Finite Group Databasebeta

← C131×#23482 #45709366

Subgroups — C131×#23482 #45709366

Order 33536.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic
2C2×#428×C131C211yesmaximal, characteristic, complemented
3C2×#417×C131C211yesmaximal, characteristic, complemented
4C2×#417×C131C211yesmaximal, characteristic, complemented
5C2×#407×C131C211yesmaximal, characteristic, complemented
6C2×#380×C131C211yesmaximal, characteristic, complemented
7#2036×C131C212yesmaximal, complemented
8#2035×C131C212yesmaximal, complemented
9#2034×C131C212yesmaximal, complemented
10#2033×C131C212yesmaximal, complemented
11#1736×C131C211yesmaximal, characteristic, complemented
12C22×#41×C131C2211yescharacteristic
13C24×C4×C131C2211yescharacteristic
14C22×M16×C131C2211yescharacteristic
15C22×M16×C131C2211yescharacteristic
16#525×C131—24no—
17#525×C131—24no—
18C2×#123×C131—21no—
19C2×C22⋊Q8×C131C2211yescharacteristic
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×#121×C131C2211yescharacteristic
22C2×#121×C131C2211yescharacteristic
23C2×#120×C131—21no—
24C2×C4×D4×C131—21no—
25C2×C4×D4×C131—21no—
26C2×#117×C131C2211yescharacteristic
27C22×C4⋊C4×C131C2211yescharacteristic
28C22×C4⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131—21no—
30#428×C131—24no—
31C2×#107×C131C2212yescomplemented
32C2×#106×C131C2212yescomplemented
33#417×C131—24no—
34#417×C131—24no—
35C2×#103×C131C2212yescomplemented
36C2×#103×C131C2212yescomplemented
37C2×#102×C131C2212yescomplemented
38C2×#102×C131C2212yescomplemented
39#407×C131—24no—
40C2×C22⋊C8×C131C2212yes—
41C2×C22⋊C8×C131C2212yes—
42#380×C131—21no—
43#380×C131—21no—
44#380×C131C2212yes—
45#380×C131C2212yes—
46C2×#95×C131—21no—
47#340×C131C2212yescomplemented
48#340×C131C2212yescomplemented
49C25×C131D411yescharacteristic
50C2×#41×C131—22no—
51C2×#41×C131—22no—
52C2×#41×C131—22no—
53C2×#41×C131—22no—
54C2×#41×C131—22no—
55C2×#41×C131D414yes—
56C22×Q8×C131C2311yescharacteristic
57C22×D4×C131—21no—
58C22×D4×C131—21no—
59C22×D4×C131—21no—
60C22×D4×C131C2311yescharacteristic
61C23×C4×C131—22no—
62C23×C4×C131—21no—
63C23×C4×C131—22no—
64C23×C4×C131—22no—
65C23×C4×C131—22no—
66C23×C4×C131—22no—
67C23×C4×C131—22no—
68C23×C4×C131—21no—
69C23×C4×C131—21no—
70C23×C4×C131D411yescharacteristic
71C23×C4×C131D411yescharacteristic
72C23×C4×C131D411yescharacteristic
73C23×C4×C131C2311yescharacteristic
74C23×C4×C131C2311yescharacteristic
75C23×C4×C131C2311yescharacteristic
76C2×M16×C131—22no—
77C2×M16×C131—22no—
78C2×M16×C131—22no—
79C2×M16×C131—22no—
80C2×M16×C131—22no—
81C2×M16×C131D414yescomplemented
82C22×C8×C131C2312yes—
83C22×C8×C131C2312yes—
84#123×C131—28no—
85C22⋊Q8×C131—22no—
86C22⋊Q8×C131—22no—
87C22⋊Q8×C131—22no—
88C22⋊Q8×C131—22no—
89#121×C131—22no—
90#121×C131—22no—
91#121×C131—22no—
92#121×C131—22no—
93#120×C131—28no—
94C4×D4×C131—28no—
95C4×D4×C131—28no—
96#117×C131—22no—
97#117×C131D414yes—
98C2×C4⋊C4×C131—21no—
99C2×C4⋊C4×C131—21no—
100C2×C4⋊C4×C131—22no—
101C2×C4⋊C4×C131—22no—
102C2×C4⋊C4×C131—22no—
103C2×C4⋊C4×C131—22no—
104C2×C4⋊C4×C131—21no—
105C2×C4⋊C4×C131—21no—
106C2×C4⋊C4×C131C2312yes—
107C2×C4⋊C4×C131C2312yes—
108C2×C4⋊C4×C131C2311yescharacteristic
109C2×C4⋊C4×C131C2311yescharacteristic
110C2×C22⋊C4×C131—21no—
111C2×C22⋊C4×C131—21no—
112C2×C22⋊C4×C131—21no—
113C2×C22⋊C4×C131—21no—
114C2×C22⋊C4×C131—21no—
115C2×C22⋊C4×C131—22no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—44no—
118C2×C42×C131—21no—
119#107×C131—24no—
120#106×C131—24no—
121#103×C131—24no—
122#103×C131—24no—
123#102×C131—24no—
124#102×C131—24no—
125C22⋊C8×C131—24no—
126C22⋊C8×C131—24no—
127#95×C131—22no—
128#95×C131—22no—
129C24×C131—22no—
130C24×C131—22no—
131C24×C131—22no—
132C24×C131—22no—
133C24×C131—22no—
134C24×C131—21no—
135C24×C131—41no—
136C24×C131—41no—
137C24×C131C2×D411yescharacteristic
138C24×C131C2×D411yescharacteristic
139C24×C131C2×D411yescharacteristic
140#41×C131—28no—
141#41×C131—28no—
142#41×C131—44no—
143#41×C131—44no—
144C2×Q8×C131—21no—
145C2×Q8×C131—21no—
146C2×Q8×C131—21no—
147C2×Q8×C131—21no—
148C2×Q8×C131—21no—
149C2×Q8×C131C2×D412yes—
150C2×D4×C131—24no—
151C2×D4×C131—24no—
152C2×D4×C131—24no—
153C2×D4×C131—21no—
154C2×D4×C131—21no—
155C2×D4×C131—21no—
156C2×D4×C131—21no—
157C2×D4×C131—21no—
158C2×D4×C131—42no—
159C2×D4×C131—42no—
160C2×D4×C131—42no—
161C2×D4×C131—42no—
162C2×D4×C131—42no—
163C2×D4×C131—42no—
164C2×D4×C131C2×D412yes—
165C22×C4×C131—22no—
166C22×C4×C131—22no—
167C22×C4×C131—22no—
168C22×C4×C131—21no—
169C22×C4×C131—21no—
170C22×C4×C131—21no—
171C22×C4×C131—22no—
172C22×C4×C131—22no—
173C22×C4×C131—24no—
174C22×C4×C131—22no—
175C22×C4×C131—22no—
176C22×C4×C131—22no—
177C22×C4×C131—22no—
178C22×C4×C131—21no—
179C22×C4×C131—21no—
180C22×C4×C131—21no—
181C22×C4×C131—21no—
182C22×C4×C131—21no—
183C22×C4×C131—21no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
186C22×C4×C131—21no—
187C22×C4×C131—21no—
188C22×C4×C131—21no—
189C22×C4×C131—21no—
190C22×C4×C131—22no—
191C22×C4×C131—22no—
192C22×C4×C131—44no—
193C22×C4×C131—44no—
194C22×C4×C131—42no—
195C22×C4×C131—44no—
196C22×C4×C131—42no—
197C22×C4×C131—44no—
198C22×C4×C131—42no—
199C22×C4×C131—42no—
200C22×C4×C131—42no—
201C22×C4×C131—42no—
202C22×C4×C131—42no—
203C22×C4×C131—42no—
204C22×C4×C131C2×D411yescharacteristic
205C22×C4×C131C2×D411yescharacteristic
206C22×C4×C131C2×D411yescharacteristic
207C22×C4×C131C2×D412yes—
208C22×C4×C131C2×D412yes—
209C22×C4×C131C2×D412yes—
210C22×C4×C131#4112yes—
211C22×C4×C131#4112yes—
212C22×C4×C131#4112yes—
213C22×C4×C131C2411yescharacteristic
214M16×C131—28no—
215M16×C131—44no—
216C2×C8×C131—22no—
217C2×C8×C131—22no—
218C2×C8×C131—22no—
219C2×C8×C131—22no—
220C2×C8×C131—22no—
221C2×C8×C131C2×D414yes—
222C4⋊C4×C131—24no—
223C4⋊C4×C131—24no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—21no—
226C4⋊C4×C131—22no—
227C4⋊C4×C131—22no—
228C4⋊C4×C131—22no—
229C4⋊C4×C131—22no—
230C4⋊C4×C131—42no—
231C4⋊C4×C131—42no—
232C4⋊C4×C131C2×D412yes—
233C4⋊C4×C131C2×D412yes—
234C22⋊C4×C131—24no—
235C22⋊C4×C131—24no—
236C22⋊C4×C131—24no—
237C22⋊C4×C131—24no—
238C22⋊C4×C131—24no—
239C22⋊C4×C131—44no—
240C22⋊C4×C131—44no—
241C42×C131—24no—
242C23×C131—21no—
243C23×C131—21no—
244C23×C131—21no—
245C23×C131—21no—
246C23×C131—28no—
247C23×C131—21no—
248C23×C131—21no—
249C23×C131—21no—
250C23×C131—21no—
251C23×C131—21no—
252C23×C131—21no—
253C23×C131—21no—
254C23×C131—21no—
255C23×C131—21no—
256C23×C131—21no—
257C23×C131—21no—
258C23×C131—21no—
259C23×C131—22no—
260C23×C131—44no—
261C23×C131—44no—
262C23×C131—44no—
263C23×C131—44no—
264C23×C131—44no—
265C23×C131—44no—
266C23×C131—41no—
267C23×C131—41no—
268C23×C131—41no—
269C23×C131—41no—
270C23×C131—41no—
271C23×C131—41no—
272C23×C131#12012yes—
273C23×C131#12112yes—
274C23×C131#12312yes—
275C23×C131AGL(1,ℤ/8)12yes—
276C23×C131#13712yes—
277C23×C131C22×D411yescharacteristic
278Q8×C131—22no—
279Q8×C131—22no—
280Q8×C131—41no—
281Q8×C131—41no—
282D4×C131—22no—
283D4×C131—22no—
284D4×C131—48no—
285D4×C131—48no—
286D4×C131—48no—
287D4×C131—41no—
288D4×C131—41no—
289C2×C4×C131—22no—
290C2×C4×C131—22no—
291C2×C4×C131—21no—
292C2×C4×C131—21no—
293C2×C4×C131—22no—
294C2×C4×C131—21no—
295C2×C4×C131—21no—
296C2×C4×C131—21no—
297C2×C4×C131—21no—
298C2×C4×C131—41no—
299C2×C4×C131—41no—
300C2×C4×C131—41no—
301C2×C4×C131—41no—
302C2×C4×C131—41no—
303C2×C4×C131—41no—
304C2×C4×C131—44no—
305C2×C4×C131—41no—
306C2×C4×C131—41no—
307C2×C4×C131—41no—
308C2×C4×C131—41no—
309C2×C4×C131—41no—
310C2×C4×C131—41no—
311C2×C4×C131—41no—
312C2×C4×C131—41no—
313C2×C4×C131—44no—
314C2×C4×C131—44no—
315C2×C4×C131—48no—
316C2×C4×C131—42no—
317C2×C4×C131—42no—
318C2×C4×C131—42no—
319C2×C4×C131—42no—
320C2×C4×C131—42no—
321C2×C4×C131—42no—
322C2×C4×C131—84no—
323C2×C4×C131—84no—
324C2×C4×C131#12012yes—
325C2×C4×C131#12114yes—
326C2×C4×C131#12114yes—
327C2×C4×C131#12112yes—
328C2×C4×C131#12314yes—
329C2×C4×C131#12312yes—
330C2×C4×C131#12414yes—
331C2×C4×C131C22×D411yescharacteristic
332C2×C4×C131C22×D411yescharacteristic
333C2×C4×C131C22×D411yescharacteristic
334C2×C4×C131C2×#4111yescharacteristic
335C2×C4×C131C2×#4111yescharacteristic
336C2×C4×C131C2×#4111yescharacteristic
337C8×C131—24no—
338C8×C131—42no—
339C22×C131—22no—
340C22×C131—22no—
341C22×C131—22no—
342C22×C131—22no—
343C22×C131—22no—
344C22×C131—22no—
345C22×C131—22no—
346C22×C131—22no—
347C22×C131—22no—
348C22×C131—22no—
349C22×C131—22no—
350C22×C131—22no—
351C22×C131—416no—
352C22×C131—41no—
353C22×C131—41no—
354C22×C131—41no—
355C22×C131—41no—
356C22×C131—41no—
357C22×C131—41no—
358C22×C131—41no—
359C22×C131—41no—
360C22×C131—42no—
361C22×C131—42no—
362C22×C131—42no—
363C22×C131—81no—
364C22×C131—81no—
365C22×C131—81no—
366C22×C131—81no—
367C22×C131#39414yes—
368C22×C131C2×#12011yescharacteristic
369C22×C131C2×#12111yescharacteristic
370C22×C131C2×#12311yescharacteristic
371C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
372C22×C131C2×#13711yescharacteristic
373C22×C131#57511yescharacteristic
374C22×C131#57511yescharacteristic
375C4×C131—41no—
376C4×C131—41no—
377C4×C131—42no—
378C4×C131—42no—
379C4×C131—42no—
380C4×C131—82no—
381C4×C131—82no—
382C4×C131#39414yes—
383C4×C131C2×#12111yescharacteristic
384C4×C131C2×#12111yescharacteristic
385C4×C131C2×#12311yescharacteristic
386C4×C131C2×#12411yescharacteristic
387C2×C131—24no—
388C2×C131—42no—
389C2×C131—42no—
390C2×C131—82no—
391C2×C131C2×#39411yescharacteristic
392C2×C131#300611yescharacteristic
393C2×C131#300711yescharacteristic
394C2×C131#305511yescharacteristic
395C2×C131#305611yescharacteristic
396C2×C131#309211yescharacteristic
397C2×C131#309311yescharacteristic
398#23482C13111yesmaximal, characteristic, direct product factor, Sylow
399C131#2348211yescharacteristic, direct product factor, Sylow
400C2×#525C2×C13111yescharacteristic
401C2×#428C2×C13111yescharacteristic, complemented
402C2×#417C2×C13111yescharacteristic, complemented
403C2×#417C2×C13111yescharacteristic, complemented
404C2×#407C2×C13111yescharacteristic, complemented
405C2×#380C2×C13111yescharacteristic, complemented
406#2036C2×C13112yescomplemented
407#2035C2×C13112yescomplemented
408#2034C2×C13112yescomplemented
409#2033C2×C13112yescomplemented
410#1736C2×C13111yescharacteristic, complemented
411C22×#41C22×C13111yescharacteristic
412C24×C4C22×C13111yescharacteristic
413C22×M16C22×C13111yescharacteristic
414C22×M16C22×C13111yescharacteristic
415#525—24no—
416#525—24no—
417C2×#123—21no—
418C2×C22⋊Q8C22×C13111yescharacteristic
419C2×C22⋊Q8C22×C13111yescharacteristic
420C2×#121C22×C13111yescharacteristic
421C2×#121C22×C13111yescharacteristic
422C2×#120—21no—
423C2×C4×D4—21no—
424C2×C4×D4—21no—
425C2×#117C22×C13111yescharacteristic
426C22×C4⋊C4C22×C13111yescharacteristic
427C22×C4⋊C4C22×C13111yescharacteristic
428C22×C22⋊C4—21no—
429#428—24no—
430C2×#107C22×C13112yescomplemented
431C2×#106C22×C13112yescomplemented
432#417—24no—
433#417—24no—
434C2×#103C22×C13112yescomplemented
435C2×#103C22×C13112yescomplemented
436C2×#102C22×C13112yescomplemented
437C2×#102C22×C13112yescomplemented
438#407—24no—
439C2×C22⋊C8C22×C13112yes—
440C2×C22⋊C8C22×C13112yes—
441#380—21no—
442#380—21no—
443#380C22×C13112yes—
444#380C22×C13112yes—
445C2×#95—21no—
446#340C22×C13112yescomplemented
447#340C22×C13112yescomplemented
448C25D4×C13111yescharacteristic
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—22no—
454C2×#41D4×C13114yes—
455C22×Q8C23×C13111yescharacteristic
456C22×D4—21no—
457C22×D4—21no—
458C22×D4—21no—
459C22×D4C23×C13111yescharacteristic
460C23×C4—21no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—21no—
468C23×C4—21no—
469C23×C4D4×C13111yescharacteristic
470C23×C4D4×C13111yescharacteristic
471C23×C4D4×C13111yescharacteristic
472C23×C4C23×C13111yescharacteristic
473C23×C4C23×C13111yescharacteristic
474C23×C4C23×C13111yescharacteristic
475C2×M16—22no—
476C2×M16—22no—
477C2×M16—22no—
478C2×M16—22no—
479C2×M16—22no—
480C2×M16D4×C13114yescomplemented
481C22×C8C23×C13112yes—
482C22×C8C23×C13112yes—
483#123—28no—
484C22⋊Q8—22no—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—22no—
488#121—22no—
489#121—22no—
490#121—22no—
491#121—22no—
492#120—28no—
493C4×D4—28no—
494C4×D4—28no—
495#117—22no—
496#117D4×C13114yes—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—22no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—22no—
502C2×C4⋊C4—22no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—21no—
505C2×C4⋊C4C23×C13112yes—
506C2×C4⋊C4C23×C13112yes—
507C2×C4⋊C4C23×C13111yescharacteristic
508C2×C4⋊C4C23×C13111yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—22no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—44no—
517C2×C42—21no—
518#107—24no—
519#106—24no—
520#103—24no—
521#103—24no—
522#102—24no—
523#102—24no—
524C22⋊C8—24no—
525C22⋊C8—24no—
526#95—22no—
527#95—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—21no—
534C24—41no—
535C24—41no—
536C24C2×D4×C13111yescharacteristic
537C24C2×D4×C13111yescharacteristic
538C24C2×D4×C13111yescharacteristic
539#41—28no—
540#41—28no—
541#41—44no—
542#41—44no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C13112yes—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—24no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4—42no—
563C2×D4C2×D4×C13112yes—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—44no—
595C22×C4—42no—
596C22×C4—44no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—42no—
600C22×C4—42no—
601C22×C4—42no—
602C22×C4—42no—
603C22×C4C2×D4×C13111yescharacteristic
604C22×C4C2×D4×C13111yescharacteristic
605C22×C4C2×D4×C13111yescharacteristic
606C22×C4C2×D4×C13112yes—
607C22×C4C2×D4×C13112yes—
608C22×C4C2×D4×C13112yes—
609C22×C4#41×C13112yes—
610C22×C4#41×C13112yes—
611C22×C4#41×C13112yes—
612C22×C4C24×C13111yescharacteristic
613M16—28no—
614M16—44no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—22no—
618C2×C8—22no—
619C2×C8—22no—
620C2×C8C2×D4×C13114yes—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—22no—
626C4⋊C4—22no—
627C4⋊C4—22no—
628C4⋊C4—22no—
629C4⋊C4—42no—
630C4⋊C4—42no—
631C4⋊C4C2×D4×C13112yes—
632C4⋊C4C2×D4×C13112yes—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—44no—
639C22⋊C4—44no—
640C42—24no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#120×C13112yes—
672C23#121×C13112yes—
673C23#123×C13112yes—
674C23AGL(1,ℤ/8)×C13112yes—
675C23#137×C13112yes—
676C23C22×D4×C13111yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—44no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—44no—
705C2×C4—44no—
706C2×C4—48no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—84no—
722C2×C4—84no—
723C2×C4#120×C13112yes—
724C2×C4#121×C13112yes—
725C2×C4#121×C13114yes—
726C2×C4#121×C13114yes—
727C2×C4#123×C13112yes—
728C2×C4#123×C13114yes—
729C2×C4#124×C13114yes—
730C2×C4C22×D4×C13111yescharacteristic
731C2×C4C22×D4×C13111yescharacteristic
732C2×C4C22×D4×C13111yescharacteristic
733C2×C4C2×#41×C13111yescharacteristic
734C2×C4C2×#41×C13111yescharacteristic
735C2×C4C2×#41×C13111yescharacteristic
736C8—24no—
737C8—42no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#394×C13114yes—
767C22C2×#120×C13111yescharacteristic
768C22C2×#121×C13111yescharacteristic
769C22C2×#123×C13111yescharacteristic
770C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
771C22C2×#137×C13111yescharacteristic
772C22#575×C13111yescharacteristic
773C22#575×C13111yescharacteristic
774C4—42no—
775C4—42no—
776C4—41no—
777C4—41no—
778C4—42no—
779C4—82no—
780C4—82no—
781C4#394×C13114yes—
782C4C2×#121×C13111yescharacteristic
783C4C2×#121×C13111yescharacteristic
784C4C2×#123×C13111yescharacteristic
785C4C2×#124×C13111yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#394×C13111yescharacteristic
791C2#3006×C13111yescharacteristic
792C2#3007×C13111yescharacteristic
793C2#3055×C13111yescharacteristic
794C2#3056×C13111yescharacteristic
795C2#3092×C13111yescharacteristic
796C2#3093×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×#525×C131C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#428×C131C2semidirect
3. C2×#417×C131C2semidirect
4. C2×#417×C131C2semidirect
5. C2×#407×C131C2semidirect
6. C2×#380×C131C2semidirect
7. #2036×C131C2semidirect
8. #2035×C131C2semidirect
9. #2034×C131C2semidirect
10. #2033×C131C2semidirect
11. #1736×C131C2semidirect
31. C2×#107×C131C22semidirect
32. C2×#106×C131C22semidirect
35. C2×#103×C131C22semidirect
36. C2×#103×C131C22semidirect
37. C2×#102×C131C22semidirect
38. C2×#102×C131C22semidirect
47. #340×C131C22semidirect
48. #340×C131C22semidirect
81. C2×M16×C131D4semidirect
398. #23482C131direct (N × H)
399. C131#23482direct (N × H)
401. C2×#428C2×C131semidirect
402. C2×#417C2×C131semidirect
403. C2×#417C2×C131semidirect
404. C2×#407C2×C131semidirect
405. C2×#380C2×C131semidirect
406. #2036C2×C131semidirect
407. #2035C2×C131semidirect
408. #2034C2×C131semidirect
409. #2033C2×C131semidirect
410. #1736C2×C131semidirect
430. C2×#107C22×C131semidirect
431. C2×#106C22×C131semidirect
434. C2×#103C22×C131semidirect
435. C2×#103C22×C131semidirect
436. C2×#102C22×C131semidirect
437. C2×#102C22×C131semidirect
446. #340C22×C131semidirect
447. #340C22×C131semidirect
480. C2×M16D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1312
C2×#428×C1312
C2×#417×C1312
C2×#407×C1312
C2×#380×C1312
#2036×C1312
#2035×C1312
#2034×C1312
#2033×C1312
#1736×C1312
#23482131