Finite Group Databasebeta

← #27399596

Subgroups — #27399596

Order 13568.

1530 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811282C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic, complemented
3C2×#16810622C211yesmaximal, characteristic, complemented
4C22×#13133140C211yesmaximal, characteristic, complemented
5#20275647C211yesmaximal, characteristic, complemented
6#20275529C211yesmaximal, characteristic, complemented
7#20275146C211yesmaximal, characteristic, complemented
8#20275141C211yesmaximal, characteristic, complemented
9#20275032C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20274717C211yesmaximal, characteristic, complemented
12#20274653C211yesmaximal, characteristic, complemented
13#20274649C211yesmaximal, characteristic, complemented
14#20274548C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C53C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×Dic106C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20#16811282—24no—
21#16811282C418yescomplemented
22C2×#13133205C2211yescharacteristic
23C2×#13133203—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133195—21no—
26C2×#13133191C2211yescharacteristic
27C2×#13133189—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×#13133177—21no—
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic
32#16810622—24no—
33C2×#13133140—24no—
34C2×#13133140C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133140C2211yescharacteristic
38C2×#13133140C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41C2×#13133140C2211yescharacteristic
42C2×#13133137C2211yescharacteristic
43C2×#13133137C2211yescharacteristic
44C2×#13133137C2211yescharacteristic
45C2×#13133137C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic
48C2×#13133128C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53C2×C4×D4×C53—21no—
54C2×C4×D4×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C22×C4⋊C4×C53C2211yescharacteristic
57C53×#389—21no—
58C53×#385—21no—
59C53×#385—21no—
60C53×#384C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C53×#380C2211yescharacteristic
63C4×C4⋊C4×C53C2211yescharacteristic
64C2×#11719945—22no—
65C2×#11719945—22no—
66C2×#11719945—22no—
67C2×#11719945—41no—
68C2×#11719945—41no—
69C2×#11719945C2×C414yescomplemented
70C22×Dic106—22no—
71C22×Dic106—22no—
72C22×Dic106—22no—
73C22×Dic106—21no—
74C22×Dic106—41no—
75C22×Dic106—41no—
76C22×Dic106C2×C414yescomplemented
77C22×Dic106C2311yescharacteristic
78C22×Dic106C2311yescharacteristic
79C22×D212C2311yescharacteristic
80C22×C22⋊D53—21no—
81C22×C22⋊D53—21no—
82C23×Dic53—21no—
83C22×C4×D53—21no—
84C2×#11719917—22no—
85C2×#11719917—22no—
86C2×#11719917—41no—
87C22×#88322—22no—
88C22×#88322—22no—
89C22×#88322—41no—
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93C22×#88322C2311yescharacteristic
94#13133205—22no—
95#13133205C2×C414yescomplemented
96#13133203—28no—
97#13133196—22no—
98#13133196C2×C414yescomplemented
99#13133195—28no—
100#13133191—22no—
101#13133191C2×C414yescomplemented
102#13133189—28no—
103C4×Dic106—22no—
104C4×Dic106C2×C414yescomplemented
105#13133177—28no—
106C2×C4⋊Dic53C2311yescharacteristic
107C2×#11719919—21no—
108C2×#11719919—21no—
109C2×C22⋊Dic53—21no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113C2×C4×Dic53—21no—
114C4⋊#88322—22no—
115#13133140—22no—
116#13133140—22no—
117#13133140—22no—
118#13133140—22no—
119#13133140—22no—
120#13133140—41no—
121#13133140—41no—
122#13133140D414yescomplemented
123#13133137—22no—
124#13133137—22no—
125#13133137—41no—
126#13133137—41no—
127C22⋊#88322—22no—
128C22⋊#88322—22no—
129#13133128—22no—
130C22×D4×C53D411yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53—21no—
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C4×D4×C53—44no—
136C4×D4×C53C2×C414yes—
137C4×D4×C53D414yes—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—21no—
140C2×C4⋊C4×C53—21no—
141C2×C4⋊C4×C53—21no—
142C2×C4⋊C4×C53—22no—
143C2×C4⋊C4×C53—22no—
144C2×C4⋊C4×C53—41no—
145C2×C4⋊C4×C53—41no—
146C2×C4⋊C4×C53D411yescharacteristic
147C2×C4⋊C4×C53C2311yescharacteristic
148C2×C4⋊C4×C53C2311yescharacteristic
149C2×C4⋊C4×C53C2311yescharacteristic
150C2×C4⋊C4×C53C2311yescharacteristic
151C2×C22⋊C4×C53—21no—
152C2×C22⋊C4×C53—21no—
153C2×C22⋊C4×C53D411yescharacteristic
154C2×C22⋊C4×C53D411yescharacteristic
155C2×C42×C53—21no—
156C2×C42×C53C2311yescharacteristic
157#95×C53—21no—
158#95×C53—21no—
159#95×C53—21no—
160C24×C53C2×D411yescharacteristic
161C24×C53C2×D411yescharacteristic
162C23×D53—21no—
163C2×D4×C53—22no—
164C2×D4×C53—22no—
165C2×D4×C53C22⋊C414yes—
166C22×C4×C53—21no—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—21no—
171C22×C4×C53—21no—
172C22×C4×C53—21no—
173C22×C4×C53—21no—
174C22×C4×C53—21no—
175C22×C4×C53—21no—
176C22×C4×C53—21no—
177C22×C4×C53—21no—
178C22×C4×C53—42no—
179C22×C4×C53—42no—
180C22×C4×C53—42no—
181C22×C4×C53—42no—
182C22×C4×C53—81no—
183C22×C4×C53—81no—
184C22×C4×C53C22×C412yes—
185C22×C4×C53C22×C412yes—
186C22×C4×C53C2×D411yescharacteristic
187C22×C4×C53C2×D411yescharacteristic
188C22×C4×C53C2×D411yescharacteristic
189C22×C4×C53C2×D411yescharacteristic
190C22×C4×C53C2×D412yes—
191C22×C4×C53C2×D412yes—
192C22×C4×C53C2411yescharacteristic
193C2×C22⋊D53—24no—
194C2×C22⋊D53—24no—
195C2×C22⋊D53—42no—
196C2×C22⋊D53—42no—
197C2×C22⋊D53—42no—
198C2×C22⋊D53—42no—
199C22×Dic53—21no—
200C22×Dic53—24no—
201C22×Dic53—21no—
202C22×Dic53—21no—
203C22×Dic53—42no—
204C22×Dic53—42no—
205#11719945—28no—
206#11719945—44no—
207#11719945—44no—
208#11719945—44no—
209C2×D212—21no—
210C2×D212—21no—
211C2×D212—21no—
212C2×D212—21no—
213C2×D212—21no—
214C2×D212C22×C412yes—
215C2×C4×D53—24no—
216C2×C4×D53—42no—
217C2×C4×D53—42no—
218C2×Dic106—21no—
219C2×Dic106—21no—
220C2×Dic106—21no—
221C2×Dic106—21no—
222C2×Dic106—21no—
223C2×Dic106—21no—
224C2×Dic106—21no—
225C2×Dic106—28no—
226C2×Dic106—24no—
227C2×Dic106—21no—
228C2×Dic106—44no—
229C2×Dic106—44no—
230C2×Dic106—44no—
231C2×Dic106—42no—
232C2×Dic106—42no—
233C2×Dic106C22×C412yes—
234C2×Dic106C22×C412yes—
235C2×Dic106C2×D412yes—
236C2×Dic106#4112yes—
237C4⋊C4×C53—21no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53—21no—
241C4⋊C4×C53—21no—
242C4⋊C4×C53—21no—
243C4⋊C4×C53—21no—
244C4⋊C4×C53—42no—
245C4⋊C4×C53—42no—
246C4⋊C4×C53—42no—
247C4⋊C4×C53—81no—
248C4⋊C4×C53C22⋊C414yes—
249C4⋊C4×C53C2×D412yes—
250C22⋊C4×C53—42no—
251C22⋊C4×C53—42no—
252C22⋊C4×C53C22⋊C414yes—
253C22⋊C4×C53C22⋊C414yes—
254C42×C53—42no—
255C42×C53C22×C412yes—
256C42×C53C2×D412yes—
257C22⋊Dic53—24no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261C4⋊Dic53—21no—
262C4⋊Dic53C22×C412yes—
263#11719919—24no—
264#11719919—24no—
265C4×Dic53—24no—
266#11719917—44no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—21no—
272C2×#88322—21no—
273C2×#88322—21no—
274C2×#88322—21no—
275C2×#88322—21no—
276C2×#88322—21no—
277C2×#88322—21no—
278C2×#88322—44no—
279C2×#88322C2×D412yes—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53—21no—
284C23×C53—21no—
285C23×C53—21no—
286C23×C53—21no—
287C23×C53—21no—
288C23×C53—21no—
289C23×C53—21no—
290C23×C53C2×C22⋊C412yes—
291C23×C53C2×C22⋊C412yes—
292C23×C53AGL(1,ℤ/8)12yes—
293C23×C53#13712yes—
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—41no—
297C22×D53—41no—
298C22×D53—41no—
299C22×D53—41no—
300C22×D53—41no—
301C22×D53—41no—
302D4×C53—28no—
303C2×C4×C53—21no—
304C2×C4×C53—21no—
305C2×C4×C53—21no—
306C2×C4×C53—21no—
307C2×C4×C53—21no—
308C2×C4×C53—21no—
309C2×C4×C53—21no—
310C2×C4×C53—21no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—41no—
321C2×C4×C53—41no—
322C2×C4×C53—41no—
323C2×C4×C53—41no—
324C2×C4×C53—41no—
325C2×C4×C53—41no—
326C2×C4×C53—41no—
327C2×C4×C53—41no—
328C2×C4×C53—41no—
329C2×C4×C53—41no—
330C2×C4×C53—41no—
331C2×C4×C53—84no—
332C2×C4×C53—84no—
333C2×C4×C53C2×C22⋊C412yes—
334C2×C4×C53C2×C22⋊C412yes—
335C2×C4×C53C2×C22⋊C412yes—
336C2×C4×C53C2×C22⋊C412yes—
337C2×C4×C53C23×C411yescharacteristic
338C2×C4×C53C22×D411yescharacteristic
339C2×C4×C53C22×D411yescharacteristic
340C2×C4×C53C2×#4111yescharacteristic
341C2×C4×C53H(5,𝔽2)11yescharacteristic
342C2×C4×C53H(5,𝔽2)11yescharacteristic
343C22⋊D53—48no—
344C22⋊D53—48no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—22no—
348C2×Dic53—22no—
349C2×Dic53—22no—
350C2×Dic53—48no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—41no—
354C2×Dic53—41no—
355D212—22no—
356D212—22no—
357D212—41no—
358D212—41no—
359C4×D53—48no—
360Dic106—22no—
361Dic106—22no—
362Dic106—22no—
363Dic106—22no—
364Dic106—22no—
365Dic106—48no—
366Dic106—41no—
367Dic106—41no—
368Dic106C4×D414yescomplemented
369#88322—22no—
370#88322—41no—
371#88322—41no—
372#88322—41no—
373#22421—531nomaximal, Sylow
374C22×C53—22no—
375C22×C53—22no—
376C22×C53—22no—
377C22×C53—22no—
378C22×C53—22no—
379C22×C53—22no—
380C22×C53—22no—
381C22×C53—22no—
382C22×C53—22no—
383C22×C53—41no—
384C22×C53—41no—
385C22×C53—41no—
386C22×C53—41no—
387C22×C53#41714yescomplemented
388C22×C53C22×C22⋊C411yescharacteristic
389C22×C53D4211yescharacteristic
390C22×C53#54611yescharacteristic
391C22×C53C2×AGL(1,ℤ/8)11yescharacteristic
392C22×C53C2×#13711yescharacteristic
393C22×C53#57711yescharacteristic
394C22×C53#57811yescharacteristic
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—81no—
399C2×D53—81no—
400C2×D53—81no—
401C2×D53—81no—
402C4×C53—22no—
403C4×C53—22no—
404C4×C53—22no—
405C4×C53—22no—
406C4×C53—42no—
407C4×C53—81no—
408C4×C53—81no—
409C4×C53—81no—
410C4×C53C2×C4×D411yescharacteristic
411C4×C53#51811yescharacteristic
412C4×C53D4211yescharacteristic
413C4×C53#54611yescharacteristic
414Dic53—24no—
415Dic53—42no—
416Dic53—42no—
417C2×#548—531no—
418C2×#435—531no—
419C2×#417—531no—
420C22×#103—531no—
421D4×C4⋊C4D5311yescharacteristic, complemented
422#1983—531no—
423#1959—531no—
424#1894—531no—
425#1893—531no—
426#1874—531no—
427#1872—531no—
428#1803—531no—
429#1788—531no—
430#1787—531no—
431#1763—531no—
432C2×C53—24no—
433C2×C53—42no—
434C2×C53D4×C22⋊C411yescharacteristic
435C2×C53C2×#41711yescharacteristic
436C2×C53#289811yescharacteristic
437C2×C53#326511yescharacteristic
438C2×C53#327011yescharacteristic
439C2×C53#330811yescharacteristic
440C2×C53#331611yescharacteristic
441D53—82no—
442C22×#41—531no—
443C23×Q8—531no—
444C22×M16—531no—
445C23×C8—531no—
446#548—538no—
447#548—1064no—
448C2×#124—531no—
449C2×#124—1061no—
450C2×C22⋊Q8—531no—
451C2×C22⋊Q8—1061no—
452C2×#121—531no—
453C2×#121—1061no—
454C2×C4×Q8—531no—
455C2×C4×D4—21no—
456C2×C4×D4—1061no—
457C2×C4×D4C2×D5311yescharacteristic
458C22×C4⋊C4C2×D5311yescharacteristic
459C22×C4⋊C4C2×D5311yescharacteristic
460#435—1064no—
461C2×C4⋊C8—531no—
462#417—1064no—
463C2×#103—531no—
464C2×#103—531no—
465C2×#103—531no—
466C2×#103—531no—
467C2×#103—531no—
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—1064no—
472C2×#102—531no—
473C2×#102—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×C22⋊C8—531no—
477C2×C22⋊C8—531no—
478C2×#97—531no—
479#389—21no—
480#385—21no—
481#385—21no—
482#384C2×D5311yescharacteristic
483#380C2×D5311yescharacteristic
484#380C2×D5311yescharacteristic
485C4×C4⋊C4C2×D5311yescharacteristic
486#340—531no—
487#340—531no—
488#340—531no—
489#340—531no—
490C53#2242111yescharacteristic, complemented, Sylow
491C2×#41—534no—
492C2×#41—1062no—
493C2×#41—1062no—
494C2×#41—1062no—
495C2×#41—2121no—
496C2×#41—2121no—
497C22×Q8—534no—
498C22×Q8—531no—
499C22×Q8—531no—
500C22×Q8—1062no—
501C22×Q8—1062no—
502C22×Q8—1062no—
503C22×Q8—1061no—
504C22×Q8—2121no—
505C22×Q8—2121no—
506C22×D4—531no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4C22⋊D5311yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4C22×D5311yescharacteristic
515C23×C4C22×D5311yescharacteristic
516C2×M16—1062no—
517C2×M16—1062no—
518C2×M16—2121no—
519C22×C8—531no—
520C22×C8—531no—
521C22×C8—531no—
522C22×C8—531no—
523C22×C8—1062no—
524C22×C8—1062no—
525C22×C8—2121no—
526#124—534no—
527#124—1068no—
528#124—1062no—
529C22⋊Q8—534no—
530C22⋊Q8—1062no—
531C22⋊Q8—1068no—
532#121—534no—
533#121—1068no—
534#121—1062no—
535C4×Q8—534no—
536C4×Q8—1062no—
537C4×D4—44no—
538C4×D4—1068no—
539C4×D4C4×D5314yes—
540C4×D4D21214yes—
541C2×C4⋊C4—22no—
542C2×C4⋊C4—22no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—41no—
548C2×C4⋊C4—41no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4C22⋊D5311yescharacteristic
553C2×C4⋊C4C22×D5311yescharacteristic
554C2×C4⋊C4C22×D5311yescharacteristic
555C2×C4⋊C4C22×D5311yescharacteristic
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4C22⋊D5311yescharacteristic
564C2×C22⋊C4C22⋊D5311yescharacteristic
565C2×C42—21no—
566C2×C42—1061no—
567C2×C42C22×D5311yescharacteristic
568C4⋊C8—1062no—
569#103—534no—
570#103—1062no—
571#103—1062no—
572#103—1062no—
573#103—1062no—
574#103—1062no—
575#103—2121no—
576#103—2121no—
577#102—1062no—
578#102—1062no—
579#102—2121no—
580#102—2121no—
581C22⋊C8—1062no—
582C22⋊C8—1062no—
583#97—1062no—
584#95—21no—
585#95—21no—
586#95—21no—
587C24—1061no—
588C24C2×C22⋊D5311yescharacteristic
589C24C2×C22⋊D5311yescharacteristic
590#41—1068no—
591#41—2124no—
592#41—2124no—
593#41—2124no—
594C2×Q8—532no—
595C2×Q8—532no—
596C2×Q8—532no—
597C2×Q8—532no—
598C2×Q8—1068no—
599C2×Q8—1064no—
600C2×Q8—1061no—
601C2×Q8—1061no—
602C2×Q8—1061no—
603C2×Q8—1061no—
604C2×Q8—1061no—
605C2×Q8—1061no—
606C2×Q8—1061no—
607C2×Q8—1061no—
608C2×Q8—2122no—
609C2×Q8—2122no—
610C2×Q8—2124no—
611C2×Q8—2124no—
612C2×Q8—2124no—
613C2×D4—22no—
614C2×D4—22no—
615C2×D4—532no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1061no—
619C2×D4—1061no—
620C2×D4—1061no—
621C2×D4—1061no—
622C2×D4—1061no—
623C2×D4—2122no—
624C2×D4—2122no—
625C2×D4—2122no—
626C2×D4—2122no—
627C2×D4#1171992114yes—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—42no—
643C22×C4—42no—
644C22×C4—81no—
645C22×C4—81no—
646C22×C4—1061no—
647C22×C4—1064no—
648C22×C4—1061no—
649C22×C4—1061no—
650C22×C4—1064no—
651C22×C4—2122no—
652C22×C4—2122no—
653C22×C4—2122no—
654C22×C4—2122no—
655C22×C4C2×C4×D5312yes—
656C22×C4C2×C4×D5312yes—
657C22×C4C2×D21212yes—
658C22×C4C2×D21212yes—
659C22×C4C2×C22⋊D5311yescharacteristic
660C22×C4C2×C22⋊D5311yescharacteristic
661C22×C4C2×C22⋊D5311yescharacteristic
662C22×C4C2×C22⋊D5311yescharacteristic
663C22×C4C23×D5311yescharacteristic
664M16—2124no—
665C2×C8—532no—
666C2×C8—1061no—
667C2×C8—1061no—
668C2×C8—1061no—
669C2×C8—1061no—
670C2×C8—1061no—
671C2×C8—1061no—
672C2×C8—1061no—
673C2×C8—1061no—
674C2×C8—1061no—
675C2×C8—1061no—
676C2×C8—1061no—
677C2×C8—2124no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—42no—
686C4⋊C4—42no—
687C4⋊C4—42no—
688C4⋊C4—81no—
689C4⋊C4—532no—
690C4⋊C4—1064no—
691C4⋊C4—1064no—
692C4⋊C4—1061no—
693C4⋊C4#1171992114yes—
694C4⋊C4D4×D5312yes—
695C22⋊C4—42no—
696C22⋊C4—42no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4#1171992114yes—
702C22⋊C4#1171992114yes—
703C42—42no—
704C42—1064no—
705C42C2×C4×D5312yes—
706C42C2×D21212yes—
707C23—21no—
708C23—21no—
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—1062no—
718C23—2121no—
719C23—2121no—
720C23—2121no—
721C23—2121no—
722C23—2121no—
723C23—2121no—
724C23C2×#1171992112yes—
725C23C2×#1171992112yes—
726C23#1313324312yes—
727C23#1313324812yes—
728C23C22×C22⋊D5311yescharacteristic
729Q8—534no—
730Q8—1062no—
731Q8—1062no—
732Q8—1062no—
733Q8—1062no—
734Q8—1062no—
735Q8—2128no—
736Q8—2121no—
737Q8—2121no—
738D4—28no—
739D4—1062no—
740D4—1062no—
741D4—2128no—
742D4—2128no—
743D4—2121no—
744D4—2121no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—84no—
774C2×C4—84no—
775C2×C4—1062no—
776C2×C4—1062no—
777C2×C4—1062no—
778C2×C4—1062no—
779C2×C4—1062no—
780C2×C4—2128no—
781C2×C4—2128no—
782C2×C4—2121no—
783C2×C4—2121no—
784C2×C4—2121no—
785C2×C4—2121no—
786C2×C4C2×#1171992112yes—
787C2×C4C2×#1171992112yes—
788C2×C4C2×#1171992112yes—
789C2×C4C2×#1171992112yes—
790C2×C4C22×C4×D5311yescharacteristic
791C2×C4C2×D4×D5311yescharacteristic
792C2×C4C22×D21211yescharacteristic
793C2×C4#41×D5311yescharacteristic
794C2×C4#1313326211yescharacteristic
795C2×C4#1313326311yescharacteristic
796C8—1062no—
797C8—2121no—
798C8—2121no—
799C8—2121no—
800C22—22no—
801C22—22no—
802C22—22no—
803C22—22no—
804C22—22no—
805C22—22no—
806C22—22no—
807C22—22no—
808C22—22no—
809C22—41no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—4241no—
814C22—4241no—
815C22—4241no—
816C22—4241no—
817C22—2122no—
818C22—2122no—
819C22—2122no—
820C22#1681062214yescomplemented
821C22C22×#1171992111yescharacteristic
822C22D4×C22⋊D5311yescharacteristic
823C22#1681126111yescharacteristic
824C22C2×#1313324311yescharacteristic
825C22C2×#1313324811yescharacteristic
826C22#1681143411yescharacteristic
827C22#1681143811yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—1064no—
837C4—2122no—
838C4—2122no—
839C4C4×D4×D5311yescharacteristic
840C4#1681109511yescharacteristic
841C4D4×D21211yescharacteristic
842C4#1681126811yescharacteristic
843C2—24no—
844C2—42no—
845C2—4242no—
846C2D4×#1171992111yescharacteristic
847C2C2×#1681062211yescharacteristic
848C2#2028324511yescharacteristic
849C2#2028620611yescharacteristic
850C2#2028628611yescharacteristic
851C2#2028670011yescharacteristic
852C2#2028682011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingD4×C4⋊C4×C53C2
socleC23×C53C22×D4
prime radicalC2×#16811282C2
cosocleC22×C4×C53C24
hypercenterD4×C4⋊C4D53
hypocenterC53#22421
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#16810695C2semidirect
3. C2×#16810622C2semidirect
4. C22×#13133140C2semidirect
5. #20275647C2semidirect
6. #20275529C2semidirect
7. #20275146C2semidirect
8. #20275141C2semidirect
9. #20275032C2semidirect
10. #20275022C2semidirect
11. #20274717C2semidirect
12. #20274653C2semidirect
13. #20274649C2semidirect
14. #20274548C2semidirect
15. D4×C4⋊C4×C53C2semidirect
21. #16811282C4semidirect
69. C2×#11719945C2×C4semidirect
76. C22×Dic106C2×C4semidirect
95. #13133205C2×C4semidirect
98. #13133196C2×C4semidirect
101. #13133191C2×C4semidirect
104. C4×Dic106C2×C4semidirect
122. #13133140D4semidirect
368. Dic106C4×D4semidirect
387. C22×C53#417semidirect
421. D4×C4⋊C4D53semidirect
490. C53#22421semidirect
820. C22#16810622semidirect

Maximal subgroups

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

subgroupindex
C2×#168112822
C2×#168106952
C2×#168106222
C22×#131331402
#202756472
#202755292
#202751462
#202751412
#202750322
#202750222
#202747172
#202746532
#202746492
#202745482
D4×C4⋊C4×C532
#2242153