Finite Group Databasebeta

← C131×#24424 #45710308

Subgroups — C131×#24424 #45710308

Order 33536.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C131C211yesmaximal, characteristic, complemented
2C2×#466×C131C211yesmaximal, characteristic, complemented
3C2×#447×C131C211yesmaximal, characteristic, complemented
4C2×#447×C131C211yesmaximal, characteristic, complemented
5C22×#102×C131C211yesmaximal, characteristic, complemented
6#2416×C131C211yesmaximal, characteristic, complemented
7#2041×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2011×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1879×C131C211yesmaximal, characteristic, complemented
12#1874×C131C211yesmaximal, characteristic, complemented
13#1869×C131C211yesmaximal, characteristic, complemented
14#1862×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
22C23×C8×C131C2211yescharacteristic, complemented
23D42×C131—24no—
24D42×C131—24no—
25C2×#127×C131C2211yescharacteristic
26C2×#121×C131—21no—
27C2×#121×C131—21no—
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#121×C131C2211yescharacteristic, complemented
31C2×#121×C131C2211yescharacteristic, complemented
32C2×#120×C131—21no—
33C2×#120×C131—21no—
34C2×C4×D4×C131C2211yescharacteristic
35C2×C4×D4×C131C2211yescharacteristic
36C22×C4⋊C4×C131C2211yescharacteristic, complemented
37#466×C131—24no—
38#447×C131—24no—
39#447×C131—24no—
40C2×#107×C131C2211yescharacteristic, complemented
41C2×#102×C131—24no—
42C2×#102×C131C2211yescharacteristic
43C2×#102×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic, complemented
46C2×#102×C131C2211yescharacteristic, complemented
47C2×#102×C131C2211yescharacteristic, complemented
48C2×#102×C131C2211yescharacteristic, complemented
49C2×#102×C131C2211yescharacteristic, complemented
50C2×#102×C131C2211yescharacteristic, complemented
51C2×#102×C131C2211yescharacteristic, complemented
52C2×C22⋊C8×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic, complemented
54C2×C22⋊C8×C131C2211yescharacteristic, complemented
55#396×C131—21no—
56#394×C131—21no—
57#390×C131C2211yescharacteristic, complemented
58#389×C131C2211yescharacteristic, complemented
59#386×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×C131—21no—
97C23×C4×C131C2311yescharacteristic
98C23×C4×C131C2311yescharacteristic
99C2×D8×C131—22no—
100C2×D8×C131—22no—
101C2×D8×C131—22no—
102C2×D8×C131—22no—
103C2×D8×C131—22no—
104C2×D8×C131—22no—
105C2×D8×C131—41no—
106C2×D8×C131—41no—
107C2×D8×C131—41no—
108C22×C8×C131—22no—
109C22×C8×C131—22no—
110C22×C8×C131—41no—
111C22×C8×C131C2311yescharacteristic
112C22×C8×C131C2311yescharacteristic
113C22×C8×C131C2311yescharacteristic
114C22×C8×C131C2311yescharacteristic
115#127×C131—22no—
116#127×C131—22no—
117#121×C131—28no—
118#121×C131—22no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131—22no—
122#121×C131—22no—
123#121×C131—22no—
124#121×C131—41no—
125#121×C131—44no—
126#121×C131D414yescomplemented
127#120×C131—28no—
128#120×C131—28no—
129C4×D4×C131—22no—
130C4×D4×C131—22no—
131C4×D4×C131—22no—
132C4×D4×C131—22no—
133C2×C4⋊C4×C131—22no—
134C2×C4⋊C4×C131—21no—
135C2×C4⋊C4×C131—21no—
136C2×C4⋊C4×C131—41no—
137C2×C4⋊C4×C131D411yescharacteristic
138C2×C4⋊C4×C131C2311yescharacteristic
139C2×C4⋊C4×C131C2311yescharacteristic
140C2×C4⋊C4×C131C2311yescharacteristic
141C2×C4⋊C4×C131C2311yescharacteristic
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×C131—21no—
149C2×C22⋊C4×C131—21no—
150C2×C22⋊C4×C131D411yescharacteristic
151C2×C22⋊C4×C131D411yescharacteristic
152C2×C42×C131C2311yescharacteristic
153#107×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—22no—
162#102×C131—41no—
163#102×C131D414yescomplemented
164C22⋊C8×C131—22no—
165C22⋊C8×C131—22no—
166C22⋊C8×C131—41no—
167#95×C131—21no—
168#95×C131—21no—
169C24×C131—21no—
170C24×C131—24no—
171C24×C131—21no—
172C24×C131—21no—
173C24×C131—24no—
174C24×C131—21no—
175C24×C131—42no—
176C24×C131—42no—
177C24×C131—42no—
178C24×C131—42no—
179C24×C131—42no—
180C24×C131—42no—
181C24×C131—42no—
182C24×C131—42no—
183C24×C131—81no—
184C24×C131—81no—
185C24×C131—81no—
186C24×C131—81no—
187C24×C131C2×D411yescharacteristic
188C24×C131C2×D411yescharacteristic
189C2×D4×C131—22no—
190C2×D4×C131—22no—
191C2×D4×C131—28no—
192C2×D4×C131—24no—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—24no—
196C2×D4×C131—24no—
197C2×D4×C131—24no—
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—42no—
239C2×D4×C131—42no—
240C2×D4×C131—81no—
241C2×D4×C131—81no—
242C2×D4×C131—81no—
243C2×D4×C131D814yescomplemented
244C2×D4×C131C2×D412yes—
245C2×D4×C131C2×D412yes—
246C2×D4×C131C2×D412yes—
247C2×D4×C131C2×D412yes—
248C2×D4×C131#4112yes—
249C22×C4×C131—21no—
250C22×C4×C131—21no—
251C22×C4×C131—21no—
252C22×C4×C131—21no—
253C22×C4×C131—24no—
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—21no—
264C22×C4×C131—42no—
265C22×C4×C131—42no—
266C22×C4×C131—42no—
267C22×C4×C131—42no—
268C22×C4×C131—81no—
269C22×C4×C131C2×D411yescharacteristic
270C22×C4×C131C2×D411yescharacteristic
271C22×C4×C131C2×D411yescharacteristic
272C22×C4×C131C2×D412yes—
273C22×C4×C131C2×D412yes—
274C22×C4×C131C2×D411yescharacteristic
275C22×C4×C131C2411yescharacteristic
276D8×C131—44no—
277D8×C131—44no—
278D8×C131—44no—
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×C131—21no—
288C2×C8×C131—21no—
289C2×C8×C131—21no—
290C2×C8×C131—44no—
291C2×C8×C131C2×D412yescomplemented
292C4⋊C4×C131—22no—
293C4⋊C4×C131—21no—
294C4⋊C4×C131—21no—
295C4⋊C4×C131—21no—
296C4⋊C4×C131—21no—
297C4⋊C4×C131—21no—
298C4⋊C4×C131—21no—
299C4⋊C4×C131—42no—
300C4⋊C4×C131—42no—
301C4⋊C4×C131C2×D412yes—
302C4⋊C4×C131C2×D412yescomplemented
303C22⋊C4×C131—24no—
304C22⋊C4×C131—24no—
305C22⋊C4×C131—22no—
306C22⋊C4×C131—24no—
307C22⋊C4×C131—22no—
308C22⋊C4×C131—42no—
309C22⋊C4×C131—42no—
310C22⋊C4×C131—42no—
311C22⋊C4×C131—42no—
312C22⋊C4×C131—81no—
313C42×C131—21no—
314C42×C131—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—21no—
318C23×C131—21no—
319C23×C131—21no—
320C23×C131—22no—
321C23×C131—21no—
322C23×C131—22no—
323C23×C131—21no—
324C23×C131—22no—
325C23×C131—21no—
326C23×C131—21no—
327C23×C131—21no—
328C23×C131—22no—
329C23×C131—22no—
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—48no—
350C23×C131—41no—
351C23×C131—41no—
352C23×C131—41no—
353C23×C131—41no—
354C23×C131—41no—
355C23×C131—41no—
356C23×C131—41no—
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—84no—
367C23×C131#12012yes—
368C23×C131C2×D812yes—
369C23×C131C2×D812yes—
370C23×C131AGL(1,ℤ/8)12yes—
371C23×C131C22×D411yescharacteristic
372D4×C131—28no—
373D4×C131—22no—
374D4×C131—22no—
375D4×C131—22no—
376D4×C131—22no—
377D4×C131—22no—
378D4×C131—22no—
379D4×C131—22no—
380D4×C131—48no—
381D4×C131—48no—
382D4×C131—48no—
383D4×C131—48no—
384D4×C131—48no—
385D4×C131—41no—
386D4×C131—41no—
387D4×C131—41no—
388D4×C131—41no—
389D4×C131—41no—
390D4×C131—41no—
391D4×C131—41no—
392D4×C131—41no—
393D4×C131—84no—
394D4×C131—84no—
395D4×C131—84no—
396D4×C131#12114yescomplemented
397C2×C4×C131—21no—
398C2×C4×C131—21no—
399C2×C4×C131—21no—
400C2×C4×C131—21no—
401C2×C4×C131—22no—
402C2×C4×C131—22no—
403C2×C4×C131—22no—
404C2×C4×C131—22no—
405C2×C4×C131—21no—
406C2×C4×C131—21no—
407C2×C4×C131—22no—
408C2×C4×C131—21no—
409C2×C4×C131—22no—
410C2×C4×C131—21no—
411C2×C4×C131—21no—
412C2×C4×C131—21no—
413C2×C4×C131—48no—
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—41no—
426C2×C4×C131—41no—
427C2×C4×C131—41no—
428C2×C4×C131—84no—
429C2×C4×C131#12012yes—
430C2×C4×C131C2×D812yes—
431C2×C4×C131C22×D411yescharacteristic
432C2×C4×C131C22×D411yescharacteristic
433C2×C4×C131C22×D411yescharacteristic
434C2×C4×C131C2×#4111yescharacteristic
435C2×C4×C131H(5,𝔽2)11yescharacteristic
436C2×C4×C131H(5,𝔽2)11yescharacteristic
437C8×C131—22no—
438C8×C131—41no—
439C8×C131—41no—
440C8×C131—41no—
441C22×C131—22no—
442C22×C131—22no—
443C22×C131—22no—
444C22×C131—22no—
445C22×C131—22no—
446C22×C131—22no—
447C22×C131—24no—
448C22×C131—22no—
449C22×C131—22no—
450C22×C131—22no—
451C22×C131—41no—
452C22×C131—42no—
453C22×C131—41no—
454C22×C131—42no—
455C22×C131—41no—
456C22×C131—42no—
457C22×C131—42no—
458C22×C131—42no—
459C22×C131—41no—
460C22×C131—42no—
461C22×C131—42no—
462C22×C131—42no—
463C22×C131—42no—
464C22×C131—42no—
465C22×C131—42no—
466C22×C131—42no—
467C22×C131—816no—
468C22×C131—816no—
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×C131—81no—
482C22×C131—81no—
483C22×C131—81no—
484C22×C131#44714yescomplemented
485C22×C131C2×#12011yescharacteristic
486C22×C131D4211yescharacteristic
487C22×C131#54611yescharacteristic
488C22×C131C22×D811yescharacteristic
489C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
490C22×C131#57611yescharacteristic
491C22×C131#57711yescharacteristic
492C4×C131—22no—
493C4×C131—22no—
494C4×C131—41no—
495C4×C131—42no—
496C4×C131—41no—
497C4×C131—42no—
498C4×C131—81no—
499C4×C131—81no—
500C4×C131C2×#12111yescharacteristic
501C4×C131#53411yescharacteristic
502C4×C131D4211yescharacteristic
503C4×C131#54611yescharacteristic
504C2×C131—24no—
505C2×C131—42no—
506C2×C131—44no—
507C2×C131—82no—
508C2×C131—82no—
509C2×C131—161no—
510C2×C131#241011yescharacteristic
511C2×C131C2×#44711yescharacteristic
512C2×C131#301211yescharacteristic
513C2×C131#326511yescharacteristic
514C2×C131D4×D811yescharacteristic
515C2×C131#329411yescharacteristic
516C2×C131#331811yescharacteristic
517#24424C13111yesmaximal, characteristic, direct product factor, Sylow
518C131#2442411yescharacteristic, direct product factor, Sylow
519C2×D42C2×C13111yescharacteristic, complemented
520C2×#466C2×C13111yescharacteristic, complemented
521C2×#447C2×C13111yescharacteristic, complemented
522C2×#447C2×C13111yescharacteristic, complemented
523C22×#102C2×C13111yescharacteristic, complemented
524#2416C2×C13111yescharacteristic, complemented
525#2041C2×C13111yescharacteristic, complemented
526#2033C2×C13111yescharacteristic, complemented
527#2011C2×C13111yescharacteristic, complemented
528#1999C2×C13111yescharacteristic, complemented
529#1879C2×C13111yescharacteristic, complemented
530#1874C2×C13111yescharacteristic, complemented
531#1869C2×C13111yescharacteristic, complemented
532#1862C2×C13111yescharacteristic, complemented
533#1786C2×C13111yescharacteristic, complemented
534C23×D4—21no—
535C23×D4C22×C13111yescharacteristic
536C23×D4C22×C13111yescharacteristic
537C22×D8C22×C13111yescharacteristic
538C22×D8C22×C13111yescharacteristic, complemented
539C22×D8C22×C13111yescharacteristic, complemented
540C23×C8C22×C13111yescharacteristic, complemented
541D42—24no—
542D42—24no—
543C2×#127C22×C13111yescharacteristic
544C2×#121—21no—
545C2×#121—21no—
546C2×#121C22×C13111yescharacteristic
547C2×#121C22×C13111yescharacteristic
548C2×#121C22×C13111yescharacteristic, complemented
549C2×#121C22×C13111yescharacteristic, complemented
550C2×#120—21no—
551C2×#120—21no—
552C2×C4×D4C22×C13111yescharacteristic
553C2×C4×D4C22×C13111yescharacteristic
554C22×C4⋊C4C22×C13111yescharacteristic, complemented
555#466—24no—
556#447—24no—
557#447—24no—
558C2×#107C22×C13111yescharacteristic, complemented
559C2×#102—24no—
560C2×#102C22×C13111yescharacteristic
561C2×#102C22×C13111yescharacteristic
562C2×#102C22×C13111yescharacteristic
563C2×#102C22×C13111yescharacteristic, complemented
564C2×#102C22×C13111yescharacteristic, complemented
565C2×#102C22×C13111yescharacteristic, complemented
566C2×#102C22×C13111yescharacteristic, complemented
567C2×#102C22×C13111yescharacteristic, complemented
568C2×#102C22×C13111yescharacteristic, complemented
569C2×#102C22×C13111yescharacteristic, complemented
570C2×C22⋊C8C22×C13111yescharacteristic, complemented
571C2×C22⋊C8C22×C13111yescharacteristic, complemented
572C2×C22⋊C8C22×C13111yescharacteristic, complemented
573#396—21no—
574#394—21no—
575#390C22×C13111yescharacteristic, complemented
576#389C22×C13111yescharacteristic, complemented
577#386—21no—
578#380C22×C13111yescharacteristic, complemented
579#340C22×C13111yescharacteristic, complemented
580#340C22×C13111yescharacteristic, complemented
581#336C22×C13111yescharacteristic, complemented
582#336C22×C13111yescharacteristic, complemented
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C13111yescharacteristic
608C22×D4D4×C13114yescomplemented
609C22×D4C23×C13111yescharacteristic
610C22×D4C23×C13111yescharacteristic
611C22×D4C23×C13111yescharacteristic
612C22×D4C23×C13111yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C13111yescharacteristic
616C23×C4C23×C13111yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C13111yescharacteristic
630C22×C8C23×C13111yescharacteristic
631C22×C8C23×C13111yescharacteristic
632C22×C8C23×C13111yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C13114yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C13111yescharacteristic
656C2×C4⋊C4C23×C13111yescharacteristic
657C2×C4⋊C4C23×C13111yescharacteristic
658C2×C4⋊C4C23×C13111yescharacteristic
659C2×C4⋊C4C23×C13111yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C13111yescharacteristic
669C2×C22⋊C4D4×C13111yescharacteristic
670C2×C42C23×C13111yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C13114yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C13111yescharacteristic
706C24C2×D4×C13111yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
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—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C13114yescomplemented
762C2×D4C2×D4×C13112yes—
763C2×D4C2×D4×C13112yes—
764C2×D4C2×D4×C13112yes—
765C2×D4C2×D4×C13112yes—
766C2×D4#41×C13112yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C13111yescharacteristic
788C22×C4C2×D4×C13111yescharacteristic
789C22×C4C2×D4×C13111yescharacteristic
790C22×C4C2×D4×C13112yes—
791C22×C4C2×D4×C13112yes—
792C22×C4C2×D4×C13111yescharacteristic
793C22×C4C24×C13111yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C13112yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C13112yes—
820C4⋊C4C2×D4×C13112yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—48no—
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—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C13112yes—
886C23C2×D8×C13112yes—
887C23C2×D8×C13112yes—
888C23AGL(1,ℤ/8)×C13112yes—
889C23C22×D4×C13111yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C13114yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C13112yes—
948C2×C4C2×D8×C13112yes—
949C2×C4C22×D4×C13111yescharacteristic
950C2×C4C22×D4×C13111yescharacteristic
951C2×C4C22×D4×C13111yescharacteristic
952C2×C4C2×#41×C13111yescharacteristic
953C2×C4H(5,𝔽2)×C13111yescharacteristic
954C2×C4H(5,𝔽2)×C13111yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—24no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—41no—
977C22—42no—
978C22—41no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22#447×C13114yescomplemented
1003C22C2×#120×C13111yescharacteristic
1004C22D42×C13111yescharacteristic
1005C22#546×C13111yescharacteristic
1006C22C22×D8×C13111yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
1008C22#576×C13111yescharacteristic
1009C22#577×C13111yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—42no—
1013C4—41no—
1014C4—42no—
1015C4—41no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C13111yescharacteristic
1019C4#534×C13111yescharacteristic
1020C4D42×C13111yescharacteristic
1021C4#546×C13111yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2#2410×C13111yescharacteristic
1029C2C2×#447×C13111yescharacteristic
1030C2#3012×C13111yescharacteristic
1031C2#3265×C13111yescharacteristic
1032C2D4×D8×C13111yescharacteristic
1033C2#3294×C13111yescharacteristic
1034C2#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×D42×C131C2semidirect
2. C2×#466×C131C2semidirect
3. C2×#447×C131C2semidirect
4. C2×#447×C131C2semidirect
5. C22×#102×C131C2semidirect
6. #2416×C131C2semidirect
7. #2041×C131C2semidirect
8. #2033×C131C2semidirect
9. #2011×C131C2semidirect
10. #1999×C131C2semidirect
11. #1879×C131C2semidirect
12. #1874×C131C2semidirect
13. #1869×C131C2semidirect
14. #1862×C131C2semidirect
15. #1786×C131C2semidirect
20. C22×D8×C131C22semidirect
21. C22×D8×C131C22semidirect
22. C23×C8×C131C22semidirect
30. C2×#121×C131C22semidirect
31. C2×#121×C131C22semidirect
36. C22×C4⋊C4×C131C22semidirect
40. C2×#107×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×#102×C131C22semidirect
52. C2×C22⋊C8×C131C22semidirect
53. C2×C22⋊C8×C131C22semidirect
54. 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
126. #121×C131D4semidirect
163. #102×C131D4semidirect
243. C2×D4×C131D8semidirect
291. C2×C8×C131C2×D4semidirect
302. C4⋊C4×C131C2×D4semidirect
396. D4×C131#121semidirect
484. C22×C131#447semidirect
517. #24424C131direct (N × H)
518. C131#24424direct (N × H)
519. C2×D42C2×C131semidirect
520. C2×#466C2×C131semidirect
521. C2×#447C2×C131semidirect
522. C2×#447C2×C131semidirect
523. C22×#102C2×C131semidirect
524. #2416C2×C131semidirect
525. #2041C2×C131semidirect
526. #2033C2×C131semidirect
527. #2011C2×C131semidirect
528. #1999C2×C131semidirect
529. #1879C2×C131semidirect
530. #1874C2×C131semidirect
531. #1869C2×C131semidirect
532. #1862C2×C131semidirect
533. #1786C2×C131semidirect
538. C22×D8C22×C131semidirect
539. C22×D8C22×C131semidirect
540. C23×C8C22×C131semidirect
548. C2×#121C22×C131semidirect
549. C2×#121C22×C131semidirect
554. C22×C4⋊C4C22×C131semidirect
558. C2×#107C22×C131semidirect
563. C2×#102C22×C131semidirect
564. C2×#102C22×C131semidirect
565. C2×#102C22×C131semidirect
566. C2×#102C22×C131semidirect
567. C2×#102C22×C131semidirect
568. C2×#102C22×C131semidirect
569. C2×#102C22×C131semidirect
570. C2×C22⋊C8C22×C131semidirect
571. C2×C22⋊C8C22×C131semidirect
572. C2×C22⋊C8C22×C131semidirect
575. #390C22×C131semidirect
576. #389C22×C131semidirect
578. #380C22×C131semidirect
579. #340C22×C131semidirect
580. #340C22×C131semidirect
581. #336C22×C131semidirect
582. #336C22×C131semidirect
608. C22×D4D4×C131semidirect
644. #121D4×C131semidirect
681. #102D4×C131semidirect
761. C2×D4D8×C131semidirect
809. C2×C8C2×D4×C131semidirect
820. C4⋊C4C2×D4×C131semidirect
914. D4#121×C131semidirect
1002. C22#447×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×#466×C1312
C2×#447×C1312
C22×#102×C1312
#2416×C1312
#2041×C1312
#2033×C1312
#2011×C1312
#1999×C1312
#1879×C1312
#1874×C1312
#1869×C1312
#1862×C1312
#1786×C1312
#24424131