Finite Group Databasebeta

← C113×#23882 #43291902

Subgroups — C113×#23882 #43291902

Order 28928.

1866 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3585C211yesmaximal, characteristic, complemented
2C113×#3484C211yesmaximal, characteristic, complemented
3C113×#3025C211yesmaximal, characteristic, complemented
4C113×#3021C211yesmaximal, characteristic, complemented
5C113×#3003C212yesmaximal, complemented
6C113×#2010C212yesmaximal, complemented
7C113×#2008C212yesmaximal, complemented
8C113×#1910C211yesmaximal, characteristic, complemented
9C113×#1904C212yesmaximal, complemented
10C113×#1891C211yesmaximal, characteristic, complemented
11C113×#1795C211yesmaximal, characteristic, complemented
12#585×C113C2211yescharacteristic, complemented
13C2×H(5,𝔽2)×C113C2211yescharacteristic
14C23×D4×C113C2211yescharacteristic, complemented
15#577×C113—24no—
16#576×C113—24no—
17#575×C113—22no—
18#575×C113C2212yescomplemented
19C2×AGL(1,ℤ/8)×C113—22no—
20C2×AGL(1,ℤ/8)×C113C2212yes—
21C2×AGL(1,ℤ/8)×C113C2212yescomplemented
22#568×C113C2211yescharacteristic, complemented
23#546×C113—22no—
24#546×C113—22no—
25D42×C113—22no—
26D42×C113—22no—
27#535×C113C2211yescharacteristic
28#535×C113C2211yescharacteristic, complemented
29#534×C113—22no—
30#525×C113C2211yescharacteristic
31#525×C113C2211yescharacteristic, complemented
32#525×C113C2212yescomplemented
33C2×#120×C113—22no—
34#518×C113C2211yescharacteristic, complemented
35#458×C113—22no—
36B(4,𝔽2)×C113—22no—
37#454×C113—22no—
38#453×C113—22no—
39#450×C113—24no—
40#447×C113—24no—
41#421×C113C2212yescomplemented
42#421×C113C2212yescomplemented
43#418×C113C2212yescomplemented
44#418×C113C2212yescomplemented
45#413×C113C2211yescharacteristic, complemented
46#410×C113C2211yescharacteristic, complemented
47#410×C113C2212yescomplemented
48#407×C113C2212yescomplemented
49#344×C113C2212yescomplemented
50H(3,ℤ/4)×C113C2212yescomplemented
51C25×C113—21no—
522−1+4×C113—22no—
532−1+4×C113—21no—
54H(5,𝔽2)×C113—24no—
55H(5,𝔽2)×C113—22no—
56H(5,𝔽2)×C113—22no—
57H(5,𝔽2)×C113—21no—
58H(5,𝔽2)×C113—42no—
59C2×#41×C113—21no—
60C2×#41×C113—22no—
61C2×#41×C113—42no—
62C2×#41×C113D412yescomplemented
63C2×#41×C113C2311yescharacteristic
64C2×#41×C113C2312yes—
65C2×#41×C113C2311yescharacteristic
66C22×D4×C113—24no—
67C22×D4×C113—22no—
68C22×D4×C113—21no—
69C22×D4×C113—22no—
70C22×D4×C113—22no—
71C22×D4×C113—24no—
72C22×D4×C113—21no—
73C22×D4×C113—42no—
74C22×D4×C113D412yescomplemented
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C23×C4×C113C2311yescharacteristic
78#137×C113—24no—
79#137×C113—22no—
80#137×C113—22no—
81AGL(1,ℤ/8)×C113—28no—
82AGL(1,ℤ/8)×C113—24no—
83AGL(1,ℤ/8)×C113—22no—
84AGL(1,ℤ/8)×C113—24no—
85AGL(1,ℤ/8)×C113—24no—
86AGL(1,ℤ/8)×C113—22no—
87AGL(1,ℤ/8)×C113—24no—
88AGL(1,ℤ/8)×C113—42no—
89#135×C113—28no—
90#135×C113—24no—
91C2×SD16×C113—24no—
92C2×SD16×C113—22no—
93C2×SD16×C113D414yescomplemented
94C2×D8×C113—24no—
95C2×D8×C113—22no—
96C2×D8×C113D414yescomplemented
97#131×C113—24no—
98C2×M16×C113—22no—
99C2×M16×C113C2312yes—
100C2×M16×C113C2312yes—
101#127×C113—21no—
102#127×C113D412yescomplemented
103#124×C113—21no—
104#124×C113D412yescomplemented
105#123×C113—24no—
106#123×C113—21no—
107#123×C113—22no—
108#123×C113D412yes—
109C22⋊Q8×C113—21no—
110C22⋊Q8×C113—21no—
111C22⋊Q8×C113—22no—
112#121×C113—24no—
113#121×C113—24no—
114#121×C113—21no—
115#121×C113—21no—
116#121×C113—22no—
117#121×C113—22no—
118#121×C113—22no—
119#120×C113—24no—
120#120×C113—24no—
121#120×C113—24no—
122#120×C113—21no—
123#120×C113—22no—
124#120×C113—22no—
125#120×C113—22no—
126#120×C113D412yes—
127C4×D4×C113—22no—
128C4×D4×C113—22no—
129C4×D4×C113—22no—
130C4×D4×C113—22no—
131C4×D4×C113—42no—
132#117×C113C2312yes—
133#117×C113C2311yescharacteristic
134#117×C113C2311yescharacteristic
135C2×C22⋊C4×C113—24no—
136C2×C22⋊C4×C113—22no—
137#104×C113—24no—
138#104×C113—42no—
139#102×C113—24no—
140#102×C113—24no—
141#101×C113—21no—
142#100×C113—21no—
143#99×C113—22no—
144#99×C113—24no—
145C22⋊C8×C113—24no—
146C24×C113—21no—
147C24×C113—24no—
148C24×C113—22no—
149C24×C113—21no—
150C24×C113—44no—
151C24×C113—84no—
152C24×C113C2×D411yescharacteristic
153#41×C113—22no—
154#41×C113—22no—
155#41×C113—24no—
156#41×C113—24no—
157#41×C113—22no—
158#41×C113—22no—
159#41×C113—22no—
160#41×C113—22no—
161#41×C113—22no—
162#41×C113—22no—
163#41×C113—42no—
164#41×C113—44no—
165#41×C113—42no—
166#41×C113—44no—
167#41×C113—42no—
168#41×C113—42no—
169#41×C113—42no—
170C2×Q8×C113—22no—
171C2×Q8×C113—42no—
172C2×Q8×C113C2×D411yescharacteristic
173C2×Q8×C113C2×D411yescharacteristic
174C2×Q8×C113C2×D412yescomplemented
175C2×D4×C113—22no—
176C2×D4×C113—24no—
177C2×D4×C113—22no—
178C2×D4×C113—24no—
179C2×D4×C113—22no—
180C2×D4×C113—22no—
181C2×D4×C113—22no—
182C2×D4×C113—21no—
183C2×D4×C113—24no—
184C2×D4×C113—24no—
185C2×D4×C113—22no—
186C2×D4×C113—21no—
187C2×D4×C113—22no—
188C2×D4×C113—21no—
189C2×D4×C113—22no—
190C2×D4×C113—22no—
191C2×D4×C113—42no—
192C2×D4×C113—44no—
193C2×D4×C113—48no—
194C2×D4×C113—44no—
195C2×D4×C113—42no—
196C2×D4×C113—48no—
197C2×D4×C113—44no—
198C2×D4×C113—44no—
199C2×D4×C113—42no—
200C2×D4×C113—44no—
201C2×D4×C113—42no—
202C2×D4×C113—88no—
203C2×D4×C113C2×D412yes—
204C2×D4×C113C2×D412yes—
205C2×D4×C113C2×D411yescharacteristic
206C2×D4×C113C2×D411yescharacteristic
207C2×D4×C113C2×D414yes—
208C2×D4×C113C2×D412yes—
209C2×D4×C113C2×D412yescomplemented
210C22×C4×C113—24no—
211C22×C4×C113—22no—
212C22×C4×C113—22no—
213C22×C4×C113—21no—
214C22×C4×C113—21no—
215C22×C4×C113—21no—
216C22×C4×C113—22no—
217C22×C4×C113—22no—
218C22×C4×C113—42no—
219C22×C4×C113C2×D411yescharacteristic
220C22×C4×C113C2×D412yes—
221C22×C4×C113C2411yescharacteristic
222Q16×C113—24no—
223SD16×C113—24no—
224SD16×C113—24no—
225SD16×C113—28no—
226SD16×C113—44no—
227D8×C113—24no—
228D8×C113—28no—
229D8×C113—44no—
230M16×C113—24no—
231M16×C113—22no—
232M16×C113—22no—
233M16×C113—22no—
234M16×C113—22no—
235C2×C8×C113—24no—
236C2×C8×C113—22no—
237C2×C8×C113C2×D414yescomplemented
238C4⋊C4×C113—22no—
239C4⋊C4×C113—22no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—22no—
243C4⋊C4×C113—42no—
244C22⋊C4×C113—22no—
245C22⋊C4×C113—24no—
246C22⋊C4×C113—24no—
247C22⋊C4×C113—22no—
248C22⋊C4×C113—22no—
249C22⋊C4×C113—21no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—24no—
252C22⋊C4×C113—22no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113C2×D412yes—
256C42×C113—21no—
257C42×C113—22no—
258C42×C113C2×D412yes—
259C23×C113—21no—
260C23×C113—22no—
261C23×C113—22no—
262C23×C113—24no—
263C23×C113—22no—
264C23×C113—21no—
265C23×C113—22no—
266C23×C113—42no—
267C23×C113—44no—
268C23×C113—48no—
269C23×C113—48no—
270C23×C113—42no—
271C23×C113—42no—
272C23×C113—88no—
273C23×C113—82no—
274C23×C113—82no—
275C23×C113—84no—
276C23×C113—84no—
277C23×C113—88no—
278C23×C113#12012yes—
279C23×C113C22×D411yescharacteristic
280Q8×C113—22no—
281Q8×C113—22no—
282Q8×C113—21no—
283Q8×C113—21no—
284Q8×C113—22no—
285Q8×C113—42no—
286D4×C113—24no—
287D4×C113—22no—
288D4×C113—21no—
289D4×C113—22no—
290D4×C113—21no—
291D4×C113—24no—
292D4×C113—22no—
293D4×C113—22no—
294D4×C113—24no—
295D4×C113—44no—
296D4×C113—42no—
297D4×C113—44no—
298D4×C113—48no—
299D4×C113—44no—
300D4×C113—44no—
301D4×C113—44no—
302D4×C113—42no—
303D4×C113—42no—
304D4×C113—42no—
305D4×C113—41no—
306D4×C113—41no—
307D4×C113—84no—
308D4×C113—84no—
309D4×C113—84no—
310D4×C113#12014yes—
311C2×C4×C113—22no—
312C2×C4×C113—22no—
313C2×C4×C113—22no—
314C2×C4×C113—22no—
315C2×C4×C113—21no—
316C2×C4×C113—21no—
317C2×C4×C113—22no—
318C2×C4×C113—22no—
319C2×C4×C113—44no—
320C2×C4×C113—44no—
321C2×C4×C113—42no—
322C2×C4×C113—41no—
323C2×C4×C113—41no—
324C2×C4×C113—42no—
325C2×C4×C113—42no—
326C2×C4×C113—42no—
327C2×C4×C113—42no—
328C2×C4×C113—42no—
329C2×C4×C113—84no—
330C2×C4×C113#12012yes—
331C2×C4×C113C22×D411yescharacteristic
332C2×C4×C113C22×D412yes—
333C2×C4×C113C22×D411yescharacteristic
334C2×C4×C113H(5,𝔽2)12yes—
335C8×C113—24no—
336C8×C113—42no—
337C22×C113—22no—
338C22×C113—24no—
339C22×C113—22no—
340C22×C113—24no—
341C22×C113—41no—
342C22×C113—42no—
343C22×C113—44no—
344C22×C113—41no—
345C22×C113—42no—
346C22×C113—42no—
347C22×C113—44no—
348C22×C113—41no—
349C22×C113—42no—
350C22×C113—41no—
351C22×C113—42no—
352C22×C113—84no—
353C22×C113—82no—
354C22×C113—84no—
355C22×C113—816no—
356C22×C113—164no—
357C22×C113—162no—
358C22×C113C2×#12011yescharacteristic
359C22×C113D4212yes—
360C4×C113—22no—
361C4×C113—42no—
362C4×C113—42no—
363C4×C113—41no—
364C4×C113—41no—
365C4×C113—42no—
366C4×C113—82no—
367C4×C113C2×#12011yescharacteristic
368C4×C113#53411yescharacteristic
369C4×C113D4212yes—
370#23882C11311yesmaximal, characteristic, direct product factor, Sylow
371C2×C113—21no—
372C2×C113—22no—
373C2×C113—42no—
374C2×C113—44no—
375C2×C113—42no—
376C2×C113—82no—
377C2×C113—81no—
378C2×C113—82no—
379C2×C113#240311yescharacteristic
380#3585C2×C11311yescharacteristic, complemented
381#3484C2×C11311yescharacteristic, complemented
382#3025C2×C11311yescharacteristic, complemented
383#3021C2×C11311yescharacteristic, complemented
384#3003C2×C11312yescomplemented
385#2010C2×C11312yescomplemented
386#2008C2×C11312yescomplemented
387#1910C2×C11311yescharacteristic, complemented
388#1904C2×C11312yescomplemented
389#1891C2×C11311yescharacteristic, complemented
390#1795C2×C11311yescharacteristic, complemented
391C113#2388211yescharacteristic, direct product factor, Sylow
392#585C22×C11311yescharacteristic, complemented
393C2×H(5,𝔽2)C22×C11311yescharacteristic
394C23×D4C22×C11311yescharacteristic, complemented
395#577—24no—
396#576—24no—
397#575—22no—
398#575C22×C11312yescomplemented
399C2×AGL(1,ℤ/8)—22no—
400C2×AGL(1,ℤ/8)C22×C11312yes—
401C2×AGL(1,ℤ/8)C22×C11312yescomplemented
402#568C22×C11311yescharacteristic, complemented
403#546—22no—
404#546—22no—
405D42—22no—
406D42—22no—
407#535C22×C11311yescharacteristic
408#535C22×C11311yescharacteristic, complemented
409#534—22no—
410#525C22×C11311yescharacteristic
411#525C22×C11311yescharacteristic, complemented
412#525C22×C11312yescomplemented
413C2×#120—22no—
414#518C22×C11311yescharacteristic, complemented
415#458—22no—
416B(4,𝔽2)—22no—
417#454—22no—
418#453—22no—
419#450—24no—
420#447—24no—
421#421C22×C11312yescomplemented
422#421C22×C11312yescomplemented
423#418C22×C11312yescomplemented
424#418C22×C11312yescomplemented
425#413C22×C11311yescharacteristic, complemented
426#410C22×C11311yescharacteristic, complemented
427#410C22×C11312yescomplemented
428#407C22×C11312yescomplemented
429#344C22×C11312yescomplemented
430H(3,ℤ/4)C22×C11312yescomplemented
431C25—21no—
4322−1+4—22no—
4332−1+4—21no—
434H(5,𝔽2)—24no—
435H(5,𝔽2)—22no—
436H(5,𝔽2)—22no—
437H(5,𝔽2)—21no—
438H(5,𝔽2)—42no—
439C2×#41—21no—
440C2×#41—22no—
441C2×#41—42no—
442C2×#41D4×C11312yescomplemented
443C2×#41C23×C11311yescharacteristic
444C2×#41C23×C11312yes—
445C2×#41C23×C11311yescharacteristic
446C22×D4—24no—
447C22×D4—22no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4—22no—
451C22×D4—24no—
452C22×D4—21no—
453C22×D4—42no—
454C22×D4D4×C11312yescomplemented
455C22×D4C23×C11311yescharacteristic
456C22×D4C23×C11311yescharacteristic
457C23×C4C23×C11311yescharacteristic
458#137—24no—
459#137—22no—
460#137—22no—
461AGL(1,ℤ/8)—28no—
462AGL(1,ℤ/8)—24no—
463AGL(1,ℤ/8)—22no—
464AGL(1,ℤ/8)—24no—
465AGL(1,ℤ/8)—24no—
466AGL(1,ℤ/8)—22no—
467AGL(1,ℤ/8)—24no—
468AGL(1,ℤ/8)—42no—
469#135—28no—
470#135—24no—
471C2×SD16—24no—
472C2×SD16—22no—
473C2×SD16D4×C11314yescomplemented
474C2×D8—24no—
475C2×D8—22no—
476C2×D8D4×C11314yescomplemented
477#131—24no—
478C2×M16—22no—
479C2×M16C23×C11312yes—
480C2×M16C23×C11312yes—
481#127—21no—
482#127D4×C11312yescomplemented
483#124—21no—
484#124D4×C11312yescomplemented
485#123—24no—
486#123—21no—
487#123—22no—
488#123D4×C11312yes—
489C22⋊Q8—21no—
490C22⋊Q8—21no—
491C22⋊Q8—22no—
492#121—24no—
493#121—24no—
494#121—21no—
495#121—21no—
496#121—22no—
497#121—22no—
498#121—22no—
499#120—24no—
500#120—24no—
501#120—24no—
502#120—21no—
503#120—22no—
504#120—22no—
505#120—22no—
506#120D4×C11312yes—
507C4×D4—22no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—42no—
512#117C23×C11312yes—
513#117C23×C11311yescharacteristic
514#117C23×C11311yescharacteristic
515C2×C22⋊C4—24no—
516C2×C22⋊C4—22no—
517#104—24no—
518#104—42no—
519#102—24no—
520#102—24no—
521#101—21no—
522#100—21no—
523#99—22no—
524#99—24no—
525C22⋊C8—24no—
526C24—21no—
527C24—24no—
528C24—22no—
529C24—21no—
530C24—44no—
531C24—84no—
532C24C2×D4×C11311yescharacteristic
533#41—22no—
534#41—22no—
535#41—24no—
536#41—24no—
537#41—22no—
538#41—22no—
539#41—22no—
540#41—22no—
541#41—22no—
542#41—22no—
543#41—42no—
544#41—44no—
545#41—42no—
546#41—44no—
547#41—42no—
548#41—42no—
549#41—42no—
550C2×Q8—22no—
551C2×Q8—42no—
552C2×Q8C2×D4×C11311yescharacteristic
553C2×Q8C2×D4×C11311yescharacteristic
554C2×Q8C2×D4×C11312yescomplemented
555C2×D4—22no—
556C2×D4—24no—
557C2×D4—22no—
558C2×D4—24no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—21no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—42no—
572C2×D4—44no—
573C2×D4—48no—
574C2×D4—44no—
575C2×D4—42no—
576C2×D4—48no—
577C2×D4—44no—
578C2×D4—44no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—42no—
582C2×D4—88no—
583C2×D4C2×D4×C11312yes—
584C2×D4C2×D4×C11312yes—
585C2×D4C2×D4×C11311yescharacteristic
586C2×D4C2×D4×C11311yescharacteristic
587C2×D4C2×D4×C11314yes—
588C2×D4C2×D4×C11312yes—
589C2×D4C2×D4×C11312yescomplemented
590C22×C4—24no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—42no—
599C22×C4C2×D4×C11311yescharacteristic
600C22×C4C2×D4×C11312yes—
601C22×C4C24×C11311yescharacteristic
602Q16—24no—
603SD16—24no—
604SD16—24no—
605SD16—28no—
606SD16—44no—
607D8—24no—
608D8—28no—
609D8—44no—
610M16—24no—
611M16—22no—
612M16—22no—
613M16—22no—
614M16—22no—
615C2×C8—24no—
616C2×C8—22no—
617C2×C8C2×D4×C11314yescomplemented
618C4⋊C4—22no—
619C4⋊C4—22no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—22no—
623C4⋊C4—42no—
624C22⋊C4—22no—
625C22⋊C4—24no—
626C22⋊C4—24no—
627C22⋊C4—22no—
628C22⋊C4—22no—
629C22⋊C4—21no—
630C22⋊C4—22no—
631C22⋊C4—24no—
632C22⋊C4—22no—
633C22⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4C2×D4×C11312yes—
636C42—21no—
637C42—22no—
638C42C2×D4×C11312yes—
639C23—21no—
640C23—22no—
641C23—22no—
642C23—24no—
643C23—22no—
644C23—21no—
645C23—22no—
646C23—42no—
647C23—44no—
648C23—48no—
649C23—48no—
650C23—42no—
651C23—42no—
652C23—88no—
653C23—82no—
654C23—82no—
655C23—84no—
656C23—84no—
657C23—88no—
658C23#120×C11312yes—
659C23C22×D4×C11311yescharacteristic
660Q8—22no—
661Q8—22no—
662Q8—21no—
663Q8—21no—
664Q8—22no—
665Q8—42no—
666D4—24no—
667D4—22no—
668D4—21no—
669D4—22no—
670D4—21no—
671D4—24no—
672D4—22no—
673D4—22no—
674D4—24no—
675D4—44no—
676D4—42no—
677D4—44no—
678D4—48no—
679D4—44no—
680D4—44no—
681D4—44no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—41no—
686D4—41no—
687D4—84no—
688D4—84no—
689D4—84no—
690D4#120×C11314yes—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—84no—
710C2×C4#120×C11312yes—
711C2×C4C22×D4×C11311yescharacteristic
712C2×C4C22×D4×C11312yes—
713C2×C4C22×D4×C11311yescharacteristic
714C2×C4H(5,𝔽2)×C11312yes—
715C8—24no—
716C8—42no—
717C22—22no—
718C22—24no—
719C22—22no—
720C22—24no—
721C22—41no—
722C22—42no—
723C22—44no—
724C22—41no—
725C22—42no—
726C22—42no—
727C22—44no—
728C22—41no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—84no—
733C22—82no—
734C22—84no—
735C22—816no—
736C22—164no—
737C22—162no—
738C22C2×#120×C11311yescharacteristic
739C22D42×C11312yes—
740C4—22no—
741C4—42no—
742C4—42no—
743C4—41no—
744C4—41no—
745C4—42no—
746C4—82no—
747C4C2×#120×C11311yescharacteristic
748C4#534×C11311yescharacteristic
749C4D42×C11312yes—
750C2—21no—
751C2—22no—
752C2—42no—
753C2—44no—
754C2—42no—
755C2—82no—
756C2—81no—
757C2—82no—
758C2C113×#240311yescharacteristic
subgroupG/H
center, socleC2×C113#2403
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C113 ◁ C22×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3585C2semidirect
2. C113×#3484C2semidirect
3. C113×#3025C2semidirect
4. C113×#3021C2semidirect
5. C113×#3003C2semidirect
6. C113×#2010C2semidirect
7. C113×#2008C2semidirect
8. C113×#1910C2semidirect
9. C113×#1904C2semidirect
10. C113×#1891C2semidirect
11. C113×#1795C2semidirect
12. #585×C113C22semidirect
14. C23×D4×C113C22semidirect
18. #575×C113C22semidirect
21. C2×AGL(1,ℤ/8)×C113C22semidirect
22. #568×C113C22semidirect
28. #535×C113C22semidirect
31. #525×C113C22semidirect
32. #525×C113C22semidirect
34. #518×C113C22semidirect
41. #421×C113C22semidirect
42. #421×C113C22semidirect
43. #418×C113C22semidirect
44. #418×C113C22semidirect
45. #413×C113C22semidirect
46. #410×C113C22semidirect
47. #410×C113C22semidirect
48. #407×C113C22semidirect
49. #344×C113C22semidirect
50. H(3,ℤ/4)×C113C22semidirect
62. C2×#41×C113D4semidirect
74. C22×D4×C113D4semidirect
93. C2×SD16×C113D4semidirect
96. C2×D8×C113D4semidirect
102. #127×C113D4semidirect
104. #124×C113D4semidirect
174. C2×Q8×C113C2×D4semidirect
209. C2×D4×C113C2×D4semidirect
237. C2×C8×C113C2×D4semidirect
370. #23882C113direct (N × H)
380. #3585C2×C113semidirect
381. #3484C2×C113semidirect
382. #3025C2×C113semidirect
383. #3021C2×C113semidirect
384. #3003C2×C113semidirect
385. #2010C2×C113semidirect
386. #2008C2×C113semidirect
387. #1910C2×C113semidirect
388. #1904C2×C113semidirect
389. #1891C2×C113semidirect
390. #1795C2×C113semidirect
391. C113#23882direct (N × H)
392. #585C22×C113semidirect
394. C23×D4C22×C113semidirect
398. #575C22×C113semidirect
401. C2×AGL(1,ℤ/8)C22×C113semidirect
402. #568C22×C113semidirect
408. #535C22×C113semidirect
411. #525C22×C113semidirect
412. #525C22×C113semidirect
414. #518C22×C113semidirect
421. #421C22×C113semidirect
422. #421C22×C113semidirect
423. #418C22×C113semidirect
424. #418C22×C113semidirect
425. #413C22×C113semidirect
426. #410C22×C113semidirect
427. #410C22×C113semidirect
428. #407C22×C113semidirect
429. #344C22×C113semidirect
430. H(3,ℤ/4)C22×C113semidirect
442. C2×#41D4×C113semidirect
454. C22×D4D4×C113semidirect
473. C2×SD16D4×C113semidirect
476. C2×D8D4×C113semidirect
482. #127D4×C113semidirect
484. #124D4×C113semidirect
554. C2×Q8C2×D4×C113semidirect
589. C2×D4C2×D4×C113semidirect
617. C2×C8C2×D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35852
C113×#34842
C113×#30252
C113×#30212
C113×#30032
C113×#20102
C113×#20082
C113×#19102
C113×#19042
C113×#18912
C113×#17952
#23882113