Finite Group Databasebeta

← #27305585

Subgroups — #27305585

Order 13568.

2882 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C2×#16810502C212yesmaximal
3C2×C4×C22⋊Dic53C212yesmaximal, complemented
4C2×#16810470C211yesmaximal, characteristic, complemented
5#20272951C212yesmaximal, complemented
6#20272946C212yesmaximal, complemented
7#20272941C211yesmaximal, characteristic, complemented
8#20272938C211yesmaximal, characteristic, complemented
9#20272936C211yesmaximal, characteristic, complemented
10#95×Dic53C211yesmaximal, characteristic, complemented
11C22×#95×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C2×C4×C22⋊D53—28no—
15C2×C4×C22⋊D53C418yescomplemented
16C22×#11719919C2211yescharacteristic
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2211yescharacteristic
19C22×#11719921C2212yes—
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×C4×Dic53C2212yes—
23C22×C4×Dic53C2212yes—
24C22×C4×Dic53C2211yescharacteristic
25#16810502C4116yescomplemented
26C4×C22⋊Dic53—28no—
27#16810470—24no—
28C2×#13133124C2211yescharacteristic
29C2×#13133124C2212yes—
30C2×#13133124C2211yescharacteristic
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C24×C4×C53C2211yescharacteristic
36C24×C4×C53C2212yes—
37C2×#95×C53—24no—
38C2×#95×C53C2211yescharacteristic
39C2×#95×C53C2212yes—
40C2×#95×C53C2211yescharacteristic
41C24×D53C2311yescharacteristic
42C22×C22⋊D53—24no—
43C22×C22⋊D53—22no—
44C22×C22⋊D53—22no—
45C22×C22⋊D53C2×C418yes—
46C22×C22⋊D53C2×C414yes—
47C23×Dic53C2312yes—
48C23×Dic53C2312yes—
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2311yescharacteristic
52C22×C4×D53—22no—
53C22×C4×D53—22no—
54C22×C4×D53—24no—
55C22×C4×D53—42no—
56C22×C4×D53C2×C414yescomplemented
57C4×C22⋊D53—232no—
58C2×#11719919—24no—
59C2×#11719919C2×C414yescomplemented
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—24no—
62C2×C22⋊Dic53C2×C414yes—
63C2×C22⋊Dic53C2×C418yescomplemented
64C2×C22⋊Dic53D418yes—
65C2×#11719921—24no—
66C2×#11719921—24no—
67C2×#11719921—24no—
68C2×#11719921—42no—
69C2×#11719921—42no—
70C2×#11719921C2×C418yescomplemented
71C2×#11719921C2×C414yescomplemented
72C2×#11719921C2×C418yescomplemented
73C2×C4×Dic53—24no—
74C2×C4×Dic53—24no—
75C2×C4×Dic53—24no—
76C2×C4×Dic53—24no—
77C2×C4×Dic53—24no—
78C2×C4×Dic53—42no—
79C2×C4×Dic53—42no—
80C2×C4×Dic53C2×C414yescomplemented
81#13133124—22no—
82#13133124—22no—
83#13133124—24no—
84#13133124—24no—
85#13133124—42no—
86#13133124C2×C418yescomplemented
87#13133124C2×C418yescomplemented
88C25×C53C2311yescharacteristic
89C23×C4×C53—24no—
90C23×C4×C53—24no—
91C23×C4×C53—24no—
92C23×C4×C53—22no—
93C23×C4×C53—24no—
94C23×C4×C53—22no—
95C23×C4×C53—24no—
96C23×C4×C53—42no—
97C23×C4×C53—42no—
98C23×C4×C53—42no—
99C23×C4×C53C2×C414yes—
100C23×C4×C53C2×C418yescomplemented
101C23×C4×C53C2311yescharacteristic
102C23×C4×C53C2312yes—
103C23×C4×C53C2312yes—
104C23×C4×C53C2311yescharacteristic
105#95×C53—22no—
106#95×C53—24no—
107#95×C53D414yescomplemented
108C24×C53—21no—
109C24×C53—21no—
110C24×C53—22no—
111C24×C53—22no—
112C24×C53—21no—
113C24×C53—21no—
114C24×C53C22×C412yes—
115C24×C53C22×C414yes—
116C24×C53C2×D414yes—
117C24×C53#4112yes—
118C24×C53#4112yes—
119C24×C53C2411yescharacteristic
120C23×D53—21no—
121C23×D53—22no—
122C23×D53—22no—
123C23×D53—21no—
124C23×D53—21no—
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—22no—
128C23×D53—21no—
129C23×D53C22×C414yes—
130C23×D53C22×C412yes—
131C22×C4×C53—22no—
132C22×C4×C53—22no—
133C22×C4×C53—22no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—28no—
138C22×C4×C53—216no—
139C22×C4×C53—21no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—21no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—28no—
150C22×C4×C53—216no—
151C22×C4×C53—44no—
152C22×C4×C53—48no—
153C22×C4×C53—48no—
154C22×C4×C53—48no—
155C22×C4×C53—48no—
156C22×C4×C53—48no—
157C22×C4×C53—48no—
158C22×C4×C53—48no—
159C22×C4×C53C22×C412yes—
160C22×C4×C53C22×C414yes—
161C22×C4×C53C22×C412yes—
162C22×C4×C53C22×C414yes—
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D414yes—
165C22×C4×C53#4112yes—
166C22×C4×C53#4114yes—
167C2×C22⋊D53—28no—
168C2×C22⋊D53—28no—
169C2×C22⋊D53—216no—
170C2×C22⋊D53—216no—
171C2×C22⋊D53C42116yescomplemented
172C22×Dic53—21no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—21no—
176C22×Dic53—21no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—22no—
180C22×Dic53—21no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53C22×C414yes—
194C22×Dic53C22×C414yes—
195C22×Dic53C22×C414yes—
196C22×Dic53C22×C412yes—
197C22×Dic53C22×C412yes—
198C22×Dic53C22×C412yes—
199C22×Dic53C2×D414yes—
200C22×Dic53C2×D414yes—
201C2×C4×D53—28no—
202C2×C4×D53—28no—
203C2×C4×D53—44no—
204C2×C4×D53—48no—
205C2×C4×D53—48no—
206C22⋊Dic53—216no—
207C22⋊Dic53C22⋊C4116yescomplemented
208#11719921—216no—
209#11719921—28no—
210#11719921—48no—
211#11719919—28no—
212C4×Dic53—28no—
213C4×Dic53—48no—
214C4×Dic53—48no—
215C23×C53—22no—
216C23×C53—24no—
217C23×C53—22no—
218C23×C53—24no—
219C23×C53—22no—
220C23×C53—24no—
221C23×C53—22no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—22no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—24no—
228C23×C53—22no—
229C23×C53—24no—
230C23×C53—22no—
231C23×C53—22no—
232C23×C53—24no—
233C23×C53C2×C4214yes—
234C23×C53C2×C22⋊C414yes—
235C23×C53#11714yes—
236C23×C53C4×D418yes—
237C23×C53C4×D418yes—
238C23×C53C23×C411yescharacteristic
239C23×C53C23×C412yes—
240C23×C53C22×D412yes—
241C23×C53C22×D411yescharacteristic
242C23×C53C2×#4111yescharacteristic
243C23×C53C2×#4111yescharacteristic
244C23×C53C2×#4112yes—
245C23×C53C2×#4111yescharacteristic
246C23×C53H(5,𝔽2)12yes—
247C23×C53H(5,𝔽2)11yescharacteristic
248C23×C532−1+411yescharacteristic
249C22×D53—22no—
250C22×D53—22no—
251C22×D53—22no—
252C22×D53—24no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—22no—
256C22×D53—24no—
257C22×D53—22no—
258C22×D53—24no—
259C22×D53—22no—
260C22×D53—24no—
261C22×D53—42no—
262C22×D53—42no—
263C22×D53—41no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53—41no—
267C22×D53—42no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—42no—
271C22×D53C2×C4214yes—
272C2×C4×C53—22no—
273C2×C4×C53—24no—
274C2×C4×C53—22no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—24no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—22no—
283C2×C4×C53—24no—
284C2×C4×C53—22no—
285C2×C4×C53—24no—
286C2×C4×C53—22no—
287C2×C4×C53—24no—
288C2×C4×C53—416no—
289C2×C4×C53—432no—
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×C53C4×D414yes—
297C2×C4×C53C4×D418yescomplemented
298C22⋊D53—232no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—24no—
303C2×Dic53—24no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—24no—
308C2×Dic53—24no—
309C2×Dic53—24no—
310C2×Dic53—24no—
311C2×Dic53—24no—
312C2×Dic53—24no—
313C2×Dic53—24no—
314C2×Dic53—24no—
315C2×Dic53—24no—
316C2×Dic53—24no—
317C2×Dic53—42no—
318C2×Dic53—42no—
319C2×Dic53—42no—
320C2×Dic53—42no—
321C2×Dic53—42no—
322C2×Dic53—42no—
323C2×Dic53—42no—
324C2×Dic53—42no—
325C2×Dic53C2×C4214yes—
326C2×Dic53C2×C22⋊C414yes—
327C2×Dic53C2×C22⋊C414yes—
328C4×D53—416no—
329#13813—531nomaximal, Sylow
330C22×C53—24no—
331C22×C53—24no—
332C22×C53—24no—
333C22×C53—24no—
334C22×C53—28no—
335C22×C53—28no—
336C22×C53—28no—
337C22×C53—28no—
338C22×C53—24no—
339C22×C53—24no—
340C22×C53C4×C22⋊C418yescomplemented
341C22×C53C22×C4211yescharacteristic
342C22×C53C22×C22⋊C411yescharacteristic
343C22×C53C2×#11711yescharacteristic
344C22×C53C2×C4×D412yes—
345C22×C53C2×C4×D411yescharacteristic
346C22×C53C2×C4×D412yes—
347C22×C53C2×C4×D412yes—
348C22×C53C4×#4111yescharacteristic
349C22×C53C4×#4112yes—
350C22×C53#51811yescharacteristic
351C22×C53#51812yes—
352C22×C53#52011yescharacteristic
353C22×C53#52012yes—
354C22×C53D4212yes—
355C22×C53#54611yescharacteristic
356C22×C53#54612yes—
357C22×C53#54612yes—
358C22×C53#54712yes—
359C22×C53#54811yescharacteristic
360C22×C53#55112yes—
361C22×C53#55211yescharacteristic
362C22×C53#55311yescharacteristic
363C22×C53#55312yes—
364C2×D53—24no—
365C2×D53—24no—
366C2×D53—24no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—44no—
372C2×D53—44no—
373C2×D53—44no—
374C2×D53—44no—
375C4×C53—24no—
376C4×C53—28no—
377C4×C53—42no—
378C4×C53—44no—
379Dic53—24no—
380Dic53—24no—
381Dic53—24no—
382Dic53—44no—
383Dic53—44no—
384C22×C4×D4—531no—
385C2×#386—532no—
386C2×C4×C22⋊C4—531no—
387C2×C4×C22⋊C4—532no—
388C22×#95D5311yescharacteristic, complemented
389#1437—532no—
390#1436—532no—
391#1434—531no—
392C22⋊#95—531no—
393C22⋊#95—531no—
394C4×#95—531no—
395C2×C53—28no—
396C2×C53C2×C4×C22⋊C411yescharacteristic
397C2×C53C42×D411yescharacteristic
398C2×C53#227511yescharacteristic
399C2×C53D4×C22⋊C411yescharacteristic
400C2×C53#233911yescharacteristic
401C2×C53#235211yescharacteristic
402C2×C53#235311yescharacteristic
403C2×C53#235812yes—
404C2×C53#235912yes—
405C2×C53#236112yes—
406C2×C53#236412yes—
407D53—44no—
408C23×D4—531no—
409C24×C4—531no—
410C24×C4C2×D5311yescharacteristic
411C24×C4C2×D5312yes—
412C2×C4×D4—538no—
413C2×C4×D4—1068no—
414C22×C4⋊C4—531no—
415C22×C22⋊C4—531no—
416C22×C22⋊C4—532no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—532no—
419C22×C22⋊C4—532no—
420C22×C42—531no—
421C22×C42—532no—
422C22×C42—532no—
423#386—5316no—
424C4×C22⋊C4—1068no—
425C4×C22⋊C4—1064no—
426C2×#95—24no—
427C2×#95—532no—
428C2×#95—532no—
429C2×#95—531no—
430C2×#95—531no—
431C2×#95—532no—
432C2×#95—532no—
433C2×#95—532no—
434C2×#95C2×D5311yescharacteristic
435C2×#95C2×D5312yes—
436C2×#95C2×D5311yescharacteristic
437C53#1381311yescharacteristic, complemented, Sylow
438C25—531no—
439C25C22×D5311yescharacteristic
440C22×D4—534no—
441C22×D4—538no—
442C22×D4—1064no—
443C22×D4—1062no—
444C22×D4—1062no—
445C23×C4—24no—
446C23×C4—24no—
447C23×C4—24no—
448C23×C4—22no—
449C23×C4—24no—
450C23×C4—22no—
451C23×C4—24no—
452C23×C4—42no—
453C23×C4—42no—
454C23×C4—42no—
455C23×C4—531no—
456C23×C4—531no—
457C23×C4—531no—
458C23×C4—532no—
459C23×C4—532no—
460C23×C4—534no—
461C23×C4—1064no—
462C23×C4—1062no—
463C23×C4—1062no—
464C23×C4—2122no—
465C23×C4C4×D5314yes—
466C23×C4C4×D5318yescomplemented
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5312yes—
469C23×C4C22×D5312yes—
470C23×C4C22×D5311yescharacteristic
471C4×D4—10632no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—1064no—
474C2×C22⋊C4—534no—
475C2×C22⋊C4—538no—
476C2×C22⋊C4—538no—
477C2×C22⋊C4—534no—
478C2×C22⋊C4—538no—
479C2×C22⋊C4—538no—
480C2×C22⋊C4—1064no—
481C2×C22⋊C4—1064no—
482C2×C22⋊C4—1064no—
483C2×C22⋊C4—1064no—
484C2×C22⋊C4—1064no—
485C2×C22⋊C4—2122no—
486C2×C22⋊C4—2122no—
487C2×C42—534no—
488C2×C42—1064no—
489C2×C42—1064no—
490C2×C42—1064no—
491C2×C42—1064no—
492C2×C42—1064no—
493C2×C42—2122no—
494C2×C42—2122no—
495#95—22no—
496#95—24no—
497#95—538no—
498#95—538no—
499#95—1064no—
500#95—1064no—
501#95—1062no—
502#95—1062no—
503#95—2122no—
504#95C22⋊D5314yescomplemented
505C24—21no—
506C24—22no—
507C24—21no—
508C24—21no—
509C24—22no—
510C24—21no—
511C24—534no—
512C24—532no—
513C24—1062no—
514C24—1061no—
515C24—1061no—
516C24—1062no—
517C24—1061no—
518C24—1061no—
519C24—1061no—
520C24—1062no—
521C24—1061no—
522C24C2×C4×D5312yes—
523C24C2×C4×D5314yes—
524C24D4×D5314yes—
525C24#1171994712yes—
526C24#1171994912yes—
527C24C23×D5311yescharacteristic
528C2×D4—5316no—
529C2×D4—1068no—
530C2×D4—1068no—
531C2×D4—10616no—
532C2×D4—10616no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—28no—
540C22×C4—216no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—28no—
552C22×C4—216no—
553C22×C4—44no—
554C22×C4—48no—
555C22×C4—48no—
556C22×C4—48no—
557C22×C4—48no—
558C22×C4—48no—
559C22×C4—48no—
560C22×C4—48no—
561C22×C4—534no—
562C22×C4—532no—
563C22×C4—532no—
564C22×C4—532no—
565C22×C4—534no—
566C22×C4—534no—
567C22×C4—534no—
568C22×C4—534no—
569C22×C4—1068no—
570C22×C4—1062no—
571C22×C4—1061no—
572C22×C4—1061no—
573C22×C4—1062no—
574C22×C4—1061no—
575C22×C4—1061no—
576C22×C4—1061no—
577C22×C4—1062no—
578C22×C4—1061no—
579C22×C4—1062no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1068no—
592C22×C4—2124no—
593C22×C4—2128no—
594C22×C4—2128no—
595C22×C4C2×C4×D5314yes—
596C22×C4C2×C4×D5312yes—
597C22×C4C2×C4×D5312yes—
598C22×C4C2×C4×D5314yes—
599C22×C4#1171994512yes—
600C22×C4#1171994514yes—
601C22×C4C2×C22⋊D5312yes—
602C22×C4C2×C22⋊D5314yes—
603C4⋊C4—1068no—
604C22⋊C4—5316no—
605C22⋊C4—1068no—
606C22⋊C4—10616no—
607C22⋊C4—10616no—
608C22⋊C4—2128no—
609C42—1068no—
610C42—2128no—
611C42—2128no—
612C23—22no—
613C23—24no—
614C23—22no—
615C23—24no—
616C23—22no—
617C23—22no—
618C23—24no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—24no—
624C23—22no—
625C23—22no—
626C23—24no—
627C23—24no—
628C23—24no—
629C23—24no—
630C23—534no—
631C23—1062no—
632C23—1062no—
633C23—1064no—
634C23—1064no—
635C23—1062no—
636C23—1064no—
637C23—1064no—
638C23—1062no—
639C23—1064no—
640C23—1062no—
641C23—1062no—
642C23—1064no—
643C23—2121no—
644C23—2122no—
645C23—2121no—
646C23—2122no—
647C23—2121no—
648C23—2121no—
649C23—2122no—
650C23—2122no—
651C23—2122no—
652C23—2122no—
653C23C42×D5314yes—
654C23C22⋊C4×D5314yes—
655C23#1313317514yes—
656C23#1313317718yes—
657C23#1313317918yes—
658C23C22×C4×D5311yescharacteristic
659C23C22×C4×D5312yes—
660C23C2×D4×D5312yes—
661C23C22×C22⋊D5311yescharacteristic
662C23C2×#1171994711yescharacteristic
663C23C2×#1171994512yes—
664C23C2×#1171994511yescharacteristic
665C23C2×#1171994911yescharacteristic
666C23#1313326211yescharacteristic
667C23#1313326212yes—
668C23#1313326511yescharacteristic
669D4—10632no—
670C2×C4—24no—
671C2×C4—24no—
672C2×C4—22no—
673C2×C4—24no—
674C2×C4—22no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—24no—
684C2×C4—24no—
685C2×C4—22no—
686C2×C4—416no—
687C2×C4—432no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—534no—
695C2×C4—534no—
696C2×C4—534no—
697C2×C4—1064no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1064no—
701C2×C4—1062no—
702C2×C4—1064no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1064no—
707C2×C4—1064no—
708C2×C4—1064no—
709C2×C4—1064no—
710C2×C4—1064no—
711C2×C4—1064no—
712C2×C4—1064no—
713C2×C4—1064no—
714C2×C4—1064no—
715C2×C4—21216no—
716C2×C4—2122no—
717C2×C4—2122no—
718C2×C4—2122no—
719C2×C4—2122no—
720C2×C4—2122no—
721C2×C4—2122no—
722C2×C4—2122no—
723C2×C4—2122no—
724C2×C4C4×C22⋊D5314yes—
725C2×C4C4×C22⋊D5318yescomplemented
726C22—28no—
727C22—24no—
728C22—24no—
729C22—24no—
730C22—24no—
731C22—24no—
732C22—24no—
733C22—28no—
734C22—28no—
735C22—28no—
736C22—1064no—
737C22—1064no—
738C22—1064no—
739C22—2124no—
740C22—2122no—
741C22—2122no—
742C22—2122no—
743C22—2122no—
744C22—2124no—
745C22—2124no—
746C22—2124no—
747C22#1681047018yescomplemented
748C22C2×C42×D5311yescharacteristic
749C22C2×C22⋊C4×D5311yescharacteristic
750C22C2×#1313317511yescharacteristic
751C22C2×#1313317712yes—
752C22C2×C4×C22⋊D5311yescharacteristic
753C22C2×C4×C22⋊D5312yes—
754C22C2×#1313317912yes—
755C22C4×#1171994512yes—
756C22C4×#1171994511yescharacteristic
757C22#1681109612yes—
758C22#1681109611yescharacteristic
759C22#1681110411yescharacteristic
760C22#1681110412yes—
761C22D4×C22⋊D5312yes—
762C22#1681126312yes—
763C22#1681126312yes—
764C22#1681126711yescharacteristic
765C22#1681127412yes—
766C22#1681128411yescharacteristic
767C22#1681129912yes—
768C22#1681130811yescharacteristic
769C22#1681132111yescharacteristic
770C22#1681132112yes—
771C4—24no—
772C4—28no—
773C4—42no—
774C4—44no—
775C4—1064no—
776C4—1064no—
777C4—1064no—
778C4—2124no—
779C4—2124no—
780C2—28no—
781C2—2124no—
782C2C2×#1681047011yescharacteristic
783C2C42×C22⋊D5311yescharacteristic
784C2#2027707311yescharacteristic
785C2C22⋊C4×C22⋊D5311yescharacteristic
786C2#2027754211yescharacteristic
787C2#2027764011yescharacteristic
788C2#2027765111yescharacteristic
789C2#2027769412yes—
790C2#2027770312yes—
791C2#2027773112yes—
792C2#2027776212yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC22×#95×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC22×#95D53
hypocenterC53#13813
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×C22⋊Dic53C2semidirect
4. C2×#16810470C2semidirect
5. #20272951C2semidirect
6. #20272946C2semidirect
7. #20272941C2semidirect
8. #20272938C2semidirect
9. #20272936C2semidirect
10. #95×Dic53C2semidirect
11. C22×#95×C53C2semidirect
15. C2×C4×C22⋊D53C4semidirect
25. #16810502C4semidirect
56. C22×C4×D53C2×C4semidirect
59. C2×#11719919C2×C4semidirect
63. C2×C22⋊Dic53C2×C4semidirect
70. C2×#11719921C2×C4semidirect
71. C2×#11719921C2×C4semidirect
72. C2×#11719921C2×C4semidirect
80. C2×C4×Dic53C2×C4semidirect
86. #13133124C2×C4semidirect
87. #13133124C2×C4semidirect
100. C23×C4×C53C2×C4semidirect
107. #95×C53D4semidirect
171. C2×C22⋊D53C42semidirect
207. C22⋊Dic53C22⋊C4semidirect
297. C2×C4×C53C4×D4semidirect
340. C22×C53C4×C22⋊C4semidirect
388. C22×#95D53semidirect
437. C53#13813semidirect
466. C23×C4C4×D53semidirect
504. #95C22⋊D53semidirect
725. C2×C4C4×C22⋊D53semidirect
747. C22#16810470semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D532
C2×#168105022
C2×C4×C22⋊Dic532
C2×#168104702
#202729512
#202729462
#202729412
#202729382
#202729362
#95×Dic532
C22×#95×C532
#1381353