Finite Group Databasebeta

← #27381900

Subgroups — #27381900

Order 13568.

1738 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
1C2×#16811095C211yesmaximal, characteristic
2C2×#16810626C211yesmaximal, characteristic
3C2×#102×D53C211yesmaximal, characteristic
4C2×#16810577C211yesmaximal, characteristic, complemented
5#20277069C211yesmaximal, characteristic, complemented
6#20274543C211yesmaximal, characteristic, complemented
7#20274542C211yesmaximal, characteristic, complemented
8#20274540C211yesmaximal, characteristic, complemented
9#20274539C211yesmaximal, characteristic, complemented
10#102×Dic53C211yesmaximal, characteristic, complemented
11C4×#13133139C211yesmaximal, characteristic, complemented
12#20274529C211yesmaximal, characteristic, complemented
13#20274433C211yesmaximal, characteristic, complemented
14#20274430C211yesmaximal, characteristic, complemented
15C4×#102×C53C211yesmaximal, characteristic, complemented
16C22×D4×D53C2211yescharacteristic
17C22×#11719912C2211yescharacteristic
18C22×C8×D53C2211yescharacteristic
19#16811095—24no—
20#16811095C418yescomplemented
21C2×C4×D212C2211yescharacteristic
22C2×D4×Dic53C2211yescharacteristic
23C2×#13133179C2211yescharacteristic
24C2×C4×C22⋊D53—21no—
25C2×#13133177—21no—
26C2×#13133175C2211yescharacteristic
27C2×#13133175C2211yescharacteristic
28C2×#13133174C2211yescharacteristic
29C2×C4⋊C4×D53C2211yescharacteristic
30C22×#11719921—21no—
31C2×C22⋊C4×D53—21no—
32#16810626C418yescomplemented
33C2×#13133139C2211yescharacteristic
34C2×#13133139C2211yescharacteristic
35C2×#13133138C2211yescharacteristic
36C2×#13133138C2211yescharacteristic
37C2×#13133137C2211yescharacteristic
38C2×#13133137C2211yescharacteristic
39#102×D53C418yescomplemented
40#16810577—24no—
41C2×#13133128C2211yescharacteristic, complemented
42C2×#13133127C2211yescharacteristic, complemented
43C2×C8×Dic53C2211yescharacteristic, complemented
44C4⋊C4×Dic53C2211yescharacteristic, complemented
45C4⋊C4×Dic53C2211yescharacteristic, complemented
46C4×#11719919—21no—
47C4×C4⋊Dic53C2211yescharacteristic, complemented
48#16810474—21no—
49C4×#11719921—21no—
50#16810470—21no—
51#16810386C2211yescharacteristic, complemented
52#16810386C2211yescharacteristic, complemented
53#16810385C2211yescharacteristic, complemented
54#16810385C2211yescharacteristic, complemented
55#16810385C2211yescharacteristic, complemented
56#16810385C2211yescharacteristic, complemented
57C2×C4×D4×C53C2211yescharacteristic
58C2×#102×C53C2211yescharacteristic
59C2×#102×C53C2211yescharacteristic
60C2×C4×C8×C53C2211yescharacteristic, complemented
61C4×C4⋊C4×C53C2211yescharacteristic, complemented
62C53×#340C2211yescharacteristic, complemented
63C53×#340C2211yescharacteristic, complemented
64C24×D53—21no—
65C22×D212C2311yescharacteristic
66C22×C22⋊D53—21no—
67C2×D4×D53—22no—
68C2×D4×D53—22no—
69C2×D4×D53—22no—
70C2×D4×D53C2×C414yes—
71C2×D4×D53C2×C414yes—
72C2×D4×D53C2×C414yes—
73C23×Dic53—21no—
74C22×C4×D53—21no—
75C22×C4×D53—21no—
76C22×C4×D53—21no—
77C22×C4×D53C2311yescharacteristic
78C2×#11719912—22no—
79C2×#11719912—22no—
80C2×#11719912C2×C414yescomplemented
81C22×#88322C2311yescharacteristic
82C22×#88322C2311yescharacteristic
83C2×C8×D53—22no—
84C2×C8×D53—22no—
85C2×C8×D53C2×C414yescomplemented
86C4×D212—22no—
87C4×D212C2×C414yescomplemented
88D4×Dic53—22no—
89D4×Dic53C2×C414yescomplemented
90#13133179—22no—
91#13133179C2×C414yescomplemented
92C4×C22⋊D53—28no—
93#13133177—28no—
94#13133175—22no—
95#13133175—22no—
96#13133175C2×C414yes—
97#13133175C2×C414yescomplemented
98#13133174C2×C414yes—
99#13133174D414yes—
100C2×C4⋊Dic53C2311yescharacteristic
101C2×C4⋊Dic53C2311yescharacteristic
102C2×C4⋊Dic53C2311yescharacteristic
103C2×#11719919—21no—
104C2×#11719919D411yescharacteristic
105C2×#11719919D411yescharacteristic
106C4⋊C4×D53—22no—
107C4⋊C4×D53C2×C414yescomplemented
108C2×C22⋊Dic53—21no—
109C2×#11719921—28no—
110C2×#11719921—21no—
111C2×#11719921—21no—
112C2×#11719921—21no—
113C2×#11719921—21no—
114C2×#11719921D411yescharacteristic
115C2×#11719921D411yescharacteristic
116C22⋊C4×D53—28no—
117C2×C4×Dic53—21no—
118C2×C4×Dic53—21no—
119C2×C4×Dic53—21no—
120C2×C4×Dic53—21no—
121C2×C4×Dic53—21no—
122C2×C4×Dic53C2311yescharacteristic
123#13133139C2×C414yescomplemented
124#13133139C2×C414yescomplemented
125#13133138C2×C414yescomplemented
126#13133138C2×C414yescomplemented
127#13133137C2×C414yescomplemented
128#13133137C2×C414yescomplemented
129#13133128—22no—
130#13133127—22no—
131C8×Dic53—22no—
132#13133124—21no—
133#13133124—21no—
134#13133124—21no—
135C22×D4×C53C2311yescharacteristic
136C23×C4×C53—21no—
137C22×C8×C53C2311yescharacteristic
138C22×C8×C53C2311yescharacteristic
139C4×D4×C53—22no—
140C4×D4×C53C2×C414yescomplemented
141C2×C4⋊C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53C2311yescharacteristic
143C2×C4⋊C4×C53C2311yescharacteristic
144C2×C22⋊C4×C53—21no—
145C2×C42×C53—21no—
146C2×C42×C53C2311yescharacteristic
147#102×C53C2×C414yescomplemented
148#102×C53C2×C414yescomplemented
149C4×C8×C53—22no—
150#95×C53—21no—
151C24×C53—21no—
152C23×D53—21no—
153C23×D53—24no—
154C23×D53—24no—
155C23×D53—24no—
156C23×D53—81no—
157C23×D53—81no—
158C23×D53—81no—
159C23×D53—81no—
160C23×D53C2×D411yescharacteristic
161C2×D4×C53—21no—
162C2×D4×C53—21no—
163C2×D4×C53—21no—
164C2×D4×C53C22×C412yes—
165C2×D4×C53C22×C412yes—
166C2×D4×C53C22×C412yes—
167C22×C4×C53—21no—
168C22×C4×C53—21no—
169C22×C4×C53—21no—
170C22×C4×C53—24no—
171C22×C4×C53—81no—
172C22×C4×C53—81no—
173C22×C4×C53C2×D411yescharacteristic
174C22×C4×C53C2×D411yescharacteristic
175C22×C4×C53C2411yescharacteristic
176C2×C22⋊D53—24no—
177C2×C22⋊D53—24no—
178C2×C22⋊D53—24no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—24no—
183C22×Dic53—81no—
184C22×Dic53—81no—
185C22×Dic53C2×D411yescharacteristic
186C22×Dic53C2×D411yescharacteristic
187C22×Dic53C2×D411yescharacteristic
188D4×D53—28no—
189D4×D53—28no—
190D4×D53—28no—
191D4×D53C42116yescomplemented
192C2×D212—21no—
193C2×D212—21no—
194C2×D212—21no—
195C2×D212C22×C412yes—
196C2×D212C22×C412yes—
197C2×D212C22×C412yes—
198C2×C4×D53—24no—
199C2×C4×D53—24no—
200C2×C4×D53—24no—
201C2×C4×D53—81no—
202C2×C4×D53—81no—
203C2×C4×D53—81no—
204C2×C4×D53—81no—
205C2×C4×D53—81no—
206C2×C4×D53—81no—
207C2×C4×D53C22×C412yes—
208C2×C4×D53C22×C412yes—
209C2×C4×D53C22×C412yes—
210C2×C4×D53C2×D412yes—
211C2×C4×D53#4112yes—
212C2×C4×D53#4112yes—
213C2×C8×C53—21no—
214C2×C8×C53—21no—
215C2×C8×C53—21no—
216C2×C8×C53—21no—
217C2×C8×C53C22×C412yes—
218C2×C8×C53C22×C412yes—
219C4⋊C4×C53—21no—
220C4⋊C4×C53—21no—
221C4⋊C4×C53—21no—
222C4⋊C4×C53C22×C412yes—
223C4⋊C4×C53C22×C412yes—
224C4⋊C4×C53C22×C412yes—
225C22⋊C4×C53—24no—
226C42×C53—81no—
227C42×C53C22×C412yes—
228C42×C53C2×D412yes—
229C22⋊Dic53—24no—
230#11719921—24no—
231#11719921—24no—
232#11719921—24no—
233#11719921—24no—
234#11719921C22⋊C414yes—
235#11719921C22⋊C414yes—
236C4⋊Dic53—21no—
237C4⋊Dic53—21no—
238C4⋊Dic53—21no—
239C4⋊Dic53C22×C412yes—
240C4⋊Dic53C22×C412yes—
241C4⋊Dic53C22×C412yes—
242#11719919—24no—
243#11719919C22⋊C414yes—
244#11719919C22⋊C414yes—
245C4×Dic53—24no—
246C4×Dic53—24no—
247C4×Dic53—81no—
248C4×Dic53—81no—
249C4×Dic53—81no—
250C4×Dic53C22×C412yes—
251C4×Dic53C2×D412yes—
252C2×#88322—21no—
253C2×#88322—21no—
254C2×#88322—21no—
255C2×#88322—21no—
256C2×#88322C22×C412yes—
257C2×#88322C22×C412yes—
258#11719912—28no—
259C8×D53—28no—
260C23×C53—22no—
261C23×C53—22no—
262C23×C53—22no—
263C23×C53—41no—
264C23×C53—41no—
265C23×C53—41no—
266C23×C53—41no—
267C23×C53C22×D411yescharacteristic
268C22×D53—21no—
269C22×D53—21no—
270C22×D53—21no—
271C22×D53—21no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—216no—
276C22×D53—41no—
277C22×D53—41no—
278C22×D53—41no—
279C22×D53—41no—
280C22×D53—84no—
281C22×D53—84no—
282C22×D53—84no—
283C22×D53—84no—
284C22×D53—84no—
285C22×D53—84no—
286C22×D53C2×C22⋊C412yes—
287C22×D53C4×D412yes—
288C22×D53C4×D412yes—
289D4×C53—22no—
290D4×C53—22no—
291D4×C53—22no—
292D4×C53C2×C4214yes—
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—41no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—41no—
304C2×C4×C53—41no—
305C2×C4×C53—41no—
306C2×C4×C53—84no—
307C2×C4×C53C2×C22⋊C412yes—
308C2×C4×C53C2×C22⋊C412yes—
309C2×C4×C53C23×C411yescharacteristic
310C2×C4×C53C23×C411yescharacteristic
311C2×C4×C53C23×C411yescharacteristic
312C2×C4×C53C22×D411yescharacteristic
313C2×C4×C53C2×#4111yescharacteristic
314C2×C4×C53C2×#4111yescharacteristic
315C22⋊D53—216no—
316C2×Dic53—21no—
317C2×Dic53—21no—
318C2×Dic53—21no—
319C2×Dic53—21no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—41no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—41no—
329C2×Dic53—84no—
330C2×Dic53C2×C22⋊C412yes—
331C2×Dic53C2×C22⋊C412yes—
332C2×Dic53C2×C22⋊C412yes—
333C2×Dic53C4×D412yes—
334C2×Dic53C4×D412yes—
335D212—22no—
336D212—22no—
337D212—22no—
338D212C2×C4214yes—
339C4×D53—84no—
340C4×D53—84no—
341C4×D53—84no—
342C4×D53C2×C4214yes—
343C4×D53#11714yes—
344C4×D53C4×D414yes—
345C4×D53C4×D414yes—
346C8×C53—22no—
347C8×C53—22no—
348#88322—22no—
349#88322—22no—
350#20416—531nomaximal, Sylow
351C22×C53—24no—
352C22×C53—42no—
353C22×C53—42no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—42no—
358C22×C53C22×C22⋊C411yescharacteristic
359C22×C53C2×C4×D411yescharacteristic
360C22×C53C2×C4×D411yescharacteristic
361C22×C53#57611yescharacteristic
362C22×C53#57611yescharacteristic
363C22×C53#57711yescharacteristic
364C22×C53#57711yescharacteristic
365C2×D53—22no—
366C2×D53—22no—
367C2×D53—22no—
368C2×D53—22no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—24no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—42no—
375C2×D53—42no—
376C2×D53—42no—
377C2×D53—42no—
378C2×D53—816no—
379C2×D53C4×C22⋊C414yes—
380C4×C53—22no—
381C4×C53—22no—
382C4×C53—42no—
383C4×C53—42no—
384C4×C53—42no—
385C4×C53C22×C4211yescharacteristic
386C4×C53C2×#11711yescharacteristic
387C4×C53C2×C4×D411yescharacteristic
388C4×C53C2×C4×D411yescharacteristic
389Dic53—22no—
390Dic53—22no—
391Dic53—42no—
392Dic53—42no—
393Dic53—42no—
394Dic53C4×C22⋊C414yes—
395C2×#518—531no—
396C2×#418—531no—
397C22×#102—531no—
398C2×#405—531no—
399#2274—531no—
400#1762—531no—
401#1762—531no—
402#1762—531no—
403#1762—531no—
404C4×#102—531no—
405C4×#102—531no—
406C4×#102—531no—
407C4×#102D5311yescharacteristic, complemented
408#1736—531no—
409#1735—531no—
410C2×C53—44no—
411C2×C53C2×C4×C22⋊C411yescharacteristic
412C2×C53#289711yescharacteristic
413C2×C53#289711yescharacteristic
414C2×C53#294611yescharacteristic
415C2×C53#294611yescharacteristic
416C2×C53#294811yescharacteristic
417C2×C53#294911yescharacteristic
418D53—24no—
419D53—44no—
420C23×D4—531no—
421C22×M16—531no—
422C23×C8—531no—
423#518—538no—
424#518—1064no—
425C2×C4×D4—531no—
426C2×C4×D4—531no—
427C2×C4×D4—531no—
428C2×C4×D4—1061no—
429C2×C4×D4—1061no—
430C2×C4×D4C2×D5311yescharacteristic
431C2×#117—531no—
432C2×#117—531no—
433C2×#117—531no—
434C22×C4⋊C4—531no—
435C22×C22⋊C4—1061no—
436C22×C22⋊C4—1061no—
437#418—538no—
438C2×#102—531no—
439C2×#102—531no—
440C2×#102—531no—
441C2×#102—531no—
442C2×#102—531no—
443C2×#102—531no—
444C2×#102—538no—
445C2×#102C2×D5311yescharacteristic
446C2×#102C2×D5311yescharacteristic
447#405—1064no—
448C2×#97—531no—
449C2×#97—531no—
450C2×C4×C8—531no—
451C2×C4×C8C2×D5311yescharacteristic, complemented
452C4×C4⋊C4—531no—
453C4×C4⋊C4—531no—
454C4×C4⋊C4—531no—
455C4×C4⋊C4—1061no—
456C4×C4⋊C4—1061no—
457C4×C4⋊C4C2×D5311yescharacteristic, complemented
458C4×C22⋊C4—1061no—
459C4×C22⋊C4—1061no—
460#340—531no—
461#340—531no—
462#340—531no—
463#340—531no—
464#340—531no—
465#340—531no—
466#340C2×D5311yescharacteristic, complemented
467#340C2×D5311yescharacteristic, complemented
468C53#2041611yescharacteristic, complemented, Sylow
469C25—1061no—
470C22×D4—534no—
471C22×D4—534no—
472C22×D4—534no—
473C22×D4—531no—
474C22×D4—1062no—
475C22×D4—1062no—
476C22×D4—1062no—
477C22×D4—1061no—
478C22×D4C22×D5311yescharacteristic
479C23×C4—21no—
480C23×C4—531no—
481C23×C4—1061no—
482C23×C4—1061no—
483C23×C4—1061no—
484C23×C4—1061no—
485C2×M16—534no—
486C2×M16—1062no—
487C2×M16—1062no—
488C22×C8—531no—
489C22×C8—531no—
490C22×C8—534no—
491C22×C8—1062no—
492C22×C8—1062no—
493C22×C8C22×D5311yescharacteristic
494C22×C8C22×D5311yescharacteristic
495C4×D4—22no—
496C4×D4—534no—
497C4×D4—534no—
498C4×D4—534no—
499C4×D4—1062no—
500C4×D4—1062no—
501C4×D4—1068no—
502C4×D4—1068no—
503C4×D4—1062no—
504C4×D4C4×D5314yescomplemented
505#117—534no—
506#117—534no—
507#117—534no—
508#117—534no—
509#117—1062no—
510#117—1062no—
511C2×C4⋊C4—531no—
512C2×C4⋊C4—531no—
513C2×C4⋊C4—531no—
514C2×C4⋊C4—531no—
515C2×C4⋊C4—531no—
516C2×C4⋊C4—534no—
517C2×C4⋊C4—1062no—
518C2×C4⋊C4—1061no—
519C2×C4⋊C4C22×D5311yescharacteristic
520C2×C4⋊C4C22×D5311yescharacteristic
521C2×C4⋊C4C22×D5311yescharacteristic
522C2×C22⋊C4—21no—
523C2×C22⋊C4—531no—
524C2×C22⋊C4—531no—
525C2×C22⋊C4—1068no—
526C2×C22⋊C4—1068no—
527C2×C22⋊C4—1061no—
528C2×C22⋊C4—1061no—
529C2×C22⋊C4—1061no—
530C2×C22⋊C4—1061no—
531C2×C22⋊C4—1061no—
532C2×C42—21no—
533C2×C42—531no—
534C2×C42—1061no—
535C2×C42—1061no—
536C2×C42—1061no—
537C2×C42—1061no—
538C2×C42—1061no—
539C2×C42C22×D5311yescharacteristic
540#102—534no—
541#102—534no—
542#102—534no—
543#102—534no—
544#102—534no—
545#102—534no—
546#102C4×D5314yescomplemented
547#102C4×D5314yescomplemented
548#97—1062no—
549#97—1062no—
550C4×C8—22no—
551C4×C8—1062no—
552#95—21no—
553#95—1061no—
554#95—1061no—
555#95—1061no—
556C24—21no—
557C24—531no—
558C24—1064no—
559C24—1064no—
560C24—1064no—
561C24—1061no—
562C24—4241no—
563C24—4241no—
564C24—4241no—
565C24—4241no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—5316no—
570C2×D4—532no—
571C2×D4—532no—
572C2×D4—532no—
573C2×D4—1068no—
574C2×D4—1068no—
575C2×D4—1068no—
576C2×D4—1064no—
577C2×D4—1064no—
578C2×D4—1064no—
579C2×D4—1061no—
580C2×D4—1061no—
581C2×D4—1061no—
582C2×D4C2×C4×D5312yes—
583C2×D4C2×C4×D5312yes—
584C2×D4C2×C4×D5312yes—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—24no—
589C22×C4—81no—
590C22×C4—81no—
591C22×C4—531no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—532no—
595C22×C4—532no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—531no—
599C22×C4—531no—
600C22×C4—1064no—
601C22×C4—1064no—
602C22×C4—1064no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1064no—
607C22×C4—4241no—
608C22×C4—4241no—
609C22×C4—4241no—
610C22×C4—4241no—
611C22×C4—4241no—
612C22×C4—4241no—
613C22×C4—4241no—
614C22×C4—4241no—
615C22×C4D4×D5311yescharacteristic
616C22×C4D4×D5311yescharacteristic
617C22×C4C23×D5311yescharacteristic
618M16—1068no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—532no—
624C2×C8—532no—
625C2×C8—1068no—
626C2×C8—1061no—
627C2×C8—1061no—
628C2×C8—1061no—
629C2×C8—1061no—
630C2×C8C2×C4×D5312yes—
631C2×C8C2×C4×D5312yes—
632C4⋊C4—21no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—534no—
636C4⋊C4—534no—
637C4⋊C4—532no—
638C4⋊C4—532no—
639C4⋊C4—532no—
640C4⋊C4—1064no—
641C4⋊C4—1061no—
642C4⋊C4—1061no—
643C4⋊C4—1061no—
644C4⋊C4C2×C4×D5312yes—
645C4⋊C4C2×C4×D5312yes—
646C4⋊C4C2×C4×D5312yes—
647C22⋊C4—24no—
648C22⋊C4—534no—
649C22⋊C4—534no—
650C22⋊C4—1064no—
651C22⋊C4—1064no—
652C22⋊C4—1064no—
653C22⋊C4—1064no—
654C22⋊C4—1064no—
655C42—81no—
656C42—532no—
657C42—532no—
658C42—1064no—
659C42—1064no—
660C42—4241no—
661C42—4241no—
662C42—4241no—
663C42C2×C4×D5312yes—
664C42D4×D5312yes—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—532no—
673C23—532no—
674C23—532no—
675C23—10616no—
676C23—1061no—
677C23—1061no—
678C23—1061no—
679C23—1061no—
680C23—1062no—
681C23—1062no—
682C23—1062no—
683C23—4244no—
684C23—4244no—
685C23—4244no—
686C23—4244no—
687C23—4244no—
688C23—4244no—
689C23—2121no—
690C23—2121no—
691C23—2121no—
692C23—2121no—
693C23C2×D4×D5311yescharacteristic
694D4—22no—
695D4—22no—
696D4—22no—
697D4—534no—
698D4—10616no—
699D4—1062no—
700D4—1062no—
701D4—1062no—
702D4C42×D5314yes—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—84no—
717C2×C4—532no—
718C2×C4—532no—
719C2×C4—532no—
720C2×C4—534no—
721C2×C4—534no—
722C2×C4—534no—
723C2×C4—534no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—1061no—
727C2×C4—1061no—
728C2×C4—1061no—
729C2×C4—1061no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1062no—
733C2×C4—4244no—
734C2×C4—4244no—
735C2×C4—4244no—
736C2×C4—4244no—
737C2×C4—2121no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4C22⋊C4×D5312yes—
744C2×C4C22⋊C4×D5312yes—
745C2×C4C22×C4×D5311yescharacteristic
746C2×C4C22×C4×D5311yescharacteristic
747C2×C4C22×C4×D5311yescharacteristic
748C2×C4C2×D4×D5311yescharacteristic
749C2×C4#41×D5311yescharacteristic
750C2×C4#41×D5311yescharacteristic
751C8—22no—
752C8—22no—
753C8—1062no—
754C8—1062no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—534no—
763C22—1062no—
764C22—1062no—
765C22—1062no—
766C22—1062no—
767C22—1062no—
768C22—1062no—
769C22—1064no—
770C22—42416no—
771C22—2122no—
772C22—2122no—
773C22—2122no—
774C22—2122no—
775C22—2122no—
776C22—2122no—
777C22C2×C22⋊C4×D5311yescharacteristic
778C22C4×D4×D5311yescharacteristic
779C22C4×D4×D5311yescharacteristic
780C22#1681142411yescharacteristic
781C22#1681142511yescharacteristic
782C22#1681142911yescharacteristic
783C22#1681143011yescharacteristic
784C4—22no—
785C4—22no—
786C4—42no—
787C4—42no—
788C4—42no—
789C4—534no—
790C4—1062no—
791C4—1062no—
792C4—2122no—
793C4—2122no—
794C4—2122no—
795C4C2×C42×D5311yescharacteristic
796C4#117×D5311yescharacteristic
797C4C4×D4×D5311yescharacteristic
798C4C4×D4×D5311yescharacteristic
799C2—44no—
800C2—1064no—
801C2—2124no—
802C2C4×C22⋊C4×D5311yescharacteristic
803C2#2028323611yescharacteristic
804C2#2028323711yescharacteristic
805C2#2028354011yescharacteristic
806C2#2028354211yescharacteristic
807C2#2028356211yescharacteristic
808C2#2028356911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutatorC4×C53C22×C42
FrattiniC22×C4C23×D53
FittingC4×#102×C53C2
socleC23×C53C22×D4
prime radicalC22×D4×D53C22
cosocleC22×C4×C53C24
hypercenterC4×#102D53
hypocenterC53#20416
LCSG ▷ C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
4. C2×#16810577C2semidirect
5. #20277069C2semidirect
6. #20274543C2semidirect
7. #20274542C2semidirect
8. #20274540C2semidirect
9. #20274539C2semidirect
10. #102×Dic53C2semidirect
11. C4×#13133139C2semidirect
12. #20274529C2semidirect
13. #20274433C2semidirect
14. #20274430C2semidirect
15. C4×#102×C53C2semidirect
20. #16811095C4semidirect
32. #16810626C4semidirect
39. #102×D53C4semidirect
41. C2×#13133128C22semidirect
42. C2×#13133127C22semidirect
43. C2×C8×Dic53C22semidirect
44. C4⋊C4×Dic53C22semidirect
45. C4⋊C4×Dic53C22semidirect
47. C4×C4⋊Dic53C22semidirect
51. #16810386C22semidirect
52. #16810386C22semidirect
53. #16810385C22semidirect
54. #16810385C22semidirect
55. #16810385C22semidirect
56. #16810385C22semidirect
60. C2×C4×C8×C53C22semidirect
61. C4×C4⋊C4×C53C22semidirect
62. C53×#340C22semidirect
63. C53×#340C22semidirect
80. C2×#11719912C2×C4semidirect
85. C2×C8×D53C2×C4semidirect
87. C4×D212C2×C4semidirect
89. D4×Dic53C2×C4semidirect
91. #13133179C2×C4semidirect
97. #13133175C2×C4semidirect
107. C4⋊C4×D53C2×C4semidirect
123. #13133139C2×C4semidirect
124. #13133139C2×C4semidirect
125. #13133138C2×C4semidirect
126. #13133138C2×C4semidirect
127. #13133137C2×C4semidirect
128. #13133137C2×C4semidirect
140. C4×D4×C53C2×C4semidirect
147. #102×C53C2×C4semidirect
148. #102×C53C2×C4semidirect
191. D4×D53C42semidirect
407. C4×#102D53semidirect
451. C2×C4×C8C2×D53semidirect
457. C4×C4⋊C4C2×D53semidirect
466. #340C2×D53semidirect
467. #340C2×D53semidirect
468. C53#20416semidirect
504. C4×D4C4×D53semidirect
546. #102C4×D53semidirect
547. #102C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168110952
C2×#168106262
C2×#102×D532
C2×#168105772
#202770692
#202745432
#202745422
#202745402
#202745392
#102×Dic532
C4×#131331392
#202745292
#202744332
#202744302
C4×#102×C532
#2041653