Finite Group Databasebeta

← C113×#24405 #43292425

Subgroups — C113×#24405 #43292425

Order 28928.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3484C211yesmaximal, characteristic
2C2×#458×C113C211yesmaximal, characteristic, complemented
3C22×#99×C113C211yesmaximal, characteristic, complemented
4C113×#2412C212yesmaximal, complemented
5C113×#2405C211yesmaximal, characteristic, complemented
6C113×#2044C212yesmaximal, complemented
7C113×#2022C212yesmaximal, complemented
8C113×#1898C212yesmaximal, complemented
9C113×#1890C211yesmaximal, characteristic, complemented
10C113×#1867C211yesmaximal, characteristic, complemented
11C113×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C113C2211yescharacteristic
13C23×D4×C113C2211yescharacteristic
14#546×C113—22no—
15#546×C113—22no—
16D42×C113—22no—
17D42×C113—22no—
18#535×C113—21no—
19#534×C113—21no—
20#534×C113C2212yes—
21#525×C113—21no—
22C2×#123×C113C2211yescharacteristic
23C2×#123×C113C2212yescomplemented
24C2×#123×C113C2211yescharacteristic, complemented
25C2×#120×C113—21no—
26C2×#120×C113C2212yes—
27#518×C113C2211yescharacteristic
28C22×C22⋊C4×C113C2211yescharacteristic, complemented
29C22×C22⋊C4×C113C2212yescomplemented
30#458×C113—24no—
31C2×#99×C113—24no—
32C2×#99×C113C2211yescharacteristic
33C2×#99×C113C2211yescharacteristic
34C2×#99×C113C2212yescomplemented
35C2×#99×C113C2212yescomplemented
36C2×#99×C113C2212yescomplemented
37#397×C113—22no—
38#394×C113—21no—
39#394×C113—21no—
40#394×C113—22no—
41#386×C113—22no—
42#386×C113C2211yescharacteristic
43#386×C113C2211yescharacteristic, complemented
44#386×C113C2212yescomplemented
45#385×C113—21no—
46#385×C113C2212yescomplemented
47#381×C113C2212yescomplemented
48#380×C113—22no—
49#379×C113—21no—
50#379×C113C2211yescharacteristic, complemented
51#342×C113C2212yescomplemented
52#342×C113C2212yescomplemented
53C25×C113D411yescharacteristic
54C25×C113C2311yescharacteristic
55H(5,𝔽2)×C113—22no—
56H(5,𝔽2)×C113—22no—
57H(5,𝔽2)×C113—42no—
58C2×#41×C113—21no—
59C2×#41×C113—22no—
60C22×D4×C113—21no—
61C22×D4×C113—22no—
62C22×D4×C113—22no—
63C22×D4×C113—22no—
64C22×D4×C113—21no—
65C22×D4×C113—21no—
66C22×D4×C113—22no—
67C22×D4×C113—22no—
68C22×D4×C113—42no—
69C22×D4×C113D411yescharacteristic
70C22×D4×C113D411yescharacteristic
71C22×D4×C113D412yes—
72C22×D4×C113D412yes—
73C22×D4×C113C2312yes—
74C22×D4×C113C2311yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C23×C4×C113—22no—
77C23×C4×C113D411yescharacteristic
78C23×C4×C113C2311yescharacteristic
79C23×C4×C113C2311yescharacteristic
80#127×C113—22no—
81#124×C113—22no—
82#123×C113—22no—
83#123×C113—22no—
84#123×C113—22no—
85#123×C113—22no—
86#123×C113—22no—
87#123×C113—24no—
88#123×C113—42no—
89#123×C113—42no—
90C22⋊Q8×C113—21no—
91C22⋊Q8×C113—21no—
92#121×C113—21no—
93#121×C113—21no—
94#121×C113—22no—
95#121×C113—22no—
96#121×C113—22no—
97#121×C113—22no—
98#121×C113—22no—
99#121×C113—22no—
100#120×C113—22no—
101#120×C113—22no—
102#120×C113—22no—
103#120×C113—22no—
104#120×C113—22no—
105#120×C113—22no—
106#120×C113—22no—
107#120×C113—22no—
108#120×C113—22no—
109C4×D4×C113—22no—
110C4×D4×C113—22no—
111C4×D4×C113—22no—
112C4×D4×C113—22no—
113#117×C113—21no—
114C2×C4⋊C4×C113—21no—
115C2×C4⋊C4×C113—22no—
116C2×C4⋊C4×C113—21no—
117C2×C4⋊C4×C113—22no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—24no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—22no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—22no—
126C2×C22⋊C4×C113—22no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113—21no—
129C2×C22⋊C4×C113—22no—
130C2×C22⋊C4×C113—21no—
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—22no—
135C2×C22⋊C4×C113—42no—
136C2×C22⋊C4×C113D412yes—
137C2×C22⋊C4×C113D412yes—
138C2×C22⋊C4×C113C2312yes—
139C2×C22⋊C4×C113C2311yescharacteristic
140C2×C22⋊C4×C113C2311yescharacteristic
141C2×C22⋊C4×C113C2312yes—
142C2×C22⋊C4×C113C2312yes—
143#99×C113—22no—
144#99×C113—24no—
145#99×C113—24no—
146#99×C113—42no—
147#99×C113D414yescomplemented
148#95×C113—22no—
149#95×C113—22no—
150#95×C113—22no—
151#95×C113—21no—
152#95×C113—21no—
153#95×C113—22no—
154C24×C113—21no—
155C24×C113—21no—
156C24×C113—22no—
157C24×C113—21no—
158C24×C113—21no—
159C24×C113—21no—
160C24×C113—22no—
161C24×C113—41no—
162C24×C113—42no—
163C24×C113—42no—
164C24×C113—81no—
165C24×C113—81no—
166C24×C113C2×D411yescharacteristic
167C24×C113C2×D412yes—
168C24×C113C2×D411yescharacteristic
169C24×C113C2×D412yes—
170C24×C113C2×D412yes—
171C24×C113C2×D411yescharacteristic
172C24×C113C2×D411yescharacteristic
173C24×C113C2411yescharacteristic
174#41×C113—44no—
175#41×C113—44no—
176#41×C113—42no—
177#41×C113—42no—
178C2×Q8×C113—21no—
179C2×D4×C113—22no—
180C2×D4×C113—22no—
181C2×D4×C113—22no—
182C2×D4×C113—21no—
183C2×D4×C113—22no—
184C2×D4×C113—22no—
185C2×D4×C113—22no—
186C2×D4×C113—22no—
187C2×D4×C113—22no—
188C2×D4×C113—21no—
189C2×D4×C113—22no—
190C2×D4×C113—22no—
191C2×D4×C113—22no—
192C2×D4×C113—22no—
193C2×D4×C113—21no—
194C2×D4×C113—22no—
195C2×D4×C113—22no—
196C2×D4×C113—22no—
197C2×D4×C113—22no—
198C2×D4×C113—22no—
199C2×D4×C113—22no—
200C2×D4×C113—22no—
201C2×D4×C113—22no—
202C2×D4×C113—22no—
203C2×D4×C113—41no—
204C2×D4×C113—41no—
205C2×D4×C113—44no—
206C2×D4×C113—44no—
207C2×D4×C113—44no—
208C2×D4×C113—44no—
209C2×D4×C113—44no—
210C2×D4×C113—44no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—44no—
214C2×D4×C113—82no—
215C2×D4×C113—82no—
216C2×D4×C113—82no—
217C2×D4×C113C2×D412yes—
218C2×D4×C113#4112yes—
219C22×C4×C113—21no—
220C22×C4×C113—22no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—22no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—22no—
227C22×C4×C113—22no—
228C22×C4×C113—21no—
229C22×C4×C113—22no—
230C22×C4×C113—22no—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—22no—
237C22×C4×C113—41no—
238C22×C4×C113—44no—
239C22×C4×C113—44no—
240C22×C4×C113—81no—
241C22×C4×C113—82no—
242C22×C4×C113C2×D412yes—
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D412yes—
246C22×C4×C113C2×D412yes—
247C4⋊C4×C113—21no—
248C4⋊C4×C113—21no—
249C4⋊C4×C113—22no—
250C4⋊C4×C113—22no—
251C4⋊C4×C113—44no—
252C4⋊C4×C113—42no—
253C4⋊C4×C113—42no—
254C4⋊C4×C113—82no—
255C22⋊C4×C113—22no—
256C22⋊C4×C113—22no—
257C22⋊C4×C113—22no—
258C22⋊C4×C113—22no—
259C22⋊C4×C113—22no—
260C22⋊C4×C113—22no—
261C22⋊C4×C113—22no—
262C22⋊C4×C113—22no—
263C22⋊C4×C113—22no—
264C22⋊C4×C113—22no—
265C22⋊C4×C113—22no—
266C22⋊C4×C113—22no—
267C22⋊C4×C113—22no—
268C22⋊C4×C113—21no—
269C22⋊C4×C113—21no—
270C22⋊C4×C113—22no—
271C22⋊C4×C113—22no—
272C22⋊C4×C113—44no—
273C22⋊C4×C113—44no—
274C22⋊C4×C113—42no—
275C22⋊C4×C113—42no—
276C22⋊C4×C113—41no—
277C22⋊C4×C113—42no—
278C22⋊C4×C113—41no—
279C22⋊C4×C113—42no—
280C22⋊C4×C113—81no—
281C22⋊C4×C113—81no—
282C22⋊C4×C113—81no—
283C22⋊C4×C113—82no—
284C22⋊C4×C113C2×D414yescomplemented
285C42×C113—22no—
286C23×C113—21no—
287C23×C113—21no—
288C23×C113—21no—
289C23×C113—22no—
290C23×C113—22no—
291C23×C113—22no—
292C23×C113—24no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—22no—
297C23×C113—22no—
298C23×C113—21no—
299C23×C113—22no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—22no—
303C23×C113—22no—
304C23×C113—42no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—42no—
310C23×C113—42no—
311C23×C113—41no—
312C23×C113—42no—
313C23×C113—42no—
314C23×C113—41no—
315C23×C113—41no—
316C23×C113—41no—
317C23×C113—41no—
318C23×C113—42no—
319C23×C113—42no—
320C23×C113—42no—
321C23×C113—42no—
322C23×C113—42no—
323C23×C113—81no—
324C23×C113—81no—
325C23×C113—82no—
326C23×C113—82no—
327C23×C113—84no—
328C23×C113—81no—
329C23×C113—81no—
330C23×C113—84no—
331C23×C113—84no—
332C23×C113#12011yescharacteristic
333C23×C113#12012yes—
334C23×C113#12011yescharacteristic
335C23×C113#12112yes—
336C23×C113C22×D411yescharacteristic
337C23×C113C22×D412yes—
338C23×C113C22×D411yescharacteristic
339C23×C113C2×#4111yescharacteristic
340C23×C113H(5,𝔽2)12yes—
341Q8×C113—42no—
342D4×C113—24no—
343D4×C113—24no—
344D4×C113—44no—
345D4×C113—42no—
346D4×C113—44no—
347D4×C113—44no—
348D4×C113—44no—
349D4×C113—42no—
350D4×C113—42no—
351D4×C113—42no—
352D4×C113—42no—
353D4×C113—42no—
354D4×C113—42no—
355D4×C113—44no—
356D4×C113—82no—
357D4×C113—82no—
358D4×C113—82no—
359D4×C113—82no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—22no—
363C2×C4×C113—22no—
364C2×C4×C113—22no—
365C2×C4×C113—21no—
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—24no—
369C2×C4×C113—22no—
370C2×C4×C113—22no—
371C2×C4×C113—42no—
372C2×C4×C113—42no—
373C2×C4×C113—44no—
374C2×C4×C113—42no—
375C2×C4×C113—42no—
376C2×C4×C113—42no—
377C2×C4×C113—42no—
378C2×C4×C113—42no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
383C2×C4×C113—42no—
384C2×C4×C113—42no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—42no—
388C2×C4×C113—42no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—42no—
396C2×C4×C113—42no—
397C2×C4×C113—42no—
398C2×C4×C113—81no—
399C2×C4×C113—81no—
400C2×C4×C113—88no—
401C2×C4×C113#12112yes—
402C22×C113—21no—
403C22×C113—22no—
404C22×C113—21no—
405C22×C113—22no—
406C22×C113—21no—
407C22×C113—21no—
408C22×C113—21no—
409C22×C113—22no—
410C22×C113—22no—
411C22×C113—22no—
412C22×C113—21no—
413C22×C113—21no—
414C22×C113—22no—
415C22×C113—41no—
416C22×C113—41no—
417C22×C113—42no—
418C22×C113—44no—
419C22×C113—44no—
420C22×C113—42no—
421C22×C113—42no—
422C22×C113—42no—
423C22×C113—42no—
424C22×C113—41no—
425C22×C113—41no—
426C22×C113—42no—
427C22×C113—41no—
428C22×C113—42no—
429C22×C113—41no—
430C22×C113—42no—
431C22×C113—41no—
432C22×C113—82no—
433C22×C113—81no—
434C22×C113—81no—
435C22×C113—81no—
436C22×C113—82no—
437C22×C113—84no—
438C22×C113—82no—
439C22×C113—82no—
440C22×C113—81no—
441C22×C113—84no—
442C22×C113—162no—
443C22×C113#45812yescomplemented
444C22×C113C2×#12011yescharacteristic
445C22×C113C2×#12111yescharacteristic
446C22×C113#53411yescharacteristic
447C22×C113D4212yes—
448C22×C113#54612yes—
449C4×C113—22no—
450C4×C113—44no—
451C4×C113—41no—
452C4×C113—42no—
453C4×C113—42no—
454C4×C113—42no—
455C4×C113—81no—
456C4×C113—81no—
457C4×C113—82no—
458C4×C113—81no—
459C4×C113—81no—
460#24405C11311yesmaximal, characteristic, direct product factor, Sylow
461C2×C113—22no—
462C2×C113—21no—
463C2×C113—21no—
464C2×C113—22no—
465C2×C113—22no—
466C2×C113—42no—
467C2×C113—41no—
468C2×C113—42no—
469C2×C113—81no—
470C2×C113—82no—
471C2×C113#241011yescharacteristic
472C2×C113C2×#45811yescharacteristic
473C2×C113#302611yescharacteristic
474#3484C2×C11311yescharacteristic
475C2×#458C2×C11311yescharacteristic, complemented
476C22×#99C2×C11311yescharacteristic, complemented
477#2412C2×C11312yescomplemented
478#2405C2×C11311yescharacteristic, complemented
479#2044C2×C11312yescomplemented
480#2022C2×C11312yescomplemented
481#1898C2×C11312yescomplemented
482#1890C2×C11311yescharacteristic, complemented
483#1867C2×C11311yescharacteristic, complemented
484#1790C2×C11311yescharacteristic, complemented
485C113#2440511yescharacteristic, direct product factor, Sylow
486C2×H(5,𝔽2)C22×C11311yescharacteristic
487C23×D4C22×C11311yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C11312yes—
495#525—21no—
496C2×#123C22×C11311yescharacteristic
497C2×#123C22×C11312yescomplemented
498C2×#123C22×C11311yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C11312yes—
501#518C22×C11311yescharacteristic
502C22×C22⋊C4C22×C11311yescharacteristic, complemented
503C22×C22⋊C4C22×C11312yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C11311yescharacteristic
507C2×#99C22×C11311yescharacteristic
508C2×#99C22×C11312yescomplemented
509C2×#99C22×C11312yescomplemented
510C2×#99C22×C11312yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C11311yescharacteristic
517#386C22×C11311yescharacteristic, complemented
518#386C22×C11312yescomplemented
519#385—21no—
520#385C22×C11312yescomplemented
521#381C22×C11312yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C11311yescharacteristic, complemented
525#342C22×C11312yescomplemented
526#342C22×C11312yescomplemented
527C25D4×C11311yescharacteristic
528C25C23×C11311yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C11311yescharacteristic
544C22×D4D4×C11311yescharacteristic
545C22×D4D4×C11312yes—
546C22×D4D4×C11312yes—
547C22×D4C23×C11312yes—
548C22×D4C23×C11311yescharacteristic
549C22×D4C23×C11311yescharacteristic
550C23×C4—22no—
551C23×C4D4×C11311yescharacteristic
552C23×C4C23×C11311yescharacteristic
553C23×C4C23×C11311yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C11312yes—
611C2×C22⋊C4D4×C11312yes—
612C2×C22⋊C4C23×C11312yes—
613C2×C22⋊C4C23×C11311yescharacteristic
614C2×C22⋊C4C23×C11311yescharacteristic
615C2×C22⋊C4C23×C11312yes—
616C2×C22⋊C4C23×C11312yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C11314yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C11311yescharacteristic
641C24C2×D4×C11312yes—
642C24C2×D4×C11311yescharacteristic
643C24C2×D4×C11312yes—
644C24C2×D4×C11312yes—
645C24C2×D4×C11311yescharacteristic
646C24C2×D4×C11311yescharacteristic
647C24C24×C11311yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C11312yes—
692C2×D4#41×C11312yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C11312yes—
717C22×C4C2×D4×C11311yescharacteristic
718C22×C4C2×D4×C11311yescharacteristic
719C22×C4C2×D4×C11312yes—
720C22×C4C2×D4×C11312yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C11314yescomplemented
759C42—22no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—24no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C11311yescharacteristic
807C23#120×C11312yes—
808C23#120×C11311yescharacteristic
809C23#121×C11312yes—
810C23C22×D4×C11311yescharacteristic
811C23C22×D4×C11312yes—
812C23C22×D4×C11311yescharacteristic
813C23C2×#41×C11311yescharacteristic
814C23H(5,𝔽2)×C11312yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—42no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—44no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C11312yes—
876C22—21no—
877C22—22no—
878C22—21no—
879C22—22no—
880C22—21no—
881C22—21no—
882C22—21no—
883C22—22no—
884C22—22no—
885C22—22no—
886C22—21no—
887C22—21no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C11312yescomplemented
918C22C2×#120×C11311yescharacteristic
919C22C2×#121×C11311yescharacteristic
920C22#534×C11311yescharacteristic
921C22D42×C11312yes—
922C22#546×C11312yes—
923C4—22no—
924C4—44no—
925C4—41no—
926C4—42no—
927C4—42no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C113×#241011yescharacteristic
945C2C2×#458×C11311yescharacteristic
946C2C113×#302611yescharacteristic
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. C2×#458×C113C2semidirect
3. C22×#99×C113C2semidirect
4. C113×#2412C2semidirect
5. C113×#2405C2semidirect
6. C113×#2044C2semidirect
7. C113×#2022C2semidirect
8. C113×#1898C2semidirect
9. C113×#1890C2semidirect
10. C113×#1867C2semidirect
11. C113×#1790C2semidirect
23. C2×#123×C113C22semidirect
24. C2×#123×C113C22semidirect
28. C22×C22⋊C4×C113C22semidirect
29. C22×C22⋊C4×C113C22semidirect
34. C2×#99×C113C22semidirect
35. C2×#99×C113C22semidirect
36. C2×#99×C113C22semidirect
43. #386×C113C22semidirect
44. #386×C113C22semidirect
46. #385×C113C22semidirect
47. #381×C113C22semidirect
50. #379×C113C22semidirect
51. #342×C113C22semidirect
52. #342×C113C22semidirect
147. #99×C113D4semidirect
284. C22⋊C4×C113C2×D4semidirect
443. C22×C113#458semidirect
460. #24405C113direct (N × H)
475. C2×#458C2×C113semidirect
476. C22×#99C2×C113semidirect
477. #2412C2×C113semidirect
478. #2405C2×C113semidirect
479. #2044C2×C113semidirect
480. #2022C2×C113semidirect
481. #1898C2×C113semidirect
482. #1890C2×C113semidirect
483. #1867C2×C113semidirect
484. #1790C2×C113semidirect
485. C113#24405direct (N × H)
497. C2×#123C22×C113semidirect
498. C2×#123C22×C113semidirect
502. C22×C22⋊C4C22×C113semidirect
503. C22×C22⋊C4C22×C113semidirect
508. C2×#99C22×C113semidirect
509. C2×#99C22×C113semidirect
510. C2×#99C22×C113semidirect
517. #386C22×C113semidirect
518. #386C22×C113semidirect
520. #385C22×C113semidirect
521. #381C22×C113semidirect
524. #379C22×C113semidirect
525. #342C22×C113semidirect
526. #342C22×C113semidirect
621. #99D4×C113semidirect
758. C22⋊C4C2×D4×C113semidirect
917. C22#458×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#34842
C2×#458×C1132
C22×#99×C1132
C113×#24122
C113×#24052
C113×#20442
C113×#20222
C113×#18982
C113×#18902
C113×#18672
C113×#17902
#24405113