Finite Group Databasebeta

← #16728144

Subgroups — #16728144

Order 3328.

1882 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13128400C211yesmaximal, characteristic
2#13123994C214yesmaximal, complemented
3#13123992C212yesmaximal, complemented
4#13123981C212yesmaximal, complemented
5#13123973C214yesmaximal, complemented
6#13123962C212yesmaximal, complemented
7#13123945C212yesmaximal, complemented
8#13123779C211yesmaximal, characteristic, complemented
9#13123766C211yesmaximal, characteristic, complemented
10#13123571C211yesmaximal, characteristic, complemented
11#13123558C212yesmaximal, complemented
12#13123528C212yesmaximal, complemented
13C2×#11718495C211yesmaximal, characteristic, complemented
14#13123493C212yesmaximal, complemented
15#13123480C211yesmaximal, characteristic, complemented
16D13×#424C212yesmaximal, complemented
17C13×#2906C211yesmaximal, characteristic, complemented
18C2×C13×#131C2212yes—
19C4×C13×#41C2211yescharacteristic
20#11719533C2212yes—
21C2×M16×D13C2212yes—
22C22×C8×D13C2212yes—
23#11719289C411yescharacteristic
24#11719286C412yes—
25#11719284C411yescharacteristic
26#11719268C411yescharacteristic
27#11719263C412yes—
28#11719261C414yes—
29#11719256C411yescharacteristic
30#11719255C412yes—
31#11719246C412yes—
32#11719233C2214yes—
33D13×#117C2212yes—
34#11719184C2212yes—
35C4×#6127C2212yes—
36C2×C4×D52C2211yescharacteristic
37#11719175C2211yescharacteristic
38C13×#424C2212yes—
39C13×#424C2214yescomplemented
40C13×#423C2211yescharacteristic
41C13×#423C2212yescomplemented
42C2×C13×C4⋊C8C2211yescharacteristic
43C2×C13×C4⋊C8C2212yescomplemented
44#11718895C2211yescharacteristic
45#11718895C2211yescharacteristic
46#11718789C2214yescomplemented
47#11718788C2214yescomplemented
48#11718788C2214yescomplemented
49#11718788C2214yescomplemented
50#11718787C2212yes—
51#11718783C2212yes—
52#11718780C2212yes—
53#11718772C2214yescomplemented
54C8×C22⋊D13C2214yescomplemented
55C8×C22⋊D13C2214yescomplemented
56C8×C22⋊D13C2214yescomplemented
57C2×#88060C2212yes—
58#11718763C2212yes—
59#11718762C2212yes—
60#11718661C2212yescomplemented
61#11718661C2212yescomplemented
62#11718660C2211yescharacteristic
63#11718660C2211yescharacteristic
64#11718586C2212yescomplemented
65#11718586C2212yescomplemented
66C4×#6099C2211yescharacteristic
67C2×C4×#1055C2211yescharacteristic
68#11718501C2214yescomplemented
69#11718501C2214yescomplemented
70#11718500C2214yescomplemented
71#11718500C2214yescomplemented
72#11718499C2212yes—
73#11718497C2214yes—
74#11718496C2214yescomplemented
75#11718495C2211yescharacteristic
76#11718495C2212yes—
77#11718495C2211yescharacteristic
78#11718495C2212yes—
79#11718495C2211yescharacteristic
80#11718495C2211yescharacteristic
81#11718495C2212yes—
82#11718494C2214yescomplemented
83D13×C4⋊C8C2214yescomplemented
84D13×C4⋊C8C2214yescomplemented
85#11718492C2212yescomplemented
86#11718492C2212yescomplemented
87#11718492C2212yescomplemented
88#11718491C2212yescomplemented
89#11718491C2212yescomplemented
90#11718491C2212yescomplemented
91#11718489C2214yescomplemented
92C2×C13×#41C2311yescharacteristic
93C2×#6127C2×C412yes—
94C22×D52C2×C411yescharacteristic
95C22×C4×D13C2312yes—
96C13×#131—44no—
97C2×C13×M16C2312yes—
98C2×C13×M16C2314yes—
99C22×C8×C13C2312yes—
100C22×C8×C13C2314yes—
101C4×Q8×C13C2×C411yescharacteristic
102C4×Q8×C13C2×C411yescharacteristic
103C4×D4×C13C2×C412yes—
104C4×D4×C13C2×C411yescharacteristic
105C4×D4×C13C2×C412yes—
106C4×D4×C13C2×C411yescharacteristic
107C13×#117C2311yescharacteristic
108C13×#117C2312yes—
109C2×C42×C13C2311yescharacteristic
110C2×C42×C13C2312yes—
111#88200C2×C412yes—
112#88200C2×C412yes—
113#88192C2×C412yes—
114#88192C2×C412yes—
115#88191C2×C414yes—
116#88189C2×C414yes—
117#88184C2×C412yes—
118#88183C2×C414yes—
119C4×C22⋊D13C2×C414yes—
120C4×C22⋊D13C2314yes—
121C4×C22⋊D13C2314yes—
122C2×#6103C2×C412yes—
123#88180C2×C412yes—
124#88180C2312yes—
125C2×C4⋊Dic13C2×C411yescharacteristic
126#88178C2×C412yes—
127#88178C2×C412yes—
128#88178C2×C412yes—
129C2×#6099C2311yescharacteristic
130C2×#6099C2311yescharacteristic
131C22×#1055C2311yescharacteristic
132C22×#1055C2311yescharacteristic
133M16×D13—44no—
134C2×#6094C2314yes—
135C2×C8×D13—44no—
136C2×C8×D13C2312yes—
137C2×C8×D13C2312yes—
138C2×C8×D13C2312yes—
139C2×C8×D13C2312yes—
140C2×C8×D13C2314yes—
141#88152C2×C414yes—
142#88150C2×C414yes—
143#88148C2×C414yes—
144#88146C2×C412yes—
145#88146C2×C412yes—
146C4⋊C4×D13C2×C412yes—
147C4⋊C4×D13C2×C412yes—
148#88143C2×C414yes—
149#88139C2×C414yes—
150#88138C2×C414yes—
151#88137C2×C414yes—
152C22⋊C4×D13C2×C414yes—
153#88133C2×C414yes—
154#88131C2×C414yes—
155#88130C2×C414yes—
156#88129C2×C412yes—
157C4×D52C2×C411yescharacteristic
158C4×D52C2×C412yes—
159C4×D52C2×C411yescharacteristic
160C4×D52C2×C412yes—
161C4×D52C2311yescharacteristic
162C4×D52C2311yescharacteristic
163C4×D52C2312yes—
164#88126C2×C414yes—
165#88126C2314yes—
166C42×D13C2314yes—
167#88124C2×C412yes—
168#88124C2×C412yes—
169#88123C2×C411yescharacteristic
170#88123C2×C411yescharacteristic
171C4×Dic26C2×C412yes—
172C4×Dic26C2312yes—
173C4×Dic26C2312yes—
174C13×C4⋊C8C2311yescharacteristic
175C13×C4⋊C8C2311yescharacteristic
176C13×C4⋊C8C2312yes—
177C13×C4⋊C8C2312yes—
178C13×C4⋊C8C2314yes—
179C13×C4⋊C8C2312yes—
180C13×C4⋊C8C2314yes—
181C22⋊#1055C2312yes—
182C22⋊#1055C2312yes—
183C22⋊#1055C2312yes—
184C22⋊#1055C2312yes—
185#88060C2312yes—
186#88060C2314yes—
187#88060C2312yes—
188#88060C2312yes—
189#88060C2312yes—
190#88060C2314yes—
191#88055C2314yes—
192#88055C2314yes—
193#88054C2314yes—
194#88054C2314yes—
195#88054C2314yes—
196#88054C2314yes—
197C8×Dic13C2314yes—
198C8×Dic13C2314yes—
199C4⋊#1055C2312yes—
200C4⋊#1055C2312yes—
201C4⋊#1055C2312yes—
202C4⋊#1055C2312yes—
203#88043C2312yes—
204C4×#1055C2311yescharacteristic
205C4×#1055C2311yescharacteristic
206C4×#1055C2311yescharacteristic
207C4×#1055C2312yes—
208C4×#1055C2311yescharacteristic
209#60271—131nomaximal, Sylow
210C23×D13C22×C412yes—
211C13×#41—22no—
212C13×#41—22no—
213C2×Q8×C13C22×C411yescharacteristic
214C2×D4×C13C22×C412yes—
215C2×D4×C13C22×C411yescharacteristic
216C22×C4×C13C22×C411yescharacteristic
217C22×C4×C13C22×C412yes—
218C22×C4×C13C22×C411yescharacteristic
219C22×C4×C13C22×C412yes—
220C22×C4×C13C2412yes—
221C22×C4×C13C2411yescharacteristic
222C2×C22⋊D13C22×C414yes—
223C2×C22⋊D13C22×C414yes—
224C22×Dic13C22×C412yes—
225#6127—28no—
226C2×D52—24no—
227C2×D52C22×C411yescharacteristic
228C2×D52C22×C412yes—
229C2×D52C22×C411yescharacteristic
230C2×C4×D13—24no—
231C2×C4×D13—24no—
232C2×C4×D13C22×C414yes—
233C2×C4×D13C22×C412yes—
234C2×C4×D13C22×C412yes—
235C2×C4×D13C22×C414yes—
236C2×C4×D13C2412yes—
237C2×C4×D13C2412yes—
238C2×Dic26C22×C412yes—
239C2×Dic26C22×C412yes—
240C13×M16—24no—
241C13×M16—44no—
242C2×C8×C13—24no—
243C2×C8×C13—44no—
244C2×C8×C13C2412yes—
245C2×C8×C13C2412yes—
246C2×C8×C13C2414yes—
247C13×C4⋊C4C22×C412yes—
248C13×C4⋊C4C22×C411yescharacteristic
249C13×C4⋊C4C22×C411yescharacteristic
250C13×C4⋊C4C22×C412yes—
251C13×C22⋊C4C22×C412yes—
252C13×C22⋊C4C22×C412yes—
253C13×C22⋊C4C22×C412yes—
254C42×C13C22×C412yes—
255C42×C13C22×C411yescharacteristic
256C42×C13C22×C411yescharacteristic
257C42×C13C22×C412yes—
258C42×C13C2411yescharacteristic
259C42×C13C2411yescharacteristic
260C42×C13C2412yes—
261C22⋊Dic13C22×C414yes—
262C22⋊Dic13C22×C414yes—
263C22⋊Dic13C22×C414yes—
264#6103C22×C412yes—
265#6103C22×C414yes—
266#6103C22×C414yes—
267#6103C22×C414yes—
268#6103C22×C412yes—
269#6103C22×C412yes—
270#6103C22×C412yes—
271#6103C22×C414yes—
272C4⋊Dic13C22×C411yescharacteristic
273C4⋊Dic13C22×C412yes—
274C4⋊Dic13C22×C412yes—
275C4⋊Dic13C22×C412yes—
276C4⋊Dic13C22×C412yes—
277C4⋊Dic13C22×C411yescharacteristic
278C4⋊Dic13C22×C412yes—
279#6101C22×C414yes—
280#6101C22×C414yes—
281#6101C22×C414yes—
282#6101C22×C414yes—
283#6101C22×C414yes—
284#6101C22×C414yes—
285C4×Dic13C22×C414yes—
286C4×Dic13C22×C414yes—
287C4×Dic13C2414yes—
288#6099—22no—
289#6099—22no—
290C2×#1055—22no—
291C2×#1055—22no—
292C2×#1055C2411yescharacteristic
293C2×#1055C2411yescharacteristic
294C2×#1055C2412yes—
295C2×#1055C2411yescharacteristic
296C2×#1055C2411yescharacteristic
297C2×#1055C2412yes—
298#6094—44no—
299C8×D13—42no—
300C8×D13—42no—
301C8×D13—42no—
302C8×D13—42no—
303C8×D13—44no—
304#3475—131no—
305#2994—134no—
306#2994—132no—
307#2993—132no—
308#2992—134no—
309#2990—132no—
310#2988—132no—
311#2962—131no—
312#2960—131no—
313D4×M16—131no—
314#2933—132no—
315#2929—132no—
316C2×C8×D4—131no—
317#2924—132no—
318#2922—131no—
319#2906D1311yescharacteristic, complemented
320C2×#424—132no—
321C23×C13C23×C412yes—
322C23×C13C23×C411yescharacteristic
323C22×D13—24no—
324C22×D13—24no—
325C22×D13—42no—
326C22×D13C23×C412yes—
327C22×D13C23×C412yes—
328Q8×C13—22no—
329D4×C13—24no—
330D4×C13—22no—
331C2×C4×C13—22no—
332C2×C4×C13—24no—
333C2×C4×C13—22no—
334C2×C4×C13—22no—
335C2×C4×C13—41no—
336C2×C4×C13—42no—
337C2×C4×C13C23×C412yes—
338C2×C4×C13C23×C412yes—
339C2×C4×C13C23×C411yescharacteristic
340C2×C4×C13C23×C411yescharacteristic
341C2×C4×C13C23×C412yes—
342C2×C4×C13C23×C411yescharacteristic
343C2×C4×C13C23×C411yescharacteristic
344C2×C4×C13C23×C411yescharacteristic
345C2×C4×C13H(5,𝔽2)12yes—
346C2×C4×C132−1+412yes—
347C2×C4×C13C2511yescharacteristic
348C22⋊D13—28no—
349C22⋊D13—44no—
350C2×Dic13—24no—
351C2×Dic13C23×C412yes—
352C2×Dic13C23×C414yes—
353C2×Dic13C23×C414yes—
354C2×Dic13C23×C412yes—
355D52—24no—
356D52—22no—
357D52#13114yescomplemented
358C4×D13—28no—
359C4×D13—24no—
360C4×D13—24no—
361C4×D13—22no—
362C4×D13—22no—
363C4×D13—22no—
364C4×D13—22no—
365C4×D13—44no—
366Dic26—24no—
367Dic26—42no—
368C8×C13—22no—
369C8×C13—22no—
370C8×C13—24no—
371#1055—21no—
372#1055—21no—
373#1055—22no—
374#1055—21no—
375#1055—21no—
376#1055—22no—
377C2×#131C2×D1312yes—
378C22×M16—132no—
379C23×C8—132no—
380#556—131no—
381#555—131no—
382#554—131no—
383#553—132no—
384#552—132no—
385#552—132no—
386#551—134no—
387#547—131no—
388#546—132no—
389#533—131no—
390#529—134no—
391#529—132no—
392#525—132no—
393C4×#41—132no—
394C4×#41C2×D1311yescharacteristic
395C2×C4×D4—131no—
396C2×#117—132no—
397#446—134no—
398#446—132no—
399#446—132no—
400#446—132no—
401C8×Q8—132no—
402C8×Q8—132no—
403C8×Q8—132no—
404#436—134no—
405#436—132no—
406#435—134no—
407#435—134no—
408#435—134no—
409#435—134no—
410#435—134no—
411C8×D4—134no—
412C8×D4—134no—
413C8×D4—134no—
414C8×D4—131no—
415C8×D4—131no—
416C8×D4—132no—
417C8×D4—131no—
418C8×D4—131no—
419C8×D4—132no—
420C8×D4—132no—
421#433—132no—
422#433—132no—
423#433—134no—
424#433—134no—
425#432—134no—
426#431—132no—
427#431—132no—
428#431—134no—
429#424—132no—
430#424—132no—
431#424—131no—
432#424—131no—
433#424—134no—
434#424—134no—
435#424C2×D1312yes—
436#424C2×D1314yescomplemented
437#423C2×D1311yescharacteristic
438#423C2×D1312yescomplemented
439C2×C4⋊C8—134no—
440C2×C4⋊C8—134no—
441C2×C4⋊C8C2×D1311yescharacteristic
442C2×C4⋊C8C2×D1312yescomplemented
443#408—131no—
444#408—131no—
445#407—132no—
446C2×C22⋊C8—132no—
447#405—132no—
448#405—132no—
449C4×M16—131no—
450C2×C4×C8—131no—
451C22×C13—21no—
452C22×C13—21no—
453C22×C13—22no—
454C22×C13—22no—
455C22×C13—22no—
456C22×C13#52012yes—
457C22×C13C24×C411yescharacteristic
458C2×D13—22no—
459C2×D13—22no—
460C2×D13—22no—
461C2×D13—22no—
462C2×D13—22no—
463C2×D13—48no—
464C2×D13C2×#13114yes—
465C4×C13—22no—
466C4×C13—22no—
467C4×C13—21no—
468C4×C13—21no—
469C4×C13—22no—
470C4×C13—21no—
471C4×C13#52012yes—
472C4×C13C2×#13112yes—
473C4×C13C2×H(5,𝔽2)11yescharacteristic
474C4×C13C2×2−1+411yescharacteristic
475Dic13—22no—
476Dic13—22no—
477Dic13—24no—
478Dic13—24no—
479C2×#41—132no—
480C2×#41C22×D1311yescharacteristic
481C22×D4—131no—
482C23×C4—132no—
483#131—44no—
484C2×M16—131no—
485C2×M16—131no—
486C2×M16—134no—
487C2×M16—524no—
488C2×M16C22×D1312yes—
489C2×M16C22×D1314yes—
490C22×C8—131no—
491C22×C8—131no—
492C22×C8—132no—
493C22×C8—132no—
494C22×C8—132no—
495C22×C8—132no—
496C22×C8—134no—
497C22×C8—524no—
498C22×C8C22×D1312yes—
499C22×C8C22×D1314yes—
500C4⋊Q8—131no—
501C4⋊Q8—131no—
502#126—134no—
503#126—134no—
504#126—134no—
505#125—134no—
506#125—132no—
507#125—132no—
508#124—134no—
509#124—132no—
510#123—134no—
511#123—134no—
512#123—134no—
513#123—134no—
514C22⋊Q8—132no—
515C22⋊Q8—132no—
516C22⋊Q8—132no—
517C22⋊Q8—132no—
518C22⋊Q8—132no—
519C22⋊Q8—134no—
520#121—132no—
521#121—132no—
522#121—132no—
523#121—134no—
524#120—134no—
525C4×Q8—132no—
526C4×Q8—132no—
527C4×Q8—132no—
528C4×Q8C4×D1311yescharacteristic
529C4×Q8C4×D1311yescharacteristic
530C4×D4—134no—
531C4×D4—134no—
532C4×D4—134no—
533C4×D4—131no—
534C4×D4—132no—
535C4×D4—131no—
536C4×D4—132no—
537C4×D4—131no—
538C4×D4—132no—
539C4×D4—131no—
540C4×D4C4×D1312yes—
541C4×D4C4×D1311yescharacteristic
542C4×D4C4×D1312yes—
543C4×D4C4×D1311yescharacteristic
544#117—132no—
545#117—132no—
546#117—132no—
547#117—132no—
548#117—134no—
549#117—134no—
550#117—134no—
551#117C22×D1311yescharacteristic
552#117C22×D1312yes—
553C2×C4⋊C4—131no—
554C2×C4⋊C4—132no—
555C2×C4⋊C4—132no—
556C2×C22⋊C4—132no—
557C2×C22⋊C4—134no—
558C2×C42—134no—
559C2×C42C22×D1311yescharacteristic
560C2×C42C22×D1312yes—
561C4⋊C8—134no—
562C4⋊C8—134no—
563C4⋊C8—134no—
564C4⋊C8—134no—
565C4⋊C8—132no—
566C4⋊C8—132no—
567C4⋊C8—132no—
568C4⋊C8—132no—
569C4⋊C8C22×D1314yes—
570C4⋊C8C22×D1314yes—
571C4⋊C8C22×D1311yescharacteristic
572C4⋊C8C22×D1311yescharacteristic
573C4⋊C8C22×D1312yes—
574C4⋊C8C22×D1312yes—
575C4⋊C8C22×D1312yes—
576C22⋊C8—132no—
577C22⋊C8—132no—
578C22⋊C8—132no—
579C22⋊C8—132no—
580C22⋊C8—132no—
581C22⋊C8—132no—
582C22⋊C8—132no—
583C22⋊C8—132no—
584C22⋊C8—134no—
585C22⋊C8—134no—
586#97—134no—
587#97—134no—
588#97—132no—
589C4×C8—134no—
590C4×C8—134no—
591C4×C8—131no—
592C4×C8—131no—
593C4×C8—131no—
594C4×C8—131no—
595C4×C8—132no—
596C2×C13—22no—
597C2×C13—42no—
598C2×C13C2×#52011yescharacteristic
599C2×C13C22×#13111yescharacteristic
600C2×C13#357311yescharacteristic
601D13—24no—
602D13—42no—
603C24—132no—
604#41—22no—
605#41—22no—
606#41—268no—
607C2×Q8—132no—
608C2×Q8—132no—
609C2×Q8C2×C4×D1311yescharacteristic
610C2×D4—134no—
611C2×D4—134no—
612C2×D4—131no—
613C2×D4—132no—
614C2×D4—131no—
615C2×D4—264no—
616C2×D4C2×C4×D1312yes—
617C2×D4C2×C4×D1311yescharacteristic
618C22×C4—132no—
619C22×C4—134no—
620C22×C4—132no—
621C22×C4—132no—
622C22×C4—132no—
623C22×C4—132no—
624C22×C4—134no—
625C22×C4—264no—
626C22×C4—264no—
627C22×C4C2×C4×D1311yescharacteristic
628C22×C4C2×C4×D1312yes—
629C22×C4C2×C4×D1311yescharacteristic
630C22×C4C2×C4×D1312yes—
631C22×C4C23×D1312yes—
632C22×C4C23×D1311yescharacteristic
633M16—24no—
634M16—44no—
635M16—262no—
636M16—262no—
637M16—524no—
638C2×C8—24no—
639C2×C8—44no—
640C2×C8—131no—
641C2×C8—132no—
642C2×C8—131no—
643C2×C8—131no—
644C2×C8—131no—
645C2×C8—132no—
646C2×C8—262no—
647C2×C8—262no—
648C2×C8—522no—
649C2×C8—522no—
650C2×C8—522no—
651C2×C8—522no—
652C2×C8—524no—
653C2×C8C23×D1312yes—
654C2×C8C23×D1314yes—
655C2×C8C23×D1312yes—
656C4⋊C4—131no—
657C4⋊C4—132no—
658C4⋊C4—132no—
659C4⋊C4—134no—
660C4⋊C4—134no—
661C4⋊C4—131no—
662C4⋊C4—132no—
663C4⋊C4—132no—
664C4⋊C4—134no—
665C4⋊C4—134no—
666C4⋊C4—134no—
667C4⋊C4—134no—
668C4⋊C4—132no—
669C4⋊C4C2×C4×D1311yescharacteristic
670C4⋊C4C2×C4×D1311yescharacteristic
671C4⋊C4C2×C4×D1312yes—
672C4⋊C4C2×C4×D1312yes—
673C22⋊C4—134no—
674C22⋊C4—134no—
675C22⋊C4—134no—
676C22⋊C4—132no—
677C22⋊C4—134no—
678C22⋊C4—134no—
679C22⋊C4—132no—
680C22⋊C4—132no—
681C22⋊C4—132no—
682C22⋊C4—134no—
683C22⋊C4—134no—
684C22⋊C4C2×C4×D1312yes—
685C22⋊C4C2×C4×D1312yes—
686C22⋊C4C2×C4×D1312yes—
687C42—134no—
688C42—134no—
689C42—134no—
690C42C2×C4×D1312yes—
691C42C2×C4×D1311yescharacteristic
692C42C2×C4×D1311yescharacteristic
693C42C2×C4×D1312yes—
694C42C23×D1311yescharacteristic
695C42C23×D1311yescharacteristic
696C42C23×D1312yes—
697C13#6027111yescharacteristic, complemented, Sylow
698C23—132no—
699C23—132no—
700C23—264no—
701C23—264no—
702C23—522no—
703C23C22×C4×D1312yes—
704C23C22×C4×D1311yescharacteristic
705Q8—22no—
706Q8—264no—
707Q8—522no—
708D4—24no—
709D4—22no—
710D4—134no—
711D4—264no—
712D4—268no—
713D4—262no—
714D4—524no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—41no—
721C2×C4—132no—
722C2×C4—134no—
723C2×C4—134no—
724C2×C4—132no—
725C2×C4—268no—
726C2×C4—264no—
727C2×C4—264no—
728C2×C4—264no—
729C2×C4—262no—
730C2×C4—262no—
731C2×C4—262no—
732C2×C4—262no—
733C2×C4—524no—
734C2×C4C22×C4×D1312yes—
735C2×C4C22×C4×D1312yes—
736C2×C4C22×C4×D1311yescharacteristic
737C2×C4C22×C4×D1312yes—
738C2×C4C22×C4×D1311yescharacteristic
739C2×C4C22×C4×D1311yescharacteristic
740C2×C4C22×C4×D1311yescharacteristic
741C2×C4C22×C4×D1311yescharacteristic
742C2×C4#8825112yes—
743C2×C4#8825412yes—
744C2×C4C24×D1311yescharacteristic
745C8—22no—
746C8—22no—
747C8—24no—
748C8—261no—
749C8—261no—
750C8—262no—
751C8—261no—
752C8—261no—
753C8—262no—
754C22—21no—
755C22—21no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—134no—
760C22—262no—
761C22—262no—
762C22—262no—
763C22—262no—
764C22—262no—
765C22—528no—
766C22#1171920912yes—
767C22C23×C4×D1311yescharacteristic
768C4—22no—
769C4—21no—
770C4—21no—
771C4—22no—
772C4—21no—
773C4—22no—
774C4—264no—
775C4—264no—
776C4—262no—
777C4—262no—
778C4#1171920912yes—
779C4D13×#13112yes—
780C4C2×#8825111yescharacteristic
781C4C2×#8825411yescharacteristic
782C2—22no—
783C2—42no—
784C2—264no—
785C2—522no—
786C2C2×#1171920911yescharacteristic
787C2C2×D13×#13111yescharacteristic
788C2#1312954911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D13
commutator, socleC22×C13C24×C4
FittingC13×#2906C2
prime radical#13128400C2
cosocleC2×C4×C13C25
hypercenter#2906D13
hypocenterC13#60271
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ #2906

Complements

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

NH ≅ G/Ntype
2. #13123994C2semidirect
3. #13123992C2semidirect
4. #13123981C2semidirect
5. #13123973C2semidirect
6. #13123962C2semidirect
7. #13123945C2semidirect
8. #13123779C2semidirect
9. #13123766C2semidirect
10. #13123571C2semidirect
11. #13123558C2semidirect
12. #13123528C2semidirect
13. C2×#11718495C2semidirect
14. #13123493C2semidirect
15. #13123480C2semidirect
16. D13×#424C2semidirect
17. C13×#2906C2semidirect
39. C13×#424C22semidirect
41. C13×#423C22semidirect
43. C2×C13×C4⋊C8C22semidirect
46. #11718789C22semidirect
47. #11718788C22semidirect
48. #11718788C22semidirect
49. #11718788C22semidirect
53. #11718772C22semidirect
54. C8×C22⋊D13C22semidirect
55. C8×C22⋊D13C22semidirect
56. C8×C22⋊D13C22semidirect
60. #11718661C22semidirect
61. #11718661C22semidirect
64. #11718586C22semidirect
65. #11718586C22semidirect
68. #11718501C22semidirect
69. #11718501C22semidirect
70. #11718500C22semidirect
71. #11718500C22semidirect
74. #11718496C22semidirect
82. #11718494C22semidirect
83. D13×C4⋊C8C22semidirect
84. D13×C4⋊C8C22semidirect
85. #11718492C22semidirect
86. #11718492C22semidirect
87. #11718492C22semidirect
88. #11718491C22semidirect
89. #11718491C22semidirect
90. #11718491C22semidirect
91. #11718489C22semidirect
319. #2906D13semidirect
357. D52#131semidirect
436. #424C2×D13semidirect
438. #423C2×D13semidirect
442. C2×C4⋊C8C2×D13semidirect
697. C13#60271semidirect

Maximal subgroups

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

subgroupindex
#131284002
#131239942
#131239922
#131239812
#131239732
#131239622
#131239452
#131237792
#131237662
#131235712
#131235582
#131235282
C2×#117184952
#131234932
#131234802
D13×#4242
C13×#29062
#6027113