Finite Group Databasebeta

← #27307227

Subgroups — #27307227

Order 13568.

2106 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13133193C211yesmaximal, characteristic
2C2×#16810530C211yesmaximal, characteristic, complemented
3C2×#16810519C211yesmaximal, characteristic, complemented
4C2×#16810480C211yesmaximal, characteristic
5C2×C4×C4⋊Dic53C211yesmaximal, characteristic, complemented
6C2×C4×#11719921C211yesmaximal, characteristic
7#20272981C212yesmaximal, complemented
8#20272959C212yesmaximal
9#20272951C212yesmaximal
10#20272943C212yesmaximal, complemented
11C2×C53×#391C211yesmaximal, characteristic, complemented
12C23×C4×D53C2211yescharacteristic
13C2×#13133193—24no—
14C2×#13133193—24no—
15C2×#13133193C418yescomplemented
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×#11719919C2212yes—
19C22×#11719919C2212yes—
20C22×#11719921C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2212yes—
26#16810530—24no—
27#16810519—24no—
28#16810480—24no—
29C4×C4⋊Dic53—24no—
30C4×#11719921—24no—
31C2×#13133124C2211yescharacteristic
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2211yescharacteristic
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C23×Q8×C53C2211yescharacteristic
39C22×C4⋊C4×C53C2211yescharacteristic
40C22×C42×C53C2211yescharacteristic
41C53×#391—24no—
42C2×#95×C53C2212yes—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C23×Dic53C2311yescharacteristic
46C23×Dic53C2312yes—
47C23×Dic53C2311yescharacteristic
48C23×Dic53C2311yescharacteristic
49C23×Dic53C2312yes—
50C22×C4×D53—22no—
51C22×C4×D53—22no—
52C22×C4×D53—22no—
53C22×C4×D53—22no—
54C22×C4×D53—22no—
55C22×C4×D53—22no—
56C22×C4×D53C2×C414yes—
57#13133193—232no—
58C2×C4⋊Dic53—22no—
59C2×C4⋊Dic53—22no—
60C2×C4⋊Dic53C2×C414yes—
61C2×C4⋊Dic53D414yes—
62C2×C4⋊Dic53D414yes—
63C2×C4⋊Dic53D414yes—
64C2×#11719919—24no—
65C2×#11719919—24no—
66C2×#11719919—24no—
67C2×#11719919—24no—
68C2×#11719919—42no—
69C2×#11719919C2×C418yes—
70C2×#11719921—22no—
71C2×#11719921—24no—
72C2×#11719921—22no—
73C2×#11719921—22no—
74C2×#11719921—22no—
75C2×#11719921—24no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—22no—
79C2×#11719921—42no—
80C2×#11719921C2×C418yes—
81C2×#11719921Q814yescomplemented
82C2×C4×Dic53—22no—
83C2×C4×Dic53—22no—
84C2×C4×Dic53—22no—
85C2×C4×Dic53—24no—
86C2×C4×Dic53—24no—
87C2×C4×Dic53—42no—
88#13133124—22no—
89#13133124—22no—
90#13133124—24no—
91#13133124—24no—
92#13133124—24no—
93#13133124—24no—
94#13133124—24no—
95C22×Q8×C53—22no—
96C22×Q8×C53—22no—
97C22×Q8×C53—22no—
98C22×Q8×C53—22no—
99C22×Q8×C53—22no—
100C22×Q8×C53—22no—
101C22×Q8×C53C2×C414yes—
102C23×C4×C53C2312yes—
103C23×C4×C53C2312yes—
104C23×C4×C53C2311yescharacteristic
105C23×C4×C53C2311yescharacteristic
106C23×C4×C53C2311yescharacteristic
107C2×C4⋊C4×C53—22no—
108C2×C4⋊C4×C53—22no—
109C2×C4⋊C4×C53—22no—
110C2×C42×C53—22no—
111C2×C42×C53—22no—
112C2×C42×C53D414yes—
113#95×C53—24no—
114#95×C53—24no—
115C24×C53C2411yescharacteristic
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×D53—21no—
125C23×D53—21no—
126C23×D53—21no—
127C23×D53—21no—
128C23×D53C22×C412yes—
129C23×D53C2×Q812yes—
130C23×D53#4112yes—
131C2×Q8×C53—28no—
132C2×Q8×C53—28no—
133C2×Q8×C53—28no—
134C2×Q8×C53—44no—
135C2×Q8×C53—44no—
136C2×Q8×C53—44no—
137C2×Q8×C53—44no—
138C22×C4×C53—21no—
139C22×C4×C53—21no—
140C22×C4×C53—21no—
141C22×C4×C53—21no—
142C22×C4×C53—22no—
143C22×C4×C53—21no—
144C22×C4×C53—22no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—21no—
148C22×C4×C53—22no—
149C22×C4×C53—22no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—21no—
153C22×C4×C53—21no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—22no—
157C22×C4×C53—22no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53C22×C414yes—
162C22×C4×C53C22×C412yes—
163C22×C4×C53C2×D412yes—
164C22×C4×C53C2×D412yes—
165C22×C4×C53C2×D412yes—
166C22×C4×C53C2×D412yes—
167C22×C4×C53C2×D412yes—
168C22×C4×C53C2×D412yes—
169C22×C4×C53C2×Q812yes—
170C22×C4×C53#4112yes—
171C22×C4×C53#4112yes—
172C22×C4×C53#4112yes—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—22no—
177C22×Dic53—21no—
178C22×Dic53—21no—
179C22×Dic53—21no—
180C22×Dic53—21no—
181C22×Dic53—21no—
182C22×Dic53—21no—
183C22×Dic53—21no—
184C22×Dic53—22no—
185C22×Dic53—21no—
186C22×Dic53—21no—
187C22×Dic53—21no—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—21no—
194C22×Dic53—21no—
195C22×Dic53—22no—
196C22×Dic53—21no—
197C22×Dic53—22no—
198C22×Dic53—21no—
199C22×Dic53—21no—
200C22×Dic53—21no—
201C22×Dic53C22×C412yes—
202C22×Dic53C22×C414yes—
203C22×Dic53C2×D414yes—
204C22×Dic53C2×D414yes—
205C22×Dic53C2×D414yes—
206C22×Dic53C2×Q812yes—
207C22×Dic53#4112yes—
208C2×C4×D53—28no—
209C2×C4×D53—28no—
210C2×C4×D53—28no—
211C2×C4×D53—44no—
212C2×C4×D53—44no—
213C2×C4×D53—44no—
214C2×C4×D53—44no—
215C4⋊C4×C53—44no—
216C42×C53—28no—
217#11719921—28no—
218#11719921—28no—
219#11719921—216no—
220#11719921—48no—
221C4⋊Dic53—28no—
222C4⋊Dic53C22⋊C4116yescomplemented
223#11719919—216no—
224#11719919—48no—
225C4×Dic53—48no—
226C4×Dic53—44no—
227C23×C53C23×C411yescharacteristic
228C23×C53C22×D411yescharacteristic
229C23×C53C22×D411yescharacteristic
230C23×C53C22×D411yescharacteristic
231C23×C53C22×D411yescharacteristic
232C23×C53C22×Q811yescharacteristic
233C23×C53C2×#4111yescharacteristic
234C23×C53C2×#4111yescharacteristic
235C23×C53C2×#4111yescharacteristic
236C23×C53C2×#4111yescharacteristic
237C23×C53C2×#4111yescharacteristic
238C23×C53H(5,𝔽2)11yescharacteristic
239C23×C532−1+411yescharacteristic
240C23×C532−1+411yescharacteristic
241C23×C532−1+411yescharacteristic
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—22no—
252C22×D53—22no—
253C22×D53—22no—
254C22×D53—22no—
255C22×D53—22no—
256C22×D53—22no—
257C22×D53—22no—
258C22×D53—22no—
259C22×D53—22no—
260C22×D53—41no—
261C22×D53—41no—
262C22×D53—41no—
263C22×D53—41no—
264C22×D53—41no—
265C22×D53—41no—
266C22×D53—41no—
267C22×D53—41no—
268C22×D53—41no—
269C22×D53—41no—
270C22×D53—41no—
271C22×D53—41no—
272C22×D53—41no—
273C22×D53—41no—
274C22×D53—41no—
275C22×D53—41no—
276C22×D53C4×Q814yes—
277Q8×C53—416no—
278C2×C4×C53—22no—
279C2×C4×C53—22no—
280C2×C4×C53—22no—
281C2×C4×C53—22no—
282C2×C4×C53—22no—
283C2×C4×C53—22no—
284C2×C4×C53—24no—
285C2×C4×C53—24no—
286C2×C4×C53—24no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—42no—
291C2×C4×C53—42no—
292C2×C4×C53—42no—
293C2×C4×C53—42no—
294C2×C4×C53—41no—
295C2×C4×C53—41no—
296C2×C4×C53—41no—
297C2×C4×C53—41no—
298C2×C4×C53—42no—
299C2×C4×C53—42no—
300C2×C4×C53—42no—
301C2×C4×C53—42no—
302C2×C4×C53—42no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53C2×C22⋊C414yes—
306C2×C4×C53C4×D414yes—
307C2×C4×C53C4×D414yes—
308C2×C4×C53#12114yes—
309C2×C4×C53#12114yes—
310C2×C4×C53C22⋊Q814yescomplemented
311C2×C4×C53#12414yes—
312C2×C4×C53#12714yes—
313C2×Dic53—24no—
314C2×Dic53—24no—
315C2×Dic53—24no—
316C2×Dic53—24no—
317C2×Dic53—24no—
318C2×Dic53—24no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—24no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—24no—
326C2×Dic53—22no—
327C2×Dic53—24no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—22no—
331C2×Dic53—41no—
332C2×Dic53—41no—
333C2×Dic53—41no—
334C2×Dic53—42no—
335C2×Dic53—41no—
336C2×Dic53—41no—
337C2×Dic53—41no—
338C2×Dic53—41no—
339C2×Dic53—41no—
340C2×Dic53—42no—
341C2×Dic53—41no—
342C2×Dic53—42no—
343C2×Dic53—41no—
344C2×Dic53—41no—
345C2×Dic53—41no—
346C2×Dic53—42no—
347C2×Dic53C2×C22⋊C418yes—
348C4×D53—416no—
349#13997—531nomaximal, Sylow
350C22×C53C22×C22⋊C411yescharacteristic
351C22×C53C2×C4×D411yescharacteristic
352C22×C53C2×C4×D411yescharacteristic
353C22×C53C2×C4×Q811yescharacteristic
354C22×C53C4×#4111yescharacteristic
355C22×C53#51911yescharacteristic
356C22×C53#52011yescharacteristic
357C22×C53C2×#12111yescharacteristic
358C22×C53C2×#12111yescharacteristic
359C22×C53C2×C22⋊Q811yescharacteristic
360C22×C53#52511yescharacteristic
361C22×C53C2×#12411yescharacteristic
362C22×C53#52911yescharacteristic
363C22×C53C2×#12711yescharacteristic
364C22×C53#53311yescharacteristic
365C22×C53#53611yescharacteristic
366C22×C53#53711yescharacteristic
367C22×C53#54111yescharacteristic
368C22×C53#54211yescharacteristic
369C22×C53#54611yescharacteristic
370C22×C53#54611yescharacteristic
371C22×C53#54611yescharacteristic
372C22×C53#54711yescharacteristic
373C22×C53#54711yescharacteristic
374C22×C53#54711yescharacteristic
375C22×C53#54811yescharacteristic
376C22×C53#54811yescharacteristic
377C22×C53#54811yescharacteristic
378C22×C53D4×Q811yescharacteristic
379C22×C53D4×Q811yescharacteristic
380C22×C53D4×Q811yescharacteristic
381C22×C53#55211yescharacteristic
382C22×C53#55211yescharacteristic
383C22×C53#55411yescharacteristic
384C22×C53#55611yescharacteristic
385C2×D53—24no—
386C2×D53—24no—
387C2×D53—24no—
388C2×D53—42no—
389C2×D53—42no—
390C2×D53—42no—
391C2×D53—42no—
392C2×D53—42no—
393C2×D53—42no—
394C2×D53—42no—
395C2×D53—42no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C4×C53—24no—
401C4×C53—42no—
402C4×C53—44no—
403C4×C53—82no—
404C4×C53#39018yes—
405Dic53—28no—
406Dic53—44no—
407Dic53—42no—
408Dic53—42no—
409Dic53—42no—
410C22×C22⋊Q8—531no—
411C2×#391—531no—
412C2×#391D5311yescharacteristic, complemented
413C2×#389—531no—
414C2×#380—531no—
415C2×C4×C4⋊C4—531no—
416C2×C4×C22⋊C4—531no—
417#1445—532no—
418#1439—532no—
419#1437—532no—
420C4⋊#95—532no—
421C2×C53C2×#39011yescharacteristic
422C2×C53C4×C22⋊Q811yescharacteristic
423C2×C53#232311yescharacteristic
424C2×C53#233911yescharacteristic
425C2×C53Q8×C22⋊C411yescharacteristic
426C2×C53#236011yescharacteristic
427C2×C53#236211yescharacteristic
428C2×C53#241511yescharacteristic
429C2×C53#241711yescharacteristic
430C2×C53#242711yescharacteristic
431C2×C53#242911yescharacteristic
432C2×C53#248911yescharacteristic
433C2×C53#249211yescharacteristic
434C2×C53#254011yescharacteristic
435C2×C53#254211yescharacteristic
436D53—44no—
437C23×Q8C2×D5311yescharacteristic
438C24×C4—531no—
439C2×C22⋊Q8—538no—
440C2×C22⋊Q8—1064no—
441C2×C22⋊Q8—1064no—
442C22×C4⋊C4—531no—
443C22×C4⋊C4—532no—
444C22×C4⋊C4—531no—
445C22×C4⋊C4—532no—
446C22×C4⋊C4C2×D5311yescharacteristic
447C22×C22⋊C4—532no—
448C22×C22⋊C4—531no—
449C22×C22⋊C4—531no—
450C22×C22⋊C4—532no—
451C22×C42—531no—
452C22×C42—532no—
453C22×C42C2×D5311yescharacteristic
454#391—24no—
455#391—1064no—
456#389—1064no—
457#380—1064no—
458C4×C4⋊C4—1064no—
459C4×C22⋊C4—1064no—
460C2×#95—531no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C2×#95—532no—
465C2×#95—532no—
466C2×#95—531no—
467C2×#95C2×D5312yes—
468C2×#95C2×D5312yes—
469C53#1399711yescharacteristic, complemented, Sylow
470C25—531no—
471C22×Q8—22no—
472C22×Q8—22no—
473C22×Q8—22no—
474C22×Q8—22no—
475C22×Q8—22no—
476C22×Q8—22no—
477C22×Q8C4×D5314yes—
478C23×C4—532no—
479C23×C4—531no—
480C23×C4—532no—
481C23×C4—531no—
482C23×C4—531no—
483C23×C4—534no—
484C23×C4—1062no—
485C23×C4—1062no—
486C23×C4—1062no—
487C23×C4—1062no—
488C23×C4—1062no—
489C23×C4—1062no—
490C23×C4C22×D5312yes—
491C23×C4C22×D5312yes—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5311yescharacteristic
494C23×C4C22×D5311yescharacteristic
495C22⋊Q8—10632no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—22no—
499C2×C4⋊C4—534no—
500C2×C4⋊C4—534no—
501C2×C4⋊C4—534no—
502C2×C4⋊C4—538no—
503C2×C4⋊C4—534no—
504C2×C4⋊C4—1064no—
505C2×C4⋊C4—1064no—
506C2×C4⋊C4—1062no—
507C2×C4⋊C4—1062no—
508C2×C4⋊C4—1064no—
509C2×C4⋊C4—1064no—
510C2×C4⋊C4—2122no—
511C2×C22⋊C4—538no—
512C2×C22⋊C4—534no—
513C2×C22⋊C4—1064no—
514C2×C22⋊C4—1064no—
515C2×C22⋊C4—1062no—
516C2×C22⋊C4—1062no—
517C2×C22⋊C4—1062no—
518C2×C22⋊C4—1062no—
519C2×C22⋊C4—1062no—
520C2×C22⋊C4—1064no—
521C2×C22⋊C4—1064no—
522C2×C22⋊C4—2122no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—1064no—
526C2×C42—1062no—
527C2×C42—1062no—
528C2×C42—1064no—
529C2×C42—1062no—
530C2×C42—2122no—
531C2×C42C22⋊D5314yes—
532#95—24no—
533#95—24no—
534#95—1064no—
535#95—1064no—
536#95—1064no—
537#95—1064no—
538#95—1064no—
539#95—1062no—
540#95—1062no—
541C24—532no—
542C24—532no—
543C24—532no—
544C24—1061no—
545C24—1061no—
546C24—1061no—
547C24—1061no—
548C24—1061no—
549C24—1061no—
550C24—1061no—
551C24—1061no—
552C24—1061no—
553C24—1061no—
554C24—1061no—
555C24—1061no—
556C24C23×D5311yescharacteristic
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—44no—
561C2×Q8—44no—
562C2×Q8—44no—
563C2×Q8—44no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—534no—
588C22×C4—534no—
589C22×C4—534no—
590C22×C4—532no—
591C22×C4—534no—
592C22×C4—532no—
593C22×C4—532no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1061no—
599C22×C4—1061no—
600C22×C4—1061no—
601C22×C4—1061no—
602C22×C4—1062no—
603C22×C4—1061no—
604C22×C4—1061no—
605C22×C4—1061no—
606C22×C4—1061no—
607C22×C4—1061no—
608C22×C4—1061no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1061no—
612C22×C4—1062no—
613C22×C4—1061no—
614C22×C4—1062no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1061no—
618C22×C4—1061no—
619C22×C4—1062no—
620C22×C4—1061no—
621C22×C4—1061no—
622C22×C4—1068no—
623C22×C4—1068no—
624C22×C4—1068no—
625C22×C4—2124no—
626C22×C4—2124no—
627C22×C4—2124no—
628C22×C4—2124no—
629C22×C4C2×C4×D5314yes—
630C22×C4C2×C4×D5312yes—
631C22×C4#1171994512yes—
632C22×C4D4×D5312yes—
633C22×C4D4×D5312yes—
634C22×C4D4×D5312yes—
635C22×C4#1171994712yes—
636C22×C4Q8×D5312yes—
637C22×C4#1171994912yes—
638C22×C4C2×C22⋊D5312yes—
639C22×C4C2×C22⋊D5312yes—
640C22×C4C2×C22⋊D5312yes—
641C4⋊C4—44no—
642C4⋊C4—5316no—
643C4⋊C4—10616no—
644C4⋊C4—1068no—
645C4⋊C4—2128no—
646C22⋊C4—10616no—
647C22⋊C4—1068no—
648C22⋊C4—1068no—
649C22⋊C4—2128no—
650C42—28no—
651C42—2128no—
652C42—2124no—
653C23—534no—
654C23—1062no—
655C23—1062no—
656C23—1062no—
657C23—1062no—
658C23—1062no—
659C23—1062no—
660C23—1062no—
661C23—1062no—
662C23—1062no—
663C23—1062no—
664C23—1062no—
665C23—1062no—
666C23—1062no—
667C23—1062no—
668C23—1062no—
669C23—1062no—
670C23—1062no—
671C23—1062no—
672C23—2121no—
673C23—2121no—
674C23—2121no—
675C23—2121no—
676C23—2121no—
677C23—2121no—
678C23—2121no—
679C23—2121no—
680C23—2121no—
681C23—2121no—
682C23—2121no—
683C23—2121no—
684C23—2121no—
685C23—2121no—
686C23—2121no—
687C23—2121no—
688C23C22×C4×D5311yescharacteristic
689C23C2×D4×D5311yescharacteristic
690C23C2×D4×D5311yescharacteristic
691C23C2×D4×D5311yescharacteristic
692C23C22×C22⋊D5311yescharacteristic
693C23C2×Q8×D5311yescharacteristic
694C23#41×D5311yescharacteristic
695C23#41×D5311yescharacteristic
696C23C2×#1171994711yescharacteristic
697C23C2×#1171994511yescharacteristic
698C23C2×#1171994911yescharacteristic
699C23#1313326311yescharacteristic
700C23#1313326411yescharacteristic
701C23#1313326511yescharacteristic
702C23#1313326511yescharacteristic
703Q8—416no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—538no—
732C2×C4—1064no—
733C2×C4—1064no—
734C2×C4—1064no—
735C2×C4—1064no—
736C2×C4—1064no—
737C2×C4—1064no—
738C2×C4—1064no—
739C2×C4—1062no—
740C2×C4—1064no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1064no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—2122no—
751C2×C4—2121no—
752C2×C4—2121no—
753C2×C4—2121no—
754C2×C4—2121no—
755C2×C4—2122no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2121no—
759C2×C4—2122no—
760C2×C4—2121no—
761C2×C4—2121no—
762C2×C4—2121no—
763C2×C4—2121no—
764C2×C4—2121no—
765C2×C4—2122no—
766C2×C4—21216no—
767C2×C4C22⋊C4×D5314yes—
768C2×C4#1313317714yes—
769C2×C4C4×C22⋊D5314yes—
770C2×C4#1313318914yes—
771C2×C4#1313319014yes—
772C2×C4#1313319314yescomplemented
773C2×C4#1313320314yes—
774C2×C4#1313321314yes—
775C22—1064no—
776C22—1064no—
777C22—1064no—
778C22—2122no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22—2122no—
786C22—2122no—
787C22—2122no—
788C22—2122no—
789C22—2122no—
790C22C2×C22⋊C4×D5311yescharacteristic
791C22C2×#1313317711yescharacteristic
792C22C2×C4×C22⋊D5311yescharacteristic
793C22C4×Q8×D5311yescharacteristic
794C22C4×#1171994911yescharacteristic
795C22#1681109911yescharacteristic
796C22#1681110511yescharacteristic
797C22C2×#1313318911yescharacteristic
798C22C2×#1313319011yescharacteristic
799C22C2×#1313319311yescharacteristic
800C22#1681113011yescharacteristic
801C22C2×#1313320311yescharacteristic
802C22#1681116011yescharacteristic
803C22C2×#1313321311yescharacteristic
804C22#1681117711yescharacteristic
805C22#1681119711yescharacteristic
806C22#1681120111yescharacteristic
807C22#1681123111yescharacteristic
808C22#1681124511yescharacteristic
809C22#1681126411yescharacteristic
810C22#1681126611yescharacteristic
811C22#1681126611yescharacteristic
812C22#1681127511yescharacteristic
813C22#1681127611yescharacteristic
814C22#1681127611yescharacteristic
815C22#1681128111yescharacteristic
816C22#1681128111yescharacteristic
817C22#1681128311yescharacteristic
818C22#1681128611yescharacteristic
819C22#1681128811yescharacteristic
820C22#1681128811yescharacteristic
821C22#1681130711yescharacteristic
822C22#1681131511yescharacteristic
823C22#1681133111yescharacteristic
824C22#1681134411yescharacteristic
825C4—24no—
826C4—42no—
827C4—44no—
828C4—82no—
829C4—1068no—
830C4—2124no—
831C4—2122no—
832C4—2122no—
833C4—2122no—
834C4#1681052318yes—
835C2—2124no—
836C2C2×#1681052311yescharacteristic
837C2C4×#1313319311yescharacteristic
838C2#2027739111yescharacteristic
839C2#2027754411yescharacteristic
840C2#2027754911yescharacteristic
841C2#2027772511yescharacteristic
842C2#2027774711yescharacteristic
843C2#2027814511yescharacteristic
844C2#2027816711yescharacteristic
845C2#2027829311yescharacteristic
846C2#2027831511yescharacteristic
847C2#2027905711yescharacteristic
848C2#2027909011yescharacteristic
849C2#2027965511yescharacteristic
850C2#2027966911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#391C2
socle, cosocleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#391D53
hypocenterC53#13997
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
2. C2×#16810530C2semidirect
3. C2×#16810519C2semidirect
5. C2×C4×C4⋊Dic53C2semidirect
7. #20272981C2semidirect
10. #20272943C2semidirect
11. C2×C53×#391C2semidirect
15. C2×#13133193C4semidirect
81. C2×#11719921Q8semidirect
222. C4⋊Dic53C22⋊C4semidirect
310. C2×C4×C53C22⋊Q8semidirect
412. C2×#391D53semidirect
469. C53#13997semidirect
772. C2×C4#13133193semidirect

Maximal subgroups

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

subgroupindex
C22×#131331932
C2×#168105302
C2×#168105192
C2×#168104802
C2×C4×C4⋊Dic532
C2×C4×#117199212
#202729812
#202729592
#202729512
#202729432
C2×C53×#3912
#1399753