Finite Group Databasebeta

← #15830410

Subgroups — #15830410

Order 3328.

1510 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×#11719496C211yesmaximal, characteristic
2C2×#11718873C211yesmaximal, characteristic, complemented
3#13113409C212yesmaximal, complemented
4#13113405C212yesmaximal, complemented
5#13113380C214yesmaximal, 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
27C22×C4⋊Dic13—21no—
28C2×#88178C411yescharacteristic, complemented
29C2×#88178C2211yescharacteristic
30C13×#407—21no—
31C13×#407—21no—
32C13×#407C2212yescomplemented
33C13×#407C2212yescomplemented
34C2×C13×C22⋊C8—21no—
35C2×C13×C22⋊C8C2212yes—
36#11718873—21no—
37#11718873—21no—
38#11718873C2212yes—
39#11718873C2212yescomplemented
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⋊Dic13—22no—
112C2×C4⋊Dic13—22no—
113C2×C4⋊Dic13—44no—
114C2×C4⋊Dic13C2×C411yescharacteristic, complemented
115C2×C4⋊Dic13C2×C411yescharacteristic, complemented
116#88178—21no—
117#88178—21no—
118#88178—21no—
119#88178—21no—
120#88178C2×C412yes—
121#88178C2×C412yescomplemented
122#88178C2×C412yescomplemented
123#88178C2312yes—
124C2×#6101—21no—
125C2×#6101—21no—
126C2×C4×Dic13—21no—
127C13×C22⋊C8—22no—
128C13×C22⋊C8—22no—
129C13×C22⋊C8—22no—
130C13×C22⋊C8C2314yes—
131#88071—22no—
132#88071C2314yes—
133#17592—131nomaximal, Sylow
134C24×C13—22no—
135C24×C13—22no—
136C24×C13—42no—
137C24×C13—42no—
138C24×C13C22⋊C411yescharacteristic
139C24×C13C22⋊C411yescharacteristic
140C24×C13C22⋊C411yescharacteristic
141C24×C13C22⋊C411yescharacteristic
142C24×C13C2×D411yescharacteristic
143C24×C13C2×D411yescharacteristic
144C24×C13C2×D411yescharacteristic
145C23×D13—21no—
146C22×C4×C13—24no—
147C22×C4×C13—24no—
148C22×C4×C13—24no—
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×C13—42no—
159C22×C4×C13—42no—
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×C13C22×C411yescharacteristic
177C22×C4×C13C22×C411yescharacteristic
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×C13C2×D411yescharacteristic
186C22×C4×C13C2×D411yescharacteristic
187C22×C4×C13C2411yescharacteristic
188C2×C22⋊D13—22no—
189C2×C22⋊D13—22no—
190C2×C22⋊D13—22no—
191C2×C22⋊D13—22no—
192C2×C22⋊D13—22no—
193C2×C22⋊D13—22no—
194C2×C22⋊D13—44no—
195C2×C22⋊D13—44no—
196C2×C22⋊D13—42no—
197C2×C22⋊D13—42no—
198C22×Dic13—21no—
199C22×Dic13—21no—
200C22×Dic13—21no—
201C22×Dic13—24no—
202C22×Dic13—44no—
203C22×Dic13—44no—
204C22×Dic13—44no—
205#6127—44no—
206#6127—44no—
207#6127—44no—
208#6127—44no—
209C2×D52—21no—
210C2×D52—42no—
211C2×D52C22×C412yes—
212C2×C4×D13—22no—
213C2×C4×D13—22no—
214C2×C4×D13—44no—
215C2×Dic26—21no—
216C2×Dic26—42no—
217C2×Dic26C22×C412yes—
218C13×M16—44no—
219C13×M16—44no—
220C2×C8×C13—24no—
221C2×C8×C13—44no—
222C22⋊Dic13—22no—
223C22⋊Dic13—22no—
224C22⋊Dic13—22no—
225C22⋊Dic13—22no—
226C22⋊Dic13—22no—
227C22⋊Dic13—22no—
228C22⋊Dic13—44no—
229C22⋊Dic13—44no—
230#6103—22no—
231#6103—22no—
232#6103—22no—
233#6103—22no—
234C4⋊Dic13—21no—
235C4⋊Dic13—21no—
236C4⋊Dic13—44no—
237C4⋊Dic13—44no—
238C4⋊Dic13C22×C412yes—
239C4⋊Dic13C22×C412yes—
240#6101—22no—
241#6101—22no—
242#6101—22no—
243#6101—22no—
244C4×Dic13—22no—
245C4×Dic13—22no—
246C2×#525—131no—
247C2×#407D1311yescharacteristic, complemented
248C2×#380—131no—
249#1520—132no—
250#1519—132no—
251#1513—134no—
252#1504—134no—
253C23×C13—21no—
254C23×C13—21no—
255C23×C13—22no—
256C23×C13—22no—
257C23×C13—21no—
258C23×C13—21no—
259C23×C13—22no—
260C23×C13—22no—
261C23×C13—22no—
262C23×C13—22no—
263C23×C13—22no—
264C23×C13—22no—
265C23×C13—22no—
266C23×C13—22no—
267C23×C13—41no—
268C23×C13—41no—
269C23×C13—41no—
270C23×C13—41no—
271C23×C13—41no—
272C23×C13—41no—
273C23×C13—41no—
274C23×C13—41no—
275C23×C13—48no—
276C23×C13—48no—
277C23×C13C2×C22⋊C411yescharacteristic
278C23×C13C2×C22⋊C411yescharacteristic
279C23×C13C2×C22⋊C411yescharacteristic
280C23×C13C2×C22⋊C411yescharacteristic
281C23×C13C2×C22⋊C411yescharacteristic
282C23×C13C2×C22⋊C411yescharacteristic
283C23×C13AGL(1,ℤ/8)12yes—
284C23×C13#13712yes—
285C23×C13C22×D411yescharacteristic
286C22×D13—22no—
287C22×D13—42no—
288C22×D13—42no—
289C22×D13—42no—
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—22no—
300C2×C4×C13—22no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—22no—
304C2×C4×C13—22no—
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—41no—
313C2×C4×C13—41no—
314C2×C4×C13—41no—
315C2×C4×C13—41no—
316C2×C4×C13—41no—
317C2×C4×C13#9914yes—
318C2×C4×C13C2×C22⋊C411yescharacteristic
319C2×C4×C13C2×C22⋊C411yescharacteristic
320C2×C4×C13C2×C22⋊C411yescharacteristic
321C2×C4×C13C2×C22⋊C411yescharacteristic
322C2×C4×C13C2×C22⋊C411yescharacteristic
323C2×C4×C13C2×C22⋊C411yescharacteristic
324C2×C4×C13C23×C411yescharacteristic
325C2×C4×C13C22×D411yescharacteristic
326C22⋊D13—44no—
327C22⋊D13—44no—
328C22⋊D13—42no—
329C22⋊D13—42no—
330C22⋊D13—44no—
331C22⋊D13—44no—
332C22⋊D13—44no—
333C2×Dic13—22no—
334C2×Dic13—22no—
335C2×Dic13—22no—
336C2×Dic13—42no—
337C2×Dic13—42no—
338C2×Dic13—42no—
339C2×Dic13—44no—
340C2×Dic13—44no—
341C2×Dic13—44no—
342C2×Dic13—88no—
343D52—42no—
344D52—42no—
345C4×D13—44no—
346C4×D13—44no—
347Dic26—42no—
348Dic26—42no—
349C8×C13—44no—
350C22×#41—131no—
351C24×C4C2×D1311yescharacteristic
352C22×M16—21no—
353#525—132no—
354#525—132no—
355#525—132no—
356#525—132no—
357#525—261no—
358#525—261no—
359#525—261no—
360#525—261no—
361C2×#123—261no—
362C2×C22⋊Q8—131no—
363C2×C22⋊Q8—131no—
364C2×#121—131no—
365C2×#121—131no—
366C2×#120—261no—
367C2×C4×D4—261no—
368C2×C4×D4—261no—
369C2×#117—131no—
370C22×C4⋊C4—261no—
371C22×C22⋊C4—261no—
372#407—21no—
373#407—21no—
374#407C2×D1312yescomplemented
375#407C2×D1312yescomplemented
376C2×C22⋊C8—21no—
377C2×C22⋊C8C2×D1312yes—
378#380—132no—
379#380—132no—
380#380—261no—
381#380—261no—
382C2×#95—132no—
383#328—138no—
384#327—138no—
385C22×C13—24no—
386C22×C13—24no—
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—21no—
396C22×C13—21no—
397C22×C13—21no—
398C22×C13—21no—
399C22×C13—21no—
400C22×C13—21no—
401C22×C13—21no—
402C22×C13—21no—
403C22×C13—42no—
404C22×C13—42no—
405C22×C13—44no—
406C22×C13—44no—
407C22×C13—44no—
408C22×C13—44no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13C2×#9912yes—
412C22×C13#41712yes—
413C22×C13#41712yes—
414C22×C13#42112yes—
415C22×C13C22×C22⋊C411yescharacteristic
416C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
417C22×C13C2×#13711yescharacteristic
418C2×D13—42no—
419C2×D13—42no—
420C2×D13—42no—
421C2×D13—84no—
422C4×C13—21no—
423C4×C13—21no—
424C4×C13—21no—
425C4×C13—21no—
426C4×C13—21no—
427C4×C13—21no—
428C4×C13C2×#9912yes—
429C4×C13C2×#9912yes—
430Dic13—42no—
431Dic13—42no—
432Dic13—42no—
433Dic13—84no—
434C25D5211yescharacteristic
435C2×#41—132no—
436C2×#41—132no—
437C2×#41—261no—
438C2×#41—261no—
439C2×#41—524no—
440C22×Q8—131no—
441C22×D4—131no—
442C22×D4—261no—
443C22×D4—261no—
444C22×D4—261no—
445C23×C4—44no—
446C23×C4—261no—
447C23×C4—262no—
448C23×C4C4×D1311yescharacteristic
449C23×C4C4×D1311yescharacteristic
450C23×C4C4×D1311yescharacteristic
451C23×C4C4×D1311yescharacteristic
452C23×C4D5211yescharacteristic
453C23×C4D5211yescharacteristic
454C23×C4D5211yescharacteristic
455C23×C4C22⋊D1311yescharacteristic
456C23×C4C22⋊D1311yescharacteristic
457C23×C4C22⋊D1311yescharacteristic
458C23×C4C22⋊D1311yescharacteristic
459C23×C4C22×D1311yescharacteristic
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C2×M16—22no—
463C2×M16—22no—
464C2×M16—44no—
465C22×C8—22no—
466#123—262no—
467#123—262no—
468#123—262no—
469#123—262no—
470C22⋊Q8—132no—
471C22⋊Q8—132no—
472C22⋊Q8—132no—
473C22⋊Q8—132no—
474C22⋊Q8—261no—
475C22⋊Q8—261no—
476C22⋊Q8—261no—
477C22⋊Q8—261no—
478#121—132no—
479#121—132no—
480#121—132no—
481#121—132no—
482#121—261no—
483#121—261no—
484#121—261no—
485#121—261no—
486#120—262no—
487#120—262no—
488#120—262no—
489#120—262no—
490C4×D4—262no—
491C4×D4—262no—
492C4×D4—262no—
493C4×D4—262no—
494C4×D4—262no—
495C4×D4—262no—
496C4×D4—262no—
497C4×D4—262no—
498#117—132no—
499#117—132no—
500#117—261no—
501#117—261no—
502C2×C4⋊C4—131no—
503C2×C4⋊C4—131no—
504C2×C4⋊C4—261no—
505C2×C4⋊C4—261no—
506C2×C4⋊C4—262no—
507C2×C4⋊C4—262no—
508C2×C4⋊C4—524no—
509C2×C22⋊C4—261no—
510C2×C22⋊C4—261no—
511C2×C22⋊C4—261no—
512C2×C22⋊C4—261no—
513C2×C22⋊C4—261no—
514C2×C22⋊C4—262no—
515C2×C22⋊C4—262no—
516C2×C22⋊C4—524no—
517C2×C42—261no—
518C22⋊C8—22no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8C22×D1314yes—
522#95—134no—
523#95—262no—
524C2×C13—21no—
525C2×C13—22no—
526C2×C13—21no—
527C2×C13—22no—
528C2×C13—22no—
529C2×C13—22no—
530C2×C13—41no—
531C2×C13—41no—
532C2×C13C22×#9911yescharacteristic
533C2×C13C2×#41711yescharacteristic
534C2×C13C2×#42111yescharacteristic
535D13—82no—
536C24—22no—
537C24—22no—
538C24—42no—
539C24—42no—
540C24—261no—
541C24#610311yescharacteristic
542C24#610311yescharacteristic
543C24#610311yescharacteristic
544C24#610311yescharacteristic
545C24C2×D5211yescharacteristic
546C24C2×D5211yescharacteristic
547C24C2×D5211yescharacteristic
548#41—524no—
549#41—524no—
550#41—524no—
551#41—524no—
552C2×Q8—132no—
553C2×Q8—261no—
554C2×Q8—522no—
555C2×D4—132no—
556C2×D4—262no—
557C2×D4—262no—
558C2×D4—262no—
559C2×D4—262no—
560C2×D4—262no—
561C2×D4—262no—
562C2×D4—261no—
563C2×D4—522no—
564C2×D4—524no—
565C2×D4—524no—
566C2×D4—522no—
567C2×D4—522no—
568C22×C4—24no—
569C22×C4—24no—
570C22×C4—24no—
571C22×C4—42no—
572C22×C4—42no—
573C22×C4—42no—
574C22×C4—42no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—42no—
581C22×C4—42no—
582C22×C4—261no—
583C22×C4—261no—
584C22×C4—261no—
585C22×C4—262no—
586C22×C4—262no—
587C22×C4—264no—
588C22×C4—524no—
589C22×C4—524no—
590C22×C4—524no—
591C22×C4—524no—
592C22×C4#610311yescharacteristic
593C22×C4#610311yescharacteristic
594C22×C4#610311yescharacteristic
595C22×C4#610311yescharacteristic
596C22×C4#610311yescharacteristic
597C22×C4#610311yescharacteristic
598C22×C4#610311yescharacteristic
599C22×C4#610311yescharacteristic
600C22×C4#610311yescharacteristic
601C22×C4#610311yescharacteristic
602C22×C4#610311yescharacteristic
603C22×C4#610311yescharacteristic
604C22×C4C2×C4×D1311yescharacteristic
605C22×C4C2×C4×D1311yescharacteristic
606C22×C4C2×C4×D1311yescharacteristic
607C22×C4C2×C4×D1311yescharacteristic
608C22×C4C2×C4×D1311yescharacteristic
609C22×C4C2×C4×D1311yescharacteristic
610C22×C4C2×D5211yescharacteristic
611C22×C4C2×D5211yescharacteristic
612C22×C4C2×D5211yescharacteristic
613C22×C4C2×C22⋊D1311yescharacteristic
614C22×C4C2×C22⋊D1311yescharacteristic
615C22×C4C2×C22⋊D1311yescharacteristic
616C22×C4C2×C22⋊D1311yescharacteristic
617C22×C4C2×C22⋊D1311yescharacteristic
618C22×C4C2×C22⋊D1311yescharacteristic
619C22×C4C23×D1311yescharacteristic
620M16—44no—
621M16—44no—
622C2×C8—24no—
623C2×C8—44no—
624C4⋊C4—132no—
625C4⋊C4—132no—
626C4⋊C4—261no—
627C4⋊C4—261no—
628C4⋊C4—262no—
629C4⋊C4—262no—
630C4⋊C4—262no—
631C4⋊C4—262no—
632C4⋊C4—524no—
633C4⋊C4—524no—
634C22⋊C4—262no—
635C22⋊C4—262no—
636C22⋊C4—262no—
637C22⋊C4—262no—
638C22⋊C4—262no—
639C22⋊C4—262no—
640C22⋊C4—262no—
641C22⋊C4—262no—
642C22⋊C4—262no—
643C22⋊C4—262no—
644C22⋊C4—524no—
645C22⋊C4—524no—
646C42—262no—
647C42—262no—
648C13#1759211yescharacteristic, complemented, Sylow
649C23—21no—
650C23—21no—
651C23—22no—
652C23—22no—
653C23—21no—
654C23—21no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—48no—
672C23—48no—
673C23—262no—
674C23—522no—
675C23—522no—
676C23—522no—
677C23#8816212yes—
678C23#8816312yes—
679C23C2×#610311yescharacteristic
680C23C2×#610311yescharacteristic
681C23C2×#610311yescharacteristic
682C23C2×#610311yescharacteristic
683C23C2×#610311yescharacteristic
684C23C2×#610311yescharacteristic
685C23C22×D5211yescharacteristic
686Q8—522no—
687Q8—522no—
688D4—522no—
689D4—524no—
690D4—524no—
691D4—522no—
692D4—522no—
693D4—524no—
694D4—524no—
695D4—524no—
696D4—522no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—262no—
725C2×C4—262no—
726C2×C4—262no—
727C2×C4—524no—
728C2×C4—522no—
729C2×C4—522no—
730C2×C4—522no—
731C2×C4—524no—
732C2×C4—524no—
733C2×C4—524no—
734C2×C4—524no—
735C2×C4—1048no—
736C2×C4#8804614yes—
737C2×C4C2×#610311yescharacteristic
738C2×C4C2×#610311yescharacteristic
739C2×C4C2×#610311yescharacteristic
740C2×C4C2×#610311yescharacteristic
741C2×C4C2×#610311yescharacteristic
742C2×C4C2×#610311yescharacteristic
743C2×C4C22×C4×D1311yescharacteristic
744C2×C4C22×C22⋊D1311yescharacteristic
745C8—44no—
746C22—24no—
747C22—24no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—21no—
755C22—21no—
756C22—21no—
757C22—21no—
758C22—21no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—42no—
765C22—42no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—42no—
771C22—42no—
772C22—522no—
773C22—522no—
774C22—522no—
775C22—1044no—
776C22C2×#8804612yes—
777C22#1171879412yes—
778C22#1171879412yes—
779C22#1171880012yes—
780C22C2×#8816211yescharacteristic
781C22C2×#8816311yescharacteristic
782C22C22×#610311yescharacteristic
783C4—21no—
784C4—21no—
785C4—21no—
786C4—21no—
787C4—21no—
788C4—21no—
789C4—522no—
790C4—522no—
791C4—522no—
792C4—1044no—
793C4C2×#8804612yes—
794C4C2×#8804612yes—
795C2—21no—
796C2—21no—
797C2—22no—
798C2—22no—
799C2—22no—
800C2—22no—
801C2—41no—
802C2—41no—
803C2—1042no—
804C2C22×#8804611yescharacteristic
805C2C2×#1171879411yescharacteristic
806C2C2×#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#17592
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×#11718873C2semidirect
3. #13113409C2semidirect
4. #13113405C2semidirect
5. #13113380C2semidirect
6. #13113341C2semidirect
7. C2×C13×#407C2semidirect
9. C22×#6127C4semidirect
17. #11719496C4semidirect
18. #11719496C4semidirect
21. C2×#88184C4semidirect
26. C2×#88180C4semidirect
28. C2×#88178C4semidirect
32. C13×#407C22semidirect
33. C13×#407C22semidirect
39. #11718873C22semidirect
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
114. C2×C4⋊Dic13C2×C4semidirect
115. C2×C4⋊Dic13C2×C4semidirect
121. #88178C2×C4semidirect
122. #88178C2×C4semidirect
247. C2×#407D13semidirect
374. #407C2×D13semidirect
375. #407C2×D13semidirect
648. C13#17592semidirect

Maximal subgroups

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

subgroupindex
C2×#117194962
C2×#117188732
#131134092
#131134052
#131133802
#131133412
C2×C13×#4072
#1759213