Finite Group Databasebeta

← C2×#20286702 #28260662

Subgroups — C2×#20286702 #28260662

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×#16811284C211yesmaximal, characteristic, complemented
2C2×#16811274C211yesmaximal, characteristic, complemented
3#20286702C2116yesmaximal, direct product factor
4C2×#16810984C211yesmaximal, characteristic, complemented
5C2×#16810957C211yesmaximal, characteristic, complemented
6C2×#16810936C211yesmaximal, characteristic, complemented
7C2×#16810916C211yesmaximal, characteristic, complemented
8C2×#16810872C211yesmaximal, characteristic, complemented
9C2×#16810859C211yesmaximal, characteristic, complemented
10C2×#16810841C211yesmaximal, characteristic, complemented
11C2×#16810771C211yesmaximal, characteristic, complemented
12C2×#16810762C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic, complemented
14C2×#16810694C211yesmaximal, characteristic, complemented
15C2×#16810623C211yesmaximal, characteristic, complemented
16C22×#103×C53C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945—21no—
19C22×#11719924C2211yescharacteristic
20C22×#11719924C2211yescharacteristic
21C22×D424C2211yescharacteristic
22C22×#11719912C2211yescharacteristic
23#16811284—24no—
24#16811284C2218yescomplemented
25#16811274—24no—
26#16811274C2218yescomplemented
27C2×#13133216C2211yescharacteristic
28C2×#13133206—21no—
29C2×#13133206C2211yescharacteristic
30C2×#13133202—21no—
31C2×#13133200—21no—
32C2×#13133195—21no—
33C2×#13133193—21no—
34C2×#13133193C2211yescharacteristic
35C2×#13133192C2211yescharacteristic
36C2×#13133191—21no—
37C2×#13133191C2211yescharacteristic
38C2×#13133191C2211yescharacteristic
39C2×Q8×Dic53C2211yescharacteristic
40C2×#13133179C2211yescharacteristic
41C2×C4×C22⋊D53—21no—
42C2×C4×C22⋊D53C2211yescharacteristic
43C2×C4⋊C4×D53C2211yescharacteristic
44#16810984C2218yescomplemented
45#16810957C2218yescomplemented
46#16810936C2218yescomplemented
47#16810916C2218yescomplemented
48#16810872C2218yescomplemented
49#16810859C2218yescomplemented
50#16810841C2218yescomplemented
51#16810771C2218yescomplemented
52#16810762C2218yescomplemented
53#16810726C2218yescomplemented
54#16810694C2218yescomplemented
55C2×#13133151C2211yescharacteristic
56C2×#13133150C2211yescharacteristic
57C2×#13133150C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59#16810623C2218yescomplemented
60C2×#13133141C2211yescharacteristic
61C2×#13133141C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133139C2211yescharacteristic
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×#13133127C2211yescharacteristic
69C23×Q8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C22×C4⋊C4×C53C2211yescharacteristic
72C2×#103×C53C2211yescharacteristic
73C2×#103×C53C2211yescharacteristic
74C2×#103×C53C2211yescharacteristic
75C2×#103×C53C2211yescharacteristic
76C2×#103×C53C2218yescomplemented
77C2×#11719949—22no—
78C2×#11719949—24no—
79C2×#11719949—42no—
80C2×#11719949C2314yes—
81C2×#11719945—28no—
82C2×#11719945—48no—
83C22×Dic106—21no—
84C22×D212—21no—
85C22×D212—21no—
86C22×D212C2311yescharacteristic
87C22×D212C2311yescharacteristic
88C22×C22⋊D53—21no—
89C22×C22⋊D53—21no—
90C22×C22⋊D53D411yescharacteristic
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53—21no—
94C22×C4×D53C2311yescharacteristic
95C2×#11719924—24no—
96C2×#11719924—42no—
97C2×#11719924C2314yes—
98C2×#11719924C2314yes—
99C2×D424—42no—
100C2×D424C2314yes—
101C2×#11719912—42no—
102C2×#11719912C2314yes—
103C22×#88322C2311yescharacteristic
104C22×#88322C2311yescharacteristic
105#13133216—22no—
106#13133216C2314yes—
107#13133206—28no—
108#13133206—22no—
109#13133206C2314yes—
110#13133202—28no—
111#13133200—28no—
112#13133195—28no—
113#13133193—28no—
114#13133193—22no—
115#13133193C2314yes—
116#13133192—22no—
117#13133192C2314yes—
118#13133191—22no—
119#13133191—22no—
120#13133191—28no—
121#13133191C2314yes—
122#13133191C2314yes—
123Q8×Dic53—22no—
124Q8×Dic53C2314yes—
125#13133179—22no—
126#13133179C2314yes—
127C4×C22⋊D53—28no—
128C4×C22⋊D53D414yes—
129C4×C22⋊D53C2314yes—
130C2×C4⋊Dic53—21no—
131C2×C4⋊Dic53C2311yescharacteristic
132C2×C4⋊Dic53C2311yescharacteristic
133C2×#11719919—21no—
134C2×#11719919—21no—
135C2×#11719919—21no—
136C2×#11719919D411yescharacteristic
137C4⋊C4×D53—22no—
138C4⋊C4×D53C2314yes—
139C2×C22⋊Dic53D411yescharacteristic
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921D411yescharacteristic
148C2×C4×Dic53—21no—
149C2×C4×Dic53C2311yescharacteristic
150#13133151C2314yes—
151#13133150C2314yes—
152#13133150C2314yes—
153#13133146C2314yes—
154#13133141C2314yes—
155#13133141C2314yes—
156#13133139C2314yes—
157#13133139C2314yes—
158#13133137C2314yes—
159#13133137C2314yes—
160C22⋊#88322C2314yes—
161#13133129C2314yes—
162#13133127C2314yes—
163C22×Q8×C53—22no—
164C22×Q8×C53—21no—
165C22×Q8×C53—24no—
166C22×Q8×C53—42no—
167C22×Q8×C53C2311yescharacteristic
168C22×Q8×C53C2314yes—
169C22×Q8×C53C2311yescharacteristic
170C23×C4×C53—21no—
171C23×C4×C53—21no—
172C23×C4×C53C2311yescharacteristic
173C22×C8×C53—42no—
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2311yescharacteristic
176C22×C8×C53C2314yes—
177C2×C4⋊C4×C53—22no—
178C2×C4⋊C4×C53—21no—
179C2×C4⋊C4×C53C2314yes—
180C2×C4⋊C4×C53C2311yescharacteristic
181C2×C4⋊C4×C53C2311yescharacteristic
182#103×C53C2314yes—
183#103×C53C2314yes—
184#103×C53C2314yes—
185#103×C53C2314yes—
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C23×D53C2×D411yescharacteristic
190C2×Q8×C53—21no—
191C2×Q8×C53—24no—
192C2×Q8×C53—21no—
193C2×Q8×C53—22no—
194C2×Q8×C53—28no—
195C2×Q8×C53—22no—
196C2×Q8×C53—22no—
197C2×Q8×C53—44no—
198C2×Q8×C53—44no—
199C2×Q8×C53—48no—
200C2×Q8×C53#4114yescomplemented
201C2×Q8×C53C2412yes—
202C2×Q8×C53C2412yes—
203C22×C4×C53—21no—
204C22×C4×C53—22no—
205C22×C4×C53—22no—
206C22×C4×C53—21no—
207C22×C4×C53—21no—
208C22×C4×C53—24no—
209C22×C4×C53—21no—
210C22×C4×C53—24no—
211C22×C4×C53—44no—
212C22×C4×C53—44no—
213C22×C4×C53C2×D411yescharacteristic
214C22×C4×C53C2×D412yes—
215C22×C4×C53C2412yes—
216C22×C4×C53C2411yescharacteristic
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—24no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53—44no—
222C2×C22⋊D53C2×D414yes—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53C2×D411yescharacteristic
226C22×Dic53C2×D411yescharacteristic
227C22×Dic53C2×D411yescharacteristic
228#11719949—28no—
229#11719949—44no—
230#11719949—48no—
231#11719945—432no—
232C2×D212—22no—
233C2×D212—22no—
234C2×D212—22no—
235C2×D212—22no—
236C2×D212—24no—
237C2×D212—24no—
238C2×D212—21no—
239C2×D212—21no—
240C2×D212—44no—
241C2×D212—44no—
242C2×D212C2412yes—
243C2×D212C2412yes—
244C2×C4×D53—22no—
245C2×C4×D53—22no—
246C2×C4×D53—24no—
247C2×C4×D53—24no—
248C2×C4×D53—24no—
249C2×C4×D53—44no—
250C2×C4×D53—44no—
251C2×C4×D53—44no—
252C2×C4×D53C2×D412yes—
253C2×C4×D53C2412yes—
254C2×Dic106—24no—
255C2×Dic106—44no—
256C2×C8×C53—22no—
257C2×C8×C53—22no—
258C2×C8×C53—44no—
259C2×C8×C53C2412yes—
260C2×C8×C53C2412yes—
261C4⋊C4×C53—21no—
262C4⋊C4×C53—21no—
263C4⋊C4×C53—24no—
264C4⋊C4×C53C2412yes—
265C4⋊C4×C53C2412yes—
266C22⋊Dic53C2×D414yes—
267#11719924—28no—
268#11719924—44no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273#11719921—24no—
274#11719921—24no—
275#11719921—24no—
276#11719921C2×D414yes—
277C4⋊Dic53—21no—
278C4⋊Dic53—21no—
279C4⋊Dic53—24no—
280C4⋊Dic53C2412yes—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285#11719919C2×D414yes—
286C4×Dic53—24no—
287C4×Dic53C2×D412yes—
288C4×Dic53C2412yes—
289C2×#88322—22no—
290C2×#88322—22no—
291C2×#88322C2412yes—
292C2×#88322C2412yes—
293D424—44no—
294#11719912—44no—
295C23×C53—22no—
296C23×C53—22no—
297C23×C53AGL(1,ℤ/8)14yes—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—22no—
303C22×D53—22no—
304C22×D53—22no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308C22×D53—42no—
309C22×D53—42no—
310C22×D53—42no—
311C22×D53C22×D412yes—
312Q8×C53—24no—
313Q8×C53—22no—
314Q8×C53—22no—
315Q8×C53—22no—
316Q8×C53—48no—
317Q8×C53—42no—
318Q8×C53C2×#4114yescomplemented
319C2×C4×C53—24no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—24no—
323C2×C4×C53—22no—
324C2×C4×C53—22no—
325C2×C4×C53—22no—
326C2×C4×C53—22no—
327C2×C4×C53—22no—
328C2×C4×C53—48no—
329C2×C4×C53—42no—
330C2×C4×C53—42no—
331C2×C4×C53—42no—
332C2×C4×C53—48no—
333C2×C4×C53C22×D412yes—
334C2×C4×C53C22×D411yescharacteristic
335C2×C4×C53C2×#4112yes—
336C2×C4×C53H(5,𝔽2)12yes—
337C2×C4×C53C2511yescharacteristic
338C22⋊D53—28no—
339C22⋊D53—48no—
340C22⋊D53—48no—
341C2×Dic53—22no—
342C2×Dic53—22no—
343C2×Dic53—22no—
344C2×Dic53—22no—
345C2×Dic53—22no—
346C2×Dic53—42no—
347C2×Dic53—42no—
348C2×Dic53C22×D412yes—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351D212—22no—
352D212—22no—
353D212—22no—
354D212—22no—
355D212—48no—
356D212—48no—
357D212—42no—
358D212—42no—
359C4×D53—24no—
360C4×D53—22no—
361C4×D53—22no—
362C4×D53—48no—
363C4×D53—48no—
364C4×D53—48no—
365Dic106—48no—
366C8×C53—22no—
367C8×C53—22no—
368#88322—22no—
369#88322—22no—
370C2×#3308—531nomaximal, Sylow
371C22×C53—22no—
372C22×C53—28no—
373C22×C53—22no—
374C22×C53#54612yes—
375C22×C53C2×AGL(1,ℤ/8)14yes—
376C22×C53C2×AGL(1,ℤ/8)12yes—
377C22×C53#57812yes—
378C22×C53C23×D411yescharacteristic
379C2×D53—22no—
380C2×D53—22no—
381C2×D53—22no—
382C2×D53—44no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—42no—
388C2×D53—42no—
389C2×D53—84no—
390C2×D53—84no—
391C4×C53—24no—
392C4×C53—22no—
393C4×C53—42no—
394C4×C53—42no—
395C4×C53—42no—
396C4×C53#54612yes—
397C4×C53C22×#4111yescharacteristic
398C4×C53C2×H(5,𝔽2)11yescharacteristic
399Dic53—22no—
400Dic53—22no—
401Dic53—22no—
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×#440—531no—
417C2×#435—531no—
418C2×#417—531no—
419C22×#103D5311yescharacteristic, complemented
420C2×C53—24no—
421C2×C53#330814yescomplemented
422C2×C53C2×#54611yescharacteristic
423C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
424C2×C53C2×#57811yescharacteristic
425D53—42no—
426D53—82no—
427D53—82no—
428C22×#41—531no—
429C22×#41—1061no—
430C23×Q8C2×D5311yescharacteristic
431C22×SD16—531no—
432C22×SD16—531no—
433C22×D8—531no—
434C22×M16—531no—
435C23×C8C2×D5311yescharacteristic
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×Q8—531no—
453C2×C4×D4—531no—
454C2×C4×D4—531no—
455C2×C4×D4—1061no—
456C22×C4⋊C4—531no—
457C22×C4⋊C4C2×D5311yescharacteristic
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#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×#103C2×D5311yescharacteristic
477C2×#103C2×D5311yescharacteristic
478C2×#103C2×D5311yescharacteristic
479C2×#103C2×D5311yescharacteristic
480C2×#103C2×D5318yescomplemented
481C2×#102—531no—
482C2×#102—531no—
483C2×#102—531no—
484C2×#102—531no—
485C2×C22⋊C8—531no—
486C2×C22⋊C8—531no—
487C2×#97—531no—
488C53C2×#330811yescharacteristic, complemented, Sylow
489C2×#41—534no—
490C2×#41—1068no—
491C2×#41—1062no—
492C2×#41—1064no—
493C2×#41—2128no—
494C2×#41—2122no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—24no—
498C22×Q8—42no—
499C22×Q8—1061no—
500C22×Q8C22×D5311yescharacteristic
501C22×Q8C22×D5314yes—
502C22×Q8C22×D5311yescharacteristic
503C22×D4—531no—
504C22×D4—531no—
505C22×D4—531no—
506C22×D4—1061no—
507C22×D4—1061no—
508C22×D4—1061no—
509C22×D4—1061no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—531no—
513C23×C4—1061no—
514C23×C4—1061no—
515C23×C4—1061no—
516C23×C4C22×D5311yescharacteristic
517C2×SD16—534no—
518C2×SD16—534no—
519C2×SD16—1064no—
520C2×SD16—2122no—
521C2×D8—534no—
522C2×D8—2122no—
523C2×M16—534no—
524C2×M16—2122no—
525C22×C8—42no—
526C22×C8—531no—
527C22×C8—531no—
528C22×C8C22×D5311yescharacteristic
529C22×C8C22×D5311yescharacteristic
530C22×C8C22×D5314yes—
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—534no—
543#121—534no—
544#121—534no—
545#121—1062no—
546#121—1068no—
547#121—1062no—
548#121—1062no—
549C4×Q8—534no—
550C4×Q8—1062no—
551C4×D4—534no—
552C4×D4—534no—
553C4×D4—534no—
554C4×D4—1062no—
555C4×D4—1068no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—531no—
559C2×C4⋊C4—531no—
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⋊C4C22×D5311yescharacteristic
568C2×C4⋊C4C22×D5311yescharacteristic
569C2×C4⋊C4C22×D5314yes—
570C2×C22⋊C4—531no—
571C2×C22⋊C4—531no—
572C2×C22⋊C4—1061no—
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#103C22×D5314yes—
588#103C22×D5314yes—
589#103C22×D5314yes—
590#103C22×D5314yes—
591#102—534no—
592#102—534no—
593#102—534no—
594#102—534no—
595C22⋊C8—534no—
596C22⋊C8—534no—
597#97—534no—
598C24—531no—
599C24—1061no—
600C24—1061no—
601C24D4×D5311yescharacteristic
602#41—1068no—
603#41—21232no—
604#41—2124no—
605#41—2128no—
606C2×Q8—21no—
607C2×Q8—24no—
608C2×Q8—21no—
609C2×Q8—22no—
610C2×Q8—28no—
611C2×Q8—22no—
612C2×Q8—22no—
613C2×Q8—44no—
614C2×Q8—44no—
615C2×Q8—48no—
616C2×Q8—1064no—
617C2×Q8—2124no—
618C2×Q8#1171994514yescomplemented
619C2×Q8C23×D5312yes—
620C2×Q8C23×D5312yes—
621C2×D4—534no—
622C2×D4—532no—
623C2×D4—532no—
624C2×D4—1064no—
625C2×D4—1064no—
626C2×D4—1064no—
627C2×D4—1064no—
628C2×D4—1064no—
629C2×D4—1061no—
630C2×D4—1061no—
631C2×D4—1062no—
632C2×D4—1062no—
633C2×D4—1062no—
634C2×D4—1062no—
635C2×D4—2124no—
636C2×D4—2124no—
637C2×D4—2124no—
638C2×D4—2124no—
639C22×C4—21no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—24no—
643C22×C4—24no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—44no—
648C22×C4—44no—
649C22×C4—531no—
650C22×C4—531no—
651C22×C4—531no—
652C22×C4—532no—
653C22×C4—532no—
654C22×C4—1064no—
655C22×C4—1064no—
656C22×C4—1064no—
657C22×C4—1062no—
658C22×C4—1062no—
659C22×C4—1061no—
660C22×C4—1061no—
661C22×C4—2124no—
662C22×C4—2124no—
663C22×C4—2124no—
664C22×C4D4×D5312yes—
665C22×C4D4×D5311yescharacteristic
666C22×C4C23×D5312yes—
667C22×C4C23×D5311yescharacteristic
668SD16—1068no—
669SD16—2124no—
670D8—2124no—
671M16—2124no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—44no—
675C2×C8—532no—
676C2×C8—532no—
677C2×C8—1062no—
678C2×C8—1062no—
679C2×C8C23×D5312yes—
680C2×C8C23×D5312yes—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—24no—
684C4⋊C4—534no—
685C4⋊C4—532no—
686C4⋊C4—532no—
687C4⋊C4—1064no—
688C4⋊C4—1064no—
689C4⋊C4—1064no—
690C4⋊C4—1064no—
691C4⋊C4—1061no—
692C4⋊C4—1061no—
693C4⋊C4C23×D5312yes—
694C4⋊C4C23×D5312yes—
695C22⋊C4—534no—
696C22⋊C4—534no—
697C22⋊C4—1064no—
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—532no—
710C23—1062no—
711C23—1062no—
712C23—1062no—
713C23—1062no—
714C23—1062no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23—2122no—
719C23—2122no—
720C23—2122no—
721C23#1313324414yes—
722C23C2×D4×D5312yes—
723C23C2×D4×D5311yescharacteristic
724Q8—22no—
725Q8—24no—
726Q8—22no—
727Q8—22no—
728Q8—48no—
729Q8—42no—
730Q8—2128no—
731Q8C2×#1171994514yescomplemented
732D4—1068no—
733D4—1062no—
734D4—1062no—
735D4—1062no—
736D4—1062no—
737D4—2128no—
738D4—2128no—
739D4—2128no—
740D4—2128no—
741D4—2122no—
742D4—2122no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—24no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—48no—
753C2×C4—42no—
754C2×C4—42no—
755C2×C4—48no—
756C2×C4—42no—
757C2×C4—532no—
758C2×C4—532no—
759C2×C4—532no—
760C2×C4—1062no—
761C2×C4—1062no—
762C2×C4—1062no—
763C2×C4—1062no—
764C2×C4—1062no—
765C2×C4—1064no—
766C2×C4—1062no—
767C2×C4—1062no—
768C2×C4—2128no—
769C2×C4—2128no—
770C2×C4—2128no—
771C2×C4—2122no—
772C2×C4—2122no—
773C2×C4C2×D4×D5312yes—
774C2×C4C2×D4×D5311yescharacteristic
775C2×C4C2×#1171994512yes—
776C2×C4#1313326212yes—
777C2×C4C24×D5311yescharacteristic
778C8—22no—
779C8—22no—
780C8—1062no—
781C8—1062no—
782C22—22no—
783C22—22no—
784C22—28no—
785C22—1062no—
786C22—1062no—
787C22—1062no—
788C22—4244no—
789C22—4244no—
790C22—2122no—
791C22—2122no—
792C22—2122no—
793C22—2122no—
794C22—2122no—
795C22—2122no—
796C22—2124no—
797C22#1681126312yes—
798C22C2×#1313324414yes—
799C22C2×#1313324412yes—
800C22#1681143612yes—
801C22C22×D4×D5311yescharacteristic
802C4—22no—
803C4—24no—
804C4—42no—
805C4—42no—
806C4—42no—
807C4—1062no—
808C4—1062no—
809C4—1062no—
810C4—2122no—
811C4—2122no—
812C4#1681126312yes—
813C4C22×#1171994511yescharacteristic
814C4C2×#1313326211yescharacteristic
815C2—24no—
816C2—4242no—
817C2—4242no—
818C2—2122no—
819C2#2028670214yesdirect product factor
820C2C2×#1681126311yescharacteristic
821C2C22×#1313324411yescharacteristic
822C2C2×#1681143611yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC22×#103×C53C2
socleC23×C53C22×D4
hypercenterC22×#103D53
hypocenterC53C2×#3308
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
1. C2×#16811284C2semidirect
2. C2×#16811274C2semidirect
3. #20286702C2direct (N × H)
4. C2×#16810984C2semidirect
5. C2×#16810957C2semidirect
6. C2×#16810936C2semidirect
7. C2×#16810916C2semidirect
8. C2×#16810872C2semidirect
9. C2×#16810859C2semidirect
10. C2×#16810841C2semidirect
11. C2×#16810771C2semidirect
12. C2×#16810762C2semidirect
13. C2×#16810726C2semidirect
14. C2×#16810694C2semidirect
15. C2×#16810623C2semidirect
16. C22×#103×C53C2semidirect
24. #16811284C22semidirect
26. #16811274C22semidirect
44. #16810984C22semidirect
45. #16810957C22semidirect
46. #16810936C22semidirect
47. #16810916C22semidirect
48. #16810872C22semidirect
49. #16810859C22semidirect
50. #16810841C22semidirect
51. #16810771C22semidirect
52. #16810762C22semidirect
53. #16810726C22semidirect
54. #16810694C22semidirect
59. #16810623C22semidirect
76. C2×#103×C53C22semidirect
200. C2×Q8×C53#41semidirect
318. Q8×C53C2×#41semidirect
419. C22×#103D53semidirect
421. C2×C53#3308semidirect
480. C2×#103C2×D53semidirect
488. C53C2×#3308semidirect
618. C2×Q8#11719945semidirect
731. Q8C2×#11719945semidirect
819. C2#20286702direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112842
C2×#168112742
#202867022
C2×#168109842
C2×#168109572
C2×#168109362
C2×#168109162
C2×#168108722
C2×#168108592
C2×#168108412
C2×#168107712
C2×#168107622
C2×#168107262
C2×#168106942
C2×#168106232
C22×#103×C532
C2×#330853