Finite Group Databasebeta

← C2×#20286619 #28260517

Subgroups — C2×#20286619 #28260517

Order 13568.

2210 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811319C211yesmaximal, characteristic, complemented
2C2×#16811282C211yesmaximal, characteristic, complemented
3#20286619C2116yesmaximal, direct product factor
4C2×#16810978C211yesmaximal, characteristic, complemented
5C2×#16810942C211yesmaximal, characteristic, complemented
6C2×#16810965C211yesmaximal, characteristic, complemented
7C2×#16810931C211yesmaximal, characteristic, complemented
8C2×#16810859C211yesmaximal, characteristic, complemented
9C2×#16810852C211yesmaximal, characteristic, complemented
10C2×#16810839C211yesmaximal, characteristic, complemented
11C2×#16810770C211yesmaximal, characteristic, complemented
12C2×#16810764C211yesmaximal, characteristic, complemented
13C2×C4×#11719913C211yesmaximal, characteristic, complemented
14C2×#16810620C211yesmaximal, characteristic, complemented
15C22×#13133142C211yesmaximal, characteristic, complemented
16C2×C8×D4×C53C211yesmaximal, characteristic, complemented
17C22×#11719945C2211yescharacteristic
18C23×Dic106C2211yescharacteristic
19C22×#11719913C2211yescharacteristic
20C22×#11719913C2211yescharacteristic
21C22×D424C2211yescharacteristic
22#16811319—24no—
23#16811319C2218yescomplemented
24#16811282—24no—
25#16811282C2218yescomplemented
26C2×#13133212—21no—
27C2×#13133209C2211yescharacteristic
28C2×#13133205C2211yescharacteristic
29C2×#13133203—21no—
30C2×#13133199—21no—
31C2×#13133196C2211yescharacteristic
32C2×#13133195—21no—
33C2×#13133191C2211yescharacteristic
34C2×#13133191C2211yescharacteristic
35C2×#13133191C2211yescharacteristic
36C2×#13133189—21no—
37C2×#13133189—21no—
38C2×C4×Dic106C2211yescharacteristic
39C2×C4×D212C2211yescharacteristic
40C2×#13133177—21no—
41C2×#13133177—21no—
42C2×#13133176C2211yescharacteristic
43C22×C4⋊Dic53C2211yescharacteristic
44#16810978C2218yescomplemented
45#16810965C2218yescomplemented
46#16810942C2218yescomplemented
47#16810931C2218yescomplemented
48#16810859C2218yescomplemented
49#16810852C2218yescomplemented
50#16810839C2218yescomplemented
51#16810770C2218yescomplemented
52#16810764C2218yescomplemented
53C4×#11719913C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133149C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57#16810620C2218yescomplemented
58C2×#13133142C2211yescharacteristic
59C2×#13133142C2211yescharacteristic
60C2×#13133142C2211yescharacteristic
61C2×#13133142C2211yescharacteristic
62C2×#13133142C2211yescharacteristic
63C2×#13133142C2211yescharacteristic
64C2×#13133142C2218yescomplemented
65C2×#13133139C2211yescharacteristic
66C2×#13133139C2211yescharacteristic
67C2×#13133139C2211yescharacteristic
68C2×#13133139C2211yescharacteristic
69C23×C8×C53C2211yescharacteristic
70C23×C8×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic
72C8×D4×C53C2218yescomplemented
73C2×C4⋊C8×C53C2211yescharacteristic
74C2×C22⋊C8×C53C2211yescharacteristic
75C2×C22⋊C8×C53C2211yescharacteristic
76C2×C4×C8×C53C2211yescharacteristic
77C2×#11719945—22no—
78C2×#11719945—24no—
79C2×#11719945—42no—
80C2×#11719945C2314yes—
81C22×Dic106—24no—
82C22×Dic106—22no—
83C22×Dic106—21no—
84C22×Dic106—42no—
85C22×Dic106C2311yescharacteristic
86C22×Dic106C2314yes—
87C22×Dic106C2311yescharacteristic
88C22×D212C2311yescharacteristic
89C22×D212C2311yescharacteristic
90C22×C22⋊D53—21no—
91C22×C22⋊D53—21no—
92C22×C22⋊D53—21no—
93C22×C22⋊D53—21no—
94C23×Dic53—21no—
95C23×Dic53—21no—
96C22×C4×D53—21no—
97C22×C4×D53—21no—
98C2×#11719913—24no—
99C2×#11719913—42no—
100C2×#11719913C2314yes—
101C2×#11719913C2314yes—
102C2×D424—42no—
103C2×D424C2314yes—
104#13133212—28no—
105#13133209—22no—
106#13133209C2314yes—
107#13133205—22no—
108#13133205C2314yes—
109#13133203—28no—
110#13133199—28no—
111#13133196—22no—
112#13133196C2314yes—
113#13133195—28no—
114#13133191—22no—
115#13133191—22no—
116#13133191—22no—
117#13133191C2314yes—
118#13133191C2314yes—
119#13133191C2314yes—
120#13133189—28no—
121#13133189—28no—
122C4×Dic106—22no—
123C4×Dic106C2314yes—
124C4×D212—22no—
125C4×D212C2314yes—
126#13133177—28no—
127#13133177—28no—
128#13133176—22no—
129#13133176C2314yes—
130C2×C4⋊Dic53—22no—
131C2×C4⋊Dic53—21no—
132C2×C4⋊Dic53C2314yes—
133C2×C4⋊Dic53C2311yescharacteristic
134C2×C4⋊Dic53C2311yescharacteristic
135C2×C4⋊Dic53C2311yescharacteristic
136C2×C4⋊Dic53C2311yescharacteristic
137C2×#11719919—21no—
138C2×#11719919—21no—
139C2×#11719919—21no—
140C2×#11719919—21no—
141C2×C22⋊Dic53—21no—
142C2×C22⋊Dic53—21no—
143C2×#11719921—21no—
144C2×#11719921—21no—
145C2×#11719921—21no—
146C2×#11719921—21no—
147C2×#11719921—21no—
148C2×#11719921—21no—
149C2×C4×Dic53—21no—
150C2×C4×Dic53—21no—
151#13133151C2314yes—
152#13133149C2314yes—
153#13133149C2314yes—
154#13133142C2314yes—
155#13133142C2314yes—
156#13133142C2314yes—
157#13133142C2314yes—
158#13133142C2314yes—
159#13133142C2314yes—
160#13133139C2314yes—
161#13133139C2314yes—
162#13133139C2314yes—
163#13133139C2314yes—
164C22×D4×C53D411yescharacteristic
165C23×C4×C53C2311yescharacteristic
166C23×C4×C53C2311yescharacteristic
167C22×C8×C53—42no—
168C22×C8×C53—42no—
169C22×C8×C53C2311yescharacteristic
170C22×C8×C53C2311yescharacteristic
171C22×C8×C53C2311yescharacteristic
172C22×C8×C53C2311yescharacteristic
173C22×C8×C53C2314yes—
174C22×C8×C53C2314yes—
175C4×D4×C53D414yes—
176C4×D4×C53C2314yes—
177C2×C4⋊C4×C53D411yescharacteristic
178C2×C22⋊C4×C53D411yescharacteristic
179C2×C22⋊C4×C53D411yescharacteristic
180C2×C42×C53C2311yescharacteristic
181C4⋊C8×C53C2314yes—
182C22⋊C8×C53C2314yes—
183C22⋊C8×C53C2314yes—
184C4×C8×C53C2314yes—
185C24×C53C2×D411yescharacteristic
186C24×C53C2×D411yescharacteristic
187C23×D53—21no—
188C23×D53—21no—
189C2×D4×C53—24no—
190C2×D4×C53C2×D414yes—
191C22×C4×C53—22no—
192C22×C4×C53—22no—
193C22×C4×C53—22no—
194C22×C4×C53—22no—
195C22×C4×C53C2×D411yescharacteristic
196C22×C4×C53C2×D411yescharacteristic
197C22×C4×C53C2×D411yescharacteristic
198C22×C4×C53C2×D411yescharacteristic
199C22×C4×C53C2×D412yes—
200C22×C4×C53C2×D412yes—
201C22×C4×C53C2412yes—
202C22×C4×C53C2412yes—
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—82no—
212C22×Dic53—21no—
213C22×Dic53—21no—
214C22×Dic53—21no—
215C22×Dic53—21no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—24no—
219C22×Dic53—24no—
220C22×Dic53—44no—
221C22×Dic53—82no—
222#11719945—28no—
223#11719945—44no—
224#11719945—48no—
225C2×D212—22no—
226C2×D212—22no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—21no—
230C2×D212—21no—
231C2×D212C2412yes—
232C2×D212C2412yes—
233C2×C4×D53—24no—
234C2×C4×D53—24no—
235C2×C4×D53—44no—
236C2×C4×D53—82no—
237C2×Dic106—21no—
238C2×Dic106—22no—
239C2×Dic106—22no—
240C2×Dic106—22no—
241C2×Dic106—28no—
242C2×Dic106—24no—
243C2×Dic106—21no—
244C2×Dic106—44no—
245C2×Dic106—48no—
246C2×Dic106—44no—
247C2×Dic106#4114yes—
248C2×Dic106C2412yes—
249C2×Dic106C2412yes—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53—22no—
253C2×C8×C53—22no—
254C2×C8×C53—44no—
255C2×C8×C53—44no—
256C2×C8×C53C2412yes—
257C2×C8×C53C2412yes—
258C2×C8×C53C2412yes—
259C2×C8×C53C2412yes—
260C4⋊C4×C53C2×D414yes—
261C22⋊C4×C53C2×D414yes—
262C22⋊C4×C53C2×D414yes—
263C42×C53C2×D412yes—
264C42×C53C2412yes—
265C22⋊Dic53—24no—
266C22⋊Dic53—24no—
267#11719921—24no—
268#11719921—24no—
269#11719921—24no—
270#11719921—24no—
271#11719921—24no—
272#11719921—24no—
273C4⋊Dic53—21no—
274C4⋊Dic53—21no—
275C4⋊Dic53—24no—
276C4⋊Dic53—21no—
277C4⋊Dic53—21no—
278C4⋊Dic53C2412yes—
279C4⋊Dic53C2412yes—
280C4⋊Dic53C2412yes—
281C4⋊Dic53C2412yes—
282#11719919—24no—
283#11719919—24no—
284#11719919—24no—
285#11719919—24no—
286C4×Dic53—24no—
287C4×Dic53—24no—
288D424—44no—
289#11719913—28no—
290#11719913—44no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—22no—
294C23×C53—22no—
295C23×C53—22no—
296C23×C53#13514yes—
297C23×C53C22×D412yes—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—42no—
308D4×C53—28no—
309C2×C4×C53—22no—
310C2×C4×C53—22no—
311C2×C4×C53—22no—
312C2×C4×C53—22no—
313C2×C4×C53—24no—
314C2×C4×C53—24no—
315C2×C4×C53—22no—
316C2×C4×C53—22no—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53C22×D412yes—
320C2×C4×C53C22×D412yes—
321C2×C4×C53C22×D412yes—
322C2×C4×C53C22×D412yes—
323C2×C4×C53C22×D411yescharacteristic
324C2×C4×C53C2×#4112yes—
325C2×C4×C53H(5,𝔽2)12yes—
326C2×C4×C53C2511yescharacteristic
327C22⋊D53—48no—
328C22⋊D53—48no—
329C22⋊D53—48no—
330C22⋊D53—84no—
331C2×Dic53—24no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—48no—
339C2×Dic53—42no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—84no—
345D212—22no—
346D212—22no—
347D212—22no—
348D212—22no—
349D212—42no—
350D212—42no—
351C4×D53—48no—
352C4×D53—84no—
353Dic106—24no—
354Dic106—22no—
355Dic106—22no—
356Dic106—22no—
357Dic106—48no—
358Dic106—42no—
359Dic106C2×#4114yes—
360C8×C53—22no—
361C8×C53—22no—
362C8×C53—22no—
363C8×C53—22no—
364C2×#3301—531nomaximal, Sylow
365C22×C53—22no—
366C22×C53—28no—
367C22×C53—22no—
368C22×C53—22no—
369C22×C53—22no—
370C22×C53—22no—
371C22×C53—44no—
372C22×C53#54612yes—
373C22×C53C2×#13514yes—
374C22×C53C2×#13512yes—
375C22×C53#57712yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—42no—
381C2×D53—42no—
382C2×D53—42no—
383C2×D53—84no—
384C2×D53—84no—
385C4×C53—22no—
386C4×C53—22no—
387C4×C53—22no—
388C4×C53—22no—
389C4×C53#54612yes—
390C4×C53C22×#4111yescharacteristic
391C4×C53C2×H(5,𝔽2)11yescharacteristic
392Dic53—24no—
393Dic53—42no—
394Dic53—42no—
395Dic53—42no—
396Dic53—42no—
397Dic53—42no—
398C2×#553—531no—
399C2×#548—531no—
400#3301—5316no—
401C2×#488—531no—
402C2×#481—531no—
403C2×#485—531no—
404C2×#479—531no—
405C2×#466—531no—
406C2×#465—531no—
407C2×#463—531no—
408C2×#449—531no—
409C2×#448—531no—
410C2×C4×SD16—531no—
411C2×C8×D4D5311yescharacteristic, complemented
412C2×#416—531no—
413C22×#103—531no—
414C2×C53—24no—
415C2×C53—42no—
416C2×C53#330114yescomplemented
417C2×C53C2×#54611yescharacteristic
418C2×C53C22×#13511yescharacteristic
419C2×C53C2×#57711yescharacteristic
420D53—82no—
421D53—82no—
422C22×#41—531no—
423C23×Q8—531no—
424C22×SD16—531no—
425C22×SD16—531no—
426C22×D8—531no—
427C23×C8C2×D5311yescharacteristic
428C23×C8C2×D5311yescharacteristic
429#553—538no—
430#553—1064no—
431#548—538no—
432#548—1064no—
433C2×#126—1061no—
434C2×#125—531no—
435C2×#124—531no—
436C2×#124—1061no—
437C2×#123—1061no—
438C2×C22⋊Q8—531no—
439C2×C22⋊Q8—1061no—
440C2×#121—531no—
441C2×#121—531no—
442C2×#121—531no—
443C2×#121—1061no—
444C2×#121—1061no—
445C2×C4×Q8—531no—
446C2×C4×D4—531no—
447C2×C4×D4—1061no—
448C2×C4×D4—1061no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×#117—531no—
451C22×C4⋊C4—531no—
452#488—538no—
453#485—538no—
454#481—538no—
455#479—538no—
456#466—538no—
457#465—538no—
458#463—538no—
459#449—538no—
460#448—538no—
461C4×SD16—538no—
462C8×D4C2×D5318yescomplemented
463C2×#107—531no—
464C2×#106—531no—
465C2×#106—531no—
466C2×C4⋊C8C2×D5311yescharacteristic
467#416—538no—
468C2×#103—531no—
469C2×#103—531no—
470C2×#103—531no—
471C2×#103—531no—
472C2×#103—531no—
473C2×#103—531no—
474C2×#103—538no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×C22⋊C8C2×D5311yescharacteristic
480C2×C22⋊C8C2×D5311yescharacteristic
481C2×C4×C8C2×D5311yescharacteristic
482C53C2×#330111yescharacteristic, complemented, Sylow
483C2×#41—534no—
484C2×#41—1064no—
485C2×#41—1062no—
486C2×#41—2122no—
487C22×Q8—531no—
488C22×Q8—531no—
489C22×Q8—534no—
490C22×Q8—1064no—
491C22×Q8—1061no—
492C22×Q8—1062no—
493C22×Q8—2122no—
494C22×D4—531no—
495C22×D4—531no—
496C22×D4—1061no—
497C22×D4—1061no—
498C22×D4—1061no—
499C22×D4—1061no—
500C22×D4D21211yescharacteristic
501C23×C4—1061no—
502C23×C4—1061no—
503C23×C4—1061no—
504C23×C4—1061no—
505C23×C4C22×D5311yescharacteristic
506C23×C4C22×D5311yescharacteristic
507C2×SD16—534no—
508C2×SD16—534no—
509C2×SD16—1064no—
510C2×SD16—2122no—
511C2×D8—534no—
512C2×D8—2122no—
513C22×C8—42no—
514C22×C8—42no—
515C22×C8C22×D5311yescharacteristic
516C22×C8C22×D5311yescharacteristic
517C22×C8C22×D5311yescharacteristic
518C22×C8C22×D5311yescharacteristic
519C22×C8C22×D5314yes—
520C22×C8C22×D5314yes—
521#126—1068no—
522#125—534no—
523#125—1062no—
524#124—534no—
525#124—1068no—
526#124—1062no—
527#123—1068no—
528C22⋊Q8—534no—
529C22⋊Q8—1062no—
530C22⋊Q8—1068no—
531#121—534no—
532#121—534no—
533#121—534no—
534#121—1068no—
535#121—1068no—
536#121—1062no—
537#121—1062no—
538#121—1062no—
539C4×Q8—534no—
540C4×Q8—1062no—
541C4×D4—534no—
542C4×D4—1068no—
543C4×D4—1068no—
544C4×D4—1062no—
545C4×D4D21214yes—
546C4×D4C22×D5314yes—
547#117—534no—
548#117—1062no—
549C2×C4⋊C4—531no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—534no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1062no—
556C2×C4⋊C4—1061no—
557C2×C4⋊C4—1061no—
558C2×C4⋊C4—1061no—
559C2×C4⋊C4—1061no—
560C2×C4⋊C4D21211yescharacteristic
561C2×C22⋊C4—1061no—
562C2×C22⋊C4—1061no—
563C2×C22⋊C4—1061no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4D21211yescharacteristic
570C2×C22⋊C4D21211yescharacteristic
571C2×C42—1061no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#106—534no—
576#106—534no—
577C4⋊C8C22×D5314yes—
578#103—534no—
579#103—534no—
580#103—534no—
581#103—534no—
582#103—534no—
583#103—534no—
584#102—534no—
585#102—534no—
586#102—534no—
587#102—534no—
588C22⋊C8C22×D5314yes—
589C22⋊C8C22×D5314yes—
590C4×C8C22×D5314yes—
591C24—1061no—
592C24—1061no—
593C24C2×D21211yescharacteristic
594C24C2×D21211yescharacteristic
595#41—1068no—
596#41—2124no—
597#41—2128no—
598C2×Q8—534no—
599C2×Q8—532no—
600C2×Q8—532no—
601C2×Q8—1068no—
602C2×Q8—1061no—
603C2×Q8—1064no—
604C2×Q8—1061no—
605C2×Q8—1062no—
606C2×Q8—1062no—
607C2×Q8—1062no—
608C2×Q8—2124no—
609C2×Q8—2124no—
610C2×Q8—2128no—
611C2×D4—24no—
612C2×D4—532no—
613C2×D4—532no—
614C2×D4—1064no—
615C2×D4—1064no—
616C2×D4—1064no—
617C2×D4—1064no—
618C2×D4—1061no—
619C2×D4—1061no—
620C2×D4—1062no—
621C2×D4—1062no—
622C2×D4—1062no—
623C2×D4—1062no—
624C2×D4—4242no—
625C2×D4—2124no—
626C2×D4—2124no—
627C2×D4—2124no—
628C2×D4C2×D21214yes—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—1061no—
634C22×C4—1064no—
635C22×C4—1064no—
636C22×C4—1061no—
637C22×C4—1061no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—4242no—
644C22×C4—4242no—
645C22×C4—2124no—
646C22×C4—2124no—
647C22×C4C2×D21212yes—
648C22×C4C2×D21212yes—
649C22×C4C2×D21211yescharacteristic
650C22×C4C2×D21211yescharacteristic
651C22×C4C2×D21211yescharacteristic
652C22×C4C2×D21211yescharacteristic
653C22×C4C23×D5312yes—
654C22×C4C23×D5312yes—
655C22×C4C23×D5311yescharacteristic
656SD16—1068no—
657SD16—2124no—
658D8—2124no—
659C2×C8—22no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—22no—
663C2×C8—44no—
664C2×C8—44no—
665C2×C8C23×D5312yes—
666C2×C8C23×D5312yes—
667C2×C8C23×D5312yes—
668C2×C8C23×D5312yes—
669C4⋊C4—532no—
670C4⋊C4—532no—
671C4⋊C4—532no—
672C4⋊C4—532no—
673C4⋊C4—1061no—
674C4⋊C4—1061no—
675C4⋊C4—1064no—
676C4⋊C4—1061no—
677C4⋊C4—1061no—
678C4⋊C4—1064no—
679C4⋊C4—1064no—
680C4⋊C4—1064no—
681C4⋊C4—1064no—
682C4⋊C4C2×D21214yes—
683C22⋊C4—1064no—
684C22⋊C4—1064no—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C22⋊C4C2×D21214yes—
692C22⋊C4C2×D21214yes—
693C42—1064no—
694C42—1064no—
695C42C2×D21212yes—
696C42C23×D5312yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—1062no—
703C23—1062no—
704C23—2122no—
705C23—2122no—
706C23—2122no—
707C23—2122no—
708C23—2122no—
709C23—2122no—
710C23#1313323914yes—
711C23C22×D21212yes—
712C23C22×D21212yes—
713C23C22×D21211yescharacteristic
714Q8—534no—
715Q8—1064no—
716Q8—1062no—
717Q8—1062no—
718Q8—1062no—
719Q8—2128no—
720Q8—2122no—
721D4—28no—
722D4—1062no—
723D4—1062no—
724D4—1062no—
725D4—1062no—
726D4—4244no—
727D4—2128no—
728D4—2128no—
729D4—2128no—
730D4—2122no—
731D4—2122no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—24no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—1064no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—1062no—
746C2×C4—1062no—
747C2×C4—1062no—
748C2×C4—1062no—
749C2×C4—4244no—
750C2×C4—4244no—
751C2×C4—2128no—
752C2×C4—2128no—
753C2×C4—2122no—
754C2×C4—2122no—
755C2×C4—2122no—
756C2×C4—2122no—
757C2×C4—2122no—
758C2×C4C22×D21212yes—
759C2×C4C22×D21212yes—
760C2×C4C22×D21212yes—
761C2×C4C22×D21212yes—
762C2×C4C22×D21211yescharacteristic
763C2×C4#41×D5312yes—
764C2×C4#1313326212yes—
765C2×C4C24×D5311yescharacteristic
766C8—22no—
767C8—22no—
768C8—22no—
769C8—22no—
770C22—28no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—4244no—
778C22—4244no—
779C22—2122no—
780C22—2122no—
781C22—2122no—
782C22—2122no—
783C22—2122no—
784C22—2122no—
785C22#1681126812yes—
786C22C2×#1313323914yes—
787C22C2×#1313323912yes—
788C22#1681143512yes—
789C22C23×D21211yescharacteristic
790C4—22no—
791C4—22no—
792C4—22no—
793C4—22no—
794C4—1064no—
795C4—2122no—
796C4—2122no—
797C4—2122no—
798C4—2122no—
799C4—2122no—
800C4#1681126812yes—
801C4C2×#41×D5311yescharacteristic
802C4C2×#1313326211yescharacteristic
803C2—24no—
804C2—42no—
805C2—4242no—
806C2—4242no—
807C2#2028661914yesdirect product factor
808C2C2×#1681126811yescharacteristic
809C2C22×#1313323911yescharacteristic
810C2C2×#1681143511yescharacteristic
subgroupG/H
centerC23C22×D212
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C8×D4×C53C2
socleC23×C53C22×D4
hypercenterC2×C8×D4D53
hypocenterC53C2×#3301
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×C8×D4

Complements

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

NH ≅ G/Ntype
1. C2×#16811319C2semidirect
2. C2×#16811282C2semidirect
3. #20286619C2direct (N × H)
4. C2×#16810978C2semidirect
5. C2×#16810942C2semidirect
6. C2×#16810965C2semidirect
7. C2×#16810931C2semidirect
8. C2×#16810859C2semidirect
9. C2×#16810852C2semidirect
10. C2×#16810839C2semidirect
11. C2×#16810770C2semidirect
12. C2×#16810764C2semidirect
13. C2×C4×#11719913C2semidirect
14. C2×#16810620C2semidirect
15. C22×#13133142C2semidirect
16. C2×C8×D4×C53C2semidirect
23. #16811319C22semidirect
25. #16811282C22semidirect
44. #16810978C22semidirect
45. #16810965C22semidirect
46. #16810942C22semidirect
47. #16810931C22semidirect
48. #16810859C22semidirect
49. #16810852C22semidirect
50. #16810839C22semidirect
51. #16810770C22semidirect
52. #16810764C22semidirect
53. C4×#11719913C22semidirect
57. #16810620C22semidirect
64. C2×#13133142C22semidirect
72. C8×D4×C53C22semidirect
411. C2×C8×D4D53semidirect
416. C2×C53#3301semidirect
462. C8×D4C2×D53semidirect
482. C53C2×#3301semidirect
807. C2#20286619direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168113192
C2×#168112822
#202866192
C2×#168109782
C2×#168109422
C2×#168109652
C2×#168109312
C2×#168108592
C2×#168108522
C2×#168108392
C2×#168107702
C2×#168107642
C2×C4×#117199132
C2×#168106202
C22×#131331422
C2×C8×D4×C532
C2×#330153