Finite Group Databasebeta

← C2×#20288729 #28292361

Subgroups — C2×#20288729 #28292361

Order 13568.

7118 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#20288729C2132yesmaximal, direct product factor
2C2×Q8×Dic106C211yesmaximal, characteristic, complemented
3C2×#16811346C212yesmaximal, complemented
4C2×#16811344C212yesmaximal, complemented
5C2×#16811340C214yesmaximal, complemented
6C2×#16811338C211yesmaximal, characteristic, complemented
7C2×#16811336C212yesmaximal, complemented
8C2×#16811288C211yesmaximal, characteristic, complemented
9C2×#16811281C212yesmaximal, complemented
10C2×#16811242C212yesmaximal, complemented
11C2×#16811239C214yesmaximal, complemented
12C2×#16811178C211yesmaximal, characteristic, complemented
13C2×#16811176C212yesmaximal, complemented
14C2×#16811160C211yesmaximal, characteristic, complemented
15C2×#16811159C212yesmaximal, complemented
16C2×#16811099C212yesmaximal, complemented
17C2×C4×#11719947C211yesmaximal, characteristic, complemented
18C2×C53×#556C211yesmaximal, characteristic, complemented
19C22×#11719947C2211yescharacteristic
20C22×Q8×D53C2212yes—
21Q8×Dic106C22116yescomplemented
22#16811346C22132yescomplemented
23#16811344C22132yescomplemented
24#16811340C22164yescomplemented
25#16811338C22116yescomplemented
26#16811336C22132yescomplemented
27#16811288C22116yescomplemented
28#16811281C22132yescomplemented
29#16811242C22132yescomplemented
30#16811239C22164yescomplemented
31#16811178C22116yescomplemented
32#16811176C22132yescomplemented
33C2×#13133217C2211yescharacteristic
34C2×#13133217C2212yes—
35C2×#13133216C2212yes—
36C2×#13133216C2212yes—
37C2×#13133216C2214yes—
38#16811160C22116yescomplemented
39#16811159C22132yescomplemented
40C2×#13133212C2212yes—
41C2×#13133212C2214yes—
42C2×#13133212C2214yes—
43C2×#13133210C2214yes—
44C2×#13133208C2211yescharacteristic
45C2×#13133208C2212yes—
46C2×#13133206C2211yescharacteristic
47C2×#13133205C2214yes—
48C2×#13133203C2214yes—
49C2×#13133203C2214yes—
50C2×#13133203C2214yes—
51C2×#13133202C2212yes—
52C2×#13133201C2214yes—
53C2×#13133197C2212yes—
54C2×#13133195C2214yes—
55C2×#13133194C2214yes—
56C2×#13133194C2214yes—
57C2×#13133193C2212yes—
58C2×#13133193C2211yescharacteristic
59C2×#13133193C2212yes—
60C2×#13133192C2211yescharacteristic
61C2×#13133191C2212yes—
62C2×#13133190C2214yes—
63C2×#13133188C2212yes—
64#16811099C22132yescomplemented
65C4×#11719947C22116yescomplemented
66C2×Q8×Dic53C2212yes—
67C2×Q8×Dic53C2212yes—
68C2×C4×Dic106C2214yes—
69C2×C4×Dic106C2214yes—
70C2×C4×Dic106C2211yescharacteristic
71C2×C4×Dic106C2212yes—
72C2×#13133182C2212yes—
73C2×#13133182C2214yes—
74C2×#13133182C2211yescharacteristic
75C2×C4×D212C2212yes—
76C2×C4×D212C2211yescharacteristic
77C2×D4×Dic53C2211yescharacteristic
78C2×#13133179C2212yes—
79C2×C4×C22⋊D53C2212yes—
80C2×#13133177C2214yes—
81C2×#13133177C2212yes—
82C2×#13133176C2212yes—
83C2×#13133175C2212yes—
84C2×#13133175C2211yescharacteristic
85C2×#13133175C2212yes—
86C2×#13133175C2214yes—
87C2×#13133174C2214yes—
88C2×#13133174C2212yes—
89C2×#13133173C2212yes—
90C22×C4×Dic53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#556C22116yescomplemented
93C2×C4⋊Q8×C53C2211yescharacteristic
94C2×#126×C53C2214yes—
95C2×#124×C53C2212yes—
96C2×C22⋊Q8×C53C2212yes—
97C2×C4×Q8×C53C2212yes—
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×D4×C53C2211yescharacteristic
100C2×#117×C53C2212yes—
101C2×#11719947—28no—
102C2×#11719947C2318yes—
103C22×Dic106C2314yes—
104C22×Dic106C2312yes—
105C22×Dic106C2314yes—
106C22×Dic106C2311yescharacteristic
107C2×Q8×D53—216no—
108C2×Q8×D53C23116yes—
109C22×D212C2311yescharacteristic
110C22×D212C2312yes—
111C22×C22⋊D53C2312yes—
112C22×C22⋊D53C2314yes—
113C23×Dic53C2312yes—
114C23×Dic53C2312yes—
115C22×C4×D53C2311yescharacteristic
116C22×C4×D53C2311yescharacteristic
117C22×C4×D53C2314yes—
118C22×C4×D53C2312yes—
119C22×C4×D53C2311yescharacteristic
120#13133217C2318yes—
121#13133217C23116yes—
122#13133216C23116yes—
123#13133216C23116yes—
124#13133216C23132yes—
125#13133212C23116yes—
126#13133212C23132yes—
127#13133212C23132yes—
128#13133210C23132yes—
129#13133208C23116yes—
130#13133208C2318yes—
131#13133206C2318yes—
132#13133205C23132yes—
133#13133203C23132yes—
134#13133203C23132yes—
135#13133203C23132yes—
136#13133202C23116yes—
137#13133201C23132yes—
138#13133197C23116yes—
139#13133195C23132yes—
140#13133194C23132yes—
141#13133194C23132yes—
142#13133193C23116yes—
143#13133193C23116yes—
144#13133193C2318yes—
145#13133192C2318yes—
146#13133191C23116yes—
147#13133190C23132yes—
148#13133188C23116yes—
149Q8×Dic53C23116yes—
150Q8×Dic53C23116yes—
151C4×Dic106C23116yes—
152C4×Dic106C2318yes—
153C4×Dic106C23132yes—
154C4×Dic106C23132yes—
155#13133182C23116yes—
156#13133182C23132yes—
157#13133182C2318yes—
158C4×D212C23116yes—
159C4×D212C2318yes—
160D4×Dic53C2318yes—
161#13133179C23116yes—
162C4×C22⋊D53C23116yes—
163#13133177C23132yes—
164#13133177C23116yes—
165#13133176C23116yes—
166#13133175C23116yes—
167#13133175C23116yes—
168#13133175C2318yes—
169#13133175C23132yes—
170#13133174C23132yes—
171#13133174C23116yes—
172#13133173C23116yes—
173C2×C4⋊Dic53C2312yes—
174C2×C4⋊Dic53C2311yescharacteristic
175C2×C4⋊Dic53C2312yes—
176C2×C4⋊Dic53C2314yes—
177C2×C4⋊Dic53C2311yescharacteristic
178C2×C4⋊Dic53C2312yes—
179C2×C4⋊Dic53C2314yes—
180C2×#11719919C2312yes—
181C2×#11719919C2312yes—
182C2×#11719919C2312yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C2×#11719919C2314yes—
186C2×#11719919C2314yes—
187C2×C22⋊Dic53C2312yes—
188C2×C22⋊Dic53C2314yes—
189C2×#11719921C2312yes—
190C2×#11719921C2314yes—
191C2×#11719921C2312yes—
192C2×#11719921C2312yes—
193C2×#11719921C2314yes—
194C2×#11719921C2312yes—
195C2×#11719921C2314yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×C4×Dic53C2311yescharacteristic
199C2×C4×Dic53C2311yescharacteristic
200C2×C4×Dic53C2311yescharacteristic
201C2×C4×Dic53C2312yes—
202C2×C4×Dic53C2312yes—
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C23116yes—
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2314yes—
207C2×C4×Dic53C2314yes—
208C42×D53C2318yes—
209C22×Q8×C53C2311yescharacteristic
210C22×Q8×C53C2312yes—
211C22×D4×C53C2311yescharacteristic
212C23×C4×C53C2312yes—
213C4⋊Q8×C53C2318yes—
214#126×C53C23132yes—
215#124×C53C23116yes—
216C22⋊Q8×C53C23116yes—
217C4×Q8×C53C23116yes—
218C4×Q8×C53C2318yes—
219C4×D4×C53C2318yes—
220#117×C53C23116yes—
221C2×C4⋊C4×C53C2311yescharacteristic
222C2×C4⋊C4×C53C2312yes—
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊C4×C53C2314yes—
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2312yes—
227C2×C22⋊C4×C53C2314yes—
228C2×C22⋊C4×C53C2312yes—
229C2×C22⋊C4×C53C2314yes—
230C2×C42×C53C2314yes—
231C2×C42×C53C2311yescharacteristic
232C2×C42×C53C2312yes—
233C24×C53C2412yes—
234C23×D53C2412yes—
235C23×D53C2411yescharacteristic
236C2×Q8×C53—28no—
237C2×Q8×C53—24no—
238C2×Q8×C53C2414yes—
239C2×Q8×C53C2418yes—
240C2×D4×C53—24no—
241C2×D4×C53C2414yes—
242C22×C4×C53—28no—
243C22×C4×C53C2412yes—
244C22×C4×C53C2412yes—
245C22×C4×C53C2411yescharacteristic
246C22×C4×C53C2412yes—
247C22×C4×C53C2414yes—
248C22×C4×C53C2418yes—
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2411yescharacteristic
251C2×C22⋊D53—28no—
252C2×C22⋊D53—48no—
253C2×C22⋊D53C2418yes—
254C2×C22⋊D53C24116yes—
255C22×Dic53—28no—
256C22×Dic53—44no—
257C22×Dic53C2411yescharacteristic
258C22×Dic53C2411yescharacteristic
259C22×Dic53C2411yescharacteristic
260C22×Dic53C2414yes—
261C22×Dic53C2412yes—
262C22×Dic53C2412yes—
263C22×Dic53C2418yes—
264C22×Dic53C2418yes—
265C22×Dic53C2412yes—
266Q8×D53—264no—
267#11719947—232no—
268C2×D212—24no—
269C2×D212—44no—
270C2×D212C2414yes—
271C2×D212C2418yes—
272C2×C4×D53—28no—
273C2×C4×D53—24no—
274C2×C4×D53—24no—
275C2×C4×D53—216no—
276C2×C4×D53—42no—
277C2×C4×D53C2414yes—
278C2×C4×D53C2414yes—
279C2×C4×D53C24116yes—
280C2×C4×D53C2418yes—
281C2×C4×D53C2414yes—
282C2×Dic106—216no—
283C2×Dic106—48no—
284C2×Dic106—44no—
285C2×Dic106#4118yes—
286C2×Dic106C24116yes—
287C2×Dic106C2418yes—
288C2×Dic106C24116yes—
289C2×Dic106C2414yes—
290C4⋊C4×C53C2414yes—
291C4⋊C4×C53C2418yes—
292C4⋊C4×C53C2414yes—
293C4⋊C4×C53C24116yes—
294C4⋊C4×C53C2418yes—
295C4⋊C4×C53C2418yes—
296C22⋊C4×C53C24116yes—
297C22⋊C4×C53C2418yes—
298C22⋊C4×C53C24116yes—
299C42×C53C24116yes—
300C42×C53C2414yes—
301C42×C53C2418yes—
302C22⋊Dic53C2418yes—
303C22⋊Dic53C24116yes—
304#11719921C2418yes—
305#11719921C24116yes—
306#11719921C2418yes—
307#11719921C2418yes—
308#11719921C24116yes—
309#11719921C2418yes—
310#11719921C24116yes—
311#11719921C2418yes—
312#11719921C2418yes—
313C4⋊Dic53C2418yes—
314C4⋊Dic53C2414yes—
315C4⋊Dic53C2418yes—
316C4⋊Dic53C24116yes—
317C4⋊Dic53C2414yes—
318C4⋊Dic53C2418yes—
319C4⋊Dic53C24116yes—
320#11719919C2418yes—
321#11719919C2418yes—
322#11719919C2418yes—
323#11719919C24116yes—
324#11719919C2418yes—
325#11719919C24116yes—
326#11719919C24116yes—
327C4×Dic53C2414yes—
328C4×Dic53C2414yes—
329C4×Dic53C2414yes—
330C4×Dic53C2418yes—
331C4×Dic53C2418yes—
332C4×Dic53C2418yes—
333C4×Dic53C24116yes—
334C4×Dic53C24116yes—
335C4×Dic53C24116yes—
336C23×C53—24no—
337C23×C53—24no—
338C23×C53—24no—
339C23×C53C2514yes—
340C23×C53C2511yescharacteristic
341C22×D53—24no—
342C22×D53—22no—
343C22×D53—22no—
344C22×D53—24no—
345C22×D53—22no—
346C22×D53—24no—
347C22×D53C2514yes—
348C22×D53C2512yes—
349Q8×C53—216no—
350Q8×C53—28no—
351D4×C53—28no—
352C2×C4×C53—28no—
353C2×C4×C53—24no—
354C2×C4×C53—24no—
355C2×C4×C53—22no—
356C2×C4×C53—24no—
357C2×C4×C53—216no—
358C2×C4×C53C2×#4114yes—
359C2×C4×C532−1+414yes—
360C2×C4×C53C2512yes—
361C2×C4×C53C2514yes—
362C2×C4×C53C2518yes—
363C2×C4×C53C2514yes—
364C2×C4×C53C2514yes—
365C2×C4×C53C2512yes—
366C2×C4×C53C2512yes—
367C22⋊D53—216no—
368C22⋊D53—416no—
369C2×Dic53—24no—
370C2×Dic53—22no—
371C2×Dic53—22no—
372C2×Dic53—24no—
373C2×Dic53—28no—
374C2×Dic53—22no—
375C2×Dic53—216no—
376C2×Dic53—48no—
377C2×Dic53C2×#4118yes—
378C2×Dic53C2514yes—
379C2×Dic53C2514yes—
380C2×Dic53C2518yes—
381C2×Dic53C2512yes—
382C2×Dic53C2512yes—
383C2×Dic53C2512yes—
384C2×Dic53C2514yes—
385D212—28no—
386D212—48no—
387C4×D53—28no—
388C4×D53—216no—
389C4×D53—28no—
390C4×D53—232no—
391C4×D53—44no—
392Dic106—232no—
393Dic106—416no—
394Dic106—48no—
395Dic106C2×#41116yes—
396C2×#3518—531nomaximal, Sylow
397C22×C53—24no—
398C22×C53—24no—
399C22×C53—24no—
400C22×C53—48no—
401C22×C53C22×#4112yes—
402C22×C53C2×2−1+412yes—
403C22×C53#58512yes—
404C22×C53C2611yescharacteristic
405C2×D53—24no—
406C2×D53—22no—
407C2×D53—22no—
408C2×D53—24no—
409C2×D53—22no—
410C2×D53—24no—
411C2×D53—48no—
412C2×D53—44no—
413C4×C53—28no—
414C4×C53—24no—
415C4×C53—24no—
416C4×C53—22no—
417C4×C53—24no—
418C4×C53C22×#4114yes—
419C4×C53C2×2−1+414yes—
420Dic53—24no—
421Dic53—22no—
422Dic53—22no—
423Dic53—24no—
424Dic53—28no—
425Dic53—22no—
426Dic53C22×#4118yes—
427#3518—5332no—
428C2×Q82—531no—
429C2×#556—534no—
430C2×#556—532no—
431C2×#556—532no—
432C2×#556D5311yescharacteristic, complemented
433C2×#555—531no—
434C2×#555—532no—
435C2×D4×Q8—531no—
436C2×#548—532no—
437C2×#542—534no—
438C2×#542—532no—
439C2×#533—531no—
440C2×#533—532no—
441C2×#529—532no—
442C2×#529—531no—
443C2×#519—532no—
444C2×C4×#41—531no—
445C2×C53—44no—
446C2×C53#351814yescomplemented
447C2×C53C23×#4111yescharacteristic
448C2×C53C22×2−1+411yescharacteristic
449C2×C53C2×#58511yescharacteristic
450D53—44no—
451D53—42no—
452C22×#41—531no—
453C23×Q8—532no—
454Q82—5316no—
455#556—5364no—
456#556—5332no—
457#556—5332no—
458#556C2×D53116yescomplemented
459#555—5316no—
460#555—5332no—
461D4×Q8—5316no—
462#548—5332no—
463#542—5364no—
464#542—5332no—
465#533—5316no—
466#533—5332no—
467C2×C4⋊Q8—532no—
468C2×C4⋊Q8—532no—
469C2×C4⋊Q8—534no—
470C2×C4⋊Q8—531no—
471C2×C4⋊Q8—532no—
472C2×C4⋊Q8C2×D5311yescharacteristic
473#529—5332no—
474#529—5316no—
475C2×#126—532no—
476C2×#126—534no—
477C2×#126—534no—
478C2×#126—534no—
479C2×#126C2×D5314yes—
480C2×#125—531no—
481C2×#125—532no—
482C2×#124—531no—
483C2×#124—534no—
484C2×#124—534no—
485C2×#124—534no—
486C2×#124—534no—
487C2×#124C2×D5312yes—
488C2×#123—532no—
489C2×#123—534no—
490C2×C22⋊Q8—531no—
491C2×C22⋊Q8—532no—
492C2×C22⋊Q8—532no—
493C2×C22⋊Q8—534no—
494C2×C22⋊Q8—532no—
495C2×C22⋊Q8—534no—
496C2×C22⋊Q8—534no—
497C2×C22⋊Q8C2×D5312yes—
498C2×#121—532no—
499C2×#121—532no—
500C2×#121—531no—
501C2×#121—534no—
502#519—5332no—
503C4×#41—5316no—
504C2×C4×Q8—532no—
505C2×C4×Q8—532no—
506C2×C4×Q8—531no—
507C2×C4×Q8—534no—
508C2×C4×Q8—532no—
509C2×C4×Q8—531no—
510C2×C4×Q8—534no—
511C2×C4×Q8—532no—
512C2×C4×Q8—534no—
513C2×C4×Q8C2×D5312yes—
514C2×C4×Q8C2×D5311yescharacteristic
515C2×C4×D4—531no—
516C2×C4×D4—532no—
517C2×C4×D4—532no—
518C2×C4×D4—532no—
519C2×C4×D4—534no—
520C2×C4×D4—532no—
521C2×C4×D4—531no—
522C2×C4×D4C2×D5311yescharacteristic
523C2×#117—532no—
524C2×#117—531no—
525C2×#117—534no—
526C2×#117—532no—
527C2×#117—532no—
528C2×#117—532no—
529C2×#117—532no—
530C2×#117—534no—
531C2×#117C2×D5312yes—
532C22×C42—532no—
533C22×C42—531no—
534C53C2×#351811yescharacteristic, complemented, Sylow
535C2×#41—538no—
536C2×#41—1068no—
537C22×Q8—5316no—
538C22×Q8—531no—
539C22×Q8—534no—
540C22×Q8—532no—
541C22×Q8—534no—
542C22×Q8—10616no—
543C22×Q8C22×D5311yescharacteristic
544C22×Q8C22×D5312yes—
545C22×D4—532no—
546C22×D4—534no—
547C22×D4—531no—
548C22×D4—532no—
549C22×D4C22×D5311yescharacteristic
550C23×C4—532no—
551C23×C4—532no—
552C23×C4—534no—
553C23×C4—532no—
554C23×C4—531no—
555C23×C4—531no—
556C23×C4—531no—
557C23×C4C22×D5312yes—
558C4⋊Q8—5316no—
559C4⋊Q8—5316no—
560C4⋊Q8—5332no—
561C4⋊Q8—538no—
562C4⋊Q8—5316no—
563C4⋊Q8C22×D5318yes—
564#126—5316no—
565#126—5332no—
566#126—5332no—
567#126—5332no—
568#126C22×D53132yes—
569#125—538no—
570#125—5316no—
571#124—538no—
572#124—5332no—
573#124—5332no—
574#124—5332no—
575#124—5332no—
576#124C22×D53116yes—
577#123—5316no—
578#123—5332no—
579C22⋊Q8—538no—
580C22⋊Q8—5316no—
581C22⋊Q8—5316no—
582C22⋊Q8—5316no—
583C22⋊Q8—5332no—
584C22⋊Q8—5332no—
585C22⋊Q8—5332no—
586C22⋊Q8C22×D53116yes—
587#121—5316no—
588#121—5316no—
589#121—538no—
590#121—5332no—
591C4×Q8—5316no—
592C4×Q8—5316no—
593C4×Q8—538no—
594C4×Q8—5332no—
595C4×Q8—5316no—
596C4×Q8—538no—
597C4×Q8—5332no—
598C4×Q8—5316no—
599C4×Q8—5332no—
600C4×Q8C22×D53116yes—
601C4×Q8C22×D5318yes—
602C4×D4—538no—
603C4×D4—5316no—
604C4×D4—5316no—
605C4×D4—5316no—
606C4×D4—5332no—
607C4×D4—5316no—
608C4×D4—538no—
609C4×D4C22×D5318yes—
610#117—5316no—
611#117—538no—
612#117—5332no—
613#117—5316no—
614#117—5316no—
615#117—5316no—
616#117—5316no—
617#117—5332no—
618#117C22×D53116yes—
619C2×C4⋊C4—532no—
620C2×C4⋊C4—531no—
621C2×C4⋊C4—532no—
622C2×C4⋊C4—532no—
623C2×C4⋊C4—531no—
624C2×C4⋊C4—534no—
625C2×C4⋊C4—532no—
626C2×C4⋊C4—532no—
627C2×C4⋊C4—534no—
628C2×C4⋊C4—532no—
629C2×C4⋊C4—534no—
630C2×C4⋊C4—532no—
631C2×C4⋊C4—534no—
632C2×C4⋊C4—534no—
633C2×C4⋊C4C22×D5311yescharacteristic
634C2×C4⋊C4C22×D5312yes—
635C2×C4⋊C4C22×D5314yes—
636C2×C4⋊C4C22×D5311yescharacteristic
637C2×C4⋊C4C22×D5312yes—
638C2×C4⋊C4C22×D5312yes—
639C2×C22⋊C4—532no—
640C2×C22⋊C4—534no—
641C2×C22⋊C4—532no—
642C2×C22⋊C4—534no—
643C2×C22⋊C4—532no—
644C2×C22⋊C4—532no—
645C2×C22⋊C4—534no—
646C2×C22⋊C4—532no—
647C2×C22⋊C4—534no—
648C2×C22⋊C4—532no—
649C2×C22⋊C4—532no—
650C2×C22⋊C4C22×D5312yes—
651C2×C22⋊C4C22×D5314yes—
652C2×C22⋊C4C22×D5314yes—
653C2×C42—532no—
654C2×C42—531no—
655C2×C42—534no—
656C2×C42—534no—
657C2×C42—531no—
658C2×C42—532no—
659C2×C42—534no—
660C2×C42—532no—
661C2×C42—5316no—
662C2×C42—531no—
663C2×C42—538no—
664C2×C42C22×D5314yes—
665C2×C42C22×D5312yes—
666C2×C42C22×D5311yescharacteristic
667C24—532no—
668C24—531no—
669C24C23×D5312yes—
670#41—10632no—
671C2×Q8—28no—
672C2×Q8—24no—
673C2×Q8—538no—
674C2×Q8—534no—
675C2×Q8—5316no—
676C2×Q8—538no—
677C2×Q8—5316no—
678C2×Q8—10616no—
679C2×Q8—10664no—
680C2×Q8—2124no—
681C2×Q8—2128no—
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—1064no—
691C2×D4—2124no—
692C2×D4—2128no—
693C2×D4C23×D5314yes—
694C22×C4—28no—
695C22×C4—532no—
696C22×C4—538no—
697C22×C4—531no—
698C22×C4—531no—
699C22×C4—531no—
700C22×C4—534no—
701C22×C4—532no—
702C22×C4—532no—
703C22×C4—538no—
704C22×C4—534no—
705C22×C4—534no—
706C22×C4—5316no—
707C22×C4—538no—
708C22×C4—534no—
709C22×C4—10616no—
710C22×C4—1068no—
711C22×C4—1068no—
712C22×C4—1064no—
713C22×C4—1064no—
714C22×C4—2122no—
715C22×C4—2124no—
716C22×C4C23×D5318yes—
717C22×C4C23×D5312yes—
718C22×C4C23×D5312yes—
719C22×C4C23×D5314yes—
720C22×C4C23×D5311yescharacteristic
721C22×C4C23×D5312yes—
722C22×C4C23×D5311yescharacteristic
723C22×C4C23×D5311yescharacteristic
724C4⋊C4—538no—
725C4⋊C4—534no—
726C4⋊C4—538no—
727C4⋊C4—538no—
728C4⋊C4—534no—
729C4⋊C4—5316no—
730C4⋊C4—538no—
731C4⋊C4—538no—
732C4⋊C4—5316no—
733C4⋊C4—538no—
734C4⋊C4—5316no—
735C4⋊C4—538no—
736C4⋊C4—5316no—
737C4⋊C4—5316no—
738C4⋊C4C23×D5314yes—
739C4⋊C4C23×D5318yes—
740C4⋊C4C23×D53116yes—
741C4⋊C4C23×D5314yes—
742C4⋊C4C23×D5318yes—
743C4⋊C4C23×D5318yes—
744C22⋊C4—538no—
745C22⋊C4—5316no—
746C22⋊C4—538no—
747C22⋊C4—5316no—
748C22⋊C4—538no—
749C22⋊C4—538no—
750C22⋊C4—5316no—
751C22⋊C4—538no—
752C22⋊C4—5316no—
753C22⋊C4—538no—
754C22⋊C4—538no—
755C22⋊C4C23×D5318yes—
756C22⋊C4C23×D53116yes—
757C22⋊C4C23×D53116yes—
758C42—534no—
759C42—538no—
760C42—534no—
761C42—534no—
762C42—538no—
763C42—538no—
764C42—5316no—
765C42—5316no—
766C42—5316no—
767C42C23×D5314yes—
768C42C23×D53116yes—
769C42C23×D5318yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—534no—
774C23—532no—
775C23—1064no—
776C23—1062no—
777C23—1062no—
778C23—1064no—
779C23—1062no—
780C23—1064no—
781C23C24×D5314yes—
782C23C24×D5311yescharacteristic
783Q8—216no—
784Q8—28no—
785Q8—5316no—
786Q8—10632no—
787Q8—2128no—
788Q8—21216no—
789D4—28no—
790D4—10616no—
791D4—1068no—
792D4—2128no—
793D4—21216no—
794C2×C4—28no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—538no—
801C2×C4—534no—
802C2×C4—532no—
803C2×C4—532no—
804C2×C4—532no—
805C2×C4—538no—
806C2×C4—534no—
807C2×C4—534no—
808C2×C4—10632no—
809C2×C4—10616no—
810C2×C4—1062no—
811C2×C4—1064no—
812C2×C4—1062no—
813C2×C4—1062no—
814C2×C4—1064no—
815C2×C4—1068no—
816C2×C4—10616no—
817C2×C4—1068no—
818C2×C4—1068no—
819C2×C4—2124no—
820C2×C4—2128no—
821C2×C4#41×D5314yes—
822C2×C4#1313326414yes—
823C2×C4C24×D5314yes—
824C2×C4C24×D5314yes—
825C2×C4C24×D5318yes—
826C2×C4C24×D5312yes—
827C2×C4C24×D5314yes—
828C2×C4C24×D5312yes—
829C2×C4C24×D5312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—1064no—
835C22—1062no—
836C22—1062no—
837C22—1064no—
838C22—1062no—
839C22—1064no—
840C22—2128no—
841C22—2124no—
842C22C2×#41×D5312yes—
843C22C2×#1313326412yes—
844C22#1681146012yes—
845C22C25×D5311yescharacteristic
846C4—28no—
847C4—24no—
848C4—24no—
849C4—22no—
850C4—24no—
851C4—538no—
852C4—1062no—
853C4—1064no—
854C4—1062no—
855C4—1062no—
856C4—1064no—
857C4—1068no—
858C4C2×#41×D5314yes—
859C4C2×#1313326414yes—
860C2—44no—
861C2—2124no—
862C2—2122no—
863C2#2028872914yesdirect product factor
864C2C22×#41×D5311yescharacteristic
865C2C22×#1313326411yescharacteristic
866C2C2×#1681146011yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#556C2
socleC23×C53C25
hypercenterC2×#556D53
hypocenterC53C2×#3518
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20288729C2direct (N × H)
2. C2×Q8×Dic106C2semidirect
3. C2×#16811346C2semidirect
4. C2×#16811344C2semidirect
5. C2×#16811340C2semidirect
6. C2×#16811338C2semidirect
7. C2×#16811336C2semidirect
8. C2×#16811288C2semidirect
9. C2×#16811281C2semidirect
10. C2×#16811242C2semidirect
11. C2×#16811239C2semidirect
12. C2×#16811178C2semidirect
13. C2×#16811176C2semidirect
14. C2×#16811160C2semidirect
15. C2×#16811159C2semidirect
16. C2×#16811099C2semidirect
17. C2×C4×#11719947C2semidirect
18. C2×C53×#556C2semidirect
21. Q8×Dic106C22semidirect
22. #16811346C22semidirect
23. #16811344C22semidirect
24. #16811340C22semidirect
25. #16811338C22semidirect
26. #16811336C22semidirect
27. #16811288C22semidirect
28. #16811281C22semidirect
29. #16811242C22semidirect
30. #16811239C22semidirect
31. #16811178C22semidirect
32. #16811176C22semidirect
38. #16811160C22semidirect
39. #16811159C22semidirect
64. #16811099C22semidirect
65. C4×#11719947C22semidirect
92. C53×#556C22semidirect
432. C2×#556D53semidirect
446. C2×C53#3518semidirect
458. #556C2×D53semidirect
534. C53C2×#3518semidirect
863. C2#20288729direct (N × H)

Maximal subgroups

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

subgroupindex
#202887292
C2×Q8×Dic1062
C2×#168113462
C2×#168113442
C2×#168113402
C2×#168113382
C2×#168113362
C2×#168112882
C2×#168112812
C2×#168112422
C2×#168112392
C2×#168111782
C2×#168111762
C2×#168111602
C2×#168111592
C2×#168110992
C2×C4×#117199472
C2×C53×#5562
C2×#351853