Finite Group Databasebeta

← C131×#24434 #45710318

Subgroups — C131×#24434 #45710318

Order 33536.

1674 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C131C211yesmaximal, characteristic, complemented
2C2×#465×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic, complemented
4C2×#447×C131C211yesmaximal, characteristic, complemented
5C22×#102×C131C211yesmaximal, characteristic, complemented
6#2416×C131C211yesmaximal, characteristic, complemented
7#2042×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2012×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1879×C131C211yesmaximal, characteristic, complemented
12#1872×C131C211yesmaximal, characteristic, complemented
13#1869×C131C211yesmaximal, characteristic, complemented
14#1864×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic, complemented
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21C23×C8×C131C2211yescharacteristic
22#546×C131—24no—
23#546×C131—24no—
24C2×#124×C131C2211yescharacteristic
25C2×#123×C131—21no—
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×#121×C131—21no—
28C2×#121×C131—21no—
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic
31C2×#121×C131C2211yescharacteristic, complemented
32C2×#120×C131—21no—
33C2×C4×D4×C131C2211yescharacteristic
34C2×C4×D4×C131C2211yescharacteristic
35C22×C4⋊C4×C131C2211yescharacteristic
36C22×C22⋊C4×C131—21no—
37#465×C131—24no—
38#449×C131—24no—
39#447×C131—24no—
40C2×#106×C131C2211yescharacteristic, complemented
41C2×#103×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#102×C131—24no—
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×#102×C131C2211yescharacteristic
51C2×#102×C131C2211yescharacteristic, complemented
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55#396×C131—21no—
56#394×C131—21no—
57#390×C131C2211yescharacteristic, complemented
58#389×C131C2211yescharacteristic, complemented
59#386×C131—21no—
60#380×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63#336×C131C2211yescharacteristic, complemented
64#336×C131C2211yescharacteristic, complemented
65C25×C131—21no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—41no—
71C2×#41×C131—41no—
72C22×Q8×C131C2311yescharacteristic
73C22×D4×C131—22no—
74C22×D4×C131—22no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—22no—
81C22×D4×C131—41no—
82C22×D4×C131—41no—
83C22×D4×C131D411yescharacteristic
84C22×D4×C131D414yescomplemented
85C22×D4×C131C2311yescharacteristic
86C22×D4×C131C2311yescharacteristic
87C22×D4×C131C2311yescharacteristic
88C23×C4×C131—21no—
89C23×C4×C131—21no—
90C23×C4×C131—21no—
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C2×SD16×C131—22no—
94C2×SD16×C131—22no—
95C2×SD16×C131—41no—
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—41no—
101C2×D8×C131—41no—
102C22×C8×C131—22no—
103C22×C8×C131—22no—
104C22×C8×C131—41no—
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109#124×C131—22no—
110#124×C131—22no—
111#123×C131—28no—
112C22⋊Q8×C131—22no—
113C22⋊Q8×C131D414yescomplemented
114#121×C131—28no—
115#121×C131—22no—
116#121×C131—22no—
117#121×C131—22no—
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—41no—
121#121×C131—44no—
122#120×C131—28no—
123C4×D4×C131—22no—
124C4×D4×C131—22no—
125C4×D4×C131—22no—
126C4×D4×C131—22no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131—22no—
129C2×C4⋊C4×C131—21no—
130C2×C4⋊C4×C131—21no—
131C2×C4⋊C4×C131—41no—
132C2×C4⋊C4×C131D411yescharacteristic
133C2×C4⋊C4×C131C2311yescharacteristic
134C2×C4⋊C4×C131C2311yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C4⋊C4×C131C2311yescharacteristic
137C2×C22⋊C4×C131—28no—
138C2×C22⋊C4×C131—21no—
139C2×C22⋊C4×C131—21no—
140C2×C22⋊C4×C131—21no—
141C2×C22⋊C4×C131—21no—
142C2×C22⋊C4×C131—21no—
143C2×C22⋊C4×C131—21no—
144C2×C22⋊C4×C131—21no—
145C2×C22⋊C4×C131—21no—
146C2×C22⋊C4×C131—21no—
147C2×C22⋊C4×C131—21no—
148C2×C22⋊C4×C131D411yescharacteristic
149C2×C22⋊C4×C131D411yescharacteristic
150C2×C42×C131C2311yescharacteristic
151#106×C131—22no—
152#103×C131—22no—
153#103×C131—22no—
154#103×C131—41no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—22no—
159#102×C131—22no—
160#102×C131—22no—
161#102×C131D414yescomplemented
162C22⋊C8×C131—22no—
163C22⋊C8×C131—22no—
164C22⋊C8×C131—41no—
165#95×C131—21no—
166#95×C131—21no—
167C24×C131—21no—
168C24×C131—21no—
169C24×C131—24no—
170C24×C131—21no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—42no—
174C24×C131—42no—
175C24×C131—81no—
176C24×C131—81no—
177C24×C131C2×D411yescharacteristic
178C24×C131C2×D411yescharacteristic
179#41×C131—44no—
180#41×C131—44no—
181#41×C131—44no—
182#41×C131—44no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131—21no—
188C2×Q8×C131C2×D412yes—
189C2×D4×C131—28no—
190C2×D4×C131—24no—
191C2×D4×C131—22no—
192C2×D4×C131—22no—
193C2×D4×C131—22no—
194C2×D4×C131—24no—
195C2×D4×C131—24no—
196C2×D4×C131—21no—
197C2×D4×C131—21no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—21no—
202C2×D4×C131—21no—
203C2×D4×C131—21no—
204C2×D4×C131—21no—
205C2×D4×C131—21no—
206C2×D4×C131—21no—
207C2×D4×C131—21no—
208C2×D4×C131—21no—
209C2×D4×C131—21no—
210C2×D4×C131—44no—
211C2×D4×C131—44no—
212C2×D4×C131—44no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—42no—
216C2×D4×C131—42no—
217C2×D4×C131—42no—
218C2×D4×C131—42no—
219C2×D4×C131—42no—
220C2×D4×C131—42no—
221C2×D4×C131—42no—
222C2×D4×C131—81no—
223C2×D4×C131—81no—
224C2×D4×C131—81no—
225C2×D4×C131C2×D412yes—
226C2×D4×C131C2×D412yes—
227C2×D4×C131C2×D412yes—
228C2×D4×C131#4112yes—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—24no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—24no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—42no—
247C22×C4×C131—42no—
248C22×C4×C131—42no—
249C22×C4×C131—42no—
250C22×C4×C131—81no—
251C22×C4×C131—81no—
252C22×C4×C131—81no—
253C22×C4×C131C2×D411yescharacteristic
254C22×C4×C131C2×D411yescharacteristic
255C22×C4×C131C2×D411yescharacteristic
256C22×C4×C131C2×D411yescharacteristic
257C22×C4×C131C2×D412yes—
258C22×C4×C131C2×D412yes—
259C22×C4×C131C2411yescharacteristic
260SD16×C131—44no—
261D8×C131—44no—
262D8×C131—44no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—21no—
271C2×C8×C131—21no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131—44no—
275C2×C8×C131C2×D412yes—
276C4⋊C4×C131—24no—
277C4⋊C4×C131—22no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—21no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—42no—
285C4⋊C4×C131—42no—
286C4⋊C4×C131C2×D412yes—
287C4⋊C4×C131C2×D412yes—
288C22⋊C4×C131—24no—
289C22⋊C4×C131—24no—
290C22⋊C4×C131—24no—
291C22⋊C4×C131—24no—
292C22⋊C4×C131—22no—
293C22⋊C4×C131—24no—
294C22⋊C4×C131—22no—
295C22⋊C4×C131—42no—
296C22⋊C4×C131—42no—
297C22⋊C4×C131—42no—
298C22⋊C4×C131—42no—
299C22⋊C4×C131—81no—
300C42×C131—21no—
301C42×C131—21no—
302C23×C131—21no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—22no—
307C23×C131—22no—
308C23×C131—22no—
309C23×C131—22no—
310C23×C131—21no—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—21no—
314C23×C131—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—48no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—41no—
322C23×C131—41no—
323C23×C131—41no—
324C23×C131—41no—
325C23×C131—41no—
326C23×C131—41no—
327C23×C131—41no—
328C23×C131—48no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131—41no—
336C23×C131—84no—
337C23×C131—84no—
338C23×C131—84no—
339C23×C131—84no—
340C23×C131—84no—
341C23×C131#12012yes—
342C23×C131#13512yes—
343C23×C131AGL(1,ℤ/8)12yes—
344C23×C131C22×D411yescharacteristic
345Q8×C131—22no—
346Q8×C131—22no—
347Q8×C131—41no—
348Q8×C131—41no—
349D4×C131—22no—
350D4×C131—22no—
351D4×C131—22no—
352D4×C131—22no—
353D4×C131—22no—
354D4×C131—48no—
355D4×C131—48no—
356D4×C131—44no—
357D4×C131—41no—
358D4×C131—41no—
359D4×C131—41no—
360D4×C131—41no—
361D4×C131—41no—
362D4×C131—41no—
363D4×C131—84no—
364D4×C131—84no—
365D4×C131—84no—
366D4×C131#12114yescomplemented
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—22no—
370C2×C4×C131—22no—
371C2×C4×C131—22no—
372C2×C4×C131—22no—
373C2×C4×C131—21no—
374C2×C4×C131—21no—
375C2×C4×C131—22no—
376C2×C4×C131—21no—
377C2×C4×C131—22no—
378C2×C4×C131—21no—
379C2×C4×C131—22no—
380C2×C4×C131—21no—
381C2×C4×C131—21no—
382C2×C4×C131—21no—
383C2×C4×C131—21no—
384C2×C4×C131—21no—
385C2×C4×C131—48no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—84no—
403C2×C4×C131—84no—
404C2×C4×C131#12012yes—
405C2×C4×C131C22×D411yescharacteristic
406C2×C4×C131C22×D411yescharacteristic
407C2×C4×C131C22×D411yescharacteristic
408C2×C4×C131C2×#4111yescharacteristic
409C2×C4×C131H(5,𝔽2)11yescharacteristic
410C2×C4×C131H(5,𝔽2)11yescharacteristic
411C8×C131—22no—
412C8×C131—41no—
413C8×C131—41no—
414C8×C131—41no—
415C22×C131—22no—
416C22×C131—22no—
417C22×C131—22no—
418C22×C131—22no—
419C22×C131—22no—
420C22×C131—22no—
421C22×C131—24no—
422C22×C131—42no—
423C22×C131—42no—
424C22×C131—42no—
425C22×C131—42no—
426C22×C131—42no—
427C22×C131—42no—
428C22×C131—41no—
429C22×C131—42no—
430C22×C131—41no—
431C22×C131—42no—
432C22×C131—41no—
433C22×C131—41no—
434C22×C131—42no—
435C22×C131—41no—
436C22×C131—41no—
437C22×C131—41no—
438C22×C131—816no—
439C22×C131—81no—
440C22×C131—81no—
441C22×C131—81no—
442C22×C131—81no—
443C22×C131—81no—
444C22×C131—81no—
445C22×C131—81no—
446C22×C131—81no—
447C22×C131—81no—
448C22×C131—81no—
449C22×C131—81no—
450C22×C131#44914yescomplemented
451C22×C131C2×#12011yescharacteristic
452C22×C131D4211yescharacteristic
453C22×C131#54611yescharacteristic
454C22×C131C2×#13511yescharacteristic
455C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
456C22×C131#57611yescharacteristic
457C22×C131#57711yescharacteristic
458C4×C131—22no—
459C4×C131—41no—
460C4×C131—42no—
461C4×C131—41no—
462C4×C131—42no—
463C4×C131—41no—
464C4×C131—42no—
465C4×C131—81no—
466C4×C131—81no—
467C4×C131C2×#12111yescharacteristic
468C4×C131#53411yescharacteristic
469C4×C131D4211yescharacteristic
470C4×C131#54611yescharacteristic
471C2×C131—24no—
472C2×C131—44no—
473C2×C131—81no—
474C2×C131—82no—
475C2×C131—161no—
476C2×C131#241011yescharacteristic
477C2×C131C2×#44911yescharacteristic
478C2×C131#301211yescharacteristic
479C2×C131#326411yescharacteristic
480C2×C131#328211yescharacteristic
481C2×C131#329711yescharacteristic
482C2×C131#330611yescharacteristic
483#24434C13111yesmaximal, characteristic, direct product factor, Sylow
484C131#2443411yescharacteristic, direct product factor, Sylow
485C2×#546C2×C13111yescharacteristic, complemented
486C2×#465C2×C13111yescharacteristic, complemented
487C2×#449C2×C13111yescharacteristic, complemented
488C2×#447C2×C13111yescharacteristic, complemented
489C22×#102C2×C13111yescharacteristic, complemented
490#2416C2×C13111yescharacteristic, complemented
491#2042C2×C13111yescharacteristic, complemented
492#2034C2×C13111yescharacteristic, complemented
493#2012C2×C13111yescharacteristic, complemented
494#1999C2×C13111yescharacteristic, complemented
495#1879C2×C13111yescharacteristic, complemented
496#1872C2×C13111yescharacteristic, complemented
497#1869C2×C13111yescharacteristic, complemented
498#1864C2×C13111yescharacteristic, complemented
499#1788C2×C13111yescharacteristic, complemented
500C22×#41C22×C13111yescharacteristic
501C23×D4C22×C13111yescharacteristic
502C22×SD16C22×C13111yescharacteristic, complemented
503C22×D8C22×C13111yescharacteristic
504C22×D8C22×C13111yescharacteristic
505C23×C8C22×C13111yescharacteristic
506#546—24no—
507#546—24no—
508C2×#124C22×C13111yescharacteristic
509C2×#123—21no—
510C2×C22⋊Q8C22×C13111yescharacteristic
511C2×#121—21no—
512C2×#121—21no—
513C2×#121C22×C13111yescharacteristic
514C2×#121C22×C13111yescharacteristic
515C2×#121C22×C13111yescharacteristic, complemented
516C2×#120—21no—
517C2×C4×D4C22×C13111yescharacteristic
518C2×C4×D4C22×C13111yescharacteristic
519C22×C4⋊C4C22×C13111yescharacteristic
520C22×C22⋊C4—21no—
521#465—24no—
522#449—24no—
523#447—24no—
524C2×#106C22×C13111yescharacteristic, complemented
525C2×#103C22×C13111yescharacteristic, complemented
526C2×#103C22×C13111yescharacteristic, complemented
527C2×#103C22×C13111yescharacteristic, complemented
528C2×#102—24no—
529C2×#102C22×C13111yescharacteristic
530C2×#102C22×C13111yescharacteristic
531C2×#102C22×C13111yescharacteristic
532C2×#102C22×C13111yescharacteristic
533C2×#102C22×C13111yescharacteristic
534C2×#102C22×C13111yescharacteristic
535C2×#102C22×C13111yescharacteristic, complemented
536C2×C22⋊C8C22×C13111yescharacteristic
537C2×C22⋊C8C22×C13111yescharacteristic, complemented
538C2×C22⋊C8C22×C13111yescharacteristic, complemented
539#396—21no—
540#394—21no—
541#390C22×C13111yescharacteristic, complemented
542#389C22×C13111yescharacteristic, complemented
543#386—21no—
544#380C22×C13111yescharacteristic, complemented
545#340C22×C13111yescharacteristic, complemented
546#340C22×C13111yescharacteristic, complemented
547#336C22×C13111yescharacteristic, complemented
548#336C22×C13111yescharacteristic, complemented
549C25—21no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—22no—
553C2×#41—22no—
554C2×#41—41no—
555C2×#41—41no—
556C22×Q8C23×C13111yescharacteristic
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—41no—
566C22×D4—41no—
567C22×D4D4×C13111yescharacteristic
568C22×D4D4×C13114yescomplemented
569C22×D4C23×C13111yescharacteristic
570C22×D4C23×C13111yescharacteristic
571C22×D4C23×C13111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4—21no—
575C23×C4C23×C13111yescharacteristic
576C23×C4C23×C13111yescharacteristic
577C2×SD16—22no—
578C2×SD16—22no—
579C2×SD16—41no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C22×C8—22no—
587C22×C8—22no—
588C22×C8—41no—
589C22×C8C23×C13111yescharacteristic
590C22×C8C23×C13111yescharacteristic
591C22×C8C23×C13111yescharacteristic
592C22×C8C23×C13111yescharacteristic
593#124—22no—
594#124—22no—
595#123—28no—
596C22⋊Q8—22no—
597C22⋊Q8D4×C13114yescomplemented
598#121—28no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—41no—
605#121—44no—
606#120—28no—
607C4×D4—22no—
608C4×D4—22no—
609C4×D4—22no—
610C4×D4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—41no—
616C2×C4⋊C4D4×C13111yescharacteristic
617C2×C4⋊C4C23×C13111yescharacteristic
618C2×C4⋊C4C23×C13111yescharacteristic
619C2×C4⋊C4C23×C13111yescharacteristic
620C2×C4⋊C4C23×C13111yescharacteristic
621C2×C22⋊C4—28no—
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⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4D4×C13111yescharacteristic
633C2×C22⋊C4D4×C13111yescharacteristic
634C2×C42C23×C13111yescharacteristic
635#106—22no—
636#103—22no—
637#103—22no—
638#103—41no—
639#102—22no—
640#102—22no—
641#102—22no—
642#102—22no—
643#102—22no—
644#102—22no—
645#102D4×C13114yescomplemented
646C22⋊C8—22no—
647C22⋊C8—22no—
648C22⋊C8—41no—
649#95—21no—
650#95—21no—
651C24—21no—
652C24—21no—
653C24—24no—
654C24—21no—
655C24—42no—
656C24—42no—
657C24—42no—
658C24—42no—
659C24—81no—
660C24—81no—
661C24C2×D4×C13111yescharacteristic
662C24C2×D4×C13111yescharacteristic
663#41—44no—
664#41—44no—
665#41—44no—
666#41—44no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8C2×D4×C13112yes—
673C2×D4—28no—
674C2×D4—24no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—24no—
679C2×D4—24no—
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—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—44no—
695C2×D4—44no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—42no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4C2×D4×C13112yes—
710C2×D4C2×D4×C13112yes—
711C2×D4C2×D4×C13112yes—
712C2×D4#41×C13112yes—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—24no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4—81no—
736C22×C4—81no—
737C22×C4C2×D4×C13111yescharacteristic
738C22×C4C2×D4×C13111yescharacteristic
739C22×C4C2×D4×C13111yescharacteristic
740C22×C4C2×D4×C13111yescharacteristic
741C22×C4C2×D4×C13112yes—
742C22×C4C2×D4×C13112yes—
743C22×C4C24×C13111yescharacteristic
744SD16—44no—
745D8—44no—
746D8—44no—
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×C8—21no—
758C2×C8—44no—
759C2×C8C2×D4×C13112yes—
760C4⋊C4—24no—
761C4⋊C4—22no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—42no—
769C4⋊C4—42no—
770C4⋊C4C2×D4×C13112yes—
771C4⋊C4C2×D4×C13112yes—
772C22⋊C4—24no—
773C22⋊C4—24no—
774C22⋊C4—24no—
775C22⋊C4—24no—
776C22⋊C4—22no—
777C22⋊C4—24no—
778C22⋊C4—22no—
779C22⋊C4—42no—
780C22⋊C4—42no—
781C22⋊C4—42no—
782C22⋊C4—42no—
783C22⋊C4—81no—
784C42—21no—
785C42—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—22no—
791C23—22no—
792C23—22no—
793C23—22no—
794C23—21no—
795C23—21no—
796C23—21no—
797C23—21no—
798C23—21no—
799C23—21no—
800C23—21no—
801C23—48no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—48no—
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—
825C23#120×C13112yes—
826C23#135×C13112yes—
827C23AGL(1,ℤ/8)×C13112yes—
828C23C22×D4×C13111yescharacteristic
829Q8—22no—
830Q8—22no—
831Q8—41no—
832Q8—41no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—22no—
838D4—48no—
839D4—48no—
840D4—44no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4#121×C13114yescomplemented
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—22no—
860C2×C4—21no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—22no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—48no—
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—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—84no—
887C2×C4—84no—
888C2×C4#120×C13112yes—
889C2×C4C22×D4×C13111yescharacteristic
890C2×C4C22×D4×C13111yescharacteristic
891C2×C4C22×D4×C13111yescharacteristic
892C2×C4C2×#41×C13111yescharacteristic
893C2×C4H(5,𝔽2)×C13111yescharacteristic
894C2×C4H(5,𝔽2)×C13111yescharacteristic
895C8—22no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—22no—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—22no—
904C22—22no—
905C22—24no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—41no—
913C22—42no—
914C22—41no—
915C22—41no—
916C22—42no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—42no—
922C22—816no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22#449×C13114yescomplemented
935C22C2×#120×C13111yescharacteristic
936C22D42×C13111yescharacteristic
937C22#546×C13111yescharacteristic
938C22C2×#135×C13111yescharacteristic
939C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
940C22#576×C13111yescharacteristic
941C22#577×C13111yescharacteristic
942C4—22no—
943C4—41no—
944C4—42no—
945C4—41no—
946C4—42no—
947C4—41no—
948C4—42no—
949C4—81no—
950C4—81no—
951C4C2×#121×C13111yescharacteristic
952C4#534×C13111yescharacteristic
953C4D42×C13111yescharacteristic
954C4#546×C13111yescharacteristic
955C2—24no—
956C2—44no—
957C2—81no—
958C2—82no—
959C2—161no—
960C2#2410×C13111yescharacteristic
961C2C2×#449×C13111yescharacteristic
962C2#3012×C13111yescharacteristic
963C2#3264×C13111yescharacteristic
964C2#3282×C13111yescharacteristic
965C2#3297×C13111yescharacteristic
966C2#3306×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×C4×D4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#546×C131C2semidirect
2. C2×#465×C131C2semidirect
3. C2×#449×C131C2semidirect
4. C2×#447×C131C2semidirect
5. C22×#102×C131C2semidirect
6. #2416×C131C2semidirect
7. #2042×C131C2semidirect
8. #2034×C131C2semidirect
9. #2012×C131C2semidirect
10. #1999×C131C2semidirect
11. #1879×C131C2semidirect
12. #1872×C131C2semidirect
13. #1869×C131C2semidirect
14. #1864×C131C2semidirect
15. #1788×C131C2semidirect
18. C22×SD16×C131C22semidirect
31. C2×#121×C131C22semidirect
40. C2×#106×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
51. C2×#102×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
54. C2×C22⋊C8×C131C22semidirect
57. #390×C131C22semidirect
58. #389×C131C22semidirect
60. #380×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
84. C22×D4×C131D4semidirect
113. C22⋊Q8×C131D4semidirect
161. #102×C131D4semidirect
366. D4×C131#121semidirect
450. C22×C131#449semidirect
483. #24434C131direct (N × H)
484. C131#24434direct (N × H)
485. C2×#546C2×C131semidirect
486. C2×#465C2×C131semidirect
487. C2×#449C2×C131semidirect
488. C2×#447C2×C131semidirect
489. C22×#102C2×C131semidirect
490. #2416C2×C131semidirect
491. #2042C2×C131semidirect
492. #2034C2×C131semidirect
493. #2012C2×C131semidirect
494. #1999C2×C131semidirect
495. #1879C2×C131semidirect
496. #1872C2×C131semidirect
497. #1869C2×C131semidirect
498. #1864C2×C131semidirect
499. #1788C2×C131semidirect
502. C22×SD16C22×C131semidirect
515. C2×#121C22×C131semidirect
524. C2×#106C22×C131semidirect
525. C2×#103C22×C131semidirect
526. C2×#103C22×C131semidirect
527. C2×#103C22×C131semidirect
535. C2×#102C22×C131semidirect
537. C2×C22⋊C8C22×C131semidirect
538. C2×C22⋊C8C22×C131semidirect
541. #390C22×C131semidirect
542. #389C22×C131semidirect
544. #380C22×C131semidirect
545. #340C22×C131semidirect
546. #340C22×C131semidirect
547. #336C22×C131semidirect
548. #336C22×C131semidirect
568. C22×D4D4×C131semidirect
597. C22⋊Q8D4×C131semidirect
645. #102D4×C131semidirect
850. D4#121×C131semidirect
934. C22#449×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1312
C2×#465×C1312
C2×#449×C1312
C2×#447×C1312
C22×#102×C1312
#2416×C1312
#2042×C1312
#2034×C1312
#2012×C1312
#1999×C1312
#1879×C1312
#1872×C1312
#1869×C1312
#1864×C1312
#1788×C1312
#24434131