Finite Group Databasebeta

← C131×#24432 #45710316

Subgroups — C131×#24432 #45710316

Order 33536.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C131C211yesmaximal, characteristic
2C2×#465×C131C211yesmaximal, characteristic, complemented
3C2×#450×C131C211yesmaximal, characteristic, complemented
4C2×#450×C131C211yesmaximal, characteristic, complemented
5C22×#102×C131C211yesmaximal, characteristic, complemented
6#2417×C131C211yesmaximal, characteristic, complemented
7#2041×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2014×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1877×C131C211yesmaximal, characteristic, complemented
12#1874×C131C211yesmaximal, characteristic, complemented
13#1869×C131C211yesmaximal, characteristic, complemented
14#1864×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131—21no—
17C23×D4×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C22×SD16×C131C2211yescharacteristic
20C22×SD16×C131C2211yescharacteristic, complemented
21C22×SD16×C131C2211yescharacteristic, complemented
22C23×C8×C131C2211yescharacteristic, complemented
23D42×C131—24no—
24D42×C131—24no—
25C2×#127×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic, complemented
27C2×C22⋊Q8×C131C2211yescharacteristic, complemented
28C2×#121×C131—21no—
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic
31C2×#120×C131—21no—
32C2×#120×C131—21no—
33C2×C4×D4×C131C2211yescharacteristic
34C2×C4×D4×C131C2211yescharacteristic
35C22×C4⋊C4×C131C2211yescharacteristic, complemented
36#465×C131—24no—
37#450×C131—24no—
38#450×C131—24no—
39C2×#106×C131C2211yescharacteristic, complemented
40C2×#103×C131C2211yescharacteristic, complemented
41C2×#102×C131—24no—
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic, complemented
47C2×#102×C131C2211yescharacteristic, complemented
48C2×#102×C131C2211yescharacteristic, complemented
49C2×#102×C131C2211yescharacteristic, complemented
50C2×#102×C131C2211yescharacteristic, complemented
51C2×C22⋊C8×C131C2211yescharacteristic, complemented
52C2×C22⋊C8×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54#398×C131—21no—
55#396×C131—21no—
56#391×C131C2211yescharacteristic, complemented
57#389×C131C2211yescharacteristic, complemented
58#386×C131—21no—
59#380×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—
66C25×C131—21no—
67C22×Q8×C131C2311yescharacteristic
68C22×D4×C131—22no—
69C22×D4×C131—22no—
70C22×D4×C131—28no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—22no—
74C22×D4×C131—22no—
75C22×D4×C131—22no—
76C22×D4×C131—22no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—22no—
81C22×D4×C131—21no—
82C22×D4×C131—41no—
83C22×D4×C131—41no—
84C22×D4×C131—41no—
85C22×D4×C131—41no—
86C22×D4×C131—44no—
87C22×D4×C131—44no—
88C22×D4×C131D411yescharacteristic
89C22×D4×C131D414yes—
90C22×D4×C131C2311yescharacteristic
91C22×D4×C131C2311yescharacteristic
92C22×D4×C131C2311yescharacteristic
93C23×C4×C131—21no—
94C23×C4×C131—21no—
95C23×C4×C131C2311yescharacteristic
96C23×C4×C131C2311yescharacteristic
97C2×SD16×C131—22no—
98C2×SD16×C131—22no—
99C2×SD16×C131—22no—
100C2×SD16×C131—22no—
101C2×SD16×C131—22no—
102C2×SD16×C131—22no—
103C2×SD16×C131—41no—
104C2×SD16×C131—41no—
105C2×SD16×C131—41no—
106C22×C8×C131—22no—
107C22×C8×C131—22no—
108C22×C8×C131—41no—
109C22×C8×C131C2311yescharacteristic
110C22×C8×C131C2311yescharacteristic
111C22×C8×C131C2311yescharacteristic
112C22×C8×C131C2311yescharacteristic
113#127×C131—22no—
114#127×C131—22no—
115C22⋊Q8×C131—22no—
116C22⋊Q8×C131—22no—
117C22⋊Q8×C131—22no—
118C22⋊Q8×C131—41no—
119#121×C131—28no—
120#121×C131—22no—
121#121×C131—22no—
122#121×C131—22no—
123#121×C131D414yes—
124#120×C131—28no—
125#120×C131—28no—
126C4×D4×C131—22no—
127C4×D4×C131—22no—
128C4×D4×C131—22no—
129C4×D4×C131—22no—
130C2×C4⋊C4×C131—22no—
131C2×C4⋊C4×C131—21no—
132C2×C4⋊C4×C131—21no—
133C2×C4⋊C4×C131—21no—
134C2×C4⋊C4×C131—21no—
135C2×C4⋊C4×C131—41no—
136C2×C4⋊C4×C131D411yescharacteristic
137C2×C4⋊C4×C131C2311yescharacteristic
138C2×C4⋊C4×C131C2311yescharacteristic
139C2×C4⋊C4×C131C2311yescharacteristic
140C2×C4⋊C4×C131C2311yescharacteristic
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×C131D411yescharacteristic
148C2×C22⋊C4×C131D411yescharacteristic
149C2×C42×C131C2311yescharacteristic
150#106×C131—22no—
151#103×C131—22no—
152#102×C131—22no—
153#102×C131—22no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—22no—
159#102×C131—41no—
160#102×C131D414yescomplemented
161C22⋊C8×C131—22no—
162C22⋊C8×C131—22no—
163C22⋊C8×C131—41no—
164#95×C131—21no—
165#95×C131—21no—
166#95×C131—21no—
167#95×C131—21no—
168C24×C131—21no—
169C24×C131—24no—
170C24×C131—21no—
171C24×C131—21no—
172C24×C131—24no—
173C24×C131—42no—
174C24×C131—42no—
175C24×C131—42no—
176C24×C131—42no—
177C24×C131—42no—
178C24×C131—42no—
179C24×C131—42no—
180C24×C131—42no—
181C24×C131—81no—
182C24×C131—81no—
183C24×C131—81no—
184C24×C131—81no—
185C24×C131C2×D411yescharacteristic
186C24×C131C2×D411yescharacteristic
187C2×Q8×C131—21no—
188C2×Q8×C131—21no—
189C2×Q8×C131—21no—
190C2×Q8×C131—21no—
191C2×Q8×C131—21no—
192C2×Q8×C131—21no—
193C2×D4×C131—22no—
194C2×D4×C131—22no—
195C2×D4×C131—28no—
196C2×D4×C131—24no—
197C2×D4×C131—24no—
198C2×D4×C131—24no—
199C2×D4×C131—24no—
200C2×D4×C131—24no—
201C2×D4×C131—24no—
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—21no—
211C2×D4×C131—21no—
212C2×D4×C131—21no—
213C2×D4×C131—21no—
214C2×D4×C131—21no—
215C2×D4×C131—44no—
216C2×D4×C131—44no—
217C2×D4×C131—44no—
218C2×D4×C131—42no—
219C2×D4×C131—42no—
220C2×D4×C131—42no—
221C2×D4×C131—42no—
222C2×D4×C131—42no—
223C2×D4×C131—44no—
224C2×D4×C131—44no—
225C2×D4×C131—432no—
226C2×D4×C131—44no—
227C2×D4×C131—42no—
228C2×D4×C131—42no—
229C2×D4×C131—42no—
230C2×D4×C131—42no—
231C2×D4×C131—44no—
232C2×D4×C131—42no—
233C2×D4×C131—81no—
234C2×D4×C131—81no—
235C2×D4×C131SD1614yescomplemented
236C2×D4×C131C2×D412yes—
237C2×D4×C131C2×D412yes—
238C2×D4×C131C2×D412yes—
239C2×D4×C131C2×D412yes—
240C2×D4×C131#4112yes—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—24no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—42no—
258C22×C4×C131—42no—
259C22×C4×C131—42no—
260C22×C4×C131—42no—
261C22×C4×C131—81no—
262C22×C4×C131C2×D411yescharacteristic
263C22×C4×C131C2×D411yescharacteristic
264C22×C4×C131C2×D411yescharacteristic
265C22×C4×C131C2×D412yes—
266C22×C4×C131C2×D412yes—
267C22×C4×C131C2×D411yescharacteristic
268C22×C4×C131C2411yescharacteristic
269SD16×C131—44no—
270SD16×C131—44no—
271SD16×C131—44no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131—21no—
275C2×C8×C131—21no—
276C2×C8×C131—21no—
277C2×C8×C131—21no—
278C2×C8×C131—21no—
279C2×C8×C131—21no—
280C2×C8×C131—21no—
281C2×C8×C131—21no—
282C2×C8×C131—21no—
283C2×C8×C131—44no—
284C2×C8×C131C2×D412yescomplemented
285C4⋊C4×C131—22no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131—21no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131—21no—
292C4⋊C4×C131—42no—
293C4⋊C4×C131—42no—
294C4⋊C4×C131—42no—
295C4⋊C4×C131—81no—
296C4⋊C4×C131C2×D412yes—
297C4⋊C4×C131C2×D412yescomplemented
298C22⋊C4×C131—24no—
299C22⋊C4×C131—24no—
300C22⋊C4×C131—22no—
301C22⋊C4×C131—24no—
302C22⋊C4×C131—22no—
303C22⋊C4×C131—42no—
304C22⋊C4×C131—42no—
305C22⋊C4×C131—81no—
306C42×C131—21no—
307C42×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—21no—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—22no—
314C23×C131—21no—
315C23×C131—22no—
316C23×C131—21no—
317C23×C131—22no—
318C23×C131—21no—
319C23×C131—21no—
320C23×C131—21no—
321C23×C131—22no—
322C23×C131—22no—
323C23×C131—48no—
324C23×C131—48no—
325C23×C131—48no—
326C23×C131—41no—
327C23×C131—41no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131—41no—
335C23×C131—41no—
336C23×C131—41no—
337C23×C131—41no—
338C23×C131—41no—
339C23×C131—41no—
340C23×C131—41no—
341C23×C131—41no—
342C23×C131—48no—
343C23×C131—84no—
344C23×C131—84no—
345C23×C131—84no—
346C23×C131—84no—
347C23×C131—84no—
348C23×C131—84no—
349C23×C131—84no—
350C23×C131—84no—
351C23×C131—84no—
352C23×C131—84no—
353C23×C131#12012yes—
354C23×C131C2×SD1612yes—
355C23×C131C2×SD1612yes—
356C23×C131AGL(1,ℤ/8)12yes—
357C23×C131C22×D411yescharacteristic
358Q8×C131—41no—
359Q8×C131—41no—
360Q8×C131—41no—
361Q8×C131—41no—
362D4×C131—28no—
363D4×C131—22no—
364D4×C131—22no—
365D4×C131—22no—
366D4×C131—22no—
367D4×C131—22no—
368D4×C131—22no—
369D4×C131—22no—
370D4×C131—48no—
371D4×C131—48no—
372D4×C131—48no—
373D4×C131—48no—
374D4×C131—48no—
375D4×C131—41no—
376D4×C131—41no—
377D4×C131—41no—
378D4×C131—41no—
379D4×C131—84no—
380D4×C131#12114yes—
381C2×C4×C131—21no—
382C2×C4×C131—21no—
383C2×C4×C131—21no—
384C2×C4×C131—21no—
385C2×C4×C131—22no—
386C2×C4×C131—22no—
387C2×C4×C131—22no—
388C2×C4×C131—22no—
389C2×C4×C131—21no—
390C2×C4×C131—21no—
391C2×C4×C131—22no—
392C2×C4×C131—22no—
393C2×C4×C131—21no—
394C2×C4×C131—21no—
395C2×C4×C131—21no—
396C2×C4×C131—21no—
397C2×C4×C131—48no—
398C2×C4×C131—41no—
399C2×C4×C131—41no—
400C2×C4×C131—41no—
401C2×C4×C131—41no—
402C2×C4×C131—41no—
403C2×C4×C131—41no—
404C2×C4×C131—41no—
405C2×C4×C131—41no—
406C2×C4×C131—41no—
407C2×C4×C131—41no—
408C2×C4×C131—41no—
409C2×C4×C131—41no—
410C2×C4×C131—41no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131—41no—
414C2×C4×C131—41no—
415C2×C4×C131—84no—
416C2×C4×C131#12012yes—
417C2×C4×C131C2×SD1612yes—
418C2×C4×C131C22×D411yescharacteristic
419C2×C4×C131C22×D411yescharacteristic
420C2×C4×C131C22×D411yescharacteristic
421C2×C4×C131C2×#4111yescharacteristic
422C2×C4×C131H(5,𝔽2)11yescharacteristic
423C2×C4×C131H(5,𝔽2)11yescharacteristic
424C8×C131—22no—
425C8×C131—41no—
426C8×C131—41no—
427C8×C131—41no—
428C22×C131—22no—
429C22×C131—22no—
430C22×C131—22no—
431C22×C131—22no—
432C22×C131—22no—
433C22×C131—22no—
434C22×C131—24no—
435C22×C131—22no—
436C22×C131—22no—
437C22×C131—22no—
438C22×C131—41no—
439C22×C131—42no—
440C22×C131—41no—
441C22×C131—42no—
442C22×C131—41no—
443C22×C131—42no—
444C22×C131—42no—
445C22×C131—42no—
446C22×C131—41no—
447C22×C131—42no—
448C22×C131—42no—
449C22×C131—42no—
450C22×C131—42no—
451C22×C131—42no—
452C22×C131—42no—
453C22×C131—42no—
454C22×C131—816no—
455C22×C131—816no—
456C22×C131—81no—
457C22×C131—81no—
458C22×C131—81no—
459C22×C131—81no—
460C22×C131—81no—
461C22×C131—81no—
462C22×C131—81no—
463C22×C131—81no—
464C22×C131#45014yescomplemented
465C22×C131C2×#12011yescharacteristic
466C22×C131D4211yescharacteristic
467C22×C131#54611yescharacteristic
468C22×C131C22×SD1611yescharacteristic
469C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C131#57611yescharacteristic
471C22×C131#57711yescharacteristic
472C4×C131—22no—
473C4×C131—22no—
474C4×C131—41no—
475C4×C131—42no—
476C4×C131—42no—
477C4×C131—41no—
478C4×C131—81no—
479C4×C131—81no—
480C4×C131—81no—
481C4×C131C2×#12111yescharacteristic
482C4×C131#53411yescharacteristic
483C4×C131D4211yescharacteristic
484C4×C131#54611yescharacteristic
485C2×C131—24no—
486C2×C131—42no—
487C2×C131—44no—
488C2×C131—82no—
489C2×C131—82no—
490C2×C131#241011yescharacteristic
491C2×C131C2×#45011yescharacteristic
492C2×C131#301211yescharacteristic
493C2×C131#326411yescharacteristic
494C2×C131D4×SD1611yescharacteristic
495C2×C131#329511yescharacteristic
496C2×C131#331011yescharacteristic
497#24432C13111yesmaximal, characteristic, direct product factor, Sylow
498C131#2443211yescharacteristic, direct product factor, Sylow
499C2×D42C2×C13111yescharacteristic
500C2×#465C2×C13111yescharacteristic, complemented
501C2×#450C2×C13111yescharacteristic, complemented
502C2×#450C2×C13111yescharacteristic, complemented
503C22×#102C2×C13111yescharacteristic, complemented
504#2417C2×C13111yescharacteristic, complemented
505#2041C2×C13111yescharacteristic, complemented
506#2034C2×C13111yescharacteristic, complemented
507#2014C2×C13111yescharacteristic, complemented
508#2000C2×C13111yescharacteristic, complemented
509#1877C2×C13111yescharacteristic, complemented
510#1874C2×C13111yescharacteristic, complemented
511#1869C2×C13111yescharacteristic, complemented
512#1864C2×C13111yescharacteristic, complemented
513#1786C2×C13111yescharacteristic, complemented
514C23×D4—21no—
515C23×D4C22×C13111yescharacteristic
516C23×D4C22×C13111yescharacteristic
517C22×SD16C22×C13111yescharacteristic
518C22×SD16C22×C13111yescharacteristic, complemented
519C22×SD16C22×C13111yescharacteristic, complemented
520C23×C8C22×C13111yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C13111yescharacteristic
524C2×C22⋊Q8C22×C13111yescharacteristic, complemented
525C2×C22⋊Q8C22×C13111yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C13111yescharacteristic
528C2×#121C22×C13111yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C13111yescharacteristic
532C2×C4×D4C22×C13111yescharacteristic
533C22×C4⋊C4C22×C13111yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C13111yescharacteristic, complemented
538C2×#103C22×C13111yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C13111yescharacteristic
541C2×#102C22×C13111yescharacteristic
542C2×#102C22×C13111yescharacteristic
543C2×#102C22×C13111yescharacteristic, complemented
544C2×#102C22×C13111yescharacteristic, complemented
545C2×#102C22×C13111yescharacteristic, complemented
546C2×#102C22×C13111yescharacteristic, complemented
547C2×#102C22×C13111yescharacteristic, complemented
548C2×#102C22×C13111yescharacteristic, complemented
549C2×C22⋊C8C22×C13111yescharacteristic, complemented
550C2×C22⋊C8C22×C13111yescharacteristic, complemented
551C2×C22⋊C8C22×C13111yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C13111yescharacteristic, complemented
555#389C22×C13111yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C13111yescharacteristic, complemented
559#340C22×C13111yescharacteristic, complemented
560#340C22×C13111yescharacteristic, complemented
561#336C22×C13111yescharacteristic, complemented
562#336C22×C13111yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C13111yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C13111yescharacteristic
587C22×D4D4×C13114yes—
588C22×D4C23×C13111yescharacteristic
589C22×D4C23×C13111yescharacteristic
590C22×D4C23×C13111yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C13111yescharacteristic
594C23×C4C23×C13111yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C13111yescharacteristic
608C22×C8C23×C13111yescharacteristic
609C22×C8C23×C13111yescharacteristic
610C22×C8C23×C13111yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C13114yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C13111yescharacteristic
635C2×C4⋊C4C23×C13111yescharacteristic
636C2×C4⋊C4C23×C13111yescharacteristic
637C2×C4⋊C4C23×C13111yescharacteristic
638C2×C4⋊C4C23×C13111yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C13111yescharacteristic
646C2×C22⋊C4D4×C13111yescharacteristic
647C2×C42C23×C13111yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C13114yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C13111yescharacteristic
684C24C2×D4×C13111yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C13114yescomplemented
734C2×D4C2×D4×C13112yes—
735C2×D4C2×D4×C13112yes—
736C2×D4C2×D4×C13112yes—
737C2×D4C2×D4×C13112yes—
738C2×D4#41×C13112yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C13111yescharacteristic
761C22×C4C2×D4×C13111yescharacteristic
762C22×C4C2×D4×C13111yescharacteristic
763C22×C4C2×D4×C13112yes—
764C22×C4C2×D4×C13112yes—
765C22×C4C2×D4×C13111yescharacteristic
766C22×C4C24×C13111yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C13112yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C13112yes—
795C4⋊C4C2×D4×C13112yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—48no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C13112yes—
852C23C2×SD16×C13112yes—
853C23C2×SD16×C13112yes—
854C23AGL(1,ℤ/8)×C13112yes—
855C23C22×D4×C13111yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C13114yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C13112yes—
915C2×C4C2×SD16×C13112yes—
916C2×C4C22×D4×C13111yescharacteristic
917C2×C4C22×D4×C13111yescharacteristic
918C2×C4C22×D4×C13111yescharacteristic
919C2×C4C2×#41×C13111yescharacteristic
920C2×C4H(5,𝔽2)×C13111yescharacteristic
921C2×C4H(5,𝔽2)×C13111yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—24no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—41no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C13114yescomplemented
963C22C2×#120×C13111yescharacteristic
964C22D42×C13111yescharacteristic
965C22#546×C13111yescharacteristic
966C22C22×SD16×C13111yescharacteristic
967C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
968C22#576×C13111yescharacteristic
969C22#577×C13111yescharacteristic
970C4—22no—
971C4—22no—
972C4—42no—
973C4—42no—
974C4—41no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C13111yescharacteristic
980C4#534×C13111yescharacteristic
981C4D42×C13111yescharacteristic
982C4#546×C13111yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2#2410×C13111yescharacteristic
989C2C2×#450×C13111yescharacteristic
990C2#3012×C13111yescharacteristic
991C2#3264×C13111yescharacteristic
992C2D4×SD16×C13111yescharacteristic
993C2#3295×C13111yescharacteristic
994C2#3310×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
prime radicalC2×D42×C131C2
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
2. C2×#465×C131C2semidirect
3. C2×#450×C131C2semidirect
4. C2×#450×C131C2semidirect
5. C22×#102×C131C2semidirect
6. #2417×C131C2semidirect
7. #2041×C131C2semidirect
8. #2034×C131C2semidirect
9. #2014×C131C2semidirect
10. #2000×C131C2semidirect
11. #1877×C131C2semidirect
12. #1874×C131C2semidirect
13. #1869×C131C2semidirect
14. #1864×C131C2semidirect
15. #1786×C131C2semidirect
20. C22×SD16×C131C22semidirect
21. C22×SD16×C131C22semidirect
22. C23×C8×C131C22semidirect
26. C2×C22⋊Q8×C131C22semidirect
27. C2×C22⋊Q8×C131C22semidirect
35. C22×C4⋊C4×C131C22semidirect
39. C2×#106×C131C22semidirect
40. C2×#103×C131C22semidirect
45. C2×#102×C131C22semidirect
46. C2×#102×C131C22semidirect
47. C2×#102×C131C22semidirect
48. C2×#102×C131C22semidirect
49. C2×#102×C131C22semidirect
50. C2×#102×C131C22semidirect
51. C2×C22⋊C8×C131C22semidirect
52. C2×C22⋊C8×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
56. #391×C131C22semidirect
57. #389×C131C22semidirect
60. #380×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
160. #102×C131D4semidirect
235. C2×D4×C131SD16semidirect
284. C2×C8×C131C2×D4semidirect
297. C4⋊C4×C131C2×D4semidirect
464. C22×C131#450semidirect
497. #24432C131direct (N × H)
498. C131#24432direct (N × H)
500. C2×#465C2×C131semidirect
501. C2×#450C2×C131semidirect
502. C2×#450C2×C131semidirect
503. C22×#102C2×C131semidirect
504. #2417C2×C131semidirect
505. #2041C2×C131semidirect
506. #2034C2×C131semidirect
507. #2014C2×C131semidirect
508. #2000C2×C131semidirect
509. #1877C2×C131semidirect
510. #1874C2×C131semidirect
511. #1869C2×C131semidirect
512. #1864C2×C131semidirect
513. #1786C2×C131semidirect
518. C22×SD16C22×C131semidirect
519. C22×SD16C22×C131semidirect
520. C23×C8C22×C131semidirect
524. C2×C22⋊Q8C22×C131semidirect
525. C2×C22⋊Q8C22×C131semidirect
533. C22×C4⋊C4C22×C131semidirect
537. C2×#106C22×C131semidirect
538. C2×#103C22×C131semidirect
543. C2×#102C22×C131semidirect
544. C2×#102C22×C131semidirect
545. C2×#102C22×C131semidirect
546. C2×#102C22×C131semidirect
547. C2×#102C22×C131semidirect
548. C2×#102C22×C131semidirect
549. C2×C22⋊C8C22×C131semidirect
550. C2×C22⋊C8C22×C131semidirect
551. C2×C22⋊C8C22×C131semidirect
554. #391C22×C131semidirect
555. #389C22×C131semidirect
558. #380C22×C131semidirect
559. #340C22×C131semidirect
560. #340C22×C131semidirect
561. #336C22×C131semidirect
562. #336C22×C131semidirect
658. #102D4×C131semidirect
733. C2×D4SD16×C131semidirect
782. C2×C8C2×D4×C131semidirect
795. C4⋊C4C2×D4×C131semidirect
962. C22#450×C131semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1312
C2×#465×C1312
C2×#450×C1312
C22×#102×C1312
#2417×C1312
#2041×C1312
#2034×C1312
#2014×C1312
#2000×C1312
#1877×C1312
#1874×C1312
#1869×C1312
#1864×C1312
#1786×C1312
#24432131