Finite Group Databasebeta

← C131×#24218 #45710102

Subgroups — C131×#24218 #45710102

Order 33536.

1612 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#535×C131C211yesmaximal, characteristic, complemented
2C2×#463×C131C211yesmaximal, characteristic, complemented
3C2×#459×C131C211yesmaximal, characteristic, complemented
4C2×#449×C131C211yesmaximal, characteristic, complemented
5C2×#447×C131C211yesmaximal, characteristic, complemented
6#2324×C131C211yesmaximal, characteristic, complemented
7#2042×C131C211yesmaximal, characteristic, complemented
8#2041×C131C211yesmaximal, characteristic, complemented
9#2012×C131C211yesmaximal, characteristic, complemented
10#2011×C131C211yesmaximal, characteristic, complemented
11#1983×C131C211yesmaximal, characteristic, complemented
12#1982×C131C211yesmaximal, characteristic, complemented
13#1798×C131C211yesmaximal, characteristic, complemented
14#1788×C131C211yesmaximal, characteristic, complemented
15#1786×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C23×D4×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic, complemented
19C22×D8×C131C2211yescharacteristic
20C22×D8×C131C2211yescharacteristic
21C22×D8×C131C2211yescharacteristic, complemented
22#535×C131—24no—
23#535×C131—24no—
24C2×#127×C131C2211yescharacteristic
25C2×#127×C131C2211yescharacteristic
26C2×#124×C131C2211yescharacteristic
27C2×#124×C131C2211yescharacteristic
28C2×#121×C131—21no—
29C2×#121×C131—21no—
30C2×#121×C131C2211yescharacteristic
31C2×#120×C131—21no—
32C2×#120×C131—21no—
33C2×C4×D4×C131C2211yescharacteristic, complemented
34C2×#117×C131C2211yescharacteristic
35#463×C131—24no—
36#459×C131—24no—
37#449×C131—24no—
38#447×C131—24no—
39C2×C4⋊C8×C131C2211yescharacteristic, complemented
40C2×C4⋊C8×C131C2211yescharacteristic, complemented
41C2×#103×C131C2211yescharacteristic, complemented
42C2×#103×C131C2211yescharacteristic, complemented
43C2×#103×C131C2211yescharacteristic, complemented
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49C2×#102×C131C2211yescharacteristic
50C2×#102×C131C2211yescharacteristic, complemented
51C2×#102×C131C2211yescharacteristic, complemented
52C2×#102×C131C2211yescharacteristic, complemented
53C2×C22⋊C8×C131C2211yescharacteristic
54C2×C22⋊C8×C131C2211yescharacteristic
55#390×C131—21no—
56#390×C131C2211yescharacteristic, complemented
57#389×C131C2211yescharacteristic, complemented
58#388×C131—21no—
59#386×C131—21no—
60#385×C131—21no—
61#380×C131C2211yescharacteristic
62C4×C4⋊C4×C131C2211yescharacteristic, complemented
63#336×C131C2211yescharacteristic, complemented
64#336×C131C2211yescharacteristic, complemented
65C25×C131—21no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—41no—
71C2×#41×C131—41no—
72C22×Q8×C131C2311yescharacteristic
73C22×D4×C131—21no—
74C22×D4×C131—21no—
75C22×D4×C131—22no—
76C22×D4×C131—22no—
77C22×D4×C131—21no—
78C22×D4×C131—21no—
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—22no—
83C22×D4×C131—22no—
84C22×D4×C131—41no—
85C22×D4×C131—41no—
86C22×D4×C131C2311yescharacteristic
87C22×D4×C131C2311yescharacteristic
88C22×D4×C131C2311yescharacteristic
89C22×D4×C131C2311yescharacteristic
90C23×C4×C131—21no—
91C23×C4×C131—21no—
92C23×C4×C131C2311yescharacteristic
93C2×SD16×C131—22no—
94C2×SD16×C131—22no—
95C2×SD16×C131—41no—
96C2×D8×C131—22no—
97C2×D8×C131—22no—
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—22no—
101C2×D8×C131—22no—
102C2×D8×C131—41no—
103C2×D8×C131—41no—
104C2×D8×C131—41no—
105C22×C8×C131C2311yescharacteristic
106C22×C8×C131C2311yescharacteristic
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109#127×C131—22no—
110#127×C131—22no—
111#127×C131—22no—
112#127×C131D414yescomplemented
113#124×C131—22no—
114#124×C131—22no—
115#124×C131—22no—
116#124×C131D414yescomplemented
117#121×C131—28no—
118#121×C131—28no—
119#121×C131—22no—
120#121×C131D414yescomplemented
121#120×C131—28no—
122#120×C131—28no—
123C4×D4×C131—22no—
124C4×D4×C131—22no—
125#117×C131—22no—
126#117×C131—22no—
127C2×C4⋊C4×C131—21no—
128C2×C4⋊C4×C131D411yescharacteristic
129C2×C4⋊C4×C131D411yescharacteristic
130C2×C4⋊C4×C131C2311yescharacteristic
131C2×C4⋊C4×C131C2311yescharacteristic
132C2×C4⋊C4×C131C2311yescharacteristic
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×C22⋊C4×C131—21no—
142C2×C22⋊C4×C131D411yescharacteristic
143C2×C22⋊C4×C131D411yescharacteristic
144C2×C42×C131—21no—
145C2×C42×C131C2311yescharacteristic
146C2×C42×C131C2311yescharacteristic
147C4⋊C8×C131—22no—
148C4⋊C8×C131—22no—
149#103×C131—22no—
150#103×C131—22no—
151#103×C131—41no—
152#102×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—41no—
159#102×C131—41no—
160#102×C131—41no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131—22no—
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—24no—
167C24×C131—21no—
168C24×C131—21no—
169C24×C131—21no—
170C24×C131—21no—
171C24×C131—42no—
172C24×C131—42no—
173C24×C131—81no—
174C24×C131—81no—
175C24×C131—81no—
176C24×C131—81no—
177C24×C131C2×D411yescharacteristic
178#41×C131—44no—
179#41×C131—44no—
180#41×C131—44no—
181#41×C131—44no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—21no—
187C2×Q8×C131C2×D412yes—
188C2×D4×C131—24no—
189C2×D4×C131—24no—
190C2×D4×C131—24no—
191C2×D4×C131—24no—
192C2×D4×C131—24no—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—21no—
196C2×D4×C131—21no—
197C2×D4×C131—21no—
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—44no—
216C2×D4×C131—44no—
217C2×D4×C131—44no—
218C2×D4×C131—44no—
219C2×D4×C131—42no—
220C2×D4×C131—42no—
221C2×D4×C131—42no—
222C2×D4×C131—42no—
223C2×D4×C131—81no—
224C2×D4×C131—81no—
225C2×D4×C131—81no—
226C2×D4×C131—81no—
227C2×D4×C131—81no—
228C2×D4×C131—81no—
229C2×D4×C131—81no—
230C2×D4×C131—81no—
231C2×D4×C131—81no—
232C2×D4×C131—81no—
233C2×D4×C131C2×D412yes—
234C2×D4×C131C2×D412yes—
235C2×D4×C131C2×D412yes—
236C2×D4×C131C2×D412yes—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—21no—
241C22×C4×C131—24no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—42no—
247C22×C4×C131—42no—
248C22×C4×C131—42no—
249C22×C4×C131—81no—
250C22×C4×C131—81no—
251C22×C4×C131C2×D411yescharacteristic
252C22×C4×C131C2×D411yescharacteristic
253C22×C4×C131C2×D411yescharacteristic
254C22×C4×C131C2×D411yescharacteristic
255C22×C4×C131C2×D411yescharacteristic
256C22×C4×C131C2×D412yes—
257C22×C4×C131#4112yes—
258C22×C4×C131C2411yescharacteristic
259SD16×C131—44no—
260D8×C131—44no—
261D8×C131—44no—
262D8×C131—44no—
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—
271C2×C8×C131—21no—
272C2×C8×C131—21no—
273C2×C8×C131—21no—
274C2×C8×C131—21no—
275C4⋊C4×C131—22no—
276C4⋊C4×C131—22no—
277C4⋊C4×C131—21no—
278C4⋊C4×C131—21no—
279C4⋊C4×C131—21no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—81no—
283C4⋊C4×C131C2×D412yes—
284C22⋊C4×C131—24no—
285C22⋊C4×C131—24no—
286C22⋊C4×C131—24no—
287C22⋊C4×C131—24no—
288C22⋊C4×C131—22no—
289C22⋊C4×C131—22no—
290C22⋊C4×C131—24no—
291C22⋊C4×C131—42no—
292C22⋊C4×C131—81no—
293C22⋊C4×C131—81no—
294C22⋊C4×C131—81no—
295C42×C131—21no—
296C42×C131—21no—
297C42×C131—81no—
298C42×C131C2×D412yes—
299C42×C131C2×D412yes—
300C23×C131—21no—
301C23×C131—21no—
302C23×C131—21no—
303C23×C131—21no—
304C23×C131—21no—
305C23×C131—21no—
306C23×C131—22no—
307C23×C131—22no—
308C23×C131—22no—
309C23×C131—22no—
310C23×C131—48no—
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—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—41no—
335C23×C131—84no—
336C23×C131—84no—
337C23×C131—84no—
338C23×C131—84no—
339C23×C131—84no—
340C23×C131—84no—
341C23×C131#12112yes—
342C23×C131C22×D411yescharacteristic
343Q8×C131—22no—
344Q8×C131—22no—
345Q8×C131—41no—
346Q8×C131—41no—
347D4×C131—22no—
348D4×C131—22no—
349D4×C131—22no—
350D4×C131—22no—
351D4×C131—22no—
352D4×C131—22no—
353D4×C131—22no—
354D4×C131—22no—
355D4×C131—48no—
356D4×C131—48no—
357D4×C131—41no—
358D4×C131—41no—
359D4×C131—41no—
360D4×C131—41no—
361D4×C131—41no—
362D4×C131—41no—
363D4×C131—41no—
364D4×C131—41no—
365D4×C131—84no—
366D4×C131—84no—
367D4×C131—84no—
368D4×C131—84no—
369D4×C131—84no—
370C2×C4×C131—21no—
371C2×C4×C131—21no—
372C2×C4×C131—21no—
373C2×C4×C131—21no—
374C2×C4×C131—21no—
375C2×C4×C131—21no—
376C2×C4×C131—22no—
377C2×C4×C131—22no—
378C2×C4×C131—22no—
379C2×C4×C131—22no—
380C2×C4×C131—21no—
381C2×C4×C131—21no—
382C2×C4×C131—22no—
383C2×C4×C131—22no—
384C2×C4×C131—21no—
385C2×C4×C131—21no—
386C2×C4×C131—21no—
387C2×C4×C131—21no—
388C2×C4×C131—48no—
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—41no—
399C2×C4×C131—84no—
400C2×C4×C131#12012yes—
401C2×C4×C131#12012yes—
402C2×C4×C131#12112yes—
403C2×C4×C131C22×D411yescharacteristic
404C2×C4×C131C22×D411yescharacteristic
405C2×C4×C131C22×D411yescharacteristic
406C2×C4×C131C2×#4111yescharacteristic
407C2×C4×C131H(5,𝔽2)11yescharacteristic
408C2×C4×C131H(5,𝔽2)11yescharacteristic
409C8×C131—41no—
410C8×C131—41no—
411C8×C131—41no—
412C8×C131—41no—
413C22×C131—22no—
414C22×C131—22no—
415C22×C131—22no—
416C22×C131—41no—
417C22×C131—41no—
418C22×C131—41no—
419C22×C131—41no—
420C22×C131—42no—
421C22×C131—42no—
422C22×C131—42no—
423C22×C131—42no—
424C22×C131—42no—
425C22×C131—42no—
426C22×C131—42no—
427C22×C131—42no—
428C22×C131—42no—
429C22×C131—42no—
430C22×C131—42no—
431C22×C131—42no—
432C22×C131—816no—
433C22×C131—81no—
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×C131—81no—
446C22×C131—81no—
447C22×C131—81no—
448C22×C131—81no—
449C22×C131C2×#12011yescharacteristic
450C22×C131C2×#12111yescharacteristic
451C22×C131#53511yescharacteristic
452C22×C131#57611yescharacteristic
453C22×C131#57611yescharacteristic
454C22×C131#57611yescharacteristic
455C22×C131#57711yescharacteristic
456C4×C131—22no—
457C4×C131—22no—
458C4×C131—22no—
459C4×C131—42no—
460C4×C131—41no—
461C4×C131—41no—
462C4×C131—42no—
463C4×C131—81no—
464C4×C131—81no—
465C4×C131D4211yescharacteristic
466C4×C131D4211yescharacteristic
467C4×C131#54611yescharacteristic
468C4×C131#54611yescharacteristic
469C2×C131—42no—
470C2×C131—82no—
471C2×C131—82no—
472C2×C131—82no—
473C2×C131—82no—
474C2×C131#240811yescharacteristic
475C2×C131#300811yescharacteristic
476C2×C131#301211yescharacteristic
477C2×C131#304111yescharacteristic
478C2×C131#304511yescharacteristic
479C2×C131#322011yescharacteristic
480C2×C131#322411yescharacteristic
481#24218C13111yesmaximal, characteristic, direct product factor, Sylow
482C131#2421811yescharacteristic, direct product factor, Sylow
483C2×#535C2×C13111yescharacteristic, complemented
484C2×#463C2×C13111yescharacteristic, complemented
485C2×#459C2×C13111yescharacteristic, complemented
486C2×#449C2×C13111yescharacteristic, complemented
487C2×#447C2×C13111yescharacteristic, complemented
488#2324C2×C13111yescharacteristic, complemented
489#2042C2×C13111yescharacteristic, complemented
490#2041C2×C13111yescharacteristic, complemented
491#2012C2×C13111yescharacteristic, complemented
492#2011C2×C13111yescharacteristic, complemented
493#1983C2×C13111yescharacteristic, complemented
494#1982C2×C13111yescharacteristic, complemented
495#1798C2×C13111yescharacteristic, complemented
496#1788C2×C13111yescharacteristic, complemented
497#1786C2×C13111yescharacteristic, complemented
498C22×#41C22×C13111yescharacteristic
499C23×D4C22×C13111yescharacteristic
500C22×SD16C22×C13111yescharacteristic, complemented
501C22×D8C22×C13111yescharacteristic
502C22×D8C22×C13111yescharacteristic
503C22×D8C22×C13111yescharacteristic, complemented
504#535—24no—
505#535—24no—
506C2×#127C22×C13111yescharacteristic
507C2×#127C22×C13111yescharacteristic
508C2×#124C22×C13111yescharacteristic
509C2×#124C22×C13111yescharacteristic
510C2×#121—21no—
511C2×#121—21no—
512C2×#121C22×C13111yescharacteristic
513C2×#120—21no—
514C2×#120—21no—
515C2×C4×D4C22×C13111yescharacteristic, complemented
516C2×#117C22×C13111yescharacteristic
517#463—24no—
518#459—24no—
519#449—24no—
520#447—24no—
521C2×C4⋊C8C22×C13111yescharacteristic, complemented
522C2×C4⋊C8C22×C13111yescharacteristic, complemented
523C2×#103C22×C13111yescharacteristic, complemented
524C2×#103C22×C13111yescharacteristic, complemented
525C2×#103C22×C13111yescharacteristic, complemented
526C2×#102C22×C13111yescharacteristic
527C2×#102C22×C13111yescharacteristic
528C2×#102C22×C13111yescharacteristic
529C2×#102C22×C13111yescharacteristic
530C2×#102C22×C13111yescharacteristic
531C2×#102C22×C13111yescharacteristic
532C2×#102C22×C13111yescharacteristic, complemented
533C2×#102C22×C13111yescharacteristic, complemented
534C2×#102C22×C13111yescharacteristic, complemented
535C2×C22⋊C8C22×C13111yescharacteristic
536C2×C22⋊C8C22×C13111yescharacteristic
537#390—21no—
538#390C22×C13111yescharacteristic, complemented
539#389C22×C13111yescharacteristic, complemented
540#388—21no—
541#386—21no—
542#385—21no—
543#380C22×C13111yescharacteristic
544C4×C4⋊C4C22×C13111yescharacteristic, complemented
545#336C22×C13111yescharacteristic, complemented
546#336C22×C13111yescharacteristic, complemented
547C25—21no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—22no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8C23×C13111yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—22no—
565C22×D4—22no—
566C22×D4—41no—
567C22×D4—41no—
568C22×D4C23×C13111yescharacteristic
569C22×D4C23×C13111yescharacteristic
570C22×D4C23×C13111yescharacteristic
571C22×D4C23×C13111yescharacteristic
572C23×C4—21no—
573C23×C4—21no—
574C23×C4C23×C13111yescharacteristic
575C2×SD16—22no—
576C2×SD16—22no—
577C2×SD16—41no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—22no—
581C2×D8—22no—
582C2×D8—22no—
583C2×D8—22no—
584C2×D8—41no—
585C2×D8—41no—
586C2×D8—41no—
587C22×C8C23×C13111yescharacteristic
588C22×C8C23×C13111yescharacteristic
589C22×C8C23×C13111yescharacteristic
590C22×C8C23×C13111yescharacteristic
591#127—22no—
592#127—22no—
593#127—22no—
594#127D4×C13114yescomplemented
595#124—22no—
596#124—22no—
597#124—22no—
598#124D4×C13114yescomplemented
599#121—28no—
600#121—28no—
601#121—22no—
602#121D4×C13114yescomplemented
603#120—28no—
604#120—28no—
605C4×D4—22no—
606C4×D4—22no—
607#117—22no—
608#117—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4D4×C13111yescharacteristic
611C2×C4⋊C4D4×C13111yescharacteristic
612C2×C4⋊C4C23×C13111yescharacteristic
613C2×C4⋊C4C23×C13111yescharacteristic
614C2×C4⋊C4C23×C13111yescharacteristic
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4D4×C13111yescharacteristic
625C2×C22⋊C4D4×C13111yescharacteristic
626C2×C42—21no—
627C2×C42C23×C13111yescharacteristic
628C2×C42C23×C13111yescharacteristic
629C4⋊C8—22no—
630C4⋊C8—22no—
631#103—22no—
632#103—22no—
633#103—41no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641#102—41no—
642#102—41no—
643C22⋊C8—22no—
644C22⋊C8—22no—
645#95—21no—
646#95—21no—
647#95—21no—
648C24—24no—
649C24—21no—
650C24—21no—
651C24—21no—
652C24—21no—
653C24—42no—
654C24—42no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24—81no—
659C24C2×D4×C13111yescharacteristic
660#41—44no—
661#41—44no—
662#41—44no—
663#41—44no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8C2×D4×C13112yes—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—24no—
673C2×D4—24no—
674C2×D4—24no—
675C2×D4—24no—
676C2×D4—24no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—44no—
698C2×D4—44no—
699C2×D4—44no—
700C2×D4—44no—
701C2×D4—42no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—42no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4—81no—
709C2×D4—81no—
710C2×D4—81no—
711C2×D4—81no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4C2×D4×C13112yes—
716C2×D4C2×D4×C13112yes—
717C2×D4C2×D4×C13112yes—
718C2×D4C2×D4×C13112yes—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—24no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—81no—
732C22×C4—81no—
733C22×C4C2×D4×C13111yescharacteristic
734C22×C4C2×D4×C13111yescharacteristic
735C22×C4C2×D4×C13111yescharacteristic
736C22×C4C2×D4×C13111yescharacteristic
737C22×C4C2×D4×C13111yescharacteristic
738C22×C4C2×D4×C13112yes—
739C22×C4#41×C13112yes—
740C22×C4C24×C13111yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744D8—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8—21no—
757C4⋊C4—22no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—81no—
765C4⋊C4C2×D4×C13112yes—
766C22⋊C4—24no—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—22no—
772C22⋊C4—24no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
777C42—21no—
778C42—21no—
779C42—81no—
780C42C2×D4×C13112yes—
781C42C2×D4×C13112yes—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—22no—
791C23—22no—
792C23—48no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
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—41no—
813C23—41no—
814C23—41no—
815C23—41no—
816C23—41no—
817C23—84no—
818C23—84no—
819C23—84no—
820C23—84no—
821C23—84no—
822C23—84no—
823C23#121×C13112yes—
824C23C22×D4×C13111yescharacteristic
825Q8—22no—
826Q8—22no—
827Q8—41no—
828Q8—41no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—22no—
833D4—22no—
834D4—22no—
835D4—22no—
836D4—22no—
837D4—48no—
838D4—48no—
839D4—41no—
840D4—41no—
841D4—41no—
842D4—41no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—84no—
848D4—84no—
849D4—84no—
850D4—84no—
851D4—84no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—48no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—84no—
882C2×C4#120×C13112yes—
883C2×C4#120×C13112yes—
884C2×C4#121×C13112yes—
885C2×C4C22×D4×C13111yescharacteristic
886C2×C4C22×D4×C13111yescharacteristic
887C2×C4C22×D4×C13111yescharacteristic
888C2×C4C2×#41×C13111yescharacteristic
889C2×C4H(5,𝔽2)×C13111yescharacteristic
890C2×C4H(5,𝔽2)×C13111yescharacteristic
891C8—41no—
892C8—41no—
893C8—41no—
894C8—41no—
895C22—22no—
896C22—22no—
897C22—22no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—41no—
902C22—42no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—42no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—816no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22C2×#120×C13111yescharacteristic
932C22C2×#121×C13111yescharacteristic
933C22#535×C13111yescharacteristic
934C22#576×C13111yescharacteristic
935C22#576×C13111yescharacteristic
936C22#576×C13111yescharacteristic
937C22#577×C13111yescharacteristic
938C4—22no—
939C4—22no—
940C4—22no—
941C4—41no—
942C4—41no—
943C4—42no—
944C4—42no—
945C4—81no—
946C4—81no—
947C4D42×C13111yescharacteristic
948C4D42×C13111yescharacteristic
949C4#546×C13111yescharacteristic
950C4#546×C13111yescharacteristic
951C2—42no—
952C2—82no—
953C2—82no—
954C2—82no—
955C2—82no—
956C2#2408×C13111yescharacteristic
957C2#3008×C13111yescharacteristic
958C2#3012×C13111yescharacteristic
959C2#3041×C13111yescharacteristic
960C2#3045×C13111yescharacteristic
961C2#3220×C13111yescharacteristic
962C2#3224×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C2×#117×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#535×C131C2semidirect
2. C2×#463×C131C2semidirect
3. C2×#459×C131C2semidirect
4. C2×#449×C131C2semidirect
5. C2×#447×C131C2semidirect
6. #2324×C131C2semidirect
7. #2042×C131C2semidirect
8. #2041×C131C2semidirect
9. #2012×C131C2semidirect
10. #2011×C131C2semidirect
11. #1983×C131C2semidirect
12. #1982×C131C2semidirect
13. #1798×C131C2semidirect
14. #1788×C131C2semidirect
15. #1786×C131C2semidirect
18. C22×SD16×C131C22semidirect
21. C22×D8×C131C22semidirect
33. C2×C4×D4×C131C22semidirect
39. C2×C4⋊C8×C131C22semidirect
40. C2×C4⋊C8×C131C22semidirect
41. C2×#103×C131C22semidirect
42. C2×#103×C131C22semidirect
43. C2×#103×C131C22semidirect
50. C2×#102×C131C22semidirect
51. C2×#102×C131C22semidirect
52. C2×#102×C131C22semidirect
56. #390×C131C22semidirect
57. #389×C131C22semidirect
62. C4×C4⋊C4×C131C22semidirect
63. #336×C131C22semidirect
64. #336×C131C22semidirect
112. #127×C131D4semidirect
116. #124×C131D4semidirect
120. #121×C131D4semidirect
481. #24218C131direct (N × H)
482. C131#24218direct (N × H)
483. C2×#535C2×C131semidirect
484. C2×#463C2×C131semidirect
485. C2×#459C2×C131semidirect
486. C2×#449C2×C131semidirect
487. C2×#447C2×C131semidirect
488. #2324C2×C131semidirect
489. #2042C2×C131semidirect
490. #2041C2×C131semidirect
491. #2012C2×C131semidirect
492. #2011C2×C131semidirect
493. #1983C2×C131semidirect
494. #1982C2×C131semidirect
495. #1798C2×C131semidirect
496. #1788C2×C131semidirect
497. #1786C2×C131semidirect
500. C22×SD16C22×C131semidirect
503. C22×D8C22×C131semidirect
515. C2×C4×D4C22×C131semidirect
521. C2×C4⋊C8C22×C131semidirect
522. C2×C4⋊C8C22×C131semidirect
523. C2×#103C22×C131semidirect
524. C2×#103C22×C131semidirect
525. C2×#103C22×C131semidirect
532. C2×#102C22×C131semidirect
533. C2×#102C22×C131semidirect
534. C2×#102C22×C131semidirect
538. #390C22×C131semidirect
539. #389C22×C131semidirect
544. C4×C4⋊C4C22×C131semidirect
545. #336C22×C131semidirect
546. #336C22×C131semidirect
594. #127D4×C131semidirect
598. #124D4×C131semidirect
602. #121D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#535×C1312
C2×#463×C1312
C2×#459×C1312
C2×#449×C1312
C2×#447×C1312
#2324×C1312
#2042×C1312
#2041×C1312
#2012×C1312
#2011×C1312
#1983×C1312
#1982×C1312
#1798×C1312
#1788×C1312
#1786×C1312
#24218131