Finite Group Databasebeta

← C131×#29600 #45715484

Subgroups — C131×#29600 #45715484

Order 33536.

1540 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#525×C131C211yesmaximal, characteristic, complemented
2C2×#482×C131C211yesmaximal, characteristic, complemented
3C2×#449×C131C211yesmaximal, characteristic, complemented
4#2847×C131C211yesmaximal, characteristic, complemented
5#2036×C131C211yesmaximal, characteristic, complemented
6#2035×C131C211yesmaximal, characteristic, complemented
7#2034×C131C211yesmaximal, characteristic, complemented
8#2033×C131C211yesmaximal, characteristic, complemented
9#2000×C131C211yesmaximal, characteristic, complemented
10#2000×C131C211yesmaximal, characteristic, complemented
11#1999×C131C211yesmaximal, characteristic, complemented
12#1999×C131C211yesmaximal, characteristic, complemented
13#1825×C131C211yesmaximal, characteristic, complemented
14#1788×C131C211yesmaximal, characteristic, complemented
15#1779×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic, complemented
19C22×D8×C131C2211yescharacteristic, complemented
20#525×C131—24no—
21#525×C131—24no—
22C2×#123×C131—21no—
23C2×C22⋊Q8×C131C2211yescharacteristic
24C2×C22⋊Q8×C131C2211yescharacteristic
25C2×#121×C131C2211yescharacteristic
26C2×#121×C131C2211yescharacteristic
27C2×#121×C131C2211yescharacteristic
28C2×#121×C131C2211yescharacteristic
29C2×#121×C131C2211yescharacteristic
30C2×#120×C131—21no—
31C2×#120×C131—21no—
32C2×C4×D4×C131—21no—
33C2×C4×D4×C131—21no—
34C2×#117×C131C2211yescharacteristic
35#482×C131—24no—
36#449×C131—24no—
37C2×#107×C131C2211yescharacteristic, complemented
38C2×#106×C131C2211yescharacteristic, complemented
39C2×#103×C131C2211yescharacteristic, complemented
40C2×#103×C131C2211yescharacteristic, complemented
41C2×#103×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
48C2×C22⋊C8×C131C2211yescharacteristic
49C2×C22⋊C8×C131C2211yescharacteristic
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53#386×C131—21no—
54#386×C131—21no—
55#386×C131—21no—
56#380×C131C2211yescharacteristic
57#380×C131C2211yescharacteristic
58#380×C131C2211yescharacteristic
59#340×C131C2211yescharacteristic, complemented
60#340×C131C2211yescharacteristic, complemented
61#340×C131C2211yescharacteristic, complemented
62#340×C131C2211yescharacteristic, complemented
63C25×C131D411yescharacteristic
64C2×#41×C131—22no—
65C2×#41×C131—41no—
66C2×#41×C131—41no—
67C2×#41×C131—41no—
68C2×#41×C131—41no—
69C2×#41×C131D414yescomplemented
70C22×Q8×C131C2311yescharacteristic
71C22×D4×C131—21no—
72C22×D4×C131—21no—
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—21no—
76C22×D4×C131—21no—
77C22×D4×C131C2311yescharacteristic
78C22×D4×C131C2311yescharacteristic
79C23×C4×C131—21no—
80C23×C4×C131—22no—
81C23×C4×C131—22no—
82C23×C4×C131—41no—
83C23×C4×C131—41no—
84C23×C4×C131—41no—
85C23×C4×C131—41no—
86C23×C4×C131D411yescharacteristic
87C23×C4×C131D411yescharacteristic
88C23×C4×C131D411yescharacteristic
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2311yescharacteristic
91C23×C4×C131C2311yescharacteristic
92C2×SD16×C131—22no—
93C2×SD16×C131—41no—
94C2×SD16×C131—41no—
95C2×D8×C131—22no—
96C2×D8×C131—41no—
97C2×D8×C131—41no—
98C22×C8×C131C2311yescharacteristic
99C22×C8×C131C2311yescharacteristic
100C22×C8×C131C2311yescharacteristic
101C22×C8×C131C2311yescharacteristic
102#123×C131—28no—
103C22⋊Q8×C131—22no—
104C22⋊Q8×C131—22no—
105C22⋊Q8×C131—22no—
106C22⋊Q8×C131—22no—
107#121×C131—22no—
108#121×C131—22no—
109#121×C131—22no—
110#121×C131—22no—
111#121×C131—22no—
112#121×C131—22no—
113#121×C131—41no—
114#121×C131—41no—
115#121×C131—41no—
116#121×C131—41no—
117#120×C131—28no—
118#120×C131—44no—
119C4×D4×C131—28no—
120C4×D4×C131—28no—
121#117×C131—22no—
122#117×C131D414yescomplemented
123C2×C4⋊C4×C131—21no—
124C2×C4⋊C4×C131—21no—
125C2×C4⋊C4×C131C2311yescharacteristic
126C2×C4⋊C4×C131C2311yescharacteristic
127C2×C4⋊C4×C131C2311yescharacteristic
128C2×C4⋊C4×C131C2311yescharacteristic
129C2×C4⋊C4×C131C2311yescharacteristic
130C2×C22⋊C4×C131—21no—
131C2×C22⋊C4×C131—21no—
132C2×C22⋊C4×C131—21no—
133C2×C22⋊C4×C131—21no—
134C2×C22⋊C4×C131—21no—
135C2×C22⋊C4×C131—21no—
136C2×C22⋊C4×C131—21no—
137C2×C22⋊C4×C131—21no—
138C2×C22⋊C4×C131—21no—
139C2×C22⋊C4×C131—21no—
140C2×C22⋊C4×C131—21no—
141C2×C42×C131—21no—
142#107×C131—22no—
143#106×C131—22no—
144#103×C131—22no—
145#103×C131—41no—
146#103×C131—41no—
147#102×C131—22no—
148#102×C131—22no—
149#102×C131—22no—
150#102×C131—41no—
151#102×C131—41no—
152C22⋊C8×C131—22no—
153C22⋊C8×C131—22no—
154C22⋊C8×C131—41no—
155C22⋊C8×C131—41no—
156C22⋊C8×C131—41no—
157C22⋊C8×C131—41no—
158#95×C131—21no—
159#95×C131—21no—
160#95×C131—21no—
161C24×C131—22no—
162C24×C131—22no—
163C24×C131—22no—
164C24×C131—21no—
165C24×C131—21no—
166C24×C131—41no—
167C24×C131—41no—
168C24×C131—41no—
169C24×C131—41no—
170C24×C131C2×D411yescharacteristic
171C24×C131C2×D411yescharacteristic
172C24×C131C2×D411yescharacteristic
173#41×C131—44no—
174#41×C131—44no—
175#41×C131—44no—
176#41×C131—44no—
177C2×Q8×C131—21no—
178C2×Q8×C131—21no—
179C2×Q8×C131—21no—
180C2×Q8×C131—21no—
181C2×Q8×C131—21no—
182C2×Q8×C131C2×D412yes—
183C2×D4×C131—24no—
184C2×D4×C131—24no—
185C2×D4×C131—24no—
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—42no—
198C2×D4×C131—42no—
199C2×D4×C131—42no—
200C2×D4×C131—42no—
201C2×D4×C131—42no—
202C2×D4×C131—42no—
203C2×D4×C131—42no—
204C2×D4×C131—42no—
205C2×D4×C131—42no—
206C2×D4×C131—42no—
207C2×D4×C131—42no—
208C2×D4×C131—42no—
209C2×D4×C131—42no—
210C2×D4×C131—42no—
211C2×D4×C131—42no—
212C2×D4×C131C2×D412yes—
213C22×C4×C131—21no—
214C22×C4×C131—21no—
215C22×C4×C131—21no—
216C22×C4×C131—21no—
217C22×C4×C131—22no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—22no—
222C22×C4×C131—22no—
223C22×C4×C131—24no—
224C22×C4×C131—21no—
225C22×C4×C131—21no—
226C22×C4×C131—21no—
227C22×C4×C131—21no—
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—41no—
240C22×C4×C131—41no—
241C22×C4×C131—41no—
242C22×C4×C131—41no—
243C22×C4×C131—41no—
244C22×C4×C131—41no—
245C22×C4×C131—44no—
246C22×C4×C131—44no—
247C22×C4×C131—44no—
248C22×C4×C131—44no—
249C22×C4×C131—42no—
250C22×C4×C131—42no—
251C22×C4×C131C2×D411yescharacteristic
252C22×C4×C131C2×D411yescharacteristic
253C22×C4×C131C2×D411yescharacteristic
254C22×C4×C131C2×D412yes—
255C22×C4×C131C2×D412yes—
256C22×C4×C131C2411yescharacteristic
257SD16×C131—44no—
258D8×C131—44no—
259C2×C8×C131—21no—
260C2×C8×C131—21no—
261C2×C8×C131—21no—
262C2×C8×C131—21no—
263C2×C8×C131—21no—
264C2×C8×C131—21no—
265C2×C8×C131—21no—
266C2×C8×C131—21no—
267C2×C8×C131—21no—
268C2×C8×C131—21no—
269C2×C8×C131—21no—
270C2×C8×C131—21no—
271C4⋊C4×C131—24no—
272C4⋊C4×C131—24no—
273C4⋊C4×C131—21no—
274C4⋊C4×C131—21no—
275C4⋊C4×C131—21no—
276C4⋊C4×C131—21no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131C2×D412yes—
282C4⋊C4×C131C2×D412yes—
283C22⋊C4×C131—24no—
284C22⋊C4×C131—24no—
285C22⋊C4×C131—24no—
286C22⋊C4×C131—24no—
287C22⋊C4×C131—24no—
288C22⋊C4×C131—42no—
289C22⋊C4×C131—42no—
290C22⋊C4×C131—42no—
291C22⋊C4×C131—42no—
292C22⋊C4×C131—42no—
293C22⋊C4×C131—42no—
294C42×C131—24no—
295C23×C131—21no—
296C23×C131—21no—
297C23×C131—21no—
298C23×C131—21no—
299C23×C131—21no—
300C23×C131—21no—
301C23×C131—21no—
302C23×C131—21no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—21no—
307C23×C131—21no—
308C23×C131—21no—
309C23×C131—21no—
310C23×C131—21no—
311C23×C131—21no—
312C23×C131—21no—
313C23×C131—22no—
314C23×C131—44no—
315C23×C131—44no—
316C23×C131—44no—
317C23×C131—44no—
318C23×C131—44no—
319C23×C131—44no—
320C23×C131—44no—
321C23×C131—41no—
322C23×C131—41no—
323C23×C131—41no—
324C23×C131—41no—
325C23×C131—41no—
326C23×C131—41no—
327C23×C131—41no—
328C23×C131—41no—
329C23×C131—41no—
330C23×C131—41no—
331C23×C131—41no—
332C23×C131—41no—
333C23×C131—41no—
334C23×C131#12012yes—
335C23×C131#13512yes—
336C23×C131AGL(1,ℤ/8)12yes—
337C23×C131C22×D411yescharacteristic
338Q8×C131—22no—
339Q8×C131—22no—
340Q8×C131—41no—
341Q8×C131—41no—
342D4×C131—22no—
343D4×C131—22no—
344D4×C131—48no—
345D4×C131—48no—
346D4×C131—48no—
347D4×C131—41no—
348D4×C131—41no—
349D4×C131—41no—
350D4×C131—41no—
351D4×C131—41no—
352D4×C131—41no—
353D4×C131—84no—
354D4×C131—84no—
355D4×C131—84no—
356C2×C4×C131—21no—
357C2×C4×C131—21no—
358C2×C4×C131—22no—
359C2×C4×C131—22no—
360C2×C4×C131—22no—
361C2×C4×C131—22no—
362C2×C4×C131—22no—
363C2×C4×C131—22no—
364C2×C4×C131—21no—
365C2×C4×C131—21no—
366C2×C4×C131—22no—
367C2×C4×C131—21no—
368C2×C4×C131—21no—
369C2×C4×C131—21no—
370C2×C4×C131—21no—
371C2×C4×C131—44no—
372C2×C4×C131—44no—
373C2×C4×C131—48no—
374C2×C4×C131—44no—
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—41no—
390C2×C4×C131—41no—
391C2×C4×C131—41no—
392C2×C4×C131—41no—
393C2×C4×C131—41no—
394C2×C4×C131—41no—
395C2×C4×C131—41no—
396C2×C4×C131—41no—
397C2×C4×C131—41no—
398C2×C4×C131#12012yes—
399C2×C4×C131C22×D411yescharacteristic
400C2×C4×C131C22×D411yescharacteristic
401C2×C4×C131H(5,𝔽2)11yescharacteristic
402C2×C4×C131H(5,𝔽2)11yescharacteristic
403C2×C4×C131H(5,𝔽2)11yescharacteristic
404C2×C4×C131H(5,𝔽2)11yescharacteristic
405C8×C131—41no—
406C8×C131—41no—
407C8×C131—41no—
408C8×C131—41no—
409C22×C131—22no—
410C22×C131—22no—
411C22×C131—22no—
412C22×C131—22no—
413C22×C131—22no—
414C22×C131—22no—
415C22×C131—22no—
416C22×C131—22no—
417C22×C131—22no—
418C22×C131—416no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—41no—
422C22×C131—41no—
423C22×C131—41no—
424C22×C131—41no—
425C22×C131—41no—
426C22×C131—41no—
427C22×C131—41no—
428C22×C131—41no—
429C22×C131—41no—
430C22×C131—41no—
431C22×C131—42no—
432C22×C131—42no—
433C22×C131—42no—
434C22×C131—81no—
435C22×C131—81no—
436C22×C131—81no—
437C22×C131—81no—
438C22×C131—81no—
439C22×C131—81no—
440C22×C131—81no—
441C22×C131—81no—
442C22×C131—81no—
443C22×C131—81no—
444C22×C131—81no—
445C22×C131C2×#12011yescharacteristic
446C22×C131#53411yescharacteristic
447C22×C131#53411yescharacteristic
448C22×C131C2×#13511yescharacteristic
449C22×C131C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C131#57511yescharacteristic
451C22×C131#57511yescharacteristic
452C4×C131—22no—
453C4×C131—41no—
454C4×C131—41no—
455C4×C131—42no—
456C4×C131—42no—
457C4×C131—42no—
458C4×C131—81no—
459C4×C131—81no—
460C4×C131—81no—
461C4×C131#53411yescharacteristic
462C4×C131#53411yescharacteristic
463C4×C131#53511yescharacteristic
464C4×C131#53511yescharacteristic
465C2×C131—42no—
466C2×C131—42no—
467C2×C131—42no—
468C2×C131—82no—
469C2×C131—161no—
470C2×C131#261311yescharacteristic
471C2×C131#300211yescharacteristic
472C2×C131#300611yescharacteristic
473C2×C131#318811yescharacteristic
474C2×C131#319111yescharacteristic
475C2×C131#319411yescharacteristic
476C2×C131#319711yescharacteristic
477#29600C13111yesmaximal, characteristic, direct product factor, Sylow
478C131#2960011yescharacteristic, direct product factor, Sylow
479C2×#525C2×C13111yescharacteristic, complemented
480C2×#482C2×C13111yescharacteristic, complemented
481C2×#449C2×C13111yescharacteristic, complemented
482#2847C2×C13111yescharacteristic, complemented
483#2036C2×C13111yescharacteristic, complemented
484#2035C2×C13111yescharacteristic, complemented
485#2034C2×C13111yescharacteristic, complemented
486#2033C2×C13111yescharacteristic, complemented
487#2000C2×C13111yescharacteristic, complemented
488#2000C2×C13111yescharacteristic, complemented
489#1999C2×C13111yescharacteristic, complemented
490#1999C2×C13111yescharacteristic, complemented
491#1825C2×C13111yescharacteristic, complemented
492#1788C2×C13111yescharacteristic, complemented
493#1779C2×C13111yescharacteristic, complemented
494C22×#41C22×C13111yescharacteristic
495C24×C4C22×C13111yescharacteristic
496C22×SD16C22×C13111yescharacteristic, complemented
497C22×D8C22×C13111yescharacteristic, complemented
498#525—24no—
499#525—24no—
500C2×#123—21no—
501C2×C22⋊Q8C22×C13111yescharacteristic
502C2×C22⋊Q8C22×C13111yescharacteristic
503C2×#121C22×C13111yescharacteristic
504C2×#121C22×C13111yescharacteristic
505C2×#121C22×C13111yescharacteristic
506C2×#121C22×C13111yescharacteristic
507C2×#121C22×C13111yescharacteristic
508C2×#120—21no—
509C2×#120—21no—
510C2×C4×D4—21no—
511C2×C4×D4—21no—
512C2×#117C22×C13111yescharacteristic
513#482—24no—
514#449—24no—
515C2×#107C22×C13111yescharacteristic, complemented
516C2×#106C22×C13111yescharacteristic, complemented
517C2×#103C22×C13111yescharacteristic, complemented
518C2×#103C22×C13111yescharacteristic, complemented
519C2×#103C22×C13111yescharacteristic, complemented
520C2×#102C22×C13111yescharacteristic, complemented
521C2×#102C22×C13111yescharacteristic, complemented
522C2×#102C22×C13111yescharacteristic, complemented
523C2×#102C22×C13111yescharacteristic, complemented
524C2×#102C22×C13111yescharacteristic, complemented
525C2×C22⋊C8C22×C13111yescharacteristic
526C2×C22⋊C8C22×C13111yescharacteristic
527C2×C22⋊C8C22×C13111yescharacteristic
528C2×C22⋊C8C22×C13111yescharacteristic
529C2×C22⋊C8C22×C13111yescharacteristic
530C2×C22⋊C8C22×C13111yescharacteristic
531#386—21no—
532#386—21no—
533#386—21no—
534#380C22×C13111yescharacteristic
535#380C22×C13111yescharacteristic
536#380C22×C13111yescharacteristic
537#340C22×C13111yescharacteristic, complemented
538#340C22×C13111yescharacteristic, complemented
539#340C22×C13111yescharacteristic, complemented
540#340C22×C13111yescharacteristic, complemented
541C25D4×C13111yescharacteristic
542C2×#41—22no—
543C2×#41—41no—
544C2×#41—41no—
545C2×#41—41no—
546C2×#41—41no—
547C2×#41D4×C13114yescomplemented
548C22×Q8C23×C13111yescharacteristic
549C22×D4—21no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—21no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4C23×C13111yescharacteristic
556C22×D4C23×C13111yescharacteristic
557C23×C4—21no—
558C23×C4—22no—
559C23×C4—22no—
560C23×C4—41no—
561C23×C4—41no—
562C23×C4—41no—
563C23×C4—41no—
564C23×C4D4×C13111yescharacteristic
565C23×C4D4×C13111yescharacteristic
566C23×C4D4×C13111yescharacteristic
567C23×C4C23×C13111yescharacteristic
568C23×C4C23×C13111yescharacteristic
569C23×C4C23×C13111yescharacteristic
570C2×SD16—22no—
571C2×SD16—41no—
572C2×SD16—41no—
573C2×D8—22no—
574C2×D8—41no—
575C2×D8—41no—
576C22×C8C23×C13111yescharacteristic
577C22×C8C23×C13111yescharacteristic
578C22×C8C23×C13111yescharacteristic
579C22×C8C23×C13111yescharacteristic
580#123—28no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585#121—22no—
586#121—22no—
587#121—22no—
588#121—22no—
589#121—22no—
590#121—22no—
591#121—41no—
592#121—41no—
593#121—41no—
594#121—41no—
595#120—28no—
596#120—44no—
597C4×D4—28no—
598C4×D4—28no—
599#117—22no—
600#117D4×C13114yescomplemented
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4C23×C13111yescharacteristic
604C2×C4⋊C4C23×C13111yescharacteristic
605C2×C4⋊C4C23×C13111yescharacteristic
606C2×C4⋊C4C23×C13111yescharacteristic
607C2×C4⋊C4C23×C13111yescharacteristic
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C42—21no—
620#107—22no—
621#106—22no—
622#103—22no—
623#103—41no—
624#103—41no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630C22⋊C8—22no—
631C22⋊C8—22no—
632C22⋊C8—41no—
633C22⋊C8—41no—
634C22⋊C8—41no—
635C22⋊C8—41no—
636#95—21no—
637#95—21no—
638#95—21no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—21no—
643C24—21no—
644C24—41no—
645C24—41no—
646C24—41no—
647C24—41no—
648C24C2×D4×C13111yescharacteristic
649C24C2×D4×C13111yescharacteristic
650C24C2×D4×C13111yescharacteristic
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8C2×D4×C13112yes—
661C2×D4—24no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4C2×D4×C13112yes—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—24no—
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—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—41no—
718C22×C4—41no—
719C22×C4—41no—
720C22×C4—41no—
721C22×C4—41no—
722C22×C4—41no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4C2×D4×C13111yescharacteristic
730C22×C4C2×D4×C13111yescharacteristic
731C22×C4C2×D4×C13111yescharacteristic
732C22×C4C2×D4×C13112yes—
733C22×C4C2×D4×C13112yes—
734C22×C4C24×C13111yescharacteristic
735SD16—44no—
736D8—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C4⋊C4—24no—
750C4⋊C4—24no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4C2×D4×C13112yes—
760C4⋊C4C2×D4×C13112yes—
761C22⋊C4—24no—
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—42no—
769C22⋊C4—42no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C42—24no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—22no—
792C23—44no—
793C23—44no—
794C23—44no—
795C23—44no—
796C23—44no—
797C23—44no—
798C23—44no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23#120×C13112yes—
813C23#135×C13112yes—
814C23AGL(1,ℤ/8)×C13112yes—
815C23C22×D4×C13111yescharacteristic
816Q8—22no—
817Q8—22no—
818Q8—41no—
819Q8—41no—
820D4—22no—
821D4—22no—
822D4—48no—
823D4—48no—
824D4—48no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—41no—
831D4—84no—
832D4—84no—
833D4—84no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—22no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—44no—
850C2×C4—44no—
851C2×C4—48no—
852C2×C4—44no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4#120×C13112yes—
877C2×C4C22×D4×C13111yescharacteristic
878C2×C4C22×D4×C13111yescharacteristic
879C2×C4H(5,𝔽2)×C13111yescharacteristic
880C2×C4H(5,𝔽2)×C13111yescharacteristic
881C2×C4H(5,𝔽2)×C13111yescharacteristic
882C2×C4H(5,𝔽2)×C13111yescharacteristic
883C8—41no—
884C8—41no—
885C8—41no—
886C8—41no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—416no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—41no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22C2×#120×C13111yescharacteristic
924C22#534×C13111yescharacteristic
925C22#534×C13111yescharacteristic
926C22C2×#135×C13111yescharacteristic
927C22C2×AGL(1,ℤ/8)×C13111yescharacteristic
928C22#575×C13111yescharacteristic
929C22#575×C13111yescharacteristic
930C4—22no—
931C4—42no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—81no—
939C4#534×C13111yescharacteristic
940C4#534×C13111yescharacteristic
941C4#535×C13111yescharacteristic
942C4#535×C13111yescharacteristic
943C2—42no—
944C2—42no—
945C2—42no—
946C2—82no—
947C2—161no—
948C2#2613×C13111yescharacteristic
949C2#3002×C13111yescharacteristic
950C2#3006×C13111yescharacteristic
951C2#3188×C13111yescharacteristic
952C2#3191×C13111yescharacteristic
953C2#3194×C13111yescharacteristic
954C2#3197×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C24×C4×C131 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#525×C131C2semidirect
2. C2×#482×C131C2semidirect
3. C2×#449×C131C2semidirect
4. #2847×C131C2semidirect
5. #2036×C131C2semidirect
6. #2035×C131C2semidirect
7. #2034×C131C2semidirect
8. #2033×C131C2semidirect
9. #2000×C131C2semidirect
10. #2000×C131C2semidirect
11. #1999×C131C2semidirect
12. #1999×C131C2semidirect
13. #1825×C131C2semidirect
14. #1788×C131C2semidirect
15. #1779×C131C2semidirect
18. C22×SD16×C131C22semidirect
19. C22×D8×C131C22semidirect
37. C2×#107×C131C22semidirect
38. C2×#106×C131C22semidirect
39. C2×#103×C131C22semidirect
40. C2×#103×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#102×C131C22semidirect
43. C2×#102×C131C22semidirect
44. C2×#102×C131C22semidirect
45. C2×#102×C131C22semidirect
46. C2×#102×C131C22semidirect
59. #340×C131C22semidirect
60. #340×C131C22semidirect
61. #340×C131C22semidirect
62. #340×C131C22semidirect
69. C2×#41×C131D4semidirect
122. #117×C131D4semidirect
477. #29600C131direct (N × H)
478. C131#29600direct (N × H)
479. C2×#525C2×C131semidirect
480. C2×#482C2×C131semidirect
481. C2×#449C2×C131semidirect
482. #2847C2×C131semidirect
483. #2036C2×C131semidirect
484. #2035C2×C131semidirect
485. #2034C2×C131semidirect
486. #2033C2×C131semidirect
487. #2000C2×C131semidirect
488. #2000C2×C131semidirect
489. #1999C2×C131semidirect
490. #1999C2×C131semidirect
491. #1825C2×C131semidirect
492. #1788C2×C131semidirect
493. #1779C2×C131semidirect
496. C22×SD16C22×C131semidirect
497. C22×D8C22×C131semidirect
515. C2×#107C22×C131semidirect
516. C2×#106C22×C131semidirect
517. C2×#103C22×C131semidirect
518. C2×#103C22×C131semidirect
519. C2×#103C22×C131semidirect
520. C2×#102C22×C131semidirect
521. C2×#102C22×C131semidirect
522. C2×#102C22×C131semidirect
523. C2×#102C22×C131semidirect
524. C2×#102C22×C131semidirect
537. #340C22×C131semidirect
538. #340C22×C131semidirect
539. #340C22×C131semidirect
540. #340C22×C131semidirect
547. C2×#41D4×C131semidirect
600. #117D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#525×C1312
C2×#482×C1312
C2×#449×C1312
#2847×C1312
#2036×C1312
#2035×C1312
#2034×C1312
#2033×C1312
#2000×C1312
#1999×C1312
#1825×C1312
#1788×C1312
#1779×C1312
#29600131