Finite Group Databasebeta

← C2×#20285392 #28253970

Subgroups — C2×#20285392 #28253970

Order 13568.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811228C211yesmaximal, characteristic, complemented
2#20285392C2116yesmaximal, direct product factor
3C2×#16811029C211yesmaximal, characteristic, complemented
4C2×#16811013C211yesmaximal, characteristic, complemented
5C2×#16810977C211yesmaximal, characteristic, complemented
6C2×#16810971C211yesmaximal, characteristic, complemented
7C2×#16810874C211yesmaximal, characteristic, complemented
8C2×#16810871C211yesmaximal, characteristic, complemented
9C2×#16810857C211yesmaximal, characteristic, complemented
10C2×#16810854C211yesmaximal, characteristic, complemented
11C2×#16810733C211yesmaximal, characteristic, complemented
12C2×#16810721C211yesmaximal, characteristic, complemented
13C2×C4×#11719924C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810579C211yesmaximal, characteristic, complemented
16C2×C53×#542C211yesmaximal, characteristic, complemented
17C22×#11719924C2211yescharacteristic
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×#11719917C2211yescharacteristic
22C23×#88322C2211yescharacteristic
23#16811228—24no—
24#16811228C2218yescomplemented
25C2×#13133214C2211yescharacteristic
26C2×#13133209C2211yescharacteristic
27C2×#13133202—21no—
28C2×#13133202—21no—
29C2×#13133191C2211yescharacteristic
30C2×#13133191C2211yescharacteristic
31C2×#13133190—21no—
32C2×#13133190—21no—
33C2×C4×D212C2211yescharacteristic
34C2×C4×D212C2211yescharacteristic
35#16811029C2218yescomplemented
36#16811013C2218yescomplemented
37#16810977C2218yescomplemented
38#16810971C2218yescomplemented
39#16810874C2218yescomplemented
40#16810871C2218yescomplemented
41#16810857C2218yescomplemented
42#16810854C2218yescomplemented
43#16810733C2218yescomplemented
44#16810721C2218yescomplemented
45C4×#11719924C2218yescomplemented
46C4×#11719922C2218yescomplemented
47C2×#13133150C2211yescharacteristic
48C2×#13133150C2211yescharacteristic
49C2×#13133148C2211yescharacteristic
50C2×#13133148C2211yescharacteristic
51C2×#13133141C2211yescharacteristic
52C2×#13133141C2211yescharacteristic
53C2×#13133138C2211yescharacteristic
54C2×#13133138C2211yescharacteristic
55C2×#13133137C2211yescharacteristic
56C2×#13133137C2211yescharacteristic
57C2×#13133137C2211yescharacteristic
58C2×#13133137C2211yescharacteristic
59#16810579C2218yescomplemented
60C2×#13133128C2211yescharacteristic
61C2×#13133128C2211yescharacteristic
62C2×C4×#88322C2211yescharacteristic
63C2×C4×#88322C2211yescharacteristic
64C53×#542—24no—
65C53×#542C2218yescomplemented
66C2×C4⋊Q8×C53C2211yescharacteristic
67C2×#126×C53—21no—
68C2×#124×C53—21no—
69C2×#124×C53C2211yescharacteristic
70C2×#123×C53—21no—
71C2×C22⋊Q8×C53—21no—
72C2×C22⋊Q8×C53C2211yescharacteristic
73C2×#121×C53C2211yescharacteristic
74C2×C4×Q8×C53C2211yescharacteristic
75C2×C4×D4×C53C2211yescharacteristic
76C2×#117×C53C2211yescharacteristic
77C22×D212—21no—
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C4×D53—21no—
84C22×C4×D53—21no—
85C2×#11719924—24no—
86C2×#11719924—24no—
87C2×#11719924C2314yes—
88C2×#11719924C2314yes—
89C2×#11719922—24no—
90C2×#11719922—24no—
91C2×#11719922C2314yes—
92C2×#11719922C2314yes—
93C2×#11719917—24no—
94C2×#11719917C2314yes—
95C22×#88322—24no—
96C22×#88322C2311yescharacteristic
97C22×#88322C2311yescharacteristic
98C22×#88322C2314yes—
99C22×#88322C2311yescharacteristic
100C22×#88322C2311yescharacteristic
101#13133214—22no—
102#13133214C2314yes—
103#13133209—22no—
104#13133209C2314yes—
105#13133202—28no—
106#13133202—28no—
107#13133191—22no—
108#13133191—22no—
109#13133191C2314yes—
110#13133191C2314yes—
111#13133190—28no—
112#13133190—28no—
113C4×D212—22no—
114C4×D212—22no—
115C4×D212C2314yes—
116C4×D212C2314yes—
117C2×C4⋊Dic53C2311yescharacteristic
118C2×C4⋊Dic53C2311yescharacteristic
119C2×#11719919—21no—
120C2×#11719919—21no—
121C2×#11719921—21no—
122C2×#11719921—21no—
123C2×#11719921—21no—
124C2×#11719921—21no—
125#13133150C2314yes—
126#13133150C2314yes—
127#13133148C2314yes—
128#13133148C2314yes—
129#13133141C2314yes—
130#13133141C2314yes—
131#13133138C2314yes—
132#13133138C2314yes—
133#13133137C2314yes—
134#13133137C2314yes—
135#13133137C2314yes—
136#13133137C2314yes—
137#13133128C2314yes—
138#13133128C2314yes—
139C4×#88322C2314yes—
140C4×#88322C2314yes—
141C22×Q8×C53—21no—
142C22×Q8×C53C2311yescharacteristic
143C22×D4×C53—21no—
144C22×D4×C53C2311yescharacteristic
145C23×C4×C53—21no—
146C23×C4×C53C2311yescharacteristic
147C4⋊Q8×C53—22no—
148C4⋊Q8×C53C2314yes—
149#126×C53—28no—
150#124×C53—28no—
151#124×C53—22no—
152#124×C53C2314yes—
153#123×C53—28no—
154C22⋊Q8×C53—28no—
155C22⋊Q8×C53—22no—
156C22⋊Q8×C53C2314yes—
157#121×C53—22no—
158#121×C53C2314yes—
159C4×Q8×C53—22no—
160C4×Q8×C53C2314yes—
161C4×D4×C53—22no—
162C4×D4×C53C2314yes—
163#117×C53D414yes—
164#117×C53C2314yes—
165C2×C4⋊C4×C53—21no—
166C2×C4⋊C4×C53—21no—
167C2×C4⋊C4×C53—21no—
168C2×C4⋊C4×C53D411yescharacteristic
169C2×C4⋊C4×C53D411yescharacteristic
170C2×C4⋊C4×C53C2311yescharacteristic
171C2×C4⋊C4×C53C2311yescharacteristic
172C2×C22⋊C4×C53—21no—
173C2×C22⋊C4×C53—21no—
174C2×C22⋊C4×C53—21no—
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C42×C53—21no—
180C2×C42×C53C2311yescharacteristic
181C2×C42×C53C2311yescharacteristic
182C24×C53—21no—
183C24×C53C2×D411yescharacteristic
184C23×D53—21no—
185C23×D53—21no—
186C2×Q8×C53—21no—
187C2×Q8×C53—24no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53—82no—
191C2×Q8×C53C2412yes—
192C2×D4×C53—24no—
193C2×D4×C53—21no—
194C2×D4×C53—22no—
195C2×D4×C53—22no—
196C2×D4×C53—82no—
197C2×D4×C53C2412yes—
198C22×C4×C53—22no—
199C22×C4×C53—22no—
200C22×C4×C53—21no—
201C22×C4×C53—21no—
202C22×C4×C53—21no—
203C22×C4×C53—24no—
204C22×C4×C53—82no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2×D411yescharacteristic
208C22×C4×C53C2×D411yescharacteristic
209C22×C4×C53C2×D411yescharacteristic
210C22×C4×C53C2×D412yes—
211C22×C4×C53C2412yes—
212C22×C4×C53C2411yescharacteristic
213C2×C22⋊D53—24no—
214C2×C22⋊D53—24no—
215C2×C22⋊D53—82no—
216C2×C22⋊D53—82no—
217C22×Dic53—21no—
218C22×Dic53—21no—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—22no—
222C2×D212—22no—
223C2×D212—21no—
224C2×D212—21no—
225C2×D212—24no—
226C2×D212—24no—
227C2×D212—82no—
228C2×D212—82no—
229C2×D212C2412yes—
230C2×D212C2412yes—
231C2×C4×D53—24no—
232C2×C4×D53—24no—
233C2×C4×D53—82no—
234C2×C4×D53—82no—
235C4⋊C4×C53—24no—
236C4⋊C4×C53—24no—
237C4⋊C4×C53—24no—
238C4⋊C4×C53—21no—
239C4⋊C4×C53—21no—
240C4⋊C4×C53C2×D414yes—
241C4⋊C4×C53C2×D414yes—
242C4⋊C4×C53C2412yes—
243C4⋊C4×C53C2412yes—
244C22⋊C4×C53—24no—
245C22⋊C4×C53—24no—
246C22⋊C4×C53—24no—
247C22⋊C4×C53—24no—
248C22⋊C4×C53—24no—
249C22⋊C4×C53C2×D414yes—
250C22⋊C4×C53C2×D414yes—
251C42×C53—24no—
252C42×C53C2×D412yes—
253C42×C53C2×D412yes—
254C42×C53C2412yes—
255C42×C53C2412yes—
256#11719924—28no—
257#11719924—28no—
258#11719922—28no—
259#11719922—28no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264C4⋊Dic53—21no—
265C4⋊Dic53—21no—
266C4⋊Dic53C2412yes—
267C4⋊Dic53C2412yes—
268#11719919—24no—
269#11719919—24no—
270#11719917—28no—
271C2×#88322—22no—
272C2×#88322—22no—
273C2×#88322—28no—
274C2×#88322#4114yes—
275C2×#88322#4114yes—
276C2×#88322C2412yes—
277C2×#88322C2412yes—
278C2×#88322C2412yes—
279C2×#88322C2412yes—
280C23×C53—22no—
281C23×C53—22no—
282C23×C53—22no—
283C23×C53—22no—
284C23×C53—42no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53C22×D412yes—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—42no—
292C22×D53—42no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297Q8×C53—22no—
298Q8×C53—22no—
299Q8×C53—42no—
300Q8×C53—84no—
301D4×C53—22no—
302D4×C53—22no—
303D4×C53—42no—
304D4×C53—84no—
305C2×C4×C53—22no—
306C2×C4×C53—22no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—24no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—22no—
314C2×C4×C53—22no—
315C2×C4×C53—22no—
316C2×C4×C53—42no—
317C2×C4×C53—42no—
318C2×C4×C53—42no—
319C2×C4×C53—84no—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D412yes—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4112yes—
327C2×C4×C53C2×#4112yes—
328C2×C4×C53C2511yescharacteristic
329C22⋊D53—84no—
330C22⋊D53—84no—
331C2×Dic53—22no—
332C2×Dic53—22no—
333C2×Dic53—42no—
334C2×Dic53—42no—
335D212—22no—
336D212—22no—
337D212—22no—
338D212—22no—
339D212—42no—
340D212—42no—
341D212—84no—
342D212—84no—
343C4×D53—84no—
344C4×D53—84no—
345#88322—22no—
346#88322—22no—
347#88322C2×#4114yes—
348#88322C2×#4114yes—
349C2×#3179—531nomaximal, Sylow
350C22×C53—22no—
351C22×C53—22no—
352C22×C53—22no—
353C22×C53—44no—
354C22×C53—42no—
355C22×C53—42no—
356C22×C53—42no—
357C22×C53—84no—
358C22×C53#53212yes—
359C22×C53#57612yes—
360C22×C53#57712yes—
361C22×C53C23×D411yescharacteristic
362C2×D53—42no—
363C2×D53—42no—
364C2×D53—42no—
365C2×D53—42no—
366C2×D53—42no—
367C2×D53—42no—
368C2×D53—84no—
369C2×D53—84no—
370C4×C53—22no—
371C4×C53—22no—
372C4×C53—22no—
373C4×C53—22no—
374C4×C53—22no—
375C4×C53—42no—
376C4×C53—42no—
377C4×C53—42no—
378C4×C53#53212yes—
379C4×C53C22×#4111yescharacteristic
380C4×C53C22×#4111yescharacteristic
381Dic53—42no—
382Dic53—42no—
383C2×#542D5311yescharacteristic, complemented
384C2×#540—531no—
385#3179—5316no—
386C2×#501—531no—
387C2×#496—531no—
388C2×#488—531no—
389C2×#486—531no—
390C2×#469—531no—
391C2×#468—531no—
392C2×#466—531no—
393C2×#465—531no—
394C2×#442—531no—
395C2×#440—531no—
396C2×C4×SD16—531no—
397C2×C4×D8—531no—
398C2×#405—531no—
399C2×C53—42no—
400C2×C53—82no—
401C2×C53#317914yescomplemented
402C2×C53C2×#53211yescharacteristic
403C2×C53C2×#57611yescharacteristic
404C2×C53C2×#57711yescharacteristic
405D53—82no—
406D53—82no—
407C22×SD16—531no—
408C22×SD16—531no—
409C22×D8—531no—
410C22×D8—531no—
411C22×M16—531no—
412C23×C8—531no—
413#542—24no—
414#542C2×D5318yescomplemented
415#540—538no—
416#540—1064no—
417C2×C4⋊Q8C2×D5311yescharacteristic
418C2×#127—531no—
419C2×#126—21no—
420C2×#125—531no—
421C2×#124—21no—
422C2×#124C2×D5311yescharacteristic
423C2×#123—21no—
424C2×#123—1061no—
425C2×#123—1061no—
426C2×C22⋊Q8—21no—
427C2×C22⋊Q8C2×D5311yescharacteristic
428C2×#121—531no—
429C2×#121—531no—
430C2×#121—1061no—
431C2×#121—1061no—
432C2×#121C2×D5311yescharacteristic
433C2×C4×Q8C2×D5311yescharacteristic
434C2×C4×D4—531no—
435C2×C4×D4—531no—
436C2×C4×D4C2×D5311yescharacteristic
437C2×#117C2×D5311yescharacteristic
438#501—538no—
439#496—538no—
440#488—538no—
441#486—538no—
442#469—538no—
443#468—538no—
444#466—538no—
445#465—538no—
446#442—538no—
447#440—538no—
448C4×SD16—538no—
449C4×D8—538no—
450C2×#107—531no—
451C2×#107—531no—
452C2×#106—531no—
453C2×#106—531no—
454C2×#103—531no—
455C2×#103—531no—
456C2×#102—531no—
457C2×#102—531no—
458C2×#102—531no—
459C2×#102—531no—
460C2×#102—531no—
461C2×#102—531no—
462#405—538no—
463C2×#97—531no—
464C2×#97—531no—
465C2×C4×C8—531no—
466C2×C4×C8—531no—
467C53C2×#317911yescharacteristic, complemented, Sylow
468C22×Q8—21no—
469C22×Q8C22×D5311yescharacteristic
470C22×D4—21no—
471C22×D4—531no—
472C22×D4—531no—
473C22×D4—1061no—
474C22×D4—1061no—
475C22×D4—1061no—
476C22×D4—1061no—
477C22×D4C22×D5311yescharacteristic
478C23×C4—21no—
479C23×C4—1061no—
480C23×C4—1061no—
481C23×C4C22×D5311yescharacteristic
482C2×SD16—534no—
483C2×SD16—534no—
484C2×SD16—1064no—
485C2×SD16—1064no—
486C2×D8—534no—
487C2×D8—534no—
488C2×D8—1064no—
489C2×D8—1064no—
490C2×M16—534no—
491C2×M16—1064no—
492C22×C8—531no—
493C22×C8—531no—
494C22×C8—531no—
495C22×C8—534no—
496C22×C8—531no—
497C22×C8—1064no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D5314yes—
500#127—534no—
501#127—1062no—
502#126—28no—
503#125—534no—
504#125—1062no—
505#124—28no—
506#124—22no—
507#124C22×D5314yes—
508#123—28no—
509#123—1068no—
510#123—1068no—
511C22⋊Q8—22no—
512C22⋊Q8—28no—
513C22⋊Q8C22×D5314yes—
514#121—22no—
515#121—534no—
516#121—534no—
517#121—1062no—
518#121—1062no—
519#121—1068no—
520#121—1068no—
521#121C22×D5314yes—
522C4×Q8—22no—
523C4×Q8C22×D5314yes—
524C4×D4—22no—
525C4×D4—534no—
526C4×D4—534no—
527C4×D4—1062no—
528C4×D4—1062no—
529C4×D4C22×D5314yes—
530#117C22⋊D5314yes—
531#117C22×D5314yes—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—531no—
536C2×C4⋊C4—531no—
537C2×C4⋊C4—1061no—
538C2×C4⋊C4—1061no—
539C2×C4⋊C4C22⋊D5311yescharacteristic
540C2×C4⋊C4C22⋊D5311yescharacteristic
541C2×C4⋊C4C22×D5311yescharacteristic
542C2×C4⋊C4C22×D5311yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1061no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4C22⋊D5311yescharacteristic
553C2×C22⋊C4C22⋊D5311yescharacteristic
554C2×C42—21no—
555C2×C42C22×D5311yescharacteristic
556C2×C42C22×D5311yescharacteristic
557#107—534no—
558#107—534no—
559#106—534no—
560#106—534no—
561#103—534no—
562#103—534no—
563#102—534no—
564#102—534no—
565#102—534no—
566#102—534no—
567#102—534no—
568#102—534no—
569#97—534no—
570#97—534no—
571C4×C8—534no—
572C4×C8—534no—
573C24—21no—
574C24—1061no—
575C24—1061no—
576C24C2×C22⋊D5311yescharacteristic
577C2×Q8—21no—
578C2×Q8—24no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—82no—
582C2×Q8C23×D5312yes—
583C2×D4—24no—
584C2×D4—21no—
585C2×D4—22no—
586C2×D4—22no—
587C2×D4—82no—
588C2×D4—532no—
589C2×D4—532no—
590C2×D4—1064no—
591C2×D4—1064no—
592C2×D4—1064no—
593C2×D4—1064no—
594C2×D4—1061no—
595C2×D4—1061no—
596C2×D4—1062no—
597C2×D4—1062no—
598C2×D4—1062no—
599C2×D4—1062no—
600C2×D4—4242no—
601C2×D4—4242no—
602C2×D4—4242no—
603C2×D4—4242no—
604C2×D4C23×D5312yes—
605C22×C4—22no—
606C22×C4—22no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—82no—
612C22×C4—1061no—
613C22×C4—1061no—
614C22×C4—1064no—
615C22×C4—1064no—
616C22×C4—4242no—
617C22×C4—4242no—
618C22×C4C2×C22⋊D5312yes—
619C22×C4C2×C22⋊D5311yescharacteristic
620C22×C4C2×C22⋊D5311yescharacteristic
621C22×C4C2×C22⋊D5311yescharacteristic
622C22×C4C2×C22⋊D5311yescharacteristic
623C22×C4C2×C22⋊D5311yescharacteristic
624C22×C4C23×D5312yes—
625C22×C4C23×D5311yescharacteristic
626SD16—1068no—
627SD16—1068no—
628D8—1068no—
629D8—1068no—
630M16—1068no—
631C2×C8—534no—
632C2×C8—534no—
633C2×C8—532no—
634C2×C8—532no—
635C2×C8—532no—
636C2×C8—532no—
637C2×C8—1068no—
638C2×C8—1062no—
639C2×C8—1062no—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—532no—
646C4⋊C4—532no—
647C4⋊C4—1061no—
648C4⋊C4—1061no—
649C4⋊C4—1064no—
650C4⋊C4—1064no—
651C4⋊C4C2×C22⋊D5314yes—
652C4⋊C4C2×C22⋊D5314yes—
653C4⋊C4C23×D5312yes—
654C4⋊C4C23×D5312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
657C22⋊C4—24no—
658C22⋊C4—24no—
659C22⋊C4—24no—
660C22⋊C4—1064no—
661C22⋊C4—1064no—
662C22⋊C4—1064no—
663C22⋊C4—1064no—
664C22⋊C4C2×C22⋊D5314yes—
665C22⋊C4C2×C22⋊D5314yes—
666C42—24no—
667C42C2×C22⋊D5312yes—
668C42C2×C22⋊D5312yes—
669C42C23×D5312yes—
670C42C23×D5312yes—
671C23—22no—
672C23—22no—
673C23—22no—
674C23—22no—
675C23—42no—
676C23—42no—
677C23—42no—
678C23—1062no—
679C23—1062no—
680C23—2122no—
681C23—2122no—
682C23—2122no—
683C23—2122no—
684C23—2122no—
685C23—2122no—
686C23C22×C22⋊D5312yes—
687C23C22×C22⋊D5311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—84no—
692D4—22no—
693D4—22no—
694D4—42no—
695D4—84no—
696D4—1062no—
697D4—1062no—
698D4—1062no—
699D4—1062no—
700D4—4244no—
701D4—4244no—
702D4—4244no—
703D4—4244no—
704D4—2122no—
705D4—2122no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—84no—
721C2×C4—1062no—
722C2×C4—1062no—
723C2×C4—4244no—
724C2×C4—4244no—
725C2×C4—2122no—
726C2×C4—2122no—
727C2×C4C22×C22⋊D5312yes—
728C2×C4C22×C22⋊D5312yes—
729C2×C4C22×C22⋊D5312yes—
730C2×C4C22×C22⋊D5312yes—
731C2×C4C22×C22⋊D5312yes—
732C2×C4C22×C22⋊D5311yescharacteristic
733C2×C4#41×D5312yes—
734C2×C4#41×D5312yes—
735C2×C4C24×D5311yescharacteristic
736C8—534no—
737C8—534no—
738C8—1062no—
739C8—1062no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—44no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—84no—
748C22—4244no—
749C22—4244no—
750C22—2122no—
751C22—2122no—
752C22—2122no—
753C22—2122no—
754C22—2122no—
755C22—2122no—
756C22#1681116912yes—
757C22#1681142612yes—
758C22#1681143112yes—
759C22C23×C22⋊D5311yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—22no—
765C4—42no—
766C4—42no—
767C4—42no—
768C4—2122no—
769C4—2122no—
770C4#1681116912yes—
771C4C2×#41×D5311yescharacteristic
772C4C2×#41×D5311yescharacteristic
773C2—42no—
774C2—82no—
775C2—4242no—
776C2—4242no—
777C2#2028539214yesdirect product factor
778C2C2×#1681116911yescharacteristic
779C2C2×#1681142611yescharacteristic
780C2C2×#1681143111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#542C2
socleC23×C53C22×D4
hypercenterC2×#542D53
hypocenterC53C2×#3179
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. C2×#16811228C2semidirect
2. #20285392C2direct (N × H)
3. C2×#16811029C2semidirect
4. C2×#16811013C2semidirect
5. C2×#16810977C2semidirect
6. C2×#16810971C2semidirect
7. C2×#16810874C2semidirect
8. C2×#16810871C2semidirect
9. C2×#16810857C2semidirect
10. C2×#16810854C2semidirect
11. C2×#16810733C2semidirect
12. C2×#16810721C2semidirect
13. C2×C4×#11719924C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810579C2semidirect
16. C2×C53×#542C2semidirect
24. #16811228C22semidirect
35. #16811029C22semidirect
36. #16811013C22semidirect
37. #16810977C22semidirect
38. #16810971C22semidirect
39. #16810874C22semidirect
40. #16810871C22semidirect
41. #16810857C22semidirect
42. #16810854C22semidirect
43. #16810733C22semidirect
44. #16810721C22semidirect
45. C4×#11719924C22semidirect
46. C4×#11719922C22semidirect
59. #16810579C22semidirect
65. C53×#542C22semidirect
383. C2×#542D53semidirect
401. C2×C53#3179semidirect
414. #542C2×D53semidirect
467. C53C2×#3179semidirect
777. C2#20285392direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112282
#202853922
C2×#168110292
C2×#168110132
C2×#168109772
C2×#168109712
C2×#168108742
C2×#168108712
C2×#168108572
C2×#168108542
C2×#168107332
C2×#168107212
C2×C4×#117199242
C2×C4×#117199222
C2×#168105792
C2×C53×#5422
C2×#317953