Finite Group Databasebeta

← #28293040

Subgroups — #28293040

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289295C218yesmaximal, complemented
2#20289188C214yesmaximal, complemented
3#20289089C214yesmaximal, complemented
4#20289023C218yesmaximal, complemented
5#20288721C214yesmaximal, complemented
6#20288676C214yesmaximal, complemented
7#20288649C218yesmaximal, complemented
8#20288627C214yesmaximal, complemented
9#20288611C212yesmaximal, complemented
10#20288602C211yesmaximal, characteristic, complemented
11#20288592C211yesmaximal, characteristic, complemented
12#20288584C214yesmaximal, complemented
13#20288508C212yesmaximal, complemented
14#20288495C211yesmaximal, characteristic, complemented
15#20288488C211yesmaximal, characteristic, complemented
16#20288369C212yesmaximal, complemented
17#20288357C212yesmaximal, complemented
18#20288011C211yesmaximal, characteristic, complemented
19C2×#16811173C211yesmaximal, characteristic, complemented
20C53×#3444C211yesmaximal, characteristic, complemented
21C2×#13133264C2212yescomplemented
22C2×#13133263C2212yes—
23C22×#11719945C2212yescomplemented
24#16811370C22116yescomplemented
25#16811363C22116yescomplemented
26#16811358C2214yescomplemented
27#16811356C2218yescomplemented
28#16811355C2218yescomplemented
29#16811352C2214yescomplemented
30#16811346C2214yescomplemented
31#16811345C2218yescomplemented
32#16811336C2218yescomplemented
33#16811329C2218yescomplemented
34#16811326C2218yescomplemented
35#16811317C22116yescomplemented
36#16811317C2218yescomplemented
37#16811315C2218yescomplemented
38#16811302C22116yescomplemented
39#16811297C22116yescomplemented
40#16811295C2214yescomplemented
41#16811294C2218yescomplemented
42#16811294C2214yescomplemented
43#16811292C2218yescomplemented
44#16811291C2218yescomplemented
45D4×Dic106C2214yescomplemented
46#16811285C2218yescomplemented
47#16811283C2218yescomplemented
48#16811282C2218yescomplemented
49#16811278C2214yescomplemented
50#16811278C2218yescomplemented
51#16811275C2218yescomplemented
52#16811273C2218yescomplemented
53#16811270C2218yescomplemented
54#16811269C2218yescomplemented
55#16811268C2218yescomplemented
56#16811268C22116yescomplemented
57#16811266C2218yescomplemented
58#16811264C2218yescomplemented
59#16811261C2218yescomplemented
60D4×D212C2214yescomplemented
61#16811257C2218yes—
62#16811246C2218yescomplemented
63#16811245C2218yescomplemented
64#16811244C2218yescomplemented
65#16811236C2214yescomplemented
66#16811229C2214yescomplemented
67#16811226C2218yescomplemented
68#16811224C22116yescomplemented
69#16811224C2218yescomplemented
70#16811214C22116yescomplemented
71#16811212C22116yescomplemented
72#16811206C22116yescomplemented
73#16811203C2218yescomplemented
74#16811199C2212yes—
75#16811199C2214yescomplemented
76#16811194C2212yescomplemented
77#16811193C2214yescomplemented
78#16811192C2214yescomplemented
79#16811192C2212yescomplemented
80#16811191C2214yescomplemented
81#16811189C2218yescomplemented
82#16811188C2218yescomplemented
83#16811187C2212yes—
84#16811183C2218yescomplemented
85#16811180C2211yescharacteristic, complemented
86#16811180C2212yescomplemented
87#16811178C2214yescomplemented
88#16811174C2214yescomplemented
89#16811174C2212yescomplemented
90#16811173C2211yescharacteristic
91#16811173C2212yescomplemented
92#16811173C2214yescomplemented
93#16811173C2214yescomplemented
94#16811173C2214yescomplemented
95#16811173C2214yescomplemented
96#16811173C2214yescomplemented
97#16811171C2212yescomplemented
98C2×#13133217C2211yescharacteristic, complemented
99C4⋊Q8×D53C2212yescomplemented
100C2×#13133214C2211yescharacteristic
101#127×D53C2212yescomplemented
102#16811157C2214yescomplemented
103#16811157C2214yescomplemented
104#16811157C2212yescomplemented
105#16811157C2212yescomplemented
106#16811157C2218yescomplemented
107C2×#13133205C2212yescomplemented
108C2×#13133205C2214yescomplemented
109#16811134C2211yescharacteristic
110#16811134C2211yescharacteristic, complemented
111#16811134C2214yescomplemented
112#16811131C2218yescomplemented
113#123×D53C2218yescomplemented
114C2×#13133191C2214yescomplemented
115#16811105C2218yescomplemented
116#16811100C2212yescomplemented
117#16811097C2212yescomplemented
118#16811095C2218yescomplemented
119C4×#11719945C2211yescharacteristic
120C4×#11719945C2214yescomplemented
121C4×#11719945C2211yescharacteristic, complemented
122C2×C4×D212C2214yescomplemented
123C53×#533C2211yescharacteristic, complemented
124C53×#533C2212yescomplemented
125C53×#532C2211yescharacteristic
126C53×#532C2212yescomplemented
127C53×#529C2214yescomplemented
128C53×#529C2214yescomplemented
129C53×#529C2214yescomplemented
130C53×#525C2212yescomplemented
131C53×#525C2214yescomplemented
132C4×#41×C53C2212yescomplemented
133C4×#41×C53C2214yescomplemented
134C22×C42×C53C2211yescharacteristic, complemented
135#13133264—48no—
136#13133263—48no—
137C2×#11719949C2318yes—
138C2×#11719949C2314yes—
139C2×#11719945—48no—
140C2×#11719945C2311yescharacteristic
141C2×#11719945C2311yescharacteristic
142C2×#11719945C2318yes—
143C2×#11719945C2318yes—
144C2×#11719945C2314yes—
145C2×#11719945C2314yes—
146C2×#11719945C2314yes—
147C2×#11719947C2318yes—
148C2×#11719947C2314yes—
149C22×Dic106C2312yes—
150C22×Dic106C2314yes—
151C2×Q8×D53C2314yes—
152C22×D212C2312yes—
153C22×D212C2314yes—
154C22×D212C2314yes—
155C22×C22⋊D53C2314yes—
156C2×D4×D53C2318yes—
157C2×D4×D53C2314yes—
158C2×D4×D53C2318yes—
159C22×C4×D53C2314yes—
160#13133217C2314yes—
161#13133217C2314yes—
162#13133217C2312yes—
163#13133217C2312yes—
164#13133217C2311yescharacteristic
165#13133217C2312yes—
166#13133216C2318yes—
167#13133215C2314yes—
168#13133214C2314yes—
169#13133214C2314yes—
170#13133214C2312yes—
171#13133214C2312yes—
172#13133214C2311yescharacteristic
173#13133213C2314yes—
174#13133213C23116yes—
175#13133213C2318yes—
176#13133212C23116yes—
177#13133212C23116yes—
178#13133211C2314yes—
179#13133211C23116yes—
180#13133211C2314yes—
181#13133209C2312yes—
182#13133209C2314yes—
183#13133208C2318yes—
184#13133208C23116yes—
185#13133206C2318yes—
186#13133206C2314yes—
187#13133205C23116yes—
188#13133205C2318yes—
189#13133205C2314yes—
190#13133205C2314yes—
191#13133205C2311yescharacteristic
192#13133205C2314yes—
193#13133205C2314yes—
194#13133205C2311yescharacteristic
195#13133205C2314yes—
196#13133204C2314yes—
197#13133203C23116yes—
198#13133203C23116yes—
199#13133202C23116yes—
200#13133202C23116yes—
201#13133201C2318yes—
202#13133201C23116yes—
203#13133200C23116yes—
204#13133200C2312yes—
205#13133200C2312yes—
206#13133200C2314yes—
207#13133200C2314yes—
208#13133199C23116yes—
209#13133199C23116yes—
210#13133199C23116yes—
211#13133199C23116yes—
212#13133198C2318yes—
213#13133197C2318yes—
214#13133197C23116yes—
215#13133196C2318yes—
216#13133196C2312yes—
217#13133196C2312yes—
218#13133196C2314yes—
219#13133196C2314yes—
220#13133195C23116yes—
221#13133195C23116yes—
222#13133194C23116yes—
223#13133193C2318yes—
224#13133192C2318yes—
225#13133192C23116yes—
226#13133192C2318yes—
227#13133192C23116yes—
228#13133192C2318yes—
229#13133191C2314yes—
230#13133191C23116yes—
231#13133191C2312yes—
232#13133191C2318yes—
233#13133191C2318yes—
234#13133191C2312yes—
235#13133191C2314yes—
236#13133191C2318yes—
237#13133191C2318yes—
238#13133191C2318yes—
239#13133190C23116yes—
240#13133190C23116yes—
241#13133190C23116yes—
242#13133190C23116yes—
243#13133189C23116yes—
244#13133188C2318yes—
245#13133188C23116yes—
246#13133187C2318yes—
247#13133187C23116yes—
248#13133187C23116yes—
249#13133186C2312yes—
250#13133186C2312yes—
251#13133185C23116yes—
252#13133185C2318yes—
253Q8×Dic53C2318yes—
254C4×Dic106C2318yes—
255C4×Dic106C2312yes—
256C4×Dic106C2312yes—
257C4×Dic106C2314yes—
258C4×Dic106C2314yes—
259#13133182C2318yes—
260C4×D212C2314yes—
261C4×D212C2318yes—
262C4×D212C2314yes—
263C4×D212C23116yes—
264C4×D212C2318yes—
265C4×D212C2312yes—
266C4×D212C2318yes—
267C4×D212C2318yes—
268C4×D212C2318yes—
269C4×D212C2312yes—
270D4×Dic53C2318yes—
271#13133179C2318yes—
272#13133179C2318yes—
273#13133179C23116yes—
274#13133179C2318yes—
275C4×C22⋊D53C2314yes—
276C4×C22⋊D53C2314yes—
277C4×C22⋊D53C2314yes—
278C4×C22⋊D53C2314yes—
279C4×C22⋊D53C23116yes—
280C4×C22⋊D53C2314yes—
281C4×C22⋊D53C2314yes—
282#13133177C23116yes—
283#13133176C2311yescharacteristic
284#13133176C2311yescharacteristic
285#13133176C2314yes—
286#13133175C2318yes—
287#13133174C23116yes—
288#13133174C2312yes—
289#13133174C2314yes—
290#13133174C2314yes—
291#13133174C2312yes—
292#13133173C2318yes—
293C2×C4⋊Dic53C2314yes—
294C4⋊C4×D53C2318yes—
295C4⋊C4×D53C23116yes—
296C2×#11719921C23116yes—
297C2×#11719921C2318yes—
298C22⋊C4×D53C2318yes—
299C22⋊C4×D53C23116yes—
300C42×D53C2312yes—
301C42×D53C2312yes—
302C2×#41×C53C2312yes—
303C2×#41×C53C2314yes—
304C23×C4×C53C2311yescharacteristic
305C23×C4×C53C2312yes—
306C4⋊Q8×C53C2311yescharacteristic
307C4⋊Q8×C53C2312yes—
308#127×C53C2311yescharacteristic
309#126×C53C2318yes—
310#125×C53C2314yes—
311#125×C53C2312yes—
312#124×C53C2314yes—
313#124×C53C2312yes—
314#123×C53C2318yes—
315#123×C53C2314yes—
316C22⋊Q8×C53C2314yes—
317C22⋊Q8×C53C2314yes—
318C22⋊Q8×C53C2314yes—
319#121×C53C2314yes—
320#121×C53C2314yes—
321#121×C53C2314yes—
322#120×C53C2314yes—
323C4×Q8×C53C2314yes—
324C4×Q8×C53C2314yes—
325C4×Q8×C53C2314yes—
326C4×D4×C53C2318yes—
327C4×D4×C53C2314yes—
328C4×D4×C53C2318yes—
329C4×D4×C53C2314yes—
330C4×D4×C53C2318yes—
331C4×D4×C53C2314yes—
332#117×C53C2318yes—
333#117×C53C2314yes—
334#117×C53C2312yes—
335#117×C53C2314yes—
336C2×C42×C53C2311yescharacteristic
337C2×C42×C53C2312yes—
338C2×C42×C53C2312yes—
339C2×C42×C53C2312yes—
340C2×C42×C53C2312yes—
341C2×C42×C53C2311yescharacteristic
342C2×C42×C53C2312yes—
343C2×C42×C53C2314yes—
344C24×C53C2411yescharacteristic
345C23×D53C2414yes—
346C23×D53C2418yes—
347#41×C53—28no—
348#41×C53—48no—
349C2×Q8×C53C2414yes—
350C2×Q8×C53C2412yes—
351C2×D4×C53C2414yes—
352C2×D4×C53C2414yes—
353C2×D4×C53C2412yes—
354C2×D4×C53C2418yes—
355C22×C4×C53—24no—
356C22×C4×C53—44no—
357C22×C4×C53C2412yes—
358C22×C4×C53C2412yes—
359C22×C4×C53C2412yes—
360C22×C4×C53C2412yes—
361C22×C4×C53C2412yes—
362C22×C4×C53C2411yescharacteristic
363C22×C4×C53C2414yes—
364C22×C4×C53C2412yes—
365C22×C4×C53C2412yes—
366C22×C4×C53C2412yes—
367C22×C4×C53C2418yes—
368C22×C4×C53C2411yescharacteristic
369C2×C22⋊D53—48no—
370C2×C22⋊D53C2412yes—
371C2×C22⋊D53C2412yes—
372C2×C22⋊D53C24116yes—
373C2×C22⋊D53C2414yes—
374C2×C22⋊D53C2414yes—
375C2×C22⋊D53C24116yes—
376C2×C22⋊D53C2418yes—
377C2×C22⋊D53C2418yes—
378C22×Dic53C2414yes—
379C22×Dic53C2418yes—
380#11719949—416no—
381#11719949—48no—
382Q8×D53—48no—
383#11719947—48no—
384#11719947—416no—
385D4×D53—416no—
386D4×D53—48no—
387D4×D53—416no—
388#11719945—24no—
389#11719945—24no—
390#11719945—416no—
391#11719945—416no—
392#11719945—48no—
393#11719945—48no—
394#11719945—48no—
395C2×D212—28no—
396C2×D212—48no—
397C2×D212—48no—
398C2×D212C2418yes—
399C2×D212C2414yes—
400C2×D212C2411yescharacteristic
401C2×D212C2414yes—
402C2×D212C2411yescharacteristic
403C2×D212C24116yes—
404C2×D212C2414yes—
405C2×D212C2418yes—
406C2×D212C2418yes—
407C2×C4×D53—48no—
408C2×C4×D53C2414yes—
409C2×C4×D53C2414yes—
410C2×C4×D53C2412yes—
411C2×C4×D53C2412yes—
412C2×C4×D53C24116yes—
413C2×C4×D53C24116yes—
414C2×C4×D53C2418yes—
415C2×C4×D53C2418yes—
416C2×Dic106—28no—
417C2×Dic106—48no—
418C2×Dic106C2414yes—
419C2×Dic106C2411yescharacteristic
420C2×Dic106C2414yes—
421C2×Dic106C2411yescharacteristic
422C2×Dic106C2414yes—
423C2×Dic106C2418yes—
424C4⋊C4×C53C2414yes—
425C4⋊C4×C53C2414yes—
426C4⋊C4×C53C2414yes—
427C4⋊C4×C53C2418yes—
428C4⋊C4×C53C2418yes—
429C4⋊C4×C53C2418yes—
430C22⋊C4×C53C2414yes—
431C22⋊C4×C53C2418yes—
432C22⋊C4×C53C2418yes—
433C22⋊C4×C53C2418yes—
434C22⋊C4×C53C2418yes—
435C42×C53C2411yescharacteristic
436C42×C53C2412yes—
437C42×C53C2411yescharacteristic
438C42×C53C2412yes—
439C42×C53C2412yes—
440C42×C53C2412yes—
441C42×C53C2411yescharacteristic
442C42×C53C2412yes—
443C42×C53C2412yes—
444C42×C53C2411yescharacteristic
445C42×C53C2418yes—
446C42×C53C2414yes—
447C22⋊Dic53C2412yes—
448C22⋊Dic53C24116yes—
449C22⋊Dic53C2412yes—
450C22⋊Dic53C2414yes—
451C22⋊Dic53C2414yes—
452#11719921C2414yes—
453#11719921C24116yes—
454#11719921C24116yes—
455#11719921C2414yes—
456#11719921C24116yes—
457#11719921C24116yes—
458#11719921C24116yes—
459#11719921C2414yes—
460#11719921C2414yes—
461#11719921C2414yes—
462#11719921C2414yes—
463#11719921C24116yes—
464C4⋊Dic53C2418yes—
465C4⋊Dic53C24116yes—
466C4⋊Dic53C2418yes—
467C4⋊Dic53C2412yes—
468C4⋊Dic53C2412yes—
469C4⋊Dic53C2414yes—
470C4⋊Dic53C2414yes—
471#11719919C2414yes—
472#11719919C24116yes—
473#11719919C24116yes—
474#11719919C2414yes—
475#11719919C2414yes—
476#11719919C2414yes—
477#11719919C2414yes—
478#11719919C2414yes—
479C4×Dic53C2412yes—
480C4×Dic53C2414yes—
481C4×Dic53C2414yes—
482C4×Dic53C2412yes—
483C4×Dic53C24116yes—
484C23×C53—22no—
485C23×C53—42no—
486C23×C53C2514yes—
487C23×C53C2512yes—
488C23×C53C2511yescharacteristic
489C22×D53—28no—
490C22×D53—48no—
491C22×D53—48no—
492C22×D53—416no—
493C22×D53C2512yes—
494C22×D53C2518yes—
495C22×D53C2512yes—
496Q8×C53—24no—
497Q8×C53—28no—
498D4×C53—28no—
499D4×C53—24no—
500D4×C53—28no—
501D4×C53—48no—
502C2×C4×C53—22no—
503C2×C4×C53—28no—
504C2×C4×C53—24no—
505C2×C4×C53—24no—
506C2×C4×C53—24no—
507C2×C4×C53—24no—
508C2×C4×C53—24no—
509C2×C4×C53—42no—
510C2×C4×C53—42no—
511C2×C4×C53—42no—
512C2×C4×C53—48no—
513C2×C4×C53H(5,𝔽2)14yes—
514C2×C4×C53C2514yes—
515C2×C4×C53C2512yes—
516C2×C4×C53C2512yes—
517C2×C4×C53C2518yes—
518C2×C4×C53C2512yes—
519C2×C4×C53C2512yes—
520C2×C4×C53C2511yescharacteristic
521C2×C4×C53C2511yescharacteristic
522C2×C4×C53C2512yes—
523C22⋊D53—24no—
524C22⋊D53—24no—
525C22⋊D53—416no—
526C22⋊D53—48no—
527C22⋊D53—48no—
528C22⋊D53—44no—
529C22⋊D53—44no—
530C22⋊D53—416no—
531C2×Dic53—28no—
532C2×Dic53—48no—
533C2×Dic53C2512yes—
534C2×Dic53C2518yes—
535C2×Dic53C2512yes—
536C2×Dic53C2514yes—
537C2×Dic53C2514yes—
538D212—28no—
539D212—28no—
540D212—22no—
541D212—22no—
542D212—216no—
543D212—48no—
544D212—48no—
545D212—44no—
546D212—416no—
547C4×D53—24no—
548C4×D53—24no—
549C4×D53—28no—
550C4×D53—28no—
551C4×D53—416no—
552C4×D53—48no—
553C4×D53—48no—
554C4×D53—416no—
555Dic106—28no—
556Dic106—28no—
557Dic106—22no—
558Dic106—22no—
559Dic106—48no—
560Dic106—44no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—24no—
564C22×C53—22no—
565C22×C53—22no—
566C22×C53—28no—
567C22×C53—22no—
568C22×C53—44no—
569C22×C53C2×H(5,𝔽2)12yes—
570C22×C53C2611yescharacteristic
571C2×D53—22no—
572C2×D53—22no—
573C2×D53—28no—
574C2×D53—24no—
575C2×D53—24no—
576C2×D53—216no—
577C2×D53—88no—
578C2×D53—168no—
579C4×C53—24no—
580C4×C53—22no—
581C4×C53—22no—
582C4×C53—28no—
583C4×C53—22no—
584C4×C53—22no—
585C4×C53C2×H(5,𝔽2)12yes—
586C4×C53C2×H(5,𝔽2)12yes—
587C4×C53#58514yes—
588Dic53—28no—
589Dic53—22no—
590Dic53—22no—
591Dic53—24no—
592Dic53—24no—
593#3562—538no—
594#3554—534no—
595#3546—534no—
596#3542—538no—
597#3517—534no—
598#3514—534no—
599#3513—538no—
600#3511—534no—
601#3510—532no—
602#3509—531no—
603#3508—531no—
604#3508—534no—
605#3500—532no—
606#3499—531no—
607#3498—531no—
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444D5311yescharacteristic, complemented
612C2×#532—531no—
613C2×C53—22no—
614C2×C53—44no—
615C2×C53—42no—
616C2×C53C22×H(5,𝔽2)11yescharacteristic
617C2×C53C2×#58512yes—
618D53—42no—
619D53—48no—
620D53—42no—
621C2×2−1+4—532no—
622C2×H(5,𝔽2)—532no—
623C22×#41—532no—
624#562—5316no—
625#560—5316no—
626#559—538no—
627#559—534no—
628#559—538no—
629#557—534no—
630#556—538no—
631#556—534no—
632#555—538no—
633#554—538no—
634#553—538no—
635#553—538no—
636#553—5316no—
637#552—538no—
638#551—5316no—
639#551—5316no—
640#550—538no—
641#550—538no—
642#550—534no—
643#550—538no—
644#550—534no—
645D4×Q8—534no—
646#548—538no—
647#548—538no—
648#548—538no—
649#547—538no—
650#547—538no—
651#547—538no—
652#547—534no—
653#546—538no—
654#546—538no—
655#546—538no—
656#546—538no—
657#546—538no—
658#546—5316no—
659#546—538no—
660D42—538no—
661D42—534no—
662#542—538no—
663#542—538no—
664#542—538no—
665#541—534no—
666#540—534no—
667#540—538no—
668#540—538no—
669#540—5316no—
670#539—5316no—
671#538—5316no—
672#538—5316no—
673#537—538no—
674#536—532no—
675#536—534no—
676#536—532no—
677#536—534no—
678#535—532no—
679#535—534no—
680#535—538no—
681#535—538no—
682#535—532no—
683#535—534no—
684#534—538no—
685#533—534no—
686#533—531no—
687#533—532no—
688#533C2×D5311yescharacteristic, complemented
689#533C2×D5312yescomplemented
690#532—532no—
691#532—534no—
692#532—532no—
693#532—534no—
694#532—534no—
695#532—534no—
696#532—534no—
697#532—531no—
698#532—532no—
699#532—534no—
700#532C2×D5311yescharacteristic
701#532C2×D5312yescomplemented
702C2×C4⋊Q8—532no—
703C2×C4⋊Q8—531no—
704C2×#127—532no—
705C2×#127—531no—
706#529—534no—
707#529—532no—
708#529—532no—
709#529—534no—
710#529—538no—
711#529C2×D5314yescomplemented
712#529C2×D5314yescomplemented
713#529C2×D5314yescomplemented
714C2×#124—532no—
715C2×#124—534no—
716#525—531no—
717#525—531no—
718#525—534no—
719#525—538no—
720#525C2×D5312yescomplemented
721#525C2×D5314yescomplemented
722C2×#123—538no—
723C2×#121—534no—
724#520—538no—
725#519—532no—
726#518—538no—
727#518—532no—
728C4×#41—531no—
729C4×#41—531no—
730C4×#41—534no—
731C4×#41C2×D5312yescomplemented
732C4×#41C2×D5314yescomplemented
733C2×C4×D4—534no—
734C22×C42C2×D5311yescharacteristic, complemented
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—2128no—
737H(5,𝔽2)—2128no—
738C2×#41—538no—
739C2×#41—534no—
740C2×#41—538no—
741C2×#41—534no—
742C2×#41—531no—
743C2×#41—531no—
744C2×#41—534no—
745C2×#41—538no—
746C2×#41—538no—
747C2×#41—534no—
748C2×#41—534no—
749C2×#41—2128no—
750C2×#41C22×D5312yes—
751C2×#41C22×D5314yes—
752C22×Q8—534no—
753C22×Q8—532no—
754C22×Q8—534no—
755C22×D4—534no—
756C22×D4—538no—
757C22×D4—538no—
758C22×D4—534no—
759C22×D4—532no—
760C22×D4—534no—
761C22×D4—534no—
762C23×C4—534no—
763C23×C4C22×D5311yescharacteristic
764C23×C4C22×D5312yes—
765C4⋊Q8—534no—
766C4⋊Q8—538no—
767C4⋊Q8—532no—
768C4⋊Q8—532no—
769C4⋊Q8—534no—
770C4⋊Q8—531no—
771C4⋊Q8—532no—
772C4⋊Q8—534no—
773C4⋊Q8C22×D5311yescharacteristic
774C4⋊Q8C22×D5312yes—
775#127—534no—
776#127—538no—
777#127—5316no—
778#127—532no—
779#127—532no—
780#127—534no—
781#127—531no—
782#127—534no—
783#127C22×D5311yescharacteristic
784#126—5316no—
785#126—5316no—
786#126—534no—
787#126—534no—
788#126—5316no—
789#126C22×D5318yes—
790#125—538no—
791#125—5316no—
792#125—532no—
793#125—534no—
794#125C22×D5312yes—
795#125C22×D5314yes—
796#124—534no—
797#124—538no—
798#124—534no—
799#124—5316no—
800#124—5316no—
801#124—531no—
802#124—534no—
803#124—534no—
804#124—538no—
805#124—534no—
806#124—534no—
807#124—5316no—
808#124—531no—
809#124—534no—
810#124C22×D5312yes—
811#124C22×D5314yes—
812#123—538no—
813#123—532no—
814#123—532no—
815#123—534no—
816#123—534no—
817#123—5316no—
818#123—5316no—
819#123—5316no—
820#123—538no—
821#123—5316no—
822#123—5316no—
823#123—5316no—
824#123—5316no—
825#123—5316no—
826#123C22×D5314yes—
827#123C22×D5318yes—
828C22⋊Q8—538no—
829C22⋊Q8—532no—
830C22⋊Q8—532no—
831C22⋊Q8—534no—
832C22⋊Q8—534no—
833C22⋊Q8—538no—
834C22⋊Q8—5316no—
835C22⋊Q8—538no—
836C22⋊Q8—5316no—
837C22⋊Q8—5316no—
838C22⋊Q8—5316no—
839C22⋊Q8C22×D5314yes—
840C22⋊Q8C22×D5314yes—
841C22⋊Q8C22×D5314yes—
842#121—538no—
843#121—5316no—
844#121—5316no—
845#121—538no—
846#121—538no—
847#121—538no—
848#121—538no—
849#121—532no—
850#121—534no—
851#121—532no—
852#121—534no—
853#121—538no—
854#121—5316no—
855#121—538no—
856#121—538no—
857#121—538no—
858#121—5316no—
859#121—5316no—
860#121—5316no—
861#121—5316no—
862#121—5316no—
863#121—5316no—
864#121C22×D5314yes—
865#121C22×D5314yes—
866#121C22×D5314yes—
867#120—532no—
868#120—532no—
869#120—538no—
870#120—5316no—
871#120—538no—
872#120—5316no—
873#120—5316no—
874#120C22×D5314yes—
875C4×Q8—538no—
876C4×Q8—538no—
877C4×Q8—532no—
878C4×Q8—532no—
879C4×Q8—534no—
880C4×Q8—534no—
881C4×Q8—538no—
882C4×Q8C22×D5314yes—
883C4×Q8C22×D5314yes—
884C4×Q8C22×D5314yes—
885C4×D4—538no—
886C4×D4—534no—
887C4×D4—534no—
888C4×D4—534no—
889C4×D4—534no—
890C4×D4—534no—
891C4×D4—534no—
892C4×D4—5316no—
893C4×D4—538no—
894C4×D4—538no—
895C4×D4—5316no—
896C4×D4—538no—
897C4×D4—5316no—
898C4×D4—538no—
899C4×D4—538no—
900C4×D4—538no—
901C4×D4—538no—
902C4×D4—532no—
903C4×D4—534no—
904C4×D4—534no—
905C4×D4—532no—
906C4×D4—538no—
907C4×D4—5316no—
908C4×D4C22×D5314yes—
909C4×D4C22×D5318yes—
910C4×D4C22×D5318yes—
911C4×D4C22×D5318yes—
912C4×D4C22×D5314yes—
913C4×D4C22×D5314yes—
914#117—531no—
915#117—531no—
916#117—534no—
917#117—538no—
918#117—538no—
919#117—534no—
920#117—534no—
921#117—532no—
922#117—532no—
923#117—5316no—
924#117C22×D5312yes—
925#117C22×D5314yes—
926#117C22×D5314yes—
927#117C22×D5318yes—
928C2×C4⋊C4—534no—
929C2×C4⋊C4—5316no—
930C2×C4⋊C4—538no—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—5316no—
933C2×C22⋊C4—538no—
934C2×C22⋊C4—5316no—
935C2×C42—532no—
936C2×C42—532no—
937C2×C42C22×D5312yes—
938C2×C42C22×D5311yescharacteristic
939C2×C42C22×D5312yes—
940C2×C42C22×D5314yes—
941C2×C42C22×D5311yescharacteristic
942C2×C42C22×D5312yes—
943C2×C42C22×D5312yes—
944C2×C42C22×D5312yes—
945C24—534no—
946C24—538no—
947C24C23×D5311yescharacteristic
948#41—28no—
949#41—48no—
950#41—1064no—
951#41—1064no—
952#41—2128no—
953#41—21216no—
954#41—21216no—
955#41—2128no—
956#41—2128no—
957#41—21216no—
958#41—2128no—
959#41—21216no—
960#41—2128no—
961C2×Q8—531no—
962C2×Q8—534no—
963C2×Q8—534no—
964C2×Q8—531no—
965C2×Q8—534no—
966C2×Q8—538no—
967C2×Q8—1068no—
968C2×Q8—2128no—
969C2×Q8—2128no—
970C2×Q8C23×D5314yes—
971C2×Q8C23×D5312yes—
972C2×D4—532no—
973C2×D4—532no—
974C2×D4—534no—
975C2×D4—5316no—
976C2×D4—534no—
977C2×D4—538no—
978C2×D4—5316no—
979C2×D4—538no—
980C2×D4—538no—
981C2×D4—531no—
982C2×D4—534no—
983C2×D4—534no—
984C2×D4—531no—
985C2×D4—534no—
986C2×D4—5316no—
987C2×D4—538no—
988C2×D4—538no—
989C2×D4—1068no—
990C2×D4—2128no—
991C2×D4—2128no—
992C2×D4—21216no—
993C2×D4—2128no—
994C2×D4—2128no—
995C2×D4—21216no—
996C2×D4C23×D5314yes—
997C2×D4C23×D5314yes—
998C2×D4C23×D5312yes—
999C2×D4C23×D5318yes—
1000C22×C4—24no—
1001C22×C4—44no—
1002C22×C4—534no—
1003C22×C4—538no—
1004C22×C4—534no—
1005C22×C4—534no—
1006C22×C4—532no—
1007C22×C4—532no—
1008C22×C4—5316no—
1009C22×C4—5316no—
1010C22×C4—538no—
1011C22×C4—538no—
1012C22×C4—2128no—
1013C22×C4C23×D5312yes—
1014C22×C4C23×D5312yes—
1015C22×C4C23×D5312yes—
1016C22×C4C23×D5312yes—
1017C22×C4C23×D5312yes—
1018C22×C4C23×D5311yescharacteristic
1019C22×C4C23×D5314yes—
1020C22×C4C23×D5312yes—
1021C22×C4C23×D5312yes—
1022C22×C4C23×D5312yes—
1023C22×C4C23×D5318yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—534no—
1026C4⋊C4—538no—
1027C4⋊C4—5316no—
1028C4⋊C4—538no—
1029C4⋊C4—5316no—
1030C4⋊C4—534no—
1031C4⋊C4—532no—
1032C4⋊C4—534no—
1033C4⋊C4—534no—
1034C4⋊C4—532no—
1035C4⋊C4—534no—
1036C4⋊C4—534no—
1037C4⋊C4—534no—
1038C4⋊C4—534no—
1039C4⋊C4—5316no—
1040C4⋊C4C23×D5314yes—
1041C4⋊C4C23×D5318yes—
1042C4⋊C4C23×D5314yes—
1043C4⋊C4C23×D5314yes—
1044C4⋊C4C23×D5318yes—
1045C4⋊C4C23×D5318yes—
1046C22⋊C4—532no—
1047C22⋊C4—5316no—
1048C22⋊C4—532no—
1049C22⋊C4—534no—
1050C22⋊C4—534no—
1051C22⋊C4—534no—
1052C22⋊C4—534no—
1053C22⋊C4—5316no—
1054C22⋊C4—5316no—
1055C22⋊C4—5316no—
1056C22⋊C4—5316no—
1057C22⋊C4—5316no—
1058C22⋊C4—534no—
1059C22⋊C4—534no—
1060C22⋊C4—534no—
1061C22⋊C4—5316no—
1062C22⋊C4—534no—
1063C22⋊C4C23×D5314yes—
1064C22⋊C4C23×D5318yes—
1065C22⋊C4C23×D5318yes—
1066C22⋊C4C23×D5318yes—
1067C22⋊C4C23×D5318yes—
1068C42—532no—
1069C42—534no—
1070C42—534no—
1071C42—532no—
1072C42—5316no—
1073C42C23×D5311yescharacteristic
1074C42C23×D5311yescharacteristic
1075C42C23×D5312yes—
1076C42C23×D5311yescharacteristic
1077C42C23×D5312yes—
1078C42C23×D5311yescharacteristic
1079C42C23×D5312yes—
1080C42C23×D5312yes—
1081C42C23×D5312yes—
1082C42C23×D5312yes—
1083C42C23×D5318yes—
1084C42C23×D5314yes—
1085C23—22no—
1086C23—42no—
1087C23—532no—
1088C23—538no—
1089C23—532no—
1090C23—1068no—
1091C23—2128no—
1092C23—21216no—
1093C23—2128no—
1094C23C24×D5314yes—
1095C23C24×D5312yes—
1096C23C24×D5311yescharacteristic
1097Q8—24no—
1098Q8—28no—
1099Q8—1068no—
1100Q8—1068no—
1101Q8—1062no—
1102Q8—1062no—
1103Q8—2128no—
1104Q8—2124no—
1105D4—28no—
1106D4—24no—
1107D4—28no—
1108D4—48no—
1109D4—1064no—
1110D4—1064no—
1111D4—1068no—
1112D4—1068no—
1113D4—1062no—
1114D4—1062no—
1115D4—10616no—
1116D4—2128no—
1117D4—2128no—
1118D4—2124no—
1119D4—21216no—
1120D4—21216no—
1121D4—2128no—
1122D4—21216no—
1123D4—2124no—
1124D4—2124no—
1125D4—2128no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—48no—
1137C2×C4—534no—
1138C2×C4—534no—
1139C2×C4—532no—
1140C2×C4—538no—
1141C2×C4—532no—
1142C2×C4—1068no—
1143C2×C4—1064no—
1144C2×C4—1064no—
1145C2×C4—1068no—
1146C2×C4—1068no—
1147C2×C4—21216no—
1148C2×C4—2128no—
1149C2×C4—2128no—
1150C2×C4—21216no—
1151C2×C4—2128no—
1152C2×C4#1313326314yes—
1153C2×C4C24×D5318yes—
1154C2×C4C24×D5312yes—
1155C2×C4C24×D5312yes—
1156C2×C4C24×D5312yes—
1157C2×C4C24×D5312yes—
1158C2×C4C24×D5314yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—22no—
1164C22—24no—
1165C22—22no—
1166C22—22no—
1167C22—28no—
1168C22—44no—
1169C22—8488no—
1170C22—1062no—
1171C22—1062no—
1172C22—1068no—
1173C22—1064no—
1174C22—1064no—
1175C22—10616no—
1176C22—4248no—
1177C22C2×#1313326312yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—28no—
1185C4—1062no—
1186C4—1062no—
1187C4—1068no—
1188C4—1064no—
1189C4—1064no—
1190C4C2×#1313326312yes—
1191C4C2×#1313326312yes—
1192C4#1681145914yes—
1193C2—22no—
1194C2—42no—
1195C2—44no—
1196C2—2122no—
1197C2—2128no—
1198C2—2122no—
1199C2C22×#1313326311yescharacteristic
1200C2C2×#1681145912yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289295C2semidirect
2. #20289188C2semidirect
3. #20289089C2semidirect
4. #20289023C2semidirect
5. #20288721C2semidirect
6. #20288676C2semidirect
7. #20288649C2semidirect
8. #20288627C2semidirect
9. #20288611C2semidirect
10. #20288602C2semidirect
11. #20288592C2semidirect
12. #20288584C2semidirect
13. #20288508C2semidirect
14. #20288495C2semidirect
15. #20288488C2semidirect
16. #20288369C2semidirect
17. #20288357C2semidirect
18. #20288011C2semidirect
19. C2×#16811173C2semidirect
20. C53×#3444C2semidirect
21. C2×#13133264C22semidirect
23. C22×#11719945C22semidirect
24. #16811370C22semidirect
25. #16811363C22semidirect
26. #16811358C22semidirect
27. #16811356C22semidirect
28. #16811355C22semidirect
29. #16811352C22semidirect
30. #16811346C22semidirect
31. #16811345C22semidirect
32. #16811336C22semidirect
33. #16811329C22semidirect
34. #16811326C22semidirect
35. #16811317C22semidirect
36. #16811317C22semidirect
37. #16811315C22semidirect
38. #16811302C22semidirect
39. #16811297C22semidirect
40. #16811295C22semidirect
41. #16811294C22semidirect
42. #16811294C22semidirect
43. #16811292C22semidirect
44. #16811291C22semidirect
45. D4×Dic106C22semidirect
46. #16811285C22semidirect
47. #16811283C22semidirect
48. #16811282C22semidirect
49. #16811278C22semidirect
50. #16811278C22semidirect
51. #16811275C22semidirect
52. #16811273C22semidirect
53. #16811270C22semidirect
54. #16811269C22semidirect
55. #16811268C22semidirect
56. #16811268C22semidirect
57. #16811266C22semidirect
58. #16811264C22semidirect
59. #16811261C22semidirect
60. D4×D212C22semidirect
62. #16811246C22semidirect
63. #16811245C22semidirect
64. #16811244C22semidirect
65. #16811236C22semidirect
66. #16811229C22semidirect
67. #16811226C22semidirect
68. #16811224C22semidirect
69. #16811224C22semidirect
70. #16811214C22semidirect
71. #16811212C22semidirect
72. #16811206C22semidirect
73. #16811203C22semidirect
75. #16811199C22semidirect
76. #16811194C22semidirect
77. #16811193C22semidirect
78. #16811192C22semidirect
79. #16811192C22semidirect
80. #16811191C22semidirect
81. #16811189C22semidirect
82. #16811188C22semidirect
84. #16811183C22semidirect
85. #16811180C22semidirect
86. #16811180C22semidirect
87. #16811178C22semidirect
88. #16811174C22semidirect
89. #16811174C22semidirect
91. #16811173C22semidirect
92. #16811173C22semidirect
93. #16811173C22semidirect
94. #16811173C22semidirect
95. #16811173C22semidirect
96. #16811173C22semidirect
97. #16811171C22semidirect
98. C2×#13133217C22semidirect
99. C4⋊Q8×D53C22semidirect
101. #127×D53C22semidirect
102. #16811157C22semidirect
103. #16811157C22semidirect
104. #16811157C22semidirect
105. #16811157C22semidirect
106. #16811157C22semidirect
107. C2×#13133205C22semidirect
108. C2×#13133205C22semidirect
110. #16811134C22semidirect
111. #16811134C22semidirect
112. #16811131C22semidirect
113. #123×D53C22semidirect
114. C2×#13133191C22semidirect
115. #16811105C22semidirect
116. #16811100C22semidirect
117. #16811097C22semidirect
118. #16811095C22semidirect
120. C4×#11719945C22semidirect
121. C4×#11719945C22semidirect
122. C2×C4×D212C22semidirect
123. C53×#533C22semidirect
124. C53×#533C22semidirect
126. C53×#532C22semidirect
127. C53×#529C22semidirect
128. C53×#529C22semidirect
129. C53×#529C22semidirect
130. C53×#525C22semidirect
131. C53×#525C22semidirect
132. C4×#41×C53C22semidirect
133. C4×#41×C53C22semidirect
134. C22×C42×C53C22semidirect
611. #3444D53semidirect
688. #533C2×D53semidirect
689. #533C2×D53semidirect
701. #532C2×D53semidirect
711. #529C2×D53semidirect
712. #529C2×D53semidirect
713. #529C2×D53semidirect
720. #525C2×D53semidirect
721. #525C2×D53semidirect
731. C4×#41C2×D53semidirect
732. C4×#41C2×D53semidirect
734. C22×C42C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202892952
#202891882
#202890892
#202890232
#202887212
#202886762
#202886492
#202886272
#202886112
#202886022
#202885922
#202885842
#202885082
#202884952
#202884882
#202883692
#202883572
#202880112
C2×#168111732
C53×#34442
#6283653