Finite Group Databasebeta

← #27312067

Subgroups — #27312067

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×#16810519C211yesmaximal, characteristic, complemented
2C2×#16810516C211yesmaximal, characteristic
3C2×#16810516C211yesmaximal, characteristic
4C2×#16810496C211yesmaximal, characteristic
5C2×#16810496C211yesmaximal, characteristic
6C2×#16810492C211yesmaximal, characteristic, complemented
7#20272979C211yesmaximal, characteristic, complemented
8#20272978C211yesmaximal, characteristic, complemented
9#20272974C211yesmaximal, characteristic, complemented
10#20272967C211yesmaximal, characteristic, complemented
11#20272958C211yesmaximal, characteristic
12#20272958C211yesmaximal, characteristic
13#20272946C211yesmaximal, characteristic, complemented
14#20272941C211yesmaximal, characteristic, complemented
15C2×C53×#385C211yesmaximal, characteristic
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
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#16810519—24no—
31#16810516—24no—
32#16810516C418yescomplemented
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—22no—
69C2×C4⋊Dic53—22no—
70C2×C4⋊Dic53—41no—
71C2×C4⋊Dic53C2×C414yescomplemented
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×#11719919—41no—
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—22no—
96C2×C22⋊Dic53—22no—
97C2×C22⋊Dic53—22no—
98C2×C22⋊Dic53—41no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53C2×C414yes—
101C2×C22⋊Dic53C2×C414yes—
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—41no—
117#13133124—41no—
118#13133124—41no—
119#13133124C2×C414yescomplemented
120#13133124C2×C414yescomplemented
121#13133124D414yes—
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—22no—
140C2×C4⋊C4×C53—41no—
141C2×C4⋊C4×C53—41no—
142C2×C22⋊C4×C53—22no—
143C2×C22⋊C4×C53—41no—
144C2×C22⋊C4×C53—41no—
145C2×C22⋊C4×C53C2×C414yes—
146C2×C22⋊C4×C53D414yes—
147C2×C22⋊C4×C53Q814yes—
148#95×C53—22no—
149#95×C53—22no—
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—44no—
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×C53C22×C412yes—
208C22×C4×C53C22×C412yes—
209C22×C4×C53C2×D412yes—
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2×D412yes—
212C22×C4×C53C2×D412yes—
213C22×C4×C53C2×Q812yes—
214C22×C4×C53C2×Q812yes—
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×Dic53—21no—
261C22×Dic53C22×C412yes—
262C22×Dic53C22×C412yes—
263C22×Dic53C22×C412yes—
264C22×Dic53C22×C412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53C2×D412yes—
267C22×Dic53C2×D412yes—
268C22×Dic53C2×D412yes—
269C22×Dic53#4112yes—
270C22×Dic53#4112yes—
271C4⋊C4×C53—44no—
272C4⋊C4×C53—44no—
273C22⋊C4×C53—44no—
274C22⋊C4×C53C4⋊C4116yescomplemented
275C22⋊Dic53—28no—
276C22⋊Dic53—28no—
277C22⋊Dic53—44no—
278C22⋊Dic53—44no—
279C4⋊Dic53—28no—
280C4⋊Dic53—44no—
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×C53C2×C4⋊C414yes—
381C2×C4×C53C2×C4⋊C414yes—
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×Dic53—41no—
436C2×Dic53C4×D414yes—
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—24no—
491C4×C53—42no—
492C4×C53—42no—
493C4×C53—81no—
494C4×C53—81no—
495Dic53—24no—
496Dic53—24no—
497Dic53—42no—
498Dic53—42no—
499Dic53—42no—
500Dic53—42no—
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—22no—
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—2121no—
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—41no—
631C2×C22⋊C4—41no—
632C2×C22⋊C4—534no—
633C2×C22⋊C4—534no—
634C2×C22⋊C4—1062no—
635C2×C22⋊C4—1062no—
636C2×C22⋊C4—1062no—
637C2×C22⋊C4—1062no—
638C2×C22⋊C4—1062no—
639C2×C22⋊C4—1062no—
640C2×C22⋊C4—1062no—
641C2×C22⋊C4—1062no—
642C2×C22⋊C4—2121no—
643C2×C22⋊C4—2121no—
644C2×C22⋊C4Dic10614yes—
645C2×C22⋊C4C4×D5314yes—
646C2×C22⋊C4C22⋊D5314yes—
647C2×C42—534no—
648C2×C42—1062no—
649C2×C42—1062no—
650C2×C42—1062no—
651C2×C42—1062no—
652C2×C42—2121no—
653#95—22no—
654#95—22no—
655#95—534no—
656#95—534no—
657#95—534no—
658#95—1062no—
659#95—1062no—
660#95—1062no—
661#95—1062no—
662#95—1062no—
663#95—1062no—
664#95—1062no—
665#95—1062no—
666#95—2121no—
667#95—2121no—
668#95—2121no—
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×Dic10612yes—
682C24C2×C4×D5312yes—
683C24C2×C22⋊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—44no—
720C22×C4—44no—
721C22×C4—44no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—44no—
725C22×C4—44no—
726C22×C4—532no—
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—1061no—
737C22×C4—1061no—
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×C4C2×Dic10612yes—
783C22×C4C2×Dic10612yes—
784C22×C4C2×C4×D5312yes—
785C22×C4C2×C4×D5312yes—
786C22×C4D4×D5312yes—
787C22×C4D4×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—44no—
801C22⋊C4—1068no—
802C22⋊C4—1068no—
803C22⋊C4—2124no—
804C22⋊C4—2124no—
805C22⋊C4#11719919116yescomplemented
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—
842C23C2×#1171991914yes—
843C23C22×C4×D5311yescharacteristic
844C23C2×D4×D5311yescharacteristic
845C23C2×D4×D5311yescharacteristic
846C23C22×C22⋊D5311yescharacteristic
847C23C22×Dic10611yescharacteristic
848C23#41×D5311yescharacteristic
849C23#41×D5311yescharacteristic
850C23#1313326211yescharacteristic
851C23#1313326211yescharacteristic
852C23#1313326211yescharacteristic
853C23#1313326211yescharacteristic
854C23#1313326411yescharacteristic
855C23#1313326411yescharacteristic
856C23#1313326511yescharacteristic
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—534no—
900C2×C4—534no—
901C2×C4—1062no—
902C2×C4—1062no—
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—2121no—
926C2×C4—2121no—
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×C4C2×#1171991914yes—
956C2×C4C2×#1171991914yes—
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—
972C22C22×#1171991911yescharacteristic
973C22C4×D4×D5311yescharacteristic
974C22C4×D4×D5311yescharacteristic
975C22#1681110211yescharacteristic
976C22#1681110211yescharacteristic
977C22#1681110411yescharacteristic
978C22#1681110411yescharacteristic
979C22#1681118311yescharacteristic
980C22#1681118811yescharacteristic
981C22#1681119011yescharacteristic
982C22#1681119611yescharacteristic
983C22#1681119611yescharacteristic
984C22#1681119711yescharacteristic
985C22#1681121611yescharacteristic
986C22#1681121911yescharacteristic
987C22#1681124111yescharacteristic
988C22#1681124311yescharacteristic
989C22#1681125411yescharacteristic
990C22#1681125411yescharacteristic
991C22#1681125511yescharacteristic
992C22D4×C22⋊D5311yescharacteristic
993C22D4×C22⋊D5311yescharacteristic
994C22#1681127211yescharacteristic
995C22#1681127211yescharacteristic
996C22#1681127511yescharacteristic
997C22#1681128311yescharacteristic
998C22D4×Dic10611yescharacteristic
999C22D4×Dic10611yescharacteristic
1000C22#1681131811yescharacteristic
1001C22#1681133211yescharacteristic
1002C22#1681133211yescharacteristic
1003C22#1681136211yescharacteristic
1004C22#1681137411yescharacteristic
1005C22#1681137411yescharacteristic
1006C22#1681137611yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—42no—
1010C4—42no—
1011C4—81no—
1012C4—81no—
1013C4—1064no—
1014C4—1064no—
1015C4—4241no—
1016C4—4241no—
1017C4—2122no—
1018C4—2122no—
1019C4—2122no—
1020C4—2122no—
1021C2—44no—
1022C2#2027733911yescharacteristic
1023C2#2027738211yescharacteristic
1024C2#2027742111yescharacteristic
1025C2D4×#1171991911yescharacteristic
1026C2D4×#1171991911yescharacteristic
1027C2#2027773411yescharacteristic
1028C2#2027790311yescharacteristic
1029C2#2028092911yescharacteristic
1030C2#2028099211yescharacteristic
1031C2#2028103011yescharacteristic
1032C2#2028105411yescharacteristic
1033C2#2028156111yescharacteristic
1034C2#2028159611yescharacteristic
1035C2#2028170111yescharacteristic
1036C2#2028248811yescharacteristic
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×#16810519C2semidirect
6. C2×#16810492C2semidirect
7. #20272979C2semidirect
8. #20272978C2semidirect
9. #20272974C2semidirect
10. #20272967C2semidirect
13. #20272946C2semidirect
14. #20272941C2semidirect
32. #16810516C4semidirect
71. C2×C4⋊Dic53C2×C4semidirect
107. C2×C4×Dic53C2×C4semidirect
119. #13133124C2×C4semidirect
120. #13133124C2×C4semidirect
274. C22⋊C4×C53C4⋊C4semidirect
576. C53#14405semidirect
805. C22⋊C4#11719919semidirect

Maximal subgroups

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

subgroupindex
C2×#168105192
C2×#168105162
C2×#168104962
C2×#168104922
#202729792
#202729782
#202729742
#202729672
#202729582
#202729462
#202729412
C2×C53×#3852
#1440553