Finite Group Databasebeta

← C101×#23901 #38806052

Subgroups — C101×#23901 #38806052

Order 25856.

2056 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3484C211yesmaximal, characteristic
2C22×#123×C101C211yesmaximal, characteristic, complemented
3C2×#458×C101C212yesmaximal, complemented
4C101×#2849C212yesmaximal, complemented
5C101×#2022C214yesmaximal, complemented
6C101×#1898C212yesmaximal, complemented
7C101×#1890C212yesmaximal, complemented
8C101×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C101C2211yescharacteristic
10C23×D4×C101C2211yescharacteristic
11C24×C4×C101C2211yescharacteristic, complemented
12#546×C101—24no—
13D42×C101—24no—
14#535×C101—21no—
15#534×C101—21no—
16#534×C101C2212yes—
17#525×C101—21no—
18C2×#123×C101—21no—
19C2×#123×C101—21no—
20C2×#123×C101—28no—
21C2×#123×C101C2212yes—
22C2×#123×C101C2212yescomplemented
23C2×#123×C101C2214yescomplemented
24C2×#120×C101—21no—
25C2×#120×C101C2212yes—
26#518×C101C2211yescharacteristic
27C22×C4⋊C4×C101—21no—
28C22×C22⋊C4×C101—21no—
29C22×C22⋊C4×C101C2211yescharacteristic, complemented
30#458×C101—28no—
31C2×#99×C101C2212yes—
32C2×#99×C101C2214yescomplemented
33C2×#99×C101C2212yescomplemented
34#386×C101—24no—
35#385×C101—24no—
36#381×C101C2214yescomplemented
37#379×C101C2212yescomplemented
38#342×C101C2214yescomplemented
39C25×C101D411yescharacteristic
40C25×C101C2311yescharacteristic
41H(5,𝔽2)×C101—24no—
42H(5,𝔽2)×C101—42no—
43C2×#41×C101—21no—
44C2×#41×C101—22no—
45C22×D4×C101—21no—
46C22×D4×C101—22no—
47C22×D4×C101—24no—
48C22×D4×C101—22no—
49C22×D4×C101—24no—
50C22×D4×C101—42no—
51C22×D4×C101D411yescharacteristic
52C22×D4×C101D411yescharacteristic
53C22×D4×C101D414yes—
54C22×D4×C101C2312yes—
55C22×D4×C101C2311yescharacteristic
56C22×D4×C101C2311yescharacteristic
57C23×C4×C101—21no—
58C23×C4×C101—21no—
59C23×C4×C101—21no—
60C23×C4×C101—24no—
61C23×C4×C101—24no—
62C23×C4×C101—42no—
63C23×C4×C101D411yescharacteristic
64C23×C4×C101C2312yes—
65#127×C101—22no—
66#124×C101—22no—
67#123×C101—28no—
68#123×C101—28no—
69#123×C101—22no—
70#123×C101—24no—
71#123×C101—22no—
72#123×C101—22no—
73#123×C101—24no—
74#123×C101—24no—
75#123×C101—28no—
76#123×C101—44no—
77#123×C101D418yescomplemented
78C22⋊Q8×C101—22no—
79#121×C101—22no—
80#121×C101—24no—
81#121×C101—24no—
82#121×C101—24no—
83#120×C101—24no—
84#120×C101—22no—
85#120×C101—22no—
86#120×C101—22no—
87#120×C101—22no—
88#120×C101—24no—
89#120×C101—22no—
90C4×D4×C101—24no—
91C4×D4×C101—24no—
92#117×C101—21no—
93C2×C4⋊C4×C101—28no—
94C2×C4⋊C4×C101—22no—
95C2×C4⋊C4×C101—22no—
96C2×C4⋊C4×C101—24no—
97C2×C22⋊C4×C101—28no—
98C2×C22⋊C4×C101—22no—
99C2×C22⋊C4×C101—22no—
100C2×C22⋊C4×C101—22no—
101C2×C22⋊C4×C101—21no—
102C2×C22⋊C4×C101—21no—
103C2×C22⋊C4×C101—24no—
104C2×C22⋊C4×C101—24no—
105C2×C22⋊C4×C101—24no—
106C2×C22⋊C4×C101D414yes—
107C2×C22⋊C4×C101C2314yes—
108C2×C22⋊C4×C101C2312yes—
109C2×C22⋊C4×C101C2312yes—
110#99×C101—24no—
111#99×C101—28no—
112#99×C101—42no—
113#95×C101—28no—
114C24×C101—22no—
115C24×C101—22no—
116C24×C101—21no—
117C24×C101—22no—
118C24×C101—22no—
119C24×C101—44no—
120C24×C101—41no—
121C24×C101—44no—
122C24×C101C2×D411yescharacteristic
123C24×C101C2×D414yes—
124C24×C101C2×D411yescharacteristic
125C24×C101C2×D412yes—
126C24×C101C2×D411yescharacteristic
127C24×C101C2×D411yescharacteristic
128C24×C101C2411yescharacteristic
129#41×C101—48no—
130#41×C101—42no—
131#41×C101—42no—
132C2×Q8×C101—21no—
133C2×D4×C101—22no—
134C2×D4×C101—22no—
135C2×D4×C101—22no—
136C2×D4×C101—21no—
137C2×D4×C101—24no—
138C2×D4×C101—22no—
139C2×D4×C101—22no—
140C2×D4×C101—22no—
141C2×D4×C101—24no—
142C2×D4×C101—22no—
143C2×D4×C101—22no—
144C2×D4×C101—22no—
145C2×D4×C101—22no—
146C2×D4×C101—22no—
147C2×D4×C101—24no—
148C2×D4×C101—24no—
149C2×D4×C101—24no—
150C2×D4×C101—22no—
151C2×D4×C101—41no—
152C2×D4×C101—41no—
153C2×D4×C101—416no—
154C2×D4×C101—48no—
155C2×D4×C101—42no—
156C2×D4×C101—42no—
157C2×D4×C101—48no—
158C2×D4×C101—84no—
159C2×D4×C101C2×D414yes—
160C22×C4×C101—24no—
161C22×C4×C101—24no—
162C22×C4×C101—21no—
163C22×C4×C101—22no—
164C22×C4×C101—24no—
165C22×C4×C101—22no—
166C22×C4×C101—24no—
167C22×C4×C101—22no—
168C22×C4×C101—22no—
169C22×C4×C101—22no—
170C22×C4×C101—24no—
171C22×C4×C101—22no—
172C22×C4×C101—22no—
173C22×C4×C101—24no—
174C22×C4×C101—41no—
175C22×C4×C101—416no—
176C22×C4×C101—44no—
177C22×C4×C101—42no—
178C22×C4×C101—42no—
179C22×C4×C101—42no—
180C22×C4×C101—42no—
181C22×C4×C101C2×D412yes—
182C22×C4×C101C2×D411yescharacteristic
183C22×C4×C101C2×D411yescharacteristic
184C22×C4×C101C2×D414yes—
185C22×C4×C101C2×D414yescomplemented
186C4⋊C4×C101—28no—
187C4⋊C4×C101—22no—
188C4⋊C4×C101—24no—
189C4⋊C4×C101—28no—
190C4⋊C4×C101—48no—
191C22⋊C4×C101—24no—
192C22⋊C4×C101—28no—
193C22⋊C4×C101—22no—
194C22⋊C4×C101—24no—
195C22⋊C4×C101—24no—
196C22⋊C4×C101—28no—
197C22⋊C4×C101—24no—
198C22⋊C4×C101—24no—
199C22⋊C4×C101—22no—
200C22⋊C4×C101—22no—
201C22⋊C4×C101—22no—
202C22⋊C4×C101—24no—
203C22⋊C4×C101—24no—
204C22⋊C4×C101—48no—
205C22⋊C4×C101—48no—
206C22⋊C4×C101C2×D414yescomplemented
207C42×C101—22no—
208C23×C101—21no—
209C23×C101—21no—
210C23×C101—24no—
211C23×C101—21no—
212C23×C101—21no—
213C23×C101—21no—
214C23×C101—28no—
215C23×C101—28no—
216C23×C101—21no—
217C23×C101—21no—
218C23×C101—21no—
219C23×C101—22no—
220C23×C101—21no—
221C23×C101—24no—
222C23×C101—44no—
223C23×C101—42no—
224C23×C101—42no—
225C23×C101—44no—
226C23×C101—48no—
227C23×C101—48no—
228C23×C101—42no—
229C23×C101—42no—
230C23×C101—48no—
231C23×C101—42no—
232C23×C101—44no—
233C23×C101—44no—
234C23×C101—82no—
235C23×C101—84no—
236C23×C101—82no—
237C23×C101#12012yes—
238C23×C101#12012yes—
239C23×C101#12012yes—
240C23×C101C22×D411yescharacteristic
241C23×C101C22×D412yes—
242C23×C101C22×D412yes—
243C23×C101H(5,𝔽2)12yes—
244Q8×C101—42no—
245D4×C101—28no—
246D4×C101—44no—
247D4×C101—42no—
248D4×C101—44no—
249D4×C101—44no—
250D4×C101—42no—
251D4×C101—42no—
252D4×C101—44no—
253D4×C101—44no—
254D4×C101—48no—
255D4×C101—84no—
256D4×C101—84no—
257C2×C4×C101—21no—
258C2×C4×C101—21no—
259C2×C4×C101—24no—
260C2×C4×C101—24no—
261C2×C4×C101—21no—
262C2×C4×C101—24no—
263C2×C4×C101—22no—
264C2×C4×C101—21no—
265C2×C4×C101—21no—
266C2×C4×C101—28no—
267C2×C4×C101—24no—
268C2×C4×C101—44no—
269C2×C4×C101—44no—
270C2×C4×C101—48no—
271C2×C4×C101—44no—
272C2×C4×C101—48no—
273C2×C4×C101—48no—
274C2×C4×C101—42no—
275C2×C4×C101—42no—
276C2×C4×C101—42no—
277C2×C4×C101—44no—
278C2×C4×C101—44no—
279C2×C4×C101—48no—
280C2×C4×C101—44no—
281C2×C4×C101—82no—
282C2×C4×C101#12012yes—
283C22×C101—24no—
284C22×C101—24no—
285C22×C101—22no—
286C22×C101—24no—
287C22×C101—22no—
288C22×C101—22no—
289C22×C101—22no—
290C22×C101—22no—
291C22×C101—24no—
292C22×C101—42no—
293C22×C101—42no—
294C22×C101—416no—
295C22×C101—42no—
296C22×C101—42no—
297C22×C101—42no—
298C22×C101—42no—
299C22×C101—42no—
300C22×C101—42no—
301C22×C101—41no—
302C22×C101—44no—
303C22×C101—42no—
304C22×C101—81no—
305C22×C101—88no—
306C22×C101—84no—
307C22×C101—81no—
308C22×C101—162no—
309C22×C101#45814yescomplemented
310C22×C101C2×#12011yescharacteristic
311C22×C101C2×#12011yescharacteristic
312C22×C101#53411yescharacteristic
313C22×C101D4214yes—
314C4×C101—22no—
315C4×C101—44no—
316C4×C101—44no—
317C4×C101—41no—
318C4×C101—42no—
319C4×C101—44no—
320C4×C101—84no—
321#23901C10111yesmaximal, characteristic, direct product factor, Sylow
322C2×C101—21no—
323C2×C101—24no—
324C2×C101—21no—
325C2×C101—24no—
326C2×C101—42no—
327C2×C101—42no—
328C2×C101—81no—
329C2×C101—82no—
330C2×C101#240311yescharacteristic
331C2×C101C2×#45812yes—
332#3484C2×C10111yescharacteristic
333C22×#123C2×C10111yescharacteristic, complemented
334C2×#458C2×C10112yescomplemented
335#2849C2×C10112yescomplemented
336#2022C2×C10114yescomplemented
337#1898C2×C10112yescomplemented
338#1890C2×C10112yescomplemented
339#1781C2×C10111yescharacteristic, complemented
340C101#2390111yescharacteristic, direct product factor, Sylow
341C2×H(5,𝔽2)C22×C10111yescharacteristic
342C23×D4C22×C10111yescharacteristic
343C24×C4C22×C10111yescharacteristic, complemented
344#546—24no—
345D42—24no—
346#535—21no—
347#534—21no—
348#534C22×C10112yes—
349#525—21no—
350C2×#123—21no—
351C2×#123—21no—
352C2×#123—28no—
353C2×#123C22×C10112yes—
354C2×#123C22×C10112yescomplemented
355C2×#123C22×C10114yescomplemented
356C2×#120—21no—
357C2×#120C22×C10112yes—
358#518C22×C10111yescharacteristic
359C22×C4⋊C4—21no—
360C22×C22⋊C4—21no—
361C22×C22⋊C4C22×C10111yescharacteristic, complemented
362#458—28no—
363C2×#99C22×C10112yes—
364C2×#99C22×C10114yescomplemented
365C2×#99C22×C10112yescomplemented
366#386—24no—
367#385—24no—
368#381C22×C10114yescomplemented
369#379C22×C10112yescomplemented
370#342C22×C10114yescomplemented
371C25D4×C10111yescharacteristic
372C25C23×C10111yescharacteristic
373H(5,𝔽2)—24no—
374H(5,𝔽2)—42no—
375C2×#41—21no—
376C2×#41—22no—
377C22×D4—21no—
378C22×D4—22no—
379C22×D4—24no—
380C22×D4—22no—
381C22×D4—24no—
382C22×D4—42no—
383C22×D4D4×C10111yescharacteristic
384C22×D4D4×C10111yescharacteristic
385C22×D4D4×C10114yes—
386C22×D4C23×C10112yes—
387C22×D4C23×C10111yescharacteristic
388C22×D4C23×C10111yescharacteristic
389C23×C4—21no—
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—42no—
395C23×C4D4×C10111yescharacteristic
396C23×C4C23×C10112yes—
397#127—22no—
398#124—22no—
399#123—28no—
400#123—28no—
401#123—22no—
402#123—24no—
403#123—22no—
404#123—22no—
405#123—24no—
406#123—24no—
407#123—28no—
408#123—44no—
409#123D4×C10118yescomplemented
410C22⋊Q8—22no—
411#121—22no—
412#121—24no—
413#121—24no—
414#121—24no—
415#120—24no—
416#120—22no—
417#120—22no—
418#120—22no—
419#120—22no—
420#120—24no—
421#120—22no—
422C4×D4—24no—
423C4×D4—24no—
424#117—21no—
425C2×C4⋊C4—28no—
426C2×C4⋊C4—22no—
427C2×C4⋊C4—22no—
428C2×C4⋊C4—24no—
429C2×C22⋊C4—28no—
430C2×C22⋊C4—22no—
431C2×C22⋊C4—22no—
432C2×C22⋊C4—22no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—24no—
436C2×C22⋊C4—24no—
437C2×C22⋊C4—24no—
438C2×C22⋊C4D4×C10114yes—
439C2×C22⋊C4C23×C10114yes—
440C2×C22⋊C4C23×C10112yes—
441C2×C22⋊C4C23×C10112yes—
442#99—24no—
443#99—28no—
444#99—42no—
445#95—28no—
446C24—22no—
447C24—22no—
448C24—21no—
449C24—22no—
450C24—22no—
451C24—44no—
452C24—41no—
453C24—44no—
454C24C2×D4×C10111yescharacteristic
455C24C2×D4×C10114yes—
456C24C2×D4×C10111yescharacteristic
457C24C2×D4×C10112yes—
458C24C2×D4×C10111yescharacteristic
459C24C2×D4×C10111yescharacteristic
460C24C24×C10111yescharacteristic
461#41—48no—
462#41—42no—
463#41—42no—
464C2×Q8—21no—
465C2×D4—22no—
466C2×D4—22no—
467C2×D4—22no—
468C2×D4—21no—
469C2×D4—24no—
470C2×D4—22no—
471C2×D4—22no—
472C2×D4—22no—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—22no—
477C2×D4—22no—
478C2×D4—22no—
479C2×D4—24no—
480C2×D4—24no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—41no—
484C2×D4—41no—
485C2×D4—416no—
486C2×D4—48no—
487C2×D4—42no—
488C2×D4—42no—
489C2×D4—48no—
490C2×D4—84no—
491C2×D4C2×D4×C10114yes—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—21no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—24no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—24no—
506C22×C4—41no—
507C22×C4—416no—
508C22×C4—44no—
509C22×C4—42no—
510C22×C4—42no—
511C22×C4—42no—
512C22×C4—42no—
513C22×C4C2×D4×C10112yes—
514C22×C4C2×D4×C10111yescharacteristic
515C22×C4C2×D4×C10111yescharacteristic
516C22×C4C2×D4×C10114yes—
517C22×C4C2×D4×C10114yescomplemented
518C4⋊C4—28no—
519C4⋊C4—22no—
520C4⋊C4—24no—
521C4⋊C4—28no—
522C4⋊C4—48no—
523C22⋊C4—24no—
524C22⋊C4—28no—
525C22⋊C4—22no—
526C22⋊C4—24no—
527C22⋊C4—24no—
528C22⋊C4—28no—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—22no—
532C22⋊C4—22no—
533C22⋊C4—22no—
534C22⋊C4—24no—
535C22⋊C4—24no—
536C22⋊C4—48no—
537C22⋊C4—48no—
538C22⋊C4C2×D4×C10114yescomplemented
539C42—22no—
540C23—24no—
541C23—21no—
542C23—21no—
543C23—28no—
544C23—21no—
545C23—21no—
546C23—21no—
547C23—28no—
548C23—21no—
549C23—21no—
550C23—21no—
551C23—22no—
552C23—21no—
553C23—24no—
554C23—44no—
555C23—42no—
556C23—42no—
557C23—44no—
558C23—48no—
559C23—48no—
560C23—42no—
561C23—42no—
562C23—48no—
563C23—42no—
564C23—44no—
565C23—44no—
566C23—82no—
567C23—84no—
568C23—82no—
569C23#120×C10112yes—
570C23#120×C10112yes—
571C23#120×C10112yes—
572C23C22×D4×C10111yescharacteristic
573C23C22×D4×C10112yes—
574C23C22×D4×C10112yes—
575C23H(5,𝔽2)×C10112yes—
576Q8—42no—
577D4—28no—
578D4—44no—
579D4—42no—
580D4—44no—
581D4—44no—
582D4—48no—
583D4—42no—
584D4—42no—
585D4—44no—
586D4—44no—
587D4—84no—
588D4—84no—
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—28no—
599C2×C4—24no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—48no—
603C2×C4—48no—
604C2×C4—48no—
605C2×C4—44no—
606C2×C4—42no—
607C2×C4—42no—
608C2×C4—42no—
609C2×C4—44no—
610C2×C4—44no—
611C2×C4—48no—
612C2×C4—44no—
613C2×C4—82no—
614C2×C4#120×C10112yes—
615C22—24no—
616C22—24no—
617C22—22no—
618C22—24no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—22no—
623C22—24no—
624C22—42no—
625C22—42no—
626C22—416no—
627C22—42no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—42no—
632C22—42no—
633C22—41no—
634C22—44no—
635C22—42no—
636C22—81no—
637C22—88no—
638C22—81no—
639C22—84no—
640C22—162no—
641C22#458×C10114yescomplemented
642C22C2×#120×C10111yescharacteristic
643C22C2×#120×C10111yescharacteristic
644C22#534×C10111yescharacteristic
645C22D42×C10114yes—
646C4—22no—
647C4—44no—
648C4—44no—
649C4—41no—
650C4—42no—
651C4—44no—
652C4—84no—
653C2—21no—
654C2—24no—
655C2—24no—
656C2—21no—
657C2—42no—
658C2—42no—
659C2—81no—
660C2—82no—
661C2C101×#240311yescharacteristic
662C2C2×#458×C10112yes—
subgroupG/H
center, socleC22×C101C2×#120
commutator, Frattini, cosocleC24C24×C101
prime radicalC101×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C101 ◁ C25×C101 ◁ G

Complements

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

NH ≅ G/Ntype
2. C22×#123×C101C2semidirect
3. C2×#458×C101C2semidirect
4. C101×#2849C2semidirect
5. C101×#2022C2semidirect
6. C101×#1898C2semidirect
7. C101×#1890C2semidirect
8. C101×#1781C2semidirect
11. C24×C4×C101C22semidirect
22. C2×#123×C101C22semidirect
23. C2×#123×C101C22semidirect
29. C22×C22⋊C4×C101C22semidirect
32. C2×#99×C101C22semidirect
33. C2×#99×C101C22semidirect
36. #381×C101C22semidirect
37. #379×C101C22semidirect
38. #342×C101C22semidirect
77. #123×C101D4semidirect
185. C22×C4×C101C2×D4semidirect
206. C22⋊C4×C101C2×D4semidirect
309. C22×C101#458semidirect
321. #23901C101direct (N × H)
333. C22×#123C2×C101semidirect
334. C2×#458C2×C101semidirect
335. #2849C2×C101semidirect
336. #2022C2×C101semidirect
337. #1898C2×C101semidirect
338. #1890C2×C101semidirect
339. #1781C2×C101semidirect
340. C101#23901direct (N × H)
343. C24×C4C22×C101semidirect
354. C2×#123C22×C101semidirect
355. C2×#123C22×C101semidirect
361. C22×C22⋊C4C22×C101semidirect
364. C2×#99C22×C101semidirect
365. C2×#99C22×C101semidirect
368. #381C22×C101semidirect
369. #379C22×C101semidirect
370. #342C22×C101semidirect
409. #123D4×C101semidirect
517. C22×C4C2×D4×C101semidirect
538. C22⋊C4C2×D4×C101semidirect
641. C22#458×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C22×#123×C1012
C2×#458×C1012
C101×#28492
C101×#20222
C101×#18982
C101×#18902
C101×#17812
#23901101