Finite Group Databasebeta

← #15784871

Subgroups — #15784871

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×#11718330C212yesmaximal
2C2×#11718637C211yesmaximal, characteristic, complemented
3C2×#11718648C211yesmaximal, characteristic
4C2×#11718648C211yesmaximal, characteristic
5C2×C4×C4⋊Dic13C211yesmaximal, characteristic, complemented
6C2×C4×#6103C211yesmaximal, characteristic
7#13113094C212yesmaximal, complemented
8#13113080C212yesmaximal
9#13113067C212yesmaximal, complemented
10#13113065C211yesmaximal, characteristic, complemented
11C13×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C42×C13C2211yescharacteristic
16C22×#6103C2212yes—
17C22×#6103C2212yes—
18C22×#6103C2211yescharacteristic
19C22×#6103C2211yescharacteristic
20C22×C4⋊Dic13C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×#6101C2212yes—
23C22×#6101C2212yes—
24C22×C4×Dic13C2212yes—
25C22×C4×Dic13C2211yescharacteristic
26C2×C13×#95C2212yes—
27C2×C13×#95C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2211yescharacteristic
35#11718648—24no—
36#11718648—24no—
37#11718637—24no—
38C4×#6103C418yescomplemented
39C4×C4⋊Dic13—24no—
40#11718330—28no—
41C24×D13C2311yescharacteristic
42C23×C4×C13C2312yes—
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2311yescharacteristic
47C23×Dic13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
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⋊C4—22no—
64C2×C13×C4⋊C4—22no—
65C2×C42×C13—22no—
66C2×C42×C13—22no—
67C2×C42×C13C2×C414yes—
68C2×#6103—22no—
69C2×#6103—22no—
70C2×#6103—24no—
71C2×#6103—24no—
72C2×#6103—24no—
73C2×#6103—24no—
74C2×#6103—42no—
75C2×#6103—42no—
76C2×#6103C2×C414yes—
77C2×#6103C2×C414yes—
78C2×#6103D414yes—
79C2×#6103Q814yes—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13D414yes—
85C2×C4⋊Dic13D414yes—
86C2×#6101—24no—
87C2×#6101—24no—
88C2×#6101—24no—
89C2×#6101—24no—
90C2×#6101—42no—
91C2×#6101—42no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—22no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—24no—
96C2×C4×Dic13—42no—
97C2×C4×Dic13C2×C414yes—
98C13×#95—24no—
99C13×#95—42no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—24no—
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—21no—
129C22×C4×C13—21no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
132C22×C4×C13—21no—
133C22×C4×C13—21no—
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—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13C22×C412yes—
149C22×C4×C13C22×C412yes—
150C22×C4×C13C22×C412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
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—22no—
170C22×Dic13—22no—
171C22×Dic13—22no—
172C22×Dic13—22no—
173C22×Dic13—22no—
174C22×Dic13—22no—
175C22×Dic13—22no—
176C22×Dic13—22no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—21no—
181C22×Dic13—22no—
182C22×Dic13—22no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13C22×C412yes—
186C22×Dic13C22×C412yes—
187C22×Dic13C22×C412yes—
188C22×Dic13C2×D414yes—
189C22×Dic13C2×D414yes—
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—44no—
202C13×C4⋊C4—44no—
203C42×C13—28no—
204#6103—28no—
205#6103—48no—
206#6103—48no—
207#6103C4⋊C4116yescomplemented
208C4⋊Dic13—28no—
209C4⋊Dic13—28no—
210#6101—48no—
211#6101—48no—
212C4×Dic13—28no—
213C4×Dic13—48no—
214C2×#388—132no—
215C2×#384—131no—
216C2×#380—131no—
217C2×#380—131no—
218C2×C4×C4⋊C4—131no—
219C2×C4×C22⋊C4—131no—
220#1442—132no—
221#1439—132no—
222#1436—132no—
223C4⋊#95—131no—
224C4⋊#95D1311yescharacteristic, complemented
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—41no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
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—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
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—24no—
326C2×Dic13—24no—
327C2×Dic13—24no—
328C2×Dic13—24no—
329C2×Dic13—24no—
330C2×Dic13—24no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—41no—
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×C42—132no—
359C22×C42C2×D1311yescharacteristic
360#388—268no—
361#384—264no—
362#380—264no—
363#380—264no—
364C4×C4⋊C4—264no—
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×#95C2×D1312yes—
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—82no—
428C4×C13—82no—
429C4×C13#38818yescomplemented
430Dic13—24no—
431Dic13—24no—
432Dic13—44no—
433Dic13—44no—
434Dic13—42no—
435C25—131no—
436C23×C4—131no—
437C23×C4—131no—
438C23×C4—132no—
439C23×C4—132no—
440C23×C4—131no—
441C23×C4—134no—
442C23×C4—262no—
443C23×C4—262no—
444C23×C4—262no—
445C23×C4—262no—
446C23×C4—262no—
447C23×C4—262no—
448C23×C4C22×D1312yes—
449C23×C4C22×D1312yes—
450C23×C4C22×D1311yescharacteristic
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—22no—
458C2×C4⋊C4—22no—
459C2×C4⋊C4—134no—
460C2×C4⋊C4—134no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—262no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—264no—
466C2×C4⋊C4—264no—
467C2×C4⋊C4—264no—
468C2×C4⋊C4—264no—
469C2×C4⋊C4—522no—
470C2×C4⋊C4—522no—
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—134no—
486C2×C42—262no—
487C2×C42—262no—
488C2×C42—264no—
489C2×C42—264no—
490C2×C42—522no—
491C2×C42C4×D1314yes—
492#95—24no—
493#95—42no—
494#95—134no—
495#95—134no—
496#95—264no—
497#95—264no—
498#95—264no—
499#95—264no—
500#95—264no—
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—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—132no—
558C22×C4—132no—
559C22×C4—132no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—132no—
564C22×C4—134no—
565C22×C4—134no—
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—262no—
575C22×C4—262no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—261no—
580C22×C4—262no—
581C22×C4—262no—
582C22×C4—262no—
583C22×C4—261no—
584C22×C4—262no—
585C22×C4—262no—
586C22×C4—261no—
587C22×C4—262no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—268no—
593C22×C4—268no—
594C22×C4—268no—
595C22×C4—524no—
596C22×C4—524no—
597C22×C4—524no—
598C22×C4—524no—
599C22×C4C2×C4×D1312yes—
600C22×C4C2×C4×D1312yes—
601C22×C4C2×C4×D1312yes—
602C22×C4#612712yes—
603C22×C4#612712yes—
604C22×C4D4×D1312yes—
605C22×C4D4×D1312yes—
606C22×C4D4×D1312yes—
607C22×C4#612912yes—
608C22×C4Q8×D1312yes—
609C22×C4#613112yes—
610C4⋊C4—44no—
611C4⋊C4—44no—
612C4⋊C4—268no—
613C4⋊C4—268no—
614C4⋊C4—528no—
615C4⋊C4—528no—
616C22⋊C4—1316no—
617C22⋊C4—268no—
618C22⋊C4—528no—
619C22⋊C4—528no—
620C42—28no—
621C42—268no—
622C42—528no—
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
660C23C2×#612711yescharacteristic
661C23C2×#612711yescharacteristic
662C23C2×D4×D1311yescharacteristic
663C23C2×D4×D1311yescharacteristic
664C23C2×D4×D1311yescharacteristic
665C23C2×#612911yescharacteristic
666C23#8825111yescharacteristic
667C23C2×Q8×D1311yescharacteristic
668C23C2×#613111yescharacteristic
669C23#8825411yescharacteristic
670C23#41×D1311yescharacteristic
671C23#41×D1311yescharacteristic
672C23#8825611yescharacteristic
673C23#8825711yescharacteristic
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—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
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—264no—
718C2×C4—262no—
719C2×C4—264no—
720C2×C4—264no—
721C2×C4—264no—
722C2×C4—264no—
723C2×C4—264no—
724C2×C4—522no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—521no—
728C2×C4—521no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—522no—
733C2×C4—522no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—5216no—
737C2×C4#8812614yes—
738C2×C4#8813514yes—
739C2×C4#8813814yes—
740C2×C4#8813914yes—
741C2×C4C4⋊C4×D1314yes—
742C2×C4#8814714yes—
743C2×C4#8814814yes—
744C2×C4#8815214yes—
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×#8813511yescharacteristic
762C22C2×#8813811yescharacteristic
763C22C2×#8813911yescharacteristic
764C22C2×C4⋊C4×D1311yescharacteristic
765C22C2×#8814711yescharacteristic
766C22#1171920911yescharacteristic
767C22C2×#8814811yescharacteristic
768C22C2×#8815211yescharacteristic
769C22D13×#11711yescharacteristic
770C22#1171922811yescharacteristic
771C22#1171925311yescharacteristic
772C22#1171925311yescharacteristic
773C22#1171926611yescharacteristic
774C22#1171926711yescharacteristic
775C22#1171928311yescharacteristic
776C22#1171928311yescharacteristic
777C22#1171928711yescharacteristic
778C22#1171928811yescharacteristic
779C22#1171930411yescharacteristic
780C22#1171931411yescharacteristic
781C22#1171931611yescharacteristic
782C22#1171932111yescharacteristic
783C22#1171933611yescharacteristic
784C22#1171933711yescharacteristic
785C22#1171934011yescharacteristic
786C22#1171934611yescharacteristic
787C22#1171938111yescharacteristic
788C22#1171938211yescharacteristic
789C22#1171939911yescharacteristic
790C22#1171940011yescharacteristic
791C22#1171942211yescharacteristic
792C22#1171943111yescharacteristic
793C22#1171943211yescharacteristic
794C22#1171943511yescharacteristic
795C4—24no—
796C4—42no—
797C4—82no—
798C4—82no—
799C4—264no—
800C4—264no—
801C4—522no—
802C4—524no—
803C4—524no—
804C4#1171833018yescomplemented
805C2—524no—
806C2#1311724011yescharacteristic
807C2C2×#1171833011yescharacteristic
808C2#1311744111yescharacteristic
809C2#1311773211yescharacteristic
810C2#1311773611yescharacteristic
811C2#1311776211yescharacteristic
812C2#1311778011yescharacteristic
813C2#1311835111yescharacteristic
814C2#1311836211yescharacteristic
815C2#1311842511yescharacteristic
816C2#1311843611yescharacteristic
817C2#1311920011yescharacteristic
818C2#1311921111yescharacteristic
819C2#1311925911yescharacteristic
820C2#1311927011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC13×C4⋊#95C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC4⋊#95D13
hypocenterC13#13876
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#11718637C2semidirect
5. C2×C4×C4⋊Dic13C2semidirect
7. #13113094C2semidirect
9. #13113067C2semidirect
10. #13113065C2semidirect
11. C13×C4⋊#95C2semidirect
38. C4×#6103C4semidirect
207. #6103C4⋊C4semidirect
224. C4⋊#95D13semidirect
429. C4×C13#388semidirect
623. C13#13876semidirect
804. C4#11718330semidirect

Maximal subgroups

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

subgroupindex
C2×#117183302
C2×#117186372
C2×#117186482
C2×C4×C4⋊Dic132
C2×C4×#61032
#131130942
#131130802
#131130672
#131130652
C13×C4⋊#952
#1387613