Finite Group Databasebeta

← #15890425

Subgroups — #15890425

Order 3328.

1650 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11718656C211yesmaximal, characteristic, complemented
2C2×#11718893C211yesmaximal, characteristic, complemented
3C2×#11718893C211yesmaximal, characteristic, complemented
4C2×#11718868C211yesmaximal, characteristic, complemented
5C2×#11718873C211yesmaximal, characteristic, complemented
6#13116036C212yesmaximal, complemented
7#13116029C212yesmaximal, complemented
8#13116022C212yesmaximal, complemented
9#13116015C212yesmaximal, complemented
10#13114557C211yesmaximal, characteristic, complemented
11C2×C13×#525C211yesmaximal, characteristic
12C22×C13×#41C2211yescharacteristic
13C24×C4×C13C2211yescharacteristic
14C13×#525—24no—
15C13×#525—24no—
16C2×C13×#123—21no—
17C2×C13×C22⋊Q8C2211yescharacteristic
18C2×C13×C22⋊Q8C2211yescharacteristic
19C2×C13×#121C2211yescharacteristic
20C2×C13×#121C2211yescharacteristic
21C2×C13×#120—21no—
22C2×C4×D4×C13—21no—
23C2×C4×D4×C13—21no—
24C2×C13×#117C2211yescharacteristic
25C22×C22⋊Dic13—21no—
26C22×C4⋊Dic13C2211yescharacteristic
27C22×C4⋊Dic13C2211yescharacteristic
28C22×#6099C2211yescharacteristic
29C22×#6099C2211yescharacteristic
30#11718893—24no—
31#11718893—24no—
32C2×#88075C2212yescomplemented
33C2×#88075C2212yescomplemented
34C2×#88072C2212yescomplemented
35C2×#88072C2212yescomplemented
36#11718873—21no—
37#11718873—21no—
38#11718873C2212yes—
39#11718873C2212yes—
40C2×#88071—21no—
41#11718868—24no—
42C2×C22⋊#1055C2212yes—
43C2×C22⋊#1055C2212yes—
44#11718656—24no—
45C2×#88048C2212yescomplemented
46C2×#88047C2212yescomplemented
47#11718121C2212yescomplemented
48#11718121C2212yescomplemented
49C25×C13D411yescharacteristic
50C2×C13×#41—22no—
51C2×C13×#41—22no—
52C2×C13×#41—22no—
53C2×C13×#41—22no—
54C2×C13×#41—22no—
55C2×C13×#41D414yes—
56C22×Q8×C13C2311yescharacteristic
57C22×D4×C13—21no—
58C22×D4×C13—21no—
59C22×D4×C13—21no—
60C22×D4×C13C2311yescharacteristic
61C23×C4×C13—21no—
62C23×C4×C13—22no—
63C23×C4×C13—22no—
64C23×C4×C13—22no—
65C23×C4×C13—22no—
66C23×C4×C13—22no—
67C23×C4×C13—22no—
68C23×C4×C13D411yescharacteristic
69C23×C4×C13D411yescharacteristic
70C23×C4×C13D411yescharacteristic
71C23×C4×C13C2311yescharacteristic
72C23×C4×C13C2311yescharacteristic
73C23×C4×C13C2311yescharacteristic
74C23×Dic13—21no—
75C23×Dic13—21no—
76C13×#123—28no—
77C13×C22⋊Q8—22no—
78C13×C22⋊Q8—22no—
79C13×C22⋊Q8—22no—
80C13×C22⋊Q8—22no—
81C13×#121—22no—
82C13×#121—22no—
83C13×#121—22no—
84C13×#121—22no—
85C13×#120—28no—
86C4×D4×C13—28no—
87C4×D4×C13—28no—
88C13×#117—22no—
89C13×#117D414yes—
90C2×C13×C4⋊C4—21no—
91C2×C13×C4⋊C4—21no—
92C2×C13×C4⋊C4C2311yescharacteristic
93C2×C13×C4⋊C4C2311yescharacteristic
94C2×C13×C22⋊C4—21no—
95C2×C13×C22⋊C4—21no—
96C2×C13×C22⋊C4—21no—
97C2×C13×C22⋊C4—21no—
98C2×C13×C22⋊C4—21no—
99C2×C42×C13—21no—
100C2×C22⋊Dic13—22no—
101C2×C22⋊Dic13—22no—
102C2×C22⋊Dic13—44no—
103C2×C4⋊Dic13—22no—
104C2×C4⋊Dic13—22no—
105C2×C4⋊Dic13—22no—
106C2×C4⋊Dic13—22no—
107C2×C4⋊Dic13—21no—
108C2×C4⋊Dic13—21no—
109C2×C4⋊Dic13C2312yes—
110C2×C4⋊Dic13C2312yes—
111C2×#6099—22no—
112C2×#6099—22no—
113C2×#6099—22no—
114C2×#6099—22no—
115C2×#6099—22no—
116C2×#6099D414yescomplemented
117C22×#1055C2312yes—
118C22×#1055C2312yes—
119#88075—24no—
120#88075—24no—
121#88072—24no—
122#88072—24no—
123#88071—22no—
124#88071—22no—
125C22⋊#1055—24no—
126C22⋊#1055—24no—
127#88048—24no—
128#88047—24no—
129#23482—131nomaximal, Sylow
130C24×C13—22no—
131C24×C13—22no—
132C24×C13—22no—
133C24×C13—22no—
134C24×C13—22no—
135C24×C13—21no—
136C24×C13—41no—
137C24×C13—41no—
138C24×C13C2×D411yescharacteristic
139C24×C13C2×D411yescharacteristic
140C24×C13C2×D411yescharacteristic
141C13×#41—28no—
142C13×#41—28no—
143C13×#41—44no—
144C13×#41—44no—
145C2×Q8×C13—21no—
146C2×Q8×C13—21no—
147C2×Q8×C13—21no—
148C2×Q8×C13—21no—
149C2×Q8×C13—21no—
150C2×Q8×C13C2×D412yes—
151C2×D4×C13—24no—
152C2×D4×C13—24no—
153C2×D4×C13—24no—
154C2×D4×C13—21no—
155C2×D4×C13—21no—
156C2×D4×C13—21no—
157C2×D4×C13—21no—
158C2×D4×C13—21no—
159C2×D4×C13—42no—
160C2×D4×C13—42no—
161C2×D4×C13—42no—
162C2×D4×C13—42no—
163C2×D4×C13—42no—
164C2×D4×C13—42no—
165C2×D4×C13C2×D412yes—
166C22×C4×C13—22no—
167C22×C4×C13—22no—
168C22×C4×C13—22no—
169C22×C4×C13—21no—
170C22×C4×C13—21no—
171C22×C4×C13—21no—
172C22×C4×C13—22no—
173C22×C4×C13—22no—
174C22×C4×C13—24no—
175C22×C4×C13—22no—
176C22×C4×C13—22no—
177C22×C4×C13—22no—
178C22×C4×C13—22no—
179C22×C4×C13—21no—
180C22×C4×C13—21no—
181C22×C4×C13—21no—
182C22×C4×C13—21no—
183C22×C4×C13—21no—
184C22×C4×C13—21no—
185C22×C4×C13—21no—
186C22×C4×C13—21no—
187C22×C4×C13—21no—
188C22×C4×C13—21no—
189C22×C4×C13—21no—
190C22×C4×C13—21no—
191C22×C4×C13—44no—
192C22×C4×C13—44no—
193C22×C4×C13—42no—
194C22×C4×C13—44no—
195C22×C4×C13—42no—
196C22×C4×C13—44no—
197C22×C4×C13C2×D412yes—
198C22×C4×C13C2×D411yescharacteristic
199C22×C4×C13C2×D411yescharacteristic
200C22×C4×C13C2×D411yescharacteristic
201C22×C4×C13C2×D412yes—
202C22×C4×C13C2×D412yes—
203C22×C4×C13#4112yes—
204C22×C4×C13#4112yes—
205C22×C4×C13#4112yes—
206C22×C4×C13C2411yescharacteristic
207C22×Dic13—22no—
208C22×Dic13—22no—
209C22×Dic13—42no—
210C22×Dic13—42no—
211C22×Dic13—42no—
212C22×Dic13—42no—
213C22×Dic13—42no—
214C22×Dic13—42no—
215C13×C4⋊C4—24no—
216C13×C4⋊C4—24no—
217C13×C4⋊C4—21no—
218C13×C4⋊C4—21no—
219C13×C4⋊C4C2×D412yes—
220C13×C4⋊C4C2×D412yes—
221C13×C22⋊C4—24no—
222C13×C22⋊C4—24no—
223C13×C22⋊C4—24no—
224C13×C22⋊C4—24no—
225C13×C22⋊C4—24no—
226C42×C13—24no—
227C22⋊Dic13—44no—
228C22⋊Dic13—44no—
229C4⋊Dic13—22no—
230C4⋊Dic13—22no—
231C4⋊Dic13—22no—
232C4⋊Dic13—22no—
233C4⋊Dic13—42no—
234C4⋊Dic13—42no—
235#6099—28no—
236#6099—44no—
237C2×#1055—22no—
238C2×#1055—22no—
239C2×#1055—22no—
240C2×#1055—22no—
241C2×#1055—22no—
242C2×#1055C2×D414yes—
243C2×#525D1311yescharacteristic
244C2×#428—131no—
245C2×#417—131no—
246C2×#417—131no—
247C2×#407—131no—
248C2×#380—131no—
249#2036—132no—
250#2035—132no—
251#2034—132no—
252#2033—132no—
253#1736—131no—
254C23×C13—21no—
255C23×C13—21no—
256C23×C13—21no—
257C23×C13—21no—
258C23×C13—28no—
259C23×C13—21no—
260C23×C13—21no—
261C23×C13—21no—
262C23×C13—21no—
263C23×C13—21no—
264C23×C13—21no—
265C23×C13—21no—
266C23×C13—21no—
267C23×C13—21no—
268C23×C13—21no—
269C23×C13—21no—
270C23×C13—21no—
271C23×C13—22no—
272C23×C13—44no—
273C23×C13—44no—
274C23×C13—44no—
275C23×C13—44no—
276C23×C13—44no—
277C23×C13—44no—
278C23×C13—41no—
279C23×C13—41no—
280C23×C13—41no—
281C23×C13—41no—
282C23×C13—41no—
283C23×C13—41no—
284C23×C13#12012yes—
285C23×C13#12112yes—
286C23×C13#12312yes—
287C23×C13AGL(1,ℤ/8)12yes—
288C23×C13#13712yes—
289C23×C13C22×D411yescharacteristic
290Q8×C13—22no—
291Q8×C13—22no—
292Q8×C13—41no—
293Q8×C13—41no—
294D4×C13—22no—
295D4×C13—22no—
296D4×C13—48no—
297D4×C13—48no—
298D4×C13—48no—
299D4×C13—41no—
300D4×C13—41no—
301C2×C4×C13—22no—
302C2×C4×C13—22no—
303C2×C4×C13—21no—
304C2×C4×C13—21no—
305C2×C4×C13—22no—
306C2×C4×C13—21no—
307C2×C4×C13—21no—
308C2×C4×C13—21no—
309C2×C4×C13—21no—
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—44no—
317C2×C4×C13—41no—
318C2×C4×C13—41no—
319C2×C4×C13—41no—
320C2×C4×C13—41no—
321C2×C4×C13—41no—
322C2×C4×C13—41no—
323C2×C4×C13—41no—
324C2×C4×C13—41no—
325C2×C4×C13—44no—
326C2×C4×C13—44no—
327C2×C4×C13—48no—
328C2×C4×C13#12012yes—
329C2×C4×C13#12114yes—
330C2×C4×C13#12114yes—
331C2×C4×C13#12112yes—
332C2×C4×C13#12314yes—
333C2×C4×C13#12312yes—
334C2×C4×C13#12414yes—
335C2×C4×C13C22×D411yescharacteristic
336C2×C4×C13C22×D411yescharacteristic
337C2×C4×C13C22×D411yescharacteristic
338C2×C4×C13C2×#4111yescharacteristic
339C2×C4×C13C2×#4111yescharacteristic
340C2×C4×C13C2×#4111yescharacteristic
341C2×Dic13—42no—
342C2×Dic13—42no—
343C2×Dic13—42no—
344C2×Dic13—42no—
345C2×Dic13—42no—
346C2×Dic13—42no—
347C2×Dic13—84no—
348C2×Dic13—84no—
349#1055—24no—
350#1055—42no—
351C22×#41C2×D1311yescharacteristic
352C24×C4C2×D1311yescharacteristic
353C22×M16—131no—
354C22×M16—131no—
355#525—24no—
356#525—24no—
357C2×#123—21no—
358C2×C22⋊Q8C2×D1311yescharacteristic
359C2×C22⋊Q8C2×D1311yescharacteristic
360C2×#121C2×D1311yescharacteristic
361C2×#121C2×D1311yescharacteristic
362C2×#120—21no—
363C2×C4×D4—21no—
364C2×C4×D4—21no—
365C2×#117C2×D1311yescharacteristic
366C22×C4⋊C4—131no—
367C22×C4⋊C4—131no—
368C22×C22⋊C4—261no—
369#428—264no—
370C2×#107—132no—
371C2×#106—132no—
372#417—264no—
373#417—264no—
374C2×#103—132no—
375C2×#103—132no—
376C2×#102—132no—
377C2×#102—132no—
378#407—264no—
379C2×C22⋊C8—132no—
380C2×C22⋊C8—132no—
381#380—132no—
382#380—132no—
383#380—261no—
384#380—261no—
385C2×#95—261no—
386#340—132no—
387#340—132no—
388C22×C13—22no—
389C22×C13—22no—
390C22×C13—22no—
391C22×C13—22no—
392C22×C13—22no—
393C22×C13—22no—
394C22×C13—22no—
395C22×C13—22no—
396C22×C13—22no—
397C22×C13—22no—
398C22×C13—22no—
399C22×C13—22no—
400C22×C13—416no—
401C22×C13—41no—
402C22×C13—41no—
403C22×C13—41no—
404C22×C13—41no—
405C22×C13—41no—
406C22×C13—41no—
407C22×C13—41no—
408C22×C13—41no—
409C22×C13—42no—
410C22×C13—42no—
411C22×C13—42no—
412C22×C13—81no—
413C22×C13—81no—
414C22×C13—81no—
415C22×C13—81no—
416C22×C13#39414yes—
417C22×C13C2×#12011yescharacteristic
418C22×C13C2×#12111yescharacteristic
419C22×C13C2×#12311yescharacteristic
420C22×C13C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C13C2×#13711yescharacteristic
422C22×C13#57511yescharacteristic
423C22×C13#57511yescharacteristic
424C4×C13—41no—
425C4×C13—41no—
426C4×C13—42no—
427C4×C13—42no—
428C4×C13—42no—
429C4×C13#39414yes—
430C4×C13C2×#12111yescharacteristic
431C4×C13C2×#12111yescharacteristic
432C4×C13C2×#12311yescharacteristic
433C4×C13C2×#12411yescharacteristic
434Dic13—82no—
435Dic13—82no—
436C25C22⋊D1311yescharacteristic
437C2×#41—22no—
438C2×#41—22no—
439C2×#41—22no—
440C2×#41—22no—
441C2×#41—22no—
442C2×#41C22⋊D1314yes—
443C22×Q8C22×D1311yescharacteristic
444C22×D4—21no—
445C22×D4—21no—
446C22×D4—21no—
447C22×D4C22×D1311yescharacteristic
448C23×C4—22no—
449C23×C4—22no—
450C23×C4—22no—
451C23×C4—22no—
452C23×C4—21no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—261no—
456C23×C4—261no—
457C23×C4C22⋊D1311yescharacteristic
458C23×C4C22⋊D1311yescharacteristic
459C23×C4C22⋊D1311yescharacteristic
460C23×C4C22×D1311yescharacteristic
461C23×C4C22×D1311yescharacteristic
462C23×C4C22×D1311yescharacteristic
463C2×M16—134no—
464C2×M16—262no—
465C2×M16—262no—
466C2×M16—262no—
467C2×M16—262no—
468C2×M16—262no—
469C22×C8—132no—
470C22×C8—132no—
471#123—28no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—22no—
475C22⋊Q8—22no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—22no—
480#120—28no—
481C4×D4—28no—
482C4×D4—28no—
483#117—22no—
484#117C22⋊D1314yes—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—132no—
488C2×C4⋊C4—132no—
489C2×C4⋊C4—262no—
490C2×C4⋊C4—262no—
491C2×C4⋊C4—262no—
492C2×C4⋊C4—262no—
493C2×C4⋊C4—261no—
494C2×C4⋊C4—261no—
495C2×C4⋊C4C22×D1311yescharacteristic
496C2×C4⋊C4C22×D1311yescharacteristic
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4—262no—
503C2×C22⋊C4—262no—
504C2×C22⋊C4—524no—
505C2×C42—21no—
506#107—264no—
507#106—264no—
508#103—264no—
509#103—264no—
510#102—264no—
511#102—264no—
512C22⋊C8—264no—
513C22⋊C8—264no—
514#95—262no—
515#95—262no—
516C2×C13—24no—
517C2×C13—42no—
518C2×C13—42no—
519C2×C13—82no—
520C2×C13C2×#39411yescharacteristic
521C2×C13#300611yescharacteristic
522C2×C13#300711yescharacteristic
523C2×C13#305511yescharacteristic
524C2×C13#305611yescharacteristic
525C2×C13#309211yescharacteristic
526C2×C13#309311yescharacteristic
527C24—22no—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—21no—
533C24—41no—
534C24—41no—
535C24C2×C22⋊D1311yescharacteristic
536C24C2×C22⋊D1311yescharacteristic
537C24C2×C22⋊D1311yescharacteristic
538#41—28no—
539#41—28no—
540#41—44no—
541#41—44no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×C22⋊D1312yes—
548C2×D4—24no—
549C2×D4—24no—
550C2×D4—24no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—42no—
557C2×D4—42no—
558C2×D4—42no—
559C2×D4—42no—
560C2×D4—42no—
561C2×D4—42no—
562C2×D4C2×C22⋊D1312yes—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—44no—
589C22×C4—42no—
590C22×C4—44no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—42no—
594C22×C4—262no—
595C22×C4—262no—
596C22×C4—522no—
597C22×C4—522no—
598C22×C4—522no—
599C22×C4—522no—
600C22×C4—522no—
601C22×C4—522no—
602C22×C4D4×D1312yes—
603C22×C4#612912yes—
604C22×C4#612912yes—
605C22×C4#612912yes—
606C22×C4C2×C22⋊D1311yescharacteristic
607C22×C4C2×C22⋊D1311yescharacteristic
608C22×C4C2×C22⋊D1311yescharacteristic
609C22×C4C2×C22⋊D1312yes—
610C22×C4C2×C22⋊D1312yes—
611C22×C4C23×D1311yescharacteristic
612M16—268no—
613M16—524no—
614C2×C8—134no—
615C2×C8—262no—
616C2×C8—262no—
617C2×C8—262no—
618C2×C8—262no—
619C2×C8—262no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—262no—
625C4⋊C4—262no—
626C4⋊C4—262no—
627C4⋊C4—262no—
628C4⋊C4—522no—
629C4⋊C4—522no—
630C4⋊C4C2×C22⋊D1312yes—
631C4⋊C4C2×C22⋊D1312yes—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—524no—
638C22⋊C4—524no—
639C42—24no—
640C13#2348211yescharacteristic, complemented, Sylow
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—28no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—22no—
659C23—44no—
660C23—44no—
661C23—44no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23#8818912yes—
672C23#8819312yes—
673C23#8820312yes—
674C23#8820512yes—
675C23#8820712yes—
676C23C22×C22⋊D1311yescharacteristic
677Q8—22no—
678Q8—22no—
679Q8—41no—
680Q8—41no—
681D4—22no—
682D4—22no—
683D4—48no—
684D4—48no—
685D4—48no—
686D4—41no—
687D4—41no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—44no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—48no—
715C2×C4—522no—
716C2×C4—522no—
717C2×C4—522no—
718C2×C4—522no—
719C2×C4—522no—
720C2×C4—522no—
721C2×C4—1044no—
722C2×C4—1044no—
723C2×C4#8818914yes—
724C2×C4#8818912yes—
725C2×C4#8819014yes—
726C2×C4#8819214yes—
727C2×C4#8819314yes—
728C2×C4#8819312yes—
729C2×C4#8820712yes—
730C2×C4C2×D4×D1311yescharacteristic
731C2×C4C2×#612911yescharacteristic
732C2×C4C2×#612911yescharacteristic
733C2×C4C2×#612911yescharacteristic
734C2×C4C22×C22⋊D1311yescharacteristic
735C2×C4C22×C22⋊D1311yescharacteristic
736C8—264no—
737C8—522no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—416no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22#1171888314yes—
767C22C2×#8818911yescharacteristic
768C22C2×#8819311yescharacteristic
769C22C2×#8820311yescharacteristic
770C22#1171952711yescharacteristic
771C22#1171952711yescharacteristic
772C22C2×#8820511yescharacteristic
773C22C2×#8820711yescharacteristic
774C4—42no—
775C4—41no—
776C4—41no—
777C4—42no—
778C4—42no—
779C4—1042no—
780C4—1042no—
781C4#1171888314yes—
782C4C2×#8818911yescharacteristic
783C4C2×#8819011yescharacteristic
784C4C2×#8819211yescharacteristic
785C4C2×#8819311yescharacteristic
786C2—24no—
787C2—42no—
788C2—42no—
789C2—82no—
790C2C2×#1171888311yescharacteristic
791C2#1312408811yescharacteristic
792C2#1312409611yescharacteristic
793C2#1312445711yescharacteristic
794C2#1312446811yescharacteristic
795C2#1312475611yescharacteristic
796C2#1312476511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D13
commutator, cosocleC22×C4×C13C24
FrattiniC22×C4C23×D13
Fitting, prime radicalC2×C13×#525C2
socleC23×C13C22×D4
hypercenterC2×#525D13
hypocenterC13#23482
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#11718656C2semidirect
2. C2×#11718893C2semidirect
3. C2×#11718893C2semidirect
4. C2×#11718868C2semidirect
5. C2×#11718873C2semidirect
6. #13116036C2semidirect
7. #13116029C2semidirect
8. #13116022C2semidirect
9. #13116015C2semidirect
10. #13114557C2semidirect
32. C2×#88075C22semidirect
33. C2×#88075C22semidirect
34. C2×#88072C22semidirect
35. C2×#88072C22semidirect
45. C2×#88048C22semidirect
46. C2×#88047C22semidirect
47. #11718121C22semidirect
48. #11718121C22semidirect
116. C2×#6099D4semidirect
640. C13#23482semidirect

Maximal subgroups

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

subgroupindex
C2×#117186562
C2×#117188932
C2×#117188682
C2×#117188732
#131160362
#131160292
#131160222
#131160152
#131145572
C2×C13×#5252
#2348213