Finite Group Databasebeta

← C2×#20289056 #28291775

Subgroups — C2×#20289056 #28291775

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289056C2132yesmaximal, direct product factor
2C2×#16811374C214yesmaximal, complemented
3C2×Q8×Dic106C211yesmaximal, characteristic, complemented
4C2×#16811338C211yesmaximal, characteristic, complemented
5C2×#16811334C211yesmaximal, characteristic, complemented
6C2×#16811311C212yesmaximal, complemented
7C2×#16811307C212yesmaximal, complemented
8C2×#16811278C212yesmaximal, complemented
9C2×#16811274C212yesmaximal, complemented
10C2×#16811254C212yesmaximal, complemented
11C2×#16811253C212yesmaximal, complemented
12C2×#16811246C212yesmaximal, complemented
13C2×#16811238C212yesmaximal, complemented
14C2×#16811196C214yesmaximal, complemented
15C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
16C2×#16811160C211yesmaximal, characteristic, complemented
17C2×#16811155C211yesmaximal, characteristic, complemented
18C2×C53×#554C211yesmaximal, characteristic, complemented
19C22×#11719945C2214yes—
20C22×Q8×D53C2212yes—
21#16811374C22164yescomplemented
22Q8×Dic106C22116yescomplemented
23#16811338C22116yescomplemented
24#16811334C22116yescomplemented
25#16811311C22132yescomplemented
26#16811307C22132yescomplemented
27#16811278C22132yescomplemented
28#16811274C22132yescomplemented
29#16811254C22132yescomplemented
30#16811253C22132yescomplemented
31#16811246C22132yescomplemented
32#16811238C22132yescomplemented
33#16811196C22164yescomplemented
34C2×#13133217C2212yes—
35C2×#13133217C2211yescharacteristic
36C2×#13133216C2214yes—
37C2×#13133216C2214yes—
38C2×#13133216C2212yes—
39C2×#13133216C2212yes—
40C2×#13133216C2212yes—
41C2×#13133215C2212yes—
42C4⋊Q8×D53C22116yescomplemented
43#16811160C22116yescomplemented
44#16811155C22116yescomplemented
45C2×#13133212C2212yes—
46C2×#13133212C2214yes—
47C2×#13133210C2212yes—
48C2×#13133210C2214yes—
49C2×#13133208C2214yes—
50C2×#13133208C2211yescharacteristic
51C2×#13133208C2211yescharacteristic
52C2×#13133208C2212yes—
53C2×#13133207C2214yes—
54C2×#13133206C2211yescharacteristic
55C2×#13133204C2211yescharacteristic
56C2×#13133203C2214yes—
57C2×#13133203C2214yes—
58C2×#13133202C2212yes—
59C2×#13133202C2214yes—
60C2×#13133200C2214yes—
61C2×#13133199C2212yes—
62C2×#13133199C2214yes—
63C2×#13133199C2214yes—
64C2×#13133197C2214yes—
65C2×#13133197C2212yes—
66C2×#13133197C2211yescharacteristic
67C2×#13133196C2214yes—
68C2×#13133196C2214yes—
69C2×#13133195C2214yes—
70C2×#13133193C2214yes—
71C2×#13133193C2211yescharacteristic
72C2×#13133192C2211yescharacteristic
73C2×#13133191C2212yes—
74C2×#13133188C2212yes—
75C2×#13133188C2211yescharacteristic
76C2×Q8×Dic53C2212yes—
77C2×C4×Dic106C2212yes—
78C2×C4×Dic106C2211yescharacteristic
79C2×C4×D212C2212yes—
80C2×C4×D212C2211yescharacteristic
81C2×#13133179C2212yes—
82C2×C4×C22⋊D53C2212yes—
83C2×#13133176C2212yes—
84C2×#13133176C2212yes—
85C2×#13133175C2214yes—
86C2×#13133175C2212yes—
87C2×#13133174C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C2×C4⋊C4×D53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#554C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#125×C53C2212yes—
95C2×C22⋊Q8×C53C2214yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×D4×C53C2212yes—
99C2×C4×D4×C53C2211yescharacteristic
100C22×C4⋊C4×C53C2212yes—
101C2×#11719945—416no—
102C2×#11719945C23132yes—
103C22×Dic106C2311yescharacteristic
104C22×Dic106C2314yes—
105C22×Dic106C2314yes—
106C22×Dic106C2312yes—
107C2×Q8×D53—48no—
108C2×Q8×D53C23116yes—
109C22×D212C2311yescharacteristic
110C22×D212C2312yes—
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2314yes—
113C22×C4×D53C2311yescharacteristic
114C22×C4×D53C2311yescharacteristic
115C22×C4×D53C2311yescharacteristic
116C22×C4×D53C2314yes—
117C22×C4×D53C2312yes—
118C22×C4×D53C2314yes—
119#13133217C23116yes—
120#13133217C2318yes—
121#13133216C23116yes—
122#13133216C23132yes—
123#13133216C23116yes—
124#13133216C23116yes—
125#13133216C23132yes—
126#13133215C23116yes—
127#13133212C23132yes—
128#13133212C23116yes—
129#13133210C23132yes—
130#13133210C23116yes—
131#13133208C23116yes—
132#13133208C23132yes—
133#13133208C2318yes—
134#13133208C2318yes—
135#13133207C23132yes—
136#13133206C2318yes—
137#13133204C2318yes—
138#13133203C23132yes—
139#13133203C23132yes—
140#13133202C23132yes—
141#13133202C23116yes—
142#13133200C23132yes—
143#13133199C23132yes—
144#13133199C23132yes—
145#13133199C23116yes—
146#13133197C2318yes—
147#13133197C23116yes—
148#13133197C23132yes—
149#13133196C23132yes—
150#13133196C23132yes—
151#13133195C23132yes—
152#13133193C2318yes—
153#13133193C23132yes—
154#13133192C2318yes—
155#13133191C23116yes—
156#13133188C2318yes—
157#13133188C23116yes—
158Q8×Dic53C23116yes—
159C4×Dic106C23116yes—
160C4×Dic106C2318yes—
161C4×D212C23116yes—
162C4×D212C2318yes—
163#13133179C23116yes—
164C4×C22⋊D53C23116yes—
165#13133176C23116yes—
166#13133176C23116yes—
167#13133175C23132yes—
168#13133175C23116yes—
169#13133174C23116yes—
170C2×C4⋊Dic53C2311yescharacteristic
171C2×C4⋊Dic53C2312yes—
172C2×C4⋊Dic53C2312yes—
173C2×C4⋊Dic53C2314yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2312yes—
176C2×C4⋊Dic53C2312yes—
177C2×C4⋊Dic53C2312yes—
178C2×C4⋊Dic53C2314yes—
179C2×#11719919C2314yes—
180C2×#11719919C2314yes—
181C2×#11719919C2314yes—
182C2×#11719919C2312yes—
183C2×#11719919C2312yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2314yes—
187C4⋊C4×D53C23116yes—
188C4⋊C4×D53C23116yes—
189C4⋊C4×D53C23116yes—
190C2×C22⋊Dic53C2312yes—
191C2×C22⋊Dic53C2314yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2312yes—
194C2×#11719921C2312yes—
195C2×#11719921C2312yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×#11719921C2314yes—
199C2×#11719921C2314yes—
200C2×#11719921C2312yes—
201C2×#11719921C2312yes—
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2314yes—
207C2×C4×Dic53C2312yes—
208C42×D53C2318yes—
209C22×Q8×C53C2311yescharacteristic
210C22×Q8×C53C2312yes—
211C22×D4×C53C2311yescharacteristic
212C23×C4×C53C2312yes—
213C23×C4×C53C2314yes—
214C4⋊Q8×C53C2318yes—
215#125×C53C23116yes—
216C22⋊Q8×C53C23116yes—
217C22⋊Q8×C53C23132yes—
218C4×Q8×C53C2318yes—
219C4×D4×C53C23116yes—
220C4×D4×C53C2318yes—
221C2×C4⋊C4×C53C23116yes—
222C2×C4⋊C4×C53C2311yescharacteristic
223C2×C4⋊C4×C53C2314yes—
224C2×C4⋊C4×C53C2312yes—
225C2×C4⋊C4×C53C2311yescharacteristic
226C2×C4⋊C4×C53C2312yes—
227C2×C4⋊C4×C53C2312yes—
228C2×C4⋊C4×C53C2314yes—
229C2×C22⋊C4×C53C2314yes—
230C2×C22⋊C4×C53C2312yes—
231C2×C42×C53C2312yes—
232C2×C42×C53C2311yescharacteristic
233C24×C53C2412yes—
234C23×D53C2412yes—
235C23×D53C2411yescharacteristic
236C2×Q8×C53—24no—
237C2×Q8×C53—44no—
238C2×Q8×C53C2414yes—
239C2×Q8×C53C2418yes—
240C2×D4×C53—24no—
241C2×D4×C53C2414yes—
242C22×C4×C53—28no—
243C22×C4×C53—48no—
244C22×C4×C53C2412yes—
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2412yes—
247C22×C4×C53C2412yes—
248C22×C4×C53C2414yes—
249C22×C4×C53C2418yes—
250C22×C4×C53C24116yes—
251C22×C4×C53C2411yescharacteristic
252C22×C4×C53C2411yescharacteristic
253C2×C22⋊D53—28no—
254C2×C22⋊D53—48no—
255C2×C22⋊D53C2418yes—
256C2×C22⋊D53C24116yes—
257C22×Dic53C2412yes—
258C22×Dic53C2411yescharacteristic
259C22×Dic53C2411yescharacteristic
260C22×Dic53C2412yes—
261C22×Dic53C2411yescharacteristic
262C22×Dic53C2414yes—
263C22×Dic53C2412yes—
264Q8×D53—432no—
265#11719945—464no—
266C2×D212—28no—
267C2×D212—24no—
268C2×D212C2414yes—
269C2×D212C2418yes—
270C2×C4×D53—24no—
271C2×C4×D53—216no—
272C2×C4×D53—24no—
273C2×C4×D53—24no—
274C2×C4×D53—28no—
275C2×C4×D53—48no—
276C2×C4×D53C2414yes—
277C2×C4×D53C2414yes—
278C2×C4×D53C2414yes—
279C2×C4×D53C24116yes—
280C2×C4×D53C2418yes—
281C2×C4×D53C24116yes—
282C2×Dic106—24no—
283C2×Dic106—48no—
284C2×Dic106—44no—
285C2×Dic106—48no—
286C2×Dic106C2414yes—
287C2×Dic106C24116yes—
288C2×Dic106C24116yes—
289C2×Dic106C2418yes—
290C4⋊C4×C53C2414yes—
291C4⋊C4×C53C24116yes—
292C4⋊C4×C53C2418yes—
293C4⋊C4×C53C2414yes—
294C4⋊C4×C53C2418yes—
295C4⋊C4×C53C2418yes—
296C4⋊C4×C53C24116yes—
297C22⋊C4×C53C24116yes—
298C22⋊C4×C53C2418yes—
299C42×C53C2418yes—
300C42×C53C2414yes—
301C22⋊Dic53C2418yes—
302C22⋊Dic53C24116yes—
303C22⋊Dic53C2418yes—
304C22⋊Dic53C2418yes—
305#11719921C2418yes—
306#11719921C2418yes—
307#11719921C2418yes—
308#11719921C2418yes—
309#11719921C24116yes—
310#11719921C24116yes—
311#11719921C2418yes—
312#11719921C2418yes—
313C4⋊Dic53C2414yes—
314C4⋊Dic53C2418yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C24116yes—
317C4⋊Dic53C2414yes—
318C4⋊Dic53C2418yes—
319C4⋊Dic53C2418yes—
320C4⋊Dic53C2418yes—
321C4⋊Dic53C24116yes—
322#11719919C24116yes—
323#11719919C24116yes—
324#11719919C24116yes—
325#11719919C2418yes—
326#11719919C2418yes—
327#11719919C2418yes—
328#11719919C2418yes—
329#11719919C24116yes—
330C4×Dic53C2414yes—
331C4×Dic53C2414yes—
332C4×Dic53C2414yes—
333C4×Dic53C24116yes—
334C4×Dic53C24116yes—
335C4×Dic53C2418yes—
336C23×C53—24no—
337C23×C53—24no—
338C23×C53—24no—
339C23×C53C2514yes—
340C23×C53C2511yescharacteristic
341C22×D53—22no—
342C22×D53—22no—
343C22×D53—24no—
344C22×D53—24no—
345C22×D53—24no—
346C22×D53H(5,𝔽2)14yes—
347C22×D53C2514yes—
348C22×D53C2512yes—
349Q8×C53—28no—
350Q8×C53—48no—
351D4×C53—28no—
352C2×C4×C53—22no—
353C2×C4×C53—24no—
354C2×C4×C53—28no—
355C2×C4×C53—24no—
356C2×C4×C53—24no—
357C2×C4×C53—216no—
358C2×C4×C53—416no—
359C2×C4×C532−1+414yes—
360C2×C4×C532−1+414yes—
361C2×C4×C53C2512yes—
362C2×C4×C53C2514yes—
363C2×C4×C53C2518yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2514yes—
366C2×C4×C53C2512yes—
367C2×C4×C53C2512yes—
368C22⋊D53—216no—
369C22⋊D53—416no—
370C2×Dic53—22no—
371C2×Dic53—28no—
372C2×Dic53—24no—
373C2×Dic53—24no—
374C2×Dic53—22no—
375C2×Dic53—22no—
376C2×Dic53—24no—
377C2×Dic53C2512yes—
378C2×Dic53C2518yes—
379C2×Dic53C2514yes—
380C2×Dic53C2514yes—
381C2×Dic53C2512yes—
382C2×Dic53C2512yes—
383C2×Dic53C2514yes—
384D212—216no—
385D212—28no—
386C4×D53—232no—
387C4×D53—28no—
388C4×D53—28no—
389C4×D53—28no—
390C4×D53—216no—
391C4×D53—416no—
392Dic106—28no—
393Dic106—416no—
394Dic106—416no—
395Dic106—48no—
396C2×#3544—531nomaximal, Sylow
397C22×C53—24no—
398C22×C53—24no—
399C22×C53—24no—
400C22×C53—48no—
401C22×C53C2×H(5,𝔽2)12yes—
402C22×C53C2×2−1+412yes—
403C22×C53C2×2−1+412yes—
404C22×C53C2611yescharacteristic
405C2×D53—22no—
406C2×D53—22no—
407C2×D53—28no—
408C2×D53—24no—
409C2×D53—24no—
410C2×D53—24no—
411C2×D53—48no—
412C2×D53C2×H(5,𝔽2)14yes—
413C4×C53—22no—
414C4×C53—24no—
415C4×C53—28no—
416C4×C53—24no—
417C4×C53—24no—
418C4×C53C2×2−1+414yes—
419C4×C53C2×2−1+414yes—
420Dic53—22no—
421Dic53—28no—
422Dic53—24no—
423Dic53—24no—
424Dic53—22no—
425Dic53—22no—
426Dic53—24no—
427#3544—5332no—
428C2×#563—534no—
429C2×Q82—531no—
430C2×#555—531no—
431C2×#554—531no—
432C2×#554D5311yescharacteristic, complemented
433C2×#552—532no—
434C2×#552—532no—
435C2×#547—532no—
436C2×#547—532no—
437C2×#544—532no—
438C2×#544—532no—
439C2×#542—532no—
440C2×#542—532no—
441C2×#536—534no—
442C22×C4⋊Q8—531no—
443C2×#529—531no—
444C2×#529—531no—
445C2×C53—44no—
446C2×C53#354414yescomplemented
447C2×C53C22×H(5,𝔽2)11yescharacteristic
448C2×C53C22×2−1+411yescharacteristic
449C2×C53C22×2−1+411yescharacteristic
450D53—24no—
451D53—44no—
452C22×#41—534no—
453C23×Q8—532no—
454#563—5364no—
455Q82—5316no—
456#555—5316no—
457#554—5316no—
458#554C2×D53116yescomplemented
459#552—5332no—
460#552—5332no—
461#547—5332no—
462#547—5332no—
463#544—5332no—
464#544—5332no—
465#542—5332no—
466#542—5332no—
467#536—5364no—
468C2×C4⋊Q8—532no—
469C2×C4⋊Q8—5316no—
470C2×C4⋊Q8—532no—
471C2×C4⋊Q8—532no—
472C2×C4⋊Q8—534no—
473C2×C4⋊Q8—534no—
474C2×C4⋊Q8—532no—
475C2×C4⋊Q8—531no—
476C2×C4⋊Q8—532no—
477C2×C4⋊Q8C2×D5311yescharacteristic
478#529—5316no—
479#529—5316no—
480C2×#126—532no—
481C2×#126—534no—
482C2×#126—532no—
483C2×#126—534no—
484C2×#125—531no—
485C2×#125—531no—
486C2×#125—534no—
487C2×#125—532no—
488C2×#125—534no—
489C2×#125C2×D5312yes—
490C2×#124—531no—
491C2×#124—531no—
492C2×#124—534no—
493C2×#124—534no—
494C2×#123—534no—
495C2×#123—532no—
496C2×#123—534no—
497C2×#123—532no—
498C2×#123—534no—
499C2×#123—534no—
500C2×C22⋊Q8—531no—
501C2×C22⋊Q8—534no—
502C2×C22⋊Q8—534no—
503C2×C22⋊Q8—534no—
504C2×C22⋊Q8—531no—
505C2×C22⋊Q8—534no—
506C2×C22⋊Q8—534no—
507C2×C22⋊Q8—532no—
508C2×C22⋊Q8C2×D5314yes—
509C2×C22⋊Q8C2×D5312yes—
510C2×#121—531no—
511C2×#121—532no—
512C2×#121—532no—
513C2×#121—531no—
514C2×C4×Q8—532no—
515C2×C4×Q8—531no—
516C2×C4×Q8—532no—
517C2×C4×Q8C2×D5311yescharacteristic
518C2×C4×D4—532no—
519C2×C4×D4—532no—
520C2×C4×D4—532no—
521C2×C4×D4—531no—
522C2×C4×D4C2×D5311yescharacteristic
523C2×C4×D4C2×D5312yes—
524C2×#117—532no—
525C2×#117—532no—
526C2×#117—534no—
527C2×#117—532no—
528C2×#117—532no—
529C22×C4⋊C4—532no—
530C22×C4⋊C4—532no—
531C22×C4⋊C4—532no—
532C22×C4⋊C4C2×D5312yes—
533C22×C42—531no—
534C53C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—5332no—
536C2×#41—21216no—
537C22×Q8—5316no—
538C22×Q8—531no—
539C22×Q8—534no—
540C22×Q8—534no—
541C22×Q8—532no—
542C22×Q8—2128no—
543C22×Q8C22×D5311yescharacteristic
544C22×Q8C22×D5312yes—
545C22×D4—532no—
546C22×D4—534no—
547C22×D4—531no—
548C22×D4—532no—
549C22×D4C22×D5311yescharacteristic
550C23×C4—534no—
551C23×C4—531no—
552C23×C4—531no—
553C23×C4—532no—
554C23×C4—531no—
555C23×C4—534no—
556C23×C4C22×D5312yes—
557C23×C4C22×D5314yes—
558C4⋊Q8—5316no—
559C4⋊Q8—5316no—
560C4⋊Q8—5316no—
561C4⋊Q8—5332no—
562C4⋊Q8—5332no—
563C4⋊Q8—5316no—
564C4⋊Q8—538no—
565C4⋊Q8—5316no—
566C4⋊Q8C22×D5318yes—
567#126—5316no—
568#126—5332no—
569#126—5316no—
570#126—5332no—
571#125—538no—
572#125—538no—
573#125—5316no—
574#125—5332no—
575#125—5332no—
576#125C22×D53116yes—
577#124—538no—
578#124—538no—
579#124—5332no—
580#124—5332no—
581#123—5332no—
582#123—5316no—
583#123—5332no—
584#123—5316no—
585#123—5332no—
586#123—5332no—
587C22⋊Q8—538no—
588C22⋊Q8—5332no—
589C22⋊Q8—5332no—
590C22⋊Q8—5332no—
591C22⋊Q8—538no—
592C22⋊Q8—5332no—
593C22⋊Q8—5316no—
594C22⋊Q8—5332no—
595C22⋊Q8C22×D53132yes—
596C22⋊Q8C22×D53116yes—
597#121—538no—
598#121—5316no—
599#121—5316no—
600#121—538no—
601C4×Q8—5316no—
602C4×Q8—538no—
603C4×Q8—5316no—
604C4×Q8C22×D5318yes—
605C4×D4—5316no—
606C4×D4—5316no—
607C4×D4—5316no—
608C4×D4—538no—
609C4×D4C22×D5318yes—
610C4×D4C22×D53116yes—
611#117—5316no—
612#117—5316no—
613#117—5332no—
614#117—5316no—
615#117—5316no—
616C2×C4⋊C4—531no—
617C2×C4⋊C4—532no—
618C2×C4⋊C4—532no—
619C2×C4⋊C4—534no—
620C2×C4⋊C4—534no—
621C2×C4⋊C4—534no—
622C2×C4⋊C4—531no—
623C2×C4⋊C4—534no—
624C2×C4⋊C4—532no—
625C2×C4⋊C4—532no—
626C2×C4⋊C4—532no—
627C2×C4⋊C4—532no—
628C2×C4⋊C4—532no—
629C2×C4⋊C4—532no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—534no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4—5316no—
634C2×C4⋊C4—5316no—
635C2×C4⋊C4—5316no—
636C2×C4⋊C4C22×D5312yes—
637C2×C4⋊C4C22×D5312yes—
638C2×C4⋊C4C22×D5311yescharacteristic
639C2×C4⋊C4C22×D5314yes—
640C2×C4⋊C4C22×D53116yes—
641C2×C4⋊C4C22×D5311yescharacteristic
642C2×C4⋊C4C22×D5314yes—
643C2×C4⋊C4C22×D5312yes—
644C2×C22⋊C4—532no—
645C2×C22⋊C4—534no—
646C2×C22⋊C4—532no—
647C2×C22⋊C4—532no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—532no—
650C2×C22⋊C4—532no—
651C2×C22⋊C4—534no—
652C2×C22⋊C4—532no—
653C2×C22⋊C4—534no—
654C2×C22⋊C4—532no—
655C2×C22⋊C4—532no—
656C2×C22⋊C4C22×D5314yes—
657C2×C22⋊C4C22×D5312yes—
658C2×C42—534no—
659C2×C42—531no—
660C2×C42—531no—
661C2×C42—532no—
662C2×C42—534no—
663C2×C42—531no—
664C2×C42—538no—
665C2×C42C22×D5312yes—
666C2×C42C22×D5311yescharacteristic
667C24—531no—
668C24—532no—
669C24C23×D5312yes—
670#41—21264no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—534no—
674C2×Q8—5316no—
675C2×Q8—5316no—
676C2×Q8—538no—
677C2×Q8—1064no—
678C2×Q8—2128no—
679C2×Q8—2124no—
680C2×Q8—2128no—
681C2×Q8—21232no—
682C2×Q8C23×D5314yes—
683C2×Q8C23×D5318yes—
684C2×D4—24no—
685C2×D4—538no—
686C2×D4—5316no—
687C2×D4—534no—
688C2×D4—538no—
689C2×D4—1068no—
690C2×D4—1068no—
691C2×D4—1064no—
692C2×D4—2128no—
693C2×D4C23×D5314yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—532no—
697C22×C4—531no—
698C22×C4—532no—
699C22×C4—531no—
700C22×C4—531no—
701C22×C4—534no—
702C22×C4—532no—
703C22×C4—534no—
704C22×C4—534no—
705C22×C4—534no—
706C22×C4—5316no—
707C22×C4—538no—
708C22×C4—5316no—
709C22×C4—1064no—
710C22×C4—10616no—
711C22×C4—1064no—
712C22×C4—1064no—
713C22×C4—1068no—
714C22×C4—2128no—
715C22×C4C23×D5318yes—
716C22×C4C23×D5312yes—
717C22×C4C23×D5312yes—
718C22×C4C23×D5311yescharacteristic
719C22×C4C23×D5312yes—
720C22×C4C23×D5314yes—
721C22×C4C23×D53116yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724C4⋊C4—534no—
725C4⋊C4—538no—
726C4⋊C4—538no—
727C4⋊C4—5316no—
728C4⋊C4—5316no—
729C4⋊C4—5316no—
730C4⋊C4—534no—
731C4⋊C4—5316no—
732C4⋊C4—538no—
733C4⋊C4—538no—
734C4⋊C4—538no—
735C4⋊C4—538no—
736C4⋊C4—538no—
737C4⋊C4—538no—
738C4⋊C4—538no—
739C4⋊C4—5316no—
740C4⋊C4—5316no—
741C4⋊C4C23×D5318yes—
742C4⋊C4C23×D5318yes—
743C4⋊C4C23×D5314yes—
744C4⋊C4C23×D53116yes—
745C4⋊C4C23×D5314yes—
746C4⋊C4C23×D53116yes—
747C4⋊C4C23×D5318yes—
748C22⋊C4—538no—
749C22⋊C4—5316no—
750C22⋊C4—538no—
751C22⋊C4—538no—
752C22⋊C4—538no—
753C22⋊C4—538no—
754C22⋊C4—538no—
755C22⋊C4—5316no—
756C22⋊C4—538no—
757C22⋊C4—5316no—
758C22⋊C4—538no—
759C22⋊C4—538no—
760C22⋊C4C23×D53116yes—
761C22⋊C4C23×D5318yes—
762C42—534no—
763C42—534no—
764C42—534no—
765C42—5316no—
766C42—538no—
767C42—5316no—
768C42C23×D5314yes—
769C42C23×D5318yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—534no—
774C23—532no—
775C23—534no—
776C23—1062no—
777C23—1062no—
778C23—1064no—
779C23—1064no—
780C23—1064no—
781C23C24×D5314yes—
782C23C24×D5311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—1068no—
786Q8—21216no—
787Q8—2128no—
788Q8—21216no—
789D4—28no—
790D4—10616no—
791D4—10616no—
792D4—1068no—
793D4—21216no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—534no—
802C2×C4—532no—
803C2×C4—532no—
804C2×C4—534no—
805C2×C4—532no—
806C2×C4—538no—
807C2×C4—534no—
808C2×C4—1068no—
809C2×C4—10632no—
810C2×C4—1068no—
811C2×C4—1062no—
812C2×C4—1064no—
813C2×C4—1062no—
814C2×C4—1064no—
815C2×C4—1062no—
816C2×C4—1064no—
817C2×C4—1068no—
818C2×C4—1068no—
819C2×C4—10616no—
820C2×C4—21216no—
821C2×C4#1313326414yes—
822C2×C4#1313326514yes—
823C2×C4C24×D5314yes—
824C2×C4C24×D5314yes—
825C2×C4C24×D5312yes—
826C2×C4C24×D5314yes—
827C2×C4C24×D5318yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—534no—
835C22—1068no—
836C22—1062no—
837C22—1062no—
838C22—1064no—
839C22—1064no—
840C22—1064no—
841C22—2128no—
842C22H(5,𝔽2)×D5312yes—
843C22C2×#1313326412yes—
844C22C2×#1313326512yes—
845C22C25×D5311yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1068no—
852C4—1062no—
853C4—1064no—
854C4—1062no—
855C4—1062no—
856C4—1064no—
857C4—1064no—
858C4C2×#1313326414yes—
859C4C2×#1313326514yes—
860C2—44no—
861C2—1064no—
862C2—2124no—
863C2#2028905614yesdirect product factor
864C2C2×H(5,𝔽2)×D5311yescharacteristic
865C2C22×#1313326411yescharacteristic
866C2C22×#1313326511yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#554C2
socleC23×C53C25
hypercenterC2×#554D53
hypocenterC53C2×#3544
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20289056C2direct (N × H)
2. C2×#16811374C2semidirect
3. C2×Q8×Dic106C2semidirect
4. C2×#16811338C2semidirect
5. C2×#16811334C2semidirect
6. C2×#16811311C2semidirect
7. C2×#16811307C2semidirect
8. C2×#16811278C2semidirect
9. C2×#16811274C2semidirect
10. C2×#16811254C2semidirect
11. C2×#16811253C2semidirect
12. C2×#16811246C2semidirect
13. C2×#16811238C2semidirect
14. C2×#16811196C2semidirect
15. C2×C4⋊Q8×D53C2semidirect
16. C2×#16811160C2semidirect
17. C2×#16811155C2semidirect
18. C2×C53×#554C2semidirect
21. #16811374C22semidirect
22. Q8×Dic106C22semidirect
23. #16811338C22semidirect
24. #16811334C22semidirect
25. #16811311C22semidirect
26. #16811307C22semidirect
27. #16811278C22semidirect
28. #16811274C22semidirect
29. #16811254C22semidirect
30. #16811253C22semidirect
31. #16811246C22semidirect
32. #16811238C22semidirect
33. #16811196C22semidirect
42. C4⋊Q8×D53C22semidirect
43. #16811160C22semidirect
44. #16811155C22semidirect
92. C53×#554C22semidirect
432. C2×#554D53semidirect
446. C2×C53#3544semidirect
458. #554C2×D53semidirect
534. C53C2×#3544semidirect
863. C2#20289056direct (N × H)

Maximal subgroups

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

subgroupindex
#202890562
C2×#168113742
C2×Q8×Dic1062
C2×#168113382
C2×#168113342
C2×#168113112
C2×#168113072
C2×#168112782
C2×#168112742
C2×#168112542
C2×#168112532
C2×#168112462
C2×#168112382
C2×#168111962
C2×C4⋊Q8×D532
C2×#168111602
C2×#168111552
C2×C53×#5542
C2×#354453