Finite Group Databasebeta

← #27312555

Subgroups — #27312555

Order 13568.

1758 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810525C211yesmaximal, characteristic
2C2×#16810515C212yesmaximal, complemented
3C2×#16810513C212yesmaximal, complemented
4#20272961C212yesmaximal, complemented
5#20272957C212yesmaximal, complemented
6#20272955C212yesmaximal
7#20272949C212yesmaximal, complemented
8#20272945C211yesmaximal, characteristic, complemented
9C53×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D212C2211yescharacteristic
11C22×C4⋊Dic53C2211yescharacteristic
12C22×C4⋊Dic53C2211yescharacteristic
13C22×C4⋊Dic53C2211yescharacteristic
14C22×#11719921C2212yes—
15C22×#11719921C2212yes—
16C22×#11719921C2212yes—
17C22×#11719921C2212yes—
18C22×#11719921C2212yes—
19C22×#11719921C2212yes—
20C22×C4×Dic53C2212yes—
21#16810525C418yescomplemented
22#16810515—28no—
23#16810513—28no—
24C2×#13133124C2212yes—
25C2×#13133124C2212yes—
26C2×#13133124C2212yes—
27C2×#13133124C2212yes—
28C2×#13133124C2212yes—
29C22×C4⋊C4×C53C2211yescharacteristic
30C22×C4⋊C4×C53C2211yescharacteristic
31C22×C42×C53C2211yescharacteristic
32C2×#95×C53C2212yes—
33C2×#95×C53C2212yes—
34C24×D53C2312yes—
35C22×D212—22no—
36C22×D212—22no—
37C22×D212—41no—
38C22×D212—41no—
39C22×D212—41no—
40C22×D212—41no—
41C22×D212C2×C414yes—
42C23×Dic53C2312yes—
43C23×Dic53C2312yes—
44C23×Dic53C2312yes—
45C2×C4⋊Dic53—22no—
46C2×C4⋊Dic53—41no—
47C2×C4⋊Dic53—41no—
48C2×C4⋊Dic53—41no—
49C2×C4⋊Dic53—41no—
50C2×C4⋊Dic53—41no—
51C2×C4⋊Dic53—41no—
52C2×C4⋊Dic53C2×C414yes—
53C2×C4⋊Dic53D414yescomplemented
54C2×#11719921—24no—
55C2×#11719921—24no—
56C2×#11719921—24no—
57C2×#11719921—24no—
58C2×#11719921—24no—
59C2×#11719921—24no—
60C2×#11719921—24no—
61C2×#11719921—24no—
62C2×#11719921—42no—
63C2×#11719921—42no—
64C2×#11719921—42no—
65C2×#11719921—42no—
66C2×#11719921—42no—
67C2×#11719921—42no—
68C2×#11719921—42no—
69C2×#11719921—42no—
70C2×#11719921C2×C418yes—
71C2×#11719921C2×C418yes—
72C2×C4×Dic53—24no—
73C2×C4×Dic53—24no—
74C2×C4×Dic53—42no—
75#13133124—24no—
76#13133124—24no—
77#13133124—24no—
78#13133124—24no—
79#13133124—42no—
80C23×C4×C53C2312yes—
81C23×C4×C53C2312yes—
82C23×C4×C53C2311yescharacteristic
83C23×C4×C53C2311yescharacteristic
84C23×C4×C53C2311yescharacteristic
85C2×C4⋊C4×C53—22no—
86C2×C4⋊C4×C53—41no—
87C2×C4⋊C4×C53—41no—
88C2×C4⋊C4×C53—41no—
89C2×C4⋊C4×C53—41no—
90C2×C4⋊C4×C53D414yescomplemented
91C2×C42×C53—41no—
92C2×C42×C53—41no—
93C2×C42×C53C2×C414yes—
94#95×C53—24no—
95#95×C53—24no—
96C24×C53C2411yescharacteristic
97C23×D53—22no—
98C23×D53—22no—
99C23×D53—22no—
100C23×D53—22no—
101C23×D53—22no—
102C23×D53—22no—
103C23×D53—22no—
104C23×D53—22no—
105C23×D53—22no—
106C23×D53—22no—
107C23×D53—22no—
108C23×D53—22no—
109C23×D53—22no—
110C23×D53—22no—
111C23×D53C22×C414yes—
112C22×C4×C53—21no—
113C22×C4×C53—21no—
114C22×C4×C53—21no—
115C22×C4×C53—21no—
116C22×C4×C53—21no—
117C22×C4×C53—21no—
118C22×C4×C53—21no—
119C22×C4×C53—21no—
120C22×C4×C53—21no—
121C22×C4×C53—21no—
122C22×C4×C53—21no—
123C22×C4×C53—21no—
124C22×C4×C53—22no—
125C22×C4×C53—22no—
126C22×C4×C53—22no—
127C22×C4×C53—22no—
128C22×C4×C53—22no—
129C22×C4×C53—22no—
130C22×C4×C53—22no—
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×C53C22×C412yes—
138C22×C4×C53C22×C412yes—
139C22×C4×C53C22×C412yes—
140C22×C4×C53C2×D414yes—
141C22×C4×C53C2×D412yes—
142C22×C4×C53C2×D412yes—
143C22×C4×C53#4112yes—
144C22×C4×C53#4112yes—
145C22×C4×C53#4112yes—
146C22×C4×C53#4112yes—
147C22×Dic53—22no—
148C22×Dic53—22no—
149C22×Dic53—22no—
150C22×Dic53—22no—
151C22×Dic53—22no—
152C22×Dic53—22no—
153C22×Dic53—22no—
154C22×Dic53—22no—
155C22×Dic53—22no—
156C22×Dic53—22no—
157C22×Dic53—22no—
158C22×Dic53—22no—
159C22×Dic53—22no—
160C22×Dic53—22no—
161C22×Dic53—22no—
162C22×Dic53—22no—
163C22×Dic53—22no—
164C22×Dic53—22no—
165C22×Dic53—22no—
166C22×Dic53C22×C414yes—
167C22×Dic53C2×D414yes—
168C2×D212—28no—
169C2×D212—44no—
170C2×D212—44no—
171C2×D212—44no—
172C2×D212—44no—
173C2×D212—44no—
174C2×D212—44no—
175C4⋊C4×C53—44no—
176C4⋊C4×C53—44no—
177C42×C53—44no—
178#11719921—216no—
179#11719921—216no—
180#11719921—48no—
181#11719921—48no—
182#11719921—48no—
183#11719921—48no—
184C4⋊Dic53—44no—
185C4⋊Dic53—44no—
186C4⋊Dic53—44no—
187C4×Dic53—48no—
188C23×C53C23×C411yescharacteristic
189C23×C53C22×D411yescharacteristic
190C23×C53C22×D411yescharacteristic
191C23×C53C2×#4111yescharacteristic
192C23×C53C2×#4111yescharacteristic
193C23×C53C2×#4111yescharacteristic
194C23×C53C2×#4111yescharacteristic
195C23×C53H(5,𝔽2)11yescharacteristic
196C23×C53H(5,𝔽2)11yescharacteristic
197C23×C53H(5,𝔽2)11yescharacteristic
198C23×C53H(5,𝔽2)11yescharacteristic
199C23×C53H(5,𝔽2)11yescharacteristic
200C23×C53H(5,𝔽2)11yescharacteristic
201C23×C532−1+411yescharacteristic
202C23×C532−1+411yescharacteristic
203C22×D53—24no—
204C22×D53—24no—
205C22×D53—24no—
206C22×D53—24no—
207C22×D53—24no—
208C22×D53—24no—
209C22×D53—24no—
210C22×D53—42no—
211C22×D53—42no—
212C22×D53—42no—
213C22×D53—42no—
214C22×D53—42no—
215C22×D53—42no—
216C22×D53—42no—
217C22×D53—42no—
218C22×D53—42no—
219C22×D53—42no—
220C22×D53—42no—
221C22×D53—42no—
222C22×D53—42no—
223C22×D53—42no—
224C22×D53—42no—
225C22×D53—42no—
226C22×D53—42no—
227C22×D53—42no—
228C22×D53—42no—
229C22×D53—42no—
230C22×D53—42no—
231C22×D53—42no—
232C22×D53—42no—
233C22×D53—42no—
234C22×D53—42no—
235C22×D53—42no—
236C22×D53—42no—
237C22×D53—42no—
238C2×C4×C53—22no—
239C2×C4×C53—22no—
240C2×C4×C53—22no—
241C2×C4×C53—22no—
242C2×C4×C53—22no—
243C2×C4×C53—22no—
244C2×C4×C53—22no—
245C2×C4×C53—22no—
246C2×C4×C53—22no—
247C2×C4×C53—22no—
248C2×C4×C53—22no—
249C2×C4×C53—22no—
250C2×C4×C53—22no—
251C2×C4×C53—22no—
252C2×C4×C53—22no—
253C2×C4×C53—22no—
254C2×C4×C53—22no—
255C2×C4×C53—22no—
256C2×C4×C53—24no—
257C2×C4×C53—24no—
258C2×C4×C53—24no—
259C2×C4×C53—42no—
260C2×C4×C53—42no—
261C2×C4×C53—42no—
262C2×C4×C53—42no—
263C2×C4×C53—42no—
264C2×C4×C53—42no—
265C2×C4×C53—42no—
266C2×C4×C53—42no—
267C2×C4×C53—42no—
268C2×C4×C53—42no—
269C2×C4×C53—42no—
270C2×C4×C53#11714yes—
271C2×C4×C53C4×D414yes—
272C2×C4×C53C4×D414yes—
273C2×Dic53—24no—
274C2×Dic53—24no—
275C2×Dic53—24no—
276C2×Dic53—24no—
277C2×Dic53—24no—
278C2×Dic53—24no—
279C2×Dic53—42no—
280C2×Dic53—42no—
281C2×Dic53—42no—
282C2×Dic53—42no—
283C2×Dic53—42no—
284C2×Dic53—42no—
285C2×Dic53—42no—
286C2×Dic53—42no—
287C2×Dic53—42no—
288C2×Dic53—42no—
289C2×Dic53—42no—
290C2×Dic53—42no—
291C2×Dic53—42no—
292C2×Dic53—42no—
293C2×Dic53—42no—
294D212—416no—
295#14445—531nomaximal, Sylow
296C22×C53C2×#11711yescharacteristic
297C22×C53C2×C4×D411yescharacteristic
298C22×C53C2×C4×D411yescharacteristic
299C22×C53#51811yescharacteristic
300C22×C53#51811yescharacteristic
301C22×C53#52011yescharacteristic
302C22×C53#52011yescharacteristic
303C22×C53#53411yescharacteristic
304C22×C53#53411yescharacteristic
305C22×C53#53711yescharacteristic
306C22×C53#53711yescharacteristic
307C22×C53#53811yescharacteristic
308C22×C53#53811yescharacteristic
309C22×C53#53811yescharacteristic
310C22×C53#53811yescharacteristic
311C22×C53#53811yescharacteristic
312C22×C53#53811yescharacteristic
313C22×C53#53911yescharacteristic
314C22×C53#53911yescharacteristic
315C22×C53D4211yescharacteristic
316C22×C53#54711yescharacteristic
317C22×C53#54711yescharacteristic
318C22×C53#55011yescharacteristic
319C22×C53#55011yescharacteristic
320C22×C53#55011yescharacteristic
321C22×C53#55011yescharacteristic
322C22×C53#55511yescharacteristic
323C22×C53#55511yescharacteristic
324C22×C53#55611yescharacteristic
325C22×C53#55611yescharacteristic
326C22×C53#55911yescharacteristic
327C22×C53H(3,𝔽4)11yescharacteristic
328C22×C53#56211yescharacteristic
329C22×C53#56211yescharacteristic
330C22×C53#56311yescharacteristic
331C2×D53—44no—
332C2×D53—44no—
333C2×D53—44no—
334C2×D53—44no—
335C2×D53—44no—
336C2×D53—44no—
337C2×D53—44no—
338C2×D53—82no—
339C2×D53—82no—
340C2×D53—82no—
341C2×D53—82no—
342C2×D53—82no—
343C2×D53—82no—
344C2×D53—82no—
345C2×D53—82no—
346C4×C53—24no—
347C4×C53—24no—
348C4×C53—24no—
349C4×C53—44no—
350C4×C53—82no—
351Dic53—44no—
352Dic53—44no—
353Dic53—82no—
354C2×#390—531no—
355C2×#388—532no—
356C2×#388—532no—
357#1439—532no—
358#1439—532no—
359#1438—532no—
360#1436—532no—
361C4⋊#95—531no—
362C4⋊#95D5311yescharacteristic, complemented
363C2×C53#231211yescharacteristic
364C2×C53#232511yescharacteristic
365C2×C53#232511yescharacteristic
366C2×C53#235411yescharacteristic
367C2×C53#235411yescharacteristic
368C2×C53#236611yescharacteristic
369C2×C53#237911yescharacteristic
370C2×C53#268211yescharacteristic
371C2×C53#268211yescharacteristic
372C2×C53#272711yescharacteristic
373C2×C53#272711yescharacteristic
374C2×C53#273311yescharacteristic
375C2×C53#273311yescharacteristic
376C2×C53#280811yescharacteristic
377C2×C53#280811yescharacteristic
378D53—84no—
379C23×D4—531no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—531no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4C2×D5311yescharacteristic
384C22×C4⋊C4C2×D5311yescharacteristic
385C22×C22⋊C4—532no—
386C22×C22⋊C4—532no—
387C22×C22⋊C4—532no—
388C22×C22⋊C4—532no—
389C22×C22⋊C4—532no—
390C22×C22⋊C4—532no—
391C22×C42—532no—
392C22×C42C2×D5311yescharacteristic
393#390—538no—
394#388—1068no—
395#388—1068no—
396C2×#95—532no—
397C2×#95—532no—
398C2×#95—532no—
399C2×#95—532no—
400C2×#95—532no—
401C2×#95C2×D5312yes—
402C2×#95C2×D5312yes—
403C53#1444511yescharacteristic, complemented, Sylow
404C25—532no—
405C22×D4—534no—
406C22×D4—1062no—
407C22×D4—1062no—
408C22×D4—2121no—
409C22×D4—2121no—
410C22×D4—2121no—
411C22×D4—2121no—
412C23×C4—532no—
413C23×C4—532no—
414C23×C4—532no—
415C23×C4C22×D5312yes—
416C23×C4C22×D5312yes—
417C23×C4C22×D5311yescharacteristic
418C23×C4C22×D5311yescharacteristic
419C23×C4C22×D5311yescharacteristic
420C2×C4⋊C4—22no—
421C2×C4⋊C4—41no—
422C2×C4⋊C4—41no—
423C2×C4⋊C4—41no—
424C2×C4⋊C4—41no—
425C2×C4⋊C4—534no—
426C2×C4⋊C4—534no—
427C2×C4⋊C4—1062no—
428C2×C4⋊C4—2121no—
429C2×C4⋊C4—2121no—
430C2×C4⋊C4—2121no—
431C2×C4⋊C4—2121no—
432C2×C4⋊C4—2121no—
433C2×C4⋊C4—2121no—
434C2×C4⋊C4D21214yescomplemented
435C2×C22⋊C4—538no—
436C2×C22⋊C4—538no—
437C2×C22⋊C4—1064no—
438C2×C22⋊C4—1064no—
439C2×C22⋊C4—1064no—
440C2×C22⋊C4—1064no—
441C2×C22⋊C4—1064no—
442C2×C22⋊C4—1064no—
443C2×C22⋊C4—1064no—
444C2×C22⋊C4—1064no—
445C2×C22⋊C4—2122no—
446C2×C22⋊C4—2122no—
447C2×C22⋊C4—2122no—
448C2×C22⋊C4—2122no—
449C2×C22⋊C4—2122no—
450C2×C22⋊C4—2122no—
451C2×C22⋊C4—2122no—
452C2×C22⋊C4—2122no—
453C2×C42—41no—
454C2×C42—41no—
455C2×C42—1064no—
456C2×C42—1064no—
457C2×C42—2122no—
458C2×C42C4×D5314yes—
459#95—24no—
460#95—24no—
461#95—1064no—
462#95—1064no—
463#95—1064no—
464#95—1064no—
465#95—2122no—
466C24—534no—
467C24—1062no—
468C24—1062no—
469C24—1062no—
470C24—1062no—
471C24—1062no—
472C24—1062no—
473C24—1062no—
474C24—1062no—
475C24—1062no—
476C24—1062no—
477C24—1062no—
478C24—1062no—
479C24—1062no—
480C24—1062no—
481C24C23×D5311yescharacteristic
482C2×D4—1068no—
483C2×D4—2124no—
484C2×D4—2124no—
485C2×D4—2124no—
486C2×D4—2124no—
487C2×D4—2124no—
488C2×D4—2124no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—21no—
496C22×C4—21no—
497C22×C4—21no—
498C22×C4—21no—
499C22×C4—21no—
500C22×C4—21no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—22no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—534no—
515C22×C4—534no—
516C22×C4—1062no—
517C22×C4—1062no—
518C22×C4—1062no—
519C22×C4—1062no—
520C22×C4—1062no—
521C22×C4—1062no—
522C22×C4—1062no—
523C22×C4—1062no—
524C22×C4—1062no—
525C22×C4—1062no—
526C22×C4—1062no—
527C22×C4—1062no—
528C22×C4—1062no—
529C22×C4—1062no—
530C22×C4—1062no—
531C22×C4—1062no—
532C22×C4—1062no—
533C22×C4—1062no—
534C22×C4—1062no—
535C22×C4C2×C4×D5312yes—
536C22×C4C2×C4×D5312yes—
537C22×C4C2×C4×D5312yes—
538C22×C4C2×D21214yes—
539C22×C4C2×D21212yes—
540C22×C4#1171994512yes—
541C22×C4D4×D5312yes—
542C22×C4#1171994712yes—
543C22×C4#1171994912yes—
544C22×C4#1171994912yes—
545C4⋊C4—44no—
546C4⋊C4—44no—
547C4⋊C4—2124no—
548C4⋊C4—2124no—
549C4⋊C4—2124no—
550C22⋊C4—10616no—
551C22⋊C4—10616no—
552C22⋊C4—2128no—
553C22⋊C4—2128no—
554C22⋊C4—2128no—
555C22⋊C4—2128no—
556C42—44no—
557C42—2128no—
558C23—1064no—
559C23—1064no—
560C23—1064no—
561C23—1064no—
562C23—1064no—
563C23—1064no—
564C23—1064no—
565C23—2122no—
566C23—2122no—
567C23—2122no—
568C23—2122no—
569C23—2122no—
570C23—2122no—
571C23—2122no—
572C23—2122no—
573C23—2122no—
574C23—2122no—
575C23—2122no—
576C23—2122no—
577C23—2122no—
578C23—2122no—
579C23—2122no—
580C23—2122no—
581C23—2122no—
582C23—2122no—
583C23—2122no—
584C23—2122no—
585C23—2122no—
586C23—2122no—
587C23—2122no—
588C23—2122no—
589C23—2122no—
590C23—2122no—
591C23—2122no—
592C23—2122no—
593C23C22×C4×D5311yescharacteristic
594C23C2×D4×D5311yescharacteristic
595C23C22×D21211yescharacteristic
596C23C2×#1171994711yescharacteristic
597C23C2×#1171994511yescharacteristic
598C23C2×#1171994911yescharacteristic
599C23C2×#1171994911yescharacteristic
600C23#1313326211yescharacteristic
601C23#1313326211yescharacteristic
602C23#1313326211yescharacteristic
603C23#1313326311yescharacteristic
604C23#1313326311yescharacteristic
605C23#1313326311yescharacteristic
606C23#1313326411yescharacteristic
607C23#1313326511yescharacteristic
608D4—21216no—
609C2×C4—22no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—24no—
628C2×C4—24no—
629C2×C4—24no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—42no—
637C2×C4—42no—
638C2×C4—42no—
639C2×C4—42no—
640C2×C4—42no—
641C2×C4—1064no—
642C2×C4—1064no—
643C2×C4—1064no—
644C2×C4—1064no—
645C2×C4—1064no—
646C2×C4—1064no—
647C2×C4—2122no—
648C2×C4—2122no—
649C2×C4—2122no—
650C2×C4—2122no—
651C2×C4—2122no—
652C2×C4—2122no—
653C2×C4—2122no—
654C2×C4—2122no—
655C2×C4—2122no—
656C2×C4—2122no—
657C2×C4—2122no—
658C2×C4—2122no—
659C2×C4—2122no—
660C2×C4—2122no—
661C2×C4—2122no—
662C2×C4#1313317514yes—
663C2×C4#1313317914yes—
664C2×C4C4×D21214yes—
665C22—4242no—
666C22—4242no—
667C22—4242no—
668C22—4242no—
669C22—4242no—
670C22—4242no—
671C22—4242no—
672C22—4242no—
673C22—2124no—
674C22—2124no—
675C22—2124no—
676C22—2124no—
677C22—2124no—
678C22—2124no—
679C22—2124no—
680C22C2×#1313317511yescharacteristic
681C22C2×#1313317911yescharacteristic
682C22C2×C4×D21211yescharacteristic
683C22#1681109611yescharacteristic
684C22#1681109711yescharacteristic
685C22#1681110311yescharacteristic
686C22#1681110411yescharacteristic
687C22#1681118111yescharacteristic
688C22#1681118511yescharacteristic
689C22#1681120011yescharacteristic
690C22#1681120411yescharacteristic
691C22#1681121011yescharacteristic
692C22#1681121011yescharacteristic
693C22#1681121111yescharacteristic
694C22#1681121311yescharacteristic
695C22#1681121311yescharacteristic
696C22#1681121311yescharacteristic
697C22#1681122011yescharacteristic
698C22#1681122211yescharacteristic
699C22D4×D21211yescharacteristic
700C22#1681127611yescharacteristic
701C22#1681127711yescharacteristic
702C22#1681129311yescharacteristic
703C22#1681129411yescharacteristic
704C22#1681129511yescharacteristic
705C22#1681129511yescharacteristic
706C22#1681133811yescharacteristic
707C22#1681133911yescharacteristic
708C22#1681134611yescharacteristic
709C22#1681134711yescharacteristic
710C22#1681135811yescharacteristic
711C22#1681136511yescharacteristic
712C22#1681136711yescharacteristic
713C22#1681137111yescharacteristic
714C22#1681137711yescharacteristic
715C4—24no—
716C4—24no—
717C4—24no—
718C4—44no—
719C4—82no—
720C4—4242no—
721C4—2124no—
722C4—2124no—
723C2—4244no—
724C2#2027731211yescharacteristic
725C2#2027741511yescharacteristic
726C2#2027741811yescharacteristic
727C2#2027766211yescharacteristic
728C2#2027766611yescharacteristic
729C2#2027777911yescharacteristic
730C2#2027788611yescharacteristic
731C2#2028107711yescharacteristic
732C2#2028107911yescharacteristic
733C2#2028167511yescharacteristic
734C2#2028167611yescharacteristic
735C2#2028174011yescharacteristic
736C2#2028174111yescharacteristic
737C2#2028269211yescharacteristic
738C2#2028269711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D53
commutatorC23×C53C23×C4
FittingC53×C4⋊#95C2
socle, cosocleC24×C53C24
prime radicalC23×D212C22
hypercenterC4⋊#95D53
hypocenterC53#14445
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#16810515C2semidirect
3. C2×#16810513C2semidirect
4. #20272961C2semidirect
5. #20272957C2semidirect
7. #20272949C2semidirect
8. #20272945C2semidirect
9. C53×C4⋊#95C2semidirect
21. #16810525C4semidirect
53. C2×C4⋊Dic53D4semidirect
90. C2×C4⋊C4×C53D4semidirect
362. C4⋊#95D53semidirect
403. C53#14445semidirect
434. C2×C4⋊C4D212semidirect

Maximal subgroups

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

subgroupindex
C2×#168105252
C2×#168105152
C2×#168105132
#202729612
#202729572
#202729552
#202729492
#202729452
C53×C4⋊#952
#1444553