Finite Group Databasebeta

← C113×#24475 #43292495

Subgroups — C113×#24475 #43292495

Order 28928.

1324 conjugacy classes of subgroups.

The subgroup lattice has 894 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3585C211yesmaximal, characteristic
2C113×#3069C211yesmaximal, characteristic, complemented
3C113×#3040C211yesmaximal, characteristic, complemented
4C113×#3022C211yesmaximal, characteristic, complemented
5C2×#455×C113C211yesmaximal, characteristic, complemented
6C113×#2901C211yesmaximal, characteristic, complemented
7C113×#2050C211yesmaximal, characteristic, complemented
8C113×#2048C211yesmaximal, characteristic, complemented
9C113×#2009C211yesmaximal, characteristic, complemented
10C113×#2003C211yesmaximal, characteristic, complemented
11C113×#1906C211yesmaximal, characteristic, complemented
12C113×#1903C211yesmaximal, characteristic, complemented
13C113×#1902C211yesmaximal, characteristic, complemented
14C113×#1861C211yesmaximal, characteristic, complemented
15C113×#1795C211yesmaximal, characteristic, complemented
16#585×C113C2211yescharacteristic
17C2×H(5,𝔽2)×C113C2211yescharacteristic
18#577×C113—22no—
19#577×C113—22no—
20#576×C113—22no—
21#576×C113—22no—
22#575×C113—22no—
23#575×C113C2211yescharacteristic
24#575×C113C2211yescharacteristic
25C2×#137×C113C2211yescharacteristic
26C2×#137×C113C2211yescharacteristic, complemented
27C2×#137×C113C2211yescharacteristic, complemented
28C2×AGL(1,ℤ/8)×C113—22no—
29C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
30C2×AGL(1,ℤ/8)×C113C2211yescharacteristic
31#568×C113C2211yescharacteristic
32#568×C113C2211yescharacteristic, complemented
33#536×C113C2211yescharacteristic, complemented
34C2×#124×C113C2211yescharacteristic, complemented
35C4×#41×C113C2211yescharacteristic, complemented
36#473×C113—22no—
37#471×C113—22no—
38#464×C113—22no—
39#463×C113—22no—
40#456×C113—22no—
41#455×C113—22no—
42#455×C113—22no—
43#455×C113—22no—
44#430×C113C2211yescharacteristic, complemented
45#423×C113C2211yescharacteristic, complemented
46#421×C113—22no—
47#421×C113C2211yescharacteristic
48#421×C113C2211yescharacteristic
49#421×C113C2211yescharacteristic, complemented
50#421×C113C2211yescharacteristic, complemented
51C2×#104×C113—22no—
52C2×#104×C113C2211yescharacteristic
53C2×#104×C113C2211yescharacteristic, complemented
54C2×#104×C113C2211yescharacteristic, complemented
55#419×C113C2211yescharacteristic, complemented
56#418×C113C2211yescharacteristic, complemented
57#418×C113C2211yescharacteristic, complemented
58#413×C113C2211yescharacteristic, complemented
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—21no—
682−1+4×C113—21no—
692−1+4×C113D412yes—
70H(5,𝔽2)×C113—22no—
71H(5,𝔽2)×C113—21no—
72H(5,𝔽2)×C113—22no—
73H(5,𝔽2)×C113—21no—
74H(5,𝔽2)×C113—22no—
75H(5,𝔽2)×C113—41no—
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×C113C2311yescharacteristic
84C2×#41×C113C2311yescharacteristic
85C2×#41×C113C2311yescharacteristic
86C2×#41×C113C2311yescharacteristic
87C22×Q8×C113C2311yescharacteristic
88C22×D4×C113—21no—
89C22×D4×C113—21no—
90C22×D4×C113—41no—
91C22×D4×C113C2311yescharacteristic
92#137×C113—24no—
93#137×C113—21no—
94#137×C113—21no—
95#137×C113—21no—
96#137×C113—22no—
97#137×C113—22no—
98#137×C113—22no—
99#137×C113—22no—
100#137×C113—22no—
101#137×C113—41no—
102#137×C113D412yes—
103AGL(1,ℤ/8)×C113—24no—
104AGL(1,ℤ/8)×C113—24no—
105AGL(1,ℤ/8)×C113—24no—
106AGL(1,ℤ/8)×C113—22no—
107AGL(1,ℤ/8)×C113—22no—
108AGL(1,ℤ/8)×C113—21no—
109AGL(1,ℤ/8)×C113—22no—
110AGL(1,ℤ/8)×C113—21no—
111AGL(1,ℤ/8)×C113—21no—
112AGL(1,ℤ/8)×C113—22no—
113AGL(1,ℤ/8)×C113D412yes—
114#135×C113—24no—
115#135×C113—24no—
116#135×C113—22no—
117#135×C113—22no—
118C2×Q16×C113—21no—
119C2×Q16×C113—21no—
120C2×Q16×C113—21no—
121C2×SD16×C113—24no—
122C2×SD16×C113—21no—
123C2×SD16×C113—21no—
124C2×SD16×C113—21no—
125C2×SD16×C113—21no—
126C2×SD16×C113D412yes—
127C2×D8×C113—24no—
128C2×D8×C113—21no—
129C2×D8×C113D412yes—
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
142C4⋊Q8×C113—21no—
143#124×C113—22no—
144#124×C113—21no—
145#124×C113—21no—
146#124×C113—21no—
147#123×C113—41no—
148C22⋊Q8×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×C113D412yes—
169#104×C113D412yes—
170#103×C113—22no—
171#102×C113—22no—
172#102×C113—41no—
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—
181C24×C113—41no—
182#41×C113—21no—
183#41×C113—21no—
184#41×C113—21no—
185#41×C113—21no—
186#41×C113—24no—
187#41×C113—22no—
188#41×C113—22no—
189#41×C113—22no—
190#41×C113—22no—
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—21no—
199#41×C113—42no—
200#41×C113—42no—
201#41×C113—42no—
202#41×C113—42no—
203#41×C113—42no—
204#41×C113—42no—
205#41×C113—41no—
206#41×C113—41no—
207#41×C113—42no—
208#41×C113C2×D412yes—
209#41×C113C2×D412yes—
210#41×C113C2×D412yes—
211#41×C113C2×D412yes—
212C2×Q8×C113—22no—
213C2×Q8×C113—22no—
214C2×Q8×C113—21no—
215C2×Q8×C113—21no—
216C2×Q8×C113—21no—
217C2×Q8×C113—21no—
218C2×Q8×C113—21no—
219C2×Q8×C113—21no—
220C2×Q8×C113—41no—
221C2×Q8×C113C2×D411yescharacteristic
222C2×Q8×C113C2×D411yescharacteristic
223C2×Q8×C113C2×D411yescharacteristic
224C2×Q8×C113#4111yescharacteristic
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—24no—
228C2×D4×C113—22no—
229C2×D4×C113—22no—
230C2×D4×C113—21no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—21no—
234C2×D4×C113—21no—
235C2×D4×C113—21no—
236C2×D4×C113—21no—
237C2×D4×C113—42no—
238C2×D4×C113—41no—
239C2×D4×C113—41no—
240C2×D4×C113—42no—
241C2×D4×C113—42no—
242C2×D4×C113—41no—
243C2×D4×C113—44no—
244C2×D4×C113—42no—
245C2×D4×C113—42no—
246C2×D4×C113—44no—
247C2×D4×C113—42no—
248C2×D4×C113C2×D411yescharacteristic
249C2×D4×C113C2×D411yescharacteristic
250C2×D4×C113C2×D412yes—
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—41no—
260C22×C4×C113—42no—
261C22×C4×C113—41no—
262C22×C4×C113C2411yescharacteristic
263Q16×C113—22no—
264Q16×C113—22no—
265Q16×C113—42no—
266Q16×C113—42no—
267Q16×C113—42no—
268SD16×C113—24no—
269SD16×C113—22no—
270SD16×C113—22no—
271SD16×C113—22no—
272SD16×C113—24no—
273SD16×C113—22no—
274SD16×C113—42no—
275SD16×C113—42no—
276SD16×C113—42no—
277D8×C113—24no—
278D8×C113—22no—
279D8×C113—22no—
280D8×C113—24no—
281M16×C113—24no—
282M16×C113—21no—
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—42no—
293M16×C113C2×D412yes—
294M16×C113C2×D412yes—
295C2×C8×C113—24no—
296C2×C8×C113—21no—
297C2×C8×C113—21no—
298C2×C8×C113—21no—
299C2×C8×C113—21no—
300C2×C8×C113—21no—
301C2×C8×C113—42no—
302C2×C8×C113C2×D412yes—
303C4⋊C4×C113—21no—
304C4⋊C4×C113—21no—
305C4⋊C4×C113—41no—
306C4⋊C4×C113—42no—
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—22no—
323C23×C113—21no—
324C23×C113—42no—
325C23×C113—44no—
326C23×C113—41no—
327C23×C113—41no—
328C23×C113—82no—
329C23×C113—162no—
330C23×C113H(5,𝔽2)11yescharacteristic
331Q8×C113—21no—
332Q8×C113—21no—
333Q8×C113—21no—
334Q8×C113—21no—
335Q8×C113—21no—
336Q8×C113—21no—
337Q8×C113—42no—
338Q8×C113—41no—
339Q8×C113—41no—
340Q8×C113—41no—
341Q8×C113—41no—
342Q8×C113#12012yes—
343Q8×C113#12112yes—
344D4×C113—22no—
345D4×C113—22no—
346D4×C113—22no—
347D4×C113—22no—
348D4×C113—21no—
349D4×C113—21no—
350D4×C113—22no—
351D4×C113—21no—
352D4×C113—21no—
353D4×C113—21no—
354D4×C113—21no—
355D4×C113—22no—
356D4×C113—42no—
357D4×C113—42no—
358D4×C113—44no—
359D4×C113—42no—
360D4×C113—44no—
361D4×C113—41no—
362D4×C113—41no—
363D4×C113—41no—
364D4×C113—41no—
365D4×C113—41no—
366D4×C113—41no—
367D4×C113#12012yes—
368D4×C113#12112yes—
369C2×C4×C113—21no—
370C2×C4×C113—21no—
371C2×C4×C113—22no—
372C2×C4×C113—22no—
373C2×C4×C113—22no—
374C2×C4×C113—22no—
375C2×C4×C113—21no—
376C2×C4×C113—21no—
377C2×C4×C113—21no—
378C2×C4×C113—21no—
379C2×C4×C113—42no—
380C2×C4×C113—42no—
381C2×C4×C113—42no—
382C2×C4×C113—44no—
383C2×C4×C113—41no—
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—42no—
411C22×C113—41no—
412C22×C113—81no—
413C22×C113—81no—
414C22×C113—81no—
415C22×C113—82no—
416C22×C113—81no—
417C22×C113—82no—
418C22×C113—161no—
419C22×C113—162no—
420C22×C113—164no—
421C22×C113#53411yescharacteristic
422C22×C113D4211yescharacteristic
423C22×C113#54611yescharacteristic
424C4×C113—22no—
425C4×C113—22no—
426C4×C113—41no—
427C4×C113—41no—
428C4×C113—41no—
429C4×C113—41no—
430C4×C113—81no—
431C4×C113—81no—
432C4×C113—81no—
433C4×C113C2×#12011yescharacteristic
434C4×C113C2×#12111yescharacteristic
435C4×C113D4211yescharacteristic
436C4×C113#54611yescharacteristic
437#24475C11311yesmaximal, characteristic, direct product factor, Sylow
438C2×C113—21no—
439C2×C113—21no—
440C2×C113—21no—
441C2×C113—42no—
442C2×C113—42no—
443C2×C113—82no—
444C2×C113—81no—
445C2×C113—81no—
446C2×C113#241011yescharacteristic
447#3585C2×C11311yescharacteristic
448#3069C2×C11311yescharacteristic, complemented
449#3040C2×C11311yescharacteristic, complemented
450#3022C2×C11311yescharacteristic, complemented
451C2×#455C2×C11311yescharacteristic, complemented
452#2901C2×C11311yescharacteristic, complemented
453#2050C2×C11311yescharacteristic, complemented
454#2048C2×C11311yescharacteristic, complemented
455#2009C2×C11311yescharacteristic, complemented
456#2003C2×C11311yescharacteristic, complemented
457#1906C2×C11311yescharacteristic, complemented
458#1903C2×C11311yescharacteristic, complemented
459#1902C2×C11311yescharacteristic, complemented
460#1861C2×C11311yescharacteristic, complemented
461#1795C2×C11311yescharacteristic, complemented
462C113#2447511yescharacteristic, direct product factor, Sylow
463#585C22×C11311yescharacteristic
464C2×H(5,𝔽2)C22×C11311yescharacteristic
465#577—22no—
466#577—22no—
467#576—22no—
468#576—22no—
469#575—22no—
470#575C22×C11311yescharacteristic
471#575C22×C11311yescharacteristic
472C2×#137C22×C11311yescharacteristic
473C2×#137C22×C11311yescharacteristic, complemented
474C2×#137C22×C11311yescharacteristic, complemented
475C2×AGL(1,ℤ/8)—22no—
476C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
477C2×AGL(1,ℤ/8)C22×C11311yescharacteristic
478#568C22×C11311yescharacteristic
479#568C22×C11311yescharacteristic, complemented
480#536C22×C11311yescharacteristic, complemented
481C2×#124C22×C11311yescharacteristic, complemented
482C4×#41C22×C11311yescharacteristic, complemented
483#473—22no—
484#471—22no—
485#464—22no—
486#463—22no—
487#456—22no—
488#455—22no—
489#455—22no—
490#455—22no—
491#430C22×C11311yescharacteristic, complemented
492#423C22×C11311yescharacteristic, complemented
493#421—22no—
494#421C22×C11311yescharacteristic
495#421C22×C11311yescharacteristic
496#421C22×C11311yescharacteristic, complemented
497#421C22×C11311yescharacteristic, complemented
498C2×#104—22no—
499C2×#104C22×C11311yescharacteristic
500C2×#104C22×C11311yescharacteristic, complemented
501C2×#104C22×C11311yescharacteristic, complemented
502#419C22×C11311yescharacteristic, complemented
503#418C22×C11311yescharacteristic, complemented
504#418C22×C11311yescharacteristic, complemented
505#413C22×C11311yescharacteristic, complemented
506#413C22×C11311yescharacteristic, complemented
507C2×#101C22×C11311yescharacteristic, complemented
508C2×#100C22×C11311yescharacteristic, complemented
509#410C22×C11311yescharacteristic, complemented
510#344C22×C11311yescharacteristic, complemented
511#344C22×C11311yescharacteristic, complemented
512#339C22×C11311yescharacteristic, complemented
513#338C22×C11311yescharacteristic, complemented
5142−1+4—21no—
5152−1+4—21no—
5162−1+4D4×C11312yes—
517H(5,𝔽2)—22no—
518H(5,𝔽2)—21no—
519H(5,𝔽2)—22no—
520H(5,𝔽2)—21no—
521H(5,𝔽2)—22no—
522H(5,𝔽2)—41no—
523H(5,𝔽2)—41no—
524H(5,𝔽2)D4×C11312yes—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—41no—
530C2×#41C23×C11311yescharacteristic
531C2×#41C23×C11311yescharacteristic
532C2×#41C23×C11311yescharacteristic
533C2×#41C23×C11311yescharacteristic
534C22×Q8C23×C11311yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—41no—
538C22×D4C23×C11311yescharacteristic
539#137—24no—
540#137—21no—
541#137—21no—
542#137—21no—
543#137—22no—
544#137—22no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137—41no—
549#137D4×C11312yes—
550AGL(1,ℤ/8)—24no—
551AGL(1,ℤ/8)—24no—
552AGL(1,ℤ/8)—24no—
553AGL(1,ℤ/8)—22no—
554AGL(1,ℤ/8)—22no—
555AGL(1,ℤ/8)—21no—
556AGL(1,ℤ/8)—22no—
557AGL(1,ℤ/8)—21no—
558AGL(1,ℤ/8)—21no—
559AGL(1,ℤ/8)—22no—
560AGL(1,ℤ/8)D4×C11312yes—
561#135—24no—
562#135—24no—
563#135—22no—
564#135—22no—
565C2×Q16—21no—
566C2×Q16—21no—
567C2×Q16—21no—
568C2×SD16—24no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—21no—
572C2×SD16—21no—
573C2×SD16D4×C11312yes—
574C2×D8—24no—
575C2×D8—21no—
576C2×D8D4×C11312yes—
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—22no—
582C2×M16—22no—
583C2×M16C23×C11311yescharacteristic
584C2×M16C23×C11311yescharacteristic
585C2×M16C23×C11311yescharacteristic
586C2×M16C23×C11311yescharacteristic
587C2×M16C23×C11311yescharacteristic
588C2×M16C23×C11311yescharacteristic
589C4⋊Q8—21no—
590#124—22no—
591#124—21no—
592#124—21no—
593#124—21no—
594#123—41no—
595C22⋊Q8—41no—
596C4×Q8—21no—
597C4×D4—21no—
598C4×D4—41no—
599#117—21no—
600#117C23×C11311yescharacteristic
601#117C23×C11311yescharacteristic
602C2×C22⋊C4—41no—
603C2×C42—21no—
604C2×C42C23×C11311yescharacteristic
605#108—22no—
606C4⋊C8—22no—
607#104—22no—
608#104—22no—
609#104—22no—
610#104—22no—
611#104—21no—
612#104—21no—
613#104—21no—
614#104—21no—
615#104D4×C11312yes—
616#104D4×C11312yes—
617#103—22no—
618#102—22no—
619#102—41no—
620#101—21no—
621#101—21no—
622#101—22no—
623#100—21no—
624#100—21no—
625#100—22no—
626#99—41no—
627C24—21no—
628C24—41no—
629#41—21no—
630#41—21no—
631#41—21no—
632#41—21no—
633#41—24no—
634#41—22no—
635#41—22no—
636#41—22no—
637#41—22no—
638#41—21no—
639#41—21no—
640#41—21no—
641#41—21no—
642#41—21no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—42no—
647#41—42no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—42no—
652#41—41no—
653#41—41no—
654#41—42no—
655#41C2×D4×C11312yes—
656#41C2×D4×C11312yes—
657#41C2×D4×C11312yes—
658#41C2×D4×C11312yes—
659C2×Q8—22no—
660C2×Q8—22no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—41no—
668C2×Q8C2×D4×C11311yescharacteristic
669C2×Q8C2×D4×C11311yescharacteristic
670C2×Q8C2×D4×C11311yescharacteristic
671C2×Q8#41×C11311yescharacteristic
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—42no—
685C2×D4—41no—
686C2×D4—41no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—41no—
690C2×D4—44no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4C2×D4×C11311yescharacteristic
696C2×D4C2×D4×C11311yescharacteristic
697C2×D4C2×D4×C11312yes—
698C2×D4C2×D4×C11311yescharacteristic
699C2×D4#41×C11311yescharacteristic
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—41no—
707C22×C4—42no—
708C22×C4—41no—
709C22×C4C24×C11311yescharacteristic
710Q16—22no—
711Q16—22no—
712Q16—42no—
713Q16—42no—
714Q16—42no—
715SD16—24no—
716SD16—22no—
717SD16—22no—
718SD16—22no—
719SD16—24no—
720SD16—22no—
721SD16—42no—
722SD16—42no—
723SD16—42no—
724D8—24no—
725D8—22no—
726D8—22no—
727D8—24no—
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—
753C4⋊C4—42no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—42no—
757C22⋊C4—42no—
758C22⋊C4—41no—
759C22⋊C4—42no—
760C42—21no—
761C42—21no—
762C42—21no—
763C42—41no—
764C42C2×D4×C11311yescharacteristic
765C42C2×D4×C11311yescharacteristic
766C23—21no—
767C23—21no—
768C23—21no—
769C23—22no—
770C23—21no—
771C23—42no—
772C23—44no—
773C23—41no—
774C23—41no—
775C23—82no—
776C23—162no—
777C23H(5,𝔽2)×C11311yescharacteristic
778Q8—21no—
779Q8—21no—
780Q8—21no—
781Q8—21no—
782Q8—21no—
783Q8—21no—
784Q8—42no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8#120×C11312yes—
790Q8#121×C11312yes—
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—21no—
796D4—21no—
797D4—22no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—21no—
802D4—22no—
803D4—42no—
804D4—42no—
805D4—44no—
806D4—42no—
807D4—44no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—41no—
814D4#120×C11312yes—
815D4#121×C11312yes—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—42no—
827C2×C4—42no—
828C2×C4—42no—
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—41no—
839C2×C4—81no—
840C2×C4—82no—
841C2×C4C22×D4×C11311yescharacteristic
842C2×C4C22×D4×C11311yescharacteristic
843C2×C4C22×D4×C11311yescharacteristic
844C2×C4C22×D4×C11311yescharacteristic
845C2×C4C2×#41×C11311yescharacteristic
846C2×C4H(5,𝔽2)×C11311yescharacteristic
847C8—22no—
848C8—22no—
849C8—22no—
850C8—41no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—42no—
858C22—41no—
859C22—81no—
860C22—81no—
861C22—82no—
862C22—81no—
863C22—81no—
864C22—82no—
865C22—161no—
866C22—162no—
867C22—164no—
868C22#534×C11311yescharacteristic
869C22D42×C11311yescharacteristic
870C22#546×C11311yescharacteristic
871C4—22no—
872C4—22no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—81no—
878C4—81no—
879C4—81no—
880C4C2×#120×C11311yescharacteristic
881C4C2×#121×C11311yescharacteristic
882C4D42×C11311yescharacteristic
883C4#546×C11311yescharacteristic
884C2—21no—
885C2—21no—
886C2—21no—
887C2—42no—
888C2—42no—
889C2—82no—
890C2—81no—
891C2—81no—
892C2C113×#241011yescharacteristic
subgroupG/H
center, socleC2×C113#2410
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#3585C2
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
2. C113×#3069C2semidirect
3. C113×#3040C2semidirect
4. C113×#3022C2semidirect
5. C2×#455×C113C2semidirect
6. C113×#2901C2semidirect
7. C113×#2050C2semidirect
8. C113×#2048C2semidirect
9. C113×#2009C2semidirect
10. C113×#2003C2semidirect
11. C113×#1906C2semidirect
12. C113×#1903C2semidirect
13. C113×#1902C2semidirect
14. C113×#1861C2semidirect
15. C113×#1795C2semidirect
26. C2×#137×C113C22semidirect
27. C2×#137×C113C22semidirect
32. #568×C113C22semidirect
33. #536×C113C22semidirect
34. C2×#124×C113C22semidirect
35. C4×#41×C113C22semidirect
44. #430×C113C22semidirect
45. #423×C113C22semidirect
49. #421×C113C22semidirect
50. #421×C113C22semidirect
53. C2×#104×C113C22semidirect
54. C2×#104×C113C22semidirect
55. #419×C113C22semidirect
56. #418×C113C22semidirect
57. #418×C113C22semidirect
58. #413×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
437. #24475C113direct (N × H)
448. #3069C2×C113semidirect
449. #3040C2×C113semidirect
450. #3022C2×C113semidirect
451. C2×#455C2×C113semidirect
452. #2901C2×C113semidirect
453. #2050C2×C113semidirect
454. #2048C2×C113semidirect
455. #2009C2×C113semidirect
456. #2003C2×C113semidirect
457. #1906C2×C113semidirect
458. #1903C2×C113semidirect
459. #1902C2×C113semidirect
460. #1861C2×C113semidirect
461. #1795C2×C113semidirect
462. C113#24475direct (N × H)
473. C2×#137C22×C113semidirect
474. C2×#137C22×C113semidirect
479. #568C22×C113semidirect
480. #536C22×C113semidirect
481. C2×#124C22×C113semidirect
482. C4×#41C22×C113semidirect
491. #430C22×C113semidirect
492. #423C22×C113semidirect
496. #421C22×C113semidirect
497. #421C22×C113semidirect
500. C2×#104C22×C113semidirect
501. C2×#104C22×C113semidirect
502. #419C22×C113semidirect
503. #418C22×C113semidirect
504. #418C22×C113semidirect
505. #413C22×C113semidirect
506. #413C22×C113semidirect
507. C2×#101C22×C113semidirect
508. C2×#100C22×C113semidirect
509. #410C22×C113semidirect
510. #344C22×C113semidirect
511. #344C22×C113semidirect
512. #339C22×C113semidirect
513. #338C22×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35852
C113×#30692
C113×#30402
C113×#30222
C2×#455×C1132
C113×#29012
C113×#20502
C113×#20482
C113×#20092
C113×#20032
C113×#19062
C113×#19032
C113×#19022
C113×#18612
C113×#17952
#24475113