Finite Group Databasebeta

← C131×#25076 #45710960

Subgroups — C131×#25076 #45710960

Order 33536.

1440 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#466×C131C211yesmaximal, characteristic, complemented
2C2×#459×C131C211yesmaximal, characteristic, complemented
3C2×#447×C131C211yesmaximal, characteristic, complemented
4C22×#102×C131C211yesmaximal, characteristic, complemented
5#2433×C131C211yesmaximal, characteristic, complemented
6#2361×C131C211yesmaximal, characteristic, complemented
7#2067×C131C211yesmaximal, characteristic, complemented
8#2054×C131C211yesmaximal, characteristic, complemented
9#2041×C131C211yesmaximal, characteristic, complemented
10#2011×C131C211yesmaximal, characteristic, complemented
11#1982×C131C211yesmaximal, characteristic, complemented
12#1925×C131C211yesmaximal, characteristic, complemented
13#1879×C131C211yesmaximal, characteristic, complemented
14#1874×C131C211yesmaximal, characteristic, complemented
15#1850×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic, complemented
20C23×C8×C131C2211yescharacteristic
21C2×#127×C131C2211yescharacteristic
22C2×#127×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×#120×C131—21no—
26C2×#120×C131—21no—
27C2×C4×D4×C131—21no—
28C2×C4×D4×C131C2211yescharacteristic, complemented
29C22×C4⋊C4×C131C2211yescharacteristic
30#466×C131—24no—
31#459×C131—24no—
32#447×C131—24no—
33C2×#107×C131C2211yescharacteristic, complemented
34C2×C4⋊C8×C131C2211yescharacteristic, complemented
35C2×C4⋊C8×C131C2211yescharacteristic, complemented
36C2×#102×C131—24no—
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic, complemented
44C2×#102×C131C2211yescharacteristic, complemented
45C2×#102×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic, complemented
47C2×C22⋊C8×C131C2211yescharacteristic
48#392×C131—21no—
49#392×C131—21no—
50#390×C131C2211yescharacteristic
51#390×C131C2211yescharacteristic
52#390×C131C2211yescharacteristic, complemented
53#389×C131C2211yescharacteristic, complemented
54#388×C131—21no—
55#386×C131—21no—
56#385×C131—21no—
57C4×C4⋊C4×C131C2211yescharacteristic, complemented
58C4×C22⋊C4×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—21no—
67C22×D4×C131—21no—
68C22×D4×C131—22no—
69C22×D4×C131—21no—
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131—22no—
75C22×D4×C131—41no—
76C22×D4×C131—41no—
77C22×D4×C131C2311yescharacteristic
78C22×D4×C131C2311yescharacteristic
79C22×D4×C131C2311yescharacteristic
80C22×D4×C131C2311yescharacteristic
81C23×C4×C131—21no—
82C23×C4×C131—21no—
83C23×C4×C131C2311yescharacteristic
84C2×D8×C131—22no—
85C2×D8×C131—22no—
86C2×D8×C131—22no—
87C2×D8×C131—22no—
88C2×D8×C131—22no—
89C2×D8×C131—22no—
90C2×D8×C131—41no—
91C2×D8×C131—41no—
92C2×D8×C131—41no—
93C22×C8×C131—22no—
94C22×C8×C131—22no—
95C22×C8×C131—41no—
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99C22×C8×C131C2311yescharacteristic
100#127×C131—22no—
101#127×C131—22no—
102#127×C131—41no—
103#127×C131—41no—
104#121×C131—22no—
105#121×C131—22no—
106#121×C131—22no—
107#121×C131D414yescomplemented
108#120×C131—44no—
109#120×C131—44no—
110C4×D4×C131—22no—
111C4×D4×C131—41no—
112C4×D4×C131—44no—
113C2×C4⋊C4×C131—22no—
114C2×C4⋊C4×C131—21no—
115C2×C4⋊C4×C131—21no—
116C2×C4⋊C4×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×C131D411yescharacteristic
131C2×C22⋊C4×C131D411yescharacteristic
132C2×C42×C131—21no—
133C2×C42×C131C2311yescharacteristic
134C2×C42×C131C2311yescharacteristic
135#107×C131—22no—
136C4⋊C8×C131—22no—
137C4⋊C8×C131—41no—
138#102×C131—22no—
139#102×C131—22no—
140#102×C131—22no—
141#102×C131—22no—
142#102×C131—22no—
143#102×C131—22no—
144#102×C131—22no—
145#102×C131—22no—
146#102×C131—41no—
147#102×C131D414yescomplemented
148C22⋊C8×C131—22no—
149#95×C131—21no—
150#95×C131—21no—
151#95×C131D411yescharacteristic
152#95×C131D411yescharacteristic
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—21no—
156C24×C131—21no—
157C24×C131—42no—
158C24×C131—42no—
159C24×C131—42no—
160C24×C131—42no—
161C24×C131—42no—
162C24×C131—81no—
163C24×C131—81no—
164C24×C131C2×D411yescharacteristic
165C2×D4×C131—28no—
166C2×D4×C131—24no—
167C2×D4×C131—21no—
168C2×D4×C131—21no—
169C2×D4×C131—21no—
170C2×D4×C131—21no—
171C2×D4×C131—21no—
172C2×D4×C131—21no—
173C2×D4×C131—21no—
174C2×D4×C131—21no—
175C2×D4×C131—21no—
176C2×D4×C131—21no—
177C2×D4×C131—21no—
178C2×D4×C131—21no—
179C2×D4×C131—21no—
180C2×D4×C131—21no—
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—44no—
189C2×D4×C131—44no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—44no—
193C2×D4×C131—42no—
194C2×D4×C131—42no—
195C2×D4×C131—42no—
196C2×D4×C131—42no—
197C2×D4×C131—42no—
198C2×D4×C131—42no—
199C2×D4×C131—42no—
200C2×D4×C131—42no—
201C2×D4×C131—42no—
202C2×D4×C131—42no—
203C2×D4×C131—42no—
204C2×D4×C131—42no—
205C2×D4×C131—42no—
206C2×D4×C131—42no—
207C2×D4×C131—81no—
208C2×D4×C131—81no—
209C2×D4×C131—81no—
210C2×D4×C131—81no—
211C2×D4×C131C2×D412yes—
212C2×D4×C131C2×D412yes—
213C2×D4×C131#4112yes—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
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×C131C2×D411yescharacteristic
229C22×C4×C131C2×D411yescharacteristic
230C22×C4×C131C2×D411yescharacteristic
231C22×C4×C131C2×D412yes—
232C22×C4×C131C2×D411yescharacteristic
233C22×C4×C131C2×D411yescharacteristic
234C22×C4×C131#4112yes—
235C22×C4×C131C2411yescharacteristic
236D8×C131—44no—
237D8×C131—44no—
238D8×C131—44no—
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×C131—21no—
246C2×C8×C131—21no—
247C2×C8×C131—21no—
248C2×C8×C131—21no—
249C2×C8×C131—21no—
250C2×C8×C131—44no—
251C2×C8×C131C2×D412yes—
252C4⋊C4×C131—21no—
253C4⋊C4×C131—21no—
254C4⋊C4×C131—21no—
255C4⋊C4×C131—21no—
256C4⋊C4×C131—21no—
257C4⋊C4×C131—21no—
258C4⋊C4×C131—42no—
259C4⋊C4×C131—42no—
260C4⋊C4×C131C2×D412yes—
261C4⋊C4×C131C2×D412yes—
262C22⋊C4×C131—22no—
263C22⋊C4×C131—24no—
264C22⋊C4×C131—42no—
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—81no—
272C22⋊C4×C131D814yescomplemented
273C42×C131—21no—
274C42×C131—21no—
275C42×C131—21no—
276C42×C131—21no—
277C42×C131—42no—
278C23×C131—21no—
279C23×C131—21no—
280C23×C131—21no—
281C23×C131—21no—
282C23×C131—22no—
283C23×C131—22no—
284C23×C131—22no—
285C23×C131—48no—
286C23×C131—41no—
287C23×C131—41no—
288C23×C131—41no—
289C23×C131—41no—
290C23×C131—41no—
291C23×C131—41no—
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—41no—
309C23×C131—41no—
310C23×C131—41no—
311C23×C131—84no—
312C23×C131—84no—
313C23×C131—84no—
314C23×C131—84no—
315C23×C131—84no—
316C23×C131—84no—
317C23×C131#12112yes—
318C23×C131C2×D812yes—
319C23×C131AGL(1,ℤ/8)12yes—
320C23×C131C22×D411yescharacteristic
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×C131—41no—
332D4×C131—41no—
333D4×C131—41no—
334D4×C131—41no—
335D4×C131—41no—
336D4×C131—41no—
337D4×C131—41no—
338D4×C131—41no—
339D4×C131—84no—
340D4×C131—84no—
341D4×C131—84no—
342D4×C131—84no—
343D4×C131—84no—
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—22no—
351C2×C4×C131—22no—
352C2×C4×C131—22no—
353C2×C4×C131—22no—
354C2×C4×C131—22no—
355C2×C4×C131—21no—
356C2×C4×C131—22no—
357C2×C4×C131—21no—
358C2×C4×C131—21no—
359C2×C4×C131—21no—
360C2×C4×C131—21no—
361C2×C4×C131—21no—
362C2×C4×C131—41no—
363C2×C4×C131—41no—
364C2×C4×C131—41no—
365C2×C4×C131—41no—
366C2×C4×C131—41no—
367C2×C4×C131—41no—
368C2×C4×C131—41no—
369C2×C4×C131—41no—
370C2×C4×C131—41no—
371C2×C4×C131—41no—
372C2×C4×C131—84no—
373C2×C4×C131—84no—
374C2×C4×C131#12112yes—
375C2×C4×C131C2×D812yes—
376C2×C4×C131C2×D812yes—
377C2×C4×C131C22×D411yescharacteristic
378C2×C4×C131C22×D411yescharacteristic
379C2×C4×C131C2×#4111yescharacteristic
380C2×C4×C131C2×#4111yescharacteristic
381C2×C4×C131H(5,𝔽2)11yescharacteristic
382C2×C4×C131H(5,𝔽2)11yescharacteristic
383C8×C131—22no—
384C8×C131—41no—
385C8×C131—41no—
386C8×C131—41no—
387C22×C131—22no—
388C22×C131—22no—
389C22×C131—22no—
390C22×C131—22no—
391C22×C131—22no—
392C22×C131—22no—
393C22×C131—42no—
394C22×C131—42no—
395C22×C131—42no—
396C22×C131—42no—
397C22×C131—42no—
398C22×C131—42no—
399C22×C131—42no—
400C22×C131—42no—
401C22×C131—42no—
402C22×C131—816no—
403C22×C131—81no—
404C22×C131—81no—
405C22×C131—81no—
406C22×C131—81no—
407C22×C131—81no—
408C22×C131—81no—
409C22×C131—81no—
410C22×C131—81no—
411C22×C131—81no—
412C22×C131—81no—
413C22×C131—81no—
414C22×C131—81no—
415C22×C131—81no—
416C22×C131—81no—
417C22×C131—81no—
418C22×C131—81no—
419C22×C131—81no—
420C22×C131—81no—
421C22×C131—81no—
422C22×C131#45914yescomplemented
423C22×C131C2×#12111yescharacteristic
424C22×C131D4211yescharacteristic
425C22×C131#54611yescharacteristic
426C22×C131C22×D811yescharacteristic
427C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
428C22×C131#57611yescharacteristic
429C22×C131#57711yescharacteristic
430C4×C131—22no—
431C4×C131—22no—
432C4×C131—22no—
433C4×C131—41no—
434C4×C131—42no—
435C4×C131—42no—
436C4×C131—41no—
437C4×C131—81no—
438C4×C131—81no—
439C4×C131#52511yescharacteristic
440C4×C131#53811yescharacteristic
441C4×C131D4211yescharacteristic
442C4×C131#54611yescharacteristic
443C2×C131—24no—
444C2×C131—82no—
445C2×C131—82no—
446C2×C131—82no—
447C2×C131—161no—
448C2×C131#242411yescharacteristic
449C2×C131C2×#45911yescharacteristic
450C2×C131#304511yescharacteristic
451C2×C131#326511yescharacteristic
452C2×C131D4×D811yescharacteristic
453C2×C131#329411yescharacteristic
454C2×C131#331811yescharacteristic
455#25076C13111yesmaximal, characteristic, direct product factor, Sylow
456C131#2507611yescharacteristic, direct product factor, Sylow
457C2×#466C2×C13111yescharacteristic, complemented
458C2×#459C2×C13111yescharacteristic, complemented
459C2×#447C2×C13111yescharacteristic, complemented
460C22×#102C2×C13111yescharacteristic, complemented
461#2433C2×C13111yescharacteristic, complemented
462#2361C2×C13111yescharacteristic, complemented
463#2067C2×C13111yescharacteristic, complemented
464#2054C2×C13111yescharacteristic, complemented
465#2041C2×C13111yescharacteristic, complemented
466#2011C2×C13111yescharacteristic, complemented
467#1982C2×C13111yescharacteristic, complemented
468#1925C2×C13111yescharacteristic, complemented
469#1879C2×C13111yescharacteristic, complemented
470#1874C2×C13111yescharacteristic, complemented
471#1850C2×C13111yescharacteristic, complemented
472C23×D4C22×C13111yescharacteristic
473C22×D8C22×C13111yescharacteristic
474C22×D8C22×C13111yescharacteristic
475C22×D8C22×C13111yescharacteristic, complemented
476C23×C8C22×C13111yescharacteristic
477C2×#127C22×C13111yescharacteristic
478C2×#127C22×C13111yescharacteristic
479C2×#121C22×C13111yescharacteristic
480C2×#121C22×C13111yescharacteristic
481C2×#120—21no—
482C2×#120—21no—
483C2×C4×D4—21no—
484C2×C4×D4C22×C13111yescharacteristic, complemented
485C22×C4⋊C4C22×C13111yescharacteristic
486#466—24no—
487#459—24no—
488#447—24no—
489C2×#107C22×C13111yescharacteristic, complemented
490C2×C4⋊C8C22×C13111yescharacteristic, complemented
491C2×C4⋊C8C22×C13111yescharacteristic, complemented
492C2×#102—24no—
493C2×#102C22×C13111yescharacteristic
494C2×#102C22×C13111yescharacteristic
495C2×#102C22×C13111yescharacteristic
496C2×#102C22×C13111yescharacteristic
497C2×#102C22×C13111yescharacteristic
498C2×#102C22×C13111yescharacteristic
499C2×#102C22×C13111yescharacteristic, complemented
500C2×#102C22×C13111yescharacteristic, complemented
501C2×#102C22×C13111yescharacteristic, complemented
502C2×#102C22×C13111yescharacteristic, complemented
503C2×C22⋊C8C22×C13111yescharacteristic
504#392—21no—
505#392—21no—
506#390C22×C13111yescharacteristic
507#390C22×C13111yescharacteristic
508#390C22×C13111yescharacteristic, complemented
509#389C22×C13111yescharacteristic, complemented
510#388—21no—
511#386—21no—
512#385—21no—
513C4×C4⋊C4C22×C13111yescharacteristic, complemented
514C4×C22⋊C4C22×C13111yescharacteristic
515#340C22×C13111yescharacteristic, complemented
516#340C22×C13111yescharacteristic, complemented
517#336C22×C13111yescharacteristic, complemented
518#336C22×C13111yescharacteristic, complemented
519C25—21no—
520C22×D4—22no—
521C22×D4—22no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—22no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4C23×C13111yescharacteristic
534C22×D4C23×C13111yescharacteristic
535C22×D4C23×C13111yescharacteristic
536C22×D4C23×C13111yescharacteristic
537C23×C4—21no—
538C23×C4—21no—
539C23×C4C23×C13111yescharacteristic
540C2×D8—22no—
541C2×D8—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—22no—
546C2×D8—41no—
547C2×D8—41no—
548C2×D8—41no—
549C22×C8—22no—
550C22×C8—22no—
551C22×C8—41no—
552C22×C8C23×C13111yescharacteristic
553C22×C8C23×C13111yescharacteristic
554C22×C8C23×C13111yescharacteristic
555C22×C8C23×C13111yescharacteristic
556#127—22no—
557#127—22no—
558#127—41no—
559#127—41no—
560#121—22no—
561#121—22no—
562#121—22no—
563#121D4×C13114yescomplemented
564#120—44no—
565#120—44no—
566C4×D4—22no—
567C4×D4—41no—
568C4×D4—44no—
569C2×C4⋊C4—22no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—41no—
573C2×C4⋊C4C23×C13111yescharacteristic
574C2×C4⋊C4C23×C13111yescharacteristic
575C2×C4⋊C4C23×C13111yescharacteristic
576C2×C4⋊C4C23×C13111yescharacteristic
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4D4×C13111yescharacteristic
587C2×C22⋊C4D4×C13111yescharacteristic
588C2×C42—21no—
589C2×C42C23×C13111yescharacteristic
590C2×C42C23×C13111yescharacteristic
591#107—22no—
592C4⋊C8—22no—
593C4⋊C8—41no—
594#102—22no—
595#102—22no—
596#102—22no—
597#102—22no—
598#102—22no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—41no—
603#102D4×C13114yescomplemented
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95D4×C13111yescharacteristic
608#95D4×C13111yescharacteristic
609C24—21no—
610C24—21no—
611C24—21no—
612C24—21no—
613C24—42no—
614C24—42no—
615C24—42no—
616C24—42no—
617C24—42no—
618C24—81no—
619C24—81no—
620C24C2×D4×C13111yescharacteristic
621C2×D4—28no—
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—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—44no—
645C2×D4—44no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—44no—
649C2×D4—42no—
650C2×D4—42no—
651C2×D4—42no—
652C2×D4—42no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C13112yes—
668C2×D4C2×D4×C13112yes—
669C2×D4#41×C13112yes—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—42no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—81no—
683C22×C4—81no—
684C22×C4C2×D4×C13111yescharacteristic
685C22×C4C2×D4×C13111yescharacteristic
686C22×C4C2×D4×C13111yescharacteristic
687C22×C4C2×D4×C13112yes—
688C22×C4C2×D4×C13111yescharacteristic
689C22×C4C2×D4×C13111yescharacteristic
690C22×C4#41×C13112yes—
691C22×C4C24×C13111yescharacteristic
692D8—44no—
693D8—44no—
694D8—44no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—44no—
707C2×C8C2×D4×C13112yes—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—42no—
715C4⋊C4—42no—
716C4⋊C4C2×D4×C13112yes—
717C4⋊C4C2×D4×C13112yes—
718C22⋊C4—22no—
719C22⋊C4—24no—
720C22⋊C4—42no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—42no—
727C22⋊C4—81no—
728C22⋊C4D8×C13114yescomplemented
729C42—21no—
730C42—21no—
731C42—21no—
732C42—21no—
733C42—42no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—48no—
742C23—41no—
743C23—41no—
744C23—41no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—84no—
768C23—84no—
769C23—84no—
770C23—84no—
771C23—84no—
772C23—84no—
773C23#121×C13112yes—
774C23C2×D8×C13112yes—
775C23AGL(1,ℤ/8)×C13112yes—
776C23C22×D4×C13111yescharacteristic
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—22no—
782D4—22no—
783D4—48no—
784D4—48no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—21no—
812C2×C4—22no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—84no—
829C2×C4—84no—
830C2×C4#121×C13112yes—
831C2×C4C2×D8×C13112yes—
832C2×C4C2×D8×C13112yes—
833C2×C4C22×D4×C13111yescharacteristic
834C2×C4C22×D4×C13111yescharacteristic
835C2×C4C2×#41×C13111yescharacteristic
836C2×C4C2×#41×C13111yescharacteristic
837C2×C4H(5,𝔽2)×C13111yescharacteristic
838C2×C4H(5,𝔽2)×C13111yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C22—22no—
844C22—22no—
845C22—22no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—42no—
850C22—42no—
851C22—42no—
852C22—42no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—816no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22#459×C13114yescomplemented
879C22C2×#121×C13111yescharacteristic
880C22D42×C13111yescharacteristic
881C22#546×C13111yescharacteristic
882C22C22×D8×C13111yescharacteristic
883C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
884C22#576×C13111yescharacteristic
885C22#577×C13111yescharacteristic
886C4—22no—
887C4—22no—
888C4—22no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—81no—
894C4—81no—
895C4#525×C13111yescharacteristic
896C4#538×C13111yescharacteristic
897C4D42×C13111yescharacteristic
898C4#546×C13111yescharacteristic
899C2—24no—
900C2—82no—
901C2—82no—
902C2—82no—
903C2—161no—
904C2#2424×C13111yescharacteristic
905C2C2×#459×C13111yescharacteristic
906C2#3045×C13111yescharacteristic
907C2#3265×C13111yescharacteristic
908C2D4×D8×C13111yescharacteristic
909C2#3294×C13111yescharacteristic
910C2#3318×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×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
1. C2×#466×C131C2semidirect
2. C2×#459×C131C2semidirect
3. C2×#447×C131C2semidirect
4. C22×#102×C131C2semidirect
5. #2433×C131C2semidirect
6. #2361×C131C2semidirect
7. #2067×C131C2semidirect
8. #2054×C131C2semidirect
9. #2041×C131C2semidirect
10. #2011×C131C2semidirect
11. #1982×C131C2semidirect
12. #1925×C131C2semidirect
13. #1879×C131C2semidirect
14. #1874×C131C2semidirect
15. #1850×C131C2semidirect
19. C22×D8×C131C22semidirect
28. C2×C4×D4×C131C22semidirect
33. C2×#107×C131C22semidirect
34. C2×C4⋊C8×C131C22semidirect
35. C2×C4⋊C8×C131C22semidirect
43. C2×#102×C131C22semidirect
44. C2×#102×C131C22semidirect
45. C2×#102×C131C22semidirect
46. C2×#102×C131C22semidirect
52. #390×C131C22semidirect
53. #389×C131C22semidirect
57. C4×C4⋊C4×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
107. #121×C131D4semidirect
147. #102×C131D4semidirect
272. C22⋊C4×C131D8semidirect
422. C22×C131#459semidirect
455. #25076C131direct (N × H)
456. C131#25076direct (N × H)
457. C2×#466C2×C131semidirect
458. C2×#459C2×C131semidirect
459. C2×#447C2×C131semidirect
460. C22×#102C2×C131semidirect
461. #2433C2×C131semidirect
462. #2361C2×C131semidirect
463. #2067C2×C131semidirect
464. #2054C2×C131semidirect
465. #2041C2×C131semidirect
466. #2011C2×C131semidirect
467. #1982C2×C131semidirect
468. #1925C2×C131semidirect
469. #1879C2×C131semidirect
470. #1874C2×C131semidirect
471. #1850C2×C131semidirect
475. C22×D8C22×C131semidirect
484. C2×C4×D4C22×C131semidirect
489. C2×#107C22×C131semidirect
490. C2×C4⋊C8C22×C131semidirect
491. C2×C4⋊C8C22×C131semidirect
499. C2×#102C22×C131semidirect
500. C2×#102C22×C131semidirect
501. C2×#102C22×C131semidirect
502. C2×#102C22×C131semidirect
508. #390C22×C131semidirect
509. #389C22×C131semidirect
513. C4×C4⋊C4C22×C131semidirect
515. #340C22×C131semidirect
516. #340C22×C131semidirect
517. #336C22×C131semidirect
518. #336C22×C131semidirect
563. #121D4×C131semidirect
603. #102D4×C131semidirect
728. C22⋊C4D8×C131semidirect
878. C22#459×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1312
C2×#459×C1312
C2×#447×C1312
C22×#102×C1312
#2433×C1312
#2361×C1312
#2067×C1312
#2054×C1312
#2041×C1312
#2011×C1312
#1982×C1312
#1925×C1312
#1879×C1312
#1874×C1312
#1850×C1312
#25076131