Finite Group Databasebeta

← #28293038

Subgroups — #28293038

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#20289305C218yesmaximal, complemented
2#20289174C214yesmaximal, complemented
3#20289075C214yesmaximal, complemented
4#20289017C218yesmaximal, complemented
5#20288716C214yesmaximal, complemented
6#20288675C214yesmaximal, complemented
7#20288656C218yesmaximal, complemented
8#20288622C214yesmaximal, complemented
9#20288606C212yesmaximal, complemented
10#20288602C211yesmaximal, characteristic, complemented
11#20288584C214yesmaximal, complemented
12#20288507C212yesmaximal, complemented
13#20288500C211yesmaximal, characteristic, complemented
14#20288491C211yesmaximal, characteristic, complemented
15#20288371C212yesmaximal, complemented
16#20288360C212yesmaximal, complemented
17#20288012C211yesmaximal, characteristic, complemented
18#20288008C211yesmaximal, characteristic, complemented
19C2×#16811171C211yesmaximal, characteristic, complemented
20C53×#3508C211yesmaximal, characteristic, complemented
21C2×#13133264C2212yescomplemented
22C2×#13133262C2212yes—
23C22×#11719947C2212yescomplemented
24#16811370C22116yescomplemented
25#16811361C22116yescomplemented
26#16811356C2218yescomplemented
27#16811355C2218yescomplemented
28#16811352C2214yescomplemented
29#16811346C2214yescomplemented
30#16811343C2218yescomplemented
31#16811338C2218yescomplemented
32#16811330C2218yescomplemented
33#16811325C22116yescomplemented
34#16811325C2218yescomplemented
35#16811325C2218yescomplemented
36#16811315C2218yescomplemented
37#16811299C22116yescomplemented
38#16811296C22116yescomplemented
39#16811293C2218yescomplemented
40#16811293C2214yescomplemented
41#16811292C2218yescomplemented
42#16811291C2218yescomplemented
43Q8×D212C2214yescomplemented
44#16811281C2218yescomplemented
45#16811279C2218yescomplemented
46#16811279C2218yescomplemented
47#16811277C2218yescomplemented
48#16811277C2214yescomplemented
49#16811277C2218yescomplemented
50#16811277C2218yescomplemented
51#16811270C2218yescomplemented
52#16811268C2218yescomplemented
53#16811268C2218yescomplemented
54#16811266C2218yescomplemented
55#16811261C2218yescomplemented
56#16811260C22116yescomplemented
57#16811258C2214yescomplemented
58D4×C22⋊D53C2218yes—
59#16811242C2218yescomplemented
60#16811242C2218yescomplemented
61#16811238C2218yescomplemented
62#16811236C2214yescomplemented
63#16811226C22116yescomplemented
64#16811226C2218yescomplemented
65#16811224C2218yescomplemented
66#16811217C22116yescomplemented
67#16811210C22116yescomplemented
68#16811209C22116yescomplemented
69#16811201C2218yescomplemented
70#16811199C2212yes—
71#16811199C2214yescomplemented
72#16811199C2212yescomplemented
73#16811193C2214yescomplemented
74#16811190C2212yes—
75#16811189C2218yescomplemented
76#16811188C2218yescomplemented
77#16811186C2214yescomplemented
78#16811186C2214yescomplemented
79#16811185C2218yescomplemented
80#16811178C2212yescomplemented
81#16811178C2214yescomplemented
82#16811177C2212yescomplemented
83#16811176C2211yescharacteristic, complemented
84#16811174C2212yescomplemented
85#16811173C2211yescharacteristic
86#16811173C2212yescomplemented
87#16811171C2214yescomplemented
88#16811171C2214yescomplemented
89#16811171C2214yescomplemented
90#16811171C2212yescomplemented
91#16811171C2214yescomplemented
92#16811171C2214yescomplemented
93#16811170C2212yescomplemented
94#16811169C2211yescharacteristic
95C2×#13133217C2211yescharacteristic, complemented
96C2×#13133217C2212yescomplemented
97#127×D53C2212yescomplemented
98#16811160C2212yescomplemented
99#16811160C2214yescomplemented
100#16811159C2214yescomplemented
101#16811158C2214yescomplemented
102#16811155C2212yescomplemented
103#16811155C2218yescomplemented
104#16811153C2214yescomplemented
105#16811151C2214yescomplemented
106C2×#13133204C2212yescomplemented
107#124×D53C2214yescomplemented
108#16811136C2214yescomplemented
109#16811135C2211yescharacteristic
110#16811135C2212yescomplemented
111#16811132C2214yescomplemented
112#16811130C2211yescharacteristic, complemented
113#16811129C2218yescomplemented
114C2×#13133201C2218yescomplemented
115C2×#13133188C2214yescomplemented
116#16811106C2218yescomplemented
117#16811100C2212yescomplemented
118#16811095C2218yescomplemented
119C4×#11719949C2214yescomplemented
120C4×#11719945C2211yescharacteristic
121C4×#11719945C2214yescomplemented
122#16811091C2212yescomplemented
123C2×D4×Dic53C2214yescomplemented
124C2×C42×D53C2211yescharacteristic, complemented
125C53×#559C2214yescomplemented
126C53×#550C2214yescomplemented
127C53×#546C2218yescomplemented
128C53×#540C2214yescomplemented
129C53×#535C2212yescomplemented
130C53×#533C2211yescharacteristic, complemented
131C53×#532C2214yescomplemented
132C2×#127×C53C2211yescharacteristic
133C53×#518C2212yescomplemented
134C4×#41×C53C2211yescharacteristic, complemented
135#13133264—48no—
136#13133262—48no—
137C2×#11719949C2314yes—
138C2×#11719945C2312yes—
139C2×#11719945C2311yescharacteristic
140C2×#11719945C2314yes—
141C2×#11719945C2314yes—
142C2×#11719947—48no—
143C2×#11719947C2318yes—
144C2×#11719947C2318yes—
145C2×#11719947C2314yes—
146C2×#11719947C2314yes—
147C2×#11719947C2314yes—
148C2×#11719947C2318yes—
149C22×Dic106C2312yes—
150C22×Dic106C2314yes—
151C2×Q8×D53C2314yes—
152C22×C22⋊D53C2314yes—
153C22×C22⋊D53C2318yes—
154C2×D4×D53C2318yes—
155C2×D4×D53C2314yes—
156C2×D4×D53C2314yes—
157C23×Dic53C2314yes—
158C22×C4×D53C2311yescharacteristic
159C22×C4×D53C2312yes—
160#13133217C2314yes—
161#13133217C2314yes—
162#13133217C2318yes—
163#13133217C2314yes—
164#13133217C2311yescharacteristic
165#13133217C2312yes—
166#13133217C2312yes—
167#13133216C2312yes—
168#13133215C2311yescharacteristic
169#13133214C2311yescharacteristic
170#13133213C2314yes—
171#13133213C23116yes—
172#13133213C2318yes—
173#13133213C2311yescharacteristic
174#13133212C2314yes—
175#13133212C23116yes—
176#13133212C2318yes—
177#13133210C23116yes—
178#13133210C23116yes—
179#13133210C2314yes—
180#13133208C2318yes—
181#13133208C23116yes—
182#13133208C2314yes—
183#13133208C2312yes—
184#13133207C2314yes—
185#13133206C2314yes—
186#13133206C2311yescharacteristic
187#13133205C2314yes—
188#13133205C2314yes—
189#13133205C2312yes—
190#13133204C2318yes—
191#13133204C2314yes—
192#13133204C2314yes—
193#13133204C2314yes—
194#13133204C2311yescharacteristic
195#13133203C23116yes—
196#13133203C23116yes—
197#13133203C23116yes—
198#13133203C2314yes—
199#13133202C2318yes—
200#13133202C2314yes—
201#13133201C23116yes—
202#13133201C23116yes—
203#13133201C2318yes—
204#13133201C23116yes—
205#13133201C23116yes—
206#13133201C2318yes—
207#13133201C2312yes—
208#13133201C2314yes—
209#13133200C23116yes—
210#13133199C23116yes—
211#13133199C23116yes—
212#13133199C2314yes—
213#13133198C2312yes—
214#13133197C2318yes—
215#13133197C2318yes—
216#13133197C2312yes—
217#13133197C2314yes—
218#13133197C23116yes—
219#13133196C23116yes—
220#13133195C2314yes—
221#13133194C23116yes—
222#13133194C23116yes—
223#13133194C2314yes—
224#13133193C2318yes—
225#13133193C2312yes—
226#13133193C2314yes—
227#13133192C2312yes—
228#13133192C2314yes—
229#13133192C2314yes—
230#13133191C23116yes—
231#13133191C23116yes—
232#13133191C2318yes—
233#13133191C2314yes—
234#13133190C23116yes—
235#13133190C2314yes—
236#13133189C23116yes—
237#13133189C23116yes—
238#13133189C23116yes—
239#13133189C23116yes—
240#13133189C2314yes—
241#13133188C2318yes—
242#13133188C23116yes—
243#13133188C2318yes—
244#13133188C2312yes—
245#13133188C2318yes—
246#13133188C2318yes—
247#13133188C2318yes—
248#13133188C2318yes—
249#13133187C23116yes—
250#13133187C2312yes—
251#13133187C2314yes—
252#13133186C2318yes—
253#13133185C23116yes—
254#13133185C23116yes—
255#13133185C2312yes—
256Q8×Dic53C2318yes—
257Q8×Dic53C2314yes—
258C4×Dic106C2318yes—
259C4×Dic106C2312yes—
260C4×Dic106C2314yes—
261C4×Dic106C2314yes—
262#13133182C2314yes—
263#13133182C2318yes—
264C4×D212C2314yes—
265C4×D212C2318yes—
266C4×D212C2314yes—
267C4×D212C2318yes—
268C4×D212C2314yes—
269C4×D212C2312yes—
270D4×Dic53C23116yes—
271D4×Dic53C23116yes—
272D4×Dic53C2318yes—
273D4×Dic53C2318yes—
274D4×Dic53C2318yes—
275D4×Dic53C2318yes—
276D4×Dic53C2318yes—
277#13133179C2314yes—
278#13133179C2314yes—
279#13133179C2318yes—
280C4×C22⋊D53C2314yes—
281C4×C22⋊D53C2314yes—
282C4×C22⋊D53C2314yes—
283C4×C22⋊D53C23116yes—
284C4×C22⋊D53C2314yes—
285C4×C22⋊D53C2314yes—
286#13133177C23116yes—
287#13133177C2318yes—
288#13133176C23116yes—
289#13133176C2311yescharacteristic
290#13133176C2314yes—
291#13133175C2318yes—
292#13133175C2318yes—
293#13133175C2314yes—
294#13133174C2314yes—
295#13133174C2312yes—
296#13133174C2314yes—
297#13133174C2314yes—
298#13133173C2318yes—
299C2×C4⋊Dic53C2314yes—
300C2×C4⋊Dic53C2318yes—
301C2×C4⋊Dic53C23116yes—
302C2×C22⋊Dic53C2318yes—
303C2×#11719921C23116yes—
304C22⋊C4×D53C23116yes—
305C2×C4×Dic53C2312yes—
306C2×C4×Dic53C2311yescharacteristic
307C42×D53C2312yes—
308C42×D53C2312yes—
309C42×D53C2312yes—
310C42×D53C2312yes—
311C42×D53C2314yes—
312C42×D53C2312yes—
313C2×#41×C53C2311yescharacteristic
314C2×#41×C53C2318yes—
315C22×D4×C53C2312yes—
316C22×D4×C53C2314yes—
317C4⋊Q8×C53C2312yes—
318#127×C53C2314yes—
319#127×C53C2314yes—
320#127×C53C2312yes—
321#127×C53C2312yes—
322#125×C53C2312yes—
323#124×C53C2318yes—
324#124×C53C2314yes—
325#123×C53C23116yes—
326C22⋊Q8×C53C2314yes—
327#121×C53C2318yes—
328#121×C53C2318yes—
329#121×C53C23116yes—
330#120×C53C2318yes—
331C4×Q8×C53C2312yes—
332C4×Q8×C53C2314yes—
333C4×D4×C53C2318yes—
334C4×D4×C53C2318yes—
335C4×D4×C53C2314yes—
336C4×D4×C53C2312yes—
337C4×D4×C53C2318yes—
338#117×C53C2311yescharacteristic
339#117×C53C2312yes—
340#117×C53C2312yes—
341C2×C22⋊C4×C53C2318yes—
342C2×C42×C53C2311yescharacteristic
343C2×C42×C53C2312yes—
344C24×C53C2414yes—
345C23×D53C2411yescharacteristic
346C23×D53C2418yes—
347#41×C53—24no—
348#41×C53—416no—
349C2×Q8×C53C2411yescharacteristic
350C2×Q8×C53C2414yes—
351C2×D4×C53—28no—
352C2×D4×C53—48no—
353C2×D4×C53C2412yes—
354C2×D4×C53C2414yes—
355C2×D4×C53C2414yes—
356C2×D4×C53C2411yescharacteristic
357C2×D4×C53C2418yes—
358C2×D4×C53C24116yes—
359C2×D4×C53C2418yes—
360C22×C4×C53C2412yes—
361C22×C4×C53C2414yes—
362C22×C4×C53C2412yes—
363C22×C4×C53C24116yes—
364C22×C4×C53C2411yescharacteristic
365C2×C22⋊D53—48no—
366C2×C22⋊D53—416no—
367C2×C22⋊D53C2414yes—
368C2×C22⋊D53C2412yes—
369C2×C22⋊D53C24116yes—
370C2×C22⋊D53C2414yes—
371C2×C22⋊D53C2414yes—
372C2×C22⋊D53C2418yes—
373C2×C22⋊D53C2418yes—
374C2×C22⋊D53C24116yes—
375C2×C22⋊D53C2418yes—
376C22×Dic53—48no—
377C22×Dic53C2411yescharacteristic
378C22×Dic53C2414yes—
379C22×Dic53C2412yes—
380C22×Dic53C24116yes—
381C22×Dic53C2418yes—
382C22×Dic53C2418yes—
383#11719949—48no—
384Q8×D53—48no—
385#11719947—416no—
386#11719947—416no—
387#11719947—48no—
388#11719947—48no—
389#11719947—48no—
390#11719947—416no—
391D4×D53—416no—
392D4×D53—48no—
393D4×D53—48no—
394#11719945—24no—
395#11719945—28no—
396#11719945—48no—
397#11719945—48no—
398C2×D212C2412yes—
399C2×D212C2414yes—
400C2×D212C2411yescharacteristic
401C2×D212C2418yes—
402C2×D212C2414yes—
403C2×C4×D53—24no—
404C2×C4×D53—44no—
405C2×C4×D53C2412yes—
406C2×C4×D53C2412yes—
407C2×C4×D53C2412yes—
408C2×C4×D53C2412yes—
409C2×C4×D53C2414yes—
410C2×C4×D53C2412yes—
411C2×C4×D53C2414yes—
412C2×C4×D53C2412yes—
413C2×C4×D53C2412yes—
414C2×C4×D53C2418yes—
415C2×C4×D53C2418yes—
416C2×Dic106—28no—
417C2×Dic106—48no—
418C2×Dic106C2414yes—
419C2×Dic106C2412yes—
420C2×Dic106C2414yes—
421C2×Dic106C2411yescharacteristic
422C2×Dic106C2414yes—
423C2×Dic106C2418yes—
424C4⋊C4×C53C2412yes—
425C4⋊C4×C53C2414yes—
426C4⋊C4×C53C2414yes—
427C4⋊C4×C53C2414yes—
428C4⋊C4×C53C2418yes—
429C22⋊C4×C53C2412yes—
430C22⋊C4×C53C2414yes—
431C22⋊C4×C53C24116yes—
432C22⋊C4×C53C2414yes—
433C22⋊C4×C53C24116yes—
434C42×C53C2411yescharacteristic
435C42×C53C2412yes—
436C42×C53C2411yescharacteristic
437C42×C53C2414yes—
438C42×C53C2412yes—
439C42×C53C2414yes—
440C22⋊Dic53C24116yes—
441C22⋊Dic53C24116yes—
442C22⋊Dic53C2412yes—
443C22⋊Dic53C2414yes—
444C22⋊Dic53C2414yes—
445C22⋊Dic53C24116yes—
446#11719921C2414yes—
447#11719921C24116yes—
448#11719921C2414yes—
449#11719921C2418yes—
450#11719921C24116yes—
451#11719921C2418yes—
452#11719921C2414yes—
453#11719921C2414yes—
454#11719921C2414yes—
455#11719921C2418yes—
456#11719921C2418yes—
457C4⋊Dic53C2414yes—
458C4⋊Dic53C2418yes—
459C4⋊Dic53C2414yes—
460C4⋊Dic53C2418yes—
461C4⋊Dic53C24116yes—
462C4⋊Dic53C2418yes—
463C4⋊Dic53C24116yes—
464C4⋊Dic53C2414yes—
465C4⋊Dic53C2412yes—
466#11719919C24116yes—
467#11719919C2414yes—
468#11719919C2418yes—
469#11719919C2414yes—
470#11719919C2414yes—
471#11719919C2414yes—
472#11719919C2414yes—
473C4×Dic53C2411yescharacteristic
474C4×Dic53C2411yescharacteristic
475C4×Dic53C2412yes—
476C4×Dic53C2412yes—
477C4×Dic53C2412yes—
478C4×Dic53C2412yes—
479C4×Dic53C2412yes—
480C4×Dic53C2414yes—
481C4×Dic53C2412yes—
482C4×Dic53C2418yes—
483C4×Dic53C24116yes—
484C23×C53—28no—
485C23×C53—48no—
486C23×C53C2512yes—
487C23×C53C2518yes—
488C23×C53C2511yescharacteristic
489C22×D53—22no—
490C22×D53—42no—
491C22×D53—48no—
492C22×D53—416no—
493C22×D53C2512yes—
494C22×D53C2514yes—
495C22×D53C2512yes—
496Q8×C53—22no—
497Q8×C53—28no—
498D4×C53—24no—
499D4×C53—28no—
500D4×C53—28no—
501D4×C53—22no—
502D4×C53—216no—
503D4×C53—48no—
504D4×C53—416no—
505C2×C4×C53—24no—
506C2×C4×C53—24no—
507C2×C4×C53—28no—
508C2×C4×C53—416no—
509C2×C4×C53H(5,𝔽2)14yes—
510C2×C4×C53C2512yes—
511C2×C4×C53C2514yes—
512C2×C4×C53C2512yes—
513C2×C4×C53C2518yes—
514C2×C4×C53C2511yescharacteristic
515C2×C4×C53C2511yescharacteristic
516C2×C4×C53C2512yes—
517C22⋊D53—28no—
518C22⋊D53—24no—
519C22⋊D53—48no—
520C22⋊D53—44no—
521C22⋊D53—44no—
522C22⋊D53—48no—
523C22⋊D53—48no—
524C22⋊D53—416no—
525C22⋊D53—416no—
526C2×Dic53—28no—
527C2×Dic53—22no—
528C2×Dic53—48no—
529C2×Dic53—42no—
530C2×Dic53—416no—
531C2×Dic53—48no—
532C2×Dic53C2518yes—
533C2×Dic53C2514yes—
534C2×Dic53C2512yes—
535C2×Dic53C2512yes—
536C2×Dic53C2514yes—
537C2×Dic53C2512yes—
538C2×Dic53C2512yes—
539D212—24no—
540D212—22no—
541D212—28no—
542D212—44no—
543D212—48no—
544C4×D53—24no—
545C4×D53—24no—
546C4×D53—24no—
547C4×D53—28no—
548C4×D53—24no—
549C4×D53—24no—
550C4×D53—28no—
551C4×D53—42no—
552C4×D53—42no—
553C4×D53—48no—
554C4×D53—48no—
555Dic106—28no—
556Dic106—28no—
557Dic106—24no—
558Dic106—22no—
559Dic106—48no—
560Dic106—44no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—22no—
564C22×C53—28no—
565C22×C53—24no—
566C22×C53—216no—
567C22×C53—88no—
568C22×C53C2×H(5,𝔽2)12yes—
569C22×C53C2611yescharacteristic
570C2×D53—22no—
571C2×D53—24no—
572C2×D53—22no—
573C2×D53—22no—
574C2×D53—22no—
575C2×D53—24no—
576C2×D53—28no—
577C2×D53—44no—
578C2×D53—168no—
579C4×C53—22no—
580C4×C53—24no—
581C4×C53—22no—
582C4×C53—28no—
583C4×C53C2×H(5,𝔽2)12yes—
584C4×C53C2×H(5,𝔽2)12yes—
585C4×C53#58514yes—
586Dic53—28no—
587Dic53—24no—
588Dic53—22no—
589Dic53—22no—
590Dic53—22no—
591Dic53—24no—
592Dic53—22no—
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—534no—
604#3508D5311yescharacteristic, complemented
605#3500—532no—
606#3499—531no—
607#3498—531no—
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444—531no—
612C2×#532—531no—
613C2×C53—22no—
614C2×C53—48no—
615C2×C53—42no—
616C2×C53C22×H(5,𝔽2)11yescharacteristic
617C2×C53C2×#58512yes—
618D53—42no—
619D53—44no—
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—538no—
628#559C2×D5314yescomplemented
629#557—534no—
630#556—534no—
631#556—538no—
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#550C2×D5314yescomplemented
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—5316no—
657#546—538no—
658#546—538no—
659#546C2×D5318yescomplemented
660D42—538no—
661D42—534no—
662#542—538no—
663#542—538no—
664#542—538no—
665#541—534no—
666#540—538no—
667#540—5316no—
668#540—538no—
669#540C2×D5314yescomplemented
670#539—5316no—
671#538—5316no—
672#538—5316no—
673#537—538no—
674#536—534no—
675#536—532no—
676#536—532no—
677#536—534no—
678#535—532no—
679#535—534no—
680#535—534no—
681#535—538no—
682#535—538no—
683#535C2×D5312yescomplemented
684#534—538no—
685#533—532no—
686#533—534no—
687#533—532no—
688#533—531no—
689#533C2×D5311yescharacteristic, complemented
690#532—531no—
691#532—532no—
692#532—534no—
693#532—534no—
694#532—534no—
695#532—534no—
696#532—532no—
697#532—534no—
698#532—532no—
699#532—531no—
700#532—532no—
701#532C2×D5314yescomplemented
702C2×C4⋊Q8—531no—
703C2×C4⋊Q8—532no—
704C2×#127—532no—
705C2×#127C2×D5311yescharacteristic
706#529—534no—
707#529—534no—
708#529—532no—
709#529—534no—
710#529—534no—
711#529—532no—
712#529—538no—
713#529—534no—
714C2×#124—532no—
715C2×#124—534no—
716#525—531no—
717#525—534no—
718#525—538no—
719#525—534no—
720#525—531no—
721#525—532no—
722C2×#123—538no—
723C2×#121—534no—
724#520—538no—
725#519—532no—
726#518—538no—
727#518C2×D5312yescomplemented
728C4×#41—534no—
729C4×#41—532no—
730C4×#41—531no—
731C4×#41—534no—
732C4×#41C2×D5311yescharacteristic, complemented
733C2×C4×D4—534no—
734C22×C42—531no—
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—2128no—
737H(5,𝔽2)—2128no—
738C2×#41—534no—
739C2×#41—538no—
740C2×#41—538no—
741C2×#41—538no—
742C2×#41—534no—
743C2×#41—534no—
744C2×#41—534no—
745C2×#41—532no—
746C2×#41—531no—
747C2×#41—534no—
748C2×#41—534no—
749C2×#41—2128no—
750C2×#41C22×D5311yescharacteristic
751C2×#41C22×D5318yes—
752C22×Q8—534no—
753C22×Q8—532no—
754C22×Q8—534no—
755C22×D4—534no—
756C22×D4—538no—
757C22×D4—538no—
758C22×D4—534no—
759C22×D4—534no—
760C22×D4C22×D5312yes—
761C22×D4C22×D5314yes—
762C23×C4—534no—
763C23×C4—531no—
764C23×C4—532no—
765C4⋊Q8—531no—
766C4⋊Q8—532no—
767C4⋊Q8—532no—
768C4⋊Q8—531no—
769C4⋊Q8—532no—
770C4⋊Q8—534no—
771C4⋊Q8—534no—
772C4⋊Q8—538no—
773C4⋊Q8—534no—
774C4⋊Q8C22×D5312yes—
775#127—534no—
776#127—538no—
777#127—531no—
778#127—5316no—
779#127—531no—
780#127C22×D5312yes—
781#127C22×D5312yes—
782#127C22×D5314yes—
783#127C22×D5314yes—
784#126—538no—
785#126—534no—
786#126—5316no—
787#126—534no—
788#126—5316no—
789#126—5316no—
790#125—532no—
791#125—534no—
792#125—534no—
793#125—538no—
794#125—5316no—
795#125C22×D5312yes—
796#124—531no—
797#124—534no—
798#124—534no—
799#124—534no—
800#124—538no—
801#124—531no—
802#124—534no—
803#124—5316no—
804#124—534no—
805#124—5316no—
806#124—5316no—
807#124—534no—
808#124—532no—
809#124—534no—
810#124C22×D5314yes—
811#124C22×D5318yes—
812#123—532no—
813#123—5316no—
814#123—534no—
815#123—538no—
816#123—532no—
817#123—534no—
818#123—538no—
819#123—538no—
820#123—5316no—
821#123—5316no—
822#123—534no—
823#123—5316no—
824#123—5316no—
825#123—5316no—
826#123—5316no—
827#123C22×D53116yes—
828C22⋊Q8—534no—
829C22⋊Q8—532no—
830C22⋊Q8—538no—
831C22⋊Q8—5316no—
832C22⋊Q8—532no—
833C22⋊Q8—534no—
834C22⋊Q8—534no—
835C22⋊Q8—538no—
836C22⋊Q8—538no—
837C22⋊Q8—5316no—
838C22⋊Q8—534no—
839C22⋊Q8—5316no—
840C22⋊Q8—5316no—
841C22⋊Q8C22×D5314yes—
842#121—538no—
843#121—538no—
844#121—538no—
845#121—538no—
846#121—534no—
847#121—532no—
848#121—5316no—
849#121—538no—
850#121—538no—
851#121—5316no—
852#121—5316no—
853#121—5316no—
854#121—5316no—
855#121—534no—
856#121—538no—
857#121—5316no—
858#121—5316no—
859#121—534no—
860#121—532no—
861#121—534no—
862#121—534no—
863#121—5316no—
864#121C22×D5318yes—
865#121C22×D5318yes—
866#121C22×D53116yes—
867#120—538no—
868#120—532no—
869#120—5316no—
870#120—5316no—
871#120—532no—
872#120—534no—
873#120—5316no—
874#120C22×D5318yes—
875C4×Q8—534no—
876C4×Q8—538no—
877C4×Q8—534no—
878C4×Q8—538no—
879C4×Q8—532no—
880C4×Q8—534no—
881C4×Q8—534no—
882C4×Q8—538no—
883C4×Q8C22×D5314yes—
884C4×Q8C22×D5312yes—
885C4×D4—538no—
886C4×D4—538no—
887C4×D4—538no—
888C4×D4—538no—
889C4×D4—5316no—
890C4×D4—5316no—
891C4×D4—538no—
892C4×D4—534no—
893C4×D4—534no—
894C4×D4—534no—
895C4×D4—534no—
896C4×D4—534no—
897C4×D4—5316no—
898C4×D4—534no—
899C4×D4—538no—
900C4×D4—534no—
901C4×D4—538no—
902C4×D4—5316no—
903C4×D4—534no—
904C4×D4—534no—
905C4×D4—538no—
906C4×D4—532no—
907C4×D4—534no—
908C4×D4—538no—
909C4×D4C22×D5314yes—
910C4×D4C22×D5312yes—
911C4×D4C22×D5318yes—
912C4×D4C22×D5318yes—
913C4×D4C22×D5318yes—
914#117—531no—
915#117—534no—
916#117—5316no—
917#117—534no—
918#117—538no—
919#117—538no—
920#117—538no—
921#117—534no—
922#117—534no—
923#117—532no—
924#117—534no—
925#117C22×D5312yes—
926#117C22×D5311yescharacteristic
927#117C22×D5312yes—
928C2×C4⋊C4—534no—
929C2×C4⋊C4—5316no—
930C2×C4⋊C4—538no—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—5316no—
933C2×C22⋊C4—5316no—
934C2×C22⋊C4C22×D5318yes—
935C2×C42—532no—
936C2×C42—531no—
937C2×C42—534no—
938C2×C42—532no—
939C2×C42—532no—
940C2×C42—532no—
941C2×C42—532no—
942C2×C42—532no—
943C2×C42C22×D5312yes—
944C2×C42C22×D5311yescharacteristic
945C24—531no—
946C24—538no—
947C24C23×D5314yes—
948#41—24no—
949#41—416no—
950#41—1064no—
951#41—1068no—
952#41—2128no—
953#41—2128no—
954#41—21216no—
955#41—21216no—
956#41—21216no—
957#41—2128no—
958#41—2128no—
959#41—2128no—
960#41—2128no—
961C2×Q8—534no—
962C2×Q8—532no—
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×D5311yescharacteristic
972C2×D4—28no—
973C2×D4—48no—
974C2×D4—534no—
975C2×D4—532no—
976C2×D4—534no—
977C2×D4—5316no—
978C2×D4—534no—
979C2×D4—538no—
980C2×D4—538no—
981C2×D4—5316no—
982C2×D4—538no—
983C2×D4—534no—
984C2×D4—531no—
985C2×D4—532no—
986C2×D4—534no—
987C2×D4—538no—
988C2×D4—21216no—
989C2×D4—2128no—
990C2×D4—2128no—
991C2×D4—2128no—
992C2×D4—21216no—
993C2×D4C23×D5318yes—
994C2×D4C23×D5312yes—
995C2×D4C23×D5314yes—
996C2×D4C23×D5311yescharacteristic
997C2×D4C23×D5314yes—
998C2×D4C23×D5318yes—
999C2×D4C23×D53116yes—
1000C22×C4—531no—
1001C22×C4—534no—
1002C22×C4—532no—
1003C22×C4—5316no—
1004C22×C4—538no—
1005C22×C4—538no—
1006C22×C4—532no—
1007C22×C4—532no—
1008C22×C4—532no—
1009C22×C4—532no—
1010C22×C4—534no—
1011C22×C4—534no—
1012C22×C4—532no—
1013C22×C4—532no—
1014C22×C4—532no—
1015C22×C4—538no—
1016C22×C4—538no—
1017C22×C4—1064no—
1018C22×C4—2124no—
1019C22×C4—2128no—
1020C22×C4C23×D5312yes—
1021C22×C4C23×D5314yes—
1022C22×C4C23×D5312yes—
1023C22×C4C23×D53116yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—534no—
1026C4⋊C4—538no—
1027C4⋊C4—534no—
1028C4⋊C4—538no—
1029C4⋊C4—5316no—
1030C4⋊C4—538no—
1031C4⋊C4—5316no—
1032C4⋊C4—534no—
1033C4⋊C4—534no—
1034C4⋊C4—534no—
1035C4⋊C4—532no—
1036C4⋊C4—534no—
1037C4⋊C4—538no—
1038C4⋊C4—534no—
1039C4⋊C4—534no—
1040C4⋊C4—5316no—
1041C4⋊C4C23×D5314yes—
1042C4⋊C4C23×D5318yes—
1043C4⋊C4C23×D5314yes—
1044C4⋊C4C23×D5312yes—
1045C4⋊C4C23×D5314yes—
1046C22⋊C4—5316no—
1047C22⋊C4—5316no—
1048C22⋊C4—532no—
1049C22⋊C4—534no—
1050C22⋊C4—534no—
1051C22⋊C4—5316no—
1052C22⋊C4—534no—
1053C22⋊C4—534no—
1054C22⋊C4—538no—
1055C22⋊C4—5316no—
1056C22⋊C4—5316no—
1057C22⋊C4—534no—
1058C22⋊C4—538no—
1059C22⋊C4—538no—
1060C22⋊C4—534no—
1061C22⋊C4—538no—
1062C22⋊C4—534no—
1063C22⋊C4C23×D53116yes—
1064C22⋊C4C23×D5312yes—
1065C22⋊C4C23×D5314yes—
1066C22⋊C4C23×D53116yes—
1067C22⋊C4C23×D5314yes—
1068C42—531no—
1069C42—532no—
1070C42—532no—
1071C42—531no—
1072C42—532no—
1073C42—532no—
1074C42—532no—
1075C42—538no—
1076C42—534no—
1077C42—532no—
1078C42—5316no—
1079C42C23×D5311yescharacteristic
1080C42C23×D5311yescharacteristic
1081C42C23×D5312yes—
1082C42C23×D5314yes—
1083C42C23×D5314yes—
1084C42C23×D5312yes—
1085C23—28no—
1086C23—48no—
1087C23—532no—
1088C23—534no—
1089C23—532no—
1090C23—1062no—
1091C23—2128no—
1092C23—21216no—
1093C23—2122no—
1094C23C24×D5318yes—
1095C23C24×D5312yes—
1096C23C24×D5311yescharacteristic
1097Q8—22no—
1098Q8—28no—
1099Q8—1068no—
1100Q8—1068no—
1101Q8—1064no—
1102Q8—1062no—
1103Q8—2128no—
1104Q8—2124no—
1105D4—24no—
1106D4—28no—
1107D4—28no—
1108D4—22no—
1109D4—216no—
1110D4—48no—
1111D4—416no—
1112D4—1064no—
1113D4—1068no—
1114D4—1062no—
1115D4—1064no—
1116D4—1068no—
1117D4—2124no—
1118D4—2128no—
1119D4—21216no—
1120D4—2128no—
1121D4—2128no—
1122D4—21216no—
1123D4—2124no—
1124D4—2124no—
1125D4—2128no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—28no—
1129C2×C4—416no—
1130C2×C4—532no—
1131C2×C4—534no—
1132C2×C4—532no—
1133C2×C4—532no—
1134C2×C4—534no—
1135C2×C4—538no—
1136C2×C4—532no—
1137C2×C4—1062no—
1138C2×C4—1068no—
1139C2×C4—1064no—
1140C2×C4—1064no—
1141C2×C4—1064no—
1142C2×C4—1068no—
1143C2×C4—1064no—
1144C2×C4—1064no—
1145C2×C4—1068no—
1146C2×C4—2122no—
1147C2×C4—2122no—
1148C2×C4—2128no—
1149C2×C4—2128no—
1150C2×C4—2122no—
1151C2×C4—21216no—
1152C2×C4—2128no—
1153C2×C4—2128no—
1154C2×C4#1313326314yes—
1155C2×C4C24×D5318yes—
1156C2×C4C24×D5312yes—
1157C2×C4C24×D5314yes—
1158C2×C4C24×D5312yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—22no—
1164C22—28no—
1165C22—24no—
1166C22—216no—
1167C22—88no—
1168C22—8488no—
1169C22—1062no—
1170C22—1064no—
1171C22—1062no—
1172C22—1062no—
1173C22—1062no—
1174C22—1064no—
1175C22—1068no—
1176C22—2124no—
1177C22C2×#1313326312yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—22no—
1182C4—28no—
1183C4—1062no—
1184C4—1062no—
1185C4—1064no—
1186C4—1068no—
1187C4—1062no—
1188C4—1062no—
1189C4—1064no—
1190C4C2×#1313326312yes—
1191C4C2×#1313326312yes—
1192C4#1681145814yes—
1193C2—22no—
1194C2—48no—
1195C2—42no—
1196C2—2122no—
1197C2—2124no—
1198C2—2122no—
1199C2C22×#1313326311yescharacteristic
1200C2C2×#1681145812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3508C2
hypercenter#3508D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #20289305C2semidirect
2. #20289174C2semidirect
3. #20289075C2semidirect
4. #20289017C2semidirect
5. #20288716C2semidirect
6. #20288675C2semidirect
7. #20288656C2semidirect
8. #20288622C2semidirect
9. #20288606C2semidirect
10. #20288602C2semidirect
11. #20288584C2semidirect
12. #20288507C2semidirect
13. #20288500C2semidirect
14. #20288491C2semidirect
15. #20288371C2semidirect
16. #20288360C2semidirect
17. #20288012C2semidirect
18. #20288008C2semidirect
19. C2×#16811171C2semidirect
20. C53×#3508C2semidirect
21. C2×#13133264C22semidirect
23. C22×#11719947C22semidirect
24. #16811370C22semidirect
25. #16811361C22semidirect
26. #16811356C22semidirect
27. #16811355C22semidirect
28. #16811352C22semidirect
29. #16811346C22semidirect
30. #16811343C22semidirect
31. #16811338C22semidirect
32. #16811330C22semidirect
33. #16811325C22semidirect
34. #16811325C22semidirect
35. #16811325C22semidirect
36. #16811315C22semidirect
37. #16811299C22semidirect
38. #16811296C22semidirect
39. #16811293C22semidirect
40. #16811293C22semidirect
41. #16811292C22semidirect
42. #16811291C22semidirect
43. Q8×D212C22semidirect
44. #16811281C22semidirect
45. #16811279C22semidirect
46. #16811279C22semidirect
47. #16811277C22semidirect
48. #16811277C22semidirect
49. #16811277C22semidirect
50. #16811277C22semidirect
51. #16811270C22semidirect
52. #16811268C22semidirect
53. #16811268C22semidirect
54. #16811266C22semidirect
55. #16811261C22semidirect
56. #16811260C22semidirect
57. #16811258C22semidirect
59. #16811242C22semidirect
60. #16811242C22semidirect
61. #16811238C22semidirect
62. #16811236C22semidirect
63. #16811226C22semidirect
64. #16811226C22semidirect
65. #16811224C22semidirect
66. #16811217C22semidirect
67. #16811210C22semidirect
68. #16811209C22semidirect
69. #16811201C22semidirect
71. #16811199C22semidirect
72. #16811199C22semidirect
73. #16811193C22semidirect
75. #16811189C22semidirect
76. #16811188C22semidirect
77. #16811186C22semidirect
78. #16811186C22semidirect
79. #16811185C22semidirect
80. #16811178C22semidirect
81. #16811178C22semidirect
82. #16811177C22semidirect
83. #16811176C22semidirect
84. #16811174C22semidirect
86. #16811173C22semidirect
87. #16811171C22semidirect
88. #16811171C22semidirect
89. #16811171C22semidirect
90. #16811171C22semidirect
91. #16811171C22semidirect
92. #16811171C22semidirect
93. #16811170C22semidirect
95. C2×#13133217C22semidirect
96. C2×#13133217C22semidirect
97. #127×D53C22semidirect
98. #16811160C22semidirect
99. #16811160C22semidirect
100. #16811159C22semidirect
101. #16811158C22semidirect
102. #16811155C22semidirect
103. #16811155C22semidirect
104. #16811153C22semidirect
105. #16811151C22semidirect
106. C2×#13133204C22semidirect
107. #124×D53C22semidirect
108. #16811136C22semidirect
110. #16811135C22semidirect
111. #16811132C22semidirect
112. #16811130C22semidirect
113. #16811129C22semidirect
114. C2×#13133201C22semidirect
115. C2×#13133188C22semidirect
116. #16811106C22semidirect
117. #16811100C22semidirect
118. #16811095C22semidirect
119. C4×#11719949C22semidirect
121. C4×#11719945C22semidirect
122. #16811091C22semidirect
123. C2×D4×Dic53C22semidirect
124. C2×C42×D53C22semidirect
125. C53×#559C22semidirect
126. C53×#550C22semidirect
127. C53×#546C22semidirect
128. C53×#540C22semidirect
129. C53×#535C22semidirect
130. C53×#533C22semidirect
131. C53×#532C22semidirect
133. C53×#518C22semidirect
134. C4×#41×C53C22semidirect
604. #3508D53semidirect
628. #559C2×D53semidirect
644. #550C2×D53semidirect
659. #546C2×D53semidirect
669. #540C2×D53semidirect
683. #535C2×D53semidirect
689. #533C2×D53semidirect
701. #532C2×D53semidirect
727. #518C2×D53semidirect
732. C4×#41C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893052
#202891742
#202890752
#202890172
#202887162
#202886752
#202886562
#202886222
#202886062
#202886022
#202885842
#202885072
#202885002
#202884912
#202883712
#202883602
#202880122
#202880082
C2×#168111712
C53×#35082
#6283653