Finite Group Databasebeta

← #27310519

Subgroups — #27310519

Order 13568.

1926 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133174C211yesmaximal, characteristic
2C2×#16810522C211yesmaximal, characteristic, complemented
3C2×#16810521C211yesmaximal, characteristic, complemented
4C2×#16810480C211yesmaximal, characteristic
5C2×#16810480C211yesmaximal, characteristic
6#20272979C212yesmaximal, complemented
7#20272970C212yesmaximal, complemented
8#20272961C212yesmaximal
9#20272959C212yesmaximal
10#20272944C211yesmaximal, characteristic, complemented
11C53×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C2×#13133174—24no—
14C2×#13133174—24no—
15C2×#13133174—24no—
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2212yes—
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2212yes—
22C22×#11719921C2211yescharacteristic
23C22×#11719921C2211yescharacteristic
24C22×#11719921C2212yes—
25C22×#11719921C2212yes—
26C22×C4×Dic53C2211yescharacteristic
27#16810522—24no—
28#16810521—24no—
29#16810480—24no—
30#16810480C418yescomplemented
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C22×C4⋊C4×C53C2211yescharacteristic
38C22×C4⋊C4×C53C2211yescharacteristic
39C22×C42×C53C2211yescharacteristic
40C2×#95×C53C2212yes—
41C2×#95×C53C2212yes—
42C24×D53C2311yescharacteristic
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2311yescharacteristic
47C23×Dic53C2311yescharacteristic
48C22×C4×D53—22no—
49C22×C4×D53—22no—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53C2×C414yes—
53C22×C4×D53D414yes—
54C22×C4×D53Q814yes—
55#13133174—232no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—22no—
58C2×C4⋊Dic53—22no—
59C2×C4⋊Dic53—22no—
60C2×C4⋊Dic53—22no—
61C2×C4⋊Dic53—24no—
62C2×C4⋊Dic53—42no—
63C2×C4⋊Dic53—42no—
64C2×C4⋊Dic53C2×C414yes—
65C2×#11719919—22no—
66C2×#11719919—22no—
67C2×#11719919—24no—
68C2×#11719919—22no—
69C2×#11719919—22no—
70C2×#11719919—22no—
71C2×#11719919—22no—
72C2×#11719919—42no—
73C2×#11719919—42no—
74C2×#11719921—22no—
75C2×#11719921—22no—
76C2×#11719921—24no—
77C2×#11719921—22no—
78C2×#11719921—22no—
79C2×#11719921—22no—
80C2×#11719921—22no—
81C2×#11719921—42no—
82C2×#11719921—42no—
83C2×#11719921—42no—
84C2×#11719921—42no—
85C2×#11719921C2×C418yes—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88C2×C4×Dic53D414yes—
89#13133124—24no—
90#13133124—24no—
91#13133124—24no—
92#13133124—42no—
93#13133124—42no—
94#13133124C2×C418yes—
95C23×C4×C53C2312yes—
96C23×C4×C53C2312yes—
97C23×C4×C53C2311yescharacteristic
98C23×C4×C53C2311yescharacteristic
99C23×C4×C53C2311yescharacteristic
100C2×C4⋊C4×C53—22no—
101C2×C4⋊C4×C53—22no—
102C2×C4⋊C4×C53—22no—
103C2×C4⋊C4×C53—22no—
104C2×C4⋊C4×C53—22no—
105C2×C4⋊C4×C53C2×C414yes—
106C2×C42×C53—22no—
107C2×C42×C53—22no—
108C2×C42×C53D414yes—
109#95×C53—42no—
110#95×C53—42no—
111C24×C53C2411yescharacteristic
112C23×D53—21no—
113C23×D53—21no—
114C23×D53—21no—
115C23×D53—21no—
116C23×D53—21no—
117C23×D53—21no—
118C23×D53—21no—
119C23×D53—21no—
120C23×D53—21no—
121C23×D53—21no—
122C23×D53—21no—
123C23×D53—21no—
124C23×D53C22×C412yes—
125C23×D53C2×D412yes—
126C23×D53C2×Q812yes—
127C22×C4×C53—21no—
128C22×C4×C53—21no—
129C22×C4×C53—21no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—21no—
134C22×C4×C53—21no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—22no—
141C22×C4×C53—21no—
142C22×C4×C53—21no—
143C22×C4×C53—21no—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53—22no—
152C22×C4×C53C22×C414yes—
153C22×C4×C53C22×C412yes—
154C22×C4×C53C2×D412yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D412yes—
158C22×C4×C53C2×D412yes—
159C22×C4×C53C2×Q812yes—
160C22×C4×C53#4112yes—
161C22×C4×C53#4112yes—
162C22×Dic53—21no—
163C22×Dic53—21no—
164C22×Dic53—21no—
165C22×Dic53—21no—
166C22×Dic53—22no—
167C22×Dic53—21no—
168C22×Dic53—21no—
169C22×Dic53—21no—
170C22×Dic53—21no—
171C22×Dic53—22no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53C22×C414yes—
192C22×Dic53C22×C412yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D412yes—
195C22×Dic53C2×D412yes—
196C22×Dic53C2×Q812yes—
197C2×C4×D53—28no—
198C2×C4×D53—28no—
199C2×C4×D53—28no—
200C2×C4×D53—28no—
201C2×C4×D53—28no—
202C2×C4×D53—28no—
203C2×C4×D53C4⋊C4116yescomplemented
204C4⋊C4×C53—28no—
205C4⋊C4×C53—44no—
206C42×C53—28no—
207#11719921—28no—
208#11719921—28no—
209#11719921—48no—
210#11719921—48no—
211C4⋊Dic53—28no—
212C4⋊Dic53—48no—
213C4⋊Dic53—44no—
214#11719919—28no—
215#11719919—28no—
216#11719919—48no—
217C4×Dic53—28no—
218C23×C53C23×C411yescharacteristic
219C23×C53C22×D411yescharacteristic
220C23×C53C22×D411yescharacteristic
221C23×C53C22×D411yescharacteristic
222C23×C53C22×Q811yescharacteristic
223C23×C53C2×#4111yescharacteristic
224C23×C53C2×#4111yescharacteristic
225C23×C53H(5,𝔽2)11yescharacteristic
226C23×C53H(5,𝔽2)11yescharacteristic
227C23×C53H(5,𝔽2)11yescharacteristic
228C23×C53H(5,𝔽2)11yescharacteristic
229C23×C532−1+411yescharacteristic
230C23×C532−1+411yescharacteristic
231C23×C532−1+411yescharacteristic
232C23×C532−1+411yescharacteristic
233C22×D53—22no—
234C22×D53—22no—
235C22×D53—22no—
236C22×D53—22no—
237C22×D53—22no—
238C22×D53—22no—
239C22×D53—22no—
240C22×D53—22no—
241C22×D53—22no—
242C22×D53—22no—
243C22×D53—22no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—41no—
252C22×D53—41no—
253C22×D53—41no—
254C22×D53—41no—
255C22×D53—41no—
256C22×D53—41no—
257C22×D53—41no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53C2×C4⋊C414yes—
268C2×C4×C53—24no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—22no—
277C2×C4×C53—41no—
278C2×C4×C53—41no—
279C2×C4×C53—42no—
280C2×C4×C53—41no—
281C2×C4×C53—41no—
282C2×C4×C53—42no—
283C2×C4×C53—41no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—41no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—42no—
295C2×C4×C53—42no—
296C2×C4×C53C2×C4⋊C414yes—
297C2×C4×C53C4×D414yes—
298C2×C4×C53C4×D414yes—
299C2×C4×C53#12014yes—
300C2×C4×C53C22⋊Q814yes—
301C2×C4×C53C22⋊Q814yes—
302C2×C4×C53#12314yes—
303C2×Dic53—22no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—24no—
310C2×Dic53—24no—
311C2×Dic53—24no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—41no—
319C2×Dic53—41no—
320C2×Dic53—42no—
321C2×Dic53—41no—
322C2×Dic53—41no—
323C2×Dic53—41no—
324C2×Dic53—41no—
325C2×Dic53—42no—
326C2×Dic53—41no—
327C2×Dic53—41no—
328C2×Dic53—42no—
329C2×Dic53—42no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335C2×Dic53—42no—
336C2×Dic53—42no—
337C2×Dic53C2×C4⋊C414yes—
338C4×D53—232no—
339#14264—531nomaximal, Sylow
340C22×C53C22×C4⋊C411yescharacteristic
341C22×C53C2×C4×D411yescharacteristic
342C22×C53C2×C4×D411yescharacteristic
343C22×C53#51811yescharacteristic
344C22×C53#51911yescharacteristic
345C22×C53#52011yescharacteristic
346C22×C53#52011yescharacteristic
347C22×C53C2×#12011yescharacteristic
348C22×C53C2×C22⋊Q811yescharacteristic
349C22×C53C2×C22⋊Q811yescharacteristic
350C22×C53C2×#12311yescharacteristic
351C22×C53#53511yescharacteristic
352C22×C53#53511yescharacteristic
353C22×C53#53511yescharacteristic
354C22×C53#53611yescharacteristic
355C22×C53#53611yescharacteristic
356C22×C53#53611yescharacteristic
357C22×C53#53711yescharacteristic
358C22×C53#53711yescharacteristic
359C22×C53#53711yescharacteristic
360C22×C53#53711yescharacteristic
361C22×C53#53711yescharacteristic
362C22×C53#53711yescharacteristic
363C22×C53#54011yescharacteristic
364C22×C53#54011yescharacteristic
365C22×C53#54111yescharacteristic
366C22×C53#54111yescharacteristic
367C22×C53#54211yescharacteristic
368C22×C53#54211yescharacteristic
369C22×C53#54211yescharacteristic
370C22×C53#54211yescharacteristic
371C22×C53#54411yescharacteristic
372C22×C53#54411yescharacteristic
373C22×C53#54411yescharacteristic
374C22×C53#54411yescharacteristic
375C2×D53—24no—
376C2×D53—24no—
377C2×D53—24no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—42no—
390C4×C53—44no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53—82no—
394C4×C53#38518yes—
395Dic53—24no—
396Dic53—44no—
397Dic53—42no—
398Dic53—42no—
399Dic53—82no—
400C22×#117—531no—
401C2×#389—531no—
402C2×#389—531no—
403C2×#380—531no—
404C2×#380—531no—
405#1444—532no—
406#1442—532no—
407#1439—532no—
408#1439—532no—
409C4⋊#95—531no—
410C4⋊#95D5311yescharacteristic, complemented
411C2×C53C2×#38511yescharacteristic
412C2×C53#231611yescharacteristic
413C2×C53#231711yescharacteristic
414C2×C53#232311yescharacteristic
415C2×C53#232311yescharacteristic
416C2×C53#232411yescharacteristic
417C2×C53#232411yescharacteristic
418C2×C53#261511yescharacteristic
419C2×C53#261611yescharacteristic
420C2×C53#262411yescharacteristic
421C2×C53#262511yescharacteristic
422C2×C53#262811yescharacteristic
423C2×C53#262811yescharacteristic
424C2×C53#262911yescharacteristic
425C2×C53#262911yescharacteristic
426D53—44no—
427C24×C4—531no—
428C2×#117—1064no—
429C2×#117—1064no—
430C2×#117—1064no—
431C22×C4⋊C4—531no—
432C22×C4⋊C4—531no—
433C22×C4⋊C4—531no—
434C22×C4⋊C4—531no—
435C22×C4⋊C4—532no—
436C22×C4⋊C4—532no—
437C22×C4⋊C4C2×D5311yescharacteristic
438C22×C4⋊C4C2×D5311yescharacteristic
439C22×C22⋊C4—532no—
440C22×C22⋊C4—531no—
441C22×C22⋊C4—531no—
442C22×C22⋊C4—532no—
443C22×C42—531no—
444C22×C42C2×D5311yescharacteristic
445#389—1064no—
446#389—1064no—
447#380—538no—
448#380—1064no—
449C2×#95—532no—
450C2×#95—532no—
451C2×#95—532no—
452C2×#95—532no—
453C2×#95—532no—
454C2×#95—532no—
455C2×#95C2×D5312yes—
456C2×#95C2×D5312yes—
457C53#1426411yescharacteristic, complemented, Sylow
458C25—531no—
459C23×C4—531no—
460C23×C4—534no—
461C23×C4—534no—
462C23×C4—534no—
463C23×C4—531no—
464C23×C4—532no—
465C23×C4—531no—
466C23×C4—532no—
467C23×C4—1062no—
468C23×C4—1062no—
469C23×C4—1062no—
470C23×C4—1062no—
471C23×C4C22×D5312yes—
472C23×C4C22×D5312yes—
473C23×C4C22×D5311yescharacteristic
474C23×C4C22×D5311yescharacteristic
475C23×C4C22×D5311yescharacteristic
476#117—10632no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—22no—
482C2×C4⋊C4—534no—
483C2×C4⋊C4—1062no—
484C2×C4⋊C4—1062no—
485C2×C4⋊C4—1062no—
486C2×C4⋊C4—1062no—
487C2×C4⋊C4—1062no—
488C2×C4⋊C4—1062no—
489C2×C4⋊C4—1062no—
490C2×C4⋊C4—1062no—
491C2×C4⋊C4—1064no—
492C2×C4⋊C4—1064no—
493C2×C4⋊C4—1062no—
494C2×C4⋊C4—1062no—
495C2×C4⋊C4—1062no—
496C2×C4⋊C4—2122no—
497C2×C4⋊C4—2122no—
498C2×C4⋊C4—2122no—
499C2×C4⋊C4—2122no—
500C2×C4⋊C4C4×D5314yes—
501C2×C22⋊C4—538no—
502C2×C22⋊C4—1062no—
503C2×C22⋊C4—1062no—
504C2×C22⋊C4—1062no—
505C2×C22⋊C4—1062no—
506C2×C22⋊C4—1062no—
507C2×C22⋊C4—1062no—
508C2×C22⋊C4—1064no—
509C2×C22⋊C4—2122no—
510C2×C22⋊C4—2122no—
511C2×C22⋊C4—2122no—
512C2×C22⋊C4—2122no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—534no—
516C2×C42—1062no—
517C2×C42—1062no—
518C2×C42D21214yes—
519#95—42no—
520#95—42no—
521#95—538no—
522#95—1064no—
523#95—1064no—
524#95—1064no—
525#95—2122no—
526#95—2122no—
527C24—532no—
528C24—532no—
529C24—532no—
530C24—1061no—
531C24—1061no—
532C24—1061no—
533C24—1061no—
534C24—1061no—
535C24—1061no—
536C24—1061no—
537C24—1061no—
538C24—1061no—
539C24—1061no—
540C24—1061no—
541C24—1061no—
542C24C23×D5311yescharacteristic
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—532no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—5316no—
572C22×C4—534no—
573C22×C4—532no—
574C22×C4—532no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1061no—
578C22×C4—1061no—
579C22×C4—1068no—
580C22×C4—1068no—
581C22×C4—1068no—
582C22×C4—1068no—
583C22×C4—1068no—
584C22×C4—1068no—
585C22×C4—1061no—
586C22×C4—1061no—
587C22×C4—1062no—
588C22×C4—1061no—
589C22×C4—1061no—
590C22×C4—1062no—
591C22×C4—1061no—
592C22×C4—1062no—
593C22×C4—1061no—
594C22×C4—1061no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1061no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1062no—
601C22×C4—1061no—
602C22×C4—1061no—
603C22×C4—1062no—
604C22×C4—1062no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4C2×C4×D5314yes—
611C22×C4C2×C4×D5312yes—
612C22×C4C2×D21212yes—
613C22×C4C2×D21212yes—
614C22×C4C2×D21212yes—
615C22×C4#1171994512yes—
616C22×C4D4×D5312yes—
617C22×C4D4×D5312yes—
618C22×C4#1171994712yes—
619C22×C4Q8×D5312yes—
620C4⋊C4—28no—
621C4⋊C4—44no—
622C4⋊C4—1068no—
623C4⋊C4—1068no—
624C4⋊C4—1068no—
625C4⋊C4—2128no—
626C4⋊C4—2128no—
627C4⋊C4—2124no—
628C22⋊C4—1068no—
629C22⋊C4—1068no—
630C22⋊C4—2128no—
631C22⋊C4—2128no—
632C42—28no—
633C42—1068no—
634C23—534no—
635C23—1062no—
636C23—1062no—
637C23—1062no—
638C23—1062no—
639C23—1062no—
640C23—1062no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—1062no—
648C23—1062no—
649C23—1062no—
650C23—1062no—
651C23—1062no—
652C23—1062no—
653C23—2121no—
654C23—2121no—
655C23—2121no—
656C23—2121no—
657C23—2121no—
658C23—2121no—
659C23—2121no—
660C23—2121no—
661C23—2121no—
662C23—2121no—
663C23—2121no—
664C23—2121no—
665C23—2121no—
666C23—2121no—
667C23—2121no—
668C23—2121no—
669C23C22×C4×D5311yescharacteristic
670C23C2×D4×D5311yescharacteristic
671C23C2×D4×D5311yescharacteristic
672C23C22×D21211yescharacteristic
673C23C2×Q8×D5311yescharacteristic
674C23C2×#1171994711yescharacteristic
675C23C2×#1171994511yescharacteristic
676C23#1313326211yescharacteristic
677C23#1313326211yescharacteristic
678C23#1313326311yescharacteristic
679C23#1313326311yescharacteristic
680C23#1313326411yescharacteristic
681C23#1313326411yescharacteristic
682C23#1313326511yescharacteristic
683C23#1313326511yescharacteristic
684C2×C4—24no—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—42no—
704C2×C4—42no—
705C2×C4—42no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—534no—
713C2×C4—1062no—
714C2×C4—1062no—
715C2×C4—1062no—
716C2×C4—1062no—
717C2×C4—1062no—
718C2×C4—1062no—
719C2×C4—10632no—
720C2×C4—1064no—
721C2×C4—1064no—
722C2×C4—1064no—
723C2×C4—1062no—
724C2×C4—1062no—
725C2×C4—1062no—
726C2×C4—1062no—
727C2×C4—1062no—
728C2×C4—1062no—
729C2×C4—2122no—
730C2×C4—2122no—
731C2×C4—2122no—
732C2×C4—2122no—
733C2×C4—2122no—
734C2×C4—2122no—
735C2×C4—2122no—
736C2×C4—2121no—
737C2×C4—2122no—
738C2×C4—2121no—
739C2×C4—2121no—
740C2×C4—2121no—
741C2×C4—2121no—
742C2×C4—2121no—
743C2×C4—2121no—
744C2×C4—2121no—
745C2×C4—2122no—
746C2×C4—2122no—
747C2×C4—2122no—
748C2×C4C4⋊C4×D5314yes—
749C2×C4#1313317714yes—
750C2×C4C4×D21214yes—
751C2×C4#1313318714yes—
752C2×C4#1313319514yes—
753C2×C4#1313319714yes—
754C2×C4#1313319914yes—
755C22—1064no—
756C22—1064no—
757C22—1064no—
758C22—2122no—
759C22—2122no—
760C22—2122no—
761C22—2122no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22—2122no—
768C22—2122no—
769C22—2122no—
770C22C2×C4⋊C4×D5311yescharacteristic
771C22C2×#1313317711yescharacteristic
772C22C2×C4×D21211yescharacteristic
773C22#1681109511yescharacteristic
774C22#1681109911yescharacteristic
775C22#1681110211yescharacteristic
776C22#1681110511yescharacteristic
777C22C2×#1313318711yescharacteristic
778C22C2×#1313319511yescharacteristic
779C22C2×#1313319711yescharacteristic
780C22C2×#1313319911yescharacteristic
781C22#1681118911yescharacteristic
782C22#1681118911yescharacteristic
783C22#1681119211yescharacteristic
784C22#1681119611yescharacteristic
785C22#1681119611yescharacteristic
786C22#1681119911yescharacteristic
787C22#1681120211yescharacteristic
788C22#1681120211yescharacteristic
789C22#1681120311yescharacteristic
790C22#1681120311yescharacteristic
791C22#1681120411yescharacteristic
792C22#1681120411yescharacteristic
793C22#1681122411yescharacteristic
794C22#1681122711yescharacteristic
795C22#1681123111yescharacteristic
796C22#1681123411yescharacteristic
797C22#1681123811yescharacteristic
798C22#1681124211yescharacteristic
799C22#1681124211yescharacteristic
800C22#1681124511yescharacteristic
801C22#1681125011yescharacteristic
802C22#1681125011yescharacteristic
803C22#1681125311yescharacteristic
804C22#1681125311yescharacteristic
805C4—42no—
806C4—42no—
807C4—44no—
808C4—82no—
809C4—1064no—
810C4—4242no—
811C4—2122no—
812C4—2122no—
813C4—2124no—
814C4#1681049718yes—
815C2—2124no—
816C2C2×#1681049711yescharacteristic
817C2#2027733011yescharacteristic
818C2#2027733711yescharacteristic
819C2#2027739811yescharacteristic
820C2#2027740011yescharacteristic
821C2#2027740911yescharacteristic
822C2#2027741111yescharacteristic
823C2#2028044111yescharacteristic
824C2#2028044611yescharacteristic
825C2#2028050711yescharacteristic
826C2#2028051511yescharacteristic
827C2#2028053911yescharacteristic
828C2#2028054211yescharacteristic
829C2#2028054811yescharacteristic
830C2#2028055011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC4⋊#95D53
hypocenterC53#14264
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16810522C2semidirect
3. C2×#16810521C2semidirect
6. #20272979C2semidirect
7. #20272970C2semidirect
10. #20272944C2semidirect
11. C53×C4⋊#95C2semidirect
30. #16810480C4semidirect
203. C2×C4×D53C4⋊C4semidirect
410. C4⋊#95D53semidirect
457. C53#14264semidirect

Maximal subgroups

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

subgroupindex
C22×#131331742
C2×#168105222
C2×#168105212
C2×#168104802
#202729792
#202729702
#202729612
#202729592
#202729442
C53×C4⋊#952
#1426453