Finite Group Databasebeta

← C2×#20282817 #27590280

Subgroups — C2×#20282817 #27590280

Order 13568.

2218 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20282817C2116yesmaximal, direct product factor
2C2×#16810565C211yesmaximal, characteristic, complemented
3C2×#16810564C211yesmaximal, characteristic, complemented
4C2×#16810558C211yesmaximal, characteristic, complemented
5C2×#16810556C211yesmaximal, characteristic, complemented
6C2×#16810553C211yesmaximal, characteristic, complemented
7C2×#16810551C211yesmaximal, characteristic, complemented
8C2×#16810550C211yesmaximal, characteristic, complemented
9C2×#16810549C211yesmaximal, characteristic, complemented
10C2×#16810547C211yesmaximal, characteristic, complemented
11C2×#16810546C211yesmaximal, characteristic, complemented
12C2×#16810539C211yesmaximal, characteristic
13C2×#16810538C211yesmaximal, characteristic
14C2×#16810502C211yesmaximal, characteristic
15C2×#16810496C211yesmaximal, characteristic, complemented
16C2×C53×#385C211yesmaximal, characteristic, complemented
17C23×C22⋊D53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×C4⋊Dic53C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×#11719919C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×#11719921C2211yescharacteristic
30C22×#11719921C2211yescharacteristic
31C22×#11719921C2211yescharacteristic
32C22×#11719921C2211yescharacteristic
33C22×#11719921C2211yescharacteristic
34C22×#11719921C2211yescharacteristic
35#16810565C2218yescomplemented
36#16810564C2218yescomplemented
37#16810558C2218yescomplemented
38#16810556C2218yescomplemented
39#16810553C2218yescomplemented
40#16810551C2218yescomplemented
41#16810550C2218yescomplemented
42#16810549C2218yescomplemented
43#16810547C2218yescomplemented
44#16810546C2218yescomplemented
45#16810539C2218yes—
46#16810538C2218yes—
47#16810502C2218yes—
48#16810496C2218yescomplemented
49C2×#13133124C2211yescharacteristic
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C24×C4×C53C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C4⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C53×#385C2218yescomplemented
65C2×#95×C53C2211yescharacteristic
66C2×#95×C53C2211yescharacteristic
67C24×D53C2311yescharacteristic
68C22×C22⋊D53—24no—
69C22×C22⋊D53—42no—
70C22×C22⋊D53—42no—
71C22×C22⋊D53C2314yes—
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C23×Dic53C2311yescharacteristic
76C23×Dic53C2311yescharacteristic
77C23×Dic53C2311yescharacteristic
78C23×Dic53C2311yescharacteristic
79C2×C4⋊Dic53—42no—
80C2×C4⋊Dic53—42no—
81C2×C4⋊Dic53C2314yes—
82C2×C4⋊Dic53C2314yes—
83C2×#11719919—42no—
84C2×#11719919—42no—
85C2×#11719919—42no—
86C2×#11719919—42no—
87C2×#11719919—42no—
88C2×#11719919—42no—
89C2×#11719919C2314yes—
90C2×#11719919C2314yes—
91C2×#11719919C2314yes—
92C2×#11719919C2314yes—
93C2×#11719919C2314yes—
94C2×#11719919C2314yes—
95C2×C22⋊Dic53—24no—
96C2×C22⋊Dic53—42no—
97C2×C22⋊Dic53—42no—
98C2×C22⋊Dic53C2314yes—
99C2×C22⋊Dic53C2314yes—
100C2×C22⋊Dic53C2314yes—
101C2×#11719921—42no—
102C2×#11719921—42no—
103C2×#11719921—42no—
104C2×#11719921—42no—
105C2×#11719921—42no—
106C2×#11719921—42no—
107C2×#11719921C2314yes—
108C2×#11719921C2314yes—
109C2×#11719921C2314yes—
110C2×#11719921C2314yes—
111C2×#11719921C2314yes—
112C2×#11719921C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122#13133124C2314yes—
123C25×C53C2311yescharacteristic
124C23×C4×C53—42no—
125C23×C4×C53—42no—
126C23×C4×C53—42no—
127C23×C4×C53C2311yescharacteristic
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C23×C4×C53C2314yes—
134C2×C4⋊C4×C53—42no—
135C2×C4⋊C4×C53—42no—
136C2×C4⋊C4×C53C2314yes—
137C2×C4⋊C4×C53C2314yes—
138C2×C22⋊C4×C53—24no—
139C2×C22⋊C4×C53—42no—
140C2×C22⋊C4×C53C2314yes—
141C2×C22⋊C4×C53C2314yes—
142#95×C53C2314yes—
143#95×C53C2314yes—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—22no—
150C24×C53#4114yes—
151C24×C53C2412yes—
152C24×C53C2411yescharacteristic
153C23×D53—22no—
154C23×D53—22no—
155C23×D53—22no—
156C23×D53—22no—
157C23×D53—22no—
158C23×D53—22no—
159C23×D53—22no—
160C23×D53C2412yes—
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×C53—22no—
171C22×C4×C53—22no—
172C22×C4×C53—22no—
173C22×C4×C53—22no—
174C22×C4×C53—22no—
175C22×C4×C53—22no—
176C22×C4×C53—22no—
177C22×C4×C53—22no—
178C22×C4×C53—22no—
179C22×C4×C53—44no—
180C22×C4×C53—44no—
181C22×C4×C53—44no—
182C22×C4×C53—416no—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
185C22×C4×C53C2412yes—
186C22×C4×C53C2412yes—
187C22×C4×C53C2412yes—
188C22×C4×C53C2412yes—
189C2×C22⋊D53—28no—
190C2×C22⋊D53—44no—
191C2×C22⋊D53—44no—
192C2×C22⋊D53—416no—
193C22×Dic53—22no—
194C22×Dic53—22no—
195C22×Dic53—22no—
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—22no—
205C22×Dic53—22no—
206C22×Dic53—22no—
207C22×Dic53—22no—
208C22×Dic53—22no—
209C22×Dic53—22no—
210C22×Dic53—22no—
211C22×Dic53—22no—
212C22×Dic53—22no—
213C22×Dic53—22no—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C22×Dic53C2412yes—
218C22×Dic53C2412yes—
219C22×Dic53C2412yes—
220C22×Dic53C2412yes—
221C4⋊C4×C53—44no—
222C4⋊C4×C53—44no—
223C22⋊C4×C53—28no—
224C22⋊C4×C53—44no—
225C22⋊Dic53—28no—
226C22⋊Dic53—44no—
227C22⋊Dic53—44no—
228#11719921—44no—
229#11719921—44no—
230#11719921—44no—
231#11719921—44no—
232#11719921—44no—
233#11719921—44no—
234C4⋊Dic53—44no—
235C4⋊Dic53—44no—
236#11719919—44no—
237#11719919—44no—
238#11719919—44no—
239#11719919—44no—
240#11719919—44no—
241#11719919—44no—
242C23×C53—28no—
243C23×C53—28no—
244C23×C53—28no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—44no—
252C23×C53—44no—
253C23×C53—44no—
254C23×C53—44no—
255C23×C53C2×#4114yes—
256C23×C53C2×#4112yes—
257C23×C53H(5,𝔽2)12yes—
258C23×C53H(5,𝔽2)12yes—
259C23×C53H(5,𝔽2)12yes—
260C23×C53H(5,𝔽2)12yes—
261C23×C532−1+412yes—
262C23×C532−1+412yes—
263C23×C53C2511yescharacteristic
264C22×D53—22no—
265C22×D53—22no—
266C22×D53—22no—
267C22×D53—22no—
268C22×D53—22no—
269C22×D53—22no—
270C22×D53—22no—
271C22×D53—44no—
272C22×D53—44no—
273C22×D53—44no—
274C22×D53—44no—
275C22×D53—44no—
276C22×D53—44no—
277C22×D53—44no—
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—22no—
285C2×C4×C53—22no—
286C2×C4×C53—22no—
287C2×C4×C53—22no—
288C2×C4×C53—22no—
289C2×C4×C53—22no—
290C2×C4×C53—22no—
291C2×C4×C53—22no—
292C2×C4×C53—22no—
293C2×C4×C53—22no—
294C2×C4×C53—22no—
295C2×C4×C53—22no—
296C2×C4×C53—416no—
297C2×C4×C53—44no—
298C2×C4×C53—44no—
299C2×C4×C53—44no—
300C2×C4×C53—44no—
301C2×C4×C53—44no—
302C2×C4×C53—44no—
303C22⋊D53—416no—
304C2×Dic53—22no—
305C2×Dic53—22no—
306C2×Dic53—22no—
307C2×Dic53—22no—
308C2×Dic53—22no—
309C2×Dic53—22no—
310C2×Dic53—22no—
311C2×Dic53—22no—
312C2×Dic53—22no—
313C2×Dic53—22no—
314C2×Dic53—22no—
315C2×Dic53—22no—
316C2×Dic53—22no—
317C2×Dic53—22no—
318C2×Dic53—22no—
319C2×Dic53—22no—
320C2×Dic53—22no—
321C2×Dic53—22no—
322C2×Dic53—22no—
323C2×Dic53—22no—
324C2×Dic53—22no—
325C2×Dic53—44no—
326C2×Dic53—44no—
327C2×Dic53—44no—
328C2×Dic53—44no—
329C2×Dic53—44no—
330C2×Dic53—44no—
331C2×Dic53—44no—
332C2×#2827—531nomaximal, Sylow
333C22×C53—24no—
334C22×C53—24no—
335C22×C53—24no—
336C22×C53—416no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53#53814yes—
342C22×C53#53914yes—
343C22×C53#53914yes—
344C22×C53#56014yes—
345C22×C53#56214yes—
346C22×C53#56214yes—
347C22×C53#56314yes—
348C22×C53C22×#4111yescharacteristic
349C22×C53C2×H(5,𝔽2)11yescharacteristic
350C22×C53C2×H(5,𝔽2)11yescharacteristic
351C22×C53C2×H(5,𝔽2)11yescharacteristic
352C22×C53C2×H(5,𝔽2)11yescharacteristic
353C22×C53C2×2−1+411yescharacteristic
354C22×C53C2×2−1+411yescharacteristic
355C2×D53—42no—
356C2×D53—42no—
357C2×D53—42no—
358C2×D53—42no—
359C2×D53—42no—
360C2×D53—42no—
361C2×D53—42no—
362C2×D53—88no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366C4×C53—42no—
367C4×C53—42no—
368C4×C53—42no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372Dic53—42no—
373Dic53—42no—
374Dic53—42no—
375Dic53—42no—
376#2827—5316no—
377C2×#400—531no—
378C2×#400—531no—
379C2×#399—531no—
380C2×#398—531no—
381C2×#398—531no—
382C2×#397—531no—
383C2×#397—531no—
384C2×#397—531no—
385C2×#396—531no—
386C2×#396—531no—
387C2×#394—531no—
388C2×#394—531no—
389C2×#386—531no—
390C2×#385—531no—
391C2×#385D5311yescharacteristic, complemented
392C2×C53—44no—
393C2×C53#282718yescomplemented
394C2×C53C2×#53811yescharacteristic
395C2×C53C2×#53911yescharacteristic
396C2×C53C2×#53911yescharacteristic
397C2×C53C2×#56011yescharacteristic
398C2×C53C2×#56211yescharacteristic
399C2×C53C2×#56211yescharacteristic
400C2×C53C2×#56311yescharacteristic
401D53—82no—
402C23×D4—531no—
403C24×C4C2×D5311yescharacteristic
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4—531no—
408C22×C4⋊C4—531no—
409C22×C4⋊C4—531no—
410C22×C4⋊C4—531no—
411C22×C4⋊C4—531no—
412C22×C4⋊C4C2×D5311yescharacteristic
413C22×C4⋊C4C2×D5311yescharacteristic
414C22×C22⋊C4—531no—
415C22×C22⋊C4—531no—
416C22×C22⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4—531no—
419C22×C22⋊C4—531no—
420C22×C22⋊C4—531no—
421C22×C22⋊C4—531no—
422C22×C22⋊C4—531no—
423C22×C22⋊C4C2×D5311yescharacteristic
424C22×C22⋊C4C2×D5311yescharacteristic
425#400—538no—
426#400—538no—
427#399—538no—
428#398—538no—
429#398—538no—
430#397—538no—
431#397—538no—
432#397—538no—
433#396—538no—
434#396—538no—
435#394—538no—
436#394—538no—
437#386—538no—
438#385—538no—
439#385C2×D5318yescomplemented
440C2×#95—531no—
441C2×#95—531no—
442C2×#95—531no—
443C2×#95—531no—
444C2×#95—531no—
445C2×#95—531no—
446C2×#95—531no—
447C2×#95—531no—
448C2×#95—531no—
449C2×#95—531no—
450C2×#95C2×D5311yescharacteristic
451C2×#95C2×D5311yescharacteristic
452C53C2×#282711yescharacteristic, complemented, Sylow
453C25—531no—
454C25C22×D5311yescharacteristic
455C22×D4—534no—
456C22×D4—1064no—
457C22×D4—2122no—
458C22×D4—2122no—
459C23×C4—42no—
460C23×C4—42no—
461C23×C4—42no—
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—531no—
465C23×C4—531no—
466C23×C4—531no—
467C23×C4—531no—
468C23×C4—531no—
469C23×C4C22×D5311yescharacteristic
470C23×C4C22×D5311yescharacteristic
471C23×C4C22×D5311yescharacteristic
472C23×C4C22×D5311yescharacteristic
473C23×C4C22×D5311yescharacteristic
474C23×C4C22×D5311yescharacteristic
475C23×C4C22×D5314yes—
476C2×C4⋊C4—42no—
477C2×C4⋊C4—42no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—534no—
480C2×C4⋊C4—534no—
481C2×C4⋊C4—534no—
482C2×C4⋊C4—534no—
483C2×C4⋊C4—534no—
484C2×C4⋊C4—534no—
485C2×C4⋊C4—534no—
486C2×C4⋊C4—2122no—
487C2×C4⋊C4—2122no—
488C2×C4⋊C4—2122no—
489C2×C4⋊C4—2122no—
490C2×C4⋊C4—2122no—
491C2×C4⋊C4—2122no—
492C2×C4⋊C4—2122no—
493C2×C4⋊C4—2122no—
494C2×C4⋊C4C22×D5314yes—
495C2×C4⋊C4C22×D5314yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—42no—
498C2×C22⋊C4—534no—
499C2×C22⋊C4—534no—
500C2×C22⋊C4—534no—
501C2×C22⋊C4—534no—
502C2×C22⋊C4—534no—
503C2×C22⋊C4—534no—
504C2×C22⋊C4—534no—
505C2×C22⋊C4—534no—
506C2×C22⋊C4—534no—
507C2×C22⋊C4—1064no—
508C2×C22⋊C4—2122no—
509C2×C22⋊C4—2122no—
510C2×C22⋊C4—2122no—
511C2×C22⋊C4—2122no—
512C2×C22⋊C4—2122no—
513C2×C22⋊C4—2122no—
514C2×C22⋊C4—2122no—
515C2×C22⋊C4—2122no—
516C2×C22⋊C4C22×D5314yes—
517C2×C22⋊C4C22×D5314yes—
518#95—534no—
519#95—534no—
520#95—534no—
521#95—534no—
522#95—534no—
523#95—534no—
524#95—534no—
525#95—534no—
526#95—534no—
527#95—534no—
528#95C22×D5314yes—
529#95C22×D5314yes—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—532no—
537C24—1062no—
538C24—1062no—
539C24—1062no—
540C24—1062no—
541C24—1062no—
542C24—1062no—
543C24—1062no—
544C24#1171994514yes—
545C24C23×D5312yes—
546C24C23×D5311yescharacteristic
547C2×D4—1068no—
548C2×D4—2124no—
549C2×D4—2124no—
550C2×D4—21216no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—44no—
570C22×C4—44no—
571C22×C4—44no—
572C22×C4—416no—
573C22×C4—532no—
574C22×C4—532no—
575C22×C4—532no—
576C22×C4—532no—
577C22×C4—532no—
578C22×C4—532no—
579C22×C4—532no—
580C22×C4—1062no—
581C22×C4—1062no—
582C22×C4—1062no—
583C22×C4—1062no—
584C22×C4—1062no—
585C22×C4—1062no—
586C22×C4—1062no—
587C22×C4—1062no—
588C22×C4—1062no—
589C22×C4—1062no—
590C22×C4—1062no—
591C22×C4—1062no—
592C22×C4—1062no—
593C22×C4—1062no—
594C22×C4—1062no—
595C22×C4—1062no—
596C22×C4—1062no—
597C22×C4—1062no—
598C22×C4—1062no—
599C22×C4—1062no—
600C22×C4—1062no—
601C22×C4C23×D5312yes—
602C22×C4C23×D5312yes—
603C22×C4C23×D5312yes—
604C22×C4C23×D5312yes—
605C22×C4C23×D5312yes—
606C22×C4C23×D5312yes—
607C4⋊C4—44no—
608C4⋊C4—44no—
609C4⋊C4—2124no—
610C4⋊C4—2124no—
611C4⋊C4—2124no—
612C4⋊C4—2124no—
613C4⋊C4—2124no—
614C4⋊C4—2124no—
615C4⋊C4—2124no—
616C4⋊C4—2124no—
617C22⋊C4—28no—
618C22⋊C4—44no—
619C22⋊C4—1068no—
620C22⋊C4—2124no—
621C22⋊C4—2124no—
622C22⋊C4—2124no—
623C22⋊C4—2124no—
624C22⋊C4—2124no—
625C22⋊C4—2124no—
626C22⋊C4—2124no—
627C22⋊C4—2124no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—28no—
635C23—28no—
636C23—28no—
637C23—44no—
638C23—44no—
639C23—44no—
640C23—44no—
641C23—1062no—
642C23—1062no—
643C23—1062no—
644C23—1062no—
645C23—1062no—
646C23—1062no—
647C23—1062no—
648C23—2124no—
649C23—2124no—
650C23—2124no—
651C23—2124no—
652C23—2124no—
653C23—2124no—
654C23—2124no—
655C23C2×#1171994514yes—
656C23C2×#1171994512yes—
657C23#1313326212yes—
658C23#1313326212yes—
659C23#1313326212yes—
660C23#1313326312yes—
661C23#1313326412yes—
662C23#1313326512yes—
663C23C24×D5311yescharacteristic
664D4—21216no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—416no—
684C2×C4—44no—
685C2×C4—44no—
686C2×C4—44no—
687C2×C4—44no—
688C2×C4—44no—
689C2×C4—44no—
690C2×C4—1062no—
691C2×C4—1062no—
692C2×C4—1062no—
693C2×C4—1062no—
694C2×C4—1062no—
695C2×C4—1062no—
696C2×C4—1062no—
697C2×C4—1062no—
698C2×C4—1062no—
699C2×C4—1062no—
700C2×C4—1062no—
701C2×C4—1062no—
702C2×C4—1062no—
703C2×C4—1062no—
704C2×C4—1062no—
705C2×C4—1062no—
706C2×C4—1062no—
707C2×C4—1062no—
708C2×C4—1062no—
709C2×C4—1062no—
710C2×C4—1062no—
711C2×C4—2124no—
712C2×C4—2124no—
713C2×C4—2124no—
714C2×C4—2124no—
715C2×C4—2124no—
716C2×C4—2124no—
717C2×C4—2124no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—416no—
726C22—4248no—
727C22—2122no—
728C22—2122no—
729C22—2122no—
730C22—2122no—
731C22—2122no—
732C22—2122no—
733C22—2122no—
734C22#1681120614yes—
735C22#1681121514yes—
736C22#1681122014yes—
737C22#1681136214yes—
738C22#1681136914yes—
739C22#1681137014yes—
740C22#1681137414yes—
741C22C22×#1171994511yescharacteristic
742C22C2×#1313326211yescharacteristic
743C22C2×#1313326211yescharacteristic
744C22C2×#1313326211yescharacteristic
745C22C2×#1313326311yescharacteristic
746C22C2×#1313326411yescharacteristic
747C22C2×#1313326511yescharacteristic
748C4—42no—
749C4—42no—
750C4—42no—
751C4—42no—
752C4—42no—
753C4—42no—
754C4—2122no—
755C4—2122no—
756C4—2122no—
757C4—2122no—
758C4—2122no—
759C4—2122no—
760C4—2122no—
761C2—44no—
762C2—4242no—
763C2#2028281718yesdirect product factor
764C2C2×#1681120611yescharacteristic
765C2C2×#1681121511yescharacteristic
766C2C2×#1681122011yescharacteristic
767C2C2×#1681136211yescharacteristic
768C2C2×#1681136911yescharacteristic
769C2C2×#1681137011yescharacteristic
770C2C2×#1681137411yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#385C2
socleC24×C53C24
prime radicalC23×C22⋊D53C22
hypercenterC2×#385D53
hypocenterC53C2×#2827
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. #20282817C2direct (N × H)
2. C2×#16810565C2semidirect
3. C2×#16810564C2semidirect
4. C2×#16810558C2semidirect
5. C2×#16810556C2semidirect
6. C2×#16810553C2semidirect
7. C2×#16810551C2semidirect
8. C2×#16810550C2semidirect
9. C2×#16810549C2semidirect
10. C2×#16810547C2semidirect
11. C2×#16810546C2semidirect
15. C2×#16810496C2semidirect
16. C2×C53×#385C2semidirect
35. #16810565C22semidirect
36. #16810564C22semidirect
37. #16810558C22semidirect
38. #16810556C22semidirect
39. #16810553C22semidirect
40. #16810551C22semidirect
41. #16810550C22semidirect
42. #16810549C22semidirect
43. #16810547C22semidirect
44. #16810546C22semidirect
48. #16810496C22semidirect
64. C53×#385C22semidirect
391. C2×#385D53semidirect
393. C2×C53#2827semidirect
439. #385C2×D53semidirect
452. C53C2×#2827semidirect
763. C2#20282817direct (N × H)

Maximal subgroups

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

subgroupindex
#202828172
C2×#168105652
C2×#168105642
C2×#168105582
C2×#168105562
C2×#168105532
C2×#168105512
C2×#168105502
C2×#168105492
C2×#168105472
C2×#168105462
C2×#168105392
C2×#168105382
C2×#168105022
C2×#168104962
C2×C53×#3852
C2×#282753