Finite Group Databasebeta

← C2×#20289187 #28291716

Subgroups — C2×#20289187 #28291716

Order 13568.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289187C2132yesmaximal, direct product factor
2C2×#16811369C214yesmaximal, complemented
3C2×#16811358C211yesmaximal, characteristic, complemented
4C2×#16811356C212yesmaximal, complemented
5C2×#16811348C211yesmaximal, characteristic, complemented
6C2×#16811334C212yesmaximal, complemented
7C2×#16811294C211yesmaximal, characteristic, complemented
8C2×#16811284C212yesmaximal, complemented
9C2×#16811275C212yesmaximal, complemented
10C2×#16811247C212yesmaximal, complemented
11C2×#16811246C212yesmaximal, complemented
12C2×#16811224C212yesmaximal, complemented
13C2×#16811219C214yesmaximal, complemented
14C2×#16811197C212yesmaximal, complemented
15C2×#16811177C211yesmaximal, characteristic, complemented
16C2×#16811174C211yesmaximal, characteristic, complemented
17C2×#16811155C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C53C211yesmaximal, characteristic, complemented
19C22×#11719949C2212yes—
20C22×#11719945C2212yes—
21#16811369C22164yescomplemented
22#16811358C22116yescomplemented
23#16811356C22132yescomplemented
24#16811348C22116yescomplemented
25#16811334C22132yescomplemented
26#16811294C22116yescomplemented
27#16811284C22132yescomplemented
28#16811275C22132yescomplemented
29#16811247C22132yescomplemented
30#16811246C22132yescomplemented
31#16811224C22132yescomplemented
32#16811219C22164yescomplemented
33#16811197C22132yescomplemented
34#16811177C22116yescomplemented
35#16811174C22116yescomplemented
36C2×#13133216C2211yescharacteristic
37C2×#13133215C2211yescharacteristic
38C2×#13133215C2212yes—
39C2×#13133214C2211yescharacteristic
40C2×#13133213C2212yes—
41#16811155C22116yescomplemented
42C2×#13133212C2214yes—
43C2×#13133210C2212yes—
44C2×#13133208C2212yes—
45C2×#13133208C2211yescharacteristic
46C2×#13133207C2212yes—
47C2×#13133207C2214yes—
48C2×#13133206C2212yes—
49C2×#13133206C2212yes—
50C2×#13133206C2214yes—
51C2×#13133205C2212yes—
52C2×#13133204C2211yescharacteristic
53C2×#13133203C2214yes—
54C2×#13133202C2214yes—
55C2×#13133202C2214yes—
56C2×#13133200C2214yes—
57C2×#13133200C2214yes—
58C2×#13133199C2214yes—
59C2×#13133199C2214yes—
60C2×#13133199C2212yes—
61C2×#13133197C2211yescharacteristic
62C2×#13133197C2214yes—
63C2×#13133197C2211yescharacteristic
64C2×#13133195C2212yes—
65C2×#13133193C2211yescharacteristic
66C2×#13133193C2214yes—
67C2×#13133193C2214yes—
68C2×#13133193C2214yes—
69C2×#13133192C2212yes—
70C2×#13133192C2212yes—
71C2×#13133191C2214yes—
72C2×#13133191C2212yes—
73C2×#13133190C2214yes—
74C2×#13133190C2214yes—
75C2×#13133188C2211yescharacteristic
76C2×Q8×Dic53C2212yes—
77C2×C4×Dic106C2211yescharacteristic
78C2×C4×Dic106C2212yes—
79C2×C4×Dic106C2211yescharacteristic
80C2×#13133182C2212yes—
81C2×C4×D212C2212yes—
82C2×#13133179C2212yes—
83C2×#13133179C2212yes—
84C2×#13133179C2212yes—
85C2×#13133179C2212yes—
86C2×C4×C22⋊D53C2214yes—
87C2×C4×C22⋊D53C2212yes—
88C2×#13133176C2212yes—
89C2×#13133174C2212yes—
90C2×C4⋊C4×D53C2214yes—
91C2×C42×D53C2211yescharacteristic
92C23×Q8×C53C2212yes—
93D4×Q8×C53C22116yescomplemented
94C2×C4⋊Q8×C53C2211yescharacteristic
95C2×C4⋊Q8×C53C2212yes—
96C2×C22⋊Q8×C53C2214yes—
97C2×C22⋊Q8×C53C2212yes—
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×D4×C53C2212yes—
100C2×C4×D4×C53C2211yescharacteristic
101C2×#11719949—48no—
102C2×#11719949C23116yes—
103C2×#11719945—48no—
104C2×#11719945C23116yes—
105C22×Dic106C2311yescharacteristic
106C22×Dic106C2311yescharacteristic
107C22×Dic106C2312yes—
108C22×D212C2312yes—
109C22×D212C2312yes—
110C22×D212C2312yes—
111C22×D212C2314yes—
112C22×C22⋊D53C2312yes—
113C22×C22⋊D53C2314yes—
114C22×C22⋊D53C2314yes—
115C22×C4×D53C2311yescharacteristic
116C22×C4×D53C2311yescharacteristic
117C22×C4×D53C2311yescharacteristic
118C22×C4×D53C2314yes—
119C22×C4×D53C2314yes—
120C22×C4×D53C2314yes—
121#13133216C2318yes—
122#13133215C23116yes—
123#13133215C2318yes—
124#13133214C2318yes—
125#13133213C23116yes—
126#13133212C23132yes—
127#13133210C23116yes—
128#13133208C2318yes—
129#13133208C23116yes—
130#13133207C23132yes—
131#13133207C23116yes—
132#13133206C23116yes—
133#13133206C23132yes—
134#13133206C23116yes—
135#13133205C23116yes—
136#13133204C2318yes—
137#13133203C23132yes—
138#13133202C23132yes—
139#13133202C23132yes—
140#13133200C23132yes—
141#13133200C23132yes—
142#13133199C23132yes—
143#13133199C23116yes—
144#13133199C23132yes—
145#13133197C2318yes—
146#13133197C23132yes—
147#13133197C2318yes—
148#13133195C23116yes—
149#13133193C2318yes—
150#13133193C23132yes—
151#13133193C23132yes—
152#13133193C23132yes—
153#13133192C23116yes—
154#13133192C23116yes—
155#13133191C23116yes—
156#13133191C23132yes—
157#13133190C23132yes—
158#13133190C23132yes—
159#13133188C2318yes—
160Q8×Dic53C23116yes—
161C4×Dic106C2318yes—
162C4×Dic106C23116yes—
163C4×Dic106C2318yes—
164#13133182C23116yes—
165C4×D212C23116yes—
166#13133179C23116yes—
167#13133179C23116yes—
168#13133179C23116yes—
169#13133179C23116yes—
170C4×C22⋊D53C23116yes—
171C4×C22⋊D53C23132yes—
172#13133176C23116yes—
173#13133174C23116yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2312yes—
176C2×C4⋊Dic53C2312yes—
177C2×C4⋊Dic53C2311yescharacteristic
178C2×C4⋊Dic53C2311yescharacteristic
179C2×C4⋊Dic53C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2314yes—
182C2×#11719919C2312yes—
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2314yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C2×#11719919C2312yes—
189C4⋊C4×D53C23132yes—
190C2×C22⋊Dic53C2312yes—
191C2×C22⋊Dic53C2312yes—
192C2×C22⋊Dic53C2312yes—
193C2×#11719921C2312yes—
194C2×#11719921C2312yes—
195C2×#11719921C2314yes—
196C2×#11719921C2312yes—
197C2×#11719921C2314yes—
198C2×#11719921C2314yes—
199C2×#11719921C2314yes—
200C2×#11719921C2314yes—
201C2×#11719921C2314yes—
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2312yes—
206C2×C4×Dic53C2312yes—
207C2×C4×Dic53C2314yes—
208C42×D53C2318yes—
209C22×Q8×C53—48no—
210C22×Q8×C53C2311yescharacteristic
211C22×Q8×C53C2312yes—
212C22×Q8×C53C23116yes—
213C22×Q8×C53C2314yes—
214C22×D4×C53C2311yescharacteristic
215C23×C4×C53C2312yes—
216C23×C4×C53C2314yes—
217C4⋊Q8×C53C23116yes—
218C4⋊Q8×C53C2318yes—
219C22⋊Q8×C53C23116yes—
220C22⋊Q8×C53C23132yes—
221C4×Q8×C53C2318yes—
222C4×D4×C53C2318yes—
223C4×D4×C53C23116yes—
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2311yescharacteristic
227C2×C4⋊C4×C53C2312yes—
228C2×C4⋊C4×C53C2314yes—
229C2×C4⋊C4×C53C2312yes—
230C2×C22⋊C4×C53C2312yes—
231C2×C22⋊C4×C53C2314yes—
232C2×C42×C53C2311yescharacteristic
233C2×C42×C53C2312yes—
234C24×C53C2412yes—
235C23×D53C2411yescharacteristic
236C23×D53C2414yes—
237C2×Q8×C53—24no—
238C2×Q8×C53—28no—
239C2×Q8×C53—48no—
240C2×Q8×C53—432no—
241C2×Q8×C53C2414yes—
242C2×Q8×C53C2418yes—
243C2×Q8×C53C24116yes—
244C2×D4×C53—24no—
245C2×D4×C53C2414yes—
246C22×C4×C53—28no—
247C22×C4×C53—48no—
248C22×C4×C53C2411yescharacteristic
249C22×C4×C53C2412yes—
250C22×C4×C53C2412yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2418yes—
254C22×C4×C53C24116yes—
255C22×C4×C53C2411yescharacteristic
256C22×C4×C53C2411yescharacteristic
257C2×C22⋊D53—48no—
258C2×C22⋊D53—44no—
259C2×C22⋊D53—48no—
260C2×C22⋊D53C2418yes—
261C2×C22⋊D53C24116yes—
262C2×C22⋊D53C24116yes—
263C22×Dic53C2412yes—
264C22×Dic53C2412yes—
265C22×Dic53C2411yescharacteristic
266C22×Dic53C2411yescharacteristic
267C22×Dic53C2411yescharacteristic
268C22×Dic53C2412yes—
269C22×Dic53C2412yes—
270#11719949—432no—
271#11719945—432no—
272C2×D212—28no—
273C2×D212—28no—
274C2×D212—44no—
275C2×D212—48no—
276C2×D212C2418yes—
277C2×D212C2418yes—
278C2×D212C2418yes—
279C2×D212C24116yes—
280C2×C4×D53—24no—
281C2×C4×D53—24no—
282C2×C4×D53—42no—
283C2×C4×D53—48no—
284C2×C4×D53—48no—
285C2×C4×D53—48no—
286C2×C4×D53C2414yes—
287C2×C4×D53C2414yes—
288C2×C4×D53C2414yes—
289C2×C4×D53C24116yes—
290C2×C4×D53C24116yes—
291C2×C4×D53C24116yes—
292C2×Dic106—24no—
293C2×Dic106—24no—
294C2×Dic106—44no—
295C2×Dic106C2414yes—
296C2×Dic106C2414yes—
297C2×Dic106C2418yes—
298C4⋊C4×C53C2414yes—
299C4⋊C4×C53C2418yes—
300C4⋊C4×C53C2414yes—
301C4⋊C4×C53C2418yes—
302C4⋊C4×C53C24116yes—
303C4⋊C4×C53C2418yes—
304C22⋊C4×C53C2418yes—
305C22⋊C4×C53C24116yes—
306C42×C53C2414yes—
307C42×C53C2418yes—
308C22⋊Dic53C2418yes—
309C22⋊Dic53C2418yes—
310C22⋊Dic53C2418yes—
311#11719921C2418yes—
312#11719921C2418yes—
313#11719921C24116yes—
314#11719921C2418yes—
315#11719921C24116yes—
316#11719921C24116yes—
317#11719921C24116yes—
318#11719921C24116yes—
319#11719921C24116yes—
320C4⋊Dic53C2418yes—
321C4⋊Dic53C2418yes—
322C4⋊Dic53C2418yes—
323C4⋊Dic53C2414yes—
324C4⋊Dic53C2414yes—
325C4⋊Dic53C24116yes—
326#11719919C2418yes—
327#11719919C24116yes—
328#11719919C2418yes—
329#11719919C2418yes—
330#11719919C2418yes—
331#11719919C24116yes—
332#11719919C2418yes—
333#11719919C2418yes—
334#11719919C2418yes—
335C4×Dic53C2414yes—
336C4×Dic53C2414yes—
337C4×Dic53C2414yes—
338C4×Dic53C2418yes—
339C4×Dic53C2418yes—
340C4×Dic53C24116yes—
341C23×C53—24no—
342C23×C53—24no—
343C23×C53—24no—
344C23×C53C2514yes—
345C23×C53C2511yescharacteristic
346C22×D53—22no—
347C22×D53—28no—
348C22×D53—22no—
349C22×D53—28no—
350C22×D53—28no—
351C22×D53—22no—
352C22×D53C2512yes—
353C22×D53C2518yes—
354Q8×C53—216no—
355Q8×C53—28no—
356Q8×C53—416no—
357D4×C53—28no—
358C2×C4×C53—24no—
359C2×C4×C53—28no—
360C2×C4×C53—24no—
361C2×C4×C53—24no—
362C2×C4×C53—22no—
363C2×C4×C53—216no—
364C2×C4×C53—416no—
365C2×C4×C53H(5,𝔽2)14yes—
366C2×C4×C532−1+414yes—
367C2×C4×C53C2514yes—
368C2×C4×C53C2514yes—
369C2×C4×C53C2512yes—
370C2×C4×C53C2518yes—
371C2×C4×C53C2514yes—
372C2×C4×C53C2512yes—
373C2×C4×C53C2512yes—
374C22⋊D53—416no—
375C22⋊D53—416no—
376C22⋊D53—48no—
377C2×Dic53—24no—
378C2×Dic53—22no—
379C2×Dic53—24no—
380C2×Dic53—22no—
381C2×Dic53—22no—
382C2×Dic53—24no—
383C2×Dic53—24no—
384C2×Dic53C2512yes—
385C2×Dic53C2514yes—
386C2×Dic53C2514yes—
387C2×Dic53C2514yes—
388C2×Dic53C2512yes—
389C2×Dic53C2514yes—
390C2×Dic53C2512yes—
391D212—216no—
392D212—216no—
393D212—48no—
394D212—416no—
395C4×D53—28no—
396C4×D53—28no—
397C4×D53—44no—
398C4×D53—416no—
399C4×D53—416no—
400C4×D53—416no—
401Dic106—28no—
402Dic106—28no—
403Dic106—48no—
404C2×#3554—531nomaximal, Sylow
405C22×C53—24no—
406C22×C53—24no—
407C22×C53—24no—
408C22×C53—48no—
409C22×C53C2×H(5,𝔽2)12yes—
410C22×C53C2×2−1+412yes—
411C22×C53#58512yes—
412C22×C53C2611yescharacteristic
413C2×D53—22no—
414C2×D53—28no—
415C2×D53—22no—
416C2×D53—28no—
417C2×D53—28no—
418C2×D53—22no—
419C2×D53—44no—
420C2×D53—416no—
421C4×C53—24no—
422C4×C53—28no—
423C4×C53—24no—
424C4×C53—24no—
425C4×C53—22no—
426C4×C53C2×H(5,𝔽2)14yes—
427C4×C53C2×2−1+414yes—
428Dic53—24no—
429Dic53—22no—
430Dic53—24no—
431Dic53—22no—
432Dic53—22no—
433Dic53—24no—
434Dic53—24no—
435#3554—5332no—
436C2×#562—534no—
437C2×#559—531no—
438C2×#559—532no—
439C2×#557—531no—
440C2×#554—532no—
441C2×#550—531no—
442C2×D4×Q8D5311yescharacteristic, complemented
443C2×#548—532no—
444C2×#547—532no—
445C2×#542—532no—
446C2×#542—532no—
447C2×#540—532no—
448C2×#539—534no—
449C2×#536—532no—
450C2×#533—531no—
451C2×#532—531no—
452C2×#529—531no—
453C2×C53—44no—
454C2×C53#355414yescomplemented
455C2×C53C22×H(5,𝔽2)11yescharacteristic
456C2×C53C22×2−1+411yescharacteristic
457C2×C53C2×#58511yescharacteristic
458D53—42no—
459D53—48no—
460C22×#41—532no—
461C22×#41—532no—
462C23×Q8C2×D5312yes—
463#562—5364no—
464#559—5316no—
465#559—5332no—
466#557—5316no—
467#554—5332no—
468#550—5316no—
469D4×Q8C2×D53116yescomplemented
470#548—5332no—
471#547—5332no—
472#542—5332no—
473#542—5332no—
474#540—5332no—
475#539—5364no—
476#536—5332no—
477#533—5316no—
478#532—5316no—
479C2×C4⋊Q8—531no—
480C2×C4⋊Q8—532no—
481C2×C4⋊Q8—531no—
482C2×C4⋊Q8C2×D5311yescharacteristic
483C2×C4⋊Q8C2×D5312yes—
484C2×#127—532no—
485C2×#127—531no—
486#529—5316no—
487C2×#126—534no—
488C2×#126—532no—
489C2×#125—531no—
490C2×#125—532no—
491C2×#125—534no—
492C2×#125—532no—
493C2×#124—532no—
494C2×#124—532no—
495C2×#124—534no—
496C2×#124—531no—
497C2×#124—534no—
498C2×#124—532no—
499C2×#123—534no—
500C2×#123—534no—
501C2×#123—534no—
502C2×#123—534no—
503C2×#123—532no—
504C2×#123—534no—
505C2×#123—534no—
506C2×C22⋊Q8—531no—
507C2×C22⋊Q8—534no—
508C2×C22⋊Q8—534no—
509C2×C22⋊Q8—534no—
510C2×C22⋊Q8—531no—
511C2×C22⋊Q8—532no—
512C2×C22⋊Q8—531no—
513C2×C22⋊Q8—534no—
514C2×C22⋊Q8C2×D5314yes—
515C2×C22⋊Q8C2×D5312yes—
516C2×#121—531no—
517C2×#121—534no—
518C2×#121—532no—
519C2×#121—532no—
520C2×#121—532no—
521C2×#121—534no—
522C2×#121—534no—
523C2×C4×Q8—532no—
524C2×C4×Q8—532no—
525C2×C4×Q8—531no—
526C2×C4×Q8—531no—
527C2×C4×Q8—532no—
528C2×C4×Q8C2×D5311yescharacteristic
529C2×C4×D4—532no—
530C2×C4×D4—534no—
531C2×C4×D4—532no—
532C2×C4×D4—532no—
533C2×C4×D4—532no—
534C2×C4×D4—532no—
535C2×C4×D4—532no—
536C2×C4×D4C2×D5311yescharacteristic
537C2×C4×D4C2×D5312yes—
538C2×#117—532no—
539C2×#117—532no—
540C22×C4⋊C4—534no—
541C22×C42—531no—
542C53C2×#355411yescharacteristic, complemented, Sylow
543C2×#41—5316no—
544C2×#41—5316no—
545C2×#41—2128no—
546C2×#41—2128no—
547C22×Q8—48no—
548C22×Q8—531no—
549C22×Q8—531no—
550C22×Q8—532no—
551C22×Q8C22×D5312yes—
552C22×Q8C22×D5311yescharacteristic
553C22×Q8C22×D5314yes—
554C22×Q8C22×D53116yes—
555C22×D4—532no—
556C22×D4—534no—
557C22×D4—534no—
558C22×D4—532no—
559C22×D4—532no—
560C22×D4—532no—
561C22×D4—534no—
562C22×D4C22×D5311yescharacteristic
563C23×C4—531no—
564C23×C4—531no—
565C23×C4—534no—
566C23×C4—534no—
567C23×C4—534no—
568C23×C4—531no—
569C23×C4C22×D5312yes—
570C23×C4C22×D5314yes—
571C4⋊Q8—538no—
572C4⋊Q8—5316no—
573C4⋊Q8—538no—
574C4⋊Q8C22×D5318yes—
575C4⋊Q8C22×D53116yes—
576#127—5316no—
577#127—538no—
578#126—5332no—
579#126—5316no—
580#125—538no—
581#125—5316no—
582#125—5332no—
583#125—5316no—
584#124—5316no—
585#124—5316no—
586#124—5332no—
587#124—538no—
588#124—5332no—
589#124—5316no—
590#123—5332no—
591#123—5332no—
592#123—5332no—
593#123—5332no—
594#123—5316no—
595#123—5332no—
596#123—5332no—
597C22⋊Q8—538no—
598C22⋊Q8—5332no—
599C22⋊Q8—5332no—
600C22⋊Q8—5332no—
601C22⋊Q8—538no—
602C22⋊Q8—538no—
603C22⋊Q8—5316no—
604C22⋊Q8—5332no—
605C22⋊Q8C22×D53132yes—
606C22⋊Q8C22×D53116yes—
607#121—538no—
608#121—5332no—
609#121—5316no—
610#121—5316no—
611#121—5316no—
612#121—5332no—
613#121—5332no—
614C4×Q8—5316no—
615C4×Q8—5316no—
616C4×Q8—538no—
617C4×Q8—538no—
618C4×Q8—5316no—
619C4×Q8C22×D5318yes—
620C4×D4—5316no—
621C4×D4—5332no—
622C4×D4—5316no—
623C4×D4—5316no—
624C4×D4—5316no—
625C4×D4—5316no—
626C4×D4—5316no—
627C4×D4C22×D5318yes—
628C4×D4C22×D53116yes—
629#117—5316no—
630#117—5316no—
631C2×C4⋊C4—532no—
632C2×C4⋊C4—532no—
633C2×C4⋊C4—534no—
634C2×C4⋊C4—532no—
635C2×C4⋊C4—532no—
636C2×C4⋊C4—532no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—531no—
639C2×C4⋊C4—532no—
640C2×C4⋊C4—531no—
641C2×C4⋊C4—532no—
642C2×C4⋊C4—534no—
643C2×C4⋊C4—532no—
644C2×C4⋊C4—534no—
645C2×C4⋊C4—532no—
646C2×C4⋊C4—5332no—
647C2×C4⋊C4C22×D5314yes—
648C2×C4⋊C4C22×D5311yescharacteristic
649C2×C4⋊C4C22×D5311yescharacteristic
650C2×C4⋊C4C22×D5312yes—
651C2×C4⋊C4C22×D5312yes—
652C2×C4⋊C4C22×D5312yes—
653C2×C22⋊C4—532no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—532no—
656C2×C22⋊C4—532no—
657C2×C22⋊C4—532no—
658C2×C22⋊C4—534no—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—534no—
661C2×C22⋊C4—534no—
662C2×C22⋊C4—532no—
663C2×C22⋊C4—534no—
664C2×C22⋊C4—534no—
665C2×C22⋊C4C22×D5312yes—
666C2×C22⋊C4C22×D5314yes—
667C2×C42—531no—
668C2×C42—532no—
669C2×C42—532no—
670C2×C42—531no—
671C2×C42—531no—
672C2×C42—534no—
673C2×C42—538no—
674C2×C42C22×D5312yes—
675C2×C42C22×D5311yescharacteristic
676C24—531no—
677C24—534no—
678C24C23×D5312yes—
679#41—21232no—
680#41—21232no—
681C2×Q8—24no—
682C2×Q8—28no—
683C2×Q8—48no—
684C2×Q8—432no—
685C2×Q8—534no—
686C2×Q8—534no—
687C2×Q8—538no—
688C2×Q8—1064no—
689C2×Q8—1064no—
690C2×Q8—2124no—
691C2×Q8C23×D5318yes—
692C2×Q8C23×D5314yes—
693C2×Q8C23×D53116yes—
694C2×D4—24no—
695C2×D4—538no—
696C2×D4—5316no—
697C2×D4—5316no—
698C2×D4—538no—
699C2×D4—538no—
700C2×D4—538no—
701C2×D4—5316no—
702C2×D4—1068no—
703C2×D4—1068no—
704C2×D4—2124no—
705C2×D4—2128no—
706C2×D4—2124no—
707C2×D4—2128no—
708C2×D4—2128no—
709C2×D4C23×D5314yes—
710C22×C4—28no—
711C22×C4—48no—
712C22×C4—532no—
713C22×C4—532no—
714C22×C4—531no—
715C22×C4—531no—
716C22×C4—531no—
717C22×C4—532no—
718C22×C4—532no—
719C22×C4—534no—
720C22×C4—534no—
721C22×C4—534no—
722C22×C4—5316no—
723C22×C4—5316no—
724C22×C4—5316no—
725C22×C4—1064no—
726C22×C4—1064no—
727C22×C4—2128no—
728C22×C4—2122no—
729C22×C4—2128no—
730C22×C4—2128no—
731C22×C4C23×D5318yes—
732C22×C4C23×D5311yescharacteristic
733C22×C4C23×D5314yes—
734C22×C4C23×D5312yes—
735C22×C4C23×D5312yes—
736C22×C4C23×D5312yes—
737C22×C4C23×D53116yes—
738C22×C4C23×D5311yescharacteristic
739C22×C4C23×D5311yescharacteristic
740C4⋊C4—538no—
741C4⋊C4—538no—
742C4⋊C4—5316no—
743C4⋊C4—538no—
744C4⋊C4—538no—
745C4⋊C4—538no—
746C4⋊C4—538no—
747C4⋊C4—534no—
748C4⋊C4—538no—
749C4⋊C4—534no—
750C4⋊C4—538no—
751C4⋊C4—5316no—
752C4⋊C4—538no—
753C4⋊C4—5316no—
754C4⋊C4—538no—
755C4⋊C4C23×D53116yes—
756C4⋊C4C23×D5314yes—
757C4⋊C4C23×D5314yes—
758C4⋊C4C23×D5318yes—
759C4⋊C4C23×D5318yes—
760C4⋊C4C23×D5318yes—
761C22⋊C4—538no—
762C22⋊C4—538no—
763C22⋊C4—538no—
764C22⋊C4—538no—
765C22⋊C4—538no—
766C22⋊C4—5316no—
767C22⋊C4—5316no—
768C22⋊C4—5316no—
769C22⋊C4—5316no—
770C22⋊C4—538no—
771C22⋊C4—5316no—
772C22⋊C4—5316no—
773C22⋊C4C23×D5318yes—
774C22⋊C4C23×D53116yes—
775C42—534no—
776C42—534no—
777C42—534no—
778C42—538no—
779C42—538no—
780C42—5316no—
781C42C23×D5314yes—
782C42C23×D5318yes—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—532no—
787C23—538no—
788C23—1062no—
789C23—1068no—
790C23—1062no—
791C23—1068no—
792C23—1068no—
793C23—1062no—
794C23C24×D5314yes—
795C23C24×D5311yescharacteristic
796Q8—28no—
797Q8—216no—
798Q8—416no—
799Q8—1068no—
800Q8—1068no—
801Q8—2128no—
802D4—28no—
803D4—10616no—
804D4—10616no—
805D4—2128no—
806D4—21216no—
807D4—2128no—
808D4—21216no—
809D4—21216no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—28no—
813C2×C4—24no—
814C2×C4—22no—
815C2×C4—216no—
816C2×C4—416no—
817C2×C4—534no—
818C2×C4—534no—
819C2×C4—532no—
820C2×C4—532no—
821C2×C4—532no—
822C2×C4—534no—
823C2×C4—534no—
824C2×C4—1062no—
825C2×C4—1064no—
826C2×C4—1062no—
827C2×C4—1064no—
828C2×C4—1064no—
829C2×C4—1062no—
830C2×C4—1064no—
831C2×C4—1068no—
832C2×C4—1068no—
833C2×C4—21216no—
834C2×C4—2124no—
835C2×C4—21216no—
836C2×C4—21216no—
837C2×C4#1313326214yes—
838C2×C4#1313326514yes—
839C2×C4C24×D5312yes—
840C2×C4C24×D5318yes—
841C2×C4C24×D5314yes—
842C2×C4C24×D5314yes—
843C2×C4C24×D5314yes—
844C2×C4C24×D5312yes—
845C2×C4C24×D5312yes—
846C22—24no—
847C22—24no—
848C22—24no—
849C22—48no—
850C22—1062no—
851C22—1068no—
852C22—1062no—
853C22—1068no—
854C22—1068no—
855C22—1062no—
856C22—2124no—
857C22—21216no—
858C22C2×#1313326212yes—
859C22C2×#1313326512yes—
860C22#1681146012yes—
861C22C25×D5311yescharacteristic
862C4—24no—
863C4—24no—
864C4—28no—
865C4—24no—
866C4—22no—
867C4—1062no—
868C4—1064no—
869C4—1062no—
870C4—1064no—
871C4—1064no—
872C4—1062no—
873C4—1064no—
874C4C2×#1313326214yes—
875C4C2×#1313326514yes—
876C2—44no—
877C2—2122no—
878C2—2128no—
879C2#2028918714yesdirect product factor
880C2C22×#1313326211yescharacteristic
881C2C22×#1313326511yescharacteristic
882C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×D4×Q8×C53C2
socleC23×C53C25
hypercenterC2×D4×Q8D53
hypocenterC53C2×#3554
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #20289187C2direct (N × H)
2. C2×#16811369C2semidirect
3. C2×#16811358C2semidirect
4. C2×#16811356C2semidirect
5. C2×#16811348C2semidirect
6. C2×#16811334C2semidirect
7. C2×#16811294C2semidirect
8. C2×#16811284C2semidirect
9. C2×#16811275C2semidirect
10. C2×#16811247C2semidirect
11. C2×#16811246C2semidirect
12. C2×#16811224C2semidirect
13. C2×#16811219C2semidirect
14. C2×#16811197C2semidirect
15. C2×#16811177C2semidirect
16. C2×#16811174C2semidirect
17. C2×#16811155C2semidirect
18. C2×D4×Q8×C53C2semidirect
21. #16811369C22semidirect
22. #16811358C22semidirect
23. #16811356C22semidirect
24. #16811348C22semidirect
25. #16811334C22semidirect
26. #16811294C22semidirect
27. #16811284C22semidirect
28. #16811275C22semidirect
29. #16811247C22semidirect
30. #16811246C22semidirect
31. #16811224C22semidirect
32. #16811219C22semidirect
33. #16811197C22semidirect
34. #16811177C22semidirect
35. #16811174C22semidirect
41. #16811155C22semidirect
93. D4×Q8×C53C22semidirect
442. C2×D4×Q8D53semidirect
454. C2×C53#3554semidirect
469. D4×Q8C2×D53semidirect
542. C53C2×#3554semidirect
879. C2#20289187direct (N × H)

Maximal subgroups

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

subgroupindex
#202891872
C2×#168113692
C2×#168113582
C2×#168113562
C2×#168113482
C2×#168113342
C2×#168112942
C2×#168112842
C2×#168112752
C2×#168112472
C2×#168112462
C2×#168112242
C2×#168112192
C2×#168111972
C2×#168111772
C2×#168111742
C2×#168111552
C2×D4×Q8×C532
C2×#355453