Finite Group Databasebeta

← C2×#20288797 #28292296

Subgroups — C2×#20288797 #28292296

Order 13568.

7758 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288797C2132yesmaximal, direct product factor
2C2×#16811355C212yesmaximal, complemented
3C2×Q8×Dic106C211yesmaximal, characteristic, complemented
4C2×#16811333C211yesmaximal, characteristic, complemented
5C2×#16811332C212yesmaximal, complemented
6C2×#16811293C211yesmaximal, characteristic, complemented
7C2×#16811281C212yesmaximal, complemented
8C2×#16811278C212yesmaximal, complemented
9C2×#16811271C214yesmaximal, complemented
10C2×#16811242C212yesmaximal, complemented
11C2×#16811241C214yesmaximal, complemented
12C2×#16811171C211yesmaximal, characteristic, complemented
13C2×#16811170C212yesmaximal, complemented
14C2×#16811160C211yesmaximal, characteristic, complemented
15C2×#16811152C212yesmaximal, complemented
16C2×#16811102C212yesmaximal, complemented
17C2×C4×Q8×D53C211yesmaximal, characteristic, complemented
18C2×C53×#559C211yesmaximal, characteristic, complemented
19C22×#11719945C2214yes—
20C22×#11719947C2212yes—
21C22×#11719947C2212yes—
22C22×Q8×D53C2211yescharacteristic
23#16811355C22132yescomplemented
24Q8×Dic106C22116yescomplemented
25#16811333C22116yescomplemented
26#16811332C22132yescomplemented
27#16811293C22116yescomplemented
28#16811281C22132yescomplemented
29#16811278C22132yescomplemented
30#16811271C22164yescomplemented
31#16811242C22132yescomplemented
32#16811241C22164yescomplemented
33#16811171C22116yescomplemented
34#16811170C22132yescomplemented
35C2×#13133217C2212yes—
36C2×#13133217C2211yescharacteristic
37C2×#13133216C2214yes—
38C2×#13133216C2212yes—
39C2×#13133213C2212yes—
40#16811160C22116yescomplemented
41#16811152C22132yescomplemented
42C2×#13133212C2212yes—
43C2×#13133210C2214yes—
44C2×#13133209C2212yes—
45C2×#13133208C2211yescharacteristic
46C2×#13133206C2211yescharacteristic
47C2×#13133204C2212yes—
48C2×#13133203C2214yes—
49C2×#13133203C2214yes—
50C2×#13133202C2212yes—
51C2×#13133201C2214yes—
52C2×#13133199C2214yes—
53C2×#13133199C2214yes—
54C2×#13133196C2214yes—
55C2×#13133195C2214yes—
56C2×#13133194C2214yes—
57C2×#13133194C2214yes—
58C2×#13133193C2212yes—
59C2×#13133193C2211yescharacteristic
60C2×#13133192C2211yescharacteristic
61C2×#13133190C2214yes—
62C2×#13133189C2214yes—
63C2×#13133188C2212yes—
64C2×#13133188C2212yes—
65C2×#13133188C2212yes—
66#16811102C22132yescomplemented
67C2×Q8×Dic53C2212yes—
68C2×Q8×Dic53C2211yescharacteristic
69C2×C4×Dic106C2211yescharacteristic
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2212yes—
72C2×#13133182C2212yes—
73C2×#13133182C2211yescharacteristic
74C4×Q8×D53C22116yescomplemented
75C2×C4×D212C2212yes—
76C2×C4×D212C2212yes—
77C2×C4×D212C2211yescharacteristic
78C2×D4×Dic53C2212yes—
79C2×D4×Dic53C2212yes—
80C2×D4×Dic53C2212yes—
81C2×C4×C22⋊D53C2214yes—
82C2×#13133177C2214yes—
83C2×#13133177C2214yes—
84C2×#13133174C2212yes—
85C2×#13133173C2214yes—
86C22×#11719919C2214yes—
87C2×C4⋊C4×D53C2212yes—
88C2×C4⋊C4×D53C2211yescharacteristic
89C2×C4⋊C4×D53C2212yes—
90C2×C42×D53C2212yes—
91C2×C42×D53C2211yescharacteristic
92C53×#559C22116yescomplemented
93C2×#127×C53C2211yescharacteristic
94C2×#124×C53C2212yes—
95C2×#124×C53C2212yes—
96C2×#123×C53C2214yes—
97C2×C4×Q8×C53C2211yescharacteristic
98C2×C4×Q8×C53C2211yescharacteristic
99C2×C4×D4×C53C2212yes—
100C2×C4×D4×C53C2212yes—
101C2×#11719945—416no—
102C2×#11719945C23132yes—
103C2×#11719947—216no—
104C2×#11719947—48no—
105C2×#11719947C23116yes—
106C2×#11719947C23116yes—
107C22×Dic106C2312yes—
108C22×Dic106C2314yes—
109C22×Dic106C2312yes—
110C22×Dic106C2311yescharacteristic
111C2×Q8×D53—28no—
112C2×Q8×D53C2318yes—
113C22×D212C2311yescharacteristic
114C22×D212C2312yes—
115C22×C22⋊D53C2314yes—
116C22×C22⋊D53C2314yes—
117C22×C22⋊D53C2314yes—
118C23×Dic53C2314yes—
119C23×Dic53C2314yes—
120C22×C4×D53C2311yescharacteristic
121C22×C4×D53C2312yes—
122C22×C4×D53C2311yescharacteristic
123C22×C4×D53C2312yes—
124C22×C4×D53C2311yescharacteristic
125C22×C4×D53C2312yes—
126C22×C4×D53C2314yes—
127#13133217C23116yes—
128#13133217C2318yes—
129#13133216C23132yes—
130#13133216C23116yes—
131#13133213C23116yes—
132#13133212C23116yes—
133#13133210C23132yes—
134#13133209C23116yes—
135#13133208C2318yes—
136#13133206C2318yes—
137#13133204C23116yes—
138#13133203C23132yes—
139#13133203C23132yes—
140#13133202C23116yes—
141#13133201C23132yes—
142#13133199C23132yes—
143#13133199C23132yes—
144#13133196C23132yes—
145#13133195C23132yes—
146#13133194C23132yes—
147#13133194C23132yes—
148#13133193C23116yes—
149#13133193C2318yes—
150#13133192C2318yes—
151#13133190C23132yes—
152#13133189C23132yes—
153#13133188C23116yes—
154#13133188C23116yes—
155#13133188C23116yes—
156Q8×Dic53C2318yes—
157Q8×Dic53C23116yes—
158C4×Dic106C23116yes—
159C4×Dic106C2318yes—
160C4×Dic106C23116yes—
161#13133182C2318yes—
162#13133182C23116yes—
163C4×D212C23116yes—
164C4×D212C2318yes—
165C4×D212C23116yes—
166D4×Dic53C23116yes—
167D4×Dic53C23116yes—
168D4×Dic53C23116yes—
169C4×C22⋊D53C23132yes—
170#13133177C23132yes—
171#13133177C23132yes—
172#13133174C23116yes—
173#13133173C23132yes—
174C2×C4⋊Dic53C2312yes—
175C2×C4⋊Dic53C2311yescharacteristic
176C2×C4⋊Dic53C2312yes—
177C2×C4⋊Dic53C2311yescharacteristic
178C2×C4⋊Dic53C2312yes—
179C2×C4⋊Dic53C2312yes—
180C2×C4⋊Dic53C2314yes—
181C2×#11719919C23132yes—
182C2×#11719919C2312yes—
183C2×#11719919C2314yes—
184C2×#11719919C2312yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2314yes—
188C2×#11719919C2312yes—
189C2×#11719919C2314yes—
190C4⋊C4×D53C23116yes—
191C4⋊C4×D53C2318yes—
192C4⋊C4×D53C23116yes—
193C2×C22⋊Dic53C2314yes—
194C2×C22⋊Dic53C2314yes—
195C2×C22⋊Dic53C2314yes—
196C2×#11719921C2312yes—
197C2×#11719921C2312yes—
198C2×#11719921C2312yes—
199C2×#11719921C2312yes—
200C2×#11719921C2314yes—
201C2×#11719921C2312yes—
202C2×C4×Dic53C2312yes—
203C2×C4×Dic53C2311yescharacteristic
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2312yes—
206C2×C4×Dic53C2311yescharacteristic
207C2×C4×Dic53C2312yes—
208C2×C4×Dic53C2314yes—
209C42×D53C23116yes—
210C42×D53C2318yes—
211C22×Q8×C53C2311yescharacteristic
212C22×Q8×C53C2311yescharacteristic
213C22×D4×C53C2312yes—
214C22×D4×C53C2312yes—
215C22×D4×C53C2312yes—
216C23×C4×C53C2314yes—
217#127×C53C2318yes—
218#124×C53C23116yes—
219#124×C53C23116yes—
220#123×C53C23132yes—
221C4×Q8×C53C2318yes—
222C4×Q8×C53C2318yes—
223C4×D4×C53C23116yes—
224C4×D4×C53C23116yes—
225C2×C4⋊C4×C53C2311yescharacteristic
226C2×C4⋊C4×C53C2311yescharacteristic
227C2×C4⋊C4×C53C2312yes—
228C2×C4⋊C4×C53C2312yes—
229C2×C22⋊C4×C53C2314yes—
230C2×C22⋊C4×C53C2314yes—
231C2×C22⋊C4×C53C2314yes—
232C2×C42×C53C2312yes—
233C2×C42×C53C2312yes—
234C2×C42×C53C2311yescharacteristic
235C24×C53C2414yes—
236C23×D53C2412yes—
237C23×D53C2411yescharacteristic
238C2×Q8×C53—24no—
239C2×Q8×C53—24no—
240C2×Q8×C53C2414yes—
241C2×Q8×C53C2414yes—
242C2×D4×C53—28no—
243C2×D4×C53—28no—
244C2×D4×C53—44no—
245C2×D4×C53C2418yes—
246C2×D4×C53C2418yes—
247C2×D4×C53C2418yes—
248C22×C4×C53—48no—
249C22×C4×C53C2412yes—
250C22×C4×C53C2412yes—
251C22×C4×C53C2412yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2411yescharacteristic
254C22×C4×C53C24116yes—
255C22×C4×C53C2411yescharacteristic
256C22×C4×C53C2411yescharacteristic
257C2×C22⋊D53—216no—
258C2×C22⋊D53—216no—
259C2×C22⋊D53—48no—
260C2×C22⋊D53C24116yes—
261C2×C22⋊D53C24116yes—
262C2×C22⋊D53C24116yes—
263C22×Dic53—216no—
264C22×Dic53—48no—
265C22×Dic53C2411yescharacteristic
266C22×Dic53C2411yescharacteristic
267C22×Dic53C2411yescharacteristic
268C22×Dic53C2412yes—
269C22×Dic53C2414yes—
270C22×Dic53C2412yes—
271C22×Dic53C24116yes—
272C22×Dic53C24116yes—
273C22×Dic53C2412yes—
274Q8×D53—232no—
275#11719947—264no—
276#11719947—432no—
277#11719945—464no—
278C2×D212—28no—
279C2×D212—24no—
280C2×D212C2414yes—
281C2×D212C2418yes—
282C2×C4×D53—24no—
283C2×C4×D53—28no—
284C2×C4×D53—24no—
285C2×C4×D53—28no—
286C2×C4×D53—24no—
287C2×C4×D53—28no—
288C2×C4×D53—48no—
289C2×C4×D53C2414yes—
290C2×C4×D53C2418yes—
291C2×C4×D53C2414yes—
292C2×C4×D53C2418yes—
293C2×C4×D53C2414yes—
294C2×C4×D53C2418yes—
295C2×C4×D53C24116yes—
296C2×Dic106—28no—
297C2×Dic106—44no—
298C2×Dic106—48no—
299C2×Dic106#4118yescomplemented
300C2×Dic106C2418yes—
301C2×Dic106C24116yes—
302C2×Dic106C2418yes—
303C2×Dic106C2414yes—
304C4⋊C4×C53C2414yes—
305C4⋊C4×C53C2414yes—
306C4⋊C4×C53C2418yes—
307C4⋊C4×C53C2418yes—
308C22⋊C4×C53C24116yes—
309C22⋊C4×C53C24116yes—
310C22⋊C4×C53C24116yes—
311C42×C53C2418yes—
312C42×C53C2418yes—
313C42×C53C2414yes—
314C22⋊Dic53C24116yes—
315C22⋊Dic53C24116yes—
316C22⋊Dic53C24116yes—
317#11719921C2418yes—
318#11719921C2418yes—
319#11719921C2418yes—
320#11719921C2418yes—
321#11719921C24116yes—
322#11719921C2418yes—
323C4⋊Dic53C2418yes—
324C4⋊Dic53C2414yes—
325C4⋊Dic53C2418yes—
326C4⋊Dic53C2414yes—
327C4⋊Dic53C2418yes—
328C4⋊Dic53C2418yes—
329C4⋊Dic53C24116yes—
330#11719919C2418yes—
331#11719919C24116yes—
332#11719919C2418yes—
333#11719919C2418yes—
334#11719919C2418yes—
335#11719919C24116yes—
336#11719919C2418yes—
337#11719919C24116yes—
338C4×Dic53C2418yes—
339C4×Dic53C2414yes—
340C4×Dic53C2414yes—
341C4×Dic53C2418yes—
342C4×Dic53C2414yes—
343C4×Dic53C2418yes—
344C4×Dic53C24116yes—
345C23×C53—28no—
346C23×C53—28no—
347C23×C53—28no—
348C23×C53C2518yes—
349C23×C53C2511yescharacteristic
350C22×D53—22no—
351C22×D53—22no—
352C22×D53—24no—
353C22×D53—24no—
354C22×D53—24no—
355C22×D53H(5,𝔽2)14yes—
356C22×D53C2514yes—
357C22×D53C2512yes—
358Q8×C53—28no—
359Q8×C53—28no—
360D4×C53—216no—
361D4×C53—216no—
362D4×C53—48no—
363C2×C4×C53—24no—
364C2×C4×C53—22no—
365C2×C4×C53—24no—
366C2×C4×C53—24no—
367C2×C4×C53—24no—
368C2×C4×C53—416no—
369C2×C4×C53C2×#4114yes—
370C2×C4×C532−1+414yes—
371C2×C4×C53C2512yes—
372C2×C4×C53C2514yes—
373C2×C4×C53C2514yes—
374C2×C4×C53C2514yes—
375C2×C4×C53C2514yes—
376C2×C4×C53C2512yes—
377C2×C4×C53C2512yes—
378C22⋊D53—232no—
379C22⋊D53—232no—
380C22⋊D53—416no—
381C2×Dic53—22no—
382C2×Dic53—24no—
383C2×Dic53—24no—
384C2×Dic53—28no—
385C2×Dic53—22no—
386C2×Dic53—22no—
387C2×Dic53—232no—
388C2×Dic53—416no—
389C2×Dic53C2×#4118yes—
390C2×Dic53C2518yes—
391C2×Dic53C2514yes—
392C2×Dic53C2512yes—
393C2×Dic53C2512yes—
394C2×Dic53C2514yes—
395C2×Dic53C2512yes—
396C2×Dic53C2514yes—
397D212—216no—
398D212—28no—
399C4×D53—216no—
400C4×D53—28no—
401C4×D53—216no—
402C4×D53—28no—
403C4×D53—28no—
404C4×D53—216no—
405C4×D53—416no—
406Dic106—216no—
407Dic106—416no—
408Dic106—48no—
409Dic106C2×#41116yescomplemented
410C2×#3522—531nomaximal, Sylow
411C22×C53—28no—
412C22×C53—28no—
413C22×C53—28no—
414C22×C53—416no—
415C22×C53C22×#4112yes—
416C22×C53C2×H(5,𝔽2)12yes—
417C22×C53C2×2−1+412yes—
418C22×C53C2611yescharacteristic
419C2×D53—22no—
420C2×D53—22no—
421C2×D53—28no—
422C2×D53—24no—
423C2×D53—24no—
424C2×D53—24no—
425C2×D53—48no—
426C2×D53C2×H(5,𝔽2)14yes—
427C4×C53—24no—
428C4×C53—22no—
429C4×C53—24no—
430C4×C53—24no—
431C4×C53—24no—
432C4×C53C22×#4114yes—
433C4×C53C2×2−1+414yes—
434Dic53—22no—
435Dic53—24no—
436Dic53—24no—
437Dic53—28no—
438Dic53—22no—
439Dic53—22no—
440Dic53C22×#4118yes—
441#3522—5332no—
442C2×#559—532no—
443C2×#559D5311yescharacteristic, complemented
444C2×Q82—531no—
445C2×#554—531no—
446C2×#554—532no—
447C2×#550—531no—
448C2×#548—532no—
449C2×#547—534no—
450C2×#547—532no—
451C2×#542—532no—
452C2×#542—534no—
453C2×#532—531no—
454C2×#532—532no—
455C2×#529—532no—
456C2×#529—531no—
457C2×#520—532no—
458C22×C4×Q8—531no—
459C2×C53—48no—
460C2×C53#352214yescomplemented
461C2×C53C23×#4111yescharacteristic
462C2×C53C22×H(5,𝔽2)11yescharacteristic
463C2×C53C22×2−1+411yescharacteristic
464D53—24no—
465D53—44no—
466C22×#41—532no—
467C22×#41—532no—
468C22×#41—534no—
469C23×Q8—531no—
470#559—5332no—
471#559C2×D53116yescomplemented
472Q82—5316no—
473#554—5316no—
474#554—5332no—
475#550—5316no—
476#548—5332no—
477#547—5364no—
478#547—5332no—
479#542—5332no—
480#542—5364no—
481#532—5316no—
482#532—5332no—
483C2×C4⋊Q8—532no—
484C2×C4⋊Q8—534no—
485C2×C4⋊Q8—531no—
486C2×C4⋊Q8—532no—
487C2×#127—532no—
488C2×#127C2×D5311yescharacteristic
489#529—5332no—
490#529—5316no—
491C2×#126—532no—
492C2×#126—534no—
493C2×#125—531no—
494C2×#125—532no—
495C2×#124—531no—
496C2×#124—532no—
497C2×#124—534no—
498C2×#124—534no—
499C2×#124C2×D5312yes—
500C2×#124C2×D5312yes—
501C2×#123—532no—
502C2×#123—534no—
503C2×#123—534no—
504C2×#123—534no—
505C2×#123C2×D5314yes—
506C2×C22⋊Q8—531no—
507C2×C22⋊Q8—532no—
508C2×C22⋊Q8—534no—
509C2×C22⋊Q8—534no—
510C2×C22⋊Q8—534no—
511C2×C22⋊Q8—534no—
512C2×#121—532no—
513C2×#121—532no—
514C2×#121—532no—
515C2×#121—534no—
516C2×#121—531no—
517C2×#121—534no—
518#520—5332no—
519C2×C4×Q8—531no—
520C2×C4×Q8—532no—
521C2×C4×Q8—5316no—
522C2×C4×Q8—531no—
523C2×C4×Q8—532no—
524C2×C4×Q8—531no—
525C2×C4×Q8—532no—
526C2×C4×Q8—532no—
527C2×C4×Q8C2×D5311yescharacteristic
528C2×C4×Q8C2×D5311yescharacteristic
529C2×C4×D4—532no—
530C2×C4×D4—532no—
531C2×C4×D4—532no—
532C2×C4×D4—534no—
533C2×C4×D4—534no—
534C2×C4×D4—534no—
535C2×C4×D4—532no—
536C2×C4×D4—531no—
537C2×C4×D4—532no—
538C2×C4×D4C2×D5312yes—
539C2×C4×D4C2×D5312yes—
540C2×#117—534no—
541C2×#117—532no—
542C22×C4⋊C4—534no—
543C22×C4⋊C4—532no—
544C22×C4⋊C4—531no—
545C22×C4⋊C4—532no—
546C22×C42—531no—
547C22×C42—532no—
548C53C2×#352211yescharacteristic, complemented, Sylow
549C2×#41—5316no—
550C2×#41—5316no—
551C2×#41—5332no—
552C2×#41—10616no—
553C2×#41—21216no—
554C2×#41—2128no—
555C22×Q8—538no—
556C22×Q8—531no—
557C22×Q8—532no—
558C22×Q8—534no—
559C22×Q8—532no—
560C22×Q8—1068no—
561C22×Q8C22×D5311yescharacteristic
562C22×Q8C22×D5311yescharacteristic
563C22×D4—534no—
564C22×D4—534no—
565C22×D4—534no—
566C22×D4—531no—
567C22×D4—532no—
568C22×D4C22×D5312yes—
569C22×D4C22×D5312yes—
570C22×D4C22×D5312yes—
571C23×C4—534no—
572C23×C4—534no—
573C23×C4—531no—
574C23×C4—532no—
575C23×C4—532no—
576C23×C4—532no—
577C23×C4—531no—
578C23×C4—531no—
579C23×C4—534no—
580C23×C4C22×D5314yes—
581C4⋊Q8—5316no—
582C4⋊Q8—5332no—
583C4⋊Q8—538no—
584C4⋊Q8—5316no—
585#127—5316no—
586#127C22×D5318yes—
587#126—5316no—
588#126—5332no—
589#125—538no—
590#125—5316no—
591#124—538no—
592#124—5316no—
593#124—5332no—
594#124—5332no—
595#124C22×D53116yes—
596#124C22×D53116yes—
597#123—5316no—
598#123—5332no—
599#123—5332no—
600#123—5332no—
601#123C22×D53132yes—
602C22⋊Q8—538no—
603C22⋊Q8—5316no—
604C22⋊Q8—5332no—
605C22⋊Q8—5332no—
606C22⋊Q8—5332no—
607C22⋊Q8—5332no—
608#121—5316no—
609#121—5316no—
610#121—5316no—
611#121—5332no—
612#121—538no—
613#121—5332no—
614C4×Q8—538no—
615C4×Q8—5316no—
616C4×Q8—538no—
617C4×Q8—5316no—
618C4×Q8—538no—
619C4×Q8—5316no—
620C4×Q8—5316no—
621C4×Q8C22×D5318yes—
622C4×Q8C22×D5318yes—
623C4×D4—5316no—
624C4×D4—5316no—
625C4×D4—5316no—
626C4×D4—5332no—
627C4×D4—5332no—
628C4×D4—5332no—
629C4×D4—5316no—
630C4×D4—538no—
631C4×D4—5316no—
632C4×D4C22×D53116yes—
633C4×D4C22×D53116yes—
634#117—5332no—
635#117—5316no—
636C2×C4⋊C4—532no—
637C2×C4⋊C4—532no—
638C2×C4⋊C4—534no—
639C2×C4⋊C4—534no—
640C2×C4⋊C4—532no—
641C2×C4⋊C4—532no—
642C2×C4⋊C4—531no—
643C2×C4⋊C4—532no—
644C2×C4⋊C4—532no—
645C2×C4⋊C4—5332no—
646C2×C4⋊C4—532no—
647C2×C4⋊C4—531no—
648C2×C4⋊C4—532no—
649C2×C4⋊C4—534no—
650C2×C4⋊C4—532no—
651C2×C4⋊C4—534no—
652C2×C4⋊C4—5316no—
653C2×C4⋊C4—538no—
654C2×C4⋊C4—5316no—
655C2×C4⋊C4C22×D5311yescharacteristic
656C2×C4⋊C4C22×D5312yes—
657C2×C4⋊C4C22×D5311yescharacteristic
658C2×C4⋊C4C22×D5312yes—
659C2×C22⋊C4—534no—
660C2×C22⋊C4—534no—
661C2×C22⋊C4—534no—
662C2×C22⋊C4—532no—
663C2×C22⋊C4—532no—
664C2×C22⋊C4—532no—
665C2×C22⋊C4—532no—
666C2×C22⋊C4—534no—
667C2×C22⋊C4—532no—
668C2×C22⋊C4C22×D5314yes—
669C2×C22⋊C4C22×D5314yes—
670C2×C22⋊C4C22×D5314yes—
671C2×C42—532no—
672C2×C42—531no—
673C2×C42—534no—
674C2×C42—531no—
675C2×C42—532no—
676C2×C42—531no—
677C2×C42—532no—
678C2×C42—538no—
679C2×C42—5316no—
680C2×C42C22×D5312yes—
681C2×C42C22×D5312yes—
682C2×C42C22×D5311yescharacteristic
683C24—531no—
684C24—532no—
685C24C23×D5314yes—
686#41—10664no—
687#41—21264no—
688#41—21232no—
689C2×Q8—24no—
690C2×Q8—24no—
691C2×Q8—538no—
692C2×Q8—534no—
693C2×Q8—538no—
694C2×Q8—5316no—
695C2×Q8—538no—
696C2×Q8—1068no—
697C2×Q8—10632no—
698C2×Q8—2128no—
699C2×Q8—2124no—
700C2×Q8C23×D5314yes—
701C2×Q8C23×D5314yes—
702C2×D4—28no—
703C2×D4—28no—
704C2×D4—44no—
705C2×D4—5316no—
706C2×D4—5316no—
707C2×D4—5316no—
708C2×D4—534no—
709C2×D4—538no—
710C2×D4—1068no—
711C2×D4—10616no—
712C2×D4—10616no—
713C2×D4—1064no—
714C2×D4—2128no—
715C2×D4C23×D5318yes—
716C2×D4C23×D5318yes—
717C2×D4C23×D5318yes—
718C22×C4—48no—
719C22×C4—532no—
720C22×C4—5316no—
721C22×C4—531no—
722C22×C4—531no—
723C22×C4—531no—
724C22×C4—532no—
725C22×C4—534no—
726C22×C4—532no—
727C22×C4—5316no—
728C22×C4—534no—
729C22×C4—534no—
730C22×C4—538no—
731C22×C4—538no—
732C22×C4—534no—
733C22×C4—538no—
734C22×C4—5316no—
735C22×C4—1068no—
736C22×C4—1068no—
737C22×C4—1064no—
738C22×C4—10616no—
739C22×C4—1064no—
740C22×C4—1068no—
741C22×C4—1064no—
742C22×C4—2128no—
743C22×C4—2128no—
744C22×C4C23×D5312yes—
745C22×C4C23×D5312yes—
746C22×C4C23×D5311yescharacteristic
747C22×C4C23×D5312yes—
748C22×C4C23×D5312yes—
749C22×C4C23×D53116yes—
750C22×C4C23×D5311yescharacteristic
751C22×C4C23×D5311yescharacteristic
752C4⋊C4—538no—
753C4⋊C4—538no—
754C4⋊C4—5316no—
755C4⋊C4—5316no—
756C4⋊C4—538no—
757C4⋊C4—538no—
758C4⋊C4—534no—
759C4⋊C4—538no—
760C4⋊C4—538no—
761C4⋊C4—538no—
762C4⋊C4—534no—
763C4⋊C4—538no—
764C4⋊C4—5316no—
765C4⋊C4—538no—
766C4⋊C4—5316no—
767C4⋊C4C23×D5314yes—
768C4⋊C4C23×D5318yes—
769C4⋊C4C23×D5314yes—
770C4⋊C4C23×D5318yes—
771C22⋊C4—5316no—
772C22⋊C4—5316no—
773C22⋊C4—5316no—
774C22⋊C4—538no—
775C22⋊C4—538no—
776C22⋊C4—538no—
777C22⋊C4—538no—
778C22⋊C4—5316no—
779C22⋊C4—538no—
780C22⋊C4C23×D53116yes—
781C22⋊C4C23×D53116yes—
782C22⋊C4C23×D53116yes—
783C42—538no—
784C42—534no—
785C42—534no—
786C42—538no—
787C42—534no—
788C42—538no—
789C42—5316no—
790C42C23×D5318yes—
791C42C23×D5314yes—
792C42C23×D5318yes—
793C23—28no—
794C23—28no—
795C23—28no—
796C23—534no—
797C23—532no—
798C23—534no—
799C23—1062no—
800C23—1062no—
801C23—1064no—
802C23—1064no—
803C23—1064no—
804C23C24×D5318yes—
805C23C24×D5311yescharacteristic
806Q8—28no—
807Q8—28no—
808Q8—5316no—
809Q8—10616no—
810Q8—21216no—
811Q8—2128no—
812D4—216no—
813D4—216no—
814D4—48no—
815D4—10616no—
816D4—10632no—
817D4—10632no—
818D4—1068no—
819D4—21216no—
820C2×C4—24no—
821C2×C4—24no—
822C2×C4—24no—
823C2×C4—22no—
824C2×C4—24no—
825C2×C4—416no—
826C2×C4—538no—
827C2×C4—534no—
828C2×C4—532no—
829C2×C4—532no—
830C2×C4—532no—
831C2×C4—534no—
832C2×C4—538no—
833C2×C4—534no—
834C2×C4—10616no—
835C2×C4—10616no—
836C2×C4—1068no—
837C2×C4—10632no—
838C2×C4—1064no—
839C2×C4—1062no—
840C2×C4—1062no—
841C2×C4—1064no—
842C2×C4—1068no—
843C2×C4—1062no—
844C2×C4—1068no—
845C2×C4—10616no—
846C2×C4—1068no—
847C2×C4—21216no—
848C2×C4—21216no—
849C2×C4#41×D5314yes—
850C2×C4#1313326414yes—
851C2×C4C24×D5314yes—
852C2×C4C24×D5314yes—
853C2×C4C24×D5312yes—
854C2×C4C24×D5314yes—
855C2×C4C24×D5314yes—
856C2×C4C24×D5312yes—
857C2×C4C24×D5312yes—
858C22—28no—
859C22—28no—
860C22—28no—
861C22—416no—
862C22—534no—
863C22—1068no—
864C22—1062no—
865C22—1062no—
866C22—1064no—
867C22—1064no—
868C22—1064no—
869C22—2128no—
870C22C2×#41×D5312yes—
871C22H(5,𝔽2)×D5312yes—
872C22C2×#1313326412yes—
873C22C25×D5311yescharacteristic
874C4—24no—
875C4—24no—
876C4—24no—
877C4—22no—
878C4—24no—
879C4—538no—
880C4—1064no—
881C4—1062no—
882C4—1062no—
883C4—1064no—
884C4—1068no—
885C4—1062no—
886C4C2×#41×D5314yes—
887C4C2×#1313326414yes—
888C2—48no—
889C2—1064no—
890C2—2124no—
891C2#2028879714yesdirect product factor
892C2C22×#41×D5311yescharacteristic
893C2C2×H(5,𝔽2)×D5311yescharacteristic
894C2C22×#1313326411yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#559C2
socleC23×C53C25
hypercenterC2×#559D53
hypocenterC53C2×#3522
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#559

Complements

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

NH ≅ G/Ntype
1. #20288797C2direct (N × H)
2. C2×#16811355C2semidirect
3. C2×Q8×Dic106C2semidirect
4. C2×#16811333C2semidirect
5. C2×#16811332C2semidirect
6. C2×#16811293C2semidirect
7. C2×#16811281C2semidirect
8. C2×#16811278C2semidirect
9. C2×#16811271C2semidirect
10. C2×#16811242C2semidirect
11. C2×#16811241C2semidirect
12. C2×#16811171C2semidirect
13. C2×#16811170C2semidirect
14. C2×#16811160C2semidirect
15. C2×#16811152C2semidirect
16. C2×#16811102C2semidirect
17. C2×C4×Q8×D53C2semidirect
18. C2×C53×#559C2semidirect
23. #16811355C22semidirect
24. Q8×Dic106C22semidirect
25. #16811333C22semidirect
26. #16811332C22semidirect
27. #16811293C22semidirect
28. #16811281C22semidirect
29. #16811278C22semidirect
30. #16811271C22semidirect
31. #16811242C22semidirect
32. #16811241C22semidirect
33. #16811171C22semidirect
34. #16811170C22semidirect
40. #16811160C22semidirect
41. #16811152C22semidirect
66. #16811102C22semidirect
74. C4×Q8×D53C22semidirect
92. C53×#559C22semidirect
299. C2×Dic106#41semidirect
409. Dic106C2×#41semidirect
443. C2×#559D53semidirect
460. C2×C53#3522semidirect
471. #559C2×D53semidirect
548. C53C2×#3522semidirect
891. C2#20288797direct (N × H)

Maximal subgroups

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

subgroupindex
#202887972
C2×#168113552
C2×Q8×Dic1062
C2×#168113332
C2×#168113322
C2×#168112932
C2×#168112812
C2×#168112782
C2×#168112712
C2×#168112422
C2×#168112412
C2×#168111712
C2×#168111702
C2×#168111602
C2×#168111522
C2×#168111022
C2×C4×Q8×D532
C2×C53×#5592
C2×#352253