Finite Group Databasebeta

← C2×#20288619 #28292460

Subgroups — C2×#20288619 #28292460

Order 13568.

7758 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288619C2132yesmaximal, direct product factor
2C2×#16811346C211yesmaximal, characteristic, complemented
3C2×#16811336C212yesmaximal, complemented
4C2×#16811331C212yesmaximal, complemented
5C2×#16811324C214yesmaximal, complemented
6C2×#16811285C212yesmaximal, complemented
7C2×#16811281C212yesmaximal, complemented
8C2×#16811277C211yesmaximal, characteristic, complemented
9C2×#16811276C211yesmaximal, characteristic, complemented
10C2×#16811239C214yesmaximal, complemented
11C2×#16811203C212yesmaximal, complemented
12C2×#16811177C212yesmaximal, complemented
13C2×#16811172C212yesmaximal, complemented
14C2×#16811170C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
16C2×#16811103C212yesmaximal, complemented
17C2×C4×#11719949C211yesmaximal, characteristic, complemented
18C2×C53×#556C211yesmaximal, characteristic, complemented
19C22×#11719949C2211yescharacteristic
20C22×#11719949C2212yes—
21C22×#11719945C2212yes—
22C22×#11719947C2212yes—
23C22×Q8×D53C2212yes—
24#16811346C22116yescomplemented
25#16811336C22132yescomplemented
26#16811331C22132yescomplemented
27#16811324C22164yescomplemented
28#16811285C22132yescomplemented
29#16811281C22132yescomplemented
30#16811277C22116yescomplemented
31#16811276C22116yescomplemented
32#16811239C22164yescomplemented
33#16811203C22132yescomplemented
34#16811177C22132yescomplemented
35#16811172C22132yescomplemented
36#16811170C22116yescomplemented
37C2×#13133217C2211yescharacteristic
38C2×#13133216C2211yescharacteristic
39C2×#13133216C2212yes—
40C2×#13133216C2212yes—
41C2×#13133215C2212yes—
42C4⋊Q8×D53C22116yescomplemented
43C2×#13133213C2211yescharacteristic
44C2×#13133212C2214yes—
45C2×#13133207C2214yes—
46C2×#13133205C2212yes—
47C2×#13133205C2214yes—
48C2×#13133203C2212yes—
49C2×#13133203C2214yes—
50C2×#13133202C2214yes—
51C2×#13133201C2214yes—
52C2×#13133197C2212yes—
53C2×#13133197C2214yes—
54C2×#13133195C2214yes—
55C2×#13133194C2214yes—
56C2×#13133193C2212yes—
57C2×#13133193C2212yes—
58C2×#13133192C2212yes—
59C2×#13133192C2214yes—
60C2×#13133192C2211yescharacteristic
61C2×#13133191C2212yes—
62C2×#13133190C2214yes—
63C2×#13133190C2214yes—
64C2×#13133190C2212yes—
65C2×#13133190C2214yes—
66C2×#13133188C2211yescharacteristic
67#16811103C22132yescomplemented
68C4×#11719949C22116yescomplemented
69C2×Q8×Dic53C2211yescharacteristic
70C2×C4×Dic106C2212yes—
71C2×C4×Dic106C2214yes—
72C2×C4×D212C2211yescharacteristic
73C2×C4×D212C2211yescharacteristic
74C2×C4×D212C2212yes—
75C2×C4×D212C2214yes—
76C2×#13133179C2212yes—
77C2×#13133179C2211yescharacteristic
78C2×C4×C22⋊D53C2212yes—
79C2×#13133177C2214yes—
80C2×#13133177C2214yes—
81C2×#13133177C2214yes—
82C2×#13133175C2212yes—
83C2×#13133175C2212yes—
84C2×#13133175C2211yescharacteristic
85C2×#13133174C2214yes—
86C22×C4⋊Dic53C2212yes—
87C2×C4⋊C4×D53C2212yes—
88C2×C4⋊C4×D53C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C2×C42×D53C2212yes—
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×#11719949—28no—
102C2×#11719949—48no—
103C2×#11719949C2318yes—
104C2×#11719949C23116yes—
105C2×#11719945—216no—
106C2×#11719945C23116yes—
107C2×#11719947—48no—
108C2×#11719947C23116yes—
109C22×Dic106C2312yes—
110C22×Dic106C2312yes—
111C22×Dic106C2314yes—
112C2×Q8×D53—48no—
113C2×Q8×D53C23116yes—
114C22×D212C2312yes—
115C22×D212C2311yescharacteristic
116C22×D212C2312yes—
117C22×D212C2311yescharacteristic
118C22×D212C2314yes—
119C22×C22⋊D53C2312yes—
120C22×C22⋊D53C2312yes—
121C22×C22⋊D53C2312yes—
122C22×C22⋊D53C2314yes—
123C23×Dic53C2314yes—
124C22×C4×D53C2311yescharacteristic
125C22×C4×D53C2312yes—
126C22×C4×D53C2312yes—
127C22×C4×D53C2311yescharacteristic
128C22×C4×D53C2312yes—
129C22×C4×D53C2312yes—
130C22×C4×D53C2314yes—
131C22×C4×D53C2314yes—
132C22×C4×D53C2311yescharacteristic
133#13133217C2318yes—
134#13133216C23116yes—
135#13133216C23116yes—
136#13133216C2318yes—
137#13133215C23116yes—
138#13133213C2318yes—
139#13133212C23132yes—
140#13133207C23132yes—
141#13133205C23132yes—
142#13133205C23116yes—
143#13133203C23132yes—
144#13133203C23116yes—
145#13133202C23132yes—
146#13133201C23132yes—
147#13133197C23116yes—
148#13133197C23132yes—
149#13133195C23132yes—
150#13133194C23132yes—
151#13133193C23116yes—
152#13133193C23116yes—
153#13133192C23116yes—
154#13133192C2318yes—
155#13133192C23132yes—
156#13133191C23116yes—
157#13133190C23132yes—
158#13133190C23116yes—
159#13133190C23132yes—
160#13133190C23132yes—
161#13133188C2318yes—
162Q8×Dic53C2318yes—
163C4×Dic106C23116yes—
164C4×Dic106C23132yes—
165C4×D212C2318yes—
166C4×D212C2318yes—
167C4×D212C23116yes—
168C4×D212C23132yes—
169#13133179C23116yes—
170#13133179C2318yes—
171C4×C22⋊D53C23116yes—
172#13133177C23132yes—
173#13133177C23132yes—
174#13133177C23132yes—
175#13133175C23116yes—
176#13133175C2318yes—
177#13133175C23116yes—
178#13133174C23132yes—
179C2×C4⋊Dic53C23116yes—
180C2×C4⋊Dic53C2311yescharacteristic
181C2×C4⋊Dic53C2312yes—
182C2×C4⋊Dic53C2312yes—
183C2×C4⋊Dic53C2314yes—
184C2×C4⋊Dic53C2312yes—
185C2×C4⋊Dic53C2311yescharacteristic
186C2×#11719919C2314yes—
187C2×#11719919C2314yes—
188C2×#11719919C2314yes—
189C2×#11719919C2312yes—
190C2×#11719919C2314yes—
191C4⋊C4×D53C23116yes—
192C4⋊C4×D53C23116yes—
193C4⋊C4×D53C23116yes—
194C2×C22⋊Dic53C2312yes—
195C2×#11719921C2314yes—
196C2×#11719921C2314yes—
197C2×#11719921C2312yes—
198C2×#11719921C2314yes—
199C2×#11719921C2312yes—
200C2×#11719921C2312yes—
201C2×#11719921C2314yes—
202C2×#11719921C2312yes—
203C2×#11719921C2312yes—
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2312yes—
206C2×C4×Dic53C2311yescharacteristic
207C2×C4×Dic53C2312yes—
208C2×C4×Dic53C2311yescharacteristic
209C2×C4×Dic53C2314yes—
210C42×D53C2318yes—
211C42×D53C23116yes—
212C22×Q8×C53C2311yescharacteristic
213C22×Q8×C53C2312yes—
214C22×D4×C53C2311yescharacteristic
215C23×C4×C53C2312yes—
216C4⋊Q8×C53C2318yes—
217#126×C53C23132yes—
218#124×C53C23116yes—
219C22⋊Q8×C53C23116yes—
220C4×Q8×C53C23116yes—
221C4×Q8×C53C2318yes—
222C4×D4×C53C2318yes—
223#117×C53C23116yes—
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C4⋊C4×C53C2312yes—
226C2×C4⋊C4×C53C2311yescharacteristic
227C2×C4⋊C4×C53C2314yes—
228C2×C4⋊C4×C53C2312yes—
229C2×C4⋊C4×C53C2312yes—
230C2×C22⋊C4×C53C2314yes—
231C2×C22⋊C4×C53C2312yes—
232C2×C22⋊C4×C53C2314yes—
233C2×C42×C53C2314yes—
234C2×C42×C53C2311yescharacteristic
235C2×C42×C53C2312yes—
236C24×C53C2412yes—
237C23×D53C2412yes—
238C23×D53C2412yes—
239C23×D53C2411yescharacteristic
240C2×Q8×C53—24no—
241C2×Q8×C53—28no—
242C2×Q8×C53C2414yes—
243C2×Q8×C53C2418yes—
244C2×D4×C53—24no—
245C2×D4×C53C2414yes—
246C22×C4×C53—28no—
247C22×C4×C53C2412yes—
248C22×C4×C53C2412yes—
249C22×C4×C53C2411yescharacteristic
250C22×C4×C53C2412yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2418yes—
253C22×C4×C53C2411yescharacteristic
254C22×C4×C53C2411yescharacteristic
255C2×C22⋊D53—28no—
256C2×C22⋊D53—28no—
257C2×C22⋊D53—28no—
258C2×C22⋊D53—48no—
259C2×C22⋊D53C2418yes—
260C2×C22⋊D53C2418yes—
261C2×C22⋊D53C2418yes—
262C2×C22⋊D53C24116yes—
263C22×Dic53—48no—
264C22×Dic53C2411yescharacteristic
265C22×Dic53C2412yes—
266C22×Dic53C2412yes—
267C22×Dic53C2414yes—
268C22×Dic53C24116yes—
269C22×Dic53C2411yescharacteristic
270C22×Dic53C2411yescharacteristic
271#11719949—232no—
272#11719949—432no—
273Q8×D53—432no—
274#11719947—432no—
275#11719945—264no—
276C2×D212—28no—
277C2×D212—28no—
278C2×D212—24no—
279C2×D212—24no—
280C2×D212—48no—
281C2×D212C2418yes—
282C2×D212C2414yes—
283C2×D212C2418yes—
284C2×D212C2414yes—
285C2×D212C24116yes—
286C2×C4×D53—28no—
287C2×C4×D53—24no—
288C2×C4×D53—28no—
289C2×C4×D53—28no—
290C2×C4×D53—24no—
291C2×C4×D53—28no—
292C2×C4×D53—48no—
293C2×C4×D53—48no—
294C2×C4×D53#4118yescomplemented
295C2×C4×D53C2414yes—
296C2×C4×D53C2418yes—
297C2×C4×D53C2418yes—
298C2×C4×D53C2414yes—
299C2×C4×D53C2418yes—
300C2×C4×D53C2418yes—
301C2×C4×D53C24116yes—
302C2×C4×D53C24116yes—
303C2×C4×D53C2414yes—
304C2×Dic106—28no—
305C2×Dic106—28no—
306C2×Dic106—48no—
307C2×Dic106C2418yes—
308C2×Dic106C2418yes—
309C2×Dic106C24116yes—
310C4⋊C4×C53C2414yes—
311C4⋊C4×C53C2418yes—
312C4⋊C4×C53C2414yes—
313C4⋊C4×C53C24116yes—
314C4⋊C4×C53C2418yes—
315C4⋊C4×C53C2418yes—
316C22⋊C4×C53C24116yes—
317C22⋊C4×C53C2418yes—
318C22⋊C4×C53C24116yes—
319C42×C53C24116yes—
320C42×C53C2414yes—
321C42×C53C2418yes—
322C22⋊Dic53C2418yes—
323#11719921C24116yes—
324#11719921C24116yes—
325#11719921C2418yes—
326#11719921C24116yes—
327#11719921C2418yes—
328#11719921C2418yes—
329#11719921C24116yes—
330#11719921C2418yes—
331#11719921C2418yes—
332C4⋊Dic53C2414yes—
333C4⋊Dic53C2418yes—
334C4⋊Dic53C2418yes—
335C4⋊Dic53C24116yes—
336C4⋊Dic53C2418yes—
337C4⋊Dic53C2414yes—
338#11719919C24116yes—
339#11719919C24116yes—
340#11719919C24116yes—
341#11719919C2418yes—
342#11719919C24116yes—
343C4×Dic53C2414yes—
344C4×Dic53C2418yes—
345C4×Dic53C2414yes—
346C4×Dic53C2418yes—
347C4×Dic53C2414yes—
348C4×Dic53C24116yes—
349C23×C53—24no—
350C23×C53—24no—
351C23×C53—24no—
352C23×C53C2514yes—
353C23×C53C2511yescharacteristic
354C22×D53—22no—
355C22×D53—22no—
356C22×D53—24no—
357C22×D53—24no—
358C22×D53—24no—
359C22×D53—24no—
360C22×D53—24no—
361C22×D53—24no—
362C22×D53C2×#4114yes—
363C22×D53C2514yes—
364C22×D53C2514yes—
365C22×D53C2512yes—
366Q8×C53—28no—
367Q8×C53—216no—
368D4×C53—28no—
369C2×C4×C53—24no—
370C2×C4×C53—24no—
371C2×C4×C53—28no—
372C2×C4×C53—24no—
373C2×C4×C53—22no—
374C2×C4×C53—216no—
375C2×C4×C53C2×#4114yes—
376C2×C4×C53H(5,𝔽2)14yes—
377C2×C4×C53C2518yes—
378C2×C4×C53C2514yes—
379C2×C4×C53C2514yes—
380C2×C4×C53C2514yes—
381C2×C4×C53C2512yes—
382C2×C4×C53C2512yes—
383C2×C4×C53C2512yes—
384C22⋊D53—216no—
385C22⋊D53—216no—
386C22⋊D53—216no—
387C22⋊D53—416no—
388C2×Dic53—24no—
389C2×Dic53—28no—
390C2×Dic53—22no—
391C2×Dic53—24no—
392C2×Dic53—416no—
393C2×Dic53C2×#4114yes—
394C2×Dic532−1+414yes—
395C2×Dic53C2512yes—
396C2×Dic53C2518yes—
397C2×Dic53C2514yes—
398C2×Dic53C2514yes—
399C2×Dic53C2512yes—
400C2×Dic53C2512yes—
401D212—216no—
402D212—216no—
403D212—28no—
404D212—28no—
405D212—416no—
406C4×D53—216no—
407C4×D53—216no—
408C4×D53—28no—
409C4×D53—216no—
410C4×D53—28no—
411C4×D53—216no—
412C4×D53—416no—
413C4×D53—416no—
414C4×D53C2×#41116yescomplemented
415Dic106—216no—
416Dic106—216no—
417Dic106—416no—
418C2×#3511—531nomaximal, Sylow
419C22×C53—24no—
420C22×C53—24no—
421C22×C53—24no—
422C22×C53—48no—
423C22×C53C22×#4112yes—
424C22×C53C2×H(5,𝔽2)12yes—
425C22×C53C2×2−1+412yes—
426C22×C53C2611yescharacteristic
427C2×D53—22no—
428C2×D53—22no—
429C2×D53—28no—
430C2×D53—24no—
431C2×D53—24no—
432C2×D53—24no—
433C2×D53—24no—
434C2×D53—24no—
435C2×D53—24no—
436C2×D53—48no—
437C2×D53—48no—
438C2×D53C22×#4114yes—
439C4×C53—24no—
440C4×C53—24no—
441C4×C53—28no—
442C4×C53—24no—
443C4×C53—22no—
444C4×C53C22×#4114yes—
445C4×C53C2×H(5,𝔽2)14yes—
446Dic53—24no—
447Dic53—28no—
448Dic53—22no—
449Dic53—24no—
450Dic53C22×#4114yes—
451Dic53C2×2−1+414yes—
452#3511—5332no—
453C2×#556—531no—
454C2×#556D5311yescharacteristic, complemented
455C2×#555—532no—
456C2×#554—532no—
457C2×#553—534no—
458C2×#548—532no—
459C2×#548—532no—
460C2×#547—531no—
461C2×#547—531no—
462C2×#542—534no—
463C2×#537—532no—
464C2×#533—532no—
465C2×#532—532no—
466C2×#532—531no—
467C22×C4⋊Q8—531no—
468C2×#520—532no—
469C2×C4×#41—531no—
470C2×C53—44no—
471C2×C53#351114yescomplemented
472C2×C53C23×#4111yescharacteristic
473C2×C53C22×H(5,𝔽2)11yescharacteristic
474C2×C53C22×2−1+411yescharacteristic
475D53—24no—
476D53—44no—
477D53—44no—
478C22×#41—531no—
479C22×#41—532no—
480C22×#41—532no—
481C22×#41—532no—
482C23×Q8—532no—
483#556—5316no—
484#556C2×D53116yescomplemented
485#555—5332no—
486#554—5332no—
487#553—5364no—
488#548—5332no—
489#548—5332no—
490#547—5316no—
491#547—5316no—
492#542—5364no—
493#537—5332no—
494#533—5332no—
495#532—5332no—
496#532—5316no—
497C2×C4⋊Q8—532no—
498C2×C4⋊Q8—5316no—
499C2×C4⋊Q8—532no—
500C2×C4⋊Q8—532no—
501C2×C4⋊Q8—531no—
502C2×C4⋊Q8—531no—
503C2×C4⋊Q8C2×D5311yescharacteristic
504C2×#127—531no—
505C2×#126—534no—
506C2×#126C2×D5314yes—
507C2×#125—534no—
508C2×#124—532no—
509C2×#124—534no—
510C2×#124—532no—
511C2×#124—534no—
512C2×#124C2×D5312yes—
513C2×#123—534no—
514C2×#123—534no—
515C2×C22⋊Q8—532no—
516C2×C22⋊Q8—532no—
517C2×C22⋊Q8—534no—
518C2×C22⋊Q8—532no—
519C2×C22⋊Q8—534no—
520C2×C22⋊Q8—534no—
521C2×C22⋊Q8C2×D5312yes—
522C2×#121—531no—
523C2×#121—532no—
524C2×#121—531no—
525C2×#121—532no—
526C2×#121—534no—
527C2×#121—534no—
528C2×#121—532no—
529C2×#121—534no—
530C2×#121—534no—
531#520—5332no—
532C4×#41—5316no—
533C2×C4×Q8—531no—
534C2×C4×Q8—534no—
535C2×C4×Q8—532no—
536C2×C4×Q8C2×D5311yescharacteristic
537C2×C4×Q8C2×D5312yes—
538C2×C4×D4—532no—
539C2×C4×D4—532no—
540C2×C4×D4—531no—
541C2×C4×D4—534no—
542C2×C4×D4—534no—
543C2×C4×D4—534no—
544C2×C4×D4—531no—
545C2×C4×D4—532no—
546C2×C4×D4—534no—
547C2×C4×D4—531no—
548C2×C4×D4C2×D5311yescharacteristic
549C2×#117—531no—
550C2×#117—532no—
551C2×#117—532no—
552C2×#117—534no—
553C2×#117C2×D5312yes—
554C22×C4⋊C4—532no—
555C22×C4⋊C4—532no—
556C22×C4⋊C4—532no—
557C22×C4⋊C4—532no—
558C22×C42—531no—
559C22×C42—532no—
560C53C2×#351111yescharacteristic, complemented, Sylow
561C2×#41—538no—
562C2×#41—5316no—
563C2×#41—5316no—
564C2×#41—5316no—
565C2×#41—10616no—
566C2×#41—1068no—
567C2×#41—2128no—
568C2×#41—2128no—
569C22×Q8—5316no—
570C22×Q8—532no—
571C22×Q8—532no—
572C22×Q8—534no—
573C22×Q8—2128no—
574C22×Q8C22×D5311yescharacteristic
575C22×Q8C22×D5312yes—
576C22×D4—532no—
577C22×D4—532no—
578C22×D4—532no—
579C22×D4—534no—
580C22×D4—532no—
581C22×D4—532no—
582C22×D4—531no—
583C22×D4—531no—
584C22×D4—534no—
585C22×D4C22×D5311yescharacteristic
586C23×C4—531no—
587C23×C4—534no—
588C23×C4—531no—
589C23×C4—532no—
590C23×C4—532no—
591C23×C4—532no—
592C23×C4—531no—
593C23×C4—532no—
594C23×C4—534no—
595C23×C4—534no—
596C23×C4C22×D5312yes—
597C4⋊Q8—5316no—
598C4⋊Q8—5316no—
599C4⋊Q8—5316no—
600C4⋊Q8—538no—
601C4⋊Q8—538no—
602C4⋊Q8C22×D5318yes—
603#127—538no—
604#126—5332no—
605#126C22×D53132yes—
606#125—5332no—
607#124—5316no—
608#124—5332no—
609#124—5316no—
610#124—5332no—
611#124C22×D53116yes—
612#123—5332no—
613#123—5332no—
614C22⋊Q8—5316no—
615C22⋊Q8—5316no—
616C22⋊Q8—5332no—
617C22⋊Q8—5316no—
618C22⋊Q8—5332no—
619C22⋊Q8—5332no—
620C22⋊Q8C22×D53116yes—
621#121—538no—
622#121—5316no—
623#121—538no—
624#121—5316no—
625#121—5332no—
626#121—5332no—
627#121—5316no—
628#121—5332no—
629#121—5332no—
630C4×Q8—538no—
631C4×Q8—5332no—
632C4×Q8—5316no—
633C4×Q8C22×D5318yes—
634C4×Q8C22×D53116yes—
635C4×D4—5316no—
636C4×D4—5316no—
637C4×D4—538no—
638C4×D4—5332no—
639C4×D4—5332no—
640C4×D4—5332no—
641C4×D4—538no—
642C4×D4—5316no—
643C4×D4—5332no—
644C4×D4—538no—
645C4×D4C22×D5318yes—
646#117—538no—
647#117—5316no—
648#117—5316no—
649#117—5332no—
650#117C22×D53116yes—
651C2×C4⋊C4—531no—
652C2×C4⋊C4—532no—
653C2×C4⋊C4—534no—
654C2×C4⋊C4—534no—
655C2×C4⋊C4—534no—
656C2×C4⋊C4—534no—
657C2×C4⋊C4—5316no—
658C2×C4⋊C4—532no—
659C2×C4⋊C4—532no—
660C2×C4⋊C4—532no—
661C2×C4⋊C4—531no—
662C2×C4⋊C4—534no—
663C2×C4⋊C4—5316no—
664C2×C4⋊C4—5316no—
665C2×C4⋊C4—5316no—
666C2×C4⋊C4C22×D5312yes—
667C2×C4⋊C4C22×D5312yes—
668C2×C4⋊C4C22×D5311yescharacteristic
669C2×C4⋊C4C22×D5312yes—
670C2×C4⋊C4C22×D5311yescharacteristic
671C2×C4⋊C4C22×D5314yes—
672C2×C22⋊C4—532no—
673C2×C22⋊C4—532no—
674C2×C22⋊C4—534no—
675C2×C22⋊C4—532no—
676C2×C22⋊C4—532no—
677C2×C22⋊C4—534no—
678C2×C22⋊C4—534no—
679C2×C22⋊C4—534no—
680C2×C22⋊C4—532no—
681C2×C22⋊C4—532no—
682C2×C22⋊C4C22×D5314yes—
683C2×C22⋊C4C22×D5314yes—
684C2×C22⋊C4C22×D5312yes—
685C2×C42—532no—
686C2×C42—534no—
687C2×C42—531no—
688C2×C42—532no—
689C2×C42—531no—
690C2×C42—531no—
691C2×C42—538no—
692C2×C42—5316no—
693C2×C42C22×D5314yes—
694C2×C42C22×D5311yescharacteristic
695C2×C42C22×D5312yes—
696C24—531no—
697C24—532no—
698C24—532no—
699C24C23×D5312yes—
700#41—10664no—
701#41—10632no—
702#41—21232no—
703#41—21232no—
704C2×Q8—24no—
705C2×Q8—28no—
706C2×Q8—538no—
707C2×Q8—538no—
708C2×Q8—5316no—
709C2×Q8—1068no—
710C2×Q8—1068no—
711C2×Q8—2128no—
712C2×Q8—21232no—
713C2×Q8C23×D5314yes—
714C2×Q8C23×D5318yes—
715C2×D4—24no—
716C2×D4—538no—
717C2×D4—538no—
718C2×D4—538no—
719C2×D4—5316no—
720C2×D4—538no—
721C2×D4—538no—
722C2×D4—534no—
723C2×D4—534no—
724C2×D4—5316no—
725C2×D4—1068no—
726C2×D4—1068no—
727C2×D4—1068no—
728C2×D4—1068no—
729C2×D4—1068no—
730C2×D4—1064no—
731C2×D4—1064no—
732C2×D4—2128no—
733C2×D4—2128no—
734C2×D4C23×D5314yes—
735C22×C4—28no—
736C22×C4—531no—
737C22×C4—531no—
738C22×C4—538no—
739C22×C4—534no—
740C22×C4—531no—
741C22×C4—532no—
742C22×C4—532no—
743C22×C4—534no—
744C22×C4—5316no—
745C22×C4—534no—
746C22×C4—538no—
747C22×C4—538no—
748C22×C4—534no—
749C22×C4—538no—
750C22×C4—538no—
751C22×C4—5316no—
752C22×C4—5316no—
753C22×C4—1064no—
754C22×C4—1068no—
755C22×C4—1068no—
756C22×C4—1068no—
757C22×C4—1064no—
758C22×C4—1068no—
759C22×C4—2128no—
760C22×C4—2128no—
761C22×C4—2128no—
762C22×C4C23×D5318yes—
763C22×C4C23×D5312yes—
764C22×C4C23×D5311yescharacteristic
765C22×C4C23×D5312yes—
766C22×C4C23×D5312yes—
767C22×C4C23×D5314yes—
768C22×C4C23×D5311yescharacteristic
769C22×C4C23×D5311yescharacteristic
770C4⋊C4—534no—
771C4⋊C4—538no—
772C4⋊C4—5316no—
773C4⋊C4—5316no—
774C4⋊C4—5316no—
775C4⋊C4—5316no—
776C4⋊C4—538no—
777C4⋊C4—538no—
778C4⋊C4—538no—
779C4⋊C4—534no—
780C4⋊C4—5316no—
781C4⋊C4C23×D5318yes—
782C4⋊C4C23×D5318yes—
783C4⋊C4C23×D5314yes—
784C4⋊C4C23×D5318yes—
785C4⋊C4C23×D5314yes—
786C4⋊C4C23×D53116yes—
787C22⋊C4—538no—
788C22⋊C4—538no—
789C22⋊C4—5316no—
790C22⋊C4—538no—
791C22⋊C4—538no—
792C22⋊C4—5316no—
793C22⋊C4—5316no—
794C22⋊C4—5316no—
795C22⋊C4—538no—
796C22⋊C4—538no—
797C22⋊C4C23×D53116yes—
798C22⋊C4C23×D53116yes—
799C22⋊C4C23×D5318yes—
800C42—534no—
801C42—538no—
802C42—534no—
803C42—538no—
804C42—534no—
805C42—5316no—
806C42C23×D5314yes—
807C42C23×D5318yes—
808C42C23×D53116yes—
809C23—24no—
810C23—24no—
811C23—24no—
812C23—534no—
813C23—532no—
814C23—534no—
815C23—534no—
816C23—1062no—
817C23—1062no—
818C23—1064no—
819C23—1064no—
820C23—1064no—
821C23—1064no—
822C23—1064no—
823C23—1064no—
824C23C24×D5314yes—
825C23C24×D5311yescharacteristic
826Q8—28no—
827Q8—216no—
828Q8—10616no—
829Q8—10616no—
830Q8—21216no—
831D4—28no—
832D4—10616no—
833D4—10616no—
834D4—10616no—
835D4—10616no—
836D4—10616no—
837D4—1068no—
838D4—1068no—
839D4—21216no—
840D4—21216no—
841C2×C4—24no—
842C2×C4—24no—
843C2×C4—28no—
844C2×C4—24no—
845C2×C4—22no—
846C2×C4—216no—
847C2×C4—534no—
848C2×C4—534no—
849C2×C4—532no—
850C2×C4—532no—
851C2×C4—5316no—
852C2×C4—532no—
853C2×C4—534no—
854C2×C4—534no—
855C2×C4—538no—
856C2×C4—1068no—
857C2×C4—10616no—
858C2×C4—10616no—
859C2×C4—1064no—
860C2×C4—1064no—
861C2×C4—1062no—
862C2×C4—1068no—
863C2×C4—10616no—
864C2×C4—1068no—
865C2×C4—10616no—
866C2×C4—21216no—
867C2×C4—21216no—
868C2×C4—21216no—
869C2×C4#41×D5314yes—
870C2×C4#1313326314yes—
871C2×C4C24×D5314yes—
872C2×C4C24×D5312yes—
873C2×C4C24×D5314yes—
874C2×C4C24×D5314yes—
875C2×C4C24×D5318yes—
876C2×C4C24×D5312yes—
877C2×C4C24×D5312yes—
878C22—24no—
879C22—24no—
880C22—24no—
881C22—48no—
882C22—534no—
883C22—1068no—
884C22—1062no—
885C22—1062no—
886C22—1064no—
887C22—1064no—
888C22—1064no—
889C22—1064no—
890C22—1064no—
891C22—1064no—
892C22—2128no—
893C22—2128no—
894C22C2×#41×D5312yes—
895C22C2×#1313326312yes—
896C222−1+4×D5312yes—
897C22C25×D5311yescharacteristic
898C4—24no—
899C4—24no—
900C4—28no—
901C4—24no—
902C4—22no—
903C4—534no—
904C4—534no—
905C4—1064no—
906C4—1064no—
907C4—1062no—
908C4—1068no—
909C4C2×#41×D5314yes—
910C4C2×#1313326314yes—
911C2—44no—
912C2—1064no—
913C2—2124no—
914C2—2124no—
915C2#2028861914yesdirect product factor
916C2C22×#41×D5311yescharacteristic
917C2C22×#1313326311yescharacteristic
918C2C2×2−1+4×D5311yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#556C2
socleC23×C53C25
hypercenterC2×#556D53
hypocenterC53C2×#3511
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20288619C2direct (N × H)
2. C2×#16811346C2semidirect
3. C2×#16811336C2semidirect
4. C2×#16811331C2semidirect
5. C2×#16811324C2semidirect
6. C2×#16811285C2semidirect
7. C2×#16811281C2semidirect
8. C2×#16811277C2semidirect
9. C2×#16811276C2semidirect
10. C2×#16811239C2semidirect
11. C2×#16811203C2semidirect
12. C2×#16811177C2semidirect
13. C2×#16811172C2semidirect
14. C2×#16811170C2semidirect
15. C2×C4⋊Q8×D53C2semidirect
16. C2×#16811103C2semidirect
17. C2×C4×#11719949C2semidirect
18. C2×C53×#556C2semidirect
24. #16811346C22semidirect
25. #16811336C22semidirect
26. #16811331C22semidirect
27. #16811324C22semidirect
28. #16811285C22semidirect
29. #16811281C22semidirect
30. #16811277C22semidirect
31. #16811276C22semidirect
32. #16811239C22semidirect
33. #16811203C22semidirect
34. #16811177C22semidirect
35. #16811172C22semidirect
36. #16811170C22semidirect
42. C4⋊Q8×D53C22semidirect
67. #16811103C22semidirect
68. C4×#11719949C22semidirect
92. C53×#556C22semidirect
294. C2×C4×D53#41semidirect
414. C4×D53C2×#41semidirect
454. C2×#556D53semidirect
471. C2×C53#3511semidirect
484. #556C2×D53semidirect
560. C53C2×#3511semidirect
915. C2#20288619direct (N × H)

Maximal subgroups

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

subgroupindex
#202886192
C2×#168113462
C2×#168113362
C2×#168113312
C2×#168113242
C2×#168112852
C2×#168112812
C2×#168112772
C2×#168112762
C2×#168112392
C2×#168112032
C2×#168111772
C2×#168111722
C2×#168111702
C2×C4⋊Q8×D532
C2×#168111032
C2×C4×#117199492
C2×C53×#5562
C2×#351153