Finite Group Databasebeta

← C131×#13967 #45699851

Subgroups — C131×#13967 #45699851

Order 33536.

4478 conjugacy classes of subgroups.

The subgroup lattice has 1062 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#120×C131C211yesmaximal, characteristic
2C22×C4×D4×C131C211yesmaximal, characteristic, complemented
3C23×C22⋊C4×C131C211yesmaximal, characteristic, complemented
4C2×#386×C131C212yesmaximal, complemented
5C2×#386×C131C211yesmaximal, characteristic, complemented
6C2×#379×C131C211yesmaximal, characteristic, complemented
7#1439×C131C212yesmaximal, complemented
8#1438×C131C212yesmaximal, complemented
9#1437×C131C212yesmaximal, complemented
10C22⋊#95×C131C211yesmaximal, characteristic, complemented
11C22⋊#95×C131C211yesmaximal, characteristic, complemented
12C26×C131C2211yescharacteristic
13C23×D4×C131C2212yes—
14C23×D4×C131C2211yescharacteristic
15C24×C4×C131C2211yescharacteristic
16C24×C4×C131C2211yescharacteristic
17C24×C4×C131C2211yescharacteristic, complemented
18C2×#120×C131—24no—
19C2×#120×C131—24no—
20C2×#120×C131C418yescomplemented
21C2×C4×D4×C131—24no—
22C2×C4×D4×C131—24no—
23C2×C4×D4×C131—24no—
24C22×C4⋊C4×C131C2211yescharacteristic, complemented
25C22×C22⋊C4×C131—24no—
26C22×C22⋊C4×C131—28no—
27C22×C22⋊C4×C131C2211yescharacteristic
28C22×C22⋊C4×C131C2212yes—
29C22×C22⋊C4×C131C2212yes—
30C22×C22⋊C4×C131C2212yes—
31C22×C22⋊C4×C131C2211yescharacteristic
32C22×C22⋊C4×C131C2212yes—
33C22×C22⋊C4×C131C2211yescharacteristic
34C22×C22⋊C4×C131C2212yes—
35C22×C22⋊C4×C131C2211yescharacteristic, complemented
36C22×C22⋊C4×C131C2212yescomplemented
37C22×C42×C131C2211yescharacteristic, complemented
38#386×C131—24no—
39#386×C131—28no—
40#379×C131—24no—
41C2×#95×C131C2212yescomplemented
42C2×#95×C131C2212yescomplemented
43C2×#95×C131C2212yescomplemented
44C2×#95×C131C2212yescomplemented
45C2×#95×C131C2212yescomplemented
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×C414yescomplemented
57C25×C131C2311yescharacteristic
58C25×C131C2312yes—
59C25×C131C2311yescharacteristic
60C22×D4×C131—22no—
61C22×D4×C131—22no—
62C22×D4×C131—22no—
63C22×D4×C131—22no—
64C22×D4×C131—24no—
65C22×D4×C131—24no—
66C22×D4×C131—24no—
67C22×D4×C131—24no—
68C22×D4×C131—42no—
69C22×D4×C131—42no—
70C22×D4×C131C2×C414yes—
71C22×D4×C131C2×C418yescomplemented
72C22×D4×C131D414yes—
73C22×D4×C131D414yes—
74C23×C4×C131—22no—
75C23×C4×C131—22no—
76C23×C4×C131—22no—
77C23×C4×C131—22no—
78C23×C4×C131—24no—
79C23×C4×C131—24no—
80C23×C4×C131—22no—
81C23×C4×C131—22no—
82C23×C4×C131—22no—
83C23×C4×C131—22no—
84C23×C4×C131—24no—
85C23×C4×C131—42no—
86C23×C4×C131—42no—
87C23×C4×C131—42no—
88C23×C4×C131D414yescomplemented
89C23×C4×C131C2312yes—
90C23×C4×C131C2312yes—
91C23×C4×C131C2311yescharacteristic
92C23×C4×C131C2311yescharacteristic
93C23×C4×C131C2311yescharacteristic
94C23×C4×C131C2312yes—
95C23×C4×C131C2311yescharacteristic
96C23×C4×C131C2311yescharacteristic
97#120×C131—232no—
98C4×D4×C131—232no—
99C2×C4⋊C4×C131—22no—
100C2×C4⋊C4×C131—22no—
101C2×C4⋊C4×C131—22no—
102C2×C22⋊C4×C131—232no—
103C2×C22⋊C4×C131—24no—
104C2×C22⋊C4×C131—22no—
105C2×C22⋊C4×C131—22no—
106C2×C22⋊C4×C131—22no—
107C2×C22⋊C4×C131—22no—
108C2×C22⋊C4×C131—22no—
109C2×C22⋊C4×C131—24no—
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—22no—
116C2×C22⋊C4×C131—22no—
117C2×C22⋊C4×C131—22no—
118C2×C22⋊C4×C131—24no—
119C2×C22⋊C4×C131—22no—
120C2×C22⋊C4×C131—24no—
121C2×C22⋊C4×C131—24no—
122C2×C22⋊C4×C131—22no—
123C2×C22⋊C4×C131—24no—
124C2×C22⋊C4×C131—24no—
125C2×C22⋊C4×C131—24no—
126C2×C22⋊C4×C131—42no—
127C2×C22⋊C4×C131—42no—
128C2×C22⋊C4×C131—42no—
129C2×C22⋊C4×C131C2×C414yescomplemented
130C2×C22⋊C4×C131C2×C418yescomplemented
131C2×C22⋊C4×C131D418yescomplemented
132C2×C22⋊C4×C131D414yescomplemented
133C2×C42×C131—22no—
134C2×C42×C131—22no—
135C2×C42×C131—22no—
136#95×C131—24no—
137#95×C131—24no—
138#95×C131—24no—
139#95×C131—42no—
140#95×C131—42no—
141C24×C131—22no—
142C24×C131—22no—
143C24×C131—22no—
144C24×C131—22no—
145C24×C131—28no—
146C24×C131—28no—
147C24×C131—216no—
148C24×C131—28no—
149C24×C131—216no—
150C24×C131—22no—
151C24×C131—22no—
152C24×C131—22no—
153C24×C131—21no—
154C24×C131—21no—
155C24×C131—22no—
156C24×C131—22no—
157C24×C131—22no—
158C24×C131—21no—
159C24×C131—21no—
160C24×C131—22no—
161C24×C131—22no—
162C24×C131—22no—
163C24×C131—22no—
164C24×C131—22no—
165C24×C131—22no—
166C24×C131—22no—
167C24×C131—22no—
168C24×C131—22no—
169C24×C131—22no—
170C24×C131—28no—
171C24×C131—28no—
172C24×C131—48no—
173C24×C131—48no—
174C24×C131—48no—
175C24×C131—48no—
176C24×C131—48no—
177C24×C131—48no—
178C24×C131—48no—
179C24×C131—48no—
180C24×C131—48no—
181C24×C131—44no—
182C24×C131—44no—
183C24×C131—48no—
184C24×C131—44no—
185C24×C131—44no—
186C24×C131—44no—
187C24×C131—44no—
188C24×C131C22×C412yes—
189C24×C131C22×C414yes—
190C24×C131C22×C412yes—
191C24×C131C2×D412yes—
192C24×C131C2×D412yes—
193C24×C131C2×D414yes—
194C24×C131C2×D412yes—
195C24×C131C2×D412yes—
196C24×C131C2×D412yes—
197C24×C131C2×D412yes—
198C24×C131#4114yes—
199C24×C131#4112yes—
200C24×C131#4112yes—
201C24×C131C2411yescharacteristic
202C2×D4×C131—28no—
203C2×D4×C131—28no—
204C2×D4×C131—28no—
205C2×D4×C131—28no—
206C2×D4×C131—28no—
207C2×D4×C131—28no—
208C2×D4×C131—216no—
209C2×D4×C131—216no—
210C2×D4×C131—48no—
211C2×D4×C131—48no—
212C2×D4×C131—48no—
213C2×D4×C131—48no—
214C2×D4×C131—48no—
215C2×D4×C131C22⋊C4116yescomplemented
216C22×C4×C131—21no—
217C22×C4×C131—21no—
218C22×C4×C131—21no—
219C22×C4×C131—21no—
220C22×C4×C131—21no—
221C22×C4×C131—21no—
222C22×C4×C131—22no—
223C22×C4×C131—28no—
224C22×C4×C131—28no—
225C22×C4×C131—28no—
226C22×C4×C131—22no—
227C22×C4×C131—22no—
228C22×C4×C131—22no—
229C22×C4×C131—21no—
230C22×C4×C131—21no—
231C22×C4×C131—22no—
232C22×C4×C131—22no—
233C22×C4×C131—22no—
234C22×C4×C131—22no—
235C22×C4×C131—22no—
236C22×C4×C131—21no—
237C22×C4×C131—21no—
238C22×C4×C131—21no—
239C22×C4×C131—21no—
240C22×C4×C131—22no—
241C22×C4×C131—22no—
242C22×C4×C131—22no—
243C22×C4×C131—22no—
244C22×C4×C131—22no—
245C22×C4×C131—22no—
246C22×C4×C131—22no—
247C22×C4×C131—22no—
248C22×C4×C131—22no—
249C22×C4×C131—22no—
250C22×C4×C131—28no—
251C22×C4×C131—22no—
252C22×C4×C131—22no—
253C22×C4×C131—22no—
254C22×C4×C131—22no—
255C22×C4×C131—22no—
256C22×C4×C131—22no—
257C22×C4×C131—22no—
258C22×C4×C131—44no—
259C22×C4×C131—48no—
260C22×C4×C131—48no—
261C22×C4×C131—48no—
262C22×C4×C131—48no—
263C22×C4×C131—48no—
264C22×C4×C131—48no—
265C22×C4×C131—44no—
266C22×C4×C131—44no—
267C22×C4×C131—44no—
268C22×C4×C131—44no—
269C22×C4×C131C22×C414yes—
270C22×C4×C131C22×C412yes—
271C22×C4×C131C2×D414yes—
272C22×C4×C131C2×D412yes—
273C22×C4×C131C2×D412yes—
274C22×C4×C131C2×D412yes—
275C22×C4×C131C2×D412yes—
276C22×C4×C131C2×D412yes—
277C22×C4×C131C2×D414yes—
278C22×C4×C131C2×D412yes—
279C4⋊C4×C131—28no—
280C22⋊C4×C131—216no—
281C22⋊C4×C131—28no—
282C22⋊C4×C131—28no—
283C22⋊C4×C131—28no—
284C22⋊C4×C131—216no—
285C22⋊C4×C131—216no—
286C22⋊C4×C131—48no—
287C22⋊C4×C131—48no—
288C22⋊C4×C131—48no—
289C22⋊C4×C131—44no—
290C42×C131—28no—
291C23×C131—24no—
292C23×C131—24no—
293C23×C131—22no—
294C23×C131—22no—
295C23×C131—24no—
296C23×C131—22no—
297C23×C131—22no—
298C23×C131—24no—
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—232no—
308C23×C131—24no—
309C23×C131—24no—
310C23×C131—22no—
311C23×C131—22no—
312C23×C131—24no—
313C23×C131—24no—
314C23×C131—24no—
315C23×C131—24no—
316C23×C131—24no—
317C23×C131—24no—
318C23×C131—24no—
319C23×C131—22no—
320C23×C131—22no—
321C23×C131—22no—
322C23×C131—22no—
323C23×C131—24no—
324C23×C131—24no—
325C23×C131—24no—
326C23×C131—24no—
327C23×C131—24no—
328C23×C131—24no—
329C23×C131—24no—
330C23×C131—24no—
331C23×C131—24no—
332C23×C131—24no—
333C23×C131—24no—
334C23×C131—24no—
335C23×C131—24no—
336C23×C131—24no—
337C23×C131—24no—
338C23×C131—432no—
339C23×C131—432no—
340C23×C131—416no—
341C23×C131—416no—
342C23×C131—416no—
343C23×C131—416no—
344C23×C131—432no—
345C23×C131—432no—
346C23×C131—416no—
347C23×C131—41no—
348C23×C131—42no—
349C23×C131—42no—
350C23×C131—42no—
351C23×C131—42no—
352C23×C131—41no—
353C23×C131—42no—
354C23×C131—41no—
355C23×C131—42no—
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×C131—42no—
367C23×C131—42no—
368C23×C131—42no—
369C23×C131—42no—
370C23×C131—42no—
371C23×C131—42no—
372C23×C131—42no—
373C23×C131—416no—
374C23×C131C2×C22⋊C414yes—
375C23×C131C2×C22⋊C414yescomplemented
376C23×C131C4×D414yes—
377C23×C131C4×D414yes—
378C23×C131C4×D418yescomplemented
379C23×C131#12014yes—
380C23×C131#12114yes—
381C23×C131#12114yes—
382C23×C131#12314yes—
383C23×C131C23×C411yescharacteristic
384C23×C131C22×D411yescharacteristic
385C23×C131C22×D411yescharacteristic
386C23×C131C22×D411yescharacteristic
387C23×C131C22×D411yescharacteristic
388C23×C131C22×D412yes—
389C23×C131C2×#4111yescharacteristic
390C23×C131C2×#4111yescharacteristic
391C23×C131C2×#4112yes—
392C23×C131H(5,𝔽2)12yes—
393C23×C131H(5,𝔽2)12yes—
394D4×C131—232no—
395D4×C131—432no—
396C2×C4×C131—22no—
397C2×C4×C131—22no—
398C2×C4×C131—22no—
399C2×C4×C131—22no—
400C2×C4×C131—22no—
401C2×C4×C131—22no—
402C2×C4×C131—22no—
403C2×C4×C131—22no—
404C2×C4×C131—24no—
405C2×C4×C131—24no—
406C2×C4×C131—24no—
407C2×C4×C131—24no—
408C2×C4×C131—24no—
409C2×C4×C131—22no—
410C2×C4×C131—22no—
411C2×C4×C131—24no—
412C2×C4×C131—22no—
413C2×C4×C131—22no—
414C2×C4×C131—22no—
415C2×C4×C131—24no—
416C2×C4×C131—24no—
417C2×C4×C131—24no—
418C2×C4×C131—24no—
419C2×C4×C131—416no—
420C2×C4×C131—416no—
421C2×C4×C131—416no—
422C2×C4×C131—41no—
423C2×C4×C131—42no—
424C2×C4×C131—41no—
425C2×C4×C131—41no—
426C2×C4×C131—41no—
427C2×C4×C131—42no—
428C2×C4×C131—42no—
429C2×C4×C131—42no—
430C2×C4×C131—42no—
431C2×C4×C131—42no—
432C2×C4×C131—42no—
433C2×C4×C131—42no—
434C2×C4×C131—42no—
435C2×C4×C131—42no—
436C2×C4×C131—42no—
437C2×C4×C131—42no—
438C2×C4×C131—42no—
439C2×C4×C131—42no—
440C2×C4×C131—42no—
441C2×C4×C131—42no—
442C2×C4×C131—42no—
443C2×C4×C131—42no—
444C2×C4×C131—42no—
445C2×C4×C131C2×C22⋊C414yescomplemented
446C2×C4×C131#12014yescomplemented
447C22×C131—24no—
448C22×C131—28no—
449C22×C131—28no—
450C22×C131—24no—
451C22×C131—24no—
452C22×C131—24no—
453C22×C131—28no—
454C22×C131—28no—
455C22×C131—24no—
456C22×C131—24no—
457C22×C131—28no—
458C22×C131—28no—
459C22×C131—28no—
460C22×C131—24no—
461C22×C131—28no—
462C22×C131—464no—
463C22×C131—42no—
464C22×C131—44no—
465C22×C131—44no—
466C22×C131—44no—
467C22×C131—44no—
468C22×C131—42no—
469C22×C131—44no—
470C22×C131—42no—
471C22×C131—44no—
472C22×C131—42no—
473C22×C131—44no—
474C22×C131—44no—
475C22×C131—44no—
476C22×C131—44no—
477C22×C131—44no—
478C22×C131—44no—
479C22×C131—44no—
480C22×C131—42no—
481C22×C131—44no—
482C22×C131—44no—
483C22×C131—42no—
484C22×C131#38618yescomplemented
485C22×C131C22×C22⋊C411yescharacteristic
486C22×C131C2×C4×D411yescharacteristic
487C22×C131C2×C4×D412yes—
488C22×C131C2×C4×D411yescharacteristic
489C22×C131#51812yes—
490C22×C131C2×#12011yescharacteristic
491C22×C131C2×#12011yescharacteristic
492C22×C131C2×#12111yescharacteristic
493C22×C131C2×#12111yescharacteristic
494C22×C131C2×#12311yescharacteristic
495C22×C131#52511yescharacteristic
496C22×C131#52512yes—
497C22×C131#53411yescharacteristic
498C22×C131#53511yescharacteristic
499C22×C131#53812yes—
500C22×C131D4212yes—
501C22×C131D4212yes—
502C22×C131D4212yes—
503C22×C131#54612yes—
504C22×C131#54612yes—
505C22×C131#54612yes—
506C22×C131#54612yes—
507C22×C131#55112yes—
508C4×C131—24no—
509C4×C131—24no—
510C4×C131—44no—
511C4×C131—42no—
512C4×C131—42no—
513C4×C131—42no—
514C4×C131—44no—
515C4×C131—82no—
516C2×C131—28no—
517C2×C131—44no—
518C2×C131—48no—
519C2×C131C2×#38611yescharacteristic
520C2×C131C4×#12011yescharacteristic
521C2×C131#232111yescharacteristic
522C2×C131D4×C22⋊C412yes—
523C2×C131#235812yes—
524C2×C131#240311yescharacteristic
525C2×C131#240411yescharacteristic
526C2×C131#240811yescharacteristic
527C2×C131#241812yes—
528C2×C131#242412yes—
529C2×C131#253411yescharacteristic
530#13967C13111yesmaximal, characteristic, direct product factor, Sylow
531C131#1396711yescharacteristic, direct product factor, Sylow
532C22×#120C2×C13111yescharacteristic
533C22×C4×D4C2×C13111yescharacteristic, complemented
534C23×C22⋊C4C2×C13111yescharacteristic, complemented
535C2×#386C2×C13112yescomplemented
536C2×#386C2×C13111yescharacteristic, complemented
537C2×#379C2×C13111yescharacteristic, complemented
538#1439C2×C13112yescomplemented
539#1438C2×C13112yescomplemented
540#1437C2×C13112yescomplemented
541C22⋊#95C2×C13111yescharacteristic, complemented
542C22⋊#95C2×C13111yescharacteristic, complemented
543C26C22×C13111yescharacteristic
544C23×D4C22×C13112yes—
545C23×D4C22×C13111yescharacteristic
546C24×C4C22×C13111yescharacteristic
547C24×C4C22×C13111yescharacteristic
548C24×C4C22×C13111yescharacteristic, complemented
549C2×#120—24no—
550C2×#120—24no—
551C2×#120C4×C13118yescomplemented
552C2×C4×D4—24no—
553C2×C4×D4—24no—
554C2×C4×D4—24no—
555C22×C4⋊C4C22×C13111yescharacteristic, complemented
556C22×C22⋊C4—24no—
557C22×C22⋊C4—28no—
558C22×C22⋊C4C22×C13112yes—
559C22×C22⋊C4C22×C13111yescharacteristic
560C22×C22⋊C4C22×C13112yes—
561C22×C22⋊C4C22×C13112yes—
562C22×C22⋊C4C22×C13111yescharacteristic
563C22×C22⋊C4C22×C13112yes—
564C22×C22⋊C4C22×C13112yes—
565C22×C22⋊C4C22×C13111yescharacteristic
566C22×C22⋊C4C22×C13111yescharacteristic, complemented
567C22×C22⋊C4C22×C13112yescomplemented
568C22×C42C22×C13111yescharacteristic, complemented
569#386—24no—
570#386—28no—
571#379—24no—
572C2×#95C22×C13112yescomplemented
573C2×#95C22×C13112yescomplemented
574C2×#95C22×C13112yescomplemented
575C2×#95C22×C13112yescomplemented
576C2×#95C22×C13112yescomplemented
577C25—24no—
578C25—22no—
579C25—24no—
580C25—22no—
581C25—22no—
582C25—22no—
583C25—22no—
584C25—22no—
585C25—42no—
586C25—42no—
587C25C2×C4×C13114yescomplemented
588C25C23×C13111yescharacteristic
589C25C23×C13112yes—
590C25C23×C13111yescharacteristic
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—22no—
595C22×D4—24no—
596C22×D4—24no—
597C22×D4—24no—
598C22×D4—24no—
599C22×D4—42no—
600C22×D4—42no—
601C22×D4C2×C4×C13114yes—
602C22×D4C2×C4×C13118yescomplemented
603C22×D4D4×C13114yes—
604C22×D4D4×C13114yes—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—22no—
608C23×C4—22no—
609C23×C4—24no—
610C23×C4—24no—
611C23×C4—22no—
612C23×C4—22no—
613C23×C4—22no—
614C23×C4—22no—
615C23×C4—24no—
616C23×C4—42no—
617C23×C4—42no—
618C23×C4—42no—
619C23×C4D4×C13114yescomplemented
620C23×C4C23×C13112yes—
621C23×C4C23×C13112yes—
622C23×C4C23×C13111yescharacteristic
623C23×C4C23×C13111yescharacteristic
624C23×C4C23×C13111yescharacteristic
625C23×C4C23×C13112yes—
626C23×C4C23×C13111yescharacteristic
627C23×C4C23×C13111yescharacteristic
628#120—232no—
629C4×D4—232no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C22⋊C4—232no—
634C2×C22⋊C4—24no—
635C2×C22⋊C4—22no—
636C2×C22⋊C4—22no—
637C2×C22⋊C4—22no—
638C2×C22⋊C4—22no—
639C2×C22⋊C4—22no—
640C2×C22⋊C4—24no—
641C2×C22⋊C4—24no—
642C2×C22⋊C4—24no—
643C2×C22⋊C4—24no—
644C2×C22⋊C4—24no—
645C2×C22⋊C4—24no—
646C2×C22⋊C4—22no—
647C2×C22⋊C4—22no—
648C2×C22⋊C4—22no—
649C2×C22⋊C4—24no—
650C2×C22⋊C4—22no—
651C2×C22⋊C4—24no—
652C2×C22⋊C4—24no—
653C2×C22⋊C4—22no—
654C2×C22⋊C4—24no—
655C2×C22⋊C4—24no—
656C2×C22⋊C4—24no—
657C2×C22⋊C4—42no—
658C2×C22⋊C4—42no—
659C2×C22⋊C4—42no—
660C2×C22⋊C4C2×C4×C13114yescomplemented
661C2×C22⋊C4C2×C4×C13118yescomplemented
662C2×C22⋊C4D4×C13118yescomplemented
663C2×C22⋊C4D4×C13114yescomplemented
664C2×C42—22no—
665C2×C42—22no—
666C2×C42—22no—
667#95—24no—
668#95—24no—
669#95—24no—
670#95—42no—
671#95—42no—
672C24—22no—
673C24—22no—
674C24—22no—
675C24—22no—
676C24—28no—
677C24—28no—
678C24—216no—
679C24—28no—
680C24—216no—
681C24—22no—
682C24—22no—
683C24—22no—
684C24—21no—
685C24—21no—
686C24—22no—
687C24—22no—
688C24—22no—
689C24—21no—
690C24—21no—
691C24—22no—
692C24—22no—
693C24—22no—
694C24—22no—
695C24—22no—
696C24—22no—
697C24—22no—
698C24—22no—
699C24—22no—
700C24—22no—
701C24—28no—
702C24—28no—
703C24—48no—
704C24—48no—
705C24—48no—
706C24—48no—
707C24—48no—
708C24—48no—
709C24—48no—
710C24—48no—
711C24—48no—
712C24—44no—
713C24—44no—
714C24—48no—
715C24—44no—
716C24—44no—
717C24—44no—
718C24—44no—
719C24C22×C4×C13112yes—
720C24C22×C4×C13114yes—
721C24C22×C4×C13112yes—
722C24C2×D4×C13112yes—
723C24C2×D4×C13112yes—
724C24C2×D4×C13114yes—
725C24C2×D4×C13112yes—
726C24C2×D4×C13112yes—
727C24C2×D4×C13112yes—
728C24C2×D4×C13112yes—
729C24#41×C13114yes—
730C24#41×C13112yes—
731C24#41×C13112yes—
732C24C24×C13111yescharacteristic
733C2×D4—28no—
734C2×D4—28no—
735C2×D4—28no—
736C2×D4—28no—
737C2×D4—28no—
738C2×D4—28no—
739C2×D4—216no—
740C2×D4—216no—
741C2×D4—48no—
742C2×D4—48no—
743C2×D4—48no—
744C2×D4—48no—
745C2×D4—48no—
746C2×D4C22⋊C4×C131116yescomplemented
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—22no—
754C22×C4—28no—
755C22×C4—28no—
756C22×C4—28no—
757C22×C4—22no—
758C22×C4—22no—
759C22×C4—22no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—22no—
763C22×C4—22no—
764C22×C4—22no—
765C22×C4—22no—
766C22×C4—22no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—22no—
772C22×C4—22no—
773C22×C4—22no—
774C22×C4—22no—
775C22×C4—22no—
776C22×C4—22no—
777C22×C4—22no—
778C22×C4—22no—
779C22×C4—22no—
780C22×C4—22no—
781C22×C4—28no—
782C22×C4—22no—
783C22×C4—22no—
784C22×C4—22no—
785C22×C4—22no—
786C22×C4—22no—
787C22×C4—22no—
788C22×C4—22no—
789C22×C4—44no—
790C22×C4—48no—
791C22×C4—48no—
792C22×C4—48no—
793C22×C4—48no—
794C22×C4—48no—
795C22×C4—48no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4C22×C4×C13114yes—
801C22×C4C22×C4×C13112yes—
802C22×C4C2×D4×C13114yes—
803C22×C4C2×D4×C13112yes—
804C22×C4C2×D4×C13112yes—
805C22×C4C2×D4×C13112yes—
806C22×C4C2×D4×C13112yes—
807C22×C4C2×D4×C13112yes—
808C22×C4C2×D4×C13114yes—
809C22×C4C2×D4×C13112yes—
810C4⋊C4—28no—
811C22⋊C4—216no—
812C22⋊C4—28no—
813C22⋊C4—28no—
814C22⋊C4—28no—
815C22⋊C4—216no—
816C22⋊C4—216no—
817C22⋊C4—48no—
818C22⋊C4—48no—
819C22⋊C4—48no—
820C22⋊C4—44no—
821C42—28no—
822C23—24no—
823C23—24no—
824C23—22no—
825C23—22no—
826C23—24no—
827C23—22no—
828C23—22no—
829C23—24no—
830C23—24no—
831C23—24no—
832C23—24no—
833C23—24no—
834C23—24no—
835C23—24no—
836C23—24no—
837C23—24no—
838C23—232no—
839C23—24no—
840C23—22no—
841C23—22no—
842C23—24no—
843C23—24no—
844C23—24no—
845C23—24no—
846C23—24no—
847C23—24no—
848C23—24no—
849C23—24no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—24no—
855C23—24no—
856C23—24no—
857C23—24no—
858C23—24no—
859C23—24no—
860C23—24no—
861C23—24no—
862C23—24no—
863C23—24no—
864C23—24no—
865C23—24no—
866C23—24no—
867C23—24no—
868C23—24no—
869C23—432no—
870C23—432no—
871C23—416no—
872C23—416no—
873C23—416no—
874C23—416no—
875C23—416no—
876C23—432no—
877C23—432no—
878C23—41no—
879C23—42no—
880C23—42no—
881C23—42no—
882C23—42no—
883C23—41no—
884C23—42no—
885C23—41no—
886C23—42no—
887C23—42no—
888C23—41no—
889C23—42no—
890C23—42no—
891C23—42no—
892C23—42no—
893C23—42no—
894C23—42no—
895C23—42no—
896C23—42no—
897C23—42no—
898C23—42no—
899C23—42no—
900C23—42no—
901C23—42no—
902C23—42no—
903C23—42no—
904C23—416no—
905C23C2×C22⋊C4×C13114yes—
906C23C2×C22⋊C4×C13114yescomplemented
907C23C4×D4×C13114yes—
908C23C4×D4×C13114yes—
909C23C4×D4×C13118yescomplemented
910C23#120×C13114yes—
911C23#121×C13114yes—
912C23#121×C13114yes—
913C23#123×C13114yes—
914C23C23×C4×C13111yescharacteristic
915C23C22×D4×C13111yescharacteristic
916C23C22×D4×C13111yescharacteristic
917C23C22×D4×C13111yescharacteristic
918C23C22×D4×C13111yescharacteristic
919C23C22×D4×C13112yes—
920C23C2×#41×C13111yescharacteristic
921C23C2×#41×C13111yescharacteristic
922C23C2×#41×C13112yes—
923C23H(5,𝔽2)×C13112yes—
924C23H(5,𝔽2)×C13112yes—
925D4—232no—
926D4—432no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—24no—
936C2×C4—24no—
937C2×C4—24no—
938C2×C4—24no—
939C2×C4—24no—
940C2×C4—22no—
941C2×C4—22no—
942C2×C4—24no—
943C2×C4—22no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—24no—
947C2×C4—24no—
948C2×C4—24no—
949C2×C4—24no—
950C2×C4—416no—
951C2×C4—416no—
952C2×C4—416no—
953C2×C4—41no—
954C2×C4—42no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—42no—
958C2×C4—41no—
959C2×C4—42no—
960C2×C4—42no—
961C2×C4—42no—
962C2×C4—42no—
963C2×C4—42no—
964C2×C4—42no—
965C2×C4—42no—
966C2×C4—42no—
967C2×C4—42no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—42no—
972C2×C4—42no—
973C2×C4—42no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4C2×C22⋊C4×C13114yescomplemented
977C2×C4#120×C13114yescomplemented
978C22—24no—
979C22—24no—
980C22—24no—
981C22—28no—
982C22—28no—
983C22—24no—
984C22—24no—
985C22—24no—
986C22—28no—
987C22—28no—
988C22—24no—
989C22—28no—
990C22—28no—
991C22—28no—
992C22—28no—
993C22—464no—
994C22—44no—
995C22—42no—
996C22—44no—
997C22—42no—
998C22—44no—
999C22—42no—
1000C22—44no—
1001C22—44no—
1002C22—44no—
1003C22—42no—
1004C22—44no—
1005C22—44no—
1006C22—42no—
1007C22—44no—
1008C22—42no—
1009C22—44no—
1010C22—44no—
1011C22—44no—
1012C22—44no—
1013C22—44no—
1014C22—44no—
1015C22#386×C13118yescomplemented
1016C22C22×C22⋊C4×C13111yescharacteristic
1017C22C2×C4×D4×C13111yescharacteristic
1018C22C2×C4×D4×C13111yescharacteristic
1019C22C2×C4×D4×C13112yes—
1020C22#518×C13112yes—
1021C22C2×#120×C13111yescharacteristic
1022C22C2×#120×C13111yescharacteristic
1023C22C2×#121×C13111yescharacteristic
1024C22C2×#121×C13111yescharacteristic
1025C22C2×#123×C13111yescharacteristic
1026C22#525×C13111yescharacteristic
1027C22#525×C13112yes—
1028C22#534×C13111yescharacteristic
1029C22#535×C13111yescharacteristic
1030C22#538×C13112yes—
1031C22D42×C13112yes—
1032C22D42×C13112yes—
1033C22D42×C13112yes—
1034C22#546×C13112yes—
1035C22#546×C13112yes—
1036C22#546×C13112yes—
1037C22#546×C13112yes—
1038C22#551×C13112yes—
1039C4—24no—
1040C4—24no—
1041C4—44no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—44no—
1046C4—82no—
1047C2—28no—
1048C2—48no—
1049C2—44no—
1050C2C2×#386×C13111yescharacteristic
1051C2C4×#120×C13111yescharacteristic
1052C2#2321×C13111yescharacteristic
1053C2D4×C22⋊C4×C13112yes—
1054C2#2358×C13112yes—
1055C2#2403×C13111yescharacteristic
1056C2#2404×C13111yescharacteristic
1057C2#2408×C13111yescharacteristic
1058C2#2418×C13112yes—
1059C2#2424×C13112yes—
1060C2#2534×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. C22×C4×D4×C131C2semidirect
3. C23×C22⋊C4×C131C2semidirect
4. C2×#386×C131C2semidirect
5. C2×#386×C131C2semidirect
6. C2×#379×C131C2semidirect
7. #1439×C131C2semidirect
8. #1438×C131C2semidirect
9. #1437×C131C2semidirect
10. C22⋊#95×C131C2semidirect
11. C22⋊#95×C131C2semidirect
17. C24×C4×C131C22semidirect
20. C2×#120×C131C4semidirect
24. C22×C4⋊C4×C131C22semidirect
35. C22×C22⋊C4×C131C22semidirect
36. C22×C22⋊C4×C131C22semidirect
37. C22×C42×C131C22semidirect
41. C2×#95×C131C22semidirect
42. C2×#95×C131C22semidirect
43. C2×#95×C131C22semidirect
44. C2×#95×C131C22semidirect
45. C2×#95×C131C22semidirect
56. C25×C131C2×C4semidirect
71. C22×D4×C131C2×C4semidirect
88. C23×C4×C131D4semidirect
129. C2×C22⋊C4×C131C2×C4semidirect
130. C2×C22⋊C4×C131C2×C4semidirect
131. C2×C22⋊C4×C131D4semidirect
132. C2×C22⋊C4×C131D4semidirect
215. C2×D4×C131C22⋊C4semidirect
375. C23×C131C2×C22⋊C4semidirect
378. C23×C131C4×D4semidirect
445. C2×C4×C131C2×C22⋊C4semidirect
446. C2×C4×C131#120semidirect
484. C22×C131#386semidirect
530. #13967C131direct (N × H)
531. C131#13967direct (N × H)
533. C22×C4×D4C2×C131semidirect
534. C23×C22⋊C4C2×C131semidirect
535. C2×#386C2×C131semidirect
536. C2×#386C2×C131semidirect
537. C2×#379C2×C131semidirect
538. #1439C2×C131semidirect
539. #1438C2×C131semidirect
540. #1437C2×C131semidirect
541. C22⋊#95C2×C131semidirect
542. C22⋊#95C2×C131semidirect
548. C24×C4C22×C131semidirect
551. C2×#120C4×C131semidirect
555. C22×C4⋊C4C22×C131semidirect
566. C22×C22⋊C4C22×C131semidirect
567. C22×C22⋊C4C22×C131semidirect
568. C22×C42C22×C131semidirect
572. C2×#95C22×C131semidirect
573. C2×#95C22×C131semidirect
574. C2×#95C22×C131semidirect
575. C2×#95C22×C131semidirect
576. C2×#95C22×C131semidirect
587. C25C2×C4×C131semidirect
602. C22×D4C2×C4×C131semidirect
619. C23×C4D4×C131semidirect
660. C2×C22⋊C4C2×C4×C131semidirect
661. C2×C22⋊C4C2×C4×C131semidirect
662. C2×C22⋊C4D4×C131semidirect
663. C2×C22⋊C4D4×C131semidirect
746. C2×D4C22⋊C4×C131semidirect
906. C23C2×C22⋊C4×C131semidirect
909. C23C4×D4×C131semidirect
976. C2×C4C2×C22⋊C4×C131semidirect
977. C2×C4#120×C131semidirect
1015. C22#386×C131semidirect

Maximal subgroups

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

subgroupindex
C22×#120×C1312
C22×C4×D4×C1312
C23×C22⋊C4×C1312
C2×#386×C1312
C2×#379×C1312
#1439×C1312
#1438×C1312
#1437×C1312
C22⋊#95×C1312
#13967131