Finite Group Databasebeta

← #15799621

Subgroups — #15799621

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×#11718609C212yesmaximal, complemented
2C2×#11718882C211yesmaximal, characteristic
3C2×#11718882C211yesmaximal, characteristic
4C2×#11718646C211yesmaximal, characteristic, complemented
5C2×#11718589C211yesmaximal, characteristic, complemented
6C2×#11718634C211yesmaximal, characteristic, complemented
7#13113081C212yesmaximal, complemented
8#13113079C212yesmaximal, complemented
9#13113079C212yesmaximal, 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⋊Dic13C2212yes—
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4⋊Dic13C2211yescharacteristic
24C22×#6101C2212yes—
25C22×#6101C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27C22×C4×Dic13C2211yescharacteristic
28C13×#390—24no—
29#11718882—24no—
30#11718882—24no—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36C2×#88071C2211yescharacteristic
37C2×#88071C2211yescharacteristic
38#11718646—24no—
39#11718634—24no—
40#11718609—28no—
41#11718589—24no—
42C25×C13C2312yes—
43C22×D4×C13—22no—
44C22×D4×C13—22no—
45C22×D4×C13—22no—
46C22×D4×C13—22no—
47C22×D4×C13—22no—
48C22×D4×C13—22no—
49C22×D4×C13Q814yes—
50C23×C4×C13C2311yescharacteristic
51C23×C4×C13C2312yes—
52C23×C4×C13C2311yescharacteristic
53C23×C4×C13C2311yescharacteristic
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2312yes—
57C23×Dic13C2312yes—
58C23×Dic13C2311yescharacteristic
59C23×Dic13C2311yescharacteristic
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4D414yes—
63C2×C13×C22⋊C4—24no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4—42no—
68C2×C13×C22⋊C4—42no—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
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—24no—
79C2×C22⋊Dic13—24no—
80C2×C22⋊Dic13—42no—
81C2×C22⋊Dic13—42no—
82C2×C22⋊Dic13—42no—
83C2×C22⋊Dic13—42no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—24no—
89C2×C4⋊Dic13—24no—
90C2×C4⋊Dic13—42no—
91C2×C4⋊Dic13D414yes—
92C2×C4⋊Dic13D414yes—
93C2×#6101—24no—
94C2×#6101—24no—
95C2×#6101—24no—
96C2×#6101—24no—
97C2×#6101—42no—
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—
105#88071—24no—
106#88071—22no—
107#88071—24no—
108#88071—24no—
109#88071—22no—
110#88071—22no—
111#88071D414yescomplemented
112#15141—131nomaximal, Sylow
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×C13—22no—
122C24×C13—22no—
123C24×C13—22no—
124C24×C13—22no—
125C24×C13—22no—
126C24×C13—22no—
127C24×C13C2×Q814yes—
128C24×C13C2411yescharacteristic
129C2×D4×C13—28no—
130C2×D4×C13—28no—
131C2×D4×C13—28no—
132C2×D4×C13—44no—
133C2×D4×C13—44no—
134C2×D4×C13—44no—
135C2×D4×C13—44no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—21no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—21no—
144C22×C4×C13—21no—
145C22×C4×C13—21no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—21no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—21no—
152C22×C4×C13—21no—
153C22×C4×C13—21no—
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—22no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—21no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—21no—
193C22×Dic13—22no—
194C22×Dic13—21no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13C2×D414yes—
201C22×Dic13C2×D414yes—
202C22×Dic13C2×D412yes—
203C22×Dic13C2×D412yes—
204C22×Dic13#4112yes—
205C22×Dic13#4112yes—
206C13×C4⋊C4—28no—
207C13×C22⋊C4—48no—
208C13×C22⋊C4—48no—
209C42×C13—44no—
210C22⋊Dic13—48no—
211C22⋊Dic13—48no—
212C22⋊Dic13—48no—
213C22⋊Dic13—48no—
214C4⋊Dic13—28no—
215C4⋊Dic13—28no—
216C4⋊Dic13—48no—
217#6101—48no—
218#6101—48no—
219C4×Dic13—44no—
220C4×Dic13—44no—
221C2×#396—132no—
222C2×#390—131no—
223C2×#390—131no—
224C2×#390D1311yescharacteristic
225C2×#389—131no—
226C2×#389—131no—
227C2×#389—131no—
228#1439—132no—
229#1439—132no—
230#1439—132no—
231C4×#95—131no—
232C23×C13—24no—
233C23×C13—24no—
234C23×C13—24no—
235C23×C13—24no—
236C23×C13—24no—
237C23×C13—24no—
238C23×C13—24no—
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×C13—42no—
260C23×C13—42no—
261C23×C13—42no—
262C23×C13—42no—
263C23×C13—42no—
264C23×C13—42no—
265C23×C13—42no—
266C23×C13—42no—
267C23×C13C22×D411yescharacteristic
268C23×C13C22×D411yescharacteristic
269C23×C13C22×D411yescharacteristic
270C23×C13C22×D411yescharacteristic
271C23×C13C22×Q811yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13C2×#4111yescharacteristic
274C23×C13C2×#4111yescharacteristic
275C23×C13C2×#4111yescharacteristic
276C23×C13C2×#4111yescharacteristic
277C23×C13C2×#4111yescharacteristic
278C23×C13H(5,𝔽2)11yescharacteristic
279C23×C13H(5,𝔽2)11yescharacteristic
280C23×C13H(5,𝔽2)11yescharacteristic
281C23×C132−1+411yescharacteristic
282D4×C13—416no—
283C2×C4×C13—24no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—24no—
288C2×C4×C13—22no—
289C2×C4×C13—22no—
290C2×C4×C13—24no—
291C2×C4×C13—22no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—42no—
304C2×C4×C13#12114yes—
305C2×C4×C13#12114yes—
306C2×C4×C13#12114yes—
307C2×C4×C13C22⋊Q814yes—
308C2×C4×C13C22⋊Q814yes—
309C2×C4×C13C22⋊Q814yes—
310C2×C4×C13#12614yes—
311C2×Dic13—24no—
312C2×Dic13—24no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—24no—
319C2×Dic13—22no—
320C2×Dic13—24no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—24no—
326C2×Dic13—24no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—41no—
336C2×Dic13—41no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—41no—
340C2×Dic13—41no—
341C2×Dic13—42no—
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—42no—
351C2×Dic13—41no—
352C2×Dic13—41no—
353C23×D4C2×D1311yescharacteristic
354C22×C4⋊C4—131no—
355C22×C4⋊C4—131no—
356C22×C4⋊C4—132no—
357C22×C4⋊C4—132no—
358C22×C4⋊C4—132no—
359C22×C4⋊C4C2×D1311yescharacteristic
360C22×C22⋊C4—132no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4—132no—
363C22×C22⋊C4—132no—
364C22×C22⋊C4C2×D1312yes—
365C22×C22⋊C4C2×D1312yes—
366C22×C42—131no—
367C22×C42—131no—
368C22×C42C2×D1311yescharacteristic
369#396—268no—
370#390—24no—
371#390—264no—
372#390—264no—
373#389—264no—
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×#95—132no—
383C22×C13—44no—
384C22×C13—44no—
385C22×C13—44no—
386C22×C13—44no—
387C22×C13—44no—
388C22×C13—44no—
389C22×C13—44no—
390C22×C13—82no—
391C22×C13—82no—
392C22×C13—82no—
393C22×C13—82no—
394C22×C13—82no—
395C22×C13—82no—
396C22×C13—82no—
397C22×C13—82no—
398C22×C13C2×#12111yescharacteristic
399C22×C13C2×#12111yescharacteristic
400C22×C13C2×#12111yescharacteristic
401C22×C13C2×C22⋊Q811yescharacteristic
402C22×C13C2×C22⋊Q811yescharacteristic
403C22×C13C2×C22⋊Q811yescharacteristic
404C22×C13C2×#12611yescharacteristic
405C22×C13#52911yescharacteristic
406C22×C13#52911yescharacteristic
407C22×C13#52911yescharacteristic
408C22×C13#53211yescharacteristic
409C22×C13#53211yescharacteristic
410C22×C13#53211yescharacteristic
411C22×C13#54011yescharacteristic
412C22×C13#54011yescharacteristic
413C22×C13#54011yescharacteristic
414C22×C13#54211yescharacteristic
415C22×C13#54211yescharacteristic
416C22×C13#54211yescharacteristic
417C22×C13D4211yescharacteristic
418C22×C13D4211yescharacteristic
419C22×C13D4211yescharacteristic
420C22×C13#54611yescharacteristic
421C22×C13#54611yescharacteristic
422C22×C13#54611yescharacteristic
423C22×C13#54811yescharacteristic
424C22×C13#54811yescharacteristic
425C22×C13#54811yescharacteristic
426C22×C13D4×Q811yescharacteristic
427C22×C13#55011yescharacteristic
428C22×C13#55011yescharacteristic
429C22×C13#55011yescharacteristic
430C22×C13#55411yescharacteristic
431C22×C13#55411yescharacteristic
432C22×C13#55411yescharacteristic
433C4×C13—42no—
434C4×C13—42no—
435C4×C13—44no—
436C4×C13#39618yescomplemented
437Dic13—42no—
438Dic13—42no—
439Dic13—44no—
440Dic13—44no—
441Dic13—42no—
442Dic13—42no—
443C25C22×D1312yes—
444C22×D4—22no—
445C22×D4—22no—
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4Dic2614yes—
451C23×C4—132no—
452C23×C4—132no—
453C23×C4—131no—
454C23×C4—131no—
455C23×C4—131no—
456C23×C4—131no—
457C23×C4C22×D1311yescharacteristic
458C23×C4C22×D1311yescharacteristic
459C23×C4C22×D1312yes—
460C23×C4C22×D1311yescharacteristic
461C2×C4⋊C4—22no—
462C2×C4⋊C4—22no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—134no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—264no—
470C2×C4⋊C4—264no—
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⋊C4—522no—
478C2×C4⋊C4C22⋊D1314yes—
479C2×C22⋊C4—24no—
480C2×C22⋊C4—24no—
481C2×C22⋊C4—24no—
482C2×C22⋊C4—24no—
483C2×C22⋊C4—42no—
484C2×C22⋊C4—42no—
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—264no—
492C2×C22⋊C4—264no—
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—134no—
507#95—262no—
508#95—262no—
509#95—264no—
510#95—264no—
511#95—262no—
512#95—264no—
513C2×C13—84no—
514C2×C13C2×#39611yescharacteristic
515C2×C13#242611yescharacteristic
516C2×C13#242611yescharacteristic
517C2×C13#242611yescharacteristic
518C2×C13#242811yescharacteristic
519C2×C13#242811yescharacteristic
520C2×C13#242811yescharacteristic
521C2×C13#245211yescharacteristic
522C2×C13#245211yescharacteristic
523C2×C13#245211yescharacteristic
524C2×C13#245411yescharacteristic
525C2×C13#245411yescharacteristic
526C2×C13#245411yescharacteristic
527C2×C13#264411yescharacteristic
528C2×C13#286011yescharacteristic
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24C2×Dic2614yes—
544C24C23×D1311yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—132no—
571C22×C4—132no—
572C22×C4—134no—
573C22×C4—134no—
574C22×C4—132no—
575C22×C4—132no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—262no—
579C22×C4—261no—
580C22×C4—262no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—261no—
590C22×C4—261no—
591C22×C4—261no—
592C22×C4—262no—
593C22×C4—261no—
594C22×C4—261no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—261no—
598C22×C4—261no—
599C22×C4—261no—
600C22×C4—261no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—261no—
604C22×C4—261no—
605C22×C4—262no—
606C22×C4—262no—
607C22×C4—261no—
608C22×C4—261no—
609C22×C4—261no—
610C22×C4—262no—
611C22×C4—261no—
612C22×C4C2×Dic2612yes—
613C22×C4#612712yes—
614C22×C4D4×D1312yes—
615C22×C4D4×D1312yes—
616C22×C4D4×D1312yes—
617C22×C4#612912yes—
618C22×C4#612912yes—
619C22×C4#612912yes—
620C22×C4C2×C22⋊D1314yes—
621C22×C4C2×C22⋊D1312yes—
622C4⋊C4—28no—
623C4⋊C4—268no—
624C4⋊C4—268no—
625C4⋊C4—528no—
626C4⋊C4—528no—
627C4⋊C4—528no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C22⋊C4—528no—
631C22⋊C4—528no—
632C22⋊C4—528no—
633C22⋊C4—528no—
634C42—44no—
635C42—524no—
636C42—524no—
637C13#1514111yescharacteristic, complemented, Sylow
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23C22×Dic2611yescharacteristic
674C23C2×#612711yescharacteristic
675C23C2×D4×D1311yescharacteristic
676C23C2×D4×D1311yescharacteristic
677C23C2×D4×D1311yescharacteristic
678C23C2×#612911yescharacteristic
679C23C2×#612911yescharacteristic
680C23C2×#612911yescharacteristic
681C23#8825111yescharacteristic
682C23#8825111yescharacteristic
683C23#41×D1311yescharacteristic
684C23#41×D1311yescharacteristic
685C23#8825611yescharacteristic
686C23#8825711yescharacteristic
687C23C22×C22⋊D1311yescharacteristic
688D4—416no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—42no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—264no—
711C2×C4—264no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—264no—
718C2×C4—262no—
719C2×C4—264no—
720C2×C4—262no—
721C2×C4—264no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—264no—
727C2×C4—262no—
728C2×C4—521no—
729C2×C4—521no—
730C2×C4—521no—
731C2×C4—522no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—522no—
735C2×C4—521no—
736C2×C4—521no—
737C2×C4—521no—
738C2×C4—522no—
739C2×C4—521no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—521no—
743C2×C4—522no—
744C2×C4—521no—
745C2×C4—522no—
746C2×C4—522no—
747C2×C4—521no—
748C2×C4—521no—
749C2×C4—521no—
750C2×C4—521no—
751C2×C4—521no—
752C2×C4#8813214yes—
753C2×C4#8813214yes—
754C2×C4#8813314yes—
755C2×C4#8813814yes—
756C2×C4#8817814yes—
757C2×C4#8819214yes—
758C2×C4#8819314yes—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22C2×#8813211yescharacteristic
775C22C2×#8813211yescharacteristic
776C22C2×#8813311yescharacteristic
777C22C2×#8813811yescharacteristic
778C22D4×Dic2611yescharacteristic
779C22#1171924411yescharacteristic
780C22#1171924411yescharacteristic
781C22#1171924811yescharacteristic
782C22#1171925311yescharacteristic
783C22#1171926211yescharacteristic
784C22#1171926611yescharacteristic
785C22#1171926711yescharacteristic
786C22#1171930111yescharacteristic
787C22#1171930311yescharacteristic
788C22#1171930411yescharacteristic
789C22#1171930511yescharacteristic
790C22#1171930811yescharacteristic
791C22#1171931411yescharacteristic
792C22#1171931711yescharacteristic
793C22#1171932411yescharacteristic
794C22#1171938111yescharacteristic
795C22#1171938211yescharacteristic
796C22#1171938511yescharacteristic
797C22#1171938711yescharacteristic
798C22#1171942111yescharacteristic
799C22#1171942211yescharacteristic
800C22#1171942311yescharacteristic
801C22#1171942411yescharacteristic
802C22C2×#8817811yescharacteristic
803C22C2×#8819211yescharacteristic
804C22D4×C22⋊D1311yescharacteristic
805C22C2×#8819311yescharacteristic
806C22#1171951111yescharacteristic
807C22#1171953611yescharacteristic
808C22#1171953911yescharacteristic
809C4—42no—
810C4—42no—
811C4—44no—
812C4—522no—
813C4—522no—
814C4—524no—
815C4—524no—
816C4—522no—
817C4—522no—
818C4#1171860918yescomplemented
819C2—84no—
820C2C2×#1171860911yescharacteristic
821C2#1311839811yescharacteristic
822C2#1311840311yescharacteristic
823C2#1311840511yescharacteristic
824C2#1311842011yescharacteristic
825C2#1311842511yescharacteristic
826C2#1311842711yescharacteristic
827C2#1311868011yescharacteristic
828C2#1311868811yescharacteristic
829C2#1311868911yescharacteristic
830C2#1311870211yescharacteristic
831C2#1311871011yescharacteristic
832C2#1311871111yescharacteristic
833C2#1312079711yescharacteristic
834C2#1312320011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#390C2
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#15141
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#11718609C2semidirect
4. C2×#11718646C2semidirect
5. C2×#11718589C2semidirect
6. C2×#11718634C2semidirect
7. #13113081C2semidirect
8. #13113079C2semidirect
9. #13113079C2semidirect
10. C4×#88071C2semidirect
111. #88071D4semidirect
436. C4×C13#396semidirect
637. C13#15141semidirect
818. C4#11718609semidirect

Maximal subgroups

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

subgroupindex
C2×#117186092
C2×#117188822
C2×#117186462
C2×#117185892
C2×#117186342
#131130812
#131130792
C4×#880712
C2×C13×#3902
#1514113