Finite Group Databasebeta

← #15799592

Subgroups — #15799592

Order 3328.

1762 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718613C212yesmaximal, complemented
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718882C211yesmaximal, characteristic
4C2×#11718634C211yesmaximal, characteristic, complemented
5#13113085C212yesmaximal, complemented
6#13113083C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#390C211yesmaximal, characteristic
12C23×D4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C22⋊C4C2212yes—
15C22×C13×C22⋊C4C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2212yes—
19C22×C22⋊Dic13C2212yes—
20C22×C22⋊Dic13C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C13×#390—24no—
27#11718882—24no—
28#11718882—24no—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2211yescharacteristic
38#11718634—24no—
39#11718613—28no—
40C25×C13C2312yes—
41C22×D4×C13—22no—
42C22×D4×C13—22no—
43C22×D4×C13—22no—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13D414yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2311yescharacteristic
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2311yescharacteristic
52C23×Dic13C2312yes—
53C23×Dic13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2312yes—
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C22⋊C4—24no—
62C2×C13×C22⋊C4—24no—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—42no—
66C2×C13×C22⋊C4—42no—
67C2×C42×C13—22no—
68C2×C42×C13—22no—
69C2×C42×C13—22no—
70C2×C22⋊Dic13—24no—
71C2×C22⋊Dic13—24no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—24no—
76C2×C22⋊Dic13—24no—
77C2×C22⋊Dic13—24no—
78C2×C22⋊Dic13—42no—
79C2×C22⋊Dic13—42no—
80C2×C22⋊Dic13—42no—
81C2×C22⋊Dic13—42no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13D414yes—
88C2×#6101—24no—
89C2×#6101—24no—
90C2×#6101—42no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13—22no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97#88071—24no—
98#88071—22no—
99#88071—24no—
100#88071—24no—
101#88071—22no—
102#88071—22no—
103#88071—42no—
104#88071—42no—
105#88071D414yescomplemented
106#15138—131nomaximal, Sylow
107C24×C13—22no—
108C24×C13—22no—
109C24×C13—22no—
110C24×C13—22no—
111C24×C13—22no—
112C24×C13—22no—
113C24×C13—22no—
114C24×C13—22no—
115C24×C13—22no—
116C24×C13—22no—
117C24×C13—22no—
118C24×C13—22no—
119C24×C13—22no—
120C24×C13—22no—
121C24×C13C2×D414yes—
122C24×C13C2411yescharacteristic
123C2×D4×C13—28no—
124C2×D4×C13—28no—
125C2×D4×C13—28no—
126C2×D4×C13—44no—
127C2×D4×C13—44no—
128C2×D4×C13—44no—
129C2×D4×C13—44no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—21no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—21no—
179C22×Dic13—22no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—21no—
186C22×Dic13—21no—
187C22×Dic13—21no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13C2×D412yes—
196C22×Dic13C2×D414yes—
197C22×Dic13C2×D412yes—
198C22×Dic13#4112yes—
199C22×Dic13#4112yes—
200C13×C4⋊C4—44no—
201C13×C22⋊C4—48no—
202C13×C22⋊C4—48no—
203C42×C13—44no—
204C22⋊Dic13—48no—
205C22⋊Dic13—48no—
206C22⋊Dic13—48no—
207C22⋊Dic13—48no—
208C4⋊Dic13—28no—
209C4⋊Dic13—44no—
210#6101—48no—
211C4×Dic13—44no—
212C4×Dic13—44no—
213C2×#397—132no—
214C2×#390—131no—
215C2×#390—131no—
216C2×#390D1311yescharacteristic
217C2×#389—131no—
218#1440—132no—
219#1440—132no—
220#1439—132no—
221C4⋊#95—131no—
222C4⋊#95—131no—
223C4×#95—131no—
224C23×C13—24no—
225C23×C13—24no—
226C23×C13—24no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—42no—
232C23×C13—42no—
233C23×C13—42no—
234C23×C13—42no—
235C23×C13—42no—
236C23×C13—42no—
237C23×C13—42no—
238C23×C13—42no—
239C23×C13—42no—
240C23×C13—42no—
241C23×C13—42no—
242C23×C13—42no—
243C23×C13—42no—
244C23×C13—42no—
245C23×C13—42no—
246C23×C13—42no—
247C23×C13—42no—
248C23×C13—42no—
249C23×C13—42no—
250C23×C13—42no—
251C23×C13—42no—
252C23×C13—42no—
253C23×C13—42no—
254C23×C13—42no—
255C23×C13—42no—
256C23×C13—42no—
257C23×C13—42no—
258C23×C13—42no—
259C23×C13C22×D411yescharacteristic
260C23×C13C22×D411yescharacteristic
261C23×C13C22×D411yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C23×C13C2×#4111yescharacteristic
270C23×C13H(5,𝔽2)11yescharacteristic
271C23×C13H(5,𝔽2)11yescharacteristic
272C23×C13H(5,𝔽2)11yescharacteristic
273C23×C132−1+411yescharacteristic
274D4×C13—416no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—41no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13#12114yes—
297C2×C4×C13#12314yes—
298C2×C4×C13#12314yes—
299C2×C4×C13#12314yes—
300C2×C4×C13#12414yes—
301C2×C4×C13#12614yes—
302C2×C4×C13#12614yes—
303C2×Dic13—24no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—24no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—24no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—42no—
323C2×Dic13—41no—
324C2×Dic13—42no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C23×D4C2×D1311yescharacteristic
346C22×C4⋊C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—132no—
349C22×C4⋊C4C2×D1311yescharacteristic
350C22×C22⋊C4—132no—
351C22×C22⋊C4—132no—
352C22×C22⋊C4—132no—
353C22×C22⋊C4—132no—
354C22×C22⋊C4C2×D1312yes—
355C22×C22⋊C4C2×D1312yes—
356C22×C42—131no—
357C22×C42—131no—
358C22×C42C2×D1311yescharacteristic
359#397—268no—
360#390—24no—
361#390—264no—
362#390—264no—
363#389—264no—
364C2×#95—131no—
365C2×#95—132no—
366C2×#95—132no—
367C2×#95—131no—
368C2×#95—131no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C22×C13—44no—
374C22×C13—44no—
375C22×C13—44no—
376C22×C13—44no—
377C22×C13—44no—
378C22×C13—44no—
379C22×C13—44no—
380C22×C13—82no—
381C22×C13—82no—
382C22×C13—82no—
383C22×C13—82no—
384C22×C13—82no—
385C22×C13—82no—
386C22×C13—82no—
387C22×C13—82no—
388C22×C13C2×#12111yescharacteristic
389C22×C13C2×#12311yescharacteristic
390C22×C13C2×#12311yescharacteristic
391C22×C13C2×#12311yescharacteristic
392C22×C13C2×#12411yescharacteristic
393C22×C13C2×#12611yescharacteristic
394C22×C13C2×#12611yescharacteristic
395C22×C13#52911yescharacteristic
396C22×C13#52911yescharacteristic
397C22×C13#52911yescharacteristic
398C22×C13#53211yescharacteristic
399C22×C13#53211yescharacteristic
400C22×C13#53211yescharacteristic
401C22×C13#54011yescharacteristic
402C22×C13#54011yescharacteristic
403C22×C13#54011yescharacteristic
404C22×C13#54211yescharacteristic
405C22×C13#54211yescharacteristic
406C22×C13#54211yescharacteristic
407C22×C13D4211yescharacteristic
408C22×C13D4211yescharacteristic
409C22×C13#54611yescharacteristic
410C22×C13#54611yescharacteristic
411C22×C13#54611yescharacteristic
412C22×C13#54711yescharacteristic
413C22×C13#54711yescharacteristic
414C22×C13#54811yescharacteristic
415C22×C13#55011yescharacteristic
416C22×C13#55011yescharacteristic
417C22×C13#55311yescharacteristic
418C22×C13#55311yescharacteristic
419C22×C13#55511yescharacteristic
420C22×C13#55611yescharacteristic
421C22×C13#55911yescharacteristic
422C22×C13#55911yescharacteristic
423C4×C13—42no—
424C4×C13—42no—
425C4×C13—82no—
426C4×C13#39718yescomplemented
427Dic13—42no—
428Dic13—42no—
429Dic13—44no—
430Dic13—42no—
431Dic13—42no—
432Dic13—82no—
433C25C22×D1312yes—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—22no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4C22⋊D1314yes—
441C23×C4—132no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—132no—
447C23×C4C22×D1312yes—
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C23×C4C22×D1311yescharacteristic
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4—264no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—522no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—24no—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—42no—
468C2×C22⋊C4—42no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—264no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—264no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—522no—
478C2×C22⋊C4—522no—
479C2×C22⋊C4—522no—
480C2×C22⋊C4—522no—
481C2×C42—22no—
482C2×C42—22no—
483C2×C42—22no—
484C2×C42—262no—
485C2×C42—262no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42—262no—
489C2×C42—262no—
490#95—134no—
491#95—262no—
492#95—262no—
493#95—264no—
494#95—264no—
495#95—264no—
496#95—262no—
497#95—522no—
498#95—522no—
499C2×C13—84no—
500C2×C13C2×#39711yescharacteristic
501C2×C13#242011yescharacteristic
502C2×C13#242211yescharacteristic
503C2×C13#242711yescharacteristic
504C2×C13#242811yescharacteristic
505C2×C13#244511yescharacteristic
506C2×C13#244511yescharacteristic
507C2×C13#244711yescharacteristic
508C2×C13#244811yescharacteristic
509C2×C13#249011yescharacteristic
510C2×C13#249111yescharacteristic
511C2×C13#251211yescharacteristic
512C2×C13#251311yescharacteristic
513C2×C13#264411yescharacteristic
514C2×C13#286011yescharacteristic
515C24—22no—
516C24—22no—
517C24—22no—
518C24—22no—
519C24—22no—
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24C2×C22⋊D1314yes—
530C24C23×D1311yescharacteristic
531C2×D4—28no—
532C2×D4—28no—
533C2×D4—28no—
534C2×D4—44no—
535C2×D4—44no—
536C2×D4—44no—
537C2×D4—44no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—134no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—262no—
565C22×C4—261no—
566C22×C4—262no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—262no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—262no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4#612712yes—
600C22×C4#612712yes—
601C22×C4D4×D1312yes—
602C22×C4D4×D1312yes—
603C22×C4#612912yes—
604C22×C4#612912yes—
605C22×C4#612912yes—
606C22×C4#612912yes—
607C22×C4C2×C22⋊D1312yes—
608C4⋊C4—44no—
609C4⋊C4—268no—
610C4⋊C4—528no—
611C4⋊C4—524no—
612C22⋊C4—48no—
613C22⋊C4—48no—
614C22⋊C4—528no—
615C22⋊C4—528no—
616C22⋊C4—528no—
617C22⋊C4—528no—
618C42—44no—
619C42—524no—
620C42—524no—
621C13#1513811yescharacteristic, complemented, Sylow
622C23—24no—
623C23—24no—
624C23—24no—
625C23—24no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—42no—
630C23—42no—
631C23—42no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23—42no—
637C23—42no—
638C23—42no—
639C23—42no—
640C23—42no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23C2×#612711yescharacteristic
658C23C2×#612711yescharacteristic
659C23C2×D4×D1311yescharacteristic
660C23C2×D4×D1311yescharacteristic
661C23C2×#612911yescharacteristic
662C23C2×#612911yescharacteristic
663C23C2×#612911yescharacteristic
664C23C2×#612911yescharacteristic
665C23#8825111yescharacteristic
666C23#8825111yescharacteristic
667C23#41×D1311yescharacteristic
668C23#41×D1311yescharacteristic
669C23#8825611yescharacteristic
670C23#8825711yescharacteristic
671C23C22×C22⋊D1311yescharacteristic
672D4—416no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—264no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—264no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—264no—
708C2×C4—262no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—521no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—522no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—522no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4#8813314yes—
737C2×C4#8813314yes—
738C2×C4#8813714yes—
739C2×C4#8813914yes—
740C2×C4#8818314yes—
741C2×C4#8818914yes—
742C2×C4#8819314yes—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—82no—
751C22—82no—
752C22—82no—
753C22—82no—
754C22—82no—
755C22—82no—
756C22—82no—
757C22—82no—
758C22C2×#8813311yescharacteristic
759C22C2×#8813311yescharacteristic
760C22C2×#8813711yescharacteristic
761C22C2×#8813911yescharacteristic
762C22#1171924711yescharacteristic
763C22#1171925311yescharacteristic
764C22#1171925811yescharacteristic
765C22#1171926211yescharacteristic
766C22#1171926411yescharacteristic
767C22#1171926411yescharacteristic
768C22#1171926611yescharacteristic
769C22#1171926711yescharacteristic
770C22#1171930111yescharacteristic
771C22#1171930511yescharacteristic
772C22#1171930811yescharacteristic
773C22#1171931611yescharacteristic
774C22#1171931911yescharacteristic
775C22#1171932111yescharacteristic
776C22#1171932311yescharacteristic
777C22#1171932411yescharacteristic
778C22#1171938111yescharacteristic
779C22#1171938211yescharacteristic
780C22#1171938511yescharacteristic
781C22#1171938711yescharacteristic
782C22#1171942111yescharacteristic
783C22#1171942211yescharacteristic
784C22#1171942311yescharacteristic
785C22#1171942411yescharacteristic
786C22C2×#8818311yescharacteristic
787C22C2×#8818911yescharacteristic
788C22D4×C22⋊D1311yescharacteristic
789C22C2×#8819311yescharacteristic
790C22#1171951111yescharacteristic
791C22#1171952911yescharacteristic
792C22#1171953411yescharacteristic
793C4—42no—
794C4—42no—
795C4—82no—
796C4—524no—
797C4—522no—
798C4—522no—
799C4—522no—
800C4—522no—
801C4—1042no—
802C4#1171861318yescomplemented
803C2—84no—
804C2C2×#1171861311yescharacteristic
805C2#1311832411yescharacteristic
806C2#1311834611yescharacteristic
807C2#1311841611yescharacteristic
808C2#1311842711yescharacteristic
809C2#1311859511yescharacteristic
810C2#1311860411yescharacteristic
811C2#1311861711yescharacteristic
812C2#1311863711yescharacteristic
813C2#1311918911yescharacteristic
814C2#1311920011yescharacteristic
815C2#1311942411yescharacteristic
816C2#1311943511yescharacteristic
817C2#1312079711yescharacteristic
818C2#1312320011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#390C2
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#15138
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#11718613C2semidirect
4. C2×#11718634C2semidirect
5. #13113085C2semidirect
6. #13113083C2semidirect
7. #13113079C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
10. C4×#88071C2semidirect
105. #88071D4semidirect
426. C4×C13#397semidirect
621. C13#15138semidirect
802. C4#11718613semidirect

Maximal subgroups

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

subgroupindex
C2×#117186132
C2×#117188822
C2×#117186342
#131130852
#131130832
#131130792
#131130662
#131130652
C4×#880712
C2×C13×#3902
#1513813