Finite Group Databasebeta

← #27308169

Subgroups — #27308169

Order 13568.

2206 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133173C211yesmaximal, characteristic, complemented
2C2×#16810526C211yesmaximal, characteristic
3C2×#16810517C211yesmaximal, characteristic, complemented
4C2×#16810511C211yesmaximal, characteristic, complemented
5C2×#16810503C211yesmaximal, characteristic
6#20272979C211yesmaximal, characteristic, complemented
7#20272958C211yesmaximal, characteristic, complemented
8#20272958C211yesmaximal, characteristic, complemented
9#20272952C211yesmaximal, characteristic, complemented
10#20272952C211yesmaximal, characteristic, complemented
11#20272949C211yesmaximal, characteristic, complemented
12#20272946C211yesmaximal, characteristic, complemented
13#20272937C211yesmaximal, characteristic, complemented
14#95×Dic53C211yesmaximal, characteristic, complemented
15C53×#1438C211yesmaximal, characteristic
16C24×Dic53C2211yescharacteristic
17C2×#13133173—24no—
18C2×#13133173—24no—
19C2×#13133173—24no—
20C22×C4⋊Dic53C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×C22⋊Dic53C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C4×Dic53C2211yescharacteristic
32C22×C4×Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35#16810526—24no—
36#16810517—24no—
37#16810511—24no—
38#16810503C418yescomplemented
39C2×#13133124C2211yescharacteristic
40C2×#13133124C2211yescharacteristic
41C2×#13133124C2211yescharacteristic
42C2×#13133124C2211yescharacteristic
43C2×#13133124C2211yescharacteristic
44C2×#13133124C2211yescharacteristic
45C2×#13133124C2211yescharacteristic
46C2×#13133124C2211yescharacteristic
47C2×#13133124C2211yescharacteristic
48C2×#13133124C2211yescharacteristic
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C23×D4×C53C2211yescharacteristic
52C22×C22⋊C4×C53C2211yescharacteristic
53C22×C22⋊C4×C53C2211yescharacteristic
54C22×C22⋊C4×C53C2211yescharacteristic
55C22×C22⋊C4×C53C2211yescharacteristic
56C2×#95×C53C2211yescharacteristic
57C2×#95×C53C2211yescharacteristic
58C23×Dic53—22no—
59C23×Dic53—22no—
60C23×Dic53—22no—
61C23×Dic53—22no—
62C23×Dic53—22no—
63C23×Dic53—22no—
64C23×Dic53C2×C414yes—
65C23×Dic53C2311yescharacteristic
66C23×Dic53C2311yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73#13133173—232no—
74C2×C4⋊Dic53—22no—
75C2×C4⋊Dic53—22no—
76C2×C4⋊Dic53—41no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919—22no—
82C2×#11719919—22no—
83C2×#11719919—41no—
84C2×#11719919—41no—
85C2×#11719919D414yescomplemented
86C2×C22⋊Dic53—22no—
87C2×C22⋊Dic53—22no—
88C2×C22⋊Dic53—22no—
89C2×C22⋊Dic53—22no—
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—22no—
99C2×C22⋊Dic53—41no—
100C2×C22⋊Dic53—41no—
101C2×C22⋊Dic53—41no—
102C2×C22⋊Dic53—41no—
103C2×C22⋊Dic53C2×C414yes—
104C2×C22⋊Dic53C2×C414yes—
105C2×C22⋊Dic53C2×C414yes—
106C2×C22⋊Dic53D414yes—
107C2×C4×Dic53—22no—
108C2×C4×Dic53—22no—
109C2×C4×Dic53—22no—
110C2×C4×Dic53—22no—
111C2×C4×Dic53—22no—
112C2×C4×Dic53—22no—
113C2×C4×Dic53—22no—
114C2×C4×Dic53—22no—
115C2×C4×Dic53—22no—
116C2×C4×Dic53—41no—
117C2×C4×Dic53—41no—
118C2×C4×Dic53D414yescomplemented
119#13133124—22no—
120#13133124—22no—
121#13133124—22no—
122#13133124—22no—
123#13133124—22no—
124#13133124—22no—
125#13133124—22no—
126#13133124—41no—
127#13133124—41no—
128#13133124—41no—
129#13133124C2×C414yes—
130#13133124C2×C414yes—
131C25×C53C2311yescharacteristic
132C25×C53C2311yescharacteristic
133C22×D4×C53—22no—
134C22×D4×C53—22no—
135C22×D4×C53—22no—
136C22×D4×C53—22no—
137C22×D4×C53—41no—
138C22×D4×C53—41no—
139C22×D4×C53C2×C414yes—
140C23×C4×C53C2311yescharacteristic
141C23×C4×C53C2311yescharacteristic
142C23×C4×C53C2311yescharacteristic
143C23×C4×C53C2311yescharacteristic
144C23×C4×C53C2311yescharacteristic
145C2×C22⋊C4×C53—22no—
146C2×C22⋊C4×C53—22no—
147C2×C22⋊C4×C53—22no—
148C2×C22⋊C4×C53—22no—
149C2×C22⋊C4×C53—22no—
150C2×C22⋊C4×C53—22no—
151C2×C22⋊C4×C53—22no—
152C2×C22⋊C4×C53—22no—
153C2×C22⋊C4×C53—41no—
154C2×C22⋊C4×C53—41no—
155C2×C22⋊C4×C53—41no—
156C2×C22⋊C4×C53—41no—
157#95×C53—22no—
158#95×C53—22no—
159C24×C53—21no—
160C24×C53—21no—
161C24×C53—21no—
162C24×C53—21no—
163C24×C53—21no—
164C24×C53—21no—
165C24×C53—21no—
166C24×C53—21no—
167C24×C53—21no—
168C24×C53—21no—
169C24×C53—21no—
170C24×C53—21no—
171C24×C53—21no—
172C24×C53—21no—
173C24×C53—21no—
174C24×C53—21no—
175C24×C53—21no—
176C24×C53—21no—
177C24×C53—21no—
178C24×C53—21no—
179C24×C53—21no—
180C24×C53—21no—
181C24×C53—21no—
182C24×C53—21no—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53C22×C412yes—
186C24×C53C22×C412yes—
187C24×C53C2×D412yes—
188C24×C53#4112yes—
189C24×C53C2411yescharacteristic
190C2×D4×C53—28no—
191C2×D4×C53—28no—
192C2×D4×C53—44no—
193C2×D4×C53—44no—
194C2×D4×C53—44no—
195C2×D4×C53—44no—
196C2×D4×C53—44no—
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×C53—21no—
211C22×C4×C53—21no—
212C22×C4×C53—21no—
213C22×C4×C53—21no—
214C22×C4×C53—21no—
215C22×C4×C53—21no—
216C22×C4×C53—21no—
217C22×C4×C53—21no—
218C22×C4×C53—21no—
219C22×C4×C53—21no—
220C22×C4×C53—21no—
221C22×C4×C53—21no—
222C22×C4×C53—21no—
223C22×C4×C53—21no—
224C22×C4×C53—21no—
225C22×C4×C53—21no—
226C22×C4×C53C22×C412yes—
227C22×C4×C53C2×D412yes—
228C22×C4×C53C2×D412yes—
229C22×C4×C53#4112yes—
230C22×C4×C53#4112yes—
231C22×C4×C53#4112yes—
232C22×Dic53—28no—
233C22×Dic53—28no—
234C22×Dic53—28no—
235C22×Dic53—28no—
236C22×Dic53—28no—
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—28no—
250C22×Dic53—28no—
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×Dic53—21no—
280C22×Dic53—21no—
281C22×Dic53—21no—
282C22×Dic53C22×C412yes—
283C22×Dic53C22×C412yes—
284C22×Dic53C22×C412yes—
285C22×Dic53C22×C412yes—
286C22×Dic53C2×D412yes—
287C22×Dic53C2×D412yes—
288C22×Dic53C2×D412yes—
289C22×Dic53C2×D412yes—
290C22×Dic53C2×D412yes—
291C22×Dic53C2×D412yes—
292C22×Dic53#4112yes—
293C22×Dic53#4112yes—
294C22×Dic53#4112yes—
295C22⋊C4×C53—28no—
296C22⋊C4×C53—44no—
297C22⋊C4×C53—44no—
298C22⋊C4×C53—44no—
299C22⋊Dic53—28no—
300C22⋊Dic53—28no—
301C22⋊Dic53—28no—
302C22⋊Dic53—44no—
303C22⋊Dic53—44no—
304C22⋊Dic53—44no—
305C22⋊Dic53—44no—
306C4⋊Dic53—44no—
307#11719919—28no—
308#11719919—28no—
309#11719919—44no—
310C4×Dic53—28no—
311C4×Dic53—28no—
312C4×Dic53—44no—
313C4×Dic53—44no—
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×C53—22no—
332C23×C53—22no—
333C23×C53—22no—
334C23×C53—22no—
335C23×C53—22no—
336C23×C53—22no—
337C23×C53—22no—
338C23×C53—22no—
339C23×C53—41no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—41no—
343C23×C53—41no—
344C23×C53—41no—
345C23×C53—41no—
346C23×C53—41no—
347C23×C53—41no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—41no—
351C23×C53—41no—
352C23×C53—41no—
353C23×C53—41no—
354C23×C53—41no—
355C23×C53—41no—
356C23×C53—41no—
357C23×C53—41no—
358C23×C53—41no—
359C23×C53—41no—
360C23×C53—41no—
361C23×C53—41no—
362C23×C53—41no—
363C23×C53—41no—
364C23×C53—41no—
365C23×C53—41no—
366C23×C53—41no—
367C23×C53—41no—
368C23×C53—41no—
369C23×C53—41no—
370C23×C53—41no—
371C23×C53—41no—
372C23×C53—41no—
373C23×C53—41no—
374C23×C53—41no—
375C23×C53—41no—
376C23×C53—41no—
377C23×C53—41no—
378C23×C53—41no—
379C23×C53—41no—
380C23×C53—41no—
381C23×C53—41no—
382C23×C53—41no—
383C23×C53C4×D414yes—
384C23×C53C23×C411yescharacteristic
385C23×C53C22×D411yescharacteristic
386C23×C53C22×D411yescharacteristic
387C23×C53C22×D411yescharacteristic
388C23×C53C2×#4111yescharacteristic
389C23×C53C2×#4111yescharacteristic
390C23×C53C2×#4111yescharacteristic
391C23×C53C2×#4111yescharacteristic
392C23×C53C2×#4111yescharacteristic
393C23×C53C2×#4111yescharacteristic
394C23×C53C2×#4111yescharacteristic
395C23×C53H(5,𝔽2)11yescharacteristic
396C23×C53H(5,𝔽2)11yescharacteristic
397C23×C53H(5,𝔽2)11yescharacteristic
398C23×C532−1+411yescharacteristic
399D4×C53—416no—
400C2×C4×C53—22no—
401C2×C4×C53—22no—
402C2×C4×C53—22no—
403C2×C4×C53—22no—
404C2×C4×C53—22no—
405C2×C4×C53—22no—
406C2×C4×C53—22no—
407C2×C4×C53—22no—
408C2×C4×C53—22no—
409C2×C4×C53—22no—
410C2×C4×C53—22no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—22no—
414C2×C4×C53—22no—
415C2×C4×C53—41no—
416C2×C4×C53—41no—
417C2×C4×C53—41no—
418C2×C4×C53—41no—
419C2×C4×C53—41no—
420C2×C4×C53—41no—
421C2×C4×C53—41no—
422C2×C4×C53—41no—
423C2×C4×C53—41no—
424C2×C4×C53—41no—
425C2×C4×C53—41no—
426C2×C4×C53—41no—
427C2×C4×C53—41no—
428C2×C4×C53—41no—
429C2×C4×C53—41no—
430C2×C4×C53—41no—
431C2×C4×C53—41no—
432C2×C4×C53—41no—
433C2×C4×C53—41no—
434C2×C4×C53#11714yescomplemented
435C2×Dic53—232no—
436C2×Dic53—22no—
437C2×Dic53—22no—
438C2×Dic53—22no—
439C2×Dic53—22no—
440C2×Dic53—22no—
441C2×Dic53—22no—
442C2×Dic53—22no—
443C2×Dic53—22no—
444C2×Dic53—22no—
445C2×Dic53—22no—
446C2×Dic53—22no—
447C2×Dic53—22no—
448C2×Dic53—22no—
449C2×Dic53—22no—
450C2×Dic53—22no—
451C2×Dic53—22no—
452C2×Dic53—22no—
453C2×Dic53—22no—
454C2×Dic53—22no—
455C2×Dic53—22no—
456C2×Dic53—22no—
457C2×Dic53—22no—
458C2×Dic53—22no—
459C2×Dic53—22no—
460C2×Dic53—22no—
461C2×Dic53—22no—
462C2×Dic53—22no—
463C2×Dic53—22no—
464C2×Dic53—22no—
465C2×Dic53—22no—
466C2×Dic53—41no—
467C2×Dic53—41no—
468C2×Dic53—41no—
469C2×Dic53—41no—
470C2×Dic53—41no—
471C2×Dic53—41no—
472C2×Dic53—41no—
473C2×Dic53—41no—
474C2×Dic53—41no—
475C2×Dic53—41no—
476C2×Dic53—41no—
477C2×Dic53—41no—
478C2×Dic53—41no—
479C2×Dic53—41no—
480C2×Dic53—41no—
481C2×Dic53—41no—
482C2×Dic53—41no—
483C2×Dic53—41no—
484C2×Dic53—41no—
485C2×Dic53—41no—
486C2×Dic53—41no—
487C2×Dic53—41no—
488C2×Dic53—41no—
489C2×Dic53C4×D414yes—
490C2×Dic53C4×D414yes—
491C2×Dic53#12014yes—
492#14071—531nomaximal, Sylow
493C22×C53—24no—
494C22×C53—24no—
495C22×C53—24no—
496C22×C53—42no—
497C22×C53—42no—
498C22×C53—42no—
499C22×C53—42no—
500C22×C53—42no—
501C22×C53—42no—
502C22×C53—42no—
503C22×C53—42no—
504C22×C53—42no—
505C22×C53—42no—
506C22×C53—42no—
507C22×C53—42no—
508C22×C53—42no—
509C22×C53—42no—
510C22×C53—42no—
511C22×C53—42no—
512C22×C53—42no—
513C22×C53—42no—
514C22×C53—42no—
515C22×C53—81no—
516C22×C53—81no—
517C22×C53—81no—
518C22×C53—81no—
519C22×C53—81no—
520C22×C53—81no—
521C22×C53—81no—
522C22×C53—81no—
523C22×C53C2×#11711yescharacteristic
524C22×C53C2×C4×D411yescharacteristic
525C22×C53C2×C4×D411yescharacteristic
526C22×C53C2×C4×D411yescharacteristic
527C22×C53C4×#4111yescharacteristic
528C22×C53#51811yescharacteristic
529C22×C53#52011yescharacteristic
530C22×C53C2×#12011yescharacteristic
531C22×C53#52511yescharacteristic
532C22×C53#52511yescharacteristic
533C22×C53#52511yescharacteristic
534C22×C53#52911yescharacteristic
535C22×C53#52911yescharacteristic
536C22×C53#53211yescharacteristic
537C22×C53#53211yescharacteristic
538C22×C53#53511yescharacteristic
539C22×C53#53711yescharacteristic
540C22×C53#54011yescharacteristic
541C22×C53#54211yescharacteristic
542C22×C53#54611yescharacteristic
543C22×C53#54611yescharacteristic
544C22×C53#54611yescharacteristic
545C22×C53#54611yescharacteristic
546C22×C53#54711yescharacteristic
547C22×C53#54711yescharacteristic
548C22×C53#55011yescharacteristic
549C22×C53#55011yescharacteristic
550C22×C53#55111yescharacteristic
551C22×C53#55111yescharacteristic
552C22×C53#55111yescharacteristic
553C22×C53#55211yescharacteristic
554C22×C53#55311yescharacteristic
555C22×C53#55511yescharacteristic
556C22×C53#55511yescharacteristic
557C22×C53#55611yescharacteristic
558C4×C53—24no—
559C4×C53—42no—
560C4×C53—42no—
561C4×C53—42no—
562C4×C53—81no—
563Dic53—24no—
564Dic53—24no—
565Dic53—24no—
566Dic53—42no—
567Dic53—42no—
568Dic53—42no—
569Dic53—42no—
570Dic53—81no—
571C22×#117—531no—
572C2×#390—531no—
573C2×#388—531no—
574C2×#388—531no—
575C2×#386—531no—
576#1444—531no—
577#1439—531no—
578#1439—531no—
579#1438D5311yescharacteristic
580#1437—531no—
581#1437—531no—
582#1436—531no—
583#1436—531no—
584C22⋊#95—531no—
585C4×#95—531no—
586C2×C53—44no—
587C2×C53—82no—
588C2×C53#229311yescharacteristic
589C2×C53C4×#12011yescharacteristic
590C2×C53#232411yescharacteristic
591C2×C53#234211yescharacteristic
592C2×C53#235411yescharacteristic
593C2×C53#235911yescharacteristic
594C2×C53#236311yescharacteristic
595C2×C53#243011yescharacteristic
596C2×C53#243111yescharacteristic
597C2×C53#247111yescharacteristic
598C2×C53#247411yescharacteristic
599C2×C53#247611yescharacteristic
600C2×C53#247911yescharacteristic
601C2×C53#260111yescharacteristic
602C2×C53#261011yescharacteristic
603C23×D4C2×D5311yescharacteristic
604C24×C4—531no—
605C2×#117—1064no—
606C2×#117—1064no—
607C2×#117—1064no—
608C22×C4⋊C4—531no—
609C22×C4⋊C4—531no—
610C22×C4⋊C4—531no—
611C22×C4⋊C4—531no—
612C22×C22⋊C4—531no—
613C22×C22⋊C4—531no—
614C22×C22⋊C4—531no—
615C22×C22⋊C4—531no—
616C22×C22⋊C4—531no—
617C22×C22⋊C4—531no—
618C22×C22⋊C4—531no—
619C22×C22⋊C4C2×D5311yescharacteristic
620C22×C22⋊C4C2×D5311yescharacteristic
621C22×C22⋊C4C2×D5311yescharacteristic
622C22×C22⋊C4C2×D5311yescharacteristic
623C22×C42—531no—
624C22×C42—531no—
625C22×C42—531no—
626C22×C42—531no—
627#390—1064no—
628#388—1064no—
629#388—1064no—
630#386—538no—
631C2×#95—531no—
632C2×#95—531no—
633C2×#95—531no—
634C2×#95—531no—
635C2×#95—531no—
636C2×#95—531no—
637C2×#95—531no—
638C2×#95—531no—
639C2×#95—531no—
640C2×#95—531no—
641C2×#95—531no—
642C2×#95—531no—
643C2×#95C2×D5311yescharacteristic
644C2×#95C2×D5311yescharacteristic
645C53#1407111yescharacteristic, complemented, Sylow
646C25C22×D5311yescharacteristic
647C25C22×D5311yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C4×D5314yes—
655C23×C4—531no—
656C23×C4—531no—
657C23×C4—531no—
658C23×C4—534no—
659C23×C4—531no—
660C23×C4—531no—
661C23×C4—531no—
662C23×C4—531no—
663C23×C4—531no—
664C23×C4—1062no—
665C23×C4—1062no—
666C23×C4—1062no—
667C23×C4—1062no—
668C23×C4—1062no—
669C23×C4—1062no—
670C23×C4C22×D5311yescharacteristic
671C23×C4C22×D5311yescharacteristic
672C23×C4C22×D5311yescharacteristic
673C23×C4C22×D5311yescharacteristic
674C23×C4C22×D5311yescharacteristic
675#117—10632no—
676C2×C4⋊C4—534no—
677C2×C4⋊C4—1062no—
678C2×C4⋊C4—1062no—
679C2×C4⋊C4—1062no—
680C2×C4⋊C4—1062no—
681C2×C4⋊C4—1062no—
682C2×C4⋊C4—1062no—
683C2×C4⋊C4—1062no—
684C2×C4⋊C4—1062no—
685C2×C4⋊C4—2121no—
686C2×C4⋊C4—2121no—
687C2×C4⋊C4—2121no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—41no—
697C2×C22⋊C4—41no—
698C2×C22⋊C4—41no—
699C2×C22⋊C4—41no—
700C2×C22⋊C4—534no—
701C2×C22⋊C4—534no—
702C2×C22⋊C4—534no—
703C2×C22⋊C4—534no—
704C2×C22⋊C4—1062no—
705C2×C22⋊C4—1062no—
706C2×C22⋊C4—1062no—
707C2×C22⋊C4—1062no—
708C2×C22⋊C4—1062no—
709C2×C22⋊C4—1062no—
710C2×C22⋊C4—1062no—
711C2×C22⋊C4—1062no—
712C2×C22⋊C4—1062no—
713C2×C22⋊C4—1062no—
714C2×C22⋊C4—1062no—
715C2×C22⋊C4—1062no—
716C2×C22⋊C4—1062no—
717C2×C22⋊C4—2121no—
718C2×C22⋊C4—2121no—
719C2×C22⋊C4—2121no—
720C2×C22⋊C4—2121no—
721C2×C42—534no—
722C2×C42—1062no—
723C2×C42—1062no—
724C2×C42—1062no—
725C2×C42—1062no—
726C2×C42—1062no—
727C2×C42—1062no—
728C2×C42—1062no—
729C2×C42—1062no—
730C2×C42—1062no—
731C2×C42—2121no—
732C2×C42—2121no—
733#95—22no—
734#95—22no—
735#95—534no—
736#95—534no—
737#95—1062no—
738#95—1062no—
739#95—1062no—
740#95—1062no—
741#95—1062no—
742#95—1062no—
743#95—1062no—
744#95—2121no—
745#95—2121no—
746#95—2121no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C2×C4×D5312yes—
774C24C2×C4×D5312yes—
775C24D4×D5312yes—
776C24#1171994712yes—
777C24C23×D5311yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—532no—
815C22×C4—532no—
816C22×C4—532no—
817C22×C4—532no—
818C22×C4—532no—
819C22×C4—532no—
820C22×C4—532no—
821C22×C4—532no—
822C22×C4—532no—
823C22×C4—532no—
824C22×C4—532no—
825C22×C4—532no—
826C22×C4—532no—
827C22×C4—1068no—
828C22×C4—1068no—
829C22×C4—1068no—
830C22×C4—1068no—
831C22×C4—1068no—
832C22×C4—1068no—
833C22×C4—1068no—
834C22×C4—1061no—
835C22×C4—1061no—
836C22×C4—1061no—
837C22×C4—1061no—
838C22×C4—1061no—
839C22×C4—1061no—
840C22×C4—1061no—
841C22×C4—1061no—
842C22×C4—1061no—
843C22×C4—1061no—
844C22×C4—1061no—
845C22×C4—1061no—
846C22×C4—1061no—
847C22×C4—1061no—
848C22×C4—1061no—
849C22×C4—1061no—
850C22×C4—1061no—
851C22×C4—1061no—
852C22×C4—1061no—
853C22×C4—1061no—
854C22×C4—1061no—
855C22×C4—1061no—
856C22×C4—1061no—
857C22×C4—1061no—
858C22×C4—1061no—
859C22×C4—1061no—
860C22×C4—1061no—
861C22×C4—1061no—
862C22×C4—1061no—
863C22×C4—1061no—
864C22×C4—1061no—
865C22×C4—1061no—
866C22×C4—1061no—
867C22×C4—1061no—
868C22×C4—1061no—
869C22×C4—1061no—
870C22×C4—1061no—
871C22×C4—1061no—
872C22×C4—1061no—
873C22×C4—1061no—
874C22×C4—1061no—
875C22×C4—1061no—
876C22×C4—1061no—
877C22×C4C2×C4×D5312yes—
878C22×C4D4×D5312yes—
879C22×C4D4×D5312yes—
880C22×C4#1171994712yes—
881C22×C4#1171994712yes—
882C22×C4#1171994712yes—
883C4⋊C4—1068no—
884C4⋊C4—1068no—
885C4⋊C4—2124no—
886C4⋊C4—2124no—
887C22⋊C4—28no—
888C22⋊C4—44no—
889C22⋊C4—44no—
890C22⋊C4—44no—
891C22⋊C4—1068no—
892C22⋊C4—1068no—
893C22⋊C4—1068no—
894C22⋊C4—2124no—
895C22⋊C4—2124no—
896C22⋊C4—2124no—
897C22⋊C4—2124no—
898C42—1068no—
899C42—1068no—
900C42—2124no—
901C42—2124no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23#1313317714yes—
972C23C22×C4×D5311yescharacteristic
973C23C2×D4×D5311yescharacteristic
974C23C2×D4×D5311yescharacteristic
975C23C2×D4×D5311yescharacteristic
976C23#41×D5311yescharacteristic
977C23#41×D5311yescharacteristic
978C23#41×D5311yescharacteristic
979C23C2×#1171994711yescharacteristic
980C23C2×#1171994711yescharacteristic
981C23C2×#1171994711yescharacteristic
982C23C2×#1171994711yescharacteristic
983C23#1313326211yescharacteristic
984C23#1313326211yescharacteristic
985C23#1313326211yescharacteristic
986C23#1313326411yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—534no—
1023C2×C4—534no—
1024C2×C4—534no—
1025C2×C4—10632no—
1026C2×C4—1062no—
1027C2×C4—1062no—
1028C2×C4—1062no—
1029C2×C4—1062no—
1030C2×C4—1062no—
1031C2×C4—1062no—
1032C2×C4—1062no—
1033C2×C4—1062no—
1034C2×C4—1062no—
1035C2×C4—1062no—
1036C2×C4—1062no—
1037C2×C4—1062no—
1038C2×C4—1062no—
1039C2×C4—1062no—
1040C2×C4—1062no—
1041C2×C4—1062no—
1042C2×C4—1062no—
1043C2×C4—1062no—
1044C2×C4—1062no—
1045C2×C4—1062no—
1046C2×C4—1062no—
1047C2×C4—1062no—
1048C2×C4—1062no—
1049C2×C4—1062no—
1050C2×C4—1062no—
1051C2×C4—1062no—
1052C2×C4—1062no—
1053C2×C4—1062no—
1054C2×C4—1062no—
1055C2×C4—1062no—
1056C2×C4—2121no—
1057C2×C4—2121no—
1058C2×C4—2121no—
1059C2×C4—2121no—
1060C2×C4—2121no—
1061C2×C4—2121no—
1062C2×C4—2121no—
1063C2×C4—2121no—
1064C2×C4—2121no—
1065C2×C4—2121no—
1066C2×C4—2121no—
1067C2×C4—2121no—
1068C2×C4—2121no—
1069C2×C4—2121no—
1070C2×C4—2121no—
1071C2×C4—2121no—
1072C2×C4—2121no—
1073C2×C4—2121no—
1074C2×C4—2121no—
1075C2×C4—2121no—
1076C2×C4—2121no—
1077C2×C4—2121no—
1078C2×C4—2121no—
1079C2×C4#1313317314yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C2×#1313317311yescharacteristic
1111C22C4×D4×D5311yescharacteristic
1112C22C4×D4×D5311yescharacteristic
1113C22C2×#1313317711yescharacteristic
1114C22C4×#1171994711yescharacteristic
1115C22#1681109611yescharacteristic
1116C22#1681110211yescharacteristic
1117C22#120×D5311yescharacteristic
1118C22#1681113111yescharacteristic
1119C22#1681113311yescharacteristic
1120C22#1681113311yescharacteristic
1121C22#1681115211yescharacteristic
1122C22#1681115411yescharacteristic
1123C22#1681116811yescharacteristic
1124C22#1681117111yescharacteristic
1125C22#1681118811yescharacteristic
1126C22#1681120211yescharacteristic
1127C22#1681122311yescharacteristic
1128C22#1681124111yescharacteristic
1129C22#1681126011yescharacteristic
1130C22#1681126011yescharacteristic
1131C22#1681126011yescharacteristic
1132C22#1681126211yescharacteristic
1133C22#1681127311yescharacteristic
1134C22#1681127311yescharacteristic
1135C22#1681129111yescharacteristic
1136C22#1681129311yescharacteristic
1137C22#1681130411yescharacteristic
1138C22#1681130411yescharacteristic
1139C22#1681130411yescharacteristic
1140C22#1681131011yescharacteristic
1141C22#1681131811yescharacteristic
1142C22#1681133711yescharacteristic
1143C22#1681133711yescharacteristic
1144C22#1681134211yescharacteristic
1145C4—24no—
1146C4—42no—
1147C4—42no—
1148C4—42no—
1149C4—81no—
1150C4—1064no—
1151C4—1064no—
1152C4—1064no—
1153C4—4241no—
1154C4—2122no—
1155C4—2122no—
1156C4—2122no—
1157C4—2122no—
1158C2—44no—
1159C2—82no—
1160C2#2027717711yescharacteristic
1161C2#2027722011yescharacteristic
1162C2#2027740511yescharacteristic
1163C2#2027756611yescharacteristic
1164C2#2027766311yescharacteristic
1165C2#2027771311yescharacteristic
1166C2#2027775611yescharacteristic
1167C2#2027831811yescharacteristic
1168C2#2027832911yescharacteristic
1169C2#2027882711yescharacteristic
1170C2#2027886611yescharacteristic
1171C2#2027889611yescharacteristic
1172C2#2027894711yescharacteristic
1173C2#2028030511yescharacteristic
1174C2#2028039511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1438C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenter#1438D53
hypocenterC53#14071
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. C22×#13133173C2semidirect
3. C2×#16810517C2semidirect
4. C2×#16810511C2semidirect
6. #20272979C2semidirect
7. #20272958C2semidirect
8. #20272958C2semidirect
9. #20272952C2semidirect
10. #20272952C2semidirect
11. #20272949C2semidirect
12. #20272946C2semidirect
13. #20272937C2semidirect
14. #95×Dic53C2semidirect
38. #16810503C4semidirect
85. C2×#11719919D4semidirect
118. C2×C4×Dic53D4semidirect
434. C2×C4×C53#117semidirect
645. C53#14071semidirect
1079. C2×C4#13133173semidirect

Maximal subgroups

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

subgroupindex
C22×#131331732
C2×#168105262
C2×#168105172
C2×#168105112
C2×#168105032
#202729792
#202729582
#202729522
#202729492
#202729462
#202729372
#95×Dic532
C53×#14382
#1407153