Finite Group Databasebeta

← C113×#24404 #43292424

Subgroups — C113×#24404 #43292424

Order 28928.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1046 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3484C211yesmaximal, characteristic, complemented
2C2×B(4,𝔽2)×C113C211yesmaximal, characteristic, complemented
3C22×#99×C113C211yesmaximal, characteristic, complemented
4C113×#2410C212yesmaximal, complemented
5C113×#2403C211yesmaximal, characteristic, complemented
6C113×#2044C212yesmaximal, complemented
7C113×#2021C212yesmaximal, complemented
8C113×#1898C212yesmaximal, complemented
9C113×#1889C211yesmaximal, characteristic, complemented
10C113×#1867C211yesmaximal, characteristic, complemented
11C113×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C113C2211yescharacteristic
13C23×D4×C113C2211yescharacteristic
14C23×D4×C113C2211yescharacteristic, complemented
15#546×C113—22no—
16#546×C113—22no—
17D42×C113—22no—
18D42×C113—22no—
19#535×C113—21no—
20#534×C113—21no—
21#534×C113C2212yes—
22#525×C113—21no—
23C2×#121×C113—22no—
24C2×#120×C113—21no—
25C2×#120×C113—21no—
26C2×#120×C113C2211yescharacteristic
27C2×#120×C113C2212yes—
28C2×#120×C113C2212yescomplemented
29C2×#120×C113C2211yescharacteristic, complemented
30#518×C113C2211yescharacteristic
31C22×C22⋊C4×C113C2212yescomplemented
32B(4,𝔽2)×C113—24no—
33C2×#99×C113—24no—
34C2×#99×C113C2211yescharacteristic
35C2×#99×C113C2211yescharacteristic
36C2×#99×C113C2212yescomplemented
37C2×#99×C113C2212yescomplemented
38C2×#99×C113C2212yescomplemented
39#394×C113—22no—
40#392×C113—21no—
41#392×C113—21no—
42#392×C113—22no—
43#386×C113—21no—
44#386×C113—22no—
45#386×C113C2211yescharacteristic
46#386×C113C2211yescharacteristic, complemented
47#386×C113C2212yescomplemented
48#385×C113C2212yescomplemented
49#379×C113C2212yescomplemented
50#379×C113C2211yescharacteristic, complemented
51#342×C113C2212yescomplemented
52#342×C113C2212yescomplemented
53C25×C113D411yescharacteristic, complemented
54C25×C113C2311yescharacteristic
55C25×C113C2311yescharacteristic
56H(5,𝔽2)×C113—22no—
57H(5,𝔽2)×C113—22no—
58H(5,𝔽2)×C113—42no—
59C2×#41×C113—21no—
60C2×#41×C113—22no—
61C22×D4×C113—21no—
62C22×D4×C113—21no—
63C22×D4×C113—22no—
64C22×D4×C113—22no—
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—21no—
68C22×D4×C113—21no—
69C22×D4×C113—22no—
70C22×D4×C113—22no—
71C22×D4×C113—21no—
72C22×D4×C113—22no—
73C22×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113—22no—
76C22×D4×C113—44no—
77C22×D4×C113—42no—
78C22×D4×C113D411yescharacteristic, complemented
79C22×D4×C113D411yescharacteristic, complemented
80C22×D4×C113D412yescomplemented
81C22×D4×C113D412yescomplemented
82C22×D4×C113C2312yes—
83C22×D4×C113C2311yescharacteristic
84C22×D4×C113C2311yescharacteristic
85C23×C4×C113—22no—
86C23×C4×C113D411yescharacteristic, complemented
87C23×C4×C113C2311yescharacteristic
88#127×C113—22no—
89#124×C113—22no—
90#123×C113—22no—
91#123×C113—22no—
92#123×C113—22no—
93C22⋊Q8×C113—21no—
94C22⋊Q8×C113—21no—
95#121×C113—21no—
96#121×C113—21no—
97#121×C113—22no—
98#121×C113—22no—
99#121×C113—22no—
100#121×C113—22no—
101#121×C113—22no—
102#121×C113—22no—
103#121×C113—48no—
104#120×C113—22no—
105#120×C113—22no—
106#120×C113—22no—
107#120×C113—22no—
108#120×C113—22no—
109#120×C113—22no—
110#120×C113—22no—
111#120×C113—22no—
112#120×C113—22no—
113#120×C113—22no—
114#120×C113—22no—
115#120×C113—24no—
116#120×C113—42no—
117#120×C113—42no—
118#120×C113—44no—
119C4×D4×C113—22no—
120C4×D4×C113—22no—
121C4×D4×C113—22no—
122C4×D4×C113—22no—
123#117×C113—21no—
124C2×C4⋊C4×C113—22no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—24no—
129C2×C22⋊C4×C113—22no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—22no—
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113—21no—
136C2×C22⋊C4×C113—22no—
137C2×C22⋊C4×C113—22no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—22no—
140C2×C22⋊C4×C113—42no—
141C2×C22⋊C4×C113D412yescomplemented
142C2×C22⋊C4×C113D412yescomplemented
143C2×C22⋊C4×C113C2312yes—
144C2×C22⋊C4×C113C2311yescharacteristic
145C2×C22⋊C4×C113C2311yescharacteristic
146C2×C22⋊C4×C113C2312yes—
147C2×C22⋊C4×C113C2312yes—
148#99×C113—22no—
149#99×C113—24no—
150#99×C113—24no—
151#99×C113—42no—
152#99×C113D414yescomplemented
153#95×C113—22no—
154#95×C113—21no—
155#95×C113—21no—
156#95×C113—22no—
157C24×C113—21no—
158C24×C113—21no—
159C24×C113—22no—
160C24×C113—21no—
161C24×C113—22no—
162C24×C113—21no—
163C24×C113—21no—
164C24×C113—21no—
165C24×C113—22no—
166C24×C113—21no—
167C24×C113—21no—
168C24×C113—22no—
169C24×C113—41no—
170C24×C113—42no—
171C24×C113—42no—
172C24×C113—42no—
173C24×C113—81no—
174C24×C113—81no—
175C24×C113—81no—
176C24×C113C2×D411yescharacteristic
177C24×C113C2×D412yes—
178C24×C113C2×D411yescharacteristic
179C24×C113C2×D412yes—
180C24×C113C2×D412yes—
181C24×C113C2×D411yescharacteristic
182C24×C113C2×D411yescharacteristic
183C24×C113C2411yescharacteristic
184#41×C113—44no—
185#41×C113—44no—
186#41×C113—42no—
187#41×C113—42no—
188C2×Q8×C113—21no—
189C2×D4×C113—22no—
190C2×D4×C113—22no—
191C2×D4×C113—22no—
192C2×D4×C113—24no—
193C2×D4×C113—21no—
194C2×D4×C113—28no—
195C2×D4×C113—22no—
196C2×D4×C113—22no—
197C2×D4×C113—22no—
198C2×D4×C113—22no—
199C2×D4×C113—22no—
200C2×D4×C113—21no—
201C2×D4×C113—22no—
202C2×D4×C113—22no—
203C2×D4×C113—22no—
204C2×D4×C113—22no—
205C2×D4×C113—21no—
206C2×D4×C113—22no—
207C2×D4×C113—22no—
208C2×D4×C113—22no—
209C2×D4×C113—22no—
210C2×D4×C113—22no—
211C2×D4×C113—22no—
212C2×D4×C113—22no—
213C2×D4×C113—22no—
214C2×D4×C113—22no—
215C2×D4×C113—41no—
216C2×D4×C113—41no—
217C2×D4×C113—42no—
218C2×D4×C113—44no—
219C2×D4×C113—44no—
220C2×D4×C113—44no—
221C2×D4×C113—44no—
222C2×D4×C113—44no—
223C2×D4×C113—44no—
224C2×D4×C113—44no—
225C2×D4×C113—44no—
226C2×D4×C113—44no—
227C2×D4×C113—42no—
228C2×D4×C113—42no—
229C2×D4×C113—44no—
230C2×D4×C113—42no—
231C2×D4×C113—41no—
232C2×D4×C113—42no—
233C2×D4×C113—41no—
234C2×D4×C113—42no—
235C2×D4×C113—44no—
236C2×D4×C113—42no—
237C2×D4×C113—42no—
238C2×D4×C113—42no—
239C2×D4×C113—44no—
240C2×D4×C113—42no—
241C2×D4×C113—82no—
242C2×D4×C113—82no—
243C2×D4×C113—81no—
244C2×D4×C113—81no—
245C2×D4×C113—82no—
246C2×D4×C113—82no—
247C2×D4×C113C2×D412yes—
248C2×D4×C113#4112yes—
249C22×C4×C113—21no—
250C22×C4×C113—22no—
251C22×C4×C113—21no—
252C22×C4×C113—21no—
253C22×C4×C113—21no—
254C22×C4×C113—22no—
255C22×C4×C113—22no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—22no—
259C22×C4×C113—22no—
260C22×C4×C113—21no—
261C22×C4×C113—21no—
262C22×C4×C113—42no—
263C22×C4×C113—41no—
264C22×C4×C113—44no—
265C22×C4×C113—44no—
266C22×C4×C113—82no—
267C22×C4×C113C2×D412yes—
268C22×C4×C113C2×D411yescharacteristic
269C22×C4×C113C2×D411yescharacteristic
270C22×C4×C113C2×D412yes—
271C22×C4×C113C2×D412yes—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—22no—
275C4⋊C4×C113—22no—
276C4⋊C4×C113—44no—
277C22⋊C4×C113—22no—
278C22⋊C4×C113—22no—
279C22⋊C4×C113—22no—
280C22⋊C4×C113—22no—
281C22⋊C4×C113—22no—
282C22⋊C4×C113—22no—
283C22⋊C4×C113—22no—
284C22⋊C4×C113—22no—
285C22⋊C4×C113—22no—
286C22⋊C4×C113—22no—
287C22⋊C4×C113—22no—
288C22⋊C4×C113—22no—
289C22⋊C4×C113—22no—
290C22⋊C4×C113—21no—
291C22⋊C4×C113—21no—
292C22⋊C4×C113—22no—
293C22⋊C4×C113—22no—
294C22⋊C4×C113—44no—
295C22⋊C4×C113—44no—
296C22⋊C4×C113—42no—
297C22⋊C4×C113—42no—
298C22⋊C4×C113—42no—
299C22⋊C4×C113—44no—
300C22⋊C4×C113—42no—
301C22⋊C4×C113—44no—
302C22⋊C4×C113—42no—
303C22⋊C4×C113—82no—
304C22⋊C4×C113—81no—
305C22⋊C4×C113C2×D414yescomplemented
306C42×C113—22no—
307C23×C113—21no—
308C23×C113—21no—
309C23×C113—21no—
310C23×C113—22no—
311C23×C113—22no—
312C23×C113—22no—
313C23×C113—24no—
314C23×C113—21no—
315C23×C113—21no—
316C23×C113—21no—
317C23×C113—22no—
318C23×C113—22no—
319C23×C113—24no—
320C23×C113—22no—
321C23×C113—21no—
322C23×C113—22no—
323C23×C113—21no—
324C23×C113—21no—
325C23×C113—22no—
326C23×C113—22no—
327C23×C113—41no—
328C23×C113—42no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—42no—
333C23×C113—41no—
334C23×C113—42no—
335C23×C113—42no—
336C23×C113—42no—
337C23×C113—41no—
338C23×C113—41no—
339C23×C113—41no—
340C23×C113—41no—
341C23×C113—42no—
342C23×C113—42no—
343C23×C113—41no—
344C23×C113—42no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—42no—
348C23×C113—42no—
349C23×C113—42no—
350C23×C113—42no—
351C23×C113—41no—
352C23×C113—41no—
353C23×C113—41no—
354C23×C113—42no—
355C23×C113—42no—
356C23×C113—42no—
357C23×C113—81no—
358C23×C113—81no—
359C23×C113—82no—
360C23×C113—82no—
361C23×C113—82no—
362C23×C113—82no—
363C23×C113—84no—
364C23×C113—84no—
365C23×C113—81no—
366C23×C113—81no—
367C23×C113—84no—
368C23×C113—84no—
369C23×C113#12011yescharacteristic
370C23×C113#12012yes—
371C23×C113#12011yescharacteristic
372C23×C113#12112yescomplemented
373C23×C113C22×D411yescharacteristic
374C23×C113C22×D412yes—
375C23×C113C22×D411yescharacteristic
376C23×C113C2×#4111yescharacteristic
377C23×C113H(5,𝔽2)12yes—
378Q8×C113—42no—
379D4×C113—24no—
380D4×C113—24no—
381D4×C113—44no—
382D4×C113—42no—
383D4×C113—44no—
384D4×C113—48no—
385D4×C113—44no—
386D4×C113—44no—
387D4×C113—44no—
388D4×C113—42no—
389D4×C113—42no—
390D4×C113—42no—
391D4×C113—42no—
392D4×C113—42no—
393D4×C113—42no—
394D4×C113—44no—
395D4×C113—44no—
396D4×C113—82no—
397D4×C113—82no—
398D4×C113—82no—
399D4×C113—82no—
400D4×C113—88no—
401D4×C113—84no—
402D4×C113—84no—
403C2×C4×C113—21no—
404C2×C4×C113—21no—
405C2×C4×C113—22no—
406C2×C4×C113—24no—
407C2×C4×C113—22no—
408C2×C4×C113—22no—
409C2×C4×C113—22no—
410C2×C4×C113—21no—
411C2×C4×C113—21no—
412C2×C4×C113—21no—
413C2×C4×C113—24no—
414C2×C4×C113—22no—
415C2×C4×C113—22no—
416C2×C4×C113—42no—
417C2×C4×C113—42no—
418C2×C4×C113—44no—
419C2×C4×C113—42no—
420C2×C4×C113—42no—
421C2×C4×C113—41no—
422C2×C4×C113—42no—
423C2×C4×C113—42no—
424C2×C4×C113—41no—
425C2×C4×C113—42no—
426C2×C4×C113—42no—
427C2×C4×C113—42no—
428C2×C4×C113—41no—
429C2×C4×C113—41no—
430C2×C4×C113—42no—
431C2×C4×C113—41no—
432C2×C4×C113—41no—
433C2×C4×C113—41no—
434C2×C4×C113—41no—
435C2×C4×C113—42no—
436C2×C4×C113—81no—
437C2×C4×C113—81no—
438C2×C4×C113—88no—
439C2×C4×C113#12112yescomplemented
440C22×C113—21no—
441C22×C113—22no—
442C22×C113—21no—
443C22×C113—22no—
444C22×C113—21no—
445C22×C113—21no—
446C22×C113—21no—
447C22×C113—22no—
448C22×C113—22no—
449C22×C113—22no—
450C22×C113—21no—
451C22×C113—21no—
452C22×C113—22no—
453C22×C113—41no—
454C22×C113—41no—
455C22×C113—42no—
456C22×C113—44no—
457C22×C113—44no—
458C22×C113—42no—
459C22×C113—42no—
460C22×C113—42no—
461C22×C113—44no—
462C22×C113—42no—
463C22×C113—42no—
464C22×C113—42no—
465C22×C113—44no—
466C22×C113—41no—
467C22×C113—41no—
468C22×C113—42no—
469C22×C113—41no—
470C22×C113—42no—
471C22×C113—42no—
472C22×C113—41no—
473C22×C113—42no—
474C22×C113—41no—
475C22×C113—82no—
476C22×C113—81no—
477C22×C113—81no—
478C22×C113—81no—
479C22×C113—82no—
480C22×C113—84no—
481C22×C113—82no—
482C22×C113—82no—
483C22×C113—81no—
484C22×C113—82no—
485C22×C113—81no—
486C22×C113—81no—
487C22×C113—82no—
488C22×C113—84no—
489C22×C113—81no—
490C22×C113—81no—
491C22×C113—162no—
492C22×C113B(4,𝔽2)12yescomplemented
493C22×C113C2×#12011yescharacteristic
494C22×C113C2×#12111yescharacteristic
495C22×C113#53411yescharacteristic
496C22×C113D4212yes—
497C22×C113#54612yes—
498C4×C113—22no—
499C4×C113—44no—
500C4×C113—41no—
501C4×C113—42no—
502C4×C113—42no—
503C4×C113—42no—
504C4×C113—42no—
505C4×C113—82no—
506C4×C113—81no—
507C4×C113—81no—
508#24404C11311yesmaximal, characteristic, direct product factor, Sylow
509C2×C113—22no—
510C2×C113—21no—
511C2×C113—21no—
512C2×C113—22no—
513C2×C113—22no—
514C2×C113—42no—
515C2×C113—41no—
516C2×C113—42no—
517C2×C113—82no—
518C2×C113—81no—
519C2×C113—82no—
520C2×C113#241011yescharacteristic
521C2×C113C2×B(4,𝔽2)11yescharacteristic
522C2×C113#302611yescharacteristic
523#3484C2×C11311yescharacteristic, complemented
524C2×B(4,𝔽2)C2×C11311yescharacteristic, complemented
525C22×#99C2×C11311yescharacteristic, complemented
526#2410C2×C11312yescomplemented
527#2403C2×C11311yescharacteristic, complemented
528#2044C2×C11312yescomplemented
529#2021C2×C11312yescomplemented
530#1898C2×C11312yescomplemented
531#1889C2×C11311yescharacteristic, complemented
532#1867C2×C11311yescharacteristic, complemented
533#1790C2×C11311yescharacteristic, complemented
534C113#2440411yescharacteristic, direct product factor, Sylow
535C2×H(5,𝔽2)C22×C11311yescharacteristic
536C23×D4C22×C11311yescharacteristic
537C23×D4C22×C11311yescharacteristic, complemented
538#546—22no—
539#546—22no—
540D42—22no—
541D42—22no—
542#535—21no—
543#534—21no—
544#534C22×C11312yes—
545#525—21no—
546C2×#121—22no—
547C2×#120—21no—
548C2×#120—21no—
549C2×#120C22×C11311yescharacteristic
550C2×#120C22×C11312yes—
551C2×#120C22×C11312yescomplemented
552C2×#120C22×C11311yescharacteristic, complemented
553#518C22×C11311yescharacteristic
554C22×C22⋊C4C22×C11312yescomplemented
555B(4,𝔽2)—24no—
556C2×#99—24no—
557C2×#99C22×C11311yescharacteristic
558C2×#99C22×C11311yescharacteristic
559C2×#99C22×C11312yescomplemented
560C2×#99C22×C11312yescomplemented
561C2×#99C22×C11312yescomplemented
562#394—22no—
563#392—21no—
564#392—21no—
565#392—22no—
566#386—21no—
567#386—22no—
568#386C22×C11311yescharacteristic
569#386C22×C11311yescharacteristic, complemented
570#386C22×C11312yescomplemented
571#385C22×C11312yescomplemented
572#379C22×C11312yescomplemented
573#379C22×C11311yescharacteristic, complemented
574#342C22×C11312yescomplemented
575#342C22×C11312yescomplemented
576C25D4×C11311yescharacteristic, complemented
577C25C23×C11311yescharacteristic
578C25C23×C11311yescharacteristic
579H(5,𝔽2)—22no—
580H(5,𝔽2)—22no—
581H(5,𝔽2)—42no—
582C2×#41—21no—
583C2×#41—22no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—22no—
599C22×D4—44no—
600C22×D4—42no—
601C22×D4D4×C11311yescharacteristic, complemented
602C22×D4D4×C11311yescharacteristic, complemented
603C22×D4D4×C11312yescomplemented
604C22×D4D4×C11312yescomplemented
605C22×D4C23×C11312yes—
606C22×D4C23×C11311yescharacteristic
607C22×D4C23×C11311yescharacteristic
608C23×C4—22no—
609C23×C4D4×C11311yescharacteristic, complemented
610C23×C4C23×C11311yescharacteristic
611#127—22no—
612#124—22no—
613#123—22no—
614#123—22no—
615#123—22no—
616C22⋊Q8—21no—
617C22⋊Q8—21no—
618#121—21no—
619#121—21no—
620#121—22no—
621#121—22no—
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—48no—
627#120—22no—
628#120—22no—
629#120—22no—
630#120—22no—
631#120—22no—
632#120—22no—
633#120—22no—
634#120—22no—
635#120—22no—
636#120—22no—
637#120—22no—
638#120—24no—
639#120—42no—
640#120—42no—
641#120—44no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645C4×D4—22no—
646#117—21no—
647C2×C4⋊C4—22no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—22no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4—22no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—22no—
663C2×C22⋊C4—42no—
664C2×C22⋊C4D4×C11312yescomplemented
665C2×C22⋊C4D4×C11312yescomplemented
666C2×C22⋊C4C23×C11312yes—
667C2×C22⋊C4C23×C11311yescharacteristic
668C2×C22⋊C4C23×C11311yescharacteristic
669C2×C22⋊C4C23×C11312yes—
670C2×C22⋊C4C23×C11312yes—
671#99—22no—
672#99—24no—
673#99—24no—
674#99—42no—
675#99D4×C11314yescomplemented
676#95—22no—
677#95—21no—
678#95—21no—
679#95—22no—
680C24—21no—
681C24—21no—
682C24—22no—
683C24—21no—
684C24—22no—
685C24—21no—
686C24—21no—
687C24—21no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—41no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24C2×D4×C11311yescharacteristic
700C24C2×D4×C11312yes—
701C24C2×D4×C11311yescharacteristic
702C24C2×D4×C11312yes—
703C24C2×D4×C11312yes—
704C24C2×D4×C11311yescharacteristic
705C24C2×D4×C11311yescharacteristic
706C24C24×C11311yescharacteristic
707#41—44no—
708#41—44no—
709#41—42no—
710#41—42no—
711C2×Q8—21no—
712C2×D4—22no—
713C2×D4—22no—
714C2×D4—22no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—28no—
718C2×D4—22no—
719C2×D4—22no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—22no—
723C2×D4—21no—
724C2×D4—22no—
725C2×D4—22no—
726C2×D4—22no—
727C2×D4—22no—
728C2×D4—21no—
729C2×D4—22no—
730C2×D4—22no—
731C2×D4—22no—
732C2×D4—22no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—22no—
737C2×D4—22no—
738C2×D4—41no—
739C2×D4—41no—
740C2×D4—42no—
741C2×D4—44no—
742C2×D4—44no—
743C2×D4—44no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—44no—
747C2×D4—44no—
748C2×D4—44no—
749C2×D4—44no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—41no—
757C2×D4—42no—
758C2×D4—44no—
759C2×D4—42no—
760C2×D4—42no—
761C2×D4—42no—
762C2×D4—44no—
763C2×D4—42no—
764C2×D4—82no—
765C2×D4—82no—
766C2×D4—81no—
767C2×D4—81no—
768C2×D4—82no—
769C2×D4—82no—
770C2×D4C2×D4×C11312yes—
771C2×D4#41×C11312yes—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—22no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—42no—
786C22×C4—41no—
787C22×C4—44no—
788C22×C4—44no—
789C22×C4—82no—
790C22×C4C2×D4×C11312yes—
791C22×C4C2×D4×C11311yescharacteristic
792C22×C4C2×D4×C11311yescharacteristic
793C22×C4C2×D4×C11312yes—
794C22×C4C2×D4×C11312yes—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—22no—
798C4⋊C4—22no—
799C4⋊C4—44no—
800C22⋊C4—22no—
801C22⋊C4—22no—
802C22⋊C4—22no—
803C22⋊C4—22no—
804C22⋊C4—22no—
805C22⋊C4—22no—
806C22⋊C4—22no—
807C22⋊C4—22no—
808C22⋊C4—22no—
809C22⋊C4—22no—
810C22⋊C4—22no—
811C22⋊C4—22no—
812C22⋊C4—22no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—22no—
816C22⋊C4—22no—
817C22⋊C4—44no—
818C22⋊C4—44no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—42no—
822C22⋊C4—44no—
823C22⋊C4—42no—
824C22⋊C4—44no—
825C22⋊C4—42no—
826C22⋊C4—82no—
827C22⋊C4—81no—
828C22⋊C4C2×D4×C11314yescomplemented
829C42—22no—
830C23—21no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—22no—
835C23—22no—
836C23—24no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—22no—
844C23—21no—
845C23—22no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—22no—
850C23—41no—
851C23—42no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—41no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—42no—
865C23—42no—
866C23—41no—
867C23—42no—
868C23—41no—
869C23—41no—
870C23—42no—
871C23—42no—
872C23—42no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—42no—
878C23—42no—
879C23—42no—
880C23—81no—
881C23—81no—
882C23—82no—
883C23—82no—
884C23—82no—
885C23—82no—
886C23—84no—
887C23—84no—
888C23—81no—
889C23—81no—
890C23—84no—
891C23—84no—
892C23#120×C11311yescharacteristic
893C23#120×C11312yes—
894C23#120×C11311yescharacteristic
895C23#121×C11312yescomplemented
896C23C22×D4×C11311yescharacteristic
897C23C22×D4×C11312yes—
898C23C22×D4×C11311yescharacteristic
899C23C2×#41×C11311yescharacteristic
900C23H(5,𝔽2)×C11312yes—
901Q8—42no—
902D4—24no—
903D4—24no—
904D4—44no—
905D4—42no—
906D4—44no—
907D4—48no—
908D4—44no—
909D4—44no—
910D4—44no—
911D4—42no—
912D4—42no—
913D4—42no—
914D4—42no—
915D4—42no—
916D4—42no—
917D4—44no—
918D4—44no—
919D4—82no—
920D4—82no—
921D4—82no—
922D4—82no—
923D4—88no—
924D4—84no—
925D4—84no—
926C2×C4—21no—
927C2×C4—21no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—21no—
935C2×C4—21no—
936C2×C4—24no—
937C2×C4—22no—
938C2×C4—22no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—44no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—41no—
945C2×C4—42no—
946C2×C4—42no—
947C2×C4—41no—
948C2×C4—42no—
949C2×C4—42no—
950C2×C4—42no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—42no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—42no—
959C2×C4—81no—
960C2×C4—81no—
961C2×C4—88no—
962C2×C4#121×C11312yescomplemented
963C22—21no—
964C22—22no—
965C22—21no—
966C22—22no—
967C22—21no—
968C22—21no—
969C22—21no—
970C22—22no—
971C22—22no—
972C22—22no—
973C22—21no—
974C22—21no—
975C22—22no—
976C22—41no—
977C22—41no—
978C22—42no—
979C22—44no—
980C22—42no—
981C22—42no—
982C22—44no—
983C22—42no—
984C22—44no—
985C22—42no—
986C22—42no—
987C22—42no—
988C22—44no—
989C22—41no—
990C22—41no—
991C22—42no—
992C22—41no—
993C22—42no—
994C22—42no—
995C22—41no—
996C22—42no—
997C22—41no—
998C22—82no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22—82no—
1003C22—84no—
1004C22—82no—
1005C22—81no—
1006C22—82no—
1007C22—82no—
1008C22—81no—
1009C22—81no—
1010C22—82no—
1011C22—84no—
1012C22—81no—
1013C22—81no—
1014C22—162no—
1015C22B(4,𝔽2)×C11312yescomplemented
1016C22C2×#120×C11311yescharacteristic
1017C22C2×#121×C11311yescharacteristic
1018C22#534×C11311yescharacteristic
1019C22D42×C11312yes—
1020C22#546×C11312yes—
1021C4—22no—
1022C4—44no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—42no—
1027C4—42no—
1028C4—82no—
1029C4—81no—
1030C4—81no—
1031C2—22no—
1032C2—21no—
1033C2—21no—
1034C2—22no—
1035C2—22no—
1036C2—41no—
1037C2—42no—
1038C2—42no—
1039C2—82no—
1040C2—81no—
1041C2—82no—
1042C2C113×#241011yescharacteristic
1043C2C2×B(4,𝔽2)×C11311yescharacteristic
1044C2C113×#302611yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC24C24×C113
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C113 ◁ C25×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3484C2semidirect
2. C2×B(4,𝔽2)×C113C2semidirect
3. C22×#99×C113C2semidirect
4. C113×#2410C2semidirect
5. C113×#2403C2semidirect
6. C113×#2044C2semidirect
7. C113×#2021C2semidirect
8. C113×#1898C2semidirect
9. C113×#1889C2semidirect
10. C113×#1867C2semidirect
11. C113×#1790C2semidirect
14. C23×D4×C113C22semidirect
28. C2×#120×C113C22semidirect
29. C2×#120×C113C22semidirect
31. C22×C22⋊C4×C113C22semidirect
36. C2×#99×C113C22semidirect
37. C2×#99×C113C22semidirect
38. C2×#99×C113C22semidirect
46. #386×C113C22semidirect
47. #386×C113C22semidirect
48. #385×C113C22semidirect
49. #379×C113C22semidirect
50. #379×C113C22semidirect
51. #342×C113C22semidirect
52. #342×C113C22semidirect
53. C25×C113D4semidirect
78. C22×D4×C113D4semidirect
79. C22×D4×C113D4semidirect
80. C22×D4×C113D4semidirect
81. C22×D4×C113D4semidirect
86. C23×C4×C113D4semidirect
141. C2×C22⋊C4×C113D4semidirect
142. C2×C22⋊C4×C113D4semidirect
152. #99×C113D4semidirect
305. C22⋊C4×C113C2×D4semidirect
372. C23×C113#121semidirect
439. C2×C4×C113#121semidirect
492. C22×C113B(4,𝔽2)semidirect
508. #24404C113direct (N × H)
523. #3484C2×C113semidirect
524. C2×B(4,𝔽2)C2×C113semidirect
525. C22×#99C2×C113semidirect
526. #2410C2×C113semidirect
527. #2403C2×C113semidirect
528. #2044C2×C113semidirect
529. #2021C2×C113semidirect
530. #1898C2×C113semidirect
531. #1889C2×C113semidirect
532. #1867C2×C113semidirect
533. #1790C2×C113semidirect
534. C113#24404direct (N × H)
537. C23×D4C22×C113semidirect
551. C2×#120C22×C113semidirect
552. C2×#120C22×C113semidirect
554. C22×C22⋊C4C22×C113semidirect
559. C2×#99C22×C113semidirect
560. C2×#99C22×C113semidirect
561. C2×#99C22×C113semidirect
569. #386C22×C113semidirect
570. #386C22×C113semidirect
571. #385C22×C113semidirect
572. #379C22×C113semidirect
573. #379C22×C113semidirect
574. #342C22×C113semidirect
575. #342C22×C113semidirect
576. C25D4×C113semidirect
601. C22×D4D4×C113semidirect
602. C22×D4D4×C113semidirect
603. C22×D4D4×C113semidirect
604. C22×D4D4×C113semidirect
609. C23×C4D4×C113semidirect
664. C2×C22⋊C4D4×C113semidirect
665. C2×C22⋊C4D4×C113semidirect
675. #99D4×C113semidirect
828. C22⋊C4C2×D4×C113semidirect
895. C23#121×C113semidirect
962. C2×C4#121×C113semidirect
1015. C22B(4,𝔽2)×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C2×B(4,𝔽2)×C1132
C22×#99×C1132
C113×#24102
C113×#24032
C113×#20442
C113×#20212
C113×#18982
C113×#18892
C113×#18672
C113×#17902
#24404113