Finite Group Databasebeta

← #15860739

Subgroups — #15860739

Order 3328.

1522 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719277C211yesmaximal, characteristic
2C2×#11718463C211yesmaximal, characteristic
3C2×D13×#103C211yesmaximal, characteristic
4C2×#11718369C211yesmaximal, characteristic
5#13117190C211yesmaximal, characteristic
6#13114668C211yesmaximal, characteristic, complemented
7#13114667C211yesmaximal, characteristic, complemented
8#13114665C211yesmaximal, characteristic, complemented
9C4×#88050C211yesmaximal, characteristic, complemented
10#103×Dic13C211yesmaximal, characteristic, complemented
11C4×#88075C211yesmaximal, characteristic, complemented
12#13114655C211yesmaximal, characteristic, complemented
13#13114554C211yesmaximal, characteristic
14#13114551C211yesmaximal, characteristic
15C13×#1763C211yesmaximal, characteristic, complemented
16C22×Q8×D13C2211yescharacteristic
17C2×C4×Q8×C13C2211yescharacteristic
18C2×Q8×Dic13C2211yescharacteristic
19C22×#6094C2211yescharacteristic
20C22×C8×D13C2211yescharacteristic
21#11719277—24no—
22#11719277C418yescomplemented
23C2×#88146—21no—
24C2×#88146C2211yescharacteristic
25C2×#88146C2211yescharacteristic
26C2×C4⋊C4×D13C2211yescharacteristic
27C2×#88141—21no—
28C2×#88141C2211yescharacteristic
29C2×#88126—21no—
30C2×#88126C2211yescharacteristic
31C2×C4×Dic26—21no—
32C2×C4×Dic26C2211yescharacteristic
33C2×C13×#103C2211yescharacteristic
34C2×C13×#103C2211yescharacteristic
35C2×C13×#97C2211yescharacteristic
36C4×C13×C4⋊C4C2211yescharacteristic
37C2×#88075C2211yescharacteristic
38C2×#88075C2211yescharacteristic
39C2×#88056C2211yescharacteristic
40C2×#88056C2211yescharacteristic
41C2×#88055C2211yescharacteristic
42C2×C8×Dic13C2211yescharacteristic
43C4⋊C4×Dic13C2211yescharacteristic
44C4⋊C4×Dic13C2211yescharacteristic
45C2×#88050C2211yescharacteristic
46C2×#88050C2211yescharacteristic
47C4×#6103—21no—
48C4×C4⋊Dic13C2211yescharacteristic
49C4×#6101—21no—
50C2×C4×#1055C2211yescharacteristic
51#11718463C418yescomplemented
52D13×#103C418yescomplemented
53#11718369—24no—
54#11718327—21no—
55#11718310—21no—
56C13×#340C2211yescharacteristic
57C13×#340C2211yescharacteristic
58#11718143C2211yescharacteristic
59#11718143C2211yescharacteristic
60#11718121C2211yescharacteristic
61#11718121C2211yescharacteristic
62#11718121C2211yescharacteristic
63#11718121C2211yescharacteristic
64C22×Q8×C13C2311yescharacteristic
65C2×Q8×D13—22no—
66C2×Q8×D13—22no—
67C2×Q8×D13—22no—
68C2×Q8×D13C2×C414yes—
69C2×Q8×D13C2×C414yes—
70C2×Q8×D13C2×C414yes—
71C22×C4×D13—21no—
72C22×C4×D13—21no—
73C22×C4×D13C2311yescharacteristic
74C22×Dic26—21no—
75C22×Dic26C2311yescharacteristic
76C22×C8×C13C2311yescharacteristic
77C22×C8×C13C2311yescharacteristic
78C4×Q8×C13—22no—
79C4×Q8×C13C2×C414yescomplemented
80C2×C13×C4⋊C4—21no—
81C2×C13×C4⋊C4C2311yescharacteristic
82C2×C13×C4⋊C4C2311yescharacteristic
83C2×C13×C4⋊C4C2311yescharacteristic
84C2×C42×C13—21no—
85C2×C42×C13—21no—
86C2×C42×C13C2311yescharacteristic
87Q8×Dic13—22no—
88Q8×Dic13C2×C414yescomplemented
89C2×#6103—21no—
90C2×#6103—21no—
91C2×#6103D411yescharacteristic
92C2×#6103D411yescharacteristic
93C2×C4⋊Dic13—21no—
94C2×C4⋊Dic13C2311yescharacteristic
95C2×C4⋊Dic13C2311yescharacteristic
96C2×C4⋊Dic13C2311yescharacteristic
97C2×#6101—21no—
98C2×#6101—21no—
99C2×#6101—21no—
100C2×#6101D411yescharacteristic
101C2×#6101D411yescharacteristic
102C2×C4×Dic13—21no—
103C2×C4×Dic13—21no—
104C2×C4×Dic13—21no—
105C2×C4×Dic13—21no—
106C2×C4×Dic13—21no—
107C2×C4×Dic13—21no—
108C2×C4×Dic13—21no—
109C2×C4×Dic13—21no—
110C2×C4×Dic13C2311yescharacteristic
111C22×#1055C2311yescharacteristic
112C22×#1055C2311yescharacteristic
113C2×#6094—22no—
114C2×#6094—22no—
115C2×#6094C2×C414yes—
116C2×C8×D13—22no—
117C2×C8×D13—22no—
118C2×C8×D13C2×C414yes—
119#88146—22no—
120#88146—22no—
121#88146—28no—
122#88146C2×C414yes—
123#88146C2×C414yes—
124C4⋊C4×D13—22no—
125C4⋊C4×D13C2×C414yes—
126#88141—28no—
127#88141—22no—
128#88141C2×C414yescomplemented
129#88126—28no—
130#88126C2×C414yes—
131#88126D414yes—
132C4×Dic26—22no—
133C4×Dic26—28no—
134C4×Dic26C2×C414yescomplemented
135C13×#103C2×C414yes—
136C13×#103C2×C414yescomplemented
137C13×#97—22no—
138C13×#95—21no—
139#88075C2×C414yes—
140#88075C2×C414yescomplemented
141#88071—21no—
142#88071—21no—
143#88071—21no—
144#88056C2×C414yes—
145#88056C2×C414yescomplemented
146#88055—22no—
147C8×Dic13—22no—
148#88050C2×C414yes—
149#88050C2×C414yescomplemented
150C4×#1055—22no—
151#20417—131nomaximal, Sylow
152C23×D13C2×D411yescharacteristic
153C2×Q8×C13—21no—
154C2×Q8×C13—21no—
155C2×Q8×C13—21no—
156C2×Q8×C13C22×C412yes—
157C2×Q8×C13C22×C412yes—
158C2×Q8×C13C22×C412yes—
159C22×C4×C13—21no—
160C22×C4×C13—21no—
161C22×C4×C13—21no—
162C22×C4×C13—21no—
163C22×C4×C13C2×D411yescharacteristic
164C22×C4×C13C2×D411yescharacteristic
165C22×C4×C13C2411yescharacteristic
166C22×Dic13—21no—
167C22×Dic13—21no—
168C22×Dic13—21no—
169C22×Dic13—21no—
170C22×Dic13C2×D411yescharacteristic
171C22×Dic13C2×D411yescharacteristic
172C22×Dic13C2×D411yescharacteristic
173Q8×D13—28no—
174Q8×D13—28no—
175Q8×D13—28no—
176Q8×D13C42116yescomplemented
177C2×C4×D13—24no—
178C2×C4×D13—24no—
179C2×C4×D13—24no—
180C2×C4×D13—24no—
181C2×C4×D13—81no—
182C2×C4×D13—81no—
183C2×C4×D13C22×C412yes—
184C2×C4×D13C22×C412yes—
185C2×C4×D13C22×C412yes—
186C2×C4×D13C2×D412yes—
187C2×C4×D13#4112yes—
188C2×C4×D13#4112yes—
189C2×Dic26—21no—
190C2×Dic26—21no—
191C2×Dic26—21no—
192C2×Dic26—24no—
193C2×Dic26—24no—
194C2×Dic26—24no—
195C2×Dic26C22×C412yes—
196C2×Dic26C22×C412yes—
197C2×Dic26C22×C412yes—
198C2×C8×C13—21no—
199C2×C8×C13—21no—
200C2×C8×C13—21no—
201C2×C8×C13—21no—
202C2×C8×C13C22×C412yes—
203C2×C8×C13C22×C412yes—
204C13×C4⋊C4—24no—
205C13×C4⋊C4—21no—
206C13×C4⋊C4—21no—
207C13×C4⋊C4—21no—
208C13×C4⋊C4C22×C412yes—
209C13×C4⋊C4C22×C412yes—
210C13×C4⋊C4C22×C412yes—
211C42×C13—24no—
212C42×C13—81no—
213C42×C13C22×C412yes—
214C42×C13C2×D412yes—
215#6103—24no—
216#6103—24no—
217#6103C22⋊C414yes—
218#6103C22⋊C414yes—
219C4⋊Dic13—21no—
220C4⋊Dic13—21no—
221C4⋊Dic13—21no—
222C4⋊Dic13—24no—
223C4⋊Dic13C22×C412yes—
224C4⋊Dic13C22×C412yes—
225C4⋊Dic13C22×C412yes—
226#6101—24no—
227#6101—24no—
228#6101—24no—
229#6101C22⋊C414yes—
230#6101C22⋊C414yes—
231C4×Dic13—24no—
232C4×Dic13—24no—
233C4×Dic13—24no—
234C4×Dic13—24no—
235C4×Dic13—24no—
236C4×Dic13—81no—
237C4×Dic13—81no—
238C4×Dic13—81no—
239C4×Dic13C22×C412yes—
240C4×Dic13C2×D412yes—
241C2×#1055—21no—
242C2×#1055—21no—
243C2×#1055—21no—
244C2×#1055—21no—
245C2×#1055C22×C412yes—
246C2×#1055C22×C412yes—
247#6094—28no—
248C8×D13—28no—
249C2×#519—131no—
250C2×#419—131no—
251C22×#103—131no—
252C2×#405—131no—
253#2274—131no—
254#1763—131no—
255#1763—131no—
256#1763—131no—
257#1763D1311yescharacteristic, complemented
258C4×#103—131no—
259C4×#103—131no—
260C4×#103—131no—
261C4×#103—131no—
262#1736—131no—
263#1735—131no—
264C23×C13C22×D411yescharacteristic
265C22×D13—21no—
266C22×D13—21no—
267C22×D13—21no—
268C22×D13—21no—
269C22×D13C2×C22⋊C412yes—
270C22×D13C4×D412yes—
271C22×D13C4×D412yes—
272Q8×C13—22no—
273Q8×C13—22no—
274Q8×C13—22no—
275Q8×C13C2×C4214yes—
276C2×C4×C13—22no—
277C2×C4×C13—22no—
278C2×C4×C13—22no—
279C2×C4×C13—21no—
280C2×C4×C13—21no—
281C2×C4×C13—21no—
282C2×C4×C13—21no—
283C2×C4×C13—22no—
284C2×C4×C13—22no—
285C2×C4×C13—22no—
286C2×C4×C13—41no—
287C2×C4×C13—41no—
288C2×C4×C13—41no—
289C2×C4×C13—41no—
290C2×C4×C13—41no—
291C2×C4×C13—41no—
292C2×C4×C13C2×C22⋊C412yes—
293C2×C4×C13C2×C22⋊C412yes—
294C2×C4×C13C23×C411yescharacteristic
295C2×C4×C13C23×C411yescharacteristic
296C2×C4×C13C23×C411yescharacteristic
297C2×C4×C13C22×D411yescharacteristic
298C2×C4×C13C2×#4111yescharacteristic
299C2×C4×C13C2×#4111yescharacteristic
300C2×Dic13—22no—
301C2×Dic13—22no—
302C2×Dic13—22no—
303C2×Dic13—21no—
304C2×Dic13—21no—
305C2×Dic13—21no—
306C2×Dic13—21no—
307C2×Dic13—22no—
308C2×Dic13—22no—
309C2×Dic13—22no—
310C2×Dic13—41no—
311C2×Dic13—41no—
312C2×Dic13—41no—
313C2×Dic13—41no—
314C2×Dic13—41no—
315C2×Dic13—41no—
316C2×Dic13C2×C22⋊C412yes—
317C2×Dic13C2×C22⋊C412yes—
318C2×Dic13C2×C22⋊C412yes—
319C2×Dic13C4×D412yes—
320C2×Dic13C4×D412yes—
321C4×D13—216no—
322C4×D13—84no—
323C4×D13C2×C4214yes—
324C4×D13#11714yes—
325C4×D13C4×D414yes—
326C4×D13C4×D414yes—
327Dic26—22no—
328Dic26—22no—
329Dic26—22no—
330Dic26—216no—
331Dic26C2×C4214yes—
332C8×C13—22no—
333C8×C13—22no—
334#1055—22no—
335#1055—22no—
336C23×Q8—131no—
337C22×M16—131no—
338C23×C8—131no—
339#519—138no—
340#519—264no—
341C2×C4×Q8—131no—
342C2×C4×Q8—131no—
343C2×C4×Q8—131no—
344C2×C4×Q8—261no—
345C2×C4×Q8—261no—
346C2×C4×Q8C2×D1311yescharacteristic
347C2×#117—131no—
348C2×#117—131no—
349C2×#117—131no—
350C2×#117—261no—
351C2×#117—261no—
352C22×C4⋊C4—131no—
353#419—138no—
354C2×#103—131no—
355C2×#103—131no—
356C2×#103—131no—
357C2×#103—131no—
358C2×#103—131no—
359C2×#103—131no—
360C2×#103—138no—
361C2×#103C2×D1311yescharacteristic
362C2×#103C2×D1311yescharacteristic
363#405—264no—
364C2×#97—131no—
365C2×#97C2×D1311yescharacteristic
366C2×C4×C8—131no—
367C2×C4×C8—131no—
368C4×C4⋊C4—131no—
369C4×C4⋊C4—131no—
370C4×C4⋊C4—131no—
371C4×C4⋊C4—261no—
372C4×C4⋊C4—261no—
373C4×C4⋊C4C2×D1311yescharacteristic
374C4×C22⋊C4—261no—
375C4×C22⋊C4—261no—
376#340—131no—
377#340—131no—
378#340—131no—
379#340—131no—
380#340—131no—
381#340—131no—
382#340C2×D1311yescharacteristic
383#340C2×D1311yescharacteristic
384C22×C13C22×C22⋊C411yescharacteristic
385C22×C13C2×C4×D411yescharacteristic
386C22×C13C2×C4×D411yescharacteristic
387C22×C13#57711yescharacteristic
388C22×C13#57711yescharacteristic
389C22×C13#57811yescharacteristic
390C22×C13#57811yescharacteristic
391C2×D13—22no—
392C2×D13—22no—
393C2×D13—22no—
394C2×D13—22no—
395C2×D13—22no—
396C2×D13—22no—
397C2×D13C4×C22⋊C414yes—
398C4×C13—22no—
399C4×C13—22no—
400C4×C13—24no—
401C4×C13—42no—
402C4×C13—42no—
403C4×C13—42no—
404C4×C13C22×C4211yescharacteristic
405C4×C13C2×#11711yescharacteristic
406C4×C13C2×C4×D411yescharacteristic
407C4×C13C2×C4×D411yescharacteristic
408Dic13—22no—
409Dic13—22no—
410Dic13—24no—
411Dic13—42no—
412Dic13—42no—
413Dic13—42no—
414Dic13C4×C22⋊C414yes—
415C22×Q8—134no—
416C22×Q8—134no—
417C22×Q8—134no—
418C22×Q8—131no—
419C22×Q8—261no—
420C22×Q8—262no—
421C22×Q8—262no—
422C22×Q8—262no—
423C22×Q8C22×D1311yescharacteristic
424C23×C4—131no—
425C23×C4—261no—
426C23×C4—261no—
427C2×M16—134no—
428C2×M16—262no—
429C2×M16—262no—
430C22×C8—131no—
431C22×C8—131no—
432C22×C8—134no—
433C22×C8—262no—
434C22×C8—262no—
435C22×C8C22×D1311yescharacteristic
436C22×C8C22×D1311yescharacteristic
437C4×Q8—22no—
438C4×Q8—134no—
439C4×Q8—134no—
440C4×Q8—134no—
441C4×Q8—268no—
442C4×Q8—262no—
443C4×Q8—262no—
444C4×Q8—268no—
445C4×Q8—262no—
446C4×Q8C4×D1314yescomplemented
447#117—134no—
448#117—134no—
449#117—134no—
450#117—134no—
451#117—268no—
452#117—268no—
453#117—262no—
454#117—262no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—131no—
457C2×C4⋊C4—131no—
458C2×C4⋊C4—131no—
459C2×C4⋊C4—131no—
460C2×C4⋊C4—131no—
461C2×C4⋊C4—134no—
462C2×C4⋊C4—262no—
463C2×C4⋊C4—261no—
464C2×C4⋊C4—261no—
465C2×C4⋊C4—261no—
466C2×C4⋊C4—261no—
467C2×C4⋊C4C22×D1311yescharacteristic
468C2×C4⋊C4C22×D1311yescharacteristic
469C2×C4⋊C4C22×D1311yescharacteristic
470C2×C22⋊C4—131no—
471C2×C22⋊C4—131no—
472C2×C22⋊C4—261no—
473C2×C22⋊C4—261no—
474C2×C42—21no—
475C2×C42—21no—
476C2×C42—131no—
477C2×C42—261no—
478C2×C42—261no—
479C2×C42—261no—
480C2×C42—261no—
481C2×C42—261no—
482C2×C42—261no—
483C2×C42—261no—
484C2×C42—261no—
485C2×C42C22×D1311yescharacteristic
486#103—134no—
487#103—134no—
488#103—134no—
489#103—134no—
490#103—134no—
491#103—134no—
492#103C4×D1314yes—
493#103C4×D1314yescomplemented
494#97—22no—
495#97—262no—
496C4×C8—262no—
497C4×C8—262no—
498#95—21no—
499#95—261no—
500#95—261no—
501#95—261no—
502C2×C13C2×C4×C22⋊C411yescharacteristic
503C2×C13#289811yescharacteristic
504C2×C13#289811yescharacteristic
505C2×C13#294711yescharacteristic
506C2×C13#294711yescharacteristic
507C2×C13#294911yescharacteristic
508C2×C13#295011yescharacteristic
509D13—24no—
510C24—131no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—1316no—
515C2×Q8—132no—
516C2×Q8—132no—
517C2×Q8—132no—
518C2×Q8—264no—
519C2×Q8—264no—
520C2×Q8—264no—
521C2×Q8—268no—
522C2×Q8—268no—
523C2×Q8—268no—
524C2×Q8—261no—
525C2×Q8—261no—
526C2×Q8—261no—
527C2×Q8C2×C4×D1312yes—
528C2×Q8C2×C4×D1312yes—
529C2×Q8C2×C4×D1312yes—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—131no—
535C22×C4—132no—
536C22×C4—132no—
537C22×C4—132no—
538C22×C4—132no—
539C22×C4—132no—
540C22×C4—132no—
541C22×C4—131no—
542C22×C4—131no—
543C22×C4—264no—
544C22×C4—264no—
545C22×C4—264no—
546C22×C4—264no—
547C22×C4—261no—
548C22×C4—261no—
549C22×C4—261no—
550C22×C4—261no—
551C22×C4—1041no—
552C22×C4—1041no—
553C22×C4D4×D1311yescharacteristic
554C22×C4D4×D1311yescharacteristic
555C22×C4C23×D1311yescharacteristic
556M16—268no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—132no—
562C2×C8—132no—
563C2×C8—268no—
564C2×C8—261no—
565C2×C8—261no—
566C2×C8—261no—
567C2×C8—261no—
568C2×C8C2×C4×D1312yes—
569C2×C8C2×C4×D1312yes—
570C4⋊C4—24no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—134no—
575C4⋊C4—134no—
576C4⋊C4—132no—
577C4⋊C4—132no—
578C4⋊C4—132no—
579C4⋊C4—264no—
580C4⋊C4—264no—
581C4⋊C4—264no—
582C4⋊C4—264no—
583C4⋊C4—261no—
584C4⋊C4—261no—
585C4⋊C4—261no—
586C4⋊C4C2×C4×D1312yes—
587C4⋊C4C2×C4×D1312yes—
588C4⋊C4C2×C4×D1312yes—
589C22⋊C4—134no—
590C22⋊C4—134no—
591C22⋊C4—264no—
592C22⋊C4—264no—
593C42—24no—
594C42—81no—
595C42—132no—
596C42—132no—
597C42—264no—
598C42—264no—
599C42—264no—
600C42—264no—
601C42—264no—
602C42—1041no—
603C42—1041no—
604C42—1041no—
605C42C2×C4×D1312yes—
606C42D4×D1312yes—
607C13#2041711yescharacteristic, complemented, Sylow
608C23—132no—
609C23—132no—
610C23—132no—
611C23—261no—
612C23—261no—
613C23—261no—
614C23—261no—
615C23C2×D4×D1311yescharacteristic
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—134no—
620Q8—2616no—
621Q8—262no—
622Q8—262no—
623Q8—262no—
624Q8C42×D1314yes—
625C2×C4—22no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—132no—
642C2×C4—132no—
643C2×C4—132no—
644C2×C4—134no—
645C2×C4—134no—
646C2×C4—134no—
647C2×C4—134no—
648C2×C4—132no—
649C2×C4—132no—
650C2×C4—2616no—
651C2×C4—262no—
652C2×C4—261no—
653C2×C4—261no—
654C2×C4—261no—
655C2×C4—261no—
656C2×C4—262no—
657C2×C4—262no—
658C2×C4—262no—
659C2×C4—262no—
660C2×C4—262no—
661C2×C4—521no—
662C2×C4—521no—
663C2×C4—521no—
664C2×C4—521no—
665C2×C4—521no—
666C2×C4—521no—
667C2×C4—1044no—
668C2×C4C22⋊C4×D1312yes—
669C2×C4C22⋊C4×D1312yes—
670C2×C4C22×C4×D1311yescharacteristic
671C2×C4C22×C4×D1311yescharacteristic
672C2×C4C22×C4×D1311yescharacteristic
673C2×C4C2×D4×D1311yescharacteristic
674C2×C4#41×D1311yescharacteristic
675C2×C4#41×D1311yescharacteristic
676C8—22no—
677C8—22no—
678C8—262no—
679C8—262no—
680C22—134no—
681C22—262no—
682C22—262no—
683C22—262no—
684C22—262no—
685C22—262no—
686C22—262no—
687C22C2×C22⋊C4×D1311yescharacteristic
688C22C4×D4×D1311yescharacteristic
689C22C4×D4×D1311yescharacteristic
690C22#1171948011yescharacteristic
691C22#1171948311yescharacteristic
692C22#1171948411yescharacteristic
693C22#1171948411yescharacteristic
694C4—22no—
695C4—22no—
696C4—24no—
697C4—42no—
698C4—42no—
699C4—42no—
700C4—134no—
701C4—262no—
702C4—262no—
703C4—264no—
704C4—522no—
705C4—522no—
706C4—522no—
707C4C2×C42×D1311yescharacteristic
708C4D13×#11711yescharacteristic
709C4C4×D4×D1311yescharacteristic
710C4C4×D4×D1311yescharacteristic
711C2—264no—
712C2C4×C22⋊C4×D1311yescharacteristic
713C2#1312336711yescharacteristic
714C2#1312336811yescharacteristic
715C2#1312367611yescharacteristic
716C2#1312367811yescharacteristic
717C2#1312369211yescharacteristic
718C2#1312370111yescharacteristic
subgroupG/H
centerC23C2×D4×D13
commutatorC4×C13C22×C42
FrattiniC22×C4C23×D13
FittingC13×#1763C2
socleC23×C13C22×D4
prime radicalC23×D13C2×D4
cosocleC22×C4×C13C24
hypercenter#1763D13
hypocenterC13#20417
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
6. #13114668C2semidirect
7. #13114667C2semidirect
8. #13114665C2semidirect
9. C4×#88050C2semidirect
10. #103×Dic13C2semidirect
11. C4×#88075C2semidirect
12. #13114655C2semidirect
15. C13×#1763C2semidirect
22. #11719277C4semidirect
51. #11718463C4semidirect
52. D13×#103C4semidirect
79. C4×Q8×C13C2×C4semidirect
88. Q8×Dic13C2×C4semidirect
128. #88141C2×C4semidirect
134. C4×Dic26C2×C4semidirect
136. C13×#103C2×C4semidirect
140. #88075C2×C4semidirect
145. #88056C2×C4semidirect
149. #88050C2×C4semidirect
176. Q8×D13C42semidirect
257. #1763D13semidirect
446. C4×Q8C4×D13semidirect
493. #103C4×D13semidirect
607. C13#20417semidirect

Maximal subgroups

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

subgroupindex
C2×#117192772
C2×#117184632
C2×D13×#1032
C2×#117183692
#131171902
#131146682
#131146672
#131146652
C4×#880502
#103×Dic132
C4×#880752
#131146552
#131145542
#131145512
C13×#17632
#2041713