Finite Group Databasebeta

← #15830377

Subgroups — #15830377

Order 3328.

1466 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718872C211yesmaximal, characteristic, complemented
3#13113393C214yesmaximal, complemented
4#13113370C212yesmaximal, complemented
5#13113366C212yesmaximal, complemented
6#13113341C214yesmaximal, complemented
7C2×C13×#407C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C22×C13×M16—21no—
11C2×#88207—21no—
12C22×C22⋊Dic13—21no—
13#11719496—21no—
14#11719496—21no—
15#11719496—21no—
16#11719496—21no—
17#11719496C412yescomplemented
18#11719496C412yescomplemented
19#11719496C2212yes—
20#11719496C2212yes—
21C2×#88184C411yescharacteristic, complemented
22C2×#88184C2211yescharacteristic
23C2×#88183—21no—
24C2×C4×C22⋊D13—21no—
25C2×C4×C22⋊D13—21no—
26C2×#88180C411yescharacteristic, complemented
27C2×#88178C411yescharacteristic, complemented
28C2×#88178C2211yescharacteristic
29C13×#407—21no—
30C13×#407—21no—
31C13×#407C2212yes—
32C13×#407C2212yescomplemented
33C2×C13×C22⋊C8—21no—
34C2×C13×C22⋊C8C2212yescomplemented
35#11718872—21no—
36#11718872—21no—
37#11718872C2212yes—
38#11718872C2212yescomplemented
39C2×#88071—21no—
40C2×#88071C2212yescomplemented
41#11718062C2218yescomplemented
42#11718059C2218yescomplemented
43C25×C13D411yescharacteristic
44C23×C4×C13—44no—
45C23×C4×C13C2×C411yescharacteristic
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×C4×C13D411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13C2311yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C22×C22⋊D13—21no—
60C22×C22⋊D13—21no—
61C22×C22⋊D13—21no—
62C23×Dic13—22no—
63C2×#6127—21no—
64C2×#6127—21no—
65C2×#6127—44no—
66C2×#6127C2×C412yes—
67C2×#6127C2×C412yescomplemented
68C22×D52C2×C411yescharacteristic, complemented
69C22×C4×D13—21no—
70C22×Dic26C2×C411yescharacteristic, complemented
71C2×C13×M16—22no—
72C2×C13×M16—22no—
73C2×C13×M16—44no—
74C22×C8×C13—22no—
75#88207—22no—
76#88207—22no—
77#88207—22no—
78#88207—22no—
79C2×C22⋊Dic13—21no—
80C2×C22⋊Dic13—21no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—22no—
83C2×C22⋊Dic13—22no—
84C2×C22⋊Dic13—44no—
85#88184—21no—
86#88184—21no—
87#88184—21no—
88#88184—21no—
89#88184C2×C412yes—
90#88184C2×C412yescomplemented
91#88184C2×C412yescomplemented
92#88184C2312yes—
93#88183—22no—
94#88183—22no—
95#88183—22no—
96#88183—22no—
97C4×C22⋊D13—22no—
98C4×C22⋊D13—22no—
99C4×C22⋊D13—22no—
100C4×C22⋊D13—22no—
101C4×C22⋊D13—22no—
102C4×C22⋊D13—22no—
103C4×C22⋊D13—22no—
104C4×C22⋊D13—22no—
105C2×#6103—21no—
106C2×#6103—21no—
107#88180—21no—
108#88180—21no—
109#88180C2×C412yes—
110#88180C2×C412yescomplemented
111C2×C4⋊Dic13C2×C411yescharacteristic, complemented
112C2×C4⋊Dic13C2×C411yescharacteristic, complemented
113#88178—21no—
114#88178—21no—
115#88178—21no—
116#88178—21no—
117#88178C2×C412yes—
118#88178C2×C412yescomplemented
119#88178C2×C412yescomplemented
120#88178C2312yes—
121C2×#6101—21no—
122C2×#6101—21no—
123C2×C4×Dic13—21no—
124C13×C22⋊C8—22no—
125C13×C22⋊C8—22no—
126C13×C22⋊C8—22no—
127C13×C22⋊C8C2314yes—
128#88071—22no—
129#88071—22no—
130#88071—22no—
131#88071C2314yes—
132#17587—131nomaximal, Sylow
133C24×C13—24no—
134C24×C13—42no—
135C24×C13—42no—
136C24×C13C22⋊C411yescharacteristic
137C24×C13C22⋊C411yescharacteristic
138C24×C13C22⋊C411yescharacteristic
139C24×C13C22⋊C411yescharacteristic
140C24×C13C2×D411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C23×D13—21no—
144C22×C4×C13—24no—
145C22×C4×C13—24no—
146C22×C4×C13—42no—
147C22×C4×C13—42no—
148C22×C4×C13—42no—
149C22×C4×C13—42no—
150C22×C4×C13—42no—
151C22×C4×C13—42no—
152C22×C4×C13—42no—
153C22×C4×C13—42no—
154C22×C4×C13—42no—
155C22×C4×C13—42no—
156C22×C4×C13—42no—
157C22×C4×C13—42no—
158C22×C4×C13C22⋊C411yescharacteristic
159C22×C4×C13C22⋊C411yescharacteristic
160C22×C4×C13C22⋊C411yescharacteristic
161C22×C4×C13C22⋊C411yescharacteristic
162C22×C4×C13C22⋊C411yescharacteristic
163C22×C4×C13C22⋊C411yescharacteristic
164C22×C4×C13C22⋊C411yescharacteristic
165C22×C4×C13C22⋊C411yescharacteristic
166C22×C4×C13C22⋊C411yescharacteristic
167C22×C4×C13C22⋊C411yescharacteristic
168C22×C4×C13C22⋊C411yescharacteristic
169C22×C4×C13C22⋊C411yescharacteristic
170C22×C4×C13C22×C411yescharacteristic
171C22×C4×C13C22×C411yescharacteristic
172C22×C4×C13C22×C411yescharacteristic
173C22×C4×C13C22×C411yescharacteristic
174C22×C4×C13C22×C411yescharacteristic
175C22×C4×C13C22×C411yescharacteristic
176C22×C4×C13C2×D411yescharacteristic
177C22×C4×C13C2×D411yescharacteristic
178C22×C4×C13C2×D411yescharacteristic
179C22×C4×C13C2×D411yescharacteristic
180C22×C4×C13C2×D411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2411yescharacteristic
186C2×C22⋊D13—22no—
187C2×C22⋊D13—22no—
188C2×C22⋊D13—22no—
189C2×C22⋊D13—22no—
190C2×C22⋊D13—22no—
191C2×C22⋊D13—22no—
192C2×C22⋊D13—44no—
193C2×C22⋊D13—44no—
194C2×C22⋊D13—44no—
195C22×Dic13—21no—
196C22×Dic13—21no—
197C22×Dic13—21no—
198C22×Dic13—24no—
199C22×Dic13—44no—
200C22×Dic13—44no—
201C22×Dic13—44no—
202#6127—44no—
203#6127—44no—
204#6127—44no—
205#6127—44no—
206C2×D52—21no—
207C2×D52—42no—
208C2×D52C22×C412yes—
209C2×C4×D13—22no—
210C2×C4×D13—22no—
211C2×C4×D13—44no—
212C2×Dic26—21no—
213C2×Dic26—42no—
214C2×Dic26C22×C412yes—
215C13×M16—44no—
216C13×M16—44no—
217C2×C8×C13—24no—
218C2×C8×C13—44no—
219C22⋊Dic13—22no—
220C22⋊Dic13—22no—
221C22⋊Dic13—22no—
222C22⋊Dic13—22no—
223C22⋊Dic13—22no—
224C22⋊Dic13—22no—
225C22⋊Dic13—44no—
226C22⋊Dic13—44no—
227#6103—22no—
228#6103—22no—
229#6103—22no—
230#6103—22no—
231C4⋊Dic13—21no—
232C4⋊Dic13—21no—
233C4⋊Dic13C22×C412yes—
234C4⋊Dic13C22×C412yes—
235#6101—22no—
236#6101—22no—
237#6101—22no—
238#6101—22no—
239C4×Dic13—22no—
240C4×Dic13—22no—
241C2×#525—131no—
242C2×#407D1311yescharacteristic, complemented
243C2×#381—131no—
244#1516—134no—
245#1511—132no—
246#1510—132no—
247#1504—134no—
248C23×C13—22no—
249C23×C13—22no—
250C23×C13—22no—
251C23×C13—22no—
252C23×C13—22no—
253C23×C13—22no—
254C23×C13—22no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—22no—
258C23×C13—22no—
259C23×C13—22no—
260C23×C13—41no—
261C23×C13—41no—
262C23×C13—41no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—416no—
269C23×C13#9914yes—
270C23×C13C2×C22⋊C411yescharacteristic
271C23×C13C2×C22⋊C411yescharacteristic
272C23×C13C2×C22⋊C411yescharacteristic
273C23×C13C2×C22⋊C411yescharacteristic
274C23×C13C2×C22⋊C411yescharacteristic
275C23×C13C2×C22⋊C411yescharacteristic
276C23×C13C22×D411yescharacteristic
277C22×D13—22no—
278C22×D13—42no—
279C22×D13—42no—
280C22×D13—42no—
281C2×C4×C13—22no—
282C2×C4×C13—22no—
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—22no—
290C2×C4×C13—22no—
291C2×C4×C13—22no—
292C2×C4×C13—22no—
293C2×C4×C13—41no—
294C2×C4×C13—41no—
295C2×C4×C13—41no—
296C2×C4×C13—41no—
297C2×C4×C13—41no—
298C2×C4×C13—41no—
299C2×C4×C13—41no—
300C2×C4×C13—41no—
301C2×C4×C13—41no—
302C2×C4×C13—41no—
303C2×C4×C13—41no—
304C2×C4×C13—41no—
305C2×C4×C13—41no—
306C2×C4×C13—41no—
307C2×C4×C13—41no—
308C2×C4×C13—41no—
309C2×C4×C13C2×C22⋊C411yescharacteristic
310C2×C4×C13C2×C22⋊C411yescharacteristic
311C2×C4×C13C2×C22⋊C411yescharacteristic
312C2×C4×C13C2×C22⋊C411yescharacteristic
313C2×C4×C13C2×C22⋊C411yescharacteristic
314C2×C4×C13C2×C22⋊C411yescharacteristic
315C2×C4×C13C23×C411yescharacteristic
316C2×C4×C13C22×D411yescharacteristic
317C22⋊D13—44no—
318C22⋊D13—44no—
319C22⋊D13—44no—
320C22⋊D13—44no—
321C22⋊D13—44no—
322C22⋊D13—44no—
323C2×Dic13—22no—
324C2×Dic13—22no—
325C2×Dic13—22no—
326C2×Dic13—42no—
327C2×Dic13—42no—
328C2×Dic13—42no—
329C2×Dic13—44no—
330C2×Dic13—44no—
331C2×Dic13—44no—
332C2×Dic13—88no—
333D52—42no—
334D52—42no—
335C4×D13—44no—
336C4×D13—44no—
337Dic26—42no—
338Dic26—42no—
339C8×C13—44no—
340C22×#41—131no—
341C24×C4C2×D1311yescharacteristic
342C22×M16—21no—
343#525—132no—
344#525—132no—
345#525—132no—
346#525—132no—
347#525—261no—
348#525—261no—
349#525—261no—
350#525—261no—
351C2×#123—261no—
352C2×C22⋊Q8—131no—
353C2×C22⋊Q8—131no—
354C2×#121—131no—
355C2×#121—131no—
356C2×#120—261no—
357C2×C4×D4—261no—
358C2×C4×D4—261no—
359C2×#117—131no—
360C22×C22⋊C4—261no—
361#407—21no—
362#407—21no—
363#407C2×D1312yes—
364#407C2×D1312yescomplemented
365C2×C22⋊C8—21no—
366C2×C22⋊C8C2×D1312yescomplemented
367#381—132no—
368#381—132no—
369#381—261no—
370#381—261no—
371C2×#95—132no—
372C2×#95—261no—
373#328—138no—
374#327—138no—
375C22×C13—28no—
376C22×C13—21no—
377C22×C13—21no—
378C22×C13—21no—
379C22×C13—21no—
380C22×C13—21no—
381C22×C13—21no—
382C22×C13—21no—
383C22×C13—21no—
384C22×C13—21no—
385C22×C13—21no—
386C22×C13—21no—
387C22×C13—21no—
388C22×C13—21no—
389C22×C13—21no—
390C22×C13—21no—
391C22×C13—21no—
392C22×C13—44no—
393C22×C13—44no—
394C22×C13—44no—
395C22×C13—44no—
396C22×C13—44no—
397C22×C13—44no—
398C22×C13C2×#9912yes—
399C22×C13C2×#9912yes—
400C22×C13C2×#9912yes—
401C22×C13#42112yes—
402C22×C13C22×C22⋊C411yescharacteristic
403C22×C13#57512yes—
404C2×D13—42no—
405C2×D13—42no—
406C2×D13—42no—
407C2×D13—84no—
408C4×C13—21no—
409C4×C13—21no—
410C4×C13—21no—
411C4×C13—21no—
412C4×C13—21no—
413C4×C13—21no—
414C4×C13—21no—
415C4×C13—21no—
416Dic13—42no—
417Dic13—42no—
418Dic13—42no—
419Dic13—84no—
420C25D5211yescharacteristic
421C2×#41—132no—
422C2×#41—132no—
423C2×#41—261no—
424C2×#41—261no—
425C2×#41—524no—
426C22×Q8—131no—
427C22×D4—131no—
428C22×D4—261no—
429C22×D4—261no—
430C22×D4—261no—
431C23×C4—44no—
432C23×C4—261no—
433C23×C4—262no—
434C23×C4C4×D1311yescharacteristic
435C23×C4C4×D1311yescharacteristic
436C23×C4C4×D1311yescharacteristic
437C23×C4C4×D1311yescharacteristic
438C23×C4D5211yescharacteristic
439C23×C4D5211yescharacteristic
440C23×C4D5211yescharacteristic
441C23×C4C22⋊D1311yescharacteristic
442C23×C4C22⋊D1311yescharacteristic
443C23×C4C22⋊D1311yescharacteristic
444C23×C4C22⋊D1311yescharacteristic
445C23×C4C22×D1311yescharacteristic
446C23×C4C22×D1311yescharacteristic
447C23×C4C22×D1311yescharacteristic
448C2×M16—22no—
449C2×M16—22no—
450C2×M16—44no—
451C22×C8—22no—
452#123—262no—
453#123—262no—
454#123—262no—
455#123—262no—
456C22⋊Q8—132no—
457C22⋊Q8—132no—
458C22⋊Q8—132no—
459C22⋊Q8—132no—
460C22⋊Q8—261no—
461C22⋊Q8—261no—
462C22⋊Q8—261no—
463C22⋊Q8—261no—
464#121—132no—
465#121—132no—
466#121—132no—
467#121—132no—
468#121—261no—
469#121—261no—
470#121—261no—
471#121—261no—
472#120—262no—
473#120—262no—
474#120—262no—
475#120—262no—
476C4×D4—262no—
477C4×D4—262no—
478C4×D4—262no—
479C4×D4—262no—
480C4×D4—262no—
481C4×D4—262no—
482C4×D4—262no—
483C4×D4—262no—
484#117—132no—
485#117—132no—
486#117—261no—
487#117—261no—
488C2×C4⋊C4—131no—
489C2×C4⋊C4—131no—
490C2×C4⋊C4—261no—
491C2×C4⋊C4—261no—
492C2×C22⋊C4—261no—
493C2×C22⋊C4—261no—
494C2×C22⋊C4—261no—
495C2×C22⋊C4—261no—
496C2×C22⋊C4—261no—
497C2×C22⋊C4—262no—
498C2×C22⋊C4—262no—
499C2×C22⋊C4—524no—
500C2×C42—261no—
501C22⋊C8—22no—
502C22⋊C8—22no—
503C22⋊C8—22no—
504C22⋊C8C22×D1314yes—
505#95—134no—
506#95—262no—
507#95—262no—
508#95—262no—
509C2×C13—22no—
510C2×C13—22no—
511C2×C13—22no—
512C2×C13—22no—
513C2×C13—22no—
514C2×C13—41no—
515C2×C13—41no—
516C2×C13C22×#9911yescharacteristic
517C2×C13#289611yescharacteristic
518C2×C13C2×#42111yescharacteristic
519D13—82no—
520C24—24no—
521C24—42no—
522C24—42no—
523C24—261no—
524C24#610311yescharacteristic
525C24#610311yescharacteristic
526C24#610311yescharacteristic
527C24#610311yescharacteristic
528C24C2×D5211yescharacteristic
529C24C2×D5211yescharacteristic
530C24C2×D5211yescharacteristic
531#41—524no—
532#41—524no—
533#41—524no—
534#41—524no—
535C2×Q8—132no—
536C2×Q8—261no—
537C2×Q8—522no—
538C2×D4—132no—
539C2×D4—262no—
540C2×D4—262no—
541C2×D4—262no—
542C2×D4—262no—
543C2×D4—262no—
544C2×D4—262no—
545C2×D4—261no—
546C2×D4—522no—
547C2×D4—524no—
548C2×D4—524no—
549C2×D4—524no—
550C22×C4—24no—
551C22×C4—24no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—42no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—261no—
565C22×C4—261no—
566C22×C4—261no—
567C22×C4—262no—
568C22×C4—262no—
569C22×C4—264no—
570C22×C4—524no—
571C22×C4—524no—
572C22×C4—524no—
573C22×C4—524no—
574C22×C4#610311yescharacteristic
575C22×C4#610311yescharacteristic
576C22×C4#610311yescharacteristic
577C22×C4#610311yescharacteristic
578C22×C4#610311yescharacteristic
579C22×C4#610311yescharacteristic
580C22×C4#610311yescharacteristic
581C22×C4#610311yescharacteristic
582C22×C4#610311yescharacteristic
583C22×C4#610311yescharacteristic
584C22×C4#610311yescharacteristic
585C22×C4#610311yescharacteristic
586C22×C4C2×C4×D1311yescharacteristic
587C22×C4C2×C4×D1311yescharacteristic
588C22×C4C2×C4×D1311yescharacteristic
589C22×C4C2×C4×D1311yescharacteristic
590C22×C4C2×C4×D1311yescharacteristic
591C22×C4C2×C4×D1311yescharacteristic
592C22×C4C2×D5211yescharacteristic
593C22×C4C2×D5211yescharacteristic
594C22×C4C2×D5211yescharacteristic
595C22×C4C2×C22⋊D1311yescharacteristic
596C22×C4C2×C22⋊D1311yescharacteristic
597C22×C4C2×C22⋊D1311yescharacteristic
598C22×C4C2×C22⋊D1311yescharacteristic
599C22×C4C2×C22⋊D1311yescharacteristic
600C22×C4C2×C22⋊D1311yescharacteristic
601C22×C4C23×D1311yescharacteristic
602M16—44no—
603M16—44no—
604C2×C8—24no—
605C2×C8—44no—
606C4⋊C4—132no—
607C4⋊C4—132no—
608C4⋊C4—261no—
609C4⋊C4—261no—
610C4⋊C4—262no—
611C4⋊C4—262no—
612C4⋊C4—262no—
613C4⋊C4—262no—
614C22⋊C4—262no—
615C22⋊C4—262no—
616C22⋊C4—262no—
617C22⋊C4—262no—
618C22⋊C4—262no—
619C22⋊C4—262no—
620C22⋊C4—262no—
621C22⋊C4—262no—
622C22⋊C4—262no—
623C22⋊C4—262no—
624C22⋊C4—524no—
625C22⋊C4—524no—
626C42—262no—
627C42—262no—
628C13#1758711yescharacteristic, complemented, Sylow
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—416no—
650C23—262no—
651C23—522no—
652C23—522no—
653C23—522no—
654C23#8804614yes—
655C23C2×#610311yescharacteristic
656C23C2×#610311yescharacteristic
657C23C2×#610311yescharacteristic
658C23C2×#610311yescharacteristic
659C23C2×#610311yescharacteristic
660C23C2×#610311yescharacteristic
661C23C22×D5211yescharacteristic
662Q8—522no—
663Q8—522no—
664D4—522no—
665D4—522no—
666D4—524no—
667D4—524no—
668D4—524no—
669D4—524no—
670D4—524no—
671D4—524no—
672C2×C4—22no—
673C2×C4—22no—
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—22no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
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—41no—
699C2×C4—41no—
700C2×C4—262no—
701C2×C4—262no—
702C2×C4—262no—
703C2×C4—524no—
704C2×C4—524no—
705C2×C4—522no—
706C2×C4—522no—
707C2×C4—522no—
708C2×C4—524no—
709C2×C4—524no—
710C2×C4—524no—
711C2×C4—1048no—
712C2×C4C2×#610311yescharacteristic
713C2×C4C2×#610311yescharacteristic
714C2×C4C2×#610311yescharacteristic
715C2×C4C2×#610311yescharacteristic
716C2×C4C2×#610311yescharacteristic
717C2×C4C2×#610311yescharacteristic
718C2×C4C22×C4×D1311yescharacteristic
719C2×C4C22×C22⋊D1311yescharacteristic
720C8—44no—
721C22—28no—
722C22—21no—
723C22—21no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—44no—
739C22—44no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—522no—
745C22—522no—
746C22—522no—
747C22—1044no—
748C22C2×#8804612yes—
749C22C2×#8804612yes—
750C22C2×#8804612yes—
751C22#1171880012yes—
752C22#1171945312yes—
753C22C22×#610311yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—21no—
758C4—21no—
759C4—21no—
760C4—21no—
761C4—21no—
762C4—522no—
763C4—522no—
764C4—522no—
765C4—1044no—
766C2—22no—
767C2—22no—
768C2—22no—
769C2—22no—
770C2—22no—
771C2—41no—
772C2—41no—
773C2—1042no—
774C2C22×#8804611yescharacteristic
775C2#1312335611yescharacteristic
776C2C2×#1171880011yescharacteristic
subgroupG/H
centerC22C22×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C13×#407C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC2×#407D13
hypocenterC13#17587
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#11718872C2semidirect
3. #13113393C2semidirect
4. #13113370C2semidirect
5. #13113366C2semidirect
6. #13113341C2semidirect
7. C2×C13×#407C2semidirect
9. C22×#6127C4semidirect
17. #11719496C4semidirect
18. #11719496C4semidirect
21. C2×#88184C4semidirect
26. C2×#88180C4semidirect
27. C2×#88178C4semidirect
32. C13×#407C22semidirect
34. C2×C13×C22⋊C8C22semidirect
38. #11718872C22semidirect
40. C2×#88071C22semidirect
41. #11718062C22semidirect
42. #11718059C22semidirect
67. C2×#6127C2×C4semidirect
68. C22×D52C2×C4semidirect
70. C22×Dic26C2×C4semidirect
90. #88184C2×C4semidirect
91. #88184C2×C4semidirect
110. #88180C2×C4semidirect
111. C2×C4⋊Dic13C2×C4semidirect
112. C2×C4⋊Dic13C2×C4semidirect
118. #88178C2×C4semidirect
119. #88178C2×C4semidirect
242. C2×#407D13semidirect
364. #407C2×D13semidirect
366. C2×C22⋊C8C2×D13semidirect
628. C13#17587semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117188722
#131133932
#131133702
#131133662
#131133412
C2×C13×#4072
#1758713