Finite Group Databasebeta

← C2×#20286699 #28260659

Subgroups — C2×#20286699 #28260659

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×#16811280C211yesmaximal, characteristic, complemented
2C2×#16811273C211yesmaximal, characteristic, complemented
3#20286699C2116yesmaximal, direct product factor
4C2×#16810981C211yesmaximal, characteristic, complemented
5C2×#16810959C211yesmaximal, characteristic, complemented
6C2×#16810935C211yesmaximal, characteristic, complemented
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810867C211yesmaximal, characteristic, complemented
9C2×#16810856C211yesmaximal, characteristic, complemented
10C2×#16810836C211yesmaximal, characteristic, complemented
11C2×#16810760C211yesmaximal, characteristic, complemented
12C2×#16810724C211yesmaximal, characteristic, complemented
13C2×#16810697C211yesmaximal, characteristic, complemented
14C2×#16810624C211yesmaximal, characteristic, complemented
15C2×#103×D53C211yesmaximal, characteristic, complemented
16C2×C53×#449C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×Q8×D53C2211yescharacteristic
19C22×#11719923C2211yescharacteristic
20C22×#11719917C2211yescharacteristic
21C22×C8×D53C2211yescharacteristic
22#16811280—24no—
23#16811280C2218yescomplemented
24#16811273—24no—
25#16811273C2218yescomplemented
26C2×#13133216C2211yescharacteristic
27C2×#13133204—21no—
28C2×#13133204C2211yescharacteristic
29C2×#13133199—21no—
30C2×#13133198—21no—
31C2×#13133196—21no—
32C2×#13133196C2211yescharacteristic
33C2×#13133194—21no—
34C2×#13133188—21no—
35C2×#13133188C2211yescharacteristic
36C2×#13133188C2211yescharacteristic
37C2×Q8×Dic53C2211yescharacteristic
38C2×D4×Dic53C2211yescharacteristic
39C2×C4×C22⋊D53—21no—
40C2×C4×C22⋊D53C2211yescharacteristic
41C22×C4⋊Dic53C2211yescharacteristic
42C2×C4⋊C4×D53C2211yescharacteristic
43#16810981C2218yescomplemented
44#16810959C2218yescomplemented
45#16810935C2218yescomplemented
46#16810916C2218yescomplemented
47#16810867C2218yescomplemented
48#16810856C2218yescomplemented
49#16810836C2218yescomplemented
50#16810760C2218yescomplemented
51#16810724C2218yescomplemented
52#16810697C2218yescomplemented
53C2×#13133151C2211yescharacteristic
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133146C2211yescharacteristic
57#16810624C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133140C2211yescharacteristic
63#103×D53C2218yescomplemented
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×#13133138C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C22×#41×C53C2211yescharacteristic
70C22×SD16×C53C2211yescharacteristic
71C22×D8×C53C2211yescharacteristic
72C2×#121×C53C2211yescharacteristic
73C53×#449C2218yescomplemented
74C2×#103×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic
76C2×C22⋊C8×C53C2211yescharacteristic
77C2×#11719947—28no—
78C2×#11719947—48no—
79C22×Dic106—21no—
80C22×Dic106—21no—
81C22×Dic106C2311yescharacteristic
82C2×Q8×D53—22no—
83C2×Q8×D53—24no—
84C2×Q8×D53—42no—
85C2×Q8×D53C2314yes—
86C22×C22⋊D53—21no—
87C22×C22⋊D53—21no—
88C22×C22⋊D53D411yescharacteristic
89C23×Dic53—21no—
90C23×Dic53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53C2311yescharacteristic
94C2×#11719923—42no—
95C2×#11719923C2314yes—
96C2×#11719917—42no—
97C2×#11719917C2314yes—
98C22×#88322C2311yescharacteristic
99C22×#88322C2311yescharacteristic
100C2×C8×D53—42no—
101C2×C8×D53C2314yes—
102#13133216—22no—
103#13133216C2314yes—
104#13133204—28no—
105#13133204—22no—
106#13133204C2314yes—
107#13133199—28no—
108#13133198—28no—
109#13133196—28no—
110#13133196—22no—
111#13133196C2314yes—
112#13133194—28no—
113#13133188—28no—
114#13133188—22no—
115#13133188—22no—
116#13133188C2314yes—
117#13133188C2314yes—
118Q8×Dic53—22no—
119Q8×Dic53C2314yes—
120D4×Dic53—22no—
121D4×Dic53C2314yes—
122C4×C22⋊D53—28no—
123C4×C22⋊D53D414yes—
124C4×C22⋊D53C2314yes—
125C2×C4⋊Dic53—22no—
126C2×C4⋊Dic53—21no—
127C2×C4⋊Dic53—21no—
128C2×C4⋊Dic53C2314yes—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×C4⋊Dic53C2311yescharacteristic
132C2×#11719919—21no—
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919D411yescharacteristic
136C4⋊C4×D53—22no—
137C4⋊C4×D53C2314yes—
138C2×C22⋊Dic53—21no—
139C2×C22⋊Dic53—21no—
140C2×C22⋊Dic53—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×C22⋊Dic53—21no—
144C2×C22⋊Dic53D411yescharacteristic
145C2×#11719921D411yescharacteristic
146C2×C4×Dic53—21no—
147C2×C4×Dic53C2311yescharacteristic
148#13133151C2314yes—
149#13133151C2314yes—
150#13133150C2314yes—
151#13133146C2314yes—
152#13133142C2314yes—
153#13133142C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133140C2314yes—
157#13133138C2314yes—
158#13133138C2314yes—
159#13133138C2314yes—
160#13133129C2314yes—
161#13133127C2314yes—
162C2×#41×C53—22no—
163C2×#41×C53—24no—
164C2×#41×C53—42no—
165C2×#41×C53C2314yes—
166C22×Q8×C53C2311yescharacteristic
167C22×D4×C53—21no—
168C22×D4×C53—21no—
169C22×D4×C53C2311yescharacteristic
170C22×D4×C53C2311yescharacteristic
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C2×SD16×C53—24no—
174C2×SD16×C53C2314yes—
175C2×D8×C53—42no—
176C2×D8×C53C2314yes—
177C22×C8×C53C2311yescharacteristic
178C22×C8×C53C2311yescharacteristic
179#121×C53—22no—
180#121×C53C2314yes—
181C2×C4⋊C4×C53C2311yescharacteristic
182C2×C22⋊C4×C53—21no—
183#103×C53C2314yes—
184#102×C53C2314yes—
185C22⋊C8×C53C2314yes—
186C24×C53—21no—
187C24×C53—21no—
188C24×C53C2×D411yescharacteristic
189C23×D53C2×D411yescharacteristic
190#41×C53—28no—
191#41×C53—44no—
192#41×C53—48no—
193C2×Q8×C53—21no—
194C2×Q8×C53—22no—
195C2×Q8×C53#4114yescomplemented
196C2×Q8×C53C2412yes—
197C2×D4×C53—24no—
198C2×D4×C53—24no—
199C2×D4×C53—21no—
200C2×D4×C53—21no—
201C2×D4×C53—22no—
202C2×D4×C53—22no—
203C2×D4×C53—22no—
204C2×D4×C53—22no—
205C2×D4×C53—44no—
206C2×D4×C53—44no—
207C2×D4×C53C2412yes—
208C2×D4×C53C2412yes—
209C22×C4×C53—21no—
210C22×C4×C53—22no—
211C22×C4×C53—22no—
212C22×C4×C53—21no—
213C22×C4×C53—24no—
214C22×C4×C53—44no—
215C22×C4×C53C2×D411yescharacteristic
216C22×C4×C53C2×D412yes—
217C22×C4×C53C2412yes—
218C22×C4×C53C2411yescharacteristic
219C2×C22⋊D53—24no—
220C2×C22⋊D53—24no—
221C2×C22⋊D53—24no—
222C2×C22⋊D53—44no—
223C2×C22⋊D53—44no—
224C2×C22⋊D53C2×D414yes—
225C22×Dic53—21no—
226C22×Dic53—21no—
227C22×Dic53—21no—
228C22×Dic53—21no—
229C22×Dic53—24no—
230C22×Dic53—24no—
231C22×Dic53—44no—
232C22×Dic53—44no—
233C22×Dic53C2×D411yescharacteristic
234C22×Dic53C2×D411yescharacteristic
235C22×Dic53C2×D411yescharacteristic
236Q8×D53—28no—
237Q8×D53—44no—
238Q8×D53—48no—
239#11719947—432no—
240C2×C4×D53—22no—
241C2×C4×D53—22no—
242C2×C4×D53—24no—
243C2×C4×D53—24no—
244C2×C4×D53—44no—
245C2×C4×D53—44no—
246C2×C4×D53C2×D412yes—
247C2×C4×D53C2412yes—
248C2×Dic106—22no—
249C2×Dic106—22no—
250C2×Dic106—21no—
251C2×Dic106—24no—
252C2×Dic106—24no—
253C2×Dic106—44no—
254C2×Dic106—44no—
255C2×Dic106C2412yes—
256SD16×C53—28no—
257D8×C53—44no—
258C2×C8×C53—22no—
259C2×C8×C53—22no—
260C2×C8×C53C2412yes—
261C2×C8×C53C2412yes—
262C4⋊C4×C53—21no—
263C4⋊C4×C53C2412yes—
264C22⋊C4×C53—24no—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267C22⋊Dic53—24no—
268C22⋊Dic53—24no—
269C22⋊Dic53—24no—
270C22⋊Dic53—24no—
271C22⋊Dic53C2×D414yes—
272#11719923—44no—
273#11719921C2×D414yes—
274C4⋊Dic53—21no—
275C4⋊Dic53—21no—
276C4⋊Dic53—24no—
277C4⋊Dic53—21no—
278C4⋊Dic53—24no—
279C4⋊Dic53C2412yes—
280C4⋊Dic53C2412yes—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285#11719919C2×D414yes—
286C4×Dic53—24no—
287C4×Dic53C2×D412yes—
288C4×Dic53C2412yes—
289#11719917—44no—
290C2×#88322—22no—
291C2×#88322—22no—
292C2×#88322C2412yes—
293C2×#88322C2412yes—
294C8×D53—44no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53—22no—
298C23×C53—22no—
299C23×C53—22no—
300C23×C53—42no—
301C23×C53—42no—
302C23×C53—42no—
303C23×C53—42no—
304C23×C53—42no—
305C23×C53—42no—
306C23×C53C22×D412yes—
307C23×C53C22×D411yescharacteristic
308C22×D53—22no—
309C22×D53—22no—
310C22×D53AGL(1,ℤ/8)14yes—
311C22×D53C22×D412yes—
312Q8×C53—24no—
313Q8×C53—22no—
314Q8×C53C2×#4114yescomplemented
315D4×C53—22no—
316D4×C53—22no—
317D4×C53—22no—
318D4×C53—22no—
319D4×C53—48no—
320D4×C53—48no—
321D4×C53—42no—
322D4×C53—42no—
323C2×C4×C53—24no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—24no—
327C2×C4×C53—22no—
328C2×C4×C53—22no—
329C2×C4×C53—22no—
330C2×C4×C53—48no—
331C2×C4×C53—42no—
332C2×C4×C53C22×D412yes—
333C2×C4×C53C22×D411yescharacteristic
334C2×C4×C53C2×#4112yes—
335C2×C4×C53H(5,𝔽2)12yes—
336C2×C4×C53C2511yescharacteristic
337C22⋊D53—28no—
338C22⋊D53—48no—
339C22⋊D53—48no—
340C2×Dic53—22no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—22no—
347C2×Dic53—48no—
348C2×Dic53—48no—
349C2×Dic53—42no—
350C2×Dic53—42no—
351C2×Dic53—42no—
352C2×Dic53—42no—
353C2×Dic53C22×D412yes—
354C2×Dic53C22×D412yes—
355C2×Dic53C22×D412yes—
356C4×D53—24no—
357C4×D53—22no—
358C4×D53—22no—
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—22no—
372C22×C53—22no—
373C22×C53—22no—
374C22×C53—44no—
375C22×C53—42no—
376C22×C53—42no—
377C22×C53—42no—
378C22×C53—42no—
379C22×C53—42no—
380C22×C53—42no—
381C22×C53—84no—
382C22×C53—84no—
383C22×C53#54612yes—
384C22×C53C2×AGL(1,ℤ/8)12yes—
385C22×C53#57812yes—
386C22×C53C23×D411yescharacteristic
387C2×D53—22no—
388C2×D53—28no—
389C2×D53—22no—
390C2×D53C2×AGL(1,ℤ/8)14yes—
391C4×C53—24no—
392C4×C53—22no—
393C4×C53—42no—
394C4×C53#54612yes—
395C4×C53C22×#4111yescharacteristic
396C4×C53C2×H(5,𝔽2)11yescharacteristic
397Dic53—22no—
398Dic53—22no—
399Dic53—22no—
400Dic53—42no—
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×#449D5311yescharacteristic, complemented
415C2×#448—531no—
416C2×#440—531no—
417C2×#435—531no—
418C2×#417—531no—
419C22×#103—531no—
420C2×C53—42no—
421C2×C53—82no—
422C2×C53—82no—
423C2×C53#330814yescomplemented
424C2×C53C2×#54611yescharacteristic
425C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
426C2×C53C2×#57811yescharacteristic
427D53—24no—
428C22×#41—1061no—
429C22×#41C2×D5311yescharacteristic
430C23×Q8—531no—
431C22×SD16—531no—
432C22×SD16C2×D5311yescharacteristic
433C22×D8C2×D5311yescharacteristic
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—1061no—
451C2×#121C2×D5311yescharacteristic
452C2×C4×Q8—531no—
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C2×C4×D4—1061no—
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#449C2×D5318yescomplemented
466#448—538no—
467#440—538no—
468#435—538no—
469C2×#107—531no—
470C2×#107—531no—
471C2×#107—531no—
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⋊C8C2×D5311yescharacteristic
487C2×#97—531no—
488C53C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—22no—
490C2×#41—24no—
491C2×#41—42no—
492C2×#41—1068no—
493C2×#41—2128no—
494C2×#41C22×D5314yes—
495C22×Q8—534no—
496C22×Q8—531no—
497C22×Q8—1061no—
498C22×Q8—1061no—
499C22×Q8—1062no—
500C22×Q8—1064no—
501C22×Q8—2122no—
502C22×Q8C22×D5311yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—531no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4C22×D5311yescharacteristic
509C22×D4C22×D5311yescharacteristic
510C23×C4—21no—
511C23×C4—531no—
512C23×C4—1061no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4—1061no—
516C23×C4C22×D5311yescharacteristic
517C2×SD16—24no—
518C2×SD16—534no—
519C2×SD16—2122no—
520C2×SD16C22×D5314yes—
521C2×D8—42no—
522C2×D8C22×D5314yes—
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—1062no—
535#124—1068no—
536#123—1068no—
537#123—1068no—
538C22⋊Q8—534no—
539C22⋊Q8—1068no—
540C22⋊Q8—1068no—
541C22⋊Q8—1062no—
542#121—22no—
543#121—534no—
544#121—534no—
545#121—1062no—
546#121—1062no—
547#121—1068no—
548#121C22×D5314yes—
549C4×Q8—534no—
550C4×Q8—1062no—
551C4×D4—534no—
552C4×D4—534no—
553C4×D4—534no—
554C4×D4—1062no—
555C4×D4—1068no—
556C2×C4⋊C4—531no—
557C2×C4⋊C4—531no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—534no—
560C2×C4⋊C4—531no—
561C2×C4⋊C4—534no—
562C2×C4⋊C4—1062no—
563C2×C4⋊C4—1061no—
564C2×C4⋊C4—1061no—
565C2×C4⋊C4—1061no—
566C2×C4⋊C4—1061no—
567C2×C4⋊C4—1062no—
568C2×C4⋊C4—1061no—
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—531no—
580C2×C42—1061no—
581#107—534no—
582#107—534no—
583#107—534no—
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⋊C8C22×D5314yes—
597#97—534no—
598C24—21no—
599C24—21no—
600C24—531no—
601C24D4×D5311yescharacteristic
602#41—28no—
603#41—44no—
604#41—48no—
605#41—21232no—
606C2×Q8—21no—
607C2×Q8—22no—
608C2×Q8—532no—
609C2×Q8—1064no—
610C2×Q8—1064no—
611C2×Q8—1061no—
612C2×Q8—1068no—
613C2×Q8—1062no—
614C2×Q8—1062no—
615C2×Q8—2124no—
616C2×Q8—2124no—
617C2×Q8—2124no—
618C2×Q8—2128no—
619C2×Q8#1171994714yescomplemented
620C2×Q8C23×D5312yes—
621C2×D4—24no—
622C2×D4—24no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—22no—
626C2×D4—22no—
627C2×D4—22no—
628C2×D4—22no—
629C2×D4—44no—
630C2×D4—44no—
631C2×D4—534no—
632C2×D4—1064no—
633C2×D4—1064no—
634C2×D4—1064no—
635C2×D4—2124no—
636C2×D4—2124no—
637C2×D4C23×D5312yes—
638C2×D4C23×D5312yes—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—21no—
643C22×C4—24no—
644C22×C4—44no—
645C22×C4—531no—
646C22×C4—531no—
647C22×C4—531no—
648C22×C4—532no—
649C22×C4—532no—
650C22×C4—1064no—
651C22×C4—1064no—
652C22×C4—1064no—
653C22×C4—1062no—
654C22×C4—1062no—
655C22×C4—1064no—
656C22×C4—1061no—
657C22×C4—1061no—
658C22×C4—1061no—
659C22×C4—1061no—
660C22×C4—2124no—
661C22×C4—2124no—
662C22×C4—2124no—
663C22×C4—2124no—
664C22×C4D4×D5312yes—
665C22×C4D4×D5311yescharacteristic
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668SD16—28no—
669SD16—2124no—
670D8—44no—
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—21no—
682C4⋊C4—534no—
683C4⋊C4—532no—
684C4⋊C4—532no—
685C4⋊C4—532no—
686C4⋊C4—1064no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1061no—
690C4⋊C4—1061no—
691C4⋊C4—1064no—
692C4⋊C4—1061no—
693C4⋊C4—1064no—
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—532no—
705C42—532no—
706C42—1064no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—42no—
713C23—42no—
714C23—42no—
715C23—42no—
716C23—42no—
717C23—42no—
718C23—534no—
719C23—532no—
720C23—1062no—
721C23—1062no—
722C23C2×D4×D5312yes—
723C23C2×D4×D5311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—1062no—
727Q8—1062no—
728Q8—2128no—
729Q8—2128no—
730Q8—2122no—
731Q8C2×#1171994714yescomplemented
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—48no—
737D4—48no—
738D4—42no—
739D4—42no—
740D4—1068no—
741D4—2128no—
742D4—2128no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—48no—
751C2×C4—42no—
752C2×C4—532no—
753C2×C4—532no—
754C2×C4—532no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—1062no—
758C2×C4—1062no—
759C2×C4—1062no—
760C2×C4—1064no—
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×C4—2122no—
773C2×C4C2×D4×D5312yes—
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4C2×#1171994712yes—
776C2×C4#1313326212yes—
777C2×C4C24×D5311yescharacteristic
778C8—22no—
779C8—22no—
780C8—1062no—
781C8—1062no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—44no—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—84no—
793C22—84no—
794C22—534no—
795C22—1062no—
796C22—1062no—
797C22—1068no—
798C22#1681126012yes—
799C22AGL(1,ℤ/8)×D5312yes—
800C22#1681143712yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—1062no—
806C4—1062no—
807C4—1062no—
808C4—2122no—
809C4—2122no—
810C4—2122no—
811C4—2122no—
812C4#1681126012yes—
813C4C22×#1171994711yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—42no—
816C2—82no—
817C2—82no—
818C2—1064no—
819C2#2028669914yesdirect product factor
820C2C2×#1681126011yescharacteristic
821C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
822C2C2×#1681143711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#449C2
socleC23×C53C22×D4
hypercenterC2×#449D53
hypocenterC53C2×#3308
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

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

NH ≅ G/Ntype
1. C2×#16811280C2semidirect
2. C2×#16811273C2semidirect
3. #20286699C2direct (N × H)
4. C2×#16810981C2semidirect
5. C2×#16810959C2semidirect
6. C2×#16810935C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810867C2semidirect
9. C2×#16810856C2semidirect
10. C2×#16810836C2semidirect
11. C2×#16810760C2semidirect
12. C2×#16810724C2semidirect
13. C2×#16810697C2semidirect
14. C2×#16810624C2semidirect
15. C2×#103×D53C2semidirect
16. C2×C53×#449C2semidirect
23. #16811280C22semidirect
25. #16811273C22semidirect
43. #16810981C22semidirect
44. #16810959C22semidirect
45. #16810935C22semidirect
46. #16810916C22semidirect
47. #16810867C22semidirect
48. #16810856C22semidirect
49. #16810836C22semidirect
50. #16810760C22semidirect
51. #16810724C22semidirect
52. #16810697C22semidirect
57. #16810624C22semidirect
63. #103×D53C22semidirect
73. C53×#449C22semidirect
195. C2×Q8×C53#41semidirect
314. Q8×C53C2×#41semidirect
414. C2×#449D53semidirect
423. C2×C53#3308semidirect
465. #449C2×D53semidirect
488. C53C2×#3308semidirect
619. C2×Q8#11719947semidirect
731. Q8C2×#11719947semidirect
819. C2#20286699direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112802
C2×#168112732
#202866992
C2×#168109812
C2×#168109592
C2×#168109352
C2×#168109162
C2×#168108672
C2×#168108562
C2×#168108362
C2×#168107602
C2×#168107242
C2×#168106972
C2×#168106242
C2×#103×D532
C2×C53×#4492
C2×#330853