Finite Group Databasebeta

← #15830081

Subgroups — #15830081

Order 3328.

1574 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719496C211yesmaximal, characteristic
2C2×#11718868C211yesmaximal, characteristic, complemented
3#13113355C212yesmaximal, complemented
4#13113351C212yesmaximal, complemented
5#13113338C214yesmaximal, complemented
6#13113325C214yesmaximal, complemented
7C2×C4×C13×C22⋊C4C211yesmaximal, characteristic, complemented
8C24×C4×C13C2211yescharacteristic
9C22×#6127C411yescharacteristic, complemented
10C22×C13×C22⋊C4—21no—
11C22×C42×C13—21no—
12C2×#88207—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
29C22×#6099—21no—
30C4×C13×C22⋊C4—21no—
31C4×C13×C22⋊C4—21no—
32C4×C13×C22⋊C4C2212yes—
33C4×C13×C22⋊C4C2212yescomplemented
34C2×C13×#95C2212yescomplemented
35#11718868—21no—
36#11718868—21no—
37#11718868C2212yes—
38#11718868C2212yescomplemented
39C2×C22⋊#1055—21no—
40C2×C22⋊#1055C2212yescomplemented
41#11718044C2218yescomplemented
42#11718043C2218yescomplemented
43C25×C13D411yescharacteristic
44C23×C4×C13—22no—
45C23×C4×C13—44no—
46C23×C4×C13C2×C411yescharacteristic
47C23×C4×C13C2×C411yescharacteristic
48C23×C4×C13C2×C411yescharacteristic
49C23×C4×C13C2×C411yescharacteristic
50C23×C4×C13D411yescharacteristic
51C23×C4×C13D411yescharacteristic
52C23×C4×C13D411yescharacteristic
53C23×C4×C13D411yescharacteristic
54C23×C4×C13D411yescharacteristic
55C23×C4×C13D411yescharacteristic
56C23×C4×C13D411yescharacteristic
57C23×C4×C13C2311yescharacteristic
58C23×C4×C13C2311yescharacteristic
59C23×C4×C13C2311yescharacteristic
60C22×C22⋊D13—21no—
61C22×C22⋊D13—21no—
62C22×C22⋊D13—21no—
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×C22⋊C4—28no—
72C2×C13×C22⋊C4—22no—
73C2×C13×C22⋊C4—22no—
74C2×C42×C13—22no—
75C2×C42×C13—22no—
76C2×C42×C13—44no—
77#88207—22no—
78#88207—22no—
79#88207—22no—
80#88207—22no—
81C2×C22⋊Dic13—21no—
82C2×C22⋊Dic13—21no—
83C2×C22⋊Dic13—21no—
84#88184—21no—
85#88184—21no—
86#88184—21no—
87#88184—21no—
88#88184C2×C412yes—
89#88184C2×C412yescomplemented
90#88184C2×C412yescomplemented
91#88184C2312yes—
92#88183—22no—
93#88183—22no—
94#88183—22no—
95#88183—22no—
96C4×C22⋊D13—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—
104C2×#6103—21no—
105C2×#6103—21no—
106#88180—21no—
107#88180—21no—
108#88180C2×C412yes—
109#88180C2×C412yescomplemented
110C2×C4⋊Dic13C2×C411yescharacteristic, complemented
111C2×C4⋊Dic13C2×C411yescharacteristic, complemented
112#88178—21no—
113#88178—21no—
114#88178—21no—
115#88178—21no—
116#88178C2×C412yes—
117#88178C2×C412yescomplemented
118#88178C2×C412yescomplemented
119#88178C2312yes—
120C2×#6101—21no—
121C2×#6101—21no—
122C2×C4×Dic13—21no—
123C2×#6099—22no—
124C2×#6099—22no—
125C2×#6099—44no—
126C22×#1055—22no—
127C13×#95—22no—
128C13×#95C2314yes—
129C22⋊#1055—22no—
130C22⋊#1055—22no—
131C22⋊#1055—22no—
132C22⋊#1055C2314yes—
133#17542—131nomaximal, Sylow
134C24×C13—24no—
135C24×C13—42no—
136C24×C13—42no—
137C24×C13C22⋊C411yescharacteristic
138C24×C13C22⋊C411yescharacteristic
139C24×C13C22⋊C411yescharacteristic
140C24×C13C22⋊C411yescharacteristic
141C24×C13C2×D411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C24×C13C2×D411yescharacteristic
144C23×D13—21no—
145C22×C4×C13—24no—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13—28no—
149C22×C4×C13—24no—
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×C13—42no—
159C22×C4×C13—42no—
160C22×C4×C13—42no—
161C22×C4×C13—44no—
162C22×C4×C13—44no—
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×C13C22×C411yescharacteristic
177C22×C4×C13C22×C411yescharacteristic
178C22×C4×C13C22×C411yescharacteristic
179C22×C4×C13C22×C411yescharacteristic
180C22×C4×C13C22×C411yescharacteristic
181C22×C4×C13C2×D411yescharacteristic
182C22×C4×C13C2×D411yescharacteristic
183C22×C4×C13C2×D411yescharacteristic
184C22×C4×C13C2×D411yescharacteristic
185C22×C4×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2×D411yescharacteristic
188C22×C4×C13C2×D411yescharacteristic
189C22×C4×C13C2×D411yescharacteristic
190C22×C4×C13C2411yescharacteristic
191C2×C22⋊D13—22no—
192C2×C22⋊D13—22no—
193C2×C22⋊D13—22no—
194C2×C22⋊D13—22no—
195C2×C22⋊D13—22no—
196C2×C22⋊D13—22no—
197C2×C22⋊D13—44no—
198C2×C22⋊D13—44no—
199C2×C22⋊D13—44no—
200C22×Dic13—21no—
201C22×Dic13—21no—
202C22×Dic13—21no—
203#6127—44no—
204#6127—44no—
205#6127—44no—
206#6127—44no—
207C2×D52—21no—
208C2×D52—42no—
209C2×D52C22×C412yes—
210C2×C4×D13—22no—
211C2×C4×D13—22no—
212C2×C4×D13—44no—
213C2×Dic26—21no—
214C2×Dic26—42no—
215C2×Dic26C22×C412yes—
216C13×C22⋊C4—28no—
217C13×C22⋊C4—28no—
218C42×C13—44no—
219C42×C13—44no—
220C22⋊Dic13—22no—
221C22⋊Dic13—22no—
222C22⋊Dic13—22no—
223C22⋊Dic13—22no—
224C22⋊Dic13—22no—
225C22⋊Dic13—22no—
226#6103—22no—
227#6103—22no—
228#6103—22no—
229#6103—22no—
230C4⋊Dic13—21no—
231C4⋊Dic13—21no—
232C4⋊Dic13C22×C412yes—
233C4⋊Dic13C22×C412yes—
234#6101—22no—
235#6101—22no—
236#6101—22no—
237#6101—22no—
238C4×Dic13—22no—
239C4×Dic13—22no—
240#6099—44no—
241#6099—44no—
242C2×#1055—24no—
243C2×#1055—44no—
244C2×#525—131no—
245C2×#407—131no—
246C2×C4×C22⋊C4D1311yescharacteristic, complemented
247#1508—132no—
248#1507—132no—
249#1504—134no—
250#1501—134no—
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—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—41no—
264C23×C13—41no—
265C23×C13—41no—
266C23×C13—41no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—416no—
272C23×C13#10414yes—
273C23×C13C2×C22⋊C411yescharacteristic
274C23×C13C2×C22⋊C411yescharacteristic
275C23×C13C2×C22⋊C411yescharacteristic
276C23×C13C2×C22⋊C411yescharacteristic
277C23×C13C2×C22⋊C411yescharacteristic
278C23×C13C2×C22⋊C411yescharacteristic
279C23×C13C22×D411yescharacteristic
280C22×D13—22no—
281C22×D13—42no—
282C22×D13—42no—
283C22×D13—42no—
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—22no—
294C2×C4×C13—22no—
295C2×C4×C13—22no—
296C2×C4×C13—22no—
297C2×C4×C13—22no—
298C2×C4×C13—22no—
299C2×C4×C13—28no—
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×C13—41no—
310C2×C4×C13—41no—
311C2×C4×C13—41no—
312C2×C4×C13—44no—
313C2×C4×C13—416no—
314C2×C4×C13—44no—
315C2×C4×C13#9914yes—
316C2×C4×C13C2×C22⋊C411yescharacteristic
317C2×C4×C13C2×C22⋊C411yescharacteristic
318C2×C4×C13C2×C22⋊C411yescharacteristic
319C2×C4×C13C2×C22⋊C411yescharacteristic
320C2×C4×C13C2×C22⋊C411yescharacteristic
321C2×C4×C13C2×C22⋊C411yescharacteristic
322C2×C4×C13C23×C411yescharacteristic
323C2×C4×C13C22×D411yescharacteristic
324C22⋊D13—44no—
325C22⋊D13—44no—
326C22⋊D13—44no—
327C22⋊D13—44no—
328C22⋊D13—44no—
329C22⋊D13—44no—
330C2×Dic13—22no—
331C2×Dic13—22no—
332C2×Dic13—22no—
333C2×Dic13—42no—
334C2×Dic13—42no—
335C2×Dic13—42no—
336D52—42no—
337D52—42no—
338C4×D13—44no—
339C4×D13—44no—
340Dic26—42no—
341Dic26—42no—
342#1055—44no—
343C22×#41—131no—
344C24×C4C2×D1311yescharacteristic
345C22×M16—261no—
346#525—132no—
347#525—132no—
348#525—132no—
349#525—132no—
350#525—261no—
351#525—261no—
352#525—261no—
353#525—261no—
354C2×#123—261no—
355C2×C22⋊Q8—131no—
356C2×C22⋊Q8—131no—
357C2×#121—131no—
358C2×#121—131no—
359C2×#120—261no—
360C2×C4×D4—261no—
361C2×C4×D4—261no—
362C2×#117—131no—
363C22×C22⋊C4—21no—
364C22×C42—21no—
365#407—132no—
366#407—132no—
367#407—261no—
368#407—261no—
369C2×C22⋊C8—132no—
370C2×C22⋊C8—261no—
371C4×C22⋊C4—21no—
372C4×C22⋊C4—21no—
373C4×C22⋊C4C2×D1312yes—
374C4×C22⋊C4C2×D1312yescomplemented
375C2×#95C2×D1312yescomplemented
376#328—138no—
377#327—138no—
378C22×C13—28no—
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—21no—
393C22×C13—21no—
394C22×C13—21no—
395C22×C13—44no—
396C22×C13—44no—
397C22×C13—44no—
398C22×C13—44no—
399C22×C13—44no—
400C22×C13—44no—
401C22×C13C2×#9912yes—
402C22×C13C2×#10412yes—
403C22×C13C2×#10412yes—
404C22×C13C2×#10412yes—
405C22×C13C22×C22⋊C411yescharacteristic
406C22×C13#57512yes—
407C2×D13—42no—
408C2×D13—42no—
409C2×D13—42no—
410C2×D13—84no—
411C4×C13—21no—
412C4×C13—21no—
413C4×C13—21no—
414C4×C13—21no—
415C4×C13—21no—
416C4×C13—21no—
417C4×C13—48no—
418C4×C13C2×#9912yes—
419C4×C13C2×#9912yes—
420Dic13—42no—
421Dic13—42no—
422Dic13—42no—
423C25C22⋊D1311yescharacteristic
424C2×#41—132no—
425C2×#41—132no—
426C2×#41—261no—
427C2×#41—261no—
428C2×#41—524no—
429C22×Q8—131no—
430C22×D4—131no—
431C22×D4—261no—
432C22×D4—261no—
433C22×D4—261no—
434C23×C4—22no—
435C23×C4—44no—
436C23×C4—261no—
437C23×C4C4×D1311yescharacteristic
438C23×C4C4×D1311yescharacteristic
439C23×C4C4×D1311yescharacteristic
440C23×C4C4×D1311yescharacteristic
441C23×C4D5211yescharacteristic
442C23×C4D5211yescharacteristic
443C23×C4D5211yescharacteristic
444C23×C4D5211yescharacteristic
445C23×C4C22⋊D1311yescharacteristic
446C23×C4C22⋊D1311yescharacteristic
447C23×C4C22⋊D1311yescharacteristic
448C23×C4C22×D1311yescharacteristic
449C23×C4C22×D1311yescharacteristic
450C23×C4C22×D1311yescharacteristic
451C2×M16—262no—
452C2×M16—262no—
453C2×M16—524no—
454C22×C8—262no—
455#123—262no—
456#123—262no—
457#123—262no—
458#123—262no—
459C22⋊Q8—132no—
460C22⋊Q8—132no—
461C22⋊Q8—132no—
462C22⋊Q8—132no—
463C22⋊Q8—261no—
464C22⋊Q8—261no—
465C22⋊Q8—261no—
466C22⋊Q8—261no—
467#121—132no—
468#121—132no—
469#121—132no—
470#121—132no—
471#121—261no—
472#121—261no—
473#121—261no—
474#121—261no—
475#120—262no—
476#120—262no—
477#120—262no—
478#120—262no—
479C4×D4—262no—
480C4×D4—262no—
481C4×D4—262no—
482C4×D4—262no—
483C4×D4—262no—
484C4×D4—262no—
485C4×D4—262no—
486C4×D4—262no—
487#117—132no—
488#117—132no—
489#117—261no—
490#117—261no—
491C2×C4⋊C4—131no—
492C2×C4⋊C4—131no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C22⋊C4—28no—
496C2×C22⋊C4—22no—
497C2×C22⋊C4—22no—
498C2×C22⋊C4—261no—
499C2×C22⋊C4—261no—
500C2×C22⋊C4—261no—
501C2×C22⋊C4—261no—
502C2×C22⋊C4—261no—
503C2×C42—22no—
504C2×C42—22no—
505C2×C42—44no—
506C2×C42—261no—
507C22⋊C8—134no—
508C22⋊C8—262no—
509C22⋊C8—262no—
510C22⋊C8—262no—
511#95—22no—
512#95C22×D1314yes—
513C2×C13—22no—
514C2×C13—22no—
515C2×C13—22no—
516C2×C13—22no—
517C2×C13—22no—
518C2×C13—41no—
519C2×C13—41no—
520C2×C13C22×#9911yescharacteristic
521C2×C13#289611yescharacteristic
522C2×C13C22×#10411yescharacteristic
523D13—82no—
524C24—24no—
525C24—42no—
526C24—42no—
527C24—261no—
528C24#610311yescharacteristic
529C24#610311yescharacteristic
530C24#610311yescharacteristic
531C24#610311yescharacteristic
532C24C2×C22⋊D1311yescharacteristic
533C24C2×C22⋊D1311yescharacteristic
534C24C2×C22⋊D1311yescharacteristic
535#41—524no—
536#41—524no—
537#41—524no—
538#41—524no—
539C2×Q8—132no—
540C2×Q8—261no—
541C2×Q8—522no—
542C2×D4—132no—
543C2×D4—262no—
544C2×D4—262no—
545C2×D4—262no—
546C2×D4—262no—
547C2×D4—262no—
548C2×D4—262no—
549C2×D4—261no—
550C2×D4—522no—
551C2×D4—524no—
552C2×D4—524no—
553C2×D4—524no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—28no—
558C22×C4—24no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—42no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—261no—
573C22×C4—261no—
574C22×C4—261no—
575C22×C4—262no—
576C22×C4—262no—
577C22×C4—524no—
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×C4#610311yescharacteristic
587C22×C4#610311yescharacteristic
588C22×C4#610311yescharacteristic
589C22×C4#610311yescharacteristic
590C22×C4C2×C4×D1311yescharacteristic
591C22×C4C2×C4×D1311yescharacteristic
592C22×C4C2×C4×D1311yescharacteristic
593C22×C4C2×C4×D1311yescharacteristic
594C22×C4C2×C4×D1311yescharacteristic
595C22×C4C2×C4×D1311yescharacteristic
596C22×C4C2×D5211yescharacteristic
597C22×C4C2×D5211yescharacteristic
598C22×C4C2×D5211yescharacteristic
599C22×C4C2×D5211yescharacteristic
600C22×C4C2×D5211yescharacteristic
601C22×C4C2×D5211yescharacteristic
602C22×C4C2×C22⋊D1311yescharacteristic
603C22×C4C2×C22⋊D1311yescharacteristic
604C22×C4C2×C22⋊D1311yescharacteristic
605C22×C4C23×D1311yescharacteristic
606M16—524no—
607M16—524no—
608C2×C8—264no—
609C2×C8—524no—
610C4⋊C4—132no—
611C4⋊C4—132no—
612C4⋊C4—261no—
613C4⋊C4—261no—
614C4⋊C4—262no—
615C4⋊C4—262no—
616C4⋊C4—262no—
617C4⋊C4—262no—
618C22⋊C4—28no—
619C22⋊C4—28no—
620C22⋊C4—262no—
621C22⋊C4—262no—
622C22⋊C4—262no—
623C22⋊C4—262no—
624C22⋊C4—262no—
625C22⋊C4—262no—
626C22⋊C4—262no—
627C22⋊C4—262no—
628C22⋊C4—262no—
629C22⋊C4—262no—
630C42—44no—
631C42—44no—
632C42—262no—
633C42—262no—
634C13#1754211yescharacteristic, complemented, Sylow
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—416no—
656C23—262no—
657C23—522no—
658C23—522no—
659C23—522no—
660C23#8804514yes—
661C23C2×#610311yescharacteristic
662C23C2×#610311yescharacteristic
663C23C2×#610311yescharacteristic
664C23C2×#610311yescharacteristic
665C23C2×#610311yescharacteristic
666C23C2×#610311yescharacteristic
667C23C22×C22⋊D1311yescharacteristic
668Q8—522no—
669Q8—522no—
670D4—522no—
671D4—524no—
672D4—524no—
673D4—524no—
674D4—524no—
675D4—524no—
676D4—524no—
677D4—522no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—28no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—44no—
707C2×C4—416no—
708C2×C4—44no—
709C2×C4—262no—
710C2×C4—262no—
711C2×C4—262no—
712C2×C4—524no—
713C2×C4—522no—
714C2×C4—522no—
715C2×C4—522no—
716C2×C4—524no—
717C2×C4#8804614yes—
718C2×C4C2×#610311yescharacteristic
719C2×C4C2×#610311yescharacteristic
720C2×C4C2×#610311yescharacteristic
721C2×C4C2×#610311yescharacteristic
722C2×C4C2×#610311yescharacteristic
723C2×C4C2×#610311yescharacteristic
724C2×C4C22×C4×D1311yescharacteristic
725C2×C4C22×D5211yescharacteristic
726C8—524no—
727C22—28no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—21no—
734C22—21no—
735C22—21no—
736C22—21no—
737C22—21no—
738C22—21no—
739C22—21no—
740C22—21no—
741C22—21no—
742C22—21no—
743C22—21no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—44no—
748C22—44no—
749C22—44no—
750C22—522no—
751C22—522no—
752C22—522no—
753C22—1044no—
754C22C2×#8804512yes—
755C22C2×#8804512yes—
756C22C2×#8804512yes—
757C22C2×#8804612yes—
758C22C22×#610311yescharacteristic
759C22#1171952712yes—
760C4—21no—
761C4—21no—
762C4—21no—
763C4—21no—
764C4—21no—
765C4—21no—
766C4—48no—
767C4—522no—
768C4—522no—
769C4—522no—
770C4C2×#8804612yes—
771C4C2×#8804612yes—
772C2—22no—
773C2—22no—
774C2—22no—
775C2—22no—
776C2—22no—
777C2—41no—
778C2—41no—
779C2—1042no—
780C2C22×#8804611yescharacteristic
781C2#1312335311yescharacteristic
782C2C22×#8804511yescharacteristic
subgroupG/H
centerC2×C4C2×#6103
commutatorC2×C4×C13C23×C4
FrattiniC22×C4C23×D13
FittingC2×C4×C13×C22⋊C4C2
socleC22×C13C22×C22⋊C4
prime radicalC2×#11719496C2
cosocleC22×C4×C13C24
hypercenterC2×C4×C22⋊C4D13
hypocenterC13#17542
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C24×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#11718868C2semidirect
3. #13113355C2semidirect
4. #13113351C2semidirect
5. #13113338C2semidirect
6. #13113325C2semidirect
7. C2×C4×C13×C22⋊C4C2semidirect
9. C22×#6127C4semidirect
17. #11719496C4semidirect
18. #11719496C4semidirect
21. C2×#88184C4semidirect
26. C2×#88180C4semidirect
27. C2×#88178C4semidirect
33. C4×C13×C22⋊C4C22semidirect
34. C2×C13×#95C22semidirect
38. #11718868C22semidirect
40. C2×C22⋊#1055C22semidirect
41. #11718044C22semidirect
42. #11718043C22semidirect
67. C2×#6127C2×C4semidirect
68. C22×D52C2×C4semidirect
70. C22×Dic26C2×C4semidirect
89. #88184C2×C4semidirect
90. #88184C2×C4semidirect
109. #88180C2×C4semidirect
110. C2×C4⋊Dic13C2×C4semidirect
111. C2×C4⋊Dic13C2×C4semidirect
117. #88178C2×C4semidirect
118. #88178C2×C4semidirect
246. C2×C4×C22⋊C4D13semidirect
374. C4×C22⋊C4C2×D13semidirect
375. C2×#95C2×D13semidirect
634. C13#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117188682
#131133552
#131133512
#131133382
#131133252
C2×C4×C13×C22⋊C42
#1754213