Finite Group Databasebeta

← #15784853

Subgroups — #15784853

Order 3328.

1702 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718638C211yesmaximal, characteristic, complemented
2C2×#11718648C211yesmaximal, characteristic
3C2×#11718648C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5#13113096C212yesmaximal, complemented
6#13113084C212yesmaximal
7#13113074C212yesmaximal
8#13113066C211yesmaximal, 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×#6103C2212yes—
18C22×#6103C2212yes—
19C22×#6103C2211yescharacteristic
20C22×#6103C2211yescharacteristic
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2211yescharacteristic
23C22×C4×Dic13C2211yescharacteristic
24C4×C13×C4⋊C4—24no—
25C2×C13×#95C2212yes—
26C2×#88071C2212yes—
27C2×#88071C2212yes—
28C2×#88071C2212yes—
29C2×#88071C2212yes—
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2211yescharacteristic
35C2×#88071C2211yescharacteristic
36#11718648—24no—
37#11718648—24no—
38#11718638—24no—
39C4×#6103C418yescomplemented
40C24×D13C2311yescharacteristic
41C23×C4×C13C2311yescharacteristic
42C23×C4×C13C2312yes—
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⋊C4D414yes—
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×C13C2×C414yes—
70C2×#6103—22no—
71C2×#6103—22no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—24no—
77C2×#6103—24no—
78C2×#6103—42no—
79C2×#6103—42no—
80C2×#6103C2×C414yes—
81C2×#6103C2×C414yes—
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×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13C2×C414yes—
91C13×#95—24no—
92#88071—24no—
93#88071—24no—
94#88071—24no—
95#88071—24no—
96#88071—24no—
97#88071—42no—
98#88071—42no—
99#88071—42no—
100#88071C2×C414yes—
101#88071C2×C414yes—
102#13875—131nomaximal, Sylow
103C24×C13C2411yescharacteristic
104C23×D13—21no—
105C23×D13—21no—
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×D13C22×C412yes—
117C23×D13#4112yes—
118C23×D13#4112yes—
119C22×C4×C13—21no—
120C22×C4×C13—21no—
121C22×C4×C13—21no—
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—21no—
126C22×C4×C13—21no—
127C22×C4×C13—22no—
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—22no—
135C22×C4×C13—21no—
136C22×C4×C13—22no—
137C22×C4×C13—22no—
138C22×C4×C13—22no—
139C22×C4×C13—21no—
140C22×C4×C13—22no—
141C22×C4×C13C22×C412yes—
142C22×C4×C13C22×C412yes—
143C22×C4×C13C22×C412yes—
144C22×C4×C13C2×D414yes—
145C22×C4×C13C2×D412yes—
146C22×C4×C13C2×D414yes—
147C22×C4×C13C2×D412yes—
148C22×C4×C13#4112yes—
149C22×C4×C13#4112yes—
150C22×C4×C13#4112yes—
151C22×C4×C13#4112yes—
152C22×C4×C13#4112yes—
153C22×C4×C13#4112yes—
154C22×Dic13—21no—
155C22×Dic13—21no—
156C22×Dic13—21no—
157C22×Dic13—21no—
158C22×Dic13—21no—
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—22no—
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×Dic13C22×C412yes—
187C22×Dic13C22×C412yes—
188C22×Dic13C22×C412yes—
189C2×C4×D13—28no—
190C2×C4×D13—28no—
191C2×C4×D13—28no—
192C2×C4×D13—44no—
193C2×C4×D13—44no—
194C2×C4×D13—44no—
195C2×C4×D13—44no—
196C13×C4⋊C4—28no—
197C13×C4⋊C4—28no—
198C42×C13—28no—
199C42×C13—48no—
200#6103—28no—
201#6103—28no—
202#6103—48no—
203#6103—48no—
204C4⋊Dic13—44no—
205C4⋊Dic13—44no—
206C4×Dic13—28no—
207C2×#382—131no—
208C2×#380—131no—
209C2×#380—131no—
210C2×C4×C4⋊C4D1311yescharacteristic, complemented
211C2×C4×C22⋊C4—131no—
212#1443—132no—
213#1440—132no—
214#1437—132no—
215C4⋊#95—131no—
216C4⋊#95—131no—
217#1434—132no—
218C23×C13C23×C411yescharacteristic
219C23×C13C22×D411yescharacteristic
220C23×C13C22×D411yescharacteristic
221C23×C13C2×#4111yescharacteristic
222C23×C13C2×#4111yescharacteristic
223C23×C13C2×#4111yescharacteristic
224C23×C13C2×#4111yescharacteristic
225C23×C13C2×#4111yescharacteristic
226C23×C13C2×#4111yescharacteristic
227C23×C13C2×#4111yescharacteristic
228C23×C13C2×#4111yescharacteristic
229C23×C13H(5,𝔽2)11yescharacteristic
230C23×C13H(5,𝔽2)11yescharacteristic
231C23×C132−1+411yescharacteristic
232C23×C132−1+411yescharacteristic
233C22×D13—22no—
234C22×D13—22no—
235C22×D13—22no—
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—41no—
252C22×D13—41no—
253C22×D13—41no—
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#11714yes—
268C2×C4×C13—22no—
269C2×C4×C13—22no—
270C2×C4×C13—22no—
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—24no—
281C2×C4×C13—24no—
282C2×C4×C13—24no—
283C2×C4×C13—42no—
284C2×C4×C13—42no—
285C2×C4×C13—42no—
286C2×C4×C13—42no—
287C2×C4×C13—42no—
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#11714yes—
296C2×C4×C13#11714yes—
297C2×C4×C13C4×D414yes—
298C2×C4×C13C4×D414yes—
299C2×C4×C13#12114yes—
300C2×C4×C13#12314yes—
301C2×C4×C13#12414yes—
302C2×C4×C13#12614yes—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13—41no—
317C2×Dic13—41no—
318C2×Dic13—41no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—41no—
322C2×Dic13—41no—
323C2×Dic13—41no—
324C2×Dic13—42no—
325C2×Dic13—42no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
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—
338C4×D13—416no—
339C24×C4—131no—
340C22×C4⋊C4—131no—
341C22×C4⋊C4—131no—
342C22×C4⋊C4C2×D1311yescharacteristic
343C22×C4⋊C4C2×D1311yescharacteristic
344C22×C22⋊C4—131no—
345C22×C22⋊C4—131no—
346C22×C22⋊C4—132no—
347C22×C22⋊C4—132no—
348C22×C42—131no—
349C22×C42C2×D1312yes—
350C22×C42C2×D1311yescharacteristic
351#382—264no—
352#380—264no—
353#380—264no—
354C4×C4⋊C4—24no—
355C4×C22⋊C4—138no—
356C2×#95—131no—
357C2×#95—131no—
358C2×#95—132no—
359C2×#95—132no—
360C2×#95—132no—
361C2×#95—132no—
362C2×#95—132no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95C2×D1312yes—
367C22×C13C2×#11711yescharacteristic
368C22×C13C2×#11711yescharacteristic
369C22×C13C2×#11711yescharacteristic
370C22×C13C2×C4×D411yescharacteristic
371C22×C13C2×C4×D411yescharacteristic
372C22×C13#52011yescharacteristic
373C22×C13#52011yescharacteristic
374C22×C13C2×#12111yescharacteristic
375C22×C13C2×#12311yescharacteristic
376C22×C13C2×#12411yescharacteristic
377C22×C13C2×#12611yescharacteristic
378C22×C13#52911yescharacteristic
379C22×C13#52911yescharacteristic
380C22×C13#52911yescharacteristic
381C22×C13#52911yescharacteristic
382C22×C13#54011yescharacteristic
383C22×C13#54111yescharacteristic
384C22×C13#54211yescharacteristic
385C22×C13#54211yescharacteristic
386C22×C13#54611yescharacteristic
387C22×C13#54611yescharacteristic
388C22×C13#54611yescharacteristic
389C22×C13#54711yescharacteristic
390C22×C13#54811yescharacteristic
391C22×C13#54811yescharacteristic
392C22×C13#54811yescharacteristic
393C22×C13#55011yescharacteristic
394C22×C13#55211yescharacteristic
395C22×C13#55211yescharacteristic
396C22×C13#55211yescharacteristic
397C22×C13#55311yescharacteristic
398C22×C13#55311yescharacteristic
399C22×C13#55311yescharacteristic
400C22×C13#55511yescharacteristic
401C22×C13#55611yescharacteristic
402C2×D13—24no—
403C2×D13—24no—
404C2×D13—24no—
405C2×D13—42no—
406C2×D13—42no—
407C2×D13—42no—
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—
417C4×C13—24no—
418C4×C13—42no—
419C4×C13—44no—
420C4×C13—44no—
421C4×C13#38818yes—
422Dic13—42no—
423Dic13—42no—
424Dic13—42no—
425Dic13—82no—
426Dic13—82no—
427C25—131no—
428C23×C4—131no—
429C23×C4—131no—
430C23×C4—131no—
431C23×C4—134no—
432C23×C4—132no—
433C23×C4—132no—
434C23×C4—262no—
435C23×C4—262no—
436C23×C4—262no—
437C23×C4—262no—
438C23×C4—262no—
439C23×C4—262no—
440C23×C4C22×D1311yescharacteristic
441C23×C4C22×D1312yes—
442C23×C4C22×D1312yes—
443C23×C4C22×D1311yescharacteristic
444C23×C4C22×D1311yescharacteristic
445C2×C4⋊C4—22no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—22no—
448C2×C4⋊C4—22no—
449C2×C4⋊C4—262no—
450C2×C4⋊C4—262no—
451C2×C4⋊C4—262no—
452C2×C4⋊C4—262no—
453C2×C4⋊C4—262no—
454C2×C4⋊C4—262no—
455C2×C4⋊C4D5214yes—
456C2×C4⋊C4C22⋊D1314yes—
457C2×C22⋊C4—134no—
458C2×C22⋊C4—134no—
459C2×C22⋊C4—262no—
460C2×C22⋊C4—262no—
461C2×C22⋊C4—262no—
462C2×C22⋊C4—262no—
463C2×C22⋊C4—264no—
464C2×C22⋊C4—264no—
465C2×C22⋊C4—264no—
466C2×C22⋊C4—264no—
467C2×C22⋊C4—522no—
468C2×C22⋊C4—522no—
469C2×C42—22no—
470C2×C42—22no—
471C2×C42—24no—
472C2×C42—24no—
473C2×C42—42no—
474C2×C42—134no—
475C2×C42—262no—
476C2×C42—262no—
477C2×C42C4×D1314yes—
478#95—24no—
479#95—134no—
480#95—134no—
481#95—264no—
482#95—264no—
483#95—264no—
484#95—264no—
485#95—264no—
486#95—522no—
487#95—522no—
488#95—522no—
489C2×C13#228311yescharacteristic
490C2×C13C2×#38811yescharacteristic
491C2×C13#231411yescharacteristic
492C2×C13#235211yescharacteristic
493C2×C13#235211yescharacteristic
494C2×C13#235211yescharacteristic
495C2×C13#235411yescharacteristic
496C2×C13#242011yescharacteristic
497C2×C13#242111yescharacteristic
498C2×C13#242611yescharacteristic
499C2×C13#242711yescharacteristic
500C2×C13#248911yescharacteristic
501C2×C13#249011yescharacteristic
502C2×C13#249411yescharacteristic
503C2×C13#249511yescharacteristic
504D13—44no—
505C24—132no—
506C24—132no—
507C24—132no—
508C24—261no—
509C24—261no—
510C24—261no—
511C24—261no—
512C24—261no—
513C24—261no—
514C24—261no—
515C24—261no—
516C24—261no—
517C24—261no—
518C24—261no—
519C24—261no—
520C24C23×D1311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—21no—
538C22×C4—22no—
539C22×C4—21no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—132no—
544C22×C4—132no—
545C22×C4—132no—
546C22×C4—261no—
547C22×C4—261no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—261no—
552C22×C4—261no—
553C22×C4—261no—
554C22×C4—261no—
555C22×C4—261no—
556C22×C4—261no—
557C22×C4—261no—
558C22×C4—261no—
559C22×C4—261no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—268no—
565C22×C4—268no—
566C22×C4—268no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—262no—
570C22×C4—262no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—262no—
574C22×C4—262no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—262no—
578C22×C4—262no—
579C22×C4—262no—
580C22×C4—262no—
581C22×C4—524no—
582C22×C4—524no—
583C22×C4—524no—
584C22×C4—524no—
585C22×C4C2×C4×D1312yes—
586C22×C4C2×C4×D1312yes—
587C22×C4C2×C4×D1312yes—
588C22×C4C2×D5214yes—
589C22×C4C2×D5212yes—
590C22×C4#612712yes—
591C22×C4#612712yes—
592C22×C4#612712yes—
593C22×C4#612712yes—
594C22×C4#612912yes—
595C22×C4#613112yes—
596C22×C4C2×C22⋊D1314yes—
597C22×C4C2×C22⋊D1312yes—
598C4⋊C4—28no—
599C4⋊C4—28no—
600C4⋊C4—524no—
601C4⋊C4—524no—
602C22⋊C4—268no—
603C22⋊C4—268no—
604C22⋊C4—528no—
605C22⋊C4—528no—
606C42—28no—
607C42—48no—
608C42—268no—
609C13#1387511yescharacteristic, complemented, Sylow
610C23—134no—
611C23—262no—
612C23—262no—
613C23—262no—
614C23—262no—
615C23—262no—
616C23—262no—
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—521no—
630C23—521no—
631C23—521no—
632C23—521no—
633C23—521no—
634C23—521no—
635C23—521no—
636C23—521no—
637C23—521no—
638C23—521no—
639C23—521no—
640C23—521no—
641C23—521no—
642C23—521no—
643C23—521no—
644C23—521no—
645C23C22×C4×D1311yescharacteristic
646C23C22×D5211yescharacteristic
647C23C2×#612711yescharacteristic
648C23C2×#612711yescharacteristic
649C23C2×#612711yescharacteristic
650C23C2×#612711yescharacteristic
651C23C2×#612911yescharacteristic
652C23#8825111yescharacteristic
653C23C2×#613111yescharacteristic
654C23#8825411yescharacteristic
655C23#41×D1311yescharacteristic
656C23#41×D1311yescharacteristic
657C23#8825611yescharacteristic
658C23#8825711yescharacteristic
659C23C22×C22⋊D1311yescharacteristic
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—24no—
674C2×C4—24no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—42no—
678C2×C4—42no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—42no—
687C2×C4—262no—
688C2×C4—262no—
689C2×C4—262no—
690C2×C4—262no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—521no—
697C2×C4—521no—
698C2×C4—521no—
699C2×C4—521no—
700C2×C4—521no—
701C2×C4—521no—
702C2×C4—521no—
703C2×C4—521no—
704C2×C4—521no—
705C2×C4—521no—
706C2×C4—521no—
707C2×C4—521no—
708C2×C4—5216no—
709C2×C4—522no—
710C2×C4—522no—
711C2×C4—522no—
712C2×C4—522no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—522no—
722C2×C4—522no—
723C2×C4#8812614yes—
724C2×C4C4×D5214yes—
725C2×C4#8812914yes—
726C2×C4#8813014yes—
727C2×C4#8814614yes—
728C2×C4C4×C22⋊D1314yes—
729C2×C4#8818314yes—
730C2×C4#8818414yes—
731C22—264no—
732C22—264no—
733C22—264no—
734C22—522no—
735C22—522no—
736C22—522no—
737C22—522no—
738C22—522no—
739C22—522no—
740C22—522no—
741C22—522no—
742C22—522no—
743C22—522no—
744C22—522no—
745C22—522no—
746C22C2×#8812611yescharacteristic
747C22C2×C4×D5211yescharacteristic
748C22C2×#8812911yescharacteristic
749C22C2×#8813011yescharacteristic
750C22C2×#8814611yescharacteristic
751C22#1171920911yescharacteristic
752C22#1171921811yescharacteristic
753C22#1171921911yescharacteristic
754C22D13×#11711yescharacteristic
755C22#1171922811yescharacteristic
756C22#1171923411yescharacteristic
757C22#1171923511yescharacteristic
758C22#1171925911yescharacteristic
759C22#1171926011yescharacteristic
760C22#1171926211yescharacteristic
761C22#1171926211yescharacteristic
762C22#1171926311yescharacteristic
763C22#1171926611yescharacteristic
764C22#1171926711yescharacteristic
765C22#1171926811yescharacteristic
766C22#1171928111yescharacteristic
767C22#1171928211yescharacteristic
768C22#1171928511yescharacteristic
769C22#1171928511yescharacteristic
770C22#1171928611yescharacteristic
771C22#1171928711yescharacteristic
772C22#1171928811yescharacteristic
773C22#1171928911yescharacteristic
774C22C2×C4×C22⋊D1311yescharacteristic
775C22C2×#8818311yescharacteristic
776C22C2×#8818411yescharacteristic
777C22#1171951111yescharacteristic
778C22#1171952211yescharacteristic
779C22#1171953411yescharacteristic
780C22#1171953611yescharacteristic
781C4—24no—
782C4—42no—
783C4—44no—
784C4—44no—
785C4—522no—
786C4—522no—
787C4—522no—
788C4—1042no—
789C4—1042no—
790C4#1171860118yes—
791C2—524no—
792C2#1311723211yescharacteristic
793C2C2×#1171860111yescharacteristic
794C2#1311744111yescharacteristic
795C2#1311776111yescharacteristic
796C2#1311776611yescharacteristic
797C2#1311776811yescharacteristic
798C2#1311778311yescharacteristic
799C2#1311832211yescharacteristic
800C2#1311833311yescharacteristic
801C2#1311839611yescharacteristic
802C2#1311840711yescharacteristic
803C2#1311917111yescharacteristic
804C2#1311918211yescharacteristic
805C2#1311923011yescharacteristic
806C2#1311924111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C4×C13×C4⋊C4C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×C4×C4⋊C4D13
hypocenterC13#13875
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×#11718638C2semidirect
5. #13113096C2semidirect
8. #13113066C2semidirect
9. #13113065C2semidirect
10. #13113063C2semidirect
11. C2×C4×C13×C4⋊C4C2semidirect
39. C4×#6103C4semidirect
210. C2×C4×C4⋊C4D13semidirect
609. C13#13875semidirect

Maximal subgroups

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

subgroupindex
C2×#117186382
C2×#117186482
C2×C4×#61032
#131130962
#131130842
#131130742
#131130662
#131130652
#131130632
C2×C4×C13×C4⋊C42
#1387513