Finite Group Databasebeta

← #27399656

Subgroups — #27399656

Order 13568.

1446 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×Dic106C211yesmaximal, characteristic
2C2×#16810695C211yesmaximal, characteristic
3C2×#16810631C211yesmaximal, characteristic, complemented
4C22×#13133140C211yesmaximal, characteristic, complemented
5#20275638C211yesmaximal, characteristic, complemented
6#20275534C211yesmaximal, characteristic, complemented
7#20275146C211yesmaximal, characteristic, complemented
8#20275136C211yesmaximal, characteristic, complemented
9#20275027C211yesmaximal, characteristic, complemented
10#20275022C211yesmaximal, characteristic, complemented
11#20274727C211yesmaximal, characteristic, complemented
12#20274649C211yesmaximal, characteristic, complemented
13#20274649C211yesmaximal, characteristic, complemented
14#20274548C211yesmaximal, characteristic, complemented
15C53×#2352C211yesmaximal, characteristic
16C23×Dic106C2211yescharacteristic
17C23×Dic106C2211yescharacteristic
18C22×#11719917C2211yescharacteristic
19C23×#88322C2211yescharacteristic
20D4×Dic106—24no—
21D4×Dic106C418yescomplemented
22C2×#13133217C2211yescharacteristic
23C2×#13133216—21no—
24C2×#13133196C2211yescharacteristic
25C2×#13133196C2211yescharacteristic
26C2×#13133194—21no—
27C2×#13133194—21no—
28C2×C4×Dic106C2211yescharacteristic
29C2×D4×Dic53—21no—
30#16810695—24no—
31C2×C4⋊#88322C2211yescharacteristic
32#16810631—24no—
33C2×#13133140—24no—
34C2×#13133140C2211yescharacteristic
35C2×#13133140C2211yescharacteristic
36C2×#13133140C2211yescharacteristic
37C2×#13133140C2211yescharacteristic
38C2×#13133140C2211yescharacteristic
39C2×#13133140C2211yescharacteristic
40C2×#13133140C2211yescharacteristic
41C2×#13133140C2211yescharacteristic
42C2×#13133140C2211yescharacteristic
43C2×#13133140C2211yescharacteristic
44C2×#13133140C2211yescharacteristic
45C2×#13133140C2211yescharacteristic
46C2×C22⋊#88322C2211yescharacteristic
47C2×C22⋊#88322C2211yescharacteristic
48C2×#13133128C2211yescharacteristic
49#16810385C2211yescharacteristic
50#16810385C2211yescharacteristic
51#16810385C2211yescharacteristic
52#16810385C2211yescharacteristic
53C2×C4×D4×C53C2211yescharacteristic
54C2×#117×C53C2211yescharacteristic
55C22×C4⋊C4×C53C2211yescharacteristic
56C53×#388—21no—
57C53×#387—21no—
58C53×#386—21no—
59C53×#382C2211yescharacteristic
60C53×#380C2211yescharacteristic
61C53×#380C2211yescharacteristic
62C4×C4⋊C4×C53C2211yescharacteristic
63C4×C22⋊C4×C53—21no—
64C22×Dic106—22no—
65C22×Dic106—22no—
66C22×Dic106—22no—
67C22×Dic106—22no—
68C22×Dic106—22no—
69C22×Dic106—22no—
70C22×Dic106—21no—
71C22×Dic106—21no—
72C22×Dic106—41no—
73C22×Dic106—41no—
74C22×Dic106—41no—
75C22×Dic106—41no—
76C22×Dic106C2×C414yes—
77C22×Dic106C2×C414yescomplemented
78C22×Dic106C2311yescharacteristic
79C22×Dic106C2311yescharacteristic
80C22×Dic106C2311yescharacteristic
81C23×Dic53—21no—
82C23×Dic53—21no—
83C2×#11719917—22no—
84C2×#11719917—22no—
85C2×#11719917—41no—
86C22×#88322—22no—
87C22×#88322—22no—
88C22×#88322—41no—
89C22×#88322C2311yescharacteristic
90C22×#88322C2311yescharacteristic
91C22×#88322C2311yescharacteristic
92C22×#88322C2311yescharacteristic
93#13133217—22no—
94#13133217C2×C414yescomplemented
95#13133216—28no—
96#13133196—22no—
97#13133196—22no—
98#13133196C2×C414yes—
99#13133196C2×C414yescomplemented
100#13133194—28no—
101#13133194—28no—
102C4×Dic106—22no—
103C4×Dic106C2×C414yescomplemented
104D4×Dic53—28no—
105C2×C4⋊Dic53—21no—
106C2×C4⋊Dic53—21no—
107C2×C4⋊Dic53C2311yescharacteristic
108C2×#11719919—21no—
109C2×#11719919—21no—
110C2×#11719919—21no—
111C2×C22⋊Dic53—21no—
112C2×C22⋊Dic53—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—22no—
121#13133140—22no—
122#13133140—41no—
123#13133140—41no—
124#13133140—41no—
125#13133140—41no—
126#13133140D414yescomplemented
127C22⋊#88322—22no—
128C22⋊#88322—22no—
129#13133128—22no—
130C22×D4×C53D411yescharacteristic
131C23×C4×C53—21no—
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C4×D4×C53C2×C414yes—
135C4×D4×C53D414yes—
136#117×C53—22no—
137#117×C53—41no—
138C2×C4⋊C4×C53—21no—
139C2×C4⋊C4×C53—22no—
140C2×C4⋊C4×C53—41no—
141C2×C4⋊C4×C53D411yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C4⋊C4×C53C2311yescharacteristic
145C2×C4⋊C4×C53C2311yescharacteristic
146C2×C22⋊C4×C53—21no—
147C2×C22⋊C4×C53—21no—
148C2×C22⋊C4×C53—21no—
149C2×C22⋊C4×C53D411yescharacteristic
150C2×C22⋊C4×C53D411yescharacteristic
151C2×C42×C53—21no—
152C2×C42×C53—21no—
153C2×C42×C53C2311yescharacteristic
154#95×C53—21no—
155#95×C53—21no—
156#95×C53—21no—
157#95×C53—21no—
158#95×C53—21no—
159C24×C53C2×D411yescharacteristic
160C24×C53C2×D411yescharacteristic
161C2×D4×C53—22no—
162C2×D4×C53—22no—
163C2×D4×C53C22⋊C414yes—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
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—42no—
177C22×C4×C53—42no—
178C22×C4×C53—81no—
179C22×C4×C53C22×C412yes—
180C22×C4×C53C22×C412yes—
181C22×C4×C53C2×D411yescharacteristic
182C22×C4×C53C2×D411yescharacteristic
183C22×C4×C53C2×D411yescharacteristic
184C22×C4×C53C2×D411yescharacteristic
185C22×C4×C53C2×D412yes—
186C22×C4×C53C2×D412yes—
187C22×C4×C53C2411yescharacteristic
188C22×Dic53—21no—
189C22×Dic53—24no—
190C22×Dic53—24no—
191C22×Dic53—21no—
192C22×Dic53—21no—
193C22×Dic53—21no—
194C22×Dic53—42no—
195C22×Dic53—42no—
196C22×Dic53—42no—
197C22×Dic53—42no—
198C2×Dic106—21no—
199C2×Dic106—21no—
200C2×Dic106—21no—
201C2×Dic106—21no—
202C2×Dic106—21no—
203C2×Dic106—21no—
204C2×Dic106—21no—
205C2×Dic106—21no—
206C2×Dic106—21no—
207C2×Dic106—21no—
208C2×Dic106—21no—
209C2×Dic106—28no—
210C2×Dic106—28no—
211C2×Dic106—24no—
212C2×Dic106—24no—
213C2×Dic106—21no—
214C2×Dic106—21no—
215C2×Dic106—44no—
216C2×Dic106—44no—
217C2×Dic106—44no—
218C2×Dic106—44no—
219C2×Dic106—44no—
220C2×Dic106—44no—
221C2×Dic106—42no—
222C2×Dic106—42no—
223C2×Dic106—42no—
224C2×Dic106—42no—
225C2×Dic106C22×C412yes—
226C2×Dic106C22×C412yes—
227C2×Dic106C22×C412yes—
228C2×Dic106C2×D412yes—
229C2×Dic106#4112yes—
230C4⋊C4×C53—21no—
231C4⋊C4×C53—21no—
232C4⋊C4×C53—21no—
233C4⋊C4×C53—21no—
234C4⋊C4×C53—21no—
235C4⋊C4×C53—21no—
236C4⋊C4×C53—21no—
237C4⋊C4×C53—42no—
238C4⋊C4×C53C22⋊C414yes—
239C4⋊C4×C53C2×D412yes—
240C22⋊C4×C53—42no—
241C22⋊C4×C53—42no—
242C22⋊C4×C53—81no—
243C22⋊C4×C53C22⋊C414yes—
244C22⋊C4×C53C22⋊C414yes—
245C42×C53—42no—
246C42×C53—81no—
247C42×C53C22×C412yes—
248C42×C53C2×D412yes—
249C22⋊Dic53—24no—
250C22⋊Dic53—24no—
251C4⋊Dic53—24no—
252C4⋊Dic53—24no—
253C4⋊Dic53—21no—
254C4⋊Dic53C22×C412yes—
255#11719919—24no—
256#11719919—24no—
257#11719919—24no—
258C4×Dic53—24no—
259#11719917—44no—
260C2×#88322—21no—
261C2×#88322—21no—
262C2×#88322—21no—
263C2×#88322—21no—
264C2×#88322—21no—
265C2×#88322—21no—
266C2×#88322—21no—
267C2×#88322—21no—
268C2×#88322—21no—
269C2×#88322—21no—
270C2×#88322—21no—
271C2×#88322—44no—
272C2×#88322C2×D412yes—
273C23×C53—21no—
274C23×C53—21no—
275C23×C53—21no—
276C23×C53—21no—
277C23×C53—21no—
278C23×C53—21no—
279C23×C53—21no—
280C23×C53—21no—
281C23×C53—21no—
282C23×C53—21no—
283C23×C53C2×C22⋊C412yes—
284C23×C53C2×C22⋊C412yes—
285C23×C53#13712yes—
286C23×C53#13712yes—
287C23×C53C22×D411yescharacteristic
288D4×C53—28no—
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—22no—
298C2×C4×C53—22no—
299C2×C4×C53—22no—
300C2×C4×C53—22no—
301C2×C4×C53—22no—
302C2×C4×C53—22no—
303C2×C4×C53—22no—
304C2×C4×C53—22no—
305C2×C4×C53—22no—
306C2×C4×C53—41no—
307C2×C4×C53—41no—
308C2×C4×C53—41no—
309C2×C4×C53—41no—
310C2×C4×C53—41no—
311C2×C4×C53—41no—
312C2×C4×C53—41no—
313C2×C4×C53—41no—
314C2×C4×C53—41no—
315C2×C4×C53—41no—
316C2×C4×C53—41no—
317C2×C4×C53—84no—
318C2×C4×C53C2×C22⋊C412yes—
319C2×C4×C53C2×C22⋊C412yes—
320C2×C4×C53C2×C22⋊C412yes—
321C2×C4×C53C2×C22⋊C412yes—
322C2×C4×C53C23×C411yescharacteristic
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C22×D411yescharacteristic
325C2×C4×C53C2×#4111yescharacteristic
326C2×C4×C53H(5,𝔽2)11yescharacteristic
327C2×C4×C53H(5,𝔽2)11yescharacteristic
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—48no—
335C2×Dic53—48no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—41no—
342Dic106—22no—
343Dic106—22no—
344Dic106—22no—
345Dic106—22no—
346Dic106—22no—
347Dic106—22no—
348Dic106—22no—
349Dic106—48no—
350Dic106—48no—
351Dic106—41no—
352Dic106—41no—
353Dic106—41no—
354Dic106—41no—
355Dic106C4×D414yes—
356#88322—22no—
357#88322—41no—
358#88322—41no—
359#88322—41no—
360#22425—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—22no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—22no—
366C22×C53—22no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—41no—
371C22×C53—41no—
372C22×C53—41no—
373C22×C53—41no—
374C22×C53#41914yescomplemented
375C22×C53C22×C22⋊C411yescharacteristic
376C22×C53D4211yescharacteristic
377C22×C53#54611yescharacteristic
378C22×C53C2×#13711yescharacteristic
379C22×C53C2×#13711yescharacteristic
380C22×C53#57711yescharacteristic
381C22×C53#57811yescharacteristic
382C4×C53—22no—
383C4×C53—22no—
384C4×C53—22no—
385C4×C53—22no—
386C4×C53—42no—
387C4×C53—81no—
388C4×C53—81no—
389C4×C53—81no—
390C4×C53C2×C4×D411yescharacteristic
391C4×C53#51811yescharacteristic
392C4×C53D4211yescharacteristic
393C4×C53#54611yescharacteristic
394Dic53—24no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×D4×Q8—531no—
399C2×#435—531no—
400C2×#419—531no—
401C22×#103—531no—
402#2352D5311yescharacteristic
403#1981—531no—
404#1960—531no—
405#1894—531no—
406#1892—531no—
407#1873—531no—
408#1872—531no—
409#1805—531no—
410#1787—531no—
411#1787—531no—
412#1763—531no—
413C2×C53—24no—
414C2×C53—42no—
415C2×C53D4×C22⋊C411yescharacteristic
416C2×C53C2×#41911yescharacteristic
417C2×C53#289811yescharacteristic
418C2×C53#326611yescharacteristic
419C2×C53#327011yescharacteristic
420C2×C53#331211yescharacteristic
421C2×C53#332011yescharacteristic
422C23×Q8—531no—
423C23×Q8—531no—
424C22×M16—531no—
425C23×C8—531no—
426D4×Q8—538no—
427D4×Q8—1064no—
428C2×C4⋊Q8—531no—
429C2×C4⋊Q8—1061no—
430C2×C22⋊Q8—531no—
431C2×C22⋊Q8—531no—
432C2×C22⋊Q8—1061no—
433C2×C22⋊Q8—1061no—
434C2×C4×Q8—531no—
435C2×C4×D4—1061no—
436C2×C4×D4C2×D5311yescharacteristic
437C2×#117C2×D5311yescharacteristic
438C22×C4⋊C4C2×D5311yescharacteristic
439#435—1064no—
440C2×C4⋊C8—531no—
441#419—1064no—
442C2×#103—531no—
443C2×#103—531no—
444C2×#103—531no—
445C2×#103—531no—
446C2×#103—531no—
447C2×#103—531no—
448C2×#103—531no—
449C2×#103—531no—
450C2×#103—531no—
451C2×#103—531no—
452C2×#103—531no—
453C2×#103—531no—
454C2×#103—1064no—
455C2×C22⋊C8—531no—
456C2×C22⋊C8—531no—
457C2×#97—531no—
458#388—21no—
459#387—21no—
460#386—21no—
461#382C2×D5311yescharacteristic
462#380C2×D5311yescharacteristic
463#380C2×D5311yescharacteristic
464C4×C4⋊C4C2×D5311yescharacteristic
465C4×C22⋊C4—21no—
466#340—531no—
467#340—531no—
468#340—531no—
469#340—531no—
470C53#2242511yescharacteristic, complemented, Sylow
471C22×Q8—534no—
472C22×Q8—534no—
473C22×Q8—531no—
474C22×Q8—531no—
475C22×Q8—531no—
476C22×Q8—1062no—
477C22×Q8—1062no—
478C22×Q8—1062no—
479C22×Q8—1062no—
480C22×Q8—1062no—
481C22×Q8—1062no—
482C22×Q8—1061no—
483C22×Q8—1061no—
484C22×Q8—2121no—
485C22×Q8—2121no—
486C22×Q8—2121no—
487C22×Q8—2121no—
488C22×D4C22⋊D5311yescharacteristic
489C23×C4—21no—
490C23×C4—1061no—
491C23×C4—1061no—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C2×M16—1062no—
495C2×M16—1062no—
496C2×M16—2121no—
497C22×C8—531no—
498C22×C8—531no—
499C22×C8—531no—
500C22×C8—531no—
501C22×C8—1062no—
502C22×C8—1062no—
503C22×C8—2121no—
504C4⋊Q8—534no—
505C4⋊Q8—1068no—
506C4⋊Q8—1062no—
507C22⋊Q8—534no—
508C22⋊Q8—534no—
509C22⋊Q8—1062no—
510C22⋊Q8—1062no—
511C22⋊Q8—1068no—
512C22⋊Q8—1068no—
513C4×Q8—534no—
514C4×Q8—1062no—
515C4×D4—1068no—
516C4×D4C4×D5314yes—
517C4×D4D21214yes—
518#117—22no—
519#117—41no—
520C2×C4⋊C4—22no—
521C2×C4⋊C4—21no—
522C2×C4⋊C4—41no—
523C2×C4⋊C4—531no—
524C2×C4⋊C4—1061no—
525C2×C4⋊C4—1061no—
526C2×C4⋊C4—1061no—
527C2×C4⋊C4—1061no—
528C2×C4⋊C4—1061no—
529C2×C4⋊C4C22⋊D5311yescharacteristic
530C2×C4⋊C4C22×D5311yescharacteristic
531C2×C4⋊C4C22×D5311yescharacteristic
532C2×C4⋊C4C22×D5311yescharacteristic
533C2×C4⋊C4C22×D5311yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4—21no—
537C2×C22⋊C4—1061no—
538C2×C22⋊C4—1061no—
539C2×C22⋊C4C22⋊D5311yescharacteristic
540C2×C22⋊C4C22⋊D5311yescharacteristic
541C2×C42—21no—
542C2×C42—21no—
543C2×C42—1061no—
544C2×C42C22×D5311yescharacteristic
545C4⋊C8—1062no—
546#103—534no—
547#103—1062no—
548#103—1062no—
549#103—1062no—
550#103—1062no—
551#103—1062no—
552#103—1062no—
553#103—1062no—
554#103—2121no—
555#103—2121no—
556#103—2121no—
557#103—2121no—
558C22⋊C8—1062no—
559C22⋊C8—1062no—
560#97—1062no—
561#95—21no—
562#95—21no—
563#95—21no—
564#95—21no—
565#95—21no—
566C24C2×C22⋊D5311yescharacteristic
567C24C2×C22⋊D5311yescharacteristic
568C2×Q8—532no—
569C2×Q8—532no—
570C2×Q8—532no—
571C2×Q8—532no—
572C2×Q8—532no—
573C2×Q8—1068no—
574C2×Q8—1068no—
575C2×Q8—1064no—
576C2×Q8—1064no—
577C2×Q8—1061no—
578C2×Q8—1061no—
579C2×Q8—1061no—
580C2×Q8—1061no—
581C2×Q8—1061no—
582C2×Q8—1061no—
583C2×Q8—1061no—
584C2×Q8—1061no—
585C2×Q8—1061no—
586C2×Q8—1061no—
587C2×Q8—1061no—
588C2×Q8—1061no—
589C2×Q8—1061no—
590C2×Q8—2122no—
591C2×Q8—2122no—
592C2×Q8—2122no—
593C2×Q8—2122no—
594C2×Q8—2124no—
595C2×Q8—2124no—
596C2×Q8—2124no—
597C2×Q8—2124no—
598C2×Q8—2124no—
599C2×Q8—2124no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4#1171992114yes—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—42no—
616C22×C4—42no—
617C22×C4—81no—
618C22×C4—1061no—
619C22×C4—1064no—
620C22×C4—1064no—
621C22×C4—1061no—
622C22×C4—1061no—
623C22×C4—1061no—
624C22×C4—2122no—
625C22×C4—2122no—
626C22×C4—2122no—
627C22×C4—2122no—
628C22×C4C2×C4×D5312yes—
629C22×C4C2×C4×D5312yes—
630C22×C4C2×D21212yes—
631C22×C4C2×D21212yes—
632C22×C4C2×C22⋊D5311yescharacteristic
633C22×C4C2×C22⋊D5311yescharacteristic
634C22×C4C2×C22⋊D5311yescharacteristic
635C22×C4C2×C22⋊D5311yescharacteristic
636C22×C4C23×D5311yescharacteristic
637M16—2124no—
638C2×C8—532no—
639C2×C8—1061no—
640C2×C8—1061no—
641C2×C8—1061no—
642C2×C8—1061no—
643C2×C8—1061no—
644C2×C8—1061no—
645C2×C8—1061no—
646C2×C8—1061no—
647C2×C8—1061no—
648C2×C8—1061no—
649C2×C8—1061no—
650C2×C8—2124no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—42no—
659C4⋊C4—532no—
660C4⋊C4—1064no—
661C4⋊C4—1064no—
662C4⋊C4—1064no—
663C4⋊C4—1064no—
664C4⋊C4—1064no—
665C4⋊C4—1061no—
666C4⋊C4#1171992114yes—
667C4⋊C4D4×D5312yes—
668C22⋊C4—42no—
669C22⋊C4—42no—
670C22⋊C4—81no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4#1171992114yes—
674C22⋊C4#1171992114yes—
675C42—42no—
676C42—81no—
677C42—1064no—
678C42C2×C4×D5312yes—
679C42C2×D21212yes—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23C2×#1171992112yes—
691C23C2×#1171992112yes—
692C23#1313324712yes—
693C23#1313324712yes—
694C23C22×C22⋊D5311yescharacteristic
695Q8—534no—
696Q8—1062no—
697Q8—1062no—
698Q8—1062no—
699Q8—1062no—
700Q8—1062no—
701Q8—1062no—
702Q8—1062no—
703Q8—2128no—
704Q8—2128no—
705Q8—2121no—
706Q8—2121no—
707Q8—2121no—
708Q8—2121no—
709D4—28no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—84no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—2128no—
746C2×C4—2128no—
747C2×C4—2121no—
748C2×C4—2121no—
749C2×C4—2121no—
750C2×C4—2121no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4C2×#1171992112yes—
754C2×C4C2×#1171992112yes—
755C2×C4C2×#1171992112yes—
756C2×C4C2×#1171992112yes—
757C2×C4C22×C4×D5311yescharacteristic
758C2×C4C2×D4×D5311yescharacteristic
759C2×C4C22×D21211yescharacteristic
760C2×C4#41×D5311yescharacteristic
761C2×C4#1313326211yescharacteristic
762C2×C4#1313326311yescharacteristic
763C8—1062no—
764C8—2121no—
765C8—2121no—
766C8—2121no—
767C22—22no—
768C22—22no—
769C22—22no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22#1681063114yescomplemented
781C22C22×#1171992111yescharacteristic
782C22D4×C22⋊D5311yescharacteristic
783C22#1681126111yescharacteristic
784C22C2×#1313324711yescharacteristic
785C22C2×#1313324711yescharacteristic
786C22#1681143411yescharacteristic
787C22#1681143811yescharacteristic
788C4—22no—
789C4—22no—
790C4—22no—
791C4—22no—
792C4—42no—
793C4—81no—
794C4—81no—
795C4—81no—
796C4—1064no—
797C4—2122no—
798C4—2122no—
799C4—2122no—
800C4C4×D4×D5311yescharacteristic
801C4#1681109511yescharacteristic
802C4D4×D21211yescharacteristic
803C4#1681126811yescharacteristic
804C2—24no—
805C2—42no—
806C2D4×#1171992111yescharacteristic
807C2C2×#1681063111yescharacteristic
808C2#2028324511yescharacteristic
809C2#2028622111yescharacteristic
810C2#2028628111yescharacteristic
811C2#2028676011yescharacteristic
812C2#2028688011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutatorC2×C4×C53C23×C4
FrattiniC22×C4C23×D53
FittingC53×#2352C2
socleC23×C53C22×D4
prime radicalC22×D4×C53D4
cosocleC22×C4×C53C24
hypercenter#2352D53
hypocenterC53#22425
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
3. C2×#16810631C2semidirect
4. C22×#13133140C2semidirect
5. #20275638C2semidirect
6. #20275534C2semidirect
7. #20275146C2semidirect
8. #20275136C2semidirect
9. #20275027C2semidirect
10. #20275022C2semidirect
11. #20274727C2semidirect
12. #20274649C2semidirect
13. #20274649C2semidirect
14. #20274548C2semidirect
21. D4×Dic106C4semidirect
77. C22×Dic106C2×C4semidirect
94. #13133217C2×C4semidirect
99. #13133196C2×C4semidirect
103. C4×Dic106C2×C4semidirect
126. #13133140D4semidirect
374. C22×C53#419semidirect
470. C53#22425semidirect
780. C22#16810631semidirect

Maximal subgroups

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

subgroupindex
C2×D4×Dic1062
C2×#168106952
C2×#168106312
C22×#131331402
#202756382
#202755342
#202751462
#202751362
#202750272
#202750222
#202747272
#202746492
#202745482
C53×#23522
#2242553