Finite Group Databasebeta

← C113×#24473 #43292493

Subgroups — C113×#24473 #43292493

Order 28928.

1314 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3586C211yesmaximal, characteristic, complemented
2C113×#3068C211yesmaximal, characteristic, complemented
3C113×#3040C211yesmaximal, characteristic, complemented
4C113×#3021C211yesmaximal, characteristic, complemented
5C2×#454×C113C211yesmaximal, characteristic, complemented
6C113×#2901C211yesmaximal, characteristic, complemented
7C113×#2050C211yesmaximal, characteristic, complemented
8C113×#2049C211yesmaximal, characteristic, complemented
9C113×#2008C211yesmaximal, characteristic, complemented
10C113×#2004C211yesmaximal, characteristic, complemented
11C113×#1906C211yesmaximal, characteristic, complemented
12C113×#1903C211yesmaximal, characteristic, complemented
13C113×#1902C211yesmaximal, characteristic, complemented
14C113×#1861C211yesmaximal, characteristic, complemented
15C113×#1796C211yesmaximal, characteristic, complemented
16#585×C113C2211yescharacteristic
17C2×2−1+4×C113C2211yescharacteristic
18#578×C113—22no—
19#578×C113—22no—
20#577×C113—22no—
21#577×C113—22no—
22#575×C113—22no—
23#575×C113C2211yescharacteristic
24#575×C113C2211yescharacteristic
25C2×#137×C113—22no—
26C2×#137×C113C2211yescharacteristic
27C2×#137×C113C2211yescharacteristic
28C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
29C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C113C2211yescharacteristic, complemented
31#568×C113C2211yescharacteristic
32#568×C113C2211yescharacteristic
33#535×C113C2211yescharacteristic
34C2×#124×C113C2211yescharacteristic, complemented
35C4×#41×C113C2211yescharacteristic
36#472×C113—22no—
37#471×C113—22no—
38#464×C113—22no—
39#463×C113—22no—
40#454×C113—22no—
41#454×C113—22no—
42#454×C113—22no—
43#453×C113—22no—
44#430×C113C2211yescharacteristic, complemented
45#423×C113C2211yescharacteristic, complemented
46#421×C113—22no—
47#421×C113C2211yescharacteristic
48#421×C113C2211yescharacteristic
49#421×C113C2211yescharacteristic
50#421×C113C2211yescharacteristic
51C2×#104×C113—22no—
52C2×#104×C113C2211yescharacteristic
53C2×#104×C113C2211yescharacteristic
54C2×#104×C113C2211yescharacteristic, complemented
55#419×C113C2211yescharacteristic, complemented
56#419×C113C2211yescharacteristic, complemented
57#418×C113C2211yescharacteristic, complemented
58#413×C113C2211yescharacteristic
59#413×C113C2211yescharacteristic, complemented
60C2×#101×C113C2211yescharacteristic, complemented
61C2×#100×C113C2211yescharacteristic, complemented
62#410×C113C2211yescharacteristic, complemented
63#344×C113C2211yescharacteristic, complemented
64#344×C113C2211yescharacteristic, complemented
65#339×C113C2211yescharacteristic, complemented
66#338×C113C2211yescharacteristic, complemented
672−1+4×C113—22no—
682−1+4×C113—22no—
692−1+4×C113—21no—
702−1+4×C113—21no—
712−1+4×C113—22no—
722−1+4×C113—41no—
732−1+4×C113D412yes—
74H(5,𝔽2)×C113—21no—
75H(5,𝔽2)×C113—21no—
76H(5,𝔽2)×C113—41no—
77H(5,𝔽2)×C113D412yes—
78C2×#41×C113—22no—
79C2×#41×C113—22no—
80C2×#41×C113—21no—
81C2×#41×C113—21no—
82C2×#41×C113—41no—
83C2×#41×C113—41no—
84C2×#41×C113C2311yescharacteristic
85C2×#41×C113C2311yescharacteristic
86C2×#41×C113C2311yescharacteristic
87C2×#41×C113C2311yescharacteristic
88C22×Q8×C113—21no—
89C22×Q8×C113—21no—
90C22×Q8×C113C2311yescharacteristic
91C22×D4×C113C2311yescharacteristic
92#137×C113—24no—
93#137×C113—24no—
94#137×C113—24no—
95#137×C113—22no—
96#137×C113—22no—
97#137×C113—21no—
98#137×C113—22no—
99#137×C113—21no—
100#137×C113—21no—
101#137×C113—22no—
102#137×C113D412yescomplemented
103AGL(1,ℤ/8)×C113—24no—
104AGL(1,ℤ/8)×C113—21no—
105AGL(1,ℤ/8)×C113—21no—
106AGL(1,ℤ/8)×C113—21no—
107AGL(1,ℤ/8)×C113—22no—
108AGL(1,ℤ/8)×C113—22no—
109AGL(1,ℤ/8)×C113—22no—
110AGL(1,ℤ/8)×C113—22no—
111AGL(1,ℤ/8)×C113—22no—
112AGL(1,ℤ/8)×C113—41no—
113AGL(1,ℤ/8)×C113D412yescomplemented
114#135×C113—24no—
115#135×C113—24no—
116#135×C113—22no—
117#135×C113—22no—
118C2×Q16×C113—24no—
119C2×Q16×C113—21no—
120C2×Q16×C113D412yescomplemented
121C2×SD16×C113—24no—
122C2×SD16×C113—21no—
123C2×SD16×C113—21no—
124C2×SD16×C113—21no—
125C2×SD16×C113—21no—
126C2×SD16×C113D412yescomplemented
127C2×D8×C113—21no—
128C2×D8×C113—21no—
129C2×D8×C113—21no—
130#131×C113—22no—
131#131×C113—22no—
132#131×C113—22no—
133#131×C113—41no—
134C2×M16×C113—22no—
135C2×M16×C113—22no—
136C2×M16×C113C2311yescharacteristic
137C2×M16×C113C2311yescharacteristic
138C2×M16×C113C2311yescharacteristic
139C2×M16×C113C2311yescharacteristic
140C2×M16×C113C2311yescharacteristic
141C2×M16×C113C2311yescharacteristic
142#127×C113—21no—
143#124×C113—22no—
144#124×C113—21no—
145#124×C113—21no—
146#124×C113—21no—
147#121×C113—41no—
148#120×C113—41no—
149C4×Q8×C113—21no—
150C4×D4×C113—21no—
151C4×D4×C113—41no—
152#117×C113—21no—
153#117×C113C2311yescharacteristic
154#117×C113C2311yescharacteristic
155C2×C22⋊C4×C113—41no—
156C2×C42×C113—21no—
157C2×C42×C113C2311yescharacteristic
158#108×C113—22no—
159C4⋊C8×C113—22no—
160#104×C113—22no—
161#104×C113—22no—
162#104×C113—22no—
163#104×C113—22no—
164#104×C113—21no—
165#104×C113—21no—
166#104×C113—21no—
167#104×C113—21no—
168#104×C113D412yescomplemented
169#104×C113D412yescomplemented
170#103×C113—22no—
171#103×C113—41no—
172#102×C113—22no—
173#101×C113—21no—
174#101×C113—21no—
175#101×C113—22no—
176#100×C113—21no—
177#100×C113—21no—
178#100×C113—22no—
179#99×C113—41no—
180C24×C113—21no—
181#41×C113—21no—
182#41×C113—21no—
183#41×C113—21no—
184#41×C113—21no—
185#41×C113—24no—
186#41×C113—22no—
187#41×C113—22no—
188#41×C113—22no—
189#41×C113—22no—
190#41×C113—21no—
191#41×C113—21no—
192#41×C113—21no—
193#41×C113—21no—
194#41×C113—21no—
195#41×C113—21no—
196#41×C113—21no—
197#41×C113—21no—
198#41×C113—42no—
199#41×C113—42no—
200#41×C113—42no—
201#41×C113—42no—
202#41×C113—42no—
203#41×C113—44no—
204#41×C113—42no—
205#41×C113—41no—
206#41×C113—41no—
207#41×C113—44no—
208#41×C113—42no—
209#41×C113C2×D412yes—
210#41×C113C2×D412yes—
211#41×C113C2×D412yes—
212#41×C113C2×D412yes—
213C2×Q8×C113—21no—
214C2×Q8×C113—24no—
215C2×Q8×C113—22no—
216C2×Q8×C113—22no—
217C2×Q8×C113—21no—
218C2×Q8×C113—21no—
219C2×Q8×C113—21no—
220C2×Q8×C113—21no—
221C2×Q8×C113—41no—
222C2×Q8×C113—42no—
223C2×Q8×C113—42no—
224C2×Q8×C113—41no—
225C2×Q8×C113—42no—
226C2×Q8×C113C2×D411yescharacteristic
227C2×Q8×C113C2×D411yescharacteristic
228C2×Q8×C113C2×D412yes—
229C2×Q8×C113C2×D411yescharacteristic
230C2×Q8×C113#4111yescharacteristic
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—22no—
234C2×D4×C113—22no—
235C2×D4×C113—21no—
236C2×D4×C113—21no—
237C2×D4×C113—21no—
238C2×D4×C113—21no—
239C2×D4×C113—21no—
240C2×D4×C113—21no—
241C2×D4×C113—21no—
242C2×D4×C113—21no—
243C2×D4×C113—42no—
244C2×D4×C113—41no—
245C2×D4×C113—42no—
246C2×D4×C113—42no—
247C2×D4×C113—41no—
248C2×D4×C113—42no—
249C2×D4×C113C2×D411yescharacteristic
250C2×D4×C113C2×D411yescharacteristic
251C2×D4×C113C2×D411yescharacteristic
252C2×D4×C113#4111yescharacteristic
253C22×C4×C113—21no—
254C22×C4×C113—21no—
255C22×C4×C113—21no—
256C22×C4×C113—21no—
257C22×C4×C113—21no—
258C22×C4×C113—21no—
259C22×C4×C113—42no—
260C22×C4×C113—41no—
261C22×C4×C113—41no—
262C22×C4×C113—41no—
263C22×C4×C113C2411yescharacteristic
264Q16×C113—24no—
265Q16×C113—22no—
266Q16×C113—22no—
267Q16×C113—24no—
268SD16×C113—24no—
269SD16×C113—22no—
270SD16×C113—22no—
271SD16×C113—22no—
272SD16×C113—22no—
273SD16×C113—24no—
274SD16×C113—42no—
275SD16×C113—42no—
276SD16×C113—42no—
277D8×C113—22no—
278D8×C113—22no—
279D8×C113—42no—
280D8×C113—42no—
281D8×C113—42no—
282M16×C113—24no—
283M16×C113—21no—
284M16×C113—21no—
285M16×C113—21no—
286M16×C113—21no—
287M16×C113—21no—
288M16×C113—21no—
289M16×C113—21no—
290M16×C113—21no—
291M16×C113—21no—
292M16×C113—21no—
293M16×C113—42no—
294M16×C113C2×D412yes—
295M16×C113C2×D412yes—
296C2×C8×C113—24no—
297C2×C8×C113—21no—
298C2×C8×C113—21no—
299C2×C8×C113—21no—
300C2×C8×C113—21no—
301C2×C8×C113—21no—
302C2×C8×C113—42no—
303C2×C8×C113C2×D412yes—
304C4⋊C4×C113—21no—
305C4⋊C4×C113—21no—
306C4⋊C4×C113—41no—
307C22⋊C4×C113—21no—
308C22⋊C4×C113—21no—
309C22⋊C4×C113—42no—
310C22⋊C4×C113—42no—
311C22⋊C4×C113—41no—
312C22⋊C4×C113—42no—
313C42×C113—21no—
314C42×C113—21no—
315C42×C113—21no—
316C42×C113—41no—
317C42×C113C2×D411yescharacteristic
318C42×C113C2×D411yescharacteristic
319C23×C113—21no—
320C23×C113—21no—
321C23×C113—21no—
322C23×C113—21no—
323C23×C113—42no—
324C23×C113—41no—
325C23×C113—41no—
326C23×C113—41no—
327C23×C113—82no—
328C23×C113H(5,𝔽2)11yescharacteristic
329Q8×C113—21no—
330Q8×C113—21no—
331Q8×C113—21no—
332Q8×C113—22no—
333Q8×C113—21no—
334Q8×C113—21no—
335Q8×C113—21no—
336Q8×C113—22no—
337Q8×C113—42no—
338Q8×C113—44no—
339Q8×C113—41no—
340Q8×C113—41no—
341Q8×C113#12012yes—
342Q8×C113#12112yes—
343D4×C113—22no—
344D4×C113—22no—
345D4×C113—22no—
346D4×C113—22no—
347D4×C113—21no—
348D4×C113—21no—
349D4×C113—21no—
350D4×C113—21no—
351D4×C113—21no—
352D4×C113—21no—
353D4×C113—42no—
354D4×C113—42no—
355D4×C113—42no—
356D4×C113—44no—
357D4×C113—41no—
358D4×C113—41no—
359D4×C113—41no—
360D4×C113—41no—
361D4×C113—41no—
362D4×C113—41no—
363D4×C113—41no—
364D4×C113—41no—
365D4×C113—162no—
366D4×C113#12012yes—
367D4×C113#12112yes—
368C2×C4×C113—21no—
369C2×C4×C113—21no—
370C2×C4×C113—22no—
371C2×C4×C113—22no—
372C2×C4×C113—22no—
373C2×C4×C113—22no—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—21no—
377C2×C4×C113—22no—
378C2×C4×C113—21no—
379C2×C4×C113—42no—
380C2×C4×C113—42no—
381C2×C4×C113—42no—
382C2×C4×C113—44no—
383C2×C4×C113—44no—
384C2×C4×C113—41no—
385C2×C4×C113—41no—
386C2×C4×C113—41no—
387C2×C4×C113—41no—
388C2×C4×C113—41no—
389C2×C4×C113—41no—
390C2×C4×C113—41no—
391C2×C4×C113—41no—
392C2×C4×C113—81no—
393C2×C4×C113—82no—
394C2×C4×C113C22×D411yescharacteristic
395C2×C4×C113C22×D411yescharacteristic
396C2×C4×C113C22×D411yescharacteristic
397C2×C4×C113C22×D411yescharacteristic
398C2×C4×C113C2×#4111yescharacteristic
399C2×C4×C113H(5,𝔽2)11yescharacteristic
400C8×C113—22no—
401C8×C113—22no—
402C8×C113—22no—
403C8×C113—41no—
404C8×C113—41no—
405C8×C113—41no—
406C22×C113—22no—
407C22×C113—22no—
408C22×C113—41no—
409C22×C113—41no—
410C22×C113—41no—
411C22×C113—81no—
412C22×C113—81no—
413C22×C113—81no—
414C22×C113—81no—
415C22×C113—82no—
416C22×C113—82no—
417C22×C113—81no—
418C22×C113—161no—
419C22×C113—162no—
420C22×C113#53411yescharacteristic
421C22×C113D4211yescharacteristic
422C22×C113#54611yescharacteristic
423C4×C113—22no—
424C4×C113—22no—
425C4×C113—41no—
426C4×C113—41no—
427C4×C113—41no—
428C4×C113—42no—
429C4×C113—41no—
430C4×C113—81no—
431C4×C113—81no—
432C4×C113C2×#12011yescharacteristic
433C4×C113C2×#12111yescharacteristic
434C4×C113D4211yescharacteristic
435C4×C113#54611yescharacteristic
436#24473C11311yesmaximal, characteristic, direct product factor, Sylow
437C2×C113—21no—
438C2×C113—21no—
439C2×C113—21no—
440C2×C113—42no—
441C2×C113—42no—
442C2×C113—81no—
443C2×C113—81no—
444C2×C113—161no—
445C2×C113#241011yescharacteristic
446#3586C2×C11311yescharacteristic, complemented
447#3068C2×C11311yescharacteristic, complemented
448#3040C2×C11311yescharacteristic, complemented
449#3021C2×C11311yescharacteristic, complemented
450C2×#454C2×C11311yescharacteristic, complemented
451#2901C2×C11311yescharacteristic, complemented
452#2050C2×C11311yescharacteristic, complemented
453#2049C2×C11311yescharacteristic, complemented
454#2008C2×C11311yescharacteristic, complemented
455#2004C2×C11311yescharacteristic, complemented
456#1906C2×C11311yescharacteristic, complemented
457#1903C2×C11311yescharacteristic, complemented
458#1902C2×C11311yescharacteristic, complemented
459#1861C2×C11311yescharacteristic, complemented
460#1796C2×C11311yescharacteristic, complemented
461C113#2447311yescharacteristic, direct product factor, Sylow
462#585C22×C11311yescharacteristic
463C2×2−1+4C22×C11311yescharacteristic
464#578—22no—
465#578—22no—
466#577—22no—
467#577—22no—
468#575—22no—
469#575C22×C11311yescharacteristic
470#575C22×C11311yescharacteristic
471C2×#137—22no—
472C2×#137C22×C11311yescharacteristic
473C2×#137C22×C11311yescharacteristic
474C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
475C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
476C2×AGL(1,ℤ/8)C22×C11311yescharacteristic, complemented
477#568C22×C11311yescharacteristic
478#568C22×C11311yescharacteristic
479#535C22×C11311yescharacteristic
480C2×#124C22×C11311yescharacteristic, complemented
481C4×#41C22×C11311yescharacteristic
482#472—22no—
483#471—22no—
484#464—22no—
485#463—22no—
486#454—22no—
487#454—22no—
488#454—22no—
489#453—22no—
490#430C22×C11311yescharacteristic, complemented
491#423C22×C11311yescharacteristic, complemented
492#421—22no—
493#421C22×C11311yescharacteristic
494#421C22×C11311yescharacteristic
495#421C22×C11311yescharacteristic
496#421C22×C11311yescharacteristic
497C2×#104—22no—
498C2×#104C22×C11311yescharacteristic
499C2×#104C22×C11311yescharacteristic
500C2×#104C22×C11311yescharacteristic, complemented
501#419C22×C11311yescharacteristic, complemented
502#419C22×C11311yescharacteristic, complemented
503#418C22×C11311yescharacteristic, complemented
504#413C22×C11311yescharacteristic
505#413C22×C11311yescharacteristic, complemented
506C2×#101C22×C11311yescharacteristic, complemented
507C2×#100C22×C11311yescharacteristic, complemented
508#410C22×C11311yescharacteristic, complemented
509#344C22×C11311yescharacteristic, complemented
510#344C22×C11311yescharacteristic, complemented
511#339C22×C11311yescharacteristic, complemented
512#338C22×C11311yescharacteristic, complemented
5132−1+4—22no—
5142−1+4—22no—
5152−1+4—21no—
5162−1+4—21no—
5172−1+4—22no—
5182−1+4—41no—
5192−1+4D4×C11312yes—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—21no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)D4×C11312yes—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—21no—
527C2×#41—21no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41C23×C11311yescharacteristic
531C2×#41C23×C11311yescharacteristic
532C2×#41C23×C11311yescharacteristic
533C2×#41C23×C11311yescharacteristic
534C22×Q8—21no—
535C22×Q8—21no—
536C22×Q8C23×C11311yescharacteristic
537C22×D4C23×C11311yescharacteristic
538#137—24no—
539#137—24no—
540#137—24no—
541#137—22no—
542#137—22no—
543#137—21no—
544#137—22no—
545#137—21no—
546#137—21no—
547#137—22no—
548#137D4×C11312yescomplemented
549AGL(1,ℤ/8)—24no—
550AGL(1,ℤ/8)—21no—
551AGL(1,ℤ/8)—21no—
552AGL(1,ℤ/8)—21no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—22no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—22no—
558AGL(1,ℤ/8)—41no—
559AGL(1,ℤ/8)D4×C11312yescomplemented
560#135—24no—
561#135—24no—
562#135—22no—
563#135—22no—
564C2×Q16—24no—
565C2×Q16—21no—
566C2×Q16D4×C11312yescomplemented
567C2×SD16—24no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16D4×C11312yescomplemented
573C2×D8—21no—
574C2×D8—21no—
575C2×D8—21no—
576#131—22no—
577#131—22no—
578#131—22no—
579#131—41no—
580C2×M16—22no—
581C2×M16—22no—
582C2×M16C23×C11311yescharacteristic
583C2×M16C23×C11311yescharacteristic
584C2×M16C23×C11311yescharacteristic
585C2×M16C23×C11311yescharacteristic
586C2×M16C23×C11311yescharacteristic
587C2×M16C23×C11311yescharacteristic
588#127—21no—
589#124—22no—
590#124—21no—
591#124—21no—
592#124—21no—
593#121—41no—
594#120—41no—
595C4×Q8—21no—
596C4×D4—21no—
597C4×D4—41no—
598#117—21no—
599#117C23×C11311yescharacteristic
600#117C23×C11311yescharacteristic
601C2×C22⋊C4—41no—
602C2×C42—21no—
603C2×C42C23×C11311yescharacteristic
604#108—22no—
605C4⋊C8—22no—
606#104—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—21no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104D4×C11312yescomplemented
615#104D4×C11312yescomplemented
616#103—22no—
617#103—41no—
618#102—22no—
619#101—21no—
620#101—21no—
621#101—22no—
622#100—21no—
623#100—21no—
624#100—22no—
625#99—41no—
626C24—21no—
627#41—21no—
628#41—21no—
629#41—21no—
630#41—21no—
631#41—24no—
632#41—22no—
633#41—22no—
634#41—22no—
635#41—22no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—42no—
645#41—42no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—44no—
650#41—42no—
651#41—41no—
652#41—41no—
653#41—44no—
654#41—42no—
655#41C2×D4×C11312yes—
656#41C2×D4×C11312yes—
657#41C2×D4×C11312yes—
658#41C2×D4×C11312yes—
659C2×Q8—21no—
660C2×Q8—24no—
661C2×Q8—22no—
662C2×Q8—22no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8—42no—
669C2×Q8—42no—
670C2×Q8—41no—
671C2×Q8—42no—
672C2×Q8C2×D4×C11311yescharacteristic
673C2×Q8C2×D4×C11311yescharacteristic
674C2×Q8C2×D4×C11312yes—
675C2×Q8C2×D4×C11311yescharacteristic
676C2×Q8#41×C11311yescharacteristic
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—22no—
680C2×D4—22no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—42no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—41no—
694C2×D4—42no—
695C2×D4C2×D4×C11311yescharacteristic
696C2×D4C2×D4×C11311yescharacteristic
697C2×D4C2×D4×C11311yescharacteristic
698C2×D4#41×C11311yescharacteristic
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—42no—
706C22×C4—41no—
707C22×C4—41no—
708C22×C4—41no—
709C22×C4C24×C11311yescharacteristic
710Q16—24no—
711Q16—22no—
712Q16—22no—
713Q16—24no—
714SD16—24no—
715SD16—22no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—42no—
721SD16—42no—
722SD16—42no—
723D8—22no—
724D8—22no—
725D8—42no—
726D8—42no—
727D8—42no—
728M16—24no—
729M16—21no—
730M16—21no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—21no—
739M16—42no—
740M16C2×D4×C11312yes—
741M16C2×D4×C11312yes—
742C2×C8—24no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—42no—
749C2×C8C2×D4×C11312yes—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—41no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—42no—
756C22⋊C4—42no—
757C22⋊C4—41no—
758C22⋊C4—42no—
759C42—21no—
760C42—21no—
761C42—21no—
762C42—41no—
763C42C2×D4×C11311yescharacteristic
764C42C2×D4×C11311yescharacteristic
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—42no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—82no—
774C23H(5,𝔽2)×C11311yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—22no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—22no—
783Q8—42no—
784Q8—44no—
785Q8—41no—
786Q8—41no—
787Q8#120×C11312yes—
788Q8#121×C11312yes—
789D4—22no—
790D4—22no—
791D4—22no—
792D4—22no—
793D4—21no—
794D4—21no—
795D4—21no—
796D4—21no—
797D4—21no—
798D4—21no—
799D4—42no—
800D4—42no—
801D4—42no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—162no—
812D4#120×C11312yes—
813D4#121×C11312yes—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—42no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—44no—
829C2×C4—44no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—82no—
840C2×C4C22×D4×C11311yescharacteristic
841C2×C4C22×D4×C11311yescharacteristic
842C2×C4C22×D4×C11311yescharacteristic
843C2×C4C22×D4×C11311yescharacteristic
844C2×C4C2×#41×C11311yescharacteristic
845C2×C4H(5,𝔽2)×C11311yescharacteristic
846C8—22no—
847C8—22no—
848C8—22no—
849C8—41no—
850C8—41no—
851C8—41no—
852C22—22no—
853C22—22no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—82no—
863C22—81no—
864C22—161no—
865C22—162no—
866C22#534×C11311yescharacteristic
867C22D42×C11311yescharacteristic
868C22#546×C11311yescharacteristic
869C4—22no—
870C4—22no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—42no—
875C4—41no—
876C4—81no—
877C4—81no—
878C4C2×#120×C11311yescharacteristic
879C4C2×#121×C11311yescharacteristic
880C4D42×C11311yescharacteristic
881C4#546×C11311yescharacteristic
882C2—21no—
883C2—21no—
884C2—21no—
885C2—42no—
886C2—42no—
887C2—81no—
888C2—81no—
889C2—161no—
890C2C113×#241011yescharacteristic
subgroupG/H
center, socleC2×C113#2410
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×#3586C2semidirect
2. C113×#3068C2semidirect
3. C113×#3040C2semidirect
4. C113×#3021C2semidirect
5. C2×#454×C113C2semidirect
6. C113×#2901C2semidirect
7. C113×#2050C2semidirect
8. C113×#2049C2semidirect
9. C113×#2008C2semidirect
10. C113×#2004C2semidirect
11. C113×#1906C2semidirect
12. C113×#1903C2semidirect
13. C113×#1902C2semidirect
14. C113×#1861C2semidirect
15. C113×#1796C2semidirect
30. C2×AGL(1,ℤ/8)×C113C22semidirect
34. C2×#124×C113C22semidirect
44. #430×C113C22semidirect
45. #423×C113C22semidirect
54. C2×#104×C113C22semidirect
55. #419×C113C22semidirect
56. #419×C113C22semidirect
57. #418×C113C22semidirect
59. #413×C113C22semidirect
60. C2×#101×C113C22semidirect
61. C2×#100×C113C22semidirect
62. #410×C113C22semidirect
63. #344×C113C22semidirect
64. #344×C113C22semidirect
65. #339×C113C22semidirect
66. #338×C113C22semidirect
102. #137×C113D4semidirect
113. AGL(1,ℤ/8)×C113D4semidirect
120. C2×Q16×C113D4semidirect
126. C2×SD16×C113D4semidirect
168. #104×C113D4semidirect
169. #104×C113D4semidirect
436. #24473C113direct (N × H)
446. #3586C2×C113semidirect
447. #3068C2×C113semidirect
448. #3040C2×C113semidirect
449. #3021C2×C113semidirect
450. C2×#454C2×C113semidirect
451. #2901C2×C113semidirect
452. #2050C2×C113semidirect
453. #2049C2×C113semidirect
454. #2008C2×C113semidirect
455. #2004C2×C113semidirect
456. #1906C2×C113semidirect
457. #1903C2×C113semidirect
458. #1902C2×C113semidirect
459. #1861C2×C113semidirect
460. #1796C2×C113semidirect
461. C113#24473direct (N × H)
476. C2×AGL(1,ℤ/8)C22×C113semidirect
480. C2×#124C22×C113semidirect
490. #430C22×C113semidirect
491. #423C22×C113semidirect
500. C2×#104C22×C113semidirect
501. #419C22×C113semidirect
502. #419C22×C113semidirect
503. #418C22×C113semidirect
505. #413C22×C113semidirect
506. C2×#101C22×C113semidirect
507. C2×#100C22×C113semidirect
508. #410C22×C113semidirect
509. #344C22×C113semidirect
510. #344C22×C113semidirect
511. #339C22×C113semidirect
512. #338C22×C113semidirect
548. #137D4×C113semidirect
559. AGL(1,ℤ/8)D4×C113semidirect
566. C2×Q16D4×C113semidirect
572. C2×SD16D4×C113semidirect
614. #104D4×C113semidirect
615. #104D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35862
C113×#30682
C113×#30402
C113×#30212
C2×#454×C1132
C113×#29012
C113×#20502
C113×#20492
C113×#20082
C113×#20042
C113×#19062
C113×#19032
C113×#19022
C113×#18612
C113×#17962
#24473113