Finite Group Databasebeta

← #15784864

Subgroups — #15784864

Order 3328.

1846 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718601C212yesmaximal
2C2×#11718637C211yesmaximal, characteristic, complemented
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×#6103C211yesmaximal, characteristic
6#13113091C212yesmaximal, complemented
7#13113080C212yesmaximal
8#13113069C212yesmaximal, complemented
9#13113066C211yesmaximal, characteristic, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C2×C4×C13×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2212yes—
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×#6101C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C4×C13×C4⋊C4—24no—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718648—24no—
37#11718648—24no—
38#11718637—24no—
39#11718601—28no—
40C4×#6103C418yescomplemented
41C24×D13C2311yescharacteristic
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2312yes—
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2312yes—
48C23×Dic13C2312yes—
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13—22no—
58C22×C4×D13C2×C414yes—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4D414yes—
64C2×C13×C4⋊C4D414yes—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13—24no—
68C2×C42×C13—24no—
69C2×C42×C13—42no—
70C2×C42×C13C2×C414yes—
71C2×#6103—22no—
72C2×#6103—22no—
73C2×#6103—24no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—42no—
78C2×#6103—42no—
79C2×#6103C2×C414yes—
80C2×#6103C2×C414yes—
81C2×#6103D414yes—
82C2×#6103Q814yes—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×#6101—24no—
90C2×#6101—24no—
91C2×#6101—24no—
92C2×#6101—24no—
93C2×#6101—42no—
94C2×#6101—42no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13C2×C414yes—
98C13×#95—24no—
99#88071—24no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—42no—
105#88071C2×C414yes—
106#88071C2×C414yes—
107#13876—131nomaximal, Sylow
108C24×C13C2411yescharacteristic
109C23×D13—21no—
110C23×D13—21no—
111C23×D13—21no—
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×D13C22×C412yes—
122C23×D13C2×D412yes—
123C23×D13C2×Q812yes—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—21no—
128C22×C4×C13—22no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
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—22no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—21no—
141C22×C4×C13—22no—
142C22×C4×C13—22no—
143C22×C4×C13—22no—
144C22×C4×C13—21no—
145C22×C4×C13—22no—
146C22×C4×C13C22×C412yes—
147C22×C4×C13C22×C412yes—
148C22×C4×C13C22×C412yes—
149C22×C4×C13C2×D414yes—
150C22×C4×C13C2×D412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D414yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×Q812yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×Dic13—21no—
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—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
179C22×Dic13—22no—
180C22×Dic13—22no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13C22×C412yes—
188C22×Dic13C22×C412yes—
189C22×Dic13C22×C412yes—
190C22×Dic13C2×D412yes—
191C22×Dic13C2×Q812yes—
192C22×Dic13#4112yes—
193C22×Dic13#4112yes—
194C2×C4×D13—28no—
195C2×C4×D13—28no—
196C2×C4×D13—28no—
197C2×C4×D13—44no—
198C2×C4×D13—44no—
199C2×C4×D13—44no—
200C2×C4×D13—44no—
201C13×C4⋊C4—28no—
202C13×C4⋊C4—28no—
203C42×C13—28no—
204C42×C13—48no—
205#6103—28no—
206#6103—48no—
207#6103—48no—
208#6103C4⋊C4116yescomplemented
209C4⋊Dic13—44no—
210C4⋊Dic13—44no—
211#6101—48no—
212#6101—48no—
213C4×Dic13—28no—
214C2×#388—132no—
215C2×#384—131no—
216C2×#380—131no—
217C2×#380—131no—
218C2×C4×C4⋊C4D1311yescharacteristic, complemented
219C2×C4×C22⋊C4—131no—
220#1442—132no—
221#1439—132no—
222#1436—132no—
223C4⋊#95—131no—
224C4⋊#95—131no—
225C23×C13C23×C411yescharacteristic
226C23×C13C22×D411yescharacteristic
227C23×C13C22×D411yescharacteristic
228C23×C13C22×D411yescharacteristic
229C23×C13C22×Q811yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13H(5,𝔽2)11yescharacteristic
237C23×C13H(5,𝔽2)11yescharacteristic
238C23×C132−1+411yescharacteristic
239C23×C132−1+411yescharacteristic
240C22×D13—22no—
241C22×D13—22no—
242C22×D13—22no—
243C22×D13—22no—
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—41no—
259C22×D13—41no—
260C22×D13—41no—
261C22×D13—41no—
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×D13C2×C4⋊C414yes—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
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—24no—
285C2×C4×C13—24no—
286C2×C4×C13—24no—
287C2×C4×C13—24no—
288C2×C4×C13—24no—
289C2×C4×C13—24no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—42no—
294C2×C4×C13—42no—
295C2×C4×C13—41no—
296C2×C4×C13—42no—
297C2×C4×C13—41no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13C2×C4⋊C414yes—
303C2×C4×C13#11714yes—
304C2×C4×C13C4×D414yes—
305C2×C4×C13C4×D414yes—
306C2×C4×C13#12114yes—
307C2×C4×C13#12314yes—
308C2×C4×C13#12414yes—
309C2×C4×C13#12614yes—
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—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—42no—
330C2×Dic13—42no—
331C2×Dic13—42no—
332C2×Dic13—42no—
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×Dic13C2×C4⋊C414yes—
344C2×Dic13#11714yes—
345C4×D13—416no—
346C24×C4—131no—
347C22×C4⋊C4—131no—
348C22×C4⋊C4—131no—
349C22×C4⋊C4—132no—
350C22×C4⋊C4—132no—
351C22×C4⋊C4C2×D1311yescharacteristic
352C22×C4⋊C4C2×D1311yescharacteristic
353C22×C22⋊C4—131no—
354C22×C22⋊C4—131no—
355C22×C22⋊C4—132no—
356C22×C22⋊C4—132no—
357C22×C42—131no—
358C22×C42C2×D1312yes—
359C22×C42C2×D1311yescharacteristic
360#388—268no—
361#384—264no—
362#380—264no—
363#380—264no—
364C4×C4⋊C4—24no—
365C4×C22⋊C4—138no—
366C2×#95—131no—
367C2×#95—131no—
368C2×#95—132no—
369C2×#95—132no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95C2×D1312yes—
375C22×C13C22×C4⋊C411yescharacteristic
376C22×C13C2×#11711yescharacteristic
377C22×C13C2×#11711yescharacteristic
378C22×C13C2×C4×D411yescharacteristic
379C22×C13C2×C4×D411yescharacteristic
380C22×C13#52011yescharacteristic
381C22×C13#52011yescharacteristic
382C22×C13C2×#12111yescharacteristic
383C22×C13C2×#12311yescharacteristic
384C22×C13C2×#12411yescharacteristic
385C22×C13C2×#12611yescharacteristic
386C22×C13#53211yescharacteristic
387C22×C13#53211yescharacteristic
388C22×C13#53311yescharacteristic
389C22×C13#53311yescharacteristic
390C22×C13#54011yescharacteristic
391C22×C13#54111yescharacteristic
392C22×C13#54211yescharacteristic
393C22×C13#54211yescharacteristic
394C22×C13D4211yescharacteristic
395C22×C13D4211yescharacteristic
396C22×C13#54611yescharacteristic
397C22×C13#54711yescharacteristic
398C22×C13#54711yescharacteristic
399C22×C13#54711yescharacteristic
400C22×C13#54811yescharacteristic
401C22×C13D4×Q811yescharacteristic
402C22×C13D4×Q811yescharacteristic
403C22×C13#55011yescharacteristic
404C22×C13#55211yescharacteristic
405C22×C13#55311yescharacteristic
406C22×C13#55411yescharacteristic
407C22×C13#55411yescharacteristic
408C22×C13#55511yescharacteristic
409C22×C13#55611yescharacteristic
410C2×D13—24no—
411C2×D13—24no—
412C2×D13—24no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—42no—
422C2×D13—42no—
423C2×D13—42no—
424C2×D13—42no—
425C4×C13—24no—
426C4×C13—42no—
427C4×C13—44no—
428C4×C13—44no—
429C4×C13#38818yescomplemented
430Dic13—24no—
431Dic13—24no—
432Dic13—42no—
433Dic13—82no—
434Dic13—82no—
435C25—131no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—131no—
439C23×C4—134no—
440C23×C4—132no—
441C23×C4—132no—
442C23×C4—262no—
443C23×C4—262no—
444C23×C4—262no—
445C23×C4—262no—
446C23×C4—262no—
447C23×C4—262no—
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1312yes—
450C23×C4C22×D1312yes—
451C23×C4C22×D1311yescharacteristic
452C23×C4C22×D1311yescharacteristic
453C2×C4⋊C4—22no—
454C2×C4⋊C4—22no—
455C2×C4⋊C4—22no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4—264no—
459C2×C4⋊C4—264no—
460C2×C4⋊C4—264no—
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—522no—
468C2×C4⋊C4—522no—
469C2×C4⋊C4D5214yes—
470C2×C4⋊C4C22⋊D1314yes—
471C2×C22⋊C4—134no—
472C2×C22⋊C4—134no—
473C2×C22⋊C4—134no—
474C2×C22⋊C4—134no—
475C2×C22⋊C4—262no—
476C2×C22⋊C4—262no—
477C2×C22⋊C4—264no—
478C2×C22⋊C4—264no—
479C2×C22⋊C4—264no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—522no—
482C2×C22⋊C4—522no—
483C2×C42—22no—
484C2×C42—22no—
485C2×C42—24no—
486C2×C42—24no—
487C2×C42—42no—
488C2×C42—134no—
489C2×C42—262no—
490C2×C42—262no—
491C2×C42C4×D1314yes—
492#95—24no—
493#95—134no—
494#95—134no—
495#95—264no—
496#95—264no—
497#95—264no—
498#95—264no—
499#95—264no—
500#95—522no—
501C2×C13#228511yescharacteristic
502C2×C13C2×#38811yescharacteristic
503C2×C13#231411yescharacteristic
504C2×C13D4×C4⋊C411yescharacteristic
505C2×C13D4×C4⋊C411yescharacteristic
506C2×C13#235211yescharacteristic
507C2×C13#235411yescharacteristic
508C2×C13#242211yescharacteristic
509C2×C13#242311yescharacteristic
510C2×C13#242811yescharacteristic
511C2×C13#242911yescharacteristic
512C2×C13#249111yescharacteristic
513C2×C13#249211yescharacteristic
514C2×C13#249611yescharacteristic
515C2×C13#249711yescharacteristic
516D13—44no—
517C24—132no—
518C24—132no—
519C24—132no—
520C24—261no—
521C24—261no—
522C24—261no—
523C24—261no—
524C24—261no—
525C24—261no—
526C24—261no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24C23×D1311yescharacteristic
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—22no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—261no—
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—268no—
577C22×C4—268no—
578C22×C4—268no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—262no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—524no—
594C22×C4—524no—
595C22×C4—524no—
596C22×C4—524no—
597C22×C4C2×C4×D1312yes—
598C22×C4C2×C4×D1312yes—
599C22×C4C2×C4×D1312yes—
600C22×C4C2×D5214yes—
601C22×C4C2×D5212yes—
602C22×C4#612712yes—
603C22×C4#612712yes—
604C22×C4#612712yes—
605C22×C4#612712yes—
606C22×C4D4×D1312yes—
607C22×C4Q8×D1312yes—
608C22×C4C2×C22⋊D1314yes—
609C22×C4C2×C22⋊D1312yes—
610C4⋊C4—28no—
611C4⋊C4—28no—
612C4⋊C4—528no—
613C4⋊C4—528no—
614C4⋊C4—524no—
615C4⋊C4—524no—
616C22⋊C4—1316no—
617C22⋊C4—268no—
618C22⋊C4—528no—
619C22⋊C4—528no—
620C42—28no—
621C42—48no—
622C42—268no—
623C13#1387611yescharacteristic, complemented, Sylow
624C23—134no—
625C23—262no—
626C23—262no—
627C23—262no—
628C23—262no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—262no—
636C23—262no—
637C23—262no—
638C23—262no—
639C23—262no—
640C23—262no—
641C23—262no—
642C23—262no—
643C23—521no—
644C23—521no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23C22×C4×D1311yescharacteristic
660C23C22×D5211yescharacteristic
661C23C2×#612711yescharacteristic
662C23C2×#612711yescharacteristic
663C23C2×#612711yescharacteristic
664C23C2×#612711yescharacteristic
665C23C2×D4×D1311yescharacteristic
666C23#8825111yescharacteristic
667C23C2×Q8×D1311yescharacteristic
668C23#8825411yescharacteristic
669C23#41×D1311yescharacteristic
670C23#41×D1311yescharacteristic
671C23#8825611yescharacteristic
672C23#8825711yescharacteristic
673C23C22×C22⋊D1311yescharacteristic
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—134no—
702C2×C4—134no—
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—262no—
717C2×C4—262no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—5216no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
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#8812614yes—
738C2×C4C4×D5214yes—
739C2×C4#8812914yes—
740C2×C4#8813014yes—
741C2×C4C4⋊C4×D1314yes—
742C2×C4C4×C22⋊D1314yes—
743C2×C4#8818314yes—
744C2×C4#8818414yes—
745C22—264no—
746C22—264no—
747C22—264no—
748C22—522no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22C2×#8812611yescharacteristic
761C22C2×C4×D5211yescharacteristic
762C22C2×#8812911yescharacteristic
763C22C2×#8813011yescharacteristic
764C22C2×C4⋊C4×D1311yescharacteristic
765C22#1171920911yescharacteristic
766C22#1171921211yescharacteristic
767C22#1171921611yescharacteristic
768C22D13×#11711yescharacteristic
769C22#1171922811yescharacteristic
770C22#1171923711yescharacteristic
771C22#1171923811yescharacteristic
772C22#1171925311yescharacteristic
773C22#1171925311yescharacteristic
774C22D4×D5211yescharacteristic
775C22#1171925611yescharacteristic
776C22#1171925911yescharacteristic
777C22#1171926311yescharacteristic
778C22#1171926611yescharacteristic
779C22#1171926711yescharacteristic
780C22Q8×D5211yescharacteristic
781C22#1171928111yescharacteristic
782C22#1171928311yescharacteristic
783C22#1171928311yescharacteristic
784C22#1171928411yescharacteristic
785C22#1171928611yescharacteristic
786C22#1171928711yescharacteristic
787C22#1171928811yescharacteristic
788C22C2×C4×C22⋊D1311yescharacteristic
789C22C2×#8818311yescharacteristic
790C22C2×#8818411yescharacteristic
791C22D4×C22⋊D1311yescharacteristic
792C22Q8×C22⋊D1311yescharacteristic
793C22#1171952911yescharacteristic
794C22#1171953911yescharacteristic
795C4—24no—
796C4—42no—
797C4—44no—
798C4—44no—
799C4—264no—
800C4—264no—
801C4—522no—
802C4—1042no—
803C4—1042no—
804C4#1171860118yescomplemented
805C2—524no—
806C2#1311724011yescharacteristic
807C2C2×#1171860111yescharacteristic
808C2#1311744111yescharacteristic
809C2C4⋊C4×C22⋊D1311yescharacteristic
810C2C4⋊C4×D5211yescharacteristic
811C2#1311776811yescharacteristic
812C2#1311778611yescharacteristic
813C2#1311834411yescharacteristic
814C2#1311835511yescharacteristic
815C2#1311841811yescharacteristic
816C2#1311842911yescharacteristic
817C2#1311919311yescharacteristic
818C2#1311920411yescharacteristic
819C2#1311925211yescharacteristic
820C2#1311926311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13876
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718637C2semidirect
6. #13113091C2semidirect
8. #13113069C2semidirect
9. #13113066C2semidirect
10. #13113065C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
40. C4×#6103C4semidirect
208. #6103C4⋊C4semidirect
218. C2×C4×C4⋊C4D13semidirect
429. C4×C13#388semidirect
623. C13#13876semidirect
804. C4#11718601semidirect

Maximal subgroups

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

subgroupindex
C2×#117186012
C2×#117186372
C2×#117186482
C2×C4×#61032
#131130912
#131130802
#131130692
#131130662
#131130652
C2×C4×C13×C4⋊C42
#1387613