Finite Group Databasebeta

← #15799660

Subgroups — #15799660

Order 3328.

1778 conjugacy classes of subgroups.

The subgroup lattice has 826 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×C4×#6101C211yesmaximal, characteristic, complemented
5#13113085C212yesmaximal, complemented
6#13113083C212yesmaximal, complemented
7#13113079C212yesmaximal, complemented
8#13113066C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, 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×#6101C2211yescharacteristic
24C22×#6101C2211yescharacteristic
25C22×C4×Dic13C2211yescharacteristic
26C22×C4×Dic13C2211yescharacteristic
27C13×#390—24no—
28#11718882—24no—
29#11718882—24no—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35C2×#88071C2212yes—
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718613—28no—
39C4×#6101—24no—
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×Dic13C2312yes—
54C23×Dic13C2311yescharacteristic
55C23×Dic13C2311yescharacteristic
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⋊Dic13—22no—
88C2×#6101—22no—
89C2×#6101—22no—
90C2×#6101—22no—
91C2×#6101—22no—
92C2×#6101—22no—
93C2×#6101D414yescomplemented
94C2×C4×Dic13—22no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13—22no—
99C2×C4×Dic13D414yes—
100#88071—24no—
101#88071—22no—
102#88071—22no—
103#88071—24no—
104#88071—24no—
105#88071—42no—
106#88071—42no—
107#88071—42no—
108#15147—131nomaximal, Sylow
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×C13—22no—
122C24×C13—22no—
123C24×C13C2×D414yes—
124C24×C13C2411yescharacteristic
125C2×D4×C13—28no—
126C2×D4×C13—28no—
127C2×D4×C13—28no—
128C2×D4×C13—44no—
129C2×D4×C13—44no—
130C2×D4×C13—44no—
131C2×D4×C13—44no—
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—21no—
143C22×C4×C13—21no—
144C22×C4×C13—22no—
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×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
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—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—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13—22no—
193C22×Dic13—22no—
194C22×Dic13—22no—
195C22×Dic13—22no—
196C22×Dic13C2×D412yes—
197C22×Dic13C2×D412yes—
198C22×Dic13C2×D412yes—
199C22×Dic13C2×D412yes—
200C22×Dic13#4112yes—
201C22×Dic13#4112yes—
202C13×C4⋊C4—44no—
203C13×C22⋊C4—48no—
204C13×C22⋊C4—48no—
205C42×C13—44no—
206C22⋊Dic13—48no—
207C22⋊Dic13—48no—
208C22⋊Dic13—48no—
209C22⋊Dic13—48no—
210C4⋊Dic13—44no—
211C4⋊Dic13—44no—
212#6101—28no—
213#6101—28no—
214C4×Dic13—28no—
215C4×Dic13—44no—
216C2×#397—132no—
217C2×#390—131no—
218C2×#390—131no—
219C2×#390D1311yescharacteristic
220C2×C4×C4⋊C4—131no—
221#1440—132no—
222#1440—132no—
223#1439—132no—
224C4⋊#95—131no—
225C4⋊#95—131no—
226C4⋊#95—131no—
227C23×C13—24no—
228C23×C13—24no—
229C23×C13—24no—
230C23×C13—24no—
231C23×C13—24no—
232C23×C13—24no—
233C23×C13—24no—
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×C13—42no—
260C23×C13—42no—
261C23×C13—42no—
262C23×C13C22×D411yescharacteristic
263C23×C13C22×D411yescharacteristic
264C23×C13C22×D411yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13C2×#4111yescharacteristic
269C23×C13C2×#4111yescharacteristic
270C23×C13C2×#4111yescharacteristic
271C23×C13C2×#4111yescharacteristic
272C23×C13C2×#4111yescharacteristic
273C23×C13H(5,𝔽2)11yescharacteristic
274C23×C13H(5,𝔽2)11yescharacteristic
275C23×C13H(5,𝔽2)11yescharacteristic
276C23×C132−1+411yescharacteristic
277D4×C13—416no—
278C2×C4×C13—22no—
279C2×C4×C13—22no—
280C2×C4×C13—22no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—42no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13#12114yes—
300C2×C4×C13#12314yes—
301C2×C4×C13#12314yes—
302C2×C4×C13#12314yes—
303C2×C4×C13#12414yes—
304C2×C4×C13#12614yes—
305C2×C4×C13#12614yes—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—22no—
320C2×Dic13—22no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—41no—
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—42no—
335C2×Dic13—42no—
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—
348C23×D4C2×D1311yescharacteristic
349C22×C4⋊C4—131no—
350C22×C4⋊C4—131no—
351C22×C4⋊C4—131no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4C2×D1311yescharacteristic
354C22×C22⋊C4—132no—
355C22×C22⋊C4—132no—
356C22×C22⋊C4—132no—
357C22×C22⋊C4—132no—
358C22×C22⋊C4C2×D1312yes—
359C22×C22⋊C4C2×D1312yes—
360C22×C42—131no—
361C22×C42—131no—
362C22×C42C2×D1311yescharacteristic
363#397—268no—
364#390—24no—
365#390—264no—
366#390—264no—
367C4×C4⋊C4—264no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95—132no—
371C2×#95—131no—
372C2×#95—131no—
373C2×#95—132no—
374C2×#95—132no—
375C2×#95—132no—
376C22×C13—44no—
377C22×C13—44no—
378C22×C13—44no—
379C22×C13—44no—
380C22×C13—44no—
381C22×C13—44no—
382C22×C13—44no—
383C22×C13—82no—
384C22×C13—82no—
385C22×C13—82no—
386C22×C13—82no—
387C22×C13—82no—
388C22×C13—82no—
389C22×C13—82no—
390C22×C13—82no—
391C22×C13C2×#12111yescharacteristic
392C22×C13C2×#12111yescharacteristic
393C22×C13C2×#12311yescharacteristic
394C22×C13C2×#12311yescharacteristic
395C22×C13C2×#12311yescharacteristic
396C22×C13#52511yescharacteristic
397C22×C13C2×#12411yescharacteristic
398C22×C13C2×#12611yescharacteristic
399C22×C13C2×#12611yescharacteristic
400C22×C13#52911yescharacteristic
401C22×C13#52911yescharacteristic
402C22×C13#53211yescharacteristic
403C22×C13#53211yescharacteristic
404C22×C13#53511yescharacteristic
405C22×C13#53711yescharacteristic
406C22×C13#54011yescharacteristic
407C22×C13#54011yescharacteristic
408C22×C13#54211yescharacteristic
409C22×C13#54211yescharacteristic
410C22×C13D4211yescharacteristic
411C22×C13#54611yescharacteristic
412C22×C13#54611yescharacteristic
413C22×C13#54711yescharacteristic
414C22×C13#54711yescharacteristic
415C22×C13#55011yescharacteristic
416C22×C13#55011yescharacteristic
417C22×C13#55311yescharacteristic
418C22×C13#55311yescharacteristic
419C22×C13#55511yescharacteristic
420C22×C13#55611yescharacteristic
421C22×C13#55611yescharacteristic
422C22×C13#55911yescharacteristic
423C22×C13#55911yescharacteristic
424C22×C13#55911yescharacteristic
425C22×C13#55911yescharacteristic
426C4×C13—42no—
427C4×C13—42no—
428C4×C13—82no—
429C4×C13#39718yescomplemented
430Dic13—24no—
431Dic13—42no—
432Dic13—42no—
433Dic13—42no—
434Dic13—82no—
435Dic13—82no—
436C25C22×D1312yes—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4C22⋊D1314yes—
444C23×C4—131no—
445C23×C4—131no—
446C23×C4—131no—
447C23×C4—131no—
448C23×C4—132no—
449C23×C4—132no—
450C23×C4C22×D1312yes—
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—134no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—262no—
467C2×C4⋊C4—262no—
468C2×C4⋊C4—262no—
469C2×C22⋊C4—24no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—24no—
472C2×C22⋊C4—24no—
473C2×C22⋊C4—42no—
474C2×C22⋊C4—42no—
475C2×C22⋊C4—264no—
476C2×C22⋊C4—264no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—264no—
482C2×C22⋊C4—264no—
483C2×C22⋊C4—522no—
484C2×C22⋊C4—522no—
485C2×C22⋊C4—522no—
486C2×C22⋊C4—522no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—134no—
491C2×C42—262no—
492C2×C42—262no—
493C2×C42—262no—
494C2×C42—262no—
495C2×C42—262no—
496#95—262no—
497#95—262no—
498#95—264no—
499#95—264no—
500#95—264no—
501#95—522no—
502#95—522no—
503#95—522no—
504C2×C13—84no—
505C2×C13C2×#39711yescharacteristic
506C2×C13#244511yescharacteristic
507C2×C13#244511yescharacteristic
508C2×C13#244711yescharacteristic
509C2×C13#244711yescharacteristic
510C2×C13#251211yescharacteristic
511C2×C13#251211yescharacteristic
512C2×C13#251311yescharacteristic
513C2×C13#251311yescharacteristic
514C2×C13#253511yescharacteristic
515C2×C13#253711yescharacteristic
516C2×C13#254811yescharacteristic
517C2×C13#259211yescharacteristic
518C2×C13#262411yescharacteristic
519C2×C13#285411yescharacteristic
520C24—22no—
521C24—22no—
522C24—22no—
523C24—22no—
524C24—22no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24C2×C22⋊D1314yes—
535C24C23×D1311yescharacteristic
536C2×D4—28no—
537C2×D4—28no—
538C2×D4—28no—
539C2×D4—44no—
540C2×D4—44no—
541C2×D4—44no—
542C2×D4—44no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—132no—
565C22×C4—132no—
566C22×C4—132no—
567C22×C4—132no—
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—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
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—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—262no—
597C22×C4—262no—
598C22×C4—262no—
599C22×C4—262no—
600C22×C4—262no—
601C22×C4—262no—
602C22×C4—262no—
603C22×C4—262no—
604C22×C4#612712yes—
605C22×C4#612712yes—
606C22×C4D4×D1312yes—
607C22×C4D4×D1312yes—
608C22×C4#612912yes—
609C22×C4#612912yes—
610C22×C4#612912yes—
611C22×C4#612912yes—
612C22×C4C2×C22⋊D1312yes—
613C4⋊C4—44no—
614C4⋊C4—268no—
615C4⋊C4—268no—
616C4⋊C4—524no—
617C4⋊C4—524no—
618C22⋊C4—48no—
619C22⋊C4—48no—
620C22⋊C4—528no—
621C22⋊C4—528no—
622C22⋊C4—528no—
623C22⋊C4—528no—
624C42—44no—
625C42—268no—
626C42—524no—
627C13#1514711yescharacteristic, complemented, Sylow
628C23—24no—
629C23—24no—
630C23—24no—
631C23—24no—
632C23—24no—
633C23—24no—
634C23—24no—
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—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23C2×#612711yescharacteristic
664C23C2×#612711yescharacteristic
665C23C2×D4×D1311yescharacteristic
666C23C2×D4×D1311yescharacteristic
667C23C2×#612911yescharacteristic
668C23C2×#612911yescharacteristic
669C23C2×#612911yescharacteristic
670C23C2×#612911yescharacteristic
671C23#8825111yescharacteristic
672C23#8825111yescharacteristic
673C23#41×D1311yescharacteristic
674C23#41×D1311yescharacteristic
675C23#8825611yescharacteristic
676C23#8825711yescharacteristic
677C23C22×C22⋊D1311yescharacteristic
678D4—416no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—134no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—262no—
713C2×C4—262no—
714C2×C4—262no—
715C2×C4—262no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4—522no—
742C2×C4#8813314yes—
743C2×C4#8813314yes—
744C2×C4#8813714yes—
745C2×C4#8813914yes—
746C2×C4#8818314yes—
747C2×C4#8818914yes—
748C2×C4#8819314yes—
749C22—44no—
750C22—44no—
751C22—44no—
752C22—44no—
753C22—44no—
754C22—44no—
755C22—44no—
756C22—82no—
757C22—82no—
758C22—82no—
759C22—82no—
760C22—82no—
761C22—82no—
762C22—82no—
763C22—82no—
764C22C2×#8813311yescharacteristic
765C22C2×#8813311yescharacteristic
766C22C2×#8813711yescharacteristic
767C22C2×#8813911yescharacteristic
768C22#1171924711yescharacteristic
769C22#1171925311yescharacteristic
770C22#1171925811yescharacteristic
771C22#1171926211yescharacteristic
772C22#1171926411yescharacteristic
773C22#1171926411yescharacteristic
774C22#1171926611yescharacteristic
775C22#1171926711yescharacteristic
776C22D13×#12111yescharacteristic
777C22#1171931111yescharacteristic
778C22#1171931211yescharacteristic
779C22#1171931311yescharacteristic
780C22#1171931611yescharacteristic
781C22#1171931911yescharacteristic
782C22#1171932111yescharacteristic
783C22#1171932311yescharacteristic
784C22#1171937611yescharacteristic
785C22#1171938511yescharacteristic
786C22#1171938611yescharacteristic
787C22#1171938711yescharacteristic
788C22#1171941811yescharacteristic
789C22#1171942111yescharacteristic
790C22#1171942311yescharacteristic
791C22#1171942411yescharacteristic
792C22C2×#8818311yescharacteristic
793C22C2×#8818911yescharacteristic
794C22D4×C22⋊D1311yescharacteristic
795C22C2×#8819311yescharacteristic
796C22#1171951111yescharacteristic
797C22#1171952911yescharacteristic
798C22#1171953411yescharacteristic
799C4—42no—
800C4—42no—
801C4—82no—
802C4—264no—
803C4—522no—
804C4—522no—
805C4—522no—
806C4—1042no—
807C4—1042no—
808C4#1171861318yescomplemented
809C2—84no—
810C2C2×#1171861311yescharacteristic
811C2#1311859511yescharacteristic
812C2#1311859711yescharacteristic
813C2#1311861711yescharacteristic
814C2#1311861911yescharacteristic
815C2#1311942311yescharacteristic
816C2#1311942411yescharacteristic
817C2#1311943411yescharacteristic
818C2#1311943511yescharacteristic
819C2#1311973511yescharacteristic
820C2#1311975011yescharacteristic
821C2#1311983711yescharacteristic
822C2#1312032111yescharacteristic
823C2#1312062811yescharacteristic
824C2#1312316611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutator, socle, cosocleC24×C13C24
FittingC2×C13×#390C2
prime radicalC23×D4×C13C22
hypercenterC2×#390D13
hypocenterC13#15147
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×C4×#6101C2semidirect
5. #13113085C2semidirect
6. #13113083C2semidirect
7. #13113079C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
10. #13113065C2semidirect
93. C2×#6101D4semidirect
429. C4×C13#397semidirect
627. C13#15147semidirect
808. 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×C4×#61012
#131130852
#131130832
#131130792
#131130662
#131130652
C2×C13×#3902
#1514713