Finite Group Databasebeta

← C131×#22443 #45708327

Subgroups — C131×#22443 #45708327

Order 33536.

1622 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C131C211yesmaximal, characteristic
2C2×#440×C131C211yesmaximal, characteristic, complemented
3C2×C4×SD16×C131C211yesmaximal, characteristic, complemented
4#2341×C131C211yesmaximal, characteristic, complemented
5D4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
6#1972×C131C211yesmaximal, characteristic, complemented
7#1970×C131C211yesmaximal, characteristic, complemented
8#1880×C131C211yesmaximal, characteristic, complemented
9#1880×C131C211yesmaximal, characteristic, complemented
10#1879×C131C211yesmaximal, characteristic, complemented
11#1879×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×Q8×C131C2211yescharacteristic, complemented
27C2×C4×Q8×C131C2211yescharacteristic, complemented
28C2×C4×D4×C131C2211yescharacteristic
29C2×C4×D4×C131C2211yescharacteristic
30C22×C22⋊C4×C131—21no—
31#440×C131—24no—
32C4×SD16×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#390×C131—21no—
47#390×C131—21no—
48#390×C131C2211yescharacteristic
49#390×C131C2211yescharacteristic
50#390×C131C2211yescharacteristic, complemented
51#390×C131C2211yescharacteristic, complemented
52#386×C131—21no—
53#386×C131—21no—
54#380×C131—21no—
55#380×C131C2211yescharacteristic
56#380×C131C2211yescharacteristic
57#379×C131—21no—
58C4×C22⋊C4×C131—21no—
59C4×C22⋊C4×C131C2211yescharacteristic
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×C414yes—
80C22×D4×C131C2311yescharacteristic
81C22×D4×C131C2311yescharacteristic
82C22×D4×C131C2311yescharacteristic
83C23×C4×C131—21no—
84C23×C4×C131—21no—
85C23×C4×C131—21no—
86C23×C4×C131C2311yescharacteristic
87AGL(1,ℤ/8)×C131—232no—
88C2×SD16×C131—22no—
89C2×SD16×C131—22no—
90C2×SD16×C131C2×C414yes—
91C2×SD16×C131C2×C414yescomplemented
92C2×SD16×C131D414yes—
93C2×SD16×C131D414yes—
94C2×D8×C131—22no—
95C2×D8×C131—22no—
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131C2×C414yes—
99C2×D8×C131C2×C414yescomplemented
100C2×M16×C131—22no—
101C2×M16×C131—22no—
102C2×M16×C131C2×C414yescomplemented
103C22×C8×C131C2311yescharacteristic
104C22×C8×C131C2311yescharacteristic
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107C4×Q8×C131—22no—
108C4×Q8×C131—22no—
109C4×Q8×C131—41no—
110C4×Q8×C131—41no—
111C4×D4×C131—22no—
112C4×D4×C131—22no—
113C4×D4×C131—41no—
114C4×D4×C131—41no—
115C2×C4⋊C4×C131—21no—
116C2×C4⋊C4×C131—21no—
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—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—44no—
134C2×C22⋊C4×C131D411yescharacteristic
135C2×C22⋊C4×C131D411yescharacteristic
136C2×C42×C131—21no—
137C2×C42×C131—21no—
138C2×C42×C131C2311yescharacteristic
139C2×C42×C131C2311yescharacteristic
140#107×C131—22no—
141#106×C131—22no—
142#103×C131—22no—
143#103×C131—22no—
144#102×C131—22no—
145#102×C131—22no—
146#102×C131—41no—
147#102×C131—41no—
148#102×C131—41no—
149#102×C131—41no—
150C22⋊C8×C131—22no—
151#97×C131—22no—
152C4×C8×C131—22no—
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×C131C22×C412yes—
176C2×Q8×C131C2×D412yes—
177C2×Q8×C131C2×D412yes—
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—21no—
193C2×D4×C131—21no—
194C2×D4×C131—44no—
195C2×D4×C131—44no—
196C2×D4×C131—44no—
197C2×D4×C131—42no—
198C2×D4×C131—42no—
199C2×D4×C131—42no—
200C2×D4×C131—42no—
201C2×D4×C131C22×C412yes—
202C2×D4×C131C22×C412yes—
203C2×D4×C131C22×C412yes—
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—81no—
223C22×C4×C131—81no—
224C22×C4×C131C22×C412yes—
225C22×C4×C131C2×D411yescharacteristic
226C22×C4×C131C2×D411yescharacteristic
227C22×C4×C131C2×D411yescharacteristic
228C22×C4×C131C2×D411yescharacteristic
229C22×C4×C131C2×D411yescharacteristic
230C22×C4×C131#4112yes—
231C22×C4×C131C2411yescharacteristic
232SD16×C131—28no—
233SD16×C131C22⋊C4116yescomplemented
234D8×C131—28no—
235D8×C131—28no—
236M16×C131—28no—
237C2×C8×C131—21no—
238C2×C8×C131—21no—
239C2×C8×C131—21no—
240C2×C8×C131—21no—
241C2×C8×C131—21no—
242C2×C8×C131—21no—
243C2×C8×C131—21no—
244C2×C8×C131—21no—
245C2×C8×C131C22×C412yes—
246C2×C8×C131C22×C412yes—
247C2×C8×C131C2×D412yes—
248C2×C8×C131C2×D412yes—
249C4⋊C4×C131—21no—
250C4⋊C4×C131—21no—
251C4⋊C4×C131—21no—
252C4⋊C4×C131—21no—
253C4⋊C4×C131—21no—
254C4⋊C4×C131—21no—
255C4⋊C4×C131—21no—
256C4⋊C4×C131—21no—
257C4⋊C4×C131—42no—
258C4⋊C4×C131—42no—
259C22⋊C4×C131—22no—
260C22⋊C4×C131—41no—
261C22⋊C4×C131—42no—
262C22⋊C4×C131—42no—
263C22⋊C4×C131—42no—
264C22⋊C4×C131—42no—
265C22⋊C4×C131—42no—
266C22⋊C4×C131—42no—
267C22⋊C4×C131—42no—
268C22⋊C4×C131—81no—
269C22⋊C4×C131—81no—
270C22⋊C4×C131—81no—
271C22⋊C4×C131—81no—
272C22⋊C4×C131—81no—
273C42×C131—21no—
274C42×C131—21no—
275C42×C131—21no—
276C42×C131—21no—
277C42×C131—42no—
278C42×C131—42no—
279C23×C131—22no—
280C23×C131—22no—
281C23×C131—22no—
282C23×C131—21no—
283C23×C131—21no—
284C23×C131—21no—
285C23×C131—21no—
286C23×C131—21no—
287C23×C131—21no—
288C23×C131—22no—
289C23×C131—22no—
290C23×C131—48no—
291C23×C131—48no—
292C23×C131—41no—
293C23×C131—41no—
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—22no—
318Q8×C131C2×C22⋊C414yescomplemented
319D4×C131—22no—
320D4×C131—22no—
321D4×C131—22no—
322D4×C131—22no—
323D4×C131—22no—
324D4×C131—22no—
325D4×C131—22no—
326D4×C131—48no—
327D4×C131—48no—
328D4×C131—41no—
329D4×C131—41no—
330D4×C131—41no—
331D4×C131—41no—
332D4×C131C2×C22⋊C414yes—
333C2×C4×C131—22no—
334C2×C4×C131—21no—
335C2×C4×C131—22no—
336C2×C4×C131—22no—
337C2×C4×C131—21no—
338C2×C4×C131—21no—
339C2×C4×C131—21no—
340C2×C4×C131—22no—
341C2×C4×C131—22no—
342C2×C4×C131—22no—
343C2×C4×C131—22no—
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—21no—
352C2×C4×C131—21no—
353C2×C4×C131—48no—
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×C131C4×D412yes—
369C2×C4×C131AGL(1,ℤ/8)12yescomplemented
370C2×C4×C131C23×C411yescharacteristic
371C2×C4×C131C22×D411yescharacteristic
372C2×C4×C131C22×D411yescharacteristic
373C2×C4×C131C2×#4111yescharacteristic
374C2×C4×C131H(5,𝔽2)11yescharacteristic
375C2×C4×C131H(5,𝔽2)11yescharacteristic
376C8×C131—22no—
377C8×C131—41no—
378C8×C131—41no—
379C8×C131C2×C22⋊C414yescomplemented
380C22×C131—22no—
381C22×C131—24no—
382C22×C131—22no—
383C22×C131—22no—
384C22×C131—42no—
385C22×C131—42no—
386C22×C131—42no—
387C22×C131—41no—
388C22×C131—41no—
389C22×C131—42no—
390C22×C131—42no—
391C22×C131—41no—
392C22×C131—41no—
393C22×C131—42no—
394C22×C131—42no—
395C22×C131—42no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—42no—
400C22×C131—816no—
401C22×C131—81no—
402C22×C131—81no—
403C22×C131—81no—
404C22×C131—81no—
405C22×C131—81no—
406C22×C131—81no—
407C22×C131—81no—
408C22×C131—81no—
409C22×C131C2×C4×D411yescharacteristic
410C22×C131D4211yescharacteristic
411C22×C131D4211yescharacteristic
412C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C131#57511yescharacteristic
414C22×C131#57611yescharacteristic
415C22×C131#57711yescharacteristic
416C4×C131—22no—
417C4×C131—24no—
418C4×C131—22no—
419C4×C131—41no—
420C4×C131—41no—
421C4×C131—41no—
422C4×C131—81no—
423C4×C131—81no—
424C4×C131—81no—
425C4×C131—81no—
426C4×C131C22×C22⋊C411yescharacteristic
427C4×C131#51811yescharacteristic
428C4×C131#54611yescharacteristic
429C4×C131#54611yescharacteristic
430C2×C131—42no—
431C2×C131—44no—
432C2×C131—82no—
433C2×C131—82no—
434C2×C131D4×C22⋊C411yescharacteristic
435C2×C131C4×AGL(1,ℤ/8)11yescharacteristic
436C2×C131#294611yescharacteristic
437C2×C131#326511yescharacteristic
438C2×C131#326811yescharacteristic
439C2×C131#327411yescharacteristic
440C2×C131#327511yescharacteristic
441#22443C13111yesmaximal, characteristic, direct product factor, Sylow
442C131#2244311yescharacteristic, direct product factor, Sylow
443C22×AGL(1,ℤ/8)C2×C13111yescharacteristic
444C2×#440C2×C13111yescharacteristic, complemented
445C2×C4×SD16C2×C13111yescharacteristic, complemented
446#2341C2×C13111yescharacteristic, complemented
447D4×C22⋊C4C2×C13111yescharacteristic, complemented
448#1972C2×C13111yescharacteristic, complemented
449#1970C2×C13111yescharacteristic, complemented
450#1880C2×C13111yescharacteristic, complemented
451#1880C2×C13111yescharacteristic, complemented
452#1879C2×C13111yescharacteristic, complemented
453#1879C2×C13111yescharacteristic, complemented
454#1809C2×C13111yescharacteristic, complemented
455#1788C2×C13111yescharacteristic, complemented
456#1786C2×C13111yescharacteristic, complemented
457#1753C2×C13111yescharacteristic, complemented
458C22×#41C22×C13111yescharacteristic
459C23×D4C22×C13111yescharacteristic
460C2×AGL(1,ℤ/8)—24no—
461C2×AGL(1,ℤ/8)—24no—
462C2×AGL(1,ℤ/8)C4×C13118yescomplemented
463C22×SD16C22×C13111yescharacteristic
464C22×SD16C22×C13111yescharacteristic
465C22×D8C22×C13111yescharacteristic
466C22×D8C22×C13111yescharacteristic
467C22×M16C22×C13111yescharacteristic
468C2×C4×Q8C22×C13111yescharacteristic, complemented
469C2×C4×Q8C22×C13111yescharacteristic, complemented
470C2×C4×D4C22×C13111yescharacteristic
471C2×C4×D4C22×C13111yescharacteristic
472C22×C22⋊C4—21no—
473#440—24no—
474C4×SD16—24no—
475C2×#107C22×C13111yescharacteristic, complemented
476C2×#106C22×C13111yescharacteristic, complemented
477C2×#103C22×C13111yescharacteristic, complemented
478C2×#103C22×C13111yescharacteristic, complemented
479C2×#102C22×C13111yescharacteristic
480C2×#102C22×C13111yescharacteristic
481C2×#102C22×C13111yescharacteristic
482C2×#102C22×C13111yescharacteristic
483C2×#102C22×C13111yescharacteristic, complemented
484C2×#102C22×C13111yescharacteristic, complemented
485C2×C22⋊C8C22×C13111yescharacteristic
486C2×#97C22×C13111yescharacteristic, complemented
487C2×C4×C8C22×C13111yescharacteristic, complemented
488#390—21no—
489#390—21no—
490#390C22×C13111yescharacteristic
491#390C22×C13111yescharacteristic
492#390C22×C13111yescharacteristic, complemented
493#390C22×C13111yescharacteristic, complemented
494#386—21no—
495#386—21no—
496#380—21no—
497#380C22×C13111yescharacteristic
498#380C22×C13111yescharacteristic
499#379—21no—
500C4×C22⋊C4—21no—
501C4×C22⋊C4C22×C13111yescharacteristic
502#340C22×C13111yescharacteristic, complemented
503#340C22×C13111yescharacteristic, complemented
504#336C22×C13111yescharacteristic, complemented
505#336C22×C13111yescharacteristic, complemented
506C25—21no—
507C2×#41—22no—
508C2×#41—22no—
509C2×#41—22no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41C2×C4×C13114yescomplemented
513C22×Q8C23×C13111yescharacteristic
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4C2×C4×C13114yes—
522C22×D4C23×C13111yescharacteristic
523C22×D4C23×C13111yescharacteristic
524C22×D4C23×C13111yescharacteristic
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4C23×C13111yescharacteristic
529AGL(1,ℤ/8)—232no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16C2×C4×C13114yes—
533C2×SD16C2×C4×C13114yescomplemented
534C2×SD16D4×C13114yes—
535C2×SD16D4×C13114yes—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8C2×C4×C13114yes—
541C2×D8C2×C4×C13114yescomplemented
542C2×M16—22no—
543C2×M16—22no—
544C2×M16C2×C4×C13114yescomplemented
545C22×C8C23×C13111yescharacteristic
546C22×C8C23×C13111yescharacteristic
547C22×C8C23×C13111yescharacteristic
548C22×C8C23×C13111yescharacteristic
549C4×Q8—22no—
550C4×Q8—22no—
551C4×Q8—41no—
552C4×Q8—41no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4C23×C13111yescharacteristic
560C2×C4⋊C4C23×C13111yescharacteristic
561C2×C4⋊C4C23×C13111yescharacteristic
562C2×C4⋊C4C23×C13111yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
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×C42—21no—
579C2×C42—21no—
580C2×C42C23×C13111yescharacteristic
581C2×C42C23×C13111yescharacteristic
582#107—22no—
583#106—22no—
584#103—22no—
585#103—22no—
586#102—22no—
587#102—22no—
588#102—41no—
589#102—41no—
590#102—41no—
591#102—41no—
592C22⋊C8—22no—
593#97—22no—
594C4×C8—22no—
595#95—21no—
596#95—21no—
597#95D4×C13111yescharacteristic
598#95D4×C13111yescharacteristic
599C24—21no—
600C24—21no—
601C24—21no—
602C24—24no—
603C24—42no—
604C24—42no—
605C24—42no—
606C24—42no—
607C24—81no—
608C24—81no—
609C24C2×D4×C13111yescharacteristic
610#41—28no—
611#41—44no—
612#41—44no—
613#41—44no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8—21no—
617C2×Q8C22×C4×C13112yes—
618C2×Q8C2×D4×C13112yes—
619C2×Q8C2×D4×C13112yes—
620C2×D4—28no—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
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—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—24no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—42no—
663C22×C4—42no—
664C22×C4—81no—
665C22×C4—81no—
666C22×C4C22×C4×C13112yes—
667C22×C4C2×D4×C13111yescharacteristic
668C22×C4C2×D4×C13111yescharacteristic
669C22×C4C2×D4×C13111yescharacteristic
670C22×C4C2×D4×C13111yescharacteristic
671C22×C4C2×D4×C13111yescharacteristic
672C22×C4#41×C13112yes—
673C22×C4C24×C13111yescharacteristic
674SD16—28no—
675SD16C22⋊C4×C131116yescomplemented
676D8—28no—
677D8—28no—
678M16—28no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8C22×C4×C13112yes—
688C2×C8C22×C4×C13112yes—
689C2×C8C2×D4×C13112yes—
690C2×C8C2×D4×C13112yes—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4—42no—
701C22⋊C4—22no—
702C22⋊C4—41no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—42no—
706C22⋊C4—42no—
707C22⋊C4—42no—
708C22⋊C4—42no—
709C22⋊C4—42no—
710C22⋊C4—81no—
711C22⋊C4—81no—
712C22⋊C4—81no—
713C22⋊C4—81no—
714C22⋊C4—81no—
715C42—21no—
716C42—21no—
717C42—21no—
718C42—21no—
719C42—42no—
720C42—42no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—22no—
732C23—48no—
733C23—48no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
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—84no—
751C23—84no—
752C23—84no—
753C23—84no—
754C23—84no—
755C23C4×D4×C13112yes—
756C23C22×D4×C13111yescharacteristic
757Q8—22no—
758Q8—22no—
759Q8—22no—
760Q8C2×C22⋊C4×C13114yescomplemented
761D4—22no—
762D4—22no—
763D4—22no—
764D4—22no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—48no—
769D4—48no—
770D4—41no—
771D4—41no—
772D4—41no—
773D4—41no—
774D4C2×C22⋊C4×C13114yes—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
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—84no—
809C2×C4—84no—
810C2×C4C4×D4×C13112yes—
811C2×C4AGL(1,ℤ/8)×C13112yescomplemented
812C2×C4C23×C4×C13111yescharacteristic
813C2×C4C22×D4×C13111yescharacteristic
814C2×C4C22×D4×C13111yescharacteristic
815C2×C4C2×#41×C13111yescharacteristic
816C2×C4H(5,𝔽2)×C13111yescharacteristic
817C2×C4H(5,𝔽2)×C13111yescharacteristic
818C8—22no—
819C8—41no—
820C8—41no—
821C8C2×C22⋊C4×C13114yescomplemented
822C22—22no—
823C22—24no—
824C22—22no—
825C22—22no—
826C22—42no—
827C22—41no—
828C22—41no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—42no—
836C22—42no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—42no—
841C22—42no—
842C22—816no—
843C22—81no—
844C22—81no—
845C22—81no—
846C22—81no—
847C22—81no—
848C22—81no—
849C22—81no—
850C22—81no—
851C22C2×C4×D4×C13111yescharacteristic
852C22D42×C13111yescharacteristic
853C22D42×C13111yescharacteristic
854C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
855C22#575×C13111yescharacteristic
856C22#576×C13111yescharacteristic
857C22#577×C13111yescharacteristic
858C4—22no—
859C4—22no—
860C4—24no—
861C4—41no—
862C4—41no—
863C4—41no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—81no—
868C4C22×C22⋊C4×C13111yescharacteristic
869C4#518×C13111yescharacteristic
870C4#546×C13111yescharacteristic
871C4#546×C13111yescharacteristic
872C2—42no—
873C2—44no—
874C2—82no—
875C2—82no—
876C2D4×C22⋊C4×C13111yescharacteristic
877C2C4×AGL(1,ℤ/8)×C13111yescharacteristic
878C2#2946×C13111yescharacteristic
879C2#3265×C13111yescharacteristic
880C2#3268×C13111yescharacteristic
881C2#3274×C13111yescharacteristic
882C2#3275×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×#440×C131C2semidirect
3. C2×C4×SD16×C131C2semidirect
4. #2341×C131C2semidirect
5. D4×C22⋊C4×C131C2semidirect
6. #1972×C131C2semidirect
7. #1970×C131C2semidirect
8. #1880×C131C2semidirect
9. #1880×C131C2semidirect
10. #1879×C131C2semidirect
11. #1879×C131C2semidirect
12. #1809×C131C2semidirect
13. #1788×C131C2semidirect
14. #1786×C131C2semidirect
15. #1753×C131C2semidirect
20. C2×AGL(1,ℤ/8)×C131C4semidirect
26. C2×C4×Q8×C131C22semidirect
27. C2×C4×Q8×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
50. #390×C131C22semidirect
51. #390×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #336×C131C22semidirect
63. #336×C131C22semidirect
70. C2×#41×C131C2×C4semidirect
91. C2×SD16×C131C2×C4semidirect
99. C2×D8×C131C2×C4semidirect
102. C2×M16×C131C2×C4semidirect
233. SD16×C131C22⋊C4semidirect
318. Q8×C131C2×C22⋊C4semidirect
369. C2×C4×C131AGL(1,ℤ/8)semidirect
379. C8×C131C2×C22⋊C4semidirect
441. #22443C131direct (N × H)
442. C131#22443direct (N × H)
444. C2×#440C2×C131semidirect
445. C2×C4×SD16C2×C131semidirect
446. #2341C2×C131semidirect
447. D4×C22⋊C4C2×C131semidirect
448. #1972C2×C131semidirect
449. #1970C2×C131semidirect
450. #1880C2×C131semidirect
451. #1880C2×C131semidirect
452. #1879C2×C131semidirect
453. #1879C2×C131semidirect
454. #1809C2×C131semidirect
455. #1788C2×C131semidirect
456. #1786C2×C131semidirect
457. #1753C2×C131semidirect
462. C2×AGL(1,ℤ/8)C4×C131semidirect
468. C2×C4×Q8C22×C131semidirect
469. C2×C4×Q8C22×C131semidirect
475. C2×#107C22×C131semidirect
476. C2×#106C22×C131semidirect
477. C2×#103C22×C131semidirect
478. C2×#103C22×C131semidirect
483. C2×#102C22×C131semidirect
484. C2×#102C22×C131semidirect
486. C2×#97C22×C131semidirect
487. C2×C4×C8C22×C131semidirect
492. #390C22×C131semidirect
493. #390C22×C131semidirect
502. #340C22×C131semidirect
503. #340C22×C131semidirect
504. #336C22×C131semidirect
505. #336C22×C131semidirect
512. C2×#41C2×C4×C131semidirect
533. C2×SD16C2×C4×C131semidirect
541. C2×D8C2×C4×C131semidirect
544. C2×M16C2×C4×C131semidirect
675. SD16C22⋊C4×C131semidirect
760. Q8C2×C22⋊C4×C131semidirect
811. C2×C4AGL(1,ℤ/8)×C131semidirect
821. 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×#440×C1312
C2×C4×SD16×C1312
#2341×C1312
D4×C22⋊C4×C1312
#1972×C1312
#1970×C1312
#1880×C1312
#1879×C1312
#1809×C1312
#1788×C1312
#1786×C1312
#1753×C1312
#22443131