Finite Group Databasebeta

← C101×#21288 #38803439

Subgroups — C101×#21288 #38803439

Order 25856.

874 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#440×C101C211yesmaximal, characteristic
2C101×#2295C211yesmaximal, characteristic, complemented
3C101×#2293C211yesmaximal, characteristic
4C101×#1973C211yesmaximal, characteristic
5C101×#1968C211yesmaximal, characteristic
6C101×#1943C211yesmaximal, characteristic, complemented
7C101×#1942C211yesmaximal, characteristic, complemented
8C101×#1936C211yesmaximal, characteristic
9C101×#1935C211yesmaximal, characteristic, complemented
10C101×#1934C211yesmaximal, characteristic
11C101×#1933C211yesmaximal, characteristic, complemented
12C101×#1776C211yesmaximal, characteristic, complemented
13C101×#1763C211yesmaximal, characteristic, complemented
14C101×#1762C211yesmaximal, characteristic
15C4×#97×C101C211yesmaximal, characteristic, complemented
16C22×SD16×C101C2211yescharacteristic
17C2×C4×Q8×C101C2211yescharacteristic
18C2×C4×D4×C101C2211yescharacteristic
19C2×#117×C101—21no—
20#440×C101C418yescomplemented
21C2×#107×C101C2211yescharacteristic
22C2×#107×C101C2211yescharacteristic
23C2×#106×C101C2211yescharacteristic
24C2×#103×C101C2211yescharacteristic
25C2×#103×C101C2211yescharacteristic
26C2×#103×C101C2211yescharacteristic
27C2×#102×C101C2211yescharacteristic
28C2×#102×C101C2211yescharacteristic
29C2×#102×C101C2211yescharacteristic
30C2×#97×C101C2211yescharacteristic
31C2×#97×C101C2211yescharacteristic
32C2×#97×C101C2211yescharacteristic
33C2×#97×C101C2211yescharacteristic
34C2×C4×C8×C101C2211yescharacteristic
35C2×C4×C8×C101C2211yescharacteristic
36#391×C101C2211yescharacteristic
37#391×C101C2211yescharacteristic
38#390×C101C2211yescharacteristic
39#390×C101C2211yescharacteristic
40#389×C101C2211yescharacteristic
41#389×C101C2211yescharacteristic
42#389×C101C2211yescharacteristic
43#389×C101C2211yescharacteristic
44#388×C101—21no—
45#388×C101—21no—
46#387×C101—21no—
47#387×C101—21no—
48C4×C4⋊C4×C101—21no—
49C4×C4⋊C4×C101C2211yescharacteristic
50C4×C4⋊C4×C101C2211yescharacteristic
51C4×C22⋊C4×C101—21no—
52#376×C101—21no—
53C43×C101C2211yescharacteristic
54#340×C101C2211yescharacteristic
55#340×C101C2211yescharacteristic
56#340×C101C2211yescharacteristic
57#340×C101C2211yescharacteristic
58#340×C101C2211yescharacteristic
59#340×C101C2211yescharacteristic
60C22×Q8×C101C2311yescharacteristic
61C22×D4×C101C2311yescharacteristic
62C23×C4×C101—21no—
63C2×SD16×C101—22no—
64C2×SD16×C101—22no—
65C2×SD16×C101C2×C414yes—
66C22×C8×C101C2311yescharacteristic
67C22×C8×C101C2311yescharacteristic
68C22×C8×C101C2311yescharacteristic
69C22×C8×C101C2311yescharacteristic
70C4×Q8×C101—22no—
71C4×Q8×C101C2×C414yes—
72C4×D4×C101—22no—
73C4×D4×C101C2×C414yes—
74#117×C101—44no—
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×C101C2311yescharacteristic
81C2×C4⋊C4×C101C2311yescharacteristic
82C2×C4⋊C4×C101C2311yescharacteristic
83C2×C4⋊C4×C101C2311yescharacteristic
84C2×C4⋊C4×C101C2311yescharacteristic
85C2×C4⋊C4×C101C2311yescharacteristic
86C2×C22⋊C4×C101—21no—
87C2×C22⋊C4×C101—21no—
88C2×C22⋊C4×C101—21no—
89C2×C22⋊C4×C101—21no—
90C2×C22⋊C4×C101—21no—
91C2×C42×C101—21no—
92C2×C42×C101—21no—
93C2×C42×C101—21no—
94C2×C42×C101D411yescharacteristic
95C2×C42×C101D411yescharacteristic
96C2×C42×C101D411yescharacteristic
97C2×C42×C101D411yescharacteristic
98C2×C42×C101C2311yescharacteristic
99C2×C42×C101C2311yescharacteristic
100C2×C42×C101C2311yescharacteristic
101#107×C101—22no—
102#107×C101C2×C414yes—
103#106×C101—22no—
104#103×C101—22no—
105#103×C101—22no—
106#103×C101C2×C414yes—
107#102×C101—22no—
108#102×C101—22no—
109#102×C101C2×C414yes—
110#97×C101—22no—
111#97×C101—22no—
112#97×C101—22no—
113#97×C101C2×C414yes—
114C4×C8×C101—22no—
115C4×C8×C101—22no—
116#95×C101—21no—
117#95×C101—21no—
118#95×C101—21no—
119#95×C101—21no—
120#95×C101—21no—
121#95×C101—21no—
122#95×C101—21no—
123#95×C101—21no—
124#95×C101—21no—
125#95×C101—21no—
126C24×C101—21no—
127C2×Q8×C101—21no—
128C2×Q8×C101—21no—
129C2×Q8×C101—21no—
130C2×Q8×C101—21no—
131C2×Q8×C101—21no—
132C2×Q8×C101C22×C412yes—
133C2×D4×C101—21no—
134C2×D4×C101—21no—
135C2×D4×C101—21no—
136C2×D4×C101—21no—
137C2×D4×C101—21no—
138C2×D4×C101C22×C412yes—
139C22×C4×C101—21no—
140C22×C4×C101—21no—
141C22×C4×C101—21no—
142C22×C4×C101—24no—
143C22×C4×C101—21no—
144C22×C4×C101—21no—
145C22×C4×C101—21no—
146C22×C4×C101—21no—
147C22×C4×C101—42no—
148C22×C4×C101—42no—
149C22×C4×C101C2×D411yescharacteristic
150C22×C4×C101C2×D411yescharacteristic
151C22×C4×C101C2×D411yescharacteristic
152C22×C4×C101C2×D411yescharacteristic
153C22×C4×C101C2×D411yescharacteristic
154C22×C4×C101C2×D411yescharacteristic
155C22×C4×C101C2411yescharacteristic
156SD16×C101—28no—
157C2×C8×C101—21no—
158C2×C8×C101—21no—
159C2×C8×C101—21no—
160C2×C8×C101—21no—
161C2×C8×C101—21no—
162C2×C8×C101—21no—
163C2×C8×C101C22×C412yes—
164C2×C8×C101C22×C412yes—
165C2×C8×C101#4112yes—
166C2×C8×C101#4112yes—
167C2×C8×C101#4112yes—
168C2×C8×C101#4112yes—
169C4⋊C4×C101—24no—
170C4⋊C4×C101—21no—
171C4⋊C4×C101—21no—
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—42no—
181C4⋊C4×C101—42no—
182C4⋊C4×C101—42no—
183C4⋊C4×C101—42no—
184C4⋊C4×C101C22×C412yes—
185C4⋊C4×C101C22×C412yes—
186C22⋊C4×C101—24no—
187C22⋊C4×C101—42no—
188C22⋊C4×C101—42no—
189C22⋊C4×C101—42no—
190C22⋊C4×C101—42no—
191C42×C101—24no—
192C42×C101—22no—
193C42×C101—22no—
194C42×C101—21no—
195C42×C101—21no—
196C42×C101—21no—
197C42×C101—21no—
198C42×C101—41no—
199C42×C101—41no—
200C42×C101—42no—
201C42×C101—42no—
202C42×C101C22×C412yes—
203C42×C101#4112yes—
204C23×C101—22no—
205C23×C101—41no—
206C23×C101—41no—
207C23×C101—41no—
208C23×C101—41no—
209C23×C101—41no—
210C23×C101—41no—
211C23×C101C22×D411yescharacteristic
212Q8×C101—22no—
213Q8×C101—22no—
214Q8×C101—41no—
215Q8×C101—41no—
216D4×C101—22no—
217D4×C101—22no—
218D4×C101—41no—
219D4×C101—41no—
220C2×C4×C101—21no—
221C2×C4×C101—21no—
222C2×C4×C101—21no—
223C2×C4×C101—21no—
224C2×C4×C101—21no—
225C2×C4×C101—21no—
226C2×C4×C101—21no—
227C2×C4×C101—21no—
228C2×C4×C101—22no—
229C2×C4×C101—22no—
230C2×C4×C101—22no—
231C2×C4×C101—21no—
232C2×C4×C101—21no—
233C2×C4×C101—21no—
234C2×C4×C101—21no—
235C2×C4×C101—21no—
236C2×C4×C101—21no—
237C2×C4×C101—48no—
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—41no—
252C2×C4×C101—41no—
253C2×C4×C101—41no—
254C2×C4×C101—41no—
255C2×C4×C101—41no—
256C2×C4×C101C4×D412yes—
257C2×C4×C101C4×D412yes—
258C2×C4×C101AGL(1,ℤ/8)12yes—
259C2×C4×C101#13712yes—
260C2×C4×C101C23×C411yescharacteristic
261C2×C4×C101C2×#4111yescharacteristic
262C2×C4×C101C2×#4111yescharacteristic
263C2×C4×C101C2×#4111yescharacteristic
264C2×C4×C101C2×#4111yescharacteristic
265C2×C4×C101C2×#4111yescharacteristic
266C8×C101—22no—
267C8×C101—22no—
268C8×C101—22no—
269C8×C101#11714yescomplemented
270C22×C101—42no—
271C22×C101—42no—
272C22×C101—42no—
273C22×C101—81no—
274C22×C101—81no—
275C22×C101—81no—
276C22×C101—81no—
277C22×C101C2×C4×D411yescharacteristic
278C22×C101#53211yescharacteristic
279C22×C101#53211yescharacteristic
280C22×C101C2×AGL(1,ℤ/8)11yescharacteristic
281C22×C101C2×#13711yescharacteristic
282C22×C101#57511yescharacteristic
283C22×C101#57511yescharacteristic
284C4×C101—22no—
285C4×C101—22no—
286C4×C101—22no—
287C4×C101—22no—
288C4×C101—41no—
289C4×C101—41no—
290C4×C101—42no—
291C4×C101—42no—
292C4×C101—42no—
293C4×C101—81no—
294C4×C101—81no—
295C4×C101—81no—
296C4×C101—81no—
297C4×C101C2×#11711yescharacteristic
298C4×C101C4×#4111yescharacteristic
299C4×C101#52911yescharacteristic
300C4×C101#52911yescharacteristic
301#21288C10111yesmaximal, characteristic, direct product factor, Sylow
302C2×C101—82no—
303C2×C101#229311yescharacteristic
304C2×C101C4×AGL(1,ℤ/8)11yescharacteristic
305C2×C101C4×#13711yescharacteristic
306C2×C101#318011yescharacteristic
307C2×C101#318111yescharacteristic
308C2×C101#318211yescharacteristic
309C2×C101#318311yescharacteristic
310C2×#440C2×C10111yescharacteristic
311#2295C2×C10111yescharacteristic, complemented
312#2293C2×C10111yescharacteristic
313#1973C2×C10111yescharacteristic
314#1968C2×C10111yescharacteristic
315#1943C2×C10111yescharacteristic, complemented
316#1942C2×C10111yescharacteristic, complemented
317#1936C2×C10111yescharacteristic
318#1935C2×C10111yescharacteristic, complemented
319#1934C2×C10111yescharacteristic
320#1933C2×C10111yescharacteristic, complemented
321#1776C2×C10111yescharacteristic, complemented
322#1763C2×C10111yescharacteristic, complemented
323#1762C2×C10111yescharacteristic
324C4×#97C2×C10111yescharacteristic, complemented
325C101#2128811yescharacteristic, direct product factor, Sylow
326C22×SD16C22×C10111yescharacteristic
327C2×C4×Q8C22×C10111yescharacteristic
328C2×C4×D4C22×C10111yescharacteristic
329C2×#117—21no—
330#440C4×C10118yescomplemented
331C2×#107C22×C10111yescharacteristic
332C2×#107C22×C10111yescharacteristic
333C2×#106C22×C10111yescharacteristic
334C2×#103C22×C10111yescharacteristic
335C2×#103C22×C10111yescharacteristic
336C2×#103C22×C10111yescharacteristic
337C2×#102C22×C10111yescharacteristic
338C2×#102C22×C10111yescharacteristic
339C2×#102C22×C10111yescharacteristic
340C2×#97C22×C10111yescharacteristic
341C2×#97C22×C10111yescharacteristic
342C2×#97C22×C10111yescharacteristic
343C2×#97C22×C10111yescharacteristic
344C2×C4×C8C22×C10111yescharacteristic
345C2×C4×C8C22×C10111yescharacteristic
346#391C22×C10111yescharacteristic
347#391C22×C10111yescharacteristic
348#390C22×C10111yescharacteristic
349#390C22×C10111yescharacteristic
350#389C22×C10111yescharacteristic
351#389C22×C10111yescharacteristic
352#389C22×C10111yescharacteristic
353#389C22×C10111yescharacteristic
354#388—21no—
355#388—21no—
356#387—21no—
357#387—21no—
358C4×C4⋊C4—21no—
359C4×C4⋊C4C22×C10111yescharacteristic
360C4×C4⋊C4C22×C10111yescharacteristic
361C4×C22⋊C4—21no—
362#376—21no—
363C43C22×C10111yescharacteristic
364#340C22×C10111yescharacteristic
365#340C22×C10111yescharacteristic
366#340C22×C10111yescharacteristic
367#340C22×C10111yescharacteristic
368#340C22×C10111yescharacteristic
369#340C22×C10111yescharacteristic
370C22×Q8C23×C10111yescharacteristic
371C22×D4C23×C10111yescharacteristic
372C23×C4—21no—
373C2×SD16—22no—
374C2×SD16—22no—
375C2×SD16C2×C4×C10114yes—
376C22×C8C23×C10111yescharacteristic
377C22×C8C23×C10111yescharacteristic
378C22×C8C23×C10111yescharacteristic
379C22×C8C23×C10111yescharacteristic
380C4×Q8—22no—
381C4×Q8C2×C4×C10114yes—
382C4×D4—22no—
383C4×D4C2×C4×C10114yes—
384#117—44no—
385C2×C4⋊C4—21no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4C23×C10111yescharacteristic
391C2×C4⋊C4C23×C10111yescharacteristic
392C2×C4⋊C4C23×C10111yescharacteristic
393C2×C4⋊C4C23×C10111yescharacteristic
394C2×C4⋊C4C23×C10111yescharacteristic
395C2×C4⋊C4C23×C10111yescharacteristic
396C2×C22⋊C4—21no—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—21no—
399C2×C22⋊C4—21no—
400C2×C22⋊C4—21no—
401C2×C42—21no—
402C2×C42—21no—
403C2×C42—21no—
404C2×C42D4×C10111yescharacteristic
405C2×C42D4×C10111yescharacteristic
406C2×C42D4×C10111yescharacteristic
407C2×C42D4×C10111yescharacteristic
408C2×C42C23×C10111yescharacteristic
409C2×C42C23×C10111yescharacteristic
410C2×C42C23×C10111yescharacteristic
411#107—22no—
412#107C2×C4×C10114yes—
413#106—22no—
414#103—22no—
415#103—22no—
416#103C2×C4×C10114yes—
417#102—22no—
418#102—22no—
419#102C2×C4×C10114yes—
420#97—22no—
421#97—22no—
422#97—22no—
423#97C2×C4×C10114yes—
424C4×C8—22no—
425C4×C8—22no—
426#95—21no—
427#95—21no—
428#95—21no—
429#95—21no—
430#95—21no—
431#95—21no—
432#95—21no—
433#95—21no—
434#95—21no—
435#95—21no—
436C24—21no—
437C2×Q8—21no—
438C2×Q8—21no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×Q8—21no—
442C2×Q8C22×C4×C10112yes—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—21no—
446C2×D4—21no—
447C2×D4—21no—
448C2×D4C22×C4×C10112yes—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—21no—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—42no—
458C22×C4—42no—
459C22×C4C2×D4×C10111yescharacteristic
460C22×C4C2×D4×C10111yescharacteristic
461C22×C4C2×D4×C10111yescharacteristic
462C22×C4C2×D4×C10111yescharacteristic
463C22×C4C2×D4×C10111yescharacteristic
464C22×C4C2×D4×C10111yescharacteristic
465C22×C4C24×C10111yescharacteristic
466SD16—28no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8C22×C4×C10112yes—
474C2×C8C22×C4×C10112yes—
475C2×C8#41×C10112yes—
476C2×C8#41×C10112yes—
477C2×C8#41×C10112yes—
478C2×C8#41×C10112yes—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—21no—
483C4⋊C4—21no—
484C4⋊C4—21no—
485C4⋊C4—21no—
486C4⋊C4—21no—
487C4⋊C4—21no—
488C4⋊C4—21no—
489C4⋊C4—21no—
490C4⋊C4—42no—
491C4⋊C4—42no—
492C4⋊C4—42no—
493C4⋊C4—42no—
494C4⋊C4C22×C4×C10112yes—
495C4⋊C4C22×C4×C10112yes—
496C22⋊C4—24no—
497C22⋊C4—42no—
498C22⋊C4—42no—
499C22⋊C4—42no—
500C22⋊C4—42no—
501C42—24no—
502C42—22no—
503C42—22no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—41no—
509C42—41no—
510C42—42no—
511C42—42no—
512C42C22×C4×C10112yes—
513C42#41×C10112yes—
514C23—22no—
515C23—41no—
516C23—41no—
517C23—41no—
518C23—41no—
519C23—41no—
520C23—41no—
521C23C22×D4×C10111yescharacteristic
522Q8—22no—
523Q8—22no—
524Q8—41no—
525Q8—41no—
526D4—22no—
527D4—22no—
528D4—41no—
529D4—41no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—22no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—48no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—41no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4C4×D4×C10112yes—
567C2×C4C4×D4×C10112yes—
568C2×C4AGL(1,ℤ/8)×C10112yes—
569C2×C4#137×C10112yes—
570C2×C4C23×C4×C10111yescharacteristic
571C2×C4C2×#41×C10111yescharacteristic
572C2×C4C2×#41×C10111yescharacteristic
573C2×C4C2×#41×C10111yescharacteristic
574C2×C4C2×#41×C10111yescharacteristic
575C2×C4C2×#41×C10111yescharacteristic
576C8—22no—
577C8—22no—
578C8—22no—
579C8#117×C10114yescomplemented
580C22—42no—
581C22—42no—
582C22—42no—
583C22—81no—
584C22—81no—
585C22—81no—
586C22—81no—
587C22C2×C4×D4×C10111yescharacteristic
588C22#532×C10111yescharacteristic
589C22#532×C10111yescharacteristic
590C22C2×AGL(1,ℤ/8)×C10111yescharacteristic
591C22C2×#137×C10111yescharacteristic
592C22#575×C10111yescharacteristic
593C22#575×C10111yescharacteristic
594C4—22no—
595C4—22no—
596C4—22no—
597C4—22no—
598C4—41no—
599C4—41no—
600C4—42no—
601C4—42no—
602C4—42no—
603C4—81no—
604C4—81no—
605C4—81no—
606C4—81no—
607C4C2×#117×C10111yescharacteristic
608C4C4×#41×C10111yescharacteristic
609C4#529×C10111yescharacteristic
610C4#529×C10111yescharacteristic
611C2—82no—
612C2C101×#229311yescharacteristic
613C2C4×AGL(1,ℤ/8)×C10111yescharacteristic
614C2C4×#137×C10111yescharacteristic
615C2C101×#318011yescharacteristic
616C2C101×#318111yescharacteristic
617C2C101×#318211yescharacteristic
618C2C101×#318311yescharacteristic
subgroupG/H
center, socleC23×C101C22×D4
commutatorC2×C4C23×C4×C101
Frattini, cosocleC22×C4C24×C101
prime radicalC22×D4×C101C23
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C101 ◁ C43×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C101×#2295C2semidirect
6. C101×#1943C2semidirect
7. C101×#1942C2semidirect
9. C101×#1935C2semidirect
11. C101×#1933C2semidirect
12. C101×#1776C2semidirect
13. C101×#1763C2semidirect
15. C4×#97×C101C2semidirect
20. #440×C101C4semidirect
269. C8×C101#117semidirect
301. #21288C101direct (N × H)
311. #2295C2×C101semidirect
315. #1943C2×C101semidirect
316. #1942C2×C101semidirect
318. #1935C2×C101semidirect
320. #1933C2×C101semidirect
321. #1776C2×C101semidirect
322. #1763C2×C101semidirect
324. C4×#97C2×C101semidirect
325. C101#21288direct (N × H)
330. #440C4×C101semidirect
579. C8#117×C101semidirect

Maximal subgroups

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

subgroupindex
C2×#440×C1012
C101×#22952
C101×#22932
C101×#19732
C101×#19682
C101×#19432
C101×#19422
C101×#19362
C101×#19352
C101×#19342
C101×#19332
C101×#17762
C101×#17632
C101×#17622
C4×#97×C1012
#21288101