Finite Group Databasebeta

← C113×#24257 #43292277

Subgroups — C113×#24257 #43292277

Order 28928.

1650 conjugacy classes of subgroups.

The subgroup lattice has 966 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#449×C113C211yesmaximal, characteristic, complemented
4C2×#447×C113C211yesmaximal, characteristic, complemented
5C2×#442×C113C211yesmaximal, characteristic, complemented
6C113×#2537C211yesmaximal, characteristic, complemented
7C113×#2035C211yesmaximal, characteristic, complemented
8C113×#2034C211yesmaximal, characteristic, complemented
9C113×#2000C211yesmaximal, characteristic, complemented
10C113×#1999C211yesmaximal, characteristic, complemented
11C113×#1959C211yesmaximal, characteristic, complemented
12C113×#1955C211yesmaximal, characteristic, complemented
13C113×#1802C211yesmaximal, characteristic, complemented
14C113×#1788C211yesmaximal, characteristic, complemented
15C113×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C23×D4×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic, complemented
19C22×D8×C113C2211yescharacteristic
20C22×D8×C113C2211yescharacteristic
21#546×C113—24no—
22#546×C113—24no—
23C2×#124×C113C2211yescharacteristic
24C2×#123×C113—21no—
25C2×C22⋊Q8×C113C2211yescharacteristic
26C2×#121×C113—21no—
27C2×#121×C113—21no—
28C2×#121×C113C2211yescharacteristic
29C2×#121×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic, complemented
31C2×#120×C113—21no—
32C2×C4×D4×C113C2211yescharacteristic
33C2×C4×D4×C113C2211yescharacteristic
34C2×C4×D4×C113C2211yescharacteristic, complemented
35C22×C22⋊C4×C113—21no—
36#463×C113—24no—
37#449×C113—24no—
38#447×C113—24no—
39#442×C113—24no—
40C2×#106×C113C2211yescharacteristic, complemented
41C2×C4⋊C8×C113C2211yescharacteristic, complemented
42C2×#103×C113C2211yescharacteristic, complemented
43C2×#103×C113C2211yescharacteristic, complemented
44C2×#103×C113C2211yescharacteristic, complemented
45C2×#102×C113C2211yescharacteristic
46C2×#102×C113C2211yescharacteristic
47C2×#102×C113C2211yescharacteristic
48C2×#102×C113C2211yescharacteristic
49C2×#102×C113C2211yescharacteristic
50C2×#102×C113C2211yescharacteristic
51C2×#102×C113C2211yescharacteristic, complemented
52C2×C22⋊C8×C113C2211yescharacteristic
53C2×C22⋊C8×C113C2211yescharacteristic
54C2×C22⋊C8×C113C2211yescharacteristic, complemented
55C2×C22⋊C8×C113C2211yescharacteristic, complemented
56C2×#97×C113C2211yescharacteristic, complemented
57#394×C113—21no—
58#394×C113—21no—
59#384×C113C2211yescharacteristic, complemented
60#380×C113—21no—
61#380×C113C2211yescharacteristic
62#380×C113C2211yescharacteristic, complemented
63#340×C113C2211yescharacteristic, complemented
64#340×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×D4×C113—21no—
74C22×D4×C113—21no—
75C22×D4×C113—22no—
76C22×D4×C113—22no—
77C22×D4×C113—22no—
78C22×D4×C113—22no—
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—41no—
83C22×D4×C113—41no—
84C22×D4×C113D411yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C22×D4×C113C2311yescharacteristic
88C23×C4×C113—21no—
89C23×C4×C113—21no—
90C23×C4×C113—21no—
91C23×C4×C113C2311yescharacteristic
92C23×C4×C113C2311yescharacteristic
93C2×SD16×C113—22no—
94C2×SD16×C113—22no—
95C2×SD16×C113—41no—
96C2×D8×C113—22no—
97C2×D8×C113—22no—
98C2×D8×C113—22no—
99C2×D8×C113—22no—
100C2×D8×C113—41no—
101C2×D8×C113D414yescomplemented
102C22×C8×C113C2311yescharacteristic
103C22×C8×C113C2311yescharacteristic
104C22×C8×C113C2311yescharacteristic
105C22×C8×C113C2311yescharacteristic
106#124×C113—22no—
107#124×C113D414yescomplemented
108#123×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—
119#120×C113—28no—
120C4×D4×C113—22no—
121C4×D4×C113—22no—
122C4×D4×C113—22no—
123C4×D4×C113—22no—
124C4×D4×C113—22no—
125C4×D4×C113D414yescomplemented
126C2×C4⋊C4×C113—21no—
127C2×C4⋊C4×C113—21no—
128C2×C4⋊C4×C113—21no—
129C2×C4⋊C4×C113D411yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C4⋊C4×C113C2311yescharacteristic
132C2×C4⋊C4×C113C2311yescharacteristic
133C2×C4⋊C4×C113C2311yescharacteristic
134C2×C22⋊C4×C113—28no—
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×C113—21no—
145C2×C22⋊C4×C113D411yescharacteristic
146C2×C22⋊C4×C113D411yescharacteristic
147C2×C42×C113C2311yescharacteristic
148#106×C113—22no—
149C4⋊C8×C113—22no—
150#103×C113—22no—
151#103×C113—22no—
152#103×C113—41no—
153#102×C113—22no—
154#102×C113—22no—
155#102×C113—22no—
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—24no—
169C24×C113—21no—
170C24×C113—21no—
171C24×C113—42no—
172C24×C113—42no—
173C24×C113—42no—
174C24×C113—42no—
175C24×C113—81no—
176C24×C113—81no—
177C24×C113C2×D411yescharacteristic
178C24×C113C2×D411yescharacteristic
179#41×C113—44no—
180#41×C113—44no—
181#41×C113—44no—
182#41×C113—44no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113—21no—
186C2×Q8×C113—21no—
187C2×Q8×C113—21no—
188C2×Q8×C113C2×D412yes—
189C2×D4×C113—24no—
190C2×D4×C113—24no—
191C2×D4×C113—22no—
192C2×D4×C113—24no—
193C2×D4×C113—22no—
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—21no—
207C2×D4×C113—41no—
208C2×D4×C113—42no—
209C2×D4×C113—42no—
210C2×D4×C113—44no—
211C2×D4×C113—44no—
212C2×D4×C113—44no—
213C2×D4×C113—42no—
214C2×D4×C113—42no—
215C2×D4×C113—44no—
216C2×D4×C113—42no—
217C2×D4×C113—42no—
218C2×D4×C113—42no—
219C2×D4×C113—42no—
220C2×D4×C113—81no—
221C2×D4×C113—81no—
222C2×D4×C113—81no—
223C2×D4×C113—81no—
224C2×D4×C113C2×D412yes—
225C2×D4×C113C2×D412yes—
226C2×D4×C113C2×D412yes—
227C2×D4×C113C2×D412yes—
228C2×D4×C113#4112yes—
229C22×C4×C113—24no—
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—21no—
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—24no—
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—42no—
249C22×C4×C113—42no—
250C22×C4×C113—42no—
251C22×C4×C113—42no—
252C22×C4×C113—42no—
253C22×C4×C113—81no—
254C22×C4×C113—81no—
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2×D411yescharacteristic
257C22×C4×C113C2×D411yescharacteristic
258C22×C4×C113C2×D411yescharacteristic
259C22×C4×C113C2411yescharacteristic
260SD16×C113—44no—
261D8×C113—28no—
262D8×C113—44no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113—21no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C2×C8×C113—21no—
272C2×C8×C113—21no—
273C2×C8×C113—21no—
274C2×C8×C113C2×D412yes—
275C4⋊C4×C113—24no—
276C4⋊C4×C113—22no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—21no—
284C4⋊C4×C113—42no—
285C4⋊C4×C113—81no—
286C4⋊C4×C113C2×D412yes—
287C22⋊C4×C113—24no—
288C22⋊C4×C113—24no—
289C22⋊C4×C113—22no—
290C22⋊C4×C113—24no—
291C22⋊C4×C113—24no—
292C22⋊C4×C113—24no—
293C22⋊C4×C113—22no—
294C22⋊C4×C113—42no—
295C22⋊C4×C113—42no—
296C22⋊C4×C113—42no—
297C22⋊C4×C113—42no—
298C22⋊C4×C113—42no—
299C42×C113C2×D412yes—
300C42×C113C2×D412yes—
301C23×C113—21no—
302C23×C113—22no—
303C23×C113—21no—
304C23×C113—22no—
305C23×C113—21no—
306C23×C113—22no—
307C23×C113—21no—
308C23×C113—21no—
309C23×C113—21no—
310C23×C113—22no—
311C23×C113—21no—
312C23×C113—22no—
313C23×C113—21no—
314C23×C113—21no—
315C23×C113—21no—
316C23×C113—21no—
317C23×C113—21no—
318C23×C113—21no—
319C23×C113—48no—
320C23×C113—48no—
321C23×C113—41no—
322C23×C113—41no—
323C23×C113—41no—
324C23×C113—41no—
325C23×C113—41no—
326C23×C113—41no—
327C23×C113—41no—
328C23×C113—41no—
329C23×C113—41no—
330C23×C113—41no—
331C23×C113—41no—
332C23×C113—41no—
333C23×C113—41no—
334C23×C113—41no—
335C23×C113—41no—
336C23×C113—41no—
337C23×C113—84no—
338C23×C113—84no—
339C23×C113—84no—
340C23×C113—84no—
341C23×C113—84no—
342C23×C113AGL(1,ℤ/8)12yes—
343C23×C113C22×D411yescharacteristic
344Q8×C113—22no—
345Q8×C113—22no—
346Q8×C113—41no—
347Q8×C113—41no—
348D4×C113—22no—
349D4×C113—22no—
350D4×C113—22no—
351D4×C113—22no—
352D4×C113—22no—
353D4×C113—22no—
354D4×C113—22no—
355D4×C113—44no—
356D4×C113—48no—
357D4×C113—48no—
358D4×C113—41no—
359D4×C113—41no—
360D4×C113—41no—
361D4×C113—41no—
362D4×C113—84no—
363D4×C113—84no—
364D4×C113—84no—
365D4×C113#12114yescomplemented
366C2×C4×C113—21no—
367C2×C4×C113—21no—
368C2×C4×C113—21no—
369C2×C4×C113—21no—
370C2×C4×C113—22no—
371C2×C4×C113—21no—
372C2×C4×C113—22no—
373C2×C4×C113—21no—
374C2×C4×C113—21no—
375C2×C4×C113—21no—
376C2×C4×C113—21no—
377C2×C4×C113—21no—
378C2×C4×C113—48no—
379C2×C4×C113—41no—
380C2×C4×C113—41no—
381C2×C4×C113—41no—
382C2×C4×C113—41no—
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—41no—
393C2×C4×C113—41no—
394C2×C4×C113—41no—
395C2×C4×C113—41no—
396C2×C4×C113—41no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—84no—
401C2×C4×C113—84no—
402C2×C4×C113#12012yes—
403C2×C4×C113#12012yes—
404C2×C4×C113C22×D411yescharacteristic
405C2×C4×C113C22×D411yescharacteristic
406C2×C4×C113C22×D411yescharacteristic
407C2×C4×C113C2×#4111yescharacteristic
408C2×C4×C113H(5,𝔽2)11yescharacteristic
409C2×C4×C113H(5,𝔽2)11yescharacteristic
410C8×C113—22no—
411C8×C113—41no—
412C8×C113—41no—
413C8×C113—41no—
414C22×C113—24no—
415C22×C113—22no—
416C22×C113—22no—
417C22×C113—22no—
418C22×C113—41no—
419C22×C113—42no—
420C22×C113—42no—
421C22×C113—41no—
422C22×C113—42no—
423C22×C113—42no—
424C22×C113—41no—
425C22×C113—42no—
426C22×C113—41no—
427C22×C113—42no—
428C22×C113—41no—
429C22×C113—42no—
430C22×C113—42no—
431C22×C113—41no—
432C22×C113—42no—
433C22×C113—41no—
434C22×C113—42no—
435C22×C113—41no—
436C22×C113—42no—
437C22×C113—41no—
438C22×C113—42no—
439C22×C113—41no—
440C22×C113—41no—
441C22×C113—816no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113—81no—
445C22×C113—81no—
446C22×C113—81no—
447C22×C113—81no—
448C22×C113—81no—
449C22×C113—81no—
450C22×C113C2×#12011yescharacteristic
451C22×C113D4211yescharacteristic
452C22×C113#54611yescharacteristic
453C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
454C22×C113#57511yescharacteristic
455C22×C113#57611yescharacteristic
456C22×C113#57711yescharacteristic
457C4×C113—22no—
458C4×C113—22no—
459C4×C113—41no—
460C4×C113—41no—
461C4×C113—42no—
462C4×C113—42no—
463C4×C113—81no—
464C4×C113—81no—
465C4×C113—81no—
466C4×C113C2×#12111yescharacteristic
467C4×C113#53511yescharacteristic
468C4×C113D4211yescharacteristic
469C4×C113#54611yescharacteristic
470#24257C11311yesmaximal, characteristic, direct product factor, Sylow
471C2×C113—42no—
472C2×C113—44no—
473C2×C113—81no—
474C2×C113—82no—
475C2×C113—82no—
476C2×C113#240811yescharacteristic
477C2×C113#300611yescharacteristic
478C2×C113#301211yescharacteristic
479C2×C113#326411yescharacteristic
480C2×C113#326711yescharacteristic
481C2×C113#330611yescharacteristic
482C2×C113#331911yescharacteristic
483C2×#546C2×C11311yescharacteristic, complemented
484C2×#463C2×C11311yescharacteristic, complemented
485C2×#449C2×C11311yescharacteristic, complemented
486C2×#447C2×C11311yescharacteristic, complemented
487C2×#442C2×C11311yescharacteristic, complemented
488#2537C2×C11311yescharacteristic, complemented
489#2035C2×C11311yescharacteristic, complemented
490#2034C2×C11311yescharacteristic, complemented
491#2000C2×C11311yescharacteristic, complemented
492#1999C2×C11311yescharacteristic, complemented
493#1959C2×C11311yescharacteristic, complemented
494#1955C2×C11311yescharacteristic, complemented
495#1802C2×C11311yescharacteristic, complemented
496#1788C2×C11311yescharacteristic, complemented
497#1786C2×C11311yescharacteristic, complemented
498C113#2425711yescharacteristic, direct product factor, Sylow
499C22×#41C22×C11311yescharacteristic
500C23×D4C22×C11311yescharacteristic
501C22×SD16C22×C11311yescharacteristic, complemented
502C22×D8C22×C11311yescharacteristic
503C22×D8C22×C11311yescharacteristic
504#546—24no—
505#546—24no—
506C2×#124C22×C11311yescharacteristic
507C2×#123—21no—
508C2×C22⋊Q8C22×C11311yescharacteristic
509C2×#121—21no—
510C2×#121—21no—
511C2×#121C22×C11311yescharacteristic
512C2×#121C22×C11311yescharacteristic
513C2×#121C22×C11311yescharacteristic, complemented
514C2×#120—21no—
515C2×C4×D4C22×C11311yescharacteristic
516C2×C4×D4C22×C11311yescharacteristic
517C2×C4×D4C22×C11311yescharacteristic, complemented
518C22×C22⋊C4—21no—
519#463—24no—
520#449—24no—
521#447—24no—
522#442—24no—
523C2×#106C22×C11311yescharacteristic, complemented
524C2×C4⋊C8C22×C11311yescharacteristic, complemented
525C2×#103C22×C11311yescharacteristic, complemented
526C2×#103C22×C11311yescharacteristic, complemented
527C2×#103C22×C11311yescharacteristic, complemented
528C2×#102C22×C11311yescharacteristic
529C2×#102C22×C11311yescharacteristic
530C2×#102C22×C11311yescharacteristic
531C2×#102C22×C11311yescharacteristic
532C2×#102C22×C11311yescharacteristic
533C2×#102C22×C11311yescharacteristic
534C2×#102C22×C11311yescharacteristic, complemented
535C2×C22⋊C8C22×C11311yescharacteristic
536C2×C22⋊C8C22×C11311yescharacteristic
537C2×C22⋊C8C22×C11311yescharacteristic, complemented
538C2×C22⋊C8C22×C11311yescharacteristic, complemented
539C2×#97C22×C11311yescharacteristic, complemented
540#394—21no—
541#394—21no—
542#384C22×C11311yescharacteristic, complemented
543#380—21no—
544#380C22×C11311yescharacteristic
545#380C22×C11311yescharacteristic, complemented
546#340C22×C11311yescharacteristic, complemented
547#340C22×C11311yescharacteristic, complemented
548C25—21no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—41no—
554C2×#41—41no—
555C22×Q8C23×C11311yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—22no—
559C22×D4—22no—
560C22×D4—22no—
561C22×D4—22no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C11311yescharacteristic
568C22×D4C23×C11311yescharacteristic
569C22×D4C23×C11311yescharacteristic
570C22×D4C23×C11311yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C11311yescharacteristic
575C23×C4C23×C11311yescharacteristic
576C2×SD16—22no—
577C2×SD16—22no—
578C2×SD16—41no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—41no—
584C2×D8D4×C11314yescomplemented
585C22×C8C23×C11311yescharacteristic
586C22×C8C23×C11311yescharacteristic
587C22×C8C23×C11311yescharacteristic
588C22×C8C23×C11311yescharacteristic
589#124—22no—
590#124D4×C11314yescomplemented
591#123—28no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—41no—
600#121—41no—
601#121—44no—
602#120—28no—
603C4×D4—22no—
604C4×D4—22no—
605C4×D4—22no—
606C4×D4—22no—
607C4×D4—22no—
608C4×D4D4×C11314yescomplemented
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4D4×C11311yescharacteristic
613C2×C4⋊C4C23×C11311yescharacteristic
614C2×C4⋊C4C23×C11311yescharacteristic
615C2×C4⋊C4C23×C11311yescharacteristic
616C2×C4⋊C4C23×C11311yescharacteristic
617C2×C22⋊C4—28no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4D4×C11311yescharacteristic
629C2×C22⋊C4D4×C11311yescharacteristic
630C2×C42C23×C11311yescharacteristic
631#106—22no—
632C4⋊C8—22no—
633#103—22no—
634#103—22no—
635#103—41no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645C22⋊C8—41no—
646C22⋊C8—41no—
647#97—22no—
648#95—21no—
649#95—21no—
650C24—21no—
651C24—24no—
652C24—21no—
653C24—21no—
654C24—42no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—81no—
659C24—81no—
660C24C2×D4×C11311yescharacteristic
661C24C2×D4×C11311yescharacteristic
662#41—44no—
663#41—44no—
664#41—44no—
665#41—44no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8C2×D4×C11312yes—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—22no—
675C2×D4—24no—
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—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—41no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—44no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—44no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4C2×D4×C11312yes—
708C2×D4C2×D4×C11312yes—
709C2×D4C2×D4×C11312yes—
710C2×D4C2×D4×C11312yes—
711C2×D4#41×C11312yes—
712C22×C4—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—24no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—42no—
735C22×C4—42no—
736C22×C4—81no—
737C22×C4—81no—
738C22×C4C2×D4×C11311yescharacteristic
739C22×C4C2×D4×C11311yescharacteristic
740C22×C4C2×D4×C11311yescharacteristic
741C22×C4C2×D4×C11311yescharacteristic
742C22×C4C24×C11311yescharacteristic
743SD16—44no—
744D8—28no—
745D8—44no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C2×C8C2×D4×C11312yes—
758C4⋊C4—24no—
759C4⋊C4—22no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C11312yes—
770C22⋊C4—24no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—42no—
778C22⋊C4—42no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C42C2×D4×C11312yes—
783C42C2×D4×C11312yes—
784C23—21no—
785C23—22no—
786C23—21no—
787C23—22no—
788C23—21no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—22no—
794C23—21no—
795C23—22no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—21no—
802C23—48no—
803C23—48no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23—84no—
824C23—84no—
825C23AGL(1,ℤ/8)×C11312yes—
826C23C22×D4×C11311yescharacteristic
827Q8—22no—
828Q8—22no—
829Q8—41no—
830Q8—41no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—44no—
839D4—48no—
840D4—48no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—84no—
846D4—84no—
847D4—84no—
848D4#121×C11314yescomplemented
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—84no—
884C2×C4—84no—
885C2×C4#120×C11312yes—
886C2×C4#120×C11312yes—
887C2×C4C22×D4×C11311yescharacteristic
888C2×C4C22×D4×C11311yescharacteristic
889C2×C4C22×D4×C11311yescharacteristic
890C2×C4C2×#41×C11311yescharacteristic
891C2×C4H(5,𝔽2)×C11311yescharacteristic
892C2×C4H(5,𝔽2)×C11311yescharacteristic
893C8—22no—
894C8—41no—
895C8—41no—
896C8—41no—
897C22—22no—
898C22—24no—
899C22—22no—
900C22—22no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—42no—
907C22—41no—
908C22—42no—
909C22—42no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—42no—
915C22—42no—
916C22—41no—
917C22—42no—
918C22—41no—
919C22—42no—
920C22—41no—
921C22—42no—
922C22—41no—
923C22—42no—
924C22—816no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22C2×#120×C11311yescharacteristic
934C22D42×C11311yescharacteristic
935C22#546×C11311yescharacteristic
936C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
937C22#575×C11311yescharacteristic
938C22#576×C11311yescharacteristic
939C22#577×C11311yescharacteristic
940C4—22no—
941C4—22no—
942C4—41no—
943C4—41no—
944C4—42no—
945C4—42no—
946C4—81no—
947C4—81no—
948C4—81no—
949C4C2×#121×C11311yescharacteristic
950C4#535×C11311yescharacteristic
951C4D42×C11311yescharacteristic
952C4#546×C11311yescharacteristic
953C2—42no—
954C2—44no—
955C2—81no—
956C2—82no—
957C2—82no—
958C2C113×#240811yescharacteristic
959C2C113×#300611yescharacteristic
960C2C113×#301211yescharacteristic
961C2C113×#326411yescharacteristic
962C2C113×#326711yescharacteristic
963C2C113×#330611yescharacteristic
964C2C113×#331911yescharacteristic
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×#546×C113C2semidirect
2. C2×#463×C113C2semidirect
3. C2×#449×C113C2semidirect
4. C2×#447×C113C2semidirect
5. C2×#442×C113C2semidirect
6. C113×#2537C2semidirect
7. C113×#2035C2semidirect
8. C113×#2034C2semidirect
9. C113×#2000C2semidirect
10. C113×#1999C2semidirect
11. C113×#1959C2semidirect
12. C113×#1955C2semidirect
13. C113×#1802C2semidirect
14. C113×#1788C2semidirect
15. C113×#1786C2semidirect
18. C22×SD16×C113C22semidirect
30. C2×#121×C113C22semidirect
34. C2×C4×D4×C113C22semidirect
40. C2×#106×C113C22semidirect
41. C2×C4⋊C8×C113C22semidirect
42. C2×#103×C113C22semidirect
43. C2×#103×C113C22semidirect
44. C2×#103×C113C22semidirect
51. C2×#102×C113C22semidirect
54. C2×C22⋊C8×C113C22semidirect
55. C2×C22⋊C8×C113C22semidirect
56. C2×#97×C113C22semidirect
59. #384×C113C22semidirect
62. #380×C113C22semidirect
63. #340×C113C22semidirect
64. #340×C113C22semidirect
101. C2×D8×C113D4semidirect
107. #124×C113D4semidirect
125. C4×D4×C113D4semidirect
365. D4×C113#121semidirect
470. #24257C113direct (N × H)
483. C2×#546C2×C113semidirect
484. C2×#463C2×C113semidirect
485. C2×#449C2×C113semidirect
486. C2×#447C2×C113semidirect
487. C2×#442C2×C113semidirect
488. #2537C2×C113semidirect
489. #2035C2×C113semidirect
490. #2034C2×C113semidirect
491. #2000C2×C113semidirect
492. #1999C2×C113semidirect
493. #1959C2×C113semidirect
494. #1955C2×C113semidirect
495. #1802C2×C113semidirect
496. #1788C2×C113semidirect
497. #1786C2×C113semidirect
498. C113#24257direct (N × H)
501. C22×SD16C22×C113semidirect
513. C2×#121C22×C113semidirect
517. C2×C4×D4C22×C113semidirect
523. C2×#106C22×C113semidirect
524. C2×C4⋊C8C22×C113semidirect
525. C2×#103C22×C113semidirect
526. C2×#103C22×C113semidirect
527. C2×#103C22×C113semidirect
534. C2×#102C22×C113semidirect
537. C2×C22⋊C8C22×C113semidirect
538. C2×C22⋊C8C22×C113semidirect
539. C2×#97C22×C113semidirect
542. #384C22×C113semidirect
545. #380C22×C113semidirect
546. #340C22×C113semidirect
547. #340C22×C113semidirect
584. C2×D8D4×C113semidirect
590. #124D4×C113semidirect
608. C4×D4D4×C113semidirect
848. D4#121×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1132
C2×#463×C1132
C2×#449×C1132
C2×#447×C1132
C2×#442×C1132
C113×#25372
C113×#20352
C113×#20342
C113×#20002
C113×#19992
C113×#19592
C113×#19552
C113×#18022
C113×#17882
C113×#17862
#24257113