Finite Group Databasebeta

← #27305277

Subgroups — #27305277

Order 13568.

2894 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133177C211yesmaximal, characteristic
2C2×#16810523C212yesmaximal
3C2×#16810474C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×Dic53C212yesmaximal, complemented
5C2×#16810470C212yesmaximal, complemented
6C2×C42×Dic53C211yesmaximal, characteristic, complemented
7#20272953C211yesmaximal, characteristic, complemented
8#20272952C211yesmaximal, characteristic, complemented
9#20272951C211yesmaximal, characteristic, complemented
10#20272943C212yesmaximal, complemented
11C53×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C24×Dic53C2211yescharacteristic
14C23×C4×D53C2211yescharacteristic
15C2×#13133177—24no—
16C2×#13133177—24no—
17C2×#13133177C418yescomplemented
18C22×#11719919C2211yescharacteristic
19C22×#11719919C2212yes—
20C22×C22⋊Dic53C2212yes—
21C22×#11719921C2211yescharacteristic
22C22×#11719921C2212yes—
23C22×#11719921C2212yes—
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2212yes—
26C22×C4×Dic53C2212yes—
27C22×C4×Dic53C2212yes—
28C22×C4×Dic53C2211yescharacteristic
29#16810523C4116yescomplemented
30#16810474—24no—
31C22⋊C4×Dic53—28no—
32#16810470—28no—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2211yescharacteristic
37C42×Dic53—24no—
38C22×C22⋊C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2212yes—
40C22×C42×C53C2211yescharacteristic
41C2×#95×C53C2212yes—
42C2×#95×C53C2211yescharacteristic
43C24×D53C2311yescharacteristic
44C22×C22⋊D53—22no—
45C22×C22⋊D53—22no—
46C22×C22⋊D53—24no—
47C22×C22⋊D53C2×C418yes—
48C22×C22⋊D53C2×C414yes—
49C23×Dic53—22no—
50C23×Dic53—22no—
51C23×Dic53—24no—
52C23×Dic53—24no—
53C23×Dic53C2×C414yes—
54C23×Dic53C2312yes—
55C23×Dic53C2311yescharacteristic
56C23×Dic53C2312yes—
57C23×Dic53C2311yescharacteristic
58C23×Dic53C2311yescharacteristic
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53—24no—
62C22×C4×D53—24no—
63C22×C4×D53C2×C414yes—
64#13133177—232no—
65C2×#11719919—22no—
66C2×#11719919—22no—
67C2×#11719919—24no—
68C2×#11719919—24no—
69C2×#11719919C2×C414yes—
70C2×#11719919C2×C418yescomplemented
71C2×C22⋊Dic53—24no—
72C2×C22⋊Dic53—24no—
73C2×C22⋊Dic53C2×C418yescomplemented
74C2×#11719921—22no—
75C2×#11719921—22no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—24no—
79C2×#11719921—24no—
80C2×#11719921C2×C414yes—
81C2×#11719921C2×C418yescomplemented
82C2×#11719921C2×C418yescomplemented
83C2×C4×Dic53—22no—
84C2×C4×Dic53—24no—
85C2×C4×Dic53—24no—
86C2×C4×Dic53—24no—
87C2×C4×Dic53—24no—
88C2×C4×Dic53—24no—
89C2×C4×Dic53—24no—
90C2×C4×Dic53—24no—
91C2×C4×Dic53—24no—
92C2×C4×Dic53C2×C414yes—
93C2×C4×Dic53C2×C418yescomplemented
94C2×C4×Dic53D414yes—
95C2×C4×Dic53D414yes—
96C2×C4×Dic53D418yescomplemented
97#13133124—24no—
98#13133124—22no—
99#13133124—24no—
100#13133124—24no—
101C25×C53C2311yescharacteristic
102C23×C4×C53C2312yes—
103C23×C4×C53C2311yescharacteristic
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2312yes—
106C2×C22⋊C4×C53—22no—
107C2×C22⋊C4×C53—22no—
108C2×C22⋊C4×C53—24no—
109C2×C22⋊C4×C53—24no—
110C2×C22⋊C4×C53C2×C414yes—
111C2×C22⋊C4×C53C2×C418yescomplemented
112C2×C42×C53—22no—
113C2×C42×C53—24no—
114#95×C53—24no—
115#95×C53—22no—
116C24×C53—22no—
117C24×C53—21no—
118C24×C53—21no—
119C24×C53—22no—
120C24×C53—22no—
121C24×C53—22no—
122C24×C53—22no—
123C24×C53C22×C412yes—
124C24×C53C22×C414yes—
125C24×C53C2411yescharacteristic
126C23×D53—22no—
127C23×D53—21no—
128C23×D53—21no—
129C23×D53—22no—
130C23×D53—22no—
131C23×D53—22no—
132C23×D53—22no—
133C23×D53C22×C412yes—
134C23×D53C22×C414yes—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—22no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—22no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53—22no—
145C22×C4×C53—21no—
146C22×C4×C53—21no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—22no—
151C22×C4×C53C22×C412yes—
152C22×C4×C53C22×C414yes—
153C22×C4×C53C22×C412yes—
154C22×C4×C53C22×C414yes—
155C22×C4×C53C2×D412yes—
156C22×C4×C53C2×D412yes—
157C22×C4×C53C2×D414yes—
158C22×C4×C53#4114yes—
159C2×C22⋊D53—28no—
160C2×C22⋊D53—28no—
161C2×C22⋊D53—216no—
162C2×C22⋊D53—216no—
163C2×C22⋊D53C42116yescomplemented
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—22no—
171C22×Dic53—22no—
172C22×Dic53—21no—
173C22×Dic53—21no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—22no—
178C22×Dic53—28no—
179C22×Dic53—216no—
180C22×Dic53—48no—
181C22×Dic53—44no—
182C22×Dic53—44no—
183C22×Dic53C22×C412yes—
184C22×Dic53C22×C414yes—
185C22×Dic53C22×C414yes—
186C22×Dic53C22×C412yes—
187C22×Dic53C22×C414yes—
188C22×Dic53C22×C412yes—
189C22×Dic53C2×D414yes—
190C22×Dic53C2×D412yes—
191C22×Dic53C2×D412yes—
192C22×Dic53C2×D412yes—
193C22×Dic53C2×D412yes—
194C22×Dic53C2×D414yes—
195C22×Dic53#4114yes—
196C22×Dic53#4114yes—
197C22×Dic53#4114yes—
198C2×C4×D53—28no—
199C2×C4×D53—216no—
200C2×C4×D53—48no—
201C2×C4×D53—44no—
202C2×C4×D53—44no—
203C22⋊C4×C53—28no—
204C22⋊C4×C53—216no—
205C42×C53—28no—
206C22⋊Dic53—216no—
207#11719921—28no—
208#11719921—216no—
209#11719921—216no—
210#11719919—28no—
211#11719919—216no—
212C4×Dic53—28no—
213C4×Dic53—216no—
214C4×Dic53—216no—
215C4×Dic53—48no—
216C4×Dic53C22⋊C4116yescomplemented
217C23×C53—22no—
218C23×C53—22no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—24no—
224C23×C53—24no—
225C23×C53—24no—
226C23×C53—24no—
227C23×C53—42no—
228C23×C53—41no—
229C23×C53—41no—
230C23×C53—41no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—41no—
234C23×C53—42no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53C2×C4214yes—
238C23×C53C23×C411yescharacteristic
239C23×C53C23×C412yes—
240C23×C53C22×D411yescharacteristic
241C23×C53C22×D411yescharacteristic
242C23×C53C22×D412yes—
243C23×C53C2×#4112yes—
244C23×C53C2×#4112yes—
245C23×C53C2×#4112yes—
246C23×C53C2×#4112yes—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—24no—
250C22×D53—24no—
251C22×D53—24no—
252C22×D53—24no—
253C22×D53—24no—
254C22×D53—24no—
255C22×D53—24no—
256C22×D53—24no—
257C22×D53—42no—
258C22×D53—41no—
259C22×D53—41no—
260C22×D53—41no—
261C22×D53—42no—
262C22×D53—42no—
263C22×D53—41no—
264C22×D53—42no—
265C22×D53—42no—
266C22×D53—42no—
267C22×D53C2×C4214yes—
268C2×C4×C53—24no—
269C2×C4×C53—24no—
270C2×C4×C53—24no—
271C2×C4×C53—24no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—24no—
275C2×C4×C53—24no—
276C2×C4×C53—24no—
277C2×C4×C53—24no—
278C2×C4×C53—22no—
279C2×C4×C53—24no—
280C2×C4×C53—24no—
281C2×C4×C53—24no—
282C2×C4×C53—24no—
283C2×C4×C53—42no—
284C2×C4×C53—41no—
285C2×C4×C53—41no—
286C2×C4×C53—42no—
287C2×C4×C53—42no—
288C2×C4×C53—42no—
289C2×C4×C53—42no—
290C2×C4×C53C2×C22⋊C414yes—
291C2×C4×C53C4×D418yescomplemented
292C22⋊D53—232no—
293C2×Dic53—24no—
294C2×Dic53—24no—
295C2×Dic53—24no—
296C2×Dic53—24no—
297C2×Dic53—24no—
298C2×Dic53—24no—
299C2×Dic53—22no—
300C2×Dic53—24no—
301C2×Dic53—24no—
302C2×Dic53—24no—
303C2×Dic53—24no—
304C2×Dic53—42no—
305C2×Dic53—41no—
306C2×Dic53—41no—
307C2×Dic53—42no—
308C2×Dic53—42no—
309C2×Dic53—42no—
310C2×Dic53—42no—
311C2×Dic53—416no—
312C2×Dic53C2×C4214yes—
313C2×Dic53C2×C22⋊C414yes—
314C2×Dic53C2×C22⋊C414yes—
315C2×Dic53#11714yes—
316C2×Dic53C4×D418yes—
317C2×Dic53C4×D418yes—
318C2×Dic53C4×D418yes—
319C2×Dic53C4×D418yescomplemented
320C2×Dic53#12118yes—
321C2×Dic53#12414yes—
322C2×Dic53#12714yes—
323C4×D53—416no—
324C4×#390—531nomaximal, Sylow
325C22×C53—24no—
326C22×C53—28no—
327C22×C53—44no—
328C22×C53—42no—
329C22×C53—44no—
330C22×C53—42no—
331C22×C53—44no—
332C22×C53—44no—
333C22×C53—44no—
334C22×C53C22×C4211yescharacteristic
335C22×C53C22×C22⋊C411yescharacteristic
336C22×C53C2×#11711yescharacteristic
337C22×C53C2×C4×D412yes—
338C22×C53C2×C4×D412yes—
339C22×C53C2×C4×D412yes—
340C22×C53C2×C4×D412yes—
341C22×C53C2×C4×D412yes—
342C22×C53C4×#4112yes—
343C22×C53C4×#4112yes—
344C22×C53C4×#4112yes—
345C22×C53C2×#12112yes—
346C22×C53#52511yescharacteristic
347C22×C53#52511yescharacteristic
348C22×C53C2×#12411yescharacteristic
349C22×C53#52912yes—
350C22×C53#52912yes—
351C22×C53C2×#12711yescharacteristic
352C22×C53#53212yes—
353C22×C53#53212yes—
354C22×C53#53212yes—
355C2×D53—24no—
356C2×D53—28no—
357C2×D53—44no—
358C2×D53—42no—
359C2×D53—44no—
360C2×D53—42no—
361C2×D53—44no—
362C2×D53—44no—
363C2×D53—44no—
364C4×C53—24no—
365C4×C53—28no—
366C4×C53—44no—
367C4×C53—42no—
368Dic53—28no—
369Dic53—44no—
370Dic53—42no—
371Dic53C4×C22⋊C418yescomplemented
372Dic53#39018yescomplemented
373C22×C4×D4—531no—
374C2×#390—532no—
375C2×C4×C4⋊C4—531no—
376C2×C4×C22⋊C4—532no—
377C2×C4×C22⋊C4—532no—
378C2×C43—531no—
379#1437—531no—
380#1437—531no—
381#1437—531no—
382#1437D5311yescharacteristic, complemented
383C4⋊#95—532no—
384C2×C53—44no—
385C2×C53C2×C4×C22⋊C411yescharacteristic
386C2×C53C42×D412yes—
387C2×C53C2×#39011yescharacteristic
388C2×C53#229312yes—
389C2×C53#229711yescharacteristic
390C2×C53C4×#12112yes—
391C2×C53C4×#12112yes—
392C2×C53C4×#12412yes—
393C2×C53C4×#12712yes—
394D53—44no—
395C23×D4—531no—
396C24×C4—531no—
397C24×C4—531no—
398C2×C4×D4—538no—
399C2×C4×D4—1064no—
400C2×C4×D4—1064no—
401C22×C4⋊C4—531no—
402C22×C4⋊C4—532no—
403C22×C22⋊C4—532no—
404C22×C22⋊C4—531no—
405C22×C22⋊C4—532no—
406C22×C22⋊C4—532no—
407C22×C22⋊C4C2×D5311yescharacteristic
408C22×C22⋊C4C2×D5312yes—
409C22×C42—531no—
410C22×C42—532no—
411C22×C42—532no—
412C22×C42—531no—
413C22×C42—532no—
414C22×C42C2×D5311yescharacteristic
415#390—5316no—
416C4×C4⋊C4—1064no—
417C4×C22⋊C4—1068no—
418C4×C22⋊C4—1068no—
419C2×#95—532no—
420C2×#95—532no—
421C2×#95—532no—
422C2×#95—531no—
423C2×#95C2×D5312yes—
424C2×#95C2×D5311yescharacteristic
425C43—1064no—
426C53C4×#39011yescharacteristic, complemented, Sylow
427C25—531no—
428C25C22×D5311yescharacteristic
429C22×D4—534no—
430C22×D4—538no—
431C22×D4—1062no—
432C22×D4—1062no—
433C22×D4—1064no—
434C23×C4—531no—
435C23×C4—531no—
436C23×C4—532no—
437C23×C4—534no—
438C23×C4—532no—
439C23×C4—531no—
440C23×C4—534no—
441C23×C4—1062no—
442C23×C4—1062no—
443C23×C4—1064no—
444C23×C4—1064no—
445C23×C4—1062no—
446C23×C4—1062no—
447C23×C4—1064no—
448C23×C4—1064no—
449C23×C4C22×D5312yes—
450C23×C4C22×D5311yescharacteristic
451C23×C4C22×D5311yescharacteristic
452C23×C4C22×D5312yes—
453C4×D4—10632no—
454C2×C4⋊C4—534no—
455C2×C4⋊C4—538no—
456C2×C4⋊C4—1062no—
457C2×C4⋊C4—1062no—
458C2×C4⋊C4—1064no—
459C2×C4⋊C4—1064no—
460C2×C22⋊C4—22no—
461C2×C22⋊C4—22no—
462C2×C22⋊C4—24no—
463C2×C22⋊C4—24no—
464C2×C22⋊C4—538no—
465C2×C22⋊C4—534no—
466C2×C22⋊C4—538no—
467C2×C22⋊C4—538no—
468C2×C22⋊C4—1064no—
469C2×C22⋊C4—1064no—
470C2×C22⋊C4—1064no—
471C2×C22⋊C4—1064no—
472C2×C22⋊C4—1062no—
473C2×C22⋊C4—1062no—
474C2×C22⋊C4—1064no—
475C2×C22⋊C4—1064no—
476C2×C22⋊C4C4×D5314yes—
477C2×C22⋊C4C4×D5318yescomplemented
478C2×C42—22no—
479C2×C42—24no—
480C2×C42—534no—
481C2×C42—534no—
482C2×C42—534no—
483C2×C42—538no—
484C2×C42—538no—
485C2×C42—1064no—
486C2×C42—1064no—
487C2×C42—1064no—
488C2×C42—1064no—
489C2×C42—1064no—
490C2×C42—1062no—
491C2×C42—1064no—
492C2×C42—1064no—
493C2×C42—1064no—
494#95—24no—
495#95—22no—
496#95—1064no—
497#95—1064no—
498#95—1064no—
499#95—1062no—
500C24—22no—
501C24—21no—
502C24—21no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—534no—
508C24—532no—
509C24—1062no—
510C24—1061no—
511C24—1061no—
512C24—1062no—
513C24—1062no—
514C24—1062no—
515C24—1062no—
516C24C2×C4×D5314yes—
517C24C2×C4×D5312yes—
518C24C23×D5311yescharacteristic
519C2×D4—5316no—
520C2×D4—1068no—
521C2×D4—1068no—
522C2×D4—10616no—
523C2×D4—10616no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—532no—
541C22×C4—534no—
542C22×C4—532no—
543C22×C4—532no—
544C22×C4—532no—
545C22×C4—532no—
546C22×C4—534no—
547C22×C4—532no—
548C22×C4—534no—
549C22×C4—534no—
550C22×C4—534no—
551C22×C4—534no—
552C22×C4—534no—
553C22×C4—534no—
554C22×C4—532no—
555C22×C4—1068no—
556C22×C4—10616no—
557C22×C4—1068no—
558C22×C4—10616no—
559C22×C4—1062no—
560C22×C4—1062no—
561C22×C4—1062no—
562C22×C4—1062no—
563C22×C4—1062no—
564C22×C4—1062no—
565C22×C4—1062no—
566C22×C4—1062no—
567C22×C4—1061no—
568C22×C4—1061no—
569C22×C4—1062no—
570C22×C4—1062no—
571C22×C4—1062no—
572C22×C4—1062no—
573C22×C4—2128no—
574C22×C4—2124no—
575C22×C4—2124no—
576C22×C4—2128no—
577C22×C4—2124no—
578C22×C4—2124no—
579C22×C4C2×C4×D5314yes—
580C22×C4C2×C4×D5312yes—
581C22×C4C2×C4×D5312yes—
582C22×C4C2×C4×D5314yes—
583C22×C4D4×D5312yes—
584C22×C4D4×D5312yes—
585C22×C4D4×D5314yes—
586C22×C4#1171994714yes—
587C4⋊C4—1068no—
588C4⋊C4—10616no—
589C22⋊C4—28no—
590C22⋊C4—216no—
591C22⋊C4—10616no—
592C22⋊C4—10616no—
593C22⋊C4—1068no—
594C22⋊C4—10616no—
595C42—28no—
596C42—5316no—
597C42—10616no—
598C42—10616no—
599C42—1068no—
600C42—2128no—
601C23—22no—
602C23—22no—
603C23—24no—
604C23—24no—
605C23—24no—
606C23—24no—
607C23—24no—
608C23—24no—
609C23—24no—
610C23—24no—
611C23—42no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—42no—
616C23—42no—
617C23—41no—
618C23—42no—
619C23—42no—
620C23—42no—
621C23—534no—
622C23—1062no—
623C23—1062no—
624C23—1064no—
625C23—1064no—
626C23—1064no—
627C23—1064no—
628C23—1064no—
629C23—1064no—
630C23—1064no—
631C23—1064no—
632C23—2122no—
633C23—2121no—
634C23—2121no—
635C23—2121no—
636C23—2122no—
637C23—2122no—
638C23—2121no—
639C23—2122no—
640C23—2122no—
641C23—2122no—
642C23C42×D5314yes—
643C23C22×C4×D5311yescharacteristic
644C23C22×C4×D5312yes—
645C23C2×D4×D5311yescharacteristic
646C23C2×D4×D5311yescharacteristic
647C23C2×D4×D5312yes—
648C23#41×D5312yes—
649C23#41×D5312yes—
650C23#41×D5312yes—
651C23C2×#1171994712yes—
652D4—10632no—
653C2×C4—24no—
654C2×C4—24no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—24no—
659C2×C4—22no—
660C2×C4—24no—
661C2×C4—24no—
662C2×C4—24no—
663C2×C4—22no—
664C2×C4—24no—
665C2×C4—24no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—42no—
669C2×C4—41no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—42no—
673C2×C4—42no—
674C2×C4—42no—
675C2×C4—534no—
676C2×C4—534no—
677C2×C4—534no—
678C2×C4—534no—
679C2×C4—538no—
680C2×C4—538no—
681C2×C4—538no—
682C2×C4—538no—
683C2×C4—534no—
684C2×C4—534no—
685C2×C4—538no—
686C2×C4—1064no—
687C2×C4—1064no—
688C2×C4—1064no—
689C2×C4—1064no—
690C2×C4—1064no—
691C2×C4—1064no—
692C2×C4—1062no—
693C2×C4—1064no—
694C2×C4—1064no—
695C2×C4—1064no—
696C2×C4—1064no—
697C2×C4—21216no—
698C2×C4—21216no—
699C2×C4—2122no—
700C2×C4—2121no—
701C2×C4—2122no—
702C2×C4—2121no—
703C2×C4—2122no—
704C2×C4—2122no—
705C2×C4—2122no—
706C2×C4C22⋊C4×D5314yes—
707C2×C4#1313317718yescomplemented
708C22—24no—
709C22—28no—
710C22—44no—
711C22—44no—
712C22—42no—
713C22—44no—
714C22—42no—
715C22—44no—
716C22—44no—
717C22—1064no—
718C22—1068no—
719C22—2124no—
720C22—2124no—
721C22—2122no—
722C22—2124no—
723C22—2122no—
724C22—2124no—
725C22—2124no—
726C22C2×C42×D5311yescharacteristic
727C22C2×C22⋊C4×D5311yescharacteristic
728C22#117×D5311yescharacteristic
729C22C4×D4×D5312yes—
730C22C4×D4×D5312yes—
731C22C4×D4×D5312yes—
732C22C4×D4×D5312yes—
733C22C2×#1313317712yes—
734C22C4×#1171994712yes—
735C22C4×#1171994712yes—
736C22#1681109112yes—
737C22#121×D5312yes—
738C22#1681112911yescharacteristic
739C22#1681113111yescharacteristic
740C22#124×D5311yescharacteristic
741C22#1681115012yes—
742C22#1681115612yes—
743C22#127×D5311yescharacteristic
744C22#1681116812yes—
745C22#1681116812yes—
746C22#1681117212yes—
747C4—24no—
748C4—28no—
749C4—44no—
750C4—42no—
751C4—538no—
752C4—538no—
753C4—1068no—
754C4—2124no—
755C4—2122no—
756C2—44no—
757C2—2124no—
758C2C4×C22⋊C4×D5311yescharacteristic
759C2C4×#1313317712yes—
760C2#390×D5311yescharacteristic
761C2#2027717512yes—
762C2#2027720011yescharacteristic
763C2#2027722512yes—
764C2#2027722712yes—
765C2#2027725612yes—
766C2#2027727912yes—
subgroupG/H
center, FrattiniC24C23×D53
commutatorC22×C53C22×C42
FittingC53×#1437C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenter#1437D53
hypocenterC53C4×#390
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
3. C2×#16810474C2semidirect
4. C2×C22⋊C4×Dic53C2semidirect
5. C2×#16810470C2semidirect
6. C2×C42×Dic53C2semidirect
7. #20272953C2semidirect
8. #20272952C2semidirect
9. #20272951C2semidirect
10. #20272943C2semidirect
11. C53×#1437C2semidirect
17. C2×#13133177C4semidirect
29. #16810523C4semidirect
70. C2×#11719919C2×C4semidirect
73. C2×C22⋊Dic53C2×C4semidirect
81. C2×#11719921C2×C4semidirect
82. C2×#11719921C2×C4semidirect
93. C2×C4×Dic53C2×C4semidirect
96. C2×C4×Dic53D4semidirect
111. C2×C22⋊C4×C53C2×C4semidirect
163. C2×C22⋊D53C42semidirect
216. C4×Dic53C22⋊C4semidirect
291. C2×C4×C53C4×D4semidirect
319. C2×Dic53C4×D4semidirect
371. Dic53C4×C22⋊C4semidirect
372. Dic53#390semidirect
382. #1437D53semidirect
426. C53C4×#390semidirect
477. C2×C22⋊C4C4×D53semidirect
707. C2×C4#13133177semidirect

Maximal subgroups

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

subgroupindex
C22×#131331772
C2×#168105232
C2×#168104742
C2×C22⋊C4×Dic532
C2×#168104702
C2×C42×Dic532
#202729532
#202729522
#202729512
#202729432
C53×#14372
C4×#39053