Finite Group Databasebeta

← #27305826

Subgroups — #27305826

Order 13568.

2574 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D53C211yesmaximal, characteristic
2C2×C4×#11719919C211yesmaximal, characteristic, complemented
3C2×C4×#11719921C211yesmaximal, characteristic, complemented
4C2×C4×#11719921C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic53C211yesmaximal, characteristic, complemented
6C2×#16810469C211yesmaximal, characteristic, complemented
7#20272981C212yesmaximal, complemented
8#20272959C212yesmaximal, complemented
9#20272958C212yesmaximal, complemented
10#20272954C212yesmaximal
11C2×C4×C22⋊C4×C53C211yesmaximal, characteristic, complemented
12C23×C22⋊D53C2211yescharacteristic
13C23×C4×D53C2211yescharacteristic
14C2×C4×C22⋊D53—24no—
15C2×C4×C22⋊D53—24no—
16C2×C4×C22⋊D53C418yescomplemented
17C22×#11719919C2212yes—
18C22×#11719919C2211yescharacteristic
19C22×C22⋊Dic53C2212yes—
20C22×C22⋊Dic53C2211yescharacteristic
21C22×#11719921C2212yes—
22C22×#11719921C2212yes—
23C22×#11719921C2211yescharacteristic
24C22×C4×Dic53C2211yescharacteristic
25C22×C4×Dic53C2211yescharacteristic
26C22×C4×Dic53C2211yescharacteristic
27C4×#11719919—24no—
28C4×#11719921—24no—
29C4×#11719921—24no—
30C4×C22⋊Dic53—24no—
31#16810469—24no—
32C2×#13133124C2212yes—
33C2×#13133124C2212yes—
34C2×#13133124C2212yes—
35C2×#13133124C2212yes—
36C2×#13133124C2212yes—
37C2×#13133124C2212yes—
38C24×C4×C53C2211yescharacteristic
39C22×C22⋊C4×C53C2212yes—
40C22×C42×C53C2211yescharacteristic
41C22×C42×C53C2211yescharacteristic
42C4×C22⋊C4×C53—24no—
43C2×#95×C53C2212yes—
44C24×D53C2311yescharacteristic
45C22×C22⋊D53—24no—
46C22×C22⋊D53—24no—
47C22×C22⋊D53—22no—
48C22×C22⋊D53—22no—
49C22×C22⋊D53C2×C414yes—
50C23×Dic53C2311yescharacteristic
51C23×Dic53C2312yes—
52C23×Dic53C2312yes—
53C23×Dic53C2311yescharacteristic
54C23×Dic53C2311yescharacteristic
55C22×C4×D53—22no—
56C22×C4×D53—22no—
57C22×C4×D53—22no—
58C22×C4×D53—22no—
59C22×C4×D53—22no—
60C22×C4×D53—22no—
61C22×C4×D53C2×C414yes—
62C4×C22⋊D53—232no—
63C2×#11719919—24no—
64C2×#11719919—22no—
65C2×#11719919—22no—
66C2×#11719919—24no—
67C2×#11719919—24no—
68C2×#11719919C2×C414yes—
69C2×C22⋊Dic53—24no—
70C2×C22⋊Dic53—22no—
71C2×C22⋊Dic53—22no—
72C2×C22⋊Dic53—24no—
73C2×C22⋊Dic53—24no—
74C2×C22⋊Dic53C2×C414yes—
75C2×#11719921—24no—
76C2×#11719921—24no—
77C2×#11719921—24no—
78C2×#11719921—24no—
79C2×#11719921—22no—
80C2×#11719921—22no—
81C2×#11719921—24no—
82C2×#11719921—24no—
83C2×#11719921C2×C414yes—
84C2×C4×Dic53—22no—
85C2×C4×Dic53—22no—
86C2×C4×Dic53—22no—
87C2×C4×Dic53—22no—
88C2×C4×Dic53—22no—
89C2×C4×Dic53C2×C414yes—
90C2×C4×Dic53D414yes—
91C2×C4×Dic53D414yes—
92C2×C4×Dic53D414yescomplemented
93#13133124—24no—
94#13133124—24no—
95#13133124—24no—
96#13133124—24no—
97#13133124—24no—
98#13133124—24no—
99C25×C53C2311yescharacteristic
100C23×C4×C53—22no—
101C23×C4×C53—22no—
102C23×C4×C53—22no—
103C23×C4×C53—22no—
104C23×C4×C53—22no—
105C23×C4×C53—22no—
106C23×C4×C53C2×C414yes—
107C23×C4×C53C2311yescharacteristic
108C23×C4×C53C2312yes—
109C23×C4×C53C2312yes—
110C23×C4×C53C2311yescharacteristic
111C2×C22⋊C4×C53—24no—
112C2×C22⋊C4×C53—24no—
113C2×C22⋊C4×C53—24no—
114C2×C42×C53—22no—
115C2×C42×C53—22no—
116C2×C42×C53—22no—
117C2×C42×C53—22no—
118C2×C42×C53—22no—
119C2×C42×C53D414yescomplemented
120#95×C53—24no—
121C24×C53—21no—
122C24×C53—21no—
123C24×C53—21no—
124C24×C53—21no—
125C24×C53—22no—
126C24×C53—21no—
127C24×C53—21no—
128C24×C53—22no—
129C24×C53—22no—
130C24×C53C22×C412yes—
131C24×C53#4114yes—
132C24×C53C2411yescharacteristic
133C23×D53—21no—
134C23×D53—21no—
135C23×D53—21no—
136C23×D53—21no—
137C23×D53—22no—
138C23×D53—22no—
139C23×D53—21no—
140C23×D53—21no—
141C23×D53—22no—
142C23×D53C22×C412yes—
143C23×D53#4114yes—
144C22×C4×C53—21no—
145C22×C4×C53—22no—
146C22×C4×C53—22no—
147C22×C4×C53—22no—
148C22×C4×C53—22no—
149C22×C4×C53—21no—
150C22×C4×C53—21no—
151C22×C4×C53—21no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
154C22×C4×C53—22no—
155C22×C4×C53—22no—
156C22×C4×C53—21no—
157C22×C4×C53—21no—
158C22×C4×C53—22no—
159C22×C4×C53—22no—
160C22×C4×C53—22no—
161C22×C4×C53—22no—
162C22×C4×C53—28no—
163C22×C4×C53—28no—
164C22×C4×C53—28no—
165C22×C4×C53—44no—
166C22×C4×C53—44no—
167C22×C4×C53—44no—
168C22×C4×C53—44no—
169C22×C4×C53C22×C412yes—
170C22×C4×C53C22×C412yes—
171C22×C4×C53C2×D414yes—
172C22×C4×C53C2×D412yes—
173C22×C4×C53C2×D412yes—
174C22×C4×C53C2×D412yes—
175C22×C4×C53C2×D412yes—
176C22×C4×C53#4114yes—
177C22×C4×C53#4112yes—
178C22×C4×C53#4112yes—
179C2×C22⋊D53—216no—
180C2×C22⋊D53—216no—
181C2×C22⋊D53—28no—
182C2×C22⋊D53—28no—
183C2×C22⋊D53—28no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—21no—
190C22×Dic53—21no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—21no—
195C22×Dic53—21no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53—22no—
199C22×Dic53—22no—
200C22×Dic53—22no—
201C22×Dic53—22no—
202C22×Dic53—22no—
203C22×Dic53—22no—
204C22×Dic53—21no—
205C22×Dic53—21no—
206C22×Dic53C22×C412yes—
207C22×Dic53C22×C412yes—
208C22×Dic53C22×C412yes—
209C22×Dic53C2×D414yes—
210C22×Dic53C2×D412yes—
211C22×Dic53C2×D412yes—
212C22×Dic53C2×D412yes—
213C22×Dic53C2×D412yes—
214C22×Dic53#4114yes—
215C2×C4×D53—28no—
216C2×C4×D53—28no—
217C2×C4×D53—28no—
218C2×C4×D53—44no—
219C2×C4×D53—44no—
220C2×C4×D53—44no—
221C2×C4×D53—44no—
222C22⋊C4×C53—216no—
223C42×C53—28no—
224C42×C53—44no—
225C22⋊Dic53—216no—
226C22⋊Dic53—28no—
227#11719921—216no—
228#11719921—216no—
229#11719921—28no—
230#11719919—216no—
231#11719919—28no—
232C4×Dic53—28no—
233C4×Dic53—44no—
234C4×Dic53C22⋊C4116yescomplemented
235C23×C53—22no—
236C23×C53—22no—
237C23×C53—22no—
238C23×C53—22no—
239C23×C53—22no—
240C23×C53—22no—
241C23×C53—24no—
242C23×C53—24no—
243C23×C53—24no—
244C23×C53—24no—
245C23×C53—24no—
246C23×C53—24no—
247C23×C53—41no—
248C23×C53—41no—
249C23×C53—42no—
250C23×C53—42no—
251C23×C53—42no—
252C23×C53—41no—
253C23×C53—42no—
254C23×C53—42no—
255C23×C53—41no—
256C23×C53—42no—
257C23×C53#11714yes—
258C23×C53C23×C411yescharacteristic
259C23×C53C22×D411yescharacteristic
260C23×C53C22×D411yescharacteristic
261C23×C53C22×D411yescharacteristic
262C23×C53C22×D411yescharacteristic
263C23×C53C2×#4112yes—
264C23×C53C2×#4112yes—
265C23×C53C2×#4111yescharacteristic
266C23×C53C2×#4112yes—
267C23×C53C2×#4111yescharacteristic
268C23×C53C2×#4112yes—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—22no—
272C22×D53—22no—
273C22×D53—22no—
274C22×D53—22no—
275C22×D53—24no—
276C22×D53—24no—
277C22×D53—24no—
278C22×D53—24no—
279C22×D53—24no—
280C22×D53—24no—
281C22×D53—41no—
282C22×D53—41no—
283C22×D53—42no—
284C22×D53—42no—
285C22×D53—42no—
286C22×D53—41no—
287C22×D53—42no—
288C22×D53—42no—
289C22×D53—41no—
290C22×D53—42no—
291C22×D53#11714yes—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—24no—
296C2×C4×C53—24no—
297C2×C4×C53—24no—
298C2×C4×C53—24no—
299C2×C4×C53—24no—
300C2×C4×C53—24no—
301C2×C4×C53—41no—
302C2×C4×C53—41no—
303C2×C4×C53—42no—
304C2×C4×C53—42no—
305C2×C4×C53—42no—
306C2×C4×C53—42no—
307C2×C4×C53—41no—
308C2×C4×C53—42no—
309C2×C4×C53—42no—
310C2×C4×C53—41no—
311C2×C4×C53—42no—
312C2×C4×C53—42no—
313C2×C4×C53—416no—
314C2×C4×C53C2×C22⋊C414yes—
315C2×C4×C53C4×D414yes—
316C2×C4×C53C4×D414yes—
317C2×C4×C53#12114yes—
318C2×C4×C53#12114yes—
319C2×C4×C53#12414yes—
320C2×C4×C53#12714yes—
321C22⋊D53—232no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—22no—
326C2×Dic53—24no—
327C2×Dic53—24no—
328C2×Dic53—24no—
329C2×Dic53—24no—
330C2×Dic53—22no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—24no—
334C2×Dic53—24no—
335C2×Dic53—24no—
336C2×Dic53—24no—
337C2×Dic53—24no—
338C2×Dic53—24no—
339C2×Dic53—41no—
340C2×Dic53—41no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—41no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53—41no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53C2×C22⋊C414yes—
352C2×Dic53C2×C22⋊C414yes—
353C4×D53—416no—
354#13847—531nomaximal, Sylow
355C22×C53—24no—
356C22×C53—24no—
357C22×C53—24no—
358C22×C53—44no—
359C22×C53—44no—
360C22×C53—44no—
361C22×C53—44no—
362C22×C53—42no—
363C22×C53—42no—
364C22×C53—42no—
365C22×C53—42no—
366C22×C53C22×C22⋊C411yescharacteristic
367C22×C53C2×#11711yescharacteristic
368C22×C53C2×#11711yescharacteristic
369C22×C53C2×C4×D411yescharacteristic
370C22×C53C2×C4×D411yescharacteristic
371C22×C53C4×#4111yescharacteristic
372C22×C53C4×#4111yescharacteristic
373C22×C53C2×#12111yescharacteristic
374C22×C53C2×#12111yescharacteristic
375C22×C53#52512yes—
376C22×C53#52512yes—
377C22×C53#52512yes—
378C22×C53#52512yes—
379C22×C53#52512yes—
380C22×C53#52512yes—
381C22×C53#52512yes—
382C22×C53C2×#12411yescharacteristic
383C22×C53#52912yes—
384C22×C53#52912yes—
385C22×C53#52912yes—
386C22×C53#52912yes—
387C22×C53C2×#12711yescharacteristic
388C22×C53#53212yes—
389C2×D53—24no—
390C2×D53—24no—
391C2×D53—24no—
392C2×D53—44no—
393C2×D53—44no—
394C2×D53—44no—
395C2×D53—44no—
396C2×D53—42no—
397C2×D53—42no—
398C2×D53—42no—
399C2×D53—42no—
400C4×C53—44no—
401C4×C53—44no—
402C4×C53—42no—
403C4×C53#39018yes—
404Dic53—24no—
405Dic53—24no—
406Dic53—44no—
407Dic53—44no—
408Dic53—42no—
409C22×C4×D4—531no—
410C2×C4×C4⋊C4—531no—
411C2×C4×C22⋊C4—531no—
412C2×C4×C22⋊C4—531no—
413C2×C4×C22⋊C4—531no—
414C2×C4×C22⋊C4D5311yescharacteristic, complemented
415C2×#376—531no—
416#1445—532no—
417#1439—532no—
418#1439—532no—
419#1438—532no—
420C2×C53—44no—
421C2×C53#228011yescharacteristic
422C2×C53#229011yescharacteristic
423C2×C53#229011yescharacteristic
424C2×C53#229011yescharacteristic
425C2×C53#229011yescharacteristic
426C2×C53C2×#39011yescharacteristic
427C2×C53#229711yescharacteristic
428C2×C53#239212yes—
429C2×C53#239212yes—
430C2×C53#239712yes—
431C2×C53#239812yes—
432D53—44no—
433C23×D4—531no—
434C24×C4—531no—
435C24×C4C2×D5311yescharacteristic
436C2×C4×D4—538no—
437C2×C4×D4—1064no—
438C2×C4×D4—1064no—
439C22×C4⋊C4—531no—
440C22×C4⋊C4—532no—
441C22×C22⋊C4—531no—
442C22×C22⋊C4—531no—
443C22×C22⋊C4—532no—
444C22×C22⋊C4—532no—
445C22×C22⋊C4—532no—
446C22×C22⋊C4C2×D5312yes—
447C22×C42—531no—
448C22×C42—531no—
449C22×C42—531no—
450C22×C42C2×D5311yescharacteristic
451C22×C42C2×D5311yescharacteristic
452C4×C4⋊C4—1064no—
453C4×C22⋊C4—24no—
454C4×C22⋊C4—1064no—
455C4×C22⋊C4—1064no—
456C4×C22⋊C4—1064no—
457#376—1064no—
458C2×#95—532no—
459C2×#95—532no—
460C2×#95—532no—
461C2×#95—532no—
462C2×#95—532no—
463C2×#95—532no—
464C2×#95C2×D5312yes—
465C53#1384711yescharacteristic, complemented, Sylow
466C25—531no—
467C25C22×D5311yescharacteristic
468C22×D4—534no—
469C22×D4—1062no—
470C22×D4—1062no—
471C22×D4—1064no—
472C22×D4—1064no—
473C23×C4—22no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—22no—
477C23×C4—22no—
478C23×C4—22no—
479C23×C4—531no—
480C23×C4—531no—
481C23×C4—532no—
482C23×C4—532no—
483C23×C4—531no—
484C23×C4—534no—
485C23×C4—1062no—
486C23×C4—1062no—
487C23×C4—1062no—
488C23×C4—1062no—
489C23×C4—1062no—
490C23×C4—1062no—
491C23×C4C4×D5314yes—
492C23×C4C22×D5311yescharacteristic
493C23×C4C22×D5312yes—
494C23×C4C22×D5312yes—
495C23×C4C22×D5311yescharacteristic
496C4×D4—10632no—
497C2×C4⋊C4—534no—
498C2×C4⋊C4—1062no—
499C2×C4⋊C4—1062no—
500C2×C4⋊C4—1064no—
501C2×C4⋊C4—1064no—
502C2×C4⋊C4—1064no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—534no—
507C2×C22⋊C4—534no—
508C2×C22⋊C4—1062no—
509C2×C22⋊C4—1062no—
510C2×C22⋊C4—1064no—
511C2×C22⋊C4—1064no—
512C2×C22⋊C4—1064no—
513C2×C22⋊C4—1064no—
514C2×C22⋊C4—1062no—
515C2×C22⋊C4—1062no—
516C2×C22⋊C4—1064no—
517C2×C22⋊C4—1064no—
518C2×C22⋊C4—1064no—
519C2×C22⋊C4—1064no—
520C2×C22⋊C4—1064no—
521C2×C42—22no—
522C2×C42—22no—
523C2×C42—22no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—534no—
527C2×C42—534no—
528C2×C42—534no—
529C2×C42—534no—
530C2×C42—1062no—
531C2×C42—1062no—
532C2×C42—1062no—
533C2×C42—1062no—
534C2×C42—1062no—
535C2×C42C22⋊D5314yescomplemented
536#95—24no—
537#95—1064no—
538#95—1064no—
539#95—1064no—
540#95—1064no—
541#95—1064no—
542#95—1064no—
543C24—21no—
544C24—21no—
545C24—21no—
546C24—21no—
547C24—22no—
548C24—22no—
549C24—21no—
550C24—22no—
551C24—21no—
552C24—532no—
553C24—534no—
554C24—1061no—
555C24—1061no—
556C24—1061no—
557C24—1061no—
558C24—1062no—
559C24—1061no—
560C24—1062no—
561C24—1061no—
562C24—1062no—
563C24C2×C4×D5312yes—
564C24#1171994514yes—
565C24C23×D5311yescharacteristic
566C2×D4—1068no—
567C2×D4—1068no—
568C2×D4—10616no—
569C2×D4—10616no—
570C2×D4—1068no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—21no—
589C22×C4—28no—
590C22×C4—28no—
591C22×C4—28no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—44no—
596C22×C4—532no—
597C22×C4—532no—
598C22×C4—532no—
599C22×C4—532no—
600C22×C4—532no—
601C22×C4—532no—
602C22×C4—532no—
603C22×C4—534no—
604C22×C4—534no—
605C22×C4—1062no—
606C22×C4—1062no—
607C22×C4—1062no—
608C22×C4—1062no—
609C22×C4—1062no—
610C22×C4—1061no—
611C22×C4—1062no—
612C22×C4—1062no—
613C22×C4—1061no—
614C22×C4—1061no—
615C22×C4—1061no—
616C22×C4—1062no—
617C22×C4—1062no—
618C22×C4—1062no—
619C22×C4—1062no—
620C22×C4—1061no—
621C22×C4—1062no—
622C22×C4—1062no—
623C22×C4—1062no—
624C22×C4—1062no—
625C22×C4—1062no—
626C22×C4—1061no—
627C22×C4—1068no—
628C22×C4—1068no—
629C22×C4—1068no—
630C22×C4—2124no—
631C22×C4—2124no—
632C22×C4—2124no—
633C22×C4—2124no—
634C22×C4C2×C4×D5312yes—
635C22×C4C2×C4×D5312yes—
636C22×C4#1171994514yes—
637C22×C4#1171994512yes—
638C22×C4D4×D5312yes—
639C22×C4D4×D5312yes—
640C22×C4D4×D5312yes—
641C22×C4#1171994712yes—
642C22×C4C2×C22⋊D5314yes—
643C22×C4C2×C22⋊D5312yes—
644C4⋊C4—1068no—
645C4⋊C4—10616no—
646C22⋊C4—216no—
647C22⋊C4—1068no—
648C22⋊C4—10616no—
649C22⋊C4—10616no—
650C22⋊C4—1068no—
651C22⋊C4—10616no—
652C42—28no—
653C42—44no—
654C42—5316no—
655C42—1068no—
656C42—2124no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—24no—
664C23—24no—
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—41no—
670C23—41no—
671C23—42no—
672C23—42no—
673C23—42no—
674C23—41no—
675C23—42no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—534no—
680C23—1062no—
681C23—1062no—
682C23—1062no—
683C23—1062no—
684C23—1062no—
685C23—1062no—
686C23—1064no—
687C23—1064no—
688C23—1064no—
689C23—1064no—
690C23—1064no—
691C23—1064no—
692C23—2121no—
693C23—2121no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23—2121no—
698C23—2122no—
699C23—2122no—
700C23—2121no—
701C23—2122no—
702C23#1313317414yes—
703C23C22×C4×D5311yescharacteristic
704C23C2×D4×D5311yescharacteristic
705C23C2×D4×D5311yescharacteristic
706C23C2×D4×D5311yescharacteristic
707C23C22×C22⋊D5311yescharacteristic
708C23#41×D5312yes—
709C23#41×D5312yes—
710C23C2×#1171994711yescharacteristic
711C23C2×#1171994512yes—
712C23C2×#1171994511yescharacteristic
713C23C2×#1171994512yes—
714D4—10632no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—24no—
721C2×C4—24no—
722C2×C4—24no—
723C2×C4—24no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—41no—
735C2×C4—42no—
736C2×C4—416no—
737C2×C4—534no—
738C2×C4—534no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1064no—
744C2×C4—1064no—
745C2×C4—1064no—
746C2×C4—1064no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—1062no—
750C2×C4—1064no—
751C2×C4—1064no—
752C2×C4—1064no—
753C2×C4—1064no—
754C2×C4—1064no—
755C2×C4—1064no—
756C2×C4—2121no—
757C2×C4—2121no—
758C2×C4—2122no—
759C2×C4—2122no—
760C2×C4—2122no—
761C2×C4—2122no—
762C2×C4—2121no—
763C2×C4—2122no—
764C2×C4—2122no—
765C2×C4—2122no—
766C2×C4—2121no—
767C2×C4—2122no—
768C2×C4—21216no—
769C2×C4C22⋊C4×D5314yes—
770C2×C4#1313317714yes—
771C2×C4C4×C22⋊D5314yes—
772C2×C4#1313318914yes—
773C2×C4#1313319014yes—
774C2×C4#1313320314yes—
775C2×C4#1313321314yes—
776C22—24no—
777C22—24no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—1064no—
788C22—1064no—
789C22—1064no—
790C22—2122no—
791C22—2122no—
792C22—2122no—
793C22—2124no—
794C22—2124no—
795C22—2122no—
796C22—2124no—
797C22—2124no—
798C22C2×C22⋊C4×D5311yescharacteristic
799C22#117×D5311yescharacteristic
800C22C2×#1313317411yescharacteristic
801C22C2×#1313317711yescharacteristic
802C22C2×C4×C22⋊D5311yescharacteristic
803C22#1681109111yescharacteristic
804C22C4×#1171994511yescharacteristic
805C22C2×#1313318911yescharacteristic
806C22C2×#1313319011yescharacteristic
807C22#1681113012yes—
808C22#1681113212yes—
809C22#1681113212yes—
810C22#1681113212yes—
811C22#1681113212yes—
812C22#1681113212yes—
813C22#1681113412yes—
814C22C2×#1313320311yescharacteristic
815C22#1681115112yes—
816C22#1681115312yes—
817C22#1681115512yes—
818C22#1681115712yes—
819C22C2×#1313321311yescharacteristic
820C22#1681117012yes—
821C4—42no—
822C4—44no—
823C4—44no—
824C4—1064no—
825C4—1064no—
826C4—2122no—
827C4—2124no—
828C4—2124no—
829C4#1681052318yes—
830C2—44no—
831C2—2124no—
832C2#2027709611yescharacteristic
833C2#2027715211yescharacteristic
834C2#2027715411yescharacteristic
835C2#2027715811yescharacteristic
836C2#2027716111yescharacteristic
837C2C2×#1681052311yescharacteristic
838C2#2027720111yescharacteristic
839C2#2027795712yes—
840C2#2027795912yes—
841C2#2027799412yes—
842C2#2027800212yes—
subgroupG/H
centerC23×C4C22×D53
commutatorC23×C53C23×C4
FrattiniC24C23×D53
FittingC2×C4×C22⋊C4×C53C2
socle, cosocleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×C4×C22⋊C4D53
hypocenterC53#13847
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C4×#11719919C2semidirect
3. C2×C4×#11719921C2semidirect
4. C2×C4×#11719921C2semidirect
5. C2×C4×C22⋊Dic53C2semidirect
6. C2×#16810469C2semidirect
7. #20272981C2semidirect
8. #20272959C2semidirect
9. #20272958C2semidirect
11. C2×C4×C22⋊C4×C53C2semidirect
16. C2×C4×C22⋊D53C4semidirect
92. C2×C4×Dic53D4semidirect
119. C2×C42×C53D4semidirect
234. C4×Dic53C22⋊C4semidirect
414. C2×C4×C22⋊C4D53semidirect
465. C53#13847semidirect
535. C2×C42C22⋊D53semidirect

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×C4×#117199192
C2×C4×#117199212
C2×C4×C22⋊Dic532
C2×#168104692
#202729812
#202729592
#202729582
#202729542
C2×C4×C22⋊C4×C532
#1384753