Finite Group Databasebeta

← #16808939

Subgroups — #16808939

Order 3328.

1862 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13131793C212yesmaximal, complemented
2#13131789C212yesmaximal, complemented
3#13131777C214yesmaximal, complemented
4#13131767C212yesmaximal, complemented
5#13131761C212yesmaximal, complemented
6#13131758C212yesmaximal, complemented
7#13131755C212yesmaximal, complemented
8#13131633C212yesmaximal, complemented
9#13131580C212yesmaximal, complemented
10#13131555C214yesmaximal, complemented
11#13131531C212yesmaximal, complemented
12#13131512C211yesmaximal, characteristic, complemented
13#13131481C212yesmaximal, complemented
14C2×#11719129C211yesmaximal, characteristic, complemented
15#13128128C211yesmaximal, characteristic
16C22×#6122C2212yes—
17C2×#88238C2214yes—
18C13×#525C411yescharacteristic
19#11719537C411yescharacteristic
20#41×Dic13C2211yescharacteristic
21#11719496C411yescharacteristic
22C22×C4×Dic13C2211yescharacteristic
23#11719354C412yes—
24#11719354C2212yes—
25#11719329C411yescharacteristic
26#11719329C2211yescharacteristic
27#11719327C411yescharacteristic
28#11719327C2211yescharacteristic
29#11719305C411yescharacteristic
30#11719305C2211yescharacteristic
31#11719301C411yescharacteristic
32#11719301C2211yescharacteristic
33#11719291C412yes—
34#11719291C2212yes—
35#11719243C412yes—
36#11719243C412yes—
37C4×#6129C2212yes—
38C4×#6129C2212yes—
39#11719227C2211yescharacteristic
40#11719222C411yescharacteristic
41#11719169C2212yes—
42#11719158C2214yescomplemented
43#11719146C2214yes—
44#11719145C2214yes—
45#11719145C2214yes—
46#11719144C2214yes—
47#11719144C2214yes—
48#11719144C2214yescomplemented
49#11719130C2212yes—
50#11719130C2212yescomplemented
51#11719129C2212yes—
52#11719129C2211yescharacteristic
53#11719129C2212yes—
54#11719129C2212yes—
55#11719129C2211yescharacteristic
56#11719129C2211yescharacteristic
57#11719129C2211yescharacteristic
58#11719129C2212yescomplemented
59#11719128C2212yes—
60#11719125C2212yes—
61C2×#88112C2212yes—
62C4×#6122C2212yes—
63#11719119C2212yes—
64#11719119C2212yescomplemented
65C2×C4⋊#1057C2212yes—
66C2×C4⋊#1057C2212yescomplemented
67#11719079C2214yescomplemented
68#11719078C2214yescomplemented
69#11719078C2214yescomplemented
70#11719077C2214yescomplemented
71#11719075C2214yescomplemented
72#11719074C2214yescomplemented
73#11719068C2214yescomplemented
74#11719067C2214yes—
75#11719067C2214yescomplemented
76#11719066C2214yes—
77#11719066C2214yes—
78#11719066C2214yescomplemented
79#11719065C2214yes—
80#11719065C2214yes—
81#11719063C2214yescomplemented
82#11719062C2214yes—
83#11719054C2212yescomplemented
84#11719052C2212yescomplemented
85#11719051C2212yescomplemented
86D13⋊(C4⋊C8)C2212yescomplemented
87C2×C13×#41C2×C411yescharacteristic
88C23×C4×C13C2×C411yescharacteristic
89C23×Dic13C2×C411yescharacteristic
90C23×Dic13C2311yescharacteristic
91C2×#6129C2×C412yes—
92C2×#6129C2312yes—
93C2×#6127C2×C411yescharacteristic
94C2×#6122—44no—
95C2×#6122C2312yes—
96C2×#6122C2312yes—
97C2×#6122C2312yes—
98C2×#6122C2314yes—
99C2×#6122C2312yes—
100C2×#6122C2314yes—
101C22×#1057C2314yes—
102C22×#1057C2314yes—
103#88238—48no—
104C2×#6118C2314yes—
105C2×D13⋊C8C2314yes—
106C13×#123C2×C412yes—
107C13×C22⋊Q8C2×C411yescharacteristic
108C13×C22⋊Q8C2×C411yescharacteristic
109C13×#121C2×C411yescharacteristic
110C13×#121C2×C411yescharacteristic
111C13×#120C2×C412yes—
112C4×D4×C13C2×C412yes—
113C4×D4×C13C2×C412yes—
114C13×#117C2×C411yescharacteristic
115#88207C2×C412yes—
116#88201C2×C411yescharacteristic
117Q8×Dic13C2×C411yescharacteristic
118Q8×Dic13C2311yescharacteristic
119#88198C2×C411yescharacteristic
120#88194C2×C411yescharacteristic
121#88193C2×C412yes—
122#88193C2×C412yes—
123#88193C2×C412yes—
124#88193C2×C412yes—
125#88190C2×C411yescharacteristic
126#88189C2×C412yes—
127#88189C2×C412yes—
128D4×Dic13C2×C412yes—
129D4×Dic13C2×C412yes—
130D4×Dic13C2×C411yescharacteristic
131D4×Dic13C2312yes—
132D4×Dic13C2312yes—
133D4×Dic13C2311yescharacteristic
134#88184C2×C411yescharacteristic
135#88184C2×C411yescharacteristic
136#88183C2×C412yes—
137C4×C22⋊D13C2×C412yes—
138C4×C22⋊D13C2×C412yes—
139C4×C22⋊D13C2×C412yes—
140C4×C22⋊D13C2×C412yes—
141#88180C2×C411yescharacteristic
142#88180C2×C412yes—
143#88178C2×C411yescharacteristic
144#88178C2×C411yescharacteristic
145C2×C4×Dic13C2×C411yescharacteristic
146C2×C4×Dic13C2×C411yescharacteristic
147C2×C4×Dic13C2×C411yescharacteristic
148C2×C4×Dic13C2×C411yescharacteristic
149C2×C4×Dic13C2×C411yescharacteristic
150C2×C4×Dic13C2×C411yescharacteristic
151C2×C4×Dic13C2311yescharacteristic
152C2×C4×Dic13C2311yescharacteristic
153C2×C4×Dic13C2311yescharacteristic
154C2×C4×Dic13C2311yescharacteristic
155C2×C4×Dic13C2311yescharacteristic
156C2×C4×Dic13C2311yescharacteristic
157C2×C4×Dic13C2312yes—
158#88152C2×C412yes—
159#88152C2×C412yes—
160#88147C2×C411yescharacteristic
161#88147C2311yescharacteristic
162#88146C2×C412yes—
163#88146C2312yes—
164#88144C2×C411yescharacteristic
165#88144C2×C411yescharacteristic
166#88143C2×C412yes—
167#88143C2×C412yes—
168#88142C2×C411yescharacteristic
169#88142C2×C411yescharacteristic
170#88141C2×C411yescharacteristic
171#88141C2×C412yes—
172#88141C2311yescharacteristic
173#88141C2312yes—
174#88140C2×C412yes—
175#88140C2×C412yes—
176#88139C2×C412yes—
177#88139C2×C412yes—
178#88135C2×C412yes—
179#88135C2×C412yes—
180#88135C2×C412yes—
181#88135C2312yes—
182#88135C2312yes—
183#88135C2312yes—
184#88133C2×C412yes—
185#88133C2×C412yes—
186#88132C2×C412yes—
187#88132C2×C412yes—
188#88132C2×C412yes—
189#88132C2×C412yes—
190#88131C2×C412yes—
191#88131C2×C412yes—
192#88131C2312yes—
193#88131C2312yes—
194#88126C2×C412yes—
195C42×D13C2312yes—
196C4×Dic26C2×C412yes—
197C4×Dic26C2×C412yes—
198C22⋊#1057C2314yes—
199C22⋊#1057C2314yes—
200C22⋊#1057C2314yes—
201C22⋊#1057C2314yes—
202#88112C2314yes—
203#88112C2312yes—
204#88112C2314yes—
205#88112C2312yes—
206#88112C2312yes—
207#88112C2312yes—
208#88112C2314yes—
209#88111C2314yes—
210#88111C2314yes—
211#88110C2314yes—
212#88110C2314yes—
213#88110C2314yes—
214C4⋊#1057C2312yes—
215C4⋊#1057C2312yes—
216C4⋊#1057C2312yes—
217C4⋊#1057C2312yes—
218C4⋊#1057C2314yes—
219C4⋊#1057C2314yes—
220C4⋊#1057C2314yes—
221C4×#1057C2314yes—
222C4×#1057C2314yes—
223C4×#1057C2314yes—
224#60266—131nomaximal, Sylow
225C24×C13C22×C411yescharacteristic
226C13×#41—42no—
227C2×Q8×C13C22×C411yescharacteristic
228C2×D4×C13C22×C412yes—
229C2×D4×C13C22×C411yescharacteristic
230C2×D4×C13C22×C412yes—
231C2×D4×C13C22×C412yes—
232C22×C4×C13—42no—
233C22×C4×C13C22×C411yescharacteristic
234C22×C4×C13C22×C411yescharacteristic
235C22×C4×C13C22×C411yescharacteristic
236C22×C4×C13C22×C412yes—
237C22×C4×C13C22×C411yescharacteristic
238C22×C4×C13C22×C411yescharacteristic
239C22×C4×C13C22×C411yescharacteristic
240C2×C22⋊D13C22×C412yes—
241C2×C22⋊D13C22×C412yes—
242C2×C22⋊D13C22×C412yes—
243C2×C22⋊D13C22×C412yes—
244C2×C22⋊D13C22×C412yes—
245C22×Dic13—22no—
246C22×Dic13—22no—
247C22×Dic13—42no—
248C22×Dic13C22×C411yescharacteristic
249C22×Dic13C22×C411yescharacteristic
250C22×Dic13C22×C411yescharacteristic
251C22×Dic13C22×C411yescharacteristic
252C22×Dic13C22×C411yescharacteristic
253C22×Dic13C22×C411yescharacteristic
254C22×Dic13C22×C412yes—
255C22×Dic13C22×C411yescharacteristic
256C22×Dic13C22×C411yescharacteristic
257C22×Dic13C22×C411yescharacteristic
258C22×Dic13C2412yes—
259C22×Dic13C2411yescharacteristic
260C22×Dic13C2411yescharacteristic
261C22×Dic13C2411yescharacteristic
262#6129—24no—
263#6129—24no—
264#6129—44no—
265#6127—42no—
266C2×D52C22×C411yescharacteristic
267C2×C4×D13C22×C412yes—
268C2×C4×D13C22×C412yes—
269C2×C4×D13C2412yes—
270C2×Dic26C22×C412yes—
271C2×Dic26C22×C412yes—
272C2×Dic26C22×C411yescharacteristic
273#6122—24no—
274#6122—24no—
275#6122—44no—
276#6122—42no—
277#6122—44no—
278#6122—42no—
279C2×#1057—28no—
280C2×#1057—44no—
281C2×#1057C2414yes—
282C2×#1057C2414yes—
283C2×#1057C2414yes—
284C2×#1057C2414yes—
285#6118—44no—
286D13⋊C8—44no—
287C13×C4⋊C4C22×C411yescharacteristic
288C13×C4⋊C4C22×C412yes—
289C13×C4⋊C4C22×C411yescharacteristic
290C13×C4⋊C4C22×C412yes—
291C13×C22⋊C4C22×C412yes—
292C13×C22⋊C4C22×C412yes—
293C13×C22⋊C4C22×C412yes—
294C13×C22⋊C4C22×C412yes—
295C13×C22⋊C4C22×C412yes—
296C42×C13C22×C412yes—
297C22⋊Dic13C22×C412yes—
298C22⋊Dic13C22×C412yes—
299C22⋊Dic13C22×C412yes—
300C22⋊Dic13C22×C412yes—
301C22⋊Dic13C22×C412yes—
302C22⋊Dic13C22×C412yes—
303C22⋊Dic13C22×C412yes—
304#6103C22×C412yes—
305#6103C22×C412yes—
306#6103C22×C412yes—
307#6103C22×C412yes—
308#6103C22×C412yes—
309#6103C22×C412yes—
310C4⋊Dic13C22×C412yes—
311C4⋊Dic13C22×C412yes—
312C4⋊Dic13C22×C412yes—
313C4⋊Dic13C22×C412yes—
314C4⋊Dic13C22×C411yescharacteristic
315C4⋊Dic13C22×C411yescharacteristic
316#6101C22×C412yes—
317#6101C22×C412yes—
318#6101C22×C412yes—
319#6101C22×C412yes—
320#6101C22×C412yes—
321#6101C22×C412yes—
322#6101C22×C412yes—
323#6101C22×C412yes—
324#6101C22×C412yes—
325#6101C22×C412yes—
326C4×Dic13C22×C411yescharacteristic
327C4×Dic13C22×C411yescharacteristic
328C4×Dic13C22×C412yes—
329C4×Dic13C22×C412yes—
330C4×Dic13C22×C411yescharacteristic
331C4×Dic13C22×C411yescharacteristic
332C4×Dic13C22×C412yes—
333C4×Dic13C22×C411yescharacteristic
334C4×Dic13C22×C411yescharacteristic
335C4×Dic13C22×C411yescharacteristic
336C4×Dic13C22×C411yescharacteristic
337C4×Dic13C22×C411yescharacteristic
338C4×Dic13C22×C411yescharacteristic
339C4×Dic13C22×C411yescharacteristic
340C4×Dic13C22×C411yescharacteristic
341C4×Dic13C2411yescharacteristic
342C4×Dic13C2412yes—
343C4×Dic13C2412yes—
344C4×Dic13C2411yescharacteristic
345C4×Dic13C2411yescharacteristic
346C4×Dic13C2411yescharacteristic
347#3444—131no—
348#2995—132no—
349#2995—132no—
350#2993—134no—
351#2991—132no—
352#2990—132no—
353#2989—132no—
354#2989—132no—
355#2962—132no—
356#2935—132no—
357#2930—134no—
358#2925—132no—
359#2920—131no—
360#2906—132no—
361C2×#423—131no—
362C23×C13—22no—
363C23×C13—41no—
364C23×C13—41no—
365C23×C13C23×C412yes—
366C23×C13C23×C411yescharacteristic
367C23×C13C23×C411yescharacteristic
368C23×C13C23×C411yescharacteristic
369C22×D13C23×C412yes—
370Q8×C13—41no—
371D4×C13—24no—
372D4×C13—42no—
373D4×C13—41no—
374D4×C13—42no—
375C2×C4×C13—22no—
376C2×C4×C13—22no—
377C2×C4×C13—22no—
378C2×C4×C13—24no—
379C2×C4×C13—41no—
380C2×C4×C13—41no—
381C2×C4×C13—41no—
382C2×C4×C13C23×C411yescharacteristic
383C2×C4×C13C23×C411yescharacteristic
384C2×C4×C13C23×C411yescharacteristic
385C2×C4×C13C23×C412yes—
386C2×C4×C13C23×C412yes—
387C2×C4×C13C23×C412yes—
388C2×C4×C13C23×C411yescharacteristic
389C22⋊D13—24no—
390C22⋊D13—24no—
391C22⋊D13—24no—
392C22⋊D13—42no—
393C22⋊D13—42no—
394C2×Dic13—22no—
395C2×Dic13—22no—
396C2×Dic13—22no—
397C2×Dic13—22no—
398C2×Dic13—22no—
399C2×Dic13—22no—
400C2×Dic13—22no—
401C2×Dic13—21no—
402C2×Dic13—21no—
403C2×Dic13—22no—
404C2×Dic13—21no—
405C2×Dic13—21no—
406C2×Dic13—42no—
407C2×Dic13—41no—
408C2×Dic13—41no—
409C2×Dic13—41no—
410C2×Dic13C23×C411yescharacteristic
411C2×Dic13C23×C411yescharacteristic
412C2×Dic13C23×C411yescharacteristic
413C2×Dic13C23×C411yescharacteristic
414C2×Dic13C23×C411yescharacteristic
415C2×Dic13C23×C412yes—
416C2×Dic13C23×C412yes—
417C2×Dic13C23×C412yes—
418C2×Dic13C23×C411yescharacteristic
419C2×Dic13C23×C411yescharacteristic
420C2×Dic13H(5,𝔽2)12yes—
421C2×Dic132−1+412yes—
422C2×Dic13C2511yescharacteristic
423D52—41no—
424C4×D13—24no—
425C4×D13—22no—
426C4×D13—22no—
427C4×D13—42no—
428Dic26—24no—
429Dic26—24no—
430Dic26—41no—
431#1057—24no—
432#1057—24no—
433#1057—24no—
434#1057—24no—
435C2×#131—134no—
436C22×M16—132no—
437#533—131no—
438#533—131no—
439#533—131no—
440#532—131no—
441#532—131no—
442#532—131no—
443#529—132no—
444#529—132no—
445#529—131no—
446#529—131no—
447#529—131no—
448#529—131no—
449#529—132no—
450#529—132no—
451#525—131no—
452#525—132no—
453#525—132no—
454#525#26111yescharacteristic
455C4×#41—131no—
456C4×#41—132no—
457C4×#41—132no—
458C4×#41—131no—
459C22×C42—131no—
460#446—134no—
461#446—134no—
462#446—134no—
463C8×Q8—134no—
464#436—134no—
465#436—134no—
466#436—134no—
467#436—134no—
468#436—134no—
469#435—134no—
470#435—134no—
471#435—134no—
472#435—134no—
473#435—134no—
474#435—134no—
475C8×D4—134no—
476#433—134no—
477#433—134no—
478#432—132no—
479#432—132no—
480#432—132no—
481#432—132no—
482#431—132no—
483#431—132no—
484#431—132no—
485#431—132no—
486#424—134no—
487#424—134no—
488#424—134no—
489#423—132no—
490#423—131no—
491#423—131no—
492#423—132no—
493#423—132no—
494#423—131no—
495#423—132no—
496#423—132no—
497#423—131no—
498C2×C4⋊C8—132no—
499C2×C4⋊C8—132no—
500C2×C4⋊C8—132no—
501C2×C4⋊C8—132no—
502#408—134no—
503#407—132no—
504#405—134no—
505C4×M16—132no—
506C22×C13—21no—
507C22×C13—21no—
508C22×C13—21no—
509C22×C13—21no—
510C22×C13—22no—
511C22×C13—21no—
512C22×C13—21no—
513C22×C13—22no—
514C22×C13—21no—
515C22×C13—21no—
516C22×C13—22no—
517C22×C13—44no—
518C22×C13#52012yes—
519C22×C13C24×C411yescharacteristic
520C2×D13—22no—
521C2×D13—22no—
522C2×D13—22no—
523C4×C13—22no—
524C4×C13—22no—
525C4×C13—21no—
526C4×C13—21no—
527C4×C13—21no—
528C4×C13—22no—
529C4×C13#56812yes—
530Dic13—22no—
531Dic13—21no—
532Dic13—21no—
533Dic13—22no—
534Dic13—22no—
535Dic13—21no—
536Dic13—21no—
537Dic13—21no—
538Dic13#52012yes—
539Dic13#56812yes—
540Dic13C2×H(5,𝔽2)11yescharacteristic
541Dic13C2×2−1+411yescharacteristic
542C2×#41—132no—
543C2×#41—132no—
544C2×#41—131no—
545C2×#41C2×#26111yescharacteristic
546C23×C4—131no—
547C23×C4—131no—
548C23×C4C2×#26111yescharacteristic
549#131—528no—
550C2×M16—132no—
551C2×M16—132no—
552C2×M16—132no—
553C2×M16—134no—
554C2×M16—132no—
555C2×M16—134no—
556C2×M16—134no—
557C2×M16—524no—
558C22×C8—134no—
559C22×C8—134no—
560C22×C8—134no—
561C4⋊Q8—131no—
562C4⋊Q8—131no—
563C4⋊Q8—131no—
564#127—131no—
565#126—132no—
566#126—132no—
567#126—132no—
568#126—132no—
569#125—132no—
570#125—132no—
571#125—131no—
572#125—131no—
573#124—131no—
574#124—131no—
575#124—132no—
576#124—132no—
577#123—132no—
578#123—132no—
579#123—132no—
580#123—132no—
581#123—132no—
582#123C2×#26112yes—
583C22⋊Q8—131no—
584C22⋊Q8—131no—
585C22⋊Q8—132no—
586C22⋊Q8—132no—
587C22⋊Q8—132no—
588C22⋊Q8—132no—
589C22⋊Q8C2×#26111yescharacteristic
590C22⋊Q8C2×#26111yescharacteristic
591#121—132no—
592#121—132no—
593#121—132no—
594#121—132no—
595#121—131no—
596#121—131no—
597#121C2×#26111yescharacteristic
598#121C2×#26111yescharacteristic
599#120—132no—
600#120C2×#26112yes—
601C4×Q8—131no—
602C4×Q8—131no—
603C4×Q8—132no—
604C4×Q8—131no—
605C4×Q8—132no—
606C4×Q8—131no—
607C4×Q8—132no—
608C4×Q8—132no—
609C4×D4—132no—
610C4×D4—132no—
611C4×D4—132no—
612C4×D4—132no—
613C4×D4—131no—
614C4×D4—131no—
615C4×D4—132no—
616C4×D4—132no—
617C4×D4—132no—
618C4×D4—132no—
619C4×D4—131no—
620C4×D4—131no—
621C4×D4—132no—
622C4×D4—132no—
623C4×D4—132no—
624C4×D4—132no—
625C4×D4—132no—
626C4×D4—132no—
627C4×D4C2×#26112yes—
628C4×D4C2×#26112yes—
629#117—131no—
630#117—132no—
631#117—132no—
632#117—132no—
633#117—132no—
634#117—132no—
635#117—132no—
636#117—132no—
637#117—132no—
638#117C2×#26111yescharacteristic
639C2×C42—132no—
640C2×C42—131no—
641C2×C42—131no—
642C2×C42—131no—
643C2×C42—131no—
644C2×C42—131no—
645C2×C42—131no—
646C2×C42—131no—
647C2×C42—131no—
648C2×C42—131no—
649C2×C42—131no—
650C2×C42—131no—
651C2×C42—131no—
652C2×C42—132no—
653C4⋊C8—132no—
654C4⋊C8—132no—
655C4⋊C8—132no—
656C4⋊C8—134no—
657C4⋊C8—134no—
658C4⋊C8—134no—
659C4⋊C8—132no—
660C4⋊C8—132no—
661C4⋊C8—134no—
662C4⋊C8—132no—
663C4⋊C8—134no—
664C4⋊C8—132no—
665C4⋊C8—134no—
666C4⋊C8—132no—
667C22⋊C8—134no—
668C22⋊C8—134no—
669C22⋊C8—134no—
670C22⋊C8—134no—
671C22⋊C8—134no—
672C22⋊C8—134no—
673#97—134no—
674#97—134no—
675#97—134no—
676C4×C8—134no—
677C4×C8—134no—
678C4×C8—134no—
679C2×C13—22no—
680C2×C13—42no—
681C2×C13—41no—
682C2×C13—41no—
683C2×C13C2×#52011yescharacteristic
684C2×C13C2×#56811yescharacteristic
685C2×C13C2×#56811yescharacteristic
686D13—42no—
687C24C22×#26111yescharacteristic
688#41—42no—
689#41—264no—
690#41—264no—
691#41—522no—
692#41—524no—
693C2×Q8—132no—
694C2×Q8—132no—
695C2×Q8—131no—
696C2×Q8C22×#26111yescharacteristic
697C2×D4—132no—
698C2×D4—132no—
699C2×D4—132no—
700C2×D4—132no—
701C2×D4—132no—
702C2×D4—131no—
703C2×D4C22×#26112yes—
704C2×D4C22×#26112yes—
705C2×D4C22×#26111yescharacteristic
706C2×D4C22×#26112yes—
707C22×C4—42no—
708C22×C4—131no—
709C22×C4—131no—
710C22×C4—131no—
711C22×C4—132no—
712C22×C4—131no—
713C22×C4—131no—
714C22×C4—131no—
715C22×C4—131no—
716C22×C4—131no—
717C22×C4—131no—
718C22×C4—131no—
719C22×C4—131no—
720C22×C4—131no—
721C22×C4—132no—
722C22×C4—132no—
723C22×C4—132no—
724C22×C4—132no—
725C22×C4—262no—
726C22×C4—262no—
727C22×C4—522no—
728C22×C4C22×#26111yescharacteristic
729C22×C4C22×#26111yescharacteristic
730C22×C4C22×#26111yescharacteristic
731C22×C4C22×#26112yes—
732C22×C4C22×#26111yescharacteristic
733C22×C4C22×#26111yescharacteristic
734C22×C4C22×#26111yescharacteristic
735M16—264no—
736M16—264no—
737M16—522no—
738M16—524no—
739M16—522no—
740M16—524no—
741M16—524no—
742C2×C8—134no—
743C2×C8—134no—
744C2×C8—134no—
745C2×C8—134no—
746C2×C8—268no—
747C2×C8—524no—
748C2×C8—524no—
749C4⋊C4—132no—
750C4⋊C4—132no—
751C4⋊C4—132no—
752C4⋊C4—132no—
753C4⋊C4—131no—
754C4⋊C4—131no—
755C4⋊C4—132no—
756C4⋊C4—132no—
757C4⋊C4—132no—
758C4⋊C4—132no—
759C4⋊C4—132no—
760C4⋊C4—132no—
761C4⋊C4—132no—
762C4⋊C4—132no—
763C4⋊C4—132no—
764C4⋊C4—132no—
765C4⋊C4C22×#26112yes—
766C4⋊C4C22×#26112yes—
767C4⋊C4C22×#26111yescharacteristic
768C4⋊C4C22×#26111yescharacteristic
769C22⋊C4—132no—
770C22⋊C4—132no—
771C22⋊C4—132no—
772C22⋊C4—132no—
773C22⋊C4—132no—
774C22⋊C4—132no—
775C22⋊C4—132no—
776C22⋊C4—132no—
777C22⋊C4—132no—
778C22⋊C4—132no—
779C22⋊C4—132no—
780C22⋊C4—132no—
781C22⋊C4—132no—
782C22⋊C4C22×#26112yes—
783C22⋊C4C22×#26112yes—
784C22⋊C4C22×#26112yes—
785C22⋊C4C22×#26112yes—
786C22⋊C4C22×#26112yes—
787C42—131no—
788C42—132no—
789C42—132no—
790C42—131no—
791C42—131no—
792C42—131no—
793C42—131no—
794C42—131no—
795C42—131no—
796C42—131no—
797C42—131no—
798C42—131no—
799C42—131no—
800C42—131no—
801C42—131no—
802C42—131no—
803C42—131no—
804C42—131no—
805C42—132no—
806C42—132no—
807C42—132no—
808C42C22×#26112yes—
809C13#6026611yescharacteristic, complemented, Sylow
810C23—22no—
811C23—41no—
812C23—41no—
813C23—132no—
814C23C23×#26112yes—
815C23C23×#26111yescharacteristic
816C23C23×#26111yescharacteristic
817C23C23×#26111yescharacteristic
818Q8—41no—
819Q8—264no—
820Q8—264no—
821Q8—521no—
822D4—24no—
823D4—41no—
824D4—42no—
825D4—42no—
826D4—264no—
827D4—264no—
828D4—264no—
829D4—521no—
830D4—522no—
831D4—522no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—24no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—132no—
840C2×C4—132no—
841C2×C4—131no—
842C2×C4—131no—
843C2×C4—131no—
844C2×C4—131no—
845C2×C4—131no—
846C2×C4—131no—
847C2×C4—131no—
848C2×C4—131no—
849C2×C4—132no—
850C2×C4—132no—
851C2×C4—132no—
852C2×C4—262no—
853C2×C4—262no—
854C2×C4—262no—
855C2×C4—261no—
856C2×C4—261no—
857C2×C4—262no—
858C2×C4—262no—
859C2×C4—261no—
860C2×C4—261no—
861C2×C4—262no—
862C2×C4—262no—
863C2×C4—262no—
864C2×C4—262no—
865C2×C4—262no—
866C2×C4—264no—
867C2×C4—522no—
868C2×C4—521no—
869C2×C4—521no—
870C2×C4—521no—
871C2×C4—522no—
872C2×C4C23×#26111yescharacteristic
873C2×C4C23×#26111yescharacteristic
874C2×C4C23×#26111yescharacteristic
875C2×C4C23×#26112yes—
876C2×C4C23×#26112yes—
877C2×C4C23×#26112yes—
878C2×C4C23×#26111yescharacteristic
879C8—264no—
880C8—264no—
881C8—264no—
882C8—264no—
883C22—21no—
884C22—21no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—21no—
890C22—22no—
891C22—21no—
892C22—21no—
893C22—22no—
894C22—44no—
895C22—262no—
896C22—262no—
897C22—262no—
898C22#1171963112yes—
899C22C24×#26111yescharacteristic
900C4—22no—
901C4—21no—
902C4—21no—
903C4—21no—
904C4—22no—
905C4—22no—
906C4—132no—
907C4—131no—
908C4—131no—
909C4—132no—
910C4—261no—
911C4—261no—
912C4—262no—
913C4—262no—
914C4—261no—
915C4—261no—
916C4—261no—
917C4—262no—
918C4#1171962112yes—
919C2—22no—
920C2—41no—
921C2—41no—
922C2—42no—
923C2—522no—
924C2C2×#1171963111yescharacteristic
925C2C2×#1171962111yescharacteristic
926C2D13⋊#56811yescharacteristic
subgroupG/H
center, FrattiniC22C24×#261
commutator, socleC22×C13C24×C4
FittingC13×#525C4
prime radical#13128128C2
cosocleC2×Dic13C25
hypercenter#525#261
hypocenterC13#60266
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #13131793C2semidirect
2. #13131789C2semidirect
3. #13131777C2semidirect
4. #13131767C2semidirect
5. #13131761C2semidirect
6. #13131758C2semidirect
7. #13131755C2semidirect
8. #13131633C2semidirect
9. #13131580C2semidirect
10. #13131555C2semidirect
11. #13131531C2semidirect
12. #13131512C2semidirect
13. #13131481C2semidirect
14. C2×#11719129C2semidirect
42. #11719158C22semidirect
48. #11719144C22semidirect
50. #11719130C22semidirect
58. #11719129C22semidirect
64. #11719119C22semidirect
66. C2×C4⋊#1057C22semidirect
67. #11719079C22semidirect
68. #11719078C22semidirect
69. #11719078C22semidirect
70. #11719077C22semidirect
71. #11719075C22semidirect
72. #11719074C22semidirect
73. #11719068C22semidirect
75. #11719067C22semidirect
78. #11719066C22semidirect
81. #11719063C22semidirect
83. #11719054C22semidirect
84. #11719052C22semidirect
85. #11719051C22semidirect
86. D13⋊(C4⋊C8)C22semidirect
809. C13#60266semidirect

Maximal subgroups

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

subgroupindex
#131317932
#131317892
#131317772
#131317672
#131317612
#131317582
#131317552
#131316332
#131315802
#131315552
#131315312
#131315122
#131314812
C2×#117191292
#131281282
#6026613