Finite Group Databasebeta

← C113×#24367 #43292387

Subgroups — C113×#24367 #43292387

Order 28928.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C113C211yesmaximal, characteristic
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#461×C113C211yesmaximal, characteristic, complemented
4C2×#450×C113C211yesmaximal, characteristic, complemented
5C113×#2432C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C113C211yesmaximal, characteristic, complemented
7C113×#2055C211yesmaximal, characteristic, complemented
8C113×#2054C211yesmaximal, characteristic, complemented
9C113×#2013C211yesmaximal, characteristic, complemented
10C113×#2012C211yesmaximal, characteristic, complemented
11C113×#1894C211yesmaximal, characteristic, complemented
12C113×#1879C211yesmaximal, characteristic, complemented
13C113×#1877C211yesmaximal, characteristic, complemented
14C113×#1851C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C113—24no—
19C2×AGL(1,ℤ/8)×C113—24no—
20C2×AGL(1,ℤ/8)×C113—24no—
21C22×SD16×C113C2211yescharacteristic
22C22×SD16×C113C2211yescharacteristic
23C22×SD16×C113C2211yescharacteristic
24C22×SD16×C113C2211yescharacteristic
25C22×D8×C113C2211yescharacteristic
26C22×D8×C113C2211yescharacteristic
27C22×M16×C113C2211yescharacteristic
28C2×C4⋊Q8×C113C2211yescharacteristic, complemented
29C2×#124×C113C2211yescharacteristic, complemented
30C2×C22⋊Q8×C113C2211yescharacteristic
31C2×C4×D4×C113C2211yescharacteristic
32C2×C4×D4×C113C2211yescharacteristic
33C22×C22⋊C4×C113—21no—
34#463×C113—24no—
35#461×C113—24no—
36#450×C113—24no—
37C2×C4⋊C8×C113C2211yescharacteristic, complemented
38C2×C4⋊C8×C113C2211yescharacteristic, complemented
39C2×#103×C113C2211yescharacteristic, complemented
40C2×#103×C113C2211yescharacteristic, complemented
41C2×#103×C113C2211yescharacteristic, complemented
42C2×#103×C113C2211yescharacteristic, complemented
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic, complemented
46C2×#102×C113C2211yescharacteristic, complemented
47C2×C22⋊C8×C113C2211yescharacteristic
48#394×C113—21no—
49#394×C113—21no—
50#391×C113C2211yescharacteristic, complemented
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#390×C113C2211yescharacteristic, complemented
54#386×C113—21no—
55#386×C113—21no—
56#385×C113—21no—
57#385×C113—21no—
58#380×C113C2211yescharacteristic
59#379×C113—21no—
60C4×C22⋊C4×C113C2211yescharacteristic
61#340×C113C2211yescharacteristic, complemented
62#340×C113C2211yescharacteristic, complemented
63#336×C113C2211yescharacteristic, complemented
64#336×C113C2211yescharacteristic, complemented
65C25×C113—21no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—41no—
71C2×#41×C113—41no—
72C22×Q8×C113C2311yescharacteristic
73C22×Q8×C113C2311yescharacteristic
74C22×D4×C113—22no—
75C22×D4×C113—22no—
76C22×D4×C113—21no—
77C22×D4×C113—21no—
78C22×D4×C113—22no—
79C22×D4×C113—41no—
80C22×D4×C113—41no—
81C22×D4×C113D414yes—
82C22×D4×C113C2311yescharacteristic
83C22×D4×C113C2311yescharacteristic
84C22×D4×C113C2311yescharacteristic
85C23×C4×C113—21no—
86C23×C4×C113—21no—
87C23×C4×C113—21no—
88C23×C4×C113C2311yescharacteristic
89AGL(1,ℤ/8)×C113—232no—
90C2×SD16×C113—22no—
91C2×SD16×C113—22no—
92C2×SD16×C113—22no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—22no—
98C2×SD16×C113—22no—
99C2×SD16×C113—41no—
100C2×SD16×C113—41no—
101C2×SD16×C113D414yes—
102C2×D8×C113—22no—
103C2×D8×C113—22no—
104C2×D8×C113—22no—
105C2×D8×C113—22no—
106C2×D8×C113—22no—
107C2×D8×C113D414yes—
108C2×M16×C113—22no—
109C2×M16×C113—22no—
110C2×M16×C113—22no—
111C22×C8×C113C2311yescharacteristic
112C22×C8×C113C2311yescharacteristic
113C22×C8×C113C2311yescharacteristic
114C22×C8×C113C2311yescharacteristic
115C4⋊Q8×C113—22no—
116C4⋊Q8×C113—41no—
117#124×C113—22no—
118#124×C113—41no—
119C22⋊Q8×C113—22no—
120C22⋊Q8×C113—22no—
121C4×D4×C113—22no—
122C4×D4×C113—22no—
123C4×D4×C113—41no—
124C4×D4×C113—41no—
125C2×C4⋊C4×C113—21no—
126C2×C4⋊C4×C113—21no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113C2311yescharacteristic
129C2×C4⋊C4×C113C2311yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113—21no—
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113—21no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113—21no—
142C2×C22⋊C4×C113—21no—
143C2×C22⋊C4×C113—44no—
144C2×C22⋊C4×C113D411yescharacteristic
145C2×C22⋊C4×C113D411yescharacteristic
146C2×C42×C113C2311yescharacteristic
147C2×C42×C113C2311yescharacteristic
148C4⋊C8×C113—22no—
149C4⋊C8×C113—22no—
150#103×C113—22no—
151#103×C113—22no—
152#103×C113—22no—
153#103×C113—41no—
154#102×C113—22no—
155#102×C113—22no—
156#102×C113—22no—
157#102×C113—41no—
158C22⋊C8×C113—22no—
159#95×C113—21no—
160#95×C113—21no—
161#95×C113—21no—
162#95×C113D411yescharacteristic
163#95×C113D411yescharacteristic
164C24×C113—21no—
165C24×C113—21no—
166C24×C113—21no—
167C24×C113—24no—
168C24×C113—42no—
169C24×C113—42no—
170C24×C113—42no—
171C24×C113—42no—
172C24×C113—81no—
173C24×C113—81no—
174C24×C113C2×D411yescharacteristic
175#41×C113—28no—
176#41×C113—44no—
177#41×C113—44no—
178#41×C113—44no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113—21no—
188C2×Q8×C113—21no—
189C2×Q8×C113—21no—
190C2×Q8×C113C2×D412yes—
191C2×D4×C113—28no—
192C2×D4×C113—24no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—21no—
203C2×D4×C113—21no—
204C2×D4×C113—21no—
205C2×D4×C113—21no—
206C2×D4×C113—44no—
207C2×D4×C113—44no—
208C2×D4×C113—44no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113C2×D412yes—
215C2×D4×C113C2×D412yes—
216C2×D4×C113C2×D412yes—
217C2×D4×C113C2×D412yes—
218C2×D4×C113C2×D412yes—
219C22×C4×C113—21no—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—42no—
229C22×C4×C113—42no—
230C22×C4×C113—42no—
231C22×C4×C113—42no—
232C22×C4×C113—42no—
233C22×C4×C113—42no—
234C22×C4×C113—42no—
235C22×C4×C113—81no—
236C22×C4×C113—81no—
237C22×C4×C113C2×D411yescharacteristic
238C22×C4×C113C2×D411yescharacteristic
239C22×C4×C113C2×D411yescharacteristic
240C22×C4×C113C2×D411yescharacteristic
241C22×C4×C113C2×D412yes—
242C22×C4×C113C2×D411yescharacteristic
243C22×C4×C113#4112yes—
244C22×C4×C113C2411yescharacteristic
245SD16×C113—28no—
246SD16×C113—28no—
247SD16×C113—44no—
248SD16×C113—44no—
249D8×C113—28no—
250D8×C113—28no—
251M16×C113—28no—
252C2×C8×C113—21no—
253C2×C8×C113—21no—
254C2×C8×C113—21no—
255C2×C8×C113—21no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113C2×D412yes—
263C2×C8×C113C2×D412yes—
264C4⋊C4×C113—21no—
265C4⋊C4×C113—21no—
266C4⋊C4×C113—21no—
267C4⋊C4×C113—21no—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
270C4⋊C4×C113—42no—
271C4⋊C4×C113—42no—
272C4⋊C4×C113—42no—
273C22⋊C4×C113—22no—
274C22⋊C4×C113—41no—
275C22⋊C4×C113—42no—
276C22⋊C4×C113—42no—
277C22⋊C4×C113—42no—
278C22⋊C4×C113—42no—
279C22⋊C4×C113—42no—
280C22⋊C4×C113—42no—
281C22⋊C4×C113—42no—
282C22⋊C4×C113—42no—
283C22⋊C4×C113—42no—
284C22⋊C4×C113—42no—
285C22⋊C4×C113—81no—
286C22⋊C4×C113—81no—
287C42×C113—21no—
288C42×C113—21no—
289C42×C113—21no—
290C42×C113—21no—
291C23×C113—22no—
292C23×C113—22no—
293C23×C113—22no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—22no—
301C23×C113—22no—
302C23×C113—48no—
303C23×C113—48no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—41no—
312C23×C113—41no—
313C23×C113—41no—
314C23×C113—41no—
315C23×C113—41no—
316C23×C113—41no—
317C23×C113—41no—
318C23×C113—41no—
319C23×C113—41no—
320C23×C113—84no—
321C23×C113—84no—
322C23×C113—84no—
323C23×C113—84no—
324C23×C113—84no—
325C23×C113#12112yes—
326C23×C113C22×D411yescharacteristic
327Q8×C113—22no—
328Q8×C113—22no—
329Q8×C113—41no—
330Q8×C113—41no—
331Q8×C113—41no—
332Q8×C113—41no—
333Q8×C113—41no—
334Q8×C113—41no—
335D4×C113—22no—
336D4×C113—22no—
337D4×C113—22no—
338D4×C113—22no—
339D4×C113—22no—
340D4×C113—22no—
341D4×C113—22no—
342D4×C113—48no—
343D4×C113—48no—
344D4×C113—41no—
345D4×C113—41no—
346D4×C113—41no—
347D4×C113—41no—
348D4×C113#12014yes—
349C2×C4×C113—21no—
350C2×C4×C113—21no—
351C2×C4×C113—21no—
352C2×C4×C113—21no—
353C2×C4×C113—22no—
354C2×C4×C113—22no—
355C2×C4×C113—22no—
356C2×C4×C113—22no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—22no—
361C2×C4×C113—21no—
362C2×C4×C113—21no—
363C2×C4×C113—21no—
364C2×C4×C113—21no—
365C2×C4×C113—21no—
366C2×C4×C113—21no—
367C2×C4×C113—48no—
368C2×C4×C113—41no—
369C2×C4×C113—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—41no—
377C2×C4×C113—41no—
378C2×C4×C113—41no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—84no—
383C2×C4×C113—84no—
384C2×C4×C113#12112yes—
385C2×C4×C113AGL(1,ℤ/8)12yescomplemented
386C2×C4×C113C22×D411yescharacteristic
387C2×C4×C113C22×D411yescharacteristic
388C2×C4×C113C22×D411yescharacteristic
389C2×C4×C113C2×#4111yescharacteristic
390C2×C4×C113H(5,𝔽2)11yescharacteristic
391C2×C4×C113H(5,𝔽2)11yescharacteristic
392C8×C113—22no—
393C8×C113—22no—
394C8×C113—41no—
395C8×C113—41no—
396C22×C113—22no—
397C22×C113—24no—
398C22×C113—22no—
399C22×C113—22no—
400C22×C113—42no—
401C22×C113—41no—
402C22×C113—41no—
403C22×C113—42no—
404C22×C113—42no—
405C22×C113—41no—
406C22×C113—41no—
407C22×C113—42no—
408C22×C113—42no—
409C22×C113—42no—
410C22×C113—42no—
411C22×C113—42no—
412C22×C113—42no—
413C22×C113—42no—
414C22×C113—42no—
415C22×C113—42no—
416C22×C113—816no—
417C22×C113—81no—
418C22×C113—81no—
419C22×C113—81no—
420C22×C113—81no—
421C22×C113—81no—
422C22×C113—81no—
423C22×C113—81no—
424C22×C113—81no—
425C22×C113C2×#12111yescharacteristic
426C22×C113D4211yescharacteristic
427C22×C113D4211yescharacteristic
428C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C113#57511yescharacteristic
430C22×C113#57711yescharacteristic
431C22×C113#57711yescharacteristic
432C4×C113—22no—
433C4×C113—22no—
434C4×C113—42no—
435C4×C113—41no—
436C4×C113—41no—
437C4×C113—41no—
438C4×C113—81no—
439C4×C113—81no—
440C4×C113—81no—
441C4×C113—81no—
442C4×C113C2×#12011yescharacteristic
443C4×C113#53411yescharacteristic
444C4×C113#54611yescharacteristic
445C4×C113#54611yescharacteristic
446#24367C11311yesmaximal, characteristic, direct product factor, Sylow
447C2×C113—42no—
448C2×C113—44no—
449C2×C113—82no—
450C2×C113—82no—
451C2×C113#241011yescharacteristic
452C2×C113#303611yescharacteristic
453C2×C113#304211yescharacteristic
454C2×C113#326511yescharacteristic
455C2×C113#326711yescharacteristic
456C2×C113#327211yescharacteristic
457C2×C113#327511yescharacteristic
458C22×AGL(1,ℤ/8)C2×C11311yescharacteristic
459C2×#463C2×C11311yescharacteristic, complemented
460C2×#461C2×C11311yescharacteristic, complemented
461C2×#450C2×C11311yescharacteristic, complemented
462#2432C2×C11311yescharacteristic, complemented
463D4×C22⋊C4C2×C11311yescharacteristic, complemented
464#2055C2×C11311yescharacteristic, complemented
465#2054C2×C11311yescharacteristic, complemented
466#2013C2×C11311yescharacteristic, complemented
467#2012C2×C11311yescharacteristic, complemented
468#1894C2×C11311yescharacteristic, complemented
469#1879C2×C11311yescharacteristic, complemented
470#1877C2×C11311yescharacteristic, complemented
471#1851C2×C11311yescharacteristic, complemented
472#1788C2×C11311yescharacteristic, complemented
473C113#2436711yescharacteristic, direct product factor, Sylow
474C22×#41C22×C11311yescharacteristic
475C23×D4C22×C11311yescharacteristic
476C2×AGL(1,ℤ/8)—24no—
477C2×AGL(1,ℤ/8)—24no—
478C2×AGL(1,ℤ/8)—24no—
479C22×SD16C22×C11311yescharacteristic
480C22×SD16C22×C11311yescharacteristic
481C22×SD16C22×C11311yescharacteristic
482C22×SD16C22×C11311yescharacteristic
483C22×D8C22×C11311yescharacteristic
484C22×D8C22×C11311yescharacteristic
485C22×M16C22×C11311yescharacteristic
486C2×C4⋊Q8C22×C11311yescharacteristic, complemented
487C2×#124C22×C11311yescharacteristic, complemented
488C2×C22⋊Q8C22×C11311yescharacteristic
489C2×C4×D4C22×C11311yescharacteristic
490C2×C4×D4C22×C11311yescharacteristic
491C22×C22⋊C4—21no—
492#463—24no—
493#461—24no—
494#450—24no—
495C2×C4⋊C8C22×C11311yescharacteristic, complemented
496C2×C4⋊C8C22×C11311yescharacteristic, complemented
497C2×#103C22×C11311yescharacteristic, complemented
498C2×#103C22×C11311yescharacteristic, complemented
499C2×#103C22×C11311yescharacteristic, complemented
500C2×#103C22×C11311yescharacteristic, complemented
501C2×#102C22×C11311yescharacteristic
502C2×#102C22×C11311yescharacteristic
503C2×#102C22×C11311yescharacteristic, complemented
504C2×#102C22×C11311yescharacteristic, complemented
505C2×C22⋊C8C22×C11311yescharacteristic
506#394—21no—
507#394—21no—
508#391C22×C11311yescharacteristic, complemented
509#390C22×C11311yescharacteristic
510#390C22×C11311yescharacteristic
511#390C22×C11311yescharacteristic, complemented
512#386—21no—
513#386—21no—
514#385—21no—
515#385—21no—
516#380C22×C11311yescharacteristic
517#379—21no—
518C4×C22⋊C4C22×C11311yescharacteristic
519#340C22×C11311yescharacteristic, complemented
520#340C22×C11311yescharacteristic, complemented
521#336C22×C11311yescharacteristic, complemented
522#336C22×C11311yescharacteristic, complemented
523C25—21no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8C23×C11311yescharacteristic
531C22×Q8C23×C11311yescharacteristic
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4D4×C11314yes—
540C22×D4C23×C11311yescharacteristic
541C22×D4C23×C11311yescharacteristic
542C22×D4C23×C11311yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C11311yescharacteristic
547AGL(1,ℤ/8)—232no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16D4×C11314yes—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8D4×C11314yes—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C22×C8C23×C11311yescharacteristic
570C22×C8C23×C11311yescharacteristic
571C22×C8C23×C11311yescharacteristic
572C22×C8C23×C11311yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575#124—22no—
576#124—41no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4C23×C11311yescharacteristic
587C2×C4⋊C4C23×C11311yescharacteristic
588C2×C4⋊C4C23×C11311yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—44no—
602C2×C22⋊C4D4×C11311yescharacteristic
603C2×C22⋊C4D4×C11311yescharacteristic
604C2×C42C23×C11311yescharacteristic
605C2×C42C23×C11311yescharacteristic
606C4⋊C8—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95D4×C11311yescharacteristic
621#95D4×C11311yescharacteristic
622C24—21no—
623C24—21no—
624C24—21no—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—42no—
630C24—81no—
631C24—81no—
632C24C2×D4×C11311yescharacteristic
633#41—28no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C11312yes—
649C2×D4—28no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C11312yes—
673C2×D4C2×D4×C11312yes—
674C2×D4C2×D4×C11312yes—
675C2×D4C2×D4×C11312yes—
676C2×D4C2×D4×C11312yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—81no—
694C22×C4—81no—
695C22×C4C2×D4×C11311yescharacteristic
696C22×C4C2×D4×C11311yescharacteristic
697C22×C4C2×D4×C11311yescharacteristic
698C22×C4C2×D4×C11311yescharacteristic
699C22×C4C2×D4×C11312yes—
700C22×C4C2×D4×C11311yescharacteristic
701C22×C4#41×C11312yes—
702C22×C4C24×C11311yescharacteristic
703SD16—28no—
704SD16—28no—
705SD16—44no—
706SD16—44no—
707D8—28no—
708D8—28no—
709M16—28no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8C2×D4×C11312yes—
721C2×C8C2×D4×C11312yes—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—22no—
760C23—48no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23#121×C11312yes—
784C23C22×D4×C11311yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4#120×C11314yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
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—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4#121×C11312yes—
843C2×C4AGL(1,ℤ/8)×C11312yescomplemented
844C2×C4C22×D4×C11311yescharacteristic
845C2×C4C22×D4×C11311yescharacteristic
846C2×C4C22×D4×C11311yescharacteristic
847C2×C4C2×#41×C11311yescharacteristic
848C2×C4H(5,𝔽2)×C11311yescharacteristic
849C2×C4H(5,𝔽2)×C11311yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C22—22no—
855C22—24no—
856C22—22no—
857C22—22no—
858C22—42no—
859C22—41no—
860C22—41no—
861C22—42no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—42no—
866C22—42no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#121×C11311yescharacteristic
884C22D42×C11311yescharacteristic
885C22D42×C11311yescharacteristic
886C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
887C22#575×C11311yescharacteristic
888C22#577×C11311yescharacteristic
889C22#577×C11311yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#120×C11311yescharacteristic
901C4#534×C11311yescharacteristic
902C4#546×C11311yescharacteristic
903C4#546×C11311yescharacteristic
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2C113×#241011yescharacteristic
909C2C113×#303611yescharacteristic
910C2C113×#304211yescharacteristic
911C2C113×#326511yescharacteristic
912C2C113×#326711yescharacteristic
913C2C113×#327211yescharacteristic
914C2C113×#327511yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC22×AGL(1,ℤ/8)×C113C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#463×C113C2semidirect
3. C2×#461×C113C2semidirect
4. C2×#450×C113C2semidirect
5. C113×#2432C2semidirect
6. D4×C22⋊C4×C113C2semidirect
7. C113×#2055C2semidirect
8. C113×#2054C2semidirect
9. C113×#2013C2semidirect
10. C113×#2012C2semidirect
11. C113×#1894C2semidirect
12. C113×#1879C2semidirect
13. C113×#1877C2semidirect
14. C113×#1851C2semidirect
15. C113×#1788C2semidirect
28. C2×C4⋊Q8×C113C22semidirect
29. C2×#124×C113C22semidirect
37. C2×C4⋊C8×C113C22semidirect
38. C2×C4⋊C8×C113C22semidirect
39. C2×#103×C113C22semidirect
40. C2×#103×C113C22semidirect
41. C2×#103×C113C22semidirect
42. C2×#103×C113C22semidirect
45. C2×#102×C113C22semidirect
46. C2×#102×C113C22semidirect
50. #391×C113C22semidirect
53. #390×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
63. #336×C113C22semidirect
64. #336×C113C22semidirect
385. C2×C4×C113AGL(1,ℤ/8)semidirect
446. #24367C113direct (N × H)
459. C2×#463C2×C113semidirect
460. C2×#461C2×C113semidirect
461. C2×#450C2×C113semidirect
462. #2432C2×C113semidirect
463. D4×C22⋊C4C2×C113semidirect
464. #2055C2×C113semidirect
465. #2054C2×C113semidirect
466. #2013C2×C113semidirect
467. #2012C2×C113semidirect
468. #1894C2×C113semidirect
469. #1879C2×C113semidirect
470. #1877C2×C113semidirect
471. #1851C2×C113semidirect
472. #1788C2×C113semidirect
473. C113#24367direct (N × H)
486. C2×C4⋊Q8C22×C113semidirect
487. C2×#124C22×C113semidirect
495. C2×C4⋊C8C22×C113semidirect
496. C2×C4⋊C8C22×C113semidirect
497. C2×#103C22×C113semidirect
498. C2×#103C22×C113semidirect
499. C2×#103C22×C113semidirect
500. C2×#103C22×C113semidirect
503. C2×#102C22×C113semidirect
504. C2×#102C22×C113semidirect
508. #391C22×C113semidirect
511. #390C22×C113semidirect
519. #340C22×C113semidirect
520. #340C22×C113semidirect
521. #336C22×C113semidirect
522. #336C22×C113semidirect
843. C2×C4AGL(1,ℤ/8)×C113semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1132
C2×#463×C1132
C2×#461×C1132
C2×#450×C1132
C113×#24322
D4×C22⋊C4×C1132
C113×#20552
C113×#20542
C113×#20132
C113×#20122
C113×#18942
C113×#18792
C113×#18772
C113×#18512
C113×#17882
#24367113