Finite Group Databasebeta

← C131×#24397 #45710281

Subgroups — C131×#24397 #45710281

Order 33536.

1508 conjugacy classes of subgroups.

The subgroup lattice has 954 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C131C211yesmaximal, characteristic, complemented
2C2×#469×C131C211yesmaximal, characteristic, complemented
3C2×#465×C131C211yesmaximal, characteristic, complemented
4C2×#449×C131C211yesmaximal, characteristic, complemented
5C2×#408×C131C211yesmaximal, characteristic, complemented
6#2615×C131C211yesmaximal, characteristic, complemented
7#2035×C131C211yesmaximal, characteristic, complemented
8#2034×C131C211yesmaximal, characteristic, complemented
9#2000×C131C211yesmaximal, characteristic, complemented
10#1999×C131C211yesmaximal, characteristic, complemented
11#1894×C131C211yesmaximal, characteristic, complemented
12#1893×C131C211yesmaximal, characteristic, complemented
13#1874×C131C211yesmaximal, characteristic, complemented
14#1853×C131C211yesmaximal, characteristic, complemented
15#1788×C131C211yesmaximal, characteristic, complemented
16C22×#41×C131C2211yescharacteristic
17C22×#41×C131C2211yescharacteristic
18C22×SD16×C131C2211yescharacteristic
19C22×D8×C131C2211yescharacteristic
20C22×M16×C131C2211yescharacteristic
21C23×C8×C131C2211yescharacteristic
22#537×C131—24no—
23#537×C131—24no—
24C2×C22⋊Q8×C131—21no—
25C2×C22⋊Q8×C131C2211yescharacteristic
26C2×C22⋊Q8×C131C2211yescharacteristic
27C2×#121×C131—21no—
28C2×#121×C131—21no—
29C2×#121×C131—21no—
30C2×#121×C131C2211yescharacteristic
31C2×#121×C131C2211yescharacteristic
32C2×#121×C131C2211yescharacteristic
33C2×#121×C131C2211yescharacteristic
34C2×#121×C131C2211yescharacteristic
35C22×C4⋊C4×C131C2211yescharacteristic
36#469×C131—24no—
37#465×C131—24no—
38#449×C131—24no—
39C2×#106×C131C2211yescharacteristic
40C2×#106×C131C2211yescharacteristic
41C2×#103×C131C2211yescharacteristic
42C2×#103×C131C2211yescharacteristic
43C2×#103×C131C2211yescharacteristic
44C2×#102×C131C2211yescharacteristic
45C2×#102×C131C2211yescharacteristic
46C2×#102×C131C2211yescharacteristic
47C2×#102×C131C2211yescharacteristic
48C2×#102×C131C2211yescharacteristic
49#408×C131—24no—
50C2×C22⋊C8×C131C2211yescharacteristic
51C2×C22⋊C8×C131C2211yescharacteristic
52C2×C22⋊C8×C131C2211yescharacteristic
53C2×C22⋊C8×C131C2211yescharacteristic
54#393×C131—21no—
55#392×C131—21no—
56#392×C131—21no—
57#392×C131—21no—
58#380×C131C2211yescharacteristic
59#380×C131C2211yescharacteristic
60#380×C131C2211yescharacteristic
61#340×C131C2211yescharacteristic
62#340×C131C2211yescharacteristic
63#340×C131C2211yescharacteristic
64#340×C131C2211yescharacteristic
65C2×#41×C131—22no—
66C2×#41×C131—22no—
67C2×#41×C131—22no—
68C2×#41×C131—22no—
69C2×#41×C131—22no—
70C2×#41×C131—22no—
71C2×#41×C131—22no—
72C2×#41×C131—22no—
73C2×#41×C131—41no—
74C2×#41×C131—41no—
75C2×#41×C131—41no—
76C2×#41×C131—41no—
77C22×Q8×C131D411yescharacteristic
78C22×Q8×C131C2311yescharacteristic
79C22×D4×C131—21no—
80C22×D4×C131—21no—
81C22×D4×C131—21no—
82C22×D4×C131—21no—
83C22×D4×C131—21no—
84C22×D4×C131—21no—
85C22×D4×C131D411yescharacteristic
86C22×D4×C131D411yescharacteristic
87C22×D4×C131D411yescharacteristic
88C22×D4×C131C2311yescharacteristic
89C22×D4×C131C2311yescharacteristic
90C23×C4×C131—21no—
91C23×C4×C131—21no—
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C23×C4×C131C2311yescharacteristic
95C2×SD16×C131—22no—
96C2×SD16×C131—22no—
97C2×SD16×C131—41no—
98C2×D8×C131—22no—
99C2×D8×C131—22no—
100C2×D8×C131—41no—
101C2×M16×C131—22no—
102C2×M16×C131—22no—
103C2×M16×C131—41no—
104C22×C8×C131—22no—
105C22×C8×C131—22no—
106C22×C8×C131—41no—
107C22×C8×C131C2311yescharacteristic
108C22×C8×C131C2311yescharacteristic
109C22×C8×C131C2311yescharacteristic
110C22×C8×C131C2311yescharacteristic
111C22⋊Q8×C131—28no—
112C22⋊Q8×C131—22no—
113C22⋊Q8×C131—22no—
114C22⋊Q8×C131—22no—
115C22⋊Q8×C131D414yescomplemented
116#121×C131—28no—
117#121×C131—28no—
118#121×C131—28no—
119#121×C131—22no—
120#121×C131—22no—
121#121×C131—22no—
122#121×C131—22no—
123#121×C131—22no—
124#121×C131—22no—
125#121×C131—22no—
126#121×C131—41no—
127#121×C131—41no—
128#121×C131D414yescomplemented
129C2×C4⋊C4×C131—21no—
130C2×C4⋊C4×C131—21no—
131C2×C4⋊C4×C131—21no—
132C2×C4⋊C4×C131—22no—
133C2×C4⋊C4×C131—22no—
134C2×C4⋊C4×C131C2311yescharacteristic
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×C131—21no—
149#106×C131—22no—
150#106×C131—22no—
151#103×C131—22no—
152#103×C131—22no—
153#103×C131—41no—
154#102×C131—22no—
155#102×C131—22no—
156#102×C131—22no—
157#102×C131—22no—
158#102×C131—41no—
159C22⋊C8×C131—22no—
160C22⋊C8×C131—22no—
161C22⋊C8×C131—22no—
162C22⋊C8×C131D414yescomplemented
163#95×C131—21no—
164#95×C131—21no—
165#95×C131—21no—
166C24×C131—21no—
167C24×C131—21no—
168C24×C131C2×D411yescharacteristic
169C24×C131C2×D411yescharacteristic
170C24×C131C2×D411yescharacteristic
171#41×C131—44no—
172#41×C131—44no—
173#41×C131—44no—
174#41×C131—44no—
175#41×C131—44no—
176#41×C131—44no—
177#41×C131—44no—
178#41×C131—44no—
179C2×Q8×C131—22no—
180C2×Q8×C131—22no—
181C2×Q8×C131—21no—
182C2×Q8×C131—21no—
183C2×Q8×C131—21no—
184C2×Q8×C131—21no—
185C2×Q8×C131—21no—
186C2×Q8×C131—41no—
187C2×Q8×C131C2×D412yes—
188C2×D4×C131—24no—
189C2×D4×C131—22no—
190C2×D4×C131—22no—
191C2×D4×C131—22no—
192C2×D4×C131—22no—
193C2×D4×C131—24no—
194C2×D4×C131—24no—
195C2×D4×C131—22no—
196C2×D4×C131—22no—
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—41no—
209C2×D4×C131—41no—
210C2×D4×C131—41no—
211C2×D4×C131—42no—
212C2×D4×C131—42no—
213C2×D4×C131—42no—
214C2×D4×C131—42no—
215C2×D4×C131—42no—
216C2×D4×C131—81no—
217C2×D4×C131—81no—
218C2×D4×C131—81no—
219C2×D4×C131—81no—
220C2×D4×C131—81no—
221C2×D4×C131—81no—
222C2×D4×C131—81no—
223C2×D4×C131—81no—
224C2×D4×C131—81no—
225C2×D4×C131—81no—
226C2×D4×C131C2×D412yes—
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—24no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—24no—
240C22×C4×C131—21no—
241C22×C4×C131—21no—
242C22×C4×C131—21no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—21no—
249C22×C4×C131—42no—
250C22×C4×C131—42no—
251C22×C4×C131—81no—
252C22×C4×C131—81no—
253C22×C4×C131C2×D411yescharacteristic
254C22×C4×C131C2×D411yescharacteristic
255C22×C4×C131C2×D412yes—
256C22×C4×C131C2×D412yes—
257C22×C4×C131C2×D411yescharacteristic
258C22×C4×C131C2×D412yes—
259C22×C4×C131#4112yes—
260C22×C4×C131C2411yescharacteristic
261SD16×C131—44no—
262D8×C131—44no—
263M16×C131—44no—
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—44no—
275C2×C8×C131C2×D412yes—
276C2×C8×C131C2×D412yes—
277C4⋊C4×C131—24no—
278C4⋊C4×C131—24no—
279C4⋊C4×C131—24no—
280C4⋊C4×C131—21no—
281C4⋊C4×C131—21no—
282C4⋊C4×C131—21no—
283C4⋊C4×C131—21no—
284C4⋊C4×C131—21no—
285C4⋊C4×C131—21no—
286C4⋊C4×C131—21no—
287C4⋊C4×C131—21no—
288C4⋊C4×C131C2×D412yes—
289C4⋊C4×C131C2×D412yes—
290C22⋊C4×C131—24no—
291C22⋊C4×C131—24no—
292C22⋊C4×C131—24no—
293C22⋊C4×C131—24no—
294C22⋊C4×C131—42no—
295C22⋊C4×C131—42no—
296C22⋊C4×C131—42no—
297C22⋊C4×C131—81no—
298C22⋊C4×C131—81no—
299C22⋊C4×C131—81no—
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—21no—
315C23×C131—21no—
316C23×C131—21no—
317C23×C131—21no—
318C23×C131—21no—
319C23×C131—21no—
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#12012yes—
334C23×C131#12112yes—
335C23×C131C22×D411yescharacteristic
336Q8×C131—22no—
337Q8×C131—22no—
338Q8×C131—44no—
339Q8×C131—41no—
340Q8×C131—41no—
341D4×C131—22no—
342D4×C131—22no—
343D4×C131—44no—
344D4×C131—44no—
345D4×C131—44no—
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—
356D4×C131—84no—
357D4×C131—84no—
358C2×C4×C131—21no—
359C2×C4×C131—21no—
360C2×C4×C131—21no—
361C2×C4×C131—21no—
362C2×C4×C131—22no—
363C2×C4×C131—22no—
364C2×C4×C131—22no—
365C2×C4×C131—22no—
366C2×C4×C131—22no—
367C2×C4×C131—22no—
368C2×C4×C131—22no—
369C2×C4×C131—22no—
370C2×C4×C131—22no—
371C2×C4×C131—22no—
372C2×C4×C131—22no—
373C2×C4×C131—21no—
374C2×C4×C131—21no—
375C2×C4×C131—21no—
376C2×C4×C131—48no—
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—84no—
397C2×C4×C131#12012yes—
398C2×C4×C131#12112yes—
399C2×C4×C131C22×D411yescharacteristic
400C2×C4×C131C22×D411yescharacteristic
401C2×C4×C131C22×D411yescharacteristic
402C2×C4×C131C2×#4111yescharacteristic
403C2×C4×C131H(5,𝔽2)11yescharacteristic
404C2×C4×C131H(5,𝔽2)11yescharacteristic
405C8×C131—22no—
406C8×C131—22no—
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—41no—
416C22×C131—41no—
417C22×C131—41no—
418C22×C131—41no—
419C22×C131—41no—
420C22×C131—41no—
421C22×C131—41no—
422C22×C131—41no—
423C22×C131—42no—
424C22×C131—41no—
425C22×C131—41no—
426C22×C131—41no—
427C22×C131—41no—
428C22×C131—42no—
429C22×C131—41no—
430C22×C131—42no—
431C22×C131—41no—
432C22×C131—41no—
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×C131C2×#12011yescharacteristic
445C22×C131C2×#12111yescharacteristic
446C22×C131#53411yescharacteristic
447C22×C131#57611yescharacteristic
448C22×C131#57711yescharacteristic
449C22×C131#57711yescharacteristic
450C22×C131#57711yescharacteristic
451C4×C131—22no—
452C4×C131—22no—
453C4×C131—41no—
454C4×C131—42no—
455C4×C131—42no—
456C4×C131—42no—
457C4×C131—81no—
458C4×C131—81no—
459C4×C131—81no—
460C4×C131D4211yescharacteristic
461C4×C131D4211yescharacteristic
462C4×C131#54611yescharacteristic
463C4×C131#54611yescharacteristic
464C2×C131—42no—
465C2×C131—42no—
466C2×C131—81no—
467C2×C131—82no—
468C2×C131—161no—
469C2×C131#241011yescharacteristic
470C2×C131#301011yescharacteristic
471C2×C131#301211yescharacteristic
472C2×C131#306011yescharacteristic
473C2×C131#306211yescharacteristic
474C2×C131#319811yescharacteristic
475C2×C131#320411yescharacteristic
476#24397C13111yesmaximal, characteristic, direct product factor, Sylow
477C131#2439711yescharacteristic, direct product factor, Sylow
478C2×#537C2×C13111yescharacteristic, complemented
479C2×#469C2×C13111yescharacteristic, complemented
480C2×#465C2×C13111yescharacteristic, complemented
481C2×#449C2×C13111yescharacteristic, complemented
482C2×#408C2×C13111yescharacteristic, complemented
483#2615C2×C13111yescharacteristic, complemented
484#2035C2×C13111yescharacteristic, complemented
485#2034C2×C13111yescharacteristic, complemented
486#2000C2×C13111yescharacteristic, complemented
487#1999C2×C13111yescharacteristic, complemented
488#1894C2×C13111yescharacteristic, complemented
489#1893C2×C13111yescharacteristic, complemented
490#1874C2×C13111yescharacteristic, complemented
491#1853C2×C13111yescharacteristic, complemented
492#1788C2×C13111yescharacteristic, complemented
493C22×#41C22×C13111yescharacteristic
494C22×#41C22×C13111yescharacteristic
495C22×SD16C22×C13111yescharacteristic
496C22×D8C22×C13111yescharacteristic
497C22×M16C22×C13111yescharacteristic
498C23×C8C22×C13111yescharacteristic
499#537—24no—
500#537—24no—
501C2×C22⋊Q8—21no—
502C2×C22⋊Q8C22×C13111yescharacteristic
503C2×C22⋊Q8C22×C13111yescharacteristic
504C2×#121—21no—
505C2×#121—21no—
506C2×#121—21no—
507C2×#121C22×C13111yescharacteristic
508C2×#121C22×C13111yescharacteristic
509C2×#121C22×C13111yescharacteristic
510C2×#121C22×C13111yescharacteristic
511C2×#121C22×C13111yescharacteristic
512C22×C4⋊C4C22×C13111yescharacteristic
513#469—24no—
514#465—24no—
515#449—24no—
516C2×#106C22×C13111yescharacteristic
517C2×#106C22×C13111yescharacteristic
518C2×#103C22×C13111yescharacteristic
519C2×#103C22×C13111yescharacteristic
520C2×#103C22×C13111yescharacteristic
521C2×#102C22×C13111yescharacteristic
522C2×#102C22×C13111yescharacteristic
523C2×#102C22×C13111yescharacteristic
524C2×#102C22×C13111yescharacteristic
525C2×#102C22×C13111yescharacteristic
526#408—24no—
527C2×C22⋊C8C22×C13111yescharacteristic
528C2×C22⋊C8C22×C13111yescharacteristic
529C2×C22⋊C8C22×C13111yescharacteristic
530C2×C22⋊C8C22×C13111yescharacteristic
531#393—21no—
532#392—21no—
533#392—21no—
534#392—21no—
535#380C22×C13111yescharacteristic
536#380C22×C13111yescharacteristic
537#380C22×C13111yescharacteristic
538#340C22×C13111yescharacteristic
539#340C22×C13111yescharacteristic
540#340C22×C13111yescharacteristic
541#340C22×C13111yescharacteristic
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—41no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C22×Q8D4×C13111yescharacteristic
555C22×Q8C23×C13111yescharacteristic
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4D4×C13111yescharacteristic
563C22×D4D4×C13111yescharacteristic
564C22×D4D4×C13111yescharacteristic
565C22×D4C23×C13111yescharacteristic
566C22×D4C23×C13111yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4C23×C13111yescharacteristic
570C23×C4C23×C13111yescharacteristic
571C23×C4C23×C13111yescharacteristic
572C2×SD16—22no—
573C2×SD16—22no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—41no—
578C2×M16—22no—
579C2×M16—22no—
580C2×M16—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C13111yescharacteristic
585C22×C8C23×C13111yescharacteristic
586C22×C8C23×C13111yescharacteristic
587C22×C8C23×C13111yescharacteristic
588C22⋊Q8—28no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8D4×C13114yescomplemented
593#121—28no—
594#121—28no—
595#121—28no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—41no—
604#121—41no—
605#121D4×C13114yescomplemented
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—22no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4C23×C13111yescharacteristic
612C2×C4⋊C4C23×C13111yescharacteristic
613C2×C4⋊C4C23×C13111yescharacteristic
614C2×C4⋊C4C23×C13111yescharacteristic
615C2×C4⋊C4C23×C13111yescharacteristic
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⋊C4—21no—
625C2×C22⋊C4—21no—
626#106—22no—
627#106—22no—
628#103—22no—
629#103—22no—
630#103—41no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—22no—
639C22⋊C8D4×C13114yescomplemented
640#95—21no—
641#95—21no—
642#95—21no—
643C24—21no—
644C24—21no—
645C24C2×D4×C13111yescharacteristic
646C24C2×D4×C13111yescharacteristic
647C24C2×D4×C13111yescharacteristic
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—21no—
663C2×Q8—41no—
664C2×Q8C2×D4×C13112yes—
665C2×D4—24no—
666C2×D4—22no—
667C2×D4—22no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
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—41no—
686C2×D4—41no—
687C2×D4—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—81no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C13112yes—
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—24no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—42no—
727C22×C4—42no—
728C22×C4—81no—
729C22×C4—81no—
730C22×C4C2×D4×C13111yescharacteristic
731C22×C4C2×D4×C13111yescharacteristic
732C22×C4C2×D4×C13112yes—
733C22×C4C2×D4×C13112yes—
734C22×C4C2×D4×C13111yescharacteristic
735C22×C4C2×D4×C13112yes—
736C22×C4#41×C13112yes—
737C22×C4C24×C13111yescharacteristic
738SD16—44no—
739D8—44no—
740M16—44no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—44no—
752C2×C8C2×D4×C13112yes—
753C2×C8C2×D4×C13112yes—
754C4⋊C4—24no—
755C4⋊C4—24no—
756C4⋊C4—24no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4C2×D4×C13112yes—
766C4⋊C4C2×D4×C13112yes—
767C22⋊C4—24no—
768C22⋊C4—24no—
769C22⋊C4—24no—
770C22⋊C4—24no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C22⋊C4—81no—
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—22no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—21no—
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#120×C13112yes—
811C23#121×C13112yes—
812C23C22×D4×C13111yescharacteristic
813Q8—22no—
814Q8—22no—
815Q8—44no—
816Q8—41no—
817Q8—41no—
818D4—22no—
819D4—22no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—48no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—21no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—48no—
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—84no—
874C2×C4#120×C13112yes—
875C2×C4#121×C13112yes—
876C2×C4C22×D4×C13111yescharacteristic
877C2×C4C22×D4×C13111yescharacteristic
878C2×C4C22×D4×C13111yescharacteristic
879C2×C4C2×#41×C13111yescharacteristic
880C2×C4H(5,𝔽2)×C13111yescharacteristic
881C2×C4H(5,𝔽2)×C13111yescharacteristic
882C8—22no—
883C8—22no—
884C8—41no—
885C8—41no—
886C22—22no—
887C22—22no—
888C22—22no—
889C22—22no—
890C22—22no—
891C22—22no—
892C22—41no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—41no—
906C22—42no—
907C22—41no—
908C22—41no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22C2×#120×C13111yescharacteristic
922C22C2×#121×C13111yescharacteristic
923C22#534×C13111yescharacteristic
924C22#576×C13111yescharacteristic
925C22#577×C13111yescharacteristic
926C22#577×C13111yescharacteristic
927C22#577×C13111yescharacteristic
928C4—22no—
929C4—22no—
930C4—42no—
931C4—42no—
932C4—41no—
933C4—42no—
934C4—81no—
935C4—81no—
936C4—81no—
937C4D42×C13111yescharacteristic
938C4D42×C13111yescharacteristic
939C4#546×C13111yescharacteristic
940C4#546×C13111yescharacteristic
941C2—42no—
942C2—42no—
943C2—81no—
944C2—82no—
945C2—161no—
946C2#2410×C13111yescharacteristic
947C2#3010×C13111yescharacteristic
948C2#3012×C13111yescharacteristic
949C2#3060×C13111yescharacteristic
950C2#3062×C13111yescharacteristic
951C2#3198×C13111yescharacteristic
952C2#3204×C13111yescharacteristic
subgroupG/H
center, socleC23×C131C22×D4
commutator, Frattini, cosocleC22×C4C24×C131
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C131 ◁ C22×#41×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#537×C131C2semidirect
2. C2×#469×C131C2semidirect
3. C2×#465×C131C2semidirect
4. C2×#449×C131C2semidirect
5. C2×#408×C131C2semidirect
6. #2615×C131C2semidirect
7. #2035×C131C2semidirect
8. #2034×C131C2semidirect
9. #2000×C131C2semidirect
10. #1999×C131C2semidirect
11. #1894×C131C2semidirect
12. #1893×C131C2semidirect
13. #1874×C131C2semidirect
14. #1853×C131C2semidirect
15. #1788×C131C2semidirect
115. C22⋊Q8×C131D4semidirect
128. #121×C131D4semidirect
162. C22⋊C8×C131D4semidirect
476. #24397C131direct (N × H)
477. C131#24397direct (N × H)
478. C2×#537C2×C131semidirect
479. C2×#469C2×C131semidirect
480. C2×#465C2×C131semidirect
481. C2×#449C2×C131semidirect
482. C2×#408C2×C131semidirect
483. #2615C2×C131semidirect
484. #2035C2×C131semidirect
485. #2034C2×C131semidirect
486. #2000C2×C131semidirect
487. #1999C2×C131semidirect
488. #1894C2×C131semidirect
489. #1893C2×C131semidirect
490. #1874C2×C131semidirect
491. #1853C2×C131semidirect
492. #1788C2×C131semidirect
592. C22⋊Q8D4×C131semidirect
605. #121D4×C131semidirect
639. C22⋊C8D4×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1312
C2×#469×C1312
C2×#465×C1312
C2×#449×C1312
C2×#408×C1312
#2615×C1312
#2035×C1312
#2034×C1312
#2000×C1312
#1999×C1312
#1894×C1312
#1893×C1312
#1874×C1312
#1853×C1312
#1788×C1312
#24397131