Finite Group Databasebeta

← #16776772

Subgroups — #16776772

Order 3328.

10836 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#11719648C212yesmaximal, complemented
2#13129620C218yesmaximal, complemented
3#13129619C218yesmaximal, complemented
4#13129613C218yesmaximal, complemented
5#13129612C218yesmaximal, complemented
6#13129609C218yesmaximal, complemented
7#13129605C218yesmaximal, complemented
8C2×#11719453C211yesmaximal, characteristic, complemented
9C2×#11719527C212yesmaximal, complemented
10D13×#575C218yesmaximal, complemented
11C2×#11719450C211yesmaximal, characteristic, complemented
12C2×C13×#575C211yesmaximal, characteristic, complemented
13C22×C13×#41C2212yescomplemented
14#11719648—24no—
15#11719648—24no—
16#11719648—24no—
17#11719648—24no—
18#11719648C2218yescomplemented
19#11719648C2218yescomplemented
20#11719648C2218yescomplemented
21#11719648C2218yescomplemented
22C2×#88257—22no—
23C2×#88257C2214yescomplemented
24C2×#88256—22no—
25C2×#88256C2214yescomplemented
26C2×#41×D13—24no—
27C2×#41×D13C2218yescomplemented
28C2×#88254C2214yescomplemented
29C2×#88251—24no—
30C2×#88251C2214yescomplemented
31C22×#6127—24no—
32C22×#6127C2211yescharacteristic
33C22×#6127C2212yescomplemented
34C13×#575C2214yescomplemented
35C13×#575C2218yescomplemented
36C13×#575C2214yescomplemented
37C2×C13×#137C2214yescomplemented
38C2×C13×AGL(1,ℤ/8)C2214yescomplemented
39C2×C13×#135C2214yescomplemented
40C22×C13×M16C2211yescharacteristic, complemented
41C2×#88205C2214yescomplemented
42#11719527C2218yescomplemented
43#11719527C2218yescomplemented
44#11719527C2218yescomplemented
45#11719527C2218yescomplemented
46C2×#88204C2218yescomplemented
47C2×#88203C2214yescomplemented
48C2×#88196C2214yescomplemented
49C2×#88186C2214yescomplemented
50C22×#6099C2211yescharacteristic, complemented
51#11719484C22132yescomplemented
52#11719483C22132yescomplemented
53#11719482C22132yescomplemented
54D13×#137C22132yescomplemented
55#11719480C22132yescomplemented
56#11719479C22132yescomplemented
57#11719478C22132yescomplemented
58D13×AGL(1,ℤ/8)C22132yescomplemented
59#11719476C22116yescomplemented
60#11719475C22132yescomplemented
61#11719474C22116yescomplemented
62#11719473C22132yescomplemented
63D13×#135C22132yescomplemented
64#11719471C22116yescomplemented
65#11719467C22132yescomplemented
66#11719462C22116yescomplemented
67#11719453C2214yescomplemented
68#11719453C2218yescomplemented
69#11719453C2214yescomplemented
70C2×#88163C2214yescomplemented
71C2×#88162C2214yescomplemented
72#11719450C2218yescomplemented
73#11719450C2218yescomplemented
74C2×#88161C2214yescomplemented
75C2×M16×D13C2214yescomplemented
76C2×#88158C2214yescomplemented
77C2×#88155C2214yescomplemented
78C2×C13×#41—22no—
79C2×C13×#41—22no—
80C2×C13×#41—22no—
81C2×C13×#41—22no—
82C2×C13×#41—22no—
83C2×C13×#41—22no—
84C2×C13×#41C2314yes—
85C2×C13×#41C2314yes—
86C2×C13×#41C2314yes—
87C2×C13×#41C2314yescomplemented
88C2×C13×#41C2314yescomplemented
89C2×C13×#41C2314yescomplemented
90C22×Q8×C13C2312yescomplemented
91C22×D4×C13—22no—
92C22×D4×C13C2312yescomplemented
93C23×C4×C13—22no—
94C23×C4×C13C2311yescharacteristic
95C22×C22⋊D13—22no—
96C22×C22⋊D13—28no—
97C22×C22⋊D13D412yes—
98#88257—28no—
99#88257—28no—
100#88257—28no—
101#88257—28no—
102#88257—28no—
103#88257—28no—
104#88257C23116yescomplemented
105#88257C23116yescomplemented
106#88256—28no—
107#88256—28no—
108#88256—28no—
109#88256—28no—
110#88256—28no—
111#88256—28no—
112#88256C23116yescomplemented
113#88256C23116yescomplemented
114#41×D13—216no—
115#41×D13—216no—
116#41×D13—216no—
117#41×D13—216no—
118#41×D13—216no—
119#41×D13—216no—
120#41×D13C23132yes—
121#41×D13C23132yescomplemented
122#88254—28no—
123#88254—28no—
124#88254C23116yescomplemented
125#88254C23116yescomplemented
126C2×#6131—24no—
127C2×#6131C2318yescomplemented
128C2×Q8×D13—24no—
129C2×Q8×D13C2318yescomplemented
130#88251—216no—
131#88251—216no—
132#88251—216no—
133#88251—216no—
134#88251—28no—
135#88251—28no—
136#88251C23116yescomplemented
137#88251C23116yescomplemented
138C2×#6129—28no—
139C2×#6129—28no—
140C2×#6129—24no—
141C2×#6129C2318yescomplemented
142C2×D4×D13—28no—
143C2×D4×D13—28no—
144C2×D4×D13—24no—
145C2×D4×D13C2318yescomplemented
146C2×#6127—22no—
147C2×#6127—22no—
148C2×#6127—22no—
149C2×#6127—22no—
150C2×#6127—22no—
151C2×#6127—22no—
152C2×#6127—28no—
153C2×#6127—216no—
154C2×#6127—216no—
155C2×#6127—216no—
156C2×#6127—216no—
157C2×#6127—24no—
158C2×#6127—28no—
159C2×#6127—24no—
160C2×#6127D414yes—
161C2×#6127D414yes—
162C2×#6127D412yes—
163C2×#6127D412yes—
164C2×#6127C2312yes—
165C2×#6127C2312yes—
166C2×#6127C2314yes—
167C2×#6127C2314yes—
168C2×#6127C2314yes—
169C2×#6127C2314yes—
170C2×#6127C2314yes—
171C2×#6127C2314yescomplemented
172C2×#6127C2314yescomplemented
173C2×#6127C2314yescomplemented
174C22×D52—24no—
175C22×D52D411yescharacteristic
176C22×D52C2312yescomplemented
177C22×C4×D13—22no—
178C22×C4×D13—28no—
179C22×C4×D13C2312yes—
180C22×Dic26—24no—
181C22×Dic26D411yescharacteristic
182C22×Dic26C2312yescomplemented
183C13×#137C23116yescomplemented
184C13×#137C23116yescomplemented
185C13×AGL(1,ℤ/8)C23116yescomplemented
186C13×AGL(1,ℤ/8)C23116yescomplemented
187C13×#135C23116yescomplemented
188C13×#135C23116yescomplemented
189C2×C13×Q16C2314yescomplemented
190C2×C13×SD16C2318yescomplemented
191C2×C13×D8C2314yescomplemented
192C2×C13×M16C2312yes—
193C2×C13×M16C2312yescomplemented
194C2×C13×M16C2314yescomplemented
195C2×C13×M16C2314yescomplemented
196C22×C8×C13C2312yescomplemented
197#88205C23116yescomplemented
198#88205C23116yescomplemented
199#88204C23132yescomplemented
200#88204C23132yescomplemented
201#88203C23116yescomplemented
202#88203C23116yescomplemented
203C2×#6107C2318yescomplemented
204#88196C23116yescomplemented
205#88196C23116yescomplemented
206C2×#6106C2318yescomplemented
207C2×#6105C2318yescomplemented
208#88186C23116yescomplemented
209#88186C23116yescomplemented
210C2×#6104C2318yescomplemented
211C2×#6099C2312yes—
212C2×#6099C2312yescomplemented
213C2×#6099C2314yescomplemented
214C2×#6099C2314yescomplemented
215C22×#1055C2312yescomplemented
216#88173C23132yescomplemented
217#88172C23164yescomplemented
218Q16×D13C23132yescomplemented
219#88170C23164yescomplemented
220#88169C23164yescomplemented
221#88168C23164yescomplemented
222SD16×D13C23164yescomplemented
223#88166C23132yescomplemented
224#88165C23164yescomplemented
225D8×D13C23132yescomplemented
226#88163C23116yescomplemented
227#88163C23116yescomplemented
228#88162C23116yescomplemented
229#88162C23116yescomplemented
230#88161C23132yescomplemented
231M16×D13C23132yescomplemented
232C2×Dic52C2314yescomplemented
233#88158C23116yescomplemented
234#88158C23116yescomplemented
235C2×D104C2314yescomplemented
236C2×#6095C2318yescomplemented
237#88155C23116yescomplemented
238#88155C23116yescomplemented
239C2×#6094C2318yescomplemented
240C2×C8×D13C2318yescomplemented
241#63090—131nomaximal, Sylow
242C24×C13—22no—
243C24×C13C2×D411yescharacteristic
244C23×D13—22no—
245C23×D13—28no—
246C23×D13C2×D412yes—
247C13×#41—24no—
248C13×#41—24no—
249C13×#41—24no—
250C13×#41—24no—
251C13×#41—24no—
252C13×#41—24no—
253C13×#41—24no—
254C13×#41—24no—
255C13×#41—24no—
256C13×#41—24no—
257C13×#41—24no—
258C13×#41—24no—
259C13×#41C2418yes—
260C13×#41C2418yes—
261C13×#41C2418yes—
262C13×#41C2418yes—
263C2×Q8×C13—22no—
264C2×Q8×C13—22no—
265C2×Q8×C13—22no—
266C2×Q8×C13C2414yes—
267C2×Q8×C13C2414yes—
268C2×Q8×C13C2414yes—
269C2×D4×C13—24no—
270C2×D4×C13—24no—
271C2×D4×C13—24no—
272C2×D4×C13—24no—
273C2×D4×C13—24no—
274C2×D4×C13—24no—
275C2×D4×C13—22no—
276C2×D4×C13—22no—
277C2×D4×C13—22no—
278C2×D4×C13C2414yes—
279C2×D4×C13C2414yes—
280C2×D4×C13C2414yes—
281C22×C4×C13—22no—
282C22×C4×C13—24no—
283C22×C4×C13—24no—
284C22×C4×C13—24no—
285C22×C4×C13—24no—
286C22×C4×C13—24no—
287C22×C4×C13—24no—
288C22×C4×C13C2×D411yescharacteristic
289C22×C4×C13C2×D412yes—
290C22×C4×C13C2×D412yes—
291C22×C4×C13C2×D411yescharacteristic
292C22×C4×C13C2×D411yescharacteristic
293C22×C4×C13C2411yescharacteristic
294C22×C4×C13C2411yescharacteristic
295C22×C4×C13C2411yescharacteristic
296C22×C4×C13C2412yes—
297C22×C4×C13C2412yes—
298C2×C22⋊D13—24no—
299C2×C22⋊D13—24no—
300C2×C22⋊D13—24no—
301C2×C22⋊D13—24no—
302C2×C22⋊D13—24no—
303C2×C22⋊D13—24no—
304C2×C22⋊D13—28no—
305C2×C22⋊D13—232no—
306C2×C22⋊D13—232no—
307C2×C22⋊D13—28no—
308C2×C22⋊D13C2×D418yes—
309C2×C22⋊D13C2×D418yes—
310C2×C22⋊D13C2×D414yes—
311C2×C22⋊D13C2×D414yes—
312C22×Dic13—22no—
313C22×Dic13—28no—
314C22×Dic13C2×D412yes—
315#6131—216no—
316#6131—216no—
317#6131—216no—
318#6131C24132yes—
319Q8×D13—216no—
320Q8×D13—216no—
321Q8×D13—216no—
322Q8×D13C24132yes—
323#6129—232no—
324#6129—232no—
325#6129—232no—
326#6129—232no—
327#6129—216no—
328#6129—216no—
329#6129—216no—
330#6129C24132yes—
331D4×D13—232no—
332D4×D13—232no—
333D4×D13—232no—
334D4×D13—232no—
335D4×D13—216no—
336D4×D13—216no—
337D4×D13—216no—
338D4×D13C24132yes—
339#6127—24no—
340#6127—24no—
341#6127—24no—
342#6127—24no—
343#6127—24no—
344#6127—24no—
345#6127—24no—
346#6127—24no—
347#6127—24no—
348#6127—24no—
349#6127—24no—
350#6127—24no—
351#6127—232no—
352#6127—232no—
353#6127—216no—
354#6127—216no—
355#6127—232no—
356#6127—232no—
357#6127—216no—
358#6127—216no—
359#6127C2×D414yes—
360#6127C2×D418yes—
361#6127C2×D418yes—
362#6127C2×D418yes—
363#6127C2×D418yes—
364#6127C2×D414yes—
365#6127C2×D418yes—
366#6127C2414yes—
367#6127C2414yes—
368#6127C2418yes—
369#6127C2418yes—
370#6127C2418yes—
371#6127C2418yes—
372#6127C2418yes—
373C2×D52—28no—
374C2×D52—22no—
375C2×D52—22no—
376C2×D52—22no—
377C2×D52—216no—
378C2×D52—216no—
379C2×D52C2×D414yes—
380C2×D52C2×D414yes—
381C2×D52C2×D412yes—
382C2×D52C2×D412yes—
383C2×D52C2414yes—
384C2×D52C2414yes—
385C2×D52C2414yes—
386C2×C4×D13—28no—
387C2×C4×D13—24no—
388C2×C4×D13—24no—
389C2×C4×D13—24no—
390C2×C4×D13—24no—
391C2×C4×D13—24no—
392C2×C4×D13—24no—
393C2×C4×D13—28no—
394C2×C4×D13—232no—
395C2×C4×D13—232no—
396C2×C4×D13C2×D418yes—
397C2×C4×D13C2×D414yes—
398C2×C4×D13C2414yes—
399C2×C4×D13C2418yes—
400C2×Dic26—22no—
401C2×Dic26—22no—
402C2×Dic26—22no—
403C2×Dic26—28no—
404C2×Dic26—216no—
405C2×Dic26—216no—
406C2×Dic26C2×D414yes—
407C2×Dic26C2×D414yes—
408C2×Dic26C2×D412yes—
409C2×Dic26C2×D412yes—
410C2×Dic26C2414yes—
411C2×Dic26C2414yes—
412C2×Dic26C2414yes—
413C13×Q16C24116yes—
414C13×SD16C24132yes—
415C13×D8C24116yes—
416C13×M16C2418yes—
417C13×M16C2418yes—
418C2×C8×C13C2414yes—
419C2×C8×C13C2414yes—
420C2×C8×C13C2414yes—
421#6107C24132yes—
422#6106C24132yes—
423#6105C24132yes—
424#6104C24132yes—
425#6099C2414yes—
426#6099C2414yes—
427#6099C2418yes—
428C2×#1055C2414yes—
429C2×#1055C2418yes—
430Dic52C24116yes—
431D104C24116yes—
432#6095C24132yes—
433#6094C24132yes—
434C8×D13C24132yes—
435C2×#585—132no—
436#3586—138no—
437#3586—138no—
438#3585—138no—
439#3585—138no—
440#3584—138no—
441#3584—138no—
442C2×#575—132no—
443C2×#575—138no—
444C2×#575—131no—
445C2×#575D1311yescharacteristic, complemented
446C2×#568—131no—
447C23×C13—24no—
448C23×C13—24no—
449C23×C13—24no—
450C23×C13—81no—
451C23×C13—84no—
452C23×C13C22×D412yes—
453C23×C13C22×D411yescharacteristic
454C23×C13C22×D412yes—
455C23×C13C22×D411yescharacteristic
456C23×C13C22×D411yescharacteristic
457C22×D13—24no—
458C22×D13—24no—
459C22×D13—24no—
460C22×D13—232no—
461C22×D13—82no—
462C22×D13—816no—
463C22×D13—84no—
464C22×D13C22×D418yes—
465C22×D13C22×D414yes—
466Q8×C13—24no—
467Q8×C13—24no—
468Q8×C13—24no—
469Q8×C13C2518yes—
470D4×C13—28no—
471D4×C13—28no—
472D4×C13—28no—
473D4×C13—28no—
474D4×C13—24no—
475D4×C13—24no—
476D4×C13—24no—
477D4×C13C2518yes—
478C2×C4×C13—24no—
479C2×C4×C13—24no—
480C2×C4×C13—24no—
481C2×C4×C13—28no—
482C2×C4×C13—28no—
483C2×C4×C13—28no—
484C2×C4×C13—28no—
485C2×C4×C13C22×D412yes—
486C2×C4×C13C22×D412yes—
487C2×C4×C13C22×D412yes—
488C2×C4×C13C22×D412yes—
489C2×C4×C13C22×D411yescharacteristic
490C2×C4×C13C22×D411yescharacteristic
491C2×C4×C13C22×D411yescharacteristic
492C2×C4×C13C22×D412yes—
493C2×C4×C13C22×D412yes—
494C2×C4×C13C22×D412yes—
495C2×C4×C13C22×D411yescharacteristic
496C2×C4×C13C22×D411yescharacteristic
497C2×C4×C13C22×D412yes—
498C2×C4×C13C2511yescharacteristic
499C2×C4×C13C2512yes—
500C2×C4×C13C2511yescharacteristic
501C2×C4×C13C2511yescharacteristic
502C2×C4×C13C2512yes—
503C22⋊D13—28no—
504C22⋊D13—28no—
505C22⋊D13—28no—
506C22⋊D13—28no—
507C22⋊D13—232no—
508C22⋊D13—232no—
509C22⋊D13C22×D418yes—
510C22⋊D13C22×D4116yes—
511C22⋊D13C22×D418yes—
512C2×Dic13—24no—
513C2×Dic13—24no—
514C2×Dic13—24no—
515C2×Dic13—232no—
516C2×Dic13C22×D418yes—
517C2×Dic13C22×D414yes—
518D52—232no—
519D52—24no—
520D52—24no—
521D52—24no—
522D52C22×D414yes—
523D52C22×D418yes—
524D52C22×D414yes—
525D52C2518yes—
526C4×D13—232no—
527C4×D13—28no—
528C4×D13—28no—
529C4×D13—28no—
530C4×D13—28no—
531C4×D13—232no—
532C4×D13C22×D418yes—
533C4×D13C22×D4116yes—
534C4×D13C2518yes—
535Dic26—24no—
536Dic26—24no—
537Dic26—24no—
538Dic26—232no—
539Dic26C22×D414yes—
540Dic26C22×D418yes—
541Dic26C22×D414yes—
542Dic26C2518yes—
543C8×C13C2518yes—
544#1055C2518yes—
545#585—138no—
546#585—138no—
547#585—138no—
548#585—138no—
549#585—264no—
550#585—264no—
551#585—264no—
552#585—264no—
553C2×2−1+4—134no—
554C2×2−1+4—134no—
555C2×2−1+4—262no—
556C2×H(5,𝔽2)—134no—
557C2×H(5,𝔽2)—134no—
558C2×H(5,𝔽2)—264no—
559C2×H(5,𝔽2)—262no—
560C22×#41—131no—
561C22×#41—138no—
562C22×#41—132no—
563C22×#41—264no—
564C22×#41—264no—
565C22×#41C2×D1312yescomplemented
566#578—1332no—
567#578—1316no—
568#578—1316no—
569#577—1332no—
570#577—1332no—
571#577—1332no—
572#577—1332no—
573#576—1332no—
574#576—1316no—
575#576—1316no—
576#575—138no—
577#575—138no—
578#575—138no—
579#575—138no—
580#575—1332no—
581#575—1332no—
582#575—1332no—
583#575—134no—
584#575—134no—
585#575—138no—
586#575C2×D1314yescomplemented
587#575C2×D1318yescomplemented
588#575C2×D1314yescomplemented
589C2×#137—134no—
590C2×#137—134no—
591C2×#137—1332no—
592C2×#137—134no—
593C2×#137C2×D1314yescomplemented
594C2×AGL(1,ℤ/8)—134no—
595C2×AGL(1,ℤ/8)—134no—
596C2×AGL(1,ℤ/8)—1332no—
597C2×AGL(1,ℤ/8)—134no—
598C2×AGL(1,ℤ/8)C2×D1314yescomplemented
599C2×#135—138no—
600C2×#135—1332no—
601C2×#135—134no—
602C2×#135C2×D1314yescomplemented
603#568—138no—
604#568—138no—
605C2×#131—134no—
606C2×#131—134no—
607C22×M16—131no—
608C22×M16—134no—
609C22×M16C2×D1311yescharacteristic, complemented
610C22×C13—28no—
611C22×C13—41no—
612C22×C13—42no—
613C22×C13—42no—
614C22×C13—41no—
615C22×C13—41no—
616C22×C13—48no—
617C22×C13—84no—
618C22×C13—84no—
619C22×C13C23×D411yescharacteristic
620C22×C13C23×D412yes—
621C22×C13C23×D412yes—
622C22×C13C23×D411yescharacteristic
623C22×C13C23×D411yescharacteristic
624C2×D13—28no—
625C2×D13—48no—
626C2×D13—44no—
627C2×D13—48no—
628C2×D13—832no—
629C2×D13—84no—
630C2×D13—84no—
631C2×D13C23×D418yes—
632C4×C13—28no—
633C4×C13C23×D411yescharacteristic
634C4×C13C23×D412yes—
635C4×C13C23×D412yes—
636C4×C13C23×D411yescharacteristic
637C4×C13C23×D411yescharacteristic
638C4×C13C2611yescharacteristic
639Dic13—28no—
640Dic13C23×D418yes—
6412−1+4—1316no—
6422−1+4—1316no—
6432−1+4—1316no—
6442−1+4—1316no—
6452−1+4—268no—
6462−1+4—268no—
6472−1+4—268no—
6482−1+4—268no—
6492−1+4—268no—
6502−1+4—268no—
6512−1+4—268no—
6522−1+4—268no—
653H(5,𝔽2)—1316no—
654H(5,𝔽2)—1316no—
655H(5,𝔽2)—1316no—
656H(5,𝔽2)—1316no—
657H(5,𝔽2)—2616no—
658H(5,𝔽2)—2616no—
659H(5,𝔽2)—2616no—
660H(5,𝔽2)—2616no—
661H(5,𝔽2)—268no—
662H(5,𝔽2)—268no—
663H(5,𝔽2)—268no—
664H(5,𝔽2)—268no—
665H(5,𝔽2)—268no—
666H(5,𝔽2)—268no—
667H(5,𝔽2)—268no—
668H(5,𝔽2)—268no—
669C2×#41—22no—
670C2×#41—22no—
671C2×#41—22no—
672C2×#41—22no—
673C2×#41—22no—
674C2×#41—22no—
675C2×#41—134no—
676C2×#41—134no—
677C2×#41—132no—
678C2×#41—132no—
679C2×#41—132no—
680C2×#41—132no—
681C2×#41—134no—
682C2×#41—134no—
683C2×#41—1332no—
684C2×#41—1332no—
685C2×#41—138no—
686C2×#41—138no—
687C2×#41—134no—
688C2×#41—134no—
689C2×#41—134no—
690C2×#41—134no—
691C2×#41—134no—
692C2×#41—134no—
693C2×#41—268no—
694C2×#41—268no—
695C2×#41—264no—
696C2×#41—264no—
697C2×#41—2616no—
698C2×#41—2616no—
699C2×#41—2616no—
700C2×#41—2616no—
701C2×#41—268no—
702C2×#41—2616no—
703C2×#41—2616no—
704C2×#41—268no—
705C2×#41—264no—
706C2×#41—264no—
707C2×#41—2616no—
708C2×#41—2616no—
709C2×#41—2616no—
710C2×#41—2616no—
711C2×#41—262no—
712C2×#41—262no—
713C2×#41—262no—
714C2×#41—262no—
715C2×#41—262no—
716C2×#41—262no—
717C2×#41C22×D1314yes—
718C2×#41C22×D1314yes—
719C2×#41C22×D1314yes—
720C2×#41C22×D1314yescomplemented
721C2×#41C22×D1314yescomplemented
722C2×#41C22×D1314yescomplemented
723C22×Q8—131no—
724C22×Q8—138no—
725C22×Q8—132no—
726C22×Q8—264no—
727C22×Q8—264no—
728C22×Q8C22×D1312yescomplemented
729C22×D4—22no—
730C22×D4—132no—
731C22×D4—138no—
732C22×D4—131no—
733C22×D4—132no—
734C22×D4—264no—
735C22×D4—268no—
736C22×D4—264no—
737C22×D4—268no—
738C22×D4—268no—
739C22×D4—262no—
740C22×D4C22×D1312yescomplemented
741C23×C4—22no—
742C23×C4—132no—
743C23×C4—268no—
744C23×C4—262no—
745C23×C4C22×D1311yescharacteristic
746#137—1316no—
747#137—1316no—
748#137—1316no—
749#137—1316no—
750#137—1364no—
751#137—1364no—
752#137—1316no—
753#137—1316no—
754#137C22×D13116yescomplemented
755#137C22×D13116yescomplemented
756AGL(1,ℤ/8)—1316no—
757AGL(1,ℤ/8)—1316no—
758AGL(1,ℤ/8)—1316no—
759AGL(1,ℤ/8)—1316no—
760AGL(1,ℤ/8)—1364no—
761AGL(1,ℤ/8)—1364no—
762AGL(1,ℤ/8)—1316no—
763AGL(1,ℤ/8)—1316no—
764AGL(1,ℤ/8)C22×D13116yescomplemented
765AGL(1,ℤ/8)C22×D13116yescomplemented
766#135—1332no—
767#135—1332no—
768#135—1332no—
769#135—1364no—
770#135—1332no—
771#135—1316no—
772#135—1316no—
773#135C22×D13116yescomplemented
774#135C22×D13116yescomplemented
775C2×Q16—138no—
776C2×Q16—1332no—
777C2×Q16—134no—
778C2×Q16C22×D1314yescomplemented
779C2×SD16—138no—
780C2×SD16—138no—
781C2×SD16—1364no—
782C2×SD16—138no—
783C2×SD16C22×D1318yescomplemented
784C2×D8—138no—
785C2×D8—1332no—
786C2×D8—134no—
787C2×D8C22×D1314yescomplemented
788#131—1332no—
789#131—1316no—
790#131—1316no—
791C2×M16—132no—
792C2×M16—132no—
793C2×M16—134no—
794C2×M16—134no—
795C2×M16—1332no—
796C2×M16—138no—
797C2×M16C22×D1312yes—
798C2×M16C22×D1312yescomplemented
799C2×M16C22×D1314yescomplemented
800C2×M16C22×D1314yescomplemented
801C22×C8—132no—
802C22×C8—138no—
803C22×C8C22×D1312yescomplemented
804C2×C13—22no—
805C2×C13—21no—
806C2×C13—21no—
807C2×C13—22no—
808C2×C13—21no—
809C2×C13—48no—
810C2×C13C24×D411yescharacteristic
811D13—28no—
812D13—48no—
813C24—22no—
814C24—132no—
815C24—268no—
816C24—262no—
817C24D4×D1311yescharacteristic
818#41—24no—
819#41—24no—
820#41—24no—
821#41—24no—
822#41—24no—
823#41—24no—
824#41—24no—
825#41—24no—
826#41—24no—
827#41—24no—
828#41—24no—
829#41—24no—
830#41—134no—
831#41—138no—
832#41—134no—
833#41—138no—
834#41—138no—
835#41—138no—
836#41—138no—
837#41—138no—
838#41—134no—
839#41—134no—
840#41—1332no—
841#41—1332no—
842#41—138no—
843#41—138no—
844#41—138no—
845#41—138no—
846#41—2632no—
847#41—2632no—
848#41—2632no—
849#41—2632no—
850#41—2616no—
851#41—2616no—
852#41—2616no—
853#41—2616no—
854#41—2632no—
855#41—2632no—
856#41—2616no—
857#41—2616no—
858#41—2632no—
859#41—2632no—
860#41—2616no—
861#41—2616no—
862#41—2616no—
863#41—2616no—
864#41—264no—
865#41—264no—
866#41—264no—
867#41—264no—
868#41—264no—
869#41—264no—
870#41—264no—
871#41—264no—
872#41—264no—
873#41—264no—
874#41—264no—
875#41—264no—
876#41C23×D1318yes—
877#41C23×D1318yes—
878#41C23×D1318yes—
879#41C23×D1318yes—
880C2×Q8—22no—
881C2×Q8—22no—
882C2×Q8—22no—
883C2×Q8—134no—
884C2×Q8—134no—
885C2×Q8—132no—
886C2×Q8—132no—
887C2×Q8—1332no—
888C2×Q8—134no—
889C2×Q8—134no—
890C2×Q8—134no—
891C2×Q8—268no—
892C2×Q8—2616no—
893C2×Q8—2616no—
894C2×Q8—2616no—
895C2×Q8—2616no—
896C2×Q8—2616no—
897C2×Q8—262no—
898C2×Q8—262no—
899C2×Q8—262no—
900C2×Q8C23×D1314yes—
901C2×Q8C23×D1314yes—
902C2×Q8C23×D1314yes—
903C2×D4—24no—
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—24no—
909C2×D4—22no—
910C2×D4—22no—
911C2×D4—22no—
912C2×D4—138no—
913C2×D4—138no—
914C2×D4—134no—
915C2×D4—134no—
916C2×D4—1332no—
917C2×D4—134no—
918C2×D4—134no—
919C2×D4—132no—
920C2×D4—132no—
921C2×D4—134no—
922C2×D4—134no—
923C2×D4—134no—
924C2×D4—2616no—
925C2×D4—2616no—
926C2×D4—268no—
927C2×D4—2616no—
928C2×D4—268no—
929C2×D4—2632no—
930C2×D4—2632no—
931C2×D4—2616no—
932C2×D4—2616no—
933C2×D4—2632no—
934C2×D4—2632no—
935C2×D4—2632no—
936C2×D4—2632no—
937C2×D4—268no—
938C2×D4—264no—
939C2×D4—264no—
940C2×D4—264no—
941C2×D4—264no—
942C2×D4—264no—
943C2×D4—264no—
944C2×D4—262no—
945C2×D4—262no—
946C2×D4—262no—
947C2×D4C23×D1314yes—
948C2×D4C23×D1314yes—
949C2×D4C23×D1314yes—
950C22×C4—22no—
951C22×C4—24no—
952C22×C4—24no—
953C22×C4—24no—
954C22×C4—24no—
955C22×C4—24no—
956C22×C4—24no—
957C22×C4—132no—
958C22×C4—138no—
959C22×C4—134no—
960C22×C4—134no—
961C22×C4—138no—
962C22×C4—268no—
963C22×C4—2632no—
964C22×C4—2632no—
965C22×C4—268no—
966C22×C4—268no—
967C22×C4—262no—
968C22×C4—264no—
969C22×C4—264no—
970C22×C4—264no—
971C22×C4—264no—
972C22×C4—264no—
973C22×C4—264no—
974C22×C4D4×D1312yes—
975C22×C4D4×D1312yes—
976C22×C4D4×D1311yescharacteristic
977C22×C4D4×D1311yescharacteristic
978C22×C4D4×D1311yescharacteristic
979C22×C4C23×D1311yescharacteristic
980C22×C4C23×D1311yescharacteristic
981C22×C4C23×D1311yescharacteristic
982C22×C4C23×D1312yes—
983C22×C4C23×D1312yes—
984Q16—1332no—
985Q16—1316no—
986Q16C23×D13116yes—
987SD16—1332no—
988SD16—1332no—
989SD16—1332no—
990SD16C23×D13132yes—
991D8—1332no—
992D8—1316no—
993D8C23×D13116yes—
994M16—138no—
995M16—134no—
996M16—134no—
997M16—1332no—
998M16C23×D1318yes—
999M16C23×D1318yes—
1000C2×C8—134no—
1001C2×C8—138no—
1002C2×C8—1332no—
1003C2×C8C23×D1314yes—
1004C2×C8C23×D1314yes—
1005C2×C8C23×D1314yes—
1006C13#6309011yescharacteristic, complemented, Sylow
1007C23—24no—
1008C23—24no—
1009C23—24no—
1010C23—81no—
1011C23—84no—
1012C23—138no—
1013C23—134no—
1014C23—2632no—
1015C23—264no—
1016C23—264no—
1017C23—264no—
1018C23—1042no—
1019C23—1044no—
1020C23—10416no—
1021C23C2×D4×D1312yes—
1022C23C2×D4×D1311yescharacteristic
1023C23C2×D4×D1312yes—
1024C23C2×D4×D1311yescharacteristic
1025C23C2×D4×D1311yescharacteristic
1026Q8—24no—
1027Q8—24no—
1028Q8—24no—
1029Q8—134no—
1030Q8—138no—
1031Q8—134no—
1032Q8—138no—
1033Q8—2632no—
1034Q8—264no—
1035Q8—264no—
1036Q8—264no—
1037Q8C24×D1318yes—
1038D4—28no—
1039D4—28no—
1040D4—28no—
1041D4—28no—
1042D4—24no—
1043D4—24no—
1044D4—24no—
1045D4—138no—
1046D4—1316no—
1047D4—138no—
1048D4—134no—
1049D4—138no—
1050D4—134no—
1051D4—138no—
1052D4—2632no—
1053D4—2632no—
1054D4—2632no—
1055D4—268no—
1056D4—268no—
1057D4—268no—
1058D4—268no—
1059D4—264no—
1060D4—264no—
1061D4—264no—
1062D4C24×D1318yes—
1063C2×C4—24no—
1064C2×C4—24no—
1065C2×C4—24no—
1066C2×C4—28no—
1067C2×C4—28no—
1068C2×C4—28no—
1069C2×C4—28no—
1070C2×C4—138no—
1071C2×C4—134no—
1072C2×C4—1316no—
1073C2×C4—138no—
1074C2×C4—138no—
1075C2×C4—2632no—
1076C2×C4—2632no—
1077C2×C4—2632no—
1078C2×C4—264no—
1079C2×C4—264no—
1080C2×C4—264no—
1081C2×C4—268no—
1082C2×C4—268no—
1083C2×C4—268no—
1084C2×C4—268no—
1085C2×C4C2×D4×D1312yes—
1086C2×C4C2×D4×D1312yes—
1087C2×C4C2×D4×D1312yes—
1088C2×C4C2×D4×D1311yescharacteristic
1089C2×C4C2×D4×D1312yes—
1090C2×C4C2×D4×D1312yes—
1091C2×C4C2×D4×D1312yes—
1092C2×C4C2×D4×D1311yescharacteristic
1093C2×C4C2×D4×D1311yescharacteristic
1094C2×C4C2×D4×D1311yescharacteristic
1095C2×C4C2×D4×D1312yes—
1096C2×C4C2×D4×D1312yes—
1097C2×C4C2×D4×D1311yescharacteristic
1098C2×C4C24×D1312yes—
1099C2×C4C24×D1311yescharacteristic
1100C2×C4C24×D1311yescharacteristic
1101C2×C4C24×D1312yes—
1102C2×C4C24×D1311yescharacteristic
1103C8—138no—
1104C8C24×D1318yes—
1105C22—28no—
1106C22—42no—
1107C22—41no—
1108C22—42no—
1109C22—41no—
1110C22—41no—
1111C22—48no—
1112C22—84no—
1113C22—84no—
1114C22—138no—
1115C22—268no—
1116C22—524no—
1117C22—528no—
1118C22—528no—
1119C22—1044no—
1120C22—1044no—
1121C22—10432no—
1122C22C22×D4×D1311yescharacteristic
1123C22C22×D4×D1312yes—
1124C22C22×D4×D1312yes—
1125C22C22×D4×D1311yescharacteristic
1126C22C22×D4×D1311yescharacteristic
1127C4—28no—
1128C4—138no—
1129C4—268no—
1130C4C22×D4×D1311yescharacteristic
1131C4C22×D4×D1312yes—
1132C4C22×D4×D1312yes—
1133C4C22×D4×D1311yescharacteristic
1134C4C22×D4×D1311yescharacteristic
1135C4C25×D1311yescharacteristic
1136C2—22no—
1137C2—21no—
1138C2—22no—
1139C2—21no—
1140C2—21no—
1141C2—48no—
1142C2—268no—
1143C2—528no—
1144C2C23×D4×D1311yescharacteristic
subgroupG/H
centerC4C22×D4×D13
commutator, cosocleC4×C13C26
FrattiniC4C25×D13
FittingC2×C13×#575C2
socleC2×C13C24×D4
hypercenterC2×#575D13
hypocenterC13#63090
LCSG ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#575

Complements

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

NH ≅ G/Ntype
1. C2×#11719648C2semidirect
2. #13129620C2semidirect
3. #13129619C2semidirect
4. #13129613C2semidirect
5. #13129612C2semidirect
6. #13129609C2semidirect
7. #13129605C2semidirect
8. C2×#11719453C2semidirect
9. C2×#11719527C2semidirect
10. D13×#575C2semidirect
11. C2×#11719450C2semidirect
12. C2×C13×#575C2semidirect
13. C22×C13×#41C22semidirect
18. #11719648C22semidirect
19. #11719648C22semidirect
20. #11719648C22semidirect
21. #11719648C22semidirect
23. C2×#88257C22semidirect
25. C2×#88256C22semidirect
27. C2×#41×D13C22semidirect
28. C2×#88254C22semidirect
30. C2×#88251C22semidirect
33. C22×#6127C22semidirect
34. C13×#575C22semidirect
35. C13×#575C22semidirect
36. C13×#575C22semidirect
37. C2×C13×#137C22semidirect
38. C2×C13×AGL(1,ℤ/8)C22semidirect
39. C2×C13×#135C22semidirect
40. C22×C13×M16C22semidirect
41. C2×#88205C22semidirect
42. #11719527C22semidirect
43. #11719527C22semidirect
44. #11719527C22semidirect
45. #11719527C22semidirect
46. C2×#88204C22semidirect
47. C2×#88203C22semidirect
48. C2×#88196C22semidirect
49. C2×#88186C22semidirect
50. C22×#6099C22semidirect
51. #11719484C22semidirect
52. #11719483C22semidirect
53. #11719482C22semidirect
54. D13×#137C22semidirect
55. #11719480C22semidirect
56. #11719479C22semidirect
57. #11719478C22semidirect
58. D13×AGL(1,ℤ/8)C22semidirect
59. #11719476C22semidirect
60. #11719475C22semidirect
61. #11719474C22semidirect
62. #11719473C22semidirect
63. D13×#135C22semidirect
64. #11719471C22semidirect
65. #11719467C22semidirect
66. #11719462C22semidirect
67. #11719453C22semidirect
68. #11719453C22semidirect
69. #11719453C22semidirect
70. C2×#88163C22semidirect
71. C2×#88162C22semidirect
72. #11719450C22semidirect
73. #11719450C22semidirect
74. C2×#88161C22semidirect
75. C2×M16×D13C22semidirect
76. C2×#88158C22semidirect
77. C2×#88155C22semidirect
87. C2×C13×#41C23semidirect
88. C2×C13×#41C23semidirect
89. C2×C13×#41C23semidirect
90. C22×Q8×C13C23semidirect
92. C22×D4×C13C23semidirect
104. #88257C23semidirect
105. #88257C23semidirect
112. #88256C23semidirect
113. #88256C23semidirect
121. #41×D13C23semidirect
124. #88254C23semidirect
125. #88254C23semidirect
127. C2×#6131C23semidirect
129. C2×Q8×D13C23semidirect
136. #88251C23semidirect
137. #88251C23semidirect
141. C2×#6129C23semidirect
145. C2×D4×D13C23semidirect
171. C2×#6127C23semidirect
172. C2×#6127C23semidirect
173. C2×#6127C23semidirect
176. C22×D52C23semidirect
182. C22×Dic26C23semidirect
183. C13×#137C23semidirect
184. C13×#137C23semidirect
185. C13×AGL(1,ℤ/8)C23semidirect
186. C13×AGL(1,ℤ/8)C23semidirect
187. C13×#135C23semidirect
188. C13×#135C23semidirect
189. C2×C13×Q16C23semidirect
190. C2×C13×SD16C23semidirect
191. C2×C13×D8C23semidirect
193. C2×C13×M16C23semidirect
194. C2×C13×M16C23semidirect
195. C2×C13×M16C23semidirect
196. C22×C8×C13C23semidirect
197. #88205C23semidirect
198. #88205C23semidirect
199. #88204C23semidirect
200. #88204C23semidirect
201. #88203C23semidirect
202. #88203C23semidirect
203. C2×#6107C23semidirect
204. #88196C23semidirect
205. #88196C23semidirect
206. C2×#6106C23semidirect
207. C2×#6105C23semidirect
208. #88186C23semidirect
209. #88186C23semidirect
210. C2×#6104C23semidirect
212. C2×#6099C23semidirect
213. C2×#6099C23semidirect
214. C2×#6099C23semidirect
215. C22×#1055C23semidirect
216. #88173C23semidirect
217. #88172C23semidirect
218. Q16×D13C23semidirect
219. #88170C23semidirect
220. #88169C23semidirect
221. #88168C23semidirect
222. SD16×D13C23semidirect
223. #88166C23semidirect
224. #88165C23semidirect
225. D8×D13C23semidirect
226. #88163C23semidirect
227. #88163C23semidirect
228. #88162C23semidirect
229. #88162C23semidirect
230. #88161C23semidirect
231. M16×D13C23semidirect
232. C2×Dic52C23semidirect
233. #88158C23semidirect
234. #88158C23semidirect
235. C2×D104C23semidirect
236. C2×#6095C23semidirect
237. #88155C23semidirect
238. #88155C23semidirect
239. C2×#6094C23semidirect
240. C2×C8×D13C23semidirect
445. C2×#575D13semidirect
565. C22×#41C2×D13semidirect
586. #575C2×D13semidirect
587. #575C2×D13semidirect
588. #575C2×D13semidirect
593. C2×#137C2×D13semidirect
598. C2×AGL(1,ℤ/8)C2×D13semidirect
602. C2×#135C2×D13semidirect
609. C22×M16C2×D13semidirect
720. C2×#41C22×D13semidirect
721. C2×#41C22×D13semidirect
722. C2×#41C22×D13semidirect
728. C22×Q8C22×D13semidirect
740. C22×D4C22×D13semidirect
754. #137C22×D13semidirect
755. #137C22×D13semidirect
764. AGL(1,ℤ/8)C22×D13semidirect
765. AGL(1,ℤ/8)C22×D13semidirect
773. #135C22×D13semidirect
774. #135C22×D13semidirect
778. C2×Q16C22×D13semidirect
783. C2×SD16C22×D13semidirect
787. C2×D8C22×D13semidirect
798. C2×M16C22×D13semidirect
799. C2×M16C22×D13semidirect
800. C2×M16C22×D13semidirect
803. C22×C8C22×D13semidirect
1006. C13#63090semidirect

Maximal subgroups

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

subgroupindex
C2×#117196482
#131296202
#131296192
#131296132
#131296122
#131296092
#131296052
C2×#117194532
C2×#117195272
D13×#5752
C2×#117194502
C2×C13×#5752
#6309013