Finite Group Databasebeta

← #394×Dic53 #27305889

Subgroups — #394×Dic53 #27305889

Order 13568.

2550 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic53C211yesmaximal, characteristic
2C2×C4⋊C4×Dic53C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×Dic53C212yesmaximal, complemented
4C2×C22⋊C4×Dic53C212yesmaximal, complemented
5#20272972C211yesmaximal, characteristic, complemented
6#20272968C211yesmaximal, characteristic, complemented
7#20272964C212yesmaximal, complemented
8#20272960C212yesmaximal, complemented
9#20272956C211yesmaximal, characteristic
10#95×Dic53C211yesmaximal, characteristic, complemented
11C2×C53×#394C211yesmaximal, characteristic
12C24×Dic53C2212yes—
13C2×D4×Dic53—28no—
14C2×D4×Dic53—24no—
15C22×C4⋊Dic53C2211yescharacteristic
16C22×C4⋊Dic53C2211yescharacteristic
17C22×C22⋊Dic53C2212yes—
18C22×C22⋊Dic53C2212yes—
19C22×C22⋊Dic53C2212yes—
20C22×C4×Dic53C2212yes—
21C22×C4×Dic53C2211yescharacteristic
22C22×C4×Dic53C2211yescharacteristic
23C22×C4×Dic53C2211yescharacteristic
24C4⋊C4×Dic53—24no—
25C22⋊C4×Dic53—28no—
26C22⋊C4×Dic53—28no—
27C2×#13133124C2211yescharacteristic
28C2×#13133124C2212yes—
29C2×#13133124C2212yes—
30C2×#13133124C2212yes—
31C2×#13133124C2212yes—
32C2×#13133124C2212yes—
33C2×#13133124C2211yescharacteristic
34C2×#13133124C2211yescharacteristic
35C23×D4×C53C2211yescharacteristic
36C22×C4⋊C4×C53C2211yescharacteristic
37C22×C22⋊C4×C53C2212yes—
38C22×C22⋊C4×C53C2212yes—
39C53×#394C418yescomplemented
40C2×#95×C53C2211yescharacteristic
41C23×Dic53—24no—
42C23×Dic53—24no—
43C23×Dic53—24no—
44C23×Dic53—24no—
45C23×Dic53—24no—
46C23×Dic53—24no—
47C23×Dic53D418yes—
48C23×Dic53C2311yescharacteristic
49C23×Dic53C2311yescharacteristic
50C23×Dic53C2312yes—
51C23×Dic53C2311yescharacteristic
52C23×Dic53C2312yes—
53C23×Dic53C2311yescharacteristic
54D4×Dic53—232no—
55C2×C4⋊Dic53—22no—
56C2×C4⋊Dic53—22no—
57C2×C4⋊Dic53—24no—
58C2×C4⋊Dic53—22no—
59C2×C4⋊Dic53—22no—
60C2×C22⋊Dic53—24no—
61C2×C22⋊Dic53—24no—
62C2×C22⋊Dic53—24no—
63C2×C22⋊Dic53—24no—
64C2×C22⋊Dic53—24no—
65C2×C22⋊Dic53—24no—
66C2×C22⋊Dic53—24no—
67C2×C22⋊Dic53—24no—
68C2×C22⋊Dic53—24no—
69C2×C4×Dic53—24no—
70C2×C4×Dic53—22no—
71C2×C4×Dic53—24no—
72C2×C4×Dic53—24no—
73C2×C4×Dic53—24no—
74C2×C4×Dic53—22no—
75C2×C4×Dic53—22no—
76C2×C4×Dic53—24no—
77C2×C4×Dic53D414yes—
78C2×C4×Dic53D414yescomplemented
79#13133124—24no—
80#13133124—22no—
81#13133124—22no—
82#13133124—24no—
83#13133124—24no—
84#13133124—24no—
85#13133124—22no—
86#13133124—24no—
87C25×C53C2312yes—
88C22×D4×C53—24no—
89C22×D4×C53—24no—
90C22×D4×C53—22no—
91C22×D4×C53—22no—
92C22×D4×C53C2×C414yes—
93C23×C4×C53C2311yescharacteristic
94C23×C4×C53C2312yes—
95C23×C4×C53C2311yescharacteristic
96C23×C4×C53C2311yescharacteristic
97C2×C4⋊C4×C53—22no—
98C2×C4⋊C4×C53—22no—
99C2×C4⋊C4×C53C2×C414yescomplemented
100C2×C22⋊C4×C53—24no—
101C2×C22⋊C4×C53—24no—
102C2×C22⋊C4×C53—24no—
103C2×C22⋊C4×C53—24no—
104C2×C22⋊C4×C53C2×C418yescomplemented
105C2×C22⋊C4×C53C2×C418yescomplemented
106#95×C53C2×C414yescomplemented
107C24×C53—22no—
108C24×C53—22no—
109C24×C53—22no—
110C24×C53—22no—
111C24×C53—22no—
112C24×C53—22no—
113C24×C53—22no—
114C24×C53—22no—
115C24×C53—22no—
116C24×C53—22no—
117C24×C53—22no—
118C24×C53—22no—
119C24×C53C22×C414yes—
120C24×C53C2×D414yes—
121C24×C53#4114yes—
122C24×C53C2411yescharacteristic
123C2×D4×C53—28no—
124C2×D4×C53—216no—
125C2×D4×C53—28no—
126C2×D4×C53—216no—
127C2×D4×C53—28no—
128C22×C4×C53—21no—
129C22×C4×C53—22no—
130C22×C4×C53—21no—
131C22×C4×C53—22no—
132C22×C4×C53—21no—
133C22×C4×C53—21no—
134C22×C4×C53—22no—
135C22×C4×C53—22no—
136C22×C4×C53—22no—
137C22×C4×C53—21no—
138C22×C4×C53—22no—
139C22×C4×C53—22no—
140C22×C4×C53—22no—
141C22×C4×C53—21no—
142C22×C4×C53—22no—
143C22×C4×C53—22no—
144C22×C4×C53C22×C414yes—
145C22×C4×C53C22×C412yes—
146C22×C4×C53C22×C412yes—
147C22×C4×C53C22×C412yes—
148C22×C4×C53C2×D412yes—
149C22×C4×C53C2×D412yes—
150C22×C4×C53#4112yes—
151C22×C4×C53#4112yes—
152C22×Dic53—21no—
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—21no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—21no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53—22no—
167C22×Dic53—22no—
168C22×Dic53—22no—
169C22×Dic53—22no—
170C22×Dic53—21no—
171C22×Dic53—21no—
172C22×Dic53—21no—
173C22×Dic53—22no—
174C22×Dic53—22no—
175C22×Dic53—22no—
176C22×Dic53—216no—
177C22×Dic53—216no—
178C22×Dic53—216no—
179C22×Dic53—48no—
180C22×Dic53—48no—
181C22×Dic53—48no—
182C22×Dic53—48no—
183C22×Dic53C2×D412yes—
184C22×Dic53C2×D414yes—
185C22×Dic53C2×D412yes—
186C22×Dic53C2×D414yes—
187C22×Dic53C2×D412yes—
188C22×Dic53C2×D412yes—
189C22×Dic53#4114yes—
190C22×Dic53#4112yes—
191C22×Dic53#4112yes—
192C22×Dic53#4114yes—
193C4⋊C4×C53—28no—
194C22⋊C4×C53—216no—
195C22⋊C4×C53—216no—
196C22⋊Dic53—216no—
197C22⋊Dic53—216no—
198C22⋊Dic53—216no—
199C4⋊Dic53—28no—
200C4⋊Dic53—28no—
201C4×Dic53—28no—
202C4×Dic53—28no—
203C4×Dic53—44no—
204C4×Dic53—48no—
205C23×C53—24no—
206C23×C53—24no—
207C23×C53—24no—
208C23×C53—24no—
209C23×C53—24no—
210C23×C53—24no—
211C23×C53—24no—
212C23×C53—24no—
213C23×C53—24no—
214C23×C53—24no—
215C23×C53—24no—
216C23×C53—24no—
217C23×C53—24no—
218C23×C53—24no—
219C23×C53—24no—
220C23×C53—24no—
221C23×C53—24no—
222C23×C53—24no—
223C23×C53—42no—
224C23×C53—42no—
225C23×C53—42no—
226C23×C53—42no—
227C23×C53—42no—
228C23×C53—42no—
229C23×C53—42no—
230C23×C53—42no—
231C23×C53—42no—
232C23×C53—42no—
233C23×C53—42no—
234C23×C53—42no—
235C23×C53—42no—
236C23×C53—42no—
237C23×C53—42no—
238C23×C53—42no—
239C23×C53C4×D418yes—
240C23×C53C23×C411yescharacteristic
241C23×C53C22×D412yes—
242C23×C53C22×D411yescharacteristic
243C23×C53C22×D411yescharacteristic
244C23×C53C2×#4111yescharacteristic
245C23×C53C2×#4112yes—
246C23×C53C2×#4111yescharacteristic
247C23×C53C2×#4112yes—
248C23×C53C2×#4112yes—
249C23×C53C2×#4111yescharacteristic
250C23×C53C2×#4111yescharacteristic
251D4×C53—232no—
252C2×C4×C53—24no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—22no—
257C2×C4×C53—22no—
258C2×C4×C53—24no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—24no—
263C2×C4×C53—24no—
264C2×C4×C53—24no—
265C2×C4×C53—22no—
266C2×C4×C53—24no—
267C2×C4×C53—41no—
268C2×C4×C53—42no—
269C2×C4×C53—42no—
270C2×C4×C53—41no—
271C2×C4×C53—42no—
272C2×C4×C53—42no—
273C2×C4×C53—42no—
274C2×C4×C53C4×D414yes—
275C2×C4×C53C4×D414yescomplemented
276C2×Dic53—24no—
277C2×Dic53—22no—
278C2×Dic53—24no—
279C2×Dic53—22no—
280C2×Dic53—24no—
281C2×Dic53—22no—
282C2×Dic53—24no—
283C2×Dic53—22no—
284C2×Dic53—24no—
285C2×Dic53—24no—
286C2×Dic53—24no—
287C2×Dic53—24no—
288C2×Dic53—22no—
289C2×Dic53—41no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294C2×Dic53—42no—
295C2×Dic53—41no—
296C2×Dic53—42no—
297C2×Dic53—42no—
298C2×Dic53—42no—
299C2×Dic53—42no—
300C2×Dic53—42no—
301C2×Dic53—42no—
302C2×Dic53—42no—
303C2×Dic53—41no—
304C2×Dic53—41no—
305C2×Dic53—432no—
306C2×Dic53#12014yes—
307C2×Dic53#12118yes—
308C2×Dic53#12114yes—
309C2×Dic53#12318yes—
310C2×Dic53#12414yes—
311C4×#394—531nomaximal, Sylow
312C22×C53—28no—
313C22×C53—28no—
314C22×C53—28no—
315C22×C53—44no—
316C22×C53—44no—
317C22×C53—44no—
318C22×C53—44no—
319C22×C53—44no—
320C22×C53—44no—
321C22×C53—44no—
322C22×C53—44no—
323C22×C53—44no—
324C22×C53—44no—
325C22×C53—44no—
326C22×C53—44no—
327C22×C53C2×C4×D412yes—
328C22×C53C2×C4×D411yescharacteristic
329C22×C53C2×C4×D411yescharacteristic
330C22×C53C4×#4111yescharacteristic
331C22×C53C4×#4112yes—
332C22×C53C2×#12011yescharacteristic
333C22×C53C2×#12111yescharacteristic
334C22×C53C2×#12112yes—
335C22×C53C2×#12312yes—
336C22×C53#52512yes—
337C22×C53#52511yescharacteristic
338C22×C53#52512yes—
339C22×C53#52511yescharacteristic
340C22×C53#52512yes—
341C22×C53C2×#12411yescharacteristic
342C22×C53#52912yes—
343C22×C53#52912yes—
344C22×C53#52912yes—
345C22×C53#52911yescharacteristic
346C22×C53#52912yes—
347C22×C53#53212yes—
348C22×C53#53211yescharacteristic
349C22×C53#53211yescharacteristic
350C4×C53—24no—
351C4×C53—24no—
352C4×C53—42no—
353C4×C53—44no—
354Dic53—44no—
355Dic53—42no—
356Dic53—42no—
357Dic53—42no—
358Dic53—44no—
359Dic53#39418yesdirect product factor
360C22×C4×D4—531no—
361C2×#394D5311yescharacteristic
362C2×C4×C4⋊C4—531no—
363C2×C4×C22⋊C4—532no—
364C2×C4×C22⋊C4—532no—
365#1442—531no—
366#1441—531no—
367#1440—532no—
368#1439—532no—
369#1438—531no—
370C4×#95—531no—
371C2×C53—48no—
372C2×C53C4×#12011yescharacteristic
373C2×C53C4×#12111yescharacteristic
374C2×C53C4×#12112yes—
375C2×C53C4×#12312yes—
376C2×C53C4×#12411yescharacteristic
377C2×C53C2×#39411yescharacteristic
378C2×C53#238811yescharacteristic
379C2×C53#239211yescharacteristic
380C2×C53#239212yes—
381C2×C53#239512yes—
382C2×C53#239811yescharacteristic
383C23×D4C2×D5311yescharacteristic
384C24×C4—532no—
385C2×C4×D4—1064no—
386C2×C4×D4—1068no—
387C22×C4⋊C4—531no—
388C22×C4⋊C4—531no—
389C22×C4⋊C4C2×D5311yescharacteristic
390C22×C22⋊C4—532no—
391C22×C22⋊C4—532no—
392C22×C22⋊C4—532no—
393C22×C22⋊C4C2×D5312yes—
394C22×C22⋊C4C2×D5312yes—
395C22×C42—531no—
396C22×C42—531no—
397C22×C42—532no—
398C22×C42—531no—
399#394Dic5318yesdirect product factor
400C4×C4⋊C4—1064no—
401C4×C22⋊C4—1068no—
402C4×C22⋊C4—1068no—
403C2×#95—531no—
404C2×#95—532no—
405C2×#95—531no—
406C2×#95—532no—
407C2×#95—532no—
408C2×#95—531no—
409C2×#95—532no—
410C2×#95—532no—
411C2×#95C2×D5311yescharacteristic
412C53C4×#39411yescharacteristic, complemented, Sylow
413C25C22×D5312yes—
414C22×D4—24no—
415C22×D4—24no—
416C22×D4—22no—
417C22×D4—22no—
418C22×D4C2×Dic5314yes—
419C23×C4—531no—
420C23×C4—538no—
421C23×C4—531no—
422C23×C4—531no—
423C23×C4—531no—
424C23×C4—532no—
425C23×C4—532no—
426C23×C4—1064no—
427C23×C4—1064no—
428C23×C4—1064no—
429C23×C4—1064no—
430C23×C4—1064no—
431C23×C4—1064no—
432C23×C4C22×D5311yescharacteristic
433C23×C4C22×D5312yes—
434C23×C4C22×D5311yescharacteristic
435C23×C4C22×D5311yescharacteristic
436C4×D4—10632no—
437C2×C4⋊C4—22no—
438C2×C4⋊C4—22no—
439C2×C4⋊C4—1064no—
440C2×C4⋊C4—1062no—
441C2×C4⋊C4—1062no—
442C2×C4⋊C4—1062no—
443C2×C4⋊C4—1062no—
444C2×C4⋊C4C2×Dic5314yescomplemented
445C2×C22⋊C4—24no—
446C2×C22⋊C4—24no—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—24no—
449C2×C22⋊C4—1064no—
450C2×C22⋊C4—1064no—
451C2×C22⋊C4—1064no—
452C2×C22⋊C4—1064no—
453C2×C22⋊C4—1064no—
454C2×C22⋊C4—1064no—
455C2×C22⋊C4—1064no—
456C2×C22⋊C4—1064no—
457C2×C22⋊C4—1064no—
458C2×C22⋊C4C2×Dic5318yescomplemented
459C2×C22⋊C4C2×Dic5318yescomplemented
460C2×C42—534no—
461C2×C42—534no—
462C2×C42—1064no—
463C2×C42—1062no—
464C2×C42—1062no—
465C2×C42—1064no—
466C2×C42—1064no—
467C2×C42—1064no—
468C2×C42—1062no—
469C2×C42—1064no—
470#95—1064no—
471#95—1064no—
472#95—1064no—
473#95—1064no—
474#95—1062no—
475#95—1064no—
476#95—1062no—
477#95—1062no—
478#95C2×Dic5314yescomplemented
479C24—22no—
480C24—22no—
481C24—22no—
482C24—22no—
483C24—22no—
484C24—22no—
485C24—22no—
486C24—22no—
487C24—22no—
488C24—22no—
489C24—22no—
490C24—22no—
491C24D4×D5314yes—
492C24#1171994714yes—
493C24C22×Dic5314yes—
494C24C23×D5311yescharacteristic
495C2×D4—28no—
496C2×D4—28no—
497C2×D4—216no—
498C2×D4—216no—
499C2×D4—28no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—21no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—21no—
516C22×C4—532no—
517C22×C4—532no—
518C22×C4—534no—
519C22×C4—532no—
520C22×C4—534no—
521C22×C4—532no—
522C22×C4—534no—
523C22×C4—532no—
524C22×C4—534no—
525C22×C4—532no—
526C22×C4—10616no—
527C22×C4—10616no—
528C22×C4—10616no—
529C22×C4—1061no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1061no—
535C22×C4—1062no—
536C22×C4—1062no—
537C22×C4—1062no—
538C22×C4—1062no—
539C22×C4—1061no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1061no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1061no—
552C22×C4—1061no—
553C22×C4—2128no—
554C22×C4—2128no—
555C22×C4—2128no—
556C22×C4—2128no—
557C22×C4D4×D5312yes—
558C22×C4D4×D5312yes—
559C22×C4#1171994712yes—
560C22×C4#1171994712yes—
561C22×C4C22×Dic5314yes—
562C22×C4C22×Dic5312yes—
563C22×C4C22×Dic5312yes—
564C22×C4C22×Dic5312yes—
565C4⋊C4—28no—
566C4⋊C4—1068no—
567C4⋊C4—1068no—
568C22⋊C4—216no—
569C22⋊C4—216no—
570C22⋊C4—10616no—
571C22⋊C4—10616no—
572C22⋊C4—10616no—
573C42—1068no—
574C42—1068no—
575C42—2124no—
576C42—2128no—
577C23—24no—
578C23—24no—
579C23—24no—
580C23—24no—
581C23—24no—
582C23—24no—
583C23—24no—
584C23—24no—
585C23—24no—
586C23—24no—
587C23—24no—
588C23—24no—
589C23—24no—
590C23—24no—
591C23—24no—
592C23—24no—
593C23—24no—
594C23—24no—
595C23—42no—
596C23—42no—
597C23—42no—
598C23—42no—
599C23—42no—
600C23—42no—
601C23—42no—
602C23—42no—
603C23—42no—
604C23—42no—
605C23—42no—
606C23—42no—
607C23—42no—
608C23—42no—
609C23—42no—
610C23—42no—
611C23D4×Dic5318yes—
612C23C23×Dic5311yescharacteristic
613C23C2×D4×D5312yes—
614C23C2×D4×D5311yescharacteristic
615C23C2×D4×D5311yescharacteristic
616C23#41×D5311yescharacteristic
617C23#41×D5312yes—
618C23#41×D5311yescharacteristic
619C23#41×D5312yes—
620C23C2×#1171994712yes—
621C23C2×#1171994711yescharacteristic
622C23C2×#1171994711yescharacteristic
623D4—232no—
624C2×C4—22no—
625C2×C4—24no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—24no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—24no—
636C2×C4—24no—
637C2×C4—22no—
638C2×C4—24no—
639C2×C4—41no—
640C2×C4—42no—
641C2×C4—41no—
642C2×C4—42no—
643C2×C4—42no—
644C2×C4—42no—
645C2×C4—42no—
646C2×C4—534no—
647C2×C4—534no—
648C2×C4—538no—
649C2×C4—538no—
650C2×C4—534no—
651C2×C4—1062no—
652C2×C4—1064no—
653C2×C4—1062no—
654C2×C4—1064no—
655C2×C4—1064no—
656C2×C4—1064no—
657C2×C4—1064no—
658C2×C4—1064no—
659C2×C4—1064no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—1064no—
663C2×C4—1062no—
664C2×C4—21232no—
665C2×C4—2121no—
666C2×C4—2122no—
667C2×C4—2122no—
668C2×C4—2122no—
669C2×C4—2122no—
670C2×C4—2121no—
671C2×C4—2122no—
672C2×C4—2122no—
673C2×C4—2122no—
674C2×C4—2122no—
675C2×C4—2122no—
676C2×C4—2122no—
677C2×C4—2122no—
678C2×C4—2122no—
679C2×C4—2121no—
680C2×C4—2121no—
681C2×C4D4×Dic5314yes—
682C2×C4D4×Dic5314yescomplemented
683C22—28no—
684C22—28no—
685C22—28no—
686C22—44no—
687C22—44no—
688C22—44no—
689C22—44no—
690C22—44no—
691C22—44no—
692C22—44no—
693C22—44no—
694C22—44no—
695C22—44no—
696C22—44no—
697C22—44no—
698C22C2×D4×Dic5311yescharacteristic
699C22C2×D4×Dic5312yes—
700C22C2×D4×Dic5311yescharacteristic
701C22#41×Dic5312yes—
702C22#41×Dic5311yescharacteristic
703C22#120×D5311yescharacteristic
704C22#121×D5311yescharacteristic
705C22#121×D5312yes—
706C22#123×D5312yes—
707C22#1681112911yescharacteristic
708C22#1681112912yes—
709C22#1681113112yes—
710C22#1681113311yescharacteristic
711C22#1681113312yes—
712C22#124×D5311yescharacteristic
713C22#1681115012yes—
714C22#1681115012yes—
715C22#1681115212yes—
716C22#1681115411yescharacteristic
717C22#1681115412yes—
718C22#1681116812yes—
719C22#1681116811yescharacteristic
720C22#1681117211yescharacteristic
721C4—24no—
722C4—24no—
723C4—42no—
724C4—44no—
725C4—538no—
726C4—2124no—
727C4—2122no—
728C4—2122no—
729C4—2122no—
730C4—2124no—
731C2—48no—
732C2#120×Dic5311yescharacteristic
733C2#121×Dic5311yescharacteristic
734C2#121×Dic5312yes—
735C2#123×Dic5312yes—
736C2#124×Dic5311yescharacteristic
737C2#394×D5311yescharacteristic
738C2#2027792911yescharacteristic
739C2#2027795411yescharacteristic
740C2#2027795812yes—
741C2#2027797112yes—
742C2#2027800311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC2×C53×#394C2
socle, cosocleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#394D53
hypocenterC53C4×#394
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊C4×Dic53C2semidirect
3. C2×C22⋊C4×Dic53C2semidirect
4. C2×C22⋊C4×Dic53C2semidirect
5. #20272972C2semidirect
6. #20272968C2semidirect
7. #20272964C2semidirect
8. #20272960C2semidirect
10. #95×Dic53C2semidirect
39. C53×#394C4semidirect
78. C2×C4×Dic53D4semidirect
99. C2×C4⋊C4×C53C2×C4semidirect
104. C2×C22⋊C4×C53C2×C4semidirect
105. C2×C22⋊C4×C53C2×C4semidirect
106. #95×C53C2×C4semidirect
275. C2×C4×C53C4×D4semidirect
359. Dic53#394direct (N × H)
399. #394Dic53direct (N × H)
412. C53C4×#394semidirect
444. C2×C4⋊C4C2×Dic53semidirect
458. C2×C22⋊C4C2×Dic53semidirect
459. C2×C22⋊C4C2×Dic53semidirect
478. #95C2×Dic53semidirect
682. C2×C4D4×Dic53semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic532
C2×C4⋊C4×Dic532
C2×C22⋊C4×Dic532
#202729722
#202729682
#202729642
#202729602
#202729562
#95×Dic532
C2×C53×#3942
C4×#39453