Finite Group Databasebeta

← C131×#13873 #45699757

Subgroups — C131×#13873 #45699757

Order 33536.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C131C211yesmaximal, characteristic
2C2×#388×C131C212yesmaximal, complemented
3C2×#380×C131C211yesmaximal, characteristic, complemented
4C2×#379×C131C211yesmaximal, characteristic
5C2×#379×C131C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
7#1440×C131C212yesmaximal, complemented
8#1439×C131C212yesmaximal, complemented
9#1437×C131C212yesmaximal, complemented
10C22⋊#95×C131C211yesmaximal, characteristic, complemented
11C22⋊#95×C131C211yesmaximal, characteristic, complemented
12C26×C131C2211yescharacteristic
13C24×C4×C131C2211yescharacteristic
14C24×C4×C131C2211yescharacteristic
15C22×C4⋊C4×C131C2212yescomplemented
16C22×C22⋊C4×C131—28no—
17C22×C22⋊C4×C131C418yescomplemented
18C22×C22⋊C4×C131C2211yescharacteristic
19C22×C22⋊C4×C131C2211yescharacteristic
20C22×C22⋊C4×C131C2212yes—
21C22×C22⋊C4×C131C2212yes—
22C22×C22⋊C4×C131C2212yes—
23C22×C22⋊C4×C131C2212yes—
24C22×C22⋊C4×C131C2211yescharacteristic
25C22×C22⋊C4×C131C2211yescharacteristic
26C22×C22⋊C4×C131C2211yescharacteristic
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2211yescharacteristic
30C22×C42×C131C2212yescomplemented
31#388×C131—28no—
32#380×C131—24no—
33#379×C131—24no—
34#379×C131—24no—
35C4×C22⋊C4×C131—24no—
36C2×#95×C131C2212yescomplemented
37C2×#95×C131C2212yescomplemented
38C2×#95×C131C2212yescomplemented
39C2×#95×C131C2212yescomplemented
40C2×#95×C131C2212yescomplemented
41C2×#95×C131C2212yescomplemented
42C25×C131—24no—
43C25×C131—24no—
44C25×C131—22no—
45C25×C131—22no—
46C25×C131—22no—
47C25×C131—22no—
48C25×C131—22no—
49C25×C131—22no—
50C25×C131—42no—
51C25×C131—42no—
52C25×C131C2×C414yes—
53C25×C131C2311yescharacteristic
54C25×C131C2311yescharacteristic
55C25×C131C2311yescharacteristic
56C23×C4×C131—22no—
57C23×C4×C131—22no—
58C23×C4×C131—22no—
59C23×C4×C131—22no—
60C23×C4×C131—24no—
61C23×C4×C131—24no—
62C23×C4×C131—42no—
63C23×C4×C131—42no—
64C23×C4×C131C2×C414yes—
65C23×C4×C131C2×C414yes—
66C23×C4×C131C2312yes—
67C23×C4×C131C2312yes—
68C23×C4×C131C2311yescharacteristic
69C23×C4×C131C2311yescharacteristic
70C23×C4×C131C2312yes—
71C23×C4×C131C2312yes—
72C23×C4×C131C2311yescharacteristic
73C23×C4×C131C2311yescharacteristic
74C2×C4⋊C4×C131—24no—
75C2×C4⋊C4×C131—24no—
76C2×C4⋊C4×C131—42no—
77C2×C22⋊C4×C131—24no—
78C2×C22⋊C4×C131—22no—
79C2×C22⋊C4×C131—22no—
80C2×C22⋊C4×C131—22no—
81C2×C22⋊C4×C131—22no—
82C2×C22⋊C4×C131—24no—
83C2×C22⋊C4×C131—24no—
84C2×C22⋊C4×C131—232no—
85C2×C22⋊C4×C131—24no—
86C2×C22⋊C4×C131—24no—
87C2×C22⋊C4×C131—22no—
88C2×C22⋊C4×C131—22no—
89C2×C22⋊C4×C131—22no—
90C2×C22⋊C4×C131—24no—
91C2×C22⋊C4×C131—24no—
92C2×C22⋊C4×C131—22no—
93C2×C22⋊C4×C131—22no—
94C2×C22⋊C4×C131—22no—
95C2×C22⋊C4×C131—24no—
96C2×C22⋊C4×C131—24no—
97C2×C22⋊C4×C131—24no—
98C2×C22⋊C4×C131—24no—
99C2×C22⋊C4×C131—42no—
100C2×C22⋊C4×C131—42no—
101C2×C22⋊C4×C131—42no—
102C2×C22⋊C4×C131—42no—
103C2×C22⋊C4×C131C2×C414yes—
104C2×C22⋊C4×C131C2×C414yes—
105C2×C22⋊C4×C131C2×C414yes—
106C2×C22⋊C4×C131C2×C414yes—
107C2×C22⋊C4×C131D414yes—
108C2×C22⋊C4×C131D414yes—
109C2×C22⋊C4×C131D418yes—
110C2×C42×C131—24no—
111C2×C42×C131—24no—
112C2×C42×C131—42no—
113#95×C131—24no—
114#95×C131—24no—
115#95×C131—24no—
116#95×C131—24no—
117#95×C131—42no—
118#95×C131—42no—
119C24×C131—22no—
120C24×C131—22no—
121C24×C131—22no—
122C24×C131—22no—
123C24×C131—216no—
124C24×C131—216no—
125C24×C131—28no—
126C24×C131—28no—
127C24×C131—28no—
128C24×C131—22no—
129C24×C131—21no—
130C24×C131—21no—
131C24×C131—21no—
132C24×C131—21no—
133C24×C131—21no—
134C24×C131—21no—
135C24×C131—22no—
136C24×C131—21no—
137C24×C131—21no—
138C24×C131—21no—
139C24×C131—21no—
140C24×C131—21no—
141C24×C131—21no—
142C24×C131—22no—
143C24×C131—22no—
144C24×C131—22no—
145C24×C131—22no—
146C24×C131—28no—
147C24×C131—28no—
148C24×C131—44no—
149C24×C131—44no—
150C24×C131—48no—
151C24×C131—48no—
152C24×C131—48no—
153C24×C131—48no—
154C24×C131—48no—
155C24×C131—48no—
156C24×C131—48no—
157C24×C131—48no—
158C24×C131—48no—
159C24×C131—48no—
160C24×C131—44no—
161C24×C131—44no—
162C24×C131—44no—
163C24×C131—44no—
164C24×C131C22×C412yes—
165C24×C131C22×C412yes—
166C24×C131C22×C412yes—
167C24×C131C2×D414yes—
168C24×C131C2×D412yes—
169C24×C131C2×D412yes—
170C24×C131#4114yes—
171C24×C131#4112yes—
172C24×C131#4112yes—
173C24×C131#4112yes—
174C24×C131#4112yes—
175C24×C131C2411yescharacteristic
176C22×C4×C131—21no—
177C22×C4×C131—21no—
178C22×C4×C131—21no—
179C22×C4×C131—21no—
180C22×C4×C131—22no—
181C22×C4×C131—22no—
182C22×C4×C131—28no—
183C22×C4×C131—28no—
184C22×C4×C131—21no—
185C22×C4×C131—21no—
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×C131—22no—
194C22×C4×C131—22no—
195C22×C4×C131—22no—
196C22×C4×C131—21no—
197C22×C4×C131—21no—
198C22×C4×C131—22no—
199C22×C4×C131—22no—
200C22×C4×C131—22no—
201C22×C4×C131—22no—
202C22×C4×C131—22no—
203C22×C4×C131—22no—
204C22×C4×C131—28no—
205C22×C4×C131—28no—
206C22×C4×C131—22no—
207C22×C4×C131—22no—
208C22×C4×C131—22no—
209C22×C4×C131—22no—
210C22×C4×C131—22no—
211C22×C4×C131—22no—
212C22×C4×C131—22no—
213C22×C4×C131—22no—
214C22×C4×C131—22no—
215C22×C4×C131—22no—
216C22×C4×C131—22no—
217C22×C4×C131—22no—
218C22×C4×C131—22no—
219C22×C4×C131—22no—
220C22×C4×C131—44no—
221C22×C4×C131—44no—
222C22×C4×C131—48no—
223C22×C4×C131—48no—
224C22×C4×C131—48no—
225C22×C4×C131—48no—
226C22×C4×C131C22×C412yes—
227C22×C4×C131C22×C412yes—
228C22×C4×C131C22×C412yes—
229C22×C4×C131C22×C412yes—
230C22×C4×C131C2×D414yes—
231C22×C4×C131C2×D414yes—
232C22×C4×C131C2×D414yes—
233C22×C4×C131C2×D414yes—
234C4⋊C4×C131—48no—
235C22⋊C4×C131—28no—
236C22⋊C4×C131—28no—
237C22⋊C4×C131—28no—
238C22⋊C4×C131—28no—
239C22⋊C4×C131—28no—
240C22⋊C4×C131—48no—
241C22⋊C4×C131—48no—
242C22⋊C4×C131—48no—
243C22⋊C4×C131—48no—
244C22⋊C4×C131—44no—
245C22⋊C4×C131—44no—
246C22⋊C4×C131C22⋊C4116yescomplemented
247C42×C131—48no—
248C23×C131—22no—
249C23×C131—22no—
250C23×C131—22no—
251C23×C131—22no—
252C23×C131—24no—
253C23×C131—24no—
254C23×C131—24no—
255C23×C131—24no—
256C23×C131—24no—
257C23×C131—24no—
258C23×C131—24no—
259C23×C131—24no—
260C23×C131—24no—
261C23×C131—24no—
262C23×C131—24no—
263C23×C131—24no—
264C23×C131—232no—
265C23×C131—22no—
266C23×C131—22no—
267C23×C131—22no—
268C23×C131—22no—
269C23×C131—22no—
270C23×C131—22no—
271C23×C131—22no—
272C23×C131—22no—
273C23×C131—22no—
274C23×C131—22no—
275C23×C131—22no—
276C23×C131—22no—
277C23×C131—24no—
278C23×C131—24no—
279C23×C131—24no—
280C23×C131—24no—
281C23×C131—24no—
282C23×C131—24no—
283C23×C131—24no—
284C23×C131—24no—
285C23×C131—24no—
286C23×C131—24no—
287C23×C131—24no—
288C23×C131—24no—
289C23×C131—416no—
290C23×C131—416no—
291C23×C131—416no—
292C23×C131—416no—
293C23×C131—416no—
294C23×C131—432no—
295C23×C131—432no—
296C23×C131—432no—
297C23×C131—432no—
298C23×C131—41no—
299C23×C131—41no—
300C23×C131—41no—
301C23×C131—41no—
302C23×C131—41no—
303C23×C131—41no—
304C23×C131—41no—
305C23×C131—41no—
306C23×C131—42no—
307C23×C131—42no—
308C23×C131—42no—
309C23×C131—42no—
310C23×C131—42no—
311C23×C131—42no—
312C23×C131—42no—
313C23×C131—42no—
314C23×C131—42no—
315C23×C131—42no—
316C23×C131—42no—
317C23×C131—42no—
318C23×C131—416no—
319C23×C131C2×C22⋊C414yes—
320C23×C131#11714yes—
321C23×C131#11714yes—
322C23×C131C4×D414yes—
323C23×C131C4×D414yes—
324C23×C131#12114yes—
325C23×C131#12314yes—
326C23×C131#12414yes—
327C23×C131#12614yes—
328C23×C131C23×C411yescharacteristic
329C23×C131C22×D412yes—
330C23×C131C22×D411yescharacteristic
331C23×C131C22×D411yescharacteristic
332C23×C131C2×#4111yescharacteristic
333C23×C131C2×#4111yescharacteristic
334C23×C131C2×#4112yes—
335C23×C131C2×#4111yescharacteristic
336C23×C131C2×#4111yescharacteristic
337C23×C131H(5,𝔽2)12yes—
338C23×C131H(5,𝔽2)12yes—
339C2×C4×C131—22no—
340C2×C4×C131—22no—
341C2×C4×C131—22no—
342C2×C4×C131—22no—
343C2×C4×C131—24no—
344C2×C4×C131—24no—
345C2×C4×C131—24no—
346C2×C4×C131—24no—
347C2×C4×C131—22no—
348C2×C4×C131—22no—
349C2×C4×C131—22no—
350C2×C4×C131—22no—
351C2×C4×C131—22no—
352C2×C4×C131—22no—
353C2×C4×C131—24no—
354C2×C4×C131—24no—
355C2×C4×C131—24no—
356C2×C4×C131—24no—
357C2×C4×C131—24no—
358C2×C4×C131—24no—
359C2×C4×C131—416no—
360C2×C4×C131—416no—
361C2×C4×C131—42no—
362C2×C4×C131—42no—
363C2×C4×C131—42no—
364C2×C4×C131—42no—
365C2×C4×C131—42no—
366C2×C4×C131—42no—
367C2×C4×C131—42no—
368C2×C4×C131—42no—
369C2×C4×C131—42no—
370C2×C4×C131—42no—
371C2×C4×C131—42no—
372C2×C4×C131—42no—
373C2×C4×C131—42no—
374C2×C4×C131—42no—
375C2×C4×C131—42no—
376C2×C4×C131—42no—
377C2×C4×C131—42no—
378C2×C4×C131—42no—
379C2×C4×C131—42no—
380C2×C4×C131—42no—
381C2×C4×C131—42no—
382C2×C4×C131—42no—
383C2×C4×C131—42no—
384C2×C4×C131—42no—
385C2×C4×C131—42no—
386C2×C4×C131—42no—
387C2×C4×C131C2×C22⋊C414yes—
388C2×C4×C131C2×C22⋊C414yes—
389C22×C131—24no—
390C22×C131—24no—
391C22×C131—24no—
392C22×C131—24no—
393C22×C131—24no—
394C22×C131—28no—
395C22×C131—28no—
396C22×C131—28no—
397C22×C131—28no—
398C22×C131—24no—
399C22×C131—24no—
400C22×C131—24no—
401C22×C131—24no—
402C22×C131—24no—
403C22×C131—24no—
404C22×C131—24no—
405C22×C131—464no—
406C22×C131—42no—
407C22×C131—42no—
408C22×C131—42no—
409C22×C131—42no—
410C22×C131—42no—
411C22×C131—42no—
412C22×C131—44no—
413C22×C131—44no—
414C22×C131—44no—
415C22×C131—44no—
416C22×C131—44no—
417C22×C131—44no—
418C22×C131—44no—
419C22×C131—44no—
420C22×C131—42no—
421C22×C131—42no—
422C22×C131#38818yescomplemented
423C22×C131C22×C22⋊C411yescharacteristic
424C22×C131C2×#11711yescharacteristic
425C22×C131C2×#11711yescharacteristic
426C22×C131C2×C4×D411yescharacteristic
427C22×C131C2×C4×D411yescharacteristic
428C22×C131#51811yescharacteristic
429C22×C131#51811yescharacteristic
430C22×C131C2×#12111yescharacteristic
431C22×C131C2×#12311yescharacteristic
432C22×C131#52512yes—
433C22×C131#52512yes—
434C22×C131C2×#12411yescharacteristic
435C22×C131C2×#12611yescharacteristic
436C22×C131#53812yes—
437C22×C131#53812yes—
438C22×C131D4212yes—
439C22×C131D4212yes—
440C22×C131#54612yes—
441C22×C131#54612yes—
442C22×C131#54612yes—
443C22×C131#54612yes—
444C22×C131#55112yes—
445C22×C131#55112yes—
446C4×C131—24no—
447C4×C131—24no—
448C4×C131—42no—
449C4×C131—42no—
450C4×C131—44no—
451C4×C131—44no—
452C4×C131—82no—
453C4×C131—82no—
454C2×C131—28no—
455C2×C131—44no—
456C2×C131—44no—
457C2×C131#228011yescharacteristic
458C2×C131C2×#38811yescharacteristic
459C2×C131#231211yescharacteristic
460C2×C131D4×C22⋊C411yescharacteristic
461C2×C131D4×C22⋊C411yescharacteristic
462C2×C131#234211yescharacteristic
463C2×C131#234211yescharacteristic
464C2×C131#241812yes—
465C2×C131#242412yes—
466C2×C131#247212yes—
467C2×C131#248012yes—
468#13873C13111yesmaximal, characteristic, direct product factor, Sylow
469C131#1387311yescharacteristic, direct product factor, Sylow
470C23×C22⋊C4C2×C13111yescharacteristic
471C2×#388C2×C13112yescomplemented
472C2×#380C2×C13111yescharacteristic, complemented
473C2×#379C2×C13111yescharacteristic
474C2×#379C2×C13111yescharacteristic
475C2×C4×C22⋊C4C2×C13111yescharacteristic, complemented
476#1440C2×C13112yescomplemented
477#1439C2×C13112yescomplemented
478#1437C2×C13112yescomplemented
479C22⋊#95C2×C13111yescharacteristic, complemented
480C22⋊#95C2×C13111yescharacteristic, complemented
481C26C22×C13111yescharacteristic
482C24×C4C22×C13111yescharacteristic
483C24×C4C22×C13111yescharacteristic
484C22×C4⋊C4C22×C13112yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C13118yescomplemented
487C22×C22⋊C4C22×C13111yescharacteristic
488C22×C22⋊C4C22×C13111yescharacteristic
489C22×C22⋊C4C22×C13112yes—
490C22×C22⋊C4C22×C13112yes—
491C22×C22⋊C4C22×C13112yes—
492C22×C22⋊C4C22×C13112yes—
493C22×C22⋊C4C22×C13111yescharacteristic
494C22×C22⋊C4C22×C13111yescharacteristic
495C22×C22⋊C4C22×C13111yescharacteristic
496C22×C22⋊C4C22×C13111yescharacteristic
497C22×C22⋊C4C22×C13111yescharacteristic
498C22×C22⋊C4C22×C13111yescharacteristic
499C22×C42C22×C13112yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C13112yescomplemented
506C2×#95C22×C13112yescomplemented
507C2×#95C22×C13112yescomplemented
508C2×#95C22×C13112yescomplemented
509C2×#95C22×C13112yescomplemented
510C2×#95C22×C13112yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C13114yes—
522C25C23×C13111yescharacteristic
523C25C23×C13111yescharacteristic
524C25C23×C13111yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C13114yes—
534C23×C4C2×C4×C13114yes—
535C23×C4C23×C13112yes—
536C23×C4C23×C13112yes—
537C23×C4C23×C13111yescharacteristic
538C23×C4C23×C13111yescharacteristic
539C23×C4C23×C13112yes—
540C23×C4C23×C13112yes—
541C23×C4C23×C13111yescharacteristic
542C23×C4C23×C13111yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C13114yes—
573C2×C22⋊C4C2×C4×C13114yes—
574C2×C22⋊C4C2×C4×C13114yes—
575C2×C22⋊C4C2×C4×C13114yes—
576C2×C22⋊C4D4×C13114yes—
577C2×C22⋊C4D4×C13114yes—
578C2×C22⋊C4D4×C13118yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C13112yes—
634C24C22×C4×C13112yes—
635C24C22×C4×C13112yes—
636C24C2×D4×C13114yes—
637C24C2×D4×C13112yes—
638C24C2×D4×C13112yes—
639C24#41×C13114yes—
640C24#41×C13112yes—
641C24#41×C13112yes—
642C24#41×C13112yes—
643C24#41×C13112yes—
644C24C24×C13111yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C13112yes—
696C22×C4C22×C4×C13112yes—
697C22×C4C22×C4×C13112yes—
698C22×C4C22×C4×C13112yes—
699C22×C4C2×D4×C13114yes—
700C22×C4C2×D4×C13114yes—
701C22×C4C2×D4×C13114yes—
702C22×C4C2×D4×C13114yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C131116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—416no—
764C23—432no—
765C23—432no—
766C23—432no—
767C23—416no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23C2×C22⋊C4×C13114yes—
789C23#117×C13114yes—
790C23#117×C13114yes—
791C23C4×D4×C13114yes—
792C23C4×D4×C13114yes—
793C23#121×C13114yes—
794C23#123×C13114yes—
795C23#124×C13114yes—
796C23#126×C13114yes—
797C23C23×C4×C13111yescharacteristic
798C23C22×D4×C13112yes—
799C23C22×D4×C13111yescharacteristic
800C23C22×D4×C13111yescharacteristic
801C23C2×#41×C13111yescharacteristic
802C23C2×#41×C13111yescharacteristic
803C23C2×#41×C13112yes—
804C23C2×#41×C13111yescharacteristic
805C23C2×#41×C13111yescharacteristic
806C23H(5,𝔽2)×C13112yes—
807C23H(5,𝔽2)×C13112yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C13114yes—
857C2×C4C2×C22⋊C4×C13114yes—
858C22—28no—
859C22—24no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—28no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—42no—
878C22—42no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—44no—
886C22—44no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#388×C13118yescomplemented
892C22C22×C22⋊C4×C13111yescharacteristic
893C22C2×#117×C13111yescharacteristic
894C22C2×#117×C13111yescharacteristic
895C22C2×C4×D4×C13111yescharacteristic
896C22C2×C4×D4×C13111yescharacteristic
897C22#518×C13111yescharacteristic
898C22#518×C13111yescharacteristic
899C22C2×#121×C13111yescharacteristic
900C22C2×#123×C13111yescharacteristic
901C22#525×C13112yes—
902C22#525×C13112yes—
903C22C2×#124×C13111yescharacteristic
904C22C2×#126×C13111yescharacteristic
905C22#538×C13112yes—
906C22#538×C13112yes—
907C22D42×C13112yes—
908C22D42×C13112yes—
909C22#546×C13112yes—
910C22#546×C13112yes—
911C22#546×C13112yes—
912C22#546×C13112yes—
913C22#551×C13112yes—
914C22#551×C13112yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2#2280×C13111yescharacteristic
927C2C2×#388×C13111yescharacteristic
928C2#2312×C13111yescharacteristic
929C2D4×C22⋊C4×C13111yescharacteristic
930C2D4×C22⋊C4×C13111yescharacteristic
931C2#2342×C13111yescharacteristic
932C2#2342×C13111yescharacteristic
933C2#2418×C13112yes—
934C2#2424×C13112yes—
935C2#2472×C13112yes—
936C2#2480×C13112yes—
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC26×C131C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C131C2semidirect
3. C2×#380×C131C2semidirect
6. C2×C4×C22⋊C4×C131C2semidirect
7. #1440×C131C2semidirect
8. #1439×C131C2semidirect
9. #1437×C131C2semidirect
10. C22⋊#95×C131C2semidirect
11. C22⋊#95×C131C2semidirect
15. C22×C4⋊C4×C131C22semidirect
17. C22×C22⋊C4×C131C4semidirect
30. C22×C42×C131C22semidirect
36. C2×#95×C131C22semidirect
37. C2×#95×C131C22semidirect
38. C2×#95×C131C22semidirect
39. C2×#95×C131C22semidirect
40. C2×#95×C131C22semidirect
41. C2×#95×C131C22semidirect
246. C22⋊C4×C131C22⋊C4semidirect
422. C22×C131#388semidirect
468. #13873C131direct (N × H)
469. C131#13873direct (N × H)
471. C2×#388C2×C131semidirect
472. C2×#380C2×C131semidirect
475. C2×C4×C22⋊C4C2×C131semidirect
476. #1440C2×C131semidirect
477. #1439C2×C131semidirect
478. #1437C2×C131semidirect
479. C22⋊#95C2×C131semidirect
480. C22⋊#95C2×C131semidirect
484. C22×C4⋊C4C22×C131semidirect
486. C22×C22⋊C4C4×C131semidirect
499. C22×C42C22×C131semidirect
505. C2×#95C22×C131semidirect
506. C2×#95C22×C131semidirect
507. C2×#95C22×C131semidirect
508. C2×#95C22×C131semidirect
509. C2×#95C22×C131semidirect
510. C2×#95C22×C131semidirect
715. C22⋊C4C22⋊C4×C131semidirect
891. C22#388×C131semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1312
C2×#388×C1312
C2×#380×C1312
C2×#379×C1312
C2×C4×C22⋊C4×C1312
#1440×C1312
#1439×C1312
#1437×C1312
C22⋊#95×C1312
#13873131