Finite Group Databasebeta

← C2×#20280745 #27550720

Subgroups — C2×#20280745 #27550720

Order 13568.

2222 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20280745C2116yesmaximal, direct product factor
2C2×#16810559C211yesmaximal, characteristic, complemented
3C2×#16810557C211yesmaximal, characteristic, complemented
4C2×#16810556C211yesmaximal, characteristic, complemented
5C2×#16810551C211yesmaximal, characteristic, complemented
6C2×#16810551C211yesmaximal, characteristic, complemented
7C2×#16810546C211yesmaximal, characteristic, complemented
8C2×#16810537C211yesmaximal, characteristic
9C2×#16810526C211yesmaximal, characteristic
10C2×#16810517C211yesmaximal, characteristic, complemented
11C2×#16810517C211yesmaximal, characteristic, complemented
12C2×#16810517C211yesmaximal, characteristic, complemented
13C2×#16810511C211yesmaximal, characteristic, complemented
14C2×#16810509C211yesmaximal, characteristic, complemented
15C2×#16810474C211yesmaximal, characteristic, complemented
16C2×C53×#394C211yesmaximal, characteristic
17C22×C4⋊Dic53C2211yescharacteristic
18C22×C4⋊Dic53C2211yescharacteristic
19C22×#11719919C2211yescharacteristic
20C22×#11719919C2211yescharacteristic
21C22×#11719919C2211yescharacteristic
22C22×#11719919C2211yescharacteristic
23C22×#11719919C2211yescharacteristic
24C22×#11719919C2211yescharacteristic
25C22×C22⋊Dic53C2211yescharacteristic
26C22×C22⋊Dic53C2211yescharacteristic
27C22×C22⋊Dic53C2211yescharacteristic
28C22×C22⋊Dic53C2211yescharacteristic
29C22×C22⋊Dic53C2211yescharacteristic
30C22×C22⋊Dic53C2211yescharacteristic
31C22×C22⋊Dic53C2211yescharacteristic
32C22×C22⋊Dic53C2211yescharacteristic
33C22×C4×Dic53C2211yescharacteristic
34C22×C4×Dic53C2211yescharacteristic
35C22×C4×Dic53C2211yescharacteristic
36#16810559C2218yescomplemented
37#16810557C2218yescomplemented
38#16810556C2218yescomplemented
39#16810551C2218yescomplemented
40#16810551C2218yescomplemented
41#16810546C2218yescomplemented
42#16810537C2218yes—
43#16810526C2218yes—
44#16810517C2218yescomplemented
45#16810517C2218yescomplemented
46#16810517C2218yescomplemented
47#16810511C2218yescomplemented
48#16810509C2218yescomplemented
49#16810474C2218yescomplemented
50C2×#13133124C2211yescharacteristic
51C2×#13133124C2211yescharacteristic
52C2×#13133124C2211yescharacteristic
53C2×#13133124C2211yescharacteristic
54C2×#13133124C2211yescharacteristic
55C2×#13133124C2211yescharacteristic
56C2×#13133124C2211yescharacteristic
57C2×#13133124C2211yescharacteristic
58C2×#13133124C2211yescharacteristic
59C23×D4×C53C2211yescharacteristic
60C22×C4⋊C4×C53C2211yescharacteristic
61C22×C22⋊C4×C53C2211yescharacteristic
62C22×C22⋊C4×C53C2211yescharacteristic
63C22×C22⋊C4×C53C2211yescharacteristic
64C22×C22⋊C4×C53C2211yescharacteristic
65C53×#394C2218yes—
66C2×#95×C53C2211yescharacteristic
67C23×Dic53C2311yescharacteristic
68C23×Dic53C2311yescharacteristic
69C23×Dic53C2311yescharacteristic
70C23×Dic53C2311yescharacteristic
71C23×Dic53C2311yescharacteristic
72C23×Dic53C2311yescharacteristic
73C23×Dic53C2311yescharacteristic
74C23×Dic53C2311yescharacteristic
75C2×C4⋊Dic53—42no—
76C2×C4⋊Dic53—42no—
77C2×C4⋊Dic53C2314yes—
78C2×C4⋊Dic53C2314yes—
79C2×#11719919—24no—
80C2×#11719919—24no—
81C2×#11719919—42no—
82C2×#11719919—42no—
83C2×#11719919—42no—
84C2×#11719919—42no—
85C2×#11719919C2314yes—
86C2×#11719919C2314yes—
87C2×#11719919C2314yes—
88C2×#11719919C2314yes—
89C2×#11719919C2314yes—
90C2×#11719919C2314yes—
91C2×C22⋊Dic53—24no—
92C2×C22⋊Dic53—24no—
93C2×C22⋊Dic53—24no—
94C2×C22⋊Dic53—24no—
95C2×C22⋊Dic53—42no—
96C2×C22⋊Dic53—42no—
97C2×C22⋊Dic53—42no—
98C2×C22⋊Dic53—42no—
99C2×C22⋊Dic53C2314yes—
100C2×C22⋊Dic53C2314yes—
101C2×C22⋊Dic53C2314yes—
102C2×C22⋊Dic53C2314yes—
103C2×C22⋊Dic53C2314yes—
104C2×C22⋊Dic53C2314yes—
105C2×C22⋊Dic53C2314yes—
106C2×C22⋊Dic53C2314yes—
107C2×C4×Dic53—24no—
108C2×C4×Dic53—42no—
109C2×C4×Dic53—42no—
110C2×C4×Dic53C2314yes—
111C2×C4×Dic53C2314yes—
112C2×C4×Dic53C2314yes—
113#13133124C2314yes—
114#13133124C2314yes—
115#13133124C2314yes—
116#13133124C2314yes—
117#13133124C2314yes—
118#13133124C2314yes—
119#13133124C2314yes—
120#13133124C2314yes—
121#13133124C2314yes—
122C25×C53C2311yescharacteristic
123C25×C53C2311yescharacteristic
124C22×D4×C53—24no—
125C22×D4×C53—42no—
126C22×D4×C53—42no—
127C22×D4×C53C2314yes—
128C23×C4×C53C2311yescharacteristic
129C23×C4×C53C2311yescharacteristic
130C23×C4×C53C2311yescharacteristic
131C23×C4×C53C2311yescharacteristic
132C23×C4×C53C2311yescharacteristic
133C2×C4⋊C4×C53—24no—
134C2×C4⋊C4×C53C2314yes—
135C2×C22⋊C4×C53—42no—
136C2×C22⋊C4×C53—42no—
137C2×C22⋊C4×C53—42no—
138C2×C22⋊C4×C53—42no—
139C2×C22⋊C4×C53C2314yes—
140C2×C22⋊C4×C53C2314yes—
141C2×C22⋊C4×C53C2314yes—
142C2×C22⋊C4×C53C2314yes—
143#95×C53C2314yes—
144C24×C53—22no—
145C24×C53—22no—
146C24×C53—22no—
147C24×C53—22no—
148C24×C53—22no—
149C24×C53—22no—
150C24×C53—22no—
151C24×C53—22no—
152C24×C53—22no—
153C24×C53—22no—
154C24×C53—22no—
155C24×C53—22no—
156C24×C53—22no—
157C24×C53—22no—
158C24×C53C2412yes—
159C24×C53C2412yes—
160C24×C53C2411yescharacteristic
161C2×D4×C53—28no—
162C2×D4×C53—44no—
163C2×D4×C53—44no—
164C2×D4×C53—416no—
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#4114yes—
180C22×C4×C53C2412yes—
181C22×C4×C53C2412yes—
182C22×C4×C53C2412yes—
183C22×C4×C53C2412yes—
184C22×C4×C53C2412yes—
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×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#4114yes—
208C22×Dic53#4114yes—
209C22×Dic53C2412yes—
210C22×Dic53C2412yes—
211C22×Dic53C2412yes—
212C22×Dic53C2412yes—
213C22×Dic53C2412yes—
214C22×Dic53C2412yes—
215C22×Dic53C2412yes—
216C22×Dic53C2412yes—
217C4⋊C4×C53—28no—
218C22⋊C4×C53—44no—
219C22⋊C4×C53—44no—
220C22⋊C4×C53—44no—
221C22⋊C4×C53—44no—
222C22⋊Dic53—28no—
223C22⋊Dic53—28no—
224C22⋊Dic53—28no—
225C22⋊Dic53—28no—
226C22⋊Dic53—44no—
227C22⋊Dic53—44no—
228C22⋊Dic53—44no—
229C22⋊Dic53—44no—
230C4⋊Dic53—44no—
231C4⋊Dic53—44no—
232#11719919—28no—
233#11719919—28no—
234#11719919—44no—
235#11719919—44no—
236#11719919—44no—
237#11719919—44no—
238C4×Dic53—28no—
239C4×Dic53—44no—
240C4×Dic53—44no—
241C23×C53—22no—
242C23×C53—22no—
243C23×C53—22no—
244C23×C53—22no—
245C23×C53—22no—
246C23×C53—22no—
247C23×C53—22no—
248C23×C53—22no—
249C23×C53—22no—
250C23×C53—22no—
251C23×C53—22no—
252C23×C53—22no—
253C23×C53—22no—
254C23×C53—22no—
255C23×C53—44no—
256C23×C53—44no—
257C23×C53—44no—
258C23×C53—44no—
259C23×C53—44no—
260C23×C53—44no—
261C23×C53—44no—
262C23×C53—44no—
263C23×C53—44no—
264C23×C53—44no—
265C23×C53—44no—
266C23×C53—44no—
267C23×C53—44no—
268C23×C53—44no—
269C23×C53C2×#4112yes—
270C23×C53C2×#4112yes—
271C23×C53C2×#4112yes—
272C23×C53H(5,𝔽2)12yes—
273C23×C53H(5,𝔽2)12yes—
274C23×C53H(5,𝔽2)12yes—
275C23×C532−1+412yes—
276C23×C53C2511yescharacteristic
277D4×C53—416no—
278C2×C4×C53—28no—
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—44no—
294C2×C4×C53—44no—
295C2×C4×C53—44no—
296C2×C4×C53—44no—
297C2×C4×C53C2×#4114yes—
298C2×Dic53—28no—
299C2×Dic53—28no—
300C2×Dic53—22no—
301C2×Dic53—22no—
302C2×Dic53—22no—
303C2×Dic53—22no—
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—44no—
323C2×Dic53—44no—
324C2×Dic53—44no—
325C2×Dic53—44no—
326C2×Dic53—44no—
327C2×Dic53—44no—
328C2×Dic53C2×#4114yes—
329C2×Dic53C2×#4114yes—
330C2×#2651—531nomaximal, Sylow
331C22×C53—42no—
332C22×C53—42no—
333C22×C53—42no—
334C22×C53—42no—
335C22×C53—42no—
336C22×C53—42no—
337C22×C53—42no—
338C22×C53—42no—
339C22×C53—42no—
340C22×C53—42no—
341C22×C53—42no—
342C22×C53—42no—
343C22×C53—42no—
344C22×C53—42no—
345C22×C53—88no—
346C22×C53—88no—
347C22×C53#52914yes—
348C22×C53#53814yes—
349C22×C53#53914yes—
350C22×C53#54014yes—
351C22×C53#54014yes—
352C22×C53#54214yes—
353C22×C53#54214yes—
354C22×C53C22×#4111yescharacteristic
355C22×C53C22×#4111yescharacteristic
356C22×C53C22×#4111yescharacteristic
357C22×C53C2×H(5,𝔽2)11yescharacteristic
358C22×C53C2×H(5,𝔽2)11yescharacteristic
359C22×C53C2×H(5,𝔽2)11yescharacteristic
360C22×C53C2×2−1+411yescharacteristic
361C4×C53—24no—
362C4×C53—42no—
363C4×C53—42no—
364C4×C53—42no—
365C4×C53—42no—
366Dic53—24no—
367Dic53—24no—
368Dic53—42no—
369Dic53—42no—
370Dic53—42no—
371Dic53—42no—
372Dic53—42no—
373Dic53—42no—
374#2651—5316no—
375C2×#399—531no—
376C2×#398—531no—
377C2×#398—531no—
378C2×#397—531no—
379C2×#397—531no—
380C2×#396—531no—
381C2×#394—531no—
382C2×#394D5311yescharacteristic
383C2×#390—531no—
384C2×#388—531no—
385C2×#388—531no—
386C2×#388—531no—
387C2×#388—531no—
388C2×#387—531no—
389C2×C4×C4⋊C4—531no—
390C2×C53—82no—
391C2×C53—82no—
392C2×C53#265118yescomplemented
393C2×C53C2×#52911yescharacteristic
394C2×C53C2×#53811yescharacteristic
395C2×C53C2×#53911yescharacteristic
396C2×C53C2×#54011yescharacteristic
397C2×C53C2×#54011yescharacteristic
398C2×C53C2×#54211yescharacteristic
399C2×C53C2×#54211yescharacteristic
400C23×D4C2×D5311yescharacteristic
401C22×C4⋊C4—531no—
402C22×C4⋊C4—531no—
403C22×C4⋊C4—531no—
404C22×C4⋊C4—531no—
405C22×C4⋊C4—531no—
406C22×C4⋊C4—531no—
407C22×C4⋊C4—531no—
408C22×C4⋊C4—531no—
409C22×C4⋊C4C2×D5311yescharacteristic
410C22×C22⋊C4—531no—
411C22×C22⋊C4—531no—
412C22×C22⋊C4—531no—
413C22×C22⋊C4—531no—
414C22×C22⋊C4—531no—
415C22×C22⋊C4—531no—
416C22×C22⋊C4—531no—
417C22×C22⋊C4—531no—
418C22×C22⋊C4C2×D5311yescharacteristic
419C22×C22⋊C4C2×D5311yescharacteristic
420C22×C22⋊C4C2×D5311yescharacteristic
421C22×C22⋊C4C2×D5311yescharacteristic
422C22×C42—531no—
423C22×C42—531no—
424C22×C42—531no—
425#399—538no—
426#398—538no—
427#398—538no—
428#397—538no—
429#397—538no—
430#396—538no—
431#394—538no—
432#394C2×D5318yes—
433#390—538no—
434#388—538no—
435#388—538no—
436#388—538no—
437#388—538no—
438#387—538no—
439C4×C4⋊C4—538no—
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×#95C2×D5311yescharacteristic
450C53C2×#265111yescharacteristic, complemented, Sylow
451C25C22×D5311yescharacteristic
452C25C22×D5311yescharacteristic
453C22×D4—24no—
454C22×D4—42no—
455C22×D4—42no—
456C22×D4C22×D5314yes—
457C23×C4—531no—
458C23×C4—531no—
459C23×C4—531no—
460C23×C4—531no—
461C23×C4—531no—
462C23×C4—531no—
463C23×C4—531no—
464C23×C4—531no—
465C23×C4C22×D5311yescharacteristic
466C23×C4C22×D5311yescharacteristic
467C23×C4C22×D5311yescharacteristic
468C23×C4C22×D5311yescharacteristic
469C23×C4C22×D5311yescharacteristic
470C2×C4⋊C4—24no—
471C2×C4⋊C4—534no—
472C2×C4⋊C4—534no—
473C2×C4⋊C4—534no—
474C2×C4⋊C4—534no—
475C2×C4⋊C4—534no—
476C2×C4⋊C4—534no—
477C2×C4⋊C4—534no—
478C2×C4⋊C4—534no—
479C2×C4⋊C4—1064no—
480C2×C4⋊C4—1064no—
481C2×C4⋊C4—2122no—
482C2×C4⋊C4—2122no—
483C2×C4⋊C4—2122no—
484C2×C4⋊C4—2122no—
485C2×C4⋊C4—2122no—
486C2×C4⋊C4—2122no—
487C2×C4⋊C4C22×D5314yes—
488C2×C22⋊C4—42no—
489C2×C22⋊C4—42no—
490C2×C22⋊C4—42no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—534no—
493C2×C22⋊C4—534no—
494C2×C22⋊C4—534no—
495C2×C22⋊C4—534no—
496C2×C22⋊C4—534no—
497C2×C22⋊C4—534no—
498C2×C22⋊C4—534no—
499C2×C22⋊C4—534no—
500C2×C22⋊C4—1064no—
501C2×C22⋊C4—1064no—
502C2×C22⋊C4—1064no—
503C2×C22⋊C4—1064no—
504C2×C22⋊C4—2122no—
505C2×C22⋊C4—2122no—
506C2×C22⋊C4—2122no—
507C2×C22⋊C4—2122no—
508C2×C22⋊C4C22×D5314yes—
509C2×C22⋊C4C22×D5314yes—
510C2×C22⋊C4C22×D5314yes—
511C2×C22⋊C4C22×D5314yes—
512C2×C42—534no—
513C2×C42—534no—
514C2×C42—534no—
515C2×C42—1064no—
516C2×C42—2122no—
517C2×C42—2122no—
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#95C22×D5314yes—
528C24—22no—
529C24—22no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C23×D5312yes—
543C24C23×D5312yes—
544C24C23×D5311yescharacteristic
545C2×D4—28no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—416no—
549C22×C4—22no—
550C22×C4—22no—
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—534no—
564C22×C4—534no—
565C22×C4—532no—
566C22×C4—532no—
567C22×C4—532no—
568C22×C4—532no—
569C22×C4—532no—
570C22×C4—532no—
571C22×C4—532no—
572C22×C4—532no—
573C22×C4—1062no—
574C22×C4—1062no—
575C22×C4—1062no—
576C22×C4—1062no—
577C22×C4—1062no—
578C22×C4—1062no—
579C22×C4—1062no—
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#1171994714yes—
596C22×C4C23×D5312yes—
597C22×C4C23×D5312yes—
598C22×C4C23×D5312yes—
599C22×C4C23×D5312yes—
600C22×C4C23×D5312yes—
601C4⋊C4—28no—
602C4⋊C4—1068no—
603C4⋊C4—1068no—
604C4⋊C4—2124no—
605C4⋊C4—2124no—
606C4⋊C4—2124no—
607C4⋊C4—2124no—
608C4⋊C4—2124no—
609C4⋊C4—2124no—
610C22⋊C4—44no—
611C22⋊C4—44no—
612C22⋊C4—44no—
613C22⋊C4—44no—
614C22⋊C4—1068no—
615C22⋊C4—1068no—
616C22⋊C4—1068no—
617C22⋊C4—1068no—
618C22⋊C4—2124no—
619C22⋊C4—2124no—
620C22⋊C4—2124no—
621C22⋊C4—2124no—
622C42—1068no—
623C42—2124no—
624C42—2124no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—44no—
640C23—44no—
641C23—44no—
642C23—44no—
643C23—44no—
644C23—44no—
645C23—44no—
646C23—44no—
647C23—44no—
648C23—44no—
649C23—44no—
650C23—44no—
651C23—44no—
652C23—44no—
653C23#41×D5312yes—
654C23#41×D5312yes—
655C23C2×#1171994712yes—
656C23#1313326212yes—
657C23#1313326212yes—
658C23#1313326212yes—
659C23#1313326412yes—
660C23C24×D5311yescharacteristic
661D4—416no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—28no—
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—44no—
678C2×C4—44no—
679C2×C4—44no—
680C2×C4—44no—
681C2×C4—534no—
682C2×C4—534no—
683C2×C4—1068no—
684C2×C4—1062no—
685C2×C4—1062no—
686C2×C4—1062no—
687C2×C4—1062no—
688C2×C4—1068no—
689C2×C4—1062no—
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—2124no—
708C2×C4—2124no—
709C2×C4—2124no—
710C2×C4—2124no—
711C2×C4—2124no—
712C2×C4—2124no—
713C2×C4C2×#1171994714yes—
714C22—42no—
715C22—42no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—42no—
728C22—88no—
729C22—88no—
730C22#1681115214yes—
731C22#1681120814yes—
732C22#1681121614yes—
733C22#1681122314yes—
734C22#1681122314yes—
735C22#1681124014yes—
736C22#1681124114yes—
737C22C2×#41×D5311yescharacteristic
738C22C2×#41×D5311yescharacteristic
739C22C22×#1171994711yescharacteristic
740C22C2×#1313326211yescharacteristic
741C22C2×#1313326211yescharacteristic
742C22C2×#1313326211yescharacteristic
743C22C2×#1313326411yescharacteristic
744C4—24no—
745C4—42no—
746C4—42no—
747C4—42no—
748C4—42no—
749C4—1064no—
750C4—1064no—
751C4—2122no—
752C4—2122no—
753C4—2122no—
754C4—2122no—
755C4—2122no—
756C4—2122no—
757C2—82no—
758C2—82no—
759C2#2028074518yesdirect product factor
760C2C2×#1681115211yescharacteristic
761C2C2×#1681120811yescharacteristic
762C2C2×#1681121611yescharacteristic
763C2C2×#1681122311yescharacteristic
764C2C2×#1681122311yescharacteristic
765C2C2×#1681124011yescharacteristic
766C2C2×#1681124111yescharacteristic
subgroupG/H
centerC24C23×D53
commutator, cosocleC23×C53C25
FrattiniC23C24×D53
FittingC2×C53×#394C2
socleC24×C53C24
prime radicalC23×D4×C53C22
hypercenterC2×#394D53
hypocenterC53C2×#2651
LCSG ▷ C23×C53 ▷ C53
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. #20280745C2direct (N × H)
2. C2×#16810559C2semidirect
3. C2×#16810557C2semidirect
4. C2×#16810556C2semidirect
5. C2×#16810551C2semidirect
6. C2×#16810551C2semidirect
7. C2×#16810546C2semidirect
10. C2×#16810517C2semidirect
11. C2×#16810517C2semidirect
12. C2×#16810517C2semidirect
13. C2×#16810511C2semidirect
14. C2×#16810509C2semidirect
15. C2×#16810474C2semidirect
36. #16810559C22semidirect
37. #16810557C22semidirect
38. #16810556C22semidirect
39. #16810551C22semidirect
40. #16810551C22semidirect
41. #16810546C22semidirect
44. #16810517C22semidirect
45. #16810517C22semidirect
46. #16810517C22semidirect
47. #16810511C22semidirect
48. #16810509C22semidirect
49. #16810474C22semidirect
392. C2×C53#2651semidirect
450. C53C2×#2651semidirect
759. C2#20280745direct (N × H)

Maximal subgroups

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

subgroupindex
#202807452
C2×#168105592
C2×#168105572
C2×#168105562
C2×#168105512
C2×#168105462
C2×#168105372
C2×#168105262
C2×#168105172
C2×#168105112
C2×#168105092
C2×#168104742
C2×C53×#3942
C2×#265153