Finite Group Databasebeta

← C109×#24056 #42142050

Subgroups — C109×#24056 #42142050

Order 27904.

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
1C109×#3484C211yesmaximal, characteristic
2C109×#2849C212yesmaximal, complemented
3C2×#386×C109C211yesmaximal, characteristic, complemented
4C109×#2044C214yesmaximal, complemented
5C109×#1898C212yesmaximal, complemented
6C109×#1867C212yesmaximal, complemented
7C109×#1790C212yesmaximal, complemented
8C109×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C109C2211yescharacteristic
10C23×D4×C109C2211yescharacteristic
11C24×C4×C109C2211yescharacteristic, complemented
12#546×C109—22no—
13#546×C109—22no—
14D42×C109—22no—
15D42×C109—22no—
16#535×C109—21no—
17#534×C109—21no—
18#534×C109C2212yes—
19#525×C109—21no—
20C2×#123×C109—22no—
21C2×#120×C109—21no—
22C2×#120×C109C2212yes—
23#518×C109C2211yescharacteristic
24C22×C22⋊C4×C109—21no—
25C22×C22⋊C4×C109C2211yescharacteristic, complemented
26C2×#99×C109C2212yes—
27C2×#99×C109C2212yescomplemented
28C2×#99×C109C2214yescomplemented
29#386×C109—21no—
30#386×C109—21no—
31#386×C109—22no—
32#386×C109C2212yes—
33#386×C109C2212yescomplemented
34#386×C109C2214yescomplemented
35#385×C109—22no—
36#385×C109C2214yescomplemented
37#381×C109—22no—
38#379×C109C2212yescomplemented
39C2×#95×C109—21no—
40#342×C109C2214yescomplemented
41C25×C109D411yescharacteristic
42C25×C109C2311yescharacteristic
43H(5,𝔽2)×C109—24no—
44H(5,𝔽2)×C109—42no—
45C2×#41×C109—21no—
46C2×#41×C109—22no—
47C22×D4×C109—21no—
48C22×D4×C109—22no—
49C22×D4×C109—22no—
50C22×D4×C109—22no—
51C22×D4×C109—21no—
52C22×D4×C109—21no—
53C22×D4×C109—24no—
54C22×D4×C109—42no—
55C22×D4×C109D411yescharacteristic
56C22×D4×C109D411yescharacteristic
57C22×D4×C109D412yes—
58C22×D4×C109D412yes—
59C22×D4×C109C2312yes—
60C22×D4×C109C2311yescharacteristic
61C22×D4×C109C2311yescharacteristic
62C23×C4×C109—21no—
63C23×C4×C109—22no—
64C23×C4×C109—21no—
65C23×C4×C109—22no—
66C23×C4×C109—21no—
67C23×C4×C109—44no—
68C23×C4×C109D411yescharacteristic
69C23×C4×C109C2312yes—
70#127×C109—22no—
71#124×C109—22no—
72#123×C109—22no—
73#123×C109—22no—
74#123×C109—22no—
75#123×C109—48no—
76C22⋊Q8×C109—21no—
77C22⋊Q8×C109—21no—
78#121×C109—21no—
79#121×C109—21no—
80#121×C109—22no—
81#121×C109—22no—
82#121×C109—22no—
83#121×C109—22no—
84#121×C109—22no—
85#121×C109—22no—
86#120×C109—22no—
87#120×C109—22no—
88#120×C109—22no—
89#120×C109—22no—
90#120×C109—22no—
91#120×C109—22no—
92#120×C109—22no—
93#120×C109—22no—
94#120×C109—22no—
95C4×D4×C109—22no—
96C4×D4×C109—22no—
97C4×D4×C109—22no—
98C4×D4×C109—22no—
99#117×C109—21no—
100C2×C4⋊C4×C109—24no—
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—22no—
105C2×C22⋊C4×C109—22no—
106C2×C22⋊C4×C109—21no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—24no—
109C2×C22⋊C4×C109—22no—
110C2×C22⋊C4×C109—42no—
111C2×C22⋊C4×C109—44no—
112C2×C22⋊C4×C109D412yes—
113C2×C22⋊C4×C109D412yes—
114C2×C22⋊C4×C109C2312yes—
115C2×C22⋊C4×C109C2314yes—
116C2×C22⋊C4×C109C2312yes—
117#99×C109—24no—
118#99×C109—42no—
119#99×C109—44no—
120#95×C109—22no—
121#95×C109—22no—
122#95×C109—24no—
123#95×C109—24no—
124C24×C109—22no—
125C24×C109—22no—
126C24×C109—21no—
127C24×C109—22no—
128C24×C109—21no—
129C24×C109—21no—
130C24×C109—42no—
131C24×C109—42no—
132C24×C109—41no—
133C24×C109—42no—
134C24×C109—42no—
135C24×C109C2×D411yescharacteristic
136C24×C109C2×D412yes—
137C24×C109C2×D412yes—
138C24×C109C2×D411yescharacteristic
139C24×C109C2×D412yes—
140C24×C109C2×D411yescharacteristic
141C24×C109C2×D411yescharacteristic
142C24×C109C2411yescharacteristic
143#41×C109—48no—
144#41×C109—42no—
145#41×C109—42no—
146C2×Q8×C109—21no—
147C2×D4×C109—22no—
148C2×D4×C109—22no—
149C2×D4×C109—22no—
150C2×D4×C109—21no—
151C2×D4×C109—22no—
152C2×D4×C109—22no—
153C2×D4×C109—22no—
154C2×D4×C109—22no—
155C2×D4×C109—22no—
156C2×D4×C109—22no—
157C2×D4×C109—22no—
158C2×D4×C109—22no—
159C2×D4×C109—22no—
160C2×D4×C109—24no—
161C2×D4×C109—22no—
162C2×D4×C109—24no—
163C2×D4×C109—22no—
164C2×D4×C109—22no—
165C2×D4×C109—22no—
166C2×D4×C109—22no—
167C2×D4×C109—22no—
168C2×D4×C109—41no—
169C2×D4×C109—41no—
170C2×D4×C109—48no—
171C2×D4×C109—48no—
172C2×D4×C109—48no—
173C2×D4×C109—42no—
174C2×D4×C109—42no—
175C2×D4×C109—44no—
176C2×D4×C109—44no—
177C2×D4×C109—82no—
178C2×D4×C109—82no—
179C2×D4×C109#4114yes—
180C22×C4×C109—21no—
181C22×C4×C109—24no—
182C22×C4×C109—22no—
183C22×C4×C109—28no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—22no—
187C22×C4×C109—24no—
188C22×C4×C109—21no—
189C22×C4×C109—21no—
190C22×C4×C109—22no—
191C22×C4×C109—24no—
192C22×C4×C109—22no—
193C22×C4×C109—44no—
194C22×C4×C109—41no—
195C22×C4×C109—44no—
196C22×C4×C109—48no—
197C22×C4×C109—42no—
198C22×C4×C109—44no—
199C22×C4×C109—42no—
200C22×C4×C109—41no—
201C22×C4×C109—41no—
202C22×C4×C109—42no—
203C22×C4×C109—42no—
204C22×C4×C109—42no—
205C22×C4×C109C2×D412yes—
206C22×C4×C109C2×D411yescharacteristic
207C22×C4×C109C2×D411yescharacteristic
208C22×C4×C109C2×D412yes—
209C22×C4×C109C2×D412yes—
210C4⋊C4×C109—21no—
211C4⋊C4×C109—21no—
212C4⋊C4×C109—22no—
213C4⋊C4×C109—22no—
214C4⋊C4×C109—48no—
215C22⋊C4×C109—22no—
216C22⋊C4×C109—22no—
217C22⋊C4×C109—22no—
218C22⋊C4×C109—22no—
219C22⋊C4×C109—22no—
220C22⋊C4×C109—22no—
221C22⋊C4×C109—22no—
222C22⋊C4×C109—22no—
223C22⋊C4×C109—22no—
224C22⋊C4×C109—22no—
225C22⋊C4×C109—22no—
226C22⋊C4×C109—24no—
227C22⋊C4×C109—24no—
228C22⋊C4×C109—24no—
229C22⋊C4×C109—44no—
230C22⋊C4×C109—44no—
231C22⋊C4×C109—48no—
232C22⋊C4×C109—44no—
233C22⋊C4×C109—42no—
234C22⋊C4×C109—44no—
235C42×C109—22no—
236C23×C109—21no—
237C23×C109—21no—
238C23×C109—22no—
239C23×C109—22no—
240C23×C109—21no—
241C23×C109—21no—
242C23×C109—21no—
243C23×C109—24no—
244C23×C109—24no—
245C23×C109—24no—
246C23×C109—24no—
247C23×C109—21no—
248C23×C109—21no—
249C23×C109—22no—
250C23×C109—21no—
251C23×C109—21no—
252C23×C109—24no—
253C23×C109—42no—
254C23×C109—41no—
255C23×C109—41no—
256C23×C109—42no—
257C23×C109—41no—
258C23×C109—41no—
259C23×C109—42no—
260C23×C109—42no—
261C23×C109—48no—
262C23×C109—48no—
263C23×C109—41no—
264C23×C109—41no—
265C23×C109—41no—
266C23×C109—41no—
267C23×C109—48no—
268C23×C109—42no—
269C23×C109—42no—
270C23×C109—42no—
271C23×C109—42no—
272C23×C109—42no—
273C23×C109—81no—
274C23×C109—81no—
275C23×C109—84no—
276C23×C109—81no—
277C23×C109—81no—
278C23×C109#12012yes—
279C23×C109#12011yescharacteristic
280C23×C109#12011yescharacteristic
281C23×C109#12312yescomplemented
282C23×C109C22×D411yescharacteristic
283C23×C109C22×D412yes—
284C23×C109C2×#4112yes—
285C23×C109H(5,𝔽2)12yes—
286Q8×C109—42no—
287D4×C109—28no—
288D4×C109—44no—
289D4×C109—42no—
290D4×C109—44no—
291D4×C109—44no—
292D4×C109—42no—
293D4×C109—42no—
294D4×C109—44no—
295D4×C109—44no—
296D4×C109—44no—
297D4×C109—44no—
298D4×C109—82no—
299D4×C109—82no—
300D4×C109—82no—
301D4×C109—82no—
302C2×C4×C109—21no—
303C2×C4×C109—21no—
304C2×C4×C109—24no—
305C2×C4×C109—28no—
306C2×C4×C109—22no—
307C2×C4×C109—22no—
308C2×C4×C109—22no—
309C2×C4×C109—21no—
310C2×C4×C109—21no—
311C2×C4×C109—21no—
312C2×C4×C109—24no—
313C2×C4×C109—42no—
314C2×C4×C109—42no—
315C2×C4×C109—44no—
316C2×C4×C109—44no—
317C2×C4×C109—42no—
318C2×C4×C109—44no—
319C2×C4×C109—48no—
320C2×C4×C109—42no—
321C2×C4×C109—42no—
322C2×C4×C109—44no—
323C2×C4×C109—42no—
324C2×C4×C109—42no—
325C2×C4×C109—44no—
326C2×C4×C109—42no—
327C2×C4×C109—44no—
328C2×C4×C109—42no—
329C2×C4×C109—42no—
330C2×C4×C109—44no—
331C2×C4×C109—81no—
332C2×C4×C109—81no—
333C2×C4×C109—84no—
334C2×C4×C109#12312yescomplemented
335C22×C109—24no—
336C22×C109—24no—
337C22×C109—21no—
338C22×C109—21no—
339C22×C109—22no—
340C22×C109—21no—
341C22×C109—21no—
342C22×C109—22no—
343C22×C109—21no—
344C22×C109—21no—
345C22×C109—22no—
346C22×C109—22no—
347C22×C109—22no—
348C22×C109—22no—
349C22×C109—42no—
350C22×C109—42no—
351C22×C109—48no—
352C22×C109—48no—
353C22×C109—42no—
354C22×C109—42no—
355C22×C109—42no—
356C22×C109—42no—
357C22×C109—41no—
358C22×C109—41no—
359C22×C109—42no—
360C22×C109—41no—
361C22×C109—42no—
362C22×C109—41no—
363C22×C109—42no—
364C22×C109—41no—
365C22×C109—81no—
366C22×C109—84no—
367C22×C109—84no—
368C22×C109—84no—
369C22×C109—81no—
370C22×C109—162no—
371C22×C109B(4,𝔽2)12yes—
372C22×C109#45812yes—
373C22×C109C2×#12011yescharacteristic
374C22×C109C2×#12311yescharacteristic
375C22×C109#53411yescharacteristic
376C22×C109#54614yes—
377C4×C109—22no—
378C4×C109—41no—
379C4×C109—42no—
380C4×C109—44no—
381C4×C109—42no—
382C4×C109—42no—
383C4×C109—84no—
384C4×C109—82no—
385#24056C10911yesmaximal, characteristic, direct product factor, Sylow
386C2×C109—21no—
387C2×C109—24no—
388C2×C109—21no—
389C2×C109—22no—
390C2×C109—22no—
391C2×C109—42no—
392C2×C109—42no—
393C2×C109—81no—
394C2×C109—82no—
395C2×C109#240511yescharacteristic
396C2×C109C2×B(4,𝔽2)11yescharacteristic
397C2×C109C2×#45811yescharacteristic
398#3484C2×C10911yescharacteristic
399#2849C2×C10912yescomplemented
400C2×#386C2×C10911yescharacteristic, complemented
401#2044C2×C10914yescomplemented
402#1898C2×C10912yescomplemented
403#1867C2×C10912yescomplemented
404#1790C2×C10912yescomplemented
405#1781C2×C10911yescharacteristic, complemented
406C109#2405611yescharacteristic, direct product factor, Sylow
407C2×H(5,𝔽2)C22×C10911yescharacteristic
408C23×D4C22×C10911yescharacteristic
409C24×C4C22×C10911yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C10912yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C10912yes—
421#518C22×C10911yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C10911yescharacteristic, complemented
424C2×#99C22×C10912yes—
425C2×#99C22×C10914yescomplemented
426C2×#99C22×C10912yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C10912yes—
431#386C22×C10914yescomplemented
432#386C22×C10912yescomplemented
433#385—22no—
434#385C22×C10914yescomplemented
435#381—22no—
436#379C22×C10912yescomplemented
437C2×#95—21no—
438#342C22×C10914yescomplemented
439C25D4×C10911yescharacteristic
440C25C23×C10911yescharacteristic
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×C10911yescharacteristic
454C22×D4D4×C10911yescharacteristic
455C22×D4D4×C10912yes—
456C22×D4D4×C10912yes—
457C22×D4C23×C10912yes—
458C22×D4C23×C10911yescharacteristic
459C22×D4C23×C10911yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C10911yescharacteristic
467C23×C4C23×C10912yes—
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×C10912yes—
511C2×C22⋊C4D4×C10912yes—
512C2×C22⋊C4C23×C10912yes—
513C2×C22⋊C4C23×C10914yes—
514C2×C22⋊C4C23×C10912yes—
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×C10911yescharacteristic
534C24C2×D4×C10912yes—
535C24C2×D4×C10912yes—
536C24C2×D4×C10911yescharacteristic
537C24C2×D4×C10912yes—
538C24C2×D4×C10911yescharacteristic
539C24C2×D4×C10911yescharacteristic
540C24C24×C10911yescharacteristic
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×C10914yes—
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×C10912yes—
604C22×C4C2×D4×C10911yescharacteristic
605C22×C4C2×D4×C10911yescharacteristic
606C22×C4C2×D4×C10912yes—
607C22×C4C2×D4×C10912yes—
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—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×C10912yes—
677C23#120×C10911yescharacteristic
678C23#120×C10911yescharacteristic
679C23#123×C10912yescomplemented
680C23C22×D4×C10911yescharacteristic
681C23C22×D4×C10912yes—
682C23C2×#41×C10912yes—
683C23H(5,𝔽2)×C10912yes—
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×C10912yescomplemented
733C22—24no—
734C22—24no—
735C22—22no—
736C22—21no—
737C22—21no—
738C22—22no—
739C22—21no—
740C22—21no—
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)×C10912yes—
770C22#458×C10912yes—
771C22C2×#120×C10911yescharacteristic
772C22C2×#123×C10911yescharacteristic
773C22#534×C10911yescharacteristic
774C22#546×C10914yes—
775C4—22no—
776C4—44no—
777C4—42no—
778C4—42no—
779C4—41no—
780C4—42no—
781C4—82no—
782C4—84no—
783C2—21no—
784C2—24no—
785C2—21no—
786C2—22no—
787C2—22no—
788C2—42no—
789C2—42no—
790C2—81no—
791C2—82no—
792C2C109×#240511yescharacteristic
793C2C2×B(4,𝔽2)×C10911yescharacteristic
794C2C2×#458×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC24C24×C109
prime radicalC109×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C25×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#2849C2semidirect
3. C2×#386×C109C2semidirect
4. C109×#2044C2semidirect
5. C109×#1898C2semidirect
6. C109×#1867C2semidirect
7. C109×#1790C2semidirect
8. C109×#1781C2semidirect
11. C24×C4×C109C22semidirect
25. C22×C22⋊C4×C109C22semidirect
27. C2×#99×C109C22semidirect
28. C2×#99×C109C22semidirect
33. #386×C109C22semidirect
34. #386×C109C22semidirect
36. #385×C109C22semidirect
38. #379×C109C22semidirect
40. #342×C109C22semidirect
281. C23×C109#123semidirect
334. C2×C4×C109#123semidirect
385. #24056C109direct (N × H)
399. #2849C2×C109semidirect
400. C2×#386C2×C109semidirect
401. #2044C2×C109semidirect
402. #1898C2×C109semidirect
403. #1867C2×C109semidirect
404. #1790C2×C109semidirect
405. #1781C2×C109semidirect
406. C109#24056direct (N × H)
409. C24×C4C22×C109semidirect
423. C22×C22⋊C4C22×C109semidirect
425. C2×#99C22×C109semidirect
426. C2×#99C22×C109semidirect
431. #386C22×C109semidirect
432. #386C22×C109semidirect
434. #385C22×C109semidirect
436. #379C22×C109semidirect
438. #342C22×C109semidirect
679. C23#123×C109semidirect
732. C2×C4#123×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#34842
C109×#28492
C2×#386×C1092
C109×#20442
C109×#18982
C109×#18672
C109×#17902
C109×#17812
#24056109