Finite Group Databasebeta

← C101×#24089 #38806240

Subgroups — C101×#24089 #38806240

Order 25856.

1334 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#547×C101C211yesmaximal, characteristic
2C2×#481×C101C211yesmaximal, characteristic, complemented
3C22×#106×C101C211yesmaximal, characteristic, complemented
4C101×#2487C211yesmaximal, characteristic, complemented
5C101×#2058C212yesmaximal, complemented
6C101×#2034C212yesmaximal, complemented
7C101×#1893C211yesmaximal, characteristic, complemented
8C101×#1869C211yesmaximal, characteristic, complemented
9C101×#1864C212yesmaximal, complemented
10C101×#1853C212yesmaximal, complemented
11C101×#1823C211yesmaximal, characteristic, complemented
12C22×#41×C101—21no—
13C23×C8×C101C2211yescharacteristic
14#547×C101—24no—
15#547×C101—24no—
16C2×C4⋊Q8×C101C2211yescharacteristic
17C2×#123×C101—21no—
18C2×#123×C101—21no—
19C2×C22⋊Q8×C101—21no—
20C2×#121×C101C2211yescharacteristic
21C2×#121×C101C2211yescharacteristic
22C2×C4×D4×C101C2211yescharacteristic
23C2×C4×D4×C101C2211yescharacteristic
24C22×C4⋊C4×C101C2211yescharacteristic
25C22×C4⋊C4×C101C2211yescharacteristic
26C22×C4⋊C4×C101C2211yescharacteristic
27#481×C101—24no—
28C2×#106×C101—24no—
29C2×#106×C101C2212yes—
30C2×#106×C101C2212yes—
31C2×#106×C101C2212yes—
32C2×#102×C101C2212yes—
33C2×#102×C101C2212yes—
34C2×C22⋊C8×C101C2212yes—
35C2×C22⋊C8×C101C2211yescharacteristic
36#400×C101—21no—
37#399×C101—21no—
38#389×C101C2212yes—
39#386×C101—21no—
40#385×C101—21no—
41#380×C101C2211yescharacteristic
42#380×C101C2212yes—
43#340×C101C2212yes—
44#340×C101C2212yes—
45#340×C101C2212yes—
46#336×C101C2212yes—
47C2×#41×C101—28no—
48C2×#41×C101—44no—
49C2×#41×C101—44no—
50C22×Q8×C101—21no—
51C22×D4×C101—21no—
52C22×D4×C101—21no—
53C22×D4×C101D411yescharacteristic
54C22×D4×C101C2311yescharacteristic
55C23×C4×C101—21no—
56C23×C4×C101—21no—
57C23×C4×C101—21no—
58C23×C4×C101—21no—
59C23×C4×C101C2311yescharacteristic
60C23×C4×C101C2311yescharacteristic
61C22×C8×C101—22no—
62C22×C8×C101—24no—
63C22×C8×C101C2312yes—
64C22×C8×C101C2312yes—
65C4⋊Q8×C101—22no—
66C4⋊Q8×C101—22no—
67#123×C101—28no—
68#123×C101—28no—
69C22⋊Q8×C101—28no—
70#121×C101—22no—
71#121×C101—22no—
72#121×C101—22no—
73#121×C101D414yes—
74C4×D4×C101—22no—
75C4×D4×C101—22no—
76C4×D4×C101—22no—
77C4×D4×C101—22no—
78C2×C4⋊C4×C101—21no—
79C2×C4⋊C4×C101—21no—
80C2×C4⋊C4×C101—22no—
81C2×C4⋊C4×C101—21no—
82C2×C4⋊C4×C101—22no—
83C2×C4⋊C4×C101—22no—
84C2×C4⋊C4×C101—22no—
85C2×C4⋊C4×C101—22no—
86C2×C4⋊C4×C101—21no—
87C2×C4⋊C4×C101—22no—
88C2×C4⋊C4×C101D411yescharacteristic
89C2×C4⋊C4×C101D414yes—
90C2×C4⋊C4×C101C2312yes—
91C2×C4⋊C4×C101C2312yes—
92C2×C4⋊C4×C101C2311yescharacteristic
93C2×C4⋊C4×C101C2311yescharacteristic
94C2×C4⋊C4×C101C2311yescharacteristic
95C2×C22⋊C4×C101—21no—
96C2×C22⋊C4×C101—21no—
97C2×C22⋊C4×C101—21no—
98C2×C22⋊C4×C101—21no—
99C2×C22⋊C4×C101—22no—
100C2×C22⋊C4×C101D411yescharacteristic
101C2×C22⋊C4×C101D411yescharacteristic
102C2×C42×C101C2311yescharacteristic
103#106×C101—24no—
104#106×C101—24no—
105#106×C101—24no—
106#102×C101—24no—
107#102×C101—24no—
108C22⋊C8×C101—22no—
109C22⋊C8×C101—24no—
110#95×C101—21no—
111#95×C101—22no—
112#95×C101—22no—
113C24×C101—21no—
114C24×C101C2×D411yescharacteristic
115C24×C101C2×D411yescharacteristic
116#41×C101—432no—
117C2×Q8×C101—24no—
118C2×Q8×C101—42no—
119C2×Q8×C101—42no—
120C2×D4×C101—22no—
121C2×D4×C101—22no—
122C2×D4×C101—24no—
123C2×D4×C101—24no—
124C2×D4×C101—21no—
125C2×D4×C101—22no—
126C2×D4×C101—22no—
127C2×D4×C101—42no—
128C2×D4×C101—42no—
129C2×D4×C101—42no—
130C2×D4×C101—42no—
131C2×D4×C101SD1614yes—
132C2×D4×C101C2×D412yes—
133C22×C4×C101—22no—
134C22×C4×C101—22no—
135C22×C4×C101—24no—
136C22×C4×C101—24no—
137C22×C4×C101—24no—
138C22×C4×C101—21no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—21no—
142C22×C4×C101—21no—
143C22×C4×C101—22no—
144C22×C4×C101—22no—
145C22×C4×C101—22no—
146C22×C4×C101—22no—
147C22×C4×C101—42no—
148C22×C4×C101—42no—
149C22×C4×C101—42no—
150C22×C4×C101—42no—
151C22×C4×C101—42no—
152C22×C4×C101—42no—
153C22×C4×C101—42no—
154C22×C4×C101—82no—
155C22×C4×C101C2×D411yescharacteristic
156C22×C4×C101C2×D411yescharacteristic
157C22×C4×C101C2×D411yescharacteristic
158C22×C4×C101C2×D412yes—
159C22×C4×C101C2×D412yes—
160C22×C4×C101C2×D411yescharacteristic
161C22×C4×C101C2411yescharacteristic
162C2×C8×C101—28no—
163C2×C8×C101—22no—
164C2×C8×C101—22no—
165C2×C8×C101—22no—
166C2×C8×C101—22no—
167C2×C8×C101—22no—
168C2×C8×C101#4114yescomplemented
169C4⋊C4×C101—24no—
170C4⋊C4×C101—24no—
171C4⋊C4×C101—24no—
172C4⋊C4×C101—22no—
173C4⋊C4×C101—21no—
174C4⋊C4×C101—21no—
175C4⋊C4×C101—21no—
176C4⋊C4×C101—22no—
177C4⋊C4×C101—22no—
178C4⋊C4×C101—22no—
179C4⋊C4×C101—22no—
180C4⋊C4×C101—42no—
181C4⋊C4×C101—82no—
182C4⋊C4×C101C2×D412yes—
183C4⋊C4×C101C2×D412yes—
184C4⋊C4×C101C2×D412yes—
185C22⋊C4×C101—24no—
186C22⋊C4×C101—24no—
187C22⋊C4×C101—22no—
188C22⋊C4×C101—24no—
189C22⋊C4×C101—22no—
190C22⋊C4×C101—42no—
191C22⋊C4×C101—82no—
192C42×C101—21no—
193C42×C101—21no—
194C23×C101—22no—
195C23×C101—22no—
196C23×C101—21no—
197C23×C101—22no—
198C23×C101—21no—
199C23×C101—22no—
200C23×C101—22no—
201C23×C101—42no—
202C23×C101—41no—
203C23×C101—41no—
204C23×C101—42no—
205C23×C101#12012yes—
206C23×C101C2×SD1612yes—
207C23×C101C2×SD1612yes—
208C23×C101AGL(1,ℤ/8)12yes—
209C23×C101C22×D411yescharacteristic
210Q8×C101—48no—
211D4×C101—28no—
212D4×C101—24no—
213D4×C101—48no—
214D4×C101—48no—
215D4×C101—41no—
216D4×C101—41no—
217C2×C4×C101—21no—
218C2×C4×C101—22no—
219C2×C4×C101—21no—
220C2×C4×C101—22no—
221C2×C4×C101—22no—
222C2×C4×C101—24no—
223C2×C4×C101—21no—
224C2×C4×C101—21no—
225C2×C4×C101—22no—
226C2×C4×C101—22no—
227C2×C4×C101—22no—
228C2×C4×C101—22no—
229C2×C4×C101—22no—
230C2×C4×C101—48no—
231C2×C4×C101—48no—
232C2×C4×C101—41no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—48no—
239C2×C4×C101—41no—
240C2×C4×C101—41no—
241C2×C4×C101—42no—
242C2×C4×C101—42no—
243C2×C4×C101—42no—
244C2×C4×C101—42no—
245C2×C4×C101—42no—
246C2×C4×C101—42no—
247C2×C4×C101—42no—
248C2×C4×C101—84no—
249C2×C4×C101#12012yes—
250C2×C4×C101C2×SD1612yes—
251C2×C4×C101C22×D411yescharacteristic
252C2×C4×C101C22×D411yescharacteristic
253C2×C4×C101C2×#4112yes—
254C2×C4×C1012−1+412yes—
255C8×C101—24no—
256C8×C101—42no—
257C22×C101—24no—
258C22×C101—24no—
259C22×C101—22no—
260C22×C101—22no—
261C22×C101—24no—
262C22×C101—22no—
263C22×C101—42no—
264C22×C101—41no—
265C22×C101—41no—
266C22×C101—42no—
267C22×C101—42no—
268C22×C101—42no—
269C22×C101—82no—
270C22×C101—82no—
271C22×C101#45014yes—
272C22×C101C2×#12011yescharacteristic
273C22×C101#54712yes—
274C22×C101C22×SD1611yescharacteristic
275C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C101#57712yes—
277C4×C101—22no—
278C4×C101—22no—
279C4×C101—41no—
280C4×C101—42no—
281C4×C101—42no—
282C4×C101—42no—
283C4×C101—41no—
284C4×C101—82no—
285C4×C101—82no—
286C4×C101#52511yescharacteristic
287C4×C101#53611yescharacteristic
288C4×C101#54712yes—
289#24089C10111yesmaximal, characteristic, direct product factor, Sylow
290C2×C101—24no—
291C2×C101—42no—
292C2×C101—82no—
293C2×C101#240611yescharacteristic
294C2×C101C2×#45011yescharacteristic
295C2×C101#301011yescharacteristic
296C2×C101#333512yes—
297C2×C101#334512yes—
298C2×#547C2×C10111yescharacteristic
299C2×#481C2×C10111yescharacteristic, complemented
300C22×#106C2×C10111yescharacteristic, complemented
301#2487C2×C10111yescharacteristic, complemented
302#2058C2×C10112yescomplemented
303#2034C2×C10112yescomplemented
304#1893C2×C10111yescharacteristic, complemented
305#1869C2×C10111yescharacteristic, complemented
306#1864C2×C10112yescomplemented
307#1853C2×C10112yescomplemented
308#1823C2×C10111yescharacteristic, complemented
309C101#2408911yescharacteristic, direct product factor, Sylow
310C22×#41—21no—
311C23×C8C22×C10111yescharacteristic
312#547—24no—
313#547—24no—
314C2×C4⋊Q8C22×C10111yescharacteristic
315C2×#123—21no—
316C2×#123—21no—
317C2×C22⋊Q8—21no—
318C2×#121C22×C10111yescharacteristic
319C2×#121C22×C10111yescharacteristic
320C2×C4×D4C22×C10111yescharacteristic
321C2×C4×D4C22×C10111yescharacteristic
322C22×C4⋊C4C22×C10111yescharacteristic
323C22×C4⋊C4C22×C10111yescharacteristic
324C22×C4⋊C4C22×C10111yescharacteristic
325#481—24no—
326C2×#106—24no—
327C2×#106C22×C10112yes—
328C2×#106C22×C10112yes—
329C2×#106C22×C10112yes—
330C2×#102C22×C10112yes—
331C2×#102C22×C10112yes—
332C2×C22⋊C8C22×C10111yescharacteristic
333C2×C22⋊C8C22×C10112yes—
334#400—21no—
335#399—21no—
336#389C22×C10112yes—
337#386—21no—
338#385—21no—
339#380C22×C10111yescharacteristic
340#380C22×C10112yes—
341#340C22×C10112yes—
342#340C22×C10112yes—
343#340C22×C10112yes—
344#336C22×C10112yes—
345C2×#41—28no—
346C2×#41—44no—
347C2×#41—44no—
348C22×Q8—21no—
349C22×D4—21no—
350C22×D4—21no—
351C22×D4D4×C10111yescharacteristic
352C22×D4C23×C10111yescharacteristic
353C23×C4—21no—
354C23×C4—21no—
355C23×C4—21no—
356C23×C4—21no—
357C23×C4C23×C10111yescharacteristic
358C23×C4C23×C10111yescharacteristic
359C22×C8—22no—
360C22×C8—24no—
361C22×C8C23×C10112yes—
362C22×C8C23×C10112yes—
363C4⋊Q8—22no—
364C4⋊Q8—22no—
365#123—28no—
366#123—28no—
367C22⋊Q8—28no—
368#121—22no—
369#121—22no—
370#121—22no—
371#121D4×C10114yes—
372C4×D4—22no—
373C4×D4—22no—
374C4×D4—22no—
375C4×D4—22no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—22no—
383C2×C4⋊C4—22no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4D4×C10111yescharacteristic
387C2×C4⋊C4D4×C10114yes—
388C2×C4⋊C4C23×C10112yes—
389C2×C4⋊C4C23×C10112yes—
390C2×C4⋊C4C23×C10111yescharacteristic
391C2×C4⋊C4C23×C10111yescharacteristic
392C2×C4⋊C4C23×C10111yescharacteristic
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—22no—
398C2×C22⋊C4D4×C10111yescharacteristic
399C2×C22⋊C4D4×C10111yescharacteristic
400C2×C42C23×C10111yescharacteristic
401#106—24no—
402#106—24no—
403#106—24no—
404#102—24no—
405#102—24no—
406C22⋊C8—22no—
407C22⋊C8—24no—
408#95—22no—
409#95—21no—
410#95—22no—
411C24—21no—
412C24C2×D4×C10111yescharacteristic
413C24C2×D4×C10111yescharacteristic
414#41—432no—
415C2×Q8—24no—
416C2×Q8—42no—
417C2×Q8—42no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4SD16×C10114yes—
430C2×D4C2×D4×C10112yes—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—42no—
449C22×C4—42no—
450C22×C4—42no—
451C22×C4—42no—
452C22×C4—82no—
453C22×C4C2×D4×C10111yescharacteristic
454C22×C4C2×D4×C10111yescharacteristic
455C22×C4C2×D4×C10111yescharacteristic
456C22×C4C2×D4×C10112yes—
457C22×C4C2×D4×C10112yes—
458C22×C4C2×D4×C10111yescharacteristic
459C22×C4C24×C10111yescharacteristic
460C2×C8—28no—
461C2×C8—22no—
462C2×C8—22no—
463C2×C8—22no—
464C2×C8—22no—
465C2×C8—22no—
466C2×C8#41×C10114yescomplemented
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—22no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—22no—
477C4⋊C4—22no—
478C4⋊C4—42no—
479C4⋊C4—82no—
480C4⋊C4C2×D4×C10112yes—
481C4⋊C4C2×D4×C10112yes—
482C4⋊C4C2×D4×C10112yes—
483C22⋊C4—24no—
484C22⋊C4—24no—
485C22⋊C4—22no—
486C22⋊C4—24no—
487C22⋊C4—22no—
488C22⋊C4—42no—
489C22⋊C4—82no—
490C42—21no—
491C42—21no—
492C23—22no—
493C23—22no—
494C23—21no—
495C23—22no—
496C23—21no—
497C23—22no—
498C23—22no—
499C23—42no—
500C23—41no—
501C23—41no—
502C23—42no—
503C23#120×C10112yes—
504C23C2×SD16×C10112yes—
505C23C2×SD16×C10112yes—
506C23AGL(1,ℤ/8)×C10112yes—
507C23C22×D4×C10111yescharacteristic
508Q8—48no—
509D4—28no—
510D4—24no—
511D4—48no—
512D4—48no—
513D4—41no—
514D4—41no—
515C2×C4—21no—
516C2×C4—22no—
517C2×C4—21no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—22no—
528C2×C4—48no—
529C2×C4—48no—
530C2×C4—48no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—42no—
540C2×C4—42no—
541C2×C4—42no—
542C2×C4—42no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—84no—
547C2×C4#120×C10112yes—
548C2×C4C2×SD16×C10112yes—
549C2×C4C22×D4×C10111yescharacteristic
550C2×C4C22×D4×C10111yescharacteristic
551C2×C4C2×#41×C10112yes—
552C2×C42−1+4×C10112yes—
553C8—24no—
554C8—42no—
555C22—22no—
556C22—22no—
557C22—24no—
558C22—24no—
559C22—22no—
560C22—24no—
561C22—41no—
562C22—41no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—42no—
567C22—82no—
568C22—82no—
569C22#450×C10114yes—
570C22C2×#120×C10111yescharacteristic
571C22#547×C10112yes—
572C22C22×SD16×C10111yescharacteristic
573C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
574C22#577×C10112yes—
575C4—22no—
576C4—22no—
577C4—41no—
578C4—42no—
579C4—42no—
580C4—42no—
581C4—41no—
582C4—82no—
583C4—82no—
584C4#525×C10111yescharacteristic
585C4#536×C10111yescharacteristic
586C4#547×C10112yes—
587C2—24no—
588C2—42no—
589C2—82no—
590C2C101×#240611yescharacteristic
591C2C2×#450×C10111yescharacteristic
592C2C101×#301011yescharacteristic
593C2C101×#333512yes—
594C2C101×#334512yes—
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC2×#547×C101C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C2×C4×D4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#481×C101C2semidirect
3. C22×#106×C101C2semidirect
4. C101×#2487C2semidirect
5. C101×#2058C2semidirect
6. C101×#2034C2semidirect
7. C101×#1893C2semidirect
8. C101×#1869C2semidirect
9. C101×#1864C2semidirect
10. C101×#1853C2semidirect
11. C101×#1823C2semidirect
168. C2×C8×C101#41semidirect
289. #24089C101direct (N × H)
299. C2×#481C2×C101semidirect
300. C22×#106C2×C101semidirect
301. #2487C2×C101semidirect
302. #2058C2×C101semidirect
303. #2034C2×C101semidirect
304. #1893C2×C101semidirect
305. #1869C2×C101semidirect
306. #1864C2×C101semidirect
307. #1853C2×C101semidirect
308. #1823C2×C101semidirect
309. C101#24089direct (N × H)
466. C2×C8#41×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1012
C2×#481×C1012
C22×#106×C1012
C101×#24872
C101×#20582
C101×#20342
C101×#18932
C101×#18692
C101×#18642
C101×#18532
C101×#18232
#24089101