Finite Group Databasebeta

← #15799619

Subgroups — #15799619

Order 3328.

1906 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718655C212yesmaximal, complemented
2C2×#11718600C211yesmaximal, characteristic
3C2×#11718649C211yesmaximal, characteristic
4C2×#11718649C211yesmaximal, characteristic
5C2×#11718646C211yesmaximal, characteristic, complemented
6C2×#11718634C211yesmaximal, characteristic, complemented
7#13113082C212yesmaximal, complemented
8#13113080C212yesmaximal, complemented
9#13113078C212yesmaximal, complemented
10C4×#88071C211yesmaximal, characteristic, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×D52C2211yescharacteristic
13C22×C13×C4⋊C4C2212yes—
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×#6103C2212yes—
22C22×#6103C2212yes—
23C22×C4⋊Dic13C2212yes—
24C22×C4⋊Dic13C2211yescharacteristic
25C22×#6101C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C13×#389—24no—
29C2×C13×#95C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718655—28no—
37#11718649—24no—
38#11718649—24no—
39#11718646—24no—
40#11718634—24no—
41#11718600—24no—
42C24×D13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2312yes—
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C22×D52—22no—
54C22×D52—22no—
55C22×D52—22no—
56C22×D52—22no—
57C22×D52—22no—
58C22×D52—22no—
59C22×D52Q814yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—24no—
65C2×C13×C4⋊C4—24no—
66C2×C13×C4⋊C4—42no—
67C2×C13×C4⋊C4D414yes—
68C2×C13×C4⋊C4D414yes—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—24no—
81C2×#6103—24no—
82C2×#6103—24no—
83C2×#6103—24no—
84C2×#6103—42no—
85C2×#6103—42no—
86C2×#6103—42no—
87C2×#6103—42no—
88C2×#6103—42no—
89C2×#6103—42no—
90C2×C4⋊Dic13—22no—
91C2×C4⋊Dic13—22no—
92C2×C4⋊Dic13—24no—
93C2×C4⋊Dic13—24no—
94C2×C4⋊Dic13—42no—
95C2×C4⋊Dic13D414yes—
96C2×#6101—24no—
97C2×#6101—24no—
98C2×#6101—42no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13—22no—
102C2×C4×Dic13—22no—
103C2×C4×Dic13—22no—
104C2×C4×Dic13—22no—
105C13×#95—24no—
106#88071—24no—
107#88071—22no—
108#88071—24no—
109#88071—22no—
110#88071—22no—
111#88071D414yescomplemented
112#15141—131nomaximal, Sylow
113C24×C13C2411yescharacteristic
114C23×D13—22no—
115C23×D13—22no—
116C23×D13—22no—
117C23×D13—22no—
118C23×D13—22no—
119C23×D13—22no—
120C23×D13—22no—
121C23×D13—22no—
122C23×D13—22no—
123C23×D13—22no—
124C23×D13—22no—
125C23×D13—22no—
126C23×D13—22no—
127C23×D13—22no—
128C23×D13C2×Q814yes—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—21no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—21no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—21no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13C2×D414yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×D414yes—
158C22×C4×C13C2×D412yes—
159C22×C4×C13C2×Q812yes—
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
162C22×C4×C13#4112yes—
163C22×C4×C13#4112yes—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—22no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—21no—
187C22×Dic13—22no—
188C22×Dic13—21no—
189C22×Dic13—21no—
190C22×Dic13—21no—
191C22×Dic13—21no—
192C22×Dic13—21no—
193C22×Dic13—21no—
194C22×Dic13C2×D414yes—
195C22×Dic13C2×D412yes—
196C22×Dic13C2×D412yes—
197C22×Dic13#4112yes—
198C22×Dic13#4112yes—
199C2×D52—28no—
200C2×D52—28no—
201C2×D52—28no—
202C2×D52—44no—
203C2×D52—44no—
204C2×D52—44no—
205C2×D52—44no—
206C13×C4⋊C4—28no—
207C13×C4⋊C4—28no—
208C13×C4⋊C4—48no—
209C42×C13—44no—
210#6103—48no—
211#6103—48no—
212#6103—48no—
213#6103—48no—
214#6103—48no—
215#6103—48no—
216C4⋊Dic13—28no—
217C4⋊Dic13—48no—
218#6101—48no—
219C4×Dic13—44no—
220C4×Dic13—44no—
221C2×#396—132no—
222C2×#390—131no—
223C2×#390—131no—
224C2×#390—131no—
225C2×#389—131no—
226C2×#389—131no—
227C2×#389D1311yescharacteristic, complemented
228#1439—132no—
229#1439—132no—
230#1439—132no—
231C4×#95—131no—
232C23×C13C22×D411yescharacteristic
233C23×C13C22×D411yescharacteristic
234C23×C13C22×D411yescharacteristic
235C23×C13C22×D411yescharacteristic
236C23×C13C22×Q811yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13C2×#4111yescharacteristic
239C23×C13C2×#4111yescharacteristic
240C23×C13C2×#4111yescharacteristic
241C23×C13C2×#4111yescharacteristic
242C23×C13C2×#4111yescharacteristic
243C23×C13H(5,𝔽2)11yescharacteristic
244C23×C13H(5,𝔽2)11yescharacteristic
245C23×C13H(5,𝔽2)11yescharacteristic
246C23×C132−1+411yescharacteristic
247C22×D13—24no—
248C22×D13—24no—
249C22×D13—24no—
250C22×D13—24no—
251C22×D13—24no—
252C22×D13—24no—
253C22×D13—24no—
254C22×D13—42no—
255C22×D13—42no—
256C22×D13—42no—
257C22×D13—42no—
258C22×D13—42no—
259C22×D13—42no—
260C22×D13—42no—
261C22×D13—42no—
262C22×D13—42no—
263C22×D13—42no—
264C22×D13—42no—
265C22×D13—42no—
266C22×D13—42no—
267C22×D13—42no—
268C22×D13—42no—
269C22×D13—42no—
270C22×D13—42no—
271C22×D13—42no—
272C22×D13—42no—
273C22×D13—42no—
274C22×D13—42no—
275C22×D13—42no—
276C22×D13—42no—
277C22×D13—42no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C22×D13—42no—
282C2×C4×C13—24no—
283C2×C4×C13—24no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—24no—
287C2×C4×C13—22no—
288C2×C4×C13—24no—
289C2×C4×C13—22no—
290C2×C4×C13—22no—
291C2×C4×C13—24no—
292C2×C4×C13—24no—
293C2×C4×C13—22no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—41no—
300C2×C4×C13—42no—
301C2×C4×C13—41no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—42no—
308C2×C4×C13—42no—
309C2×C4×C13—41no—
310C2×C4×C13#12114yes—
311C2×C4×C13#12114yes—
312C2×C4×C13#12114yes—
313C2×C4×C13C22⋊Q814yes—
314C2×C4×C13C22⋊Q814yes—
315C2×C4×C13C22⋊Q814yes—
316C2×C4×C13#12614yes—
317C2×Dic13—24no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—24no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—24no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—42no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—41no—
341C2×Dic13—41no—
342C2×Dic13—42no—
343C2×Dic13—41no—
344C2×Dic13—41no—
345C2×Dic13—41no—
346C2×Dic13—41no—
347C2×Dic13—41no—
348C2×Dic13—41no—
349C2×Dic13—42no—
350C2×Dic13—41no—
351C2×Dic13—41no—
352D52—416no—
353C23×D4—131no—
354C22×C4⋊C4—131no—
355C22×C4⋊C4—132no—
356C22×C4⋊C4—132no—
357C22×C4⋊C4C2×D1312yes—
358C22×C4⋊C4C2×D1311yescharacteristic
359C22×C4⋊C4C2×D1311yescharacteristic
360C22×C22⋊C4—132no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4—132no—
363C22×C22⋊C4—132no—
364C22×C22⋊C4—132no—
365C22×C22⋊C4—132no—
366C22×C42—131no—
367C22×C42—131no—
368C22×C42C2×D1311yescharacteristic
369#396—268no—
370#390—264no—
371#390—264no—
372#390—264no—
373#389—24no—
374#389—264no—
375#389—264no—
376C2×#95—131no—
377C2×#95—131no—
378C2×#95—131no—
379C2×#95—131no—
380C2×#95—132no—
381C2×#95—132no—
382C2×#95C2×D1312yes—
383C22×C13C2×#12111yescharacteristic
384C22×C13C2×#12111yescharacteristic
385C22×C13C2×#12111yescharacteristic
386C22×C13C2×C22⋊Q811yescharacteristic
387C22×C13C2×C22⋊Q811yescharacteristic
388C22×C13C2×C22⋊Q811yescharacteristic
389C22×C13C2×#12611yescharacteristic
390C22×C13#52911yescharacteristic
391C22×C13#52911yescharacteristic
392C22×C13#52911yescharacteristic
393C22×C13#53211yescharacteristic
394C22×C13#53211yescharacteristic
395C22×C13#53211yescharacteristic
396C22×C13#54011yescharacteristic
397C22×C13#54011yescharacteristic
398C22×C13#54011yescharacteristic
399C22×C13#54211yescharacteristic
400C22×C13#54211yescharacteristic
401C22×C13#54211yescharacteristic
402C22×C13D4211yescharacteristic
403C22×C13D4211yescharacteristic
404C22×C13D4211yescharacteristic
405C22×C13#54611yescharacteristic
406C22×C13#54611yescharacteristic
407C22×C13#54611yescharacteristic
408C22×C13#54811yescharacteristic
409C22×C13#54811yescharacteristic
410C22×C13#54811yescharacteristic
411C22×C13D4×Q811yescharacteristic
412C22×C13#55011yescharacteristic
413C22×C13#55011yescharacteristic
414C22×C13#55011yescharacteristic
415C22×C13#55411yescharacteristic
416C22×C13#55411yescharacteristic
417C22×C13#55411yescharacteristic
418C2×D13—44no—
419C2×D13—44no—
420C2×D13—44no—
421C2×D13—44no—
422C2×D13—44no—
423C2×D13—44no—
424C2×D13—44no—
425C2×D13—82no—
426C2×D13—82no—
427C2×D13—82no—
428C2×D13—82no—
429C2×D13—82no—
430C2×D13—82no—
431C2×D13—82no—
432C2×D13—82no—
433C4×C13—42no—
434C4×C13—44no—
435C4×C13—44no—
436C4×C13—42no—
437C4×C13#39618yescomplemented
438Dic13—42no—
439Dic13—42no—
440Dic13—42no—
441Dic13—44no—
442Dic13—42no—
443C25—132no—
444C22×D4—134no—
445C22×D4—262no—
446C22×D4—262no—
447C22×D4—262no—
448C22×D4—262no—
449C22×D4—262no—
450C22×D4—262no—
451C23×C4—132no—
452C23×C4—131no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4C22×D1312yes—
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C23×C4C22×D1312yes—
460C23×C4C22×D1311yescharacteristic
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—22no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—24no—
466C2×C4⋊C4—24no—
467C2×C4⋊C4—42no—
468C2×C4⋊C4—134no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—264no—
472C2×C4⋊C4—264no—
473C2×C4⋊C4—264no—
474C2×C4⋊C4—264no—
475C2×C4⋊C4—522no—
476C2×C4⋊C4—522no—
477C2×C4⋊C4D5214yes—
478C2×C4⋊C4C22⋊D1314yes—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—264no—
482C2×C22⋊C4—264no—
483C2×C22⋊C4—264no—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—264no—
486C2×C22⋊C4—264no—
487C2×C22⋊C4—264no—
488C2×C22⋊C4—264no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
491C2×C22⋊C4—522no—
492C2×C22⋊C4—522no—
493C2×C22⋊C4—522no—
494C2×C22⋊C4—522no—
495C2×C22⋊C4—522no—
496C2×C22⋊C4—522no—
497C2×C42—22no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—262no—
501C2×C42—262no—
502C2×C42—262no—
503C2×C42—262no—
504C2×C42—262no—
505C2×C42—262no—
506#95—24no—
507#95—134no—
508#95—262no—
509#95—262no—
510#95—264no—
511#95—264no—
512#95—262no—
513C2×C13C2×#39611yescharacteristic
514C2×C13#242611yescharacteristic
515C2×C13#242611yescharacteristic
516C2×C13#242611yescharacteristic
517C2×C13#242811yescharacteristic
518C2×C13#242811yescharacteristic
519C2×C13#242811yescharacteristic
520C2×C13#245211yescharacteristic
521C2×C13#245211yescharacteristic
522C2×C13#245211yescharacteristic
523C2×C13#245411yescharacteristic
524C2×C13#245411yescharacteristic
525C2×C13#245411yescharacteristic
526C2×C13#264411yescharacteristic
527C2×C13#286011yescharacteristic
528D13—84no—
529C24—134no—
530C24—262no—
531C24—262no—
532C24—262no—
533C24—262no—
534C24—262no—
535C24—262no—
536C24—262no—
537C24—262no—
538C24—262no—
539C24—262no—
540C24—262no—
541C24—262no—
542C24—262no—
543C24—262no—
544C24C23×D1311yescharacteristic
545C2×D4—268no—
546C2×D4—268no—
547C2×D4—268no—
548C2×D4—524no—
549C2×D4—524no—
550C2×D4—524no—
551C2×D4—524no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—132no—
577C22×C4—132no—
578C22×C4—134no—
579C22×C4—132no—
580C22×C4—132no—
581C22×C4—261no—
582C22×C4—262no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—262no—
591C22×C4—261no—
592C22×C4—261no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—261no—
596C22×C4—261no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—261no—
602C22×C4—261no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—261no—
611C22×C4C2×D5214yes—
612C22×C4C2×D5212yes—
613C22×C4#612712yes—
614C22×C4D4×D1312yes—
615C22×C4D4×D1312yes—
616C22×C4#612912yes—
617C22×C4Q8×D1312yes—
618C22×C4#613112yes—
619C22×C4#613112yes—
620C22×C4C2×C22⋊D1314yes—
621C22×C4C2×C22⋊D1312yes—
622C4⋊C4—28no—
623C4⋊C4—28no—
624C4⋊C4—48no—
625C4⋊C4—268no—
626C4⋊C4—528no—
627C4⋊C4—528no—
628C22⋊C4—528no—
629C22⋊C4—528no—
630C22⋊C4—528no—
631C22⋊C4—528no—
632C22⋊C4—528no—
633C22⋊C4—528no—
634C42—44no—
635C42—524no—
636C42—524no—
637C13#1514111yescharacteristic, complemented, Sylow
638C23—264no—
639C23—264no—
640C23—264no—
641C23—264no—
642C23—264no—
643C23—264no—
644C23—264no—
645C23—522no—
646C23—522no—
647C23—522no—
648C23—522no—
649C23—522no—
650C23—522no—
651C23—522no—
652C23—522no—
653C23—522no—
654C23—522no—
655C23—522no—
656C23—522no—
657C23—522no—
658C23—522no—
659C23—522no—
660C23—522no—
661C23—522no—
662C23—522no—
663C23—522no—
664C23—522no—
665C23—522no—
666C23—522no—
667C23—522no—
668C23—522no—
669C23—522no—
670C23—522no—
671C23—522no—
672C23—522no—
673C23C22×D5211yescharacteristic
674C23C2×#612711yescharacteristic
675C23C2×D4×D1311yescharacteristic
676C23C2×D4×D1311yescharacteristic
677C23C2×#612911yescharacteristic
678C23#8825111yescharacteristic
679C23C2×Q8×D1311yescharacteristic
680C23C2×#613111yescharacteristic
681C23C2×#613111yescharacteristic
682C23#8825411yescharacteristic
683C23#41×D1311yescharacteristic
684C23#41×D1311yescharacteristic
685C23#8825611yescharacteristic
686C23#8825611yescharacteristic
687C23C22×C22⋊D1311yescharacteristic
688D4—5216no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—262no—
718C2×C4—264no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—264no—
728C2×C4—262no—
729C2×C4—264no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—522no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—522no—
739C2×C4—521no—
740C2×C4—521no—
741C2×C4—521no—
742C2×C4—521no—
743C2×C4—521no—
744C2×C4—522no—
745C2×C4—521no—
746C2×C4—521no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—522no—
752C2×C4#8814914yes—
753C2×C4#8815014yes—
754C2×C4#8815114yes—
755C2×C4#8815214yes—
756C2×C4#8818414yes—
757C2×C4#8819314yes—
758C2×C4#8820014yes—
759C22—524no—
760C22—524no—
761C22—524no—
762C22—524no—
763C22—524no—
764C22—524no—
765C22—524no—
766C22—1042no—
767C22—1042no—
768C22—1042no—
769C22—1042no—
770C22—1042no—
771C22—1042no—
772C22—1042no—
773C22—1042no—
774C22C2×#8814911yescharacteristic
775C22C2×#8815011yescharacteristic
776C22C2×#8815111yescharacteristic
777C22C2×#8815211yescharacteristic
778C22#1171925311yescharacteristic
779C22D4×D5211yescharacteristic
780C22#1171925911yescharacteristic
781C22#1171926711yescharacteristic
782C22#1171928111yescharacteristic
783C22#1171928211yescharacteristic
784C22#1171928511yescharacteristic
785C22#1171928711yescharacteristic
786C22#1171930111yescharacteristic
787C22#1171930411yescharacteristic
788C22#1171931411yescharacteristic
789C22#1171932411yescharacteristic
790C22#1171932911yescharacteristic
791C22#1171933511yescharacteristic
792C22#1171933811yescharacteristic
793C22#1171934811yescharacteristic
794C22#1171939511yescharacteristic
795C22#1171939511yescharacteristic
796C22#1171939611yescharacteristic
797C22#1171940311yescharacteristic
798C22#1171943011yescharacteristic
799C22#1171943211yescharacteristic
800C22#1171943511yescharacteristic
801C22#1171943811yescharacteristic
802C22C2×#8818411yescharacteristic
803C22D4×C22⋊D1311yescharacteristic
804C22C2×#8819311yescharacteristic
805C22C2×#8820011yescharacteristic
806C22#1171952211yescharacteristic
807C22#1171953411yescharacteristic
808C22#1171953911yescharacteristic
809C4—42no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—522no—
814C4—522no—
815C4—522no—
816C4—522no—
817C4—524no—
818C4#1171865518yescomplemented
819C2—1044no—
820C2C2×#1171865511yescharacteristic
821C2#1311839611yescharacteristic
822C2#1311840011yescharacteristic
823C2#1311840411yescharacteristic
824C2#1311841811yescharacteristic
825C2#1311842211yescharacteristic
826C2#1311842611yescharacteristic
827C2#1311868211yescharacteristic
828C2#1311868411yescharacteristic
829C2#1311868711yescharacteristic
830C2#1311870411yescharacteristic
831C2#1311870611yescharacteristic
832C2#1311870911yescharacteristic
833C2#1312079911yescharacteristic
834C2#1312320411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#389C2
prime radicalC23×D52C22
hypercenterC2×#389D13
hypocenterC13#15141
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C2×#11718655C2semidirect
5. C2×#11718646C2semidirect
6. C2×#11718634C2semidirect
7. #13113082C2semidirect
8. #13113080C2semidirect
9. #13113078C2semidirect
10. C4×#88071C2semidirect
11. C2×C13×#389C2semidirect
111. #88071D4semidirect
227. C2×#389D13semidirect
437. C4×C13#396semidirect
637. C13#15141semidirect
818. C4#11718655semidirect

Maximal subgroups

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

subgroupindex
C2×#117186552
C2×#117186002
C2×#117186492
C2×#117186462
C2×#117186342
#131130822
#131130802
#131130782
C4×#880712
C2×C13×#3892
#1514113