Finite Group Databasebeta

← #15785751

Subgroups — #15785751

Order 3328.

1746 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718589C211yesmaximal, characteristic, complemented
2C2×#11718648C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5#13113091C212yesmaximal, complemented
6#13113080C212yesmaximal
7#13113074C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113063C212yesmaximal, 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×#6103C2211yescharacteristic
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×#6103C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×#6101C2212yes—
24C22×C4×Dic13C2211yescharacteristic
25C4×C13×C4⋊C4—24no—
26C2×C13×#95C2212yes—
27C2×#88071C2211yescharacteristic
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2211yescharacteristic
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36#11718648—24no—
37#11718648C418yescomplemented
38C4×#6103—24no—
39#11718589—24no—
40C24×D13C2311yescharacteristic
41C23×C4×C13C2312yes—
42C23×C4×C13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×Dic13C2312yes—
47C23×Dic13C2312yes—
48C23×Dic13C2311yescharacteristic
49C23×Dic13C2311yescharacteristic
50C23×Dic13C2311yescharacteristic
51C22×C4×D13—22no—
52C22×C4×D13—22no—
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13C2×C414yes—
58C2×C13×C4⋊C4—22no—
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4C2×C414yes—
63C2×C13×C4⋊C4D414yes—
64C2×C42×C13—22no—
65C2×C42×C13—22no—
66C2×C42×C13—24no—
67C2×C42×C13—24no—
68C2×C42×C13—42no—
69C2×C42×C13D414yes—
70C2×#6103—22no—
71C2×#6103—22no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103—22no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—42no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×#6103C2×C418yes—
81C2×#6103Q814yes—
82C2×C4⋊Dic13—22no—
83C2×C4⋊Dic13—22no—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—22no—
87C2×C4⋊Dic13C2×C414yes—
88C2×#6101—24no—
89C2×#6101—42no—
90C2×#6101—42no—
91C2×C4×Dic13—22no—
92C2×C4×Dic13—22no—
93C2×C4×Dic13—22no—
94C13×#95—24no—
95#88071—24no—
96#88071—22no—
97#88071—22no—
98#88071—24no—
99#88071—24no—
100#88071—42no—
101#88071—42no—
102#88071—42no—
103#88071C2×C418yes—
104#13973—131nomaximal, Sylow
105C24×C13C2411yescharacteristic
106C23×D13—21no—
107C23×D13—21no—
108C23×D13—21no—
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×D13C22×C412yes—
119C23×D13C2×Q812yes—
120C23×D13#4112yes—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—21no—
125C22×C4×C13—21no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—21no—
129C22×C4×C13—21no—
130C22×C4×C13—22no—
131C22×C4×C13—21no—
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—21no—
141C22×C4×C13—21no—
142C22×C4×C13—22no—
143C22×C4×C13C22×C414yes—
144C22×C4×C13C22×C412yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D412yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13C2×D414yes—
149C22×C4×C13C2×D412yes—
150C22×C4×C13C2×Q812yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—22no—
161C22×Dic13—21no—
162C22×Dic13—21no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—22no—
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—22no—
176C22×Dic13—22no—
177C22×Dic13—22no—
178C22×Dic13—22no—
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×Dic13C22×C412yes—
188C22×Dic13C22×C414yes—
189C22×Dic13C2×Q812yes—
190C22×Dic13#4112yes—
191C2×C4×D13—28no—
192C2×C4×D13—28no—
193C2×C4×D13—28no—
194C2×C4×D13—44no—
195C2×C4×D13—44no—
196C2×C4×D13—44no—
197C2×C4×D13—44no—
198C13×C4⋊C4—28no—
199C13×C4⋊C4—28no—
200C42×C13—28no—
201C42×C13—48no—
202#6103—28no—
203#6103—28no—
204#6103—48no—
205#6103—48no—
206C4⋊Dic13—28no—
207C4⋊Dic13—44no—
208#6101—48no—
209C4×Dic13—44no—
210C2×#389—131no—
211C2×#380—131no—
212C2×#380—131no—
213C2×C4×C4⋊C4D1311yescharacteristic, complemented
214C2×C4×C22⋊C4—131no—
215#1442—132no—
216#1439—132no—
217#1437—132no—
218C4⋊#95—131no—
219C4⋊#95—131no—
220#1434—132no—
221C23×C13C23×C411yescharacteristic
222C23×C13C22×D411yescharacteristic
223C23×C13C22×D411yescharacteristic
224C23×C13C22×Q811yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13C2×#4111yescharacteristic
230C23×C13C2×#4111yescharacteristic
231C23×C13C2×#4111yescharacteristic
232C23×C13H(5,𝔽2)11yescharacteristic
233C23×C13H(5,𝔽2)11yescharacteristic
234C23×C13H(5,𝔽2)11yescharacteristic
235C23×C132−1+411yescharacteristic
236C22×D13—22no—
237C22×D13—22no—
238C22×D13—22no—
239C22×D13—22no—
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—41no—
255C22×D13—41no—
256C22×D13—41no—
257C22×D13—41no—
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×D13C4×Q814yes—
271C2×C4×C13—22no—
272C2×C4×C13—22no—
273C2×C4×C13—22no—
274C2×C4×C13—22no—
275C2×C4×C13—22no—
276C2×C4×C13—22no—
277C2×C4×C13—24no—
278C2×C4×C13—24no—
279C2×C4×C13—24no—
280C2×C4×C13—22no—
281C2×C4×C13—24no—
282C2×C4×C13—22no—
283C2×C4×C13—22no—
284C2×C4×C13—24no—
285C2×C4×C13—24no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—41no—
290C2×C4×C13—42no—
291C2×C4×C13—41no—
292C2×C4×C13—42no—
293C2×C4×C13—41no—
294C2×C4×C13—42no—
295C2×C4×C13—42no—
296C2×C4×C13—41no—
297C2×C4×C13—42no—
298C2×C4×C13#11714yes—
299C2×C4×C13C4×D414yes—
300C2×C4×C13C4×D414yes—
301C2×C4×C13#12114yes—
302C2×C4×C13C22⋊Q814yes—
303C2×C4×C13#12314yes—
304C2×C4×C13#12414yes—
305C2×C4×C13#12614yes—
306C2×Dic13—22no—
307C2×Dic13—24no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—24no—
311C2×Dic13—24no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—42no—
325C2×Dic13—41no—
326C2×Dic13—41no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—42no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—41no—
333C2×Dic13—41no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C4×D13—416no—
342C24×C4—131no—
343C22×C4⋊C4—131no—
344C22×C4⋊C4—131no—
345C22×C4⋊C4—132no—
346C22×C4⋊C4C2×D1311yescharacteristic
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C22⋊C4—131no—
349C22×C22⋊C4—132no—
350C22×C22⋊C4—131no—
351C22×C22⋊C4—132no—
352C22×C42—131no—
353C22×C42C2×D1312yes—
354C22×C42C2×D1311yescharacteristic
355#389—264no—
356#380—138no—
357#380—264no—
358C4×C4⋊C4—24no—
359C4×C22⋊C4—264no—
360C2×#95—132no—
361C2×#95—131no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—131no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95C2×D1312yes—
370C22×C13C2×#11711yescharacteristic
371C22×C13C2×C4×D411yescharacteristic
372C22×C13C2×C4×D411yescharacteristic
373C22×C13C2×C4×Q811yescharacteristic
374C22×C13C4×#4111yescharacteristic
375C22×C13#51811yescharacteristic
376C22×C13#52011yescharacteristic
377C22×C13C2×#12111yescharacteristic
378C22×C13C2×C22⋊Q811yescharacteristic
379C22×C13C2×#12311yescharacteristic
380C22×C13#52511yescharacteristic
381C22×C13C2×#12411yescharacteristic
382C22×C13C2×#12611yescharacteristic
383C22×C13#52911yescharacteristic
384C22×C13#53311yescharacteristic
385C22×C13#53511yescharacteristic
386C22×C13#53711yescharacteristic
387C22×C13#54011yescharacteristic
388C22×C13#54211yescharacteristic
389C22×C13#54611yescharacteristic
390C22×C13#54611yescharacteristic
391C22×C13D4×Q811yescharacteristic
392C22×C13#55011yescharacteristic
393C22×C13#55211yescharacteristic
394C22×C13#55211yescharacteristic
395C22×C13#55211yescharacteristic
396C22×C13#55311yescharacteristic
397C22×C13#55311yescharacteristic
398C22×C13#55311yescharacteristic
399C22×C13#55411yescharacteristic
400C22×C13#55411yescharacteristic
401C22×C13#55411yescharacteristic
402C22×C13#55511yescharacteristic
403C22×C13#55511yescharacteristic
404C22×C13#55511yescharacteristic
405C2×D13—24no—
406C2×D13—24no—
407C2×D13—24no—
408C2×D13—42no—
409C2×D13—42no—
410C2×D13—42no—
411C2×D13—42no—
412C2×D13—42no—
413C2×D13—42no—
414C2×D13—42no—
415C2×D13—42no—
416C2×D13—42no—
417C2×D13—42no—
418C2×D13—42no—
419C2×D13—42no—
420C4×C13—24no—
421C4×C13—44no—
422C4×C13—42no—
423C4×C13—44no—
424C4×C13#38818yes—
425Dic13—42no—
426Dic13—42no—
427Dic13—44no—
428Dic13—42no—
429Dic13—82no—
430C25—131no—
431C23×C4—132no—
432C23×C4—131no—
433C23×C4—131no—
434C23×C4—131no—
435C23×C4—134no—
436C23×C4—132no—
437C23×C4—262no—
438C23×C4—262no—
439C23×C4—262no—
440C23×C4—262no—
441C23×C4—262no—
442C23×C4—262no—
443C23×C4C22×D1312yes—
444C23×C4C22×D1311yescharacteristic
445C23×C4C22×D1312yes—
446C23×C4C22×D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448C2×C4⋊C4—22no—
449C2×C4⋊C4—22no—
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—134no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4—264no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—262no—
458C2×C4⋊C4—262no—
459C2×C4⋊C4—522no—
460C2×C4⋊C4—522no—
461C2×C4⋊C4C4×D1314yes—
462C2×C4⋊C4C22⋊D1314yes—
463C2×C22⋊C4—134no—
464C2×C22⋊C4—138no—
465C2×C22⋊C4—262no—
466C2×C22⋊C4—262no—
467C2×C22⋊C4—262no—
468C2×C22⋊C4—262no—
469C2×C22⋊C4—262no—
470C2×C22⋊C4—264no—
471C2×C22⋊C4—264no—
472C2×C22⋊C4—522no—
473C2×C22⋊C4—522no—
474C2×C22⋊C4—522no—
475C2×C42—22no—
476C2×C42—22no—
477C2×C42—24no—
478C2×C42—24no—
479C2×C42—42no—
480C2×C42—262no—
481C2×C42—262no—
482C2×C42—262no—
483C2×C42D5214yes—
484#95—24no—
485#95—138no—
486#95—264no—
487#95—262no—
488#95—262no—
489#95—264no—
490#95—264no—
491#95—522no—
492#95—522no—
493#95—522no—
494C2×C13C2×#38811yescharacteristic
495C2×C13C4×C22⋊Q811yescharacteristic
496C2×C13#232411yescharacteristic
497C2×C13#234511yescharacteristic
498C2×C13#234611yescharacteristic
499C2×C13#236011yescharacteristic
500C2×C13#236311yescharacteristic
501C2×C13#241411yescharacteristic
502C2×C13#241711yescharacteristic
503C2×C13#242011yescharacteristic
504C2×C13#242311yescharacteristic
505C2×C13#249511yescharacteristic
506C2×C13#249711yescharacteristic
507C2×C13#256211yescharacteristic
508C2×C13#256311yescharacteristic
509D13—44no—
510C24—132no—
511C24—132no—
512C24—132no—
513C24—261no—
514C24—261no—
515C24—261no—
516C24—261no—
517C24—261no—
518C24—261no—
519C24—261no—
520C24—261no—
521C24—261no—
522C24—261no—
523C24—261no—
524C24—261no—
525C24C23×D1311yescharacteristic
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
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—21no—
540C22×C4—21no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—132no—
549C22×C4—134no—
550C22×C4—132no—
551C22×C4—132no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—262no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—262no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—261no—
572C22×C4—261no—
573C22×C4—262no—
574C22×C4—262no—
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—524no—
587C22×C4—524no—
588C22×C4—524no—
589C22×C4—524no—
590C22×C4C2×C4×D1314yes—
591C22×C4C2×C4×D1312yes—
592C22×C4C2×D5212yes—
593C22×C4C2×D5212yes—
594C22×C4C2×D5212yes—
595C22×C4#612712yes—
596C22×C4#612712yes—
597C22×C4#612712yes—
598C22×C4#612712yes—
599C22×C4#612912yes—
600C22×C4Q8×D1312yes—
601C22×C4C2×C22⋊D1314yes—
602C22×C4C2×C22⋊D1312yes—
603C4⋊C4—28no—
604C4⋊C4—28no—
605C4⋊C4—268no—
606C4⋊C4—528no—
607C4⋊C4—524no—
608C22⋊C4—268no—
609C22⋊C4—268no—
610C22⋊C4—528no—
611C22⋊C4—528no—
612C42—28no—
613C42—48no—
614C42—524no—
615C13#1397311yescharacteristic, complemented, Sylow
616C23—134no—
617C23—262no—
618C23—262no—
619C23—262no—
620C23—262no—
621C23—262no—
622C23—262no—
623C23—262no—
624C23—262no—
625C23—262no—
626C23—262no—
627C23—262no—
628C23—262no—
629C23—262no—
630C23—262no—
631C23—262no—
632C23—262no—
633C23—262no—
634C23—262no—
635C23—521no—
636C23—521no—
637C23—521no—
638C23—521no—
639C23—521no—
640C23—521no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—521no—
645C23—521no—
646C23—521no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23C22×C4×D1311yescharacteristic
652C23C22×D5211yescharacteristic
653C23C2×#612711yescharacteristic
654C23C2×#612711yescharacteristic
655C23C2×#612711yescharacteristic
656C23C2×#612711yescharacteristic
657C23C2×#612911yescharacteristic
658C23#8825111yescharacteristic
659C23C2×Q8×D1311yescharacteristic
660C23#8825411yescharacteristic
661C23#41×D1311yescharacteristic
662C23#41×D1311yescharacteristic
663C23#8825611yescharacteristic
664C23#8825611yescharacteristic
665C23C22×C22⋊D1311yescharacteristic
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—42no—
693C2×C4—262no—
694C2×C4—264no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—262no—
699C2×C4—264no—
700C2×C4—262no—
701C2×C4—264no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—262no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—521no—
709C2×C4—522no—
710C2×C4—521no—
711C2×C4—522no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—521no—
716C2×C4—522no—
717C2×C4—521no—
718C2×C4—521no—
719C2×C4—521no—
720C2×C4—522no—
721C2×C4—5216no—
722C2×C4—522no—
723C2×C4—522no—
724C2×C4—522no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4#8812614yes—
730C2×C4C4×D5214yes—
731C2×C4#8812914yes—
732C2×C4#8813014yes—
733C2×C4#8815114yes—
734C2×C4C4×C22⋊D1314yes—
735C2×C4#8818314yes—
736C2×C4#8818414yes—
737C22—264no—
738C22—264no—
739C22—264no—
740C22—522no—
741C22—522no—
742C22—522no—
743C22—522no—
744C22—522no—
745C22—522no—
746C22—522no—
747C22—522no—
748C22—522no—
749C22—522no—
750C22—522no—
751C22—522no—
752C22C2×#8812611yescharacteristic
753C22C2×C4×D5211yescharacteristic
754C22C2×#8812911yescharacteristic
755C22C2×#8813011yescharacteristic
756C22C2×#8815111yescharacteristic
757C22#1171921511yescharacteristic
758C22#1171921611yescharacteristic
759C22#1171921811yescharacteristic
760C22#1171922911yescharacteristic
761C22#1171923011yescharacteristic
762C22#1171923511yescharacteristic
763C22#1171923711yescharacteristic
764C22C4×#612911yescharacteristic
765C22#1171925011yescharacteristic
766C22#1171926211yescharacteristic
767C22#1171926311yescharacteristic
768C22#1171926311yescharacteristic
769C22#1171926711yescharacteristic
770C22#1171926811yescharacteristic
771C22#1171926811yescharacteristic
772C22C4×Q8×D1311yescharacteristic
773C22#1171927911yescharacteristic
774C22#1171928311yescharacteristic
775C22#1171928411yescharacteristic
776C22#1171928411yescharacteristic
777C22#1171928611yescharacteristic
778C22#1171928611yescharacteristic
779C22#1171928711yescharacteristic
780C22C2×C4×C22⋊D1311yescharacteristic
781C22C2×#8818311yescharacteristic
782C22C2×#8818411yescharacteristic
783C22#1171951111yescharacteristic
784C22Q8×C22⋊D1311yescharacteristic
785C22#1171953411yescharacteristic
786C22#1171953911yescharacteristic
787C4—24no—
788C4—42no—
789C4—44no—
790C4—44no—
791C4—522no—
792C4—522no—
793C4—524no—
794C4—522no—
795C4—1042no—
796C4#1171860118yes—
797C2—524no—
798C2C2×#1171860111yescharacteristic
799C2C4×#8815111yescharacteristic
800C2#1311753011yescharacteristic
801C2#1311770911yescharacteristic
802C2#1311771711yescharacteristic
803C2#1311783711yescharacteristic
804C2#1311787011yescharacteristic
805C2#1311824811yescharacteristic
806C2#1311828111yescharacteristic
807C2#1311832211yescharacteristic
808C2#1311835511yescharacteristic
809C2#1311924111yescharacteristic
810C2#1311926311yescharacteristic
811C2#1311999711yescharacteristic
812C2#1312000511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13973
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11718589C2semidirect
5. #13113091C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113063C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
37. #11718648C4semidirect
213. C2×C4×C4⋊C4D13semidirect
615. C13#13973semidirect

Maximal subgroups

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

subgroupindex
C2×#117185892
C2×#117186482
C2×C4×#61032
#131130912
#131130802
#131130742
#131130652
#131130632
C2×C4×C13×C4⋊C42
#1397313