Finite Group Databasebeta

← C131×#13995 #45699879

Subgroups — C131×#13995 #45699879

Order 33536.

4210 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C131C211yesmaximal, characteristic
2C23×C22⋊C4×C131C211yesmaximal, characteristic, complemented
3C2×#390×C131C212yesmaximal, complemented
4C2×#386×C131C211yesmaximal, characteristic, complemented
5C2×#386×C131C211yesmaximal, characteristic, complemented
6C2×#385×C131C211yesmaximal, characteristic, complemented
7C2×#379×C131C211yesmaximal, characteristic, complemented
8C2×C4×C22⋊C4×C131C211yesmaximal, characteristic, complemented
9#1439×C131C212yesmaximal, complemented
10#1438×C131C212yesmaximal, complemented
11#1437×C131C212yesmaximal, complemented
12C26×C131C2211yescharacteristic
13C23×D4×C131C2211yescharacteristic
14C23×D4×C131C2212yes—
15C24×C4×C131C2211yescharacteristic
16C24×C4×C131C2211yescharacteristic
17C2×#120×C131—24no—
18C2×#120×C131—24no—
19C2×#120×C131C418yescomplemented
20C22×C4⋊C4×C131C2212yescomplemented
21C22×C22⋊C4×C131—24no—
22C22×C22⋊C4×C131—28no—
23C22×C22⋊C4×C131C2211yescharacteristic
24C22×C22⋊C4×C131C2212yes—
25C22×C22⋊C4×C131C2212yes—
26C22×C22⋊C4×C131C2212yes—
27C22×C22⋊C4×C131C2212yes—
28C22×C22⋊C4×C131C2211yescharacteristic
29C22×C22⋊C4×C131C2212yes—
30C22×C22⋊C4×C131C2211yescharacteristic
31C22×C22⋊C4×C131C2211yescharacteristic, complemented
32C22×C22⋊C4×C131C2212yescomplemented
33C22×C22⋊C4×C131C2211yescharacteristic, complemented
34C22×C42×C131C2212yescomplemented
35#390×C131—28no—
36#386×C131—24no—
37#386×C131—24no—
38#385×C131—24no—
39#379×C131—24no—
40C4×C22⋊C4×C131—24no—
41C2×#95×C131C2212yescomplemented
42C2×#95×C131C2212yescomplemented
43C2×#95×C131C2211yescharacteristic, complemented
44C2×#95×C131C2212yescomplemented
45C2×#95×C131C2211yescharacteristic, complemented
46C25×C131—24no—
47C25×C131—22no—
48C25×C131—24no—
49C25×C131—22no—
50C25×C131—22no—
51C25×C131—22no—
52C25×C131—22no—
53C25×C131—22no—
54C25×C131—42no—
55C25×C131—42no—
56C25×C131C2×C414yes—
57C25×C131C2311yescharacteristic
58C25×C131C2312yes—
59C25×C131C2311yescharacteristic
60C22×D4×C131—24no—
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—22no—
65C22×D4×C131—24no—
66C22×D4×C131—22no—
67C22×D4×C131—22no—
68C22×D4×C131—24no—
69C22×D4×C131—24no—
70C22×D4×C131—42no—
71C22×D4×C131—42no—
72C22×D4×C131C2×C414yes—
73C22×D4×C131C2×C418yescomplemented
74C23×C4×C131—22no—
75C23×C4×C131—22no—
76C23×C4×C131—22no—
77C23×C4×C131—24no—
78C23×C4×C131—24no—
79C23×C4×C131—22no—
80C23×C4×C131—22no—
81C23×C4×C131—42no—
82C23×C4×C131—42no—
83C23×C4×C131D414yescomplemented
84C23×C4×C131C2311yescharacteristic
85C23×C4×C131C2311yescharacteristic
86C23×C4×C131C2311yescharacteristic
87C23×C4×C131C2312yes—
88C23×C4×C131C2312yes—
89C23×C4×C131C2311yescharacteristic
90C23×C4×C131C2312yes—
91C23×C4×C131C2311yescharacteristic
92#120×C131—232no—
93C2×C4⋊C4×C131—24no—
94C2×C4⋊C4×C131—24no—
95C2×C4⋊C4×C131—42no—
96C2×C22⋊C4×C131—232no—
97C2×C22⋊C4×C131—24no—
98C2×C22⋊C4×C131—22no—
99C2×C22⋊C4×C131—22no—
100C2×C22⋊C4×C131—24no—
101C2×C22⋊C4×C131—24no—
102C2×C22⋊C4×C131—24no—
103C2×C22⋊C4×C131—24no—
104C2×C22⋊C4×C131—24no—
105C2×C22⋊C4×C131—24no—
106C2×C22⋊C4×C131—24no—
107C2×C22⋊C4×C131—22no—
108C2×C22⋊C4×C131—22no—
109C2×C22⋊C4×C131—22no—
110C2×C22⋊C4×C131—24no—
111C2×C22⋊C4×C131—24no—
112C2×C22⋊C4×C131—24no—
113C2×C22⋊C4×C131—24no—
114C2×C22⋊C4×C131—24no—
115C2×C22⋊C4×C131—24no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—42no—
119C2×C22⋊C4×C131—42no—
120C2×C22⋊C4×C131—42no—
121C2×C22⋊C4×C131—42no—
122C2×C22⋊C4×C131C2×C414yes—
123C2×C22⋊C4×C131C2×C418yescomplemented
124C2×C22⋊C4×C131D414yes—
125C2×C22⋊C4×C131D414yes—
126C2×C22⋊C4×C131D418yescomplemented
127C2×C22⋊C4×C131D414yescomplemented
128C2×C42×C131—24no—
129C2×C42×C131—24no—
130C2×C42×C131—42no—
131#95×C131—24no—
132#95×C131—24no—
133#95×C131—24no—
134#95×C131—22no—
135#95×C131—22no—
136C24×C131—22no—
137C24×C131—22no—
138C24×C131—22no—
139C24×C131—22no—
140C24×C131—28no—
141C24×C131—28no—
142C24×C131—216no—
143C24×C131—216no—
144C24×C131—28no—
145C24×C131—22no—
146C24×C131—22no—
147C24×C131—22no—
148C24×C131—22no—
149C24×C131—22no—
150C24×C131—22no—
151C24×C131—22no—
152C24×C131—22no—
153C24×C131—22no—
154C24×C131—22no—
155C24×C131—22no—
156C24×C131—22no—
157C24×C131—28no—
158C24×C131—28no—
159C24×C131—21no—
160C24×C131—22no—
161C24×C131—21no—
162C24×C131—21no—
163C24×C131—21no—
164C24×C131—21no—
165C24×C131—21no—
166C24×C131—22no—
167C24×C131—22no—
168C24×C131—22no—
169C24×C131—48no—
170C24×C131—48no—
171C24×C131—48no—
172C24×C131—48no—
173C24×C131—48no—
174C24×C131—48no—
175C24×C131—48no—
176C24×C131—48no—
177C24×C131—48no—
178C24×C131—44no—
179C24×C131—44no—
180C24×C131—48no—
181C24×C131—44no—
182C24×C131—44no—
183C24×C131—44no—
184C24×C131—44no—
185C24×C131C22×C412yes—
186C24×C131C22×C414yes—
187C24×C131C22×C412yes—
188C24×C131C2×D414yes—
189C24×C131C2×D412yes—
190C24×C131C2×D412yes—
191C24×C131C2×D412yes—
192C24×C131C2×D412yes—
193C24×C131#4114yes—
194C24×C131#4112yes—
195C24×C131#4112yes—
196C24×C131C2411yescharacteristic
197C2×D4×C131—28no—
198C2×D4×C131—28no—
199C2×D4×C131—28no—
200C2×D4×C131—216no—
201C2×D4×C131—216no—
202C2×D4×C131—48no—
203C2×D4×C131—48no—
204C2×D4×C131—48no—
205C2×D4×C131—48no—
206C2×D4×C131—48no—
207C2×D4×C131—44no—
208C2×D4×C131—44no—
209C2×D4×C131—44no—
210C2×D4×C131—44no—
211C22×C4×C131—21no—
212C22×C4×C131—22no—
213C22×C4×C131—21no—
214C22×C4×C131—22no—
215C22×C4×C131—22no—
216C22×C4×C131—22no—
217C22×C4×C131—22no—
218C22×C4×C131—28no—
219C22×C4×C131—28no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—21no—
223C22×C4×C131—22no—
224C22×C4×C131—22no—
225C22×C4×C131—22no—
226C22×C4×C131—22no—
227C22×C4×C131—22no—
228C22×C4×C131—22no—
229C22×C4×C131—22no—
230C22×C4×C131—21no—
231C22×C4×C131—21no—
232C22×C4×C131—22no—
233C22×C4×C131—22no—
234C22×C4×C131—21no—
235C22×C4×C131—21no—
236C22×C4×C131—21no—
237C22×C4×C131—22no—
238C22×C4×C131—22no—
239C22×C4×C131—22no—
240C22×C4×C131—22no—
241C22×C4×C131—22no—
242C22×C4×C131—28no—
243C22×C4×C131—21no—
244C22×C4×C131—21no—
245C22×C4×C131—21no—
246C22×C4×C131—21no—
247C22×C4×C131—21no—
248C22×C4×C131—22no—
249C22×C4×C131—21no—
250C22×C4×C131—22no—
251C22×C4×C131—22no—
252C22×C4×C131—22no—
253C22×C4×C131—44no—
254C22×C4×C131—48no—
255C22×C4×C131—48no—
256C22×C4×C131—48no—
257C22×C4×C131—48no—
258C22×C4×C131—44no—
259C22×C4×C131—44no—
260C22×C4×C131C22×C412yes—
261C22×C4×C131C22×C414yes—
262C22×C4×C131C2×D414yes—
263C22×C4×C131C2×D412yes—
264C22×C4×C131C2×D414yes—
265C22×C4×C131C2×D414yes—
266C22×C4×C131C2×D414yes—
267C22×C4×C131C2×D412yes—
268C22×C4×C131C2×D414yes—
269C4⋊C4×C131—48no—
270C22⋊C4×C131—216no—
271C22⋊C4×C131—28no—
272C22⋊C4×C131—216no—
273C22⋊C4×C131—216no—
274C22⋊C4×C131—48no—
275C22⋊C4×C131—48no—
276C22⋊C4×C131—48no—
277C22⋊C4×C131—44no—
278C22⋊C4×C131—44no—
279C22⋊C4×C131—44no—
280C22⋊C4×C131C22⋊C4116yescomplemented
281C42×C131—48no—
282C23×C131—24no—
283C23×C131—24no—
284C23×C131—22no—
285C23×C131—22no—
286C23×C131—24no—
287C23×C131—22no—
288C23×C131—22no—
289C23×C131—24no—
290C23×C131—24no—
291C23×C131—24no—
292C23×C131—24no—
293C23×C131—24no—
294C23×C131—24no—
295C23×C131—24no—
296C23×C131—24no—
297C23×C131—24no—
298C23×C131—232no—
299C23×C131—24no—
300C23×C131—24no—
301C23×C131—24no—
302C23×C131—24no—
303C23×C131—24no—
304C23×C131—24no—
305C23×C131—24no—
306C23×C131—24no—
307C23×C131—24no—
308C23×C131—24no—
309C23×C131—24no—
310C23×C131—24no—
311C23×C131—24no—
312C23×C131—24no—
313C23×C131—24no—
314C23×C131—24no—
315C23×C131—24no—
316C23×C131—24no—
317C23×C131—22no—
318C23×C131—22no—
319C23×C131—24no—
320C23×C131—22no—
321C23×C131—24no—
322C23×C131—432no—
323C23×C131—432no—
324C23×C131—416no—
325C23×C131—416no—
326C23×C131—416no—
327C23×C131—432no—
328C23×C131—416no—
329C23×C131—432no—
330C23×C131—416no—
331C23×C131—42no—
332C23×C131—42no—
333C23×C131—42no—
334C23×C131—42no—
335C23×C131—42no—
336C23×C131—42no—
337C23×C131—42no—
338C23×C131—42no—
339C23×C131—42no—
340C23×C131—42no—
341C23×C131—42no—
342C23×C131—42no—
343C23×C131—42no—
344C23×C131—42no—
345C23×C131—42no—
346C23×C131—42no—
347C23×C131—416no—
348C23×C131—41no—
349C23×C131—41no—
350C23×C131—41no—
351C23×C131—41no—
352C23×C131—42no—
353C23×C131—41no—
354C23×C131—41no—
355C23×C131—41no—
356C23×C131—41no—
357C23×C131—42no—
358C23×C131—42no—
359C23×C131—42no—
360C23×C131—42no—
361C23×C131—42no—
362C23×C131—42no—
363C23×C131—42no—
364C23×C131—42no—
365C23×C131—42no—
366C23×C131C2×C22⋊C414yes—
367C23×C131C4×D418yes—
368C23×C131C4×D414yes—
369C23×C131C4×D414yes—
370C23×C131#12114yes—
371C23×C131#12114yes—
372C23×C131#12414yes—
373C23×C131#12714yes—
374C23×C131C23×C411yescharacteristic
375C23×C131C22×D411yescharacteristic
376C23×C131C22×D411yescharacteristic
377C23×C131C22×D411yescharacteristic
378C23×C131C22×D412yes—
379C23×C131C22×D411yescharacteristic
380C23×C131C2×#4111yescharacteristic
381C23×C131C2×#4111yescharacteristic
382C23×C131C2×#4112yes—
383C23×C131H(5,𝔽2)12yes—
384C23×C131H(5,𝔽2)12yes—
385D4×C131—432no—
386D4×C131—416no—
387C2×C4×C131—24no—
388C2×C4×C131—24no—
389C2×C4×C131—22no—
390C2×C4×C131—22no—
391C2×C4×C131—24no—
392C2×C4×C131—24no—
393C2×C4×C131—24no—
394C2×C4×C131—24no—
395C2×C4×C131—24no—
396C2×C4×C131—24no—
397C2×C4×C131—22no—
398C2×C4×C131—22no—
399C2×C4×C131—22no—
400C2×C4×C131—22no—
401C2×C4×C131—24no—
402C2×C4×C131—24no—
403C2×C4×C131—22no—
404C2×C4×C131—22no—
405C2×C4×C131—24no—
406C2×C4×C131—24no—
407C2×C4×C131—24no—
408C2×C4×C131—24no—
409C2×C4×C131—416no—
410C2×C4×C131—416no—
411C2×C4×C131—41no—
412C2×C4×C131—41no—
413C2×C4×C131—42no—
414C2×C4×C131—41no—
415C2×C4×C131—42no—
416C2×C4×C131—41no—
417C2×C4×C131—42no—
418C2×C4×C131—42no—
419C2×C4×C131—42no—
420C2×C4×C131—42no—
421C2×C4×C131—42no—
422C2×C4×C131—42no—
423C2×C4×C131—42no—
424C2×C4×C131—42no—
425C2×C4×C131—41no—
426C2×C4×C131—41no—
427C2×C4×C131—41no—
428C2×C4×C131—41no—
429C2×C4×C131—41no—
430C2×C4×C131—41no—
431C2×C4×C131—42no—
432C2×C4×C131—42no—
433C2×C4×C131—42no—
434C2×C4×C131—42no—
435C2×C4×C131C2×C22⋊C418yescomplemented
436C2×C4×C131#12014yescomplemented
437C22×C131—24no—
438C22×C131—28no—
439C22×C131—28no—
440C22×C131—24no—
441C22×C131—24no—
442C22×C131—28no—
443C22×C131—24no—
444C22×C131—28no—
445C22×C131—24no—
446C22×C131—24no—
447C22×C131—28no—
448C22×C131—28no—
449C22×C131—28no—
450C22×C131—464no—
451C22×C131—44no—
452C22×C131—44no—
453C22×C131—44no—
454C22×C131—44no—
455C22×C131—44no—
456C22×C131—44no—
457C22×C131—44no—
458C22×C131—44no—
459C22×C131—44no—
460C22×C131—44no—
461C22×C131—44no—
462C22×C131—44no—
463C22×C131—42no—
464C22×C131—44no—
465C22×C131—44no—
466C22×C131—42no—
467C22×C131—42no—
468C22×C131—81no—
469C22×C131—81no—
470C22×C131—82no—
471C22×C131—81no—
472C22×C131—82no—
473C22×C131—81no—
474C22×C131#39018yescomplemented
475C22×C131C22×C22⋊C411yescharacteristic
476C22×C131C2×C4×D411yescharacteristic
477C22×C131C2×C4×D412yes—
478C22×C131C2×C4×D411yescharacteristic
479C22×C131#51812yes—
480C22×C131C2×#12011yescharacteristic
481C22×C131C2×#12111yescharacteristic
482C22×C131C2×#12111yescharacteristic
483C22×C131#52511yescharacteristic
484C22×C131#52512yes—
485C22×C131C2×#12411yescharacteristic
486C22×C131C2×#12711yescharacteristic
487C22×C131#53411yescharacteristic
488C22×C131#53511yescharacteristic
489C22×C131#53812yes—
490C22×C131D4212yes—
491C22×C131D4212yes—
492C22×C131D4212yes—
493C22×C131#54612yes—
494C22×C131#54612yes—
495C22×C131#54612yes—
496C22×C131#54612yes—
497C22×C131#55112yes—
498C4×C131—28no—
499C4×C131—24no—
500C4×C131—42no—
501C4×C131—44no—
502C4×C131—44no—
503C4×C131—42no—
504C4×C131—81no—
505C4×C131—81no—
506C2×C131—28no—
507C2×C131—48no—
508C2×C131—82no—
509C2×C131C2×#39011yescharacteristic
510C2×C131C4×#12011yescharacteristic
511C2×C131#232111yescharacteristic
512C2×C131D4×C22⋊C412yes—
513C2×C131#235812yes—
514C2×C131#241011yescharacteristic
515C2×C131#241111yescharacteristic
516C2×C131#242412yes—
517C2×C131#243311yescharacteristic
518C2×C131#247212yes—
519C2×C131#253911yescharacteristic
520#13995C13111yesmaximal, characteristic, direct product factor, Sylow
521C131#1399511yescharacteristic, direct product factor, Sylow
522C22×#120C2×C13111yescharacteristic
523C23×C22⋊C4C2×C13111yescharacteristic, complemented
524C2×#390C2×C13112yescomplemented
525C2×#386C2×C13111yescharacteristic, complemented
526C2×#386C2×C13111yescharacteristic, complemented
527C2×#385C2×C13111yescharacteristic, complemented
528C2×#379C2×C13111yescharacteristic, complemented
529C2×C4×C22⋊C4C2×C13111yescharacteristic, complemented
530#1439C2×C13112yescomplemented
531#1438C2×C13112yescomplemented
532#1437C2×C13112yescomplemented
533C26C22×C13111yescharacteristic
534C23×D4C22×C13111yescharacteristic
535C23×D4C22×C13112yes—
536C24×C4C22×C13111yescharacteristic
537C24×C4C22×C13111yescharacteristic
538C2×#120—24no—
539C2×#120—24no—
540C2×#120C4×C13118yescomplemented
541C22×C4⋊C4C22×C13112yescomplemented
542C22×C22⋊C4—24no—
543C22×C22⋊C4—28no—
544C22×C22⋊C4C22×C13112yes—
545C22×C22⋊C4C22×C13111yescharacteristic
546C22×C22⋊C4C22×C13112yes—
547C22×C22⋊C4C22×C13112yes—
548C22×C22⋊C4C22×C13112yes—
549C22×C22⋊C4C22×C13112yes—
550C22×C22⋊C4C22×C13111yescharacteristic
551C22×C22⋊C4C22×C13111yescharacteristic
552C22×C22⋊C4C22×C13111yescharacteristic, complemented
553C22×C22⋊C4C22×C13112yescomplemented
554C22×C22⋊C4C22×C13111yescharacteristic, complemented
555C22×C42C22×C13112yescomplemented
556#390—28no—
557#386—24no—
558#386—24no—
559#385—24no—
560#379—24no—
561C4×C22⋊C4—24no—
562C2×#95C22×C13111yescharacteristic, complemented
563C2×#95C22×C13112yescomplemented
564C2×#95C22×C13112yescomplemented
565C2×#95C22×C13112yescomplemented
566C2×#95C22×C13111yescharacteristic, complemented
567C25—24no—
568C25—22no—
569C25—24no—
570C25—22no—
571C25—22no—
572C25—22no—
573C25—22no—
574C25—22no—
575C25—42no—
576C25—42no—
577C25C2×C4×C13114yes—
578C25C23×C13111yescharacteristic
579C25C23×C13112yes—
580C25C23×C13111yescharacteristic
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—22no—
584C22×D4—22no—
585C22×D4—24no—
586C22×D4—24no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—24no—
590C22×D4—24no—
591C22×D4—42no—
592C22×D4—42no—
593C22×D4C2×C4×C13114yes—
594C22×D4C2×C4×C13118yescomplemented
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—24no—
599C23×C4—24no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—42no—
603C23×C4—42no—
604C23×C4D4×C13114yescomplemented
605C23×C4C23×C13111yescharacteristic
606C23×C4C23×C13111yescharacteristic
607C23×C4C23×C13111yescharacteristic
608C23×C4C23×C13112yes—
609C23×C4C23×C13112yes—
610C23×C4C23×C13111yescharacteristic
611C23×C4C23×C13112yes—
612C23×C4C23×C13111yescharacteristic
613#120—232no—
614C2×C4⋊C4—24no—
615C2×C4⋊C4—24no—
616C2×C4⋊C4—42no—
617C2×C22⋊C4—232no—
618C2×C22⋊C4—24no—
619C2×C22⋊C4—22no—
620C2×C22⋊C4—22no—
621C2×C22⋊C4—24no—
622C2×C22⋊C4—24no—
623C2×C22⋊C4—24no—
624C2×C22⋊C4—24no—
625C2×C22⋊C4—24no—
626C2×C22⋊C4—24no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—24no—
631C2×C22⋊C4—24no—
632C2×C22⋊C4—24no—
633C2×C22⋊C4—24no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—24no—
638C2×C22⋊C4—24no—
639C2×C22⋊C4—42no—
640C2×C22⋊C4—42no—
641C2×C22⋊C4—42no—
642C2×C22⋊C4—42no—
643C2×C22⋊C4C2×C4×C13114yes—
644C2×C22⋊C4C2×C4×C13118yescomplemented
645C2×C22⋊C4D4×C13114yes—
646C2×C22⋊C4D4×C13114yes—
647C2×C22⋊C4D4×C13118yescomplemented
648C2×C22⋊C4D4×C13114yescomplemented
649C2×C42—24no—
650C2×C42—24no—
651C2×C42—42no—
652#95—24no—
653#95—24no—
654#95—24no—
655#95—22no—
656#95—22no—
657C24—22no—
658C24—22no—
659C24—22no—
660C24—22no—
661C24—28no—
662C24—28no—
663C24—216no—
664C24—216no—
665C24—28no—
666C24—22no—
667C24—22no—
668C24—22no—
669C24—22no—
670C24—22no—
671C24—22no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—22no—
677C24—22no—
678C24—28no—
679C24—28no—
680C24—21no—
681C24—22no—
682C24—21no—
683C24—21no—
684C24—21no—
685C24—21no—
686C24—21no—
687C24—22no—
688C24—22no—
689C24—22no—
690C24—48no—
691C24—48no—
692C24—48no—
693C24—48no—
694C24—48no—
695C24—48no—
696C24—48no—
697C24—48no—
698C24—48no—
699C24—44no—
700C24—44no—
701C24—48no—
702C24—44no—
703C24—44no—
704C24—44no—
705C24—44no—
706C24C22×C4×C13112yes—
707C24C22×C4×C13114yes—
708C24C22×C4×C13112yes—
709C24C2×D4×C13114yes—
710C24C2×D4×C13112yes—
711C24C2×D4×C13112yes—
712C24C2×D4×C13112yes—
713C24C2×D4×C13112yes—
714C24#41×C13114yes—
715C24#41×C13112yes—
716C24#41×C13112yes—
717C24C24×C13111yescharacteristic
718C2×D4—28no—
719C2×D4—28no—
720C2×D4—28no—
721C2×D4—216no—
722C2×D4—216no—
723C2×D4—48no—
724C2×D4—48no—
725C2×D4—48no—
726C2×D4—48no—
727C2×D4—48no—
728C2×D4—44no—
729C2×D4—44no—
730C2×D4—44no—
731C2×D4—44no—
732C22×C4—21no—
733C22×C4—22no—
734C22×C4—21no—
735C22×C4—22no—
736C22×C4—22no—
737C22×C4—22no—
738C22×C4—22no—
739C22×C4—28no—
740C22×C4—28no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—22no—
745C22×C4—22no—
746C22×C4—22no—
747C22×C4—22no—
748C22×C4—22no—
749C22×C4—22no—
750C22×C4—22no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—22no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—22no—
761C22×C4—22no—
762C22×C4—22no—
763C22×C4—28no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—22no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—44no—
775C22×C4—48no—
776C22×C4—48no—
777C22×C4—48no—
778C22×C4—48no—
779C22×C4—44no—
780C22×C4—44no—
781C22×C4C22×C4×C13112yes—
782C22×C4C22×C4×C13114yes—
783C22×C4C2×D4×C13114yes—
784C22×C4C2×D4×C13112yes—
785C22×C4C2×D4×C13114yes—
786C22×C4C2×D4×C13114yes—
787C22×C4C2×D4×C13114yes—
788C22×C4C2×D4×C13112yes—
789C22×C4C2×D4×C13114yes—
790C4⋊C4—48no—
791C22⋊C4—216no—
792C22⋊C4—28no—
793C22⋊C4—216no—
794C22⋊C4—216no—
795C22⋊C4—48no—
796C22⋊C4—48no—
797C22⋊C4—48no—
798C22⋊C4—44no—
799C22⋊C4—44no—
800C22⋊C4—44no—
801C22⋊C4C22⋊C4×C131116yescomplemented
802C42—48no—
803C23—24no—
804C23—24no—
805C23—22no—
806C23—22no—
807C23—24no—
808C23—22no—
809C23—22no—
810C23—24no—
811C23—24no—
812C23—24no—
813C23—24no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—232no—
820C23—24no—
821C23—24no—
822C23—24no—
823C23—24no—
824C23—24no—
825C23—24no—
826C23—24no—
827C23—24no—
828C23—24no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—24no—
842C23—24no—
843C23—432no—
844C23—432no—
845C23—416no—
846C23—416no—
847C23—416no—
848C23—416no—
849C23—432no—
850C23—416no—
851C23—432no—
852C23—416no—
853C23—42no—
854C23—42no—
855C23—42no—
856C23—42no—
857C23—42no—
858C23—42no—
859C23—42no—
860C23—42no—
861C23—42no—
862C23—42no—
863C23—42no—
864C23—42no—
865C23—42no—
866C23—42no—
867C23—42no—
868C23—42no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—42no—
874C23—41no—
875C23—41no—
876C23—41no—
877C23—41no—
878C23—42no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—42no—
884C23—42no—
885C23—42no—
886C23—42no—
887C23C2×C22⋊C4×C13114yes—
888C23C4×D4×C13118yes—
889C23C4×D4×C13114yes—
890C23C4×D4×C13114yes—
891C23#121×C13114yes—
892C23#121×C13114yes—
893C23#124×C13114yes—
894C23#127×C13114yes—
895C23C23×C4×C13111yescharacteristic
896C23C22×D4×C13111yescharacteristic
897C23C22×D4×C13111yescharacteristic
898C23C22×D4×C13111yescharacteristic
899C23C22×D4×C13112yes—
900C23C22×D4×C13111yescharacteristic
901C23C2×#41×C13111yescharacteristic
902C23C2×#41×C13111yescharacteristic
903C23C2×#41×C13112yes—
904C23H(5,𝔽2)×C13112yes—
905C23H(5,𝔽2)×C13112yes—
906D4—432no—
907D4—416no—
908C2×C4—24no—
909C2×C4—24no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—24no—
913C2×C4—24no—
914C2×C4—24no—
915C2×C4—24no—
916C2×C4—24no—
917C2×C4—24no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—24no—
923C2×C4—24no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—24no—
927C2×C4—24no—
928C2×C4—24no—
929C2×C4—24no—
930C2×C4—416no—
931C2×C4—416no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—42no—
935C2×C4—41no—
936C2×C4—42no—
937C2×C4—41no—
938C2×C4—42no—
939C2×C4—42no—
940C2×C4—42no—
941C2×C4—42no—
942C2×C4—42no—
943C2×C4—42no—
944C2×C4—42no—
945C2×C4—42no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—42no—
953C2×C4—42no—
954C2×C4—42no—
955C2×C4—42no—
956C2×C4C2×C22⋊C4×C13118yescomplemented
957C2×C4#120×C13114yescomplemented
958C22—24no—
959C22—24no—
960C22—24no—
961C22—28no—
962C22—28no—
963C22—24no—
964C22—24no—
965C22—28no—
966C22—24no—
967C22—28no—
968C22—28no—
969C22—28no—
970C22—28no—
971C22—464no—
972C22—44no—
973C22—44no—
974C22—44no—
975C22—44no—
976C22—44no—
977C22—44no—
978C22—44no—
979C22—44no—
980C22—44no—
981C22—44no—
982C22—44no—
983C22—44no—
984C22—42no—
985C22—42no—
986C22—42no—
987C22—44no—
988C22—44no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—82no—
993C22—81no—
994C22—82no—
995C22#390×C13118yescomplemented
996C22C22×C22⋊C4×C13111yescharacteristic
997C22C2×C4×D4×C13111yescharacteristic
998C22C2×C4×D4×C13111yescharacteristic
999C22C2×C4×D4×C13112yes—
1000C22#518×C13112yes—
1001C22C2×#120×C13111yescharacteristic
1002C22C2×#121×C13111yescharacteristic
1003C22C2×#121×C13111yescharacteristic
1004C22#525×C13111yescharacteristic
1005C22#525×C13112yes—
1006C22C2×#124×C13111yescharacteristic
1007C22C2×#127×C13111yescharacteristic
1008C22#534×C13111yescharacteristic
1009C22#535×C13111yescharacteristic
1010C22#538×C13112yes—
1011C22D42×C13112yes—
1012C22D42×C13112yes—
1013C22D42×C13112yes—
1014C22#546×C13112yes—
1015C22#546×C13112yes—
1016C22#546×C13112yes—
1017C22#546×C13112yes—
1018C22#551×C13112yes—
1019C4—28no—
1020C4—24no—
1021C4—42no—
1022C4—42no—
1023C4—44no—
1024C4—44no—
1025C4—81no—
1026C4—81no—
1027C2—28no—
1028C2—48no—
1029C2—82no—
1030C2C2×#390×C13111yescharacteristic
1031C2C4×#120×C13111yescharacteristic
1032C2#2321×C13111yescharacteristic
1033C2D4×C22⋊C4×C13112yes—
1034C2#2358×C13112yes—
1035C2#2410×C13111yescharacteristic
1036C2#2411×C13111yescharacteristic
1037C2#2424×C13112yes—
1038C2#2433×C13111yescharacteristic
1039C2#2472×C13112yes—
1040C2#2539×C13111yescharacteristic
subgroupG/H
center, socleC24×C131C24
commutatorC23C23×C4×C131
Frattini, cosocleC24C24×C131
prime radicalC22×#120×C131C2
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C131 ◁ G

Complements

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

NH ≅ G/Ntype
2. C23×C22⋊C4×C131C2semidirect
3. C2×#390×C131C2semidirect
4. C2×#386×C131C2semidirect
5. C2×#386×C131C2semidirect
6. C2×#385×C131C2semidirect
7. C2×#379×C131C2semidirect
8. C2×C4×C22⋊C4×C131C2semidirect
9. #1439×C131C2semidirect
10. #1438×C131C2semidirect
11. #1437×C131C2semidirect
19. C2×#120×C131C4semidirect
20. C22×C4⋊C4×C131C22semidirect
31. C22×C22⋊C4×C131C22semidirect
32. C22×C22⋊C4×C131C22semidirect
33. C22×C22⋊C4×C131C22semidirect
34. C22×C42×C131C22semidirect
41. C2×#95×C131C22semidirect
42. C2×#95×C131C22semidirect
43. C2×#95×C131C22semidirect
44. C2×#95×C131C22semidirect
45. C2×#95×C131C22semidirect
73. C22×D4×C131C2×C4semidirect
83. C23×C4×C131D4semidirect
123. C2×C22⋊C4×C131C2×C4semidirect
126. C2×C22⋊C4×C131D4semidirect
127. C2×C22⋊C4×C131D4semidirect
280. C22⋊C4×C131C22⋊C4semidirect
435. C2×C4×C131C2×C22⋊C4semidirect
436. C2×C4×C131#120semidirect
474. C22×C131#390semidirect
520. #13995C131direct (N × H)
521. C131#13995direct (N × H)
523. C23×C22⋊C4C2×C131semidirect
524. C2×#390C2×C131semidirect
525. C2×#386C2×C131semidirect
526. C2×#386C2×C131semidirect
527. C2×#385C2×C131semidirect
528. C2×#379C2×C131semidirect
529. C2×C4×C22⋊C4C2×C131semidirect
530. #1439C2×C131semidirect
531. #1438C2×C131semidirect
532. #1437C2×C131semidirect
540. C2×#120C4×C131semidirect
541. C22×C4⋊C4C22×C131semidirect
552. C22×C22⋊C4C22×C131semidirect
553. C22×C22⋊C4C22×C131semidirect
554. C22×C22⋊C4C22×C131semidirect
555. C22×C42C22×C131semidirect
562. C2×#95C22×C131semidirect
563. C2×#95C22×C131semidirect
564. C2×#95C22×C131semidirect
565. C2×#95C22×C131semidirect
566. C2×#95C22×C131semidirect
594. C22×D4C2×C4×C131semidirect
604. C23×C4D4×C131semidirect
644. C2×C22⋊C4C2×C4×C131semidirect
647. C2×C22⋊C4D4×C131semidirect
648. C2×C22⋊C4D4×C131semidirect
801. C22⋊C4C22⋊C4×C131semidirect
956. C2×C4C2×C22⋊C4×C131semidirect
957. C2×C4#120×C131semidirect
995. C22#390×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1312
C23×C22⋊C4×C1312
C2×#390×C1312
C2×#386×C1312
C2×#385×C1312
C2×#379×C1312
C2×C4×C22⋊C4×C1312
#1439×C1312
#1438×C1312
#1437×C1312
#13995131