Finite Group Databasebeta

← C2×#20284957 #28252385

Subgroups — C2×#20284957 #28252385

Order 13568.

2338 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811224C211yesmaximal, characteristic, complemented
2C2×#16811095C211yesmaximal, characteristic, complemented
3#20284957C2116yesmaximal, direct product factor
4C2×#16810949C211yesmaximal, characteristic, complemented
5C2×#16810946C211yesmaximal, characteristic, complemented
6C2×#16810925C211yesmaximal, characteristic, complemented
7C2×#16810922C211yesmaximal, characteristic, complemented
8C2×#16810817C211yesmaximal, characteristic, complemented
9C2×#16810816C211yesmaximal, characteristic, complemented
10C2×#16810758C211yesmaximal, characteristic, complemented
11C2×#16810755C211yesmaximal, characteristic, complemented
12C2×#16810736C211yesmaximal, characteristic, complemented
13C2×C4×#11719922C211yesmaximal, characteristic, complemented
14C2×C4×#11719922C211yesmaximal, characteristic, complemented
15C2×#16810685C211yesmaximal, characteristic, complemented
16C2×C53×#442C211yesmaximal, characteristic, complemented
17C22×D4×D53C2211yescharacteristic
18C22×D424C2211yescharacteristic
19C22×#11719922C2211yescharacteristic
20C22×#11719922C2211yescharacteristic
21#16811224—24no—
22#16811224C2218yescomplemented
23C2×#13133213C2211yescharacteristic, complemented
24C2×#13133208C2211yescharacteristic, complemented
25C2×#13133200—21no—
26C2×#13133199—21no—
27C2×#13133192C2211yescharacteristic
28C2×#13133191—21no—
29C2×#13133190—21no—
30C2×#13133188C2211yescharacteristic
31#16811095—24no—
32#16811095C2218yescomplemented
33C2×C4×D212C2211yescharacteristic
34C2×C4×D212C2211yescharacteristic, complemented
35C2×D4×Dic53C2211yescharacteristic
36C2×#13133179C2211yescharacteristic
37C2×C4×C22⋊D53—21no—
38C2×#13133177—21no—
39C2×#13133175C2211yescharacteristic
40C2×#13133174C2211yescharacteristic
41C22×#11719921—21no—
42C2×C22⋊C4×D53—21no—
43#16810949C2218yescomplemented
44#16810946C2218yescomplemented
45#16810925C2218yescomplemented
46#16810922C2218yescomplemented
47#16810817C2218yescomplemented
48#16810816C2218yescomplemented
49#16810758C2218yescomplemented
50#16810755C2218yescomplemented
51#16810736C2218yescomplemented
52C4×#11719922C2218yescomplemented
53C4×#11719922C2218yescomplemented
54#16810685C2218yescomplemented
55C2×#13133150C2211yescharacteristic, complemented
56C2×#13133150C2211yescharacteristic, complemented
57C2×#13133149C2211yescharacteristic, complemented
58C2×#13133146C2211yescharacteristic, complemented
59C2×#13133146C2211yescharacteristic, complemented
60C2×#13133139C2211yescharacteristic
61C2×#13133139C2211yescharacteristic, complemented
62C2×#13133138C2211yescharacteristic
63C2×#13133138C2211yescharacteristic, complemented
64C2×#13133137C2211yescharacteristic
65C2×#13133137C2211yescharacteristic, complemented
66C2×#13133129C2211yescharacteristic
67C2×#13133129C2211yescharacteristic
68C2×C4×#88322C2211yescharacteristic, complemented
69C22×D8×C53C2211yescharacteristic
70C2×C4×D4×C53C2211yescharacteristic
71C2×C4×D4×C53C2211yescharacteristic, complemented
72C53×#442C2218yescomplemented
73C2×#106×C53C2211yescharacteristic, complemented
74C2×#102×C53C2211yescharacteristic
75C2×#102×C53C2211yescharacteristic, complemented
76C2×#97×C53C2211yescharacteristic, complemented
77C24×D53—21no—
78C22×D212—21no—
79C22×D212C2311yescharacteristic
80C22×D212C2311yescharacteristic
81C22×C22⋊D53—21no—
82C22×C22⋊D53—21no—
83C22×C22⋊D53—21no—
84C22×C22⋊D53—21no—
85C2×D4×D53—24no—
86C2×D4×D53—24no—
87C2×D4×D53—22no—
88C2×D4×D53C2314yes—
89C23×Dic53—21no—
90C22×C4×D53—21no—
91C22×C4×D53—21no—
92C22×C4×D53—21no—
93C22×C4×D53C2311yescharacteristic
94C2×D424—24no—
95C2×D424C2314yes—
96C2×#11719922—24no—
97C2×#11719922—24no—
98C2×#11719922C2314yes—
99C2×#11719922C2314yes—
100C22×#88322C2311yescharacteristic
101C22×#88322C2311yescharacteristic
102#13133213—22no—
103#13133213C2314yescomplemented
104#13133208—22no—
105#13133208C2314yescomplemented
106#13133200—28no—
107#13133199—28no—
108#13133192—22no—
109#13133192C2314yes—
110#13133191—28no—
111#13133190—28no—
112#13133188—22no—
113#13133188C2314yes—
114C4×D212—22no—
115C4×D212—22no—
116C4×D212C2314yes—
117C4×D212C2314yescomplemented
118D4×Dic53—22no—
119D4×Dic53C2314yes—
120#13133179—22no—
121#13133179C2314yes—
122C4×C22⋊D53—28no—
123#13133177—28no—
124#13133175—22no—
125#13133175C2314yes—
126#13133174D414yes—
127#13133174C2314yes—
128C2×C4⋊Dic53—21no—
129C2×C4⋊Dic53C2311yescharacteristic
130C2×C4⋊Dic53C2311yescharacteristic
131C2×#11719919—21no—
132C2×#11719919D411yescharacteristic
133C2×#11719919D411yescharacteristic
134C2×C22⋊Dic53—21no—
135C2×C22⋊Dic53—21no—
136C2×#11719921—28no—
137C2×#11719921—21no—
138C2×#11719921—21no—
139C2×#11719921—21no—
140C2×#11719921—21no—
141C2×#11719921—21no—
142C2×#11719921D411yescharacteristic
143C2×#11719921D411yescharacteristic
144C22⋊C4×D53—28no—
145C2×C4×Dic53—21no—
146C2×C4×Dic53C2311yescharacteristic
147#13133150C2314yescomplemented
148#13133150C2314yescomplemented
149#13133149C2314yescomplemented
150#13133146C2314yescomplemented
151#13133146C2314yescomplemented
152#13133139C2314yes—
153#13133139C2314yescomplemented
154#13133138C2314yes—
155#13133138C2314yescomplemented
156#13133137C2314yes—
157#13133137C2314yescomplemented
158#13133129C2314yes—
159#13133129C2314yes—
160C4×#88322C2314yescomplemented
161C22×D4×C53C2311yescharacteristic
162C22×D4×C53C2311yescharacteristic
163C23×C4×C53—21no—
164C23×C4×C53—21no—
165C2×D8×C53—24no—
166C2×D8×C53C2314yes—
167C22×C8×C53C2311yescharacteristic
168C22×C8×C53C2311yescharacteristic
169C4×D4×C53—22no—
170C4×D4×C53—22no—
171C4×D4×C53C2314yes—
172C4×D4×C53C2314yescomplemented
173C2×C4⋊C4×C53C2311yescharacteristic
174C2×C4⋊C4×C53C2311yescharacteristic
175C2×C22⋊C4×C53—21no—
176C2×C22⋊C4×C53—21no—
177C2×C42×C53C2311yescharacteristic
178#106×C53C2314yescomplemented
179#102×C53C2314yes—
180#102×C53C2314yescomplemented
181#97×C53C2314yescomplemented
182C24×C53—21no—
183C24×C53—21no—
184C23×D53—21no—
185C23×D53—28no—
186C23×D53—24no—
187C23×D53—21no—
188C23×D53—82no—
189C23×D53—82no—
190C23×D53C2×D411yescharacteristic
191C2×D4×C53—21no—
192C2×D4×C53—21no—
193C2×D4×C53—22no—
194C2×D4×C53—22no—
195C2×D4×C53—22no—
196C2×D4×C53#4114yes—
197C2×D4×C53C2412yes—
198C2×D4×C53C2412yes—
199C22×C4×C53—21no—
200C22×C4×C53—21no—
201C22×C4×C53—24no—
202C22×C4×C53—24no—
203C22×C4×C53—82no—
204C22×C4×C53—82no—
205C22×C4×C53C2×D411yescharacteristic
206C22×C4×C53C2×D411yescharacteristic
207C22×C4×C53C2411yescharacteristic
208C2×C22⋊D53—28no—
209C2×C22⋊D53—24no—
210C2×C22⋊D53—24no—
211C2×C22⋊D53—24no—
212C2×C22⋊D53—24no—
213C2×C22⋊D53—82no—
214C2×C22⋊D53—82no—
215C2×C22⋊D53—82no—
216C22×Dic53—21no—
217C22×Dic53—21no—
218C22×Dic53—24no—
219C22×Dic53—82no—
220C22×Dic53C2×D411yescharacteristic
221C22×Dic53C2×D411yescharacteristic
222C22×Dic53C2×D411yescharacteristic
223D4×D53—216no—
224D4×D53—28no—
225D4×D53—28no—
226C2×D212—21no—
227C2×D212—22no—
228C2×D212—22no—
229C2×D212—22no—
230C2×D212—21no—
231C2×D212—24no—
232C2×D212—82no—
233C2×D212#4114yes—
234C2×D212C2412yes—
235C2×D212C2412yes—
236C2×C4×D53—22no—
237C2×C4×D53—22no—
238C2×C4×D53—24no—
239C2×C4×D53—24no—
240C2×C4×D53—24no—
241C2×C4×D53—82no—
242C2×C4×D53—82no—
243C2×C4×D53—82no—
244C2×C4×D53C2×D412yes—
245C2×C4×D53C2412yes—
246D8×C53—28no—
247C2×C8×C53—22no—
248C2×C8×C53—22no—
249C2×C8×C53C2412yes—
250C2×C8×C53C2412yes—
251C4⋊C4×C53—21no—
252C4⋊C4×C53—21no—
253C4⋊C4×C53C2412yes—
254C4⋊C4×C53C2412yes—
255C22⋊C4×C53—24no—
256C22⋊C4×C53—24no—
257C42×C53C2×D412yes—
258C42×C53C2412yes—
259C22⋊Dic53—24no—
260C22⋊Dic53—24no—
261#11719922—28no—
262#11719922—28no—
263#11719921—24no—
264#11719921—24no—
265#11719921—24no—
266#11719921—24no—
267#11719921—24no—
268#11719921C2×D414yes—
269#11719921C2×D414yes—
270C4⋊Dic53—21no—
271C4⋊Dic53—21no—
272C4⋊Dic53—24no—
273C4⋊Dic53C2412yes—
274C4⋊Dic53C2412yes—
275#11719919—24no—
276#11719919C2×D414yes—
277#11719919C2×D414yes—
278C4×Dic53—24no—
279C4×Dic53C2×D412yes—
280C4×Dic53C2412yes—
281C2×#88322—22no—
282C2×#88322—22no—
283C2×#88322C2412yes—
284C2×#88322C2412yes—
285D424—28no—
286C23×C53—24no—
287C23×C53—22no—
288C23×C53—22no—
289C23×C53—42no—
290C23×C53—42no—
291C23×C53—42no—
292C23×C53—42no—
293C23×C53—42no—
294C23×C53C22×D411yescharacteristic
295C22×D53—22no—
296C22×D53—24no—
297C22×D53—22no—
298C22×D53—22no—
299C22×D53—22no—
300C22×D53—216no—
301C22×D53—22no—
302C22×D53—42no—
303C22×D53—42no—
304C22×D53—42no—
305C22×D53—42no—
306C22×D53—42no—
307C22×D53—84no—
308C22×D53—84no—
309C22×D53—816no—
310C22×D53C22×D412yes—
311D4×C53—24no—
312D4×C53—22no—
313D4×C53—22no—
314D4×C53—22no—
315D4×C53—42no—
316D4×C53C2×#4114yes—
317C2×C4×C53—22no—
318C2×C4×C53—22no—
319C2×C4×C53—22no—
320C2×C4×C53—22no—
321C2×C4×C53—42no—
322C2×C4×C53—42no—
323C2×C4×C53—84no—
324C2×C4×C53—84no—
325C2×C4×C53C22×D412yes—
326C2×C4×C53C22×D412yes—
327C2×C4×C53C22×D411yescharacteristic
328C2×C4×C53C2×#4112yes—
329C2×C4×C53C2×#4112yes—
330C2×C4×C53C2511yescharacteristic
331C22⋊D53—216no—
332C22⋊D53—84no—
333C22⋊D53—84no—
334C22⋊D53—84no—
335C2×Dic53—22no—
336C2×Dic53—22no—
337C2×Dic53—22no—
338C2×Dic53—22no—
339C2×Dic53—22no—
340C2×Dic53—42no—
341C2×Dic53—42no—
342C2×Dic53—84no—
343C2×Dic53C22×D412yes—
344C2×Dic53C22×D412yes—
345C2×Dic53C22×D412yes—
346D212—24no—
347D212—22no—
348D212—22no—
349D212—22no—
350D212—42no—
351D212—84no—
352D212C2×#4114yes—
353C4×D53—24no—
354C4×D53—22no—
355C4×D53—22no—
356C4×D53—84no—
357C4×D53—84no—
358C4×D53—84no—
359C8×C53—22no—
360C8×C53—22no—
361#88322—22no—
362#88322—22no—
363C2×#3122—531nomaximal, Sylow
364C22×C53—24no—
365C22×C53—48no—
366C22×C53—42no—
367C22×C53—42no—
368C22×C53—42no—
369C22×C53—42no—
370C22×C53—42no—
371C22×C53—84no—
372C22×C53#52512yes—
373C22×C53#57612yes—
374C22×C53#57612yes—
375C22×C53C23×D411yescharacteristic
376C2×D53—22no—
377C2×D53—24no—
378C2×D53—22no—
379C2×D53—22no—
380C2×D53—44no—
381C2×D53—48no—
382C2×D53—42no—
383C2×D53—42no—
384C2×D53—42no—
385C2×D53—42no—
386C2×D53—42no—
387C2×D53—816no—
388C2×D53—84no—
389C4×C53—22no—
390C4×C53—22no—
391C4×C53—42no—
392C4×C53—42no—
393C4×C53#52512yes—
394C4×C53C22×#4111yescharacteristic
395C4×C53C22×#4111yescharacteristic
396Dic53—22no—
397Dic53—22no—
398Dic53—22no—
399Dic53—42no—
400Dic53—42no—
401C2×#540—531no—
402C2×#518—531no—
403#3122—5316no—
404C2×#482—531no—
405C2×#482—531no—
406C2×#478—531no—
407C2×#478—531no—
408C2×#459—531no—
409C2×#459—531no—
410C2×#447—531no—
411C2×#447—531no—
412C2×#442—531no—
413C2×#442D5311yescharacteristic, complemented
414C2×C4×D8—531no—
415C2×C4×D8—531no—
416C2×#433—531no—
417C2×C53—44no—
418C2×C53—82no—
419C2×C53#312214yescomplemented
420C2×C53C2×#52511yescharacteristic
421C2×C53C2×#57611yescharacteristic
422C2×C53C2×#57611yescharacteristic
423D53—42no—
424D53—44no—
425D53—82no—
426C23×D4—531no—
427C22×D8—531no—
428C22×D8—531no—
429C22×D8—531no—
430C22×D8C2×D5311yescharacteristic
431#540—538no—
432#540—1064no—
433C2×#127—531no—
434C2×#125—531no—
435C2×#123—1061no—
436C2×#123—1061no—
437C2×#121—531no—
438C2×#121—531no—
439C2×#121—1061no—
440C2×#121—1061no—
441#518—538no—
442#518—1064no—
443C2×C4×D4—531no—
444C2×C4×D4—531no—
445C2×C4×D4—531no—
446C2×C4×D4—531no—
447C2×C4×D4—1061no—
448C2×C4×D4—1061no—
449C2×C4×D4C2×D5311yescharacteristic
450C2×C4×D4C2×D5311yescharacteristic, complemented
451C2×#117—531no—
452C2×#117—531no—
453C22×C22⋊C4—1061no—
454C22×C22⋊C4—1061no—
455#482—538no—
456#482—538no—
457#478—538no—
458#478—538no—
459#459—538no—
460#459—538no—
461#447—538no—
462#447—538no—
463#442—538no—
464#442C2×D5318yescomplemented
465C4×D8—538no—
466C4×D8—538no—
467#433—538no—
468C2×#107—531no—
469C2×#107—531no—
470C2×#106—531no—
471C2×#106C2×D5311yescharacteristic, complemented
472C2×C4⋊C8—531no—
473C2×C4⋊C8—531no—
474C2×#102—531no—
475C2×#102—531no—
476C2×#102—531no—
477C2×#102—531no—
478C2×#102—531no—
479C2×#102—531no—
480C2×#102C2×D5311yescharacteristic
481C2×#102C2×D5311yescharacteristic, complemented
482C2×C22⋊C8—531no—
483C2×C22⋊C8—531no—
484C2×#97C2×D5311yescharacteristic, complemented
485C2×C4×C8—531no—
486C53C2×#312211yescharacteristic, complemented, Sylow
487C25—1061no—
488C22×D4—534no—
489C22×D4—531no—
490C22×D4—531no—
491C22×D4—1061no—
492C22×D4—1062no—
493C22×D4—1061no—
494C22×D4—1061no—
495C22×D4—1061no—
496C22×D4—1064no—
497C22×D4—1064no—
498C22×D4—1061no—
499C22×D4C22×D5311yescharacteristic
500C22×D4C22×D5311yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—531no—
504C23×C4—1061no—
505C23×C4—1061no—
506C23×C4—1061no—
507C23×C4—1061no—
508C2×D8—24no—
509C2×D8—534no—
510C2×D8—534no—
511C2×D8—534no—
512C2×D8—1064no—
513C2×D8—1064no—
514C2×D8—1064no—
515C2×D8C22×D5314yes—
516C22×C8—531no—
517C22×C8—531no—
518C22×C8C22×D5311yescharacteristic
519C22×C8C22×D5311yescharacteristic
520#127—534no—
521#127—1062no—
522#125—534no—
523#125—1062no—
524#123—1068no—
525#123—1068no—
526#121—534no—
527#121—534no—
528#121—1068no—
529#121—1068no—
530#121—1062no—
531#121—1062no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—534no—
535C4×D4—534no—
536C4×D4—534no—
537C4×D4—534no—
538C4×D4—1062no—
539C4×D4—1062no—
540C4×D4—1068no—
541C4×D4—1068no—
542C4×D4—1062no—
543C4×D4—1062no—
544C4×D4C22×D5314yes—
545C4×D4C22×D5314yescomplemented
546#117—534no—
547#117—534no—
548#117—534no—
549#117—1062no—
550C2×C4⋊C4—531no—
551C2×C4⋊C4—531no—
552C2×C4⋊C4—531no—
553C2×C4⋊C4—531no—
554C2×C4⋊C4—1061no—
555C2×C4⋊C4—1061no—
556C2×C4⋊C4C22×D5311yescharacteristic
557C2×C4⋊C4C22×D5311yescharacteristic
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—531no—
561C2×C22⋊C4—531no—
562C2×C22⋊C4—1068no—
563C2×C22⋊C4—1068no—
564C2×C22⋊C4—1061no—
565C2×C22⋊C4—1061no—
566C2×C22⋊C4—1061no—
567C2×C22⋊C4—1061no—
568C2×C22⋊C4—1061no—
569C2×C22⋊C4—1061no—
570C2×C22⋊C4—1061no—
571C2×C42—531no—
572C2×C42—1061no—
573C2×C42C22×D5311yescharacteristic
574#107—534no—
575#107—534no—
576#106—534no—
577#106C22×D5314yescomplemented
578C4⋊C8—534no—
579C4⋊C8—534no—
580#102—534no—
581#102—534no—
582#102—534no—
583#102—534no—
584#102—534no—
585#102—534no—
586#102C22×D5314yes—
587#102C22×D5314yescomplemented
588C22⋊C8—534no—
589C22⋊C8—534no—
590#97C22×D5314yescomplemented
591C4×C8—534no—
592C24—21no—
593C24—21no—
594C24—531no—
595C24—1064no—
596C24—1068no—
597C24—1061no—
598C24—1061no—
599C24—4242no—
600C24—4242no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—534no—
607C2×D4—532no—
608C2×D4—532no—
609C2×D4—1064no—
610C2×D4—1064no—
611C2×D4—1064no—
612C2×D4—1064no—
613C2×D4—1068no—
614C2×D4—10616no—
615C2×D4—1068no—
616C2×D4—1068no—
617C2×D4—1064no—
618C2×D4—1061no—
619C2×D4—1061no—
620C2×D4—1062no—
621C2×D4—1062no—
622C2×D4—1062no—
623C2×D4—4242no—
624C2×D4—4242no—
625C2×D4—4242no—
626C2×D4—4242no—
627C2×D4#1171994514yes—
628C2×D4C23×D5312yes—
629C2×D4C23×D5312yes—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—24no—
633C22×C4—24no—
634C22×C4—82no—
635C22×C4—82no—
636C22×C4—531no—
637C22×C4—531no—
638C22×C4—531no—
639C22×C4—532no—
640C22×C4—532no—
641C22×C4—1064no—
642C22×C4—1064no—
643C22×C4—1062no—
644C22×C4—1062no—
645C22×C4—1061no—
646C22×C4—1061no—
647C22×C4—1064no—
648C22×C4—1064no—
649C22×C4—4242no—
650C22×C4—4242no—
651C22×C4—4242no—
652C22×C4—4242no—
653C22×C4D4×D5311yescharacteristic
654C22×C4D4×D5311yescharacteristic
655C22×C4C23×D5311yescharacteristic
656D8—28no—
657D8—1068no—
658D8—1068no—
659D8—1068no—
660C2×C8—22no—
661C2×C8—22no—
662C2×C8—532no—
663C2×C8—532no—
664C2×C8—1062no—
665C2×C8—1062no—
666C2×C8C23×D5312yes—
667C2×C8C23×D5312yes—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—534no—
671C4⋊C4—534no—
672C4⋊C4—532no—
673C4⋊C4—532no—
674C4⋊C4—1064no—
675C4⋊C4—1064no—
676C4⋊C4—1061no—
677C4⋊C4—1061no—
678C4⋊C4C23×D5312yes—
679C4⋊C4C23×D5312yes—
680C22⋊C4—24no—
681C22⋊C4—24no—
682C22⋊C4—534no—
683C22⋊C4—534no—
684C22⋊C4—1064no—
685C22⋊C4—1064no—
686C22⋊C4—1064no—
687C22⋊C4—1064no—
688C22⋊C4—1064no—
689C22⋊C4—1064no—
690C22⋊C4—1064no—
691C42—532no—
692C42—532no—
693C42—1064no—
694C42D4×D5312yes—
695C42C23×D5312yes—
696C23—24no—
697C23—22no—
698C23—22no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—532no—
705C23—10616no—
706C23—1062no—
707C23—1064no—
708C23—1062no—
709C23—1062no—
710C23—1062no—
711C23—1062no—
712C23—4244no—
713C23—4244no—
714C23—42416no—
715C23—2122no—
716C23—2122no—
717C23—2122no—
718C23—2122no—
719C23—2122no—
720C23C2×D4×D5311yescharacteristic
721D4—24no—
722D4—22no—
723D4—22no—
724D4—22no—
725D4—42no—
726D4—534no—
727D4—10616no—
728D4—1064no—
729D4—1062no—
730D4—1062no—
731D4—1062no—
732D4—4244no—
733D4—4244no—
734D4—4244no—
735D4—4244no—
736D4—2122no—
737D4C2×#1171994514yes—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—532no—
747C2×C4—532no—
748C2×C4—532no—
749C2×C4—1062no—
750C2×C4—1062no—
751C2×C4—1062no—
752C2×C4—1064no—
753C2×C4—1062no—
754C2×C4—1062no—
755C2×C4—1062no—
756C2×C4—1062no—
757C2×C4—4244no—
758C2×C4—4244no—
759C2×C4—4244no—
760C2×C4—4244no—
761C2×C4—2122no—
762C2×C4—2122no—
763C2×C4C2×D4×D5312yes—
764C2×C4C2×D4×D5312yes—
765C2×C4C2×D4×D5311yescharacteristic
766C2×C4#41×D5312yes—
767C2×C4C2×#1171994512yes—
768C2×C4C24×D5311yescharacteristic
769C8—22no—
770C8—22no—
771C8—1062no—
772C8—1062no—
773C22—24no—
774C22—48no—
775C22—42no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—84no—
781C22—1062no—
782C22—1062no—
783C22—1062no—
784C22—1064no—
785C22—42416no—
786C22—4244no—
787C22—2122no—
788C22—2122no—
789C22—2122no—
790C22—2124no—
791C22—2128no—
792C22—2122no—
793C22—2122no—
794C22#1681113212yes—
795C22#1681142712yes—
796C22#1681142712yes—
797C22C22×D4×D5311yescharacteristic
798C4—22no—
799C4—22no—
800C4—42no—
801C4—42no—
802C4—1062no—
803C4—1062no—
804C4—1062no—
805C4—2122no—
806C4—2122no—
807C4#1681113212yes—
808C4C2×#41×D5311yescharacteristic
809C4C22×#1171994511yescharacteristic
810C2—44no—
811C2—82no—
812C2—4242no—
813C2—2122no—
814C2—2124no—
815C2#2028495714yesdirect product factor
816C2C2×#1681113211yescharacteristic
817C2C2×#1681142711yescharacteristic
818C2C2×#1681142711yescharacteristic
subgroupG/H
centerC23C2×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC2×C53×#442C2
socleC23×C53C22×D4
hypercenterC2×#442D53
hypocenterC53C2×#3122
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#16811224C2semidirect
2. C2×#16811095C2semidirect
3. #20284957C2direct (N × H)
4. C2×#16810949C2semidirect
5. C2×#16810946C2semidirect
6. C2×#16810925C2semidirect
7. C2×#16810922C2semidirect
8. C2×#16810817C2semidirect
9. C2×#16810816C2semidirect
10. C2×#16810758C2semidirect
11. C2×#16810755C2semidirect
12. C2×#16810736C2semidirect
13. C2×C4×#11719922C2semidirect
14. C2×C4×#11719922C2semidirect
15. C2×#16810685C2semidirect
16. C2×C53×#442C2semidirect
22. #16811224C22semidirect
23. C2×#13133213C22semidirect
24. C2×#13133208C22semidirect
32. #16811095C22semidirect
34. C2×C4×D212C22semidirect
43. #16810949C22semidirect
44. #16810946C22semidirect
45. #16810925C22semidirect
46. #16810922C22semidirect
47. #16810817C22semidirect
48. #16810816C22semidirect
49. #16810758C22semidirect
50. #16810755C22semidirect
51. #16810736C22semidirect
52. C4×#11719922C22semidirect
53. C4×#11719922C22semidirect
54. #16810685C22semidirect
55. C2×#13133150C22semidirect
56. C2×#13133150C22semidirect
57. C2×#13133149C22semidirect
58. C2×#13133146C22semidirect
59. C2×#13133146C22semidirect
61. C2×#13133139C22semidirect
63. C2×#13133138C22semidirect
65. C2×#13133137C22semidirect
68. C2×C4×#88322C22semidirect
71. C2×C4×D4×C53C22semidirect
72. C53×#442C22semidirect
73. C2×#106×C53C22semidirect
75. C2×#102×C53C22semidirect
76. C2×#97×C53C22semidirect
103. #13133213C23semidirect
105. #13133208C23semidirect
117. C4×D212C23semidirect
147. #13133150C23semidirect
148. #13133150C23semidirect
149. #13133149C23semidirect
150. #13133146C23semidirect
151. #13133146C23semidirect
153. #13133139C23semidirect
155. #13133138C23semidirect
157. #13133137C23semidirect
160. C4×#88322C23semidirect
172. C4×D4×C53C23semidirect
178. #106×C53C23semidirect
180. #102×C53C23semidirect
181. #97×C53C23semidirect
413. C2×#442D53semidirect
419. C2×C53#3122semidirect
450. C2×C4×D4C2×D53semidirect
464. #442C2×D53semidirect
471. C2×#106C2×D53semidirect
481. C2×#102C2×D53semidirect
484. C2×#97C2×D53semidirect
486. C53C2×#3122semidirect
545. C4×D4C22×D53semidirect
577. #106C22×D53semidirect
587. #102C22×D53semidirect
590. #97C22×D53semidirect
815. C2#20284957direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168112242
C2×#168110952
#202849572
C2×#168109492
C2×#168109462
C2×#168109252
C2×#168109222
C2×#168108172
C2×#168108162
C2×#168107582
C2×#168107552
C2×#168107362
C2×C4×#117199222
C2×#168106852
C2×C53×#4422
C2×#312253