Finite Group Databasebeta

← C131×#22442 #45708326

Subgroups — C131×#22442 #45708326

Order 33536.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C131C211yesmaximal, characteristic
2C2×#442×C131C211yesmaximal, characteristic, complemented
3C2×C4×D8×C131C211yesmaximal, characteristic, complemented
4#2339×C131C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
6#1973×C131C211yesmaximal, characteristic, complemented
7#1968×C131C211yesmaximal, characteristic, complemented
8#1879×C131C211yesmaximal, characteristic, complemented
9#1879×C131C211yesmaximal, characteristic, complemented
10#1877×C131C211yesmaximal, characteristic, complemented
11#1877×C131C211yesmaximal, characteristic, complemented
12#1809×C131C211yesmaximal, characteristic, complemented
13#1788×C131C211yesmaximal, characteristic, complemented
14#1786×C131C211yesmaximal, characteristic, complemented
15#1753×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C131—24no—
19C2×AGL(1,ℤ/8)×C131—24no—
20C2×AGL(1,ℤ/8)×C131C418yescomplemented
21C22×SD16×C131C2211yescharacteristic
22C22×SD16×C131C2211yescharacteristic
23C22×D8×C131C2211yescharacteristic
24C22×D8×C131C2211yescharacteristic
25C22×M16×C131C2211yescharacteristic
26C2×C4×D4×C131C2211yescharacteristic
27C2×C4×D4×C131C2211yescharacteristic
28C2×C4×D4×C131C2211yescharacteristic, complemented
29C2×C4×D4×C131C2211yescharacteristic, complemented
30C22×C22⋊C4×C131—21no—
31#442×C131—24no—
32C4×D8×C131—24no—
33C2×#107×C131C2211yescharacteristic, complemented
34C2×#106×C131C2211yescharacteristic, complemented
35C2×#103×C131C2211yescharacteristic, complemented
36C2×#103×C131C2211yescharacteristic, complemented
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic, complemented
42C2×#102×C131C2211yescharacteristic, complemented
43C2×C22⋊C8×C131C2211yescharacteristic
44C2×#97×C131C2211yescharacteristic, complemented
45C2×C4×C8×C131C2211yescharacteristic, complemented
46#391×C131C2211yescharacteristic, complemented
47#391×C131C2211yescharacteristic, complemented
48#390×C131C2211yescharacteristic
49#390×C131C2211yescharacteristic
50#386×C131—21no—
51#386×C131—21no—
52#386×C131—21no—
53#386×C131—21no—
54#381×C131—21no—
55#380×C131C2211yescharacteristic
56#380×C131C2211yescharacteristic
57#379×C131—21no—
58C4×C22⋊C4×C131C2211yescharacteristic
59C2×#95×C131—21no—
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63#336×C131C2211yescharacteristic, complemented
64C25×C131—21no—
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—41no—
69C2×#41×C131—41no—
70C2×#41×C131C2×C414yescomplemented
71C22×Q8×C131C2311yescharacteristic
72C22×D4×C131—22no—
73C22×D4×C131—22no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—22no—
77C22×D4×C131—41no—
78C22×D4×C131—41no—
79C22×D4×C131C2×C414yescomplemented
80C22×D4×C131C2311yescharacteristic
81C22×D4×C131C2311yescharacteristic
82C22×D4×C131C2311yescharacteristic
83C23×C4×C131—21no—
84C23×C4×C131—21no—
85C23×C4×C131—21no—
86C23×C4×C131—21no—
87C23×C4×C131—21no—
88C23×C4×C131C2311yescharacteristic
89AGL(1,ℤ/8)×C131—232no—
90C2×SD16×C131—22no—
91C2×SD16×C131—22no—
92C2×SD16×C131—22no—
93C2×SD16×C131—22no—
94C2×SD16×C131C2×C414yescomplemented
95C2×SD16×C131C2×C414yescomplemented
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131C2×C414yes—
99C2×D8×C131C2×C414yescomplemented
100C2×D8×C131D414yes—
101C2×D8×C131D414yes—
102C2×M16×C131—22no—
103C2×M16×C131—22no—
104C2×M16×C131C2×C414yescomplemented
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109C4×D4×C131—22no—
110C4×D4×C131—22no—
111C4×D4×C131—22no—
112C4×D4×C131—22no—
113C4×D4×C131—41no—
114C4×D4×C131—41no—
115C4×D4×C131—41no—
116C4×D4×C131—41no—
117C2×C4⋊C4×C131C2311yescharacteristic
118C2×C4⋊C4×C131C2311yescharacteristic
119C2×C4⋊C4×C131C2311yescharacteristic
120C2×C4⋊C4×C131C2311yescharacteristic
121C2×C22⋊C4×C131—21no—
122C2×C22⋊C4×C131—21no—
123C2×C22⋊C4×C131—21no—
124C2×C22⋊C4×C131—21no—
125C2×C22⋊C4×C131—21no—
126C2×C22⋊C4×C131—21no—
127C2×C22⋊C4×C131—21no—
128C2×C22⋊C4×C131—21no—
129C2×C22⋊C4×C131—21no—
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—44no—
132C2×C22⋊C4×C131D411yescharacteristic
133C2×C22⋊C4×C131D411yescharacteristic
134C2×C42×C131C2311yescharacteristic
135C2×C42×C131C2311yescharacteristic
136#107×C131—22no—
137#106×C131—22no—
138#103×C131—41no—
139#103×C131—41no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—22no—
143#102×C131—22no—
144#102×C131—41no—
145#102×C131—41no—
146C22⋊C8×C131—22no—
147#97×C131—22no—
148C4×C8×C131—22no—
149#95×C131—21no—
150#95×C131—21no—
151#95×C131—21no—
152#95×C131—21no—
153#95×C131—21no—
154#95×C131—21no—
155#95×C131D411yescharacteristic
156#95×C131D411yescharacteristic
157C24×C131—21no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—24no—
161C24×C131—42no—
162C24×C131—42no—
163C24×C131—42no—
164C24×C131—42no—
165C24×C131—81no—
166C24×C131—81no—
167C24×C131C2×D411yescharacteristic
168#41×C131—28no—
169#41×C131—44no—
170#41×C131—44no—
171#41×C131—44no—
172C2×Q8×C131—21no—
173C2×Q8×C131—21no—
174C2×Q8×C131—21no—
175C2×Q8×C131—21no—
176C2×Q8×C131—21no—
177C2×Q8×C131C22×C412yes—
178C2×D4×C131—28no—
179C2×D4×C131—24no—
180C2×D4×C131—24no—
181C2×D4×C131—21no—
182C2×D4×C131—21no—
183C2×D4×C131—21no—
184C2×D4×C131—21no—
185C2×D4×C131—21no—
186C2×D4×C131—21no—
187C2×D4×C131—21no—
188C2×D4×C131—21no—
189C2×D4×C131—21no—
190C2×D4×C131—21no—
191C2×D4×C131—21no—
192C2×D4×C131—44no—
193C2×D4×C131—44no—
194C2×D4×C131—44no—
195C2×D4×C131—42no—
196C2×D4×C131—42no—
197C2×D4×C131—42no—
198C2×D4×C131—42no—
199C2×D4×C131C22×C412yes—
200C2×D4×C131C22×C412yes—
201C2×D4×C131C22×C412yes—
202C2×D4×C131C2×D412yes—
203C2×D4×C131C2×D412yes—
204C2×D4×C131C2×D412yes—
205C2×D4×C131C2×D412yes—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—24no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—42no—
217C22×C4×C131—42no—
218C22×C4×C131—42no—
219C22×C4×C131—42no—
220C22×C4×C131—42no—
221C22×C4×C131—42no—
222C22×C4×C131—42no—
223C22×C4×C131—42no—
224C22×C4×C131—42no—
225C22×C4×C131—42no—
226C22×C4×C131—81no—
227C22×C4×C131—81no—
228C22×C4×C131—81no—
229C22×C4×C131—81no—
230C22×C4×C131C22×C412yes—
231C22×C4×C131C2×D411yescharacteristic
232C22×C4×C131C2×D411yescharacteristic
233C22×C4×C131C2×D411yescharacteristic
234C22×C4×C131C2×D411yescharacteristic
235C22×C4×C131C2×D411yescharacteristic
236C22×C4×C131#4112yes—
237C22×C4×C131C2411yescharacteristic
238SD16×C131—28no—
239SD16×C131—28no—
240D8×C131—28no—
241D8×C131C22⋊C4116yescomplemented
242M16×C131—28no—
243C2×C8×C131—21no—
244C2×C8×C131—21no—
245C2×C8×C131—21no—
246C2×C8×C131—21no—
247C2×C8×C131—21no—
248C2×C8×C131—21no—
249C2×C8×C131—21no—
250C2×C8×C131—21no—
251C2×C8×C131C22×C412yes—
252C2×C8×C131C22×C412yes—
253C2×C8×C131C2×D412yes—
254C2×C8×C131C2×D412yes—
255C4⋊C4×C131—21no—
256C4⋊C4×C131—21no—
257C4⋊C4×C131—21no—
258C4⋊C4×C131—21no—
259C4⋊C4×C131—21no—
260C4⋊C4×C131—21no—
261C4⋊C4×C131—21no—
262C4⋊C4×C131—21no—
263C22⋊C4×C131—22no—
264C22⋊C4×C131—41no—
265C22⋊C4×C131—42no—
266C22⋊C4×C131—42no—
267C22⋊C4×C131—42no—
268C22⋊C4×C131—42no—
269C22⋊C4×C131—42no—
270C22⋊C4×C131—42no—
271C22⋊C4×C131—42no—
272C22⋊C4×C131—81no—
273C22⋊C4×C131—81no—
274C22⋊C4×C131—81no—
275C42×C131—21no—
276C42×C131—21no—
277C42×C131—21no—
278C42×C131—21no—
279C23×C131—22no—
280C23×C131—22no—
281C23×C131—22no—
282C23×C131—22no—
283C23×C131—22no—
284C23×C131—22no—
285C23×C131—21no—
286C23×C131—21no—
287C23×C131—21no—
288C23×C131—21no—
289C23×C131—21no—
290C23×C131—21no—
291C23×C131—22no—
292C23×C131—48no—
293C23×C131—48no—
294C23×C131—41no—
295C23×C131—41no—
296C23×C131—41no—
297C23×C131—41no—
298C23×C131—41no—
299C23×C131—41no—
300C23×C131—41no—
301C23×C131—41no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—41no—
307C23×C131—41no—
308C23×C131—84no—
309C23×C131—84no—
310C23×C131—84no—
311C23×C131—84no—
312C23×C131—84no—
313C23×C131C4×D412yes—
314C23×C131C22×D411yescharacteristic
315Q8×C131—22no—
316Q8×C131—22no—
317Q8×C131—41no—
318Q8×C131—41no—
319D4×C131—22no—
320D4×C131—22no—
321D4×C131—22no—
322D4×C131—22no—
323D4×C131—22no—
324D4×C131—22no—
325D4×C131—22no—
326D4×C131—22no—
327D4×C131—48no—
328D4×C131—48no—
329D4×C131—41no—
330D4×C131—41no—
331D4×C131C2×C22⋊C414yes—
332D4×C131C2×C22⋊C414yescomplemented
333C2×C4×C131—21no—
334C2×C4×C131—21no—
335C2×C4×C131—21no—
336C2×C4×C131—21no—
337C2×C4×C131—22no—
338C2×C4×C131—22no—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—22no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—21no—
346C2×C4×C131—21no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—48no—
352C2×C4×C131—41no—
353C2×C4×C131—41no—
354C2×C4×C131—41no—
355C2×C4×C131—41no—
356C2×C4×C131—41no—
357C2×C4×C131—41no—
358C2×C4×C131—41no—
359C2×C4×C131—41no—
360C2×C4×C131—41no—
361C2×C4×C131—41no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—84no—
367C2×C4×C131—84no—
368C2×C4×C131—84no—
369C2×C4×C131—84no—
370C2×C4×C131C4×D412yes—
371C2×C4×C131AGL(1,ℤ/8)12yescomplemented
372C2×C4×C131C23×C411yescharacteristic
373C2×C4×C131C22×D411yescharacteristic
374C2×C4×C131C22×D411yescharacteristic
375C2×C4×C131C2×#4111yescharacteristic
376C2×C4×C131H(5,𝔽2)11yescharacteristic
377C2×C4×C131H(5,𝔽2)11yescharacteristic
378C8×C131—22no—
379C8×C131—41no—
380C8×C131—41no—
381C8×C131C2×C22⋊C414yescomplemented
382C22×C131—22no—
383C22×C131—24no—
384C22×C131—24no—
385C22×C131—22no—
386C22×C131—22no—
387C22×C131—42no—
388C22×C131—42no—
389C22×C131—42no—
390C22×C131—42no—
391C22×C131—42no—
392C22×C131—42no—
393C22×C131—41no—
394C22×C131—41no—
395C22×C131—42no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—41no—
399C22×C131—42no—
400C22×C131—42no—
401C22×C131—41no—
402C22×C131—42no—
403C22×C131—42no—
404C22×C131—42no—
405C22×C131—42no—
406C22×C131—816no—
407C22×C131—81no—
408C22×C131—81no—
409C22×C131—81no—
410C22×C131—81no—
411C22×C131C2×C4×D411yescharacteristic
412C22×C131D4211yescharacteristic
413C22×C131D4211yescharacteristic
414C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
415C22×C131#57511yescharacteristic
416C22×C131#57611yescharacteristic
417C22×C131#57711yescharacteristic
418C4×C131—22no—
419C4×C131—22no—
420C4×C131—42no—
421C4×C131—41no—
422C4×C131—41no—
423C4×C131—41no—
424C4×C131—81no—
425C4×C131—81no—
426C4×C131—81no—
427C4×C131—81no—
428C4×C131C22×C22⋊C411yescharacteristic
429C4×C131#51811yescharacteristic
430C4×C131#54611yescharacteristic
431C4×C131#54611yescharacteristic
432C2×C131—42no—
433C2×C131—44no—
434C2×C131—44no—
435C2×C131—82no—
436C2×C131D4×C22⋊C411yescharacteristic
437C2×C131C4×AGL(1,ℤ/8)11yescharacteristic
438C2×C131#294611yescharacteristic
439C2×C131#326411yescharacteristic
440C2×C131#326711yescharacteristic
441C2×C131#327211yescharacteristic
442C2×C131#327311yescharacteristic
443#22442C13111yesmaximal, characteristic, direct product factor, Sylow
444C131#2244211yescharacteristic, direct product factor, Sylow
445C22×AGL(1,ℤ/8)C2×C13111yescharacteristic
446C2×#442C2×C13111yescharacteristic, complemented
447C2×C4×D8C2×C13111yescharacteristic, complemented
448#2339C2×C13111yescharacteristic, complemented
449D4×C22⋊C4C2×C13111yescharacteristic, complemented
450#1973C2×C13111yescharacteristic, complemented
451#1968C2×C13111yescharacteristic, complemented
452#1879C2×C13111yescharacteristic, complemented
453#1879C2×C13111yescharacteristic, complemented
454#1877C2×C13111yescharacteristic, complemented
455#1877C2×C13111yescharacteristic, complemented
456#1809C2×C13111yescharacteristic, complemented
457#1788C2×C13111yescharacteristic, complemented
458#1786C2×C13111yescharacteristic, complemented
459#1753C2×C13111yescharacteristic, complemented
460C22×#41C22×C13111yescharacteristic
461C23×D4C22×C13111yescharacteristic
462C2×AGL(1,ℤ/8)—24no—
463C2×AGL(1,ℤ/8)—24no—
464C2×AGL(1,ℤ/8)C4×C13118yescomplemented
465C22×SD16C22×C13111yescharacteristic
466C22×SD16C22×C13111yescharacteristic
467C22×D8C22×C13111yescharacteristic
468C22×D8C22×C13111yescharacteristic
469C22×M16C22×C13111yescharacteristic
470C2×C4×D4C22×C13111yescharacteristic
471C2×C4×D4C22×C13111yescharacteristic
472C2×C4×D4C22×C13111yescharacteristic, complemented
473C2×C4×D4C22×C13111yescharacteristic, complemented
474C22×C22⋊C4—21no—
475#442—24no—
476C4×D8—24no—
477C2×#107C22×C13111yescharacteristic, complemented
478C2×#106C22×C13111yescharacteristic, complemented
479C2×#103C22×C13111yescharacteristic, complemented
480C2×#103C22×C13111yescharacteristic, complemented
481C2×#102C22×C13111yescharacteristic
482C2×#102C22×C13111yescharacteristic
483C2×#102C22×C13111yescharacteristic
484C2×#102C22×C13111yescharacteristic
485C2×#102C22×C13111yescharacteristic, complemented
486C2×#102C22×C13111yescharacteristic, complemented
487C2×C22⋊C8C22×C13111yescharacteristic
488C2×#97C22×C13111yescharacteristic, complemented
489C2×C4×C8C22×C13111yescharacteristic, complemented
490#391C22×C13111yescharacteristic, complemented
491#391C22×C13111yescharacteristic, complemented
492#390C22×C13111yescharacteristic
493#390C22×C13111yescharacteristic
494#386—21no—
495#386—21no—
496#386—21no—
497#386—21no—
498#381—21no—
499#380C22×C13111yescharacteristic
500#380C22×C13111yescharacteristic
501#379—21no—
502C4×C22⋊C4C22×C13111yescharacteristic
503C2×#95—21no—
504#340C22×C13111yescharacteristic, complemented
505#340C22×C13111yescharacteristic, complemented
506#336C22×C13111yescharacteristic, complemented
507#336C22×C13111yescharacteristic, complemented
508C25—21no—
509C2×#41—22no—
510C2×#41—22no—
511C2×#41—22no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41C2×C4×C13114yescomplemented
515C22×Q8C23×C13111yescharacteristic
516C22×D4—22no—
517C22×D4—22no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2×C4×C13114yescomplemented
524C22×D4C23×C13111yescharacteristic
525C22×D4C23×C13111yescharacteristic
526C22×D4C23×C13111yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4C23×C13111yescharacteristic
533AGL(1,ℤ/8)—232no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16C2×C4×C13114yescomplemented
539C2×SD16C2×C4×C13114yescomplemented
540C2×D8—22no—
541C2×D8—22no—
542C2×D8C2×C4×C13114yes—
543C2×D8C2×C4×C13114yescomplemented
544C2×D8D4×C13114yes—
545C2×D8D4×C13114yes—
546C2×M16—22no—
547C2×M16—22no—
548C2×M16C2×C4×C13114yescomplemented
549C22×C8C23×C13111yescharacteristic
550C22×C8C23×C13111yescharacteristic
551C22×C8C23×C13111yescharacteristic
552C22×C8C23×C13111yescharacteristic
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C2×C4⋊C4C23×C13111yescharacteristic
562C2×C4⋊C4C23×C13111yescharacteristic
563C2×C4⋊C4C23×C13111yescharacteristic
564C2×C4⋊C4C23×C13111yescharacteristic
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—44no—
576C2×C22⋊C4D4×C13111yescharacteristic
577C2×C22⋊C4D4×C13111yescharacteristic
578C2×C42C23×C13111yescharacteristic
579C2×C42C23×C13111yescharacteristic
580#107—22no—
581#106—22no—
582#103—41no—
583#103—41no—
584#102—22no—
585#102—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590C22⋊C8—22no—
591#97—22no—
592C4×C8—22no—
593#95—21no—
594#95—21no—
595#95—21no—
596#95—21no—
597#95—21no—
598#95—21no—
599#95D4×C13111yescharacteristic
600#95D4×C13111yescharacteristic
601C24—21no—
602C24—21no—
603C24—21no—
604C24—24no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—81no—
610C24—81no—
611C24C2×D4×C13111yescharacteristic
612#41—28no—
613#41—44no—
614#41—44no—
615#41—44no—
616C2×Q8—21no—
617C2×Q8—21no—
618C2×Q8—21no—
619C2×Q8—21no—
620C2×Q8—21no—
621C2×Q8C22×C4×C13112yes—
622C2×D4—28no—
623C2×D4—24no—
624C2×D4—24no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—21no—
634C2×D4—21no—
635C2×D4—21no—
636C2×D4—44no—
637C2×D4—44no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4C22×C4×C13112yes—
644C2×D4C22×C4×C13112yes—
645C2×D4C22×C4×C13112yes—
646C2×D4C2×D4×C13112yes—
647C2×D4C2×D4×C13112yes—
648C2×D4C2×D4×C13112yes—
649C2×D4C2×D4×C13112yes—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—24no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—42no—
668C22×C4—42no—
669C22×C4—42no—
670C22×C4—81no—
671C22×C4—81no—
672C22×C4—81no—
673C22×C4—81no—
674C22×C4C22×C4×C13112yes—
675C22×C4C2×D4×C13111yescharacteristic
676C22×C4C2×D4×C13111yescharacteristic
677C22×C4C2×D4×C13111yescharacteristic
678C22×C4C2×D4×C13111yescharacteristic
679C22×C4C2×D4×C13111yescharacteristic
680C22×C4#41×C13112yes—
681C22×C4C24×C13111yescharacteristic
682SD16—28no—
683SD16—28no—
684D8—28no—
685D8C22⋊C4×C131116yescomplemented
686M16—28no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8C22×C4×C13112yes—
696C2×C8C22×C4×C13112yes—
697C2×C8C2×D4×C13112yes—
698C2×C8C2×D4×C13112yes—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C22⋊C4—22no—
708C22⋊C4—41no—
709C22⋊C4—42no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—81no—
717C22⋊C4—81no—
718C22⋊C4—81no—
719C42—21no—
720C42—21no—
721C42—21no—
722C42—21no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—22no—
736C23—48no—
737C23—48no—
738C23—41no—
739C23—41no—
740C23—41no—
741C23—41no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23—84no—
756C23—84no—
757C23C4×D4×C13112yes—
758C23C22×D4×C13111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—41no—
762Q8—41no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—41no—
774D4—41no—
775D4C2×C22⋊C4×C13114yes—
776D4C2×C22⋊C4×C13114yescomplemented
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—48no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—41no—
801C2×C4—41no—
802C2×C4—41no—
803C2×C4—41no—
804C2×C4—41no—
805C2×C4—41no—
806C2×C4—41no—
807C2×C4—41no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—84no—
811C2×C4—84no—
812C2×C4—84no—
813C2×C4—84no—
814C2×C4C4×D4×C13112yes—
815C2×C4AGL(1,ℤ/8)×C13112yescomplemented
816C2×C4C23×C4×C13111yescharacteristic
817C2×C4C22×D4×C13111yescharacteristic
818C2×C4C22×D4×C13111yescharacteristic
819C2×C4C2×#41×C13111yescharacteristic
820C2×C4H(5,𝔽2)×C13111yescharacteristic
821C2×C4H(5,𝔽2)×C13111yescharacteristic
822C8—22no—
823C8—41no—
824C8—41no—
825C8C2×C22⋊C4×C13114yescomplemented
826C22—22no—
827C22—24no—
828C22—24no—
829C22—22no—
830C22—22no—
831C22—42no—
832C22—42no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—41no—
839C22—42no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—42no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22C2×C4×D4×C13111yescharacteristic
856C22D42×C13111yescharacteristic
857C22D42×C13111yescharacteristic
858C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
859C22#575×C13111yescharacteristic
860C22#576×C13111yescharacteristic
861C22#577×C13111yescharacteristic
862C4—22no—
863C4—22no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—42no—
868C4—81no—
869C4—81no—
870C4—81no—
871C4—81no—
872C4C22×C22⋊C4×C13111yescharacteristic
873C4#518×C13111yescharacteristic
874C4#546×C13111yescharacteristic
875C4#546×C13111yescharacteristic
876C2—42no—
877C2—44no—
878C2—44no—
879C2—82no—
880C2D4×C22⋊C4×C13111yescharacteristic
881C2C4×AGL(1,ℤ/8)×C13111yescharacteristic
882C2#2946×C13111yescharacteristic
883C2#3264×C13111yescharacteristic
884C2#3267×C13111yescharacteristic
885C2#3272×C13111yescharacteristic
886C2#3273×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutatorC2×C4C23×C4×C131
Frattini, cosocleC22×C4C24×C131
prime radicalC22×AGL(1,ℤ/8)×C131C2
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×#442×C131C2semidirect
3. C2×C4×D8×C131C2semidirect
4. #2339×C131C2semidirect
5. D4×C22⋊C4×C131C2semidirect
6. #1973×C131C2semidirect
7. #1968×C131C2semidirect
8. #1879×C131C2semidirect
9. #1879×C131C2semidirect
10. #1877×C131C2semidirect
11. #1877×C131C2semidirect
12. #1809×C131C2semidirect
13. #1788×C131C2semidirect
14. #1786×C131C2semidirect
15. #1753×C131C2semidirect
20. C2×AGL(1,ℤ/8)×C131C4semidirect
28. C2×C4×D4×C131C22semidirect
29. C2×C4×D4×C131C22semidirect
33. C2×#107×C131C22semidirect
34. C2×#106×C131C22semidirect
35. C2×#103×C131C22semidirect
36. C2×#103×C131C22semidirect
41. C2×#102×C131C22semidirect
42. C2×#102×C131C22semidirect
44. C2×#97×C131C22semidirect
45. C2×C4×C8×C131C22semidirect
46. #391×C131C22semidirect
47. #391×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #336×C131C22semidirect
63. #336×C131C22semidirect
70. C2×#41×C131C2×C4semidirect
79. C22×D4×C131C2×C4semidirect
94. C2×SD16×C131C2×C4semidirect
95. C2×SD16×C131C2×C4semidirect
99. C2×D8×C131C2×C4semidirect
104. C2×M16×C131C2×C4semidirect
241. D8×C131C22⋊C4semidirect
332. D4×C131C2×C22⋊C4semidirect
371. C2×C4×C131AGL(1,ℤ/8)semidirect
381. C8×C131C2×C22⋊C4semidirect
443. #22442C131direct (N × H)
444. C131#22442direct (N × H)
446. C2×#442C2×C131semidirect
447. C2×C4×D8C2×C131semidirect
448. #2339C2×C131semidirect
449. D4×C22⋊C4C2×C131semidirect
450. #1973C2×C131semidirect
451. #1968C2×C131semidirect
452. #1879C2×C131semidirect
453. #1879C2×C131semidirect
454. #1877C2×C131semidirect
455. #1877C2×C131semidirect
456. #1809C2×C131semidirect
457. #1788C2×C131semidirect
458. #1786C2×C131semidirect
459. #1753C2×C131semidirect
464. C2×AGL(1,ℤ/8)C4×C131semidirect
472. C2×C4×D4C22×C131semidirect
473. C2×C4×D4C22×C131semidirect
477. C2×#107C22×C131semidirect
478. C2×#106C22×C131semidirect
479. C2×#103C22×C131semidirect
480. C2×#103C22×C131semidirect
485. C2×#102C22×C131semidirect
486. C2×#102C22×C131semidirect
488. C2×#97C22×C131semidirect
489. C2×C4×C8C22×C131semidirect
490. #391C22×C131semidirect
491. #391C22×C131semidirect
504. #340C22×C131semidirect
505. #340C22×C131semidirect
506. #336C22×C131semidirect
507. #336C22×C131semidirect
514. C2×#41C2×C4×C131semidirect
523. C22×D4C2×C4×C131semidirect
538. C2×SD16C2×C4×C131semidirect
539. C2×SD16C2×C4×C131semidirect
543. C2×D8C2×C4×C131semidirect
548. C2×M16C2×C4×C131semidirect
685. D8C22⋊C4×C131semidirect
776. D4C2×C22⋊C4×C131semidirect
815. C2×C4AGL(1,ℤ/8)×C131semidirect
825. C8C2×C22⋊C4×C131semidirect

Maximal subgroups

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

subgroupindex
C22×AGL(1,ℤ/8)×C1312
C2×#442×C1312
C2×C4×D8×C1312
#2339×C1312
D4×C22⋊C4×C1312
#1973×C1312
#1968×C1312
#1879×C1312
#1877×C1312
#1809×C1312
#1788×C1312
#1786×C1312
#1753×C1312
#22442131