Finite Group Databasebeta

← #27312065

Subgroups — #27312065

Order 13568.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810520C211yesmaximal, characteristic, complemented
2C2×#16810517C211yesmaximal, characteristic
3C2×#16810511C211yesmaximal, characteristic
4C2×#16810496C211yesmaximal, characteristic
5C2×#16810496C211yesmaximal, characteristic
6C2×#16810492C211yesmaximal, characteristic, complemented
7#20272978C211yesmaximal, characteristic, complemented
8#20272978C211yesmaximal, characteristic, complemented
9#20272970C211yesmaximal, characteristic, complemented
10#20272965C211yesmaximal, characteristic, complemented
11#20272960C211yesmaximal, characteristic
12#20272958C211yesmaximal, characteristic
13#20272946C211yesmaximal, characteristic, complemented
14#20272940C211yesmaximal, characteristic, complemented
15C2×C53×#385C211yesmaximal, characteristic
16C22×C4⋊Dic53C2211yescharacteristic
17C22×#11719919C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30#16810520—24no—
31#16810517C418yescomplemented
32#16810511—24no—
33#16810496—24no—
34#16810496—24no—
35#16810492—24no—
36C2×#13133124C2211yescharacteristic
37C2×#13133124C2211yescharacteristic
38C2×#13133124C2211yescharacteristic
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C24×C4×C53C2211yescharacteristic
51C22×C4⋊C4×C53C2211yescharacteristic
52C22×C4⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C53×#385—24no—
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2311yescharacteristic
64C23×Dic53C2311yescharacteristic
65C23×Dic53C2311yescharacteristic
66C2×C4⋊Dic53—22no—
67C2×C4⋊Dic53—22no—
68C2×C4⋊Dic53—41no—
69C2×#11719919—22no—
70C2×#11719919—22no—
71C2×#11719919—22no—
72C2×#11719919—22no—
73C2×#11719919—22no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—41no—
81C2×#11719919—41no—
82C2×#11719919—41no—
83C2×#11719919—41no—
84C2×#11719919—41no—
85C2×#11719919—41no—
86C2×#11719919—41no—
87C2×#11719919—41no—
88C2×#11719919C2×C414yescomplemented
89C2×#11719919D414yes—
90C2×C22⋊Dic53—22no—
91C2×C22⋊Dic53—22no—
92C2×C22⋊Dic53—22no—
93C2×C22⋊Dic53—22no—
94C2×C22⋊Dic53—22no—
95C2×C22⋊Dic53—41no—
96C2×C22⋊Dic53—41no—
97C2×C22⋊Dic53—41no—
98C2×C22⋊Dic53C2×C414yes—
99C2×C22⋊Dic53C2×C414yes—
100C2×C22⋊Dic53D414yes—
101C2×C22⋊Dic53Q814yes—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—41no—
107C2×C4×Dic53C2×C414yescomplemented
108#13133124—22no—
109#13133124—22no—
110#13133124—22no—
111#13133124—22no—
112#13133124—22no—
113#13133124—22no—
114#13133124—22no—
115#13133124—22no—
116#13133124—22no—
117#13133124—41no—
118#13133124—41no—
119#13133124—41no—
120#13133124C2×C414yescomplemented
121#13133124C2×C414yescomplemented
122C25×C53C2311yescharacteristic
123C23×C4×C53—22no—
124C23×C4×C53—22no—
125C23×C4×C53—22no—
126C23×C4×C53—41no—
127C23×C4×C53—41no—
128C23×C4×C53—41no—
129C23×C4×C53—41no—
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2311yescharacteristic
134C23×C4×C53C2311yescharacteristic
135C23×C4×C53C2311yescharacteristic
136C2×C4⋊C4×C53—22no—
137C2×C4⋊C4×C53—22no—
138C2×C4⋊C4×C53—22no—
139C2×C4⋊C4×C53—41no—
140C2×C4⋊C4×C53—41no—
141C2×C4⋊C4×C53—41no—
142C2×C22⋊C4×C53—22no—
143C2×C22⋊C4×C53—22no—
144C2×C22⋊C4×C53—22no—
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—41no—
147C2×C22⋊C4×C53C2×C414yes—
148#95×C53—22no—
149#95×C53D414yes—
150C24×C53—21no—
151C24×C53—21no—
152C24×C53—21no—
153C24×C53—21no—
154C24×C53—21no—
155C24×C53—21no—
156C24×C53—21no—
157C24×C53—21no—
158C24×C53—21no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53C22×C412yes—
163C24×C53C2×D412yes—
164C24×C53C2×Q812yes—
165C24×C53C2411yescharacteristic
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—21no—
179C22×C4×C53—21no—
180C22×C4×C53—21no—
181C22×C4×C53—21no—
182C22×C4×C53—21no—
183C22×C4×C53—21no—
184C22×C4×C53—21no—
185C22×C4×C53—21no—
186C22×C4×C53—21no—
187C22×C4×C53—21no—
188C22×C4×C53—21no—
189C22×C4×C53—21no—
190C22×C4×C53—21no—
191C22×C4×C53—21no—
192C22×C4×C53—21no—
193C22×C4×C53—21no—
194C22×C4×C53—21no—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—44no—
202C22×C4×C53—44no—
203C22×C4×C53—44no—
204C22×C4×C53—44no—
205C22×C4×C53—44no—
206C22×C4×C53—44no—
207C22×C4×C53—44no—
208C22×C4×C53C22×C412yes—
209C22×C4×C53C22×C412yes—
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2×D412yes—
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2×D412yes—
214C22×C4×C53#4112yes—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C22×Dic53—21no—
220C22×Dic53—21no—
221C22×Dic53—21no—
222C22×Dic53—21no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—21no—
230C22×Dic53—21no—
231C22×Dic53—21no—
232C22×Dic53—21no—
233C22×Dic53—21no—
234C22×Dic53—21no—
235C22×Dic53—21no—
236C22×Dic53—21no—
237C22×Dic53—21no—
238C22×Dic53—21no—
239C22×Dic53—21no—
240C22×Dic53—21no—
241C22×Dic53—21no—
242C22×Dic53—21no—
243C22×Dic53—21no—
244C22×Dic53—21no—
245C22×Dic53—21no—
246C22×Dic53—21no—
247C22×Dic53—21no—
248C22×Dic53—21no—
249C22×Dic53—21no—
250C22×Dic53—21no—
251C22×Dic53—21no—
252C22×Dic53—21no—
253C22×Dic53—21no—
254C22×Dic53—21no—
255C22×Dic53—21no—
256C22×Dic53—21no—
257C22×Dic53—21no—
258C22×Dic53—21no—
259C22×Dic53—21no—
260C22×Dic53C22×C412yes—
261C22×Dic53C22×C412yes—
262C22×Dic53C22×C412yes—
263C22×Dic53C22×C412yes—
264C22×Dic53C2×D412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53C2×D412yes—
267C22×Dic53C2×D412yes—
268C22×Dic53C2×Q812yes—
269C22×Dic53C2×Q812yes—
270C22×Dic53#4112yes—
271C4⋊C4×C53—44no—
272C4⋊C4×C53—44no—
273C22⋊C4×C53—28no—
274C22⋊C4×C53—44no—
275C22⋊Dic53—28no—
276C22⋊Dic53—44no—
277C22⋊Dic53—44no—
278C22⋊Dic53C4⋊C4116yescomplemented
279C4⋊Dic53—44no—
280#11719919—28no—
281#11719919—44no—
282#11719919—44no—
283#11719919—44no—
284#11719919—44no—
285#11719919—44no—
286#11719919—44no—
287C4×Dic53—28no—
288C4×Dic53—44no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—22no—
301C23×C53—22no—
302C23×C53—22no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—41no—
308C23×C53—41no—
309C23×C53—41no—
310C23×C53—41no—
311C23×C53—41no—
312C23×C53—41no—
313C23×C53—41no—
314C23×C53—41no—
315C23×C53—41no—
316C23×C53—41no—
317C23×C53—41no—
318C23×C53—41no—
319C23×C53—41no—
320C23×C53—41no—
321C23×C53—41no—
322C23×C53—41no—
323C23×C53C2×C4⋊C414yes—
324C23×C53C23×C411yescharacteristic
325C23×C53C22×D411yescharacteristic
326C23×C53C22×D411yescharacteristic
327C23×C53C22×D411yescharacteristic
328C23×C53C22×Q811yescharacteristic
329C23×C53C2×#4111yescharacteristic
330C23×C53C2×#4111yescharacteristic
331C23×C53H(5,𝔽2)11yescharacteristic
332C23×C53H(5,𝔽2)11yescharacteristic
333C23×C53H(5,𝔽2)11yescharacteristic
334C23×C53H(5,𝔽2)11yescharacteristic
335C23×C532−1+411yescharacteristic
336C23×C532−1+411yescharacteristic
337C23×C532−1+411yescharacteristic
338C23×C532−1+411yescharacteristic
339C2×C4×C53—22no—
340C2×C4×C53—22no—
341C2×C4×C53—22no—
342C2×C4×C53—22no—
343C2×C4×C53—22no—
344C2×C4×C53—22no—
345C2×C4×C53—22no—
346C2×C4×C53—22no—
347C2×C4×C53—22no—
348C2×C4×C53—22no—
349C2×C4×C53—22no—
350C2×C4×C53—22no—
351C2×C4×C53—22no—
352C2×C4×C53—22no—
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—416no—
358C2×C4×C53—41no—
359C2×C4×C53—41no—
360C2×C4×C53—41no—
361C2×C4×C53—41no—
362C2×C4×C53—41no—
363C2×C4×C53—41no—
364C2×C4×C53—41no—
365C2×C4×C53—41no—
366C2×C4×C53—41no—
367C2×C4×C53—41no—
368C2×C4×C53—41no—
369C2×C4×C53—41no—
370C2×C4×C53—41no—
371C2×C4×C53—41no—
372C2×C4×C53—41no—
373C2×C4×C53—41no—
374C2×C4×C53—41no—
375C2×C4×C53—41no—
376C2×C4×C53—41no—
377C2×C4×C53—41no—
378C2×C4×C53—41no—
379C2×C4×C53—41no—
380C2×C4×C53—41no—
381C2×C4×C53C4×D414yes—
382C2×Dic53—22no—
383C2×Dic53—22no—
384C2×Dic53—22no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—22no—
388C2×Dic53—22no—
389C2×Dic53—22no—
390C2×Dic53—22no—
391C2×Dic53—22no—
392C2×Dic53—22no—
393C2×Dic53—22no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—22no—
397C2×Dic53—22no—
398C2×Dic53—22no—
399C2×Dic53—22no—
400C2×Dic53—22no—
401C2×Dic53—22no—
402C2×Dic53—22no—
403C2×Dic53—22no—
404C2×Dic53—22no—
405C2×Dic53—22no—
406C2×Dic53—41no—
407C2×Dic53—41no—
408C2×Dic53—41no—
409C2×Dic53—41no—
410C2×Dic53—41no—
411C2×Dic53—41no—
412C2×Dic53—41no—
413C2×Dic53—41no—
414C2×Dic53—41no—
415C2×Dic53—41no—
416C2×Dic53—41no—
417C2×Dic53—41no—
418C2×Dic53—41no—
419C2×Dic53—41no—
420C2×Dic53—41no—
421C2×Dic53—41no—
422C2×Dic53—41no—
423C2×Dic53—41no—
424C2×Dic53—41no—
425C2×Dic53—41no—
426C2×Dic53—41no—
427C2×Dic53—41no—
428C2×Dic53—41no—
429C2×Dic53—41no—
430C2×Dic53—41no—
431C2×Dic53—41no—
432C2×Dic53—41no—
433C2×Dic53—41no—
434C2×Dic53—41no—
435C2×Dic53C2×C4⋊C414yes—
436C2×Dic53C2×C4⋊C414yes—
437C2×Dic53C4×D414yes—
438#14405—531nomaximal, Sylow
439C22×C53—24no—
440C22×C53—24no—
441C22×C53—24no—
442C22×C53—42no—
443C22×C53—42no—
444C22×C53—42no—
445C22×C53—42no—
446C22×C53—42no—
447C22×C53—42no—
448C22×C53—42no—
449C22×C53—42no—
450C22×C53—42no—
451C22×C53—42no—
452C22×C53—42no—
453C22×C53—42no—
454C22×C53C22×C4⋊C411yescharacteristic
455C22×C53C2×C4×D411yescharacteristic
456C22×C53C2×C4×D411yescharacteristic
457C22×C53#52011yescharacteristic
458C22×C53#52011yescharacteristic
459C22×C53#52011yescharacteristic
460C22×C53#52011yescharacteristic
461C22×C53#53411yescharacteristic
462C22×C53#53511yescharacteristic
463C22×C53#53511yescharacteristic
464C22×C53#53611yescharacteristic
465C22×C53#53611yescharacteristic
466C22×C53#53611yescharacteristic
467C22×C53#53911yescharacteristic
468C22×C53#53911yescharacteristic
469C22×C53#54211yescharacteristic
470C22×C53#54211yescharacteristic
471C22×C53#54411yescharacteristic
472C22×C53#54411yescharacteristic
473C22×C53D4211yescharacteristic
474C22×C53D4211yescharacteristic
475C22×C53D4211yescharacteristic
476C22×C53#54711yescharacteristic
477C22×C53#54711yescharacteristic
478C22×C53#54711yescharacteristic
479C22×C53#54811yescharacteristic
480C22×C53D4×Q811yescharacteristic
481C22×C53D4×Q811yescharacteristic
482C22×C53#55311yescharacteristic
483C22×C53#55411yescharacteristic
484C22×C53#55411yescharacteristic
485C22×C53#56011yescharacteristic
486C22×C53#56311yescharacteristic
487C22×C53#56311yescharacteristic
488C22×C53#56311yescharacteristic
489C4×C53—24no—
490C4×C53—42no—
491C4×C53—42no—
492C4×C53—42no—
493C4×C53—42no—
494C4×C53—81no—
495Dic53—24no—
496Dic53—24no—
497Dic53—24no—
498Dic53—42no—
499Dic53—42no—
500Dic53—81no—
501Dic53—81no—
502Dic53—81no—
503C2×#389—531no—
504C2×#388—531no—
505C2×#388—531no—
506C2×#385—531no—
507C2×#385—531no—
508C2×#385D5311yescharacteristic
509C2×#384—531no—
510#1444—531no—
511#1444—531no—
512#1442—531no—
513#1441—531no—
514#1439—531no—
515#1439—531no—
516#1436—531no—
517#1434—531no—
518C2×C53—44no—
519C2×C53#231711yescharacteristic
520C2×C53#232211yescharacteristic
521C2×C53#232611yescharacteristic
522C2×C53D4×C4⋊C411yescharacteristic
523C2×C53D4×C4⋊C411yescharacteristic
524C2×C53#236111yescharacteristic
525C2×C53#238311yescharacteristic
526C2×C53#266911yescharacteristic
527C2×C53#267411yescharacteristic
528C2×C53#267711yescharacteristic
529C2×C53#268011yescharacteristic
530C2×C53#271811yescharacteristic
531C2×C53#272011yescharacteristic
532C2×C53#272911yescharacteristic
533C2×C53#279011yescharacteristic
534C24×C4C2×D5311yescharacteristic
535C22×C4⋊C4—531no—
536C22×C4⋊C4—531no—
537C22×C4⋊C4—531no—
538C22×C4⋊C4—531no—
539C22×C4⋊C4—531no—
540C22×C4⋊C4—531no—
541C22×C4⋊C4—531no—
542C22×C4⋊C4—531no—
543C22×C4⋊C4C2×D5311yescharacteristic
544C22×C4⋊C4C2×D5311yescharacteristic
545C22×C22⋊C4—531no—
546C22×C22⋊C4—531no—
547C22×C22⋊C4—531no—
548C22×C22⋊C4—531no—
549C22×C22⋊C4C2×D5311yescharacteristic
550C22×C22⋊C4C2×D5311yescharacteristic
551C22×C42—531no—
552C22×C42—531no—
553#389—1064no—
554#388—538no—
555#388—1064no—
556#385—24no—
557#385—1064no—
558#385—1064no—
559#384—1064no—
560C2×#95—531no—
561C2×#95—531no—
562C2×#95—531no—
563C2×#95—531no—
564C2×#95—531no—
565C2×#95—531no—
566C2×#95—531no—
567C2×#95—531no—
568C2×#95—531no—
569C2×#95—531no—
570C2×#95—531no—
571C2×#95—531no—
572C2×#95—531no—
573C2×#95—531no—
574C2×#95C2×D5311yescharacteristic
575C2×#95C2×D5311yescharacteristic
576C53#1440511yescharacteristic, complemented, Sylow
577C25C22×D5311yescharacteristic
578C23×C4—22no—
579C23×C4—22no—
580C23×C4—22no—
581C23×C4—41no—
582C23×C4—41no—
583C23×C4—41no—
584C23×C4—41no—
585C23×C4—531no—
586C23×C4—531no—
587C23×C4—531no—
588C23×C4—531no—
589C23×C4—531no—
590C23×C4—531no—
591C23×C4—531no—
592C23×C4—531no—
593C23×C4C22×D5311yescharacteristic
594C23×C4C22×D5311yescharacteristic
595C23×C4C22×D5311yescharacteristic
596C23×C4C22×D5311yescharacteristic
597C23×C4C22×D5311yescharacteristic
598C23×C4C22×D5311yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—534no—
606C2×C4⋊C4—534no—
607C2×C4⋊C4—1062no—
608C2×C4⋊C4—1062no—
609C2×C4⋊C4—1062no—
610C2×C4⋊C4—1062no—
611C2×C4⋊C4—1062no—
612C2×C4⋊C4—1062no—
613C2×C4⋊C4—1062no—
614C2×C4⋊C4—1062no—
615C2×C4⋊C4—1062no—
616C2×C4⋊C4—1062no—
617C2×C4⋊C4—1062no—
618C2×C4⋊C4—1062no—
619C2×C4⋊C4—1062no—
620C2×C4⋊C4—2121no—
621C2×C4⋊C4—2121no—
622C2×C4⋊C4—2121no—
623C2×C4⋊C4—2121no—
624C2×C4⋊C4—2121no—
625C2×C4⋊C4—2121no—
626C2×C4⋊C4—2121no—
627C2×C4⋊C4—2121no—
628C2×C4⋊C4—2121no—
629C2×C22⋊C4—22no—
630C2×C22⋊C4—22no—
631C2×C22⋊C4—22no—
632C2×C22⋊C4—22no—
633C2×C22⋊C4—41no—
634C2×C22⋊C4—534no—
635C2×C22⋊C4—534no—
636C2×C22⋊C4—534no—
637C2×C22⋊C4—534no—
638C2×C22⋊C4—1062no—
639C2×C22⋊C4—1062no—
640C2×C22⋊C4—1062no—
641C2×C22⋊C4—1062no—
642C2×C22⋊C4—1062no—
643C2×C22⋊C4—2121no—
644C2×C22⋊C4—2121no—
645C2×C22⋊C4—2121no—
646C2×C22⋊C4C4×D5314yes—
647C2×C42—534no—
648C2×C42—1062no—
649C2×C42—1062no—
650C2×C42—1062no—
651C2×C42—1062no—
652C2×C42—2121no—
653#95—22no—
654#95—534no—
655#95—534no—
656#95—1062no—
657#95—1062no—
658#95—1062no—
659#95—1062no—
660#95—1062no—
661#95—1062no—
662#95—1062no—
663#95—1062no—
664#95—1062no—
665#95—2121no—
666#95—2121no—
667#95—2121no—
668#95C22⋊D5314yes—
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D5312yes—
682C24D4×D5312yes—
683C24Q8×D5312yes—
684C24C23×D5311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—44no—
727C22×C4—532no—
728C22×C4—532no—
729C22×C4—532no—
730C22×C4—532no—
731C22×C4—532no—
732C22×C4—532no—
733C22×C4—532no—
734C22×C4—532no—
735C22×C4—532no—
736C22×C4—532no—
737C22×C4—532no—
738C22×C4—1061no—
739C22×C4—1061no—
740C22×C4—1061no—
741C22×C4—1061no—
742C22×C4—1061no—
743C22×C4—1061no—
744C22×C4—1061no—
745C22×C4—1061no—
746C22×C4—1061no—
747C22×C4—1061no—
748C22×C4—1061no—
749C22×C4—1061no—
750C22×C4—1061no—
751C22×C4—1061no—
752C22×C4—1061no—
753C22×C4—1061no—
754C22×C4—1061no—
755C22×C4—1061no—
756C22×C4—1061no—
757C22×C4—1061no—
758C22×C4—1061no—
759C22×C4—1061no—
760C22×C4—1061no—
761C22×C4—1061no—
762C22×C4—1061no—
763C22×C4—1061no—
764C22×C4—1061no—
765C22×C4—1061no—
766C22×C4—1061no—
767C22×C4—1061no—
768C22×C4—1061no—
769C22×C4—1061no—
770C22×C4—1061no—
771C22×C4—1061no—
772C22×C4—1061no—
773C22×C4—1061no—
774C22×C4—1061no—
775C22×C4—1061no—
776C22×C4—1061no—
777C22×C4—1061no—
778C22×C4—1061no—
779C22×C4—1061no—
780C22×C4—1061no—
781C22×C4—1061no—
782C22×C4—1061no—
783C22×C4C2×C4×D5312yes—
784C22×C4C2×C4×D5312yes—
785C22×C4#1171994512yes—
786C22×C4D4×D5312yes—
787C22×C4C2×C22⋊D5312yes—
788C22×C4C2×C22⋊D5312yes—
789C22×C4C2×C22⋊D5312yes—
790C4⋊C4—44no—
791C4⋊C4—44no—
792C4⋊C4—1068no—
793C4⋊C4—2124no—
794C4⋊C4—2124no—
795C4⋊C4—2124no—
796C4⋊C4—2124no—
797C4⋊C4—2124no—
798C4⋊C4—2124no—
799C4⋊C4—2124no—
800C22⋊C4—28no—
801C22⋊C4—44no—
802C22⋊C4—5316no—
803C22⋊C4—1068no—
804C22⋊C4—2124no—
805C22⋊C4—2124no—
806C42—1068no—
807C42—2124no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C4⋊C4×D5314yes—
843C23C22×C4×D5311yescharacteristic
844C23C2×D4×D5311yescharacteristic
845C23C2×D4×D5311yescharacteristic
846C23C22×C22⋊D5311yescharacteristic
847C23C2×Q8×D5311yescharacteristic
848C23#41×D5311yescharacteristic
849C23C2×#1171994511yescharacteristic
850C23#1313326211yescharacteristic
851C23#1313326211yescharacteristic
852C23#1313326211yescharacteristic
853C23#1313326211yescharacteristic
854C23#1313326411yescharacteristic
855C23#1313326411yescharacteristic
856C23#1313326411yescharacteristic
857C23#1313326511yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—416no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—534no—
901C2×C4—534no—
902C2×C4—534no—
903C2×C4—1062no—
904C2×C4—1062no—
905C2×C4—1062no—
906C2×C4—1062no—
907C2×C4—1062no—
908C2×C4—1062no—
909C2×C4—1062no—
910C2×C4—1062no—
911C2×C4—1062no—
912C2×C4—1062no—
913C2×C4—1062no—
914C2×C4—1062no—
915C2×C4—1062no—
916C2×C4—1062no—
917C2×C4—1062no—
918C2×C4—1062no—
919C2×C4—1062no—
920C2×C4—1062no—
921C2×C4—1062no—
922C2×C4—1062no—
923C2×C4—1062no—
924C2×C4—1062no—
925C2×C4—1062no—
926C2×C4—1062no—
927C2×C4—2121no—
928C2×C4—2121no—
929C2×C4—2121no—
930C2×C4—2121no—
931C2×C4—2121no—
932C2×C4—2121no—
933C2×C4—2121no—
934C2×C4—2121no—
935C2×C4—2121no—
936C2×C4—2121no—
937C2×C4—2121no—
938C2×C4—2121no—
939C2×C4—2121no—
940C2×C4—2121no—
941C2×C4—2121no—
942C2×C4—2121no—
943C2×C4—2121no—
944C2×C4—2121no—
945C2×C4—2121no—
946C2×C4—2121no—
947C2×C4—2121no—
948C2×C4—2121no—
949C2×C4—2121no—
950C2×C4—2121no—
951C2×C4—2121no—
952C2×C4—2121no—
953C2×C4—2121no—
954C2×C4—2121no—
955C2×C4—2121no—
956C2×C4C4×C22⋊D5314yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C2×C4⋊C4×D5311yescharacteristic
973C22C4×D4×D5311yescharacteristic
974C22C2×C4×C22⋊D5311yescharacteristic
975C22#1681110211yescharacteristic
976C22#1681110211yescharacteristic
977C22#1681110211yescharacteristic
978C22#1681110411yescharacteristic
979C22#1681118311yescharacteristic
980C22#1681118811yescharacteristic
981C22#1681119011yescharacteristic
982C22#1681119411yescharacteristic
983C22#1681119511yescharacteristic
984C22#1681119611yescharacteristic
985C22#1681121611yescharacteristic
986C22#1681121911yescharacteristic
987C22#1681123811yescharacteristic
988C22#1681123811yescharacteristic
989C22#1681125211yescharacteristic
990C22#1681125211yescharacteristic
991C22#1681125511yescharacteristic
992C22D4×C22⋊D5311yescharacteristic
993C22D4×C22⋊D5311yescharacteristic
994C22#1681127111yescharacteristic
995C22#1681127211yescharacteristic
996C22#1681127411yescharacteristic
997C22#1681128211yescharacteristic
998C22#1681128611yescharacteristic
999C22Q8×C22⋊D5311yescharacteristic
1000C22#1681132211yescharacteristic
1001C22#1681132711yescharacteristic
1002C22#1681132811yescharacteristic
1003C22#1681136211yescharacteristic
1004C22#1681137411yescharacteristic
1005C22#1681137411yescharacteristic
1006C22#1681137611yescharacteristic
1007C4—24no—
1008C4—42no—
1009C4—42no—
1010C4—42no—
1011C4—42no—
1012C4—81no—
1013C4—1064no—
1014C4—1064no—
1015C4—1064no—
1016C4—4241no—
1017C4—4241no—
1018C4—4241no—
1019C4—2122no—
1020C4—2122no—
1021C2—44no—
1022C2#2027733411yescharacteristic
1023C2#2027738211yescharacteristic
1024C2#2027742711yescharacteristic
1025C2#2027761311yescharacteristic
1026C2C4⋊C4×C22⋊D5311yescharacteristic
1027C2#2027773211yescharacteristic
1028C2#2027790311yescharacteristic
1029C2#2028092911yescharacteristic
1030C2#2028100011yescharacteristic
1031C2#2028102611yescharacteristic
1032C2#2028105211yescharacteristic
1033C2#2028156911yescharacteristic
1034C2#2028158911yescharacteristic
1035C2#2028169711yescharacteristic
1036C2#2028248611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#385C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC2×#385D53
hypocenterC53#14405
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C2×#16810520C2semidirect
6. C2×#16810492C2semidirect
7. #20272978C2semidirect
8. #20272978C2semidirect
9. #20272970C2semidirect
10. #20272965C2semidirect
13. #20272946C2semidirect
14. #20272940C2semidirect
31. #16810517C4semidirect
88. C2×#11719919C2×C4semidirect
107. C2×C4×Dic53C2×C4semidirect
120. #13133124C2×C4semidirect
121. #13133124C2×C4semidirect
278. C22⋊Dic53C4⋊C4semidirect
576. C53#14405semidirect

Maximal subgroups

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

subgroupindex
C2×#168105202
C2×#168105172
C2×#168105112
C2×#168104962
C2×#168104922
#202729782
#202729702
#202729652
#202729602
#202729582
#202729462
#202729402
C2×C53×#3852
#1440553