Finite Group Databasebeta

← C2×#20285409 #28253999

Subgroups — C2×#20285409 #28253999

Order 13568.

2278 conjugacy classes of subgroups.

The subgroup lattice has 794 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811170C211yesmaximal, characteristic, complemented
2C2×#16811160C211yesmaximal, characteristic, complemented
3#20285409C2116yesmaximal, direct product factor
4C2×#16811031C211yesmaximal, characteristic, complemented
5C2×#16811009C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810984C211yesmaximal, characteristic, complemented
8C2×#16810860C211yesmaximal, characteristic, complemented
9C2×#16810858C211yesmaximal, characteristic, complemented
10C2×#16810855C211yesmaximal, characteristic, complemented
11C2×#16810849C211yesmaximal, characteristic, complemented
12C2×#16810736C211yesmaximal, characteristic, complemented
13C2×#16810733C211yesmaximal, characteristic, complemented
14C2×#16810721C211yesmaximal, characteristic, complemented
15C2×#97×D53C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719924C2211yescharacteristic
19C22×D424C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811170—24no—
24#16811170C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133213C2211yescharacteristic
27#16811160—24no—
28#16811160C2218yescomplemented
29C2×#13133212—21no—
30C2×#13133208C2211yescharacteristic
31C2×#13133206C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133202—21no—
34C2×#13133193C2211yescharacteristic
35C2×#13133192C2211yescharacteristic
36C2×#13133192C2211yescharacteristic
37C2×#13133190—21no—
38C2×#13133188C2211yescharacteristic
39C2×C4×D212—21no—
40C2×C4×D212C2211yescharacteristic
41C2×C4×D212C2211yescharacteristic
42C2×C4×C22⋊D53—21no—
43C2×#13133174—21no—
44C2×C42×D53C2211yescharacteristic
45#16811031C2218yescomplemented
46#16811009C2218yescomplemented
47#16810986C2218yescomplemented
48#16810984C2218yescomplemented
49#16810860C2218yescomplemented
50#16810858C2218yescomplemented
51#16810855C2218yescomplemented
52#16810849C2218yescomplemented
53#16810736C2218yescomplemented
54#16810733C2218yescomplemented
55#16810721C2218yescomplemented
56C2×#13133150C2211yescharacteristic
57C2×#13133149C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133141C2211yescharacteristic
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133137C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133128C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68#97×D53C2218yescomplemented
69C22×SD16×C53C2211yescharacteristic
70C2×C4×Q8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#440C2218yescomplemented
73C2×#107×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×D212—21no—
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×D212C2311yescharacteristic
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53—21no—
89C22×C4×D53D411yescharacteristic
90C22×C4×D53D411yescharacteristic
91C22×C4×D53C2311yescharacteristic
92C2×#11719924—24no—
93C2×#11719924C2314yes—
94C2×D424—24no—
95C2×D424C2314yes—
96C2×#11719922—24no—
97C2×#11719922C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C2×C8×D53—24no—
101C2×C8×D53—24no—
102C2×C8×D53C2314yes—
103C2×C8×D53C2314yes—
104#13133216—22no—
105#13133216C2314yes—
106#13133213—22no—
107#13133213C2314yes—
108#13133212—28no—
109#13133208—22no—
110#13133208C2314yes—
111#13133206—22no—
112#13133206C2314yes—
113#13133203—28no—
114#13133202—28no—
115#13133193—22no—
116#13133193C2314yes—
117#13133192—22no—
118#13133192—22no—
119#13133192C2314yes—
120#13133192C2314yes—
121#13133190—28no—
122#13133188—22no—
123#13133188C2314yes—
124C4×D212—22no—
125C4×D212—22no—
126C4×D212—28no—
127C4×D212C2314yes—
128C4×D212C2314yes—
129C4×C22⋊D53—28no—
130#13133174—28no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×C22⋊Dic53—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×C4×Dic53D411yescharacteristic
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53C2311yescharacteristic
148C42×D53D414yes—
149C42×D53C2314yes—
150#13133150C2314yes—
151#13133149C2314yes—
152#13133148C2314yes—
153#13133141C2314yes—
154#13133139C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133137C2314yes—
158#13133137C2314yes—
159#13133128C2314yes—
160#13133127C2314yes—
161#13133127C2314yes—
162C22×Q8×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C2×SD16×C53—24no—
166C2×SD16×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×Q8×C53—22no—
170C4×Q8×C53C2314yes—
171C4×D4×C53—22no—
172C4×D4×C53C2314yes—
173C2×C4⋊C4×C53—21no—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C42×C53—21no—
178C2×C42×C53C2311yescharacteristic
179#107×C53C2314yes—
180#103×C53C2314yes—
181#102×C53C2314yes—
182#97×C53C2314yes—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C2×Q8×C53—21no—
188C2×Q8×C53—22no—
189C2×Q8×C53—22no—
190C2×Q8×C53C2412yes—
191C2×D4×C53—21no—
192C2×D4×C53—22no—
193C2×D4×C53—22no—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—21no—
198C22×C4×C53—24no—
199C22×C4×C53—44no—
200C22×C4×C53C2×D411yescharacteristic
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2411yescharacteristic
203C2×C22⋊D53—24no—
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—44no—
207C2×C22⋊D53—44no—
208C2×C22⋊D53—44no—
209C22×Dic53—21no—
210C22×Dic53—21no—
211C22×Dic53C2×D411yescharacteristic
212C22×Dic53C2×D411yescharacteristic
213C22×Dic53C2×D411yescharacteristic
214#11719945—432no—
215C2×D212—22no—
216C2×D212—22no—
217C2×D212—22no—
218C2×D212—22no—
219C2×D212—24no—
220C2×D212—24no—
221C2×D212—21no—
222C2×D212—21no—
223C2×D212—44no—
224C2×D212—44no—
225C2×D212C2412yes—
226C2×D212C2412yes—
227C2×C4×D53—24no—
228C2×C4×D53—22no—
229C2×C4×D53—22no—
230C2×C4×D53—24no—
231C2×C4×D53—24no—
232C2×C4×D53—42no—
233C2×C4×D53—44no—
234C2×C4×D53—44no—
235C2×C4×D53C2×D412yes—
236C2×C4×D53C2×D414yes—
237C2×C4×D53C2×D414yes—
238C2×C4×D53C2412yes—
239C2×Dic106—24no—
240C2×Dic106—44no—
241SD16×C53—28no—
242C2×C8×C53—22no—
243C2×C8×C53#4114yescomplemented
244C2×C8×C53C2412yes—
245C2×C8×C53C2412yes—
246C4⋊C4×C53—24no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53—21no—
249C4⋊C4×C53C2412yes—
250C4⋊C4×C53C2412yes—
251C22⋊C4×C53—24no—
252C42×C53—24no—
253C42×C53C2×D412yes—
254C42×C53C2412yes—
255C22⋊Dic53—24no—
256#11719924—28no—
257#11719922—28no—
258#11719921—24no—
259#11719921—24no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263#11719921—24no—
264#11719921—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—24no—
268C4⋊Dic53C2412yes—
269C4⋊Dic53C2412yes—
270#11719919—24no—
271#11719919—24no—
272#11719919—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2×D414yes—
275C4×Dic53C2×D414yes—
276C4×Dic53C2412yes—
277C2×#88322—22no—
278C2×#88322#4114yescomplemented
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281D424—28no—
282C8×D53—28no—
283C8×D53—28no—
284C23×C53—22no—
285C23×C53—42no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53C22×D411yescharacteristic
289C22×D53—22no—
290C22×D53—22no—
291C22×D53—22no—
292C22×D53—22no—
293C22×D53—42no—
294C22×D53—42no—
295C22×D53—42no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53AGL(1,ℤ/8)14yes—
300C22×D53C22×D412yes—
301Q8×C53—22no—
302Q8×C53—22no—
303Q8×C53—42no—
304D4×C53—22no—
305D4×C53—22no—
306D4×C53—42no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—48no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53—42no—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D412yes—
318C2×C4×C53C22×D411yescharacteristic
319C2×C4×C53C2×#4112yes—
320C2×C4×C53C2×#4112yes—
321C2×C4×C53C2511yescharacteristic
322C22⋊D53—48no—
323C22⋊D53—48no—
324C22⋊D53—48no—
325C2×Dic53—22no—
326C2×Dic53—22no—
327C2×Dic53—22no—
328C2×Dic53—22no—
329C2×Dic53—22no—
330C2×Dic53—42no—
331C2×Dic53—42no—
332C2×Dic53C22×D412yes—
333C2×Dic53C22×D412yes—
334C2×Dic53C22×D412yes—
335D212—22no—
336D212—22no—
337D212—22no—
338D212—22no—
339D212—48no—
340D212—48no—
341D212—42no—
342D212—42no—
343C4×D53—28no—
344C4×D53—24no—
345C4×D53—22no—
346C4×D53—22no—
347C4×D53—44no—
348C4×D53—48no—
349C4×D53—48no—
350Dic106—48no—
351C8×C53—22no—
352C8×C53C2×#4114yescomplemented
353#88322—22no—
354#88322C2×#4114yescomplemented
355C2×#3180—531nomaximal, Sylow
356C22×C53—42no—
357C22×C53—42no—
358C22×C53—42no—
359C22×C53—84no—
360C22×C53#53212yes—
361C22×C53C2×AGL(1,ℤ/8)12yes—
362C22×C53#57512yes—
363C22×C53C23×D411yescharacteristic
364C2×D53—28no—
365C2×D53—22no—
366C2×D53—22no—
367C2×D53—42no—
368C2×D53—42no—
369C2×D53—42no—
370C2×D53—42no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—84no—
374C2×D53—84no—
375C2×D53C2×AGL(1,ℤ/8)14yes—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53—42no—
381C4×C53#53212yes—
382C4×C53C22×#4111yescharacteristic
383C4×C53C22×#4111yescharacteristic
384Dic53—22no—
385Dic53—22no—
386Dic53—22no—
387Dic53—42no—
388Dic53—42no—
389C2×#532—531no—
390C2×#529—531no—
391#3180—5316no—
392C2×#501—531no—
393C2×#496—531no—
394C2×#490—531no—
395C2×#489—531no—
396C2×#466—531no—
397C2×#466—531no—
398C2×#465—531no—
399C2×#465—531no—
400C2×#442—531no—
401C2×#442—531no—
402C2×#440—531no—
403C2×#440D5311yescharacteristic, complemented
404C22×#97—531no—
405C2×C53—82no—
406C2×C53#318014yescomplemented
407C2×C53C2×#53211yescharacteristic
408C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
409C2×C53C2×#57511yescharacteristic
410D53—24no—
411D53—82no—
412D53—82no—
413C22×#41—1061no—
414C22×SD16—531no—
415C22×SD16C2×D5311yescharacteristic
416C22×D8—531no—
417C22×D8—531no—
418C23×C8—531no—
419C23×C8—531no—
420#532—538no—
421#532—1064no—
422C2×C4⋊Q8—531no—
423C2×#127—531no—
424#529—538no—
425#529—1064no—
426C2×#126—1061no—
427C2×#125—531no—
428C2×#124—531no—
429C2×#124—1061no—
430C2×#123—1061no—
431C2×C22⋊Q8—531no—
432C2×#121—531no—
433C2×#121—531no—
434C2×#121—531no—
435C2×#121—1061no—
436C2×C4×Q8C2×D5311yescharacteristic
437C2×C4×D4—531no—
438C2×C4×D4—531no—
439C2×C4×D4—1061no—
440C2×C4×D4—1061no—
441C2×C4×D4C2×D5311yescharacteristic
442C2×#117—1061no—
443C22×C42—531no—
444#501—538no—
445#496—538no—
446#490—538no—
447#489—538no—
448#466—538no—
449#466—538no—
450#465—538no—
451#465—538no—
452#442—538no—
453#442—538no—
454#440—538no—
455#440C2×D5318yescomplemented
456C2×#107—531no—
457C2×#107C2×D5311yescharacteristic
458C2×#106—531no—
459C2×#106—531no—
460C2×#103—531no—
461C2×#103C2×D5311yescharacteristic
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102—531no—
467C2×#102C2×D5311yescharacteristic
468C2×#97—531no—
469C2×#97—531no—
470C2×#97—531no—
471C2×#97—538no—
472C2×#97C2×D5311yescharacteristic
473C53C2×#318011yescharacteristic, complemented, Sylow
474C2×#41—1068no—
475C2×#41—2128no—
476C22×Q8—1061no—
477C22×Q8C22×D5311yescharacteristic
478C22×D4—531no—
479C22×D4—531no—
480C22×D4—1061no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4—1061no—
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—531no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—1061no—
491C23×C4—1061no—
492C2×SD16—24no—
493C2×SD16—534no—
494C2×SD16—1064no—
495C2×SD16C22×D5314yes—
496C2×D8—534no—
497C2×D8—534no—
498C2×D8—1064no—
499C2×D8—1064no—
500C22×C8—531no—
501C22×C8—531no—
502C22×C8—534no—
503C22×C8—534no—
504C22×C8—1064no—
505C22×C8—1064no—
506C22×C8C22×D5311yescharacteristic
507C22×C8C22×D5311yescharacteristic
508C4⋊Q8—534no—
509C4⋊Q8—1062no—
510#127—534no—
511#127—1062no—
512#126—1068no—
513#125—534no—
514#125—1062no—
515#124—534no—
516#124—1068no—
517#124—1062no—
518#123—1068no—
519C22⋊Q8—534no—
520C22⋊Q8—1062no—
521#121—534no—
522#121—534no—
523#121—534no—
524#121—1068no—
525#121—1062no—
526#121—1062no—
527#121—1062no—
528C4×Q8—22no—
529C4×Q8C22×D5314yes—
530C4×D4—22no—
531C4×D4—534no—
532C4×D4—534no—
533C4×D4—1068no—
534C4×D4—1068no—
535C4×D4—1062no—
536C4×D4—1062no—
537C4×D4C22×D5314yes—
538#117—1068no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—531no—
542C2×C4⋊C4—1061no—
543C2×C4⋊C4—1061no—
544C2×C4⋊C4—1061no—
545C2×C4⋊C4—1061no—
546C2×C4⋊C4C22×D5311yescharacteristic
547C2×C4⋊C4C22×D5311yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—1061no—
550C2×C22⋊C4—1061no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C42—21no—
558C2×C42—531no—
559C2×C42—531no—
560C2×C42—531no—
561C2×C42—534no—
562C2×C42—534no—
563C2×C42C22×D5311yescharacteristic
564#107—534no—
565#107C22×D5314yes—
566#106—534no—
567#106—534no—
568#103—534no—
569#103C22×D5314yes—
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574#102—534no—
575#102C22×D5314yes—
576#97—534no—
577#97—534no—
578#97—534no—
579#97C22×D5314yes—
580C24—21no—
581C24—531no—
582C24—1061no—
583C24—1061no—
584#41—21232no—
585C2×Q8—21no—
586C2×Q8—22no—
587C2×Q8—22no—
588C2×Q8—1064no—
589C2×Q8—2124no—
590C2×Q8C23×D5312yes—
591C2×D4—21no—
592C2×D4—22no—
593C2×D4—22no—
594C2×D4—532no—
595C2×D4—532no—
596C2×D4—1064no—
597C2×D4—1064no—
598C2×D4—1064no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1061no—
602C2×D4—1061no—
603C2×D4—1062no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—1062no—
607C2×D4—2124no—
608C2×D4—2124no—
609C2×D4—2124no—
610C2×D4—2124no—
611C2×D4—2124no—
612C2×D4C23×D5312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—24no—
617C22×C4—44no—
618C22×C4—531no—
619C22×C4—531no—
620C22×C4—531no—
621C22×C4—532no—
622C22×C4—534no—
623C22×C4—532no—
624C22×C4—534no—
625C22×C4—1064no—
626C22×C4—1062no—
627C22×C4—1062no—
628C22×C4—1061no—
629C22×C4—1061no—
630C22×C4—1064no—
631C22×C4—1064no—
632C22×C4—2122no—
633C22×C4—2124no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638SD16—28no—
639SD16—1068no—
640D8—1068no—
641D8—1068no—
642C2×C8—22no—
643C2×C8—534no—
644C2×C8—532no—
645C2×C8—532no—
646C2×C8—1068no—
647C2×C8—1062no—
648C2×C8—1068no—
649C2×C8#1171994514yescomplemented
650C2×C8C23×D5312yes—
651C2×C8C23×D5312yes—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—532no—
656C4⋊C4—532no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1064no—
661C4⋊C4—1061no—
662C4⋊C4—1061no—
663C4⋊C4C23×D5312yes—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—1064no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C42—24no—
675C42—534no—
676C42—534no—
677C42—532no—
678C42—532no—
679C42D4×D5312yes—
680C42C23×D5312yes—
681C23—22no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—534no—
686C23—532no—
687C23—1062no—
688C23—1062no—
689C23—1062no—
690C23—1062no—
691C23—2122no—
692C23—2122no—
693C23—2122no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23C2×D4×D5311yescharacteristic
698Q8—22no—
699Q8—22no—
700Q8—42no—
701Q8—2128no—
702D4—22no—
703D4—22no—
704D4—42no—
705D4—1062no—
706D4—1062no—
707D4—1062no—
708D4—1062no—
709D4—2128no—
710D4—2128no—
711D4—2128no—
712D4—2128no—
713D4—2128no—
714D4—2122no—
715D4—2122no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—532no—
728C2×C4—1068no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1062no—
732C2×C4—1064no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—2124no—
738C2×C4—2128no—
739C2×C4—2128no—
740C2×C4—2122no—
741C2×C4—2122no—
742C2×C4C2×D4×D5312yes—
743C2×C4C2×D4×D5312yes—
744C2×C4C2×D4×D5311yescharacteristic
745C2×C4#41×D5312yes—
746C2×C4C2×#1171994512yes—
747C2×C4C24×D5311yescharacteristic
748C8—22no—
749C8—534no—
750C8—1062no—
751C8C2×#1171994514yescomplemented
752C22—42no—
753C22—42no—
754C22—42no—
755C22—84no—
756C22—534no—
757C22—1062no—
758C22—1068no—
759C22—1062no—
760C22—4244no—
761C22—4244no—
762C22—2122no—
763C22—2122no—
764C22—2122no—
765C22—2122no—
766C22—2122no—
767C22—2122no—
768C22#1681117012yes—
769C22AGL(1,ℤ/8)×D5312yes—
770C22#1681142212yes—
771C22C22×D4×D5311yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—42no—
777C4—1062no—
778C4—1062no—
779C4—1062no—
780C4—2122no—
781C4—2122no—
782C4#1681117012yes—
783C4C2×#41×D5311yescharacteristic
784C4C22×#1171994511yescharacteristic
785C2—82no—
786C2—1064no—
787C2—4242no—
788C2—4242no—
789C2#2028540914yesdirect product factor
790C2C2×#1681117011yescharacteristic
791C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
792C2C2×#1681142211yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
hypercenterC2×#440D53
hypocenterC53C2×#3180
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C2×#16811170C2semidirect
2. C2×#16811160C2semidirect
3. #20285409C2direct (N × H)
4. C2×#16811031C2semidirect
5. C2×#16811009C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810984C2semidirect
8. C2×#16810860C2semidirect
9. C2×#16810858C2semidirect
10. C2×#16810855C2semidirect
11. C2×#16810849C2semidirect
12. C2×#16810736C2semidirect
13. C2×#16810733C2semidirect
14. C2×#16810721C2semidirect
15. C2×#97×D53C2semidirect
16. C2×C53×#440C2semidirect
24. #16811170C22semidirect
28. #16811160C22semidirect
45. #16811031C22semidirect
46. #16811009C22semidirect
47. #16810986C22semidirect
48. #16810984C22semidirect
49. #16810860C22semidirect
50. #16810858C22semidirect
51. #16810855C22semidirect
52. #16810849C22semidirect
53. #16810736C22semidirect
54. #16810733C22semidirect
55. #16810721C22semidirect
68. #97×D53C22semidirect
72. C53×#440C22semidirect
243. C2×C8×C53#41semidirect
278. C2×#88322#41semidirect
352. C8×C53C2×#41semidirect
354. #88322C2×#41semidirect
403. C2×#440D53semidirect
406. C2×C53#3180semidirect
455. #440C2×D53semidirect
473. C53C2×#3180semidirect
649. C2×C8#11719945semidirect
751. C8C2×#11719945semidirect
789. C2#20285409direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111702
C2×#168111602
#202854092
C2×#168110312
C2×#168110092
C2×#168109862
C2×#168109842
C2×#168108602
C2×#168108582
C2×#168108552
C2×#168108492
C2×#168107362
C2×#168107332
C2×#168107212
C2×#97×D532
C2×C53×#4402
C2×#318053