Finite Group Databasebeta

← C101×#24056 #38806207

Subgroups — C101×#24056 #38806207

Order 25856.

1820 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C101×#3484C211yesmaximal, characteristic
2C101×#2849C212yesmaximal, complemented
3C2×#386×C101C211yesmaximal, characteristic, complemented
4C101×#2044C214yesmaximal, complemented
5C101×#1898C212yesmaximal, complemented
6C101×#1867C212yesmaximal, complemented
7C101×#1790C212yesmaximal, complemented
8C101×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C101C2211yescharacteristic
10C23×D4×C101C2211yescharacteristic
11C24×C4×C101C2211yescharacteristic, complemented
12#546×C101—22no—
13#546×C101—22no—
14D42×C101—22no—
15D42×C101—22no—
16#535×C101—21no—
17#534×C101—21no—
18#534×C101C2212yes—
19#525×C101—21no—
20C2×#123×C101—22no—
21C2×#120×C101—21no—
22C2×#120×C101C2212yes—
23#518×C101C2211yescharacteristic
24C22×C22⋊C4×C101—21no—
25C22×C22⋊C4×C101C2211yescharacteristic, complemented
26C2×#99×C101C2212yes—
27C2×#99×C101C2214yescomplemented
28C2×#99×C101C2212yescomplemented
29#386×C101—21no—
30#386×C101—21no—
31#386×C101—22no—
32#386×C101C2212yes—
33#386×C101C2212yescomplemented
34#386×C101C2214yescomplemented
35#385×C101—22no—
36#385×C101C2214yescomplemented
37#381×C101—22no—
38#379×C101C2212yescomplemented
39C2×#95×C101—21no—
40#342×C101C2214yescomplemented
41C25×C101D411yescharacteristic
42C25×C101C2311yescharacteristic
43H(5,𝔽2)×C101—24no—
44H(5,𝔽2)×C101—42no—
45C2×#41×C101—21no—
46C2×#41×C101—22no—
47C22×D4×C101—21no—
48C22×D4×C101—22no—
49C22×D4×C101—22no—
50C22×D4×C101—22no—
51C22×D4×C101—21no—
52C22×D4×C101—21no—
53C22×D4×C101—24no—
54C22×D4×C101—42no—
55C22×D4×C101D411yescharacteristic
56C22×D4×C101D411yescharacteristic
57C22×D4×C101D412yes—
58C22×D4×C101D412yes—
59C22×D4×C101C2312yes—
60C22×D4×C101C2311yescharacteristic
61C22×D4×C101C2311yescharacteristic
62C23×C4×C101—21no—
63C23×C4×C101—22no—
64C23×C4×C101—21no—
65C23×C4×C101—22no—
66C23×C4×C101—21no—
67C23×C4×C101—44no—
68C23×C4×C101D411yescharacteristic
69C23×C4×C101C2312yes—
70#127×C101—22no—
71#124×C101—22no—
72#123×C101—22no—
73#123×C101—22no—
74#123×C101—22no—
75#123×C101—48no—
76C22⋊Q8×C101—21no—
77C22⋊Q8×C101—21no—
78#121×C101—21no—
79#121×C101—21no—
80#121×C101—22no—
81#121×C101—22no—
82#121×C101—22no—
83#121×C101—22no—
84#121×C101—22no—
85#121×C101—22no—
86#120×C101—22no—
87#120×C101—22no—
88#120×C101—22no—
89#120×C101—22no—
90#120×C101—22no—
91#120×C101—22no—
92#120×C101—22no—
93#120×C101—22no—
94#120×C101—22no—
95C4×D4×C101—22no—
96C4×D4×C101—22no—
97C4×D4×C101—22no—
98C4×D4×C101—22no—
99#117×C101—21no—
100C2×C4⋊C4×C101—24no—
101C2×C22⋊C4×C101—21no—
102C2×C22⋊C4×C101—21no—
103C2×C22⋊C4×C101—21no—
104C2×C22⋊C4×C101—22no—
105C2×C22⋊C4×C101—22no—
106C2×C22⋊C4×C101—21no—
107C2×C22⋊C4×C101—22no—
108C2×C22⋊C4×C101—24no—
109C2×C22⋊C4×C101—22no—
110C2×C22⋊C4×C101—42no—
111C2×C22⋊C4×C101—44no—
112C2×C22⋊C4×C101D412yes—
113C2×C22⋊C4×C101D412yes—
114C2×C22⋊C4×C101C2314yes—
115C2×C22⋊C4×C101C2312yes—
116C2×C22⋊C4×C101C2312yes—
117#99×C101—24no—
118#99×C101—42no—
119#99×C101—44no—
120#95×C101—22no—
121#95×C101—22no—
122#95×C101—24no—
123#95×C101—24no—
124C24×C101—22no—
125C24×C101—22no—
126C24×C101—21no—
127C24×C101—22no—
128C24×C101—21no—
129C24×C101—21no—
130C24×C101—42no—
131C24×C101—42no—
132C24×C101—41no—
133C24×C101—42no—
134C24×C101—42no—
135C24×C101C2×D411yescharacteristic
136C24×C101C2×D412yes—
137C24×C101C2×D412yes—
138C24×C101C2×D411yescharacteristic
139C24×C101C2×D412yes—
140C24×C101C2×D411yescharacteristic
141C24×C101C2×D411yescharacteristic
142C24×C101C2411yescharacteristic
143#41×C101—48no—
144#41×C101—42no—
145#41×C101—42no—
146C2×Q8×C101—21no—
147C2×D4×C101—22no—
148C2×D4×C101—22no—
149C2×D4×C101—22no—
150C2×D4×C101—21no—
151C2×D4×C101—22no—
152C2×D4×C101—22no—
153C2×D4×C101—22no—
154C2×D4×C101—22no—
155C2×D4×C101—22no—
156C2×D4×C101—22no—
157C2×D4×C101—22no—
158C2×D4×C101—22no—
159C2×D4×C101—22no—
160C2×D4×C101—24no—
161C2×D4×C101—22no—
162C2×D4×C101—24no—
163C2×D4×C101—22no—
164C2×D4×C101—22no—
165C2×D4×C101—22no—
166C2×D4×C101—22no—
167C2×D4×C101—22no—
168C2×D4×C101—41no—
169C2×D4×C101—41no—
170C2×D4×C101—48no—
171C2×D4×C101—48no—
172C2×D4×C101—48no—
173C2×D4×C101—42no—
174C2×D4×C101—42no—
175C2×D4×C101—44no—
176C2×D4×C101—44no—
177C2×D4×C101—82no—
178C2×D4×C101—82no—
179C2×D4×C101#4114yes—
180C22×C4×C101—21no—
181C22×C4×C101—24no—
182C22×C4×C101—22no—
183C22×C4×C101—28no—
184C22×C4×C101—21no—
185C22×C4×C101—21no—
186C22×C4×C101—22no—
187C22×C4×C101—24no—
188C22×C4×C101—21no—
189C22×C4×C101—21no—
190C22×C4×C101—22no—
191C22×C4×C101—24no—
192C22×C4×C101—22no—
193C22×C4×C101—44no—
194C22×C4×C101—41no—
195C22×C4×C101—44no—
196C22×C4×C101—48no—
197C22×C4×C101—42no—
198C22×C4×C101—44no—
199C22×C4×C101—42no—
200C22×C4×C101—41no—
201C22×C4×C101—41no—
202C22×C4×C101—42no—
203C22×C4×C101—42no—
204C22×C4×C101—42no—
205C22×C4×C101C2×D412yes—
206C22×C4×C101C2×D411yescharacteristic
207C22×C4×C101C2×D411yescharacteristic
208C22×C4×C101C2×D412yes—
209C22×C4×C101C2×D412yes—
210C4⋊C4×C101—21no—
211C4⋊C4×C101—21no—
212C4⋊C4×C101—22no—
213C4⋊C4×C101—22no—
214C4⋊C4×C101—48no—
215C22⋊C4×C101—22no—
216C22⋊C4×C101—22no—
217C22⋊C4×C101—22no—
218C22⋊C4×C101—22no—
219C22⋊C4×C101—22no—
220C22⋊C4×C101—22no—
221C22⋊C4×C101—22no—
222C22⋊C4×C101—22no—
223C22⋊C4×C101—22no—
224C22⋊C4×C101—22no—
225C22⋊C4×C101—22no—
226C22⋊C4×C101—24no—
227C22⋊C4×C101—24no—
228C22⋊C4×C101—24no—
229C22⋊C4×C101—44no—
230C22⋊C4×C101—44no—
231C22⋊C4×C101—48no—
232C22⋊C4×C101—44no—
233C22⋊C4×C101—42no—
234C22⋊C4×C101—44no—
235C42×C101—22no—
236C23×C101—21no—
237C23×C101—21no—
238C23×C101—22no—
239C23×C101—22no—
240C23×C101—21no—
241C23×C101—21no—
242C23×C101—21no—
243C23×C101—24no—
244C23×C101—24no—
245C23×C101—24no—
246C23×C101—24no—
247C23×C101—21no—
248C23×C101—21no—
249C23×C101—22no—
250C23×C101—21no—
251C23×C101—21no—
252C23×C101—24no—
253C23×C101—42no—
254C23×C101—41no—
255C23×C101—41no—
256C23×C101—42no—
257C23×C101—41no—
258C23×C101—41no—
259C23×C101—42no—
260C23×C101—42no—
261C23×C101—48no—
262C23×C101—48no—
263C23×C101—41no—
264C23×C101—41no—
265C23×C101—41no—
266C23×C101—41no—
267C23×C101—48no—
268C23×C101—42no—
269C23×C101—42no—
270C23×C101—42no—
271C23×C101—42no—
272C23×C101—42no—
273C23×C101—81no—
274C23×C101—81no—
275C23×C101—84no—
276C23×C101—81no—
277C23×C101—81no—
278C23×C101#12012yes—
279C23×C101#12011yescharacteristic
280C23×C101#12011yescharacteristic
281C23×C101#12312yescomplemented
282C23×C101C22×D411yescharacteristic
283C23×C101C22×D412yes—
284C23×C101C2×#4112yes—
285C23×C101H(5,𝔽2)12yes—
286Q8×C101—42no—
287D4×C101—28no—
288D4×C101—44no—
289D4×C101—42no—
290D4×C101—44no—
291D4×C101—44no—
292D4×C101—42no—
293D4×C101—42no—
294D4×C101—44no—
295D4×C101—44no—
296D4×C101—44no—
297D4×C101—44no—
298D4×C101—82no—
299D4×C101—82no—
300D4×C101—82no—
301D4×C101—82no—
302C2×C4×C101—21no—
303C2×C4×C101—21no—
304C2×C4×C101—24no—
305C2×C4×C101—28no—
306C2×C4×C101—22no—
307C2×C4×C101—22no—
308C2×C4×C101—22no—
309C2×C4×C101—21no—
310C2×C4×C101—21no—
311C2×C4×C101—21no—
312C2×C4×C101—24no—
313C2×C4×C101—42no—
314C2×C4×C101—42no—
315C2×C4×C101—44no—
316C2×C4×C101—44no—
317C2×C4×C101—42no—
318C2×C4×C101—44no—
319C2×C4×C101—48no—
320C2×C4×C101—42no—
321C2×C4×C101—42no—
322C2×C4×C101—44no—
323C2×C4×C101—42no—
324C2×C4×C101—42no—
325C2×C4×C101—44no—
326C2×C4×C101—42no—
327C2×C4×C101—44no—
328C2×C4×C101—42no—
329C2×C4×C101—42no—
330C2×C4×C101—44no—
331C2×C4×C101—81no—
332C2×C4×C101—81no—
333C2×C4×C101—84no—
334C2×C4×C101#12312yescomplemented
335C22×C101—24no—
336C22×C101—24no—
337C22×C101—21no—
338C22×C101—21no—
339C22×C101—22no—
340C22×C101—21no—
341C22×C101—21no—
342C22×C101—22no—
343C22×C101—21no—
344C22×C101—21no—
345C22×C101—22no—
346C22×C101—22no—
347C22×C101—22no—
348C22×C101—22no—
349C22×C101—42no—
350C22×C101—42no—
351C22×C101—48no—
352C22×C101—48no—
353C22×C101—42no—
354C22×C101—42no—
355C22×C101—42no—
356C22×C101—42no—
357C22×C101—41no—
358C22×C101—41no—
359C22×C101—42no—
360C22×C101—41no—
361C22×C101—42no—
362C22×C101—41no—
363C22×C101—42no—
364C22×C101—41no—
365C22×C101—81no—
366C22×C101—84no—
367C22×C101—84no—
368C22×C101—84no—
369C22×C101—81no—
370C22×C101—162no—
371C22×C101B(4,𝔽2)12yes—
372C22×C101#45812yes—
373C22×C101C2×#12011yescharacteristic
374C22×C101C2×#12311yescharacteristic
375C22×C101#53411yescharacteristic
376C22×C101#54614yes—
377C4×C101—22no—
378C4×C101—41no—
379C4×C101—42no—
380C4×C101—44no—
381C4×C101—42no—
382C4×C101—42no—
383C4×C101—84no—
384C4×C101—82no—
385#24056C10111yesmaximal, characteristic, direct product factor, Sylow
386C2×C101—21no—
387C2×C101—24no—
388C2×C101—21no—
389C2×C101—22no—
390C2×C101—22no—
391C2×C101—42no—
392C2×C101—42no—
393C2×C101—81no—
394C2×C101—82no—
395C2×C101#240511yescharacteristic
396C2×C101C2×B(4,𝔽2)11yescharacteristic
397C2×C101C2×#45811yescharacteristic
398#3484C2×C10111yescharacteristic
399#2849C2×C10112yescomplemented
400C2×#386C2×C10111yescharacteristic, complemented
401#2044C2×C10114yescomplemented
402#1898C2×C10112yescomplemented
403#1867C2×C10112yescomplemented
404#1790C2×C10112yescomplemented
405#1781C2×C10111yescharacteristic, complemented
406C101#2405611yescharacteristic, direct product factor, Sylow
407C2×H(5,𝔽2)C22×C10111yescharacteristic
408C23×D4C22×C10111yescharacteristic
409C24×C4C22×C10111yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C10112yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C10112yes—
421#518C22×C10111yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C10111yescharacteristic, complemented
424C2×#99C22×C10112yes—
425C2×#99C22×C10114yescomplemented
426C2×#99C22×C10112yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C10112yes—
431#386C22×C10114yescomplemented
432#386C22×C10112yescomplemented
433#385—22no—
434#385C22×C10114yescomplemented
435#381—22no—
436#379C22×C10112yescomplemented
437C2×#95—21no—
438#342C22×C10114yescomplemented
439C25D4×C10111yescharacteristic
440C25C23×C10111yescharacteristic
441H(5,𝔽2)—24no—
442H(5,𝔽2)—42no—
443C2×#41—21no—
444C2×#41—22no—
445C22×D4—21no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—24no—
452C22×D4—42no—
453C22×D4D4×C10111yescharacteristic
454C22×D4D4×C10111yescharacteristic
455C22×D4D4×C10112yes—
456C22×D4D4×C10112yes—
457C22×D4C23×C10112yes—
458C22×D4C23×C10111yescharacteristic
459C22×D4C23×C10111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C10111yescharacteristic
467C23×C4C23×C10112yes—
468#127—22no—
469#124—22no—
470#123—22no—
471#123—22no—
472#123—22no—
473#123—48no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—22no—
482#121—22no—
483#121—22no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—22no—
488#120—22no—
489#120—22no—
490#120—22no—
491#120—22no—
492#120—22no—
493C4×D4—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—22no—
497#117—21no—
498C2×C4⋊C4—24no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—22no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—22no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—44no—
510C2×C22⋊C4D4×C10112yes—
511C2×C22⋊C4D4×C10112yes—
512C2×C22⋊C4C23×C10112yes—
513C2×C22⋊C4C23×C10114yes—
514C2×C22⋊C4C23×C10112yes—
515#99—24no—
516#99—42no—
517#99—44no—
518#95—22no—
519#95—22no—
520#95—24no—
521#95—24no—
522C24—22no—
523C24—22no—
524C24—21no—
525C24—22no—
526C24—21no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—41no—
531C24—42no—
532C24—42no—
533C24C2×D4×C10111yescharacteristic
534C24C2×D4×C10112yes—
535C24C2×D4×C10112yes—
536C24C2×D4×C10111yescharacteristic
537C24C2×D4×C10112yes—
538C24C2×D4×C10111yescharacteristic
539C24C2×D4×C10111yescharacteristic
540C24C24×C10111yescharacteristic
541#41—48no—
542#41—42no—
543#41—42no—
544C2×Q8—21no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—24no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—48no—
569C2×D4—48no—
570C2×D4—48no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—44no—
574C2×D4—44no—
575C2×D4—82no—
576C2×D4—82no—
577C2×D4#41×C10114yes—
578C22×C4—21no—
579C22×C4—24no—
580C22×C4—22no—
581C22×C4—28no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—24no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—24no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—41no—
593C22×C4—44no—
594C22×C4—48no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—41no—
599C22×C4—41no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C10112yes—
604C22×C4C2×D4×C10111yescharacteristic
605C22×C4C2×D4×C10111yescharacteristic
606C22×C4C2×D4×C10112yes—
607C22×C4C2×D4×C10112yes—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—22no—
611C4⋊C4—22no—
612C4⋊C4—48no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—24no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—44no—
628C22⋊C4—44no—
629C22⋊C4—48no—
630C22⋊C4—44no—
631C22⋊C4—42no—
632C22⋊C4—44no—
633C42—22no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—21no—
638C23—24no—
639C23—24no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—24no—
644C23—24no—
645C23—21no—
646C23—21no—
647C23—22no—
648C23—21no—
649C23—21no—
650C23—24no—
651C23—42no—
652C23—41no—
653C23—41no—
654C23—42no—
655C23—41no—
656C23—41no—
657C23—42no—
658C23—42no—
659C23—48no—
660C23—48no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—48no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—81no—
672C23—81no—
673C23—84no—
674C23—81no—
675C23—81no—
676C23#120×C10112yes—
677C23#120×C10111yescharacteristic
678C23#120×C10111yescharacteristic
679C23#123×C10112yescomplemented
680C23C22×D4×C10111yescharacteristic
681C23C22×D4×C10112yes—
682C23C2×#41×C10112yes—
683C23H(5,𝔽2)×C10112yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—44no—
691D4—44no—
692D4—42no—
693D4—42no—
694D4—44no—
695D4—44no—
696D4—82no—
697D4—82no—
698D4—82no—
699D4—82no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—24no—
703C2×C4—28no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—24no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—42no—
716C2×C4—44no—
717C2×C4—48no—
718C2×C4—42no—
719C2×C4—44no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—44no—
724C2×C4—42no—
725C2×C4—44no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—44no—
729C2×C4—81no—
730C2×C4—81no—
731C2×C4—84no—
732C2×C4#123×C10112yescomplemented
733C22—24no—
734C22—24no—
735C22—21no—
736C22—21no—
737C22—22no—
738C22—21no—
739C22—21no—
740C22—22no—
741C22—21no—
742C22—21no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—42no—
748C22—42no—
749C22—48no—
750C22—48no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—41no—
756C22—41no—
757C22—42no—
758C22—41no—
759C22—42no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—81no—
764C22—84no—
765C22—84no—
766C22—81no—
767C22—84no—
768C22—162no—
769C22B(4,𝔽2)×C10112yes—
770C22#458×C10112yes—
771C22C2×#120×C10111yescharacteristic
772C22C2×#123×C10111yescharacteristic
773C22#534×C10111yescharacteristic
774C22#546×C10114yes—
775C4—22no—
776C4—41no—
777C4—42no—
778C4—44no—
779C4—42no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C101×#240511yescharacteristic
793C2C2×B(4,𝔽2)×C10111yescharacteristic
794C2C2×#458×C10111yescharacteristic
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. C101×#2849C2semidirect
3. C2×#386×C101C2semidirect
4. C101×#2044C2semidirect
5. C101×#1898C2semidirect
6. C101×#1867C2semidirect
7. C101×#1790C2semidirect
8. C101×#1781C2semidirect
11. C24×C4×C101C22semidirect
25. C22×C22⋊C4×C101C22semidirect
27. C2×#99×C101C22semidirect
28. C2×#99×C101C22semidirect
33. #386×C101C22semidirect
34. #386×C101C22semidirect
36. #385×C101C22semidirect
38. #379×C101C22semidirect
40. #342×C101C22semidirect
281. C23×C101#123semidirect
334. C2×C4×C101#123semidirect
385. #24056C101direct (N × H)
399. #2849C2×C101semidirect
400. C2×#386C2×C101semidirect
401. #2044C2×C101semidirect
402. #1898C2×C101semidirect
403. #1867C2×C101semidirect
404. #1790C2×C101semidirect
405. #1781C2×C101semidirect
406. C101#24056direct (N × H)
409. C24×C4C22×C101semidirect
423. C22×C22⋊C4C22×C101semidirect
425. C2×#99C22×C101semidirect
426. C2×#99C22×C101semidirect
431. #386C22×C101semidirect
432. #386C22×C101semidirect
434. #385C22×C101semidirect
436. #379C22×C101semidirect
438. #342C22×C101semidirect
679. C23#123×C101semidirect
732. C2×C4#123×C101semidirect

Maximal subgroups

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

subgroupindex
C101×#34842
C101×#28492
C2×#386×C1012
C101×#20442
C101×#18982
C101×#18672
C101×#17902
C101×#17812
#24056101