Finite Group Databasebeta

← C131×#22874 #45708758

Subgroups — C131×#22874 #45708758

Order 33536.

1314 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C131C211yesmaximal, characteristic
2C2×C4×SD16×C131C211yesmaximal, characteristic, complemented
3C22×#102×C131C211yesmaximal, characteristic
4#2360×C131C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C131C211yesmaximal, characteristic
6#1968×C131C211yesmaximal, characteristic, complemented
7#1934×C131C211yesmaximal, characteristic, complemented
8#1926×C131C211yesmaximal, characteristic, complemented
9#1892×C131C211yesmaximal, characteristic, complemented
10#1880×C131C211yesmaximal, characteristic, complemented
11#1877×C131C211yesmaximal, characteristic, complemented
12#1864×C131C211yesmaximal, characteristic, complemented
13#1853×C131C211yesmaximal, characteristic, complemented
14C4×#102×C131C211yesmaximal, characteristic, complemented
15C8×C22⋊C4×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×SD16×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C23×C8×C131C2211yescharacteristic
20C2×C22⋊Q8×C131C2211yescharacteristic
21C2×C4×Q8×C131C2211yescharacteristic, complemented
22C2×C4×D4×C131C2211yescharacteristic
23C2×C4×D4×C131C2211yescharacteristic
24C22×C4⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131—21no—
26#450×C131C418yescomplemented
27C4×SD16×C131—24no—
28C2×#106×C131C2211yescharacteristic, complemented
29C2×#106×C131C2211yescharacteristic, complemented
30C2×#103×C131C2211yescharacteristic, complemented
31C2×#103×C131C2211yescharacteristic, complemented
32C2×#102×C131—24no—
33C2×#102×C131C2211yescharacteristic
34C2×#102×C131C2211yescharacteristic
35C2×#102×C131C2211yescharacteristic
36C2×#102×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×C22⋊C8×C131C2211yescharacteristic
40C2×C4×C8×C131C2211yescharacteristic, complemented
41C2×C4×C8×C131C2211yescharacteristic, complemented
42#391×C131C2211yescharacteristic, complemented
43#390×C131C2211yescharacteristic
44#390×C131C2211yescharacteristic
45#389×C131—21no—
46#389×C131C2211yescharacteristic, complemented
47#387×C131—21no—
48#386×C131—21no—
49#386×C131—21no—
50#385×C131—21no—
51#380×C131C2211yescharacteristic
52#379×C131—21no—
53C4×C4⋊C4×C131C2211yescharacteristic, complemented
54C4×C22⋊C4×C131—21no—
55C4×C22⋊C4×C131C2211yescharacteristic
56#340×C131C2211yescharacteristic, complemented
57#340×C131C2211yescharacteristic, complemented
58#340×C131C2211yescharacteristic, complemented
59#340×C131C2211yescharacteristic, complemented
60#336×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62C25×C131—21no—
63C22×Q8×C131C2311yescharacteristic
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—21no—
67C22×D4×C131—22no—
68C22×D4×C131—41no—
69C22×D4×C131—41no—
70C22×D4×C131C2×C414yes—
71C22×D4×C131C2311yescharacteristic
72C22×D4×C131C2311yescharacteristic
73C23×C4×C131—21no—
74C23×C4×C131—21no—
75C23×C4×C131—21no—
76C23×C4×C131C2311yescharacteristic
77C2×SD16×C131—22no—
78C2×SD16×C131—22no—
79C2×SD16×C131—41no—
80C2×SD16×C131—41no—
81C2×SD16×C131C2×C414yescomplemented
82C2×SD16×C131C2×C414yescomplemented
83C22×C8×C131—22no—
84C22×C8×C131—22no—
85C22×C8×C131—41no—
86C22×C8×C131C2311yescharacteristic
87C22×C8×C131C2311yescharacteristic
88C22×C8×C131C2311yescharacteristic
89C22×C8×C131C2311yescharacteristic
90C22⋊Q8×C131—22no—
91C22⋊Q8×C131C2×C414yescomplemented
92C4×Q8×C131—22no—
93C4×Q8×C131—41no—
94C4×D4×C131—22no—
95C4×D4×C131—22no—
96C4×D4×C131—41no—
97C4×D4×C131—41no—
98C2×C4⋊C4×C131—21no—
99C2×C4⋊C4×C131—22no—
100C2×C4⋊C4×C131—21no—
101C2×C4⋊C4×C131—21no—
102C2×C4⋊C4×C131—21no—
103C2×C4⋊C4×C131—41no—
104C2×C4⋊C4×C131C2311yescharacteristic
105C2×C4⋊C4×C131C2311yescharacteristic
106C2×C4⋊C4×C131C2311yescharacteristic
107C2×C4⋊C4×C131C2311yescharacteristic
108C2×C4⋊C4×C131C2311yescharacteristic
109C2×C22⋊C4×C131—21no—
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—21no—
116C2×C22⋊C4×C131—21no—
117C2×C22⋊C4×C131—44no—
118C2×C22⋊C4×C131D411yescharacteristic
119C2×C22⋊C4×C131D411yescharacteristic
120C2×C42×C131—21no—
121C2×C42×C131—21no—
122C2×C42×C131C2311yescharacteristic
123C2×C42×C131C2311yescharacteristic
124#106×C131—22no—
125#106×C131—41no—
126#103×C131—22no—
127#103×C131—41no—
128#102×C131—22no—
129#102×C131—22no—
130#102×C131—22no—
131#102×C131C2×C414yescomplemented
132#102×C131C2×C414yescomplemented
133#102×C131D414yes—
134C22⋊C8×C131C2×C414yescomplemented
135C4×C8×C131—22no—
136C4×C8×C131—41no—
137#95×C131—21no—
138#95×C131—21no—
139#95×C131—21no—
140#95×C131—21no—
141#95×C131—21no—
142#95×C131D411yescharacteristic
143#95×C131D411yescharacteristic
144C24×C131—21no—
145C24×C131—21no—
146C24×C131—24no—
147C24×C131—42no—
148C24×C131—42no—
149C24×C131—42no—
150C24×C131—42no—
151C24×C131—81no—
152C24×C131—81no—
153C24×C131C2×D411yescharacteristic
154C2×Q8×C131—21no—
155C2×Q8×C131—21no—
156C2×Q8×C131—21no—
157C2×Q8×C131—21no—
158C2×Q8×C131—21no—
159C2×Q8×C131C22×C412yes—
160C2×D4×C131—28no—
161C2×D4×C131—24no—
162C2×D4×C131—21no—
163C2×D4×C131—21no—
164C2×D4×C131—21no—
165C2×D4×C131—21no—
166C2×D4×C131—21no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—44no—
171C2×D4×C131—44no—
172C2×D4×C131—44no—
173C2×D4×C131—42no—
174C2×D4×C131—42no—
175C2×D4×C131C22×C412yes—
176C2×D4×C131C22×C412yes—
177C2×D4×C131C2×D412yes—
178C2×D4×C131#4112yes—
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—42no—
190C22×C4×C131—42no—
191C22×C4×C131—42no—
192C22×C4×C131—42no—
193C22×C4×C131—42no—
194C22×C4×C131—42no—
195C22×C4×C131—81no—
196C22×C4×C131—81no—
197C22×C4×C131—81no—
198C22×C4×C131C22×C412yes—
199C22×C4×C131C2×D411yescharacteristic
200C22×C4×C131C2×D411yescharacteristic
201C22×C4×C131C2×D411yescharacteristic
202C22×C4×C131C2×D411yescharacteristic
203C22×C4×C131C2×D411yescharacteristic
204C22×C4×C131#4112yes—
205C22×C4×C131C2411yescharacteristic
206SD16×C131—28no—
207SD16×C131—44no—
208C2×C8×C131—21no—
209C2×C8×C131—21no—
210C2×C8×C131—21no—
211C2×C8×C131—21no—
212C2×C8×C131—21no—
213C2×C8×C131—21no—
214C2×C8×C131—21no—
215C2×C8×C131—21no—
216C2×C8×C131—21no—
217C2×C8×C131—44no—
218C2×C8×C131C22×C412yes—
219C2×C8×C131C22×C412yes—
220C2×C8×C131C2×D412yes—
221C4⋊C4×C131—24no—
222C4⋊C4×C131—21no—
223C4⋊C4×C131—21no—
224C4⋊C4×C131—21no—
225C4⋊C4×C131—21no—
226C4⋊C4×C131—21no—
227C4⋊C4×C131—21no—
228C4⋊C4×C131—21no—
229C4⋊C4×C131—21no—
230C4⋊C4×C131—42no—
231C4⋊C4×C131—42no—
232C4⋊C4×C131—81no—
233C4⋊C4×C131C22×C412yes—
234C4⋊C4×C131C2×D412yes—
235C22⋊C4×C131—24no—
236C22⋊C4×C131—22no—
237C22⋊C4×C131—42no—
238C22⋊C4×C131—42no—
239C22⋊C4×C131—42no—
240C22⋊C4×C131—42no—
241C22⋊C4×C131—42no—
242C22⋊C4×C131—81no—
243C22⋊C4×C131—81no—
244C22⋊C4×C131SD1614yescomplemented
245C42×C131—21no—
246C42×C131—21no—
247C42×C131—21no—
248C42×C131—21no—
249C42×C131—42no—
250C42×C131—81no—
251C23×C131—21no—
252C23×C131—21no—
253C23×C131—21no—
254C23×C131—21no—
255C23×C131—22no—
256C23×C131—22no—
257C23×C131—22no—
258C23×C131—22no—
259C23×C131—48no—
260C23×C131—41no—
261C23×C131—41no—
262C23×C131—41no—
263C23×C131—41no—
264C23×C131—41no—
265C23×C131—41no—
266C23×C131—41no—
267C23×C131—41no—
268C23×C131—41no—
269C23×C131—41no—
270C23×C131—48no—
271C23×C131—84no—
272C23×C131—84no—
273C23×C131—84no—
274C23×C131—84no—
275C23×C131—84no—
276C23×C131C4×D412yes—
277C23×C131C2×SD1612yes—
278C23×C131#13512yes—
279C23×C131C22×D411yescharacteristic
280Q8×C131—22no—
281Q8×C131—22no—
282Q8×C131—41no—
283Q8×C131—41no—
284D4×C131—22no—
285D4×C131—22no—
286D4×C131—22no—
287D4×C131—22no—
288D4×C131—22no—
289D4×C131—48no—
290D4×C131—41no—
291D4×C131—41no—
292D4×C131C4×D414yes—
293C2×C4×C131—21no—
294C2×C4×C131—21no—
295C2×C4×C131—21no—
296C2×C4×C131—21no—
297C2×C4×C131—21no—
298C2×C4×C131—21no—
299C2×C4×C131—22no—
300C2×C4×C131—22no—
301C2×C4×C131—22no—
302C2×C4×C131—22no—
303C2×C4×C131—22no—
304C2×C4×C131—22no—
305C2×C4×C131—21no—
306C2×C4×C131—22no—
307C2×C4×C131—21no—
308C2×C4×C131—21no—
309C2×C4×C131—21no—
310C2×C4×C131—21no—
311C2×C4×C131—21no—
312C2×C4×C131—41no—
313C2×C4×C131—41no—
314C2×C4×C131—41no—
315C2×C4×C131—41no—
316C2×C4×C131—41no—
317C2×C4×C131—41no—
318C2×C4×C131—41no—
319C2×C4×C131—41no—
320C2×C4×C131—41no—
321C2×C4×C131—41no—
322C2×C4×C131—41no—
323C2×C4×C131—41no—
324C2×C4×C131—41no—
325C2×C4×C131—41no—
326C2×C4×C131—41no—
327C2×C4×C131—84no—
328C2×C4×C131—84no—
329C2×C4×C131—84no—
330C2×C4×C131C4×D412yes—
331C2×C4×C131C2×SD1612yes—
332C2×C4×C131C2×SD1612yes—
333C2×C4×C131C23×C411yescharacteristic
334C2×C4×C131C22×D411yescharacteristic
335C2×C4×C131C2×#4111yescharacteristic
336C2×C4×C131C2×#4111yescharacteristic
337C2×C4×C131H(5,𝔽2)11yescharacteristic
338C2×C4×C131H(5,𝔽2)11yescharacteristic
339C8×C131—22no—
340C8×C131—22no—
341C8×C131—22no—
342C8×C131—41no—
343C22×C131—22no—
344C22×C131—22no—
345C22×C131—22no—
346C22×C131—22no—
347C22×C131—22no—
348C22×C131—22no—
349C22×C131—24no—
350C22×C131—42no—
351C22×C131—42no—
352C22×C131—42no—
353C22×C131—42no—
354C22×C131—42no—
355C22×C131—42no—
356C22×C131—42no—
357C22×C131—42no—
358C22×C131—42no—
359C22×C131—816no—
360C22×C131—81no—
361C22×C131—81no—
362C22×C131—81no—
363C22×C131—81no—
364C22×C131C4×SD1614yescomplemented
365C22×C131C2×C4×D411yescharacteristic
366C22×C131D4211yescharacteristic
367C22×C131#54611yescharacteristic
368C22×C131C22×SD1611yescharacteristic
369C22×C131C2×#13511yescharacteristic
370C22×C131#57611yescharacteristic
371C22×C131#57711yescharacteristic
372C4×C131—22no—
373C4×C131—22no—
374C4×C131—22no—
375C4×C131—42no—
376C4×C131—42no—
377C4×C131—41no—
378C4×C131—42no—
379C4×C131—41no—
380C4×C131—81no—
381C4×C131—81no—
382C4×C131—81no—
383C4×C131C2×C4×D411yescharacteristic
384C4×C131#51811yescharacteristic
385C4×C131#54611yescharacteristic
386C4×C131#55111yescharacteristic
387C2×C131—24no—
388C2×C131—44no—
389C2×C131—82no—
390C2×C131#235811yescharacteristic
391C2×C131C2×C4×SD1611yescharacteristic
392C2×C131#294611yescharacteristic
393C2×C131#328011yescharacteristic
394C2×C131D4×SD1611yescharacteristic
395C2×C131#329511yescharacteristic
396C2×C131#329611yescharacteristic
397#22874C13111yesmaximal, characteristic, direct product factor, Sylow
398C131#2287411yescharacteristic, direct product factor, Sylow
399C2×#450C2×C13111yescharacteristic
400C2×C4×SD16C2×C13111yescharacteristic, complemented
401C22×#102C2×C13111yescharacteristic
402#2360C2×C13111yescharacteristic, complemented
403D4×C22⋊C4C2×C13111yescharacteristic
404#1968C2×C13111yescharacteristic, complemented
405#1934C2×C13111yescharacteristic, complemented
406#1926C2×C13111yescharacteristic, complemented
407#1892C2×C13111yescharacteristic, complemented
408#1880C2×C13111yescharacteristic, complemented
409#1877C2×C13111yescharacteristic, complemented
410#1864C2×C13111yescharacteristic, complemented
411#1853C2×C13111yescharacteristic, complemented
412C4×#102C2×C13111yescharacteristic, complemented
413C8×C22⋊C4C2×C13111yescharacteristic, complemented
414C23×D4C22×C13111yescharacteristic
415C22×SD16C22×C13111yescharacteristic
416C22×SD16C22×C13111yescharacteristic
417C23×C8C22×C13111yescharacteristic
418C2×C22⋊Q8C22×C13111yescharacteristic
419C2×C4×Q8C22×C13111yescharacteristic, complemented
420C2×C4×D4C22×C13111yescharacteristic
421C2×C4×D4C22×C13111yescharacteristic
422C22×C4⋊C4C22×C13111yescharacteristic
423C22×C22⋊C4—21no—
424#450C4×C13118yescomplemented
425C4×SD16—24no—
426C2×#106C22×C13111yescharacteristic, complemented
427C2×#106C22×C13111yescharacteristic, complemented
428C2×#103C22×C13111yescharacteristic, complemented
429C2×#103C22×C13111yescharacteristic, complemented
430C2×#102—24no—
431C2×#102C22×C13111yescharacteristic
432C2×#102C22×C13111yescharacteristic
433C2×#102C22×C13111yescharacteristic
434C2×#102C22×C13111yescharacteristic
435C2×#102C22×C13111yescharacteristic
436C2×#102C22×C13111yescharacteristic
437C2×C22⋊C8C22×C13111yescharacteristic
438C2×C4×C8C22×C13111yescharacteristic, complemented
439C2×C4×C8C22×C13111yescharacteristic, complemented
440#391C22×C13111yescharacteristic, complemented
441#390C22×C13111yescharacteristic
442#390C22×C13111yescharacteristic
443#389—21no—
444#389C22×C13111yescharacteristic, complemented
445#387—21no—
446#386—21no—
447#386—21no—
448#385—21no—
449#380C22×C13111yescharacteristic
450#379—21no—
451C4×C4⋊C4C22×C13111yescharacteristic, complemented
452C4×C22⋊C4—21no—
453C4×C22⋊C4C22×C13111yescharacteristic
454#340C22×C13111yescharacteristic, complemented
455#340C22×C13111yescharacteristic, complemented
456#340C22×C13111yescharacteristic, complemented
457#340C22×C13111yescharacteristic, complemented
458#336C22×C13111yescharacteristic, complemented
459#336C22×C13111yescharacteristic, complemented
460C25—21no—
461C22×Q8C23×C13111yescharacteristic
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—21no—
465C22×D4—22no—
466C22×D4—41no—
467C22×D4—41no—
468C22×D4C2×C4×C13114yes—
469C22×D4C23×C13111yescharacteristic
470C22×D4C23×C13111yescharacteristic
471C23×C4—21no—
472C23×C4—21no—
473C23×C4—21no—
474C23×C4C23×C13111yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16—41no—
478C2×SD16—41no—
479C2×SD16C2×C4×C13114yescomplemented
480C2×SD16C2×C4×C13114yescomplemented
481C22×C8—22no—
482C22×C8—22no—
483C22×C8—41no—
484C22×C8C23×C13111yescharacteristic
485C22×C8C23×C13111yescharacteristic
486C22×C8C23×C13111yescharacteristic
487C22×C8C23×C13111yescharacteristic
488C22⋊Q8—22no—
489C22⋊Q8C2×C4×C13114yescomplemented
490C4×Q8—22no—
491C4×Q8—41no—
492C4×D4—22no—
493C4×D4—22no—
494C4×D4—41no—
495C4×D4—41no—
496C2×C4⋊C4—21no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—21no—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—21no—
501C2×C4⋊C4—41no—
502C2×C4⋊C4C23×C13111yescharacteristic
503C2×C4⋊C4C23×C13111yescharacteristic
504C2×C4⋊C4C23×C13111yescharacteristic
505C2×C4⋊C4C23×C13111yescharacteristic
506C2×C4⋊C4C23×C13111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—44no—
516C2×C22⋊C4D4×C13111yescharacteristic
517C2×C22⋊C4D4×C13111yescharacteristic
518C2×C42—21no—
519C2×C42—21no—
520C2×C42C23×C13111yescharacteristic
521C2×C42C23×C13111yescharacteristic
522#106—22no—
523#106—41no—
524#103—22no—
525#103—41no—
526#102—22no—
527#102—22no—
528#102—22no—
529#102C2×C4×C13114yescomplemented
530#102C2×C4×C13114yescomplemented
531#102D4×C13114yes—
532C22⋊C8C2×C4×C13114yescomplemented
533C4×C8—22no—
534C4×C8—41no—
535#95—21no—
536#95—21no—
537#95—21no—
538#95—21no—
539#95—21no—
540#95D4×C13111yescharacteristic
541#95D4×C13111yescharacteristic
542C24—21no—
543C24—21no—
544C24—24no—
545C24—42no—
546C24—42no—
547C24—42no—
548C24—42no—
549C24—81no—
550C24—81no—
551C24C2×D4×C13111yescharacteristic
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8—21no—
555C2×Q8—21no—
556C2×Q8—21no—
557C2×Q8C22×C4×C13112yes—
558C2×D4—28no—
559C2×D4—24no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—44no—
569C2×D4—44no—
570C2×D4—44no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4C22×C4×C13112yes—
574C2×D4C22×C4×C13112yes—
575C2×D4C2×D4×C13112yes—
576C2×D4#41×C13112yes—
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—42no—
588C22×C4—42no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—81no—
594C22×C4—81no—
595C22×C4—81no—
596C22×C4C22×C4×C13112yes—
597C22×C4C2×D4×C13111yescharacteristic
598C22×C4C2×D4×C13111yescharacteristic
599C22×C4C2×D4×C13111yescharacteristic
600C22×C4C2×D4×C13111yescharacteristic
601C22×C4C2×D4×C13111yescharacteristic
602C22×C4#41×C13112yes—
603C22×C4C24×C13111yescharacteristic
604SD16—28no—
605SD16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—44no—
616C2×C8C22×C4×C13112yes—
617C2×C8C22×C4×C13112yes—
618C2×C8C2×D4×C13112yes—
619C4⋊C4—24no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—42no—
629C4⋊C4—42no—
630C4⋊C4—81no—
631C4⋊C4C22×C4×C13112yes—
632C4⋊C4C2×D4×C13112yes—
633C22⋊C4—24no—
634C22⋊C4—22no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—42no—
639C22⋊C4—42no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4SD16×C13114yescomplemented
643C42—21no—
644C42—21no—
645C42—21no—
646C42—21no—
647C42—42no—
648C42—81no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—48no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—48no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—84no—
670C23—84no—
671C23—84no—
672C23—84no—
673C23—84no—
674C23C4×D4×C13112yes—
675C23C2×SD16×C13112yes—
676C23#135×C13112yes—
677C23C22×D4×C13111yescharacteristic
678Q8—22no—
679Q8—22no—
680Q8—41no—
681Q8—41no—
682D4—22no—
683D4—22no—
684D4—22no—
685D4—22no—
686D4—22no—
687D4—48no—
688D4—41no—
689D4—41no—
690D4C4×D4×C13114yes—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—21no—
704C2×C4—22no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—84no—
726C2×C4—84no—
727C2×C4—84no—
728C2×C4C4×D4×C13112yes—
729C2×C4C2×SD16×C13112yes—
730C2×C4C2×SD16×C13112yes—
731C2×C4C23×C4×C13111yescharacteristic
732C2×C4C22×D4×C13111yescharacteristic
733C2×C4C2×#41×C13111yescharacteristic
734C2×C4C2×#41×C13111yescharacteristic
735C2×C4H(5,𝔽2)×C13111yescharacteristic
736C2×C4H(5,𝔽2)×C13111yescharacteristic
737C8—22no—
738C8—22no—
739C8—22no—
740C8—41no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—24no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—816no—
758C22—81no—
759C22—81no—
760C22—81no—
761C22—81no—
762C22C4×SD16×C13114yescomplemented
763C22C2×C4×D4×C13111yescharacteristic
764C22D42×C13111yescharacteristic
765C22#546×C13111yescharacteristic
766C22C22×SD16×C13111yescharacteristic
767C22C2×#135×C13111yescharacteristic
768C22#576×C13111yescharacteristic
769C22#577×C13111yescharacteristic
770C4—22no—
771C4—22no—
772C4—22no—
773C4—41no—
774C4—42no—
775C4—41no—
776C4—42no—
777C4—42no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4C2×C4×D4×C13111yescharacteristic
782C4#518×C13111yescharacteristic
783C4#546×C13111yescharacteristic
784C4#551×C13111yescharacteristic
785C2—24no—
786C2—44no—
787C2—82no—
788C2#2358×C13111yescharacteristic
789C2C2×C4×SD16×C13111yescharacteristic
790C2#2946×C13111yescharacteristic
791C2#3280×C13111yescharacteristic
792C2D4×SD16×C13111yescharacteristic
793C2#3295×C13111yescharacteristic
794C2#3296×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC22×C4C24×C131
prime radicalC23×D4×C131C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C4×C22⋊C4×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C131C2semidirect
4. #2360×C131C2semidirect
6. #1968×C131C2semidirect
7. #1934×C131C2semidirect
8. #1926×C131C2semidirect
9. #1892×C131C2semidirect
10. #1880×C131C2semidirect
11. #1877×C131C2semidirect
12. #1864×C131C2semidirect
13. #1853×C131C2semidirect
14. C4×#102×C131C2semidirect
15. C8×C22⋊C4×C131C2semidirect
21. C2×C4×Q8×C131C22semidirect
26. #450×C131C4semidirect
28. C2×#106×C131C22semidirect
29. C2×#106×C131C22semidirect
30. C2×#103×C131C22semidirect
31. C2×#103×C131C22semidirect
40. C2×C4×C8×C131C22semidirect
41. C2×C4×C8×C131C22semidirect
42. #391×C131C22semidirect
46. #389×C131C22semidirect
53. C4×C4⋊C4×C131C22semidirect
56. #340×C131C22semidirect
57. #340×C131C22semidirect
58. #340×C131C22semidirect
59. #340×C131C22semidirect
60. #336×C131C22semidirect
61. #336×C131C22semidirect
81. C2×SD16×C131C2×C4semidirect
82. C2×SD16×C131C2×C4semidirect
91. C22⋊Q8×C131C2×C4semidirect
131. #102×C131C2×C4semidirect
132. #102×C131C2×C4semidirect
134. C22⋊C8×C131C2×C4semidirect
244. C22⋊C4×C131SD16semidirect
364. C22×C131C4×SD16semidirect
397. #22874C131direct (N × H)
398. C131#22874direct (N × H)
400. C2×C4×SD16C2×C131semidirect
402. #2360C2×C131semidirect
404. #1968C2×C131semidirect
405. #1934C2×C131semidirect
406. #1926C2×C131semidirect
407. #1892C2×C131semidirect
408. #1880C2×C131semidirect
409. #1877C2×C131semidirect
410. #1864C2×C131semidirect
411. #1853C2×C131semidirect
412. C4×#102C2×C131semidirect
413. C8×C22⋊C4C2×C131semidirect
419. C2×C4×Q8C22×C131semidirect
424. #450C4×C131semidirect
426. C2×#106C22×C131semidirect
427. C2×#106C22×C131semidirect
428. C2×#103C22×C131semidirect
429. C2×#103C22×C131semidirect
438. C2×C4×C8C22×C131semidirect
439. C2×C4×C8C22×C131semidirect
440. #391C22×C131semidirect
444. #389C22×C131semidirect
451. C4×C4⋊C4C22×C131semidirect
454. #340C22×C131semidirect
455. #340C22×C131semidirect
456. #340C22×C131semidirect
457. #340C22×C131semidirect
458. #336C22×C131semidirect
459. #336C22×C131semidirect
479. C2×SD16C2×C4×C131semidirect
480. C2×SD16C2×C4×C131semidirect
489. C22⋊Q8C2×C4×C131semidirect
529. #102C2×C4×C131semidirect
530. #102C2×C4×C131semidirect
532. C22⋊C8C2×C4×C131semidirect
642. C22⋊C4SD16×C131semidirect
762. C22C4×SD16×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1312
C2×C4×SD16×C1312
C22×#102×C1312
#2360×C1312
D4×C22⋊C4×C1312
#1968×C1312
#1934×C1312
#1926×C1312
#1892×C1312
#1880×C1312
#1877×C1312
#1864×C1312
#1853×C1312
C4×#102×C1312
C8×C22⋊C4×C1312
#22874131