Finite Group Databasebeta

← #27307646

Subgroups — #27307646

Order 13568.

1702 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810512C211yesmaximal, characteristic
2C2×#16810510C211yesmaximal, characteristic, complemented
3C2×#16810497C211yesmaximal, characteristic
4C2×#16810474C211yesmaximal, characteristic, complemented
5C2×C4×#11719921C211yesmaximal, characteristic
6#20272973C211yesmaximal, characteristic, complemented
7#20272972C211yesmaximal, characteristic, complemented
8#20272963C211yesmaximal, characteristic
9#20272959C211yesmaximal, characteristic
10#20272951C211yesmaximal, characteristic
11#20272948C211yesmaximal, characteristic, complemented
12#20272946C211yesmaximal, characteristic, complemented
13#20272941C211yesmaximal, characteristic, complemented
14#20272936C211yesmaximal, characteristic
15C53×#1434C211yesmaximal, characteristic, complemented
16C23×C4×D53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2211yescharacteristic
25C22×#11719921C2211yescharacteristic
26C22×#11719921C2211yescharacteristic
27C22×C4×Dic53C2211yescharacteristic
28C22×C4×Dic53C2211yescharacteristic
29C22×C4×Dic53C2211yescharacteristic
30#16810512C418yescomplemented
31#16810510—24no—
32#16810497—24no—
33#16810474—24no—
34C4×#11719921—24no—
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
49C22×C42×C53C2211yescharacteristic
50C2×#95×C53C2211yescharacteristic
51C2×#95×C53C2211yescharacteristic
52C2×#95×C53C2211yescharacteristic
53C2×#95×C53C2211yescharacteristic
54C2×#95×C53C2211yescharacteristic
55C2×#95×C53C2211yescharacteristic
56C24×D53C2311yescharacteristic
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C23×Dic53C2311yescharacteristic
60C23×Dic53C2311yescharacteristic
61C23×Dic53C2311yescharacteristic
62C23×Dic53C2311yescharacteristic
63C23×Dic53C2311yescharacteristic
64C22×C4×D53—22no—
65C22×C4×D53—22no—
66C22×C4×D53—22no—
67C22×C4×D53—22no—
68C22×C4×D53—22no—
69C22×C4×D53—41no—
70C22×C4×D53—41no—
71C2×C4⋊Dic53—22no—
72C2×C4⋊Dic53—22no—
73C2×C4⋊Dic53—41no—
74C2×#11719919—22no—
75C2×#11719919—22no—
76C2×#11719919—22no—
77C2×#11719919—22no—
78C2×#11719919—22no—
79C2×#11719919—22no—
80C2×#11719919—22no—
81C2×#11719919C2×C414yescomplemented
82C2×#11719919D414yes—
83C2×#11719921—22no—
84C2×#11719921—22no—
85C2×#11719921—22no—
86C2×#11719921—22no—
87C2×#11719921—22no—
88C2×#11719921—22no—
89C2×#11719921—22no—
90C2×#11719921—22no—
91C2×#11719921—22no—
92C2×#11719921—22no—
93C2×#11719921—22no—
94C2×#11719921—22no—
95C2×#11719921—22no—
96C2×#11719921—41no—
97C2×#11719921—41no—
98C2×#11719921C2×C414yes—
99C2×#11719921C2×C414yes—
100C2×#11719921C2×C414yes—
101C2×C4×Dic53—22no—
102C2×C4×Dic53—22no—
103C2×C4×Dic53—22no—
104C2×C4×Dic53—22no—
105C2×C4×Dic53—22no—
106C2×C4×Dic53—22no—
107C2×C4×Dic53—41no—
108C2×C4×Dic53—41no—
109C2×C4×Dic53C2×C414yescomplemented
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—22no—
119#13133124—41no—
120#13133124—41no—
121#13133124—41no—
122#13133124C2×C414yescomplemented
123#13133124D414yes—
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C2×C42×C53—22no—
132C2×C42×C53—22no—
133C2×C42×C53—41no—
134#95×C53—22no—
135#95×C53—22no—
136#95×C53—22no—
137#95×C53—22no—
138#95×C53—41no—
139#95×C53C2×C414yescomplemented
140C24×C53C2411yescharacteristic
141C23×D53—21no—
142C23×D53—21no—
143C23×D53—21no—
144C23×D53—21no—
145C23×D53—21no—
146C23×D53—21no—
147C23×D53—21no—
148C23×D53—21no—
149C23×D53—21no—
150C23×D53—21no—
151C23×D53—21no—
152C23×D53—21no—
153C23×D53C22×C412yes—
154C23×D53#4112yes—
155C23×D53#4112yes—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—21no—
159C22×C4×C53—21no—
160C22×C4×C53—21no—
161C22×C4×C53—21no—
162C22×C4×C53—21no—
163C22×C4×C53—21no—
164C22×C4×C53—21no—
165C22×C4×C53—21no—
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×C53C22×C412yes—
198C22×C4×C53C22×C412yes—
199C22×C4×C53C22×C412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2×D412yes—
202C22×C4×C53#4112yes—
203C22×C4×C53#4112yes—
204C22×C4×C53#4112yes—
205C22×Dic53—21no—
206C22×Dic53—21no—
207C22×Dic53—21no—
208C22×Dic53—21no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
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×Dic53C22×C412yes—
245C22×Dic53C22×C412yes—
246C22×Dic53C22×C412yes—
247C22×Dic53C2×D412yes—
248C22×Dic53C2×D412yes—
249C22×Dic53C2×D412yes—
250C22×Dic53C2×D412yes—
251C22×Dic53#4112yes—
252C22×Dic53#4112yes—
253C22×Dic53#4112yes—
254C2×C4×D53—28no—
255C2×C4×D53—44no—
256C2×C4×D53—44no—
257C2×C4×D53—44no—
258C2×C4×D53—44no—
259C2×C4×D53—44no—
260C2×C4×D53—44no—
261C42×C53—44no—
262#11719921—28no—
263#11719921—28no—
264#11719921—28no—
265#11719921—28no—
266#11719921—44no—
267#11719921—44no—
268C4⋊Dic53—44no—
269#11719919—28no—
270#11719919—28no—
271#11719919—28no—
272C4×Dic53—28no—
273C4×Dic53—44no—
274C4×Dic53—44no—
275C23×C53C23×C411yescharacteristic
276C23×C53C22×D411yescharacteristic
277C23×C53C22×D411yescharacteristic
278C23×C53C2×#4111yescharacteristic
279C23×C53C2×#4111yescharacteristic
280C23×C53C2×#4111yescharacteristic
281C23×C53C2×#4111yescharacteristic
282C23×C53C2×#4111yescharacteristic
283C23×C53C2×#4111yescharacteristic
284C23×C53C2×#4111yescharacteristic
285C23×C53C2×#4111yescharacteristic
286C23×C53H(5,𝔽2)11yescharacteristic
287C23×C53H(5,𝔽2)11yescharacteristic
288C23×C532−1+411yescharacteristic
289C23×C532−1+411yescharacteristic
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—22no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—22no—
307C22×D53—22no—
308C22×D53—41no—
309C22×D53—41no—
310C22×D53—41no—
311C22×D53—41no—
312C22×D53—41no—
313C22×D53—41no—
314C22×D53—41no—
315C22×D53—41no—
316C22×D53—41no—
317C22×D53—41no—
318C22×D53—41no—
319C22×D53—41no—
320C22×D53—41no—
321C22×D53—41no—
322C22×D53—41no—
323C22×D53—41no—
324C22×D53#11714yes—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—22no—
331C2×C4×C53—22no—
332C2×C4×C53—22no—
333C2×C4×C53—22no—
334C2×C4×C53—22no—
335C2×C4×C53—22no—
336C2×C4×C53—22no—
337C2×C4×C53—22no—
338C2×C4×C53—22no—
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—41no—
347C2×C4×C53—41no—
348C2×C4×C53—41no—
349C2×C4×C53—41no—
350C2×C4×C53—41no—
351C2×C4×C53—41no—
352C2×C4×C53—41no—
353C2×C4×C53—41no—
354C2×C4×C53—41no—
355C2×C4×C53—41no—
356C2×C4×C53—41no—
357C2×C4×C53—41no—
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#12314yes—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—22no—
377C2×Dic53—22no—
378C2×Dic53—22no—
379C2×Dic53—22no—
380C2×Dic53—22no—
381C2×Dic53—22no—
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—41no—
399C2×Dic53—41no—
400C2×Dic53—41no—
401C2×Dic53—41no—
402C2×Dic53—41no—
403C2×Dic53—41no—
404C2×Dic53—41no—
405C2×Dic53—41no—
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×Dic53C4×D414yes—
422C2×Dic53C4×D414yes—
423C4×D53—416no—
424#14032—531nomaximal, Sylow
425C22×C53C2×#11711yescharacteristic
426C22×C53C2×C4×D411yescharacteristic
427C22×C53C2×C4×D411yescharacteristic
428C22×C53C4×#4111yescharacteristic
429C22×C53C4×#4111yescharacteristic
430C22×C53#52011yescharacteristic
431C22×C53#52011yescharacteristic
432C22×C53C2×#12311yescharacteristic
433C22×C53#52511yescharacteristic
434C22×C53#52511yescharacteristic
435C22×C53#52511yescharacteristic
436C22×C53#52911yescharacteristic
437C22×C53#52911yescharacteristic
438C22×C53#52911yescharacteristic
439C22×C53#52911yescharacteristic
440C22×C53#53811yescharacteristic
441C22×C53#53911yescharacteristic
442C22×C53#54111yescharacteristic
443C22×C53#54211yescharacteristic
444C22×C53D4211yescharacteristic
445C22×C53#54611yescharacteristic
446C22×C53#54611yescharacteristic
447C22×C53#54711yescharacteristic
448C22×C53#54811yescharacteristic
449C22×C53#54811yescharacteristic
450C22×C53#54811yescharacteristic
451C22×C53#55111yescharacteristic
452C22×C53#55111yescharacteristic
453C22×C53#55211yescharacteristic
454C22×C53#55211yescharacteristic
455C22×C53#55211yescharacteristic
456C22×C53#55311yescharacteristic
457C22×C53#55311yescharacteristic
458C22×C53#55611yescharacteristic
459C22×C53#55911yescharacteristic
460C2×D53—24no—
461C2×D53—24no—
462C2×D53—24no—
463C2×D53—42no—
464C2×D53—42no—
465C2×D53—42no—
466C2×D53—42no—
467C2×D53—42no—
468C2×D53—42no—
469C2×D53—42no—
470C2×D53—42no—
471C2×D53—42no—
472C2×D53—42no—
473C2×D53—42no—
474C2×D53—42no—
475C4×C53—24no—
476C4×C53—42no—
477C4×C53—42no—
478C4×C53—42no—
479C4×C53—42no—
480C4×C53—42no—
481C4×C53—81no—
482Dic53—24no—
483Dic53—24no—
484Dic53—42no—
485Dic53—42no—
486Dic53—42no—
487Dic53—42no—
488Dic53—81no—
489C2×#388—531no—
490C2×#387—531no—
491C2×#385—531no—
492C2×C4×C4⋊C4—531no—
493C2×C4×C22⋊C4—531no—
494#1442—531no—
495#1442—531no—
496#1440—531no—
497#1439—531no—
498#1437—531no—
499#1436—531no—
500#1436—531no—
501#1434—531no—
502#1434D5311yescharacteristic, complemented
503C22⋊#95—531no—
504C2×C53#229011yescharacteristic
505C2×C53C4×#12311yescharacteristic
506C2×C53#233411yescharacteristic
507C2×C53#234311yescharacteristic
508C2×C53#235211yescharacteristic
509C2×C53#236111yescharacteristic
510C2×C53#236711yescharacteristic
511C2×C53#241811yescharacteristic
512C2×C53#242111yescharacteristic
513C2×C53#245811yescharacteristic
514C2×C53#246311yescharacteristic
515C2×C53#246811yescharacteristic
516C2×C53#247511yescharacteristic
517C2×C53#257311yescharacteristic
518C2×C53#259511yescharacteristic
519D53—44no—
520C24×C4—531no—
521C22×C4⋊C4—531no—
522C22×C4⋊C4—531no—
523C22×C4⋊C4—531no—
524C22×C4⋊C4—531no—
525C22×C22⋊C4—531no—
526C22×C22⋊C4—531no—
527C22×C22⋊C4—531no—
528C22×C22⋊C4—531no—
529C22×C22⋊C4—531no—
530C22×C22⋊C4—531no—
531C22×C42—531no—
532C22×C42—531no—
533C22×C42—531no—
534C22×C42C2×D5311yescharacteristic
535#388—538no—
536#387—1064no—
537#385—1064no—
538C4×C4⋊C4—1064no—
539C4×C22⋊C4—1064no—
540C2×#95—531no—
541C2×#95—531no—
542C2×#95—531no—
543C2×#95—531no—
544C2×#95—531no—
545C2×#95—531no—
546C2×#95—531no—
547C2×#95—531no—
548C2×#95—531no—
549C2×#95—531no—
550C2×#95—531no—
551C2×#95—531no—
552C2×#95—531no—
553C2×#95—531no—
554C2×#95C2×D5311yescharacteristic
555C2×#95C2×D5311yescharacteristic
556C2×#95C2×D5311yescharacteristic
557C2×#95C2×D5311yescharacteristic
558C2×#95C2×D5311yescharacteristic
559C2×#95C2×D5311yescharacteristic
560C53#1403211yescharacteristic, complemented, Sylow
561C25—531no—
562C23×C4—531no—
563C23×C4—531no—
564C23×C4—531no—
565C23×C4—531no—
566C23×C4—531no—
567C23×C4—531no—
568C23×C4—531no—
569C23×C4—1062no—
570C23×C4—1062no—
571C23×C4—1062no—
572C23×C4—1062no—
573C23×C4—1062no—
574C23×C4—2121no—
575C23×C4—2121no—
576C23×C4C22×D5311yescharacteristic
577C23×C4C22×D5311yescharacteristic
578C23×C4C22×D5311yescharacteristic
579C23×C4C22×D5311yescharacteristic
580C23×C4C22×D5311yescharacteristic
581C23×C4C22×D5311yescharacteristic
582C23×C4C22×D5311yescharacteristic
583C2×C4⋊C4—534no—
584C2×C4⋊C4—534no—
585C2×C4⋊C4—1062no—
586C2×C4⋊C4—1062no—
587C2×C4⋊C4—1062no—
588C2×C4⋊C4—1062no—
589C2×C4⋊C4—1062no—
590C2×C4⋊C4—1062no—
591C2×C4⋊C4—1062no—
592C2×C4⋊C4—1062no—
593C2×C4⋊C4—1062no—
594C2×C4⋊C4—2121no—
595C2×C22⋊C4—534no—
596C2×C22⋊C4—534no—
597C2×C22⋊C4—534no—
598C2×C22⋊C4—1062no—
599C2×C22⋊C4—1062no—
600C2×C22⋊C4—1062no—
601C2×C22⋊C4—1062no—
602C2×C22⋊C4—1062no—
603C2×C22⋊C4—1062no—
604C2×C22⋊C4—1062no—
605C2×C22⋊C4—1062no—
606C2×C22⋊C4—1062no—
607C2×C22⋊C4—1062no—
608C2×C22⋊C4—1062no—
609C2×C22⋊C4—1062no—
610C2×C22⋊C4—1062no—
611C2×C22⋊C4—2121no—
612C2×C22⋊C4—2121no—
613C2×C42—22no—
614C2×C42—22no—
615C2×C42—41no—
616C2×C42—534no—
617C2×C42—1062no—
618C2×C42—1062no—
619C2×C42—1062no—
620C2×C42—1062no—
621C2×C42—1062no—
622C2×C42—1062no—
623C2×C42—2121no—
624C2×C42—2121no—
625#95—22no—
626#95—22no—
627#95—22no—
628#95—22no—
629#95—41no—
630#95—534no—
631#95—534no—
632#95—1062no—
633#95—1062no—
634#95—1062no—
635#95—1062no—
636#95—1062no—
637#95—1062no—
638#95—1062no—
639#95—1062no—
640#95—1062no—
641#95—2121no—
642#95—2121no—
643#95—2121no—
644#95C4×D5314yescomplemented
645C24—532no—
646C24—532no—
647C24—532no—
648C24—1061no—
649C24—1061no—
650C24—1061no—
651C24—1061no—
652C24—1061no—
653C24—1061no—
654C24—1061no—
655C24—1061no—
656C24—1061no—
657C24—1061no—
658C24—1061no—
659C24—1061no—
660C24C23×D5311yescharacteristic
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—21no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—21no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
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—532no—
703C22×C4—532no—
704C22×C4—532no—
705C22×C4—532no—
706C22×C4—532no—
707C22×C4—532no—
708C22×C4—532no—
709C22×C4—532no—
710C22×C4—532no—
711C22×C4—532no—
712C22×C4—1068no—
713C22×C4—1061no—
714C22×C4—1061no—
715C22×C4—1061no—
716C22×C4—1061no—
717C22×C4—1061no—
718C22×C4—1061no—
719C22×C4—1061no—
720C22×C4—1061no—
721C22×C4—1061no—
722C22×C4—1061no—
723C22×C4—1061no—
724C22×C4—1061no—
725C22×C4—1061no—
726C22×C4—1061no—
727C22×C4—1061no—
728C22×C4—1061no—
729C22×C4—1061no—
730C22×C4—1061no—
731C22×C4—1061no—
732C22×C4—1061no—
733C22×C4—1061no—
734C22×C4—1061no—
735C22×C4—1061no—
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—2124no—
753C22×C4—2124no—
754C22×C4—2124no—
755C22×C4—2124no—
756C22×C4—2124no—
757C22×C4—2124no—
758C22×C4C2×C4×D5312yes—
759C22×C4C2×C4×D5312yes—
760C22×C4C2×C4×D5312yes—
761C22×C4#1171994512yes—
762C22×C4#1171994512yes—
763C22×C4D4×D5312yes—
764C22×C4D4×D5312yes—
765C22×C4#1171994912yes—
766C4⋊C4—1068no—
767C4⋊C4—1068no—
768C4⋊C4—1068no—
769C4⋊C4—2124no—
770C22⋊C4—1068no—
771C22⋊C4—1068no—
772C22⋊C4—1068no—
773C22⋊C4—1068no—
774C22⋊C4—2124no—
775C22⋊C4—2124no—
776C42—44no—
777C42—1068no—
778C42—2124no—
779C42—2124no—
780C23—534no—
781C23—1062no—
782C23—1062no—
783C23—1062no—
784C23—1062no—
785C23—1062no—
786C23—1062no—
787C23—1062no—
788C23—1062no—
789C23—1062no—
790C23—1062no—
791C23—1062no—
792C23—1062no—
793C23—1062no—
794C23—1062no—
795C23—1062no—
796C23—1062no—
797C23—1062no—
798C23—1062no—
799C23—2121no—
800C23—2121no—
801C23—2121no—
802C23—2121no—
803C23—2121no—
804C23—2121no—
805C23—2121no—
806C23—2121no—
807C23—2121no—
808C23—2121no—
809C23—2121no—
810C23—2121no—
811C23—2121no—
812C23—2121no—
813C23—2121no—
814C23—2121no—
815C23C22×C4×D5311yescharacteristic
816C23C2×D4×D5311yescharacteristic
817C23C2×D4×D5311yescharacteristic
818C23#41×D5311yescharacteristic
819C23#41×D5311yescharacteristic
820C23#41×D5311yescharacteristic
821C23#41×D5311yescharacteristic
822C23#41×D5311yescharacteristic
823C23C2×#1171994511yescharacteristic
824C23C2×#1171994511yescharacteristic
825C23C2×#1171994911yescharacteristic
826C23#1313326211yescharacteristic
827C23#1313326311yescharacteristic
828C23#1313326411yescharacteristic
829C23#1313326411yescharacteristic
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—534no—
879C2×C4—534no—
880C2×C4—1062no—
881C2×C4—1062no—
882C2×C4—1062no—
883C2×C4—1062no—
884C2×C4—1062no—
885C2×C4—1062no—
886C2×C4—1062no—
887C2×C4—1062no—
888C2×C4—1062no—
889C2×C4—1062no—
890C2×C4—1062no—
891C2×C4—1062no—
892C2×C4—1062no—
893C2×C4—1062no—
894C2×C4—1062no—
895C2×C4—1062no—
896C2×C4—1062no—
897C2×C4—1062no—
898C2×C4—1062no—
899C2×C4—1062no—
900C2×C4—1062no—
901C2×C4—1062no—
902C2×C4—1062no—
903C2×C4—1062no—
904C2×C4—21216no—
905C2×C4—2121no—
906C2×C4—2121no—
907C2×C4—2121no—
908C2×C4—2121no—
909C2×C4—2121no—
910C2×C4—2121no—
911C2×C4—2121no—
912C2×C4—2121no—
913C2×C4—2121no—
914C2×C4—2121no—
915C2×C4—2121no—
916C2×C4—2121no—
917C2×C4—2121no—
918C2×C4—2121no—
919C2×C4—2121no—
920C2×C4—2121no—
921C2×C4—2121no—
922C2×C4—2121no—
923C2×C4—2121no—
924C2×C4—2121no—
925C2×C4—2121no—
926C2×C4—2121no—
927C2×C4—2121no—
928C2×C4#1313320214yes—
929C22—1064no—
930C22—1064no—
931C22—1064no—
932C22—2122no—
933C22—2122no—
934C22—2122no—
935C22—2122no—
936C22—2122no—
937C22—2122no—
938C22—2122no—
939C22—2122no—
940C22—2122no—
941C22—2122no—
942C22—2122no—
943C22—2122no—
944C22#117×D5311yescharacteristic
945C22C4×D4×D5311yescharacteristic
946C22C4×D4×D5311yescharacteristic
947C22C4×#1171994511yescharacteristic
948C22C4×#1171994911yescharacteristic
949C22#1681110211yescharacteristic
950C22#1681110311yescharacteristic
951C22C2×#1313320211yescharacteristic
952C22#1681113111yescharacteristic
953C22#1681113211yescharacteristic
954C22#1681113611yescharacteristic
955C22#1681115111yescharacteristic
956C22#1681115611yescharacteristic
957C22#1681115811yescharacteristic
958C22#1681116011yescharacteristic
959C22#1681121311yescharacteristic
960C22#1681121411yescharacteristic
961C22#1681123611yescharacteristic
962C22#1681124111yescharacteristic
963C22#1681125711yescharacteristic
964C22#1681126211yescharacteristic
965C22#1681126311yescharacteristic
966C22#1681127111yescharacteristic
967C22#1681128111yescharacteristic
968C22#1681128111yescharacteristic
969C22#1681128211yescharacteristic
970C22#1681129711yescharacteristic
971C22#1681129711yescharacteristic
972C22#1681130911yescharacteristic
973C22#1681131211yescharacteristic
974C22#1681131211yescharacteristic
975C22#1681131811yescharacteristic
976C22#1681132411yescharacteristic
977C22#1681134111yescharacteristic
978C22#1681135611yescharacteristic
979C4—24no—
980C4—42no—
981C4—42no—
982C4—42no—
983C4—42no—
984C4—42no—
985C4—81no—
986C4—1064no—
987C4—1064no—
988C4—4241no—
989C4—2122no—
990C4—2122no—
991C4—2122no—
992C4—2122no—
993C2—2124no—
994C2#2027715311yescharacteristic
995C2C4×#1313320211yescharacteristic
996C2#2027749311yescharacteristic
997C2#2027757611yescharacteristic
998C2#2027764311yescharacteristic
999C2#2027772811yescharacteristic
1000C2#2027778711yescharacteristic
1001C2#2027818311yescharacteristic
1002C2#2027822111yescharacteristic
1003C2#2027864311yescharacteristic
1004C2#2027870911yescharacteristic
1005C2#2027877811yescharacteristic
1006C2#2027889311yescharacteristic
1007C2#2027997211yescharacteristic
1008C2#2028024311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×#1434C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenter#1434D53
hypocenterC53#14032
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
2. C2×#16810510C2semidirect
4. C2×#16810474C2semidirect
6. #20272973C2semidirect
7. #20272972C2semidirect
11. #20272948C2semidirect
12. #20272946C2semidirect
13. #20272941C2semidirect
15. C53×#1434C2semidirect
30. #16810512C4semidirect
81. C2×#11719919C2×C4semidirect
109. C2×C4×Dic53C2×C4semidirect
122. #13133124C2×C4semidirect
139. #95×C53C2×C4semidirect
502. #1434D53semidirect
560. C53#14032semidirect
644. #95C4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168105122
C2×#168105102
C2×#168104972
C2×#168104742
C2×C4×#117199212
#202729732
#202729722
#202729632
#202729592
#202729512
#202729482
#202729462
#202729412
#202729362
C53×#14342
#1403253