Finite Group Databasebeta

← #15785571

Subgroups — #15785571

Order 3328.

2006 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
1C22×#88146C211yesmaximal, characteristic
2C2×#11718646C211yesmaximal, characteristic, complemented
3C2×#11718648C211yesmaximal, characteristic
4C2×C4×#6103C211yesmaximal, characteristic
5#13113082C212yesmaximal
6#13113078C212yesmaximal
7#13113066C211yesmaximal, characteristic, complemented
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C212yesmaximal, complemented
10#13113060C212yesmaximal, complemented
11C2×C13×#389C211yesmaximal, characteristic, complemented
12C23×C4×D13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2212yes—
15C22×C13×C4⋊C4C2211yescharacteristic
16C22×C42×C13C2211yescharacteristic
17C22×#6103C2211yescharacteristic
18C22×#6103C2211yescharacteristic
19C22×#6103C2212yes—
20C22×#6103C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4⋊Dic13C2212yes—
23C22×C4⋊Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C22×C4×Dic13C2212yes—
26C2×#88146—24no—
27C2×#88146—24no—
28C2×#88146C418yescomplemented
29C13×#389—24no—
30C2×C13×#95C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2211yescharacteristic
34C2×#88071C2212yes—
35C2×#88071C2212yes—
36C2×#88071C2211yescharacteristic
37C2×#88071C2212yes—
38C2×#88071C2212yes—
39#11718648—24no—
40#11718646—24no—
41C4×#6103—24no—
42C24×D13C2311yescharacteristic
43C23×C4×C13C2312yes—
44C23×C4×C13C2311yescharacteristic
45C23×C4×C13C2311yescharacteristic
46C23×C4×C13C2312yes—
47C23×C4×C13C2311yescharacteristic
48C23×Dic13C2312yes—
49C23×Dic13C2312yes—
50C23×Dic13C2311yescharacteristic
51C23×Dic13C2311yescharacteristic
52C23×Dic13C2311yescharacteristic
53C22×C4×D13—22no—
54C22×C4×D13—22no—
55C22×C4×D13—22no—
56C22×C4×D13—22no—
57C22×C4×D13C2×C414yes—
58C22×C4×D13D414yes—
59C22×C4×D13Q814yes—
60C2×C13×C4⋊C4—24no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4—24no—
64C2×C13×C4⋊C4—22no—
65C2×C13×C4⋊C4—42no—
66C2×C13×C4⋊C4C2×C414yes—
67C2×C13×C4⋊C4D414yes—
68C2×C13×C4⋊C4D414yes—
69C2×C42×C13—22no—
70C2×C42×C13—22no—
71C2×C42×C13—22no—
72C2×#6103—22no—
73C2×#6103—22no—
74C2×#6103—24no—
75C2×#6103—24no—
76C2×#6103—22no—
77C2×#6103—22no—
78C2×#6103—22no—
79C2×#6103—22no—
80C2×#6103—24no—
81C2×#6103—42no—
82C2×#6103—42no—
83C2×#6103C2×C418yes—
84C2×C4⋊Dic13—22no—
85C2×C4⋊Dic13—22no—
86C2×C4⋊Dic13—24no—
87C2×C4⋊Dic13—22no—
88C2×C4⋊Dic13—22no—
89C2×C4⋊Dic13—22no—
90C2×C4⋊Dic13—24no—
91C2×C4⋊Dic13—42no—
92C2×C4⋊Dic13C2×C414yes—
93C2×C4×Dic13—24no—
94C2×C4×Dic13—24no—
95C2×C4×Dic13—22no—
96C2×C4×Dic13—22no—
97C2×C4×Dic13—22no—
98C2×C4×Dic13C2×C418yes—
99#88146—232no—
100C13×#95—24no—
101#88071—24no—
102#88071—24no—
103#88071—22no—
104#88071—22no—
105#88071—24no—
106#88071—24no—
107#88071—42no—
108#88071—42no—
109#13951—131nomaximal, Sylow
110C24×C13C2411yescharacteristic
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×D13—21no—
122C23×D13—21no—
123C23×D13C22×C412yes—
124C23×D13C2×D412yes—
125C23×D13C2×Q812yes—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
130C22×C4×C13—21no—
131C22×C4×C13—21no—
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—22no—
143C22×C4×C13—22no—
144C22×C4×C13—22no—
145C22×C4×C13—22no—
146C22×C4×C13—22no—
147C22×C4×C13—22no—
148C22×C4×C13—22no—
149C22×C4×C13C22×C414yes—
150C22×C4×C13C22×C412yes—
151C22×C4×C13C2×D414yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13C2×D412yes—
154C22×C4×C13C2×D414yes—
155C22×C4×C13C2×D412yes—
156C22×C4×C13C2×Q812yes—
157C22×C4×C13#4112yes—
158C22×C4×C13#4112yes—
159C22×C4×C13#4112yes—
160C22×C4×C13#4112yes—
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—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—22no—
178C22×Dic13—21no—
179C22×Dic13—21no—
180C22×Dic13—22no—
181C22×Dic13—21no—
182C22×Dic13—21no—
183C22×Dic13—22no—
184C22×Dic13—22no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13C22×C414yes—
191C22×Dic13C22×C412yes—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×Q812yes—
194C22×Dic13#4112yes—
195C22×Dic13#4112yes—
196C2×C4×D13—28no—
197C2×C4×D13—28no—
198C2×C4×D13—28no—
199C2×C4×D13—28no—
200C2×C4×D13—28no—
201C2×C4×D13—28no—
202C2×C4×D13C4⋊C4116yescomplemented
203C13×C4⋊C4—48no—
204C13×C4⋊C4—44no—
205C13×C4⋊C4C22⋊C4116yescomplemented
206C42×C13—44no—
207#6103—28no—
208#6103—28no—
209#6103—216no—
210#6103—48no—
211C4⋊Dic13—28no—
212C4⋊Dic13—48no—
213C4⋊Dic13—44no—
214C4×Dic13—216no—
215C4×Dic13—44no—
216C22×#117—131no—
217C2×#389—131no—
218C2×#389D1311yescharacteristic, complemented
219C2×#380—131no—
220C2×C4×C22⋊C4—131no—
221#1439—132no—
222#1439—132no—
223C4⋊#95—131no—
224C4⋊#95—131no—
225C4⋊#95—132no—
226#1434—132no—
227C23×C13C23×C411yescharacteristic
228C23×C13C22×D411yescharacteristic
229C23×C13C22×D411yescharacteristic
230C23×C13C22×D411yescharacteristic
231C23×C13C22×Q811yescharacteristic
232C23×C13C2×#4111yescharacteristic
233C23×C13C2×#4111yescharacteristic
234C23×C13C2×#4111yescharacteristic
235C23×C13C2×#4111yescharacteristic
236C23×C13C2×#4111yescharacteristic
237C23×C13C2×#4111yescharacteristic
238C23×C13H(5,𝔽2)11yescharacteristic
239C23×C13H(5,𝔽2)11yescharacteristic
240C23×C132−1+411yescharacteristic
241C23×C132−1+411yescharacteristic
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—22no—
259C22×D13—22no—
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×D13—41no—
275C22×D13—41no—
276C22×D13C2×C4⋊C414yes—
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—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—22no—
287C2×C4×C13—22no—
288C2×C4×C13—22no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13—41no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—42no—
298C2×C4×C13—42no—
299C2×C4×C13—42no—
300C2×C4×C13—42no—
301C2×C4×C13—42no—
302C2×C4×C13—42no—
303C2×C4×C13—42no—
304C2×C4×C13C2×C22⋊C418yes—
305C2×C4×C13C2×C22⋊C414yes—
306C2×C4×C13C2×C4⋊C414yes—
307C2×C4×C13#11714yes—
308C2×C4×C13#12114yes—
309C2×C4×C13#12114yes—
310C2×C4×C13C22⋊Q814yes—
311C2×C4×C13C22⋊Q814yes—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—22no—
315C2×Dic13—22no—
316C2×Dic13—22no—
317C2×Dic13—22no—
318C2×Dic13—24no—
319C2×Dic13—24no—
320C2×Dic13—24no—
321C2×Dic13—22no—
322C2×Dic13—22no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—22no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—42no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336C2×Dic13—41no—
337C2×Dic13—41no—
338C2×Dic13—41no—
339C2×Dic13—42no—
340C2×Dic13—42no—
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13C2×C4⋊C414yes—
347C4×D13—232no—
348C24×C4—131no—
349C2×#117—138no—
350C2×#117—264no—
351C2×#117—264no—
352C22×C4⋊C4—131no—
353C22×C4⋊C4—131no—
354C22×C4⋊C4—132no—
355C22×C4⋊C4C2×D1311yescharacteristic
356C22×C4⋊C4C2×D1312yes—
357C22×C4⋊C4C2×D1311yescharacteristic
358C22×C22⋊C4—132no—
359C22×C22⋊C4—131no—
360C22×C22⋊C4—131no—
361C22×C22⋊C4—132no—
362C22×C42—132no—
363C22×C42—131no—
364C22×C42C2×D1311yescharacteristic
365#389—24no—
366#389—264no—
367#380—264no—
368C4×C22⋊C4—264no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95—132no—
372C2×#95—132no—
373C2×#95—132no—
374C2×#95—131no—
375C2×#95—132no—
376C2×#95—132no—
377C2×#95C2×D1312yes—
378C22×C13C22×C22⋊C411yescharacteristic
379C22×C13C22×C4⋊C411yescharacteristic
380C22×C13C2×#11711yescharacteristic
381C22×C13C4×#4111yescharacteristic
382C22×C13C4×#4111yescharacteristic
383C22×C13#52011yescharacteristic
384C22×C13#52011yescharacteristic
385C22×C13C2×#12111yescharacteristic
386C22×C13C2×#12111yescharacteristic
387C22×C13C2×C22⋊Q811yescharacteristic
388C22×C13C2×C22⋊Q811yescharacteristic
389C22×C13#52511yescharacteristic
390C22×C13#52511yescharacteristic
391C22×C13#53311yescharacteristic
392C22×C13#53311yescharacteristic
393C22×C13#53511yescharacteristic
394C22×C13#53611yescharacteristic
395C22×C13#54411yescharacteristic
396C22×C13#54411yescharacteristic
397C22×C13#54611yescharacteristic
398C22×C13#54611yescharacteristic
399C22×C13#54711yescharacteristic
400C22×C13#54711yescharacteristic
401C22×C13#54811yescharacteristic
402C22×C13#54811yescharacteristic
403C22×C13#55011yescharacteristic
404C22×C13#55011yescharacteristic
405C22×C13#55211yescharacteristic
406C22×C13#55211yescharacteristic
407C22×C13#55311yescharacteristic
408C22×C13#55311yescharacteristic
409C22×C13#55511yescharacteristic
410C22×C13#55511yescharacteristic
411C22×C13#55611yescharacteristic
412C22×C13#55611yescharacteristic
413C2×D13—24no—
414C2×D13—24no—
415C2×D13—24no—
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—
425C2×D13—42no—
426C2×D13—42no—
427C2×D13—42no—
428C4×C13—28no—
429C4×C13—42no—
430C4×C13—42no—
431C4×C13—82no—
432C4×C13#38018yes—
433Dic13—24no—
434Dic13—44no—
435Dic13—42no—
436Dic13—42no—
437Dic13—82no—
438C25—131no—
439C23×C4—131no—
440C23×C4—134no—
441C23×C4—134no—
442C23×C4—134no—
443C23×C4—131no—
444C23×C4—132no—
445C23×C4—131no—
446C23×C4—132no—
447C23×C4—262no—
448C23×C4—262no—
449C23×C4—262no—
450C23×C4—262no—
451C23×C4C22×D1312yes—
452C23×C4C22×D1311yescharacteristic
453C23×C4C22×D1311yescharacteristic
454C23×C4C22×D1312yes—
455C23×C4C22×D1311yescharacteristic
456#117—2632no—
457C2×C4⋊C4—22no—
458C2×C4⋊C4—24no—
459C2×C4⋊C4—22no—
460C2×C4⋊C4—24no—
461C2×C4⋊C4—22no—
462C2×C4⋊C4—42no—
463C2×C4⋊C4—134no—
464C2×C4⋊C4—262no—
465C2×C4⋊C4—262no—
466C2×C4⋊C4—264no—
467C2×C4⋊C4—264no—
468C2×C4⋊C4—262no—
469C2×C4⋊C4—262no—
470C2×C4⋊C4—262no—
471C2×C4⋊C4—522no—
472C2×C4⋊C4C4×D1314yes—
473C2×C4⋊C4D5214yes—
474C2×C4⋊C4C22⋊D1314yes—
475C2×C22⋊C4—138no—
476C2×C22⋊C4—262no—
477C2×C22⋊C4—262no—
478C2×C22⋊C4—262no—
479C2×C22⋊C4—262no—
480C2×C22⋊C4—264no—
481C2×C22⋊C4—262no—
482C2×C22⋊C4—262no—
483C2×C22⋊C4—264no—
484C2×C22⋊C4—264no—
485C2×C22⋊C4—522no—
486C2×C22⋊C4—522no—
487C2×C42—22no—
488C2×C42—22no—
489C2×C42—22no—
490C2×C42—138no—
491C2×C42—264no—
492C2×C42—264no—
493C2×C42—262no—
494C2×C42—262no—
495C2×C42—262no—
496#95—24no—
497#95—264no—
498#95—262no—
499#95—262no—
500#95—264no—
501#95—264no—
502#95—264no—
503#95—522no—
504#95—522no—
505C2×C13C2×#38011yescharacteristic
506C2×C13#229611yescharacteristic
507C2×C13#231711yescharacteristic
508C2×C13#233911yescharacteristic
509C2×C13#234111yescharacteristic
510C2×C13#234611yescharacteristic
511C2×C13#234711yescharacteristic
512C2×C13#241411yescharacteristic
513C2×C13#241411yescharacteristic
514C2×C13#241511yescharacteristic
515C2×C13#241511yescharacteristic
516C2×C13#243911yescharacteristic
517C2×C13#243911yescharacteristic
518C2×C13#244111yescharacteristic
519C2×C13#244111yescharacteristic
520D13—44no—
521C24—132no—
522C24—132no—
523C24—132no—
524C24—261no—
525C24—261no—
526C24—261no—
527C24—261no—
528C24—261no—
529C24—261no—
530C24—261no—
531C24—261no—
532C24—261no—
533C24—261no—
534C24—261no—
535C24—261no—
536C24C23×D1311yescharacteristic
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
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—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—132no—
561C22×C4—132no—
562C22×C4—132no—
563C22×C4—1316no—
564C22×C4—134no—
565C22×C4—132no—
566C22×C4—132no—
567C22×C4—261no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—268no—
572C22×C4—268no—
573C22×C4—268no—
574C22×C4—268no—
575C22×C4—268no—
576C22×C4—268no—
577C22×C4—261no—
578C22×C4—262no—
579C22×C4—261no—
580C22×C4—261no—
581C22×C4—261no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—262no—
585C22×C4—261no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—262no—
589C22×C4—261no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—261no—
593C22×C4—261no—
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×C4C2×C4×D1314yes—
603C22×C4C2×C4×D1312yes—
604C22×C4C2×D5214yes—
605C22×C4C2×D5212yes—
606C22×C4D4×D1312yes—
607C22×C4#612912yes—
608C22×C4#612912yes—
609C22×C4Q8×D1312yes—
610C22×C4#613112yes—
611C22×C4#613112yes—
612C22×C4C2×C22⋊D1314yes—
613C22×C4C2×C22⋊D1312yes—
614C4⋊C4—48no—
615C4⋊C4—44no—
616C4⋊C4—268no—
617C4⋊C4—528no—
618C4⋊C4—524no—
619C4⋊C4#6103116yescomplemented
620C22⋊C4—268no—
621C22⋊C4—268no—
622C22⋊C4—2616no—
623C22⋊C4—528no—
624C42—44no—
625C42—2616no—
626C42—524no—
627C13#1395111yescharacteristic, complemented, Sylow
628C23—134no—
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—262no—
644C23—262no—
645C23—262no—
646C23—262no—
647C23—521no—
648C23—521no—
649C23—521no—
650C23—521no—
651C23—521no—
652C23—521no—
653C23—521no—
654C23—521no—
655C23—521no—
656C23—521no—
657C23—521no—
658C23—521no—
659C23—521no—
660C23—521no—
661C23—521no—
662C23—521no—
663C23C22×C4×D1311yescharacteristic
664C23C22×D5211yescharacteristic
665C23C2×D4×D1311yescharacteristic
666C23C2×#612911yescharacteristic
667C23C2×#612911yescharacteristic
668C23#8825111yescharacteristic
669C23C2×Q8×D1311yescharacteristic
670C23C2×#613111yescharacteristic
671C23C2×#613111yescharacteristic
672C23#8825411yescharacteristic
673C23#41×D1311yescharacteristic
674C23#41×D1311yescharacteristic
675C23#8825611yescharacteristic
676C23#8825711yescharacteristic
677C23C22×C22⋊D1311yescharacteristic
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—24no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—134no—
706C2×C4—262no—
707C2×C4—262no—
708C2×C4—262no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—2632no—
713C2×C4—264no—
714C2×C4—262no—
715C2×C4—264no—
716C2×C4—264no—
717C2×C4—262no—
718C2×C4—262no—
719C2×C4—262no—
720C2×C4—262no—
721C2×C4—262no—
722C2×C4—521no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—521no—
726C2×C4—521no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—521no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4—521no—
733C2×C4—521no—
734C2×C4—522no—
735C2×C4—522no—
736C2×C4—522no—
737C2×C4—522no—
738C2×C4—522no—
739C2×C4—522no—
740C2×C4—522no—
741C2×C4C4⋊C4×D1314yes—
742C2×C4#8814614yes—
743C2×C4#8814914yes—
744C2×C4#8815114yes—
745C2×C4C2×#610318yes—
746C2×C4C2×#610314yes—
747C2×C4#8819214yes—
748C2×C4#8820014yes—
749C22—264no—
750C22—264no—
751C22—264no—
752C22—522no—
753C22—522no—
754C22—522no—
755C22—522no—
756C22—522no—
757C22—522no—
758C22—522no—
759C22—522no—
760C22—522no—
761C22—522no—
762C22—522no—
763C22—522no—
764C22C2×C4⋊C4×D1311yescharacteristic
765C22C2×#8814611yescharacteristic
766C22C2×#8814911yescharacteristic
767C22C2×#8815111yescharacteristic
768C22C4×#612911yescharacteristic
769C22#1171925111yescharacteristic
770C22#1171925911yescharacteristic
771C22#1171926011yescharacteristic
772C22C4×#613111yescharacteristic
773C22#1171927911yescharacteristic
774C22#1171928111yescharacteristic
775C22#1171928211yescharacteristic
776C22#1171931111yescharacteristic
777C22#1171931211yescharacteristic
778C22#1171932111yescharacteristic
779C22#1171932311yescharacteristic
780C22#1171933211yescharacteristic
781C22#1171933311yescharacteristic
782C22#1171934611yescharacteristic
783C22#1171934711yescharacteristic
784C22#1171939311yescharacteristic
785C22#1171939411yescharacteristic
786C22#1171939911yescharacteristic
787C22#1171940011yescharacteristic
788C22#1171943311yescharacteristic
789C22#1171943411yescharacteristic
790C22#1171943711yescharacteristic
791C22#1171943911yescharacteristic
792C22C22×#610311yescharacteristic
793C22C2×#8819211yescharacteristic
794C22#1171951111yescharacteristic
795C22C2×#8820011yescharacteristic
796C22#1171952211yescharacteristic
797C22#1171952911yescharacteristic
798C22#1171953911yescharacteristic
799C4—28no—
800C4—42no—
801C4—42no—
802C4—82no—
803C4—264no—
804C4—522no—
805C4—522no—
806C4—524no—
807C4—1042no—
808C4#1171864818yes—
809C2—524no—
810C2C2×#1171864811yescharacteristic
811C2#1311731711yescharacteristic
812C2#1311745811yescharacteristic
813C2#1311766111yescharacteristic
814C2#1311767411yescharacteristic
815C2#1311772011yescharacteristic
816C2#1311772811yescharacteristic
817C2#1311825011yescharacteristic
818C2#1311825211yescharacteristic
819C2#1311826111yescharacteristic
820C2#1311826311yescharacteristic
821C2#1311852311yescharacteristic
822C2#1311852511yescharacteristic
823C2#1311854511yescharacteristic
824C2#1311854711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#389C2
socle, cosocleC24×C13C24
prime radicalC24×D13C23
hypercenterC2×#389D13
hypocenterC13#13951
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C2×#11718646C2semidirect
7. #13113066C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113060C2semidirect
11. C2×C13×#389C2semidirect
28. C2×#88146C4semidirect
202. C2×C4×D13C4⋊C4semidirect
205. C13×C4⋊C4C22⋊C4semidirect
218. C2×#389D13semidirect
619. C4⋊C4#6103semidirect
627. C13#13951semidirect

Maximal subgroups

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

subgroupindex
C22×#881462
C2×#117186462
C2×#117186482
C2×C4×#61032
#131130822
#131130782
#131130662
#131130652
#131130602
C2×C13×#3892
#1395113