Finite Group Databasebeta

← C131×#24044 #45709928

Subgroups — C131×#24044 #45709928

Order 33536.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C131C211yesmaximal, characteristic
2C2×#482×C131C211yesmaximal, characteristic, complemented
3C2×#418×C131C211yesmaximal, characteristic, complemented
4#2485×C131C211yesmaximal, characteristic, complemented
5#2041×C131C211yesmaximal, characteristic, complemented
6#2041×C131C211yesmaximal, characteristic, complemented
7#2034×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#1895×C131C211yesmaximal, characteristic, complemented
10#1870×C131C211yesmaximal, characteristic, complemented
11#1864×C131C211yesmaximal, characteristic, complemented
12#1862×C131C211yesmaximal, characteristic, complemented
13#1786×C131C211yesmaximal, characteristic, complemented
14#1786×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131—21no—
17C23×D4×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C22×M16×C131C2211yescharacteristic, complemented
20D42×C131—24no—
21D42×C131—24no—
22C2×#127×C131C2211yescharacteristic
23C2×#121×C131—21no—
24C2×#121×C131C2211yescharacteristic
25C2×#121×C131C2211yescharacteristic
26C2×#120×C131—21no—
27C2×#120×C131—21no—
28C2×C4×D4×C131C2211yescharacteristic
29C2×C4×D4×C131C2211yescharacteristic
30C2×#117×C131C2211yescharacteristic, complemented
31#482×C131—24no—
32C2×#107×C131C2211yescharacteristic, complemented
33C2×#106×C131C2211yescharacteristic, complemented
34#418×C131—24no—
35C2×#102×C131C2211yescharacteristic
36C2×#102×C131C2211yescharacteristic
37C2×#102×C131C2211yescharacteristic
38C2×#102×C131C2211yescharacteristic
39C2×#102×C131C2211yescharacteristic, complemented
40C2×#102×C131C2211yescharacteristic, complemented
41C2×#102×C131C2211yescharacteristic, complemented
42C2×#102×C131C2211yescharacteristic, complemented
43C2×#102×C131C2211yescharacteristic, complemented
44C2×#102×C131C2211yescharacteristic, complemented
45C2×#102×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic, complemented
47C2×C22⋊C8×C131C2211yescharacteristic, complemented
48C2×C22⋊C8×C131C2211yescharacteristic, complemented
49C2×C22⋊C8×C131C2211yescharacteristic, complemented
50#397×C131—21no—
51#394×C131—21no—
52#389×C131C2211yescharacteristic, complemented
53#389×C131C2211yescharacteristic, complemented
54#388×C131—21no—
55#387×C131—21no—
56#380×C131C2211yescharacteristic, complemented
57#380×C131C2211yescharacteristic, complemented
58#380×C131C2211yescharacteristic, complemented
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#336×C131C2211yescharacteristic, complemented
62#336×C131C2211yescharacteristic, complemented
63C25×C131—21no—
64C25×C131—21no—
65C22×D4×C131—22no—
66C22×D4×C131—22no—
67C22×D4×C131—28no—
68C22×D4×C131—21no—
69C22×D4×C131—21no—
70C22×D4×C131—22no—
71C22×D4×C131—22no—
72C22×D4×C131—22no—
73C22×D4×C131—22no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131—22no—
78C22×D4×C131—21no—
79C22×D4×C131—41no—
80C22×D4×C131—41no—
81C22×D4×C131—41no—
82C22×D4×C131—41no—
83C22×D4×C131—44no—
84C22×D4×C131—44no—
85C22×D4×C131D411yescharacteristic
86C22×D4×C131D414yes—
87C22×D4×C131C2311yescharacteristic
88C22×D4×C131C2311yescharacteristic
89C22×D4×C131C2311yescharacteristic
90C23×C4×C131—21no—
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C2×M16×C131—22no—
94C2×M16×C131—41no—
95C2×M16×C131—41no—
96C22×C8×C131C2311yescharacteristic
97C22×C8×C131C2311yescharacteristic
98C22×C8×C131C2311yescharacteristic
99C22×C8×C131C2311yescharacteristic
100#127×C131—22no—
101#127×C131—22no—
102#121×C131—28no—
103#121×C131—22no—
104#121×C131—22no—
105#121×C131—22no—
106#121×C131D414yes—
107#120×C131—28no—
108#120×C131—28no—
109C4×D4×C131—22no—
110C4×D4×C131—22no—
111C4×D4×C131—22no—
112C4×D4×C131—22no—
113#117×C131—22no—
114#117×C131—22no—
115C2×C4⋊C4×C131—21no—
116C2×C4⋊C4×C131—21no—
117C2×C4⋊C4×C131D411yescharacteristic
118C2×C4⋊C4×C131C2311yescharacteristic
119C2×C4⋊C4×C131C2311yescharacteristic
120C2×C4⋊C4×C131C2311yescharacteristic
121C2×C4⋊C4×C131C2311yescharacteristic
122C2×C4⋊C4×C131C2311yescharacteristic
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
134#107×C131—22no—
135#106×C131—22no—
136#102×C131—22no—
137#102×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×C131—41no—
146#102×C131—41no—
147#102×C131—41no—
148C22⋊C8×C131—22no—
149C22⋊C8×C131—41no—
150C22⋊C8×C131—41no—
151#95×C131—21no—
152#95×C131—21no—
153#95×C131—21no—
154#95×C131—21no—
155#95×C131—21no—
156C24×C131—21no—
157C24×C131—24no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—24no—
161C24×C131—42no—
162C24×C131—42no—
163C24×C131—42no—
164C24×C131—42no—
165C24×C131—42no—
166C24×C131—42no—
167C24×C131—42no—
168C24×C131—42no—
169C24×C131—81no—
170C24×C131—81no—
171C24×C131—81no—
172C24×C131—81no—
173C24×C131C2×D411yescharacteristic
174C24×C131C2×D411yescharacteristic
175C2×D4×C131—22no—
176C2×D4×C131—22no—
177C2×D4×C131—28no—
178C2×D4×C131—24no—
179C2×D4×C131—24no—
180C2×D4×C131—24no—
181C2×D4×C131—24no—
182C2×D4×C131—24no—
183C2×D4×C131—24no—
184C2×D4×C131—22no—
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—21no—
195C2×D4×C131—21no—
196C2×D4×C131—21no—
197C2×D4×C131—21no—
198C2×D4×C131—44no—
199C2×D4×C131—44no—
200C2×D4×C131—44no—
201C2×D4×C131—42no—
202C2×D4×C131—42no—
203C2×D4×C131—42no—
204C2×D4×C131—42no—
205C2×D4×C131—42no—
206C2×D4×C131—44no—
207C2×D4×C131—44no—
208C2×D4×C131—432no—
209C2×D4×C131—44no—
210C2×D4×C131—42no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—44no—
215C2×D4×C131—42no—
216C2×D4×C131—81no—
217C2×D4×C131—81no—
218C2×D4×C131C2×D412yes—
219C2×D4×C131C2×D412yes—
220C2×D4×C131C2×D412yes—
221C2×D4×C131#4112yes—
222C2×D4×C131#4112yes—
223C22×C4×C131—21no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—24no—
228C22×C4×C131—21no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—21no—
233C22×C4×C131—21no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—42no—
240C22×C4×C131—42no—
241C22×C4×C131C2×D411yescharacteristic
242C22×C4×C131C2×D411yescharacteristic
243C22×C4×C131C2×D411yescharacteristic
244C22×C4×C131C2×D412yes—
245C22×C4×C131C2×D412yes—
246C22×C4×C131C2×D411yescharacteristic
247C22×C4×C131C2411yescharacteristic
248M16×C131—44no—
249C2×C8×C131—21no—
250C2×C8×C131—21no—
251C2×C8×C131—21no—
252C2×C8×C131—21no—
253C2×C8×C131—21no—
254C2×C8×C131—21no—
255C2×C8×C131—21no—
256C2×C8×C131—21no—
257C2×C8×C131—21no—
258C2×C8×C131—21no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C4⋊C4×C131—22no—
262C4⋊C4×C131—21no—
263C4⋊C4×C131—21no—
264C4⋊C4×C131—21no—
265C4⋊C4×C131—21no—
266C4⋊C4×C131—21no—
267C4⋊C4×C131—21no—
268C4⋊C4×C131—21no—
269C4⋊C4×C131—21no—
270C4⋊C4×C131—21no—
271C4⋊C4×C131—42no—
272C4⋊C4×C131—81no—
273C4⋊C4×C131C2×D412yes—
274C22⋊C4×C131—24no—
275C22⋊C4×C131—24no—
276C22⋊C4×C131—22no—
277C22⋊C4×C131—24no—
278C22⋊C4×C131—22no—
279C22⋊C4×C131—42no—
280C22⋊C4×C131—42no—
281C22⋊C4×C131—81no—
282C22⋊C4×C131—81no—
283C42×C131—21no—
284C42×C131—21no—
285C42×C131—42no—
286C23×C131—21no—
287C23×C131—22no—
288C23×C131—21no—
289C23×C131—21no—
290C23×C131—21no—
291C23×C131—21no—
292C23×C131—22no—
293C23×C131—22no—
294C23×C131—21no—
295C23×C131—21no—
296C23×C131—21no—
297C23×C131—21no—
298C23×C131—21no—
299C23×C131—21no—
300C23×C131—21no—
301C23×C131—22no—
302C23×C131—22no—
303C23×C131—48no—
304C23×C131—48no—
305C23×C131—48no—
306C23×C131—48no—
307C23×C131—41no—
308C23×C131—41no—
309C23×C131—41no—
310C23×C131—41no—
311C23×C131—41no—
312C23×C131—41no—
313C23×C131—41no—
314C23×C131—41no—
315C23×C131—41no—
316C23×C131—41no—
317C23×C131—41no—
318C23×C131—41no—
319C23×C131—41no—
320C23×C131—41no—
321C23×C131—41no—
322C23×C131—41no—
323C23×C131—84no—
324C23×C131—84no—
325C23×C131—84no—
326C23×C131—84no—
327C23×C131—84no—
328C23×C131—84no—
329C23×C131—84no—
330C23×C131—84no—
331C23×C131—84no—
332C23×C131—84no—
333C23×C131#12012yes—
334C23×C131AGL(1,ℤ/8)12yes—
335C23×C131C22×D411yescharacteristic
336D4×C131—28no—
337D4×C131—22no—
338D4×C131—22no—
339D4×C131—22no—
340D4×C131—22no—
341D4×C131—22no—
342D4×C131—22no—
343D4×C131—22no—
344D4×C131—48no—
345D4×C131—48no—
346D4×C131—48no—
347D4×C131—48no—
348D4×C131—48no—
349D4×C131—41no—
350D4×C131—41no—
351D4×C131—41no—
352D4×C131—41no—
353D4×C131—84no—
354D4×C131#12314yes—
355C2×C4×C131—21no—
356C2×C4×C131—21no—
357C2×C4×C131—21no—
358C2×C4×C131—21no—
359C2×C4×C131—22no—
360C2×C4×C131—22no—
361C2×C4×C131—22no—
362C2×C4×C131—22no—
363C2×C4×C131—21no—
364C2×C4×C131—21no—
365C2×C4×C131—22no—
366C2×C4×C131—21no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—21no—
370C2×C4×C131—48no—
371C2×C4×C131—41no—
372C2×C4×C131—41no—
373C2×C4×C131—41no—
374C2×C4×C131—41no—
375C2×C4×C131—41no—
376C2×C4×C131—41no—
377C2×C4×C131—41no—
378C2×C4×C131—41no—
379C2×C4×C131—41no—
380C2×C4×C131—41no—
381C2×C4×C131—41no—
382C2×C4×C131—41no—
383C2×C4×C131—41no—
384C2×C4×C131—41no—
385C2×C4×C131—41no—
386C2×C4×C131—41no—
387C2×C4×C131—41no—
388C2×C4×C131—41no—
389C2×C4×C131#12012yes—
390C2×C4×C131AGL(1,ℤ/8)12yes—
391C2×C4×C131C22×D411yescharacteristic
392C2×C4×C131C22×D411yescharacteristic
393C2×C4×C131C2×#4111yescharacteristic
394C2×C4×C131C2×#4111yescharacteristic
395C2×C4×C131H(5,𝔽2)11yescharacteristic
396C2×C4×C131H(5,𝔽2)11yescharacteristic
397C8×C131—41no—
398C8×C131—41no—
399C8×C131—41no—
400C8×C131—41no—
401C22×C131—22no—
402C22×C131—24no—
403C22×C131—22no—
404C22×C131—22no—
405C22×C131—22no—
406C22×C131—22no—
407C22×C131—22no—
408C22×C131—41no—
409C22×C131—42no—
410C22×C131—41no—
411C22×C131—42no—
412C22×C131—41no—
413C22×C131—42no—
414C22×C131—41no—
415C22×C131—42no—
416C22×C131—41no—
417C22×C131—41no—
418C22×C131—42no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—42no—
422C22×C131—42no—
423C22×C131—42no—
424C22×C131—42no—
425C22×C131—42no—
426C22×C131—42no—
427C22×C131—42no—
428C22×C131—816no—
429C22×C131—816no—
430C22×C131—81no—
431C22×C131—81no—
432C22×C131—81no—
433C22×C131—81no—
434C22×C131—81no—
435C22×C131—81no—
436C22×C131—81no—
437C22×C131—81no—
438C22×C131C2×#12011yescharacteristic
439C22×C131#54611yescharacteristic
440C22×C131#54611yescharacteristic
441C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C131#57611yescharacteristic
444C22×C131#57711yescharacteristic
445C4×C131—22no—
446C4×C131—22no—
447C4×C131—41no—
448C4×C131—42no—
449C4×C131—41no—
450C4×C131—81no—
451C4×C131—81no—
452C4×C131—81no—
453C4×C131—81no—
454C4×C131C2×#12311yescharacteristic
455C4×C131#53411yescharacteristic
456C4×C131#54611yescharacteristic
457C4×C131#54611yescharacteristic
458C2×C131—42no—
459C2×C131—42no—
460C2×C131—44no—
461C2×C131—82no—
462C2×C131—82no—
463C2×C131#240511yescharacteristic
464C2×C131#300311yescharacteristic
465C2×C131#301211yescharacteristic
466C2×C131#331011yescharacteristic
467C2×C131#331811yescharacteristic
468C2×C131#332411yescharacteristic
469C2×C131#332511yescharacteristic
470#24044C13111yesmaximal, characteristic, direct product factor, Sylow
471C131#2404411yescharacteristic, direct product factor, Sylow
472C2×D42C2×C13111yescharacteristic
473C2×#482C2×C13111yescharacteristic, complemented
474C2×#418C2×C13111yescharacteristic, complemented
475#2485C2×C13111yescharacteristic, complemented
476#2041C2×C13111yescharacteristic, complemented
477#2041C2×C13111yescharacteristic, complemented
478#2034C2×C13111yescharacteristic, complemented
479#2033C2×C13111yescharacteristic, complemented
480#1895C2×C13111yescharacteristic, complemented
481#1870C2×C13111yescharacteristic, complemented
482#1864C2×C13111yescharacteristic, complemented
483#1862C2×C13111yescharacteristic, complemented
484#1786C2×C13111yescharacteristic, complemented
485#1786C2×C13111yescharacteristic, complemented
486#1786C2×C13111yescharacteristic, complemented
487C23×D4—21no—
488C23×D4C22×C13111yescharacteristic
489C23×D4C22×C13111yescharacteristic
490C22×M16C22×C13111yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C13111yescharacteristic
494C2×#121—21no—
495C2×#121C22×C13111yescharacteristic
496C2×#121C22×C13111yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C13111yescharacteristic
500C2×C4×D4C22×C13111yescharacteristic
501C2×#117C22×C13111yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C13111yescharacteristic, complemented
504C2×#106C22×C13111yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C13111yescharacteristic
507C2×#102C22×C13111yescharacteristic
508C2×#102C22×C13111yescharacteristic
509C2×#102C22×C13111yescharacteristic
510C2×#102C22×C13111yescharacteristic, complemented
511C2×#102C22×C13111yescharacteristic, complemented
512C2×#102C22×C13111yescharacteristic, complemented
513C2×#102C22×C13111yescharacteristic, complemented
514C2×#102C22×C13111yescharacteristic, complemented
515C2×#102C22×C13111yescharacteristic, complemented
516C2×#102C22×C13111yescharacteristic, complemented
517C2×#102C22×C13111yescharacteristic, complemented
518C2×C22⋊C8C22×C13111yescharacteristic, complemented
519C2×C22⋊C8C22×C13111yescharacteristic, complemented
520C2×C22⋊C8C22×C13111yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C13111yescharacteristic, complemented
524#389C22×C13111yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C13111yescharacteristic, complemented
528#380C22×C13111yescharacteristic, complemented
529#380C22×C13111yescharacteristic, complemented
530#340C22×C13111yescharacteristic, complemented
531#340C22×C13111yescharacteristic, complemented
532#336C22×C13111yescharacteristic, complemented
533#336C22×C13111yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C13111yescharacteristic
557C22×D4D4×C13114yes—
558C22×D4C23×C13111yescharacteristic
559C22×D4C23×C13111yescharacteristic
560C22×D4C23×C13111yescharacteristic
561C23×C4—21no—
562C23×C4C23×C13111yescharacteristic
563C23×C4C23×C13111yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C13111yescharacteristic
568C22×C8C23×C13111yescharacteristic
569C22×C8C23×C13111yescharacteristic
570C22×C8C23×C13111yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C13114yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C13111yescharacteristic
589C2×C4⋊C4C23×C13111yescharacteristic
590C2×C4⋊C4C23×C13111yescharacteristic
591C2×C4⋊C4C23×C13111yescharacteristic
592C2×C4⋊C4C23×C13111yescharacteristic
593C2×C4⋊C4C23×C13111yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C13111yescharacteristic
602C2×C22⋊C4D4×C13111yescharacteristic
603C2×C42—21no—
604C2×C42C23×C13111yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C13111yescharacteristic
645C24C2×D4×C13111yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C13112yes—
690C2×D4C2×D4×C13112yes—
691C2×D4C2×D4×C13112yes—
692C2×D4#41×C13112yes—
693C2×D4#41×C13112yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C13111yescharacteristic
713C22×C4C2×D4×C13111yescharacteristic
714C22×C4C2×D4×C13111yescharacteristic
715C22×C4C2×D4×C13112yes—
716C22×C4C2×D4×C13112yes—
717C22×C4C2×D4×C13111yescharacteristic
718C22×C4C24×C13111yescharacteristic
719M16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C13112yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C13112yes—
805C23AGL(1,ℤ/8)×C13112yes—
806C23C22×D4×C13111yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C13114yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C13112yes—
861C2×C4AGL(1,ℤ/8)×C13112yes—
862C2×C4C22×D4×C13111yescharacteristic
863C2×C4C22×D4×C13111yescharacteristic
864C2×C4C2×#41×C13111yescharacteristic
865C2×C4C2×#41×C13111yescharacteristic
866C2×C4H(5,𝔽2)×C13111yescharacteristic
867C2×C4H(5,𝔽2)×C13111yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—24no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C13111yescharacteristic
910C22#546×C13111yescharacteristic
911C22#546×C13111yescharacteristic
912C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
913C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
914C22#576×C13111yescharacteristic
915C22#577×C13111yescharacteristic
916C4—22no—
917C4—22no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C13111yescharacteristic
926C4#534×C13111yescharacteristic
927C4#546×C13111yescharacteristic
928C4#546×C13111yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2#2405×C13111yescharacteristic
935C2#3003×C13111yescharacteristic
936C2#3012×C13111yescharacteristic
937C2#3310×C13111yescharacteristic
938C2#3318×C13111yescharacteristic
939C2#3324×C13111yescharacteristic
940C2#3325×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×#482×C131C2semidirect
3. C2×#418×C131C2semidirect
4. #2485×C131C2semidirect
5. #2041×C131C2semidirect
6. #2041×C131C2semidirect
7. #2034×C131C2semidirect
8. #2033×C131C2semidirect
9. #1895×C131C2semidirect
10. #1870×C131C2semidirect
11. #1864×C131C2semidirect
12. #1862×C131C2semidirect
13. #1786×C131C2semidirect
14. #1786×C131C2semidirect
15. #1786×C131C2semidirect
19. C22×M16×C131C22semidirect
30. C2×#117×C131C22semidirect
32. C2×#107×C131C22semidirect
33. C2×#106×C131C22semidirect
39. C2×#102×C131C22semidirect
40. C2×#102×C131C22semidirect
41. C2×#102×C131C22semidirect
42. C2×#102×C131C22semidirect
43. C2×#102×C131C22semidirect
44. C2×#102×C131C22semidirect
45. C2×#102×C131C22semidirect
46. C2×#102×C131C22semidirect
47. C2×C22⋊C8×C131C22semidirect
48. C2×C22⋊C8×C131C22semidirect
49. C2×C22⋊C8×C131C22semidirect
52. #389×C131C22semidirect
53. #389×C131C22semidirect
56. #380×C131C22semidirect
57. #380×C131C22semidirect
58. #380×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #336×C131C22semidirect
62. #336×C131C22semidirect
470. #24044C131direct (N × H)
471. C131#24044direct (N × H)
473. C2×#482C2×C131semidirect
474. C2×#418C2×C131semidirect
475. #2485C2×C131semidirect
476. #2041C2×C131semidirect
477. #2041C2×C131semidirect
478. #2034C2×C131semidirect
479. #2033C2×C131semidirect
480. #1895C2×C131semidirect
481. #1870C2×C131semidirect
482. #1864C2×C131semidirect
483. #1862C2×C131semidirect
484. #1786C2×C131semidirect
485. #1786C2×C131semidirect
486. #1786C2×C131semidirect
490. C22×M16C22×C131semidirect
501. C2×#117C22×C131semidirect
503. C2×#107C22×C131semidirect
504. C2×#106C22×C131semidirect
510. C2×#102C22×C131semidirect
511. C2×#102C22×C131semidirect
512. C2×#102C22×C131semidirect
513. C2×#102C22×C131semidirect
514. C2×#102C22×C131semidirect
515. C2×#102C22×C131semidirect
516. C2×#102C22×C131semidirect
517. C2×#102C22×C131semidirect
518. C2×C22⋊C8C22×C131semidirect
519. C2×C22⋊C8C22×C131semidirect
520. C2×C22⋊C8C22×C131semidirect
523. #389C22×C131semidirect
524. #389C22×C131semidirect
527. #380C22×C131semidirect
528. #380C22×C131semidirect
529. #380C22×C131semidirect
530. #340C22×C131semidirect
531. #340C22×C131semidirect
532. #336C22×C131semidirect
533. #336C22×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×#482×C1312
C2×#418×C1312
#2485×C1312
#2041×C1312
#2034×C1312
#2033×C1312
#1895×C1312
#1870×C1312
#1864×C1312
#1862×C1312
#1786×C1312
#24044131