Finite Group Databasebeta

← #15799539

Subgroups — #15799539

Order 3328.

1626 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718613C212yesmaximal
2C2×#11718634C211yesmaximal, characteristic, complemented
3C2×#11718873C211yesmaximal, characteristic
4C2×C4×C22⋊Dic13C211yesmaximal, characteristic
5#13113097C212yesmaximal, complemented
6#13113091C212yesmaximal, complemented
7#13113085C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×#6101C2212yes—
22C22×C4×Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C13×#380—24no—
25C2×C13×#95C2212yes—
26#11718873—24no—
27C4×C22⋊Dic13—24no—
28C2×#88071C2211yescharacteristic
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2211yescharacteristic
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718634—24no—
39#11718613—28no—
40C25×C13C2311yescharacteristic
41C23×C4×C13—22no—
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13D414yes—
48C23×C4×C13C2312yes—
49C23×C4×C13C2312yes—
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×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C22⋊C4—24no—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C22⋊Dic13—22no—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—24no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—42no—
75C2×C22⋊Dic13D414yes—
76C2×C4⋊Dic13—22no—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13D414yes—
82C2×#6101—24no—
83C2×#6101—24no—
84C2×#6101—42no—
85C2×C4×Dic13—22no—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C13×#95—24no—
92#88071—22no—
93#88071—22no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—24no—
98#88071—24no—
99#88071—24no—
100#88071—24no—
101#88071—42no—
102#15132—131nomaximal, Sylow
103C24×C13—21no—
104C24×C13—21no—
105C24×C13—21no—
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13C2×D412yes—
116C24×C13C2×D412yes—
117C24×C13#4112yes—
118C24×C13C2411yescharacteristic
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—28no—
126C22×C4×C13—28no—
127C22×C4×C13—28no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—22no—
131C22×C4×C13—22no—
132C22×C4×C13—22no—
133C22×C4×C13—22no—
134C22×C4×C13—22no—
135C22×C4×C13—22no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—22no—
141C22×C4×C13—22no—
142C22×C4×C13—44no—
143C22×C4×C13—44no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D412yes—
149C22×C4×C13#4112yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—22no—
160C22×Dic13—21no—
161C22×Dic13—22no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—22no—
169C22×Dic13—22no—
170C22×Dic13—21no—
171C22×Dic13—21no—
172C22×Dic13—21no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—22no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—21no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13C2×D412yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×D414yes—
194C22×Dic13#4112yes—
195C22×Dic13#4112yes—
196C13×C4⋊C4—44no—
197C13×C4⋊C4—44no—
198C13×C22⋊C4—48no—
199C22⋊Dic13—28no—
200C22⋊Dic13—28no—
201C22⋊Dic13—48no—
202C4⋊Dic13—28no—
203C4⋊Dic13—44no—
204#6101—48no—
205C4×Dic13—44no—
206C4×Dic13—44no—
207C2×#397—132no—
208C2×#389—131no—
209C2×#380—131no—
210C2×#380D1311yescharacteristic
211C2×C4×C22⋊C4—131no—
212#1443—132no—
213#1442—132no—
214#1440—132no—
215C4⋊#95—131no—
216C4⋊#95—131no—
217C4⋊#95—131no—
218C23×C13—22no—
219C23×C13—22no—
220C23×C13—22no—
221C23×C13—22no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—41no—
237C23×C13—41no—
238C23×C13—41no—
239C23×C13—41no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13#12114yes—
253C23×C13C22×D411yescharacteristic
254C23×C13C22×D411yescharacteristic
255C23×C13C22×D411yescharacteristic
256C23×C13C2×#4111yescharacteristic
257C23×C13C2×#4111yescharacteristic
258C23×C13C2×#4111yescharacteristic
259C23×C13C2×#4111yescharacteristic
260C23×C13C2×#4111yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13H(5,𝔽2)11yescharacteristic
265C23×C132−1+411yescharacteristic
266C23×C132−1+411yescharacteristic
267C23×C132−1+411yescharacteristic
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
271C2×C4×C13—41no—
272C2×C4×C13—41no—
273C2×C4×C13—41no—
274C2×C4×C13—41no—
275C2×C4×C13—416no—
276C2×C4×C13—42no—
277C2×C4×C13—42no—
278C2×C4×C13—42no—
279C2×C4×C13—42no—
280C2×C4×C13—42no—
281C2×C4×C13—42no—
282C2×C4×C13—42no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13#12114yes—
291C2×C4×C13#12314yes—
292C2×C4×C13#12314yes—
293C2×C4×C13#12314yes—
294C2×C4×C13#12414yes—
295C2×C4×C13#12614yes—
296C2×C4×C13#12614yes—
297C2×Dic13—22no—
298C2×Dic13—22no—
299C2×Dic13—24no—
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—24no—
304C2×Dic13—22no—
305C2×Dic13—24no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—42no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—42no—
322C2×Dic13—41no—
323C2×Dic13—42no—
324C2×Dic13—41no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—42no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C24×C4C2×D1311yescharacteristic
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4—132no—
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C4⋊C4C2×D1311yescharacteristic
345C22×C22⋊C4—131no—
346C22×C22⋊C4—131no—
347C22×C22⋊C4—132no—
348C22×C22⋊C4C2×D1312yes—
349C22×C42—131no—
350C22×C42—131no—
351#397—268no—
352#389—264no—
353#380—24no—
354#380—264no—
355C4×C22⋊C4—264no—
356C2×#95—132no—
357C2×#95—132no—
358C2×#95—132no—
359C2×#95—132no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—131no—
363C2×#95—132no—
364C2×#95—131no—
365C2×#95—132no—
366C2×#95C2×D1312yes—
367C22×C13—24no—
368C22×C13—24no—
369C22×C13—24no—
370C22×C13—42no—
371C22×C13—42no—
372C22×C13—42no—
373C22×C13—42no—
374C22×C13—42no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13C2×#12111yescharacteristic
383C22×C13C2×#12111yescharacteristic
384C22×C13C2×#12311yescharacteristic
385C22×C13C2×#12311yescharacteristic
386C22×C13C2×#12311yescharacteristic
387C22×C13#52511yescharacteristic
388C22×C13C2×#12411yescharacteristic
389C22×C13C2×#12611yescharacteristic
390C22×C13C2×#12611yescharacteristic
391C22×C13#52911yescharacteristic
392C22×C13#52911yescharacteristic
393C22×C13#53211yescharacteristic
394C22×C13#53211yescharacteristic
395C22×C13#53611yescharacteristic
396C22×C13#53711yescharacteristic
397C22×C13#54111yescharacteristic
398C22×C13#54111yescharacteristic
399C22×C13#54211yescharacteristic
400C22×C13#54211yescharacteristic
401C22×C13D4211yescharacteristic
402C22×C13#54711yescharacteristic
403C22×C13#54711yescharacteristic
404C22×C13#54711yescharacteristic
405C22×C13#54711yescharacteristic
406C22×C13#54811yescharacteristic
407C22×C13#54811yescharacteristic
408C22×C13#55211yescharacteristic
409C22×C13#55211yescharacteristic
410C22×C13#55211yescharacteristic
411C22×C13#55211yescharacteristic
412C22×C13#55311yescharacteristic
413C22×C13#55311yescharacteristic
414C22×C13#55511yescharacteristic
415C22×C13#55611yescharacteristic
416C22×C13#55611yescharacteristic
417C4×C13—42no—
418C4×C13—82no—
419C4×C13—82no—
420C4×C13#39718yescomplemented
421Dic13—42no—
422Dic13—42no—
423Dic13—44no—
424Dic13—42no—
425Dic13—42no—
426Dic13—82no—
427C25C22×D1311yescharacteristic
428C23×C4—22no—
429C23×C4—22no—
430C23×C4—22no—
431C23×C4—22no—
432C23×C4—22no—
433C23×C4—22no—
434C23×C4—132no—
435C23×C4—131no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—132no—
440C23×C4C22⋊D1314yes—
441C23×C4C22×D1312yes—
442C23×C4C22×D1312yes—
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—134no—
452C2×C4⋊C4—262no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—264no—
455C2×C4⋊C4—264no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—522no—
460C2×C22⋊C4—24no—
461C2×C22⋊C4—24no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—134no—
464C2×C22⋊C4—262no—
465C2×C22⋊C4—262no—
466C2×C22⋊C4—262no—
467C2×C22⋊C4—262no—
468C2×C22⋊C4—262no—
469C2×C22⋊C4—264no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—522no—
472C2×C42—262no—
473C2×C42—262no—
474C2×C42—262no—
475C2×C42—262no—
476C2×C42—262no—
477C2×C42—262no—
478#95—24no—
479#95—264no—
480#95—264no—
481#95—264no—
482#95—264no—
483#95—264no—
484#95—264no—
485#95—264no—
486#95—262no—
487#95—262no—
488#95—522no—
489C2×C13—44no—
490C2×C13C2×#39711yescharacteristic
491C2×C13#241511yescharacteristic
492C2×C13#241611yescharacteristic
493C2×C13#242111yescharacteristic
494C2×C13#242211yescharacteristic
495C2×C13#248511yescharacteristic
496C2×C13#248611yescharacteristic
497C2×C13#248911yescharacteristic
498C2×C13#249111yescharacteristic
499C2×C13#249411yescharacteristic
500C2×C13#249511yescharacteristic
501C2×C13#249611yescharacteristic
502C2×C13#249611yescharacteristic
503C2×C13#262511yescharacteristic
504C2×C13#285411yescharacteristic
505C24—21no—
506C24—21no—
507C24—21no—
508C24—21no—
509C24—21no—
510C24—21no—
511C24—21no—
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24D4×D1312yes—
518C24#612912yes—
519C24C2×C22⋊D1312yes—
520C24C23×D1311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—28no—
528C22×C4—28no—
529C22×C4—28no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—44no—
545C22×C4—44no—
546C22×C4—44no—
547C22×C4—44no—
548C22×C4—132no—
549C22×C4—132no—
550C22×C4—134no—
551C22×C4—132no—
552C22×C4—132no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—262no—
558C22×C4—261no—
559C22×C4—262no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—262no—
566C22×C4—261no—
567C22×C4—261no—
568C22×C4—262no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—262no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—262no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4#612712yes—
591C22×C4#612712yes—
592C22×C4D4×D1312yes—
593C22×C4#612912yes—
594C22×C4#612912yes—
595C22×C4#612912yes—
596C22×C4C2×C22⋊D1312yes—
597C22×C4C2×C22⋊D1312yes—
598C4⋊C4—44no—
599C4⋊C4—44no—
600C4⋊C4—268no—
601C4⋊C4—528no—
602C4⋊C4—524no—
603C22⋊C4—48no—
604C22⋊C4—268no—
605C22⋊C4—268no—
606C22⋊C4—528no—
607C42—524no—
608C42—524no—
609C13#1513211yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—22no—
615C23—22no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23#8819214yes—
645C23C2×#612711yescharacteristic
646C23C2×#612711yescharacteristic
647C23C2×D4×D1311yescharacteristic
648C23C2×D4×D1311yescharacteristic
649C23C2×#612911yescharacteristic
650C23C2×#612911yescharacteristic
651C23C2×#612911yescharacteristic
652C23C2×#612911yescharacteristic
653C23#8825411yescharacteristic
654C23#8825411yescharacteristic
655C23#41×D1311yescharacteristic
656C23#41×D1311yescharacteristic
657C23#8825611yescharacteristic
658C23#8825711yescharacteristic
659C23C22×C22⋊D1311yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—416no—
668C2×C4—42no—
669C2×C4—42no—
670C2×C4—42no—
671C2×C4—42no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—264no—
683C2×C4—262no—
684C2×C4—262no—
685C2×C4—262no—
686C2×C4—262no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—264no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—264no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—522no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—522no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—522no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—521no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4#8813314yes—
725C2×C4#8813314yes—
726C2×C4#8813714yes—
727C2×C4#8813914yes—
728C2×C4#8818314yes—
729C2×C4#8818914yes—
730C2×C4#8819314yes—
731C22—24no—
732C22—24no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—42no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—42no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22C2×#8813311yescharacteristic
747C22C2×#8813311yescharacteristic
748C22C2×#8813711yescharacteristic
749C22C2×#8813911yescharacteristic
750C22#1171921211yescharacteristic
751C22#1171921211yescharacteristic
752C22#1171921811yescharacteristic
753C22#1171921811yescharacteristic
754C22#1171923411yescharacteristic
755C22#1171923511yescharacteristic
756C22#1171923711yescharacteristic
757C22#1171923811yescharacteristic
758C22#1171930111yescharacteristic
759C22#1171930111yescharacteristic
760C22#1171930311yescharacteristic
761C22#1171930511yescharacteristic
762C22#1171930511yescharacteristic
763C22#1171931411yescharacteristic
764C22#1171931611yescharacteristic
765C22#1171932311yescharacteristic
766C22#1171933011yescharacteristic
767C22#1171933011yescharacteristic
768C22#1171933611yescharacteristic
769C22#1171933811yescharacteristic
770C22#1171934411yescharacteristic
771C22#1171934611yescharacteristic
772C22#1171934811yescharacteristic
773C22#1171934811yescharacteristic
774C22C2×#8818311yescharacteristic
775C22C2×#8818911yescharacteristic
776C22C2×#8819211yescharacteristic
777C22C2×#8819311yescharacteristic
778C22#1171952111yescharacteristic
779C22#1171953311yescharacteristic
780C22#1171953811yescharacteristic
781C4—42no—
782C4—82no—
783C4—82no—
784C4—522no—
785C4—522no—
786C4—524no—
787C4—522no—
788C4—522no—
789C4—1042no—
790C4#1171861318yescomplemented
791C2—44no—
792C2C2×#1171861311yescharacteristic
793C2#1311826611yescharacteristic
794C2#1311827711yescharacteristic
795C2#1311834111yescharacteristic
796C2#1311835211yescharacteristic
797C2#1311912711yescharacteristic
798C2#1311913811yescharacteristic
799C2#1311917311yescharacteristic
800C2#1311919511yescharacteristic
801C2#1311923211yescharacteristic
802C2#1311924911yescharacteristic
803C2#1311925411yescharacteristic
804C2#1311926011yescharacteristic
805C2#1312063411yescharacteristic
806C2#1312316211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#380C2
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#15132
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C2×#11718634C2semidirect
5. #13113097C2semidirect
6. #13113091C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113065C2semidirect
420. C4×C13#397semidirect
609. C13#15132semidirect
790. 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×#117186342
C2×#117188732
C2×C4×C22⋊Dic132
#131130972
#131130912
#131130852
#131130652
C2×C13×#3802
#1513213