Finite Group Databasebeta

← #27307898

Subgroups — #27307898

Order 13568.

2266 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133195C211yesmaximal, characteristic
2C2×#16810527C211yesmaximal, characteristic, complemented
3C2×#16810494C211yesmaximal, characteristic
4C2×C4×#11719921C211yesmaximal, characteristic
5C2×#95×D53C211yesmaximal, characteristic
6#20272985C211yesmaximal, characteristic, complemented
7#20272983C211yesmaximal, characteristic, complemented
8#20272966C211yesmaximal, characteristic, complemented
9#20272965C211yesmaximal, characteristic, complemented
10#20272948C211yesmaximal, characteristic, complemented
11#20272946C211yesmaximal, characteristic, complemented
12#20272936C211yesmaximal, characteristic
13#20272936C211yesmaximal, characteristic
14#20272936C211yesmaximal, characteristic
15C53×C4⋊#95C211yesmaximal, characteristic, complemented
16C23×Dic106C2211yescharacteristic
17C23×C4×D53C2211yescharacteristic
18C23×C4×D53C2211yescharacteristic
19C23×C4×D53C2211yescharacteristic
20C2×#13133195—24no—
21C2×#13133195—24no—
22C2×#13133195C418yescomplemented
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×#11719921C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×C4×Dic53C2211yescharacteristic
31#16810527—24no—
32#16810494—24no—
33C4×#11719921—24no—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2211yescharacteristic
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
50#95×D53—24no—
51C22×C4⋊C4×C53C2211yescharacteristic
52C22×C4⋊C4×C53C2211yescharacteristic
53C22×C42×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C24×D53C2311yescharacteristic
59C22×Dic106—22no—
60C22×Dic106—22no—
61C22×Dic106—22no—
62C22×Dic106—22no—
63C22×Dic106—41no—
64C22×Dic106—41no—
65C22×Dic106C2×C414yescomplemented
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C22×C4×D53—22no—
74C22×C4×D53—22no—
75C22×C4×D53—22no—
76C22×C4×D53—22no—
77C22×C4×D53—22no—
78C22×C4×D53—22no—
79C22×C4×D53—22no—
80C22×C4×D53—22no—
81C22×C4×D53—22no—
82C22×C4×D53—22no—
83C22×C4×D53—22no—
84C22×C4×D53—22no—
85C22×C4×D53—22no—
86C22×C4×D53—41no—
87C22×C4×D53—41no—
88C22×C4×D53—41no—
89C22×C4×D53—41no—
90C22×C4×D53—41no—
91C22×C4×D53—41no—
92C22×C4×D53C2×C414yes—
93C22×C4×D53Q814yescomplemented
94#13133195—232no—
95C2×#11719919—22no—
96C2×#11719919—22no—
97C2×#11719919—22no—
98C2×#11719919—22no—
99C2×#11719919—22no—
100C2×#11719919—22no—
101C2×#11719919—41no—
102C2×#11719919C2×C414yescomplemented
103C2×#11719919C2×C414yescomplemented
104C2×#11719921—22no—
105C2×#11719921—22no—
106C2×#11719921—22no—
107C2×#11719921—22no—
108C2×#11719921—22no—
109C2×#11719921—22no—
110C2×#11719921—22no—
111C2×#11719921C2×C414yes—
112C2×#11719921C2×C414yes—
113C2×#11719921D414yes—
114C2×#11719921D414yes—
115C2×#11719921Q814yescomplemented
116C2×C4×Dic53—22no—
117C2×C4×Dic53—22no—
118C2×C4×Dic53—41no—
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—22no—
124#13133124—22no—
125#13133124—22no—
126#13133124—22no—
127#13133124—22no—
128#13133124—22no—
129#13133124—22no—
130#13133124—41no—
131#13133124—41no—
132#13133124—41no—
133#13133124—41no—
134#13133124D414yes—
135C23×C4×C53C2311yescharacteristic
136C23×C4×C53C2311yescharacteristic
137C23×C4×C53C2311yescharacteristic
138C23×C4×C53C2311yescharacteristic
139C23×C4×C53C2311yescharacteristic
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C2×C4⋊C4×C53—22no—
143C2×C4⋊C4×C53—22no—
144C2×C4⋊C4×C53—22no—
145C2×C4⋊C4×C53—22no—
146C2×C4⋊C4×C53—41no—
147C2×C4⋊C4×C53C2×C414yescomplemented
148C2×C42×C53—22no—
149C2×C42×C53—22no—
150C2×C42×C53—41no—
151#95×C53—22no—
152#95×C53—22no—
153#95×C53—41no—
154#95×C53—41no—
155C24×C53C2411yescharacteristic
156C23×D53—21no—
157C23×D53—21no—
158C23×D53—21no—
159C23×D53—21no—
160C23×D53—21no—
161C23×D53—21no—
162C23×D53—21no—
163C23×D53—21no—
164C23×D53C22×C412yes—
165C23×D53C2×D412yes—
166C23×D53C2×D412yes—
167C23×D53C2×Q812yes—
168C23×D53C2×Q812yes—
169C23×D53#4112yes—
170C23×D53#4112yes—
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—21no—
202C22×C4×C53—21no—
203C22×C4×C53—21no—
204C22×C4×C53—21no—
205C22×C4×C53—21no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—21no—
209C22×C4×C53—21no—
210C22×C4×C53C22×C412yes—
211C22×C4×C53C22×C412yes—
212C22×C4×C53C22×C412yes—
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2×D412yes—
216C22×C4×C53C2×Q812yes—
217C22×C4×C53C2×Q812yes—
218C22×C4×C53#4112yes—
219C22×C4×C53#4112yes—
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×Dic53C22×C412yes—
260C22×Dic53C22×C412yes—
261C22×Dic53C22×C412yes—
262C22×Dic53C2×D412yes—
263C22×Dic53C2×D412yes—
264C22×Dic53C2×D412yes—
265C22×Dic53C2×D412yes—
266C22×Dic53C2×Q812yes—
267C22×Dic53C2×Q812yes—
268C22×Dic53#4112yes—
269C2×C4×D53—28no—
270C2×C4×D53—28no—
271C2×C4×D53—28no—
272C2×C4×D53—28no—
273C2×C4×D53—28no—
274C2×C4×D53—44no—
275C2×C4×D53—44no—
276C2×C4×D53—44no—
277C2×C4×D53—44no—
278C2×C4×D53—44no—
279C2×C4×D53—44no—
280C2×C4×D53—44no—
281C2×C4×D53—44no—
282C2×C4×D53—44no—
283C2×C4×D53—44no—
284C2×C4×D53—44no—
285C2×C4×D53—44no—
286C2×C4×D53—44no—
287C2×C4×D53—44no—
288C2×C4×D53—44no—
289C2×C4×D53—44no—
290C2×Dic106—28no—
291C2×Dic106—28no—
292C2×Dic106—44no—
293C2×Dic106—44no—
294C2×Dic106—44no—
295C2×Dic106—44no—
296C2×Dic106—44no—
297C4⋊C4×C53—28no—
298C4⋊C4×C53—44no—
299C42×C53—44no—
300#11719921—28no—
301#11719921—28no—
302#11719921—44no—
303#11719921C22⋊C4116yes—
304#11719919—28no—
305#11719919—28no—
306#11719919—44no—
307C4×Dic53—44no—
308C23×C53C23×C411yescharacteristic
309C23×C53C22×D411yescharacteristic
310C23×C53C22×D411yescharacteristic
311C23×C53C22×D411yescharacteristic
312C23×C53C22×Q811yescharacteristic
313C23×C53C22×Q811yescharacteristic
314C23×C53C2×#4111yescharacteristic
315C23×C53C2×#4111yescharacteristic
316C23×C53C2×#4111yescharacteristic
317C23×C53C2×#4111yescharacteristic
318C23×C53C2×#4111yescharacteristic
319C23×C53H(5,𝔽2)11yescharacteristic
320C23×C53H(5,𝔽2)11yescharacteristic
321C23×C53H(5,𝔽2)11yescharacteristic
322C23×C532−1+411yescharacteristic
323C22×D53—22no—
324C22×D53—22no—
325C22×D53—22no—
326C22×D53—22no—
327C22×D53—22no—
328C22×D53—22no—
329C22×D53—22no—
330C22×D53—22no—
331C22×D53—22no—
332C22×D53—22no—
333C22×D53—22no—
334C22×D53—22no—
335C22×D53—22no—
336C22×D53—22no—
337C22×D53—22no—
338C22×D53—22no—
339C22×D53—22no—
340C22×D53—22no—
341C22×D53—22no—
342C22×D53—22no—
343C22×D53—22no—
344C22×D53—22no—
345C22×D53—22no—
346C22×D53—22no—
347C22×D53—22no—
348C22×D53—22no—
349C22×D53—22no—
350C22×D53—22no—
351C22×D53C2×C22⋊C414yes—
352C22×D53C4×Q814yes—
353C22×D53C4×Q814yes—
354C22×D53C22⋊Q814yes—
355C22×D53C22⋊Q814yes—
356C22×D53#12414yes—
357C22×D53C4⋊Q814yes—
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—22no—
378C2×C4×C53—22no—
379C2×C4×C53—22no—
380C2×C4×C53—22no—
381C2×C4×C53—22no—
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×C53—41no—
397C2×C4×C53—41no—
398C2×C4×C53—41no—
399C2×C4×C53—41no—
400C2×C4×C53—41no—
401C2×C4×C53—41no—
402C2×C4×C53—41no—
403C2×C4×C53—41no—
404C2×C4×C53—41no—
405C2×C4×C53C2×C22⋊C414yes—
406C2×C4×C53C22⋊Q814yescomplemented
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—22no—
423C2×Dic53—22no—
424C2×Dic53—22no—
425C2×Dic53—22no—
426C2×Dic53—22no—
427C2×Dic53—22no—
428C2×Dic53—22no—
429C2×Dic53—22no—
430C2×Dic53—22no—
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×Dic53—41no—
453C2×Dic53—41no—
454C2×Dic53C2×C22⋊C414yes—
455C2×Dic53C4×D414yes—
456C4×D53—416no—
457C4×D53—416no—
458C4×D53—416no—
459Dic106—416no—
460#14052—531nomaximal, Sylow
461C22×C53C22×C22⋊C411yescharacteristic
462C22×C53C2×C4×D411yescharacteristic
463C22×C53C2×C4×Q811yescharacteristic
464C22×C53C2×C4×Q811yescharacteristic
465C22×C53C4×#4111yescharacteristic
466C22×C53#51811yescharacteristic
467C22×C53#52011yescharacteristic
468C22×C53C2×C22⋊Q811yescharacteristic
469C22×C53C2×C22⋊Q811yescharacteristic
470C22×C53C2×C22⋊Q811yescharacteristic
471C22×C53#52511yescharacteristic
472C22×C53C2×#12411yescharacteristic
473C22×C53#52911yescharacteristic
474C22×C53C2×C4⋊Q811yescharacteristic
475C22×C53#53311yescharacteristic
476C22×C53#53811yescharacteristic
477C22×C53#53911yescharacteristic
478C22×C53#54311yescharacteristic
479C22×C53#54411yescharacteristic
480C22×C53D4211yescharacteristic
481C22×C53D4211yescharacteristic
482C22×C53#54611yescharacteristic
483C22×C53#54611yescharacteristic
484C22×C53#54611yescharacteristic
485C22×C53#54611yescharacteristic
486C22×C53#54611yescharacteristic
487C22×C53#54711yescharacteristic
488C22×C53#54711yescharacteristic
489C22×C53D4×Q811yescharacteristic
490C22×C53#55111yescharacteristic
491C22×C53#55111yescharacteristic
492C22×C53#55211yescharacteristic
493C22×C53#55411yescharacteristic
494C22×C53#55411yescharacteristic
495C22×C53#55411yescharacteristic
496C2×D53—24no—
497C2×D53—24no—
498C2×D53—24no—
499C2×D53—24no—
500C2×D53—24no—
501C2×D53—24no—
502C2×D53—24no—
503C2×D53—24no—
504C2×D53—24no—
505C2×D53—24no—
506C2×D53—24no—
507C2×D53—24no—
508C2×D53—24no—
509C2×D53—24no—
510C2×D53#39118yescomplemented
511C4×C53—24no—
512C4×C53—24no—
513C4×C53—42no—
514C4×C53—42no—
515C4×C53—42no—
516C4×C53—42no—
517C4×C53—81no—
518Dic53—24no—
519Dic53—24no—
520Dic53—42no—
521Dic53—42no—
522Dic53—42no—
523Dic53—42no—
524Dic53—81no—
525C22×C22⋊Q8—531no—
526C2×#391—531no—
527C2×#385—531no—
528C2×C4×C22⋊C4—531no—
529C22×#95—531no—
530#1446—531no—
531#1445—531no—
532#1441—531no—
533#1441—531no—
534#1436—531no—
535#1436—531no—
536C4⋊#95D5311yescharacteristic, complemented
537C22⋊#95—531no—
538C22⋊#95—531no—
539C22⋊#95—531no—
540C2×C53C2×#39111yescharacteristic
541C2×C53C4×C22⋊Q811yescharacteristic
542C2×C53#232911yescharacteristic
543C2×C53D4×C22⋊C411yescharacteristic
544C2×C53#233911yescharacteristic
545C2×C53#236011yescharacteristic
546C2×C53#236811yescharacteristic
547C2×C53#243711yescharacteristic
548C2×C53#243811yescharacteristic
549C2×C53#244011yescharacteristic
550C2×C53#244911yescharacteristic
551C2×C53#245011yescharacteristic
552C2×C53#247211yescharacteristic
553C2×C53#248811yescharacteristic
554C2×C53#254911yescharacteristic
555D53—28no—
556C23×Q8—531no—
557C24×C4—531no—
558C24×C4—531no—
559C24×C4—531no—
560C2×C22⋊Q8—538no—
561C2×C22⋊Q8—1064no—
562C2×C22⋊Q8—1064no—
563C22×C4⋊C4—531no—
564C22×C4⋊C4—531no—
565C22×C4⋊C4—531no—
566C22×C4⋊C4C2×D5311yescharacteristic
567C22×C4⋊C4C2×D5311yescharacteristic
568C22×C22⋊C4—531no—
569C22×C22⋊C4—531no—
570C22×C22⋊C4—531no—
571C22×C22⋊C4—531no—
572C22×C42—531no—
573C22×C42C2×D5311yescharacteristic
574#391—1064no—
575#385—1064no—
576C4×C22⋊C4—1064no—
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×#95—531no—
589C2×#95—531no—
590C2×#95—531no—
591C2×#95—531no—
592C2×#95—531no—
593C2×#95—1064no—
594C2×#95C2×D5311yescharacteristic
595C2×#95C2×D5311yescharacteristic
596C2×#95C2×D5311yescharacteristic
597C2×#95C2×D5311yescharacteristic
598C53#1405211yescharacteristic, complemented, Sylow
599C25—531no—
600C22×Q8—534no—
601C22×Q8—1062no—
602C22×Q8—1062no—
603C22×Q8—1062no—
604C22×Q8—1062no—
605C22×Q8—2121no—
606C22×Q8—2121no—
607C23×C4—531no—
608C23×C4—531no—
609C23×C4—531no—
610C23×C4—531no—
611C23×C4—531no—
612C23×C4—531no—
613C23×C4—534no—
614C23×C4—534no—
615C23×C4—531no—
616C23×C4—1062no—
617C23×C4—1062no—
618C23×C4—1062no—
619C23×C4—1062no—
620C23×C4—1062no—
621C23×C4—1062no—
622C23×C4—1062no—
623C23×C4—1062no—
624C23×C4—1062no—
625C23×C4—1062no—
626C23×C4—1062no—
627C23×C4—1062no—
628C23×C4—1062no—
629C23×C4—2121no—
630C23×C4—2121no—
631C23×C4—2121no—
632C23×C4—2121no—
633C23×C4—2121no—
634C23×C4—2121no—
635C23×C4C22×D5311yescharacteristic
636C23×C4C22×D5311yescharacteristic
637C23×C4C22×D5311yescharacteristic
638C23×C4C22×D5311yescharacteristic
639C23×C4C22×D5311yescharacteristic
640C23×C4C22×D5311yescharacteristic
641C23×C4C22×D5311yescharacteristic
642C22⋊Q8—10632no—
643C2×C4⋊C4—22no—
644C2×C4⋊C4—22no—
645C2×C4⋊C4—22no—
646C2×C4⋊C4—22no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—534no—
649C2×C4⋊C4—534no—
650C2×C4⋊C4—1062no—
651C2×C4⋊C4—1062no—
652C2×C4⋊C4—1062no—
653C2×C4⋊C4—1062no—
654C2×C4⋊C4—1062no—
655C2×C4⋊C4—1062no—
656C2×C4⋊C4—2121no—
657C2×C4⋊C4C4×D5314yescomplemented
658C2×C22⋊C4—534no—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—534no—
661C2×C22⋊C4—534no—
662C2×C22⋊C4—534no—
663C2×C22⋊C4—1062no—
664C2×C22⋊C4—1062no—
665C2×C22⋊C4—1062no—
666C2×C22⋊C4—1062no—
667C2×C22⋊C4—1062no—
668C2×C22⋊C4—1062no—
669C2×C22⋊C4—1062no—
670C2×C42—22no—
671C2×C42—22no—
672C2×C42—41no—
673C2×C42—1062no—
674C2×C42—1062no—
675C2×C42—2121no—
676#95—22no—
677#95—22no—
678#95—41no—
679#95—41no—
680#95—534no—
681#95—1062no—
682#95—1062no—
683#95—1062no—
684#95—1062no—
685#95—1062no—
686#95—1062no—
687#95—1062no—
688#95—1062no—
689#95—1062no—
690#95—1062no—
691#95—1062no—
692#95—2121no—
693#95—2121no—
694#95—2121no—
695#95—2121no—
696C24—532no—
697C24—532no—
698C24—532no—
699C24—532no—
700C24—532no—
701C24—532no—
702C24—532no—
703C24—1061no—
704C24—1061no—
705C24—1061no—
706C24—1061no—
707C24—1061no—
708C24—1061no—
709C24—1061no—
710C24—1061no—
711C24C23×D5311yescharacteristic
712C2×Q8—1068no—
713C2×Q8—1068no—
714C2×Q8—2124no—
715C2×Q8—2124no—
716C2×Q8—2124no—
717C2×Q8—2124no—
718C2×Q8—2124no—
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—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
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—1068no—
769C22×C4—1068no—
770C22×C4—1068no—
771C22×C4—1068no—
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—1068no—
805C22×C4—1061no—
806C22×C4—1061no—
807C22×C4—1061no—
808C22×C4—1061no—
809C22×C4—1061no—
810C22×C4—1061no—
811C22×C4—1061no—
812C22×C4—2124no—
813C22×C4—2124no—
814C22×C4—2124no—
815C22×C4—2124no—
816C22×C4—2124no—
817C22×C4—2124no—
818C22×C4—2124no—
819C22×C4—2124no—
820C22×C4—2124no—
821C22×C4—2124no—
822C22×C4—2124no—
823C22×C4—2124no—
824C22×C4—2124no—
825C22×C4—2124no—
826C22×C4—2124no—
827C22×C4—2124no—
828C22×C4C2×C4×D5312yes—
829C22×C4C2×C4×D5312yes—
830C22×C4C2×C4×D5312yes—
831C22×C4#1171994512yes—
832C22×C4#1171994512yes—
833C22×C4D4×D5312yes—
834C22×C4D4×D5312yes—
835C22×C4D4×D5312yes—
836C22×C4Q8×D5312yes—
837C22×C4Q8×D5312yes—
838C4⋊C4—28no—
839C4⋊C4—44no—
840C4⋊C4—1068no—
841C4⋊C4—1068no—
842C4⋊C4—2124no—
843C22⋊C4—5316no—
844C22⋊C4—1068no—
845C22⋊C4—1068no—
846C22⋊C4—2124no—
847C42—44no—
848C42—2124no—
849C23—534no—
850C23—534no—
851C23—534no—
852C23—534no—
853C23—534no—
854C23—534no—
855C23—534no—
856C23—1062no—
857C23—1062no—
858C23—1062no—
859C23—1062no—
860C23—1062no—
861C23—1062no—
862C23—1062no—
863C23—1062no—
864C23—1062no—
865C23—1062no—
866C23—1062no—
867C23—1062no—
868C23—1062no—
869C23—1062no—
870C23—1062no—
871C23—1062no—
872C23—1062no—
873C23—1062no—
874C23—1062no—
875C23—1062no—
876C23—1062no—
877C23—1062no—
878C23—1062no—
879C23—1062no—
880C23—1062no—
881C23—1062no—
882C23—1062no—
883C23—1062no—
884C23C22×C4×D5311yescharacteristic
885C23C2×D4×D5311yescharacteristic
886C23C2×D4×D5311yescharacteristic
887C23C2×D4×D5311yescharacteristic
888C23C2×Q8×D5311yescharacteristic
889C23C2×Q8×D5311yescharacteristic
890C23#41×D5311yescharacteristic
891C23#41×D5311yescharacteristic
892C23#41×D5311yescharacteristic
893C23C2×#1171994511yescharacteristic
894C23C2×#1171994511yescharacteristic
895C23#1313326211yescharacteristic
896C23#1313326211yescharacteristic
897C23#1313326311yescharacteristic
898C23#1313326511yescharacteristic
899Q8—21216no—
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—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—534no—
948C2×C4—534no—
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—1062no—
958C2×C4—1062no—
959C2×C4—1062no—
960C2×C4—1062no—
961C2×C4—1062no—
962C2×C4—1062no—
963C2×C4—1062no—
964C2×C4—1062no—
965C2×C4—1062no—
966C2×C4—1062no—
967C2×C4—1062no—
968C2×C4—1062no—
969C2×C4—1062no—
970C2×C4—1062no—
971C2×C4—1062no—
972C2×C4—1062no—
973C2×C4—21216no—
974C2×C4—21216no—
975C2×C4—21216no—
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×C4—2121no—
988C2×C4—2121no—
989C2×C4—2121no—
990C2×C4—2121no—
991C2×C4—2121no—
992C2×C4—2121no—
993C2×C4—2121no—
994C2×C4—2121no—
995C2×C4—2121no—
996C2×C4—2121no—
997C2×C4—2121no—
998C2×C4—2121no—
999C2×C4C22⋊C4×D5314yes—
1000C2×C4#1313319514yescomplemented
1001C22—538no—
1002C22—1064no—
1003C22—1064no—
1004C22—1064no—
1005C22—1064no—
1006C22—1064no—
1007C22—1064no—
1008C22—1064no—
1009C22—1064no—
1010C22—1064no—
1011C22—1064no—
1012C22—1064no—
1013C22—1064no—
1014C22—1064no—
1015C22—1064no—
1016C22C2×C22⋊C4×D5311yescharacteristic
1017C22C4×D4×D5311yescharacteristic
1018C22C4×Q8×D5311yescharacteristic
1019C22C4×Q8×D5311yescharacteristic
1020C22C4×#1171994511yescharacteristic
1021C22#1681109511yescharacteristic
1022C22#1681110411yescharacteristic
1023C22C22⋊Q8×D5311yescharacteristic
1024C22C22⋊Q8×D5311yescharacteristic
1025C22C2×#1313319511yescharacteristic
1026C22#1681113211yescharacteristic
1027C22#124×D5311yescharacteristic
1028C22#1681115111yescharacteristic
1029C22C4⋊Q8×D5311yescharacteristic
1030C22#1681117711yescharacteristic
1031C22#1681120511yescharacteristic
1032C22#1681122111yescharacteristic
1033C22#1681124811yescharacteristic
1034C22#1681125011yescharacteristic
1035C22#1681125711yescharacteristic
1036C22#1681125811yescharacteristic
1037C22#1681126211yescharacteristic
1038C22#1681126311yescharacteristic
1039C22#1681126311yescharacteristic
1040C22#1681126611yescharacteristic
1041C22#1681127011yescharacteristic
1042C22#1681127411yescharacteristic
1043C22#1681127411yescharacteristic
1044C22#1681128811yescharacteristic
1045C22#1681129711yescharacteristic
1046C22#1681130211yescharacteristic
1047C22#1681130511yescharacteristic
1048C22#1681132711yescharacteristic
1049C22#1681132811yescharacteristic
1050C22#1681133311yescharacteristic
1051C4—24no—
1052C4—24no—
1053C4—42no—
1054C4—42no—
1055C4—42no—
1056C4—42no—
1057C4—81no—
1058C4—1064no—
1059C4—1064no—
1060C4—4241no—
1061C4—2122no—
1062C4—2122no—
1063C4—2122no—
1064C4—2122no—
1065C2—1068no—
1066C2#391×D5311yescharacteristic
1067C2C4×#1313319511yescharacteristic
1068C2#2027744911yescharacteristic
1069C2#2027753611yescharacteristic
1070C2#2027754211yescharacteristic
1071C2#2027771711yescharacteristic
1072C2#2027779911yescharacteristic
1073C2#2027838311yescharacteristic
1074C2#2027839811yescharacteristic
1075C2#2027842011yescharacteristic
1076C2#2027853111yescharacteristic
1077C2#2027854611yescharacteristic
1078C2#2027884711yescharacteristic
1079C2#2027903811yescharacteristic
1080C2#2027972411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC4⋊#95D53
hypocenterC53#14052
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16810527C2semidirect
6. #20272985C2semidirect
7. #20272983C2semidirect
8. #20272966C2semidirect
9. #20272965C2semidirect
10. #20272948C2semidirect
11. #20272946C2semidirect
15. C53×C4⋊#95C2semidirect
22. C2×#13133195C4semidirect
65. C22×Dic106C2×C4semidirect
93. C22×C4×D53Q8semidirect
102. C2×#11719919C2×C4semidirect
103. C2×#11719919C2×C4semidirect
115. C2×#11719921Q8semidirect
147. C2×C4⋊C4×C53C2×C4semidirect
406. C2×C4×C53C22⋊Q8semidirect
510. C2×D53#391semidirect
536. C4⋊#95D53semidirect
598. C53#14052semidirect
657. C2×C4⋊C4C4×D53semidirect
1000. C2×C4#13133195semidirect

Maximal subgroups

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

subgroupindex
C22×#131331952
C2×#168105272
C2×#168104942
C2×C4×#117199212
C2×#95×D532
#202729852
#202729832
#202729662
#202729652
#202729482
#202729462
#202729362
C53×C4⋊#952
#1405253