Finite Group Databasebeta

← C113×#24056 #43292076

Subgroups — C113×#24056 #43292076

Order 28928.

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
1C113×#3484C211yesmaximal, characteristic
2C113×#2849C212yesmaximal, complemented
3C2×#386×C113C211yesmaximal, characteristic, complemented
4C113×#2044C214yesmaximal, complemented
5C113×#1898C212yesmaximal, complemented
6C113×#1867C212yesmaximal, complemented
7C113×#1790C212yesmaximal, complemented
8C113×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C113C2211yescharacteristic
10C23×D4×C113C2211yescharacteristic
11C24×C4×C113C2211yescharacteristic, complemented
12#546×C113—22no—
13#546×C113—22no—
14D42×C113—22no—
15D42×C113—22no—
16#535×C113—21no—
17#534×C113—21no—
18#534×C113C2212yes—
19#525×C113—21no—
20C2×#123×C113—22no—
21C2×#120×C113—21no—
22C2×#120×C113C2212yes—
23#518×C113C2211yescharacteristic
24C22×C22⋊C4×C113—21no—
25C22×C22⋊C4×C113C2211yescharacteristic, complemented
26C2×#99×C113C2212yes—
27C2×#99×C113C2212yescomplemented
28C2×#99×C113C2214yescomplemented
29#386×C113—21no—
30#386×C113—21no—
31#386×C113—22no—
32#386×C113C2212yes—
33#386×C113C2212yescomplemented
34#386×C113C2214yescomplemented
35#385×C113—22no—
36#385×C113C2214yescomplemented
37#381×C113—22no—
38#379×C113C2212yescomplemented
39C2×#95×C113—21no—
40#342×C113C2214yescomplemented
41C25×C113D411yescharacteristic
42C25×C113C2311yescharacteristic
43H(5,𝔽2)×C113—24no—
44H(5,𝔽2)×C113—42no—
45C2×#41×C113—21no—
46C2×#41×C113—22no—
47C22×D4×C113—21no—
48C22×D4×C113—22no—
49C22×D4×C113—22no—
50C22×D4×C113—22no—
51C22×D4×C113—21no—
52C22×D4×C113—21no—
53C22×D4×C113—24no—
54C22×D4×C113—42no—
55C22×D4×C113D411yescharacteristic
56C22×D4×C113D411yescharacteristic
57C22×D4×C113D412yes—
58C22×D4×C113D412yes—
59C22×D4×C113C2312yes—
60C22×D4×C113C2311yescharacteristic
61C22×D4×C113C2311yescharacteristic
62C23×C4×C113—21no—
63C23×C4×C113—22no—
64C23×C4×C113—21no—
65C23×C4×C113—22no—
66C23×C4×C113—21no—
67C23×C4×C113—44no—
68C23×C4×C113D411yescharacteristic
69C23×C4×C113C2312yes—
70#127×C113—22no—
71#124×C113—22no—
72#123×C113—22no—
73#123×C113—22no—
74#123×C113—22no—
75#123×C113—48no—
76C22⋊Q8×C113—21no—
77C22⋊Q8×C113—21no—
78#121×C113—21no—
79#121×C113—21no—
80#121×C113—22no—
81#121×C113—22no—
82#121×C113—22no—
83#121×C113—22no—
84#121×C113—22no—
85#121×C113—22no—
86#120×C113—22no—
87#120×C113—22no—
88#120×C113—22no—
89#120×C113—22no—
90#120×C113—22no—
91#120×C113—22no—
92#120×C113—22no—
93#120×C113—22no—
94#120×C113—22no—
95C4×D4×C113—22no—
96C4×D4×C113—22no—
97C4×D4×C113—22no—
98C4×D4×C113—22no—
99#117×C113—21no—
100C2×C4⋊C4×C113—24no—
101C2×C22⋊C4×C113—21no—
102C2×C22⋊C4×C113—21no—
103C2×C22⋊C4×C113—21no—
104C2×C22⋊C4×C113—22no—
105C2×C22⋊C4×C113—22no—
106C2×C22⋊C4×C113—21no—
107C2×C22⋊C4×C113—22no—
108C2×C22⋊C4×C113—24no—
109C2×C22⋊C4×C113—22no—
110C2×C22⋊C4×C113—42no—
111C2×C22⋊C4×C113—44no—
112C2×C22⋊C4×C113D412yes—
113C2×C22⋊C4×C113D412yes—
114C2×C22⋊C4×C113C2312yes—
115C2×C22⋊C4×C113C2314yes—
116C2×C22⋊C4×C113C2312yes—
117#99×C113—24no—
118#99×C113—42no—
119#99×C113—44no—
120#95×C113—22no—
121#95×C113—22no—
122#95×C113—24no—
123#95×C113—24no—
124C24×C113—22no—
125C24×C113—22no—
126C24×C113—21no—
127C24×C113—22no—
128C24×C113—21no—
129C24×C113—21no—
130C24×C113—42no—
131C24×C113—42no—
132C24×C113—41no—
133C24×C113—42no—
134C24×C113—42no—
135C24×C113C2×D411yescharacteristic
136C24×C113C2×D412yes—
137C24×C113C2×D412yes—
138C24×C113C2×D411yescharacteristic
139C24×C113C2×D412yes—
140C24×C113C2×D411yescharacteristic
141C24×C113C2×D411yescharacteristic
142C24×C113C2411yescharacteristic
143#41×C113—48no—
144#41×C113—42no—
145#41×C113—42no—
146C2×Q8×C113—21no—
147C2×D4×C113—22no—
148C2×D4×C113—22no—
149C2×D4×C113—22no—
150C2×D4×C113—21no—
151C2×D4×C113—22no—
152C2×D4×C113—22no—
153C2×D4×C113—22no—
154C2×D4×C113—22no—
155C2×D4×C113—22no—
156C2×D4×C113—22no—
157C2×D4×C113—22no—
158C2×D4×C113—22no—
159C2×D4×C113—22no—
160C2×D4×C113—24no—
161C2×D4×C113—22no—
162C2×D4×C113—24no—
163C2×D4×C113—22no—
164C2×D4×C113—22no—
165C2×D4×C113—22no—
166C2×D4×C113—22no—
167C2×D4×C113—22no—
168C2×D4×C113—41no—
169C2×D4×C113—41no—
170C2×D4×C113—48no—
171C2×D4×C113—48no—
172C2×D4×C113—48no—
173C2×D4×C113—42no—
174C2×D4×C113—42no—
175C2×D4×C113—44no—
176C2×D4×C113—44no—
177C2×D4×C113—82no—
178C2×D4×C113—82no—
179C2×D4×C113#4114yes—
180C22×C4×C113—21no—
181C22×C4×C113—24no—
182C22×C4×C113—22no—
183C22×C4×C113—28no—
184C22×C4×C113—21no—
185C22×C4×C113—21no—
186C22×C4×C113—22no—
187C22×C4×C113—24no—
188C22×C4×C113—21no—
189C22×C4×C113—21no—
190C22×C4×C113—22no—
191C22×C4×C113—24no—
192C22×C4×C113—22no—
193C22×C4×C113—44no—
194C22×C4×C113—41no—
195C22×C4×C113—44no—
196C22×C4×C113—48no—
197C22×C4×C113—42no—
198C22×C4×C113—44no—
199C22×C4×C113—42no—
200C22×C4×C113—41no—
201C22×C4×C113—41no—
202C22×C4×C113—42no—
203C22×C4×C113—42no—
204C22×C4×C113—42no—
205C22×C4×C113C2×D412yes—
206C22×C4×C113C2×D411yescharacteristic
207C22×C4×C113C2×D411yescharacteristic
208C22×C4×C113C2×D412yes—
209C22×C4×C113C2×D412yes—
210C4⋊C4×C113—21no—
211C4⋊C4×C113—21no—
212C4⋊C4×C113—22no—
213C4⋊C4×C113—22no—
214C4⋊C4×C113—48no—
215C22⋊C4×C113—22no—
216C22⋊C4×C113—22no—
217C22⋊C4×C113—22no—
218C22⋊C4×C113—22no—
219C22⋊C4×C113—22no—
220C22⋊C4×C113—22no—
221C22⋊C4×C113—22no—
222C22⋊C4×C113—22no—
223C22⋊C4×C113—22no—
224C22⋊C4×C113—22no—
225C22⋊C4×C113—22no—
226C22⋊C4×C113—24no—
227C22⋊C4×C113—24no—
228C22⋊C4×C113—24no—
229C22⋊C4×C113—44no—
230C22⋊C4×C113—44no—
231C22⋊C4×C113—48no—
232C22⋊C4×C113—44no—
233C22⋊C4×C113—42no—
234C22⋊C4×C113—44no—
235C42×C113—22no—
236C23×C113—21no—
237C23×C113—21no—
238C23×C113—22no—
239C23×C113—22no—
240C23×C113—21no—
241C23×C113—21no—
242C23×C113—21no—
243C23×C113—24no—
244C23×C113—24no—
245C23×C113—24no—
246C23×C113—24no—
247C23×C113—21no—
248C23×C113—21no—
249C23×C113—22no—
250C23×C113—21no—
251C23×C113—21no—
252C23×C113—24no—
253C23×C113—42no—
254C23×C113—41no—
255C23×C113—41no—
256C23×C113—42no—
257C23×C113—41no—
258C23×C113—41no—
259C23×C113—42no—
260C23×C113—42no—
261C23×C113—48no—
262C23×C113—48no—
263C23×C113—41no—
264C23×C113—41no—
265C23×C113—41no—
266C23×C113—41no—
267C23×C113—48no—
268C23×C113—42no—
269C23×C113—42no—
270C23×C113—42no—
271C23×C113—42no—
272C23×C113—42no—
273C23×C113—81no—
274C23×C113—81no—
275C23×C113—84no—
276C23×C113—81no—
277C23×C113—81no—
278C23×C113#12012yes—
279C23×C113#12011yescharacteristic
280C23×C113#12011yescharacteristic
281C23×C113#12312yescomplemented
282C23×C113C22×D411yescharacteristic
283C23×C113C22×D412yes—
284C23×C113C2×#4112yes—
285C23×C113H(5,𝔽2)12yes—
286Q8×C113—42no—
287D4×C113—28no—
288D4×C113—44no—
289D4×C113—42no—
290D4×C113—44no—
291D4×C113—44no—
292D4×C113—42no—
293D4×C113—42no—
294D4×C113—44no—
295D4×C113—44no—
296D4×C113—44no—
297D4×C113—44no—
298D4×C113—82no—
299D4×C113—82no—
300D4×C113—82no—
301D4×C113—82no—
302C2×C4×C113—21no—
303C2×C4×C113—21no—
304C2×C4×C113—24no—
305C2×C4×C113—28no—
306C2×C4×C113—22no—
307C2×C4×C113—22no—
308C2×C4×C113—22no—
309C2×C4×C113—21no—
310C2×C4×C113—21no—
311C2×C4×C113—21no—
312C2×C4×C113—24no—
313C2×C4×C113—42no—
314C2×C4×C113—42no—
315C2×C4×C113—44no—
316C2×C4×C113—44no—
317C2×C4×C113—42no—
318C2×C4×C113—44no—
319C2×C4×C113—48no—
320C2×C4×C113—42no—
321C2×C4×C113—42no—
322C2×C4×C113—44no—
323C2×C4×C113—42no—
324C2×C4×C113—42no—
325C2×C4×C113—44no—
326C2×C4×C113—42no—
327C2×C4×C113—44no—
328C2×C4×C113—42no—
329C2×C4×C113—42no—
330C2×C4×C113—44no—
331C2×C4×C113—81no—
332C2×C4×C113—81no—
333C2×C4×C113—84no—
334C2×C4×C113#12312yescomplemented
335C22×C113—24no—
336C22×C113—24no—
337C22×C113—21no—
338C22×C113—21no—
339C22×C113—22no—
340C22×C113—21no—
341C22×C113—21no—
342C22×C113—22no—
343C22×C113—21no—
344C22×C113—21no—
345C22×C113—22no—
346C22×C113—22no—
347C22×C113—22no—
348C22×C113—22no—
349C22×C113—42no—
350C22×C113—42no—
351C22×C113—48no—
352C22×C113—48no—
353C22×C113—42no—
354C22×C113—42no—
355C22×C113—42no—
356C22×C113—42no—
357C22×C113—41no—
358C22×C113—41no—
359C22×C113—42no—
360C22×C113—41no—
361C22×C113—42no—
362C22×C113—41no—
363C22×C113—42no—
364C22×C113—41no—
365C22×C113—81no—
366C22×C113—84no—
367C22×C113—84no—
368C22×C113—84no—
369C22×C113—81no—
370C22×C113—162no—
371C22×C113B(4,𝔽2)12yes—
372C22×C113#45812yes—
373C22×C113C2×#12011yescharacteristic
374C22×C113C2×#12311yescharacteristic
375C22×C113#53411yescharacteristic
376C22×C113#54614yes—
377C4×C113—22no—
378C4×C113—41no—
379C4×C113—42no—
380C4×C113—44no—
381C4×C113—42no—
382C4×C113—42no—
383C4×C113—84no—
384C4×C113—82no—
385#24056C11311yesmaximal, characteristic, direct product factor, Sylow
386C2×C113—21no—
387C2×C113—24no—
388C2×C113—21no—
389C2×C113—22no—
390C2×C113—22no—
391C2×C113—42no—
392C2×C113—42no—
393C2×C113—81no—
394C2×C113—82no—
395C2×C113#240511yescharacteristic
396C2×C113C2×B(4,𝔽2)11yescharacteristic
397C2×C113C2×#45811yescharacteristic
398#3484C2×C11311yescharacteristic
399#2849C2×C11312yescomplemented
400C2×#386C2×C11311yescharacteristic, complemented
401#2044C2×C11314yescomplemented
402#1898C2×C11312yescomplemented
403#1867C2×C11312yescomplemented
404#1790C2×C11312yescomplemented
405#1781C2×C11311yescharacteristic, complemented
406C113#2405611yescharacteristic, direct product factor, Sylow
407C2×H(5,𝔽2)C22×C11311yescharacteristic
408C23×D4C22×C11311yescharacteristic
409C24×C4C22×C11311yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C11312yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C11312yes—
421#518C22×C11311yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C11311yescharacteristic, complemented
424C2×#99C22×C11312yes—
425C2×#99C22×C11314yescomplemented
426C2×#99C22×C11312yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C11312yes—
431#386C22×C11314yescomplemented
432#386C22×C11312yescomplemented
433#385—22no—
434#385C22×C11314yescomplemented
435#381—22no—
436#379C22×C11312yescomplemented
437C2×#95—21no—
438#342C22×C11314yescomplemented
439C25D4×C11311yescharacteristic
440C25C23×C11311yescharacteristic
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×C11311yescharacteristic
454C22×D4D4×C11311yescharacteristic
455C22×D4D4×C11312yes—
456C22×D4D4×C11312yes—
457C22×D4C23×C11312yes—
458C22×D4C23×C11311yescharacteristic
459C22×D4C23×C11311yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C11311yescharacteristic
467C23×C4C23×C11312yes—
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×C11312yes—
511C2×C22⋊C4D4×C11312yes—
512C2×C22⋊C4C23×C11312yes—
513C2×C22⋊C4C23×C11314yes—
514C2×C22⋊C4C23×C11312yes—
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×C11311yescharacteristic
534C24C2×D4×C11312yes—
535C24C2×D4×C11312yes—
536C24C2×D4×C11311yescharacteristic
537C24C2×D4×C11312yes—
538C24C2×D4×C11311yescharacteristic
539C24C2×D4×C11311yescharacteristic
540C24C24×C11311yescharacteristic
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×C11314yes—
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×C11312yes—
604C22×C4C2×D4×C11311yescharacteristic
605C22×C4C2×D4×C11311yescharacteristic
606C22×C4C2×D4×C11312yes—
607C22×C4C2×D4×C11312yes—
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—42no—
631C22⋊C4—44no—
632C22⋊C4—44no—
633C42—22no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—24no—
642C23—24no—
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×C11312yes—
677C23#120×C11311yescharacteristic
678C23#120×C11311yescharacteristic
679C23#123×C11312yescomplemented
680C23C22×D4×C11311yescharacteristic
681C23C22×D4×C11312yes—
682C23C2×#41×C11312yes—
683C23H(5,𝔽2)×C11312yes—
684Q8—42no—
685D4—28no—
686D4—44no—
687D4—42no—
688D4—44no—
689D4—44no—
690D4—42no—
691D4—42no—
692D4—44no—
693D4—44no—
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—42no—
720C2×C4—44no—
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×C11312yescomplemented
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)×C11312yes—
770C22#458×C11312yes—
771C22C2×#120×C11311yescharacteristic
772C22C2×#123×C11311yescharacteristic
773C22#534×C11311yescharacteristic
774C22#546×C11314yes—
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—
792C2C113×#240511yescharacteristic
793C2C2×B(4,𝔽2)×C11311yescharacteristic
794C2C2×#458×C11311yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
prime radicalC113×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2849C2semidirect
3. C2×#386×C113C2semidirect
4. C113×#2044C2semidirect
5. C113×#1898C2semidirect
6. C113×#1867C2semidirect
7. C113×#1790C2semidirect
8. C113×#1781C2semidirect
11. C24×C4×C113C22semidirect
25. C22×C22⋊C4×C113C22semidirect
27. C2×#99×C113C22semidirect
28. C2×#99×C113C22semidirect
33. #386×C113C22semidirect
34. #386×C113C22semidirect
36. #385×C113C22semidirect
38. #379×C113C22semidirect
40. #342×C113C22semidirect
281. C23×C113#123semidirect
334. C2×C4×C113#123semidirect
385. #24056C113direct (N × H)
399. #2849C2×C113semidirect
400. C2×#386C2×C113semidirect
401. #2044C2×C113semidirect
402. #1898C2×C113semidirect
403. #1867C2×C113semidirect
404. #1790C2×C113semidirect
405. #1781C2×C113semidirect
406. C113#24056direct (N × H)
409. C24×C4C22×C113semidirect
423. C22×C22⋊C4C22×C113semidirect
425. C2×#99C22×C113semidirect
426. C2×#99C22×C113semidirect
431. #386C22×C113semidirect
432. #386C22×C113semidirect
434. #385C22×C113semidirect
436. #379C22×C113semidirect
438. #342C22×C113semidirect
679. C23#123×C113semidirect
732. C2×C4#123×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C113×#28492
C2×#386×C1132
C113×#20442
C113×#18982
C113×#18672
C113×#17902
C113×#17812
#24056113