Finite Group Databasebeta

← C131×#24440 #45710324

Subgroups — C131×#24440 #45710324

Order 33536.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C131C211yesmaximal, characteristic, complemented
2C2×#469×C131C211yesmaximal, characteristic, complemented
3C2×#447×C131C211yesmaximal, characteristic, complemented
4C2×#447×C131C211yesmaximal, characteristic, complemented
5C2×#418×C131C211yesmaximal, characteristic, complemented
6#2414×C131C211yesmaximal, characteristic, complemented
7#2041×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2011×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1879×C131C211yesmaximal, characteristic, complemented
12#1875×C131C211yesmaximal, characteristic, complemented
13#1870×C131C211yesmaximal, characteristic, complemented
14#1864×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C23×D4×C131—21no—
17C23×D4×C131C2211yescharacteristic
18C23×D4×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic, complemented
21C22×D8×C131C2211yescharacteristic, complemented
22C22×M16×C131C2211yescharacteristic, complemented
23D42×C131—24no—
24D42×C131—24no—
25C2×#127×C131C2211yescharacteristic
26C2×#121×C131—21no—
27C2×#121×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic, complemented
30C2×#121×C131C2211yescharacteristic, complemented
31C2×#120×C131—21no—
32C2×#120×C131—21no—
33C2×C4×D4×C131C2211yescharacteristic
34C2×C4×D4×C131C2211yescharacteristic
35C2×#117×C131C2211yescharacteristic, complemented
36#469×C131—24no—
37#447×C131—24no—
38#447×C131—24no—
39C2×#106×C131C2211yescharacteristic, complemented
40#418×C131—24no—
41C2×#102×C131C2211yescharacteristic
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic, complemented
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#394×C131—21no—
55#392×C131—21no—
56#390×C131—21no—
57#390×C131C2211yescharacteristic, complemented
58#389×C131C2211yescharacteristic, complemented
59#388×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×D4×C131—22no—
68C22×D4×C131—22no—
69C22×D4×C131—28no—
70C22×D4×C131—21no—
71C22×D4×C131—21no—
72C22×D4×C131—22no—
73C22×D4×C131—22no—
74C22×D4×C131—22no—
75C22×D4×C131—22no—
76C22×D4×C131—21no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—22no—
82C22×D4×C131—21no—
83C22×D4×C131—41no—
84C22×D4×C131—41no—
85C22×D4×C131—41no—
86C22×D4×C131—41no—
87C22×D4×C131—44no—
88C22×D4×C131—44no—
89C22×D4×C131D411yescharacteristic
90C22×D4×C131D414yescomplemented
91C22×D4×C131C2311yescharacteristic
92C22×D4×C131C2311yescharacteristic
93C22×D4×C131C2311yescharacteristic
94C22×D4×C131C2311yescharacteristic
95C23×C4×C131—21no—
96C23×C4×C131C2311yescharacteristic
97C23×C4×C131C2311yescharacteristic
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—22no—
101C2×D8×C131—22no—
102C2×D8×C131—22no—
103C2×D8×C131—22no—
104C2×D8×C131—41no—
105C2×D8×C131—41no—
106C2×D8×C131—41no—
107C2×M16×C131—22no—
108C2×M16×C131—22no—
109C2×M16×C131—41no—
110C22×C8×C131C2311yescharacteristic
111C22×C8×C131C2311yescharacteristic
112C22×C8×C131C2311yescharacteristic
113C22×C8×C131C2311yescharacteristic
114#127×C131—22no—
115#127×C131—22no—
116#121×C131—28no—
117#121×C131—22no—
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131—22no—
122#121×C131—22no—
123#121×C131—41no—
124#121×C131D414yescomplemented
125#120×C131—28no—
126#120×C131—28no—
127C4×D4×C131—22no—
128C4×D4×C131—22no—
129C4×D4×C131—22no—
130C4×D4×C131—22no—
131#117×C131—22no—
132#117×C131—41no—
133C2×C4⋊C4×C131—21no—
134C2×C4⋊C4×C131D411yescharacteristic
135C2×C4⋊C4×C131C2311yescharacteristic
136C2×C4⋊C4×C131C2311yescharacteristic
137C2×C4⋊C4×C131C2311yescharacteristic
138C2×C4⋊C4×C131C2311yescharacteristic
139C2×C22⋊C4×C131—21no—
140C2×C22⋊C4×C131—21no—
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×C131—21no—
148C2×C22⋊C4×C131D411yescharacteristic
149C2×C22⋊C4×C131D411yescharacteristic
150C2×C42×C131—21no—
151C2×C42×C131C2311yescharacteristic
152#106×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—22no—
160#102×C131—22no—
161#102×C131—41no—
162#102×C131D414yescomplemented
163C22⋊C8×C131—22no—
164C22⋊C8×C131—22no—
165C22⋊C8×C131—41no—
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—21no—
174C24×C131—42no—
175C24×C131—42no—
176C24×C131—42no—
177C24×C131—42no—
178C24×C131—42no—
179C24×C131—42no—
180C24×C131—42no—
181C24×C131—42no—
182C24×C131—81no—
183C24×C131—81no—
184C24×C131—81no—
185C24×C131—81no—
186C24×C131C2×D411yescharacteristic
187C24×C131C2×D411yescharacteristic
188C2×D4×C131—22no—
189C2×D4×C131—22no—
190C2×D4×C131—28no—
191C2×D4×C131—24no—
192C2×D4×C131—24no—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—24no—
196C2×D4×C131—24no—
197C2×D4×C131—22no—
198C2×D4×C131—21no—
199C2×D4×C131—21no—
200C2×D4×C131—21no—
201C2×D4×C131—21no—
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—21no—
216C2×D4×C131—21no—
217C2×D4×C131—44no—
218C2×D4×C131—44no—
219C2×D4×C131—44no—
220C2×D4×C131—42no—
221C2×D4×C131—42no—
222C2×D4×C131—42no—
223C2×D4×C131—42no—
224C2×D4×C131—42no—
225C2×D4×C131—42no—
226C2×D4×C131—44no—
227C2×D4×C131—44no—
228C2×D4×C131—432no—
229C2×D4×C131—44no—
230C2×D4×C131—42no—
231C2×D4×C131—42no—
232C2×D4×C131—42no—
233C2×D4×C131—42no—
234C2×D4×C131—44no—
235C2×D4×C131—42no—
236C2×D4×C131—42no—
237C2×D4×C131—42no—
238C2×D4×C131—81no—
239C2×D4×C131—81no—
240C2×D4×C131—81no—
241C2×D4×C131—81no—
242C2×D4×C131—81no—
243C2×D4×C131C2×D412yes—
244C2×D4×C131C2×D412yes—
245C2×D4×C131C2×D412yes—
246C2×D4×C131C2×D412yes—
247C2×D4×C131#4112yes—
248C22×C4×C131—21no—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—24no—
253C22×C4×C131—21no—
254C22×C4×C131—21no—
255C22×C4×C131—21no—
256C22×C4×C131—21no—
257C22×C4×C131—21no—
258C22×C4×C131—21no—
259C22×C4×C131—21no—
260C22×C4×C131—21no—
261C22×C4×C131—21no—
262C22×C4×C131—21no—
263C22×C4×C131—42no—
264C22×C4×C131—42no—
265C22×C4×C131C2×D411yescharacteristic
266C22×C4×C131C2×D411yescharacteristic
267C22×C4×C131C2×D411yescharacteristic
268C22×C4×C131C2×D412yes—
269C22×C4×C131C2×D412yes—
270C22×C4×C131C2×D411yescharacteristic
271C22×C4×C131C2411yescharacteristic
272D8×C131—44no—
273D8×C131—44no—
274D8×C131—44no—
275M16×C131—44no—
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—21no—
284C2×C8×C131—21no—
285C2×C8×C131—21no—
286C2×C8×C131—21no—
287C2×C8×C131C2×D412yescomplemented
288C4⋊C4×C131—22no—
289C4⋊C4×C131—21no—
290C4⋊C4×C131—21no—
291C4⋊C4×C131—21no—
292C4⋊C4×C131—21no—
293C4⋊C4×C131—21no—
294C4⋊C4×C131—21no—
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—42no—
306C22⋊C4×C131—42no—
307C22⋊C4×C131—81no—
308C22⋊C4×C131—81no—
309C42×C131—21no—
310C42×C131—21no—
311C42×C131—42no—
312C23×C131—21no—
313C23×C131—22no—
314C23×C131—21no—
315C23×C131—21no—
316C23×C131—22no—
317C23×C131—21no—
318C23×C131—21no—
319C23×C131—22no—
320C23×C131—21no—
321C23×C131—21no—
322C23×C131—21no—
323C23×C131—21no—
324C23×C131—21no—
325C23×C131—21no—
326C23×C131—21no—
327C23×C131—22no—
328C23×C131—22no—
329C23×C131—48no—
330C23×C131—48no—
331C23×C131—48no—
332C23×C131—48no—
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—41no—
343C23×C131—41no—
344C23×C131—41no—
345C23×C131—41no—
346C23×C131—41no—
347C23×C131—41no—
348C23×C131—41no—
349C23×C131—41no—
350C23×C131—41no—
351C23×C131—41no—
352C23×C131—41no—
353C23×C131—41no—
354C23×C131—41no—
355C23×C131—41no—
356C23×C131—84no—
357C23×C131—84no—
358C23×C131—84no—
359C23×C131—84no—
360C23×C131—84no—
361C23×C131—84no—
362C23×C131—84no—
363C23×C131—84no—
364C23×C131—84no—
365C23×C131—84no—
366C23×C131#12012yes—
367C23×C131AGL(1,ℤ/8)12yes—
368C23×C131C22×D411yescharacteristic
369D4×C131—28no—
370D4×C131—22no—
371D4×C131—22no—
372D4×C131—22no—
373D4×C131—22no—
374D4×C131—22no—
375D4×C131—22no—
376D4×C131—22no—
377D4×C131—48no—
378D4×C131—48no—
379D4×C131—48no—
380D4×C131—48no—
381D4×C131—48no—
382D4×C131—41no—
383D4×C131—41no—
384D4×C131—41no—
385D4×C131—41no—
386D4×C131—41no—
387D4×C131—41no—
388D4×C131—41no—
389D4×C131—41no—
390D4×C131—84no—
391D4×C131—84no—
392D4×C131—84no—
393D4×C131#12114yes—
394C2×C4×C131—21no—
395C2×C4×C131—21no—
396C2×C4×C131—21no—
397C2×C4×C131—21no—
398C2×C4×C131—22no—
399C2×C4×C131—22no—
400C2×C4×C131—22no—
401C2×C4×C131—22no—
402C2×C4×C131—21no—
403C2×C4×C131—21no—
404C2×C4×C131—22no—
405C2×C4×C131—22no—
406C2×C4×C131—21no—
407C2×C4×C131—21no—
408C2×C4×C131—21no—
409C2×C4×C131—21no—
410C2×C4×C131—48no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131—41no—
414C2×C4×C131—41no—
415C2×C4×C131—41no—
416C2×C4×C131—41no—
417C2×C4×C131—41no—
418C2×C4×C131—41no—
419C2×C4×C131—41no—
420C2×C4×C131—41no—
421C2×C4×C131—41no—
422C2×C4×C131—41no—
423C2×C4×C131—41no—
424C2×C4×C131—41no—
425C2×C4×C131#12012yes—
426C2×C4×C131AGL(1,ℤ/8)12yes—
427C2×C4×C131C22×D411yescharacteristic
428C2×C4×C131C22×D411yescharacteristic
429C2×C4×C131C22×D411yescharacteristic
430C2×C4×C131C2×#4111yescharacteristic
431C2×C4×C131H(5,𝔽2)11yescharacteristic
432C2×C4×C131H(5,𝔽2)11yescharacteristic
433C8×C131—22no—
434C8×C131—41no—
435C8×C131—41no—
436C8×C131—41no—
437C22×C131—22no—
438C22×C131—24no—
439C22×C131—22no—
440C22×C131—22no—
441C22×C131—22no—
442C22×C131—22no—
443C22×C131—22no—
444C22×C131—41no—
445C22×C131—42no—
446C22×C131—41no—
447C22×C131—42no—
448C22×C131—41no—
449C22×C131—42no—
450C22×C131—41no—
451C22×C131—41no—
452C22×C131—42no—
453C22×C131—41no—
454C22×C131—42no—
455C22×C131—41no—
456C22×C131—41no—
457C22×C131—42no—
458C22×C131—42no—
459C22×C131—42no—
460C22×C131—42no—
461C22×C131—42no—
462C22×C131—42no—
463C22×C131—42no—
464C22×C131—816no—
465C22×C131—816no—
466C22×C131—81no—
467C22×C131—81no—
468C22×C131—81no—
469C22×C131—81no—
470C22×C131—81no—
471C22×C131—81no—
472C22×C131—81no—
473C22×C131—81no—
474C22×C131—81no—
475C22×C131—81no—
476C22×C131—81no—
477C22×C131—81no—
478C22×C131—81no—
479C22×C131—81no—
480C22×C131—81no—
481C22×C131C2×#12011yescharacteristic
482C22×C131D4211yescharacteristic
483C22×C131#54611yescharacteristic
484C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
485C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C131#57611yescharacteristic
487C22×C131#57611yescharacteristic
488C4×C131—22no—
489C4×C131—22no—
490C4×C131—41no—
491C4×C131—42no—
492C4×C131—41no—
493C4×C131—42no—
494C4×C131—81no—
495C4×C131—81no—
496C4×C131C2×#12111yescharacteristic
497C4×C131#53411yescharacteristic
498C4×C131D4211yescharacteristic
499C4×C131#54611yescharacteristic
500C2×C131—42no—
501C2×C131—42no—
502C2×C131—44no—
503C2×C131—82no—
504C2×C131—82no—
505C2×C131—161no—
506C2×C131#241011yescharacteristic
507C2×C131#300311yescharacteristic
508C2×C131#300811yescharacteristic
509C2×C131#326411yescharacteristic
510C2×C131#327411yescharacteristic
511C2×C131#331811yescharacteristic
512C2×C131#332511yescharacteristic
513#24440C13111yesmaximal, characteristic, direct product factor, Sylow
514C131#2444011yescharacteristic, direct product factor, Sylow
515C2×D42C2×C13111yescharacteristic, complemented
516C2×#469C2×C13111yescharacteristic, complemented
517C2×#447C2×C13111yescharacteristic, complemented
518C2×#447C2×C13111yescharacteristic, complemented
519C2×#418C2×C13111yescharacteristic, complemented
520#2414C2×C13111yescharacteristic, complemented
521#2041C2×C13111yescharacteristic, complemented
522#2034C2×C13111yescharacteristic, complemented
523#2011C2×C13111yescharacteristic, complemented
524#1999C2×C13111yescharacteristic, complemented
525#1879C2×C13111yescharacteristic, complemented
526#1875C2×C13111yescharacteristic, complemented
527#1870C2×C13111yescharacteristic, complemented
528#1864C2×C13111yescharacteristic, complemented
529#1786C2×C13111yescharacteristic, complemented
530C23×D4—21no—
531C23×D4C22×C13111yescharacteristic
532C23×D4C22×C13111yescharacteristic
533C22×D8C22×C13111yescharacteristic
534C22×D8C22×C13111yescharacteristic, complemented
535C22×D8C22×C13111yescharacteristic, complemented
536C22×M16C22×C13111yescharacteristic, complemented
537D42—24no—
538D42—24no—
539C2×#127C22×C13111yescharacteristic
540C2×#121—21no—
541C2×#121C22×C13111yescharacteristic
542C2×#121C22×C13111yescharacteristic
543C2×#121C22×C13111yescharacteristic, complemented
544C2×#121C22×C13111yescharacteristic, complemented
545C2×#120—21no—
546C2×#120—21no—
547C2×C4×D4C22×C13111yescharacteristic
548C2×C4×D4C22×C13111yescharacteristic
549C2×#117C22×C13111yescharacteristic, complemented
550#469—24no—
551#447—24no—
552#447—24no—
553C2×#106C22×C13111yescharacteristic, complemented
554#418—24no—
555C2×#102C22×C13111yescharacteristic
556C2×#102C22×C13111yescharacteristic
557C2×#102C22×C13111yescharacteristic
558C2×#102C22×C13111yescharacteristic, complemented
559C2×#102C22×C13111yescharacteristic, complemented
560C2×#102C22×C13111yescharacteristic, complemented
561C2×#102C22×C13111yescharacteristic, complemented
562C2×#102C22×C13111yescharacteristic, complemented
563C2×#102C22×C13111yescharacteristic, complemented
564C2×#102C22×C13111yescharacteristic, complemented
565C2×C22⋊C8C22×C13111yescharacteristic, complemented
566C2×C22⋊C8C22×C13111yescharacteristic, complemented
567C2×C22⋊C8C22×C13111yescharacteristic, complemented
568#394—21no—
569#392—21no—
570#390—21no—
571#390C22×C13111yescharacteristic, complemented
572#389C22×C13111yescharacteristic, complemented
573#388—21no—
574#380C22×C13111yescharacteristic, complemented
575#340C22×C13111yescharacteristic, complemented
576#340C22×C13111yescharacteristic, complemented
577#336C22×C13111yescharacteristic, complemented
578#336C22×C13111yescharacteristic, complemented
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C13111yescharacteristic
604C22×D4D4×C13114yescomplemented
605C22×D4C23×C13111yescharacteristic
606C22×D4C23×C13111yescharacteristic
607C22×D4C23×C13111yescharacteristic
608C22×D4C23×C13111yescharacteristic
609C23×C4—21no—
610C23×C4C23×C13111yescharacteristic
611C23×C4C23×C13111yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C13111yescharacteristic
625C22×C8C23×C13111yescharacteristic
626C22×C8C23×C13111yescharacteristic
627C22×C8C23×C13111yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C13114yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C13111yescharacteristic
649C2×C4⋊C4C23×C13111yescharacteristic
650C2×C4⋊C4C23×C13111yescharacteristic
651C2×C4⋊C4C23×C13111yescharacteristic
652C2×C4⋊C4C23×C13111yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C13111yescharacteristic
663C2×C22⋊C4D4×C13111yescharacteristic
664C2×C42—21no—
665C2×C42C23×C13111yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C13114yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C13111yescharacteristic
701C24C2×D4×C13111yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C13112yes—
758C2×D4C2×D4×C13112yes—
759C2×D4C2×D4×C13112yes—
760C2×D4C2×D4×C13112yes—
761C2×D4#41×C13112yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C13111yescharacteristic
780C22×C4C2×D4×C13111yescharacteristic
781C22×C4C2×D4×C13111yescharacteristic
782C22×C4C2×D4×C13112yes—
783C22×C4C2×D4×C13112yes—
784C22×C4C2×D4×C13111yescharacteristic
785C22×C4C24×C13111yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C13112yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C13112yes—
811C4⋊C4C2×D4×C13112yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C13112yes—
881C23AGL(1,ℤ/8)×C13112yes—
882C23C22×D4×C13111yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C13114yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C13112yes—
940C2×C4AGL(1,ℤ/8)×C13112yes—
941C2×C4C22×D4×C13111yescharacteristic
942C2×C4C22×D4×C13111yescharacteristic
943C2×C4C22×D4×C13111yescharacteristic
944C2×C4C2×#41×C13111yescharacteristic
945C2×C4H(5,𝔽2)×C13111yescharacteristic
946C2×C4H(5,𝔽2)×C13111yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C13111yescharacteristic
996C22D42×C13111yescharacteristic
997C22#546×C13111yescharacteristic
998C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
999C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
1000C22#576×C13111yescharacteristic
1001C22#576×C13111yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—42no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C13111yescharacteristic
1011C4#534×C13111yescharacteristic
1012C4D42×C13111yescharacteristic
1013C4#546×C13111yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2#2410×C13111yescharacteristic
1021C2#3003×C13111yescharacteristic
1022C2#3008×C13111yescharacteristic
1023C2#3264×C13111yescharacteristic
1024C2#3274×C13111yescharacteristic
1025C2#3318×C13111yescharacteristic
1026C2#3325×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×D42×C131C2semidirect
2. C2×#469×C131C2semidirect
3. C2×#447×C131C2semidirect
4. C2×#447×C131C2semidirect
5. C2×#418×C131C2semidirect
6. #2414×C131C2semidirect
7. #2041×C131C2semidirect
8. #2034×C131C2semidirect
9. #2011×C131C2semidirect
10. #1999×C131C2semidirect
11. #1879×C131C2semidirect
12. #1875×C131C2semidirect
13. #1870×C131C2semidirect
14. #1864×C131C2semidirect
15. #1786×C131C2semidirect
20. C22×D8×C131C22semidirect
21. C22×D8×C131C22semidirect
22. C22×M16×C131C22semidirect
29. C2×#121×C131C22semidirect
30. C2×#121×C131C22semidirect
35. C2×#117×C131C22semidirect
39. C2×#106×C131C22semidirect
44. C2×#102×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
57. #390×C131C22semidirect
58. #389×C131C22semidirect
60. #380×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
90. C22×D4×C131D4semidirect
124. #121×C131D4semidirect
162. #102×C131D4semidirect
287. C2×C8×C131C2×D4semidirect
297. C4⋊C4×C131C2×D4semidirect
513. #24440C131direct (N × H)
514. C131#24440direct (N × H)
515. C2×D42C2×C131semidirect
516. C2×#469C2×C131semidirect
517. C2×#447C2×C131semidirect
518. C2×#447C2×C131semidirect
519. C2×#418C2×C131semidirect
520. #2414C2×C131semidirect
521. #2041C2×C131semidirect
522. #2034C2×C131semidirect
523. #2011C2×C131semidirect
524. #1999C2×C131semidirect
525. #1879C2×C131semidirect
526. #1875C2×C131semidirect
527. #1870C2×C131semidirect
528. #1864C2×C131semidirect
529. #1786C2×C131semidirect
534. C22×D8C22×C131semidirect
535. C22×D8C22×C131semidirect
536. C22×M16C22×C131semidirect
543. C2×#121C22×C131semidirect
544. C2×#121C22×C131semidirect
549. C2×#117C22×C131semidirect
553. C2×#106C22×C131semidirect
558. C2×#102C22×C131semidirect
559. C2×#102C22×C131semidirect
560. C2×#102C22×C131semidirect
561. C2×#102C22×C131semidirect
562. C2×#102C22×C131semidirect
563. C2×#102C22×C131semidirect
564. C2×#102C22×C131semidirect
565. C2×C22⋊C8C22×C131semidirect
566. C2×C22⋊C8C22×C131semidirect
567. C2×C22⋊C8C22×C131semidirect
571. #390C22×C131semidirect
572. #389C22×C131semidirect
574. #380C22×C131semidirect
575. #340C22×C131semidirect
576. #340C22×C131semidirect
577. #336C22×C131semidirect
578. #336C22×C131semidirect
604. C22×D4D4×C131semidirect
638. #121D4×C131semidirect
676. #102D4×C131semidirect
801. C2×C8C2×D4×C131semidirect
811. C4⋊C4C2×D4×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×#469×C1312
C2×#447×C1312
C2×#418×C1312
#2414×C1312
#2041×C1312
#2034×C1312
#2011×C1312
#1999×C1312
#1879×C1312
#1875×C1312
#1870×C1312
#1864×C1312
#1786×C1312
#24440131