Finite Group Databasebeta

← C2×#20286711 #28260671

Subgroups — C2×#20286711 #28260671

Order 13568.

2374 conjugacy classes of subgroups.

The subgroup lattice has 824 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811285C211yesmaximal, characteristic, complemented
2C2×#16811278C211yesmaximal, characteristic, complemented
3#20286711C2116yesmaximal, direct product factor
4C2×#16810983C211yesmaximal, characteristic, complemented
5C2×#16810960C211yesmaximal, characteristic, complemented
6C2×#16810938C211yesmaximal, characteristic, complemented
7C2×#16810918C211yesmaximal, characteristic, complemented
8C2×#16810868C211yesmaximal, characteristic, complemented
9C2×#16810858C211yesmaximal, characteristic, complemented
10C2×#16810838C211yesmaximal, characteristic, complemented
11C2×#16810767C211yesmaximal, characteristic, complemented
12C2×#16810760C211yesmaximal, characteristic, complemented
13C2×#16810696C211yesmaximal, characteristic, complemented
14C2×#16810623C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#440C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945—21no—
19C22×Q8×D53C2211yescharacteristic
20C22×#11719923C2211yescharacteristic
21C22×#11719922C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23C22×C8×D53C2211yescharacteristic
24#16811285—24no—
25#16811285C2218yescomplemented
26#16811278—24no—
27#16811278C2218yescomplemented
28C2×#13133217C2211yescharacteristic
29C2×#13133205—21no—
30C2×#13133205C2211yescharacteristic
31C2×#13133199—21no—
32C2×#13133199—21no—
33C2×#13133197—21no—
34C2×#13133197C2211yescharacteristic
35C2×#13133196—21no—
36C2×#13133192—21no—
37C2×#13133192C2211yescharacteristic
38C2×#13133188C2211yescharacteristic
39C2×#13133188C2211yescharacteristic
40C2×C4×D212—21no—
41C2×C4×D212C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810983C2218yescomplemented
45#16810960C2218yescomplemented
46#16810938C2218yescomplemented
47#16810918C2218yescomplemented
48#16810868C2218yescomplemented
49#16810858C2218yescomplemented
50#16810838C2218yescomplemented
51#16810767C2218yescomplemented
52#16810760C2218yescomplemented
53#16810696C2218yescomplemented
54C2×#13133150C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×C4⋊#88322C2211yescharacteristic
57#16810623C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63#103×D53C2218yescomplemented
64C2×#13133139C2211yescharacteristic
65C2×#13133139C2211yescharacteristic
66C2×#13133137C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133129C2211yescharacteristic
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×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C2×#11719945—28no—
82C2×#11719945—48no—
83C22×Dic106—21no—
84C22×Dic106—21no—
85C22×Dic106C2311yescharacteristic
86C2×Q8×D53—22no—
87C2×Q8×D53—24no—
88C2×Q8×D53—42no—
89C2×Q8×D53C2314yes—
90C22×D212—21no—
91C22×D212—21no—
92C22×D212D411yescharacteristic
93C22×D212C2311yescharacteristic
94C22×C22⋊D53—21no—
95C22×C22⋊D53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C22×C4×D53—21no—
99C22×C4×D53—21no—
100C22×C4×D53C2311yescharacteristic
101C22×C4×D53C2311yescharacteristic
102C2×#11719923—42no—
103C2×#11719923C2314yes—
104C2×#11719922—42no—
105C2×#11719922C2314yes—
106C2×#11719912—42no—
107C2×#11719912C2314yes—
108C22×#88322C2311yescharacteristic
109C22×#88322C2311yescharacteristic
110C2×C8×D53—42no—
111C2×C8×D53C2314yes—
112#13133217—22no—
113#13133217C2314yes—
114#13133205—22no—
115#13133205—28no—
116#13133205C2314yes—
117#13133199—28no—
118#13133199—28no—
119#13133197—28no—
120#13133197—22no—
121#13133197C2314yes—
122#13133196—28no—
123#13133192—28no—
124#13133192—22no—
125#13133192C2314yes—
126#13133188—22no—
127#13133188—22no—
128#13133188C2314yes—
129#13133188C2314yes—
130C4×D212—28no—
131C4×D212D414yes—
132C4×D212C2314yes—
133C2×C4⋊Dic53—21no—
134C2×C4⋊Dic53—21no—
135C2×C4⋊Dic53D411yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×C4⋊Dic53C2311yescharacteristic
138C2×#11719919—21no—
139C2×#11719919—21no—
140C4⋊C4×D53—22no—
141C4⋊C4×D53—22no—
142C4⋊C4×D53C2314yes—
143C4⋊C4×D53C2314yes—
144C2×C22⋊Dic53—21no—
145C2×C22⋊Dic53—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×#11719921—21no—
150C2×#11719921D411yescharacteristic
151C2×#11719921D411yescharacteristic
152#13133150C2314yes—
153#13133150C2314yes—
154C4⋊#88322C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133141C2314yes—
158#13133141C2314yes—
159#13133140C2314yes—
160#13133139C2314yes—
161#13133139C2314yes—
162#13133137C2314yes—
163#13133129C2314yes—
164#13133129C2314yes—
165C22×Q8×C53C2311yescharacteristic
166C22×D4×C53C2311yescharacteristic
167C23×C4×C53—21no—
168C2×SD16×C53—24no—
169C2×SD16×C53C2314yes—
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C4×Q8×C53—22no—
173C4×Q8×C53C2314yes—
174C4×D4×C53—22no—
175C4×D4×C53C2314yes—
176C2×C4⋊C4×C53—21no—
177C2×C4⋊C4×C53C2311yescharacteristic
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180C2×C42×C53—21no—
181C2×C42×C53C2311yescharacteristic
182#107×C53C2314yes—
183#103×C53C2314yes—
184#102×C53C2314yes—
185#97×C53C2314yes—
186C24×C53—21no—
187C23×D53—21no—
188C23×D53C2×D411yescharacteristic
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53#4114yescomplemented
193C2×Q8×C53C2412yes—
194C2×D4×C53—21no—
195C2×D4×C53—22no—
196C2×D4×C53—22no—
197C2×D4×C53C2412yes—
198C22×C4×C53—21no—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—44no—
203C22×C4×C53C2×D411yescharacteristic
204C22×C4×C53C2×D411yescharacteristic
205C22×C4×C53C2411yescharacteristic
206C2×C22⋊D53—24no—
207C2×C22⋊D53—24no—
208C2×C22⋊D53—44no—
209C2×C22⋊D53—44no—
210C22×Dic53—21no—
211C22×Dic53—21no—
212C22×Dic53—21no—
213C22×Dic53C2×D411yescharacteristic
214C22×Dic53C2×D411yescharacteristic
215#11719949—28no—
216#11719949—44no—
217#11719949—48no—
218Q8×D53—28no—
219Q8×D53—44no—
220Q8×D53—48no—
221#11719945—432no—
222C2×D212—24no—
223C2×D212—22no—
224C2×D212—22no—
225C2×D212—24no—
226C2×D212—24no—
227C2×D212—21no—
228C2×D212—44no—
229C2×D212—44no—
230C2×D212C2×D414yes—
231C2×D212C2412yes—
232C2×C4×D53—22no—
233C2×C4×D53—22no—
234C2×C4×D53—22no—
235C2×C4×D53—22no—
236C2×C4×D53—24no—
237C2×C4×D53—24no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—44no—
241C2×C4×D53—44no—
242C2×C4×D53—44no—
243C2×C4×D53—44no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2×D412yes—
246C2×C4×D53C2412yes—
247C2×C4×D53C2412yes—
248C2×Dic106—22no—
249C2×Dic106—22no—
250C2×Dic106—24no—
251C2×Dic106—21no—
252C2×Dic106—24no—
253C2×Dic106—44no—
254C2×Dic106—44no—
255C2×Dic106C2412yes—
256SD16×C53—28no—
257C2×C8×C53—22no—
258C2×C8×C53—22no—
259C2×C8×C53C2412yes—
260C2×C8×C53C2412yes—
261C4⋊C4×C53—24no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—21no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊C4×C53—24no—
267C42×C53—24no—
268C42×C53C2×D412yes—
269C42×C53C2412yes—
270C22⋊Dic53—24no—
271C22⋊Dic53—24no—
272#11719923—44no—
273#11719922—44no—
274#11719921—24no—
275#11719921—24no—
276#11719921—24no—
277#11719921—24no—
278#11719921C2×D414yes—
279#11719921C2×D414yes—
280C4⋊Dic53—21no—
281C4⋊Dic53—21no—
282C4⋊Dic53—24no—
283C4⋊Dic53—24no—
284C4⋊Dic53C2×D414yes—
285C4⋊Dic53C2412yes—
286C4⋊Dic53C2412yes—
287#11719919—24no—
288#11719919—24no—
289C2×#88322—22no—
290C2×#88322—22no—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293#11719912—44no—
294C8×D53—44no—
295C23×C53—22no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53—42no—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—22no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53AGL(1,ℤ/8)14yes—
310C22×D53C22×D412yes—
311C22×D53C22×D412yes—
312Q8×C53—24no—
313Q8×C53—22no—
314Q8×C53C2×#4114yescomplemented
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—42no—
318C2×C4×C53—24no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—22no—
324C2×C4×C53—48no—
325C2×C4×C53—42no—
326C2×C4×C53—42no—
327C2×C4×C53C22×D412yes—
328C2×C4×C53C22×D412yes—
329C2×C4×C53C22×D411yescharacteristic
330C2×C4×C53C2×#4112yes—
331C2×C4×C53H(5,𝔽2)12yes—
332C2×C4×C53C2511yescharacteristic
333C22⋊D53—48no—
334C22⋊D53—48no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345D212—28no—
346D212—22no—
347D212—22no—
348D212—48no—
349D212—48no—
350D212—42no—
351C4×D53—24no—
352C4×D53—24no—
353C4×D53—22no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—22no—
357C4×D53—48no—
358C4×D53—48no—
359C4×D53—48no—
360C4×D53—48no—
361Dic106—22no—
362Dic106—22no—
363Dic106—48no—
364Dic106—48no—
365Dic106—42no—
366C8×C53—22no—
367C8×C53—22no—
368#88322—22no—
369#88322—22no—
370C2×#3308—531nomaximal, Sylow
371C22×C53—42no—
372C22×C53—42no—
373C22×C53—42no—
374C22×C53—84no—
375C22×C53#54612yes—
376C22×C53C2×AGL(1,ℤ/8)12yes—
377C22×C53#57812yes—
378C22×C53C23×D411yescharacteristic
379C2×D53—22no—
380C2×D53—28no—
381C2×D53—22no—
382C2×D53—22no—
383C2×D53—22no—
384C2×D53—22no—
385C2×D53—44no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—84no—
390C2×D53C2×AGL(1,ℤ/8)14yes—
391C4×C53—24no—
392C4×C53—22no—
393C4×C53—22no—
394C4×C53—42no—
395C4×C53—42no—
396C4×C53#54612yes—
397C4×C53C22×#4111yescharacteristic
398C4×C53C2×H(5,𝔽2)11yescharacteristic
399Dic53—22no—
400Dic53—22no—
401Dic53—42no—
402Dic53—42no—
403Dic53—42no—
404C2×#548—531no—
405C2×#547—531no—
406#3308—5316no—
407C2×#489—531no—
408C2×#484—531no—
409C2×#480—531no—
410C2×#477—531no—
411C2×#468—531no—
412C2×#466—531no—
413C2×#463—531no—
414C2×#449—531no—
415C2×#448—531no—
416C2×#440D5311yescharacteristic, complemented
417C2×#435—531no—
418C2×#417—531no—
419C22×#103—531no—
420C2×C53—82no—
421C2×C53#330814yescomplemented
422C2×C53C2×#54611yescharacteristic
423C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C53C2×#57811yescharacteristic
425D53—24no—
426D53—42no—
427D53—82no—
428C22×#41—531no—
429C22×#41—1061no—
430C23×Q8—531no—
431C22×SD16—531no—
432C22×SD16C2×D5311yescharacteristic
433C22×D8—531no—
434C22×M16—531no—
435C23×C8—531no—
436#548—538no—
437#548—1064no—
438#547—538no—
439#547—1064no—
440C2×C4⋊Q8—531no—
441C2×#124—531no—
442C2×#124—1061no—
443C2×#123—1061no—
444C2×#123—1061no—
445C2×C22⋊Q8—531no—
446C2×C22⋊Q8—1061no—
447C2×C22⋊Q8—1061no—
448C2×#121—531no—
449C2×#121—531no—
450C2×#121—531no—
451C2×#121—1061no—
452C2×C4×Q8C2×D5311yescharacteristic
453C2×C4×D4—531no—
454C2×C4×D4—1061no—
455C2×C4×D4C2×D5311yescharacteristic
456C22×C4⋊C4—531no—
457C22×C4⋊C4—531no—
458#489—538no—
459#484—538no—
460#480—538no—
461#477—538no—
462#468—538no—
463#466—538no—
464#463—538no—
465#449—538no—
466#448—538no—
467#440C2×D5318yescomplemented
468#435—538no—
469C2×#107—531no—
470C2×#107—531no—
471C2×#107C2×D5311yescharacteristic
472C2×C4⋊C8—531no—
473#417—538no—
474C2×#103—531no—
475C2×#103—531no—
476C2×#103—531no—
477C2×#103—531no—
478C2×#103—531no—
479C2×#103—538no—
480C2×#103C2×D5311yescharacteristic
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102C2×D5311yescharacteristic
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×#97C2×D5311yescharacteristic
488C53C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—534no—
490C2×#41—1068no—
491C2×#41—1062no—
492C2×#41—1064no—
493C2×#41—2128no—
494C2×#41—2122no—
495C22×Q8—534no—
496C22×Q8—531no—
497C22×Q8—1061no—
498C22×Q8—1062no—
499C22×Q8—1061no—
500C22×Q8—1064no—
501C22×Q8—2122no—
502C22×Q8C22×D5311yescharacteristic
503C22×D4—531no—
504C22×D4—531no—
505C22×D4—1061no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4C22×D5311yescharacteristic
510C23×C4—21no—
511C23×C4—531no—
512C23×C4—531no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4—1061no—
516C23×C4—1061no—
517C2×SD16—24no—
518C2×SD16—534no—
519C2×SD16—2122no—
520C2×SD16C22×D5314yes—
521C2×D8—534no—
522C2×D8—2122no—
523C2×M16—534no—
524C2×M16—2122no—
525C22×C8—531no—
526C22×C8—531no—
527C22×C8—534no—
528C22×C8—2122no—
529C22×C8C22×D5311yescharacteristic
530C22×C8C22×D5311yescharacteristic
531C4⋊Q8—534no—
532C4⋊Q8—1062no—
533#124—534no—
534#124—1068no—
535#124—1062no—
536#123—1068no—
537#123—1068no—
538C22⋊Q8—534no—
539C22⋊Q8—1068no—
540C22⋊Q8—1062no—
541C22⋊Q8—1068no—
542#121—534no—
543#121—534no—
544#121—534no—
545#121—1062no—
546#121—1068no—
547#121—1062no—
548#121—1062no—
549C4×Q8—22no—
550C4×Q8C22×D5314yes—
551C4×D4—22no—
552C4×D4—534no—
553C4×D4—534no—
554C4×D4—1068no—
555C4×D4C22×D5314yes—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
560C2×C4⋊C4—534no—
561C2×C4⋊C4—534no—
562C2×C4⋊C4—1062no—
563C2×C4⋊C4—1062no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1061no—
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C4⋊C4C22×D5311yescharacteristic
570C2×C22⋊C4—21no—
571C2×C22⋊C4—531no—
572C2×C22⋊C4—531no—
573C2×C22⋊C4—1061no—
574C2×C22⋊C4—1061no—
575C2×C22⋊C4—1061no—
576C2×C22⋊C4—1061no—
577C2×C22⋊C4—1061no—
578C2×C22⋊C4—1061no—
579C2×C42—21no—
580C2×C42C22×D5311yescharacteristic
581#107—534no—
582#107—534no—
583#107C22×D5314yes—
584C4⋊C8—534no—
585#103—534no—
586#103—534no—
587#103—534no—
588#103—534no—
589#103—534no—
590#103C22×D5314yes—
591#102—534no—
592#102—534no—
593#102—534no—
594#102C22×D5314yes—
595C22⋊C8—534no—
596C22⋊C8—534no—
597#97C22×D5314yes—
598C24—21no—
599C24—531no—
600C24—531no—
601C24—1061no—
602#41—1068no—
603#41—21232no—
604#41—2124no—
605#41—2128no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—532no—
609C2×Q8—1064no—
610C2×Q8—1061no—
611C2×Q8—1064no—
612C2×Q8—1068no—
613C2×Q8—1062no—
614C2×Q8—1062no—
615C2×Q8—2124no—
616C2×Q8—2124no—
617C2×Q8—2124no—
618C2×Q8—2128no—
619C2×Q8#1171994514yescomplemented
620C2×Q8C23×D5312yes—
621C2×D4—21no—
622C2×D4—22no—
623C2×D4—22no—
624C2×D4—534no—
625C2×D4—532no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1064no—
629C2×D4—1064no—
630C2×D4—1064no—
631C2×D4—1061no—
632C2×D4—1062no—
633C2×D4—1062no—
634C2×D4—2124no—
635C2×D4—2124no—
636C2×D4—2124no—
637C2×D4—2124no—
638C2×D4C23×D5312yes—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—24no—
643C22×C4—44no—
644C22×C4—531no—
645C22×C4—531no—
646C22×C4—532no—
647C22×C4—532no—
648C22×C4—532no—
649C22×C4—532no—
650C22×C4—1064no—
651C22×C4—1064no—
652C22×C4—1064no—
653C22×C4—1064no—
654C22×C4—1062no—
655C22×C4—1062no—
656C22×C4—1062no—
657C22×C4—1062no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—2124no—
662C22×C4—2124no—
663C22×C4—2124no—
664C22×C4—2124no—
665C22×C4D4×D5311yescharacteristic
666C22×C4D4×D5311yescharacteristic
667C22×C4C23×D5311yescharacteristic
668SD16—28no—
669SD16—2124no—
670D8—2124no—
671M16—2124no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—532no—
675C2×C8—532no—
676C2×C8—1062no—
677C2×C8—1062no—
678C2×C8—2124no—
679C2×C8C23×D5312yes—
680C2×C8C23×D5312yes—
681C4⋊C4—24no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—534no—
685C4⋊C4—532no—
686C4⋊C4—532no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1061no—
691C4⋊C4—1061no—
692C4⋊C4—1064no—
693C4⋊C4C23×D5312yes—
694C4⋊C4C23×D5312yes—
695C22⋊C4—24no—
696C22⋊C4—534no—
697C22⋊C4—534no—
698C22⋊C4—1064no—
699C22⋊C4—1064no—
700C22⋊C4—1064no—
701C22⋊C4—1064no—
702C22⋊C4—1064no—
703C22⋊C4—1064no—
704C42—24no—
705C42D4×D5312yes—
706C42C23×D5312yes—
707C23—22no—
708C23—42no—
709C23—42no—
710C23—42no—
711C23—534no—
712C23—532no—
713C23—532no—
714C23—1062no—
715C23—1062no—
716C23—1062no—
717C23—1062no—
718C23—1062no—
719C23—1062no—
720C23—2122no—
721C23—2122no—
722C23—2122no—
723C23C2×D4×D5311yescharacteristic
724Q8—24no—
725Q8—22no—
726Q8—1062no—
727Q8—1062no—
728Q8—2128no—
729Q8—2128no—
730Q8—2122no—
731Q8C2×#1171994514yescomplemented
732D4—22no—
733D4—22no—
734D4—42no—
735D4—1068no—
736D4—1062no—
737D4—1062no—
738D4—2128no—
739D4—2128no—
740D4—2128no—
741D4—2128no—
742D4—2122no—
743C2×C4—24no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—48no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—532no—
753C2×C4—532no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1064no—
757C2×C4—1064no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—2128no—
766C2×C4—2128no—
767C2×C4—2128no—
768C2×C4—2128no—
769C2×C4—2122no—
770C2×C4—2122no—
771C2×C4—2122no—
772C2×C4C2×D4×D5312yes—
773C2×C4C2×D4×D5312yes—
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4C2×#1171994512yes—
776C2×C4#1313326312yes—
777C2×C4C24×D5311yescharacteristic
778C8—22no—
779C8—22no—
780C8—1062no—
781C8—1062no—
782C22—42no—
783C22—42no—
784C22—42no—
785C22—84no—
786C22—534no—
787C22—1062no—
788C22—1062no—
789C22—1068no—
790C22—1062no—
791C22—1062no—
792C22—1062no—
793C22—4244no—
794C22—2122no—
795C22—2122no—
796C22—2122no—
797C22—2124no—
798C22#1681126912yes—
799C22AGL(1,ℤ/8)×D5312yes—
800C22#1681143912yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—24no—
804C4—22no—
805C4—42no—
806C4—42no—
807C4—1062no—
808C4—1062no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126912yes—
813C4C22×#1171994511yescharacteristic
814C4C2×#1313326311yescharacteristic
815C2—82no—
816C2—1064no—
817C2—4242no—
818C2—2122no—
819C2#2028671114yesdirect product factor
820C2C2×#1681126911yescharacteristic
821C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
822C2C2×#1681143911yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#440C2
socleC23×C53C22×D4
hypercenterC2×#440D53
hypocenterC53C2×#3308
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×#16811285C2semidirect
2. C2×#16811278C2semidirect
3. #20286711C2direct (N × H)
4. C2×#16810983C2semidirect
5. C2×#16810960C2semidirect
6. C2×#16810938C2semidirect
7. C2×#16810918C2semidirect
8. C2×#16810868C2semidirect
9. C2×#16810858C2semidirect
10. C2×#16810838C2semidirect
11. C2×#16810767C2semidirect
12. C2×#16810760C2semidirect
13. C2×#16810696C2semidirect
14. C2×#16810623C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#440C2semidirect
25. #16811285C22semidirect
27. #16811278C22semidirect
44. #16810983C22semidirect
45. #16810960C22semidirect
46. #16810938C22semidirect
47. #16810918C22semidirect
48. #16810868C22semidirect
49. #16810858C22semidirect
50. #16810838C22semidirect
51. #16810767C22semidirect
52. #16810760C22semidirect
53. #16810696C22semidirect
57. #16810623C22semidirect
63. #103×D53C22semidirect
72. C53×#440C22semidirect
192. C2×Q8×C53#41semidirect
314. Q8×C53C2×#41semidirect
416. C2×#440D53semidirect
421. C2×C53#3308semidirect
467. #440C2×D53semidirect
488. C53C2×#3308semidirect
619. C2×Q8#11719945semidirect
731. Q8C2×#11719945semidirect
819. C2#20286711direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112852
C2×#168112782
#202867112
C2×#168109832
C2×#168109602
C2×#168109382
C2×#168109182
C2×#168108682
C2×#168108582
C2×#168108382
C2×#168107672
C2×#168107602
C2×#168106962
C2×#168106232
C2×#103×D532
C2×C53×#4402
C2×#330853