Finite Group Databasebeta

← C2×#20280913 #27550690

Subgroups — C2×#20280913 #27550690

Order 13568.

2158 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280913C2116yesmaximal, direct product factor
2C2×#16810558C211yesmaximal, characteristic
3C2×#16810558C211yesmaximal, characteristic
4C2×#16810556C211yesmaximal, characteristic, complemented
5C2×#16810554C211yesmaximal, characteristic, complemented
6C2×#16810554C211yesmaximal, characteristic, complemented
7C2×#16810553C211yesmaximal, characteristic, complemented
8C2×#16810545C211yesmaximal, characteristic
9C2×#16810545C211yesmaximal, characteristic
10C2×#16810520C211yesmaximal, characteristic, complemented
11C2×#16810507C211yesmaximal, characteristic, complemented
12C2×#16810506C211yesmaximal, characteristic, complemented
13C2×#16810485C211yesmaximal, characteristic
14C2×#16810482C211yesmaximal, characteristic
15C2×C4×#11719921C211yesmaximal, characteristic
16C2×C53×#389C211yesmaximal, characteristic, complemented
17C23×C4×D53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×#11719919C2211yescharacteristic
27C22×#11719919C2211yescharacteristic
28C22×#11719921C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35#16810558C2218yes—
36#16810558C2218yes—
37#16810556C2218yescomplemented
38#16810554C2218yescomplemented
39#16810554C2218yescomplemented
40#16810553C2218yescomplemented
41#16810545C2218yes—
42#16810545C2218yes—
43#16810520C2218yescomplemented
44#16810507C2218yescomplemented
45#16810506C2218yescomplemented
46#16810485C2218yes—
47#16810482C2218yes—
48C4×#11719921C2218yes—
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C22×C4⋊C4×C53C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C4⋊C4×C53C2211yescharacteristic
63C22×C42×C53C2211yescharacteristic
64C53×#389C2218yescomplemented
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C24×D53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C22×C4×D53—42no—
76C22×C4×D53—42no—
77C22×C4×D53Q818yes—
78C22×C4×D53C2314yes—
79C2×C4⋊Dic53—24no—
80C2×C4⋊Dic53—42no—
81C2×C4⋊Dic53C2314yes—
82C2×C4⋊Dic53C2314yes—
83C2×#11719919—24no—
84C2×#11719919—24no—
85C2×#11719919—42no—
86C2×#11719919—42no—
87C2×#11719919—42no—
88C2×#11719919—42no—
89C2×#11719919—42no—
90C2×#11719919—42no—
91C2×#11719919C2314yes—
92C2×#11719919C2314yes—
93C2×#11719919C2314yes—
94C2×#11719919C2314yes—
95C2×#11719919C2314yes—
96C2×#11719919C2314yes—
97C2×#11719919C2314yes—
98C2×#11719919C2314yes—
99C2×#11719921—24no—
100C2×#11719921—24no—
101C2×#11719921—42no—
102C2×#11719921—42no—
103C2×#11719921—42no—
104C2×#11719921—42no—
105C2×#11719921C2314yes—
106C2×#11719921C2314yes—
107C2×#11719921C2314yes—
108C2×#11719921C2314yes—
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×C4×Dic53—42no—
112C2×C4×Dic53C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123C23×C4×C53C2311yescharacteristic
124C23×C4×C53C2311yescharacteristic
125C23×C4×C53C2311yescharacteristic
126C23×C4×C53C2311yescharacteristic
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C2×C4⋊C4×C53—24no—
131C2×C4⋊C4×C53—42no—
132C2×C4⋊C4×C53—42no—
133C2×C4⋊C4×C53—42no—
134C2×C4⋊C4×C53C2314yes—
135C2×C4⋊C4×C53C2314yes—
136C2×C4⋊C4×C53C2314yes—
137C2×C4⋊C4×C53C2314yes—
138C2×C42×C53—42no—
139C2×C42×C53C2314yes—
140#95×C53C2314yes—
141#95×C53C2314yes—
142C24×C53C2411yescharacteristic
143C23×D53—22no—
144C23×D53—22no—
145C23×D53—22no—
146C23×D53—22no—
147C23×D53—22no—
148C23×D53—22no—
149C23×D53C2×Q814yes—
150C23×D53C2412yes—
151C22×C4×C53—22no—
152C22×C4×C53—22no—
153C22×C4×C53—22no—
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×C53—22no—
162C22×C4×C53—22no—
163C22×C4×C53—22no—
164C22×C4×C53—22no—
165C22×C4×C53—22no—
166C22×C4×C53—22no—
167C22×C4×C53—22no—
168C22×C4×C53—22no—
169C22×C4×C53—22no—
170C22×C4×C53C2×Q814yes—
171C22×C4×C53#4114yes—
172C22×C4×C53C2412yes—
173C22×C4×C53C2412yes—
174C22×C4×C53C2412yes—
175C22×C4×C53C2412yes—
176C22×C4×C53C2412yes—
177C22×C4×C53C2412yes—
178C22×C4×C53C2412yes—
179C22×Dic53—22no—
180C22×Dic53—22no—
181C22×Dic53—22no—
182C22×Dic53—22no—
183C22×Dic53—22no—
184C22×Dic53—22no—
185C22×Dic53—22no—
186C22×Dic53—22no—
187C22×Dic53—22no—
188C22×Dic53—22no—
189C22×Dic53—22no—
190C22×Dic53—22no—
191C22×Dic53—22no—
192C22×Dic53—22no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
196C22×Dic53—22no—
197C22×Dic53—22no—
198C22×Dic53C2×Q814yes—
199C22×Dic53#4114yes—
200C22×Dic53C2412yes—
201C22×Dic53C2412yes—
202C22×Dic53C2412yes—
203C22×Dic53C2412yes—
204C22×Dic53C2412yes—
205C22×Dic53C2412yes—
206C22×Dic53C2412yes—
207C2×C4×D53—416no—
208C2×C4×D53—44no—
209C2×C4×D53—44no—
210C2×C4×D53C2×Q8116yes—
211C4⋊C4×C53—28no—
212C4⋊C4×C53—44no—
213C4⋊C4×C53—44no—
214C4⋊C4×C53—44no—
215C42×C53—44no—
216#11719921—28no—
217#11719921—28no—
218#11719921—44no—
219#11719921—44no—
220#11719921—44no—
221#11719921—44no—
222C4⋊Dic53—28no—
223C4⋊Dic53—44no—
224#11719919—28no—
225#11719919—28no—
226#11719919—44no—
227#11719919—44no—
228#11719919—44no—
229#11719919—44no—
230#11719919—44no—
231#11719919—44no—
232C4×Dic53—44no—
233C23×C53C22×Q812yes—
234C23×C53C2×#4112yes—
235C23×C53C2×#4112yes—
236C23×C53H(5,𝔽2)12yes—
237C23×C53H(5,𝔽2)12yes—
238C23×C53H(5,𝔽2)12yes—
239C23×C532−1+412yes—
240C23×C53C2511yescharacteristic
241C22×D53—28no—
242C22×D53—28no—
243C22×D53—28no—
244C22×D53—22no—
245C22×D53—22no—
246C22×D53—22no—
247C22×D53—22no—
248C22×D53—22no—
249C22×D53—22no—
250C22×D53—44no—
251C22×D53—44no—
252C22×D53—44no—
253C22×D53—44no—
254C22×D53C22×Q814yes—
255C2×C4×C53—28no—
256C2×C4×C53—28no—
257C2×C4×C53—22no—
258C2×C4×C53—22no—
259C2×C4×C53—22no—
260C2×C4×C53—22no—
261C2×C4×C53—22no—
262C2×C4×C53—22no—
263C2×C4×C53—22no—
264C2×C4×C53—22no—
265C2×C4×C53—22no—
266C2×C4×C53—22no—
267C2×C4×C53—22no—
268C2×C4×C53—22no—
269C2×C4×C53—22no—
270C2×C4×C53—22no—
271C2×C4×C53—22no—
272C2×C4×C53—22no—
273C2×C4×C53—22no—
274C2×C4×C53—22no—
275C2×C4×C53—22no—
276C2×C4×C53—44no—
277C2×C4×C53—44no—
278C2×C4×C53—44no—
279C2×C4×C53—44no—
280C2×C4×C53—44no—
281C2×C4×C53C22×Q814yes—
282C2×C4×C53C2×#4114yes—
283C2×Dic53—28no—
284C2×Dic53—28no—
285C2×Dic53—22no—
286C2×Dic53—22no—
287C2×Dic53—22no—
288C2×Dic53—22no—
289C2×Dic53—22no—
290C2×Dic53—22no—
291C2×Dic53—22no—
292C2×Dic53—22no—
293C2×Dic53—22no—
294C2×Dic53—22no—
295C2×Dic53—22no—
296C2×Dic53—22no—
297C2×Dic53—22no—
298C2×Dic53—22no—
299C2×Dic53—22no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
304C2×Dic53—44no—
305C2×Dic53—44no—
306C2×Dic53—44no—
307C2×Dic53—44no—
308C2×Dic53—44no—
309C2×Dic53C22×Q814yes—
310C2×Dic53C2×#4114yes—
311C4×D53—416no—
312C2×#2667—531nomaximal, Sylow
313C22×C53#53314yes—
314C22×C53#53914yes—
315C22×C53#53914yes—
316C22×C53#54014yes—
317C22×C53#54014yes—
318C22×C53#54314yes—
319C22×C53#54414yes—
320C22×C53C23×Q811yescharacteristic
321C22×C53C22×#4111yescharacteristic
322C22×C53C22×#4111yescharacteristic
323C22×C53C2×H(5,𝔽2)11yescharacteristic
324C22×C53C2×H(5,𝔽2)11yescharacteristic
325C22×C53C2×H(5,𝔽2)11yescharacteristic
326C22×C53C2×2−1+411yescharacteristic
327C2×D53—24no—
328C2×D53—24no—
329C2×D53—24no—
330C2×D53—416no—
331C2×D53—42no—
332C2×D53—42no—
333C2×D53—42no—
334C2×D53—42no—
335C4×C53—24no—
336C4×C53—24no—
337C4×C53—42no—
338C4×C53—42no—
339C4×C53—42no—
340C4×C53—42no—
341C4×C53—42no—
342Dic53—24no—
343Dic53—24no—
344Dic53—42no—
345Dic53—42no—
346Dic53—42no—
347Dic53—42no—
348Dic53—42no—
349#2667—5316no—
350C2×#399—531no—
351C2×#399—531no—
352C2×#398—531no—
353C2×#398—531no—
354C2×#398—531no—
355C2×#398—531no—
356C2×#396—531no—
357C2×#396—531no—
358C2×#389—531no—
359C2×#389D5311yescharacteristic, complemented
360C2×#387—531no—
361C2×#387—531no—
362C2×#381—531no—
363C2×#380—531no—
364C2×C4×C22⋊C4—531no—
365C2×C53#266718yescomplemented
366C2×C53C2×#53311yescharacteristic
367C2×C53C2×#53911yescharacteristic
368C2×C53C2×#53911yescharacteristic
369C2×C53C2×#54011yescharacteristic
370C2×C53C2×#54011yescharacteristic
371C2×C53C2×#54311yescharacteristic
372C2×C53C2×#54411yescharacteristic
373D53—44no—
374C24×C4—531no—
375C22×C4⋊C4—531no—
376C22×C4⋊C4—531no—
377C22×C4⋊C4—531no—
378C22×C4⋊C4—531no—
379C22×C4⋊C4—531no—
380C22×C4⋊C4—531no—
381C22×C4⋊C4—531no—
382C22×C4⋊C4—531no—
383C22×C4⋊C4—531no—
384C22×C4⋊C4—531no—
385C22×C4⋊C4C2×D5311yescharacteristic
386C22×C4⋊C4C2×D5311yescharacteristic
387C22×C4⋊C4C2×D5311yescharacteristic
388C22×C4⋊C4C2×D5311yescharacteristic
389C22×C22⋊C4—531no—
390C22×C22⋊C4—531no—
391C22×C22⋊C4—531no—
392C22×C22⋊C4—531no—
393C22×C22⋊C4—531no—
394C22×C22⋊C4—531no—
395C22×C42—531no—
396C22×C42C2×D5311yescharacteristic
397#399—538no—
398#399—538no—
399#398—538no—
400#398—538no—
401#398—538no—
402#398—538no—
403#396—538no—
404#396—538no—
405#389—538no—
406#389C2×D5318yescomplemented
407#387—538no—
408#387—538no—
409#381—538no—
410#380—538no—
411C4×C22⋊C4—538no—
412C2×#95—531no—
413C2×#95—531no—
414C2×#95—531no—
415C2×#95—531no—
416C2×#95—531no—
417C2×#95—531no—
418C2×#95—531no—
419C2×#95—531no—
420C2×#95—531no—
421C2×#95—531no—
422C2×#95C2×D5311yescharacteristic
423C2×#95C2×D5311yescharacteristic
424C53C2×#266711yescharacteristic, complemented, Sylow
425C25—531no—
426C23×C4—531no—
427C23×C4—531no—
428C23×C4—538no—
429C23×C4—534no—
430C23×C4—531no—
431C23×C4—531no—
432C23×C4—531no—
433C23×C4—531no—
434C23×C4—531no—
435C23×C4—2122no—
436C23×C4—2122no—
437C23×C4C22×D5311yescharacteristic
438C23×C4C22×D5311yescharacteristic
439C23×C4C22×D5311yescharacteristic
440C23×C4C22×D5311yescharacteristic
441C23×C4C22×D5311yescharacteristic
442C23×C4C22×D5311yescharacteristic
443C23×C4C22×D5311yescharacteristic
444C2×C4⋊C4—24no—
445C2×C4⋊C4—42no—
446C2×C4⋊C4—42no—
447C2×C4⋊C4—42no—
448C2×C4⋊C4—534no—
449C2×C4⋊C4—534no—
450C2×C4⋊C4—534no—
451C2×C4⋊C4—534no—
452C2×C4⋊C4—534no—
453C2×C4⋊C4—534no—
454C2×C4⋊C4—534no—
455C2×C4⋊C4—534no—
456C2×C4⋊C4—534no—
457C2×C4⋊C4—534no—
458C2×C4⋊C4—1064no—
459C2×C4⋊C4—1064no—
460C2×C4⋊C4—1064no—
461C2×C4⋊C4—2122no—
462C2×C4⋊C4—2122no—
463C2×C4⋊C4—2122no—
464C2×C4⋊C4—2122no—
465C2×C4⋊C4—2122no—
466C2×C4⋊C4—2122no—
467C2×C4⋊C4—2122no—
468C2×C4⋊C4C22×D5314yes—
469C2×C4⋊C4C22×D5314yes—
470C2×C4⋊C4C22×D5314yes—
471C2×C4⋊C4C22×D5314yes—
472C2×C22⋊C4—534no—
473C2×C22⋊C4—534no—
474C2×C22⋊C4—534no—
475C2×C22⋊C4—534no—
476C2×C22⋊C4—534no—
477C2×C22⋊C4—534no—
478C2×C22⋊C4—1064no—
479C2×C22⋊C4—1064no—
480C2×C22⋊C4—2122no—
481C2×C22⋊C4—2122no—
482C2×C22⋊C4—2122no—
483C2×C22⋊C4—2122no—
484C2×C42—42no—
485C2×C42—534no—
486C2×C42—2122no—
487C2×C42C22×D5314yes—
488#95—534no—
489#95—534no—
490#95—534no—
491#95—534no—
492#95—534no—
493#95—534no—
494#95—534no—
495#95—534no—
496#95—534no—
497#95—534no—
498#95C22×D5314yes—
499#95C22×D5314yes—
500C24—534no—
501C24—532no—
502C24—1062no—
503C24—1062no—
504C24—1062no—
505C24—1062no—
506C24—1062no—
507C24—1062no—
508C24C23×D5311yescharacteristic
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—22no—
513C22×C4—22no—
514C22×C4—22no—
515C22×C4—22no—
516C22×C4—22no—
517C22×C4—22no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—534no—
529C22×C4—534no—
530C22×C4—532no—
531C22×C4—532no—
532C22×C4—5316no—
533C22×C4—532no—
534C22×C4—532no—
535C22×C4—532no—
536C22×C4—532no—
537C22×C4—532no—
538C22×C4—1062no—
539C22×C4—1062no—
540C22×C4—1062no—
541C22×C4—1062no—
542C22×C4—1062no—
543C22×C4—1062no—
544C22×C4—1062no—
545C22×C4—1062no—
546C22×C4—1062no—
547C22×C4—1062no—
548C22×C4—1062no—
549C22×C4—1062no—
550C22×C4—1062no—
551C22×C4—1062no—
552C22×C4—1062no—
553C22×C4—1062no—
554C22×C4—1062no—
555C22×C4—1062no—
556C22×C4—1062no—
557C22×C4—2124no—
558C22×C4—2124no—
559C22×C4—21216no—
560C22×C4#1171994514yes—
561C22×C4Q8×D5314yes—
562C22×C4C23×D5312yes—
563C22×C4C23×D5312yes—
564C22×C4C23×D5312yes—
565C22×C4C23×D5312yes—
566C22×C4C23×D5312yes—
567C22×C4C23×D5312yes—
568C22×C4C23×D5312yes—
569C4⋊C4—28no—
570C4⋊C4—44no—
571C4⋊C4—44no—
572C4⋊C4—44no—
573C4⋊C4—1068no—
574C4⋊C4—1068no—
575C4⋊C4—1068no—
576C4⋊C4—2124no—
577C4⋊C4—2124no—
578C4⋊C4—2124no—
579C4⋊C4—2124no—
580C4⋊C4—2124no—
581C4⋊C4—2124no—
582C4⋊C4—2124no—
583C22⋊C4—1068no—
584C22⋊C4—1068no—
585C22⋊C4—2124no—
586C22⋊C4—2124no—
587C22⋊C4—2124no—
588C22⋊C4—2124no—
589C42—44no—
590C42—2124no—
591C23—534no—
592C23—1068no—
593C23—1062no—
594C23—1062no—
595C23—1062no—
596C23—1062no—
597C23—1062no—
598C23—1062no—
599C23—1068no—
600C23—1068no—
601C23—2124no—
602C23—2124no—
603C23—2124no—
604C23—2124no—
605C23C2×Q8×D5312yes—
606C23#41×D5312yes—
607C23C2×#1171994512yes—
608C23#1313326212yes—
609C23#1313326212yes—
610C23#1313326312yes—
611C23#1313326512yes—
612C23C24×D5311yescharacteristic
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—28no—
618C2×C4—28no—
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—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—44no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—534no—
640C2×C4—534no—
641C2×C4—1062no—
642C2×C4—1062no—
643C2×C4—1062no—
644C2×C4—1062no—
645C2×C4—1068no—
646C2×C4—1068no—
647C2×C4—1062no—
648C2×C4—1062no—
649C2×C4—1062no—
650C2×C4—1062no—
651C2×C4—1062no—
652C2×C4—1062no—
653C2×C4—1062no—
654C2×C4—1062no—
655C2×C4—1062no—
656C2×C4—1062no—
657C2×C4—1062no—
658C2×C4—1062no—
659C2×C4—1062no—
660C2×C4—1062no—
661C2×C4—1062no—
662C2×C4—21216no—
663C2×C4—2124no—
664C2×C4—2124no—
665C2×C4—2124no—
666C2×C4—2124no—
667C2×C4—2124no—
668C2×C4C2×Q8×D5314yes—
669C2×C4C2×#1171994514yes—
670C22—1064no—
671C22—1064no—
672C22—1064no—
673C22—2122no—
674C22—2122no—
675C22—2122no—
676C22—2122no—
677C22—21216no—
678C22#1681117714yes—
679C22#1681122014yes—
680C22#1681122114yes—
681C22#1681122314yes—
682C22#1681122414yes—
683C22#1681124814yes—
684C22#1681125014yes—
685C22C22×Q8×D5311yescharacteristic
686C22C2×#41×D5311yescharacteristic
687C22C22×#1171994511yescharacteristic
688C22C2×#1313326211yescharacteristic
689C22C2×#1313326211yescharacteristic
690C22C2×#1313326311yescharacteristic
691C22C2×#1313326511yescharacteristic
692C4—24no—
693C4—24no—
694C4—42no—
695C4—42no—
696C4—42no—
697C4—42no—
698C4—42no—
699C4—1064no—
700C4—1064no—
701C4—2122no—
702C4—2122no—
703C4—2122no—
704C4—2122no—
705C4—2122no—
706C2—2124no—
707C2#2028091318yesdirect product factor
708C2C2×#1681117711yescharacteristic
709C2C2×#1681122011yescharacteristic
710C2C2×#1681122111yescharacteristic
711C2C2×#1681122311yescharacteristic
712C2C2×#1681122411yescharacteristic
713C2C2×#1681124811yescharacteristic
714C2C2×#1681125011yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#389C2
socleC24×C53C24
prime radicalC24×D53C23
hypercenterC2×#389D53
hypocenterC53C2×#2667
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. #20280913C2direct (N × H)
4. C2×#16810556C2semidirect
5. C2×#16810554C2semidirect
6. C2×#16810554C2semidirect
7. C2×#16810553C2semidirect
10. C2×#16810520C2semidirect
11. C2×#16810507C2semidirect
12. C2×#16810506C2semidirect
16. C2×C53×#389C2semidirect
37. #16810556C22semidirect
38. #16810554C22semidirect
39. #16810554C22semidirect
40. #16810553C22semidirect
43. #16810520C22semidirect
44. #16810507C22semidirect
45. #16810506C22semidirect
64. C53×#389C22semidirect
359. C2×#389D53semidirect
365. C2×C53#2667semidirect
406. #389C2×D53semidirect
424. C53C2×#2667semidirect
707. C2#20280913direct (N × H)

Maximal subgroups

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

subgroupindex
#202809132
C2×#168105582
C2×#168105562
C2×#168105542
C2×#168105532
C2×#168105452
C2×#168105202
C2×#168105072
C2×#168105062
C2×#168104852
C2×#168104822
C2×C4×#117199212
C2×C53×#3892
C2×#266753