Finite Group Databasebeta

← C131×#25124 #45711008

Subgroups — C131×#25124 #45711008

Order 33536.

1362 conjugacy classes of subgroups.

The subgroup lattice has 900 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#469×C131C211yesmaximal, characteristic, complemented
2C2×#447×C131C211yesmaximal, characteristic, complemented
3C2×#435×C131C211yesmaximal, characteristic, complemented
4C22×#102×C131C211yesmaximal, characteristic, complemented
5#2416×C131C211yesmaximal, characteristic, complemented
6#2408×C131C211yesmaximal, characteristic, complemented
7#2065×C131C211yesmaximal, characteristic, complemented
8#2054×C131C211yesmaximal, characteristic, complemented
9#2034×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1972×C131C211yesmaximal, characteristic, complemented
12#1936×C131C211yesmaximal, characteristic, complemented
13#1895×C131C211yesmaximal, characteristic, complemented
14#1893×C131C211yesmaximal, characteristic, complemented
15#1853×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131C2211yescharacteristic
17C22×D8×C131C2211yescharacteristic
18C22×D8×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic, complemented
20C23×C8×C131C2211yescharacteristic
21C2×#121×C131—21no—
22C2×#121×C131C2211yescharacteristic
23C2×#121×C131C2211yescharacteristic
24C2×#121×C131C2211yescharacteristic
25C2×#121×C131C2211yescharacteristic, complemented
26C2×#120×C131—21no—
27C2×C4×D4×C131C2211yescharacteristic
28C22×C4⋊C4×C131C2211yescharacteristic
29#469×C131—24no—
30#447×C131—24no—
31#435×C131—24no—
32C2×#106×C131C2211yescharacteristic, complemented
33C2×#106×C131C2211yescharacteristic, complemented
34C2×C4⋊C8×C131C2211yescharacteristic, complemented
35C2×#102×C131—24no—
36C2×#102×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic
40C2×#102×C131C2211yescharacteristic
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic, complemented
43C2×#102×C131C2211yescharacteristic, complemented
44C2×C22⋊C8×C131C2211yescharacteristic
45C2×C22⋊C8×C131C2211yescharacteristic, complemented
46C2×#97×C131C2211yescharacteristic, complemented
47#396×C131—21no—
48#394×C131—21no—
49#394×C131—21no—
50#392×C131—21no—
51#390×C131C2211yescharacteristic
52#390×C131C2211yescharacteristic
53#390×C131C2211yescharacteristic, complemented
54#389×C131C2211yescharacteristic, complemented
55#386×C131—21no—
56#380×C131C2211yescharacteristic
57#380×C131C2211yescharacteristic, complemented
58#379×C131—21no—
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C22×D4×C131—22no—
65C22×D4×C131—22no—
66C22×D4×C131—21no—
67C22×D4×C131—21no—
68C22×D4×C131—21no—
69C22×D4×C131—21no—
70C22×D4×C131—22no—
71C22×D4×C131—21no—
72C22×D4×C131—22no—
73C22×D4×C131—41no—
74C22×D4×C131—41no—
75C22×D4×C131D411yescharacteristic
76C22×D4×C131C2311yescharacteristic
77C22×D4×C131C2311yescharacteristic
78C22×D4×C131C2311yescharacteristic
79C23×C4×C131—21no—
80C23×C4×C131C2311yescharacteristic
81C23×C4×C131C2311yescharacteristic
82C2×D8×C131—22no—
83C2×D8×C131—22no—
84C2×D8×C131—22no—
85C2×D8×C131—22no—
86C2×D8×C131—41no—
87C2×D8×C131—41no—
88C2×M16×C131—22no—
89C2×M16×C131—22no—
90C2×M16×C131—41no—
91C22×C8×C131—22no—
92C22×C8×C131—22no—
93C22×C8×C131—41no—
94C22×C8×C131C2311yescharacteristic
95C22×C8×C131C2311yescharacteristic
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98#121×C131—22no—
99#121×C131—22no—
100#121×C131—22no—
101#121×C131—22no—
102#121×C131—22no—
103#121×C131—41no—
104#121×C131—41no—
105#121×C131—41no—
106#121×C131—44no—
107#120×C131—44no—
108C4×D4×C131—22no—
109C4×D4×C131—22no—
110C2×C4⋊C4×C131—22no—
111C2×C4⋊C4×C131—21no—
112C2×C4⋊C4×C131—21no—
113C2×C4⋊C4×C131—41no—
114C2×C4⋊C4×C131D411yescharacteristic
115C2×C4⋊C4×C131C2311yescharacteristic
116C2×C4⋊C4×C131C2311yescharacteristic
117C2×C4⋊C4×C131C2311yescharacteristic
118C2×C4⋊C4×C131C2311yescharacteristic
119C2×C4⋊C4×C131C2311yescharacteristic
120C2×C22⋊C4×C131—21no—
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×C131D411yescharacteristic
133C2×C22⋊C4×C131D411yescharacteristic
134C2×C42×C131C2311yescharacteristic
135#106×C131—22no—
136#106×C131—41no—
137C4⋊C8×C131—22no—
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—41no—
145#102×C131D414yescomplemented
146C22⋊C8×C131—22no—
147C22⋊C8×C131D414yescomplemented
148#97×C131—22no—
149#95×C131—21no—
150#95×C131—21no—
151#95×C131—21no—
152C24×C131—21no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—42no—
156C24×C131—42no—
157C24×C131—42no—
158C24×C131—42no—
159C24×C131—42no—
160C24×C131—81no—
161C24×C131—81no—
162C24×C131C2×D411yescharacteristic
163C24×C131C2×D411yescharacteristic
164C2×D4×C131—28no—
165C2×D4×C131—22no—
166C2×D4×C131—22no—
167C2×D4×C131—22no—
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—44no—
185C2×D4×C131—44no—
186C2×D4×C131—42no—
187C2×D4×C131—42no—
188C2×D4×C131—44no—
189C2×D4×C131—42no—
190C2×D4×C131—42no—
191C2×D4×C131—42no—
192C2×D4×C131—42no—
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—81no—
200C2×D4×C131—81no—
201C2×D4×C131—81no—
202C2×D4×C131C2×D412yes—
203C2×D4×C131#4112yes—
204C22×C4×C131—21no—
205C22×C4×C131—21no—
206C22×C4×C131—21no—
207C22×C4×C131—21no—
208C22×C4×C131—21no—
209C22×C4×C131—21no—
210C22×C4×C131—21no—
211C22×C4×C131—21no—
212C22×C4×C131—21no—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—42no—
220C22×C4×C131—42no—
221C22×C4×C131—81no—
222C22×C4×C131C2×D411yescharacteristic
223C22×C4×C131C2×D411yescharacteristic
224C22×C4×C131C2×D411yescharacteristic
225C22×C4×C131C2×D411yescharacteristic
226C22×C4×C131C2×D412yes—
227C22×C4×C131#4112yes—
228C22×C4×C131C2411yescharacteristic
229D8×C131—44no—
230D8×C131—44no—
231M16×C131—44no—
232C2×C8×C131—21no—
233C2×C8×C131—21no—
234C2×C8×C131—21no—
235C2×C8×C131—21no—
236C2×C8×C131—21no—
237C2×C8×C131—21no—
238C2×C8×C131—21no—
239C2×C8×C131—21no—
240C2×C8×C131—21no—
241C2×C8×C131—44no—
242C2×C8×C131C2×D412yes—
243C2×C8×C131C2×D412yes—
244C2×C8×C131C2×D412yes—
245C4⋊C4×C131—22no—
246C4⋊C4×C131—21no—
247C4⋊C4×C131—21no—
248C4⋊C4×C131—21no—
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—42no—
256C4⋊C4×C131—42no—
257C4⋊C4×C131C2×D412yes—
258C22⋊C4×C131—22no—
259C22⋊C4×C131—22no—
260C22⋊C4×C131—42no—
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—42no—
269C22⋊C4×C131—81no—
270C22⋊C4×C131—81no—
271C22⋊C4×C131—81no—
272C42×C131—21no—
273C42×C131—21no—
274C23×C131—21no—
275C23×C131—21no—
276C23×C131—21no—
277C23×C131—21no—
278C23×C131—21no—
279C23×C131—22no—
280C23×C131—21no—
281C23×C131—22no—
282C23×C131—21no—
283C23×C131—21no—
284C23×C131—21no—
285C23×C131—21no—
286C23×C131—21no—
287C23×C131—48no—
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—84no—
308C23×C131—84no—
309C23×C131—84no—
310C23×C131—84no—
311C23×C131—84no—
312C23×C131—84no—
313C23×C131#12112yes—
314C23×C131AGL(1,ℤ/8)12yes—
315C23×C131AGL(1,ℤ/8)12yes—
316C23×C131C22×D411yescharacteristic
317D4×C131—22no—
318D4×C131—22no—
319D4×C131—22no—
320D4×C131—22no—
321D4×C131—48no—
322D4×C131—44no—
323D4×C131—41no—
324D4×C131—41no—
325D4×C131—41no—
326D4×C131—41no—
327D4×C131—41no—
328D4×C131—41no—
329D4×C131—41no—
330D4×C131—41no—
331D4×C131—84no—
332D4×C131—84no—
333D4×C131—84no—
334D4×C131—84no—
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—21no—
342C2×C4×C131—21no—
343C2×C4×C131—21no—
344C2×C4×C131—21no—
345C2×C4×C131—22no—
346C2×C4×C131—21no—
347C2×C4×C131—21no—
348C2×C4×C131—21no—
349C2×C4×C131—21no—
350C2×C4×C131—21no—
351C2×C4×C131—41no—
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—41no—
367C2×C4×C131—41no—
368C2×C4×C131—41no—
369C2×C4×C131—84no—
370C2×C4×C131#12112yes—
371C2×C4×C131C22×D411yescharacteristic
372C2×C4×C131C22×D411yescharacteristic
373C2×C4×C131C2×#4111yescharacteristic
374C2×C4×C131C2×#4111yescharacteristic
375C2×C4×C131H(5,𝔽2)11yescharacteristic
376C2×C4×C131H(5,𝔽2)11yescharacteristic
377C8×C131—22no—
378C8×C131—22no—
379C8×C131—22no—
380C8×C131—41no—
381C22×C131—22no—
382C22×C131—22no—
383C22×C131—22no—
384C22×C131—22no—
385C22×C131—22no—
386C22×C131—22no—
387C22×C131—41no—
388C22×C131—42no—
389C22×C131—42no—
390C22×C131—41no—
391C22×C131—42no—
392C22×C131—41no—
393C22×C131—42no—
394C22×C131—41no—
395C22×C131—42no—
396C22×C131—41no—
397C22×C131—41no—
398C22×C131—41no—
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×C131—81no—
410C22×C131—81no—
411C22×C131—81no—
412C22×C131—81no—
413C22×C131—81no—
414C22×C131—81no—
415C22×C131—81no—
416C22×C131#46914yescomplemented
417C22×C131C2×#12111yescharacteristic
418C22×C131D4211yescharacteristic
419C22×C131#54611yescharacteristic
420C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
422C22×C131#57611yescharacteristic
423C22×C131#57711yescharacteristic
424C4×C131—22no—
425C4×C131—41no—
426C4×C131—42no—
427C4×C131—41no—
428C4×C131—41no—
429C4×C131—81no—
430C4×C131—81no—
431C4×C131—81no—
432C4×C131—81no—
433C4×C131#52511yescharacteristic
434C4×C131#53811yescharacteristic
435C4×C131D4211yescharacteristic
436C4×C131#54611yescharacteristic
437C2×C131—24no—
438C2×C131—81no—
439C2×C131—82no—
440C2×C131—82no—
441C2×C131—161no—
442C2×C131#242411yescharacteristic
443C2×C131C2×#46911yescharacteristic
444C2×C131#306211yescharacteristic
445C2×C131#326411yescharacteristic
446C2×C131#326511yescharacteristic
447C2×C131#330611yescharacteristic
448C2×C131#331811yescharacteristic
449#25124C13111yesmaximal, characteristic, direct product factor, Sylow
450C131#2512411yescharacteristic, direct product factor, Sylow
451C2×#469C2×C13111yescharacteristic, complemented
452C2×#447C2×C13111yescharacteristic, complemented
453C2×#435C2×C13111yescharacteristic, complemented
454C22×#102C2×C13111yescharacteristic, complemented
455#2416C2×C13111yescharacteristic, complemented
456#2408C2×C13111yescharacteristic, complemented
457#2065C2×C13111yescharacteristic, complemented
458#2054C2×C13111yescharacteristic, complemented
459#2034C2×C13111yescharacteristic, complemented
460#1999C2×C13111yescharacteristic, complemented
461#1972C2×C13111yescharacteristic, complemented
462#1936C2×C13111yescharacteristic, complemented
463#1895C2×C13111yescharacteristic, complemented
464#1893C2×C13111yescharacteristic, complemented
465#1853C2×C13111yescharacteristic, complemented
466C23×D4C22×C13111yescharacteristic
467C22×D8C22×C13111yescharacteristic
468C22×D8C22×C13111yescharacteristic
469C22×M16C22×C13111yescharacteristic, complemented
470C23×C8C22×C13111yescharacteristic
471C2×#121—21no—
472C2×#121C22×C13111yescharacteristic
473C2×#121C22×C13111yescharacteristic
474C2×#121C22×C13111yescharacteristic
475C2×#121C22×C13111yescharacteristic, complemented
476C2×#120—21no—
477C2×C4×D4C22×C13111yescharacteristic
478C22×C4⋊C4C22×C13111yescharacteristic
479#469—24no—
480#447—24no—
481#435—24no—
482C2×#106C22×C13111yescharacteristic, complemented
483C2×#106C22×C13111yescharacteristic, complemented
484C2×C4⋊C8C22×C13111yescharacteristic, complemented
485C2×#102—24no—
486C2×#102C22×C13111yescharacteristic
487C2×#102C22×C13111yescharacteristic
488C2×#102C22×C13111yescharacteristic
489C2×#102C22×C13111yescharacteristic
490C2×#102C22×C13111yescharacteristic
491C2×#102C22×C13111yescharacteristic
492C2×#102C22×C13111yescharacteristic, complemented
493C2×#102C22×C13111yescharacteristic, complemented
494C2×C22⋊C8C22×C13111yescharacteristic
495C2×C22⋊C8C22×C13111yescharacteristic, complemented
496C2×#97C22×C13111yescharacteristic, complemented
497#396—21no—
498#394—21no—
499#394—21no—
500#392—21no—
501#390C22×C13111yescharacteristic
502#390C22×C13111yescharacteristic
503#390C22×C13111yescharacteristic, complemented
504#389C22×C13111yescharacteristic, complemented
505#386—21no—
506#380C22×C13111yescharacteristic
507#380C22×C13111yescharacteristic, complemented
508#379—21no—
509#340C22×C13111yescharacteristic, complemented
510#340C22×C13111yescharacteristic, complemented
511#340C22×C13111yescharacteristic, complemented
512#340C22×C13111yescharacteristic, complemented
513C25—21no—
514C22×D4—22no—
515C22×D4—22no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—22no—
521C22×D4—21no—
522C22×D4—22no—
523C22×D4—41no—
524C22×D4—41no—
525C22×D4D4×C13111yescharacteristic
526C22×D4C23×C13111yescharacteristic
527C22×D4C23×C13111yescharacteristic
528C22×D4C23×C13111yescharacteristic
529C23×C4—21no—
530C23×C4C23×C13111yescharacteristic
531C23×C4C23×C13111yescharacteristic
532C2×D8—22no—
533C2×D8—22no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×M16—22no—
539C2×M16—22no—
540C2×M16—41no—
541C22×C8—22no—
542C22×C8—22no—
543C22×C8—41no—
544C22×C8C23×C13111yescharacteristic
545C22×C8C23×C13111yescharacteristic
546C22×C8C23×C13111yescharacteristic
547C22×C8C23×C13111yescharacteristic
548#121—22no—
549#121—22no—
550#121—22no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—44no—
557#120—44no—
558C4×D4—22no—
559C4×D4—22no—
560C2×C4⋊C4—22no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—41no—
564C2×C4⋊C4D4×C13111yescharacteristic
565C2×C4⋊C4C23×C13111yescharacteristic
566C2×C4⋊C4C23×C13111yescharacteristic
567C2×C4⋊C4C23×C13111yescharacteristic
568C2×C4⋊C4C23×C13111yescharacteristic
569C2×C4⋊C4C23×C13111yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—21no—
574C2×C22⋊C4—21no—
575C2×C22⋊C4—21no—
576C2×C22⋊C4—21no—
577C2×C22⋊C4—21no—
578C2×C22⋊C4—21no—
579C2×C22⋊C4—21no—
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
582C2×C22⋊C4D4×C13111yescharacteristic
583C2×C22⋊C4D4×C13111yescharacteristic
584C2×C42C23×C13111yescharacteristic
585#106—22no—
586#106—41no—
587C4⋊C8—22no—
588#102—22no—
589#102—22no—
590#102—22no—
591#102—22no—
592#102—22no—
593#102—22no—
594#102—41no—
595#102D4×C13114yescomplemented
596C22⋊C8—22no—
597C22⋊C8D4×C13114yescomplemented
598#97—22no—
599#95—21no—
600#95—21no—
601#95—21no—
602C24—21no—
603C24—21no—
604C24—21no—
605C24—42no—
606C24—42no—
607C24—42no—
608C24—42no—
609C24—42no—
610C24—81no—
611C24—81no—
612C24C2×D4×C13111yescharacteristic
613C24C2×D4×C13111yescharacteristic
614C2×D4—28no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
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—44no—
635C2×D4—44no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—44no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—42no—
646C2×D4—42no—
647C2×D4—42no—
648C2×D4—42no—
649C2×D4—81no—
650C2×D4—81no—
651C2×D4—81no—
652C2×D4C2×D4×C13112yes—
653C2×D4#41×C13112yes—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—42no—
670C22×C4—42no—
671C22×C4—81no—
672C22×C4C2×D4×C13111yescharacteristic
673C22×C4C2×D4×C13111yescharacteristic
674C22×C4C2×D4×C13111yescharacteristic
675C22×C4C2×D4×C13111yescharacteristic
676C22×C4C2×D4×C13112yes—
677C22×C4#41×C13112yes—
678C22×C4C24×C13111yescharacteristic
679D8—44no—
680D8—44no—
681M16—44no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—44no—
692C2×C8C2×D4×C13112yes—
693C2×C8C2×D4×C13112yes—
694C2×C8C2×D4×C13112yes—
695C4⋊C4—22no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—42no—
706C4⋊C4—42no—
707C4⋊C4C2×D4×C13112yes—
708C22⋊C4—22no—
709C22⋊C4—22no—
710C22⋊C4—42no—
711C22⋊C4—42no—
712C22⋊C4—42no—
713C22⋊C4—42no—
714C22⋊C4—42no—
715C22⋊C4—42no—
716C22⋊C4—42no—
717C22⋊C4—42no—
718C22⋊C4—42no—
719C22⋊C4—81no—
720C22⋊C4—81no—
721C22⋊C4—81no—
722C42—21no—
723C42—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—22no—
730C23—21no—
731C23—22no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
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—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—84no—
758C23—84no—
759C23—84no—
760C23—84no—
761C23—84no—
762C23—84no—
763C23#121×C13112yes—
764C23AGL(1,ℤ/8)×C13112yes—
765C23AGL(1,ℤ/8)×C13112yes—
766C23C22×D4×C13111yescharacteristic
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—44no—
773D4—41no—
774D4—41no—
775D4—41no—
776D4—41no—
777D4—41no—
778D4—41no—
779D4—41no—
780D4—41no—
781D4—84no—
782D4—84no—
783D4—84no—
784D4—84no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—22no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
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—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—84no—
820C2×C4#121×C13112yes—
821C2×C4C22×D4×C13111yescharacteristic
822C2×C4C22×D4×C13111yescharacteristic
823C2×C4C2×#41×C13111yescharacteristic
824C2×C4C2×#41×C13111yescharacteristic
825C2×C4H(5,𝔽2)×C13111yescharacteristic
826C2×C4H(5,𝔽2)×C13111yescharacteristic
827C8—22no—
828C8—22no—
829C8—22no—
830C8—41no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—22no—
837C22—41no—
838C22—42no—
839C22—41no—
840C22—42no—
841C22—41no—
842C22—42no—
843C22—41no—
844C22—41no—
845C22—41no—
846C22—42no—
847C22—41no—
848C22—42no—
849C22—42no—
850C22—816no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22#469×C13114yescomplemented
867C22C2×#121×C13111yescharacteristic
868C22D42×C13111yescharacteristic
869C22#546×C13111yescharacteristic
870C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
871C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
872C22#576×C13111yescharacteristic
873C22#577×C13111yescharacteristic
874C4—22no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4—81no—
883C4#525×C13111yescharacteristic
884C4#538×C13111yescharacteristic
885C4D42×C13111yescharacteristic
886C4#546×C13111yescharacteristic
887C2—24no—
888C2—81no—
889C2—82no—
890C2—82no—
891C2—161no—
892C2#2424×C13111yescharacteristic
893C2C2×#469×C13111yescharacteristic
894C2#3062×C13111yescharacteristic
895C2#3264×C13111yescharacteristic
896C2#3265×C13111yescharacteristic
897C2#3306×C13111yescharacteristic
898C2#3318×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
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
1. C2×#469×C131C2semidirect
2. C2×#447×C131C2semidirect
3. C2×#435×C131C2semidirect
4. C22×#102×C131C2semidirect
5. #2416×C131C2semidirect
6. #2408×C131C2semidirect
7. #2065×C131C2semidirect
8. #2054×C131C2semidirect
9. #2034×C131C2semidirect
10. #1999×C131C2semidirect
11. #1972×C131C2semidirect
12. #1936×C131C2semidirect
13. #1895×C131C2semidirect
14. #1893×C131C2semidirect
15. #1853×C131C2semidirect
19. C22×M16×C131C22semidirect
25. C2×#121×C131C22semidirect
32. C2×#106×C131C22semidirect
33. C2×#106×C131C22semidirect
34. C2×C4⋊C8×C131C22semidirect
42. C2×#102×C131C22semidirect
43. C2×#102×C131C22semidirect
45. C2×C22⋊C8×C131C22semidirect
46. C2×#97×C131C22semidirect
53. #390×C131C22semidirect
54. #389×C131C22semidirect
57. #380×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
145. #102×C131D4semidirect
147. C22⋊C8×C131D4semidirect
416. C22×C131#469semidirect
449. #25124C131direct (N × H)
450. C131#25124direct (N × H)
451. C2×#469C2×C131semidirect
452. C2×#447C2×C131semidirect
453. C2×#435C2×C131semidirect
454. C22×#102C2×C131semidirect
455. #2416C2×C131semidirect
456. #2408C2×C131semidirect
457. #2065C2×C131semidirect
458. #2054C2×C131semidirect
459. #2034C2×C131semidirect
460. #1999C2×C131semidirect
461. #1972C2×C131semidirect
462. #1936C2×C131semidirect
463. #1895C2×C131semidirect
464. #1893C2×C131semidirect
465. #1853C2×C131semidirect
469. C22×M16C22×C131semidirect
475. C2×#121C22×C131semidirect
482. C2×#106C22×C131semidirect
483. C2×#106C22×C131semidirect
484. C2×C4⋊C8C22×C131semidirect
492. C2×#102C22×C131semidirect
493. C2×#102C22×C131semidirect
495. C2×C22⋊C8C22×C131semidirect
496. C2×#97C22×C131semidirect
503. #390C22×C131semidirect
504. #389C22×C131semidirect
507. #380C22×C131semidirect
509. #340C22×C131semidirect
510. #340C22×C131semidirect
511. #340C22×C131semidirect
512. #340C22×C131semidirect
595. #102D4×C131semidirect
597. C22⋊C8D4×C131semidirect
866. C22#469×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#469×C1312
C2×#447×C1312
C2×#435×C1312
C22×#102×C1312
#2416×C1312
#2408×C1312
#2065×C1312
#2054×C1312
#2034×C1312
#1999×C1312
#1972×C1312
#1936×C1312
#1895×C1312
#1893×C1312
#1853×C1312
#25124131