Finite Group Databasebeta

← C113×#24256 #43292276

Subgroups — C113×#24256 #43292276

Order 28928.

1510 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
1C2×#548×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#448×C113C211yesmaximal, characteristic, complemented
5C2×#440×C113C211yesmaximal, characteristic, complemented
6C113×#2537C211yesmaximal, characteristic, complemented
7C113×#2036C211yesmaximal, characteristic, complemented
8C113×#2033C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1959C211yesmaximal, characteristic, complemented
12C113×#1955C211yesmaximal, characteristic, complemented
13C113×#1803C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×Q8×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×SD16×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21#548×C113—24no—
22#548×C113—24no—
23C2×#124×C113—21no—
24C2×#124×C113C2211yescharacteristic
25C2×C22⋊Q8×C113—21no—
26C2×C22⋊Q8×C113C2211yescharacteristic
27C2×#121×C113—21no—
28C2×#121×C113—21no—
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×#121×C113C2211yescharacteristic
32C2×C4×Q8×C113C2211yescharacteristic
33C2×C4×D4×C113—21no—
34C2×C4×D4×C113C2211yescharacteristic
35C2×C4×D4×C113C2211yescharacteristic
36#463×C113—24no—
37#449×C113—24no—
38#448×C113—24no—
39#440×C113—24no—
40C2×#107×C113C2211yescharacteristic
41C2×C4⋊C8×C113C2211yescharacteristic
42C2×#103×C113C2211yescharacteristic
43C2×#103×C113C2211yescharacteristic
44C2×#103×C113C2211yescharacteristic
45C2×#103×C113C2211yescharacteristic
46C2×#103×C113C2211yescharacteristic
47C2×#103×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic
55C2×C22⋊C8×C113C2211yescharacteristic
56C2×#97×C113C2211yescharacteristic
57#394×C113—21no—
58#394×C113—21no—
59#384×C113C2211yescharacteristic
60#380×C113—21no—
61#380×C113C2211yescharacteristic
62#380×C113C2211yescharacteristic
63#340×C113C2211yescharacteristic
64#340×C113C2211yescharacteristic
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—41no—
70C2×#41×C113—41no—
71C22×Q8×C113—22no—
72C22×Q8×C113—22no—
73C22×Q8×C113—21no—
74C22×Q8×C113—22no—
75C22×Q8×C113—22no—
76C22×Q8×C113—41no—
77C22×Q8×C113—41no—
78C22×Q8×C113C2311yescharacteristic
79C22×Q8×C113C2311yescharacteristic
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113D411yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C23×C4×C113—21no—
88C23×C4×C113—21no—
89C23×C4×C113—21no—
90C23×C4×C113C2311yescharacteristic
91C23×C4×C113C2311yescharacteristic
92C2×SD16×C113—22no—
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—22no—
96C2×SD16×C113—41no—
97C2×SD16×C113D414yescomplemented
98C2×D8×C113—22no—
99C2×D8×C113—22no—
100C2×D8×C113—41no—
101C22×C8×C113C2311yescharacteristic
102C22×C8×C113C2311yescharacteristic
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105#124×C113—28no—
106#124×C113—22no—
107#124×C113D414yescomplemented
108C22⋊Q8×C113—28no—
109C22⋊Q8×C113—22no—
110C22⋊Q8×C113—22no—
111#121×C113—28no—
112#121×C113—22no—
113#121×C113—22no—
114#121×C113—22no—
115#121×C113—22no—
116#121×C113—41no—
117#121×C113—41no—
118#121×C113—44no—
119C4×Q8×C113—22no—
120C4×Q8×C113D414yescomplemented
121C4×D4×C113—28no—
122C4×D4×C113—22no—
123C4×D4×C113—22no—
124C4×D4×C113—22no—
125C4×D4×C113—22no—
126C2×C4⋊C4×C113—21no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113—21no—
130C2×C4⋊C4×C113D411yescharacteristic
131C2×C4⋊C4×C113C2311yescharacteristic
132C2×C4⋊C4×C113C2311yescharacteristic
133C2×C4⋊C4×C113C2311yescharacteristic
134C2×C4⋊C4×C113C2311yescharacteristic
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—21no—
144C2×C22⋊C4×C113D411yescharacteristic
145C2×C22⋊C4×C113D411yescharacteristic
146C2×C42×C113—21no—
147C2×C42×C113C2311yescharacteristic
148#107×C113—22no—
149C4⋊C8×C113—22no—
150#103×C113—22no—
151#103×C113—22no—
152#103×C113—22no—
153#103×C113—22no—
154#103×C113—22no—
155#103×C113—41no—
156#102×C113—22no—
157#102×C113—22no—
158#102×C113—22no—
159#102×C113—41no—
160C22⋊C8×C113—22no—
161C22⋊C8×C113—22no—
162C22⋊C8×C113—41no—
163C22⋊C8×C113—41no—
164#97×C113—22no—
165#95×C113—21no—
166#95×C113—21no—
167C24×C113—21no—
168C24×C113—21no—
169C24×C113C2×D411yescharacteristic
170C24×C113C2×D411yescharacteristic
171#41×C113—44no—
172#41×C113—44no—
173#41×C113—44no—
174#41×C113—44no—
175C2×Q8×C113—24no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—42no—
185C2×Q8×C113—42no—
186C2×Q8×C113—44no—
187C2×Q8×C113—44no—
188C2×Q8×C113—44no—
189C2×Q8×C113—44no—
190C2×Q8×C113C2×D412yes—
191C2×Q8×C113C2×D412yes—
192C2×Q8×C113C2×D412yes—
193C2×Q8×C113#4112yes—
194C2×D4×C113—24no—
195C2×D4×C113—24no—
196C2×D4×C113—22no—
197C2×D4×C113—22no—
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—21no—
207C2×D4×C113—21no—
208C2×D4×C113—41no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—42no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—42no—
216C2×D4×C113—42no—
217C2×D4×C113—81no—
218C2×D4×C113—81no—
219C2×D4×C113C2×D412yes—
220C2×D4×C113C2×D412yes—
221C22×C4×C113—21no—
222C22×C4×C113—24no—
223C22×C4×C113—24no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—21no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—21no—
231C22×C4×C113—21no—
232C22×C4×C113—21no—
233C22×C4×C113—21no—
234C22×C4×C113—21no—
235C22×C4×C113—21no—
236C22×C4×C113—21no—
237C22×C4×C113—21no—
238C22×C4×C113—21no—
239C22×C4×C113—21no—
240C22×C4×C113—21no—
241C22×C4×C113—42no—
242C22×C4×C113—42no—
243C22×C4×C113—42no—
244C22×C4×C113—42no—
245C22×C4×C113—42no—
246C22×C4×C113—42no—
247C22×C4×C113—42no—
248C22×C4×C113C2×D411yescharacteristic
249C22×C4×C113C2×D411yescharacteristic
250C22×C4×C113C2×D411yescharacteristic
251C22×C4×C113C2×D411yescharacteristic
252C22×C4×C113C2411yescharacteristic
253SD16×C113—28no—
254SD16×C113—44no—
255D8×C113—44no—
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×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113C2×D412yes—
268C4⋊C4×C113—24no—
269C4⋊C4×C113—24no—
270C4⋊C4×C113—22no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—42no—
279C4⋊C4×C113—81no—
280C4⋊C4×C113C2×D412yes—
281C22⋊C4×C113—24no—
282C22⋊C4×C113—24no—
283C22⋊C4×C113—24no—
284C22⋊C4×C113—24no—
285C22⋊C4×C113—22no—
286C22⋊C4×C113—22no—
287C22⋊C4×C113—42no—
288C22⋊C4×C113—42no—
289C22⋊C4×C113—42no—
290C22⋊C4×C113—42no—
291C22⋊C4×C113—42no—
292C42×C113—24no—
293C42×C113C2×D412yes—
294C42×C113C2×D412yes—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—21no—
298C23×C113—21no—
299C23×C113—21no—
300C23×C113—21no—
301C23×C113—21no—
302C23×C113—22no—
303C23×C113—22no—
304C23×C113—21no—
305C23×C113—21no—
306C23×C113—21no—
307C23×C113—21no—
308C23×C113—21no—
309C23×C113—21no—
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—41no—
321C23×C113—41no—
322C23×C113AGL(1,ℤ/8)12yes—
323C23×C113C22×D411yescharacteristic
324Q8×C113—22no—
325Q8×C113—22no—
326Q8×C113—22no—
327Q8×C113—22no—
328Q8×C113—22no—
329Q8×C113—48no—
330Q8×C113—41no—
331Q8×C113—41no—
332Q8×C113#12114yescomplemented
333D4×C113—22no—
334D4×C113—22no—
335D4×C113—22no—
336D4×C113—22no—
337D4×C113—44no—
338D4×C113—48no—
339D4×C113—48no—
340D4×C113—41no—
341D4×C113—41no—
342D4×C113—41no—
343D4×C113—41no—
344D4×C113—84no—
345D4×C113—84no—
346C2×C4×C113—22no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
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—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—48no—
362C2×C4×C113—48no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—41no—
367C2×C4×C113—41no—
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—41no—
383C2×C4×C113—41no—
384C2×C4×C113—84no—
385C2×C4×C113#12012yes—
386C2×C4×C113#12012yes—
387C2×C4×C113C22×D411yescharacteristic
388C2×C4×C113C22×D411yescharacteristic
389C2×C4×C113C22×D411yescharacteristic
390C2×C4×C113C2×#4111yescharacteristic
391C2×C4×C113H(5,𝔽2)11yescharacteristic
392C2×C4×C113H(5,𝔽2)11yescharacteristic
393C8×C113—22no—
394C8×C113—41no—
395C8×C113—41no—
396C8×C113—41no—
397C22×C113—22no—
398C22×C113—22no—
399C22×C113—22no—
400C22×C113—41no—
401C22×C113—41no—
402C22×C113—41no—
403C22×C113—41no—
404C22×C113—42no—
405C22×C113—41no—
406C22×C113—42no—
407C22×C113—41no—
408C22×C113—42no—
409C22×C113—41no—
410C22×C113—42no—
411C22×C113—41no—
412C22×C113—42no—
413C22×C113—41no—
414C22×C113—42no—
415C22×C113—41no—
416C22×C113—41no—
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×#12011yescharacteristic
426C22×C113D4211yescharacteristic
427C22×C113#54611yescharacteristic
428C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
429C22×C113#57511yescharacteristic
430C22×C113#57711yescharacteristic
431C22×C113#57811yescharacteristic
432C4×C113—24no—
433C4×C113—22no—
434C4×C113—22no—
435C4×C113—41no—
436C4×C113—41no—
437C4×C113—42no—
438C4×C113—42no—
439C4×C113—81no—
440C4×C113—81no—
441C4×C113—81no—
442C4×C113C2×#12111yescharacteristic
443C4×C113#53511yescharacteristic
444C4×C113D4211yescharacteristic
445C4×C113#54611yescharacteristic
446#24256C11311yesmaximal, characteristic, direct product factor, Sylow
447C2×C113—42no—
448C2×C113—81no—
449C2×C113—82no—
450C2×C113—82no—
451C2×C113#240811yescharacteristic
452C2×C113#300611yescharacteristic
453C2×C113#301311yescharacteristic
454C2×C113#326511yescharacteristic
455C2×C113#326911yescharacteristic
456C2×C113#330811yescharacteristic
457C2×C113#332111yescharacteristic
458C2×#548C2×C11311yescharacteristic, complemented
459C2×#463C2×C11311yescharacteristic, complemented
460C2×#449C2×C11311yescharacteristic, complemented
461C2×#448C2×C11311yescharacteristic, complemented
462C2×#440C2×C11311yescharacteristic, complemented
463#2537C2×C11311yescharacteristic, complemented
464#2036C2×C11311yescharacteristic, complemented
465#2033C2×C11311yescharacteristic, complemented
466#2000C2×C11311yescharacteristic, complemented
467#1999C2×C11311yescharacteristic, complemented
468#1959C2×C11311yescharacteristic, complemented
469#1955C2×C11311yescharacteristic, complemented
470#1803C2×C11311yescharacteristic, complemented
471#1788C2×C11311yescharacteristic, complemented
472#1787C2×C11311yescharacteristic, complemented
473C113#2425611yescharacteristic, direct product factor, Sylow
474C22×#41C22×C11311yescharacteristic
475C23×Q8C22×C11311yescharacteristic
476C22×SD16C22×C11311yescharacteristic
477C22×SD16C22×C11311yescharacteristic
478C22×D8C22×C11311yescharacteristic
479#548—24no—
480#548—24no—
481C2×#124—21no—
482C2×#124C22×C11311yescharacteristic
483C2×C22⋊Q8—21no—
484C2×C22⋊Q8C22×C11311yescharacteristic
485C2×#121—21no—
486C2×#121—21no—
487C2×#121C22×C11311yescharacteristic
488C2×#121C22×C11311yescharacteristic
489C2×#121C22×C11311yescharacteristic
490C2×C4×Q8C22×C11311yescharacteristic
491C2×C4×D4—21no—
492C2×C4×D4C22×C11311yescharacteristic
493C2×C4×D4C22×C11311yescharacteristic
494#463—24no—
495#449—24no—
496#448—24no—
497#440—24no—
498C2×#107C22×C11311yescharacteristic
499C2×C4⋊C8C22×C11311yescharacteristic
500C2×#103C22×C11311yescharacteristic
501C2×#103C22×C11311yescharacteristic
502C2×#103C22×C11311yescharacteristic
503C2×#103C22×C11311yescharacteristic
504C2×#103C22×C11311yescharacteristic
505C2×#103C22×C11311yescharacteristic
506C2×#102C22×C11311yescharacteristic
507C2×#102C22×C11311yescharacteristic
508C2×#102C22×C11311yescharacteristic
509C2×#102C22×C11311yescharacteristic
510C2×C22⋊C8C22×C11311yescharacteristic
511C2×C22⋊C8C22×C11311yescharacteristic
512C2×C22⋊C8C22×C11311yescharacteristic
513C2×C22⋊C8C22×C11311yescharacteristic
514C2×#97C22×C11311yescharacteristic
515#394—21no—
516#394—21no—
517#384C22×C11311yescharacteristic
518#380—21no—
519#380C22×C11311yescharacteristic
520#380C22×C11311yescharacteristic
521#340C22×C11311yescharacteristic
522#340C22×C11311yescharacteristic
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—21no—
532C22×Q8—22no—
533C22×Q8—22no—
534C22×Q8—41no—
535C22×Q8—41no—
536C22×Q8C23×C11311yescharacteristic
537C22×Q8C23×C11311yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4D4×C11311yescharacteristic
543C22×D4C23×C11311yescharacteristic
544C22×D4C23×C11311yescharacteristic
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4C23×C11311yescharacteristic
549C23×C4C23×C11311yescharacteristic
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—41no—
555C2×SD16D4×C11314yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—41no—
559C22×C8C23×C11311yescharacteristic
560C22×C8C23×C11311yescharacteristic
561C22×C8C23×C11311yescharacteristic
562C22×C8C23×C11311yescharacteristic
563#124—28no—
564#124—22no—
565#124D4×C11314yescomplemented
566C22⋊Q8—28no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569#121—28no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—44no—
577C4×Q8—22no—
578C4×Q8D4×C11314yescomplemented
579C4×D4—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C11311yescharacteristic
589C2×C4⋊C4C23×C11311yescharacteristic
590C2×C4⋊C4C23×C11311yescharacteristic
591C2×C4⋊C4C23×C11311yescharacteristic
592C2×C4⋊C4C23×C11311yescharacteristic
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—21no—
602C2×C22⋊C4D4×C11311yescharacteristic
603C2×C22⋊C4D4×C11311yescharacteristic
604C2×C42—21no—
605C2×C42C23×C11311yescharacteristic
606#107—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—22no—
613#103—41no—
614#102—22no—
615#102—22no—
616#102—22no—
617#102—41no—
618C22⋊C8—22no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#97—22no—
623#95—21no—
624#95—21no—
625C24—21no—
626C24—21no—
627C24C2×D4×C11311yescharacteristic
628C24C2×D4×C11311yescharacteristic
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—24no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—42no—
643C2×Q8—42no—
644C2×Q8—44no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8C2×D4×C11312yes—
649C2×Q8C2×D4×C11312yes—
650C2×Q8C2×D4×C11312yes—
651C2×Q8#41×C11312yes—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—22no—
655C2×D4—22no—
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—21no—
665C2×D4—21no—
666C2×D4—41no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—81no—
676C2×D4—81no—
677C2×D4C2×D4×C11312yes—
678C2×D4C2×D4×C11312yes—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—24no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4—42no—
702C22×C4—42no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4C2×D4×C11311yescharacteristic
707C22×C4C2×D4×C11311yescharacteristic
708C22×C4C2×D4×C11311yescharacteristic
709C22×C4C2×D4×C11311yescharacteristic
710C22×C4C24×C11311yescharacteristic
711SD16—28no—
712SD16—44no—
713D8—44no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8C2×D4×C11312yes—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—22no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—81no—
738C4⋊C4C2×D4×C11312yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—22no—
744C22⋊C4—22no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—42no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C42—24no—
751C42C2×D4×C11312yes—
752C42C2×D4×C11312yes—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—22no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23AGL(1,ℤ/8)×C11312yes—
781C23C22×D4×C11311yescharacteristic
782Q8—22no—
783Q8—22no—
784Q8—22no—
785Q8—22no—
786Q8—22no—
787Q8—48no—
788Q8—41no—
789Q8—41no—
790Q8#121×C11314yescomplemented
791D4—22no—
792D4—22no—
793D4—22no—
794D4—22no—
795D4—44no—
796D4—48no—
797D4—48no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—84no—
803D4—84no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—48no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
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—41no—
841C2×C4—41no—
842C2×C4—84no—
843C2×C4#120×C11312yes—
844C2×C4#120×C11312yes—
845C2×C4C22×D4×C11311yescharacteristic
846C2×C4C22×D4×C11311yescharacteristic
847C2×C4C22×D4×C11311yescharacteristic
848C2×C4C2×#41×C11311yescharacteristic
849C2×C4H(5,𝔽2)×C11311yescharacteristic
850C2×C4H(5,𝔽2)×C11311yescharacteristic
851C8—22no—
852C8—41no—
853C8—41no—
854C8—41no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—42no—
865C22—41no—
866C22—42no—
867C22—41no—
868C22—42no—
869C22—41no—
870C22—42no—
871C22—41no—
872C22—42no—
873C22—41no—
874C22—42no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#120×C11311yescharacteristic
884C22D42×C11311yescharacteristic
885C22#546×C11311yescharacteristic
886C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
887C22#575×C11311yescharacteristic
888C22#577×C11311yescharacteristic
889C22#578×C11311yescharacteristic
890C4—24no—
891C4—22no—
892C4—22no—
893C4—41no—
894C4—41no—
895C4—42no—
896C4—42no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#121×C11311yescharacteristic
901C4#535×C11311yescharacteristic
902C4D42×C11311yescharacteristic
903C4#546×C11311yescharacteristic
904C2—42no—
905C2—81no—
906C2—82no—
907C2—82no—
908C2C113×#240811yescharacteristic
909C2C113×#300611yescharacteristic
910C2C113×#301311yescharacteristic
911C2C113×#326511yescharacteristic
912C2C113×#326911yescharacteristic
913C2C113×#330811yescharacteristic
914C2C113×#332111yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#548×C113C2semidirect
2. C2×#463×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#448×C113C2semidirect
5. C2×#440×C113C2semidirect
6. C113×#2537C2semidirect
7. C113×#2036C2semidirect
8. C113×#2033C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1959C2semidirect
12. C113×#1955C2semidirect
13. C113×#1803C2semidirect
14. C113×#1788C2semidirect
15. C113×#1787C2semidirect
97. C2×SD16×C113D4semidirect
107. #124×C113D4semidirect
120. C4×Q8×C113D4semidirect
332. Q8×C113#121semidirect
446. #24256C113direct (N × H)
458. C2×#548C2×C113semidirect
459. C2×#463C2×C113semidirect
460. C2×#449C2×C113semidirect
461. C2×#448C2×C113semidirect
462. C2×#440C2×C113semidirect
463. #2537C2×C113semidirect
464. #2036C2×C113semidirect
465. #2033C2×C113semidirect
466. #2000C2×C113semidirect
467. #1999C2×C113semidirect
468. #1959C2×C113semidirect
469. #1955C2×C113semidirect
470. #1803C2×C113semidirect
471. #1788C2×C113semidirect
472. #1787C2×C113semidirect
473. C113#24256direct (N × H)
555. C2×SD16D4×C113semidirect
565. #124D4×C113semidirect
578. C4×Q8D4×C113semidirect
790. Q8#121×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1132
C2×#463×C1132
C2×#449×C1132
C2×#448×C1132
C2×#440×C1132
C113×#25372
C113×#20362
C113×#20332
C113×#20002
C113×#19992
C113×#19592
C113×#19552
C113×#18032
C113×#17882
C113×#17872
#24256113