101—21no—
256C4×C101—21no—
257C4×C101—42no—
258C4×C101—42no—
259C4×C101—42no—
260C4×C101—42no—
261C4×C101—42no—
262C4×C101—81no—
263C4×C101#45412yes—
264C4×C101#57611yescharacteristic
265C4×C101#57711yescharacteristic
266C4×C101#57711yescharacteristic
267C4×C101#57811yescharacteristic
268#18697C10111yesmaximal, characteristic, direct product factor, Sylow
269C2×C101—41no—
270C2×C101—82no—
271C2×C101—161no—
272C2×C101#301211yescharacteristic
273C2×C101#301311yescharacteristic
274C2×C101C2×#45411yescharacteristic
275#3550C2×C10111yescharacteristic, complemented
276#3254C2×C10111yescharacteristic, complemented
277#3253C2×C10111yescharacteristic
278#3131C2×C10111yescharacteristic, complemented
279#1638C2×C10112yescomplemented
280#1637C2×C10112yescomplemented
281#1628C2×C10112yescomplemented
282#1627C2×C10112yescomplemented
283#1561C2×C10111yescharacteristic, complemented
284#1493C2×C10111yescharacteristic, complemented
285#1492C2×C10111yescharacteristic, complemented
286C101#1869711yescharacteristic, direct product factor, Sylow
287#563—22no—
288#559—21no—
289Q82—21no—
290#556—21no—
291#556C22×C10112yes—
292D4×Q8—21no—
293D4×Q8C22×C10112yes—
294#542—22no—
295#542—22no—
296#536—22no—
297#533C22×C10111yescharacteristic
298#533C22×C10111yescharacteristic
299#532C22×C10111yescharacteristic
300#532C22×C10111yescharacteristic
301#488—22no—
302#487C22×C10111yescharacteristic
303#487C22×C10111yescharacteristic
304#486C22×C10111yescharacteristic
305#486C22×C10111yescharacteristic
306#477C22×C10112yes—
307#476—21no—
308#476C22×C10112yes—
309#474—21no—
310#469—22no—
311#468—22no—
312#461—21no—
313#460C22×C10112yes—
314#459—21no—
315#459C22×C10112yes—
316#423C22×C10111yescharacteristic
317#423C22×C10111yescharacteristic
318#416—22no—
319C2×C4×C8C22×C10111yescharacteristic
320#332C22×C10112yes—
321#332C22×C10112yes—
322Q8⋊C8C22×C10112yes—
323Q8⋊C8C22×C10112yes—
324D4⋊C8C22×C10112yes—
325D4⋊C8C22×C10112yes—
326C2×#41—21no—
327C2×#41—21no—
328C22×Q8—22no—
329C2×SD16—22no—
330C2×D8—22no—
331C2×M16—21no—
332C2×M16—21no—
333C22×C8—21no—
334C4⋊Q8—24no—
335C4⋊Q8—22no—
336C4⋊Q8—22no—
337C4⋊Q8D4×C10111yescharacteristic
338C4⋊Q8D4×C10111yescharacteristic
339C4⋊Q8D4×C10111yescharacteristic
340C4⋊Q8C23×C10111yescharacteristic
341C4⋊Q8C23×C10111yescharacteristic
342C4⋊Q8C23×C10111yescharacteristic
343#127D4×C10111yescharacteristic
344#127C23×C10111yescharacteristic
345#126—24no—
346#126—24no—
347#125—21no—
348#125D4×C10112yes—
349#124—24no—
350#124—22no—
351#124—22no—
352#124—21no—
353#124—21no—
354#123—24no—
355#123—24no—
356C22⋊Q8—24no—
357C22⋊Q8—22no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C22⋊Q8—21no—
361C22⋊Q8—22no—
362C22⋊Q8—24no—
363C22⋊Q8D4×C10112yes—
364#121—21no—
365#121—21no—
366#121—21no—
367#121D4×C10112yes—
368C4×Q8—22no—
369C4×Q8—22no—
370C4×Q8—21no—
371C4×Q8—21no—
372C4×Q8—21no—
373C4×Q8C23×C10112yes—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—21no—
377C4×D4—21no—
378C4×D4—21no—
379C4×D4C23×C10112yes—
380#117—21no—
381#117—22no—
382#117D4×C10112yes—
383C2×C42C23×C10111yescharacteristic
384#107—22no—
385#106—22no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8C23×C10112yes—
389C4⋊C8C23×C10112yes—
390#103—22no—
391#103—22no—
392#103—22no—
393#102—22no—
394#102—22no—
395#102—22no—
396#102—22no—
397#102—22no—
398C4×C8—21no—
399C4×C8C23×C10111yescharacteristic
400C4×C8C23×C10111yescharacteristic
401#41—44no—
402#41—81no—
403#41—81no—
404C2×Q8—24no—
405C2×Q8—21no—
406C2×Q8—21no—
407C2×Q8—21no—
408C2×Q8—21no—
409C2×Q8—21no—
410C2×Q8—82no—
411C2×Q8—82no—
412C2×Q8C2×D4×C10112yes—
413C2×D4—22no—
414C2×D4—21no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—41no—
420C2×D4C2×D4×C10112yes—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—41no—
424C22×C4C2×D4×C10111yescharacteristic
425C22×C4C2×D4×C10111yescharacteristic
426C22×C4C2×D4×C10111yescharacteristic
427SD16—82no—
428D8—82no—
429M16—81no—
430M16—81no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—42no—
436C4⋊C4—24no—
437C4⋊C4—24no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—22no—
443C4⋊C4—22no—
444C4⋊C4—22no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4C2×D4×C10112yes—
451C4⋊C4C2×D4×C10112yes—
452C4⋊C4C2×D4×C10112yes—
453C4⋊C4C2×D4×C10112yes—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—24no—
457C22⋊C4—22no—
458C22⋊C4—22no—
459C22⋊C4—22no—
460C22⋊C4—22no—
461C22⋊C4—41no—
462C22⋊C4—41no—
463C42—24no—
464C42—22no—
465C42—22no—
466C42C2×D4×C10111yescharacteristic
467C42C2×D4×C10111yescharacteristic
468C42C2×D4×C10111yescharacteristic
469C42C24×C10111yescharacteristic
470C23—22no—
471C23—41no—
472C23#120×C10111yescharacteristic
473Q8—22no—
474Q8—22no—
475Q8—42no—
476Q8—42no—
477Q8—41no—
478Q8—41no—
479Q8—41no—
480Q8—41no—
481Q8—81no—
482Q8—84no—
483D4—22no—
484D4—22no—
485D4—42no—
486D4—42no—
487D4—41no—
488D4—41no—
489D4—41no—
490D4—41no—
491D4—81no—
492D4—82no—
493D4—82no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—41no—
507C2×C4—84no—
508C2×C4—82no—
509C2×C4#120×C10111yescharacteristic
510C2×C4#120×C10111yescharacteristic
511C2×C4#120×C10111yescharacteristic
512C2×C4C22×D4×C10111yescharacteristic
513C2×C4C22×D4×C10111yescharacteristic
514C2×C4C22×D4×C10111yescharacteristic
515C8—41no—
516C8—41no—
517C8—42no—
518C8—42no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—42no—
523C22—42no—
524C22—42no—
525C22—81no—
526C22—81no—
527C22—81no—
528C22C2×#120×C10111yescharacteristic
529C4—21no—
530C4—21no—
531C4—21no—
532C4—42no—
533C4—42no—
534C4—42no—
535C4—42no—
536C4—42no—
537C4—81no—
538C4#454×C10112yes—
539C4#576×C10111yescharacteristic
540C4#577×C10111yescharacteristic
541C4#577×C10111yescharacteristic
542C4#578×C10111yescharacteristic
543C2—41no—
544C2—82no—
545C2—161no—
546C2C101×#301211yescharacteristic
547C2C101×#301311yescharacteristic
548C2C2×#454×C10111yescharacteristic
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC42C24×C101
prime radicalC101×#3253C2
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×#3550C2semidirect
2. C101×#3254C2semidirect
4. C101×#3131C2semidirect
5. C101×#1638C2semidirect
6. C101×#1637C2semidirect
7. C101×#1628C2semidirect
8. C101×#1627C2semidirect
9. C101×#1561C2semidirect
10. C101×#1493C2semidirect
11. C101×#1492C2semidirect
268. #18697C101direct (N × H)
275. #3550C2×C101semidirect
276. #3254C2×C101semidirect
278. #3131C2×C101semidirect
279. #1638C2×C101semidirect
280. #1637C2×C101semidirect
281. #1628C2×C101semidirect
282. #1627C2×C101semidirect
283. #1561C2×C101semidirect
284. #1493C2×C101semidirect
285. #1492C2×C101semidirect
286. C101#18697direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#35502
C101×#32542
C101×#32532
C101×#31312
C101×#16382
C101×#16372
C101×#16282
C101×#16272
C101×#15612
C101×#14932
C101×#14922
#18697101