Finite Group Databasebeta

← C2×#20284859 #28252211

Subgroups — C2×#20284859 #28252211

Order 13568.

2430 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811168C211yesmaximal, characteristic, complemented
2C2×#41×Dic53C211yesmaximal, characteristic, complemented
3#20284859C2116yesmaximal, direct product factor
4C2×#16810948C211yesmaximal, characteristic, complemented
5C2×#16810944C211yesmaximal, characteristic, complemented
6C2×#16810906C211yesmaximal, characteristic, complemented
7C2×#16810901C211yesmaximal, characteristic, complemented
8C2×#16810821C211yesmaximal, characteristic, complemented
9C2×#16810816C211yesmaximal, characteristic, complemented
10C2×#16810768C211yesmaximal, characteristic, complemented
11C2×#16810735C211yesmaximal, characteristic, complemented
12C2×#16810732C211yesmaximal, characteristic, complemented
13C2×#16810726C211yesmaximal, characteristic, complemented
14C2×#16810724C211yesmaximal, characteristic, complemented
15C2×#16810677C211yesmaximal, characteristic, complemented
16C2×C53×#449C211yesmaximal, characteristic, complemented
17C22×#11719947—21no—
18C22×#11719924C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20#16811168—24no—
21#16811168C2218yescomplemented
22C2×#13133216C2211yescharacteristic
23C2×#13133213C2211yescharacteristic
24C2×#13133203—21no—
25C2×#13133191C2211yescharacteristic
26C2×#13133189—21no—
27#41×Dic53—24no—
28#41×Dic53C2218yescomplemented
29C2×Q8×Dic53C2211yescharacteristic
30C2×Q8×Dic53C2211yescharacteristic
31C2×D4×Dic53—21no—
32C2×D4×Dic53—21no—
33C2×D4×Dic53C2211yescharacteristic
34C2×D4×Dic53C2211yescharacteristic
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×#13133177—21no—
38C2×#13133176—21no—
39C2×#13133176C2211yescharacteristic
40C22×C4×Dic53—21no—
41C22×C4×Dic53C2211yescharacteristic
42#16810948C2218yescomplemented
43#16810944C2218yescomplemented
44#16810906C2218yescomplemented
45#16810901C2218yescomplemented
46#16810821C2218yescomplemented
47#16810816C2218yescomplemented
48#16810768C2218yescomplemented
49#16810735C2218yescomplemented
50#16810732C2218yescomplemented
51#16810726C2218yescomplemented
52#16810724C2218yescomplemented
53#16810677C2218yescomplemented
54C2×#13133151C2211yescharacteristic
55C2×#13133150C2211yescharacteristic
56C2×#13133149C2211yescharacteristic
57C2×#13133148C2211yescharacteristic
58C2×#13133146C2211yescharacteristic
59C2×#13133146C2211yescharacteristic
60C2×#13133141C2211yescharacteristic
61C2×#13133139C2211yescharacteristic
62C2×#13133139C2211yescharacteristic
63C2×#13133138C2211yescharacteristic
64C2×#13133138C2211yescharacteristic
65C2×#13133138C2211yescharacteristic
66C2×C22⋊#88322C2211yescharacteristic
67C2×#13133127C2211yescharacteristic
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×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C23×Dic53—21no—
85C23×Dic53—21no—
86C23×Dic53—21no—
87C23×Dic53D411yescharacteristic
88C23×Dic53D411yescharacteristic
89C22×C4×D53—21no—
90C2×#11719924—24no—
91C2×#11719924C2314yes—
92C2×#11719922—24no—
93C2×#11719922C2314yes—
94C22×#88322C2311yescharacteristic
95C22×#88322C2311yescharacteristic
96#13133216—22no—
97#13133216C2314yes—
98#13133213—22no—
99#13133213C2314yes—
100#13133203—28no—
101#13133191—22no—
102#13133191C2314yes—
103#13133189—28no—
104Q8×Dic53—22no—
105Q8×Dic53—22no—
106Q8×Dic53C2314yes—
107Q8×Dic53C2314yes—
108D4×Dic53—22no—
109D4×Dic53—22no—
110D4×Dic53—22no—
111D4×Dic53—28no—
112D4×Dic53—28no—
113D4×Dic53C2314yes—
114D4×Dic53C2314yes—
115D4×Dic53C2314yes—
116#13133179—22no—
117#13133179C2314yes—
118#13133177—28no—
119#13133176—28no—
120#13133176—22no—
121#13133176C2314yes—
122C2×C4⋊Dic53—21no—
123C2×C4⋊Dic53—21no—
124C2×C4⋊Dic53C2311yescharacteristic
125C2×C4⋊Dic53C2311yescharacteristic
126C2×C4⋊Dic53C2311yescharacteristic
127C2×#11719919—21no—
128C2×C22⋊Dic53—21no—
129C2×C22⋊Dic53—21no—
130C2×C22⋊Dic53—21no—
131C2×C22⋊Dic53—21no—
132C2×#11719921—21no—
133C2×#11719921—21no—
134C2×C4×Dic53—28no—
135C2×C4×Dic53—21no—
136C2×C4×Dic53—21no—
137C2×C4×Dic53—21no—
138C2×C4×Dic53D411yescharacteristic
139C2×C4×Dic53D411yescharacteristic
140C2×C4×Dic53D414yes—
141C2×C4×Dic53C2311yescharacteristic
142C2×C4×Dic53C2311yescharacteristic
143C2×C4×Dic53C2314yes—
144#13133151C2314yes—
145#13133150C2314yes—
146#13133149C2314yes—
147#13133148C2314yes—
148#13133146C2314yes—
149#13133146C2314yes—
150#13133141C2314yes—
151#13133139C2314yes—
152#13133139C2314yes—
153#13133138C2314yes—
154#13133138C2314yes—
155#13133138C2314yes—
156C22⋊#88322C2314yes—
157#13133127C2314yes—
158#13133127C2314yes—
159C2×#41×C53—24no—
160C2×#41×C53—24no—
161C2×#41×C53—22no—
162C2×#41×C53C2314yes—
163C22×Q8×C53C2311yescharacteristic
164C22×D4×C53—21no—
165C22×D4×C53—21no—
166C22×D4×C53C2311yescharacteristic
167C22×D4×C53C2311yescharacteristic
168C23×C4×C53—21no—
169C23×C4×C53C2311yescharacteristic
170C2×SD16×C53—24no—
171C2×SD16×C53C2314yes—
172C2×D8×C53—24no—
173C2×D8×C53C2314yes—
174C22×C8×C53C2311yescharacteristic
175C22×C8×C53C2311yescharacteristic
176#121×C53—22no—
177#121×C53C2314yes—
178C2×C4⋊C4×C53C2311yescharacteristic
179C2×C22⋊C4×C53—21no—
180#103×C53C2314yes—
181#102×C53C2314yes—
182C22⋊C8×C53C2314yes—
183C24×C53—21no—
184C24×C53—21no—
185C24×C53C2×D411yescharacteristic
186C23×D53—21no—
187#41×C53—216no—
188#41×C53—28no—
189#41×C53—28no—
190C2×Q8×C53—21no—
191C2×Q8×C53—22no—
192C2×Q8×C53#4114yescomplemented
193C2×Q8×C53C2412yes—
194C2×D4×C53—28no—
195C2×D4×C53—24no—
196C2×D4×C53—24no—
197C2×D4×C53—21no—
198C2×D4×C53—21no—
199C2×D4×C53—22no—
200C2×D4×C53—22no—
201C2×D4×C53—22no—
202C2×D4×C53—44no—
203C2×D4×C53#4114yescomplemented
204C2×D4×C53C2412yes—
205C2×D4×C53C2412yes—
206C22×C4×C53—28no—
207C22×C4×C53—21no—
208C22×C4×C53—24no—
209C22×C4×C53—22no—
210C22×C4×C53—22no—
211C22×C4×C53—21no—
212C22×C4×C53C2×D411yescharacteristic
213C22×C4×C53C2×D412yes—
214C22×C4×C53C2412yes—
215C22×C4×C53C2411yescharacteristic
216C2×C22⋊D53—24no—
217C2×C22⋊D53—24no—
218C2×C22⋊D53—24no—
219C2×C22⋊D53—44no—
220C2×C22⋊D53—44no—
221C2×C22⋊D53—44no—
222C22×Dic53—24no—
223C22×Dic53—21no—
224C22×Dic53—21no—
225C22×Dic53—21no—
226C22×Dic53—24no—
227C22×Dic53—24no—
228C22×Dic53—24no—
229C22×Dic53—42no—
230C22×Dic53—44no—
231C22×Dic53—44no—
232C22×Dic53—44no—
233C22×Dic53C2×D411yescharacteristic
234C22×Dic53C2×D411yescharacteristic
235C22×Dic53C2×D411yescharacteristic
236C22×Dic53C2×D414yes—
237C22×Dic53C2×D414yes—
238C22×Dic53C2×D411yescharacteristic
239#11719947—432no—
240C2×D212—22no—
241C2×D212—22no—
242C2×D212—21no—
243C2×D212C2412yes—
244C2×C4×D53—24no—
245C2×C4×D53—44no—
246C2×Dic106—24no—
247C2×Dic106—44no—
248SD16×C53—28no—
249D8×C53—28no—
250C2×C8×C53—22no—
251C2×C8×C53—22no—
252C2×C8×C53C2412yes—
253C2×C8×C53C2412yes—
254C4⋊C4×C53—21no—
255C4⋊C4×C53C2412yes—
256C22⋊C4×C53—24no—
257C22⋊Dic53—24no—
258C22⋊Dic53—24no—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261#11719924—28no—
262#11719922—28no—
263#11719921—24no—
264#11719921—24no—
265C4⋊Dic53—21no—
266C4⋊Dic53—21no—
267C4⋊Dic53—21no—
268C4⋊Dic53—24no—
269C4⋊Dic53—24no—
270C4⋊Dic53C2412yes—
271C4⋊Dic53C2412yes—
272C4⋊Dic53C2412yes—
273#11719919—24no—
274C4×Dic53—24no—
275C4×Dic53—24no—
276C4×Dic53—24no—
277C4×Dic53C2×D414yes—
278C4×Dic53C2×D414yes—
279C4×Dic53C2×D412yes—
280C4×Dic53C2×D412yes—
281C4×Dic53C2412yes—
282C4×Dic53C2412yes—
283C2×#88322—22no—
284C2×#88322—22no—
285C2×#88322C2412yes—
286C2×#88322C2412yes—
287C23×C53—22no—
288C23×C53—24no—
289C23×C53—22no—
290C23×C53—22no—
291C23×C53—22no—
292C23×C53—22no—
293C23×C53—42no—
294C23×C53—42no—
295C23×C53—42no—
296C23×C53—42no—
297C23×C53—42no—
298C23×C53C22×D412yes—
299C23×C53C22×D411yescharacteristic
300C22×D53—22no—
301C22×D53—42no—
302C22×D53—42no—
303C22×D53—42no—
304Q8×C53—24no—
305Q8×C53—22no—
306Q8×C53C2×#4114yescomplemented
307D4×C53—216no—
308D4×C53—24no—
309D4×C53—22no—
310D4×C53—22no—
311D4×C53—22no—
312D4×C53—48no—
313D4×C53—42no—
314D4×C53C2×#4114yescomplemented
315C2×C4×C53—216no—
316C2×C4×C53—22no—
317C2×C4×C53—24no—
318C2×C4×C53—22no—
319C2×C4×C53—24no—
320C2×C4×C53—22no—
321C2×C4×C53—22no—
322C2×C4×C53—22no—
323C2×C4×C53—42no—
324C2×C4×C53C22×D412yes—
325C2×C4×C53C22×D411yescharacteristic
326C2×C4×C53C2×#4112yes—
327C2×C4×C53C2×#4112yes—
328C2×C4×C53C2511yescharacteristic
329C22⋊D53—48no—
330C22⋊D53—48no—
331C22⋊D53—48no—
332C2×Dic53—22no—
333C2×Dic53—22no—
334C2×Dic53—22no—
335C2×Dic53—28no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—44no—
340C2×Dic53—48no—
341C2×Dic53—48no—
342C2×Dic53—42no—
343C2×Dic53—42no—
344C2×Dic53—42no—
345C2×Dic53—48no—
346C2×Dic53AGL(1,ℤ/8)14yes—
347C2×Dic53C22×D412yes—
348C2×Dic53C22×D412yes—
349C2×Dic53C22×D412yes—
350C2×Dic53C22×D412yes—
351D212—22no—
352D212—22no—
353D212—42no—
354C4×D53—48no—
355Dic106—48no—
356C8×C53—22no—
357C8×C53—22no—
358#88322—22no—
359#88322—22no—
360C2×#3115—531nomaximal, Sylow
361C22×C53—22no—
362C22×C53—24no—
363C22×C53—22no—
364C22×C53—22no—
365C22×C53—44no—
366C22×C53—48no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—42no—
372C22×C53—84no—
373C22×C53#52512yes—
374C22×C53C2×AGL(1,ℤ/8)12yes—
375C22×C53#57512yes—
376C22×C53C23×D411yescharacteristic
377C2×D53—42no—
378C2×D53—42no—
379C2×D53—42no—
380C2×D53—84no—
381C4×C53—22no—
382C4×C53—24no—
383C4×C53—42no—
384C4×C53#52512yes—
385C4×C53C22×#4111yescharacteristic
386C4×C53C22×#4111yescharacteristic
387Dic53—22no—
388Dic53—22no—
389Dic53—22no—
390Dic53—42no—
391Dic53—42no—
392Dic53—42no—
393Dic53C2×AGL(1,ℤ/8)14yes—
394C2×#532—531no—
395C2×C4×#41—531no—
396#3115—5316no—
397C2×#482—531no—
398C2×#482—531no—
399C2×#475—531no—
400C2×#474—531no—
401C2×#460—531no—
402C2×#459—531no—
403C2×#449—531no—
404C2×#449D5311yescharacteristic, complemented
405C2×#442—531no—
406C2×#442—531no—
407C2×#440—531no—
408C2×#440—531no—
409C2×#432—531no—
410C2×C53—42no—
411C2×C53—44no—
412C2×C53—82no—
413C2×C53#311514yescomplemented
414C2×C53C2×#52511yescharacteristic
415C2×C53C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C53C2×#57511yescharacteristic
417D53—82no—
418C22×#41—1061no—
419C22×#41C2×D5311yescharacteristic
420C22×SD16—531no—
421C22×SD16C2×D5311yescharacteristic
422C22×D8—531no—
423C22×D8C2×D5311yescharacteristic
424#532—538no—
425#532—1064no—
426C2×C4⋊Q8—531no—
427C2×#127—531no—
428C2×#124—1061no—
429C2×#121—531no—
430C2×#121—1061no—
431C2×#121C2×D5311yescharacteristic
432C4×#41—538no—
433C4×#41—1064no—
434C2×C4×Q8—531no—
435C2×C4×Q8—531no—
436C2×C4×D4—531no—
437C2×C4×D4—531no—
438C2×C4×D4—531no—
439C2×C4×D4—531no—
440C2×C4×D4—1061no—
441C2×C4×D4—1061no—
442C2×C4×D4—1061no—
443C2×#117—531no—
444C2×#117—1061no—
445C22×C42—531no—
446C22×C42—1061no—
447#482—538no—
448#482—538no—
449#475—538no—
450#474—538no—
451#460—538no—
452#459—538no—
453#449—538no—
454#449C2×D5318yescomplemented
455#442—538no—
456#442—538no—
457#440—538no—
458#440—538no—
459#432—538no—
460C2×#107—531no—
461C2×#107—531no—
462C2×#106—531no—
463C2×#106—531no—
464C2×C4⋊C8—531no—
465C2×C4⋊C8—531no—
466C2×#103—531no—
467C2×#103C2×D5311yescharacteristic
468C2×#102—531no—
469C2×#102—531no—
470C2×#102—531no—
471C2×#102—531no—
472C2×#102—531no—
473C2×#102C2×D5311yescharacteristic
474C2×C22⋊C8—531no—
475C2×C22⋊C8C2×D5311yescharacteristic
476C2×#97—531no—
477C2×#97—531no—
478C53C2×#311511yescharacteristic, complemented, Sylow
479C2×#41—24no—
480C2×#41—24no—
481C2×#41—22no—
482C2×#41—1068no—
483C2×#41—2128no—
484C2×#41C22×D5314yes—
485C22×Q8—1061no—
486C22×Q8C22×D5311yescharacteristic
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—531no—
490C22×D4—1061no—
491C22×D4—1061no—
492C22×D4—1061no—
493C22×D4C22×D5311yescharacteristic
494C22×D4C22×D5311yescharacteristic
495C23×C4—21no—
496C23×C4—531no—
497C23×C4—531no—
498C23×C4—1061no—
499C23×C4—1061no—
500C23×C4—1061no—
501C23×C4—1061no—
502C23×C4C22×D5311yescharacteristic
503C2×SD16—24no—
504C2×SD16—534no—
505C2×SD16—1064no—
506C2×SD16C22×D5314yes—
507C2×D8—24no—
508C2×D8—534no—
509C2×D8—1064no—
510C2×D8C22×D5314yes—
511C22×C8—531no—
512C22×C8—531no—
513C22×C8C22×D5311yescharacteristic
514C22×C8C22×D5311yescharacteristic
515C4⋊Q8—534no—
516C4⋊Q8—1062no—
517#127—534no—
518#127—1062no—
519#124—1068no—
520#121—22no—
521#121—534no—
522#121—1068no—
523#121—1062no—
524#121C22×D5314yes—
525C4×Q8—534no—
526C4×Q8—534no—
527C4×Q8—1062no—
528C4×Q8—1062no—
529C4×D4—534no—
530C4×D4—534no—
531C4×D4—534no—
532C4×D4—534no—
533C4×D4—1068no—
534C4×D4—1062no—
535C4×D4—1062no—
536C4×D4—1062no—
537C4×D4—1062no—
538C4×D4—1068no—
539C4×D4—1068no—
540#117—534no—
541#117—1068no—
542#117—1062no—
543C2×C4⋊C4—531no—
544C2×C4⋊C4—531no—
545C2×C4⋊C4—531no—
546C2×C4⋊C4—1061no—
547C2×C4⋊C4—1061no—
548C2×C4⋊C4—1061no—
549C2×C4⋊C4C22×D5311yescharacteristic
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1061no—
552C2×C22⋊C4—1061no—
553C2×C22⋊C4—1061no—
554C2×C22⋊C4—1061no—
555C2×C22⋊C4—1061no—
556C2×C22⋊C4—1061no—
557C2×C42—531no—
558C2×C42—534no—
559C2×C42—531no—
560C2×C42—531no—
561C2×C42—531no—
562C2×C42—534no—
563C2×C42—1068no—
564C2×C42—1061no—
565C2×C42—1061no—
566C2×C42—1061no—
567#107—534no—
568#107—534no—
569#106—534no—
570#106—534no—
571C4⋊C8—534no—
572C4⋊C8—534no—
573#103—534no—
574#103C22×D5314yes—
575#102—534no—
576#102—534no—
577#102—534no—
578#102—534no—
579#102—534no—
580#102C22×D5314yes—
581C22⋊C8—534no—
582C22⋊C8C22×D5314yes—
583#97—534no—
584#97—534no—
585C24—21no—
586C24—21no—
587C24—1061no—
588C24D4×D5311yescharacteristic
589#41—216no—
590#41—28no—
591#41—28no—
592#41—21232no—
593C2×Q8—21no—
594C2×Q8—22no—
595C2×Q8—1064no—
596C2×Q8—2124no—
597C2×Q8#1171994714yescomplemented
598C2×Q8C23×D5312yes—
599C2×D4—28no—
600C2×D4—24no—
601C2×D4—24no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—44no—
608C2×D4—532no—
609C2×D4—1064no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1061no—
613C2×D4—1062no—
614C2×D4—1062no—
615C2×D4—2124no—
616C2×D4—2124no—
617C2×D4—2124no—
618C2×D4#1171994714yescomplemented
619C2×D4C23×D5312yes—
620C2×D4C23×D5312yes—
621C22×C4—28no—
622C22×C4—21no—
623C22×C4—24no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—21no—
627C22×C4—531no—
628C22×C4—534no—
629C22×C4—531no—
630C22×C4—531no—
631C22×C4—531no—
632C22×C4—534no—
633C22×C4—1064no—
634C22×C4—1064no—
635C22×C4—1064no—
636C22×C4—1064no—
637C22×C4—1064no—
638C22×C4—1061no—
639C22×C4—1061no—
640C22×C4—1061no—
641C22×C4—2124no—
642C22×C4—2124no—
643C22×C4—2122no—
644C22×C4—2124no—
645C22×C4—2124no—
646C22×C4D4×D5312yes—
647C22×C4D4×D5311yescharacteristic
648C22×C4C23×D5312yes—
649C22×C4C23×D5311yescharacteristic
650SD16—28no—
651SD16—1068no—
652D8—28no—
653D8—1068no—
654C2×C8—22no—
655C2×C8—22no—
656C2×C8—532no—
657C2×C8—532no—
658C2×C8—1062no—
659C2×C8—1062no—
660C2×C8C23×D5312yes—
661C2×C8C23×D5312yes—
662C4⋊C4—21no—
663C4⋊C4—532no—
664C4⋊C4—532no—
665C4⋊C4—532no—
666C4⋊C4—1064no—
667C4⋊C4—1064no—
668C4⋊C4—1064no—
669C4⋊C4—1061no—
670C4⋊C4—1061no—
671C4⋊C4—1061no—
672C4⋊C4C23×D5312yes—
673C22⋊C4—24no—
674C22⋊C4—1064no—
675C22⋊C4—1064no—
676C22⋊C4—1064no—
677C22⋊C4—1064no—
678C22⋊C4—1064no—
679C22⋊C4—1064no—
680C42—534no—
681C42—534no—
682C42—532no—
683C42—532no—
684C42—532no—
685C42—532no—
686C42—1064no—
687C42—1064no—
688C42—1064no—
689C23—22no—
690C23—24no—
691C23—22no—
692C23—22no—
693C23—22no—
694C23—22no—
695C23—42no—
696C23—42no—
697C23—42no—
698C23—42no—
699C23—42no—
700C23—1062no—
701C23—2122no—
702C23—2122no—
703C23—2122no—
704C23C2×D4×D5312yes—
705C23C2×D4×D5311yescharacteristic
706Q8—24no—
707Q8—22no—
708Q8—2128no—
709Q8C2×#1171994714yescomplemented
710D4—216no—
711D4—24no—
712D4—22no—
713D4—22no—
714D4—22no—
715D4—48no—
716D4—42no—
717D4—1062no—
718D4—1062no—
719D4—2128no—
720D4—2128no—
721D4—2128no—
722D4—2122no—
723D4C2×#1171994714yescomplemented
724C2×C4—216no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—42no—
733C2×C4—534no—
734C2×C4—532no—
735C2×C4—532no—
736C2×C4—532no—
737C2×C4—532no—
738C2×C4—1068no—
739C2×C4—1062no—
740C2×C4—1062no—
741C2×C4—1062no—
742C2×C4—1062no—
743C2×C4—1062no—
744C2×C4—1062no—
745C2×C4—2128no—
746C2×C4—2128no—
747C2×C4—2124no—
748C2×C4—2128no—
749C2×C4—2128no—
750C2×C4—2122no—
751C2×C4—2122no—
752C2×C4—2122no—
753C2×C4C2×D4×D5312yes—
754C2×C4C2×D4×D5311yescharacteristic
755C2×C4C2×#1171994712yes—
756C2×C4C2×#1171994712yes—
757C2×C4C24×D5311yescharacteristic
758C8—22no—
759C8—22no—
760C8—1062no—
761C8—1062no—
762C22—22no—
763C22—22no—
764C22—22no—
765C22—24no—
766C22—42no—
767C22—42no—
768C22—44no—
769C22—48no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—84no—
774C22—4244no—
775C22—2122no—
776C22—2122no—
777C22—2122no—
778C22#1681112912yes—
779C22AGL(1,ℤ/8)×D5312yes—
780C22#1681142012yes—
781C22C22×D4×D5311yescharacteristic
782C4—22no—
783C4—24no—
784C4—42no—
785C4—534no—
786C4—1062no—
787C4—1062no—
788C4—1062no—
789C4—2122no—
790C4—2122no—
791C4—2122no—
792C4#1681112912yes—
793C4C22×#1171994711yescharacteristic
794C4C22×#1171994711yescharacteristic
795C2—42no—
796C2—44no—
797C2—82no—
798C2—4242no—
799C2#2028485914yesdirect product factor
800C2C2×#1681112911yescharacteristic
801C2C2×AGL(1,ℤ/8)×D5311yescharacteristic
802C2C2×#1681142011yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#449C2
socleC23×C53C22×D4
hypercenterC2×#449D53
hypocenterC53C2×#3115
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×#16811168C2semidirect
2. C2×#41×Dic53C2semidirect
3. #20284859C2direct (N × H)
4. C2×#16810948C2semidirect
5. C2×#16810944C2semidirect
6. C2×#16810906C2semidirect
7. C2×#16810901C2semidirect
8. C2×#16810821C2semidirect
9. C2×#16810816C2semidirect
10. C2×#16810768C2semidirect
11. C2×#16810735C2semidirect
12. C2×#16810732C2semidirect
13. C2×#16810726C2semidirect
14. C2×#16810724C2semidirect
15. C2×#16810677C2semidirect
16. C2×C53×#449C2semidirect
21. #16811168C22semidirect
28. #41×Dic53C22semidirect
42. #16810948C22semidirect
43. #16810944C22semidirect
44. #16810906C22semidirect
45. #16810901C22semidirect
46. #16810821C22semidirect
47. #16810816C22semidirect
48. #16810768C22semidirect
49. #16810735C22semidirect
50. #16810732C22semidirect
51. #16810726C22semidirect
52. #16810724C22semidirect
53. #16810677C22semidirect
73. C53×#449C22semidirect
192. C2×Q8×C53#41semidirect
203. C2×D4×C53#41semidirect
306. Q8×C53C2×#41semidirect
314. D4×C53C2×#41semidirect
404. C2×#449D53semidirect
413. C2×C53#3115semidirect
454. #449C2×D53semidirect
478. C53C2×#3115semidirect
597. C2×Q8#11719947semidirect
618. C2×D4#11719947semidirect
709. Q8C2×#11719947semidirect
723. D4C2×#11719947semidirect
799. C2#20284859direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168111682
C2×#41×Dic532
#202848592
C2×#168109482
C2×#168109442
C2×#168109062
C2×#168109012
C2×#168108212
C2×#168108162
C2×#168107682
C2×#168107352
C2×#168107322
C2×#168107262
C2×#168107242
C2×#168106772
C2×C53×#4492
C2×#311553