Finite Group Databasebeta

← #27399604

Subgroups — #27399604

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×#16810625C211yesmaximal, characteristic, complemented
3C22×#13133142C211yesmaximal, characteristic, complemented
4D4×C4⋊Dic53C211yesmaximal, characteristic, complemented
5#20275645C211yesmaximal, characteristic, complemented
6#20275531C211yesmaximal, characteristic, complemented
7#20275148C211yesmaximal, characteristic, complemented
8#20275143C211yesmaximal, characteristic, complemented
9#20275030C211yesmaximal, characteristic, complemented
10#20275020C211yesmaximal, characteristic, complemented
11#20274721C211yesmaximal, characteristic, complemented
12#20274656C211yesmaximal, characteristic, complemented
13#20274651C211yesmaximal, characteristic, complemented
14#20274546C211yesmaximal, characteristic, complemented
15C2×C53×#435C211yesmaximal, characteristic, complemented
16C22×#11719945C2211yescharacteristic
17C23×Dic106C2211yescharacteristic
18#16811282—24no—
19#16811282C418yescomplemented
20C2×#13133205C2211yescharacteristic
21C2×#13133203—21no—
22C2×#13133196C2211yescharacteristic
23C2×#13133195—21no—
24C2×#13133191C2211yescharacteristic
25C2×#13133189—21no—
26C2×C4×Dic106C2211yescharacteristic
27C2×D4×Dic53—21no—
28C2×#13133177—21no—
29C22×C4⋊Dic53C2211yescharacteristic
30C22×C4⋊Dic53C2211yescharacteristic
31#16810625—24no—
32C2×#13133142—24no—
33C2×#13133142C2211yescharacteristic
34C2×#13133142C2211yescharacteristic
35C2×#13133142C2211yescharacteristic
36C2×#13133142C2211yescharacteristic
37C2×#13133142C2211yescharacteristic
38C2×#13133142C2211yescharacteristic
39C2×#13133142C2211yescharacteristic
40C2×#13133142C2211yescharacteristic
41C2×#13133139C2211yescharacteristic
42C2×#13133139C2211yescharacteristic
43C2×#13133139C2211yescharacteristic
44C2×#13133139C2211yescharacteristic
45#16810522—21no—
46#16810498—21no—
47#16810498—21no—
48#16810493C2211yescharacteristic
49#16810483C2211yescharacteristic
50#16810483C2211yescharacteristic
51C4×C4⋊Dic53C2211yescharacteristic
52#16810386C2211yescharacteristic
53#16810386C2211yescharacteristic
54#16810386C2211yescharacteristic
55#16810386C2211yescharacteristic
56C22×M16×C53C2211yescharacteristic
57C23×C8×C53C2211yescharacteristic
58C2×C4×D4×C53C2211yescharacteristic
59C53×#435—24no—
60C2×C4⋊C8×C53C2211yescharacteristic
61C2×C22⋊C8×C53C2211yescharacteristic
62C2×C22⋊C8×C53C2211yescharacteristic
63C2×#97×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—
83C23×Dic53—21no—
84C23×Dic53—21no—
85C22×C4×D53—21no—
86#13133205—22no—
87#13133205C2×C414yescomplemented
88#13133203—28no—
89#13133196—22no—
90#13133196C2×C414yescomplemented
91#13133195—28no—
92#13133191—22no—
93#13133191C2×C414yescomplemented
94#13133189—28no—
95C4×Dic106—22no—
96C4×Dic106C2×C414yescomplemented
97D4×Dic53—44no—
98#13133177—28no—
99C2×C4⋊Dic53—21no—
100C2×C4⋊Dic53—21no—
101C2×C4⋊Dic53—21no—
102C2×C4⋊Dic53—21no—
103C2×C4⋊Dic53—22no—
104C2×C4⋊Dic53—22no—
105C2×C4⋊Dic53—41no—
106C2×C4⋊Dic53—41no—
107C2×C4⋊Dic53C2311yescharacteristic
108C2×C4⋊Dic53C2311yescharacteristic
109C2×C4⋊Dic53C2311yescharacteristic
110C2×C4⋊Dic53C2311yescharacteristic
111C2×C4⋊Dic53C2311yescharacteristic
112C2×#11719919—21no—
113C2×#11719919—21no—
114C2×C22⋊Dic53—21no—
115C2×C22⋊Dic53—21no—
116C2×C22⋊Dic53—21no—
117C2×#11719921—21no—
118C2×#11719921—21no—
119C2×#11719921—21no—
120C2×C4×Dic53—21no—
121C2×C4×Dic53—21no—
122#13133142—22no—
123#13133142—22no—
124#13133142—22no—
125#13133142—22no—
126#13133142—22no—
127#13133142—41no—
128#13133142—41no—
129#13133142D414yescomplemented
130#13133139—22no—
131#13133139—22no—
132#13133139—41no—
133#13133139—41no—
134#13133124—21no—
135#13133124—21no—
136#13133124—21no—
137C22×D4×C53D411yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C2×M16×C53—22no—
141C2×M16×C53—22no—
142C2×M16×C53—41no—
143C22×C8×C53—22no—
144C22×C8×C53—22no—
145C22×C8×C53—41no—
146C22×C8×C53C2311yescharacteristic
147C22×C8×C53C2311yescharacteristic
148C22×C8×C53C2311yescharacteristic
149C22×C8×C53C2311yescharacteristic
150C4×D4×C53C2×C414yes—
151C4×D4×C53D414yes—
152C2×C4⋊C4×C53D411yescharacteristic
153C2×C22⋊C4×C53D411yescharacteristic
154C2×C22⋊C4×C53D411yescharacteristic
155C2×C42×C53C2311yescharacteristic
156C4⋊C8×C53—22no—
157C22⋊C8×C53—22no—
158C22⋊C8×C53—22no—
159#97×C53—22no—
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×C53C22×C412yes—
175C22×C4×C53C22×C412yes—
176C22×C4×C53C2×D411yescharacteristic
177C22×C4×C53C2×D411yescharacteristic
178C22×C4×C53C2×D411yescharacteristic
179C22×C4×C53C2×D411yescharacteristic
180C22×C4×C53C2×D412yes—
181C22×C4×C53C2×D412yes—
182C22×C4×C53C2411yescharacteristic
183C2×C22⋊D53—24no—
184C2×C22⋊D53—24no—
185C2×C22⋊D53—42no—
186C2×C22⋊D53—42no—
187C2×C22⋊D53—42no—
188C2×C22⋊D53—42no—
189C22×Dic53—21no—
190C22×Dic53—24no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—21no—
197C22×Dic53—42no—
198C22×Dic53—42no—
199C22×Dic53—42no—
200C22×Dic53—42no—
201C22×Dic53—42no—
202C22×Dic53—42no—
203C22×Dic53—81no—
204C22×Dic53—81no—
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—
237M16×C53—44no—
238C2×C8×C53—21no—
239C2×C8×C53—21no—
240C2×C8×C53—21no—
241C2×C8×C53—21no—
242C2×C8×C53—21no—
243C2×C8×C53—21no—
244C2×C8×C53—21no—
245C2×C8×C53—21no—
246C2×C8×C53—21no—
247C2×C8×C53—21no—
248C2×C8×C53—21no—
249C2×C8×C53—44no—
250C2×C8×C53C2×D412yes—
251C4⋊C4×C53C22⋊C414yes—
252C22⋊C4×C53C22⋊C414yes—
253C22⋊C4×C53C22⋊C414yes—
254C42×C53C22×C412yes—
255C42×C53C2×D412yes—
256C22⋊Dic53—24no—
257C22⋊Dic53—42no—
258C22⋊Dic53—42no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262C4⋊Dic53—21no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—21no—
269C4⋊Dic53—21no—
270C4⋊Dic53—42no—
271C4⋊Dic53—42no—
272C4⋊Dic53—42no—
273C4⋊Dic53—81no—
274C4⋊Dic53C22×C412yes—
275C4⋊Dic53C2×D412yes—
276#11719919—24no—
277#11719919—24no—
278C4×Dic53—24no—
279C4×Dic53—42no—
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×C53C2×C22⋊C412yes—
320C2×C4×C53C2×C22⋊C412yes—
321C2×C4×C53C2×C22⋊C412yes—
322C2×C4×C53C2×C22⋊C412yes—
323C2×C4×C53C23×C411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4111yescharacteristic
327C2×C4×C53H(5,𝔽2)11yescharacteristic
328C2×C4×C53H(5,𝔽2)11yescharacteristic
329C22⋊D53—48no—
330C22⋊D53—48no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—48no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342C2×Dic53—41no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—41no—
347C2×Dic53—41no—
348C2×Dic53—41no—
349C2×Dic53—41no—
350C2×Dic53—41no—
351C2×Dic53—41no—
352C2×Dic53—41no—
353C2×Dic53—84no—
354C2×Dic53—84no—
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
369C8×C53—22no—
370C8×C53—41no—
371C8×C53—41no—
372C8×C53—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×C53C2×C4×D411yescharacteristic
407C4×C53#51811yescharacteristic
408C4×C53D4211yescharacteristic
409C4×C53#54611yescharacteristic
410Dic53—24no—
411Dic53—42no—
412Dic53—42no—
413Dic53—42no—
414Dic53—81no—
415Dic53—81no—
416Dic53—81no—
417C2×#548—531no—
418C2×#435D5311yescharacteristic, complemented
419C2×#417—531no—
420C22×#103—531no—
421D4×C4⋊C4—531no—
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×M16C2×D5311yescharacteristic
445C23×C8C2×D5311yescharacteristic
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—1061no—
456C2×C4×D4—1061no—
457C2×C4×D4C2×D5311yescharacteristic
458C22×C4⋊C4—531no—
459C22×C4⋊C4—531no—
460#435—24no—
461C2×C4⋊C8C2×D5311yescharacteristic
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⋊C8C2×D5311yescharacteristic
477C2×C22⋊C8C2×D5311yescharacteristic
478C2×#97C2×D5311yescharacteristic
479#389—1061no—
480#385—1061no—
481#385—1061no—
482#384—531no—
483#380—531no—
484#380—531no—
485C4×C4⋊C4—531no—
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—1061no—
503C22×Q8—1062no—
504C22×Q8—2121no—
505C22×Q8—2121no—
506C22×D4—531no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4D21211yescharacteristic
510C23×C4—1061no—
511C23×C4—1061no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4C22×D5311yescharacteristic
515C23×C4C22×D5311yescharacteristic
516C2×M16—22no—
517C2×M16—22no—
518C2×M16—41no—
519C22×C8—22no—
520C22×C8—22no—
521C22×C8—41no—
522C22×C8C22×D5311yescharacteristic
523C22×C8C22×D5311yescharacteristic
524C22×C8C22×D5311yescharacteristic
525C22×C8C22×D5311yescharacteristic
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—1068no—
538C4×D4—2124no—
539C4×D4C4×D5314yes—
540C4×D4C22⋊D5314yes—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—531no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—531no—
546C2×C4⋊C4—1062no—
547C2×C4⋊C4—1062no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4—1061no—
550C2×C4⋊C4—1061no—
551C2×C4⋊C4—1061no—
552C2×C4⋊C4—1061no—
553C2×C4⋊C4—1061no—
554C2×C4⋊C4—2121no—
555C2×C4⋊C4—2121no—
556C2×C4⋊C4D21211yescharacteristic
557C2×C22⋊C4—1061no—
558C2×C22⋊C4—1061no—
559C2×C22⋊C4—1061no—
560C2×C22⋊C4—1061no—
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4D21211yescharacteristic
564C2×C22⋊C4D21211yescharacteristic
565C2×C42—1061no—
566C2×C42—1061no—
567C2×C42C22×D5311yescharacteristic
568C4⋊C8—22no—
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—22no—
582C22⋊C8—22no—
583#97—22no—
584#95—1061no—
585#95—1061no—
586#95—1061no—
587C24—1061no—
588C24C2×D21211yescharacteristic
589C24C2×D21211yescharacteristic
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—1061no—
637C22×C4—1064no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1064no—
642C22×C4—1061no—
643C22×C4—1061no—
644C22×C4—1061no—
645C22×C4—4241no—
646C22×C4—4241no—
647C22×C4—2122no—
648C22×C4—2122no—
649C22×C4—2122no—
650C22×C4—2122no—
651C22×C4—2122no—
652C22×C4—2122no—
653C22×C4—2122no—
654C22×C4—2122no—
655C22×C4C2×C4×D5312yes—
656C22×C4C2×C4×D5312yes—
657C22×C4C2×D21211yescharacteristic
658C22×C4C2×D21211yescharacteristic
659C22×C4C2×D21211yescharacteristic
660C22×C4C2×D21211yescharacteristic
661C22×C4C2×C22⋊D5312yes—
662C22×C4C2×C22⋊D5312yes—
663C22×C4C23×D5311yescharacteristic
664M16—44no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—44no—
677C2×C8D4×D5312yes—
678C4⋊C4—532no—
679C4⋊C4—532no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4—1061no—
683C4⋊C4—1061no—
684C4⋊C4—1061no—
685C4⋊C4—1061no—
686C4⋊C4—1061no—
687C4⋊C4—1061no—
688C4⋊C4—1061no—
689C4⋊C4—1061no—
690C4⋊C4—4241no—
691C4⋊C4—2122no—
692C4⋊C4—2122no—
693C4⋊C4—2122no—
694C4⋊C4#1171992114yes—
695C22⋊C4—1064no—
696C22⋊C4—1064no—
697C22⋊C4—1064no—
698C22⋊C4—1064no—
699C22⋊C4—2122no—
700C22⋊C4—2122no—
701C22⋊C4#1171992114yes—
702C22⋊C4#1171992114yes—
703C42—1064no—
704C42—2122no—
705C42C2×C4×D5312yes—
706C42C2×C22⋊D5312yes—
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#1313324512yes—
727C23#1313325012yes—
728C23C22×D21211yescharacteristic
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—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1062no—
766C2×C4—1062no—
767C2×C4—4244no—
768C2×C4—4244no—
769C2×C4—2128no—
770C2×C4—2128no—
771C2×C4—2121no—
772C2×C4—2121no—
773C2×C4—2121no—
774C2×C4—2121no—
775C2×C4—2121no—
776C2×C4—2121no—
777C2×C4—2121no—
778C2×C4—2121no—
779C2×C4—2121no—
780C2×C4—2121no—
781C2×C4—2121no—
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×C22⋊D5311yescharacteristic
793C2×C4#41×D5311yescharacteristic
794C2×C4#1313326211yescharacteristic
795C2×C4#1313326311yescharacteristic
796C8—22no—
797C8—41no—
798C8—41no—
799C8—41no—
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#1681062514yescomplemented
821C22C22×#1171992111yescharacteristic
822C22D4×D21211yescharacteristic
823C22#1681126811yescharacteristic
824C22C2×#1313324511yescharacteristic
825C22C2×#1313325011yescharacteristic
826C22#1681143511yescharacteristic
827C22#1681144011yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—1064no—
833C4—4241no—
834C4—4241no—
835C4—4241no—
836C4—2122no—
837C4—2122no—
838C4—2122no—
839C4C4×D4×D5311yescharacteristic
840C4#1681109511yescharacteristic
841C4D4×C22⋊D5311yescharacteristic
842C4#1681126111yescharacteristic
843C2—24no—
844C2—42no—
845C2—4242no—
846C2D4×#1171992111yescharacteristic
847C2C2×#1681062511yescharacteristic
848C2#2028324911yescharacteristic
849C2#2028621511yescharacteristic
850C2#2028629011yescharacteristic
851C2#2028670811yescharacteristic
852C2#2028682811yescharacteristic
subgroupG/H
centerC23C22×D212
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC2×C53×#435C2
socleC23×C53C22×D4
prime radicalC2×#16811282C2
cosocleC22×C4×C53C24
hypercenterC2×#435D53
hypocenterC53#22421
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#16810625C2semidirect
3. C22×#13133142C2semidirect
4. D4×C4⋊Dic53C2semidirect
5. #20275645C2semidirect
6. #20275531C2semidirect
7. #20275148C2semidirect
8. #20275143C2semidirect
9. #20275030C2semidirect
10. #20275020C2semidirect
11. #20274721C2semidirect
12. #20274656C2semidirect
13. #20274651C2semidirect
14. #20274546C2semidirect
15. C2×C53×#435C2semidirect
19. #16811282C4semidirect
69. C2×#11719945C2×C4semidirect
76. C22×Dic106C2×C4semidirect
87. #13133205C2×C4semidirect
90. #13133196C2×C4semidirect
93. #13133191C2×C4semidirect
96. C4×Dic106C2×C4semidirect
129. #13133142D4semidirect
368. Dic106C4×D4semidirect
387. C22×C53#417semidirect
418. C2×#435D53semidirect
490. C53#22421semidirect
820. C22#16810625semidirect

Maximal subgroups

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

subgroupindex
C2×#168112822
C2×#168106252
C22×#131331422
D4×C4⋊Dic532
#202756452
#202755312
#202751482
#202751432
#202750302
#202750202
#202747212
#202746562
#202746512
#202745462
C2×C53×#4352
#2242153