Finite Group Databasebeta

← #28292980

Subgroups — #28292980

Order 13568.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289157C214yesmaximal, complemented
2#20289153C214yesmaximal, complemented
3#20289147C218yesmaximal, complemented
4#20289051C218yesmaximal, complemented
5#20288625C214yesmaximal, complemented
6#20288616C214yesmaximal, complemented
7#20288601C211yesmaximal, characteristic, complemented
8#20288600C212yesmaximal, complemented
9#20288599C211yesmaximal, characteristic, complemented
10#20288531C214yesmaximal, complemented
11#20288526C214yesmaximal, complemented
12#20288496C212yesmaximal, complemented
13#20288495C211yesmaximal, characteristic, complemented
14#20288417C218yesmaximal, complemented
15#20288364C212yesmaximal, complemented
16#20288363C212yesmaximal, complemented
17#20288010C211yesmaximal, characteristic, complemented
18#20288008C211yesmaximal, characteristic, complemented
19C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
20C53×#3499C211yesmaximal, characteristic, complemented
21C2×#13133264C2212yes—
22C22×Q8×D53C2212yes—
23#16811376C22116yescomplemented
24#16811374C22116yescomplemented
25#16811353C2218yescomplemented
26#16811351C2214yescomplemented
27#16811348C2214yescomplemented
28#16811348C2218yescomplemented
29#16811347C2214yescomplemented
30#16811343C2214yescomplemented
31#16811342C2218yescomplemented
32#16811337C2218yescomplemented
33#16811334C2218yes—
34#16811332C2218yescomplemented
35#16811328C2218yes—
36#16811328C2218yescomplemented
37#16811327C22116yes—
38#16811323C2218yes—
39#16811320C2218yes—
40#16811318C22116yes—
41#16811313C2218yes—
42#16811310C22116yes—
43#16811308C2218yes—
44D4×Dic106C2214yescomplemented
45#16811288C2218yes—
46Q8×C22⋊D53C2218yes—
47Q8×C22⋊D53C2218yes—
48Q8×C22⋊D53C2218yescomplemented
49#16811286C2218yes—
50#16811283C2218yes—
51#16811281C2218yes—
52#16811280C2218yes—
53#16811280C2218yes—
54#16811278C2214yescomplemented
55#16811273C2218yes—
56#16811272C22116yes—
57#16811272C2218yescomplemented
58#16811254C2218yescomplemented
59#16811252C22116yescomplemented
60#16811250C2218yes—
61#16811250C2218yescomplemented
62#16811241C22116yescomplemented
63#16811240C2218yescomplemented
64#16811238C2218yescomplemented
65#16811235C2214yescomplemented
66#16811234C2214yescomplemented
67#16811233C2218yescomplemented
68#16811219C22116yes—
69#16811216C22116yes—
70#16811202C2218yes—
71#16811197C2212yes—
72#16811197C2214yescomplemented
73#16811195C2218yes—
74#16811194C2218yes—
75#16811194C2212yes—
76#16811194C2212yes—
77#16811194C2214yescomplemented
78#16811193C2214yescomplemented
79#16811180C2211yescharacteristic
80#16811180C2214yescomplemented
81#16811178C2212yes—
82#16811178C2214yescomplemented
83#16811177C2212yes—
84#16811176C2211yescharacteristic
85#16811175C2218yescomplemented
86#16811171C2212yes—
87#16811171C2212yescomplemented
88#16811170C2212yes—
89#16811169C2211yescharacteristic
90#16811169C2214yescomplemented
91C2×#13133217C2211yescharacteristic
92C2×#13133216C2214yes—
93C2×#13133215C2212yes—
94C2×#13133215C2214yescomplemented
95C4⋊Q8×D53C2214yes—
96C4⋊Q8×D53C2214yes—
97C4⋊Q8×D53C2214yes—
98C4⋊Q8×D53C2214yes—
99C4⋊Q8×D53C2212yescomplemented
100#16811160C2212yes—
101#16811155C2212yes—
102#16811155C2214yes—
103#16811154C2214yes—
104#16811153C2214yes—
105#16811152C2214yes—
106#16811151C2214yes—
107#16811135C2211yescharacteristic
108#16811133C2214yes—
109#16811132C2214yes—
110#16811131C2218yes—
111#16811130C2211yescharacteristic
112#16811130C2212yes—
113#16811130C2218yes—
114#16811104C2218yes—
115#16811102C2218yes—
116#16811101C2212yes—
117#16811100C2212yes—
118#41×Dic53C2212yes—
119C4×#11719945C2214yes—
120C4×#11719945C2211yescharacteristic
121C4×#11719947C2214yes—
122C2×C4⋊C4×D53C2214yes—
123C2×C42×D53C2211yescharacteristic
124C2×2−1+4×C53C2212yes—
125D4×Q8×C53C2214yescomplemented
126C53×#547C2218yes—
127C53×#547C2214yescomplemented
128C53×#536C2212yes—
129C53×#536C2214yescomplemented
130C53×#532C2211yescharacteristic
131C53×#532C2212yescomplemented
132C2×C4⋊Q8×C53C2211yescharacteristic
133C2×C4⋊Q8×C53C2212yescomplemented
134C4×#41×C53C2211yescharacteristic
135#13133264—48no—
136C2×#11719945C2314yes—
137C2×#11719945C2311yescharacteristic
138C2×#11719945C2314yes—
139C2×#11719947C2314yes—
140C2×#11719947C2318yes—
141C2×#11719947C2314yes—
142C22×Dic106C2312yes—
143C22×Dic106C2314yes—
144C22×Dic106C2314yes—
145C2×Q8×D53—48no—
146C2×Q8×D53C2318yes—
147C2×Q8×D53C2318yes—
148C2×Q8×D53C2314yes—
149C22×C4×D53C2312yes—
150C22×C4×D53C2311yescharacteristic
151C22×C4×D53C2314yes—
152#13133217C2314yes—
153#13133217C2312yes—
154#13133217C2312yes—
155#13133217C2312yes—
156#13133216C2318yes—
157#13133216C23116yes—
158#13133216C2318yes—
159#13133216C2318yes—
160#13133216C2318yes—
161#13133216C2318yes—
162#13133216C2312yes—
163#13133215C23116yes—
164#13133215C2318yes—
165#13133215C2314yes—
166#13133215C2314yes—
167#13133215C2314yes—
168#13133215C23116yes—
169#13133215C2314yes—
170#13133215C2314yes—
171#13133215C2311yescharacteristic
172#13133213C2311yescharacteristic
173#13133212C23116yes—
174#13133212C2314yes—
175#13133210C23116yes—
176#13133210C23116yes—
177#13133210C23116yes—
178#13133210C2318yes—
179#13133210C2314yes—
180#13133209C2318yes—
181#13133209C2312yes—
182#13133208C2318yes—
183#13133208C23116yes—
184#13133208C2314yes—
185#13133208C2312yes—
186#13133207C23116yes—
187#13133207C23116yes—
188#13133207C23116yes—
189#13133207C23116yes—
190#13133207C2314yes—
191#13133206C2314yes—
192#13133206C2311yescharacteristic
193#13133204C23116yes—
194#13133204C2314yes—
195#13133204C2314yes—
196#13133204C2314yes—
197#13133204C2311yescharacteristic
198#13133203C23116yes—
199#13133203C2314yes—
200#13133202C2314yes—
201#13133201C2312yes—
202#13133200C2318yes—
203#13133200C23116yes—
204#13133199C23116yes—
205#13133199C2314yes—
206#13133199C2318yes—
207#13133198C2318yes—
208#13133198C23116yes—
209#13133198C2318yes—
210#13133198C2312yes—
211#13133198C2314yes—
212#13133197C2312yes—
213#13133197C2318yes—
214#13133197C2314yes—
215#13133196C23116yes—
216#13133196C2318yes—
217#13133196C2318yes—
218#13133196C23116yes—
219#13133196C23116yes—
220#13133196C2314yes—
221#13133196C2318yes—
222#13133195C23116yes—
223#13133195C23116yes—
224#13133195C2314yes—
225#13133194C23116yes—
226#13133194C23116yes—
227#13133194C2314yes—
228#13133194C23116yes—
229#13133193C23116yes—
230#13133193C2318yes—
231#13133193C2312yes—
232#13133193C2314yes—
233#13133193C23116yes—
234#13133192C2312yes—
235#13133190C23116yes—
236#13133190C2314yes—
237#13133189C2314yes—
238#13133189C23116yes—
239#13133188C2318yes—
240#13133188C2312yes—
241#13133188C2314yes—
242#13133188C23116yes—
243#13133188C2314yes—
244#13133187C2312yes—
245#13133185C2312yes—
246#13133185C2314yes—
247Q8×Dic53C2318yes—
248Q8×Dic53C2318yes—
249Q8×Dic53C2314yes—
250C4×Dic106C2318yes—
251C4×Dic106C2312yes—
252C4×Dic106C2318yes—
253C4×Dic106C2314yes—
254C4×Dic106C2314yes—
255C4×Dic106C2314yes—
256#13133182C2318yes—
257#13133182C2318yes—
258#13133182C23116yes—
259#13133182C2314yes—
260C4×D212C2312yes—
261C4×D212C2314yes—
262C4×D212C2314yes—
263D4×Dic53C2318yes—
264D4×Dic53C2314yes—
265D4×Dic53C2318yes—
266D4×Dic53C2314yes—
267#13133179C23116yes—
268C4×C22⋊D53C23116yes—
269C4×C22⋊D53C2314yes—
270C4×C22⋊D53C2314yes—
271C4×C22⋊D53C2314yes—
272C4×C22⋊D53C2318yes—
273C4×C22⋊D53C23116yes—
274C4×C22⋊D53C23116yes—
275C4×C22⋊D53C2314yes—
276C4×C22⋊D53C2314yes—
277#13133177C23116yes—
278#13133177C2318yes—
279#13133176C2318yes—
280#13133176C2318yes—
281#13133176C2311yescharacteristic
282#13133176C2314yes—
283#13133176C2312yes—
284#13133176C2314yes—
285#13133175C2318yes—
286#13133175C2314yes—
287#13133174C2314yes—
288#13133174C2312yes—
289#13133174C2314yes—
290#13133173C2318yes—
291#13133173C23116yes—
292#13133173C2318yes—
293C2×C4⋊Dic53C2314yes—
294C2×#11719919C2318yes—
295C2×#11719919C23116yes—
296C4⋊C4×D53C2318yes—
297C4⋊C4×D53C2318yes—
298C4⋊C4×D53C2318yes—
299C4⋊C4×D53C2318yes—
300C4⋊C4×D53C2318yes—
301C2×C4×Dic53C2311yescharacteristic
302C2×C4×Dic53C2312yes—
303C2×C4×Dic53C2314yes—
304C42×D53C2312yes—
305C42×D53C2312yes—
306C42×D53C2312yes—
307C42×D53C2312yes—
308C42×D53C2312yes—
3092−1+4×C53—48no—
310C2×#41×C53C2311yescharacteristic
311C2×#41×C53C2312yes—
312C2×#41×C53C2318yes—
313C2×#41×C53C2314yes—
314C2×#41×C53C2314yes—
315C22×Q8×C53C2312yes—
316C22×Q8×C53C2314yes—
317C22×Q8×C53C2314yes—
318C4⋊Q8×C53C2314yes—
319C4⋊Q8×C53C2312yes—
320C4⋊Q8×C53C2312yes—
321C4⋊Q8×C53C2314yes—
322C4⋊Q8×C53C2311yescharacteristic
323C4⋊Q8×C53C2318yes—
324#127×C53C2311yescharacteristic
325#124×C53C2314yes—
326#124×C53C2312yes—
327#123×C53C2318yes—
328#123×C53C23116yes—
329C22⋊Q8×C53C2318yes—
330C22⋊Q8×C53C23116yes—
331#121×C53C2314yes—
332#121×C53C2318yes—
333C4×Q8×C53C2312yes—
334C4×D4×C53C2314yes—
335C4×D4×C53C2314yes—
336C4×D4×C53C2312yes—
337C4×D4×C53C2318yes—
338#117×C53C2311yescharacteristic
339#117×C53C2312yes—
340C2×C4⋊C4×C53C2314yes—
341C2×C4⋊C4×C53C2318yes—
342C2×C42×C53C2311yescharacteristic
343C2×C42×C53C2312yes—
344C23×D53C2411yescharacteristic
345#41×C53—24no—
346#41×C53—28no—
347#41×C53—416no—
348#41×C53—48no—
349#41×C53—48no—
350C2×Q8×C53—28no—
351C2×Q8×C53—48no—
352C2×Q8×C53—48no—
353C2×Q8×C53C2411yescharacteristic
354C2×Q8×C53C2414yes—
355C2×Q8×C53C2414yes—
356C2×Q8×C53C2412yes—
357C2×Q8×C53C2418yes—
358C2×D4×C53C2414yes—
359C2×D4×C53C2412yes—
360C2×D4×C53C2411yescharacteristic
361C2×D4×C53C2414yes—
362C2×D4×C53C2412yes—
363C2×D4×C53C2418yes—
364C22×C4×C53C2412yes—
365C22×C4×C53C2414yes—
366C22×C4×C53C2412yes—
367C22×C4×C53C2414yes—
368C22×C4×C53C2414yes—
369C22×C4×C53C2418yes—
370C22×C4×C53C2418yes—
371C22×C4×C53C2411yescharacteristic
372C2×C22⋊D53C2418yes—
373C2×C22⋊D53C2414yes—
374C2×C22⋊D53C2414yes—
375C2×C22⋊D53C2412yes—
376C2×C22⋊D53C2418yes—
377C22×Dic53C2412yes—
378C22×Dic53C2411yescharacteristic
379C22×Dic53C2418yes—
380C22×Dic53C2414yes—
381C22×Dic53C2418yes—
382Q8×D53—416no—
383Q8×D53—416no—
384Q8×D53—48no—
385#11719947—216no—
386#11719947—48no—
387#11719947—416no—
388#11719945—24no—
389#11719945—216no—
390#11719945—48no—
391C2×D212C2414yes—
392C2×D212C2411yescharacteristic
393C2×C4×D53—24no—
394C2×C4×D53—28no—
395C2×C4×D53—48no—
396C2×C4×D53C2412yes—
397C2×C4×D53C2412yes—
398C2×C4×D53C2412yes—
399C2×C4×D53C2412yes—
400C2×C4×D53C2412yes—
401C2×C4×D53C2414yes—
402C2×C4×D53C2412yes—
403C2×C4×D53C24116yes—
404C2×C4×D53C2418yes—
405C2×C4×D53C2412yes—
406C2×Dic106—28no—
407C2×Dic106—48no—
408C2×Dic106—48no—
409C2×Dic106C2414yes—
410C2×Dic106C2414yes—
411C2×Dic106C2414yes—
412C2×Dic106C2414yes—
413C2×Dic106C2411yescharacteristic
414C2×Dic106C2418yes—
415C2×Dic106C24116yes—
416C4⋊C4×C53C2418yes—
417C4⋊C4×C53C2414yes—
418C4⋊C4×C53C2418yes—
419C4⋊C4×C53C24116yes—
420C4⋊C4×C53C2412yes—
421C4⋊C4×C53C2414yes—
422C22⋊C4×C53C2412yes—
423C22⋊C4×C53C2414yes—
424C22⋊C4×C53C24116yes—
425C22⋊C4×C53C2418yes—
426C42×C53C2411yescharacteristic
427C42×C53C2411yescharacteristic
428C42×C53C2412yes—
429C42×C53C2412yes—
430C42×C53C2414yes—
431C22⋊Dic53C2414yes—
432C22⋊Dic53C24116yes—
433C22⋊Dic53C2418yes—
434C22⋊Dic53C2412yes—
435C22⋊Dic53C24116yes—
436C22⋊Dic53C2414yes—
437C22⋊Dic53C2414yes—
438C22⋊Dic53C2418yes—
439#11719921C2414yes—
440#11719921C2414yes—
441#11719921C2414yes—
442#11719921C2414yes—
443#11719921C2414yes—
444#11719921C2418yes—
445#11719921C24116yes—
446C4⋊Dic53C2418yes—
447C4⋊Dic53C2418yes—
448C4⋊Dic53C2414yes—
449C4⋊Dic53C2414yes—
450C4⋊Dic53C2418yes—
451C4⋊Dic53C2412yes—
452C4⋊Dic53C2414yes—
453C4⋊Dic53C2414yes—
454C4⋊Dic53C24116yes—
455#11719919C24116yes—
456#11719919C24116yes—
457#11719919C24116yes—
458#11719919C2414yes—
459#11719919C24116yes—
460#11719919C24116yes—
461#11719919C2414yes—
462#11719919C2418yes—
463#11719919C2418yes—
464#11719919C24116yes—
465#11719919C2414yes—
466#11719919C2414yes—
467#11719919C2414yes—
468C4×Dic53C2411yescharacteristic
469C4×Dic53C2412yes—
470C4×Dic53C2412yes—
471C4×Dic53C2411yescharacteristic
472C4×Dic53C2412yes—
473C4×Dic53C2412yes—
474C4×Dic53C2412yes—
475C4×Dic53C2414yes—
476C4×Dic53C2412yes—
477C4×Dic53C2418yes—
478C4×Dic53C2414yes—
479C4×Dic53C24116yes—
480C4×Dic53C24116yes—
481C23×C53C2514yes—
482C23×C53C2512yes—
483C23×C53C2511yescharacteristic
484C22×D53—22no—
485C22×D53—24no—
486C22×D53C2512yes—
487C22×D53C2512yes—
488Q8×C53—28no—
489Q8×C53—28no—
490Q8×C53—24no—
491Q8×C53—22no—
492Q8×C53—48no—
493D4×C53—28no—
494D4×C53—24no—
495D4×C53—24no—
496D4×C53—22no—
497D4×C53—28no—
498D4×C53—48no—
499C2×C4×C53—28no—
500C2×C4×C53—28no—
501C2×C4×C53—24no—
502C2×C4×C53—24no—
503C2×C4×C53—28no—
504C2×C4×C53—48no—
505C2×C4×C53—48no—
506C2×C4×C53H(5,𝔽2)14yes—
507C2×C4×C53C2514yes—
508C2×C4×C53C2518yes—
509C2×C4×C53C2514yes—
510C2×C4×C53C2512yes—
511C2×C4×C53C2512yes—
512C2×C4×C53C2511yescharacteristic
513C2×C4×C53C2511yescharacteristic
514C2×C4×C53C2512yes—
515C22⋊D53—24no—
516C22⋊D53—28no—
517C22⋊D53—216no—
518C22⋊D53—28no—
519C22⋊D53—48no—
520C2×Dic53—28no—
521C2×Dic53—22no—
522C2×Dic53—24no—
523C2×Dic53—216no—
524C2×Dic53—48no—
525C2×Dic53C2512yes—
526C2×Dic53C2518yes—
527C2×Dic53C2512yes—
528C2×Dic53C2514yes—
529C2×Dic53C2518yes—
530C2×Dic53C2512yes—
531C2×Dic53C2512yes—
532D212—28no—
533D212—22no—
534C4×D53—24no—
535C4×D53—24no—
536C4×D53—24no—
537C4×D53—24no—
538C4×D53—24no—
539C4×D53—28no—
540C4×D53—24no—
541C4×D53—416no—
542C4×D53—48no—
543C4×D532−1+418yescomplemented
544Dic106—28no—
545Dic106—28no—
546Dic106—22no—
547Dic106—28no—
548Dic106—28no—
549Dic106—48no—
550Dic106—416no—
551#62833—531nomaximal, Sylow
552C22×C53—22no—
553C22×C53—24no—
554C22×C53—22no—
555C22×C53—28no—
556C22×C53—24no—
557C22×C53C2×H(5,𝔽2)12yes—
558C22×C53C2611yescharacteristic
559C2×D53—28no—
560C2×D53—22no—
561C2×D53—22no—
562C2×D53—22no—
563C2×D53—24no—
564C2×D53C2×2−1+414yes—
565C4×C53—24no—
566C4×C53—28no—
567C4×C53—22no—
568C4×C53—24no—
569C4×C53—22no—
570C4×C53C2×H(5,𝔽2)12yes—
571C4×C53C2×H(5,𝔽2)12yes—
572C4×C53C2×2−1+414yes—
573Dic53—28no—
574Dic53—22no—
575Dic53—22no—
576Dic53—24no—
577Dic53—28no—
578Dic53—22no—
579Dic53C2×2−1+414yes—
580#3552—534no—
581#3552—534no—
582#3552—538no—
583#3544—538no—
584#3511—534no—
585#3511—534no—
586#3509—532no—
587#3509—531no—
588#3509—531no—
589#3503—534no—
590#3503—534no—
591#3499—532no—
592#3499—531no—
593#3499D5311yescharacteristic, complemented
594#3492—538no—
595#3486—532no—
596#3486—532no—
597#3444—531no—
598#3444—531no—
599C22×C4⋊Q8—531no—
600C2×C53—22no—
601C2×C53—44no—
602C2×C53—42no—
603C2×C53C22×H(5,𝔽2)11yescharacteristic
604C2×C53C22×2−1+412yes—
605D53—24no—
606D53—42no—
607C2×2−1+4—532no—
608C2×2−1+4C2×D5312yes—
609C23×Q8—532no—
610#563—5316no—
611#563—5316no—
612Q82—538no—
613#557—538no—
614#557—534no—
615#557—534no—
616#556—534no—
617#556—538no—
618#556—534no—
619#555—538no—
620#554—538no—
621#554—5316no—
622#554—538no—
623#554—538no—
624#554—538no—
625#553—5316no—
626#553—538no—
627#553—538no—
628#552—5316no—
629#552—538no—
630#552—538no—
631D4×Q8—538no—
632D4×Q8—538no—
633D4×Q8—538no—
634D4×Q8—538no—
635D4×Q8—538no—
636D4×Q8—534no—
637D4×Q8C2×D5314yescomplemented
638#548—538no—
639#548—538no—
640#548—538no—
641#548—538no—
642#547—5316no—
643#547—538no—
644#547—538no—
645#547—534no—
646#547C2×D5318yes—
647#547C2×D5314yescomplemented
648#544—538no—
649#544—538no—
650#544—5316no—
651#544—538no—
652#542—5316no—
653#542—538no—
654#542—538no—
655#541—534no—
656#541—538no—
657#541—534no—
658#539—5316no—
659#539—5316no—
660#537—538no—
661#536—532no—
662#536—532no—
663#536—538no—
664#536—534no—
665#536—532no—
666#536—534no—
667#536—534no—
668#536—538no—
669#536C2×D5312yes—
670#536C2×D5314yescomplemented
671#533—532no—
672#533—534no—
673#533—538no—
674#533—532no—
675#533—531no—
676#533—531no—
677#533—534no—
678#532—531no—
679#532—534no—
680#532—532no—
681#532—532no—
682#532—532no—
683#532C2×D5311yescharacteristic
684#532C2×D5312yescomplemented
685C2×C4⋊Q8—532no—
686C2×C4⋊Q8—534no—
687C2×C4⋊Q8—534no—
688C2×C4⋊Q8—534no—
689C2×C4⋊Q8—534no—
690C2×C4⋊Q8—534no—
691C2×C4⋊Q8—532no—
692C2×C4⋊Q8—534no—
693C2×C4⋊Q8—531no—
694C2×C4⋊Q8C2×D5311yescharacteristic
695C2×C4⋊Q8C2×D5312yescomplemented
696#529—534no—
697#529—534no—
698#529—532no—
699#529—534no—
700#529—534no—
701#529—532no—
702#529—534no—
703#525—532no—
704#525—531no—
705#525—538no—
706#525—538no—
707#525—534no—
708#525—534no—
709#525—531no—
710#520—538no—
711#520—538no—
712#519—532no—
713#519—532no—
714C4×#41—532no—
715C4×#41—534no—
716C4×#41—531no—
717C4×#41—534no—
718C4×#41C2×D5311yescharacteristic
719C22×C4⋊C4—534no—
720C22×C42—531no—
721C53#6283311yescharacteristic, complemented, Sylow
7222−1+4—48no—
7232−1+4—2128no—
724C2×#41—534no—
725C2×#41—538no—
726C2×#41—534no—
727C2×#41—534no—
728C2×#41—531no—
729C2×#41—534no—
730C2×#41C22×D5312yes—
731C2×#41C22×D5311yescharacteristic
732C2×#41C22×D5318yes—
733C2×#41C22×D5314yes—
734C2×#41C22×D5314yes—
735C22×Q8—538no—
736C22×Q8—538no—
737C22×Q8—534no—
738C22×Q8—532no—
739C22×Q8—534no—
740C22×Q8—534no—
741C22×Q8—2128no—
742C22×Q8C22×D5312yes—
743C22×Q8C22×D5314yes—
744C22×Q8C22×D5314yes—
745C23×C4—532no—
746C23×C4—531no—
747C23×C4—534no—
748C4⋊Q8—534no—
749C4⋊Q8—531no—
750C4⋊Q8—534no—
751C4⋊Q8—538no—
752C4⋊Q8—534no—
753C4⋊Q8—534no—
754C4⋊Q8—534no—
755C4⋊Q8—5316no—
756C4⋊Q8—5316no—
757C4⋊Q8—538no—
758C4⋊Q8—538no—
759C4⋊Q8—538no—
760C4⋊Q8—538no—
761C4⋊Q8—538no—
762C4⋊Q8—532no—
763C4⋊Q8—5316no—
764C4⋊Q8—532no—
765C4⋊Q8—532no—
766C4⋊Q8—534no—
767C4⋊Q8—532no—
768C4⋊Q8C22×D5312yes—
769C4⋊Q8C22×D5312yes—
770C4⋊Q8C22×D5314yes—
771C4⋊Q8C22×D5311yescharacteristic
772C4⋊Q8C22×D5314yes—
773C4⋊Q8C22×D5318yes—
774#127—531no—
775#127C22×D5311yescharacteristic
776#126—534no—
777#126—5316no—
778#126—534no—
779#126—538no—
780#126—5316no—
781#126—5316no—
782#126—5316no—
783#125—532no—
784#125—534no—
785#125—534no—
786#125—5316no—
787#125—538no—
788#125—5316no—
789#125—5316no—
790#125—5316no—
791#125—5316no—
792#125—532no—
793#125—538no—
794#124—531no—
795#124—534no—
796#124—531no—
797#124—534no—
798#124—534no—
799#124—534no—
800#124—5316no—
801#124—534no—
802#124—5316no—
803#124C22×D5312yes—
804#124C22×D5314yes—
805#123—534no—
806#123—532no—
807#123—538no—
808#123—538no—
809#123—5316no—
810#123—538no—
811#123—5316no—
812#123—534no—
813#123—532no—
814#123—534no—
815#123—538no—
816#123—5316no—
817#123C22×D5318yes—
818#123C22×D53116yes—
819C22⋊Q8—534no—
820C22⋊Q8—532no—
821C22⋊Q8—5316no—
822C22⋊Q8—538no—
823C22⋊Q8—5316no—
824C22⋊Q8—534no—
825C22⋊Q8—538no—
826C22⋊Q8—538no—
827C22⋊Q8—538no—
828C22⋊Q8—5316no—
829C22⋊Q8—5316no—
830C22⋊Q8—5316no—
831C22⋊Q8—532no—
832C22⋊Q8—534no—
833C22⋊Q8—534no—
834C22⋊Q8—5316no—
835C22⋊Q8—538no—
836C22⋊Q8—5316no—
837C22⋊Q8—534no—
838C22⋊Q8—5316no—
839C22⋊Q8—5316no—
840C22⋊Q8—5316no—
841C22⋊Q8C22×D5318yes—
842C22⋊Q8C22×D53116yes—
843#121—534no—
844#121—534no—
845#121—532no—
846#121—534no—
847#121—5316no—
848#121—538no—
849#121—5316no—
850#121—532no—
851#121—534no—
852#121—5316no—
853#121C22×D5314yes—
854#121C22×D5318yes—
855#120—534no—
856#120—532no—
857#120—532no—
858C4×Q8—534no—
859C4×Q8—538no—
860C4×Q8—538no—
861C4×Q8—534no—
862C4×Q8—538no—
863C4×Q8—5316no—
864C4×Q8—538no—
865C4×Q8—532no—
866C4×Q8—534no—
867C4×Q8—534no—
868C4×Q8—534no—
869C4×Q8—538no—
870C4×Q8—538no—
871C4×Q8C22×D5312yes—
872C4×D4—538no—
873C4×D4—534no—
874C4×D4—534no—
875C4×D4—538no—
876C4×D4—534no—
877C4×D4—538no—
878C4×D4—534no—
879C4×D4—534no—
880C4×D4—534no—
881C4×D4—534no—
882C4×D4—5316no—
883C4×D4—5316no—
884C4×D4—5316no—
885C4×D4—5316no—
886C4×D4—538no—
887C4×D4—5316no—
888C4×D4—534no—
889C4×D4—534no—
890C4×D4—532no—
891C4×D4C22×D5314yes—
892C4×D4C22×D5314yes—
893C4×D4C22×D5312yes—
894C4×D4C22×D5318yes—
895#117—532no—
896#117—531no—
897#117—534no—
898#117—534no—
899#117—538no—
900#117—538no—
901#117—534no—
902#117—538no—
903#117—538no—
904#117—538no—
905#117—5316no—
906#117—534no—
907#117—532no—
908#117—534no—
909#117C22×D5311yescharacteristic
910#117C22×D5312yes—
911C2×C4⋊C4—538no—
912C2×C4⋊C4—534no—
913C2×C4⋊C4—5316no—
914C2×C4⋊C4—538no—
915C2×C4⋊C4—538no—
916C2×C4⋊C4—538no—
917C2×C4⋊C4—538no—
918C2×C4⋊C4—538no—
919C2×C4⋊C4C22×D5314yes—
920C2×C4⋊C4C22×D5318yes—
921C2×C42—534no—
922C2×C42—531no—
923C2×C42—532no—
924C2×C42—532no—
925C2×C42—532no—
926C2×C42—532no—
927C2×C42—532no—
928C2×C42—532no—
929C2×C42C22×D5312yes—
930C2×C42C22×D5311yescharacteristic
931C24—531no—
932#41—24no—
933#41—28no—
934#41—416no—
935#41—48no—
936#41—48no—
937#41—10616no—
938#41—10616no—
939#41—1064no—
940#41—2128no—
941#41—21216no—
942#41—2128no—
943C2×Q8—28no—
944C2×Q8—48no—
945C2×Q8—48no—
946C2×Q8—534no—
947C2×Q8—534no—
948C2×Q8—534no—
949C2×Q8—531no—
950C2×Q8—534no—
951C2×Q8—538no—
952C2×Q8—5316no—
953C2×Q8—1068no—
954C2×Q8—2128no—
955C2×Q8—2128no—
956C2×Q8—21216no—
957C2×Q8—21216no—
958C2×Q8—2128no—
959C2×Q8C23×D5314yes—
960C2×Q8C23×D5312yes—
961C2×Q8C23×D5314yes—
962C2×Q8C23×D5311yescharacteristic
963C2×Q8C23×D5318yes—
964C2×D4—534no—
965C2×D4—538no—
966C2×D4—534no—
967C2×D4—532no—
968C2×D4—538no—
969C2×D4—534no—
970C2×D4—531no—
971C2×D4C23×D5314yes—
972C2×D4C23×D5314yes—
973C2×D4C23×D5312yes—
974C2×D4C23×D5312yes—
975C2×D4C23×D5311yescharacteristic
976C2×D4C23×D5318yes—
977C22×C4—532no—
978C22×C4—532no—
979C22×C4—531no—
980C22×C4—538no—
981C22×C4—534no—
982C22×C4—538no—
983C22×C4—532no—
984C22×C4—532no—
985C22×C4—532no—
986C22×C4—532no—
987C22×C4—532no—
988C22×C4—534no—
989C22×C4—532no—
990C22×C4—5316no—
991C22×C4—538no—
992C22×C4—1068no—
993C22×C4—1064no—
994C22×C4—2128no—
995C22×C4C23×D5312yes—
996C22×C4C23×D5314yes—
997C22×C4C23×D5314yes—
998C22×C4C23×D5312yes—
999C22×C4C23×D5314yes—
1000C22×C4C23×D5318yes—
1001C22×C4C23×D5318yes—
1002C22×C4C23×D5311yescharacteristic
1003C4⋊C4—5316no—
1004C4⋊C4—534no—
1005C4⋊C4—538no—
1006C4⋊C4—5316no—
1007C4⋊C4—538no—
1008C4⋊C4—5316no—
1009C4⋊C4—5316no—
1010C4⋊C4—5316no—
1011C4⋊C4—534no—
1012C4⋊C4—534no—
1013C4⋊C4—532no—
1014C4⋊C4—534no—
1015C4⋊C4—534no—
1016C4⋊C4—538no—
1017C4⋊C4—538no—
1018C4⋊C4—534no—
1019C4⋊C4—534no—
1020C4⋊C4—538no—
1021C4⋊C4—534no—
1022C4⋊C4—534no—
1023C4⋊C4—5316no—
1024C4⋊C4—5316no—
1025C4⋊C4C23×D5318yes—
1026C4⋊C4C23×D5314yes—
1027C4⋊C4C23×D5318yes—
1028C4⋊C4C23×D53116yes—
1029C4⋊C4C23×D5312yes—
1030C4⋊C4C23×D5314yes—
1031C22⋊C4—532no—
1032C22⋊C4—534no—
1033C22⋊C4—5316no—
1034C22⋊C4—5316no—
1035C22⋊C4—534no—
1036C22⋊C4—534no—
1037C22⋊C4—538no—
1038C22⋊C4—538no—
1039C22⋊C4—538no—
1040C22⋊C4—534no—
1041C22⋊C4—534no—
1042C22⋊C4—5316no—
1043C22⋊C4—534no—
1044C22⋊C4—534no—
1045C22⋊C4—534no—
1046C22⋊C4C23×D5312yes—
1047C22⋊C4C23×D53116yes—
1048C22⋊C4C23×D5318yes—
1049C22⋊C4C23×D5314yes—
1050C42—531no—
1051C42—532no—
1052C42—531no—
1053C42—532no—
1054C42—532no—
1055C42—532no—
1056C42—532no—
1057C42—538no—
1058C42—534no—
1059C42—534no—
1060C42—532no—
1061C42—5316no—
1062C42—5316no—
1063C42C23×D5311yescharacteristic
1064C42C23×D5311yescharacteristic
1065C42C23×D5312yes—
1066C42C23×D5314yes—
1067C42C23×D5312yes—
1068C23—532no—
1069C23—532no—
1070C23—1064no—
1071C23—1062no—
1072C23C24×D5312yes—
1073C23C24×D5314yes—
1074C23C24×D5311yescharacteristic
1075Q8—28no—
1076Q8—28no—
1077Q8—22no—
1078Q8—24no—
1079Q8—48no—
1080Q8—1068no—
1081Q8—1068no—
1082Q8—1068no—
1083Q8—1062no—
1084Q8—1068no—
1085Q8—21216no—
1086Q8—2128no—
1087D4—24no—
1088D4—28no—
1089D4—22no—
1090D4—24no—
1091D4—28no—
1092D4—48no—
1093D4—1068no—
1094D4—1068no—
1095D4—1068no—
1096D4—10616no—
1097D4—1064no—
1098D4—1062no—
1099D4—2128no—
1100C2×C4—28no—
1101C2×C4—24no—
1102C2×C4—28no—
1103C2×C4—24no—
1104C2×C4—28no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—532no—
1108C2×C4—538no—
1109C2×C4—534no—
1110C2×C4—538no—
1111C2×C4—532no—
1112C2×C4—532no—
1113C2×C4—532no—
1114C2×C4—538no—
1115C2×C4—1064no—
1116C2×C4—1064no—
1117C2×C4—1064no—
1118C2×C4—10616no—
1119C2×C4—1062no—
1120C2×C4—1068no—
1121C2×C4—1064no—
1122C2×C4—1064no—
1123C2×C4—1064no—
1124C2×C4—1064no—
1125C2×C4—1068no—
1126C2×C4—21216no—
1127C2×C4—2128no—
1128C2×C4—2128no—
1129C2×C4#1313326214yes—
1130C2×C4C24×D5314yes—
1131C2×C4C24×D5312yes—
1132C2×C4C24×D5314yes—
1133C2×C4C24×D5318yes—
1134C2×C4C24×D5312yes—
1135C2×C4C24×D5311yescharacteristic
1136C2×C4C24×D5311yescharacteristic
1137C2×C4C24×D5312yes—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—24no—
1142C22—28no—
1143C22—534no—
1144C22—1068no—
1145C22—1062no—
1146C22—1062no—
1147C22—1062no—
1148C22—1064no—
1149C22C2×#1313326212yes—
1150C22C25×D5311yescharacteristic
1151C4—22no—
1152C4—24no—
1153C4—28no—
1154C4—22no—
1155C4—24no—
1156C4—534no—
1157C4—1062no—
1158C4—1062no—
1159C4—1068no—
1160C4—1062no—
1161C4—1068no—
1162C4—1064no—
1163C4C2×#1313326212yes—
1164C4C2×#1313326212yes—
1165C42−1+4×D5314yes—
1166C2—22no—
1167C2—42no—
1168C2—44no—
1169C2—1064no—
1170C2—2122no—
1171C2C22×#1313326211yescharacteristic
1172C2C2×2−1+4×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3499C2
hypercenter#3499D53
hypocenterC53#62833
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #20289157C2semidirect
2. #20289153C2semidirect
3. #20289147C2semidirect
4. #20289051C2semidirect
5. #20288625C2semidirect
6. #20288616C2semidirect
7. #20288601C2semidirect
8. #20288600C2semidirect
9. #20288599C2semidirect
10. #20288531C2semidirect
11. #20288526C2semidirect
12. #20288496C2semidirect
13. #20288495C2semidirect
14. #20288417C2semidirect
15. #20288364C2semidirect
16. #20288363C2semidirect
17. #20288010C2semidirect
18. #20288008C2semidirect
19. C2×C4⋊Q8×D53C2semidirect
20. C53×#3499C2semidirect
23. #16811376C22semidirect
24. #16811374C22semidirect
25. #16811353C22semidirect
26. #16811351C22semidirect
27. #16811348C22semidirect
28. #16811348C22semidirect
29. #16811347C22semidirect
30. #16811343C22semidirect
31. #16811342C22semidirect
32. #16811337C22semidirect
34. #16811332C22semidirect
36. #16811328C22semidirect
44. D4×Dic106C22semidirect
48. Q8×C22⋊D53C22semidirect
54. #16811278C22semidirect
57. #16811272C22semidirect
58. #16811254C22semidirect
59. #16811252C22semidirect
61. #16811250C22semidirect
62. #16811241C22semidirect
63. #16811240C22semidirect
64. #16811238C22semidirect
65. #16811235C22semidirect
66. #16811234C22semidirect
67. #16811233C22semidirect
72. #16811197C22semidirect
77. #16811194C22semidirect
78. #16811193C22semidirect
80. #16811180C22semidirect
82. #16811178C22semidirect
85. #16811175C22semidirect
87. #16811171C22semidirect
90. #16811169C22semidirect
94. C2×#13133215C22semidirect
99. C4⋊Q8×D53C22semidirect
125. D4×Q8×C53C22semidirect
127. C53×#547C22semidirect
129. C53×#536C22semidirect
131. C53×#532C22semidirect
133. C2×C4⋊Q8×C53C22semidirect
543. C4×D532−1+4semidirect
593. #3499D53semidirect
637. D4×Q8C2×D53semidirect
647. #547C2×D53semidirect
670. #536C2×D53semidirect
684. #532C2×D53semidirect
695. C2×C4⋊Q8C2×D53semidirect
721. C53#62833semidirect

Maximal subgroups

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

subgroupindex
#202891572
#202891532
#202891472
#202890512
#202886252
#202886162
#202886012
#202886002
#202885992
#202885312
#202885262
#202884962
#202884952
#202884172
#202883642
#202883632
#202880102
#202880082
C2×C4⋊Q8×D532
C53×#34992
#6283353