Finite Group Databasebeta

← #15799563

Subgroups — #15799563

Order 3328.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718653C212yesmaximal
2C2×#11718589C211yesmaximal, characteristic, complemented
3C2×#11718637C211yesmaximal, characteristic, complemented
4C2×#11718648C211yesmaximal, characteristic
5C2×#11718648C211yesmaximal, characteristic
6C2×C4×#6103C211yesmaximal, characteristic
7#13113102C212yesmaximal, complemented
8#13113099C212yesmaximal, complemented
9#13113080C212yesmaximal
10#13113065C211yesmaximal, characteristic, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×#6101C2212yes—
25C22×#6101C2212yes—
26C22×C4×Dic13C2211yescharacteristic
27C13×#389—24no—
28C2×C13×#95C2212yes—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718653—28no—
37#11718648—24no—
38#11718648—24no—
39#11718637—24no—
40C4×#6103—24no—
41#11718589—24no—
42C24×D13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2312yes—
46C23×C4×C13C2311yescharacteristic
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13—22no—
59C22×C4×D13Q814yes—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—24no—
63C2×C13×C4⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—22no—
66C2×C13×C4⋊C4—24no—
67C2×C13×C4⋊C4—42no—
68C2×C13×C4⋊C4D414yes—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—22no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—24no—
79C2×#6103—24no—
80C2×#6103—42no—
81C2×#6103—42no—
82C2×#6103D414yes—
83C2×#6103Q814yes—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13D414yes—
90C2×#6101—24no—
91C2×#6101—24no—
92C2×#6101—24no—
93C2×#6101—24no—
94C2×#6101—24no—
95C2×#6101—24no—
96C2×#6101—42no—
97C2×#6101—42no—
98C2×#6101—42no—
99C2×C4×Dic13—22no—
100C2×C4×Dic13—22no—
101C2×C4×Dic13D414yes—
102C13×#95—24no—
103#88071—24no—
104#88071—24no—
105#88071—22no—
106#88071—22no—
107#88071—24no—
108#88071—24no—
109#88071—24no—
110#15135—131nomaximal, Sylow
111C24×C13C2411yescharacteristic
112C23×D13—21no—
113C23×D13—21no—
114C23×D13—21no—
115C23×D13—21no—
116C23×D13—21no—
117C23×D13—21no—
118C23×D13—21no—
119C23×D13—21no—
120C23×D13—21no—
121C23×D13—21no—
122C23×D13—21no—
123C23×D13—21no—
124C23×D13C2×D412yes—
125C23×D13C2×Q812yes—
126C23×D13C2×Q812yes—
127C22×C4×C13—21no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
134C22×C4×C13—22no—
135C22×C4×C13—21no—
136C22×C4×C13—21no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13—21no—
142C22×C4×C13—21no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13—22no—
150C22×C4×C13—22no—
151C22×C4×C13—22no—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D412yes—
155C22×C4×C13C2×D414yes—
156C22×C4×C13C2×D412yes—
157C22×C4×C13C2×Q812yes—
158C22×C4×C13C2×Q812yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
161C22×C4×C13#4112yes—
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—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13C2×D414yes—
190C22×Dic13C2×D412yes—
191C22×Dic13C2×D412yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×Q812yes—
194C22×Dic13C2×Q812yes—
195C22×Dic13#4112yes—
196C22×Dic13#4112yes—
197C2×C4×D13—28no—
198C2×C4×D13—28no—
199C2×C4×D13—28no—
200C2×C4×D13—44no—
201C2×C4×D13—44no—
202C2×C4×D13—44no—
203C2×C4×D13—44no—
204C13×C4⋊C4—28no—
205C13×C4⋊C4—48no—
206C13×C4⋊C4—44no—
207C42×C13—44no—
208#6103—28no—
209#6103—28no—
210#6103—48no—
211#6103—48no—
212C4⋊Dic13—28no—
213C4⋊Dic13—44no—
214#6101—48no—
215#6101—48no—
216#6101—48no—
217C4×Dic13—28no—
218C2×#399—132no—
219C2×#389—131no—
220C2×#389D1311yescharacteristic, complemented
221C2×#384—131no—
222C2×#380—131no—
223C2×#380—131no—
224C2×C4×C22⋊C4—131no—
225#1445—132no—
226#1444—132no—
227#1439—132no—
228C4⋊#95—131no—
229C23×C13C22×D411yescharacteristic
230C23×C13C22×D411yescharacteristic
231C23×C13C22×D411yescharacteristic
232C23×C13C22×D411yescharacteristic
233C23×C13C22×Q811yescharacteristic
234C23×C13C22×Q811yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13C2×#4111yescharacteristic
239C23×C13C2×#4111yescharacteristic
240C23×C13H(5,𝔽2)11yescharacteristic
241C23×C13H(5,𝔽2)11yescharacteristic
242C23×C132−1+411yescharacteristic
243C23×C132−1+411yescharacteristic
244C22×D13—22no—
245C22×D13—22no—
246C22×D13—22no—
247C22×D13—22no—
248C22×D13—22no—
249C22×D13—22no—
250C22×D13—22no—
251C22×D13—22no—
252C22×D13—22no—
253C22×D13—22no—
254C22×D13—22no—
255C22×D13—22no—
256C22×D13—22no—
257C22×D13—22no—
258C22×D13—22no—
259C22×D13—22no—
260C22×D13—22no—
261C22×D13—22no—
262C22×D13—41no—
263C22×D13—41no—
264C22×D13—41no—
265C22×D13—41no—
266C22×D13—41no—
267C22×D13—41no—
268C22×D13—41no—
269C22×D13—41no—
270C22×D13—41no—
271C22×D13—41no—
272C22×D13—41no—
273C22×D13—41no—
274C22×D13—41no—
275C22×D13—41no—
276C22×D13—41no—
277C22×D13—41no—
278C22×D13C4⋊Q814yes—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—24no—
284C2×C4×C13—22no—
285C2×C4×C13—24no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—42no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13—42no—
305C2×C4×C13—42no—
306C2×C4×C13—42no—
307C2×C4×C13C22⋊Q814yes—
308C2×C4×C13C22⋊Q814yes—
309C2×C4×C13C22⋊Q814yes—
310C2×C4×C13#12314yes—
311C2×C4×C13#12314yes—
312C2×C4×C13#12314yes—
313C2×C4×C13#12714yes—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—22no—
328C2×Dic13—22no—
329C2×Dic13—24no—
330C2×Dic13—24no—
331C2×Dic13—24no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
335C2×Dic13—41no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13#12114yes—
348C2×Dic13C22⋊Q814yes—
349C4×D13—416no—
350C24×C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—132no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—132no—
355C22×C4⋊C4—132no—
356C22×C4⋊C4C2×D1311yescharacteristic
357C22×C4⋊C4C2×D1312yes—
358C22×C4⋊C4C2×D1311yescharacteristic
359C22×C22⋊C4—131no—
360C22×C22⋊C4—131no—
361C22×C22⋊C4—132no—
362C22×C22⋊C4—132no—
363C22×C42—131no—
364C22×C42C2×D1311yescharacteristic
365#399—268no—
366#389—24no—
367#389—264no—
368#384—264no—
369#380—264no—
370#380—264no—
371C4×C22⋊C4—264no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95—132no—
375C2×#95—131no—
376C2×#95—132no—
377C2×#95—132no—
378C2×#95—131no—
379C2×#95C2×D1312yes—
380C22×C13C2×#12111yescharacteristic
381C22×C13C2×C22⋊Q811yescharacteristic
382C22×C13C2×C22⋊Q811yescharacteristic
383C22×C13C2×C22⋊Q811yescharacteristic
384C22×C13C2×C22⋊Q811yescharacteristic
385C22×C13C2×#12311yescharacteristic
386C22×C13C2×#12311yescharacteristic
387C22×C13C2×#12311yescharacteristic
388C22×C13C2×#12711yescharacteristic
389C22×C13C2×C4⋊Q811yescharacteristic
390C22×C13#53211yescharacteristic
391C22×C13#53311yescharacteristic
392C22×C13#53311yescharacteristic
393C22×C13#53511yescharacteristic
394C22×C13#53611yescharacteristic
395C22×C13#54211yescharacteristic
396C22×C13#54211yescharacteristic
397C22×C13#54411yescharacteristic
398C22×C13#54411yescharacteristic
399C22×C13D4211yescharacteristic
400C22×C13D4211yescharacteristic
401C22×C13#54711yescharacteristic
402C22×C13#54711yescharacteristic
403C22×C13#54711yescharacteristic
404C22×C13#54711yescharacteristic
405C22×C13D4×Q811yescharacteristic
406C22×C13D4×Q811yescharacteristic
407C22×C13#55011yescharacteristic
408C22×C13#55011yescharacteristic
409C22×C13#55211yescharacteristic
410C22×C13#55211yescharacteristic
411C22×C13#55311yescharacteristic
412C22×C13#55311yescharacteristic
413C22×C13#55411yescharacteristic
414C22×C13#55411yescharacteristic
415C2×D13—24no—
416C2×D13—24no—
417C2×D13—24no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C2×D13—42no—
429C2×D13—42no—
430C4×C13—44no—
431C4×C13—42no—
432C4×C13—42no—
433C4×C13—82no—
434C4×C13#39918yescomplemented
435Dic13—24no—
436Dic13—24no—
437Dic13—42no—
438Dic13—44no—
439Dic13—82no—
440C25—131no—
441C23×C4—131no—
442C23×C4—131no—
443C23×C4—132no—
444C23×C4—131no—
445C23×C4—134no—
446C23×C4—132no—
447C23×C4—262no—
448C23×C4—262no—
449C23×C4—262no—
450C23×C4—262no—
451C23×C4—262no—
452C23×C4—262no—
453C23×C4C22×D1312yes—
454C23×C4C22×D1311yescharacteristic
455C23×C4C22×D1311yescharacteristic
456C23×C4C22×D1312yes—
457C23×C4C22×D1311yescharacteristic
458C2×C4⋊C4—22no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—22no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—24no—
463C2×C4⋊C4—24no—
464C2×C4⋊C4—22no—
465C2×C4⋊C4—42no—
466C2×C4⋊C4—134no—
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—262no—
476C2×C4⋊C4—262no—
477C2×C4⋊C4—262no—
478C2×C4⋊C4—522no—
479C2×C4⋊C4—522no—
480C2×C4⋊C4—522no—
481C2×C4⋊C4C22⋊D1314yes—
482C2×C22⋊C4—134no—
483C2×C22⋊C4—134no—
484C2×C22⋊C4—262no—
485C2×C22⋊C4—262no—
486C2×C22⋊C4—262no—
487C2×C22⋊C4—262no—
488C2×C22⋊C4—264no—
489C2×C22⋊C4—264no—
490C2×C22⋊C4—264no—
491C2×C22⋊C4—264no—
492C2×C22⋊C4—522no—
493C2×C22⋊C4—522no—
494C2×C42—22no—
495C2×C42—22no—
496C2×C42—22no—
497C2×C42—134no—
498C2×C42—262no—
499C2×C42—262no—
500#95—24no—
501#95—264no—
502#95—262no—
503#95—262no—
504#95—264no—
505#95—264no—
506#95—264no—
507#95—264no—
508C2×C13C2×#39911yescharacteristic
509C2×C13#242211yescharacteristic
510C2×C13#242211yescharacteristic
511C2×C13#242311yescharacteristic
512C2×C13#242311yescharacteristic
513C2×C13#244011yescharacteristic
514C2×C13#244011yescharacteristic
515C2×C13#244111yescharacteristic
516C2×C13#244111yescharacteristic
517C2×C13#248611yescharacteristic
518C2×C13#248711yescharacteristic
519C2×C13#254111yescharacteristic
520C2×C13#254211yescharacteristic
521C2×C13#262811yescharacteristic
522C2×C13#285711yescharacteristic
523D13—44no—
524C24—132no—
525C24—132no—
526C24—132no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24—261no—
533C24—261no—
534C24—261no—
535C24—261no—
536C24—261no—
537C24—261no—
538C24—261no—
539C24C23×D1311yescharacteristic
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—132no—
566C22×C4—132no—
567C22×C4—132no—
568C22×C4—132no—
569C22×C4—132no—
570C22×C4—132no—
571C22×C4—134no—
572C22×C4—132no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—262no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—261no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—261no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—261no—
593C22×C4—268no—
594C22×C4—268no—
595C22×C4—268no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—524no—
604C22×C4—524no—
605C22×C4—524no—
606C22×C4—524no—
607C22×C4#612712yes—
608C22×C4#612712yes—
609C22×C4D4×D1312yes—
610C22×C4D4×D1312yes—
611C22×C4D4×D1312yes—
612C22×C4Q8×D1312yes—
613C22×C4Q8×D1312yes—
614C22×C4#613112yes—
615C22×C4C2×C22⋊D1314yes—
616C22×C4C2×C22⋊D1312yes—
617C4⋊C4—28no—
618C4⋊C4—48no—
619C4⋊C4—44no—
620C4⋊C4—268no—
621C4⋊C4—528no—
622C4⋊C4—528no—
623C4⋊C4—528no—
624C4⋊C4—524no—
625C22⋊C4—268no—
626C22⋊C4—268no—
627C22⋊C4—528no—
628C22⋊C4—528no—
629C42—44no—
630C42—268no—
631C13#1513511yescharacteristic, complemented, Sylow
632C23—134no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23—262no—
644C23—262no—
645C23—262no—
646C23—262no—
647C23—262no—
648C23—262no—
649C23—262no—
650C23—262no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23—521no—
660C23—521no—
661C23—521no—
662C23—521no—
663C23—521no—
664C23—521no—
665C23—521no—
666C23—521no—
667C23C2×#612711yescharacteristic
668C23C2×#612711yescharacteristic
669C23C2×D4×D1311yescharacteristic
670C23C2×D4×D1311yescharacteristic
671C23C2×D4×D1311yescharacteristic
672C23#8825111yescharacteristic
673C23C2×Q8×D1311yescharacteristic
674C23C2×Q8×D1311yescharacteristic
675C23C2×#613111yescharacteristic
676C23#8825411yescharacteristic
677C23#41×D1311yescharacteristic
678C23#41×D1311yescharacteristic
679C23#8825611yescharacteristic
680C23#8825711yescharacteristic
681C23C22×C22⋊D1311yescharacteristic
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—134no—
711C2×C4—134no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—262no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—262no—
723C2×C4—262no—
724C2×C4—264no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—262no—
728C2×C4—264no—
729C2×C4—264no—
730C2×C4—522no—
731C2×C4—521no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—521no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—5216no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4—522no—
743C2×C4—522no—
744C2×C4—522no—
745C2×C4—522no—
746C2×C4#8814814yes—
747C2×C4#8814814yes—
748C2×C4#8815014yes—
749C2×C4#8815014yes—
750C2×C4#8818314yes—
751C2×C4#8819414yes—
752C2×C4#8820014yes—
753C22—264no—
754C22—264no—
755C22—264no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22—522no—
765C22—522no—
766C22—522no—
767C22—522no—
768C22C2×#8814811yescharacteristic
769C22C2×#8814811yescharacteristic
770C22C2×#8815011yescharacteristic
771C22C2×#8815011yescharacteristic
772C22#1171925311yescharacteristic
773C22#1171925611yescharacteristic
774C22#1171926311yescharacteristic
775C22#1171926611yescharacteristic
776C22#1171928311yescharacteristic
777C22#1171928411yescharacteristic
778C22#1171928611yescharacteristic
779C22#1171928711yescharacteristic
780C22#1171930411yescharacteristic
781C22D13×#12111yescharacteristic
782C22#1171931211yescharacteristic
783C22#1171931411yescharacteristic
784C22D13×C22⋊Q811yescharacteristic
785C22#1171933311yescharacteristic
786C22#1171933611yescharacteristic
787C22#1171933711yescharacteristic
788C22#1171939311yescharacteristic
789C22#1171939411yescharacteristic
790C22#1171939911yescharacteristic
791C22#1171940011yescharacteristic
792C22D13×C4⋊Q811yescharacteristic
793C22#1171943111yescharacteristic
794C22#1171943411yescharacteristic
795C22#1171943511yescharacteristic
796C22C2×#8818311yescharacteristic
797C22D4×C22⋊D1311yescharacteristic
798C22C2×#8819411yescharacteristic
799C22C2×#8820011yescharacteristic
800C22Q8×C22⋊D1311yescharacteristic
801C22#1171952911yescharacteristic
802C22#1171953911yescharacteristic
803C4—42no—
804C4—42no—
805C4—44no—
806C4—82no—
807C4—264no—
808C4—264no—
809C4—522no—
810C4—524no—
811C4—1042no—
812C4#1171865318yescomplemented
813C2—524no—
814C2C2×#1171865311yescharacteristic
815C2#1311834411yescharacteristic
816C2#1311835111yescharacteristic
817C2#1311835511yescharacteristic
818C2#1311836211yescharacteristic
819C2#1311853411yescharacteristic
820C2#1311854011yescharacteristic
821C2#1311854511yescharacteristic
822C2#1311855111yescharacteristic
823C2#1311914211yescharacteristic
824C2#1311915111yescharacteristic
825C2#1311977911yescharacteristic
826C2#1311978611yescharacteristic
827C2#1312066311yescharacteristic
828C2#1312318711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#389C2
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#15135
LCSG ▷ C24×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11718589C2semidirect
3. C2×#11718637C2semidirect
7. #13113102C2semidirect
8. #13113099C2semidirect
10. #13113065C2semidirect
11. C2×C13×#389C2semidirect
220. C2×#389D13semidirect
434. C4×C13#399semidirect
631. C13#15135semidirect
812. C4#11718653semidirect

Maximal subgroups

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

subgroupindex
C2×#117186532
C2×#117185892
C2×#117186372
C2×#117186482
C2×C4×#61032
#131131022
#131130992
#131130802
#131130652
C2×C13×#3892
#1513513