Finite Group Databasebeta

← C2×#20283935 #28250431

Subgroups — C2×#20283935 #28250431

Order 13568.

5130 conjugacy classes of subgroups.

The subgroup lattice has 1044 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#41×D53C211yesmaximal, characteristic, complemented
2C22×#13133239C211yesmaximal, characteristic, complemented
3C22×#13133237C211yesmaximal, characteristic, complemented
4C2×#16811135C211yesmaximal, characteristic, complemented
5#20283935C2116yesmaximal, direct product factor
6C2×#16810788C211yesmaximal, characteristic, complemented
7C2×#16810786C211yesmaximal, characteristic, complemented
8C2×#16810771C211yesmaximal, characteristic, complemented
9C2×#16810769C211yesmaximal, characteristic, complemented
10C2×#16810780C211yesmaximal, characteristic, complemented
11C2×#16810763C211yesmaximal, characteristic, complemented
12C2×#16810775C211yesmaximal, characteristic, complemented
13C2×#16810758C211yesmaximal, characteristic, complemented
14C2×#16810617C211yesmaximal, characteristic, complemented
15C22×#13133129C211yesmaximal, characteristic, complemented
16C2×C53×#416C211yesmaximal, characteristic, complemented
17C22×#11719949C2211yescharacteristic
18C22×#11719945—21no—
19C22×#11719945C2211yescharacteristic
20C22×#11719945C2211yescharacteristic, complemented
21C22×#11719947—21no—
22C22×#11719947C2211yescharacteristic
23C2×#41×D53—28no—
24C2×#41×D53—24no—
25C2×#41×D53—28no—
26C2×#41×D53C2218yescomplemented
27C22×Q8×D53C2211yescharacteristic
28C22×D4×D53—21no—
29C22×D4×D53C2211yescharacteristic
30C23×C4×D53—21no—
31C23×C4×D53C2211yescharacteristic
32C2×#13133239—28no—
33C2×#13133239C2218yescomplemented
34C2×#13133237—28no—
35C2×#13133237C2218yescomplemented
36C22×Dic212C2211yescharacteristic, complemented
37C22×#11719925C2211yescharacteristic, complemented
38C22×#11719913C2211yescharacteristic, complemented
39C22×#11719913C2211yescharacteristic, complemented
40C22×#11719923C2211yescharacteristic, complemented
41C22×#11719924C2211yescharacteristic, complemented
42C22×D424C2211yescharacteristic, complemented
43C22×#11719922C2211yescharacteristic, complemented
44C23×#88322C2211yescharacteristic, complemented
45#16811135—24no—
46#16811135C2218yescomplemented
47C2×#13133201—21no—
48C2×#13133197C2211yescharacteristic
49C2×#13133197C2211yescharacteristic, complemented
50C2×#13133192C2211yescharacteristic
51C2×#13133192C2211yescharacteristic, complemented
52C2×#13133187—21no—
53C2×C4×D212—21no—
54C2×C4×D212—21no—
55#16810788C2218yescomplemented
56#16810786C2218yescomplemented
57#16810780C2218yescomplemented
58#16810775C2218yescomplemented
59#16810771C2218yescomplemented
60#16810769C2218yescomplemented
61#16810763C2218yescomplemented
62#16810758C2218yescomplemented
63#16810617C2218yescomplemented
64C2×#13133140C2211yescharacteristic, complemented
65C2×#13133140C2211yescharacteristic, complemented
66C2×#13133137C2211yescharacteristic, complemented
67C2×#13133137C2211yescharacteristic, complemented
68C2×#13133129C2211yescharacteristic
69C2×#13133129C2211yescharacteristic
70C2×#13133129C2211yescharacteristic, complemented
71C2×#13133129C2211yescharacteristic, complemented
72C2×#13133129C2218yescomplemented
73C22×#41×C53C2211yescharacteristic
74C23×C8×C53C2211yescharacteristic, complemented
75C2×#117×C53C2211yescharacteristic, complemented
76C53×#416C2218yescomplemented
77C2×#103×C53C2211yescharacteristic, complemented
78C2×#103×C53C2211yescharacteristic, complemented
79C2×#102×C53C2211yescharacteristic, complemented
80C2×#102×C53C2211yescharacteristic, complemented
81C24×D53—21no—
82C24×D53D411yescharacteristic
83C2×#11719949—24no—
84C2×#11719949—24no—
85C2×#11719949—22no—
86C2×#11719949C2314yes—
87C2×#11719945—216no—
88C2×#11719945—24no—
89C2×#11719945—22no—
90C2×#11719945—22no—
91C2×#11719945—28no—
92C2×#11719945—24no—
93C2×#11719945—24no—
94C2×#11719945D418yescomplemented
95C2×#11719945C2314yes—
96C2×#11719945C2314yescomplemented
97C2×#11719947—216no—
98C2×#11719947—24no—
99C2×#11719947—28no—
100C2×#11719947—22no—
101C2×#11719947—24no—
102C2×#11719947C2314yes—
103#41×D53—264no—
104#41×D53—232no—
105#41×D53—232no—
106C22×Dic106—21no—
107C22×Dic106C2311yescharacteristic
108C22×Dic106C2311yescharacteristic
109C2×Q8×D53—24no—
110C2×Q8×D53—22no—
111C2×Q8×D53—24no—
112C2×Q8×D53C2314yes—
113C22×D212—21no—
114C22×D212—21no—
115C22×D212—21no—
116C22×D212C2311yescharacteristic
117C22×D212C2311yescharacteristic
118C22×C22⋊D53—21no—
119C22×C22⋊D53—21no—
120C22×C22⋊D53—21no—
121C22×C22⋊D53—21no—
122C2×D4×D53—216no—
123C2×D4×D53—28no—
124C2×D4×D53—24no—
125C2×D4×D53—24no—
126C2×D4×D53—22no—
127C2×D4×D53C2314yes—
128C23×Dic53—21no—
129C23×Dic53D411yescharacteristic
130C22×C4×D53—216no—
131C22×C4×D53—21no—
132C22×C4×D53—21no—
133C22×C4×D53—24no—
134C22×C4×D53—24no—
135C22×C4×D53—21no—
136C22×C4×D53—28no—
137C22×C4×D53—21no—
138C22×C4×D53D411yescharacteristic
139C22×C4×D53D411yescharacteristic
140C22×C4×D53D414yes—
141C22×C4×D53C2311yescharacteristic
142C22×C4×D53C2311yescharacteristic
143C22×C4×D53C2314yes—
144#13133239—232no—
145#13133237—232no—
146C2×Dic212—24no—
147C2×Dic212C2314yescomplemented
148C2×#11719925—24no—
149C2×#11719925C2314yescomplemented
150C2×#11719913—24no—
151C2×#11719913—24no—
152C2×#11719913C2314yescomplemented
153C2×#11719913C2314yescomplemented
154C2×#11719923—24no—
155C2×#11719923C2314yescomplemented
156C2×#11719924—24no—
157C2×#11719924C2314yescomplemented
158C2×D424—24no—
159C2×D424C2314yescomplemented
160C2×#11719922—24no—
161C2×#11719922C2314yescomplemented
162C22×#88322—24no—
163C22×#88322C2311yescharacteristic
164C22×#88322C2311yescharacteristic
165C22×#88322C2314yescomplemented
166#13133201—28no—
167#13133197—22no—
168#13133197—22no—
169#13133197C2314yes—
170#13133197C2314yescomplemented
171#13133192—22no—
172#13133192—22no—
173#13133192C2314yes—
174#13133192C2314yescomplemented
175#13133187—28no—
176C4×D212—28no—
177C4×D212—28no—
178C2×C4⋊Dic53—21no—
179C2×C4⋊Dic53—21no—
180C2×#11719921—21no—
181C2×#11719921—21no—
182C2×#11719921—21no—
183C2×#11719921—21no—
184#13133140C2314yescomplemented
185#13133140C2314yescomplemented
186#13133137C2314yescomplemented
187#13133137C2314yescomplemented
188#13133129C2314yes—
189#13133129C2314yes—
190#13133129C2314yescomplemented
191#13133129C2314yescomplemented
192C2×#41×C53—24no—
193C2×#41×C53—22no—
194C2×#41×C53D418yescomplemented
195C2×#41×C53C2314yes—
196C22×Q8×C53C2311yescharacteristic
197C22×D4×C53—21no—
198C22×D4×C53C2311yescharacteristic
199C23×C4×C53—21no—
200C23×C4×C53C2311yescharacteristic
201C22×C8×C53—24no—
202C22×C8×C53C2311yescharacteristic
203C22×C8×C53C2311yescharacteristic
204C22×C8×C53C2314yescomplemented
205#117×C53—22no—
206#117×C53C2314yescomplemented
207C2×C4⋊C4×C53C2311yescharacteristic
208C2×C4⋊C4×C53C2311yescharacteristic
209C2×C22⋊C4×C53—21no—
210C2×C42×C53—21no—
211#103×C53C2314yescomplemented
212#103×C53C2314yescomplemented
213#102×C53C2314yescomplemented
214#102×C53C2314yescomplemented
215C24×C53—21no—
216C24×C53C2×D411yescharacteristic
217C23×D53—28no—
218C23×D53—24no—
219C23×D53—21no—
220C23×D53—24no—
221C23×D53—24no—
222C23×D53—21no—
223C23×D53—42no—
224C23×D53—44no—
225C23×D53—44no—
226C23×D53C2×D411yescharacteristic
227C23×D53C2×D414yes—
228C23×D53C2×D411yescharacteristic
229#41×C53—216no—
230#41×C53—28no—
231#41×C53C2×D4116yescomplemented
232C2×Q8×C53—22no—
233C2×Q8×C53—21no—
234C2×Q8×C53C2×D414yes—
235C2×Q8×C53C2412yes—
236C2×D4×C53—28no—
237C2×D4×C53—24no—
238C2×D4×C53—21no—
239C2×D4×C53—22no—
240C2×D4×C53C2×D414yes—
241C2×D4×C53C2412yes—
242C22×C4×C53—21no—
243C22×C4×C53—28no—
244C22×C4×C53—24no—
245C22×C4×C53—21no—
246C22×C4×C53—21no—
247C22×C4×C53C2×D412yes—
248C22×C4×C53C2×D411yescharacteristic
249C22×C4×C53C2×D414yes—
250C22×C4×C53C2×D414yes—
251C22×C4×C53C2411yescharacteristic
252C22×C4×C53C2412yes—
253C2×C22⋊D53—28no—
254C2×C22⋊D53—28no—
255C2×C22⋊D53—28no—
256C2×C22⋊D53—24no—
257C2×C22⋊D53—24no—
258C2×C22⋊D53—24no—
259C2×C22⋊D53—24no—
260C2×C22⋊D53—44no—
261C22×Dic53—28no—
262C22×Dic53—24no—
263C22×Dic53—21no—
264C22×Dic53—24no—
265C22×Dic53—21no—
266C22×Dic53C2×D411yescharacteristic
267C22×Dic53C2×D411yescharacteristic
268C22×Dic53C2×D414yes—
269#11719949—216no—
270#11719949—28no—
271#11719949—28no—
272Q8×D53—216no—
273Q8×D53—28no—
274Q8×D53—28no—
275#11719947—264no—
276#11719947—216no—
277#11719947—28no—
278#11719947—28no—
279D4×D53—264no—
280D4×D53—216no—
281D4×D53—28no—
282D4×D53—28no—
283#11719945—264no—
284#11719945—216no—
285#11719945—28no—
286#11719945—28no—
287#11719945—28no—
288#11719945—48no—
289#11719945C2×D4116yescomplemented
290C2×D212—28no—
291C2×D212—24no—
292C2×D212—21no—
293C2×D212—22no—
294C2×D212—22no—
295C2×D212—22no—
296C2×D212—24no—
297C2×D212—24no—
298C2×D212—21no—
299C2×D212—44no—
300C2×D212—44no—
301C2×D212C2×D414yes—
302C2×D212C2412yes—
303C2×D212C2412yes—
304C2×C4×D53—28no—
305C2×C4×D53—264no—
306C2×C4×D53—28no—
307C2×C4×D53—24no—
308C2×C4×D53—24no—
309C2×C4×D53—28no—
310C2×C4×D53—216no—
311C2×C4×D53—24no—
312C2×C4×D53—24no—
313C2×C4×D53—22no—
314C2×C4×D53—22no—
315C2×C4×D53—28no—
316C2×C4×D53—28no—
317C2×C4×D53—22no—
318C2×C4×D53—22no—
319C2×C4×D53—24no—
320C2×C4×D53—24no—
321C2×C4×D53—44no—
322C2×C4×D53C2×D414yes—
323C2×C4×D53C2×D414yes—
324C2×C4×D53C2×D412yes—
325C2×C4×D53C2×D412yes—
326C2×C4×D53C2412yes—
327C2×C4×D53C2412yes—
328C2×Dic106—28no—
329C2×Dic106—21no—
330C2×Dic106—22no—
331C2×Dic106—24no—
332C2×Dic106—22no—
333C2×Dic106—22no—
334C2×Dic106—21no—
335C2×Dic106C2×D414yes—
336C2×Dic106C2412yes—
337C2×Dic106C2412yes—
338C2×C8×C53—22no—
339C2×C8×C53—22no—
340C2×C8×C53—28no—
341C2×C8×C53C2412yes—
342C2×C8×C53C2412yes—
343C4⋊C4×C53—21no—
344C4⋊C4×C53—21no—
345C4⋊C4×C53C2412yes—
346C4⋊C4×C53C2412yes—
347C22⋊C4×C53—24no—
348C42×C53—24no—
349#11719925—28no—
350#11719924—28no—
351#11719923—28no—
352#11719922—28no—
353#11719921—24no—
354#11719921—24no—
355#11719921—24no—
356#11719921—24no—
357C4⋊Dic53—24no—
358C4⋊Dic53—24no—
359C2×#88322—22no—
360C2×#88322—22no—
361C2×#88322—28no—
362C2×#88322C2412yes—
363C2×#88322C2412yes—
364Dic212—28no—
365D424—28no—
366#11719913—28no—
367#11719913—28no—
368C23×C53—22no—
369C23×C53—22no—
370C23×C53—24no—
371C23×C53—22no—
372C23×C53—42no—
373C23×C53—42no—
374C23×C53#12014yes—
375C23×C53C22×D412yes—
376C23×C53C22×D411yescharacteristic
377C22×D53—22no—
378C22×D53—22no—
379C22×D53—216no—
380C22×D53—22no—
381C22×D53—24no—
382C22×D53—28no—
383C22×D53—22no—
384C22×D53—22no—
385C22×D53—22no—
386C22×D53—28no—
387C22×D53—22no—
388C22×D53—44no—
389C22×D53—416no—
390C22×D53—432no—
391C22×D53—48no—
392C22×D53—42no—
393C22×D53—42no—
394C22×D53—48no—
395C22×D53—42no—
396C22×D53—42no—
397C22×D53—42no—
398C22×D53#13514yescomplemented
399C22×D53C22×D412yes—
400C22×D53C22×D412yes—
401Q8×C53—24no—
402Q8×C53—22no—
403Q8×C53C22×D414yes—
404D4×C53—216no—
405D4×C53—24no—
406D4×C53—22no—
407D4×C53C22×D414yes—
408C2×C4×C53—24no—
409C2×C4×C53—22no—
410C2×C4×C53—216no—
411C2×C4×C53—22no—
412C2×C4×C53—22no—
413C2×C4×C53—42no—
414C2×C4×C53—42no—
415C2×C4×C53#12014yes—
416C2×C4×C53#12018yes—
417C2×C4×C53C22×D411yescharacteristic
418C2×C4×C53C22×D412yes—
419C2×C4×C53C22×D412yes—
420C2×C4×C53C22×D414yes—
421C2×C4×C53C22×D412yes—
422C2×C4×C53C22×D414yes—
423C2×C4×C53C2511yescharacteristic
424C22⋊D53—216no—
425C22⋊D53—216no—
426C22⋊D53—216no—
427C22⋊D53—48no—
428C2×Dic53—216no—
429C2×Dic53—22no—
430C2×Dic53—24no—
431C2×Dic53—22no—
432C2×Dic53—28no—
433C2×Dic53—22no—
434C2×Dic53—22no—
435C2×Dic53—42no—
436C2×Dic53C22×D412yes—
437C2×Dic53C22×D412yes—
438D212—216no—
439D212—24no—
440D212—22no—
441D212—22no—
442D212—22no—
443D212—48no—
444D212—48no—
445D212—42no—
446D212C22×D414yes—
447C4×D53—216no—
448C4×D53—216no—
449C4×D53—28no—
450C4×D53—216no—
451C4×D53—28no—
452C4×D53—24no—
453C4×D53—24no—
454C4×D53—22no—
455C4×D53—22no—
456C4×D53—22no—
457C4×D53—22no—
458C4×D53—48no—
459Dic106—216no—
460Dic106—24no—
461Dic106—22no—
462Dic106—22no—
463Dic106—22no—
464Dic106—42no—
465Dic106C22×D414yes—
466C8×C53—22no—
467C8×C53—22no—
468#88322—22no—
469#88322—22no—
470C2×#3002—531nomaximal, Sylow
471C22×C53—28no—
472C22×C53—22no—
473C22×C53—22no—
474C22×C53—24no—
475C22×C53—48no—
476C22×C53—42no—
477C22×C53—42no—
478C22×C53C2×#12014yes—
479C22×C53C2×#12012yes—
480C22×C53C2×#13512yes—
481C22×C53#57512yes—
482C22×C53C23×D411yescharacteristic
483C2×D53—22no—
484C2×D53—28no—
485C2×D53—22no—
486C2×D53—22no—
487C2×D53—24no—
488C2×D53—22no—
489C2×D53—22no—
490C2×D53—416no—
491C2×D53—432no—
492C2×D53—44no—
493C2×D53—48no—
494C2×D53—42no—
495C2×D53—42no—
496C2×D53—42no—
497C2×D53—42no—
498C2×D53—42no—
499C2×D53—84no—
500C2×D53C2×#13514yescomplemented
501C4×C53—24no—
502C4×C53—42no—
503C4×C53—42no—
504C4×C53C2×#12012yes—
505C4×C53C2×#12014yes—
506C4×C53C23×D411yescharacteristic
507C4×C53C23×D411yescharacteristic
508Dic53—22no—
509Dic53—24no—
510Dic53—22no—
511Dic53—42no—
512C23×#41—531no—
513C22×#135—531no—
514C22×#135—531no—
515C2×#525—531no—
516#3002—5316no—
517C2×#452—531no—
518C2×#452—531no—
519C2×#449—531no—
520C2×#449—531no—
521C2×#451—531no—
522C2×#448—531no—
523C2×#450—531no—
524C2×#447—531no—
525C2×#416—531no—
526C2×#416D5311yescharacteristic, complemented
527C22×C22⋊C8—531no—
528C2×C53—24no—
529C2×C53—44no—
530C2×C53#300214yescomplemented
531C2×C53C22×#12011yescharacteristic
532C2×C53C22×#13511yescharacteristic
533C2×C53C2×#57511yescharacteristic
534D53—24no—
535D53—42no—
536D53—44no—
537D53—82no—
538C22×#41—538no—
539C22×#41—531no—
540C22×#41—531no—
541C22×#41—531no—
542C22×#41—531no—
543C22×#41—1061no—
544C22×#41—1061no—
545C22×#41—1064no—
546C22×#41—1068no—
547C22×#41—1068no—
548C22×#41C2×D5311yescharacteristic
549C23×Q8—531no—
550C23×D4—531no—
551C23×D4—1061no—
552C24×C4—531no—
553C24×C4—1061no—
554C2×#135—538no—
555C2×#135—538no—
556C2×#135—1068no—
557C2×#135—1068no—
558C22×Q16—531no—
559C22×Q16—531no—
560C22×SD16—531no—
561C22×SD16—531no—
562C22×SD16—531no—
563C22×SD16—531no—
564C22×D8—531no—
565C22×D8—531no—
566C23×C8—531no—
567C23×C8C2×D5311yescharacteristic, complemented
568#525—538no—
569#525—1064no—
570C2×#123—1061no—
571C2×C22⋊Q8—531no—
572C2×C22⋊Q8—531no—
573C2×#121—531no—
574C2×#121—531no—
575C2×#120—1061no—
576C2×C4×D4—1061no—
577C2×C4×D4—1061no—
578C2×#117C2×D5311yescharacteristic, complemented
579#452—538no—
580#452—538no—
581#451—538no—
582#450—538no—
583#449—538no—
584#449—538no—
585#448—538no—
586#447—538no—
587#416—538no—
588#416C2×D5318yescomplemented
589C2×#103—531no—
590C2×#103—531no—
591C2×#103C2×D5311yescharacteristic, complemented
592C2×#103C2×D5311yescharacteristic, complemented
593C2×#102—531no—
594C2×#102—531no—
595C2×#102C2×D5311yescharacteristic, complemented
596C2×#102C2×D5311yescharacteristic, complemented
597C2×C22⋊C8—531no—
598C2×C22⋊C8—531no—
599C2×C22⋊C8—531no—
600C2×C22⋊C8—531no—
601C2×C22⋊C8—538no—
602C53C2×#300211yescharacteristic, complemented, Sylow
603C25—531no—
604C25—1061no—
605C2×#41—24no—
606C2×#41—22no—
607C2×#41—534no—
608C2×#41—534no—
609C2×#41—538no—
610C2×#41—534no—
611C2×#41—534no—
612C2×#41—1068no—
613C2×#41—10616no—
614C2×#41—1068no—
615C2×#41—1062no—
616C2×#41—1062no—
617C2×#41—1064no—
618C2×#41—10616no—
619C2×#41—1064no—
620C2×#41—10632no—
621C2×#41—10664no—
622C2×#41—10632no—
623C2×#41—1064no—
624C2×#41—1064no—
625C2×#41—1064no—
626C2×#41—1062no—
627C2×#41—1062no—
628C2×#41—1064no—
629C2×#41—1064no—
630C2×#41D21218yescomplemented
631C2×#41C22×D5314yes—
632C22×Q8—534no—
633C22×Q8—531no—
634C22×Q8—531no—
635C22×Q8—1061no—
636C22×Q8—1062no—
637C22×Q8—1064no—
638C22×Q8—1064no—
639C22×Q8C22×D5311yescharacteristic
640C22×D4—21no—
641C22×D4—534no—
642C22×D4—531no—
643C22×D4—531no—
644C22×D4—1061no—
645C22×D4—1061no—
646C22×D4—1061no—
647C22×D4—1062no—
648C22×D4—1061no—
649C22×D4—1064no—
650C22×D4—1068no—
651C22×D4—10616no—
652C22×D4—1061no—
653C22×D4—1061no—
654C22×D4—1064no—
655C22×D4—1061no—
656C22×D4C22×D5311yescharacteristic
657C23×C4—21no—
658C23×C4—531no—
659C23×C4—534no—
660C23×C4—531no—
661C23×C4—531no—
662C23×C4—531no—
663C23×C4—531no—
664C23×C4—534no—
665C23×C4—1061no—
666C23×C4—1068no—
667C23×C4—1061no—
668C23×C4—10616no—
669C23×C4—1061no—
670C23×C4—1064no—
671C23×C4—1064no—
672C23×C4—1061no—
673C23×C4—1061no—
674C23×C4C22×D5311yescharacteristic
675#135—10632no—
676#135—10632no—
677C2×Q16—534no—
678C2×Q16—534no—
679C2×Q16—1064no—
680C2×Q16—1064no—
681C2×SD16—534no—
682C2×SD16—534no—
683C2×SD16—534no—
684C2×SD16—534no—
685C2×SD16—1064no—
686C2×SD16—1064no—
687C2×SD16—1064no—
688C2×SD16—1064no—
689C2×D8—534no—
690C2×D8—534no—
691C2×D8—1064no—
692C2×D8—1064no—
693C22×C8—24no—
694C22×C8—531no—
695C22×C8—531no—
696C22×C8—534no—
697C22×C8—1064no—
698C22×C8C22×D5311yescharacteristic
699C22×C8C22×D5311yescharacteristic
700C22×C8C22×D5314yescomplemented
701#123—1068no—
702C22⋊Q8—534no—
703C22⋊Q8—534no—
704C22⋊Q8—1062no—
705C22⋊Q8—1062no—
706#121—534no—
707#121—534no—
708#121—1062no—
709#121—1062no—
710#120—1068no—
711C4×D4—1068no—
712C4×D4—1068no—
713#117—22no—
714#117C22×D5314yescomplemented
715C2×C4⋊C4—1061no—
716C2×C4⋊C4—1061no—
717C2×C4⋊C4C22×D5311yescharacteristic
718C2×C4⋊C4C22×D5311yescharacteristic
719C2×C22⋊C4—21no—
720C2×C22⋊C4—1061no—
721C2×C22⋊C4—1061no—
722C2×C22⋊C4—1061no—
723C2×C22⋊C4—1061no—
724C2×C42—21no—
725#103—534no—
726#103—534no—
727#103C22×D5314yescomplemented
728#103C22×D5314yescomplemented
729#102—534no—
730#102—534no—
731#102C22×D5314yescomplemented
732#102C22×D5314yescomplemented
733C22⋊C8—534no—
734C22⋊C8—534no—
735C22⋊C8—534no—
736C22⋊C8—534no—
737C24—21no—
738C24—531no—
739C24—531no—
740C24—534no—
741C24—1064no—
742C24—1064no—
743C24—1068no—
744C24—1064no—
745C24—1061no—
746C24—1061no—
747C24—2122no—
748C24—2124no—
749C24—2124no—
750C24D4×D5311yescharacteristic
751#41—216no—
752#41—28no—
753#41—5316no—
754#41—10664no—
755#41—1068no—
756#41—10664no—
757#41—10616no—
758#41—1068no—
759#41—10616no—
760#41—1068no—
761#41—1068no—
762#41—10616no—
763#41—1068no—
764#41—1068no—
765#41—1068no—
766#41—2128no—
767#41C2×D212116yescomplemented
768C2×Q8—22no—
769C2×Q8—21no—
770C2×Q8—534no—
771C2×Q8—532no—
772C2×Q8—532no—
773C2×Q8—1064no—
774C2×Q8—1068no—
775C2×Q8—1068no—
776C2×Q8—10616no—
777C2×Q8—1068no—
778C2×Q8—1061no—
779C2×Q8—1061no—
780C2×Q8—1062no—
781C2×Q8—1062no—
782C2×Q8—1062no—
783C2×Q8C2×D21214yes—
784C2×Q8C23×D5312yes—
785C2×D4—28no—
786C2×D4—24no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—534no—
790C2×D4—532no—
791C2×D4—532no—
792C2×D4—1064no—
793C2×D4—1068no—
794C2×D4—1064no—
795C2×D4—1064no—
796C2×D4—1064no—
797C2×D4—1068no—
798C2×D4—10664no—
799C2×D4—10616no—
800C2×D4—1064no—
801C2×D4—1068no—
802C2×D4—1068no—
803C2×D4—1068no—
804C2×D4—1064no—
805C2×D4—1068no—
806C2×D4—1064no—
807C2×D4—1061no—
808C2×D4—1062no—
809C2×D4—1061no—
810C2×D4—1062no—
811C2×D4—1062no—
812C2×D4—2124no—
813C2×D4—2124no—
814C2×D4—2124no—
815C2×D4C2×D21214yes—
816C2×D4C23×D5312yes—
817C22×C4—21no—
818C22×C4—28no—
819C22×C4—24no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—531no—
823C22×C4—531no—
824C22×C4—534no—
825C22×C4—534no—
826C22×C4—534no—
827C22×C4—532no—
828C22×C4—532no—
829C22×C4—532no—
830C22×C4—532no—
831C22×C4—1064no—
832C22×C4—1064no—
833C22×C4—1068no—
834C22×C4—1068no—
835C22×C4—10664no—
836C22×C4—1064no—
837C22×C4—1068no—
838C22×C4—1064no—
839C22×C4—1061no—
840C22×C4—1064no—
841C22×C4—1064no—
842C22×C4—10616no—
843C22×C4—1068no—
844C22×C4—1062no—
845C22×C4—1062no—
846C22×C4—1068no—
847C22×C4—1064no—
848C22×C4—1062no—
849C22×C4—1062no—
850C22×C4—1068no—
851C22×C4—1061no—
852C22×C4—1064no—
853C22×C4—2124no—
854C22×C4C2×D21214yes—
855C22×C4D4×D5312yes—
856C22×C4D4×D5314yes—
857C22×C4D4×D5311yescharacteristic
858C22×C4C23×D5311yescharacteristic
859C22×C4C23×D5312yes—
860Q16—1068no—
861Q16—1068no—
862SD16—1068no—
863SD16—1068no—
864SD16—1068no—
865SD16—1068no—
866D8—1068no—
867D8—1068no—
868C2×C8—22no—
869C2×C8—22no—
870C2×C8—28no—
871C2×C8—532no—
872C2×C8—532no—
873C2×C8—1062no—
874C2×C8—1062no—
875C2×C8—1068no—
876C2×C8C23×D5312yes—
877C2×C8C23×D5312yes—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—1064no—
881C4⋊C4—1064no—
882C4⋊C4C23×D5312yes—
883C4⋊C4C23×D5312yes—
884C22⋊C4—24no—
885C22⋊C4—1064no—
886C22⋊C4—1064no—
887C22⋊C4—1064no—
888C22⋊C4—1064no—
889C42—24no—
890C23—22no—
891C23—22no—
892C23—24no—
893C23—22no—
894C23—42no—
895C23—42no—
896C23—534no—
897C23—532no—
898C23—532no—
899C23—1068no—
900C23—10616no—
901C23—1062no—
902C23—1062no—
903C23—1064no—
904C23—1068no—
905C23—1062no—
906C23—1062no—
907C23—1062no—
908C23—1062no—
909C23—1062no—
910C23—2124no—
911C23—21216no—
912C23—2128no—
913C23—21232no—
914C23—2128no—
915C23—2122no—
916C23—2122no—
917C23—2122no—
918C23—2122no—
919C23—2122no—
920C23#1313318714yes—
921C23C2×D4×D5312yes—
922C23C2×D4×D5311yescharacteristic
923Q8—24no—
924Q8—22no—
925Q8—534no—
926Q8—10616no—
927Q8—1064no—
928Q8—1062no—
929Q8—1062no—
930Q8—1062no—
931Q8—2122no—
932Q8C22×D21214yes—
933D4—216no—
934D4—24no—
935D4—22no—
936D4—534no—
937D4—10616no—
938D4—10616no—
939D4—10616no—
940D4—10616no—
941D4—1064no—
942D4—1062no—
943D4—1062no—
944D4—1062no—
945D4—2128no—
946D4—2128no—
947D4—2128no—
948D4—2122no—
949D4C22×D21214yes—
950C2×C4—24no—
951C2×C4—22no—
952C2×C4—216no—
953C2×C4—22no—
954C2×C4—22no—
955C2×C4—42no—
956C2×C4—42no—
957C2×C4—532no—
958C2×C4—532no—
959C2×C4—10616no—
960C2×C4—10616no—
961C2×C4—10616no—
962C2×C4—1062no—
963C2×C4—1062no—
964C2×C4—1068no—
965C2×C4—1064no—
966C2×C4—1062no—
967C2×C4—1068no—
968C2×C4—1064no—
969C2×C4—1064no—
970C2×C4—1068no—
971C2×C4—10616no—
972C2×C4—1062no—
973C2×C4—1062no—
974C2×C4—1062no—
975C2×C4—1062no—
976C2×C4—1062no—
977C2×C4—2122no—
978C2×C4—2128no—
979C2×C4#1313318714yes—
980C2×C4#1313318718yes—
981C2×C4C2×D4×D5312yes—
982C2×C4C2×D4×D5311yescharacteristic
983C2×C4C2×D4×D5312yes—
984C2×C4C2×D4×D5314yes—
985C2×C4C22×D21212yes—
986C2×C4C22×D21214yes—
987C2×C4C24×D5311yescharacteristic
988C8—22no—
989C8—22no—
990C8—1062no—
991C8—1062no—
992C22—28no—
993C22—22no—
994C22—22no—
995C22—24no—
996C22—48no—
997C22—42no—
998C22—42no—
999C22—534no—
1000C22—1068no—
1001C22—1062no—
1002C22—1062no—
1003C22—1062no—
1004C22—1062no—
1005C22—1064no—
1006C22—1062no—
1007C22—4244no—
1008C22—21216no—
1009C22—21232no—
1010C22—2122no—
1011C22—2122no—
1012C22—2122no—
1013C22—2124no—
1014C22—2128no—
1015C22—2122no—
1016C22—2122no—
1017C22C2×#1313318714yes—
1018C22C2×#1313318712yes—
1019C22#135×D5312yes—
1020C22#1681142012yes—
1021C22C22×D4×D5311yescharacteristic
1022C4—24no—
1023C4—42no—
1024C4—42no—
1025C4—1062no—
1026C4—1062no—
1027C4—1064no—
1028C4—2122no—
1029C4C2×#1313318714yes—
1030C4C2×#1313318712yes—
1031C4C22×D4×D5311yescharacteristic
1032C4C23×D21211yescharacteristic
1033C2—24no—
1034C2—44no—
1035C2—1064no—
1036C2—4242no—
1037C2—2122no—
1038C2—2124no—
1039C2#2028393514yesdirect product factor
1040C2C22×#1313318711yescharacteristic
1041C2C2×#135×D5311yescharacteristic
1042C2C2×#1681142011yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#416C2
socleC23×C53C22×D4
hypercenterC2×#416D53
hypocenterC53C2×#3002
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C22×#41×D53C2semidirect
2. C22×#13133239C2semidirect
3. C22×#13133237C2semidirect
4. C2×#16811135C2semidirect
5. #20283935C2direct (N × H)
6. C2×#16810788C2semidirect
7. C2×#16810786C2semidirect
8. C2×#16810771C2semidirect
9. C2×#16810769C2semidirect
10. C2×#16810780C2semidirect
11. C2×#16810763C2semidirect
12. C2×#16810775C2semidirect
13. C2×#16810758C2semidirect
14. C2×#16810617C2semidirect
15. C22×#13133129C2semidirect
16. C2×C53×#416C2semidirect
20. C22×#11719945C22semidirect
26. C2×#41×D53C22semidirect
33. C2×#13133239C22semidirect
35. C2×#13133237C22semidirect
36. C22×Dic212C22semidirect
37. C22×#11719925C22semidirect
38. C22×#11719913C22semidirect
39. C22×#11719913C22semidirect
40. C22×#11719923C22semidirect
41. C22×#11719924C22semidirect
42. C22×D424C22semidirect
43. C22×#11719922C22semidirect
44. C23×#88322C22semidirect
46. #16811135C22semidirect
49. C2×#13133197C22semidirect
51. C2×#13133192C22semidirect
55. #16810788C22semidirect
56. #16810786C22semidirect
57. #16810780C22semidirect
58. #16810775C22semidirect
59. #16810771C22semidirect
60. #16810769C22semidirect
61. #16810763C22semidirect
62. #16810758C22semidirect
63. #16810617C22semidirect
64. C2×#13133140C22semidirect
65. C2×#13133140C22semidirect
66. C2×#13133137C22semidirect
67. C2×#13133137C22semidirect
70. C2×#13133129C22semidirect
71. C2×#13133129C22semidirect
72. C2×#13133129C22semidirect
74. C23×C8×C53C22semidirect
75. C2×#117×C53C22semidirect
76. C53×#416C22semidirect
77. C2×#103×C53C22semidirect
78. C2×#103×C53C22semidirect
79. C2×#102×C53C22semidirect
80. C2×#102×C53C22semidirect
94. C2×#11719945D4semidirect
96. C2×#11719945C23semidirect
147. C2×Dic212C23semidirect
149. C2×#11719925C23semidirect
152. C2×#11719913C23semidirect
153. C2×#11719913C23semidirect
155. C2×#11719923C23semidirect
157. C2×#11719924C23semidirect
159. C2×D424C23semidirect
161. C2×#11719922C23semidirect
165. C22×#88322C23semidirect
170. #13133197C23semidirect
174. #13133192C23semidirect
184. #13133140C23semidirect
185. #13133140C23semidirect
186. #13133137C23semidirect
187. #13133137C23semidirect
190. #13133129C23semidirect
191. #13133129C23semidirect
194. C2×#41×C53D4semidirect
204. C22×C8×C53C23semidirect
206. #117×C53C23semidirect
211. #103×C53C23semidirect
212. #103×C53C23semidirect
213. #102×C53C23semidirect
214. #102×C53C23semidirect
231. #41×C53C2×D4semidirect
289. #11719945C2×D4semidirect
398. C22×D53#135semidirect
500. C2×D53C2×#135semidirect
526. C2×#416D53semidirect
530. C2×C53#3002semidirect
567. C23×C8C2×D53semidirect
578. C2×#117C2×D53semidirect
588. #416C2×D53semidirect
591. C2×#103C2×D53semidirect
592. C2×#103C2×D53semidirect
595. C2×#102C2×D53semidirect
596. C2×#102C2×D53semidirect
602. C53C2×#3002semidirect
630. C2×#41D212semidirect
700. C22×C8C22×D53semidirect
714. #117C22×D53semidirect
727. #103C22×D53semidirect
728. #103C22×D53semidirect
731. #102C22×D53semidirect
732. #102C22×D53semidirect
767. #41C2×D212semidirect
1039. C2#20283935direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D532
C22×#131332392
C22×#131332372
C2×#168111352
#202839352
C2×#168107882
C2×#168107862
C2×#168107712
C2×#168107692
C2×#168107802
C2×#168107632
C2×#168107752
C2×#168107582
C2×#168106172
C22×#131331292
C2×C53×#4162
C2×#300253