Finite Group Databasebeta

← D53×#3509 #28292526

Subgroups — D53×#3509 #28292526

Order 13568.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288602C211yesmaximal, characteristic, complemented
2#20288601C211yesmaximal, characteristic, complemented
3#20288600C212yesmaximal, complemented
4#20288599C211yesmaximal, characteristic, complemented
5#20288598C214yesmaximal, complemented
6#20288597C214yesmaximal, complemented
7#20288596C212yesmaximal, complemented
8#20288595C214yesmaximal, complemented
9#20288594C214yesmaximal, complemented
10#20288593C218yesmaximal, complemented
11#557×D53C214yesmaximal, complemented
12#556×D53C214yesmaximal, complemented
13#552×D53C218yesmaximal, complemented
14#541×D53C214yesmaximal, complemented
15#536×D53C212yesmaximal
16#533×D53C214yesmaximal, complemented
17#533×D53C211yesmaximal, characteristic, complemented
18C2×C4⋊Q8×D53C211yesmaximal, characteristic, complemented
19#519×D53C212yesmaximal, complemented
20C4×#41×D53C211yesmaximal, characteristic
21C53×#3509C211yesmaximal, characteristic, complemented
22C2×#41×D53C2211yescharacteristic
23C22×Q8×D53C2212yes—
24#16811352C2214yescomplemented
25#16811351C2218yescomplemented
26#16811351C2214yescomplemented
27#16811350C2218yescomplemented
28#16811350C22116yescomplemented
29#16811349C2218yescomplemented
30#16811348C2214yescomplemented
31#16811348C2218yescomplemented
32#16811347C2214yescomplemented
33#16811346C2214yescomplemented
34#16811345C2218yescomplemented
35#16811344C2218yescomplemented
36#16811343C2214yescomplemented
37#16811342C2218yescomplemented
38#16811341C2218yescomplemented
39#16811340C22116yescomplemented
40#16811315C2218yescomplemented
41#16811314C2218yescomplemented
42#16811313C2218yescomplemented
43#16811312C2218yescomplemented
44#16811311C2218yescomplemented
45#16811310C22116yescomplemented
46#16811309C22116yescomplemented
47#16811308C2218yescomplemented
48#16811307C2218yescomplemented
49#16811306C22116yescomplemented
50#16811305C22116yescomplemented
51#16811236C2214yescomplemented
52#16811235C2214yescomplemented
53#16811234C2214yescomplemented
54#16811233C2218yescomplemented
55#16811232C22116yescomplemented
56#16811231C2218yescomplemented
57#16811230C22116yescomplemented
58#16811199C2212yes—
59#16811198C2214yes—
60#16811197C2212yes—
61#16811196C2218yes—
62#16811195C2218yes—
63#16811194C2212yes—
64#16811193C2214yes—
65#16811180C2214yescomplemented
66#16811180C2211yescharacteristic, complemented
67#16811179C2218yescomplemented
68#16811179C2212yescomplemented
69#16811178C2212yescomplemented
70#16811178C2214yescomplemented
71#16811178C2214yescomplemented
72#16811177C2218yescomplemented
73#16811177C2214yescomplemented
74#16811177C2218yescomplemented
75#16811176C2218yescomplemented
76#16811176C2212yescomplemented
77#16811175C2214yescomplemented
78#16811175C2218yescomplemented
79#16811175C2218yescomplemented
80C2×#13133217C2211yescharacteristic, complemented
81C2×#13133216C2214yescomplemented
82C2×#13133215C2212yescomplemented
83C4⋊Q8×D53C2212yes—
84C4⋊Q8×D53C2212yes—
85C4⋊Q8×D53C2214yes—
86C4⋊Q8×D53C2214yes—
87C4⋊Q8×D53C2212yes—
88C4⋊Q8×D53C2212yescomplemented
89C4⋊Q8×D53C2214yescomplemented
90C4⋊Q8×D53C2212yescomplemented
91#126×D53C22116yes—
92#125×D53C2218yes—
93#125×D53C2212yes—
94#125×D53C22116yes—
95#124×D53C2214yes—
96#123×D53C2218yes—
97C22⋊Q8×D53C2218yes—
98C22⋊Q8×D53C2218yes—
99C22⋊Q8×D53C2214yes—
100#16811101C2212yescomplemented
101#16811100C2218yescomplemented
102#16811100C2212yescomplemented
103#16811100C2212yescomplemented
104#16811099C2218yescomplemented
105#16811099C2218yescomplemented
106#41×Dic53C2211yescharacteristic
107C4×#11719949C2212yes—
108C4×#11719945C2212yes—
109C4×#11719945C2211yescharacteristic
110#16811091C2211yescharacteristic
111#16811091C2212yes—
112C4×#11719947C2214yes—
113C4×#11719947C2212yes—
114C4×Q8×D53C2214yes—
115C4×Q8×D53C2218yes—
116C4×Q8×D53C2218yes—
117C4×Q8×D53C2218yes—
118C4×Q8×D53C2212yes—
119C4×D4×D53C2212yes—
120C4×D4×D53C2214yes—
121#117×D53C2218yes—
122#117×D53C2212yes—
123#117×D53C2212yes—
124#117×D53C2211yescharacteristic
125#117×D53C2218yes—
126C2×C4⋊C4×D53C2214yes—
127C2×C42×D53C2212yes—
128C2×C42×D53C2211yescharacteristic
129C53×#557C2214yescomplemented
130C53×#556C2214yescomplemented
131C53×#552C2218yescomplemented
132C53×#541C2214yescomplemented
133C53×#536C2212yes—
134C53×#533C2214yescomplemented
135C53×#533C2211yescharacteristic, complemented
136C2×C4⋊Q8×C53C2211yescharacteristic, complemented
137C53×#519C2212yescomplemented
138C4×#41×C53C2211yescharacteristic
139C2×#11719949C2311yescharacteristic
140C2×#11719945C2312yes—
141C2×#11719945C2311yescharacteristic
142C2×#11719947C2311yescharacteristic
143C2×#11719947C2312yes—
144#41×D53—28no—
145C22×Dic106C2312yes—
146C22×Dic106C2314yes—
147C2×Q8×D53—216no—
148C2×Q8×D53C2314yes—
149C2×Q8×D53C2314yes—
150C2×Q8×D53C2314yes—
151C2×Q8×D53C2311yescharacteristic
152C2×Q8×D53C2314yes—
153C2×Q8×D53C2314yes—
154C2×D4×D53C2312yes—
155C2×D4×D53C2311yescharacteristic
156C22×C4×D53C2312yes—
157C22×C4×D53C2314yes—
158C22×C4×D53C2312yes—
159C22×C4×D53C2314yes—
160C22×C4×D53C2311yescharacteristic
161#13133217C2314yes—
162#13133217C2314yes—
163#13133217C2312yes—
164#13133217C2312yes—
165#13133217C2312yes—
166#13133216C2318yes—
167#13133216C2318yes—
168#13133216C23116yes—
169#13133216C2318yes—
170#13133216C2318yes—
171#13133216C2314yes—
172#13133216C2314yes—
173#13133215C2318yes—
174#13133215C2314yes—
175#13133215C2314yes—
176#13133215C2314yes—
177#13133215C2314yes—
178#13133215C2314yes—
179#13133212C23116yes—
180#13133212C23116yes—
181#13133212C23116yes—
182#13133211C23116yes—
183#13133210C23116yes—
184#13133210C23116yes—
185#13133210C23116yes—
186#13133209C23116yes—
187#13133209C2318yes—
188#13133209C2312yes—
189#13133208C2318yes—
190#13133208C23116yes—
191#13133208C23116yes—
192#13133208C2318yes—
193#13133208C2314yes—
194#13133207C23116yes—
195#13133207C23116yes—
196#13133207C23116yes—
197#13133207C23116yes—
198#13133207C23116yes—
199#13133207C23116yes—
200#13133207C2318yes—
201#13133206C2314yes—
202#13133205C2314yes—
203#13133204C2314yes—
204#13133203C23116yes—
205#13133202C23116yes—
206#13133201C2318yes—
207#13133200C2318yes—
208#13133199C23116yes—
209#13133198C2318yes—
210#13133197C2318yes—
211#13133197C2314yes—
212#13133197C2318yes—
213#13133196C2314yes—
214#13133196C2318yes—
215#13133196C2318yes—
216#13133195C2318yes—
217#13133195C23116yes—
218#13133195C23116yes—
219#13133194C2318yes—
220#13133194C23116yes—
221#13133194C23116yes—
222#13133193C2314yes—
223#13133193C2318yes—
224#13133193C2318yes—
225Q8×Dic53C2318yes—
226Q8×Dic53C2318yes—
227Q8×Dic53C2314yes—
228Q8×Dic53C2312yes—
229Q8×Dic53C2318yes—
230C4×Dic106C23116yes—
231C4×Dic106C2318yes—
232C4×Dic106C23116yes—
233C4×Dic106C2318yes—
234C4×Dic106C2318yes—
235C4×Dic106C2314yes—
236C4×Dic106C2312yes—
237C4×Dic106C2314yes—
238C4×Dic106C23116yes—
239C4×Dic106C2318yes—
240#13133182C23116yes—
241#13133182C2318yes—
242#13133182C2318yes—
243#13133182C23116yes—
244#13133182C2314yes—
245#13133182C2318yes—
246#13133182C2314yes—
247#13133182C2312yes—
248#13133182C2318yes—
249#13133182C23116yes—
250C4×D212C2314yes—
251C4×D212C2312yes—
252D4×Dic53C2314yes—
253D4×Dic53C2312yes—
254#13133179C2314yes—
255#13133179C2312yes—
256C4×C22⋊D53C2314yes—
257C4×C22⋊D53C2314yes—
258C4×C22⋊D53C2314yes—
259#13133177C2314yes—
260#13133177C2314yes—
261#13133177C2314yes—
262#13133176C2318yes—
263#13133176C2318yes—
264#13133176C2311yescharacteristic
265#13133176C2312yes—
266#13133176C2312yes—
267#13133175C23116yes—
268#13133175C2318yes—
269#13133175C2318yes—
270#13133175C2312yes—
271#13133175C2314yes—
272#13133175C2314yes—
273#13133174C23116yes—
274#13133174C23116yes—
275#13133174C2312yes—
276#13133174C2312yes—
277#13133174C2312yes—
278#13133174C2314yes—
279#13133173C2318yes—
280#13133173C23116yes—
281#13133173C2318yes—
282#13133173C2312yes—
283#13133173C2314yes—
284#13133173C2314yes—
285C2×C4⋊Dic53C2314yes—
286C2×#11719919C2318yes—
287C4⋊C4×D53C2318yes—
288C4⋊C4×D53C2318yes—
289C4⋊C4×D53C2318yes—
290C4⋊C4×D53C2318yes—
291C4⋊C4×D53C2314yes—
292C4⋊C4×D53C2312yes—
293C4⋊C4×D53C2314yes—
294C4⋊C4×D53C2314yes—
295C4⋊C4×D53C23116yes—
296C4⋊C4×D53C23116yes—
297C4⋊C4×D53C2318yes—
298C22⋊C4×D53C2312yes—
299C22⋊C4×D53C2314yes—
300C22⋊C4×D53C2314yes—
301C22⋊C4×D53C23116yes—
302C2×C4×Dic53C2312yes—
303C2×C4×Dic53C2314yes—
304C2×C4×Dic53C2311yescharacteristic
305C2×C4×Dic53C2312yes—
306C42×D53C2311yescharacteristic
307C42×D53C2312yes—
308C42×D53C2311yescharacteristic
309C42×D53C2314yes—
310C42×D53C2312yes—
311C42×D53C2312yes—
312C42×D53C2314yes—
313C42×D53C2311yescharacteristic
314C42×D53C2312yes—
315C42×D53C2311yescharacteristic
316C42×D53C2312yes—
317C42×D53C23116yes—
318C42×D53C2314yes—
319C2×#41×C53C2311yescharacteristic
320C22×Q8×C53C2312yes—
321C4⋊Q8×C53C2312yes—
322C4⋊Q8×C53C2312yes—
323C4⋊Q8×C53C2314yes—
324C4⋊Q8×C53C2312yes—
325C4⋊Q8×C53C2314yes—
326#126×C53C23116yes—
327#125×C53C23116yes—
328#125×C53C2318yes—
329#125×C53C2312yes—
330#124×C53C2314yes—
331#123×C53C2318yes—
332C22⋊Q8×C53C2318yes—
333C22⋊Q8×C53C2318yes—
334C22⋊Q8×C53C2314yes—
335C4×Q8×C53C2312yes—
336C4×Q8×C53C2318yes—
337C4×Q8×C53C2318yes—
338C4×Q8×C53C2318yes—
339C4×Q8×C53C2314yes—
340C4×D4×C53C2314yes—
341C4×D4×C53C2312yes—
342#117×C53C2311yescharacteristic
343#117×C53C2312yes—
344#117×C53C2318yes—
345#117×C53C2312yes—
346#117×C53C2318yes—
347C2×C4⋊C4×C53C2314yes—
348C2×C42×C53C2311yescharacteristic
349C2×C42×C53C2312yes—
350C23×D53C2412yes—
351C23×D53C2411yescharacteristic
352#41×C53—24no—
353C2×Q8×C53—28no—
354C2×Q8×C53C2414yes—
355C2×Q8×C53C2414yes—
356C2×Q8×C53C2414yes—
357C2×Q8×C53C2411yescharacteristic
358C2×D4×C53C2412yes—
359C2×D4×C53C2411yescharacteristic
360C22×C4×C53C2412yes—
361C22×C4×C53C2414yes—
362C22×C4×C53C2412yes—
363C22×C4×C53C2414yes—
364C22×C4×C53C2411yescharacteristic
365C2×C22⋊D53C2412yes—
366C2×C22⋊D53C2412yes—
367C2×C22⋊D53C2412yes—
368C22×Dic53C2412yes—
369C22×Dic53C2414yes—
370C22×Dic53C2412yes—
371C22×Dic53C2414yes—
372C22×Dic53C2411yescharacteristic
373#11719949—24no—
374Q8×D53—216no—
375Q8×D53—216no—
376Q8×D53—216no—
377Q8×D53—216no—
378Q8×D53—24no—
379Q8×D53—216no—
380#11719947—28no—
381#11719947—24no—
382D4×D53—28no—
383D4×D53—24no—
384#11719945—24no—
385#11719945—28no—
386C2×D212C2412yes—
387C2×D212C2411yescharacteristic
388C2×C4×D53—216no—
389C2×C4×D53—28no—
390C2×C4×D53—28no—
391C2×C4×D53—216no—
392C2×C4×D53#4118yes—
393C2×C4×D53C2414yes—
394C2×C4×D53C2418yes—
395C2×C4×D53C2412yes—
396C2×C4×D53C2418yes—
397C2×C4×D53C2412yes—
398C2×C4×D53C2412yes—
399C2×C4×D53C2412yes—
400C2×C4×D53C2414yes—
401C2×C4×D53C2412yes—
402C2×C4×D53C2414yes—
403C2×C4×D53C2412yes—
404C2×C4×D53C2418yes—
405C2×C4×D53C2411yescharacteristic
406C2×C4×D53C2411yescharacteristic
407C2×C4×D53C2411yescharacteristic
408C2×C4×D53C2411yescharacteristic
409C2×C4×D53C2412yes—
410C2×Dic106—28no—
411C2×Dic106—216no—
412C2×Dic106C2418yes—
413C2×Dic106C2414yes—
414C2×Dic106C2418yes—
415C2×Dic106C2414yes—
416C2×Dic106C2418yes—
417C2×Dic106C2414yes—
418C2×Dic106C2411yescharacteristic
419C2×Dic106C2412yes—
420C4⋊C4×C53C2418yes—
421C4⋊C4×C53C2418yes—
422C4⋊C4×C53C2414yes—
423C4⋊C4×C53C2412yes—
424C4⋊C4×C53C2414yes—
425C4⋊C4×C53C2414yes—
426C4⋊C4×C53C24116yes—
427C4⋊C4×C53C24116yes—
428C4⋊C4×C53C2418yes—
429C22⋊C4×C53C2412yes—
430C22⋊C4×C53C2414yes—
431C22⋊C4×C53C2414yes—
432C22⋊C4×C53C24116yes—
433C42×C53C2411yescharacteristic
434C42×C53C2412yes—
435C42×C53C2411yescharacteristic
436C42×C53C2414yes—
437C42×C53C2412yes—
438C42×C53C24116yes—
439C42×C53C2414yes—
440C22⋊Dic53C2412yes—
441C22⋊Dic53C2414yes—
442C22⋊Dic53C2414yes—
443C22⋊Dic53C24116yes—
444#11719921C2414yes—
445#11719921C2418yes—
446#11719921C2414yes—
447#11719921C2414yes—
448#11719921C24116yes—
449#11719921C24116yes—
450C4⋊Dic53C2418yes—
451C4⋊Dic53C2418yes—
452C4⋊Dic53C2414yes—
453C4⋊Dic53C2412yes—
454C4⋊Dic53C2414yes—
455C4⋊Dic53C2414yes—
456C4⋊Dic53C24116yes—
457C4⋊Dic53C24116yes—
458C4⋊Dic53C2418yes—
459#11719919C24116yes—
460#11719919C24116yes—
461#11719919C2418yes—
462#11719919C2414yes—
463#11719919C2414yes—
464#11719919C2414yes—
465#11719919C24116yes—
466#11719919C2418yes—
467#11719919C24116yes—
468#11719919C24116yes—
469#11719919C2418yes—
470#11719919C24116yes—
471#11719919C2418yes—
472C4×Dic53C2411yescharacteristic
473C4×Dic53C2412yes—
474C4×Dic53C2414yes—
475C4×Dic53C2412yes—
476C4×Dic53C2412yes—
477C4×Dic53C2411yescharacteristic
478C4×Dic53C2412yes—
479C4×Dic53C2414yes—
480C4×Dic53C2414yes—
481C4×Dic53C2412yes—
482C4×Dic53C2414yes—
483C4×Dic53C2412yes—
484C4×Dic53C24116yes—
485C4×Dic53C24116yes—
486C4×Dic53C24116yes—
487C4×Dic53C2418yes—
488C4×Dic53C2414yes—
489C23×C53C2512yes—
490C23×C53C2511yescharacteristic
491C22×D53—24no—
492C22×D53—24no—
493C22×D53—28no—
494C22×D53C2×#4114yes—
495C22×D53C2512yes—
496C22×D53C2511yescharacteristic
497C22×D53C2511yescharacteristic
498Q8×C53—28no—
499Q8×C53—28no—
500Q8×C53—22no—
501Q8×C53—28no—
502D4×C53—24no—
503D4×C53—22no—
504C2×C4×C53—28no—
505C2×C4×C53—24no—
506C2×C4×C53—24no—
507C2×C4×C53—28no—
508C2×C4×C53C2×#4114yes—
509C2×C4×C53C2518yes—
510C2×C4×C53C2512yes—
511C2×C4×C53C2518yes—
512C2×C4×C53C2514yes—
513C2×C4×C53C2512yes—
514C2×C4×C53C2511yescharacteristic
515C2×C4×C53C2511yescharacteristic
516C2×C4×C53C2512yes—
517C22⋊D53—24no—
518C22⋊D53—24no—
519C22⋊D53—24no—
520C2×Dic53—28no—
521C2×Dic53—24no—
522C2×Dic53—24no—
523C2×Dic53—28no—
524C2×Dic53C2×#4114yes—
525C2×Dic53C2518yes—
526C2×Dic53C2512yes—
527C2×Dic53C2518yes—
528C2×Dic53C2514yes—
529C2×Dic53C2512yes—
530C2×Dic53C2511yescharacteristic
531C2×Dic53C2511yescharacteristic
532C2×Dic53C2512yes—
533D212—24no—
534D212—22no—
535C4×D53—24no—
536C4×D53—216no—
537C4×D53—216no—
538C4×D53—28no—
539C4×D53—24no—
540C4×D53—216no—
541C4×D53—24no—
542C4×D53—24no—
543C4×D53—28no—
544C4×D53—24no—
545C4×D53—24no—
546C4×D53—28no—
547C4×D53C2×#4114yes—
548C4×D53C2×#4114yes—
549C4×D53C2×#4114yes—
550C4×D53C2×#4114yes—
551C4×D532−1+418yes—
552Dic106—28no—
553Dic106—28no—
554Dic106—22no—
555Dic106—28no—
556Dic106—216no—
557Dic106—216no—
558Dic106—24no—
559Dic106—216no—
560C2×#3509—531nomaximal, Sylow
561C22×C53—22no—
562C22×C53—22no—
563C22×C53—24no—
564C22×C53C22×#4112yes—
565C22×C53C2611yescharacteristic
566C2×D53—22no—
567C2×D53—28no—
568C2×D53—22no—
569C2×D53—24no—
570C2×D53—48no—
571C2×D53C22×#4112yes—
572C2×D53C22×#4112yes—
573C2×D53C2×2−1+414yes—
574C4×C53—28no—
575C4×C53—22no—
576C4×C53—28no—
577C4×C53—24no—
578C4×C53—22no—
579C4×C53C22×#4112yes—
580C4×C53C22×#4112yes—
581C4×C53C2×2−1+414yes—
582Dic53—28no—
583Dic53—22no—
584Dic53—28no—
585Dic53—24no—
586Dic53—22no—
587Dic53C22×#4112yes—
588Dic53C22×#4112yes—
589Dic53C2×2−1+414yes—
590#3509—534no—
591#3509—534no—
592#3509—538no—
593#3509—534no—
594#3509—532no—
595#3509—534no—
596#3509—531no—
597#3509—531no—
598#3509—532no—
599#3509—531no—
600#3509D5311yescharacteristic, direct product factor
601C2×#557—534no—
602C2×#556—534no—
603C2×#552—538no—
604C2×#541—534no—
605C2×#536—532no—
606C2×#533—531no—
607C2×#533—534no—
608C22×C4⋊Q8—531no—
609C2×#519—532no—
610C2×C4×#41—531no—
611C2×C53—22no—
612C2×C53—42no—
613C2×C53C23×#4111yescharacteristic
614C2×C53C22×2−1+412yes—
615D53—22no—
616D53—42no—
617D53#350914yesdirect product factor
618C22×#41—531no—
619C23×Q8—532no—
620#557—538no—
621#557—534no—
622#557—5316no—
623#557—538no—
624#557—538no—
625#557—538no—
626#557—534no—
627#557—534no—
628#557C2×D5314yescomplemented
629#556—534no—
630#556—5316no—
631#556—538no—
632#556—538no—
633#556—538no—
634#556—534no—
635#556—534no—
636#556—538no—
637#556C2×D5314yescomplemented
638#552—5316no—
639#552—5316no—
640#552—538no—
641#552—5316no—
642#552—538no—
643#552—538no—
644#552—538no—
645#552—538no—
646#552—5316no—
647#552—538no—
648#552—538no—
649#552C2×D5318yescomplemented
650#541—534no—
651#541—5316no—
652#541—5316no—
653#541—534no—
654#541—538no—
655#541—538no—
656#541—534no—
657#541C2×D5314yescomplemented
658#536—532no—
659#536—532no—
660#536—534no—
661#536—534no—
662#536—538no—
663#536—538no—
664#536—532no—
665#536C2×D5312yes—
666#533—532no—
667#533—534no—
668#533—534no—
669#533—532no—
670#533—538no—
671#533—534no—
672#533—538no—
673#533—538no—
674#533—534no—
675#533—538no—
676#533—538no—
677#533—532no—
678#533—538no—
679#533—531no—
680#533—534no—
681#533C2×D5311yescharacteristic, complemented
682#533C2×D5314yescomplemented
683C2×C4⋊Q8—532no—
684C2×C4⋊Q8—532no—
685C2×C4⋊Q8—532no—
686C2×C4⋊Q8—534no—
687C2×C4⋊Q8—532no—
688C2×C4⋊Q8—532no—
689C2×C4⋊Q8—534no—
690C2×C4⋊Q8—532no—
691C2×C4⋊Q8—534no—
692C2×C4⋊Q8—534no—
693C2×C4⋊Q8—531no—
694C2×C4⋊Q8C2×D5311yescharacteristic, complemented
695C2×#126—5316no—
696C2×#125—532no—
697C2×#125—538no—
698C2×#125—5316no—
699C2×#124—534no—
700C2×#123—538no—
701C2×C22⋊Q8—538no—
702C2×C22⋊Q8—534no—
703C2×C22⋊Q8—538no—
704#519—532no—
705#519—538no—
706#519—538no—
707#519—532no—
708#519—532no—
709#519—538no—
710#519C2×D5312yescomplemented
711C4×#41—531no—
712C4×#41—532no—
713C4×#41—534no—
714C4×#41—532no—
715C4×#41—531no—
716C4×#41—532no—
717C4×#41—532no—
718C4×#41—531no—
719C4×#41C2×D5311yescharacteristic
720C2×C4×Q8—532no—
721C2×C4×Q8—538no—
722C2×C4×Q8—538no—
723C2×C4×Q8—538no—
724C2×C4×Q8—534no—
725C2×C4×D4—534no—
726C2×C4×D4—532no—
727C2×#117—531no—
728C2×#117—532no—
729C2×#117—532no—
730C2×#117—538no—
731C2×#117—538no—
732C22×C4⋊C4—534no—
733C22×C42—531no—
734C22×C42—532no—
735C53C2×#350911yescharacteristic, complemented, Sylow
736C2×#41—531no—
737C2×#41—532no—
738C2×#41—531no—
739C2×#41—532no—
740C2×#41—531no—
741C2×#41—1068no—
742C2×#41C22×D5311yescharacteristic
743C22×Q8—534no—
744C22×Q8—534no—
745C22×Q8—534no—
746C22×Q8—531no—
747C22×Q8—534no—
748C22×Q8—534no—
749C22×Q8—534no—
750C22×Q8—532no—
751C22×Q8—10616no—
752C22×Q8C22×D5312yes—
753C22×D4—532no—
754C22×D4—531no—
755C23×C4—531no—
756C23×C4—534no—
757C23×C4—532no—
758C23×C4—534no—
759C23×C4—532no—
760C4⋊Q8—534no—
761C4⋊Q8—534no—
762C4⋊Q8—538no—
763C4⋊Q8—534no—
764C4⋊Q8—534no—
765C4⋊Q8—534no—
766C4⋊Q8—538no—
767C4⋊Q8—538no—
768C4⋊Q8—538no—
769C4⋊Q8—538no—
770C4⋊Q8—534no—
771C4⋊Q8—534no—
772C4⋊Q8—5316no—
773C4⋊Q8—532no—
774C4⋊Q8—532no—
775C4⋊Q8—534no—
776C4⋊Q8—532no—
777C4⋊Q8—534no—
778C4⋊Q8C22×D5312yes—
779C4⋊Q8C22×D5312yes—
780C4⋊Q8C22×D5314yes—
781C4⋊Q8C22×D5312yes—
782C4⋊Q8C22×D5314yes—
783#126—5316no—
784#126—5316no—
785#126—5316no—
786#126—5316no—
787#126—5316no—
788#126—5316no—
789#126—5316no—
790#126C22×D53116yes—
791#125—538no—
792#125—534no—
793#125—5316no—
794#125—5316no—
795#125—538no—
796#125—538no—
797#125—5316no—
798#125—5316no—
799#125—5316no—
800#125—5316no—
801#125—5316no—
802#125—5316no—
803#125—532no—
804#125—538no—
805#125—5316no—
806#125C22×D5312yes—
807#125C22×D5318yes—
808#125C22×D53116yes—
809#124—534no—
810#124—534no—
811#124—5316no—
812#124—534no—
813#124C22×D5314yes—
814#123—538no—
815#123—538no—
816#123—5316no—
817#123—5316no—
818#123—538no—
819#123C22×D5318yes—
820C22⋊Q8—538no—
821C22⋊Q8—534no—
822C22⋊Q8—538no—
823C22⋊Q8—538no—
824C22⋊Q8—534no—
825C22⋊Q8—538no—
826C22⋊Q8—5316no—
827C22⋊Q8—538no—
828C22⋊Q8—538no—
829C22⋊Q8—534no—
830C22⋊Q8—5316no—
831C22⋊Q8—538no—
832C22⋊Q8—5316no—
833C22⋊Q8—538no—
834C22⋊Q8—5316no—
835C22⋊Q8C22×D5318yes—
836C22⋊Q8C22×D5314yes—
837C22⋊Q8C22×D5318yes—
838C4×Q8—532no—
839C4×Q8—538no—
840C4×Q8—538no—
841C4×Q8—538no—
842C4×Q8—534no—
843C4×Q8—534no—
844C4×Q8—532no—
845C4×Q8—5316no—
846C4×Q8—538no—
847C4×Q8—5316no—
848C4×Q8—538no—
849C4×Q8—5316no—
850C4×Q8—538no—
851C4×Q8—538no—
852C4×Q8—534no—
853C4×Q8—532no—
854C4×Q8—534no—
855C4×Q8—5316no—
856C4×Q8—538no—
857C4×Q8—538no—
858C4×Q8—5316no—
859C4×Q8—5316no—
860C4×Q8—538no—
861C4×Q8—538no—
862C4×Q8—534no—
863C4×Q8C22×D5312yes—
864C4×Q8C22×D5318yes—
865C4×Q8C22×D5318yes—
866C4×Q8C22×D5318yes—
867C4×Q8C22×D5314yes—
868C4×D4—534no—
869C4×D4—532no—
870C4×D4—534no—
871C4×D4—534no—
872C4×D4—534no—
873C4×D4—534no—
874C4×D4—532no—
875C4×D4—534no—
876C4×D4—534no—
877C4×D4—534no—
878C4×D4—534no—
879C4×D4—532no—
880C4×D4C22×D5314yes—
881C4×D4C22×D5312yes—
882#117—531no—
883#117—532no—
884#117—532no—
885#117—538no—
886#117—538no—
887#117—532no—
888#117—534no—
889#117—534no—
890#117—5316no—
891#117—538no—
892#117—538no—
893#117—532no—
894#117—534no—
895#117—534no—
896#117—538no—
897#117—538no—
898#117—5316no—
899#117—532no—
900#117—532no—
901#117—532no—
902#117—534no—
903#117—5316no—
904#117—5316no—
905#117C22×D5311yescharacteristic
906#117C22×D5312yes—
907#117C22×D5312yes—
908#117C22×D5318yes—
909#117C22×D5318yes—
910C2×C4⋊C4—538no—
911C2×C4⋊C4—534no—
912C2×C4⋊C4—538no—
913C2×C4⋊C4—538no—
914C2×C4⋊C4—538no—
915C2×C4⋊C4—538no—
916C2×C4⋊C4—534no—
917C2×C4⋊C4—532no—
918C2×C4⋊C4—534no—
919C2×C4⋊C4—534no—
920C2×C4⋊C4—5316no—
921C2×C4⋊C4—5316no—
922C2×C4⋊C4—538no—
923C2×C4⋊C4C22×D5314yes—
924C2×C22⋊C4—532no—
925C2×C22⋊C4—534no—
926C2×C22⋊C4—534no—
927C2×C22⋊C4—5316no—
928C2×C42—532no—
929C2×C42—531no—
930C2×C42—532no—
931C2×C42—534no—
932C2×C42—532no—
933C2×C42—5316no—
934C2×C42—531no—
935C2×C42—534no—
936C2×C42—534no—
937C2×C42—532no—
938C2×C42—532no—
939C2×C42—531no—
940C2×C42—531no—
941C2×C42—534no—
942C2×C42—532no—
943C2×C42—532no—
944C2×C42—531no—
945C2×C42C22×D5311yescharacteristic
946C2×C42C22×D5312yes—
947C24—531no—
948C24—532no—
949#41—24no—
950#41—1068no—
951#41—1068no—
952#41—1064no—
953#41—1064no—
954#41—1064no—
955C2×Q8—28no—
956C2×Q8—538no—
957C2×Q8—534no—
958C2×Q8—538no—
959C2×Q8—534no—
960C2×Q8—538no—
961C2×Q8—534no—
962C2×Q8—532no—
963C2×Q8—531no—
964C2×Q8—10616no—
965C2×Q8—10616no—
966C2×Q8—10616no—
967C2×Q8—10616no—
968C2×Q8—10616no—
969C2×Q8—10616no—
970C2×Q8—1064no—
971C2×Q8—1068no—
972C2×Q8C23×D5314yes—
973C2×Q8C23×D5314yes—
974C2×Q8C23×D5314yes—
975C2×Q8C23×D5311yescharacteristic
976C2×D4—532no—
977C2×D4—532no—
978C2×D4—532no—
979C2×D4—532no—
980C2×D4—531no—
981C2×D4—1064no—
982C2×D4—1068no—
983C2×D4C23×D5312yes—
984C2×D4C23×D5311yescharacteristic
985C22×C4—531no—
986C22×C4—538no—
987C22×C4—531no—
988C22×C4—532no—
989C22×C4—531no—
990C22×C4—531no—
991C22×C4—531no—
992C22×C4—532no—
993C22×C4—534no—
994C22×C4—532no—
995C22×C4—534no—
996C22×C4—534no—
997C22×C4—538no—
998C22×C4—532no—
999C22×C4—538no—
1000C22×C4—532no—
1001C22×C4—532no—
1002C22×C4—532no—
1003C22×C4—534no—
1004C22×C4—534no—
1005C22×C4—532no—
1006C22×C4—532no—
1007C22×C4—538no—
1008C22×C4—1068no—
1009C22×C4—10616no—
1010C22×C4—1068no—
1011C22×C4—10616no—
1012C22×C4C23×D5312yes—
1013C22×C4C23×D5314yes—
1014C22×C4C23×D5312yes—
1015C22×C4C23×D5314yes—
1016C22×C4C23×D5311yescharacteristic
1017C4⋊C4—5316no—
1018C4⋊C4—538no—
1019C4⋊C4—5316no—
1020C4⋊C4—538no—
1021C4⋊C4—538no—
1022C4⋊C4—534no—
1023C4⋊C4—534no—
1024C4⋊C4—532no—
1025C4⋊C4—534no—
1026C4⋊C4—534no—
1027C4⋊C4—534no—
1028C4⋊C4—538no—
1029C4⋊C4—534no—
1030C4⋊C4—5316no—
1031C4⋊C4—5316no—
1032C4⋊C4—5316no—
1033C4⋊C4—5316no—
1034C4⋊C4—5316no—
1035C4⋊C4—5316no—
1036C4⋊C4—538no—
1037C4⋊C4—538no—
1038C4⋊C4—538no—
1039C4⋊C4C23×D5318yes—
1040C4⋊C4C23×D5318yes—
1041C4⋊C4C23×D5314yes—
1042C4⋊C4C23×D5312yes—
1043C4⋊C4C23×D5314yes—
1044C4⋊C4C23×D5314yes—
1045C4⋊C4C23×D53116yes—
1046C4⋊C4C23×D53116yes—
1047C4⋊C4C23×D5318yes—
1048C22⋊C4—532no—
1049C22⋊C4—534no—
1050C22⋊C4—534no—
1051C22⋊C4—5316no—
1052C22⋊C4—534no—
1053C22⋊C4—538no—
1054C22⋊C4—534no—
1055C22⋊C4—534no—
1056C22⋊C4—5316no—
1057C22⋊C4—5316no—
1058C22⋊C4C23×D5312yes—
1059C22⋊C4C23×D5314yes—
1060C22⋊C4C23×D5314yes—
1061C22⋊C4C23×D53116yes—
1062C42—531no—
1063C42—532no—
1064C42—534no—
1065C42—532no—
1066C42—532no—
1067C42—531no—
1068C42—534no—
1069C42—534no—
1070C42—534no—
1071C42—532no—
1072C42—532no—
1073C42—532no—
1074C42—5316no—
1075C42—5316no—
1076C42—5316no—
1077C42—538no—
1078C42—534no—
1079C42C23×D5311yescharacteristic
1080C42C23×D5312yes—
1081C42C23×D5311yescharacteristic
1082C42C23×D5314yes—
1083C42C23×D5312yes—
1084C42C23×D53116yes—
1085C42C23×D5314yes—
1086C23—531no—
1087C23—534no—
1088C23—531no—
1089C23—532no—
1090C23—1064no—
1091C23—1064no—
1092C23—1068no—
1093C23C24×D5312yes—
1094C23C24×D5311yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—22no—
1098Q8—28no—
1099Q8—10616no—
1100Q8—10616no—
1101Q8—10616no—
1102Q8—1064no—
1103Q8—1068no—
1104Q8—1068no—
1105Q8—1062no—
1106Q8—1068no—
1107D4—24no—
1108D4—22no—
1109D4—1064no—
1110D4—1064no—
1111D4—1064no—
1112D4—1064no—
1113D4—1062no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—24no—
1117C2×C4—28no—
1118C2×C4—534no—
1119C2×C4—531no—
1120C2×C4—532no—
1121C2×C4—531no—
1122C2×C4—534no—
1123C2×C4—534no—
1124C2×C4—534no—
1125C2×C4—534no—
1126C2×C4—538no—
1127C2×C4—534no—
1128C2×C4—538no—
1129C2×C4—532no—
1130C2×C4—538no—
1131C2×C4—532no—
1132C2×C4—1064no—
1133C2×C4—1068no—
1134C2×C4—1064no—
1135C2×C4—1068no—
1136C2×C4—1064no—
1137C2×C4—1064no—
1138C2×C4—10616no—
1139C2×C4—10616no—
1140C2×C4—10616no—
1141C2×C4—1064no—
1142C2×C4—1068no—
1143C2×C4—1064no—
1144C2×C4—1068no—
1145C2×C4—1064no—
1146C2×C4—1064no—
1147C2×C4—1068no—
1148C2×C4#41×D5314yes—
1149C2×C4C24×D5314yes—
1150C2×C4C24×D5318yes—
1151C2×C4C24×D5312yes—
1152C2×C4C24×D5318yes—
1153C2×C4C24×D5312yes—
1154C2×C4C24×D5311yescharacteristic
1155C2×C4C24×D5311yescharacteristic
1156C2×C4C24×D5312yes—
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—532no—
1161C22—534no—
1162C22—532no—
1163C22—1068no—
1164C22—1062no—
1165C22—1062no—
1166C22—1064no—
1167C22—2128no—
1168C22C2×#41×D5312yes—
1169C22C25×D5311yescharacteristic
1170C4—22no—
1171C4—28no—
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—532no—
1176C4—532no—
1177C4—534no—
1178C4—1062no—
1179C4—1068no—
1180C4—1064no—
1181C4—1062no—
1182C4—1068no—
1183C4C2×#41×D5312yes—
1184C4C2×#41×D5312yes—
1185C42−1+4×D5314yes—
1186C2—22no—
1187C2—42no—
1188C2—534no—
1189C2—1062no—
1190C2—2122no—
1191C2C22×#41×D5311yescharacteristic
1192C2C2×2−1+4×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3509C2
prime radicalC2×#41×D53C22
hypercenter#3509D53
hypocenterC53C2×#3509
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #20288602C2semidirect
2. #20288601C2semidirect
3. #20288600C2semidirect
4. #20288599C2semidirect
5. #20288598C2semidirect
6. #20288597C2semidirect
7. #20288596C2semidirect
8. #20288595C2semidirect
9. #20288594C2semidirect
10. #20288593C2semidirect
11. #557×D53C2semidirect
12. #556×D53C2semidirect
13. #552×D53C2semidirect
14. #541×D53C2semidirect
16. #533×D53C2semidirect
17. #533×D53C2semidirect
18. C2×C4⋊Q8×D53C2semidirect
19. #519×D53C2semidirect
21. C53×#3509C2semidirect
24. #16811352C22semidirect
25. #16811351C22semidirect
26. #16811351C22semidirect
27. #16811350C22semidirect
28. #16811350C22semidirect
29. #16811349C22semidirect
30. #16811348C22semidirect
31. #16811348C22semidirect
32. #16811347C22semidirect
33. #16811346C22semidirect
34. #16811345C22semidirect
35. #16811344C22semidirect
36. #16811343C22semidirect
37. #16811342C22semidirect
38. #16811341C22semidirect
39. #16811340C22semidirect
40. #16811315C22semidirect
41. #16811314C22semidirect
42. #16811313C22semidirect
43. #16811312C22semidirect
44. #16811311C22semidirect
45. #16811310C22semidirect
46. #16811309C22semidirect
47. #16811308C22semidirect
48. #16811307C22semidirect
49. #16811306C22semidirect
50. #16811305C22semidirect
51. #16811236C22semidirect
52. #16811235C22semidirect
53. #16811234C22semidirect
54. #16811233C22semidirect
55. #16811232C22semidirect
56. #16811231C22semidirect
57. #16811230C22semidirect
65. #16811180C22semidirect
66. #16811180C22semidirect
67. #16811179C22semidirect
68. #16811179C22semidirect
69. #16811178C22semidirect
70. #16811178C22semidirect
71. #16811178C22semidirect
72. #16811177C22semidirect
73. #16811177C22semidirect
74. #16811177C22semidirect
75. #16811176C22semidirect
76. #16811176C22semidirect
77. #16811175C22semidirect
78. #16811175C22semidirect
79. #16811175C22semidirect
80. C2×#13133217C22semidirect
81. C2×#13133216C22semidirect
82. C2×#13133215C22semidirect
88. C4⋊Q8×D53C22semidirect
89. C4⋊Q8×D53C22semidirect
90. C4⋊Q8×D53C22semidirect
100. #16811101C22semidirect
101. #16811100C22semidirect
102. #16811100C22semidirect
103. #16811100C22semidirect
104. #16811099C22semidirect
105. #16811099C22semidirect
129. C53×#557C22semidirect
130. C53×#556C22semidirect
131. C53×#552C22semidirect
132. C53×#541C22semidirect
134. C53×#533C22semidirect
135. C53×#533C22semidirect
136. C2×C4⋊Q8×C53C22semidirect
137. C53×#519C22semidirect
600. #3509D53direct (N × H)
617. D53#3509direct (N × H)
628. #557C2×D53semidirect
637. #556C2×D53semidirect
649. #552C2×D53semidirect
657. #541C2×D53semidirect
681. #533C2×D53semidirect
682. #533C2×D53semidirect
694. C2×C4⋊Q8C2×D53semidirect
710. #519C2×D53semidirect
735. C53C2×#3509semidirect

Maximal subgroups

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

subgroupindex
#202886022
#202886012
#202886002
#202885992
#202885982
#202885972
#202885962
#202885952
#202885942
#202885932
#557×D532
#556×D532
#552×D532
#541×D532
#536×D532
#533×D532
C2×C4⋊Q8×D532
#519×D532
C4×#41×D532
C53×#35092
C2×#350953