Finite Group Databasebeta

← #15786022

Subgroups — #15786022

Order 3328.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718646C211yesmaximal, characteristic, complemented
2C2×#11718612C212yesmaximal
3C2×#11718873C211yesmaximal, characteristic
4C2×C4⋊C4×Dic13C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic13C211yesmaximal, characteristic
6#13113093C212yesmaximal, complemented
7#13113085C212yesmaximal
8#13113065C211yesmaximal, characteristic, complemented
9#13113065C211yesmaximal, characteristic, complemented
10#13113061C212yesmaximal, complemented
11C2×C13×#380C211yesmaximal, characteristic
12C24×C4×C13C2211yescharacteristic
13C22×C13×C4⋊C4C2211yescharacteristic
14C22×C13×C4⋊C4C2211yescharacteristic
15C22×C13×C22⋊C4C2212yes—
16C22×C22⋊Dic13C2211yescharacteristic
17C22×C22⋊Dic13C2212yes—
18C22×C22⋊Dic13C2211yescharacteristic
19C22×C4⋊Dic13C2211yescharacteristic
20C22×C4⋊Dic13C2212yes—
21C22×C4⋊Dic13C2211yescharacteristic
22C22×C4×Dic13C2212yes—
23C22×C4×Dic13C2211yescharacteristic
24C22×C4×Dic13C2211yescharacteristic
25C13×#380C418yescomplemented
26C2×C13×#95C2212yes—
27#11718873—24no—
28C4×C22⋊Dic13—24no—
29C2×#88071C2211yescharacteristic
30C2×#88071C2212yes—
31C2×#88071C2212yes—
32C2×#88071C2212yes—
33C2×#88071C2212yes—
34C2×#88071C2212yes—
35C2×#88071C2211yescharacteristic
36C2×#88071C2212yes—
37C2×#88071C2212yes—
38#11718646—24no—
39C4⋊C4×Dic13—24no—
40#11718612—28no—
41C25×C13C2311yescharacteristic
42C23×C4×C13—22no—
43C23×C4×C13—22no—
44C23×C4×C13—22no—
45C23×C4×C13—22no—
46C23×C4×C13—22no—
47C23×C4×C13—22no—
48C23×C4×C13C2×C414yes—
49C23×C4×C13C2312yes—
50C23×C4×C13C2312yes—
51C23×C4×C13C2311yescharacteristic
52C23×C4×C13C2311yescharacteristic
53C23×Dic13C2312yes—
54C23×Dic13C2312yes—
55C23×Dic13C2311yescharacteristic
56C23×Dic13C2311yescharacteristic
57C23×Dic13C2311yescharacteristic
58C23×Dic13C2311yescharacteristic
59C2×C13×C4⋊C4—22no—
60C2×C13×C4⋊C4—22no—
61C2×C13×C4⋊C4—22no—
62C2×C13×C4⋊C4—22no—
63C2×C13×C4⋊C4C2×C414yes—
64C2×C13×C4⋊C4C2×C414yes—
65C2×C13×C22⋊C4—24no—
66C2×C13×C22⋊C4—24no—
67C2×C13×C22⋊C4C2×C418yes—
68C2×C22⋊Dic13—22no—
69C2×C22⋊Dic13—22no—
70C2×C22⋊Dic13—22no—
71C2×C22⋊Dic13—22no—
72C2×C22⋊Dic13—22no—
73C2×C22⋊Dic13—24no—
74C2×C22⋊Dic13—24no—
75C2×C22⋊Dic13—42no—
76C2×C22⋊Dic13D414yes—
77C2×C4⋊Dic13—22no—
78C2×C4⋊Dic13—22no—
79C2×C4⋊Dic13—22no—
80C2×C4⋊Dic13—22no—
81C2×C4⋊Dic13—22no—
82C2×C4⋊Dic13—24no—
83C2×C4⋊Dic13—24no—
84C2×C4⋊Dic13—42no—
85C2×C4⋊Dic13D414yes—
86C2×C4×Dic13—22no—
87C2×C4×Dic13—22no—
88C2×C4×Dic13—22no—
89C2×C4×Dic13—22no—
90C2×C4×Dic13—22no—
91C2×C4×Dic13—24no—
92C2×C4×Dic13—24no—
93C2×C4×Dic13—24no—
94C2×C4×Dic13D414yes—
95C13×#95C2×C418yes—
96#88071—24no—
97#88071—24no—
98#88071—22no—
99#88071—22no—
100#88071—24no—
101#88071—24no—
102#88071—24no—
103#88071—24no—
104#88071—42no—
105#13994—131nomaximal, Sylow
106C24×C13—21no—
107C24×C13—21no—
108C24×C13—21no—
109C24×C13—21no—
110C24×C13—21no—
111C24×C13—21no—
112C24×C13—21no—
113C24×C13—21no—
114C24×C13—21no—
115C24×C13—21no—
116C24×C13—21no—
117C24×C13—21no—
118C24×C13C22×C412yes—
119C24×C13C2×D412yes—
120C24×C13#4112yes—
121C24×C13C2411yescharacteristic
122C22×C4×C13—21no—
123C22×C4×C13—21no—
124C22×C4×C13—22no—
125C22×C4×C13—22no—
126C22×C4×C13—22no—
127C22×C4×C13—22no—
128C22×C4×C13—22no—
129C22×C4×C13—22no—
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—21no—
138C22×C4×C13—22no—
139C22×C4×C13—22no—
140C22×C4×C13—28no—
141C22×C4×C13—28no—
142C22×C4×C13—28no—
143C22×C4×C13—44no—
144C22×C4×C13—44no—
145C22×C4×C13—44no—
146C22×C4×C13—44no—
147C22×C4×C13C22×C412yes—
148C22×C4×C13C22×C414yes—
149C22×C4×C13C22×C414yes—
150C22×C4×C13C22×C412yes—
151C22×C4×C13C2×D412yes—
152C22×C4×C13C2×D412yes—
153C22×C4×C13#4112yes—
154C22×C4×C13#4112yes—
155C22×C4×C13#4112yes—
156C22×C4×C13#4112yes—
157C22×Dic13—21no—
158C22×Dic13—21no—
159C22×Dic13—21no—
160C22×Dic13—21no—
161C22×Dic13—21no—
162C22×Dic13—22no—
163C22×Dic13—21no—
164C22×Dic13—21no—
165C22×Dic13—21no—
166C22×Dic13—22no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13—22no—
171C22×Dic13—21no—
172C22×Dic13—22no—
173C22×Dic13—21no—
174C22×Dic13—21no—
175C22×Dic13—21no—
176C22×Dic13—21no—
177C22×Dic13—21no—
178C22×Dic13—21no—
179C22×Dic13—22no—
180C22×Dic13—21no—
181C22×Dic13—21no—
182C22×Dic13—22no—
183C22×Dic13—21no—
184C22×Dic13—21no—
185C22×Dic13—22no—
186C22×Dic13—22no—
187C22×Dic13—22no—
188C22×Dic13—22no—
189C22×Dic13—22no—
190C22×Dic13—22no—
191C22×Dic13—22no—
192C22×Dic13C2×D412yes—
193C22×Dic13C2×D412yes—
194C22×Dic13C2×D414yes—
195C22×Dic13C2×D412yes—
196C22×Dic13C2×D412yes—
197C22×Dic13#4112yes—
198C22×Dic13#4112yes—
199C13×C4⋊C4—28no—
200C13×C4⋊C4—28no—
201C13×C22⋊C4—216no—
202C22⋊Dic13—28no—
203C22⋊Dic13—28no—
204C22⋊Dic13—48no—
205C4⋊Dic13—28no—
206C4⋊Dic13—48no—
207C4⋊Dic13—44no—
208C4×Dic13—28no—
209C4×Dic13—44no—
210C4×Dic13—48no—
211C2×#389—131no—
212C2×#388—132no—
213C2×#380—131no—
214C2×#380D1311yescharacteristic
215C2×C4×C4⋊C4—131no—
216C2×C4×C22⋊C4—131no—
217#1442—132no—
218#1440—132no—
219C4⋊#95—131no—
220C4⋊#95—131no—
221#1434—132no—
222C23×C13—22no—
223C23×C13—22no—
224C23×C13—22no—
225C23×C13—22no—
226C23×C13—22no—
227C23×C13—22no—
228C23×C13—22no—
229C23×C13—22no—
230C23×C13—22no—
231C23×C13—22no—
232C23×C13—22no—
233C23×C13—22no—
234C23×C13—22no—
235C23×C13—22no—
236C23×C13—22no—
237C23×C13—22no—
238C23×C13—22no—
239C23×C13—22no—
240C23×C13—41no—
241C23×C13—41no—
242C23×C13—41no—
243C23×C13—41no—
244C23×C13—41no—
245C23×C13—41no—
246C23×C13—41no—
247C23×C13—41no—
248C23×C13—41no—
249C23×C13—41no—
250C23×C13—41no—
251C23×C13—41no—
252C23×C13—41no—
253C23×C13—41no—
254C23×C13—41no—
255C23×C13—41no—
256C23×C13C4×D414yes—
257C23×C13C23×C411yescharacteristic
258C23×C13C22×D411yescharacteristic
259C23×C13C22×D411yescharacteristic
260C23×C13C22×D411yescharacteristic
261C23×C13C2×#4111yescharacteristic
262C23×C13C2×#4111yescharacteristic
263C23×C13C2×#4111yescharacteristic
264C23×C13C2×#4111yescharacteristic
265C23×C13C2×#4111yescharacteristic
266C23×C13C2×#4111yescharacteristic
267C23×C13C2×#4111yescharacteristic
268C23×C13H(5,𝔽2)11yescharacteristic
269C23×C132−1+411yescharacteristic
270C23×C132−1+411yescharacteristic
271C23×C132−1+411yescharacteristic
272C2×C4×C13—22no—
273C2×C4×C13—24no—
274C2×C4×C13—24no—
275C2×C4×C13—24no—
276C2×C4×C13—24no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—24no—
280C2×C4×C13—24no—
281C2×C4×C13—42no—
282C2×C4×C13—41no—
283C2×C4×C13—41no—
284C2×C4×C13—42no—
285C2×C4×C13—41no—
286C2×C4×C13—41no—
287C2×C4×C13—42no—
288C2×C4×C13—42no—
289C2×C4×C13—42no—
290C2×C4×C13—42no—
291C2×C4×C13—42no—
292C2×C4×C13—42no—
293C2×C4×C13—416no—
294C2×C4×C13#11714yes—
295C2×C4×C13C4×D414yes—
296C2×C4×C13C4×D414yes—
297C2×C4×C13#12114yes—
298C2×C4×C13#12314yes—
299C2×C4×C13#12414yes—
300C2×C4×C13#12614yes—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—22no—
304C2×Dic13—22no—
305C2×Dic13—22no—
306C2×Dic13—22no—
307C2×Dic13—24no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—22no—
311C2×Dic13—22no—
312C2×Dic13—22no—
313C2×Dic13—22no—
314C2×Dic13—24no—
315C2×Dic13—22no—
316C2×Dic13—24no—
317C2×Dic13—22no—
318C2×Dic13—22no—
319C2×Dic13—41no—
320C2×Dic13—41no—
321C2×Dic13—42no—
322C2×Dic13—41no—
323C2×Dic13—42no—
324C2×Dic13—41no—
325C2×Dic13—42no—
326C2×Dic13—41no—
327C2×Dic13—41no—
328C2×Dic13—41no—
329C2×Dic13—41no—
330C2×Dic13—41no—
331C2×Dic13—41no—
332C2×Dic13—42no—
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#12114yes—
343C24×C4C2×D1311yescharacteristic
344C22×C4⋊C4—131no—
345C22×C4⋊C4—131no—
346C22×C4⋊C4—132no—
347C22×C4⋊C4C2×D1311yescharacteristic
348C22×C4⋊C4C2×D1311yescharacteristic
349C22×C22⋊C4—131no—
350C22×C22⋊C4—131no—
351C22×C22⋊C4—132no—
352C22×C22⋊C4C2×D1312yes—
353C22×C42—131no—
354C22×C42—132no—
355C22×C42—131no—
356#389—264no—
357#388—268no—
358#380—264no—
359#380Dic1318yescomplemented
360C4×C4⋊C4—264no—
361C4×C22⋊C4—264no—
362C2×#95—131no—
363C2×#95—132no—
364C2×#95—132no—
365C2×#95—132no—
366C2×#95—132no—
367C2×#95—132no—
368C2×#95—132no—
369C2×#95—131no—
370C2×#95—132no—
371C2×#95C2×D1312yes—
372C22×C13—24no—
373C22×C13—24no—
374C22×C13—24no—
375C22×C13—42no—
376C22×C13—42no—
377C22×C13—42no—
378C22×C13—42no—
379C22×C13—42no—
380C22×C13—42no—
381C22×C13—42no—
382C22×C13—42no—
383C22×C13—42no—
384C22×C13—42no—
385C22×C13—42no—
386C22×C13—42no—
387C22×C13C2×#11711yescharacteristic
388C22×C13C2×C4×D411yescharacteristic
389C22×C13C2×C4×D411yescharacteristic
390C22×C13C2×C4×D411yescharacteristic
391C22×C13C4×#4111yescharacteristic
392C22×C13#51911yescharacteristic
393C22×C13#52011yescharacteristic
394C22×C13C2×#12111yescharacteristic
395C22×C13C2×#12111yescharacteristic
396C22×C13C2×#12311yescharacteristic
397C22×C13#52511yescharacteristic
398C22×C13C2×#12411yescharacteristic
399C22×C13C2×#12611yescharacteristic
400C22×C13#52911yescharacteristic
401C22×C13#53211yescharacteristic
402C22×C13#53611yescharacteristic
403C22×C13#53711yescharacteristic
404C22×C13#54111yescharacteristic
405C22×C13#54211yescharacteristic
406C22×C13D4211yescharacteristic
407C22×C13#54711yescharacteristic
408C22×C13#54711yescharacteristic
409C22×C13#54711yescharacteristic
410C22×C13#54711yescharacteristic
411C22×C13#54811yescharacteristic
412C22×C13#54811yescharacteristic
413C22×C13#55211yescharacteristic
414C22×C13#55211yescharacteristic
415C22×C13#55211yescharacteristic
416C22×C13#55211yescharacteristic
417C22×C13#55211yescharacteristic
418C22×C13#55311yescharacteristic
419C22×C13#55511yescharacteristic
420C22×C13#55511yescharacteristic
421C22×C13#55611yescharacteristic
422C4×C13—44no—
423C4×C13—42no—
424C4×C13—44no—
425C4×C13#38818yescomplemented
426Dic13—24no—
427Dic13—42no—
428Dic13—42no—
429Dic13—44no—
430Dic13—42no—
431Dic13—82no—
432C25C22×D1311yescharacteristic
433C23×C4—22no—
434C23×C4—22no—
435C23×C4—22no—
436C23×C4—22no—
437C23×C4—22no—
438C23×C4—22no—
439C23×C4—131no—
440C23×C4—131no—
441C23×C4—132no—
442C23×C4—131no—
443C23×C4—131no—
444C23×C4—132no—
445C23×C4C2×Dic1314yes—
446C23×C4C22×D1312yes—
447C23×C4C22×D1312yes—
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—134no—
455C2×C4⋊C4—262no—
456C2×C4⋊C4—262no—
457C2×C4⋊C4—264no—
458C2×C4⋊C4—264no—
459C2×C4⋊C4—262no—
460C2×C4⋊C4—262no—
461C2×C4⋊C4—262no—
462C2×C4⋊C4—522no—
463C2×C4⋊C4C2×Dic1314yes—
464C2×C4⋊C4C2×Dic1314yes—
465C2×C22⋊C4—24no—
466C2×C22⋊C4—24no—
467C2×C22⋊C4—134no—
468C2×C22⋊C4—262no—
469C2×C22⋊C4—262no—
470C2×C22⋊C4—262no—
471C2×C22⋊C4—262no—
472C2×C22⋊C4—262no—
473C2×C22⋊C4—264no—
474C2×C22⋊C4—264no—
475C2×C22⋊C4—522no—
476C2×C22⋊C4C2×Dic1318yes—
477C2×C42—134no—
478C2×C42—262no—
479C2×C42—262no—
480C2×C42—264no—
481C2×C42—264no—
482C2×C42—264no—
483C2×C42—262no—
484C2×C42—262no—
485C2×C42—262no—
486#95—264no—
487#95—262no—
488#95—262no—
489#95—264no—
490#95—264no—
491#95—264no—
492#95—264no—
493#95—264no—
494#95—522no—
495#95C2×Dic1318yes—
496C2×C13—44no—
497C2×C13C2×#38811yescharacteristic
498C2×C13C4×#12111yescharacteristic
499C2×C13#232311yescharacteristic
500C2×C13#234411yescharacteristic
501C2×C13#234611yescharacteristic
502C2×C13#236111yescharacteristic
503C2×C13#236211yescharacteristic
504C2×C13#248511yescharacteristic
505C2×C13#248611yescharacteristic
506C2×C13#248911yescharacteristic
507C2×C13#249111yescharacteristic
508C2×C13#249511yescharacteristic
509C2×C13#249611yescharacteristic
510C2×C13#253611yescharacteristic
511C2×C13#253711yescharacteristic
512C24—21no—
513C24—21no—
514C24—21no—
515C24—21no—
516C24—21no—
517C24—21no—
518C24—21no—
519C24—21no—
520C24—21no—
521C24—21no—
522C24—21no—
523C24—21no—
524C24D4×D1312yes—
525C24#612912yes—
526C24C22×Dic1312yes—
527C24C23×D1311yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—28no—
547C22×C4—28no—
548C22×C4—28no—
549C22×C4—44no—
550C22×C4—44no—
551C22×C4—44no—
552C22×C4—44no—
553C22×C4—132no—
554C22×C4—132no—
555C22×C4—132no—
556C22×C4—132no—
557C22×C4—132no—
558C22×C4—134no—
559C22×C4—132no—
560C22×C4—261no—
561C22×C4—261no—
562C22×C4—261no—
563C22×C4—261no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—262no—
568C22×C4—261no—
569C22×C4—261no—
570C22×C4—261no—
571C22×C4—262no—
572C22×C4—262no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—261no—
576C22×C4—261no—
577C22×C4—261no—
578C22×C4—261no—
579C22×C4—262no—
580C22×C4—261no—
581C22×C4—262no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—262no—
586C22×C4—261no—
587C22×C4—261no—
588C22×C4—262no—
589C22×C4—262no—
590C22×C4—262no—
591C22×C4—262no—
592C22×C4—262no—
593C22×C4—262no—
594C22×C4—262no—
595C22×C4#612712yes—
596C22×C4#612712yes—
597C22×C4D4×D1312yes—
598C22×C4D4×D1312yes—
599C22×C4#612912yes—
600C22×C4#612912yes—
601C22×C4C22×Dic1312yes—
602C22×C4C22×Dic1314yes—
603C22×C4C22×Dic1314yes—
604C22×C4C22×Dic1312yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—268no—
608C4⋊C4—528no—
609C4⋊C4—524no—
610C22⋊C4—216no—
611C22⋊C4—268no—
612C22⋊C4—268no—
613C22⋊C4—528no—
614C42—268no—
615C42—528no—
616C42—524no—
617C13#1399411yescharacteristic, complemented, Sylow
618C23—22no—
619C23—22no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23D4×Dic1314yes—
653C23C2×#612711yescharacteristic
654C23C2×#612711yescharacteristic
655C23C2×D4×D1311yescharacteristic
656C23C2×D4×D1311yescharacteristic
657C23C2×D4×D1311yescharacteristic
658C23C2×#612911yescharacteristic
659C23C2×#612911yescharacteristic
660C23C2×#612911yescharacteristic
661C23#8825411yescharacteristic
662C23#8825411yescharacteristic
663C23#41×D1311yescharacteristic
664C23#41×D1311yescharacteristic
665C23#8825611yescharacteristic
666C23#8825711yescharacteristic
667C23C23×Dic1311yescharacteristic
668C2×C4—22no—
669C2×C4—24no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—24no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—42no—
682C2×C4—42no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—416no—
690C2×C4—134no—
691C2×C4—262no—
692C2×C4—262no—
693C2×C4—262no—
694C2×C4—262no—
695C2×C4—262no—
696C2×C4—262no—
697C2×C4—262no—
698C2×C4—264no—
699C2×C4—262no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—262no—
704C2×C4—264no—
705C2×C4—262no—
706C2×C4—262no—
707C2×C4—264no—
708C2×C4—262no—
709C2×C4—521no—
710C2×C4—521no—
711C2×C4—522no—
712C2×C4—521no—
713C2×C4—521no—
714C2×C4—521no—
715C2×C4—522no—
716C2×C4—521no—
717C2×C4—521no—
718C2×C4—522no—
719C2×C4—521no—
720C2×C4—521no—
721C2×C4—521no—
722C2×C4—522no—
723C2×C4—521no—
724C2×C4—521no—
725C2×C4—522no—
726C2×C4—522no—
727C2×C4—522no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—522no—
732C2×C4#8813314yes—
733C2×C4#8813714yes—
734C2×C4#8813814yes—
735C2×C4#8813914yes—
736C2×C4#8818014yes—
737C2×C4D4×Dic1314yes—
738C2×C4D4×Dic1314yes—
739C22—24no—
740C22—24no—
741C22—24no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22C2×#8813311yescharacteristic
755C22C2×#8813711yescharacteristic
756C22C2×#8813811yescharacteristic
757C22C2×#8813911yescharacteristic
758C22#1171921211yescharacteristic
759C22#1171921211yescharacteristic
760C22#1171921811yescharacteristic
761C22#1171921811yescharacteristic
762C22#1171923411yescharacteristic
763C22#1171923411yescharacteristic
764C22#1171923711yescharacteristic
765C22#1171923711yescharacteristic
766C22#1171930111yescharacteristic
767C22#1171930311yescharacteristic
768C22#1171930511yescharacteristic
769C22D13×#12111yescharacteristic
770C22#1171931111yescharacteristic
771C22#1171931411yescharacteristic
772C22#1171931611yescharacteristic
773C22#1171932311yescharacteristic
774C22#1171933011yescharacteristic
775C22#1171933311yescharacteristic
776C22#1171933411yescharacteristic
777C22#1171933611yescharacteristic
778C22#1171933811yescharacteristic
779C22#1171934411yescharacteristic
780C22#1171934611yescharacteristic
781C22#1171934811yescharacteristic
782C22C2×#8818011yescharacteristic
783C22C2×D4×Dic1311yescharacteristic
784C22C2×D4×Dic1311yescharacteristic
785C22C2×D4×Dic1311yescharacteristic
786C22#1171951711yescharacteristic
787C22#41×Dic1311yescharacteristic
788C22#1171953211yescharacteristic
789C4—42no—
790C4—44no—
791C4—44no—
792C4—264no—
793C4—522no—
794C4—524no—
795C4—522no—
796C4—522no—
797C4—1042no—
798C4#1171861218yescomplemented
799C2—44no—
800C2C2×#1171861211yescharacteristic
801C2#121×Dic1311yescharacteristic
802C2#1311752011yescharacteristic
803C2#1311770511yescharacteristic
804C2#1311772111yescharacteristic
805C2#1311785611yescharacteristic
806C2#1311786711yescharacteristic
807C2#1311912911yescharacteristic
808C2#1311914011yescharacteristic
809C2#1311917311yescharacteristic
810C2#1311919511yescharacteristic
811C2#1311924911yescharacteristic
812C2#1311926011yescharacteristic
813C2#1311974711yescharacteristic
814C2#1311975111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D13
commutatorC23×C13C23×C4
FittingC2×C13×#380C2
socle, cosocleC24×C13C24
prime radicalC25×C13C23
hypercenterC2×#380D13
hypocenterC13#13994
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C2×#11718646C2semidirect
4. C2×C4⋊C4×Dic13C2semidirect
6. #13113093C2semidirect
8. #13113065C2semidirect
9. #13113065C2semidirect
10. #13113061C2semidirect
25. C13×#380C4semidirect
359. #380Dic13semidirect
425. C4×C13#388semidirect
617. C13#13994semidirect
798. C4#11718612semidirect

Maximal subgroups

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

subgroupindex
C2×#117186462
C2×#117186122
C2×#117188732
C2×C4⋊C4×Dic132
C2×C4×C22⋊Dic132
#131130932
#131130852
#131130652
#131130612
C2×C13×#3802
#1399413