Finite Group Databasebeta

← C101×#9241 #38791392

Subgroups — C101×#9241 #38791392

Order 25856.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#449×C101C211yesmaximal, characteristic
2C101×#2880C211yesmaximal, characteristic, complemented
3C101×#1789C211yesmaximal, characteristic, complemented
4C101×#1507C211yesmaximal, characteristic, complemented
5C101×#1471C211yesmaximal, characteristic, complemented
6C101×#1293C211yesmaximal, characteristic, complemented
7C101×#1282C211yesmaximal, characteristic, complemented
8C22×#41×C101C2211yescharacteristic
9C22×SD16×C101C411yescharacteristic, complemented
10C22×D8×C101C411yescharacteristic, complemented
11C2×#131×C101—21no—
12C2×#121×C101C2211yescharacteristic
13#449×C101—21no—
14#449×C101—21no—
15#449×C101—21no—
16#449×C101—21no—
17C2×#104×C101—21no—
18C2×#104×C101—21no—
19C2×#103×C101C411yescharacteristic, complemented
20C2×#102×C101C411yescharacteristic, complemented
21#408×C101—21no—
22#408×C101—22no—
23#407×C101—21no—
24#407×C101C2211yescharacteristic
25#407×C101C2211yescharacteristic
26C2×C22⋊C8×C101—21no—
27C2×C22⋊C8×C101C2211yescharacteristic
28C2×C22⋊C8×C101C2211yescharacteristic
29C4×C22⋊C4×C101C2211yescharacteristic
30#327×C101—22no—
31#323×C101—21no—
32#323×C101—21no—
33C2×#41×C101—21no—
34C2×#41×C101—21no—
35C2×#41×C101—42no—
36C2×#41×C101—42no—
37C2×#41×C101D411yescharacteristic
38C2×#41×C101D411yescharacteristic
39C2×#41×C101D411yescharacteristic
40C2×#41×C101D411yescharacteristic
41C22×Q8×C101C2×C411yescharacteristic
42C22×D4×C101—21no—
43C22×D4×C101—21no—
44C22×D4×C101C2×C411yescharacteristic
45C22×D4×C101C2×C411yescharacteristic
46C23×C4×C101—21no—
47C23×C4×C101C2311yescharacteristic
48C2×SD16×C101—21no—
49C2×SD16×C101—21no—
50C2×SD16×C101—42no—
51C2×D8×C101—21no—
52C2×D8×C101—21no—
53C2×D8×C101—42no—
54#131×C101—42no—
55#131×C101—42no—
56C2×M16×C101—22no—
57C2×M16×C101—21no—
58C2×M16×C101—21no—
59C22×C8×C101—22no—
60C22×C8×C101—21no—
61C22×C8×C101C2×C411yescharacteristic
62C22×C8×C101C2×C411yescharacteristic
63#121×C101—21no—
64#121×C101—21no—
65#121×C101—21no—
66#121×C101—21no—
67C2×C4⋊C4×C101C2×C411yescharacteristic
68C2×C22⋊C4×C101—21no—
69C2×C22⋊C4×C101—21no—
70C2×C42×C101—21no—
71#104×C101—42no—
72#104×C101—42no—
73#103×C101—21no—
74#103×C101—21no—
75#102×C101—21no—
76#102×C101—21no—
77C22⋊C8×C101—22no—
78C22⋊C8×C101—22no—
79C22⋊C8×C101—21no—
80C22⋊C8×C101—21no—
81C22⋊C8×C101—21no—
82C22⋊C8×C101—21no—
83C22⋊C8×C101—21no—
84C22⋊C8×C101—21no—
85C22⋊C8×C101D411yescharacteristic
86C22⋊C8×C101D411yescharacteristic
87C22⋊C8×C101D412yes—
88#95×C101—21no—
89C24×C101—21no—
90C24×C101—21no—
91C24×C101#4111yescharacteristic
92#41×C101—22no—
93#41×C101—22no—
94#41×C101—22no—
95#41×C101—22no—
96#41×C101—41no—
97#41×C101—41no—
98#41×C101—41no—
99#41×C101—41no—
100#41×C101—44no—
101#41×C101—44no—
102C2×Q8×C101—21no—
103C2×Q8×C101—22no—
104C2×Q8×C101—41no—
105C2×Q8×C101C22⋊C411yescharacteristic
106C2×Q8×C101C22⋊C411yescharacteristic
107C2×D4×C101—21no—
108C2×D4×C101—22no—
109C2×D4×C101—21no—
110C2×D4×C101—21no—
111C2×D4×C101—21no—
112C2×D4×C101—21no—
113C2×D4×C101—21no—
114C2×D4×C101—21no—
115C2×D4×C101—41no—
116C2×D4×C101—41no—
117C2×D4×C101—41no—
118C2×D4×C101—44no—
119C2×D4×C101—41no—
120C2×D4×C101—41no—
121C2×D4×C101—82no—
122C2×D4×C101C22⋊C411yescharacteristic
123C2×D4×C101C22⋊C411yescharacteristic
124C22×C4×C101—21no—
125C22×C4×C101—21no—
126C22×C4×C101—21no—
127C22×C4×C101—21no—
128C22×C4×C101—21no—
129C22×C4×C101—21no—
130C22×C4×C101—41no—
131C22×C4×C101—41no—
132C22×C4×C101—44no—
133C22×C4×C101—41no—
134C22×C4×C101C22×C411yescharacteristic
135C22×C4×C101C2×D411yescharacteristic
136C22×C4×C101C2×D411yescharacteristic
137C22×C4×C101C2×D411yescharacteristic
138C22×C4×C101C2×D411yescharacteristic
139C22×C4×C101#4111yescharacteristic
140SD16×C101—42no—
141SD16×C101—42no—
142D8×C101—42no—
143D8×C101—42no—
144M16×C101—44no—
145M16×C101—41no—
146M16×C101—41no—
147M16×C101—41no—
148M16×C101—41no—
149C2×C8×C101—21no—
150C2×C8×C101—21no—
151C2×C8×C101—21no—
152C2×C8×C101—22no—
153C2×C8×C101—21no—
154C2×C8×C101—44no—
155C2×C8×C101—41no—
156C2×C8×C101—41no—
157C2×C8×C101—41no—
158C2×C8×C101—41no—
159C2×C8×C101—41no—
160C4⋊C4×C101—21no—
161C4⋊C4×C101—21no—
162C22⋊C4×C101—22no—
163C22⋊C4×C101—41no—
164C22⋊C4×C101—41no—
165C22⋊C4×C101—41no—
166C42×C101—41no—
167C42×C101—41no—
168C23×C101—21no—
169C23×C101—21no—
170C23×C101—21no—
171C23×C101—21no—
172C23×C101—41no—
173C23×C101—41no—
174C23×C101—42no—
175C23×C101—41no—
176C23×C101—41no—
177C23×C101—41no—
178C23×C101—41no—
179C23×C101—41no—
180C23×C101—81no—
181C23×C101—81no—
182C23×C101—81no—
183C23×C101C4×D411yescharacteristic
184C23×C101#12111yescharacteristic
185C23×C101#12311yescharacteristic
186Q8×C101—21no—
187Q8×C101—21no—
188Q8×C101—21no—
189Q8×C101—42no—
190Q8×C101#9912yes—
191D4×C101—24no—
192D4×C101—21no—
193D4×C101—21no—
194D4×C101—21no—
195D4×C101—42no—
196D4×C101—42no—
197D4×C101—42no—
198D4×C101—42no—
199D4×C101—41no—
200D4×C101—41no—
201D4×C101—81no—
202D4×C101—82no—
203D4×C101—82no—
204D4×C101#9912yes—
205C2×C4×C101—24no—
206C2×C4×C101—21no—
207C2×C4×C101—21no—
208C2×C4×C101—21no—
209C2×C4×C101—21no—
210C2×C4×C101—21no—
211C2×C4×C101—21no—
212C2×C4×C101—21no—
213C2×C4×C101—21no—
214C2×C4×C101—41no—
215C2×C4×C101—41no—
216C2×C4×C101—41no—
217C2×C4×C101—42no—
218C2×C4×C101—42no—
219C2×C4×C101—42no—
220C2×C4×C101—42no—
221C2×C4×C101—42no—
222C2×C4×C101—41no—
223C2×C4×C101—81no—
224C2×C4×C101—81no—
225C2×C4×C101—81no—
226C2×C4×C101C2×C22⋊C411yescharacteristic
227C2×C4×C101C4×D411yescharacteristic
228C2×C4×C101#12011yescharacteristic
229C2×C4×C101#12111yescharacteristic
230C8×C101—41no—
231C8×C101—42no—
232C8×C101—41no—
233C8×C101—41no—
234C8×C101—41no—
235C8×C101—81no—
236C22×C101—21no—
237C22×C101—21no—
238C22×C101—21no—
239C22×C101—21no—
240C22×C101—21no—
241C22×C101—21no—
242C22×C101—22no—
243C22×C101—21no—
244C22×C101—21no—
245C22×C101—41no—
246C22×C101—41no—
247C22×C101—41no—
248C22×C101—41no—
249C22×C101—41no—
250C22×C101—81no—
251C22×C101—81no—
252C22×C101—82no—
253C22×C101—82no—
254C22×C101—81no—
255C22×C101—81no—
256C22×C101—81no—
257C22×C101—161no—
258C22×C101—161no—
259C22×C101#38611yescharacteristic
260C22×C101#44311yescharacteristic
261C22×C101#44411yescharacteristic
262C4×C101—21no—
263C4×C101—21no—
264C4×C101—22no—
265C4×C101—21no—
266C4×C101—41no—
267C4×C101—82no—
268C4×C101—81no—
269C4×C101C2×#9911yescharacteristic
270C4×C101C2×#9911yescharacteristic
271#9241C10111yesmaximal, characteristic, direct product factor, Sylow
272C2×C101—21no—
273C2×C101—21no—
274C2×C101—41no—
275C2×C101—41no—
276C2×C101—42no—
277C2×C101—81no—
278C2×C101—161no—
279C2×C101#187611yescharacteristic
280C2×C101#189811yescharacteristic
281C2×C101#190311yescharacteristic
282C2×#449C2×C10111yescharacteristic
283#2880C2×C10111yescharacteristic, complemented
284#1789C2×C10111yescharacteristic, complemented
285#1507C2×C10111yescharacteristic, complemented
286#1471C2×C10111yescharacteristic, complemented
287#1293C2×C10111yescharacteristic, complemented
288#1282C2×C10111yescharacteristic, complemented
289C101#924111yescharacteristic, direct product factor, Sylow
290C22×#41C22×C10111yescharacteristic
291C22×SD16C4×C10111yescharacteristic, complemented
292C22×D8C4×C10111yescharacteristic, complemented
293C2×#131—21no—
294C2×#121C22×C10111yescharacteristic
295#449—21no—
296#449—21no—
297#449—21no—
298#449—21no—
299C2×#104—21no—
300C2×#104—21no—
301C2×#103C4×C10111yescharacteristic, complemented
302C2×#102C4×C10111yescharacteristic, complemented
303#408—21no—
304#408—22no—
305#407—21no—
306#407C22×C10111yescharacteristic
307#407C22×C10111yescharacteristic
308C2×C22⋊C8—21no—
309C2×C22⋊C8C22×C10111yescharacteristic
310C2×C22⋊C8C22×C10111yescharacteristic
311C4×C22⋊C4C22×C10111yescharacteristic
312#327—22no—
313#323—21no—
314#323—21no—
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D4×C10111yescharacteristic
320C2×#41D4×C10111yescharacteristic
321C2×#41D4×C10111yescharacteristic
322C2×#41D4×C10111yescharacteristic
323C22×Q8C2×C4×C10111yescharacteristic
324C22×D4—21no—
325C22×D4—21no—
326C22×D4C2×C4×C10111yescharacteristic
327C22×D4C2×C4×C10111yescharacteristic
328C23×C4—21no—
329C23×C4C23×C10111yescharacteristic
330C2×SD16—21no—
331C2×SD16—21no—
332C2×SD16—42no—
333C2×D8—21no—
334C2×D8—21no—
335C2×D8—42no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—21no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8C2×C4×C10111yescharacteristic
344C22×C8C2×C4×C10111yescharacteristic
345#121—21no—
346#121—21no—
347#121—21no—
348#121—21no—
349C2×C4⋊C4C2×C4×C10111yescharacteristic
350C2×C22⋊C4—21no—
351C2×C22⋊C4—21no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—21no—
356#103—21no—
357#102—21no—
358#102—21no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—21no—
364C22⋊C8—21no—
365C22⋊C8—21no—
366C22⋊C8—21no—
367C22⋊C8D4×C10111yescharacteristic
368C22⋊C8D4×C10111yescharacteristic
369C22⋊C8D4×C10112yes—
370#95—21no—
371C24—21no—
372C24—21no—
373C24#41×C10111yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8C22⋊C4×C10111yescharacteristic
388C2×Q8C22⋊C4×C10111yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—21no—
396C2×D4—21no—
397C2×D4—41no—
398C2×D4—41no—
399C2×D4—41no—
400C2×D4—44no—
401C2×D4—41no—
402C2×D4—41no—
403C2×D4—82no—
404C2×D4C22⋊C4×C10111yescharacteristic
405C2×D4C22⋊C4×C10111yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—41no—
413C22×C4—41no—
414C22×C4—44no—
415C22×C4—41no—
416C22×C4C22×C4×C10111yescharacteristic
417C22×C4C2×D4×C10111yescharacteristic
418C22×C4C2×D4×C10111yescharacteristic
419C22×C4C2×D4×C10111yescharacteristic
420C22×C4C2×D4×C10111yescharacteristic
421C22×C4#41×C10111yescharacteristic
422SD16—42no—
423SD16—42no—
424D8—42no—
425D8—42no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—41no—
430M16—41no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—22no—
435C2×C8—21no—
436C2×C8—44no—
437C2×C8—41no—
438C2×C8—41no—
439C2×C8—41no—
440C2×C8—41no—
441C2×C8—41no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C42—41no—
449C42—41no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—41no—
460C23—41no—
461C23—41no—
462C23—81no—
463C23—81no—
464C23—81no—
465C23C4×D4×C10111yescharacteristic
466C23#121×C10111yescharacteristic
467C23#123×C10111yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#99×C10112yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—41no—
482D4—41no—
483D4—81no—
484D4—82no—
485D4—82no—
486D4#99×C10112yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—41no—
505C2×C4—81no—
506C2×C4—81no—
507C2×C4—81no—
508C2×C4C2×C22⋊C4×C10111yescharacteristic
509C2×C4C4×D4×C10111yescharacteristic
510C2×C4#120×C10111yescharacteristic
511C2×C4#121×C10111yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—41no—
516C8—41no—
517C8—81no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—81no—
537C22—81no—
538C22—81no—
539C22—161no—
540C22—161no—
541C22#386×C10111yescharacteristic
542C22#443×C10111yescharacteristic
543C22#444×C10111yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—81no—
551C4C2×#99×C10111yescharacteristic
552C4C2×#99×C10111yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—161no—
560C2C101×#187611yescharacteristic
561C2C101×#189811yescharacteristic
562C2C101×#190311yescharacteristic
subgroupG/H
center, socleC22×C101#386
commutatorC22×C4C22×C4×C101
Frattini, cosocleC23×C4C23×C101
prime radicalC2×#449×C101C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C101 ◁ C23×C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2880C2semidirect
3. C101×#1789C2semidirect
4. C101×#1507C2semidirect
5. C101×#1471C2semidirect
6. C101×#1293C2semidirect
7. C101×#1282C2semidirect
9. C22×SD16×C101C4semidirect
10. C22×D8×C101C4semidirect
19. C2×#103×C101C4semidirect
20. C2×#102×C101C4semidirect
271. #9241C101direct (N × H)
283. #2880C2×C101semidirect
284. #1789C2×C101semidirect
285. #1507C2×C101semidirect
286. #1471C2×C101semidirect
287. #1293C2×C101semidirect
288. #1282C2×C101semidirect
289. C101#9241direct (N × H)
291. C22×SD16C4×C101semidirect
292. C22×D8C4×C101semidirect
301. C2×#103C4×C101semidirect
302. C2×#102C4×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#449×C1012
C101×#28802
C101×#17892
C101×#15072
C101×#14712
C101×#12932
C101×#12822
#9241101