Finite Group Databasebeta

← #28319541

Subgroups — #28319541

Order 13568.

1458 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133304C211yesmaximal, characteristic
2C2×#16811629C211yesmaximal, characteristic, complemented
3C2×#16811626C211yesmaximal, characteristic, complemented
4C2×#16811596C211yesmaximal, characteristic
5#20290663C211yesmaximal, characteristic, complemented
6#20290662C211yesmaximal, characteristic, complemented
7#20290662C211yesmaximal, characteristic, complemented
8#20290661C211yesmaximal, characteristic, complemented
9#20290660C211yesmaximal, characteristic, complemented
10#20290660C211yesmaximal, characteristic, complemented
11#20290659C211yesmaximal, characteristic, complemented
12#20290658C211yesmaximal, characteristic, complemented
13#20290381C211yesmaximal, characteristic, complemented
14C2×#16811489C211yesmaximal, characteristic, complemented
15#20277200C211yesmaximal, characteristic
16C2×#13133304—24no—
17C2×#13133304—24no—
18C2×#13133304—24no—
19C22×#11719936C2211yescharacteristic
20C22×#11719940C2211yescharacteristic
21C22×#11719940C2211yescharacteristic
22C22×#11719940C2211yescharacteristic
23C22×D53⋊C8C2211yescharacteristic
24C23×#88324C2211yescharacteristic
25C23×#88324C2211yescharacteristic
26C23×#88324C2211yescharacteristic
27#16811629—24no—
28#16811626—24no—
29C2×#13133284C2211yescharacteristic
30C2×#13133284C2211yescharacteristic
31C2×#13133284C2211yescharacteristic
32C2×#13133284C2211yescharacteristic
33C2×C4⋊#88324C2211yescharacteristic
34C2×C4⋊#88324C2211yescharacteristic
35C2×C4⋊#88324C2211yescharacteristic
36C2×C4⋊#88324C2211yescharacteristic
37#16811596—24no—
38C2×#13133274C2211yescharacteristic
39C2×#13133274C2211yescharacteristic
40C2×C22⋊#88324C2211yescharacteristic
41C2×C22⋊#88324C2211yescharacteristic
42#16811489C2211yescharacteristic
43#16811489C2211yescharacteristic
44#16811489C2211yescharacteristic
45#16811489C2211yescharacteristic
46#16811489C2211yescharacteristic
47#16811489C2211yescharacteristic
48#16811489C2211yescharacteristic
49#16811489C2211yescharacteristic
50C22×#11719947C2211yescharacteristic
51C2×#13133173C2211yescharacteristic
52C22×C4×Dic53C2211yescharacteristic
53#16810527C411yescharacteristic
54#16810527C411yescharacteristic
55#16810523C411yescharacteristic
56#16810523C411yescharacteristic
57#16810503C411yescharacteristic
58#16810502C411yescharacteristic
59#16810500C411yescharacteristic
60C22⋊C4×Dic53C2211yescharacteristic
61C22⋊C4×Dic53C2211yescharacteristic
62#16810470C2211yescharacteristic
63#16810470C2211yescharacteristic
64C53×#386C411yescharacteristic
65#13133304—232no—
66C2×#11719936—22no—
67C2×#11719936—22no—
68C2×#11719936—22no—
69C2×#11719940—22no—
70C2×#11719940—22no—
71C2×#11719940—22no—
72C2×#11719940—22no—
73C2×#11719940—22no—
74C2×#11719940—22no—
75C2×#11719940—22no—
76C2×#11719940—22no—
77C2×#11719940D414yes—
78C2×D53⋊C8—22no—
79C2×D53⋊C8—22no—
80C2×D53⋊C8—22no—
81C22×#88324—22no—
82C22×#88324—22no—
83C22×#88324—22no—
84C22×#88324—22no—
85C22×#88324—22no—
86C22×#88324—22no—
87C22×#88324—22no—
88C22×#88324—22no—
89C22×#88324D414yes—
90C22×#88324C2311yescharacteristic
91C22×#88324C2311yescharacteristic
92C22×#88324C2311yescharacteristic
93C22×#88324C2311yescharacteristic
94C22×#88324C2311yescharacteristic
95C22×#88324C2311yescharacteristic
96C22×#88324C2311yescharacteristic
97C22×#88324C2311yescharacteristic
98#13133284—22no—
99#13133284—22no—
100#13133284—22no—
101#13133284—22no—
102C4⋊#88324—22no—
103C4⋊#88324—22no—
104C4⋊#88324—22no—
105C4⋊#88324—22no—
106#13133274—22no—
107#13133274—22no—
108C22⋊#88324—22no—
109C22⋊#88324—22no—
110C2×#11719947—22no—
111C2×#11719947—22no—
112C2×#11719947—22no—
113C2×#11719947—22no—
114C2×#11719947D414yes—
115C2×#11719947Q814yes—
116C22×Dic106C2×C411yescharacteristic
117C22×C22⋊D53C2×C411yescharacteristic
118C22×C22⋊D53C2×C411yescharacteristic
119C23×Dic53C2×C411yescharacteristic
120C23×Dic53C2311yescharacteristic
121C23×Dic53C2311yescharacteristic
122C22×C4×D53C2311yescharacteristic
123#13133173—22no—
124#13133173—22no—
125C2×#11719919C2×C411yescharacteristic
126C2×#11719919C2×C411yescharacteristic
127C2×C22⋊Dic53C2×C411yescharacteristic
128C2×C22⋊Dic53C2×C411yescharacteristic
129C2×C22⋊Dic53C2×C411yescharacteristic
130C2×#11719921C2×C411yescharacteristic
131C2×#11719921C2×C411yescharacteristic
132C2×#11719921C2×C411yescharacteristic
133C2×#11719921C2×C411yescharacteristic
134C2×C4×Dic53—22no—
135C2×C4×Dic53—22no—
136C2×C4×Dic53C2×C411yescharacteristic
137C2×C4×Dic53C2×C411yescharacteristic
138C2×C4×Dic53C2311yescharacteristic
139C2×C4×Dic53C2311yescharacteristic
140C2×C4×Dic53C2311yescharacteristic
141C2×C4×Dic53C2311yescharacteristic
142#13133124C2×C411yescharacteristic
143#13133124C2×C411yescharacteristic
144#13133124C2×C411yescharacteristic
145#13133124C2×C411yescharacteristic
146#13133124C2×C411yescharacteristic
147#13133124C2×C411yescharacteristic
148C22×D4×C53C2×C411yescharacteristic
149C23×C4×C53C2×C411yescharacteristic
150C2×C22⋊C4×C53C2×C411yescharacteristic
151C2×C22⋊C4×C53C2×C411yescharacteristic
152C2×C22⋊C4×C53C2×C411yescharacteristic
153#95×C53C2×C411yescharacteristic
154#95×C53C2×C411yescharacteristic
155C24×C53C22×C411yescharacteristic
156C24×C53C22×C411yescharacteristic
157C23×D53C22×C411yescharacteristic
158C2×D4×C53—22no—
159C2×D4×C53—22no—
160C2×D4×C53C4⋊C414yes—
161C22×C4×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—41no—
164C22×C4×C53C22×C411yescharacteristic
165C22×C4×C53C22×C411yescharacteristic
166C22×C4×C53C22×C411yescharacteristic
167C22×C4×C53C22×C411yescharacteristic
168C22×C4×C53C22×C411yescharacteristic
169C2×C22⋊D53—22no—
170C2×C22⋊D53—22no—
171C2×C22⋊D53—22no—
172C2×C22⋊D53—22no—
173C2×C22⋊D53C4⋊C414yes—
174C2×C22⋊D53C4⋊C414yes—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—41no—
182C22×Dic53C22×C411yescharacteristic
183C22×Dic53C22×C411yescharacteristic
184C22×Dic53C22×C411yescharacteristic
185C22×Dic53C22×C411yescharacteristic
186C22×Dic53C22×C411yescharacteristic
187C22×Dic53C22×C411yescharacteristic
188C22×Dic53C2×D412yes—
189C22×Dic53C2×D412yes—
190C22×Dic53C2×D412yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×Q812yes—
193C22×Dic53C2×Q812yes—
194C22×Dic53#4112yes—
195C22×Dic53#4112yes—
196C22×Dic53C2411yescharacteristic
197#11719947—28no—
198#11719947—28no—
199#11719947—28no—
200#11719947—28no—
201C2×C4×D53—21no—
202C2×C4×D53—21no—
203C2×C4×D53—21no—
204C2×C4×D53—21no—
205C2×C4×D53C2×D412yes—
206C2×C4×D53C2×Q812yes—
207C2×Dic106—22no—
208C2×Dic106—22no—
209C2×Dic106C4⋊C414yes—
210#11719940—28no—
211#11719940—28no—
212#11719940—44no—
213C2×#88324—28no—
214C2×#88324—28no—
215C2×#88324—21no—
216C2×#88324—21no—
217C2×#88324—21no—
218C2×#88324—21no—
219C2×#88324—21no—
220C2×#88324—21no—
221C2×#88324—21no—
222C2×#88324—21no—
223C2×#88324—21no—
224C2×#88324—21no—
225C2×#88324—21no—
226C2×#88324—21no—
227C2×#88324—21no—
228C2×#88324—21no—
229C2×#88324—21no—
230C2×#88324—21no—
231C2×#88324—21no—
232C2×#88324—21no—
233C2×#88324—21no—
234C2×#88324—21no—
235C2×#88324—44no—
236C2×#88324C2×D412yes—
237C2×#88324C2×D412yes—
238C2×#88324C2×D412yes—
239C2×#88324C2×D412yes—
240#11719936—28no—
241D53⋊C8—28no—
242C22⋊C4×C53—22no—
243C22⋊C4×C53—22no—
244C22⋊C4×C53—41no—
245C22⋊Dic53—22no—
246C22⋊Dic53—22no—
247C22⋊Dic53—41no—
248#11719921—22no—
249#11719921—22no—
250#11719921—41no—
251#11719921—41no—
252#11719919—22no—
253#11719919—22no—
254C4×Dic53—22no—
255C4×Dic53—22no—
256C4×Dic53—21no—
257C4×Dic53—21no—
258C4×Dic53—21no—
259C4×Dic53—21no—
260C4×Dic53—21no—
261C4×Dic53—21no—
262C4×Dic53—21no—
263C4×Dic53—21no—
264C23×C53—21no—
265C23×C53—21no—
266C23×C53—21no—
267C23×C53—21no—
268C23×C53—21no—
269C23×C53—21no—
270C23×C53—21no—
271C23×C53—21no—
272C23×C53—21no—
273C23×C53—21no—
274C23×C53C2×C4⋊C412yes—
275C23×C53C2×C4⋊C412yes—
276C23×C53C4×D412yes—
277C23×C53C4×D412yes—
278C23×C53C23×C411yescharacteristic
279C22×D53—21no—
280C22×D53—21no—
281C22×D53—21no—
282C22×D53—21no—
283C22×D53—21no—
284C22×D53—21no—
285C22×D53C2×C4⋊C412yes—
286D4×C53—28no—
287C2×C4×C53—21no—
288C2×C4×C53—21no—
289C2×C4×C53—21no—
290C2×C4×C53—21no—
291C2×C4×C53—21no—
292C2×C4×C53—21no—
293C2×C4×C53—21no—
294C2×C4×C53—21no—
295C2×C4×C53—21no—
296C2×C4×C53—21no—
297C2×C4×C53—21no—
298C2×C4×C53—21no—
299C2×C4×C53—21no—
300C2×C4×C53—44no—
301C2×C4×C53C2×C4⋊C412yes—
302C2×C4×C53#13112yescomplemented
303C22⋊D53—28no—
304C22⋊D53—28no—
305C2×Dic53—21no—
306C2×Dic53—21no—
307C2×Dic53—21no—
308C2×Dic53—21no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—21no—
314C2×Dic53—21no—
315C2×Dic53—21no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—21no—
321C2×Dic53—21no—
322C2×Dic53—44no—
323C2×Dic53C2×C4⋊C412yes—
324C2×Dic53C2×C4⋊C412yes—
325C2×Dic53C4×D412yes—
326C2×Dic53C4×D412yes—
327C2×Dic53#12014yes—
328C2×Dic53C22⋊Q814yes—
329C2×Dic53C22⋊Q814yes—
330C2×Dic53#12314yes—
331C2×Dic53#13112yescomplemented
332C2×Dic53C22×D411yescharacteristic
333C2×Dic53C22×D411yescharacteristic
334C2×Dic53C22×D411yescharacteristic
335C2×Dic53C22×Q811yescharacteristic
336C2×Dic53C2×#4111yescharacteristic
337C2×Dic53C2×#4111yescharacteristic
338C4×D53—22no—
339C4×D53—22no—
340C4×D53—22no—
341C4×D53—22no—
342Dic106—28no—
343#88324—22no—
344#88324—22no—
345#88324—22no—
346#88324—22no—
347#88324—41no—
348#88324—41no—
349#88324—41no—
350#88324—41no—
351#20839—531nomaximal, Sylow
352C22×C53—22no—
353C22×C53—22no—
354C22×C53—22no—
355C22×C53—22no—
356C22×C53—22no—
357C22×C53—22no—
358C22×C53—22no—
359C22×C53—22no—
360C22×C53—22no—
361C22×C53—41no—
362C22×C53—41no—
363C22×C53—41no—
364C22×C53—41no—
365C22×C53#38514yes—
366C22×C53C22×C4⋊C411yescharacteristic
367C22×C53C2×C4×D411yescharacteristic
368C22×C53C2×C4×D411yescharacteristic
369C22×C53C2×#13111yescharacteristic
370C22×C53C2×#13111yescharacteristic
371C22×C53#56811yescharacteristic
372C22×C53#56811yescharacteristic
373C2×D53—22no—
374C2×D53—22no—
375C2×D53—22no—
376C2×D53—41no—
377C2×D53—41no—
378C2×D53—41no—
379C2×D53—41no—
380C4×C53—22no—
381C4×C53—22no—
382C4×C53—41no—
383C4×C53—41no—
384C4×C53—41no—
385Dic53—22no—
386Dic53—22no—
387Dic53—41no—
388Dic53—41no—
389Dic53—41no—
390Dic53#38514yes—
391Dic53C2×#12011yescharacteristic
392Dic53C2×C22⋊Q811yescharacteristic
393Dic53C2×C22⋊Q811yescharacteristic
394Dic53C2×#12311yescharacteristic
395C22×#131—531no—
396C2×#424—531no—
397C2×#423—531no—
398C2×#408—531no—
399#2297—531no—
400#1851—531no—
401#1851—531no—
402#1851—531no—
403#1851—531no—
404#1850—531no—
405#1850—531no—
406#1850—531no—
407#1850—531no—
408#1729—531no—
409C2×#336—531no—
410C2×C53—24no—
411C2×C53—42no—
412C2×C53C2×#38511yescharacteristic
413C2×C53#290611yescharacteristic
414C2×C53#290611yescharacteristic
415C2×C53#293111yescharacteristic
416C2×C53#293211yescharacteristic
417C2×C53#293311yescharacteristic
418C2×C53#293311yescharacteristic
419D53—42no—
420C22×#41—531no—
421C2×#131—1064no—
422C2×#131—1064no—
423C2×#131—1064no—
424C22×M16—531no—
425C22×M16—531no—
426C22×M16—531no—
427C22×M16—531no—
428C23×C8—531no—
429C23×C8—531no—
430C23×C8—531no—
431C23×C8—531no—
432C2×#117—531no—
433C22×C42—531no—
434#424—1064no—
435#423—1064no—
436C2×C4⋊C8—531no—
437C2×C4⋊C8—531no—
438C2×C4⋊C8—531no—
439C2×C4⋊C8—531no—
440C2×C4⋊C8—531no—
441C2×C4⋊C8—531no—
442C2×C4⋊C8—531no—
443C2×C4⋊C8—531no—
444#408—1064no—
445C2×C22⋊C8—531no—
446C2×C22⋊C8—531no—
447C2×C22⋊C8—531no—
448C2×C22⋊C8—531no—
449#391—531no—
450#391—531no—
451#390—531no—
452#390—531no—
453#386—531no—
454#386—531no—
455#386—531no—
456#386#615711yescharacteristic
457C4×C22⋊C4—531no—
458C4×C22⋊C4—531no—
459C4×C22⋊C4—531no—
460C4×C22⋊C4—531no—
461#336—531no—
462#336—531no—
463#336—531no—
464#336—531no—
465#336—531no—
466#336—531no—
467#336—531no—
468#336—531no—
469C53#2083911yescharacteristic, complemented, Sylow
470C2×#41—534no—
471C2×#41—534no—
472C2×#41—1062no—
473C2×#41—1062no—
474C2×#41—1062no—
475C2×#41—1062no—
476C22×Q8—531no—
477C22×D4—531no—
478C22×D4—531no—
479C22×D4C2×#615711yescharacteristic
480C23×C4—531no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—531no—
484C23×C4C2×#615711yescharacteristic
485#131—10632no—
486C2×M16—534no—
487C2×M16—1062no—
488C2×M16—1062no—
489C2×M16—1062no—
490C2×M16—1062no—
491C2×M16—1062no—
492C2×M16—1062no—
493C2×M16—1062no—
494C2×M16—1062no—
495C2×M16—1062no—
496C2×M16—1062no—
497C2×M16—1062no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—534no—
503C22×C8—531no—
504C22×C8—531no—
505C22×C8—531no—
506C22×C8—531no—
507C22×C8—1062no—
508C22×C8—1062no—
509C22×C8—1062no—
510C22×C8—1062no—
511C22×C8—1062no—
512C22×C8—1062no—
513C22×C8—1062no—
514C22×C8—1062no—
515C22×C8—1062no—
516C22×C8—1062no—
517C22×C8—1062no—
518#117—1062no—
519#117—1062no—
520C2×C4⋊C4—531no—
521C2×C4⋊C4—531no—
522C2×C22⋊C4—531no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4—531no—
525C2×C22⋊C4—531no—
526C2×C22⋊C4—531no—
527C2×C22⋊C4—531no—
528C2×C22⋊C4—531no—
529C2×C22⋊C4C2×#615711yescharacteristic
530C2×C22⋊C4C2×#615711yescharacteristic
531C2×C22⋊C4C2×#615711yescharacteristic
532C2×C42—531no—
533C2×C42—531no—
534C2×C42—531no—
535C2×C42—531no—
536C2×C42—531no—
537C2×C42—531no—
538C2×C42—1062no—
539C2×C42—1062no—
540C4⋊C8—1062no—
541C4⋊C8—1062no—
542C4⋊C8—1062no—
543C4⋊C8—1062no—
544C4⋊C8—1062no—
545C4⋊C8—1062no—
546C4⋊C8—1062no—
547C4⋊C8—1062no—
548C22⋊C8—1062no—
549C22⋊C8—1062no—
550C22⋊C8—1062no—
551C22⋊C8—1062no—
552#95—531no—
553#95—531no—
554#95—531no—
555#95—531no—
556#95—531no—
557#95—531no—
558#95C2×#615711yescharacteristic
559#95C2×#615711yescharacteristic
560C24—531no—
561C24C22×#615711yescharacteristic
562C24C22×#615711yescharacteristic
563#41—1068no—
564#41—1068no—
565#41—1068no—
566#41—1068no—
567C2×Q8—534no—
568C2×Q8—1062no—
569C2×Q8—1062no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—534no—
573C2×D4—534no—
574C2×D4—1062no—
575C2×D4—1062no—
576C2×D4—1062no—
577C2×D4—1062no—
578C2×D4C4⋊#615714yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—41no—
582C22×C4—532no—
583C22×C4—532no—
584C22×C4—532no—
585C22×C4—532no—
586C22×C4—532no—
587C22×C4—532no—
588C22×C4—531no—
589C22×C4—531no—
590C22×C4—532no—
591C22×C4—532no—
592C22×C4—531no—
593C22×C4—531no—
594C22×C4—532no—
595C22×C4—532no—
596C22×C4—531no—
597C22×C4—531no—
598C22×C4—531no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—2121no—
610C22×C4C22×#615711yescharacteristic
611C22×C4C22×#615711yescharacteristic
612C22×C4C22×#615711yescharacteristic
613C22×C4C22×#615711yescharacteristic
614C22×C4C22×#615711yescharacteristic
615M16—1068no—
616M16—1068no—
617M16—1068no—
618M16—2124no—
619C2×C8—532no—
620C2×C8—532no—
621C2×C8—532no—
622C2×C8—532no—
623C2×C8—1061no—
624C2×C8—1061no—
625C2×C8—1061no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C2×C8—1061no—
630C2×C8—1061no—
631C2×C8—1068no—
632C2×C8—1068no—
633C2×C8—1068no—
634C2×C8—1061no—
635C2×C8—1061no—
636C2×C8—1061no—
637C2×C8—1061no—
638C2×C8—1061no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8—1061no—
646C2×C8—2124no—
647C4⋊C4—1062no—
648C4⋊C4—1062no—
649C22⋊C4—22no—
650C22⋊C4—22no—
651C22⋊C4—41no—
652C22⋊C4—1062no—
653C22⋊C4—1062no—
654C22⋊C4—1062no—
655C22⋊C4—1062no—
656C22⋊C4—2121no—
657C22⋊C4—2121no—
658C22⋊C4—2121no—
659C42—1061no—
660C42—1061no—
661C42—1061no—
662C42—1061no—
663C42—1062no—
664C42—1061no—
665C42—1062no—
666C42—1061no—
667C42—1061no—
668C42—1061no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—532no—
680C23—1061no—
681C23—1061no—
682C23—1061no—
683C23—1061no—
684C23—1061no—
685C23—1061no—
686C23C2×C4⋊#615712yes—
687C23C2×C4⋊#615712yes—
688C23D4×#615712yes—
689C23D4×#615712yes—
690C23C23×#615711yescharacteristic
691Q8—1068no—
692D4—28no—
693D4—1068no—
694D4—1068no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—44no—
709C2×C4—534no—
710C2×C4—534no—
711C2×C4—534no—
712C2×C4—534no—
713C2×C4—532no—
714C2×C4—531no—
715C2×C4—531no—
716C2×C4—532no—
717C2×C4—532no—
718C2×C4—531no—
719C2×C4—531no—
720C2×C4—531no—
721C2×C4—531no—
722C2×C4—532no—
723C2×C4—532no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1061no—
733C2×C4—1061no—
734C2×C4—1061no—
735C2×C4—1061no—
736C2×C4—1061no—
737C2×C4—1061no—
738C2×C4—1061no—
739C2×C4—1061no—
740C2×C4—1061no—
741C2×C4—1061no—
742C2×C4—1061no—
743C2×C4—1061no—
744C2×C4—1061no—
745C2×C4—2124no—
746C2×C4C2×C4⋊#615712yes—
747C2×C4#1313330412yescomplemented
748C8—1062no—
749C8—1062no—
750C8—1062no—
751C8—1062no—
752C8—2121no—
753C8—2121no—
754C8—2121no—
755C8—2121no—
756C22—22no—
757C22—22no—
758C22—22no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—41no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—1062no—
770C22—1062no—
771C22—1062no—
772C22—2121no—
773C22—2121no—
774C22—2121no—
775C22—2121no—
776C22#1681157014yes—
777C22C22×C4⋊#615711yescharacteristic
778C22C2×D4×#615711yescharacteristic
779C22C2×D4×#615711yescharacteristic
780C22C2×#1313330411yescharacteristic
781C22D53⋊#13111yescharacteristic
782C22#1681170111yescharacteristic
783C22#1681170211yescharacteristic
784C4—22no—
785C4—22no—
786C4—41no—
787C4—41no—
788C4—41no—
789C4—531no—
790C4—531no—
791C4—531no—
792C4—531no—
793C4—534no—
794C4—1062no—
795C4—1062no—
796C4—2121no—
797C4—2121no—
798C4—2121no—
799C2—24no—
800C2—42no—
801C2—2122no—
802C2C2×#1681157011yescharacteristic
803C2#2029136011yescharacteristic
804C2#2029136211yescharacteristic
805C2#2029143811yescharacteristic
806C2#2029144311yescharacteristic
807C2#2029144711yescharacteristic
808C2#2029144911yescharacteristic
subgroupG/H
center, FrattiniC23C23×#6157
commutator, socleC23×C53C23×C4
FittingC53×#386C4
prime radicalC22×#11719947C22
cosocleC22×Dic53C24
hypercenter#386#6157
hypocenterC53#20839
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×#16811629C2semidirect
3. C2×#16811626C2semidirect
5. #20290663C2semidirect
6. #20290662C2semidirect
7. #20290662C2semidirect
8. #20290661C2semidirect
9. #20290660C2semidirect
10. #20290660C2semidirect
11. #20290659C2semidirect
12. #20290658C2semidirect
13. #20290381C2semidirect
14. C2×#16811489C2semidirect
302. C2×C4×C53#131semidirect
331. C2×Dic53#131semidirect
469. C53#20839semidirect
747. C2×C4#13133304semidirect

Maximal subgroups

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

subgroupindex
C22×#131333042
C2×#168116292
C2×#168116262
C2×#168115962
#202906632
#202906622
#202906612
#202906602
#202906592
#202906582
#202903812
C2×#168114892
#202772002
#2083953