Finite Group Databasebeta

← C2×#20288618 #28292461

Subgroups — C2×#20288618 #28292461

Order 13568.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288618C2132yesmaximal, direct product factor
2C2×#16811341C212yesmaximal, complemented
3C2×#16811336C212yesmaximal, complemented
4C2×#16811328C212yesmaximal, complemented
5C2×#16811322C214yesmaximal, complemented
6C2×#16811282C214yesmaximal, complemented
7C2×#16811274C212yesmaximal, complemented
8C2×#16811245C212yesmaximal, complemented
9C2×#16811238C212yesmaximal, complemented
10C2×#16811204C211yesmaximal, characteristic, complemented
11C2×#16811201C211yesmaximal, characteristic, complemented
12C2×#16811177C212yesmaximal, complemented
13C2×#16811170C212yesmaximal, complemented
14C2×#16811169C211yesmaximal, characteristic, complemented
15C22×#13133216C211yesmaximal, characteristic, complemented
16C2×#16811103C211yesmaximal, characteristic, complemented
17C2×#16811091C211yesmaximal, characteristic, complemented
18C2×C53×#520C211yesmaximal, characteristic, complemented
19C22×#11719945C2211yescharacteristic
20C22×#11719945C2211yescharacteristic
21C22×#11719945C2214yes—
22C23×Dic106C2212yes—
23#16811341C22132yescomplemented
24#16811336C22132yescomplemented
25#16811328C22132yescomplemented
26#16811322C22164yescomplemented
27#16811282C22164yescomplemented
28#16811274C22132yescomplemented
29#16811245C22132yescomplemented
30#16811238C22132yescomplemented
31#16811204C22116yescomplemented
32#16811201C22116yescomplemented
33#16811177C22132yescomplemented
34#16811170C22132yescomplemented
35#16811169C22116yescomplemented
36C2×#13133216C2212yes—
37C2×#13133216C2212yes—
38C2×#13133216C2212yes—
39C2×#13133216C2212yes—
40C2×#13133216C22116yescomplemented
41C2×#13133215C2211yescharacteristic
42C2×#13133213C2211yescharacteristic
43C2×#13133211C2214yes—
44C2×#13133210C2214yes—
45C2×#13133207C2214yes—
46C2×#13133206C2211yescharacteristic
47C2×#13133205C2214yes—
48C2×#13133204C2211yescharacteristic
49C2×#13133203C2214yes—
50C2×#13133203C2214yes—
51C2×#13133202C2214yes—
52C2×#13133200C2214yes—
53C2×#13133197C2212yes—
54C2×#13133197C2212yes—
55C2×#13133196C2212yes—
56C2×#13133196C2214yes—
57C2×#13133195C2214yes—
58C2×#13133195C2214yes—
59C2×#13133193C2212yes—
60C2×#13133192C2212yes—
61C2×#13133192C2212yes—
62C2×#13133191C2212yes—
63C2×#13133191C2214yes—
64C2×#13133190C2214yes—
65C2×#13133189C2214yes—
66C2×#13133189C2212yes—
67C2×#13133189C2212yes—
68C2×#13133188C2212yes—
69#16811103C22116yescomplemented
70#16811091C22116yescomplemented
71C2×C4×Dic106C2214yes—
72C2×C4×Dic106C2212yes—
73C2×#13133182C2211yescharacteristic
74C2×#13133182C2211yescharacteristic
75C2×C4×D212C2212yes—
76C2×#13133179C2211yescharacteristic
77C2×#13133179C2211yescharacteristic
78C2×C4×C22⋊D53C2212yes—
79C2×C4×C22⋊D53C2214yes—
80C2×C4×C22⋊D53C2212yes—
81C2×#13133177C2212yes—
82C2×#13133177C2212yes—
83C2×#13133177C2214yes—
84C2×#13133175C2212yes—
85C2×#13133174C2214yes—
86C2×#13133174C2212yes—
87C22×C4⋊Dic53C2211yescharacteristic
88C22×#11719919C2212yes—
89C2×C4⋊C4×D53C2212yes—
90C22×C4×Dic53C2211yescharacteristic
91C2×C42×D53C2212yes—
92C22×#41×C53C2211yescharacteristic
93C53×#520C22116yescomplemented
94C2×C4×Q8×C53C2212yes—
95C2×C4×D4×C53C2212yes—
96C2×C4×D4×C53C2214yes—
97C2×#117×C53C2212yes—
98C2×#117×C53C2211yescharacteristic
99C22×C4⋊C4×C53C2211yescharacteristic
100C22×C4⋊C4×C53C2212yes—
101C2×#11719945—28no—
102C2×#11719945—28no—
103C2×#11719945—416no—
104C2×#11719945C2318yes—
105C2×#11719945C2318yes—
106C2×#11719945C23132yes—
107C22×Dic106—48no—
108C22×Dic106C2311yescharacteristic
109C22×Dic106C2311yescharacteristic
110C22×Dic106C2314yes—
111C22×Dic106C23116yes—
112C22×Dic106C2314yes—
113C22×D212C2311yescharacteristic
114C22×D212C2311yescharacteristic
115C22×D212C2314yes—
116C22×C22⋊D53C2312yes—
117C22×C22⋊D53C2312yes—
118C22×C22⋊D53C2312yes—
119C22×C22⋊D53C2312yes—
120C22×C22⋊D53C2314yes—
121C23×Dic53C2311yescharacteristic
122C23×Dic53C2311yescharacteristic
123C23×Dic53C2312yes—
124C22×C4×D53C2312yes—
125C22×C4×D53C2312yes—
126C22×C4×D53C2312yes—
127C22×C4×D53C2312yes—
128C22×C4×D53C2314yes—
129#13133216C23116yes—
130#13133216C23116yes—
131#13133216C23116yes—
132#13133216C23116yes—
133#13133215C2318yes—
134#13133213C2318yes—
135#13133211C23132yes—
136#13133210C23132yes—
137#13133207C23132yes—
138#13133206C2318yes—
139#13133205C23132yes—
140#13133204C2318yes—
141#13133203C23132yes—
142#13133203C23132yes—
143#13133202C23132yes—
144#13133200C23132yes—
145#13133197C23116yes—
146#13133197C23116yes—
147#13133196C23132yes—
148#13133196C23116yes—
149#13133195C23132yes—
150#13133195C23132yes—
151#13133193C23116yes—
152#13133192C23116yes—
153#13133192C23116yes—
154#13133191C23116yes—
155#13133191C23132yes—
156#13133190C23132yes—
157#13133189C23116yes—
158#13133189C23132yes—
159#13133189C23116yes—
160#13133188C23116yes—
161C4×Dic106C23132yes—
162C4×Dic106C23116yes—
163#13133182C2318yes—
164#13133182C2318yes—
165C4×D212C23116yes—
166#13133179C2318yes—
167#13133179C2318yes—
168C4×C22⋊D53C23116yes—
169C4×C22⋊D53C23132yes—
170C4×C22⋊D53C23116yes—
171#13133177C23116yes—
172#13133177C23132yes—
173#13133177C23116yes—
174#13133175C23116yes—
175#13133174C23132yes—
176#13133174C23116yes—
177C2×C4⋊Dic53C2312yes—
178C2×C4⋊Dic53C2312yes—
179C2×C4⋊Dic53C2318yes—
180C2×C4⋊Dic53C2314yes—
181C2×#11719919C23116yes—
182C2×#11719919C2314yes—
183C2×#11719919C2314yes—
184C2×#11719919C2314yes—
185C2×#11719919C2312yes—
186C2×#11719919C2312yes—
187C2×#11719919C2312yes—
188C2×#11719919C2312yes—
189C2×#11719919C2314yes—
190C4⋊C4×D53C23116yes—
191C2×C22⋊Dic53C2314yes—
192C2×C22⋊Dic53C2312yes—
193C2×C22⋊Dic53C2312yes—
194C2×#11719921C2312yes—
195C2×#11719921C2312yes—
196C2×#11719921C2314yes—
197C2×#11719921C2314yes—
198C2×#11719921C2314yes—
199C2×#11719921C2312yes—
200C2×#11719921C2312yes—
201C2×#11719921C2314yes—
202C2×C4×Dic53C2311yescharacteristic
203C2×C4×Dic53C2312yes—
204C2×C4×Dic53C2312yes—
205C2×C4×Dic53C2311yescharacteristic
206C2×C4×Dic53C2311yescharacteristic
207C2×C4×Dic53C2311yescharacteristic
208C2×C4×Dic53C2318yes—
209C2×C4×Dic53C2314yes—
210C42×D53C23116yes—
211C2×#41×C53—28no—
212C2×#41×C53C2318yes—
213C22×Q8×C53C2311yescharacteristic
214C22×D4×C53C2311yescharacteristic
215C22×D4×C53C2312yes—
216C23×C4×C53C2312yes—
217C23×C4×C53C2312yes—
218C23×C4×C53C2314yes—
219C23×C4×C53C2311yescharacteristic
220C4×Q8×C53C23116yes—
221C4×D4×C53C23132yes—
222C4×D4×C53C23116yes—
223#117×C53C23116yes—
224#117×C53C2318yes—
225C2×C4⋊C4×C53C23116yes—
226C2×C4⋊C4×C53C2311yescharacteristic
227C2×C4⋊C4×C53C2312yes—
228C2×C4⋊C4×C53C2312yes—
229C2×C4⋊C4×C53C2314yes—
230C2×C4⋊C4×C53C2318yes—
231C2×C4⋊C4×C53C2311yescharacteristic
232C2×C22⋊C4×C53C2312yes—
233C2×C22⋊C4×C53C2314yes—
234C2×C42×C53C2312yes—
235C2×C42×C53C2314yes—
236C24×C53C2412yes—
237C24×C53C2411yescharacteristic
238C23×D53C2412yes—
239C23×D53C2412yes—
240#41×C53—232no—
241C2×Q8×C53—24no—
242C2×Q8×C53C2414yes—
243C2×D4×C53—28no—
244C2×D4×C53—24no—
245C2×D4×C53C2414yes—
246C2×D4×C53C2418yes—
247C22×C4×C53—28no—
248C22×C4×C53—44no—
249C22×C4×C53—48no—
250C22×C4×C53#4118yescomplemented
251C22×C4×C53C2412yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2414yes—
255C22×C4×C53C2418yes—
256C22×C4×C53C2418yes—
257C22×C4×C53C24116yes—
258C22×C4×C53C2411yescharacteristic
259C22×C4×C53C2411yescharacteristic
260C22×C4×C53C2414yes—
261C2×C22⋊D53—28no—
262C2×C22⋊D53—28no—
263C2×C22⋊D53—28no—
264C2×C22⋊D53—28no—
265C2×C22⋊D53—48no—
266C2×C22⋊D53C2418yes—
267C2×C22⋊D53C2418yes—
268C2×C22⋊D53C2418yes—
269C2×C22⋊D53C2418yes—
270C2×C22⋊D53C24116yes—
271C22×Dic53—24no—
272C22×Dic53—24no—
273C22×Dic53—44no—
274C22×Dic53C2411yescharacteristic
275C22×Dic53C2411yescharacteristic
276C22×Dic53C2412yes—
277C22×Dic53C2412yes—
278C22×Dic53C2414yes—
279C22×Dic53C2414yes—
280C22×Dic53C2414yes—
281C22×Dic53C2418yes—
282C22×Dic53C2411yescharacteristic
283C22×Dic53C2411yescharacteristic
284#11719945—232no—
285#11719945—232no—
286#11719945—464no—
287C2×D212—24no—
288C2×D212—24no—
289C2×D212—48no—
290C2×D212C2414yes—
291C2×D212C2414yes—
292C2×D212C24116yes—
293C2×C4×D53—28no—
294C2×C4×D53—28no—
295C2×C4×D53—28no—
296C2×C4×D53—28no—
297C2×C4×D53—48no—
298C2×C4×D53C2418yes—
299C2×C4×D53C2418yes—
300C2×C4×D53C2418yes—
301C2×C4×D53C2418yes—
302C2×C4×D53C24116yes—
303C2×Dic106—24no—
304C2×Dic106—24no—
305C2×Dic106—216no—
306C2×Dic106—432no—
307C2×Dic106—48no—
308C2×Dic106C2414yes—
309C2×Dic106C2414yes—
310C2×Dic106C24116yes—
311C2×Dic106C24116yes—
312C4⋊C4×C53C2414yes—
313C4⋊C4×C53C2418yes—
314C4⋊C4×C53C2418yes—
315C4⋊C4×C53C24116yes—
316C4⋊C4×C53C2414yes—
317C22⋊C4×C53C2418yes—
318C22⋊C4×C53C24116yes—
319C42×C53C2418yes—
320C42×C53C24116yes—
321C22⋊Dic53C24116yes—
322C22⋊Dic53C2418yes—
323C22⋊Dic53C2418yes—
324#11719921C2418yes—
325#11719921C2418yes—
326#11719921C24116yes—
327#11719921C24116yes—
328#11719921C24116yes—
329#11719921C2418yes—
330#11719921C2418yes—
331#11719921C24116yes—
332C4⋊Dic53C2418yes—
333C4⋊Dic53C2418yes—
334C4⋊Dic53C24116yes—
335#11719919C24116yes—
336#11719919C24116yes—
337#11719919C24116yes—
338#11719919C2418yes—
339#11719919C2418yes—
340#11719919C2418yes—
341#11719919C2418yes—
342#11719919C24116yes—
343C4×Dic53C2414yes—
344C4×Dic53C2418yes—
345C4×Dic53C2418yes—
346C4×Dic53C2414yes—
347C4×Dic53C2414yes—
348C4×Dic53C2414yes—
349C4×Dic53C24116yes—
350C23×C53—22no—
351C23×C53—22no—
352C23×C53—24no—
353C23×C53—24no—
354C23×C53—24no—
355C23×C53C2×#4114yes—
356C23×C53C2514yes—
357C23×C53C2512yes—
358C23×C53C2511yescharacteristic
359C22×D53—24no—
360C22×D53—24no—
361C22×D53—24no—
362C22×D53—24no—
363C22×D53—24no—
364C22×D53—24no—
365C22×D53C2514yes—
366C22×D53C2514yes—
367Q8×C53—28no—
368D4×C53—216no—
369D4×C53—28no—
370C2×C4×C53—24no—
371C2×C4×C53—28no—
372C2×C4×C53—24no—
373C2×C4×C53—24no—
374C2×C4×C53—216no—
375C2×C4×C53—48no—
376C2×C4×C53—416no—
377C2×C4×C53C2×#4114yes—
378C2×C4×C53C2×#4114yes—
379C2×C4×C53C2×#41116yescomplemented
380C2×C4×C53C2518yes—
381C2×C4×C53C2514yes—
382C2×C4×C53C2514yes—
383C2×C4×C53C2514yes—
384C2×C4×C53C2512yes—
385C2×C4×C53C2512yes—
386C22⋊D53—216no—
387C22⋊D53—216no—
388C22⋊D53—216no—
389C22⋊D53—216no—
390C22⋊D53—416no—
391C2×Dic53—24no—
392C2×Dic53—24no—
393C2×Dic53—28no—
394C2×Dic53—22no—
395C2×Dic53—22no—
396C2×Dic53—28no—
397C2×Dic53—28no—
398C2×Dic53—48no—
399C2×Dic53H(5,𝔽2)14yes—
400C2×Dic532−1+414yes—
401C2×Dic53C2512yes—
402C2×Dic53C2518yes—
403C2×Dic53C2514yes—
404C2×Dic53C2514yes—
405C2×Dic53C2512yes—
406C2×Dic53C2512yes—
407C2×Dic53C2512yes—
408D212—28no—
409D212—28no—
410D212—416no—
411C4×D53—216no—
412C4×D53—216no—
413C4×D53—216no—
414C4×D53—216no—
415C4×D53—416no—
416Dic106—28no—
417Dic106—28no—
418Dic106—232no—
419Dic106—416no—
420C2×#3511—531nomaximal, Sylow
421C22×C53—22no—
422C22×C53—22no—
423C22×C53—28no—
424C22×C53—24no—
425C22×C53—24no—
426C22×C53—24no—
427C22×C53—48no—
428C22×C53C22×#4114yes—
429C22×C53C22×#4112yes—
430C22×C53C2×H(5,𝔽2)12yes—
431C22×C53C2×2−1+412yes—
432C22×C53C2611yescharacteristic
433C2×D53—24no—
434C2×D53—24no—
435C2×D53—24no—
436C2×D53—24no—
437C2×D53—24no—
438C2×D53—24no—
439C2×D53—48no—
440C2×D53—48no—
441C4×C53—24no—
442C4×C53—28no—
443C4×C53—24no—
444C4×C53—24no—
445C4×C53C22×#4114yes—
446C4×C53C22×#4114yes—
447Dic53—24no—
448Dic53—24no—
449Dic53—28no—
450Dic53—22no—
451Dic53—22no—
452Dic53C2×H(5,𝔽2)14yes—
453Dic53C2×2−1+414yes—
454#3511—5332no—
455C2×#556—532no—
456C2×#555—532no—
457C2×#554—532no—
458C2×#553—534no—
459C2×#548—534no—
460C2×#547—532no—
461C2×#542—532no—
462C2×#542—532no—
463C2×#537—531no—
464C2×#537—531no—
465C2×#533—532no—
466C2×#532—531no—
467C2×#532—532no—
468C22×C4⋊Q8—531no—
469C2×#520—531no—
470C2×#520D5311yescharacteristic, complemented
471C2×C4×#41—531no—
472C2×C53—24no—
473C2×C53—44no—
474C2×C53#351114yescomplemented
475C2×C53C23×#4111yescharacteristic
476C2×C53C22×H(5,𝔽2)11yescharacteristic
477C2×C53C22×2−1+411yescharacteristic
478D53—44no—
479D53—44no—
480C22×#41—531no—
481C22×#41—531no—
482C22×#41—534no—
483C22×#41C2×D5311yescharacteristic
484C23×Q8—532no—
485#556—5332no—
486#555—5332no—
487#554—5332no—
488#553—5364no—
489#548—5364no—
490#547—5332no—
491#542—5332no—
492#542—5332no—
493#537—5316no—
494#537—5316no—
495#533—5332no—
496#532—5316no—
497#532—5332no—
498C2×C4⋊Q8—531no—
499C2×C4⋊Q8—532no—
500C2×C4⋊Q8—532no—
501C2×C4⋊Q8—532no—
502C2×C4⋊Q8—532no—
503C2×C4⋊Q8—5316no—
504C2×#127—531no—
505C2×#126—534no—
506C2×#126—534no—
507C2×#125—534no—
508C2×#124—531no—
509C2×#124—531no—
510C2×#124—534no—
511C2×#124—534no—
512C2×#124—534no—
513C2×#123—534no—
514C2×#123—534no—
515C2×C22⋊Q8—532no—
516C2×C22⋊Q8—532no—
517C2×C22⋊Q8—534no—
518C2×C22⋊Q8—534no—
519C2×C22⋊Q8—534no—
520C2×C22⋊Q8—532no—
521C2×C22⋊Q8—532no—
522C2×#121—532no—
523C2×#121—532no—
524C2×#121—532no—
525C2×#121—534no—
526C2×#121—532no—
527C2×#121—534no—
528C2×#121—532no—
529C2×#121—532no—
530C2×#121—534no—
531#520—5316no—
532#520C2×D53116yescomplemented
533C4×#41—5316no—
534C2×C4×Q8—531no—
535C2×C4×Q8—531no—
536C2×C4×Q8—532no—
537C2×C4×Q8—534no—
538C2×C4×Q8C2×D5312yes—
539C2×C4×D4—532no—
540C2×C4×D4—534no—
541C2×C4×D4—532no—
542C2×C4×D4—531no—
543C2×C4×D4—531no—
544C2×C4×D4—532no—
545C2×C4×D4—532no—
546C2×C4×D4—534no—
547C2×C4×D4—532no—
548C2×C4×D4C2×D5312yes—
549C2×C4×D4C2×D5314yes—
550C2×#117—532no—
551C2×#117—532no—
552C2×#117—534no—
553C2×#117C2×D5311yescharacteristic
554C2×#117C2×D5312yes—
555C22×C4⋊C4—532no—
556C22×C4⋊C4—531no—
557C22×C4⋊C4—532no—
558C22×C4⋊C4C2×D5311yescharacteristic
559C22×C4⋊C4C2×D5312yes—
560C22×C42—531no—
561C22×C42—532no—
562C53C2×#351111yescharacteristic, complemented, Sylow
563C2×#41—28no—
564C2×#41—538no—
565C2×#41—538no—
566C2×#41—5332no—
567C2×#41—1068no—
568C2×#41—1068no—
569C2×#41—21216no—
570C2×#41C22×D5318yes—
571C22×Q8—531no—
572C22×Q8—531no—
573C22×Q8—534no—
574C22×Q8—534no—
575C22×Q8—5316no—
576C22×Q8—2128no—
577C22×Q8C22×D5311yescharacteristic
578C22×D4—532no—
579C22×D4—532no—
580C22×D4—532no—
581C22×D4—532no—
582C22×D4—534no—
583C22×D4—531no—
584C22×D4—531no—
585C22×D4—534no—
586C22×D4C22×D5312yes—
587C22×D4C22×D5311yescharacteristic
588C23×C4—531no—
589C23×C4—531no—
590C23×C4—532no—
591C23×C4—532no—
592C23×C4—532no—
593C23×C4—532no—
594C23×C4—532no—
595C23×C4—534no—
596C23×C4C22×D5312yes—
597C23×C4C22×D5312yes—
598C23×C4C22×D5314yes—
599C23×C4C22×D5311yescharacteristic
600C4⋊Q8—538no—
601C4⋊Q8—5316no—
602C4⋊Q8—5316no—
603C4⋊Q8—5316no—
604C4⋊Q8—5316no—
605#127—538no—
606#126—5332no—
607#126—5332no—
608#125—5332no—
609#124—538no—
610#124—538no—
611#124—5332no—
612#124—5332no—
613#124—5332no—
614#123—5332no—
615#123—5332no—
616C22⋊Q8—5316no—
617C22⋊Q8—5316no—
618C22⋊Q8—5332no—
619C22⋊Q8—5316no—
620C22⋊Q8—5332no—
621C22⋊Q8—5316no—
622C22⋊Q8—5332no—
623#121—5316no—
624#121—5316no—
625#121—5316no—
626#121—5332no—
627#121—5316no—
628#121—5332no—
629#121—5316no—
630#121—5316no—
631#121—5332no—
632C4×Q8—538no—
633C4×Q8—538no—
634C4×Q8—5316no—
635C4×Q8—5332no—
636C4×Q8C22×D53116yes—
637C4×D4—5316no—
638C4×D4—5332no—
639C4×D4—5316no—
640C4×D4—538no—
641C4×D4—538no—
642C4×D4—5316no—
643C4×D4—5316no—
644C4×D4—5332no—
645C4×D4—5316no—
646C4×D4C22×D53116yes—
647C4×D4C22×D53132yes—
648#117—5316no—
649#117—5316no—
650#117—5332no—
651#117C22×D5318yes—
652#117C22×D53116yes—
653C2×C4⋊C4—532no—
654C2×C4⋊C4—534no—
655C2×C4⋊C4—532no—
656C2×C4⋊C4—534no—
657C2×C4⋊C4—538no—
658C2×C4⋊C4—534no—
659C2×C4⋊C4—5316no—
660C2×C4⋊C4—532no—
661C2×C4⋊C4—532no—
662C2×C4⋊C4—532no—
663C2×C4⋊C4—532no—
664C2×C4⋊C4—534no—
665C2×C4⋊C4—534no—
666C2×C4⋊C4—5316no—
667C2×C4⋊C4C22×D5311yescharacteristic
668C2×C4⋊C4C22×D5312yes—
669C2×C4⋊C4C22×D5312yes—
670C2×C4⋊C4C22×D5314yes—
671C2×C4⋊C4C22×D5318yes—
672C2×C4⋊C4C22×D53116yes—
673C2×C4⋊C4C22×D5311yescharacteristic
674C2×C22⋊C4—534no—
675C2×C22⋊C4—532no—
676C2×C22⋊C4—532no—
677C2×C22⋊C4—534no—
678C2×C22⋊C4—532no—
679C2×C22⋊C4—532no—
680C2×C22⋊C4—534no—
681C2×C22⋊C4—534no—
682C2×C22⋊C4—534no—
683C2×C22⋊C4—532no—
684C2×C22⋊C4—532no—
685C2×C22⋊C4C22×D5312yes—
686C2×C22⋊C4C22×D5314yes—
687C2×C42—534no—
688C2×C42—531no—
689C2×C42—532no—
690C2×C42—531no—
691C2×C42—531no—
692C2×C42—532no—
693C2×C42—538no—
694C2×C42—531no—
695C2×C42—5316no—
696C2×C42C22×D5312yes—
697C2×C42C22×D5314yes—
698C24—532no—
699C24—532no—
700C24C23×D5312yes—
701C24C23×D5311yescharacteristic
702#41—232no—
703#41—10632no—
704#41—10632no—
705#41—21264no—
706C2×Q8—24no—
707C2×Q8—534no—
708C2×Q8—534no—
709C2×Q8—5316no—
710C2×Q8—5316no—
711C2×Q8—10616no—
712C2×Q8—1064no—
713C2×Q8—1064no—
714C2×Q8—2128no—
715C2×Q8—21232no—
716C2×Q8C23×D5314yes—
717C2×D4—28no—
718C2×D4—24no—
719C2×D4—538no—
720C2×D4—538no—
721C2×D4—538no—
722C2×D4—538no—
723C2×D4—5316no—
724C2×D4—534no—
725C2×D4—534no—
726C2×D4—5316no—
727C2×D4—1068no—
728C2×D4—1068no—
729C2×D4—1068no—
730C2×D4—1068no—
731C2×D4—1064no—
732C2×D4—1064no—
733C2×D4—2128no—
734C2×D4—2128no—
735C2×D4C23×D5318yes—
736C2×D4C23×D5314yes—
737C22×C4—28no—
738C22×C4—44no—
739C22×C4—48no—
740C22×C4—531no—
741C22×C4—531no—
742C22×C4—534no—
743C22×C4—534no—
744C22×C4—531no—
745C22×C4—531no—
746C22×C4—532no—
747C22×C4—532no—
748C22×C4—534no—
749C22×C4—538no—
750C22×C4—538no—
751C22×C4—538no—
752C22×C4—538no—
753C22×C4—538no—
754C22×C4—5316no—
755C22×C4—1068no—
756C22×C4—1068no—
757C22×C4—1064no—
758C22×C4—1064no—
759C22×C4—1068no—
760C22×C4—1068no—
761C22×C4—2128no—
762C22×C4—2124no—
763C22×C4#1171994518yescomplemented
764C22×C4C23×D5318yes—
765C22×C4C23×D5312yes—
766C22×C4C23×D5312yes—
767C22×C4C23×D5312yes—
768C22×C4C23×D5314yes—
769C22×C4C23×D5318yes—
770C22×C4C23×D53116yes—
771C22×C4C23×D5311yescharacteristic
772C22×C4C23×D5311yescharacteristic
773C22×C4C23×D5314yes—
774C4⋊C4—538no—
775C4⋊C4—5316no—
776C4⋊C4—538no—
777C4⋊C4—5316no—
778C4⋊C4—5316no—
779C4⋊C4—538no—
780C4⋊C4—538no—
781C4⋊C4—538no—
782C4⋊C4—538no—
783C4⋊C4—5316no—
784C4⋊C4—5316no—
785C4⋊C4C23×D5314yes—
786C4⋊C4C23×D5318yes—
787C4⋊C4C23×D5318yes—
788C4⋊C4C23×D53116yes—
789C4⋊C4C23×D5314yes—
790C22⋊C4—5316no—
791C22⋊C4—538no—
792C22⋊C4—538no—
793C22⋊C4—5316no—
794C22⋊C4—538no—
795C22⋊C4—538no—
796C22⋊C4—5316no—
797C22⋊C4—5316no—
798C22⋊C4—5316no—
799C22⋊C4—538no—
800C22⋊C4—538no—
801C22⋊C4C23×D5318yes—
802C22⋊C4C23×D53116yes—
803C42—534no—
804C42—534no—
805C42—538no—
806C42—534no—
807C42—534no—
808C42—538no—
809C42—5316no—
810C42C23×D5318yes—
811C42C23×D53116yes—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—534no—
818C23—534no—
819C23—1064no—
820C23—1064no—
821C23—1064no—
822C23—1064no—
823C23—1064no—
824C23—1064no—
825C23C2×#1171994514yes—
826C23C24×D5314yes—
827C23C24×D5312yes—
828C23C24×D5311yescharacteristic
829Q8—28no—
830Q8—10632no—
831Q8—1068no—
832Q8—1068no—
833Q8—21216no—
834D4—216no—
835D4—28no—
836D4—10616no—
837D4—10616no—
838D4—10616no—
839D4—10616no—
840D4—1068no—
841D4—1068no—
842D4—21216no—
843D4—21216no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—24no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—416no—
851C2×C4—534no—
852C2×C4—534no—
853C2×C4—532no—
854C2×C4—532no—
855C2×C4—532no—
856C2×C4—532no—
857C2×C4—534no—
858C2×C4—534no—
859C2×C4—538no—
860C2×C4—10616no—
861C2×C4—10616no—
862C2×C4—1068no—
863C2×C4—1068no—
864C2×C4—1064no—
865C2×C4—1064no—
866C2×C4—1062no—
867C2×C4—1068no—
868C2×C4—1062no—
869C2×C4—10616no—
870C2×C4—10616no—
871C2×C4—21216no—
872C2×C4—2128no—
873C2×C4C2×#1171994514yes—
874C2×C4C2×#1171994514yes—
875C2×C4C2×#11719945116yescomplemented
876C2×C4C24×D5314yes—
877C2×C4C24×D5314yes—
878C2×C4C24×D5314yes—
879C2×C4C24×D5318yes—
880C2×C4C24×D5312yes—
881C2×C4C24×D5312yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—48no—
889C22—1064no—
890C22—1064no—
891C22—1064no—
892C22—1064no—
893C22—1064no—
894C22—1064no—
895C22—2128no—
896C22—2128no—
897C22C22×#1171994514yes—
898C22C22×#1171994512yes—
899C22H(5,𝔽2)×D5312yes—
900C222−1+4×D5312yes—
901C22C25×D5311yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—24no—
906C4—534no—
907C4—534no—
908C4—1064no—
909C4—1064no—
910C4—1062no—
911C4—1068no—
912C4—1062no—
913C4C22×#1171994514yes—
914C4C22×#1171994514yes—
915C2—24no—
916C2—44no—
917C2—2124no—
918C2—2124no—
919C2#2028861814yesdirect product factor
920C2C23×#1171994511yescharacteristic
921C2C2×H(5,𝔽2)×D5311yescharacteristic
922C2C2×2−1+4×D5311yescharacteristic
subgroupG/H
centerC23C24×D53
commutator, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC2×C53×#520C2
socleC23×C53C25
hypercenterC2×#520D53
hypocenterC53C2×#3511
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×#520

Complements

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

NH ≅ G/Ntype
1. #20288618C2direct (N × H)
2. C2×#16811341C2semidirect
3. C2×#16811336C2semidirect
4. C2×#16811328C2semidirect
5. C2×#16811322C2semidirect
6. C2×#16811282C2semidirect
7. C2×#16811274C2semidirect
8. C2×#16811245C2semidirect
9. C2×#16811238C2semidirect
10. C2×#16811204C2semidirect
11. C2×#16811201C2semidirect
12. C2×#16811177C2semidirect
13. C2×#16811170C2semidirect
14. C2×#16811169C2semidirect
15. C22×#13133216C2semidirect
16. C2×#16811103C2semidirect
17. C2×#16811091C2semidirect
18. C2×C53×#520C2semidirect
23. #16811341C22semidirect
24. #16811336C22semidirect
25. #16811328C22semidirect
26. #16811322C22semidirect
27. #16811282C22semidirect
28. #16811274C22semidirect
29. #16811245C22semidirect
30. #16811238C22semidirect
31. #16811204C22semidirect
32. #16811201C22semidirect
33. #16811177C22semidirect
34. #16811170C22semidirect
35. #16811169C22semidirect
40. C2×#13133216C22semidirect
69. #16811103C22semidirect
70. #16811091C22semidirect
93. C53×#520C22semidirect
250. C22×C4×C53#41semidirect
379. C2×C4×C53C2×#41semidirect
470. C2×#520D53semidirect
474. C2×C53#3511semidirect
532. #520C2×D53semidirect
562. C53C2×#3511semidirect
763. C22×C4#11719945semidirect
875. C2×C4C2×#11719945semidirect
919. C2#20288618direct (N × H)

Maximal subgroups

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

subgroupindex
#202886182
C2×#168113412
C2×#168113362
C2×#168113282
C2×#168113222
C2×#168112822
C2×#168112742
C2×#168112452
C2×#168112382
C2×#168112042
C2×#168112012
C2×#168111772
C2×#168111702
C2×#168111692
C22×#131332162
C2×#168111032
C2×#168110912
C2×C53×#5202
C2×#351153