Finite Group Databasebeta

← #27307299

Subgroups — #27307299

Order 13568.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810520C211yesmaximal, characteristic, complemented
2C2×#16810496C211yesmaximal, characteristic
3C2×#16810496C211yesmaximal, characteristic
4C2×#16810496C211yesmaximal, characteristic
5C2×#16810483C211yesmaximal, characteristic
6C2×C4×C22⋊Dic53C211yesmaximal, characteristic
7#20272979C211yesmaximal, characteristic, complemented
8#20272973C211yesmaximal, characteristic, complemented
9#20272969C211yesmaximal, characteristic, complemented
10#20272966C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272946C211yesmaximal, characteristic, complemented
13#20272943C211yesmaximal, characteristic, complemented
14#20272938C211yesmaximal, characteristic
15C22×#95×C53C211yesmaximal, 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#16810520—24no—
31#16810496—24no—
32#16810496—24no—
33#16810496C418yescomplemented
34#16810483—24no—
35C4×C22⋊Dic53—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
51C24×C4×C53C2211yescharacteristic
52C24×C4×C53C2211yescharacteristic
53C2×#95×C53—24no—
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
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⋊Dic53—41no—
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—22no—
81C2×#11719919—22no—
82C2×#11719919—41no—
83C2×#11719919—41no—
84C2×#11719919—41no—
85C2×#11719919—41no—
86C2×#11719919—41no—
87C2×#11719919—41no—
88C2×#11719919C2×C414yescomplemented
89C2×#11719919C2×C414yescomplemented
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⋊Dic53C2×C414yes—
98C2×C22⋊Dic53C2×C414yes—
99C2×C22⋊Dic53D414yes—
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×Dic53—41no—
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—22no—
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—22no—
127C23×C4×C53—22no—
128C23×C4×C53—22no—
129C23×C4×C53—22no—
130C23×C4×C53—22no—
131C23×C4×C53—22no—
132C23×C4×C53—22no—
133C23×C4×C53—22no—
134C23×C4×C53—22no—
135C23×C4×C53—22no—
136C23×C4×C53—41no—
137C23×C4×C53—41no—
138C23×C4×C53—41no—
139C23×C4×C53—41no—
140C23×C4×C53—41no—
141C23×C4×C53—41no—
142C23×C4×C53C2×C414yes—
143C23×C4×C53Q814yes—
144C23×C4×C53C2311yescharacteristic
145C23×C4×C53C2311yescharacteristic
146C23×C4×C53C2311yescharacteristic
147C23×C4×C53C2311yescharacteristic
148C23×C4×C53C2311yescharacteristic
149C23×C4×C53C2311yescharacteristic
150#95×C53—22no—
151#95×C53—22no—
152#95×C53—22no—
153#95×C53D414yes—
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×D412yes—
165C24×C53C2×Q812yes—
166C24×C53C2×Q812yes—
167C24×C53#4112yes—
168C24×C53#4112yes—
169C24×C53C2411yescharacteristic
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—28no—
179C22×C4×C53—28no—
180C22×C4×C53—28no—
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—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—28no—
206C22×C4×C53—28no—
207C22×C4×C53—44no—
208C22×C4×C53—44no—
209C22×C4×C53—44no—
210C22×C4×C53—44no—
211C22×C4×C53—44no—
212C22×C4×C53—44no—
213C22×C4×C53—44no—
214C22×C4×C53—44no—
215C22×C4×C53—44no—
216C22×C4×C53—44no—
217C22×C4×C53—44no—
218C22×C4×C53—44no—
219C22×C4×C53—44no—
220C22×C4×C53—44no—
221C22×C4×C53—44no—
222C22×C4×C53—44no—
223C22×C4×C53C22×C412yes—
224C22×C4×C53C22×C412yes—
225C22×C4×C53C2×D412yes—
226C22×C4×C53C2×D412yes—
227C22×C4×C53C2×D412yes—
228C22×C4×C53C2×Q812yes—
229C22×C4×C53C2×Q812yes—
230C22×C4×C53#4112yes—
231C22×C4×C53#4112yes—
232C22×C4×C53#4112yes—
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×Dic53—21no—
262C22×Dic53—21no—
263C22×Dic53—21no—
264C22×Dic53—21no—
265C22×Dic53—21no—
266C22×Dic53—21no—
267C22×Dic53—21no—
268C22×Dic53—21no—
269C22×Dic53—21no—
270C22×Dic53—21no—
271C22×Dic53—21no—
272C22×Dic53—21no—
273C22×Dic53—21no—
274C22×Dic53—21no—
275C22×Dic53—21no—
276C22×Dic53—21no—
277C22×Dic53—21no—
278C22×Dic53—21no—
279C22×Dic53C22×C412yes—
280C22×Dic53C22×C412yes—
281C22×Dic53C22×C412yes—
282C22×Dic53C22×C412yes—
283C22×Dic53C2×D412yes—
284C22×Dic53C2×D412yes—
285C22×Dic53C2×D412yes—
286C22×Dic53C2×D412yes—
287C22×Dic53C2×Q812yes—
288C22×Dic53C2×Q812yes—
289C22⋊Dic53—28no—
290C22⋊Dic53—28no—
291C22⋊Dic53—44no—
292C22⋊Dic53C4⋊C4116yescomplemented
293C4⋊Dic53—44no—
294C4⋊Dic53—44no—
295#11719919—28no—
296#11719919—44no—
297#11719919—44no—
298#11719919—44no—
299#11719919—44no—
300#11719919—44no—
301C4×Dic53—44no—
302C4×Dic53—44no—
303C23×C53—22no—
304C23×C53—22no—
305C23×C53—22no—
306C23×C53—22no—
307C23×C53—22no—
308C23×C53—22no—
309C23×C53—22no—
310C23×C53—22no—
311C23×C53—22no—
312C23×C53—22no—
313C23×C53—22no—
314C23×C53—22no—
315C23×C53—22no—
316C23×C53—22no—
317C23×C53—22no—
318C23×C53—22no—
319C23×C53—22no—
320C23×C53—22no—
321C23×C53—22no—
322C23×C53—22no—
323C23×C53—22no—
324C23×C53—22no—
325C23×C53—22no—
326C23×C53—22no—
327C23×C53—22no—
328C23×C53—22no—
329C23×C53—22no—
330C23×C53—22no—
331C23×C53C2×C4⋊C414yes—
332C23×C53C4×D414yes—
333C23×C53C4×Q814yes—
334C23×C53#12114yes—
335C23×C53C22⋊Q814yes—
336C23×C53#12514yes—
337C23×C53C4⋊Q814yes—
338C23×C53C23×C411yescharacteristic
339C23×C53C22×D411yescharacteristic
340C23×C53C22×D411yescharacteristic
341C23×C53C22×D411yescharacteristic
342C23×C53C22×Q811yescharacteristic
343C23×C53C22×Q811yescharacteristic
344C23×C53C2×#4111yescharacteristic
345C23×C53C2×#4111yescharacteristic
346C23×C53C2×#4111yescharacteristic
347C23×C53C2×#4111yescharacteristic
348C23×C53C2×#4111yescharacteristic
349C23×C53H(5,𝔽2)11yescharacteristic
350C23×C53H(5,𝔽2)11yescharacteristic
351C23×C53H(5,𝔽2)11yescharacteristic
352C23×C532−1+411yescharacteristic
353C2×C4×C53—22no—
354C2×C4×C53—22no—
355C2×C4×C53—22no—
356C2×C4×C53—22no—
357C2×C4×C53—22no—
358C2×C4×C53—22no—
359C2×C4×C53—22no—
360C2×C4×C53—22no—
361C2×C4×C53—22no—
362C2×C4×C53—22no—
363C2×C4×C53—22no—
364C2×C4×C53—22no—
365C2×C4×C53—22no—
366C2×C4×C53—22no—
367C2×C4×C53—22no—
368C2×C4×C53—22no—
369C2×C4×C53—22no—
370C2×C4×C53—22no—
371C2×C4×C53—22no—
372C2×C4×C53—22no—
373C2×C4×C53—22no—
374C2×C4×C53—22no—
375C2×C4×C53—22no—
376C2×C4×C53—22no—
377C2×C4×C53—416no—
378C2×C4×C53—416no—
379C2×C4×C53—416no—
380C2×C4×C53—41no—
381C2×C4×C53—41no—
382C2×C4×C53—41no—
383C2×C4×C53—41no—
384C2×C4×C53—41no—
385C2×C4×C53—41no—
386C2×C4×C53—41no—
387C2×C4×C53—41no—
388C2×C4×C53—41no—
389C2×C4×C53—41no—
390C2×C4×C53—41no—
391C2×C4×C53—41no—
392C2×C4×C53—41no—
393C2×C4×C53—41no—
394C2×C4×C53—41no—
395C2×C4×C53—41no—
396C2×C4×C53C4×D414yes—
397C2×C4×C53C22⋊Q814yes—
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—22no—
407C2×Dic53—22no—
408C2×Dic53—22no—
409C2×Dic53—22no—
410C2×Dic53—22no—
411C2×Dic53—22no—
412C2×Dic53—22no—
413C2×Dic53—22no—
414C2×Dic53—22no—
415C2×Dic53—22no—
416C2×Dic53—22no—
417C2×Dic53—22no—
418C2×Dic53—22no—
419C2×Dic53—22no—
420C2×Dic53—22no—
421C2×Dic53—22no—
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×Dic53—41no—
437C2×Dic53—41no—
438C2×Dic53—41no—
439C2×Dic53—41no—
440C2×Dic53—41no—
441C2×Dic53—41no—
442C2×Dic53—41no—
443C2×Dic53—41no—
444C2×Dic53—41no—
445C2×Dic53—41no—
446C2×Dic53—41no—
447C2×Dic53—41no—
448C2×Dic53—41no—
449C2×Dic53—41no—
450C2×Dic53—41no—
451C2×Dic53—41no—
452C2×Dic53C2×C4⋊C414yes—
453C2×Dic53C2×C4⋊C414yes—
454#14004—531nomaximal, Sylow
455C22×C53—24no—
456C22×C53—24no—
457C22×C53—24no—
458C22×C53—24no—
459C22×C53—24no—
460C22×C53—24no—
461C22×C53—24no—
462C22×C53—24no—
463C22×C53—24no—
464C22×C53—24no—
465C22×C53—24no—
466C22×C53—24no—
467C22×C53—24no—
468C22×C53—24no—
469C22×C53#38918yescomplemented
470C22×C53C22×C4⋊C411yescharacteristic
471C22×C53C2×C4×D411yescharacteristic
472C22×C53C2×C4×D411yescharacteristic
473C22×C53C2×C4×Q811yescharacteristic
474C22×C53C4×#4111yescharacteristic
475C22×C53#51811yescharacteristic
476C22×C53#52011yescharacteristic
477C22×C53C2×#12111yescharacteristic
478C22×C53C2×C22⋊Q811yescharacteristic
479C22×C53C2×C22⋊Q811yescharacteristic
480C22×C53#52511yescharacteristic
481C22×C53C2×#12511yescharacteristic
482C22×C53#52911yescharacteristic
483C22×C53C2×C4⋊Q811yescharacteristic
484C22×C53#53311yescharacteristic
485C22×C53#53811yescharacteristic
486C22×C53#53911yescharacteristic
487C22×C53#54311yescharacteristic
488C22×C53#54411yescharacteristic
489C22×C53D4211yescharacteristic
490C22×C53D4211yescharacteristic
491C22×C53#54611yescharacteristic
492C22×C53#54611yescharacteristic
493C22×C53#54611yescharacteristic
494C22×C53#54611yescharacteristic
495C22×C53#54611yescharacteristic
496C22×C53#54711yescharacteristic
497C22×C53#54711yescharacteristic
498C22×C53D4×Q811yescharacteristic
499C22×C53#55111yescharacteristic
500C22×C53#55111yescharacteristic
501C22×C53#55211yescharacteristic
502C22×C53#55411yescharacteristic
503C22×C53#55411yescharacteristic
504C22×C53#55411yescharacteristic
505C4×C53—24no—
506C4×C53—24no—
507C4×C53—42no—
508C4×C53—42no—
509C4×C53—42no—
510C4×C53—42no—
511Dic53—24no—
512Dic53—24no—
513Dic53—42no—
514Dic53—42no—
515Dic53—42no—
516Dic53—42no—
517Dic53—81no—
518Dic53—81no—
519C2×#389—531no—
520C2×#385—531no—
521C2×#385—531no—
522C2×#385—531no—
523C2×#380—531no—
524C2×C4×C22⋊C4—531no—
525C22×#95D5311yescharacteristic
526#1444—531no—
527#1442—531no—
528#1441—531no—
529#1441—531no—
530#1436—531no—
531#1436—531no—
532C4⋊#95—531no—
533C22⋊#95—531no—
534C2×C53—28no—
535C2×C53C2×#38911yescharacteristic
536C2×C53C4×C22⋊Q811yescharacteristic
537C2×C53#232911yescharacteristic
538C2×C53D4×C4⋊C411yescharacteristic
539C2×C53#234911yescharacteristic
540C2×C53#235811yescharacteristic
541C2×C53#235911yescharacteristic
542C2×C53#242411yescharacteristic
543C2×C53#242511yescharacteristic
544C2×C53#243711yescharacteristic
545C2×C53#243811yescharacteristic
546C2×C53#244011yescharacteristic
547C2×C53#247311yescharacteristic
548C2×C53#250511yescharacteristic
549C2×C53#254911yescharacteristic
550C24×C4C2×D5311yescharacteristic
551C24×C4C2×D5311yescharacteristic
552C24×C4C2×D5311yescharacteristic
553C22×C4⋊C4—531no—
554C22×C4⋊C4—531no—
555C22×C4⋊C4—531no—
556C22×C4⋊C4—531no—
557C22×C4⋊C4—531no—
558C22×C4⋊C4—531no—
559C22×C4⋊C4—531no—
560C22×C4⋊C4—531no—
561C22×C22⋊C4—531no—
562C22×C22⋊C4—531no—
563C22×C22⋊C4—531no—
564C22×C22⋊C4—531no—
565C22×C42—531no—
566C22×C42—531no—
567#389—1064no—
568#385—538no—
569#385—1064no—
570#385—1064no—
571#380—1064no—
572C4×C22⋊C4—1064no—
573C2×#95—24no—
574C2×#95—531no—
575C2×#95—531no—
576C2×#95—531no—
577C2×#95—531no—
578C2×#95—531no—
579C2×#95—531no—
580C2×#95—531no—
581C2×#95—531no—
582C2×#95—531no—
583C2×#95—531no—
584C2×#95—531no—
585C2×#95—531no—
586C2×#95—531no—
587C2×#95—531no—
588C2×#95C2×D5311yescharacteristic
589C2×#95C2×D5311yescharacteristic
590C2×#95C2×D5311yescharacteristic
591C2×#95C2×D5311yescharacteristic
592C53#1400411yescharacteristic, complemented, Sylow
593C25C22×D5311yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4—531no—
614C23×C4—531no—
615C23×C4—531no—
616C23×C4—531no—
617C23×C4—531no—
618C23×C4—531no—
619C23×C4—531no—
620C23×C4—531no—
621C23×C4Dic10614yes—
622C23×C4C4×D5314yes—
623C23×C4C22×D5311yescharacteristic
624C23×C4C22×D5311yescharacteristic
625C23×C4C22×D5311yescharacteristic
626C23×C4C22×D5311yescharacteristic
627C23×C4C22×D5311yescharacteristic
628C23×C4C22×D5311yescharacteristic
629C2×C4⋊C4—534no—
630C2×C4⋊C4—534no—
631C2×C4⋊C4—1062no—
632C2×C4⋊C4—1062no—
633C2×C4⋊C4—1062no—
634C2×C4⋊C4—1062no—
635C2×C4⋊C4—1062no—
636C2×C4⋊C4—1062no—
637C2×C4⋊C4—1062no—
638C2×C4⋊C4—1062no—
639C2×C4⋊C4—1062no—
640C2×C4⋊C4—1062no—
641C2×C4⋊C4—1062no—
642C2×C4⋊C4—1062no—
643C2×C4⋊C4—1062no—
644C2×C4⋊C4—1062no—
645C2×C4⋊C4—2121no—
646C2×C4⋊C4—2121no—
647C2×C4⋊C4—2121no—
648C2×C4⋊C4—2121no—
649C2×C4⋊C4—2121no—
650C2×C4⋊C4—2121no—
651C2×C4⋊C4—2121no—
652C2×C4⋊C4—2121no—
653C2×C22⋊C4—534no—
654C2×C22⋊C4—534no—
655C2×C22⋊C4—534no—
656C2×C22⋊C4—534no—
657C2×C22⋊C4—534no—
658C2×C22⋊C4—1062no—
659C2×C22⋊C4—1062no—
660C2×C22⋊C4—1062no—
661C2×C22⋊C4—1062no—
662C2×C22⋊C4—1062no—
663C2×C22⋊C4—1062no—
664C2×C22⋊C4—1062no—
665C2×C42—1062no—
666C2×C42—1062no—
667C2×C42—1062no—
668C2×C42—1062no—
669C2×C42—2121no—
670C2×C42—2121no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—534no—
675#95—534no—
676#95—1062no—
677#95—1062no—
678#95—1062no—
679#95—1062no—
680#95—1062no—
681#95—1062no—
682#95—1062no—
683#95—1062no—
684#95—1062no—
685#95—1062no—
686#95—2121no—
687#95—2121no—
688#95C22⋊D5314yes—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C2×Dic10612yes—
698C24C2×C4×D5312yes—
699C24#1171994512yes—
700C24D4×D5312yes—
701C24D4×D5312yes—
702C24#1171994712yes—
703C24Q8×D5312yes—
704C24C23×D5311yescharacteristic
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—28no—
714C22×C4—28no—
715C22×C4—28no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—28no—
741C22×C4—28no—
742C22×C4—44no—
743C22×C4—44no—
744C22×C4—44no—
745C22×C4—44no—
746C22×C4—44no—
747C22×C4—44no—
748C22×C4—44no—
749C22×C4—44no—
750C22×C4—44no—
751C22×C4—44no—
752C22×C4—44no—
753C22×C4—44no—
754C22×C4—44no—
755C22×C4—44no—
756C22×C4—44no—
757C22×C4—44no—
758C22×C4—532no—
759C22×C4—532no—
760C22×C4—532no—
761C22×C4—532no—
762C22×C4—532no—
763C22×C4—532no—
764C22×C4—532no—
765C22×C4—532no—
766C22×C4—532no—
767C22×C4—532no—
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×C4—1061no—
784C22×C4—1061no—
785C22×C4—1061no—
786C22×C4—1061no—
787C22×C4—1061no—
788C22×C4—1061no—
789C22×C4—1061no—
790C22×C4—1061no—
791C22×C4—1061no—
792C22×C4—1061no—
793C22×C4—1061no—
794C22×C4—1061no—
795C22×C4—1061no—
796C22×C4—1061no—
797C22×C4—1061no—
798C22×C4—1061no—
799C22×C4—1061no—
800C22×C4—1061no—
801C22×C4—1061no—
802C22×C4—1061no—
803C22×C4—1061no—
804C22×C4—1061no—
805C22×C4—1061no—
806C22×C4—1061no—
807C22×C4—1061no—
808C22×C4—1061no—
809C22×C4—1061no—
810C22×C4—1061no—
811C22×C4—1061no—
812C22×C4—1061no—
813C22×C4—1061no—
814C22×C4C2×Dic10612yes—
815C22×C4C2×Dic10612yes—
816C22×C4C2×C4×D5312yes—
817C22×C4C2×C4×D5312yes—
818C22×C4#1171994512yes—
819C22×C4#1171994512yes—
820C22×C4#1171994512yes—
821C22×C4C2×C22⋊D5312yes—
822C22×C4C2×C22⋊D5312yes—
823C22×C4C2×C22⋊D5312yes—
824C4⋊C4—1068no—
825C4⋊C4—2124no—
826C4⋊C4—2124no—
827C4⋊C4—2124no—
828C4⋊C4—2124no—
829C4⋊C4—2124no—
830C4⋊C4—2124no—
831C4⋊C4—2124no—
832C22⋊C4—5316no—
833C22⋊C4—1068no—
834C22⋊C4—1068no—
835C22⋊C4—2124no—
836C42—2124no—
837C42—2124no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C4⋊C4×D5314yes—
867C23#1313317714yes—
868C23C4×Dic10614yes—
869C23#1313319014yes—
870C23#1313319414yes—
871C23#1313320714yes—
872C23#1313321614yes—
873C23C22×C4×D5311yescharacteristic
874C23C2×D4×D5311yescharacteristic
875C23C2×D4×D5311yescharacteristic
876C23C22×C22⋊D5311yescharacteristic
877C23C2×Q8×D5311yescharacteristic
878C23C22×Dic10611yescharacteristic
879C23C2×#1171994711yescharacteristic
880C23C2×#1171994511yescharacteristic
881C23C2×#1171994511yescharacteristic
882C23C2×#1171994511yescharacteristic
883C23C2×#1171994511yescharacteristic
884C23#1313326211yescharacteristic
885C23#1313326211yescharacteristic
886C23#1313326211yescharacteristic
887C23#1313326511yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—416no—
913C2×C4—416no—
914C2×C4—416no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—534no—
932C2×C4—534no—
933C2×C4—1062no—
934C2×C4—1062no—
935C2×C4—1062no—
936C2×C4—1062no—
937C2×C4—1062no—
938C2×C4—1062no—
939C2×C4—1062no—
940C2×C4—1062no—
941C2×C4—1062no—
942C2×C4—1062no—
943C2×C4—1062no—
944C2×C4—1062no—
945C2×C4—1062no—
946C2×C4—1062no—
947C2×C4—1062no—
948C2×C4—1062no—
949C2×C4—1062no—
950C2×C4—1062no—
951C2×C4—1062no—
952C2×C4—1062no—
953C2×C4—1062no—
954C2×C4—1062no—
955C2×C4—1062no—
956C2×C4—1062no—
957C2×C4—2121no—
958C2×C4—2121no—
959C2×C4—2121no—
960C2×C4—2121no—
961C2×C4—2121no—
962C2×C4—2121no—
963C2×C4—2121no—
964C2×C4—2121no—
965C2×C4—2121no—
966C2×C4—2121no—
967C2×C4—2121no—
968C2×C4—2121no—
969C2×C4—2121no—
970C2×C4—2121no—
971C2×C4—2121no—
972C2×C4—2121no—
973C2×C4—2121no—
974C2×C4—2121no—
975C2×C4—2121no—
976C2×C4—2121no—
977C2×C4—2121no—
978C2×C4—2121no—
979C2×C4—2121no—
980C2×C4—2121no—
981C2×C4—2121no—
982C2×C4—2121no—
983C2×C4—2121no—
984C2×C4—2121no—
985C2×C4—2121no—
986C2×C4—2121no—
987C2×C4C4×C22⋊D5314yes—
988C2×C4#1313319614yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#1681052018yescomplemented
1004C22C2×C4⋊C4×D5311yescharacteristic
1005C22C2×#1313317711yescharacteristic
1006C22C2×C4×C22⋊D5311yescharacteristic
1007C22C2×C4×Dic10611yescharacteristic
1008C22C4×#1171994511yescharacteristic
1009C22#1681109611yescharacteristic
1010C22#1681110411yescharacteristic
1011C22C2×#1313319011yescharacteristic
1012C22C2×#1313319411yescharacteristic
1013C22C2×#1313319611yescharacteristic
1014C22#1681113411yescharacteristic
1015C22C2×#1313320711yescharacteristic
1016C22#1681115711yescharacteristic
1017C22C2×#1313321611yescharacteristic
1018C22#1681118011yescharacteristic
1019C22#1681121111yescharacteristic
1020C22#1681122011yescharacteristic
1021C22#1681124911yescharacteristic
1022C22#1681125411yescharacteristic
1023C22D4×C22⋊D5311yescharacteristic
1024C22D4×C22⋊D5311yescharacteristic
1025C22#1681126311yescharacteristic
1026C22#1681126311yescharacteristic
1027C22#1681126311yescharacteristic
1028C22#1681126311yescharacteristic
1029C22#1681126711yescharacteristic
1030C22#1681127411yescharacteristic
1031C22#1681127411yescharacteristic
1032C22Q8×C22⋊D5311yescharacteristic
1033C22#1681129911yescharacteristic
1034C22#1681129911yescharacteristic
1035C22#1681130811yescharacteristic
1036C22#1681132811yescharacteristic
1037C22#1681132811yescharacteristic
1038C22#1681132811yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—42no—
1042C4—42no—
1043C4—42no—
1044C4—42no—
1045C4—1064no—
1046C4—1064no—
1047C4—4241no—
1048C4—4241no—
1049C4—2122no—
1050C4—2122no—
1051C4—2122no—
1052C4—2122no—
1053C2—28no—
1054C2C2×#1681052011yescharacteristic
1055C2C4×#1313319611yescharacteristic
1056C2#2027744811yescharacteristic
1057C2C4⋊C4×C22⋊D5311yescharacteristic
1058C2#2027762211yescharacteristic
1059C2#2027769411yescharacteristic
1060C2#2027770311yescharacteristic
1061C2#2027825111yescharacteristic
1062C2#2027826611yescharacteristic
1063C2#2027837611yescharacteristic
1064C2#2027839111yescharacteristic
1065C2#2027841111yescharacteristic
1066C2#2027885011yescharacteristic
1067C2#2027921611yescharacteristic
1068C2#2027972611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC22×#95×C53C2
socle, cosocleC24×C53C24
prime radicalC25×C53C23
hypercenterC22×#95D53
hypocenterC53#14004
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
1. C2×#16810520C2semidirect
7. #20272979C2semidirect
8. #20272973C2semidirect
9. #20272969C2semidirect
10. #20272966C2semidirect
11. #20272949C2semidirect
12. #20272946C2semidirect
13. #20272943C2semidirect
33. #16810496C4semidirect
88. C2×#11719919C2×C4semidirect
89. C2×#11719919C2×C4semidirect
120. #13133124C2×C4semidirect
121. #13133124C2×C4semidirect
292. C22⋊Dic53C4⋊C4semidirect
469. C22×C53#389semidirect
592. C53#14004semidirect
1003. C22#16810520semidirect

Maximal subgroups

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

subgroupindex
C2×#168105202
C2×#168104962
C2×#168104832
C2×C4×C22⋊Dic532
#202729792
#202729732
#202729692
#202729662
#202729492
#202729462
#202729432
#202729382
C22×#95×C532
#1400453