Finite Group Databasebeta

← C131×#16298 #45702182

Subgroups — C131×#16298 #45702182

Order 33536.

2830 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#399×C131C211yesmaximal, characteristic, complemented
2C2×#396×C131C212yesmaximal, complemented
3C2×#379×C131C211yesmaximal, characteristic
4C2×#379×C131C212yesmaximal
5#1439×C131C212yesmaximal, complemented
6#1439×C131C212yesmaximal, complemented
7#1439×C131C212yesmaximal, complemented
8#1439×C131C212yesmaximal, complemented
9#1439×C131C211yesmaximal, characteristic, complemented
10C26×C131C2211yescharacteristic
11C22×C4⋊C4×C131C2211yescharacteristic, complemented
12C22×C4⋊C4×C131C2212yescomplemented
13C22×C4⋊C4×C131C2212yescomplemented
14C22×C4⋊C4×C131C2211yescharacteristic, complemented
15C22×C22⋊C4×C131C2212yes—
16C22×C22⋊C4×C131C2212yes—
17C22×C22⋊C4×C131C2212yes—
18C22×C22⋊C4×C131C2212yes—
19C22×C22⋊C4×C131C2212yes—
20C22×C22⋊C4×C131C2212yes—
21C22×C22⋊C4×C131C2212yes—
22C22×C22⋊C4×C131C2211yescharacteristic
23C22×C22⋊C4×C131C2212yes—
24C22×C22⋊C4×C131C2211yescharacteristic
25#399×C131—24no—
26#396×C131—28no—
27#379×C131—28no—
28#379×C131—24no—
29C2×#95×C131C2212yescomplemented
30C2×#95×C131C2211yescharacteristic, complemented
31C2×#95×C131C2212yescomplemented
32C2×#95×C131C2212yescomplemented
33C2×#95×C131C2211yescharacteristic, complemented
34C2×#95×C131C2212yescomplemented
35C25×C131—24no—
36C25×C131—22no—
37C25×C131—22no—
38C25×C131—24no—
39C25×C131—41no—
40C25×C131—42no—
41C25×C131—42no—
42C25×C131—41no—
43C25×C131—41no—
44C25×C131—41no—
45C25×C131Q814yes—
46C25×C131C2312yes—
47C25×C131C2311yescharacteristic
48C23×C4×C131C2312yes—
49C23×C4×C131C2312yes—
50C23×C4×C131C2312yes—
51C23×C4×C131C2311yescharacteristic
52C23×C4×C131C2312yes—
53C23×C4×C131C2312yes—
54C23×C4×C131C2311yescharacteristic
55C2×C4⋊C4×C131—24no—
56C2×C4⋊C4×C131—24no—
57C2×C4⋊C4×C131—24no—
58C2×C4⋊C4×C131—24no—
59C2×C4⋊C4×C131—22no—
60C2×C4⋊C4×C131—41no—
61C2×C4⋊C4×C131—42no—
62C2×C4⋊C4×C131—42no—
63C2×C4⋊C4×C131—42no—
64C2×C4⋊C4×C131—41no—
65C2×C4⋊C4×C131—41no—
66C2×C22⋊C4×C131—24no—
67C2×C22⋊C4×C131—24no—
68C2×C22⋊C4×C131—24no—
69C2×C22⋊C4×C131—24no—
70C2×C22⋊C4×C131—22no—
71C2×C22⋊C4×C131—24no—
72C2×C22⋊C4×C131—24no—
73C2×C22⋊C4×C131—24no—
74C2×C22⋊C4×C131—24no—
75C2×C22⋊C4×C131—24no—
76C2×C22⋊C4×C131—24no—
77C2×C22⋊C4×C131—24no—
78C2×C22⋊C4×C131—24no—
79C2×C22⋊C4×C131—24no—
80C2×C22⋊C4×C131—42no—
81C2×C22⋊C4×C131—41no—
82C2×C22⋊C4×C131—42no—
83C2×C22⋊C4×C131—41no—
84C2×C22⋊C4×C131—42no—
85C2×C22⋊C4×C131—42no—
86C2×C22⋊C4×C131—42no—
87C2×C22⋊C4×C131—42no—
88C2×C22⋊C4×C131—42no—
89C2×C22⋊C4×C131—42no—
90C2×C22⋊C4×C131—41no—
91C2×C22⋊C4×C131—42no—
92C2×C22⋊C4×C131—42no—
93C2×C22⋊C4×C131—41no—
94C2×C22⋊C4×C131D418yes—
95C2×C22⋊C4×C131D414yes—
96#95×C131—24no—
97#95×C131—22no—
98#95×C131—42no—
99#95×C131—41no—
100#95×C131—42no—
101#95×C131—42no—
102C24×C131—22no—
103C24×C131—22no—
104C24×C131—22no—
105C24×C131—22no—
106C24×C131—22no—
107C24×C131—22no—
108C24×C131—22no—
109C24×C131—21no—
110C24×C131—21no—
111C24×C131—22no—
112C24×C131—21no—
113C24×C131—22no—
114C24×C131—22no—
115C24×C131—21no—
116C24×C131—22no—
117C24×C131—22no—
118C24×C131—22no—
119C24×C131—22no—
120C24×C131—22no—
121C24×C131—22no—
122C24×C131—216no—
123C24×C131—28no—
124C24×C131—44no—
125C24×C131—48no—
126C24×C131—44no—
127C24×C131—44no—
128C24×C131—48no—
129C24×C131—48no—
130C24×C131—48no—
131C24×C131—48no—
132C24×C131—48no—
133C24×C131—44no—
134C24×C131—48no—
135C24×C131—44no—
136C24×C131—48no—
137C24×C131—44no—
138C24×C131—44no—
139C24×C131—48no—
140C24×C131—44no—
141C24×C131—48no—
142C24×C131—44no—
143C24×C131—44no—
144C24×C131—48no—
145C24×C131C2×D414yes—
146C24×C131C2×D412yes—
147C24×C131C2×Q814yes—
148C24×C131C2×Q812yes—
149C24×C131#4112yes—
150C24×C131#4114yes—
151C24×C131C2411yescharacteristic
152C22×C4×C131—22no—
153C22×C4×C131—22no—
154C22×C4×C131—22no—
155C22×C4×C131—22no—
156C22×C4×C131—22no—
157C22×C4×C131—22no—
158C22×C4×C131—21no—
159C22×C4×C131—22no—
160C22×C4×C131—22no—
161C22×C4×C131—22no—
162C22×C4×C131—22no—
163C22×C4×C131—21no—
164C22×C4×C131—22no—
165C22×C4×C131—21no—
166C22×C4×C131—22no—
167C22×C4×C131—21no—
168C22×C4×C131—22no—
169C22×C4×C131—22no—
170C22×C4×C131—22no—
171C22×C4×C131—22no—
172C22×C4×C131—22no—
173C22×C4×C131—22no—
174C22×C4×C131—22no—
175C22×C4×C131—22no—
176C22×C4×C131—22no—
177C22×C4×C131—22no—
178C22×C4×C131—22no—
179C22×C4×C131—22no—
180C22×C4×C131—22no—
181C22×C4×C131—22no—
182C22×C4×C131—22no—
183C22×C4×C131—22no—
184C22×C4×C131—22no—
185C22×C4×C131—22no—
186C22×C4×C131—22no—
187C22×C4×C131—22no—
188C22×C4×C131—22no—
189C22×C4×C131—22no—
190C22×C4×C131—22no—
191C22×C4×C131—22no—
192C22×C4×C131—22no—
193C22×C4×C131C2×D412yes—
194C22×C4×C131C2×D414yes—
195C22×C4×C131C2×D414yes—
196C22×C4×C131C2×D412yes—
197C4⋊C4×C131—44no—
198C4⋊C4×C131—48no—
199C4⋊C4×C131—48no—
200C4⋊C4×C131—44no—
201C22⋊C4×C131—48no—
202C22⋊C4×C131—44no—
203C22⋊C4×C131—48no—
204C22⋊C4×C131—48no—
205C22⋊C4×C131—48no—
206C22⋊C4×C131—48no—
207C22⋊C4×C131—48no—
208C22⋊C4×C131—48no—
209C22⋊C4×C131—48no—
210C22⋊C4×C131—44no—
211C23×C131—24no—
212C23×C131—24no—
213C23×C131—24no—
214C23×C131—24no—
215C23×C131—22no—
216C23×C131—24no—
217C23×C131—22no—
218C23×C131—22no—
219C23×C131—24no—
220C23×C131—22no—
221C23×C131—24no—
222C23×C131—22no—
223C23×C131—24no—
224C23×C131—24no—
225C23×C131—22no—
226C23×C131—24no—
227C23×C131—24no—
228C23×C131—24no—
229C23×C131—24no—
230C23×C131—24no—
231C23×C131—24no—
232C23×C131—24no—
233C23×C131—24no—
234C23×C131—24no—
235C23×C131—24no—
236C23×C131—24no—
237C23×C131—24no—
238C23×C131—24no—
239C23×C131—24no—
240C23×C131—24no—
241C23×C131—416no—
242C23×C131—432no—
243C23×C131—432no—
244C23×C131—416no—
245C23×C131—416no—
246C23×C131—416no—
247C23×C131—416no—
248C23×C131—432no—
249C23×C131—432no—
250C23×C131—416no—
251C23×C131—416no—
252C23×C131—42no—
253C23×C131—42no—
254C23×C131—42no—
255C23×C131—42no—
256C23×C131—42no—
257C23×C131—42no—
258C23×C131—42no—
259C23×C131—42no—
260C23×C131—42no—
261C23×C131—42no—
262C23×C131—42no—
263C23×C131—42no—
264C23×C131—41no—
265C23×C131—42no—
266C23×C131—42no—
267C23×C131—42no—
268C23×C131—42no—
269C23×C131—42no—
270C23×C131—41no—
271C23×C131—42no—
272C23×C131—41no—
273C23×C131—41no—
274C23×C131—42no—
275C23×C131—42no—
276C23×C131—42no—
277C23×C131—42no—
278C23×C131C22⋊Q818yes—
279C23×C131C22⋊Q814yes—
280C23×C131C22×D412yes—
281C23×C131C22×D411yescharacteristic
282C23×C131C22×Q811yescharacteristic
283C23×C131C2×#4111yescharacteristic
284C23×C131C2×#4112yes—
285C23×C131H(5,𝔽2)11yescharacteristic
286C23×C131H(5,𝔽2)11yescharacteristic
287C23×C131H(5,𝔽2)11yescharacteristic
288C23×C131H(5,𝔽2)12yes—
289C23×C131H(5,𝔽2)12yes—
290C23×C131H(5,𝔽2)11yescharacteristic
291C2×C4×C131—24no—
292C2×C4×C131—22no—
293C2×C4×C131—24no—
294C2×C4×C131—22no—
295C2×C4×C131—24no—
296C2×C4×C131—24no—
297C2×C4×C131—24no—
298C2×C4×C131—24no—
299C2×C4×C131—24no—
300C2×C4×C131—24no—
301C2×C4×C131—42no—
302C2×C4×C131—42no—
303C2×C4×C131—42no—
304C2×C4×C131—42no—
305C2×C4×C131—42no—
306C2×C4×C131—42no—
307C2×C4×C131—41no—
308C2×C4×C131—42no—
309C2×C4×C131—42no—
310C2×C4×C131—41no—
311C2×C4×C131—42no—
312C2×C4×C131—41no—
313C2×C4×C131—42no—
314C2×C4×C131—41no—
315C2×C4×C131—42no—
316C2×C4×C131—42no—
317C2×C4×C131—42no—
318C2×C4×C131—42no—
319C2×C4×C131—42no—
320C2×C4×C131—42no—
321C2×C4×C131—42no—
322C2×C4×C131—42no—
323C2×C4×C131—42no—
324C2×C4×C131—42no—
325C2×C4×C131—42no—
326C2×C4×C131—42no—
327C2×C4×C131—42no—
328C2×C4×C131—42no—
329C2×C4×C131—42no—
330C2×C4×C131—42no—
331C2×C4×C131—42no—
332C2×C4×C131—42no—
333C2×C4×C131—42no—
334C2×C4×C131—42no—
335C2×C4×C131—42no—
336C22×C131—28no—
337C22×C131—24no—
338C22×C131—28no—
339C22×C131—28no—
340C22×C131—28no—
341C22×C131—464no—
342C22×C131—44no—
343C22×C131—42no—
344C22×C131—44no—
345C22×C131—44no—
346C22×C131—44no—
347C22×C131—44no—
348C22×C131—42no—
349C22×C131—42no—
350C22×C131—44no—
351C22×C131—44no—
352C22×C131—44no—
353C22×C131—44no—
354C22×C131—44no—
355C22×C131—44no—
356C22×C131—44no—
357C22×C131—42no—
358C22×C131—44no—
359C22×C131—42no—
360C22×C131—44no—
361C22×C131—42no—
362C22×C131—44no—
363C22×C131C2×C22⋊Q812yes—
364C22×C131C2×C22⋊Q811yescharacteristic
365C22×C131#53412yes—
366C22×C131#53411yescharacteristic
367C22×C131#53512yes—
368C22×C131#53511yescharacteristic
369C22×C131#53811yescharacteristic
370C22×C131#53812yes—
371C22×C131#53811yescharacteristic
372C22×C131#53812yes—
373C22×C131#54311yescharacteristic
374C22×C131#54312yes—
375C22×C131#54311yescharacteristic
376C22×C131D4211yescharacteristic
377C22×C131D4212yes—
378C22×C131#54612yes—
379C22×C131#54612yes—
380C22×C131#54612yes—
381C22×C131#55112yes—
382C22×C131#55111yescharacteristic
383C22×C131#56011yescharacteristic
384C22×C131#56011yescharacteristic
385C22×C131#56012yes—
386C4×C131—44no—
387C4×C131—42no—
388C4×C131—44no—
389C4×C131—42no—
390C4×C131—82no—
391C4×C131—82no—
392C4×C131—82no—
393C2×C131—48no—
394C2×C131—44no—
395C2×C131#243711yescharacteristic
396C2×C131#243712yes—
397C2×C131#262612yes—
398C2×C131#262611yescharacteristic
399C2×C131#266811yescharacteristic
400C2×C131#266911yescharacteristic
401C2×C131#267812yes—
402C2×C131#268512yes—
403C2×C131#269711yescharacteristic
404C2×C131#273511yescharacteristic
405C2×C131#284211yescharacteristic
406#16298C13111yesmaximal, characteristic, direct product factor, Sylow
407C131#1629811yescharacteristic, direct product factor, Sylow
408C2×#399C2×C13111yescharacteristic, complemented
409C2×#396C2×C13112yescomplemented
410C2×#379C2×C13111yescharacteristic
411C2×#379C2×C13112yes—
412#1439C2×C13112yescomplemented
413#1439C2×C13112yescomplemented
414#1439C2×C13112yescomplemented
415#1439C2×C13112yescomplemented
416#1439C2×C13111yescharacteristic, complemented
417C26C22×C13111yescharacteristic
418C22×C4⋊C4C22×C13111yescharacteristic, complemented
419C22×C4⋊C4C22×C13112yescomplemented
420C22×C4⋊C4C22×C13112yescomplemented
421C22×C4⋊C4C22×C13111yescharacteristic, complemented
422C22×C22⋊C4C22×C13112yes—
423C22×C22⋊C4C22×C13112yes—
424C22×C22⋊C4C22×C13112yes—
425C22×C22⋊C4C22×C13112yes—
426C22×C22⋊C4C22×C13112yes—
427C22×C22⋊C4C22×C13112yes—
428C22×C22⋊C4C22×C13112yes—
429C22×C22⋊C4C22×C13111yescharacteristic
430C22×C22⋊C4C22×C13112yes—
431C22×C22⋊C4C22×C13111yescharacteristic
432#399—24no—
433#396—28no—
434#379—28no—
435#379—24no—
436C2×#95C22×C13112yescomplemented
437C2×#95C22×C13111yescharacteristic, complemented
438C2×#95C22×C13112yescomplemented
439C2×#95C22×C13112yescomplemented
440C2×#95C22×C13111yescharacteristic, complemented
441C2×#95C22×C13112yescomplemented
442C25—24no—
443C25—22no—
444C25—22no—
445C25—24no—
446C25—41no—
447C25—42no—
448C25—42no—
449C25—41no—
450C25—41no—
451C25—41no—
452C25Q8×C13114yes—
453C25C23×C13112yes—
454C25C23×C13111yescharacteristic
455C23×C4C23×C13112yes—
456C23×C4C23×C13112yes—
457C23×C4C23×C13112yes—
458C23×C4C23×C13111yescharacteristic
459C23×C4C23×C13112yes—
460C23×C4C23×C13112yes—
461C23×C4C23×C13111yescharacteristic
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—24no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—22no—
467C2×C4⋊C4—41no—
468C2×C4⋊C4—42no—
469C2×C4⋊C4—42no—
470C2×C4⋊C4—42no—
471C2×C4⋊C4—41no—
472C2×C4⋊C4—41no—
473C2×C22⋊C4—24no—
474C2×C22⋊C4—22no—
475C2×C22⋊C4—24no—
476C2×C22⋊C4—24no—
477C2×C22⋊C4—24no—
478C2×C22⋊C4—24no—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—24no—
484C2×C22⋊C4—24no—
485C2×C22⋊C4—24no—
486C2×C22⋊C4—24no—
487C2×C22⋊C4—42no—
488C2×C22⋊C4—41no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—41no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—42no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—42no—
496C2×C22⋊C4—42no—
497C2×C22⋊C4—41no—
498C2×C22⋊C4—42no—
499C2×C22⋊C4—42no—
500C2×C22⋊C4—41no—
501C2×C22⋊C4D4×C13118yes—
502C2×C22⋊C4D4×C13114yes—
503#95—24no—
504#95—22no—
505#95—42no—
506#95—41no—
507#95—42no—
508#95—42no—
509C24—22no—
510C24—22no—
511C24—22no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—22no—
516C24—21no—
517C24—21no—
518C24—22no—
519C24—21no—
520C24—22no—
521C24—22no—
522C24—21no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—216no—
530C24—28no—
531C24—44no—
532C24—48no—
533C24—44no—
534C24—44no—
535C24—48no—
536C24—48no—
537C24—48no—
538C24—48no—
539C24—48no—
540C24—44no—
541C24—48no—
542C24—44no—
543C24—48no—
544C24—44no—
545C24—44no—
546C24—48no—
547C24—44no—
548C24—48no—
549C24—44no—
550C24—44no—
551C24—48no—
552C24C2×D4×C13114yes—
553C24C2×D4×C13112yes—
554C24C2×Q8×C13114yes—
555C24C2×Q8×C13112yes—
556C24#41×C13112yes—
557C24#41×C13114yes—
558C24C24×C13111yescharacteristic
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4C2×D4×C13112yes—
601C22×C4C2×D4×C13114yes—
602C22×C4C2×D4×C13114yes—
603C22×C4C2×D4×C13112yes—
604C4⋊C4—44no—
605C4⋊C4—48no—
606C4⋊C4—48no—
607C4⋊C4—44no—
608C22⋊C4—48no—
609C22⋊C4—44no—
610C22⋊C4—48no—
611C22⋊C4—48no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—48no—
615C22⋊C4—48no—
616C22⋊C4—48no—
617C22⋊C4—44no—
618C23—24no—
619C23—24no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—22no—
628C23—24no—
629C23—22no—
630C23—24no—
631C23—24no—
632C23—22no—
633C23—24no—
634C23—24no—
635C23—24no—
636C23—24no—
637C23—24no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—416no—
649C23—432no—
650C23—432no—
651C23—416no—
652C23—416no—
653C23—416no—
654C23—416no—
655C23—416no—
656C23—432no—
657C23—432no—
658C23—416no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—41no—
672C23—42no—
673C23—42no—
674C23—42no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—41no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23C22⋊Q8×C13118yes—
686C23C22⋊Q8×C13114yes—
687C23C22×D4×C13112yes—
688C23C22×D4×C13111yescharacteristic
689C23C22×Q8×C13111yescharacteristic
690C23C2×#41×C13111yescharacteristic
691C23C2×#41×C13112yes—
692C23H(5,𝔽2)×C13111yescharacteristic
693C23H(5,𝔽2)×C13111yescharacteristic
694C23H(5,𝔽2)×C13111yescharacteristic
695C23H(5,𝔽2)×C13112yes—
696C23H(5,𝔽2)×C13112yes—
697C23H(5,𝔽2)×C13111yescharacteristic
698C2×C4—24no—
699C2×C4—22no—
700C2×C4—24no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—41no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C22—28no—
744C22—24no—
745C22—28no—
746C22—28no—
747C22—28no—
748C22—464no—
749C22—42no—
750C22—44no—
751C22—44no—
752C22—42no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—44no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—42no—
767C22—44no—
768C22—42no—
769C22—44no—
770C22C2×C22⋊Q8×C13112yes—
771C22C2×C22⋊Q8×C13111yescharacteristic
772C22#534×C13112yes—
773C22#534×C13111yescharacteristic
774C22#535×C13112yes—
775C22#535×C13111yescharacteristic
776C22#538×C13111yescharacteristic
777C22#538×C13112yes—
778C22#538×C13111yescharacteristic
779C22#538×C13112yes—
780C22#543×C13111yescharacteristic
781C22#543×C13112yes—
782C22#543×C13111yescharacteristic
783C22D42×C13111yescharacteristic
784C22D42×C13112yes—
785C22#546×C13112yes—
786C22#546×C13112yes—
787C22#546×C13112yes—
788C22#551×C13112yes—
789C22#551×C13111yescharacteristic
790C22#560×C13111yescharacteristic
791C22#560×C13111yescharacteristic
792C22#560×C13112yes—
793C4—44no—
794C4—42no—
795C4—44no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—82no—
800C2—48no—
801C2—44no—
802C2#2437×C13111yescharacteristic
803C2#2437×C13112yes—
804C2#2626×C13112yes—
805C2#2626×C13111yescharacteristic
806C2#2668×C13111yescharacteristic
807C2#2669×C13111yescharacteristic
808C2#2678×C13112yes—
809C2#2685×C13112yes—
810C2#2697×C13111yescharacteristic
811C2#2735×C13111yescharacteristic
812C2#2842×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutator, Frattini, cosocleC24C24×C131
prime radicalC26×C131C22
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#399×C131C2semidirect
2. C2×#396×C131C2semidirect
5. #1439×C131C2semidirect
6. #1439×C131C2semidirect
7. #1439×C131C2semidirect
8. #1439×C131C2semidirect
9. #1439×C131C2semidirect
11. C22×C4⋊C4×C131C22semidirect
12. C22×C4⋊C4×C131C22semidirect
13. C22×C4⋊C4×C131C22semidirect
14. C22×C4⋊C4×C131C22semidirect
29. C2×#95×C131C22semidirect
30. C2×#95×C131C22semidirect
31. C2×#95×C131C22semidirect
32. C2×#95×C131C22semidirect
33. C2×#95×C131C22semidirect
34. C2×#95×C131C22semidirect
406. #16298C131direct (N × H)
407. C131#16298direct (N × H)
408. C2×#399C2×C131semidirect
409. C2×#396C2×C131semidirect
412. #1439C2×C131semidirect
413. #1439C2×C131semidirect
414. #1439C2×C131semidirect
415. #1439C2×C131semidirect
416. #1439C2×C131semidirect
418. C22×C4⋊C4C22×C131semidirect
419. C22×C4⋊C4C22×C131semidirect
420. C22×C4⋊C4C22×C131semidirect
421. C22×C4⋊C4C22×C131semidirect
436. C2×#95C22×C131semidirect
437. C2×#95C22×C131semidirect
438. C2×#95C22×C131semidirect
439. C2×#95C22×C131semidirect
440. C2×#95C22×C131semidirect
441. C2×#95C22×C131semidirect

Maximal subgroups

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

subgroupindex
C2×#399×C1312
C2×#396×C1312
C2×#379×C1312
#1439×C1312
#16298131