Finite Group Databasebeta

← C2×#20285411 #28254001

Subgroups — C2×#20285411 #28254001

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×#16811155C211yesmaximal, characteristic, complemented
3#20285411C2116yesmaximal, direct product factor
4C2×#16811030C211yesmaximal, characteristic, complemented
5C2×#16811011C211yesmaximal, characteristic, complemented
6C2×#16810986C211yesmaximal, characteristic, complemented
7C2×#16810981C211yesmaximal, characteristic, complemented
8C2×#16810858C211yesmaximal, characteristic, complemented
9C2×#16810856C211yesmaximal, characteristic, complemented
10C2×#16810853C211yesmaximal, characteristic, complemented
11C2×#16810851C211yesmaximal, characteristic, complemented
12C2×#16810733C211yesmaximal, characteristic, complemented
13C2×#16810725C211yesmaximal, characteristic, complemented
14C2×#16810723C211yesmaximal, characteristic, complemented
15C2×#97×D53C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C22×#11719945—21no—
18C22×#11719913C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22C22×C8×D53C2211yescharacteristic
23#16811170—24no—
24#16811170C2218yescomplemented
25C2×#13133216C2211yescharacteristic
26C2×#13133213C2211yescharacteristic
27#16811155—24no—
28#16811155C2218yescomplemented
29C2×#13133210—21no—
30C2×#13133208C2211yescharacteristic
31C2×#13133204C2211yescharacteristic
32C2×#13133203—21no—
33C2×#13133199—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133192C2211yescharacteristic
36C2×#13133190—21no—
37C2×#13133188C2211yescharacteristic
38C2×#13133188C2211yescharacteristic
39C2×C4×Dic106C2211yescharacteristic
40C2×C4×D212C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53—21no—
43C2×#13133176—21no—
44C2×C42×D53C2211yescharacteristic
45#16811030C2218yescomplemented
46#16811011C2218yescomplemented
47#16810986C2218yescomplemented
48#16810981C2218yescomplemented
49#16810858C2218yescomplemented
50#16810856C2218yescomplemented
51#16810853C2218yescomplemented
52#16810851C2218yescomplemented
53#16810733C2218yescomplemented
54#16810725C2218yescomplemented
55#16810723C2218yescomplemented
56C2×#13133151C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133148C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133140C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133128C2211yescharacteristic
66C2×#13133127C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
68#97×D53C2218yescomplemented
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×#97×C53C2211yescharacteristic
77C2×#11719945—28no—
78C2×#11719945—48no—
79C22×Dic106—21no—
80C22×Dic106C2311yescharacteristic
81C22×D212—21no—
82C22×D212C2311yescharacteristic
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C22×C22⋊D53—21no—
86C22×C22⋊D53—21no—
87C22×C4×D53—21no—
88C22×C4×D53D411yescharacteristic
89C22×C4×D53D411yescharacteristic
90C22×C4×D53C2311yescharacteristic
91C2×#11719913—24no—
92C2×#11719913C2314yes—
93C2×#11719923—24no—
94C2×#11719923C2314yes—
95C2×#11719922—24no—
96C2×#11719922C2314yes—
97C22×#88322C2311yescharacteristic
98C22×#88322C2311yescharacteristic
99C2×C8×D53—24no—
100C2×C8×D53—24no—
101C2×C8×D53C2314yes—
102C2×C8×D53C2314yes—
103#13133216—22no—
104#13133216C2314yes—
105#13133213—22no—
106#13133213C2314yes—
107#13133210—28no—
108#13133208—22no—
109#13133208C2314yes—
110#13133204—22no—
111#13133204C2314yes—
112#13133203—28no—
113#13133199—28no—
114#13133197—22no—
115#13133197C2314yes—
116#13133192—22no—
117#13133192C2314yes—
118#13133190—28no—
119#13133188—22no—
120#13133188—22no—
121#13133188C2314yes—
122#13133188C2314yes—
123C4×Dic106—22no—
124C4×Dic106C2314yes—
125C4×D212—22no—
126C4×D212C2314yes—
127C4×C22⋊D53—28no—
128C4×C22⋊D53—28no—
129#13133176—28no—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2311yescharacteristic
133C2×C4⋊Dic53C2311yescharacteristic
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919—21no—
137C2×C22⋊Dic53—21no—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×C4×Dic53—21no—
145C2×C4×Dic53D411yescharacteristic
146C2×C4×Dic53D411yescharacteristic
147C2×C4×Dic53C2311yescharacteristic
148C42×D53D414yes—
149C42×D53C2314yes—
150#13133151C2314yes—
151#13133150C2314yes—
152#13133148C2314yes—
153#13133142C2314yes—
154#13133140C2314yes—
155#13133139C2314yes—
156#13133138C2314yes—
157#13133138C2314yes—
158#13133137C2314yes—
159#13133128C2314yes—
160#13133127C2314yes—
161#13133127C2314yes—
162C22×D4×C53C2311yescharacteristic
163C22×D4×C53C2311yescharacteristic
164C23×C4×C53—21no—
165C23×C4×C53—21no—
166C2×D8×C53—24no—
167C2×D8×C53C2314yes—
168C22×C8×C53C2311yescharacteristic
169C22×C8×C53C2311yescharacteristic
170C4×D4×C53—22no—
171C4×D4×C53—22no—
172C4×D4×C53C2314yes—
173C4×D4×C53C2314yes—
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C4⋊C4×C53C2311yescharacteristic
176C2×C22⋊C4×C53—21no—
177C2×C22⋊C4×C53—21no—
178C2×C42×C53C2311yescharacteristic
179#106×C53C2314yes—
180#102×C53C2314yes—
181#102×C53C2314yes—
182#97×C53C2314yes—
183C24×C53—21no—
184C24×C53—21no—
185C23×D53—21no—
186C23×D53C2×D411yescharacteristic
187C2×D4×C53—21no—
188C2×D4×C53—21no—
189C2×D4×C53—22no—
190C2×D4×C53—22no—
191C2×D4×C53—22no—
192C2×D4×C53—22no—
193C2×D4×C53C2412yes—
194C2×D4×C53C2412yes—
195C22×C4×C53—21no—
196C22×C4×C53—21no—
197C22×C4×C53—24no—
198C22×C4×C53—24no—
199C22×C4×C53—44no—
200C22×C4×C53—44no—
201C22×C4×C53C2×D411yescharacteristic
202C22×C4×C53C2×D411yescharacteristic
203C22×C4×C53C2411yescharacteristic
204C2×C22⋊D53—24no—
205C2×C22⋊D53—24no—
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—44no—
209C2×C22⋊D53—44no—
210C2×C22⋊D53—44no—
211C2×C22⋊D53—44no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53C2×D411yescharacteristic
216C22×Dic53C2×D411yescharacteristic
217C22×Dic53C2×D411yescharacteristic
218#11719945—432no—
219C2×D212—22no—
220C2×D212—22no—
221C2×D212—24no—
222C2×D212—21no—
223C2×D212—44no—
224C2×D212C2412yes—
225C2×C4×D53—24no—
226C2×C4×D53—22no—
227C2×C4×D53—22no—
228C2×C4×D53—24no—
229C2×C4×D53—42no—
230C2×C4×D53—44no—
231C2×C4×D53C2×D412yes—
232C2×C4×D53C2×D414yes—
233C2×C4×D53C2×D414yes—
234C2×C4×D53C2412yes—
235C2×Dic106—22no—
236C2×Dic106—22no—
237C2×Dic106—21no—
238C2×Dic106—24no—
239C2×Dic106—44no—
240C2×Dic106C2412yes—
241D8×C53—28no—
242C2×C8×C53—22no—
243C2×C8×C53#4114yescomplemented
244C2×C8×C53C2412yes—
245C2×C8×C53C2412yes—
246C4⋊C4×C53—21no—
247C4⋊C4×C53—21no—
248C4⋊C4×C53C2412yes—
249C4⋊C4×C53C2412yes—
250C22⋊C4×C53—24no—
251C22⋊C4×C53—24no—
252C42×C53C2×D412yes—
253C42×C53C2412yes—
254C22⋊Dic53—24no—
255C22⋊Dic53—24no—
256C22⋊Dic53—24no—
257C22⋊Dic53—24no—
258#11719923—28no—
259#11719922—28no—
260#11719921—24no—
261#11719921—24no—
262#11719921—24no—
263C4⋊Dic53—21no—
264C4⋊Dic53—21no—
265C4⋊Dic53—24no—
266C4⋊Dic53—24no—
267C4⋊Dic53C2412yes—
268C4⋊Dic53C2412yes—
269#11719919—24no—
270#11719919—24no—
271#11719919—24no—
272C4×Dic53—24no—
273C4×Dic53C2×D412yes—
274C4×Dic53C2×D414yes—
275C4×Dic53C2×D414yes—
276C4×Dic53C2412yes—
277C2×#88322—22no—
278C2×#88322#4114yescomplemented
279C2×#88322C2412yes—
280C2×#88322C2412yes—
281#11719913—28no—
282C8×D53—28no—
283C8×D53—28no—
284C23×C53—22no—
285C23×C53—22no—
286C23×C53—42no—
287C23×C53—42no—
288C23×C53—42no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53C22×D411yescharacteristic
293C22×D53—22no—
294C22×D53—22no—
295C22×D53—22no—
296C22×D53—42no—
297C22×D53—42no—
298C22×D53—42no—
299C22×D53AGL(1,ℤ/8)14yes—
300C22×D53C22×D412yes—
301D4×C53—22no—
302D4×C53—22no—
303D4×C53—22no—
304D4×C53—22no—
305D4×C53—42no—
306D4×C53—42no—
307C2×C4×C53—22no—
308C2×C4×C53—22no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—48no—
312C2×C4×C53—48no—
313C2×C4×C53—42no—
314C2×C4×C53—42no—
315C2×C4×C53C22×D412yes—
316C2×C4×C53C22×D412yes—
317C2×C4×C53C22×D411yescharacteristic
318C2×C4×C53C2×#4112yes—
319C2×C4×C53C2×#4112yes—
320C2×C4×C53C2511yescharacteristic
321C22⋊D53—48no—
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—22no—
331C2×Dic53—42no—
332C2×Dic53—42no—
333C2×Dic53—42no—
334C2×Dic53C22×D412yes—
335C2×Dic53C22×D412yes—
336C2×Dic53C22×D412yes—
337D212—22no—
338D212—22no—
339D212—48no—
340D212—42no—
341C4×D53—28no—
342C4×D53—24no—
343C4×D53—22no—
344C4×D53—22no—
345C4×D53—44no—
346C4×D53—48no—
347Dic106—22no—
348Dic106—22no—
349Dic106—48no—
350Dic106—42no—
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—42no—
360C22×C53—42no—
361C22×C53—42no—
362C22×C53—84no—
363C22×C53—84no—
364C22×C53#53212yes—
365C22×C53C2×AGL(1,ℤ/8)12yes—
366C22×C53#57512yes—
367C22×C53C23×D411yescharacteristic
368C2×D53—28no—
369C2×D53—22no—
370C2×D53—22no—
371C2×D53—42no—
372C2×D53—42no—
373C2×D53—42no—
374C2×D53—84no—
375C2×D53C2×AGL(1,ℤ/8)14yes—
376C4×C53—22no—
377C4×C53—22no—
378C4×C53—42no—
379C4×C53—42no—
380C4×C53#53212yes—
381C4×C53C22×#4111yescharacteristic
382C4×C53C22×#4111yescharacteristic
383Dic53—22no—
384Dic53—22no—
385Dic53—22no—
386Dic53—42no—
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×#442D5311yescharacteristic, complemented
402C2×#440—531no—
403C2×#440—531no—
404C22×#97—531no—
405C2×C53—82no—
406C2×C53—82no—
407C2×C53#318014yescomplemented
408C2×C53C2×#53211yescharacteristic
409C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
410C2×C53C2×#57511yescharacteristic
411D53—24no—
412D53—82no—
413C22×#41—1061no—
414C22×SD16—531no—
415C22×SD16—531no—
416C22×D8—531no—
417C22×D8C2×D5311yescharacteristic
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×Q8—531no—
437C2×C4×D4—531no—
438C2×C4×D4—1061no—
439C2×C4×D4—1061no—
440C2×C4×D4C2×D5311yescharacteristic
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#442C2×D5318yescomplemented
454#440—538no—
455#440—538no—
456C2×#107—531no—
457C2×#107—531no—
458C2×#106—531no—
459C2×#106C2×D5311yescharacteristic
460C2×#103—531no—
461C2×#103—531no—
462C2×#102—531no—
463C2×#102—531no—
464C2×#102—531no—
465C2×#102—531no—
466C2×#102C2×D5311yescharacteristic
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—531no—
477C22×Q8—1061no—
478C22×D4—531no—
479C22×D4—1061no—
480C22×D4—1061no—
481C22×D4—1061no—
482C22×D4—1061no—
483C22×D4—1061no—
484C22×D4C22×D5311yescharacteristic
485C22×D4C22×D5311yescharacteristic
486C23×C4—21no—
487C23×C4—21no—
488C23×C4—531no—
489C23×C4—531no—
490C23×C4—531no—
491C23×C4—1061no—
492C2×SD16—534no—
493C2×SD16—534no—
494C2×SD16—1064no—
495C2×SD16—1064no—
496C2×D8—24no—
497C2×D8—534no—
498C2×D8—1064no—
499C2×D8C22×D5314yes—
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—534no—
529C4×Q8—1062no—
530C4×D4—22no—
531C4×D4—22no—
532C4×D4—534no—
533C4×D4—1068no—
534C4×D4—1068no—
535C4×D4—1062no—
536C4×D4C22×D5314yes—
537C4×D4C22×D5314yes—
538#117—1068no—
539C2×C4⋊C4—531no—
540C2×C4⋊C4—531no—
541C2×C4⋊C4—1061no—
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—21no—
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—531no—
558C2×C42—531no—
559C2×C42—531no—
560C2×C42—534no—
561C2×C42—534no—
562C2×C42—1061no—
563C2×C42C22×D5311yescharacteristic
564#107—534no—
565#107—534no—
566#106—534no—
567#106C22×D5314yes—
568#103—534no—
569#103—534no—
570#102—534no—
571#102—534no—
572#102—534no—
573#102—534no—
574#102C22×D5314yes—
575#102C22×D5314yes—
576#97—534no—
577#97—534no—
578#97—534no—
579#97C22×D5314yes—
580C24—21no—
581C24—21no—
582C24—531no—
583C24—1061no—
584#41—21232no—
585C2×Q8—532no—
586C2×Q8—1064no—
587C2×Q8—1061no—
588C2×Q8—1062no—
589C2×Q8—1062no—
590C2×Q8—2124no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—532no—
598C2×D4—1064no—
599C2×D4—1064no—
600C2×D4—1064no—
601C2×D4—1064no—
602C2×D4—1064no—
603C2×D4—1061no—
604C2×D4—1062no—
605C2×D4—1062no—
606C2×D4—2124no—
607C2×D4—2124no—
608C2×D4—2124no—
609C2×D4—2124no—
610C2×D4—2124no—
611C2×D4C23×D5312yes—
612C2×D4C23×D5312yes—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—24no—
616C22×C4—24no—
617C22×C4—44no—
618C22×C4—44no—
619C22×C4—531no—
620C22×C4—531no—
621C22×C4—531no—
622C22×C4—532no—
623C22×C4—534no—
624C22×C4—532no—
625C22×C4—534no—
626C22×C4—1064no—
627C22×C4—1062no—
628C22×C4—1062no—
629C22×C4—1061no—
630C22×C4—1061no—
631C22×C4—1061no—
632C22×C4—1064no—
633C22×C4—2122no—
634C22×C4—2124no—
635C22×C4D4×D5311yescharacteristic
636C22×C4D4×D5311yescharacteristic
637C22×C4C23×D5311yescharacteristic
638SD16—1068no—
639SD16—1068no—
640D8—28no—
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—21no—
653C4⋊C4—21no—
654C4⋊C4—532no—
655C4⋊C4—532no—
656C4⋊C4—1064no—
657C4⋊C4—1064no—
658C4⋊C4—1064no—
659C4⋊C4—1064no—
660C4⋊C4—1061no—
661C4⋊C4—1061no—
662C4⋊C4—1064no—
663C4⋊C4C23×D5312yes—
664C4⋊C4C23×D5312yes—
665C22⋊C4—24no—
666C22⋊C4—24no—
667C22⋊C4—1064no—
668C22⋊C4—1064no—
669C22⋊C4—1064no—
670C22⋊C4—1064no—
671C22⋊C4—1064no—
672C22⋊C4—1064no—
673C22⋊C4—1064no—
674C42—534no—
675C42—534no—
676C42—532no—
677C42—532no—
678C42—1064no—
679C42D4×D5312yes—
680C42C23×D5312yes—
681C23—22no—
682C23—22no—
683C23—42no—
684C23—42no—
685C23—42no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—534no—
690C23—532no—
691C23—1062no—
692C23—1062no—
693C23—1062no—
694C23—2122no—
695C23—2122no—
696C23—2122no—
697C23C2×D4×D5311yescharacteristic
698Q8—1062no—
699Q8—1062no—
700Q8—2128no—
701Q8—2122no—
702D4—22no—
703D4—22no—
704D4—22no—
705D4—22no—
706D4—42no—
707D4—42no—
708D4—1062no—
709D4—1062no—
710D4—2128no—
711D4—2128no—
712D4—2128no—
713D4—2128no—
714D4—2128no—
715D4—2122no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—48no—
721C2×C4—48no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—532no—
725C2×C4—532no—
726C2×C4—532no—
727C2×C4—1068no—
728C2×C4—1062no—
729C2×C4—1062no—
730C2×C4—1062no—
731C2×C4—1064no—
732C2×C4—1062no—
733C2×C4—1062no—
734C2×C4—1062no—
735C2×C4—1062no—
736C2×C4—1062no—
737C2×C4—2124no—
738C2×C4—2128no—
739C2×C4—2122no—
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—42no—
756C22—42no—
757C22—42no—
758C22—84no—
759C22—84no—
760C22—534no—
761C22—1062no—
762C22—1068no—
763C22—1062no—
764C22—4244no—
765C22—2122no—
766C22—2122no—
767C22—2122no—
768C22#1681117012yes—
769C22AGL(1,ℤ/8)×D5312yes—
770C22#1681141912yes—
771C22C22×D4×D5311yescharacteristic
772C4—22no—
773C4—22no—
774C4—42no—
775C4—42no—
776C4—1062no—
777C4—1062no—
778C4—1062no—
779C4—2122no—
780C4—2122no—
781C4—2122no—
782C4#1681117012yes—
783C4C2×#41×D5311yescharacteristic
784C4C22×#1171994511yescharacteristic
785C2—82no—
786C2—82no—
787C2—1064no—
788C2—4242no—
789C2#2028541114yesdirect product factor
790C2C2×#1681117011yescharacteristic
791C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
792C2C2×#1681141911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
hypercenterC2×#442D53
hypocenterC53C2×#3180
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811170C2semidirect
2. C2×#16811155C2semidirect
3. #20285411C2direct (N × H)
4. C2×#16811030C2semidirect
5. C2×#16811011C2semidirect
6. C2×#16810986C2semidirect
7. C2×#16810981C2semidirect
8. C2×#16810858C2semidirect
9. C2×#16810856C2semidirect
10. C2×#16810853C2semidirect
11. C2×#16810851C2semidirect
12. C2×#16810733C2semidirect
13. C2×#16810725C2semidirect
14. C2×#16810723C2semidirect
15. C2×#97×D53C2semidirect
16. C2×C53×#442C2semidirect
24. #16811170C22semidirect
28. #16811155C22semidirect
45. #16811030C22semidirect
46. #16811011C22semidirect
47. #16810986C22semidirect
48. #16810981C22semidirect
49. #16810858C22semidirect
50. #16810856C22semidirect
51. #16810853C22semidirect
52. #16810851C22semidirect
53. #16810733C22semidirect
54. #16810725C22semidirect
55. #16810723C22semidirect
68. #97×D53C22semidirect
72. C53×#442C22semidirect
243. C2×C8×C53#41semidirect
278. C2×#88322#41semidirect
352. C8×C53C2×#41semidirect
354. #88322C2×#41semidirect
401. C2×#442D53semidirect
407. C2×C53#3180semidirect
453. #442C2×D53semidirect
473. C53C2×#3180semidirect
649. C2×C8#11719945semidirect
751. C8C2×#11719945semidirect
789. C2#20285411direct (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×#168111552
#202854112
C2×#168110302
C2×#168110112
C2×#168109862
C2×#168109812
C2×#168108582
C2×#168108562
C2×#168108532
C2×#168108512
C2×#168107332
C2×#168107252
C2×#168107232
C2×#97×D532
C2×C53×#4422
C2×#318053