Finite Group Databasebeta

← C107×#24056 #41050020

Subgroups — C107×#24056 #41050020

Order 27392.

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
1C107×#3484C211yesmaximal, characteristic
2C107×#2849C212yesmaximal, complemented
3C2×#386×C107C211yesmaximal, characteristic, complemented
4C107×#2044C214yesmaximal, complemented
5C107×#1898C212yesmaximal, complemented
6C107×#1867C212yesmaximal, complemented
7C107×#1790C212yesmaximal, complemented
8C107×#1781C211yesmaximal, characteristic, complemented
9C2×H(5,𝔽2)×C107C2211yescharacteristic
10C23×D4×C107C2211yescharacteristic
11C24×C4×C107C2211yescharacteristic, complemented
12#546×C107—22no—
13#546×C107—22no—
14D42×C107—22no—
15D42×C107—22no—
16#535×C107—21no—
17#534×C107—21no—
18#534×C107C2212yes—
19#525×C107—21no—
20C2×#123×C107—22no—
21C2×#120×C107—21no—
22C2×#120×C107C2212yes—
23#518×C107C2211yescharacteristic
24C22×C22⋊C4×C107—21no—
25C22×C22⋊C4×C107C2211yescharacteristic, complemented
26C2×#99×C107C2212yes—
27C2×#99×C107C2214yescomplemented
28C2×#99×C107C2212yescomplemented
29#386×C107—21no—
30#386×C107—21no—
31#386×C107—22no—
32#386×C107C2212yes—
33#386×C107C2212yescomplemented
34#386×C107C2214yescomplemented
35#385×C107—22no—
36#385×C107C2214yescomplemented
37#381×C107—22no—
38#379×C107C2212yescomplemented
39C2×#95×C107—21no—
40#342×C107C2214yescomplemented
41C25×C107D411yescharacteristic
42C25×C107C2311yescharacteristic
43H(5,𝔽2)×C107—24no—
44H(5,𝔽2)×C107—42no—
45C2×#41×C107—21no—
46C2×#41×C107—22no—
47C22×D4×C107—21no—
48C22×D4×C107—22no—
49C22×D4×C107—22no—
50C22×D4×C107—22no—
51C22×D4×C107—21no—
52C22×D4×C107—21no—
53C22×D4×C107—24no—
54C22×D4×C107—42no—
55C22×D4×C107D411yescharacteristic
56C22×D4×C107D411yescharacteristic
57C22×D4×C107D412yes—
58C22×D4×C107D412yes—
59C22×D4×C107C2312yes—
60C22×D4×C107C2311yescharacteristic
61C22×D4×C107C2311yescharacteristic
62C23×C4×C107—21no—
63C23×C4×C107—22no—
64C23×C4×C107—21no—
65C23×C4×C107—22no—
66C23×C4×C107—21no—
67C23×C4×C107—44no—
68C23×C4×C107D411yescharacteristic
69C23×C4×C107C2312yes—
70#127×C107—22no—
71#124×C107—22no—
72#123×C107—22no—
73#123×C107—22no—
74#123×C107—22no—
75#123×C107—48no—
76C22⋊Q8×C107—21no—
77C22⋊Q8×C107—21no—
78#121×C107—21no—
79#121×C107—21no—
80#121×C107—22no—
81#121×C107—22no—
82#121×C107—22no—
83#121×C107—22no—
84#121×C107—22no—
85#121×C107—22no—
86#120×C107—22no—
87#120×C107—22no—
88#120×C107—22no—
89#120×C107—22no—
90#120×C107—22no—
91#120×C107—22no—
92#120×C107—22no—
93#120×C107—22no—
94#120×C107—22no—
95C4×D4×C107—22no—
96C4×D4×C107—22no—
97C4×D4×C107—22no—
98C4×D4×C107—22no—
99#117×C107—21no—
100C2×C4⋊C4×C107—24no—
101C2×C22⋊C4×C107—21no—
102C2×C22⋊C4×C107—21no—
103C2×C22⋊C4×C107—21no—
104C2×C22⋊C4×C107—22no—
105C2×C22⋊C4×C107—22no—
106C2×C22⋊C4×C107—21no—
107C2×C22⋊C4×C107—22no—
108C2×C22⋊C4×C107—22no—
109C2×C22⋊C4×C107—24no—
110C2×C22⋊C4×C107—42no—
111C2×C22⋊C4×C107—44no—
112C2×C22⋊C4×C107D412yes—
113C2×C22⋊C4×C107D412yes—
114C2×C22⋊C4×C107C2312yes—
115C2×C22⋊C4×C107C2314yes—
116C2×C22⋊C4×C107C2312yes—
117#99×C107—24no—
118#99×C107—42no—
119#99×C107—44no—
120#95×C107—22no—
121#95×C107—22no—
122#95×C107—24no—
123#95×C107—24no—
124C24×C107—22no—
125C24×C107—22no—
126C24×C107—21no—
127C24×C107—22no—
128C24×C107—21no—
129C24×C107—21no—
130C24×C107—42no—
131C24×C107—42no—
132C24×C107—41no—
133C24×C107—42no—
134C24×C107—42no—
135C24×C107C2×D411yescharacteristic
136C24×C107C2×D412yes—
137C24×C107C2×D412yes—
138C24×C107C2×D411yescharacteristic
139C24×C107C2×D412yes—
140C24×C107C2×D411yescharacteristic
141C24×C107C2×D411yescharacteristic
142C24×C107C2411yescharacteristic
143#41×C107—48no—
144#41×C107—42no—
145#41×C107—42no—
146C2×Q8×C107—21no—
147C2×D4×C107—22no—
148C2×D4×C107—22no—
149C2×D4×C107—22no—
150C2×D4×C107—21no—
151C2×D4×C107—22no—
152C2×D4×C107—22no—
153C2×D4×C107—22no—
154C2×D4×C107—22no—
155C2×D4×C107—22no—
156C2×D4×C107—22no—
157C2×D4×C107—22no—
158C2×D4×C107—22no—
159C2×D4×C107—22no—
160C2×D4×C107—24no—
161C2×D4×C107—22no—
162C2×D4×C107—24no—
163C2×D4×C107—22no—
164C2×D4×C107—22no—
165C2×D4×C107—22no—
166C2×D4×C107—22no—
167C2×D4×C107—22no—
168C2×D4×C107—41no—
169C2×D4×C107—41no—
170C2×D4×C107—48no—
171C2×D4×C107—48no—
172C2×D4×C107—48no—
173C2×D4×C107—42no—
174C2×D4×C107—42no—
175C2×D4×C107—44no—
176C2×D4×C107—44no—
177C2×D4×C107—82no—
178C2×D4×C107—82no—
179C2×D4×C107#4114yes—
180C22×C4×C107—21no—
181C22×C4×C107—24no—
182C22×C4×C107—22no—
183C22×C4×C107—28no—
184C22×C4×C107—21no—
185C22×C4×C107—21no—
186C22×C4×C107—22no—
187C22×C4×C107—24no—
188C22×C4×C107—21no—
189C22×C4×C107—21no—
190C22×C4×C107—22no—
191C22×C4×C107—24no—
192C22×C4×C107—22no—
193C22×C4×C107—44no—
194C22×C4×C107—41no—
195C22×C4×C107—44no—
196C22×C4×C107—48no—
197C22×C4×C107—42no—
198C22×C4×C107—44no—
199C22×C4×C107—42no—
200C22×C4×C107—41no—
201C22×C4×C107—41no—
202C22×C4×C107—42no—
203C22×C4×C107—42no—
204C22×C4×C107—42no—
205C22×C4×C107C2×D412yes—
206C22×C4×C107C2×D411yescharacteristic
207C22×C4×C107C2×D411yescharacteristic
208C22×C4×C107C2×D412yes—
209C22×C4×C107C2×D412yes—
210C4⋊C4×C107—21no—
211C4⋊C4×C107—21no—
212C4⋊C4×C107—22no—
213C4⋊C4×C107—22no—
214C4⋊C4×C107—48no—
215C22⋊C4×C107—22no—
216C22⋊C4×C107—22no—
217C22⋊C4×C107—22no—
218C22⋊C4×C107—22no—
219C22⋊C4×C107—22no—
220C22⋊C4×C107—22no—
221C22⋊C4×C107—22no—
222C22⋊C4×C107—22no—
223C22⋊C4×C107—22no—
224C22⋊C4×C107—22no—
225C22⋊C4×C107—22no—
226C22⋊C4×C107—24no—
227C22⋊C4×C107—24no—
228C22⋊C4×C107—24no—
229C22⋊C4×C107—44no—
230C22⋊C4×C107—44no—
231C22⋊C4×C107—48no—
232C22⋊C4×C107—44no—
233C22⋊C4×C107—42no—
234C22⋊C4×C107—44no—
235C42×C107—22no—
236C23×C107—21no—
237C23×C107—21no—
238C23×C107—22no—
239C23×C107—22no—
240C23×C107—21no—
241C23×C107—21no—
242C23×C107—21no—
243C23×C107—24no—
244C23×C107—24no—
245C23×C107—24no—
246C23×C107—24no—
247C23×C107—21no—
248C23×C107—21no—
249C23×C107—22no—
250C23×C107—21no—
251C23×C107—21no—
252C23×C107—24no—
253C23×C107—42no—
254C23×C107—41no—
255C23×C107—41no—
256C23×C107—42no—
257C23×C107—41no—
258C23×C107—41no—
259C23×C107—42no—
260C23×C107—42no—
261C23×C107—48no—
262C23×C107—48no—
263C23×C107—41no—
264C23×C107—41no—
265C23×C107—41no—
266C23×C107—41no—
267C23×C107—48no—
268C23×C107—42no—
269C23×C107—42no—
270C23×C107—42no—
271C23×C107—42no—
272C23×C107—42no—
273C23×C107—81no—
274C23×C107—81no—
275C23×C107—84no—
276C23×C107—81no—
277C23×C107—81no—
278C23×C107#12012yes—
279C23×C107#12011yescharacteristic
280C23×C107#12011yescharacteristic
281C23×C107#12312yescomplemented
282C23×C107C22×D411yescharacteristic
283C23×C107C22×D412yes—
284C23×C107C2×#4112yes—
285C23×C107H(5,𝔽2)12yes—
286Q8×C107—42no—
287D4×C107—28no—
288D4×C107—44no—
289D4×C107—42no—
290D4×C107—44no—
291D4×C107—44no—
292D4×C107—42no—
293D4×C107—42no—
294D4×C107—44no—
295D4×C107—44no—
296D4×C107—44no—
297D4×C107—44no—
298D4×C107—82no—
299D4×C107—82no—
300D4×C107—82no—
301D4×C107—82no—
302C2×C4×C107—21no—
303C2×C4×C107—21no—
304C2×C4×C107—24no—
305C2×C4×C107—28no—
306C2×C4×C107—22no—
307C2×C4×C107—22no—
308C2×C4×C107—22no—
309C2×C4×C107—21no—
310C2×C4×C107—21no—
311C2×C4×C107—21no—
312C2×C4×C107—24no—
313C2×C4×C107—42no—
314C2×C4×C107—42no—
315C2×C4×C107—44no—
316C2×C4×C107—44no—
317C2×C4×C107—42no—
318C2×C4×C107—44no—
319C2×C4×C107—48no—
320C2×C4×C107—42no—
321C2×C4×C107—42no—
322C2×C4×C107—44no—
323C2×C4×C107—42no—
324C2×C4×C107—42no—
325C2×C4×C107—44no—
326C2×C4×C107—42no—
327C2×C4×C107—44no—
328C2×C4×C107—42no—
329C2×C4×C107—42no—
330C2×C4×C107—44no—
331C2×C4×C107—81no—
332C2×C4×C107—81no—
333C2×C4×C107—84no—
334C2×C4×C107#12312yescomplemented
335C22×C107—24no—
336C22×C107—24no—
337C22×C107—21no—
338C22×C107—21no—
339C22×C107—22no—
340C22×C107—21no—
341C22×C107—21no—
342C22×C107—22no—
343C22×C107—21no—
344C22×C107—21no—
345C22×C107—22no—
346C22×C107—22no—
347C22×C107—22no—
348C22×C107—22no—
349C22×C107—42no—
350C22×C107—42no—
351C22×C107—48no—
352C22×C107—48no—
353C22×C107—42no—
354C22×C107—42no—
355C22×C107—42no—
356C22×C107—42no—
357C22×C107—41no—
358C22×C107—41no—
359C22×C107—42no—
360C22×C107—41no—
361C22×C107—42no—
362C22×C107—41no—
363C22×C107—42no—
364C22×C107—41no—
365C22×C107—81no—
366C22×C107—84no—
367C22×C107—84no—
368C22×C107—84no—
369C22×C107—81no—
370C22×C107—162no—
371C22×C107B(4,𝔽2)12yes—
372C22×C107#45812yes—
373C22×C107C2×#12011yescharacteristic
374C22×C107C2×#12311yescharacteristic
375C22×C107#53411yescharacteristic
376C22×C107#54614yes—
377C4×C107—22no—
378C4×C107—41no—
379C4×C107—42no—
380C4×C107—44no—
381C4×C107—42no—
382C4×C107—42no—
383C4×C107—84no—
384C4×C107—82no—
385#24056C10711yesmaximal, characteristic, direct product factor, Sylow
386C2×C107—21no—
387C2×C107—24no—
388C2×C107—21no—
389C2×C107—22no—
390C2×C107—22no—
391C2×C107—42no—
392C2×C107—42no—
393C2×C107—81no—
394C2×C107—82no—
395C2×C107#240511yescharacteristic
396C2×C107C2×B(4,𝔽2)11yescharacteristic
397C2×C107C2×#45811yescharacteristic
398#3484C2×C10711yescharacteristic
399#2849C2×C10712yescomplemented
400C2×#386C2×C10711yescharacteristic, complemented
401#2044C2×C10714yescomplemented
402#1898C2×C10712yescomplemented
403#1867C2×C10712yescomplemented
404#1790C2×C10712yescomplemented
405#1781C2×C10711yescharacteristic, complemented
406C107#2405611yescharacteristic, direct product factor, Sylow
407C2×H(5,𝔽2)C22×C10711yescharacteristic
408C23×D4C22×C10711yescharacteristic
409C24×C4C22×C10711yescharacteristic, complemented
410#546—22no—
411#546—22no—
412D42—22no—
413D42—22no—
414#535—21no—
415#534—21no—
416#534C22×C10712yes—
417#525—21no—
418C2×#123—22no—
419C2×#120—21no—
420C2×#120C22×C10712yes—
421#518C22×C10711yescharacteristic
422C22×C22⋊C4—21no—
423C22×C22⋊C4C22×C10711yescharacteristic, complemented
424C2×#99C22×C10712yes—
425C2×#99C22×C10714yescomplemented
426C2×#99C22×C10712yescomplemented
427#386—22no—
428#386—21no—
429#386—21no—
430#386C22×C10712yes—
431#386C22×C10714yescomplemented
432#386C22×C10712yescomplemented
433#385—22no—
434#385C22×C10714yescomplemented
435#381—22no—
436#379C22×C10712yescomplemented
437C2×#95—21no—
438#342C22×C10714yescomplemented
439C25D4×C10711yescharacteristic
440C25C23×C10711yescharacteristic
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×C10711yescharacteristic
454C22×D4D4×C10711yescharacteristic
455C22×D4D4×C10712yes—
456C22×D4D4×C10712yes—
457C22×D4C23×C10712yes—
458C22×D4C23×C10711yescharacteristic
459C22×D4C23×C10711yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—21no—
463C23×C4—22no—
464C23×C4—21no—
465C23×C4—44no—
466C23×C4D4×C10711yescharacteristic
467C23×C4C23×C10712yes—
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×C10712yes—
511C2×C22⋊C4D4×C10712yes—
512C2×C22⋊C4C23×C10712yes—
513C2×C22⋊C4C23×C10714yes—
514C2×C22⋊C4C23×C10712yes—
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×C10711yescharacteristic
534C24C2×D4×C10712yes—
535C24C2×D4×C10712yes—
536C24C2×D4×C10711yescharacteristic
537C24C2×D4×C10712yes—
538C24C2×D4×C10711yescharacteristic
539C24C2×D4×C10711yescharacteristic
540C24C24×C10711yescharacteristic
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×C10714yes—
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×C10712yes—
604C22×C4C2×D4×C10711yescharacteristic
605C22×C4C2×D4×C10711yescharacteristic
606C22×C4C2×D4×C10712yes—
607C22×C4C2×D4×C10712yes—
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—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×C10712yes—
677C23#120×C10711yescharacteristic
678C23#120×C10711yescharacteristic
679C23#123×C10712yescomplemented
680C23C22×D4×C10711yescharacteristic
681C23C22×D4×C10712yes—
682C23C2×#41×C10712yes—
683C23H(5,𝔽2)×C10712yes—
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×C10712yescomplemented
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)×C10712yes—
770C22#458×C10712yes—
771C22C2×#120×C10711yescharacteristic
772C22C2×#123×C10711yescharacteristic
773C22#534×C10711yescharacteristic
774C22#546×C10714yes—
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—
792C2C107×#240511yescharacteristic
793C2C2×B(4,𝔽2)×C10711yescharacteristic
794C2C2×#458×C10711yescharacteristic
subgroupG/H
center, socleC22×C107C2×#120
commutator, Frattini, cosocleC24C24×C107
prime radicalC107×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C107 ◁ C25×C107 ◁ G

Complements

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

NH ≅ G/Ntype
2. C107×#2849C2semidirect
3. C2×#386×C107C2semidirect
4. C107×#2044C2semidirect
5. C107×#1898C2semidirect
6. C107×#1867C2semidirect
7. C107×#1790C2semidirect
8. C107×#1781C2semidirect
11. C24×C4×C107C22semidirect
25. C22×C22⋊C4×C107C22semidirect
27. C2×#99×C107C22semidirect
28. C2×#99×C107C22semidirect
33. #386×C107C22semidirect
34. #386×C107C22semidirect
36. #385×C107C22semidirect
38. #379×C107C22semidirect
40. #342×C107C22semidirect
281. C23×C107#123semidirect
334. C2×C4×C107#123semidirect
385. #24056C107direct (N × H)
399. #2849C2×C107semidirect
400. C2×#386C2×C107semidirect
401. #2044C2×C107semidirect
402. #1898C2×C107semidirect
403. #1867C2×C107semidirect
404. #1790C2×C107semidirect
405. #1781C2×C107semidirect
406. C107#24056direct (N × H)
409. C24×C4C22×C107semidirect
423. C22×C22⋊C4C22×C107semidirect
425. C2×#99C22×C107semidirect
426. C2×#99C22×C107semidirect
431. #386C22×C107semidirect
432. #386C22×C107semidirect
434. #385C22×C107semidirect
436. #379C22×C107semidirect
438. #342C22×C107semidirect
679. C23#123×C107semidirect
732. C2×C4#123×C107semidirect

Maximal subgroups

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

subgroupindex
C107×#34842
C107×#28492
C2×#386×C1072
C107×#20442
C107×#18982
C107×#18672
C107×#17902
C107×#17812
#24056107