Finite Group Databasebeta

← C101×#26765 #38808916

Subgroups — C101×#26765 #38808916

Order 25856.

732 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#2506C211yesmaximal, characteristic, complemented
2C101×#2367C211yesmaximal, characteristic
3C101×#2072C211yesmaximal, characteristic, complemented
4C101×#2068C211yesmaximal, characteristic, complemented
5C101×#2042C211yesmaximal, characteristic
6C101×#2042C211yesmaximal, characteristic
7C101×#1934C211yesmaximal, characteristic
8C101×#1925C211yesmaximal, characteristic
9C101×#1921C211yesmaximal, characteristic, complemented
10C101×#1920C211yesmaximal, characteristic, complemented
11C101×#1916C211yesmaximal, characteristic, complemented
12C101×#1865C211yesmaximal, characteristic, complemented
13C101×#1864C211yesmaximal, characteristic
14C101×#1802C211yesmaximal, characteristic
15C4×#103×C101C211yesmaximal, characteristic, complemented
16C2×#125×C101—21no—
17C2×#124×C101C2211yescharacteristic
18C2×C4×Q8×C101C2211yescharacteristic
19C2×C4×D4×C101C2211yescharacteristic
20C2×#107×C101C2211yescharacteristic
21C2×#106×C101C2211yescharacteristic
22C2×C4⋊C8×C101C2211yescharacteristic
23C2×#103×C101C2211yescharacteristic
24C2×#103×C101C2211yescharacteristic
25C2×#103×C101C2211yescharacteristic
26C2×#103×C101C2211yescharacteristic
27C2×#102×C101C2211yescharacteristic
28C2×#102×C101C2211yescharacteristic
29C2×#102×C101C2211yescharacteristic
30C2×#102×C101C2211yescharacteristic
31C2×C4×C8×C101C2211yescharacteristic
32#400×C101—21no—
33#398×C101—21no—
34#391×C101C2211yescharacteristic
35#390×C101C2211yescharacteristic
36#389×C101C2211yescharacteristic
37#389×C101C2211yescharacteristic
38#389×C101C2211yescharacteristic
39#389×C101C2211yescharacteristic
40#388×C101—21no—
41#388×C101—21no—
42#387×C101—21no—
43#385×C101—21no—
44#384×C101C2211yescharacteristic
45C4×C4⋊C4×C101C2211yescharacteristic
46C4×C4⋊C4×C101C2211yescharacteristic
47C4×C4⋊C4×C101C2211yescharacteristic
48C4×C22⋊C4×C101—21no—
49#340×C101C2211yescharacteristic
50#340×C101C2211yescharacteristic
51#340×C101C2211yescharacteristic
52#340×C101C2211yescharacteristic
53#340×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#336×C101C2211yescharacteristic
56#336×C101C2211yescharacteristic
57#336×C101C2211yescharacteristic
58#336×C101C2211yescharacteristic
59C22×Q8×C101C2311yescharacteristic
60C22×D4×C101C2311yescharacteristic
61C23×C4×C101—21no—
62C22×C8×C101C2311yescharacteristic
63C22×C8×C101C2311yescharacteristic
64C22×C8×C101C2311yescharacteristic
65C22×C8×C101C2311yescharacteristic
66#125×C101—44no—
67#124×C101—22no—
68#124×C101—22no—
69C4×Q8×C101—22no—
70C4×Q8×C101—41no—
71C4×D4×C101—22no—
72C4×D4×C101—41no—
73C2×C4⋊C4×C101—21no—
74C2×C4⋊C4×C101—21no—
75C2×C4⋊C4×C101—21no—
76C2×C4⋊C4×C101—21no—
77C2×C4⋊C4×C101—21no—
78C2×C4⋊C4×C101—21no—
79C2×C4⋊C4×C101—21no—
80C2×C4⋊C4×C101D411yescharacteristic
81C2×C4⋊C4×C101D411yescharacteristic
82C2×C4⋊C4×C101C2311yescharacteristic
83C2×C4⋊C4×C101C2311yescharacteristic
84C2×C4⋊C4×C101C2311yescharacteristic
85C2×C4⋊C4×C101C2311yescharacteristic
86C2×C4⋊C4×C101C2311yescharacteristic
87C2×C4⋊C4×C101C2311yescharacteristic
88C2×C22⋊C4×C101—21no—
89C2×C22⋊C4×C101—21no—
90C2×C22⋊C4×C101—21no—
91C2×C22⋊C4×C101—21no—
92C2×C22⋊C4×C101—21no—
93C2×C42×C101—21no—
94C2×C42×C101—21no—
95C2×C42×C101—21no—
96C2×C42×C101C2311yescharacteristic
97C2×C42×C101C2311yescharacteristic
98C2×C42×C101C2311yescharacteristic
99#107×C101—22no—
100#106×C101—22no—
101C4⋊C8×C101—41no—
102#103×C101—22no—
103#103×C101—22no—
104#103×C101—22no—
105#103×C101—41no—
106#102×C101—22no—
107#102×C101—22no—
108#102×C101—22no—
109#102×C101—41no—
110C4×C8×C101—41no—
111#95×C101—21no—
112#95×C101—21no—
113#95×C101—21no—
114#95×C101—21no—
115#95×C101—21no—
116#95×C101—21no—
117#95×C101—21no—
118#95×C101—21no—
119#95×C101D411yescharacteristic
120#95×C101D411yescharacteristic
121C24×C101—21no—
122C2×Q8×C101—21no—
123C2×Q8×C101—21no—
124C2×Q8×C101—21no—
125C2×Q8×C101—21no—
126C2×Q8×C101—21no—
127C2×Q8×C101#4112yes—
128C2×D4×C101—21no—
129C2×D4×C101—21no—
130C2×D4×C101—21no—
131C2×D4×C101—21no—
132C2×D4×C101—21no—
133C2×D4×C101#4112yes—
134C22×C4×C101—21no—
135C22×C4×C101—21no—
136C22×C4×C101—21no—
137C22×C4×C101—21no—
138C22×C4×C101—21no—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—42no—
142C22×C4×C101—42no—
143C22×C4×C101—81no—
144C22×C4×C101C2×D411yescharacteristic
145C22×C4×C101C2×D411yescharacteristic
146C22×C4×C101C2×D411yescharacteristic
147C22×C4×C101C2×D411yescharacteristic
148C22×C4×C101C2×D411yescharacteristic
149C22×C4×C101C2×D411yescharacteristic
150C22×C4×C101C2411yescharacteristic
151C2×C8×C101—21no—
152C2×C8×C101—21no—
153C2×C8×C101—21no—
154C2×C8×C101—21no—
155C2×C8×C101—21no—
156C2×C8×C101—21no—
157C2×C8×C101—21no—
158C2×C8×C101—21no—
159C2×C8×C101—21no—
160C2×C8×C101—21no—
161C2×C8×C101—21no—
162C2×C8×C101—21no—
163C4⋊C4×C101—22no—
164C4⋊C4×C101—22no—
165C4⋊C4×C101—21no—
166C4⋊C4×C101—21no—
167C4⋊C4×C101—21no—
168C4⋊C4×C101—21no—
169C4⋊C4×C101—21no—
170C4⋊C4×C101—21no—
171C4⋊C4×C101—21no—
172C4⋊C4×C101—21no—
173C4⋊C4×C101—21no—
174C4⋊C4×C101—21no—
175C4⋊C4×C101—42no—
176C4⋊C4×C101—42no—
177C4⋊C4×C101—42no—
178C4⋊C4×C101—42no—
179C4⋊C4×C101—42no—
180C4⋊C4×C101—42no—
181C4⋊C4×C101—42no—
182C4⋊C4×C101#4112yes—
183C4⋊C4×C101#4112yes—
184C22⋊C4×C101—24no—
185C22⋊C4×C101—24no—
186C22⋊C4×C101—42no—
187C22⋊C4×C101—42no—
188C22⋊C4×C101—81no—
189C42×C101—21no—
190C42×C101—21no—
191C42×C101—21no—
192C42×C101—21no—
193C42×C101—21no—
194C42×C101—21no—
195C42×C101—42no—
196C42×C101—42no—
197C42×C101—81no—
198C23×C101—22no—
199C23×C101—41no—
200C23×C101—41no—
201C23×C101—41no—
202C23×C101—41no—
203C23×C101—41no—
204C23×C101—41no—
205C23×C101C22×D411yescharacteristic
206Q8×C101—22no—
207Q8×C101—22no—
208Q8×C101—41no—
209Q8×C101—41no—
210D4×C101—22no—
211D4×C101—22no—
212D4×C101—41no—
213D4×C101—41no—
214C2×C4×C101—21no—
215C2×C4×C101—21no—
216C2×C4×C101—21no—
217C2×C4×C101—21no—
218C2×C4×C101—21no—
219C2×C4×C101—21no—
220C2×C4×C101—22no—
221C2×C4×C101—21no—
222C2×C4×C101—21no—
223C2×C4×C101—22no—
224C2×C4×C101—22no—
225C2×C4×C101—21no—
226C2×C4×C101—21no—
227C2×C4×C101—21no—
228C2×C4×C101—21no—
229C2×C4×C101—21no—
230C2×C4×C101—21no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
233C2×C4×C101—41no—
234C2×C4×C101—41no—
235C2×C4×C101—41no—
236C2×C4×C101—41no—
237C2×C4×C101—41no—
238C2×C4×C101—41no—
239C2×C4×C101—41no—
240C2×C4×C101—41no—
241C2×C4×C101—41no—
242C2×C4×C101—41no—
243C2×C4×C101—41no—
244C2×C4×C101—41no—
245C2×C4×C101—41no—
246C2×C4×C101—41no—
247C2×C4×C101—41no—
248C2×C4×C101—41no—
249C2×C4×C101—41no—
250C2×C4×C101—41no—
251C2×C4×C101—84no—
252C2×C4×C101#13512yes—
253C2×C4×C101AGL(1,ℤ/8)12yes—
254C2×C4×C101C2×#4111yescharacteristic
255C2×C4×C101C2×#4111yescharacteristic
256C2×C4×C101C2×#4111yescharacteristic
257C2×C4×C101C2×#4111yescharacteristic
258C2×C4×C101H(5,𝔽2)11yescharacteristic
259C2×C4×C1012−1+411yescharacteristic
260C8×C101—41no—
261C8×C101—41no—
262C8×C101—41no—
263C8×C101—41no—
264C22×C101—42no—
265C22×C101—42no—
266C22×C101—42no—
267C22×C101—81no—
268C22×C101—81no—
269C22×C101—81no—
270C22×C101—81no—
271C22×C101#52511yescharacteristic
272C22×C101#54611yescharacteristic
273C22×C101#54811yescharacteristic
274C22×C101C2×#13511yescharacteristic
275C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
276C22×C101#57711yescharacteristic
277C22×C101#57811yescharacteristic
278C4×C101—22no—
279C4×C101—22no—
280C4×C101—41no—
281C4×C101—42no—
282C4×C101—41no—
283C4×C101—42no—
284C4×C101—41no—
285C4×C101—42no—
286C4×C101—41no—
287C4×C101—81no—
288C4×C101—81no—
289C4×C101—81no—
290C4×C101—81no—
291C4×C101#52911yescharacteristic
292C4×C101#53911yescharacteristic
293C4×C101#55211yescharacteristic
294C4×C101#55311yescharacteristic
295#26765C10111yesmaximal, characteristic, direct product factor, Sylow
296C2×C101—82no—
297C2×C101#246011yescharacteristic
298C2×C101#310611yescharacteristic
299C2×C101#312011yescharacteristic
300C2×C101#329611yescharacteristic
301C2×C101#330811yescharacteristic
302C2×C101#336411yescharacteristic
303C2×C101#337311yescharacteristic
304#2506C2×C10111yescharacteristic, complemented
305#2367C2×C10111yescharacteristic
306#2072C2×C10111yescharacteristic, complemented
307#2068C2×C10111yescharacteristic, complemented
308#2042C2×C10111yescharacteristic
309#2042C2×C10111yescharacteristic
310#1934C2×C10111yescharacteristic
311#1925C2×C10111yescharacteristic
312#1921C2×C10111yescharacteristic, complemented
313#1920C2×C10111yescharacteristic, complemented
314#1916C2×C10111yescharacteristic, complemented
315#1865C2×C10111yescharacteristic, complemented
316#1864C2×C10111yescharacteristic
317#1802C2×C10111yescharacteristic
318C4×#103C2×C10111yescharacteristic, complemented
319C101#2676511yescharacteristic, direct product factor, Sylow
320C2×#125—21no—
321C2×#124C22×C10111yescharacteristic
322C2×C4×Q8C22×C10111yescharacteristic
323C2×C4×D4C22×C10111yescharacteristic
324C2×#107C22×C10111yescharacteristic
325C2×#106C22×C10111yescharacteristic
326C2×C4⋊C8C22×C10111yescharacteristic
327C2×#103C22×C10111yescharacteristic
328C2×#103C22×C10111yescharacteristic
329C2×#103C22×C10111yescharacteristic
330C2×#103C22×C10111yescharacteristic
331C2×#102C22×C10111yescharacteristic
332C2×#102C22×C10111yescharacteristic
333C2×#102C22×C10111yescharacteristic
334C2×#102C22×C10111yescharacteristic
335C2×C4×C8C22×C10111yescharacteristic
336#400—21no—
337#398—21no—
338#391C22×C10111yescharacteristic
339#390C22×C10111yescharacteristic
340#389C22×C10111yescharacteristic
341#389C22×C10111yescharacteristic
342#389C22×C10111yescharacteristic
343#389C22×C10111yescharacteristic
344#388—21no—
345#388—21no—
346#387—21no—
347#385—21no—
348#384C22×C10111yescharacteristic
349C4×C4⋊C4C22×C10111yescharacteristic
350C4×C4⋊C4C22×C10111yescharacteristic
351C4×C4⋊C4C22×C10111yescharacteristic
352C4×C22⋊C4—21no—
353#340C22×C10111yescharacteristic
354#340C22×C10111yescharacteristic
355#340C22×C10111yescharacteristic
356#340C22×C10111yescharacteristic
357#340C22×C10111yescharacteristic
358#340C22×C10111yescharacteristic
359#336C22×C10111yescharacteristic
360#336C22×C10111yescharacteristic
361#336C22×C10111yescharacteristic
362#336C22×C10111yescharacteristic
363C22×Q8C23×C10111yescharacteristic
364C22×D4C23×C10111yescharacteristic
365C23×C4—21no—
366C22×C8C23×C10111yescharacteristic
367C22×C8C23×C10111yescharacteristic
368C22×C8C23×C10111yescharacteristic
369C22×C8C23×C10111yescharacteristic
370#125—44no—
371#124—22no—
372#124—22no—
373C4×Q8—22no—
374C4×Q8—41no—
375C4×D4—22no—
376C4×D4—41no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4D4×C10111yescharacteristic
385C2×C4⋊C4D4×C10111yescharacteristic
386C2×C4⋊C4C23×C10111yescharacteristic
387C2×C4⋊C4C23×C10111yescharacteristic
388C2×C4⋊C4C23×C10111yescharacteristic
389C2×C4⋊C4C23×C10111yescharacteristic
390C2×C4⋊C4C23×C10111yescharacteristic
391C2×C4⋊C4C23×C10111yescharacteristic
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C22⋊C4—21no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—21no—
400C2×C42C23×C10111yescharacteristic
401C2×C42C23×C10111yescharacteristic
402C2×C42C23×C10111yescharacteristic
403#107—22no—
404#106—22no—
405C4⋊C8—41no—
406#103—22no—
407#103—22no—
408#103—22no—
409#103—41no—
410#102—22no—
411#102—22no—
412#102—22no—
413#102—41no—
414C4×C8—41no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95D4×C10111yescharacteristic
424#95D4×C10111yescharacteristic
425C24—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×Q8#41×C10112yes—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4#41×C10112yes—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—81no—
448C22×C4C2×D4×C10111yescharacteristic
449C22×C4C2×D4×C10111yescharacteristic
450C22×C4C2×D4×C10111yescharacteristic
451C22×C4C2×D4×C10111yescharacteristic
452C22×C4C2×D4×C10111yescharacteristic
453C22×C4C2×D4×C10111yescharacteristic
454C22×C4C24×C10111yescharacteristic
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4—42no—
484C4⋊C4—42no—
485C4⋊C4—42no—
486C4⋊C4#41×C10112yes—
487C4⋊C4#41×C10112yes—
488C22⋊C4—24no—
489C22⋊C4—24no—
490C22⋊C4—42no—
491C22⋊C4—42no—
492C22⋊C4—81no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—21no—
498C42—21no—
499C42—42no—
500C42—42no—
501C42—81no—
502C23—22no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23C22×D4×C10111yescharacteristic
510Q8—22no—
511Q8—22no—
512Q8—41no—
513Q8—41no—
514D4—22no—
515D4—22no—
516D4—41no—
517D4—41no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—22no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—84no—
556C2×C4#135×C10112yes—
557C2×C4AGL(1,ℤ/8)×C10112yes—
558C2×C4C2×#41×C10111yescharacteristic
559C2×C4C2×#41×C10111yescharacteristic
560C2×C4C2×#41×C10111yescharacteristic
561C2×C4C2×#41×C10111yescharacteristic
562C2×C4H(5,𝔽2)×C10111yescharacteristic
563C2×C42−1+4×C10111yescharacteristic
564C8—41no—
565C8—41no—
566C8—41no—
567C8—41no—
568C22—42no—
569C22—42no—
570C22—42no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22#525×C10111yescharacteristic
576C22#546×C10111yescharacteristic
577C22#548×C10111yescharacteristic
578C22C2×#135×C10111yescharacteristic
579C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
580C22#577×C10111yescharacteristic
581C22#578×C10111yescharacteristic
582C4—22no—
583C4—22no—
584C4—42no—
585C4—41no—
586C4—42no—
587C4—41no—
588C4—41no—
589C4—42no—
590C4—41no—
591C4—81no—
592C4—81no—
593C4—81no—
594C4—81no—
595C4#529×C10111yescharacteristic
596C4#539×C10111yescharacteristic
597C4#552×C10111yescharacteristic
598C4#553×C10111yescharacteristic
599C2—82no—
600C2C101×#246011yescharacteristic
601C2C101×#310611yescharacteristic
602C2C101×#312011yescharacteristic
603C2C101×#329611yescharacteristic
604C2C101×#330811yescharacteristic
605C2C101×#336411yescharacteristic
606C2C101×#337311yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutator, Frattini, cosocleC22×C4C24×C101
prime radicalC22×D4×C101C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C4×C4⋊C4×C101 ◁ G

Complements

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

NH ≅ G/Ntype
1. C101×#2506C2semidirect
3. C101×#2072C2semidirect
4. C101×#2068C2semidirect
9. C101×#1921C2semidirect
10. C101×#1920C2semidirect
11. C101×#1916C2semidirect
12. C101×#1865C2semidirect
15. C4×#103×C101C2semidirect
295. #26765C101direct (N × H)
304. #2506C2×C101semidirect
306. #2072C2×C101semidirect
307. #2068C2×C101semidirect
312. #1921C2×C101semidirect
313. #1920C2×C101semidirect
314. #1916C2×C101semidirect
315. #1865C2×C101semidirect
318. C4×#103C2×C101semidirect
319. C101#26765direct (N × H)

Maximal subgroups

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

subgroupindex
C101×#25062
C101×#23672
C101×#20722
C101×#20682
C101×#20422
C101×#19342
C101×#19252
C101×#19212
C101×#19202
C101×#19162
C101×#18652
C101×#18642
C101×#18022
C4×#103×C1012
#26765101