Finite Group Databasebeta

← #28293295

Subgroups — #28293295

Order 13568.

6866 conjugacy classes of subgroups.

The subgroup lattice has 1254 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288603C218yesmaximal, complemented
2#20288593C218yesmaximal, complemented
3#20288575C214yesmaximal, complemented
4#20288571C214yesmaximal, complemented
5#20288458C218yesmaximal, complemented
6#20288454C218yesmaximal, complemented
7#20288414C211yesmaximal, characteristic, complemented
8#20288413C211yesmaximal, characteristic, complemented
9#20288412C211yesmaximal, characteristic, complemented
10#20288411C212yesmaximal, complemented
11#20288408C212yesmaximal, complemented
12#20288145C214yesmaximal, complemented
13#20288144C214yesmaximal, complemented
14#20288117C211yesmaximal, characteristic, complemented
15#20288041C211yesmaximal, characteristic
16C2×#16811195C212yesmaximal, complemented
17#20287913C212yesmaximal, complemented
18C2×#16811100C211yesmaximal, characteristic, complemented
19C53×#3491C211yesmaximal, characteristic, complemented
20C22×#11719947C2212yes—
21C23×Dic106C2211yescharacteristic
22#16811357C2218yescomplemented
23#16811356C2214yescomplemented
24#16811355C2214yescomplemented
25#16811350C2214yescomplemented
26#16811350C2218yescomplemented
27#16811349C2214yescomplemented
28#16811345C2214yescomplemented
29#16811344C2218yescomplemented
30#16811342C2214yescomplemented
31#16811341C2218yescomplemented
32#16811340C2218yescomplemented
33#16811340C2218yescomplemented
34#16811340C2218yescomplemented
35#16811332C2214yescomplemented
36#16811329C2214yescomplemented
37#16811327C2218yescomplemented
38#16811315C2218yescomplemented
39#16811313C2218yescomplemented
40#16811310C2218yescomplemented
41#16811310C2218yescomplemented
42#16811310C2218yescomplemented
43#16811309C2218yescomplemented
44#16811308C2218yescomplemented
45#16811306C2218yescomplemented
46#16811306C2218yescomplemented
47#16811306C2218yescomplemented
48#16811305C2218yescomplemented
49#16811304C2218yescomplemented
50#16811302C2218yescomplemented
51#16811300C2218yescomplemented
52#16811299C2218yescomplemented
53#16811299C2218yescomplemented
54#16811297C2218yescomplemented
55#16811296C2218yescomplemented
56#16811252C2214yescomplemented
57#16811252C2218yescomplemented
58#16811249C2212yes—
59#16811249C2211yescharacteristic
60#16811243C2218yescomplemented
61#16811241C2218yescomplemented
62#16811239C2218yescomplemented
63#16811237C2218yescomplemented
64#16811232C2218yescomplemented
65#16811232C2218yescomplemented
66#16811230C2218yescomplemented
67#16811230C2218yescomplemented
68#16811222C2214yescomplemented
69#16811220C2214yescomplemented
70#16811218C2214yescomplemented
71#16811217C2218yescomplemented
72#16811215C2218yescomplemented
73#16811200C2214yes—
74#16811195C2218yes—
75#16811195C2218yes—
76#16811195C2214yes—
77#16811195C2214yescomplemented
78#16811195C2214yescomplemented
79#16811195C2214yescomplemented
80#16811195C2214yescomplemented
81#16811188C2214yes—
82#16811185C2211yescharacteristic
83#16811182C2212yes—
84#16811179C2218yescomplemented
85#16811177C2218yescomplemented
86#16811176C2218yescomplemented
87#16811175C2214yescomplemented
88#16811175C2218yescomplemented
89#16811175C2218yescomplemented
90#16811168C2214yes—
91C2×#13133216C2214yescomplemented
92#16811159C2214yescomplemented
93#16811157C2214yescomplemented
94#16811156C2218yescomplemented
95#16811154C2214yescomplemented
96#16811153C2218yescomplemented
97#16811153C2218yescomplemented
98#16811151C2218yescomplemented
99#16811150C2218yescomplemented
100#16811150C2218yescomplemented
101C2×#13133203C2214yescomplemented
102#16811131C2214yes—
103#16811129C2214yes—
104C2×#13133201C2212yes—
105C2×#13133200C2212yes—
106C2×#13133198C2212yes—
107C2×#13133195C2214yescomplemented
108C2×#13133194C2214yescomplemented
109#16811102C2218yes—
110#16811102C2218yescomplemented
111#16811100C2214yescomplemented
112#16811100C2218yescomplemented
113#16811100C2218yescomplemented
114#16811098C2212yes—
115#16811096C2212yes—
116#16811096C2212yes—
117#16811096C2214yescomplemented
118C4×#11719947C2218yes—
119C4×#11719947C2218yescomplemented
120C2×C4×Dic106C2212yescomplemented
121C2×C4×Dic106C2212yescomplemented
122C2×#13133182C2212yescomplemented
123C2×#13133182C2212yescomplemented
124C2×#13133176C2211yescharacteristic
125C2×#13133173C2212yes—
126C2×#13133173C2211yescharacteristic
127C2×#13133173C2211yescharacteristic
128C2×#13133173C2211yescharacteristic
129C2×#13133173C2211yescharacteristic
130C2×#13133173C2214yescomplemented
131#117×D53C2214yescomplemented
132C53×#552C2218yescomplemented
133C53×#551C2218yescomplemented
134C53×#543C2211yescharacteristic
135C53×#539C2214yescomplemented
136C53×#534C2211yescharacteristic
137C53×#529C2214yescomplemented
138C2×#123×C53C2212yes—
139C53×#518C2212yes—
140C2×#117×C53C2211yescharacteristic
141C2×#11719947—216no—
142C2×#11719947C2314yes—
143C2×#11719947C2314yes—
144C2×#11719947C2314yes—
145C2×#11719947C2314yes—
146C22×Dic106—28no—
147C22×Dic106C2311yescharacteristic
148C22×Dic106C2311yescharacteristic
149C22×Dic106C2311yescharacteristic
150C22×Dic106C2311yescharacteristic
151C22×Dic106C2314yes—
152C22×Dic106C2314yes—
153C22×Dic106C2312yes—
154C22×C22⋊D53C2312yes—
155C22×C22⋊D53C2312yes—
156C23×Dic53C2311yescharacteristic
157C23×Dic53C2312yes—
158C23×Dic53C2311yescharacteristic
159C22×C4×D53C2312yes—
160#13133216C2314yes—
161#13133216C2318yes—
162#13133216C2318yes—
163#13133216C2314yes—
164#13133216C2318yes—
165#13133216C2318yes—
166#13133216C2318yes—
167#13133215C2314yes—
168#13133215C2318yes—
169#13133213C2314yes—
170#13133212C2318yes—
171#13133212C2318yes—
172#13133212C2318yes—
173#13133212C2318yes—
174#13133212C2318yes—
175#13133212C2318yes—
176#13133211C2318yes—
177#13133211C2318yes—
178#13133210C2318yes—
179#13133210C2318yes—
180#13133210C2318yes—
181#13133210C2318yes—
182#13133210C2318yes—
183#13133210C2318yes—
184#13133209C2318yes—
185#13133209C2314yes—
186#13133208C2318yes—
187#13133208C2314yes—
188#13133208C2318yes—
189#13133208C2314yes—
190#13133207C2318yes—
191#13133207C2318yes—
192#13133207C2318yes—
193#13133207C2318yes—
194#13133207C2318yes—
195#13133207C2318yes—
196#13133207C2318yes—
197#13133207C2318yes—
198#13133207C2318yes—
199#13133206C2314yes—
200#13133205C2314yes—
201#13133204C2314yes—
202#13133203C2318yes—
203#13133203C2318yes—
204#13133203C2318yes—
205#13133203C2318yes—
206#13133203C2318yes—
207#13133203C2318yes—
208#13133203C2318yes—
209#13133202C2318yes—
210#13133202C2318yes—
211#13133201C2318yes—
212#13133201C2318yes—
213#13133201C2314yes—
214#13133201C2314yes—
215#13133201C2314yes—
216#13133200C2318yes—
217#13133200C2318yes—
218#13133200C2314yes—
219#13133200C2314yes—
220#13133200C2314yes—
221#13133199C2318yes—
222#13133199C2318yes—
223#13133198C2318yes—
224#13133198C2318yes—
225#13133198C2314yes—
226#13133198C2314yes—
227#13133198C2314yes—
228#13133197C2318yes—
229#13133196C2318yes—
230#13133196C2318yes—
231#13133196C2314yes—
232#13133195C2318yes—
233#13133195C2318yes—
234#13133195C2318yes—
235#13133195C2318yes—
236#13133195C2318yes—
237#13133195C2318yes—
238#13133195C2318yes—
239#13133194C2318yes—
240#13133194C2318yes—
241#13133194C2318yes—
242#13133194C2318yes—
243#13133194C2318yes—
244#13133194C2318yes—
245#13133194C2318yes—
246#13133194C2318yes—
247#13133194C2318yes—
248#13133194C2318yes—
249#13133193C2318yes—
250#13133191C2314yes—
251#13133190C2318yes—
252#13133189C2318yes—
253#13133189C2318yes—
254#13133187C2314yes—
255#13133186C2314yes—
256#13133185C2314yes—
257Q8×Dic53C2314yes—
258Q8×Dic53C2314yes—
259C4×Dic106C2314yes—
260C4×Dic106C2314yes—
261C4×Dic106C2318yes—
262C4×Dic106C2314yes—
263C4×Dic106C2314yes—
264C4×Dic106C2318yes—
265C4×Dic106C2314yes—
266C4×Dic106C2318yes—
267C4×Dic106C2318yes—
268C4×Dic106C2318yes—
269#13133182C2318yes—
270#13133182C2318yes—
271#13133182C2314yes—
272#13133182C2314yes—
273#13133182C2318yes—
274#13133182C2318yes—
275#13133182C2318yes—
276#13133182C2318yes—
277#13133182C2318yes—
278#13133182C2318yes—
279C4×D212C2314yes—
280D4×Dic53C2318yes—
281D4×Dic53C2314yes—
282D4×Dic53C2314yes—
283D4×Dic53C2318yes—
284#13133179C2314yes—
285#13133179C2314yes—
286C4×C22⋊D53C2318yes—
287C4×C22⋊D53C2318yes—
288C4×C22⋊D53C2318yes—
289C4×C22⋊D53C2318yes—
290C4×C22⋊D53C2318yes—
291#13133177C2318yes—
292#13133177C2318yes—
293#13133177C2318yes—
294#13133177C2318yes—
295#13133177C2318yes—
296#13133177C2318yes—
297#13133176C2318yes—
298#13133176C2318yes—
299#13133176C2314yes—
300#13133175C2318yes—
301#13133175C2318yes—
302#13133175C2318yes—
303#13133174C2318yes—
304#13133174C2318yes—
305#13133174C2318yes—
306#13133173C2318yes—
307#13133173C2318yes—
308#13133173C2318yes—
309#13133173C2318yes—
310#13133173C2314yes—
311#13133173C2318yes—
312#13133173C2314yes—
313#13133173C2314yes—
314#13133173C2314yes—
315#13133173C2314yes—
316#13133173C2314yes—
317#13133173C2314yes—
318#13133173C2314yes—
319#13133173C2314yes—
320#13133173C2314yes—
321#13133173C2318yes—
322C2×C4⋊Dic53C2314yes—
323C2×C4⋊Dic53C2312yes—
324C2×#11719919C2314yes—
325C2×#11719919C2314yes—
326C2×#11719919C2318yes—
327C2×#11719919C2312yes—
328C2×#11719919C2312yes—
329C2×#11719919C2312yes—
330C2×#11719919C2312yes—
331C2×#11719919C2314yes—
332C4⋊C4×D53C2318yes—
333C2×C22⋊Dic53C2314yes—
334C2×C22⋊Dic53C2314yes—
335C2×C22⋊Dic53C2311yescharacteristic
336C2×C22⋊Dic53C2311yescharacteristic
337C2×C22⋊Dic53C2312yes—
338C2×#11719921C2314yes—
339C2×#11719921C2314yes—
340C22⋊C4×D53C2314yes—
341C22⋊C4×D53C2314yes—
342C2×C4×Dic53C2312yes—
343C2×C4×Dic53C2312yes—
344C2×C4×Dic53C2312yes—
345C2×C4×Dic53C2312yes—
346C2×C4×Dic53C2314yes—
347C2×C4×Dic53C2318yes—
348C2×C4×Dic53C2312yes—
349C42×D53C2318yes—
350C22×D4×C53C2312yes—
351C23×C4×C53C2311yescharacteristic
352#126×C53C2318yes—
353#126×C53C2318yes—
354#125×C53C2318yes—
355#125×C53C2314yes—
356#124×C53C2314yes—
357#123×C53C2318yes—
358#123×C53C2314yes—
359#123×C53C2314yes—
360#123×C53C2314yes—
361#123×C53C2318yes—
362C22⋊Q8×C53C2318yes—
363C22⋊Q8×C53C2314yes—
364C22⋊Q8×C53C2318yes—
365#121×C53C2314yes—
366#120×C53C2314yes—
367C4×Q8×C53C2314yes—
368C4×D4×C53C2318yes—
369C4×D4×C53C2318yes—
370C4×D4×C53C2314yes—
371#117×C53C2318yes—
372#117×C53C2314yes—
373#117×C53C2318yes—
374C2×C4⋊C4×C53C2312yes—
375C2×C4⋊C4×C53C2314yes—
376C2×C22⋊C4×C53C2311yescharacteristic
377C2×C22⋊C4×C53C2311yescharacteristic
378C2×C22⋊C4×C53C2314yes—
379C2×C22⋊C4×C53C2312yes—
380C2×C22⋊C4×C53C2314yes—
381C2×C42×C53C2312yes—
382C24×C53C2412yes—
383C24×C53C2411yescharacteristic
384C23×D53C2412yes—
385C2×Q8×C53C2414yes—
386C2×D4×C53—28no—
387C2×D4×C53C2414yes—
388C2×D4×C53C2414yes—
389C2×D4×C53C2414yes—
390C22×C4×C53—24no—
391C22×C4×C53C2411yescharacteristic
392C22×C4×C53C2414yes—
393C22×C4×C53C2412yes—
394C22×C4×C53C2411yescharacteristic
395C22×C4×C53C2412yes—
396C22×C4×C53C2412yes—
397C22×C4×C53C2414yes—
398C22×C4×C53C2418yes—
399C2×C22⋊D53—28no—
400C2×C22⋊D53—28no—
401C2×C22⋊D53C2414yes—
402C2×C22⋊D53C2414yes—
403C2×C22⋊D53C2414yes—
404C2×C22⋊D53C2414yes—
405C2×C22⋊D53C2418yes—
406C22×Dic53—24no—
407C22×Dic53—28no—
408C22×Dic53#4118yes—
409C22×Dic53C2411yescharacteristic
410C22×Dic53C2411yescharacteristic
411C22×Dic53C2414yes—
412C22×Dic53C2414yes—
413C22×Dic53C2412yes—
414C22×Dic53C2414yes—
415C22×Dic53C2412yes—
416C22×Dic53C2412yes—
417C22×Dic53C2414yes—
418C22×Dic53C2418yes—
419C22×Dic53C2411yescharacteristic
420C22×Dic53C2411yescharacteristic
421C22×Dic53C2412yes—
422C22×Dic53C2412yes—
423#11719947—216no—
424#11719947—216no—
425#11719947—216no—
426#11719947—216no—
427C2×D212C2414yes—
428C2×C4×D53—28no—
429C2×C4×D53C2414yes—
430C2×C4×D53C2414yes—
431C2×C4×D53C2418yes—
432C2×C4×D53C2418yes—
433C2×Dic106—216no—
434C2×Dic106—216no—
435C2×Dic106—24no—
436C2×Dic106—24no—
437C2×Dic106—24no—
438C2×Dic106—24no—
439C2×Dic106—28no—
440C2×Dic106C2412yes—
441C2×Dic106C2414yes—
442C2×Dic106C2412yes—
443C2×Dic106C2414yes—
444C2×Dic106C2414yes—
445C2×Dic106C2412yes—
446C2×Dic106C2414yes—
447C2×Dic106C2412yes—
448C2×Dic106C2414yes—
449C2×Dic106C2418yes—
450C4⋊C4×C53C2418yes—
451C4⋊C4×C53C2418yes—
452C4⋊C4×C53C2418yes—
453C4⋊C4×C53C2418yes—
454C4⋊C4×C53C2418yes—
455C4⋊C4×C53C2414yes—
456C4⋊C4×C53C2414yes—
457C22⋊C4×C53C2414yes—
458C22⋊C4×C53C2414yes—
459C22⋊C4×C53C2414yes—
460C22⋊C4×C53C2418yes—
461C22⋊C4×C53C2414yes—
462C22⋊C4×C53C2418yes—
463C22⋊C4×C53C2418yes—
464C22⋊C4×C53C2418yes—
465C42×C53C2414yes—
466C42×C53C2414yes—
467C42×C53C2418yes—
468C22⋊Dic53C2414yes—
469C22⋊Dic53C2414yes—
470C22⋊Dic53C2414yes—
471C22⋊Dic53C2414yes—
472C22⋊Dic53C2418yes—
473C22⋊Dic53C2418yes—
474C22⋊Dic53C2418yes—
475C22⋊Dic53C2418yes—
476#11719921C2418yes—
477#11719921C2418yes—
478#11719921C2418yes—
479#11719921C2418yes—
480#11719921C2418yes—
481#11719921C2418yes—
482#11719921C2418yes—
483#11719921C2418yes—
484C4⋊Dic53C2418yes—
485C4⋊Dic53C2418yes—
486C4⋊Dic53C2414yes—
487C4⋊Dic53C2414yes—
488C4⋊Dic53C2418yes—
489C4⋊Dic53C2418yes—
490C4⋊Dic53C2414yes—
491C4⋊Dic53C2414yes—
492#11719919C2414yes—
493#11719919C2418yes—
494#11719919C2414yes—
495#11719919C2418yes—
496#11719919C2418yes—
497#11719919C2418yes—
498#11719919C2418yes—
499#11719919C2418yes—
500#11719919C2414yes—
501#11719919C2414yes—
502#11719919C2418yes—
503#11719919C2418yes—
504#11719919C2418yes—
505#11719919C2418yes—
506#11719919C2418yes—
507#11719919C2418yes—
508#11719919C2418yes—
509#11719919C2418yes—
510C4×Dic53C2418yes—
511C4×Dic53C2418yes—
512C4×Dic53C2418yes—
513C4×Dic53C2414yes—
514C4×Dic53C2418yes—
515C4×Dic53C2418yes—
516C4×Dic53C2418yes—
517C4×Dic53C2414yes—
518C4×Dic53C2414yes—
519C4×Dic53C2418yes—
520C4×Dic53C2414yes—
521C4×Dic53C2418yes—
522C23×C53—24no—
523C23×C53—42no—
524C23×C53—44no—
525C23×C53C2×#4114yes—
526C23×C53C2514yes—
527C23×C53C2511yescharacteristic
528C23×C53C2512yes—
529C22×D53—24no—
530C22×D53—44no—
531C22×D53C2514yes—
532Q8×C53—44no—
533D4×C53—28no—
534D4×C53—28no—
535D4×C53—44no—
536C2×C4×C53—28no—
537C2×C4×C53—22no—
538C2×C4×C53—22no—
539C2×C4×C53—24no—
540C2×C4×C53—44no—
541C2×C4×C53—48no—
542C2×C4×C53—42no—
543C2×C4×C53—42no—
544C2×C4×C53C2512yes—
545C2×C4×C53C2512yes—
546C2×C4×C53C2514yes—
547C2×C4×C53C2518yes—
548C2×C4×C53C2514yes—
549C2×C4×C53C2514yes—
550C22⋊D53—28no—
551C22⋊D53—28no—
552C22⋊D53—28no—
553C22⋊D53—28no—
554C22⋊D53—48no—
555C2×Dic53—28no—
556C2×Dic53—22no—
557C2×Dic53—22no—
558C2×Dic53—24no—
559C2×Dic53—28no—
560C2×Dic53—28no—
561C2×Dic53—44no—
562C2×Dic53—48no—
563C2×Dic53—42no—
564C2×Dic53—42no—
565C2×Dic53C2×#4118yes—
566C2×Dic53C2×#4118yes—
567C2×Dic53C2×#4114yes—
568C2×Dic53C2×#4114yes—
569C2×Dic53C2512yes—
570C2×Dic53C2512yes—
571C2×Dic53C2518yes—
572C2×Dic53C2514yes—
573C2×Dic53C2514yes—
574C2×Dic53C2514yes—
575C2×Dic53C2511yescharacteristic
576C2×Dic53C2512yes—
577C2×Dic53C2511yescharacteristic
578D212—44no—
579C4×D53—28no—
580C4×D53—28no—
581C4×D53—48no—
582C4×D53—48no—
583Dic106—24no—
584Dic106—24no—
585Dic106—28no—
586Dic106—28no—
587Dic106—24no—
588Dic106—24no—
589Dic106—28no—
590Dic106—28no—
591Dic106—44no—
592Dic106—48no—
593#62860—531nomaximal, Sylow
594C22×C53—22no—
595C22×C53—24no—
596C22×C53—24no—
597C22×C53—28no—
598C22×C53—44no—
599C22×C53—84no—
600C22×C53C22×#4114yes—
601C22×C53C22×#4112yes—
602C22×C53C2611yescharacteristic
603C2×D53—24no—
604C2×D53—28no—
605C2×D53—84no—
606C4×C53—22no—
607C4×C53—22no—
608C4×C53—24no—
609C4×C53—28no—
610C4×C53—24no—
611C4×C53—24no—
612Dic53—22no—
613Dic53—22no—
614Dic53—24no—
615Dic53—28no—
616Dic53—24no—
617Dic53—24no—
618Dic53C22×#4112yes—
619Dic53C22×#4114yes—
620Dic53C22×#4112yes—
621#3510—538no—
622#3509—538no—
623#3507—534no—
624#3507—534no—
625#3495—538no—
626#3495—538no—
627#3491—531no—
628#3491—531no—
629#3491—532no—
630#3491—532no—
631#3491—531no—
632#3491D5311yescharacteristic, complemented
633#3461—534no—
634#3461—534no—
635#3458—531no—
636#3449—531no—
637C2×#536—532no—
638#3428—532no—
639C2×#519—531no—
640C2×C53—24no—
641C2×C53—22no—
642C2×C53—44no—
643C2×C53C23×#4111yescharacteristic
644C2×C532−1+612yes—
645D53—44no—
646C22×#41—532no—
647C23×Q8—531no—
648#559—534no—
649#559—538no—
650#559—534no—
651#557—538no—
652#557—534no—
653#557—534no—
654#556—538no—
655#556—538no—
656#556—538no—
657#556—534no—
658#556—538no—
659#556—534no—
660#556—538no—
661#554—534no—
662#554—538no—
663#554—534no—
664#552—538no—
665#552—538no—
666#552—538no—
667#552—538no—
668#552—538no—
669#552—538no—
670#552—538no—
671#552—538no—
672#552—538no—
673#552—538no—
674#552—538no—
675#552C2×D5318yescomplemented
676#551—538no—
677#551—538no—
678#551—538no—
679#551—538no—
680#551—538no—
681#551—538no—
682#551—538no—
683#551C2×D5318yescomplemented
684#544—534no—
685#544—538no—
686#543—532no—
687#543—531no—
688#543C2×D5311yescharacteristic
689#542—538no—
690#542—538no—
691#542—538no—
692#542—538no—
693#541—538no—
694#541—538no—
695#541—538no—
696#541—538no—
697#539—538no—
698#539—534no—
699#539—534no—
700#539—538no—
701#539—534no—
702#539C2×D5314yescomplemented
703#537—534no—
704#536—534no—
705#536—534no—
706#536—538no—
707#536—534no—
708#536—534no—
709#536—538no—
710#536—534no—
711#535—534no—
712#534—532no—
713#534—531no—
714#534C2×D5311yescharacteristic
715#533—538no—
716#533—534no—
717#533—538no—
718#533—538no—
719#533—538no—
720#533—538no—
721#532—534no—
722C2×C4⋊Q8—534no—
723#529—538no—
724#529—538no—
725#529—538no—
726#529—534no—
727#529—534no—
728#529—538no—
729#529—538no—
730#529—538no—
731#529—534no—
732#529C2×D5314yescomplemented
733C2×#124—534no—
734#525—534no—
735#525—534no—
736C2×#123—532no—
737C2×#123—532no—
738C2×#123—532no—
739C2×#123C2×D5312yes—
740C2×C22⋊Q8—534no—
741C2×C22⋊Q8—534no—
742#520—538no—
743#520—538no—
744#519—538no—
745#519—538no—
746#519—534no—
747#518—532no—
748#518—532no—
749#518—532no—
750#518—534no—
751#518C2×D5312yes—
752C4×#41—538no—
753C4×#41—538no—
754C2×C4×Q8—532no—
755C2×C4×Q8—532no—
756C2×C4×Q8—532no—
757C2×C4×Q8—532no—
758C2×#117—531no—
759C2×#117—534no—
760C2×#117—531no—
761C2×#117—531no—
762C2×#117—531no—
763C2×#117—531no—
764C2×#117—532no—
765C2×#117—534no—
766C2×#117C2×D5311yescharacteristic
767C53#6286011yescharacteristic, complemented, Sylow
768C2×#41—534no—
769C2×#41—534no—
770C2×#41—534no—
771C2×#41—534no—
772C2×#41—10616no—
773C22×Q8—531no—
774C22×Q8—531no—
775C22×Q8—531no—
776C22×Q8—531no—
777C22×Q8—534no—
778C22×Q8—534no—
779C22×Q8—532no—
780C22×Q8—1068no—
781C22×D4—532no—
782C22×D4—532no—
783C22×D4C22×D5312yes—
784C23×C4—531no—
785C23×C4—532no—
786C23×C4—531no—
787C23×C4—532no—
788C23×C4C22×D5311yescharacteristic
789C4⋊Q8—538no—
790C4⋊Q8—534no—
791C4⋊Q8—538no—
792C4⋊Q8—538no—
793C4⋊Q8—538no—
794C4⋊Q8—538no—
795C4⋊Q8—534no—
796C4⋊Q8—538no—
797C4⋊Q8—534no—
798#127—534no—
799#126—538no—
800#126—538no—
801#126—538no—
802#126—538no—
803#126—538no—
804#126—538no—
805#126—538no—
806#126—538no—
807#126—538no—
808#126—538no—
809#126—538no—
810#126—538no—
811#126—538no—
812#126—538no—
813#126C22×D5318yes—
814#126C22×D5318yes—
815#125—538no—
816#125—538no—
817#125—538no—
818#125—538no—
819#125—534no—
820#125—534no—
821#125—538no—
822#125—538no—
823#125—538no—
824#125—538no—
825#125—538no—
826#125—538no—
827#125—538no—
828#125—534no—
829#125—538no—
830#125C22×D5314yes—
831#125C22×D5318yes—
832#124—534no—
833#124—534no—
834#124—538no—
835#124—538no—
836#124—538no—
837#124—538no—
838#124—538no—
839#124—538no—
840#124—538no—
841#124—534no—
842#124C22×D5314yes—
843#123—534no—
844#123—534no—
845#123—538no—
846#123—534no—
847#123—538no—
848#123—534no—
849#123—534no—
850#123—538no—
851#123—534no—
852#123—538no—
853#123—538no—
854#123—538no—
855#123—534no—
856#123—534no—
857#123—538no—
858#123—534no—
859#123—538no—
860#123—538no—
861#123—538no—
862#123C22×D5314yes—
863#123C22×D5314yes—
864#123C22×D5318yes—
865#123C22×D5314yes—
866#123C22×D5318yes—
867C22⋊Q8—538no—
868C22⋊Q8—534no—
869C22⋊Q8—538no—
870C22⋊Q8—538no—
871C22⋊Q8—538no—
872C22⋊Q8—538no—
873C22⋊Q8—538no—
874C22⋊Q8—538no—
875C22⋊Q8—538no—
876C22⋊Q8—538no—
877C22⋊Q8—538no—
878C22⋊Q8—538no—
879C22⋊Q8—538no—
880C22⋊Q8—538no—
881C22⋊Q8—538no—
882C22⋊Q8—538no—
883C22⋊Q8—538no—
884C22⋊Q8—538no—
885C22⋊Q8—538no—
886C22⋊Q8—538no—
887C22⋊Q8—538no—
888C22⋊Q8—538no—
889C22⋊Q8C22×D5314yes—
890C22⋊Q8C22×D5318yes—
891C22⋊Q8C22×D5318yes—
892#121—538no—
893#121—538no—
894#121—534no—
895#121—538no—
896#121C22×D5314yes—
897#120—534no—
898#120—534no—
899#120—534no—
900#120C22×D5314yes—
901C4×Q8—534no—
902C4×Q8—534no—
903C4×Q8—538no—
904C4×Q8—538no—
905C4×Q8—538no—
906C4×Q8—538no—
907C4×Q8—538no—
908C4×Q8—538no—
909C4×Q8—534no—
910C4×Q8—538no—
911C4×Q8—534no—
912C4×Q8—538no—
913C4×Q8—538no—
914C4×Q8—538no—
915C4×Q8—534no—
916C4×Q8—534no—
917C4×Q8—534no—
918C4×Q8—534no—
919C4×Q8—538no—
920C4×Q8—538no—
921C4×Q8—534no—
922C4×Q8—538no—
923C4×Q8C22×D5314yes—
924C4×D4—538no—
925C4×D4—538no—
926C4×D4—534no—
927C4×D4—534no—
928C4×D4—538no—
929C4×D4—538no—
930C4×D4—538no—
931C4×D4—538no—
932C4×D4—538no—
933C4×D4—534no—
934C4×D4—534no—
935C4×D4—538no—
936C4×D4—538no—
937C4×D4—538no—
938C4×D4—538no—
939C4×D4—538no—
940C4×D4—538no—
941C4×D4—534no—
942C4×D4C22×D5318yes—
943C4×D4C22×D5318yes—
944C4×D4C22×D5314yes—
945#117—534no—
946#117—538no—
947#117—538no—
948#117—538no—
949#117—538no—
950#117—538no—
951#117—534no—
952#117—534no—
953#117—534no—
954#117—534no—
955#117—538no—
956#117—534no—
957#117—534no—
958#117—534no—
959#117—534no—
960#117—534no—
961#117—538no—
962#117—538no—
963#117—534no—
964#117—538no—
965#117—538no—
966#117—538no—
967#117—538no—
968#117—538no—
969#117—538no—
970#117C22×D5314yes—
971#117C22×D5318yes—
972#117C22×D5318yes—
973C2×C4⋊C4—532no—
974C2×C4⋊C4—532no—
975C2×C4⋊C4—532no—
976C2×C4⋊C4—532no—
977C2×C4⋊C4—532no—
978C2×C4⋊C4—534no—
979C2×C4⋊C4—538no—
980C2×C4⋊C4—534no—
981C2×C4⋊C4—534no—
982C2×C4⋊C4—534no—
983C2×C4⋊C4—538no—
984C2×C4⋊C4C22×D5312yes—
985C2×C4⋊C4C22×D5314yes—
986C2×C22⋊C4—531no—
987C2×C22⋊C4—531no—
988C2×C22⋊C4—532no—
989C2×C22⋊C4—534no—
990C2×C22⋊C4—534no—
991C2×C22⋊C4—534no—
992C2×C22⋊C4—534no—
993C2×C22⋊C4—534no—
994C2×C22⋊C4—534no—
995C2×C22⋊C4C22×D5311yescharacteristic
996C2×C22⋊C4C22×D5311yescharacteristic
997C2×C22⋊C4C22×D5312yes—
998C2×C22⋊C4C22×D5314yes—
999C2×C22⋊C4C22×D5314yes—
1000C2×C42—532no—
1001C2×C42—532no—
1002C2×C42—532no—
1003C2×C42—532no—
1004C2×C42—532no—
1005C2×C42—534no—
1006C2×C42—538no—
1007C2×C42—538no—
1008C2×C42C22×D5312yes—
1009C24—532no—
1010C24C23×D5312yes—
1011C24C23×D5311yescharacteristic
1012#41—10616no—
1013#41—10616no—
1014#41—10616no—
1015#41—10616no—
1016C2×Q8—532no—
1017C2×Q8—532no—
1018C2×Q8—534no—
1019C2×Q8—534no—
1020C2×Q8—534no—
1021C2×Q8—532no—
1022C2×Q8—532no—
1023C2×Q8—534no—
1024C2×Q8—538no—
1025C2×Q8—534no—
1026C2×Q8—10616no—
1027C2×Q8—10616no—
1028C2×Q8—1064no—
1029C2×Q8—1064no—
1030C2×Q8—1064no—
1031C2×Q8—1064no—
1032C2×Q8—1068no—
1033C2×Q8C23×D5314yes—
1034C2×D4—28no—
1035C2×D4—534no—
1036C2×D4—534no—
1037C2×D4—534no—
1038C2×D4—534no—
1039C2×D4—538no—
1040C2×D4—534no—
1041C2×D4—1068no—
1042C2×D4—1068no—
1043C2×D4C23×D5314yes—
1044C2×D4C23×D5314yes—
1045C2×D4C23×D5314yes—
1046C22×C4—24no—
1047C22×C4—538no—
1048C22×C4—531no—
1049C22×C4—531no—
1050C22×C4—532no—
1051C22×C4—532no—
1052C22×C4—531no—
1053C22×C4—531no—
1054C22×C4—534no—
1055C22×C4—534no—
1056C22×C4—532no—
1057C22×C4—534no—
1058C22×C4—532no—
1059C22×C4—532no—
1060C22×C4—534no—
1061C22×C4—538no—
1062C22×C4—534no—
1063C22×C4—534no—
1064C22×C4—538no—
1065C22×C4—538no—
1066C22×C4—1068no—
1067C22×C4—1068no—
1068C22×C4—1064no—
1069C22×C4C23×D5311yescharacteristic
1070C22×C4C23×D5311yescharacteristic
1071C22×C4C23×D5314yes—
1072C22×C4C23×D5312yes—
1073C22×C4C23×D5312yes—
1074C22×C4C23×D5312yes—
1075C22×C4C23×D5314yes—
1076C22×C4C23×D5318yes—
1077C4⋊C4—534no—
1078C4⋊C4—538no—
1079C4⋊C4—534no—
1080C4⋊C4—538no—
1081C4⋊C4—538no—
1082C4⋊C4—538no—
1083C4⋊C4—538no—
1084C4⋊C4—538no—
1085C4⋊C4—538no—
1086C4⋊C4—534no—
1087C4⋊C4—534no—
1088C4⋊C4—534no—
1089C4⋊C4—534no—
1090C4⋊C4—538no—
1091C4⋊C4—538no—
1092C4⋊C4—538no—
1093C4⋊C4—538no—
1094C4⋊C4—538no—
1095C4⋊C4—538no—
1096C4⋊C4—538no—
1097C4⋊C4—538no—
1098C4⋊C4—538no—
1099C4⋊C4—538no—
1100C4⋊C4—534no—
1101C4⋊C4—538no—
1102C4⋊C4—534no—
1103C4⋊C4C23×D5318yes—
1104C4⋊C4C23×D5318yes—
1105C4⋊C4C23×D5318yes—
1106C4⋊C4C23×D5318yes—
1107C4⋊C4C23×D5318yes—
1108C4⋊C4C23×D5314yes—
1109C4⋊C4C23×D5314yes—
1110C22⋊C4—534no—
1111C22⋊C4—534no—
1112C22⋊C4—534no—
1113C22⋊C4—534no—
1114C22⋊C4—538no—
1115C22⋊C4—538no—
1116C22⋊C4—538no—
1117C22⋊C4—538no—
1118C22⋊C4—538no—
1119C22⋊C4—538no—
1120C22⋊C4—538no—
1121C22⋊C4—538no—
1122C22⋊C4—538no—
1123C22⋊C4—538no—
1124C22⋊C4—538no—
1125C22⋊C4—538no—
1126C22⋊C4C23×D5314yes—
1127C22⋊C4C23×D5314yes—
1128C22⋊C4C23×D5314yes—
1129C22⋊C4C23×D5314yes—
1130C22⋊C4C23×D5318yes—
1131C22⋊C4C23×D5318yes—
1132C22⋊C4C23×D5318yes—
1133C22⋊C4C23×D5318yes—
1134C42—538no—
1135C42—538no—
1136C42—538no—
1137C42—538no—
1138C42—538no—
1139C42—538no—
1140C42—534no—
1141C42—534no—
1142C42—538no—
1143C42—534no—
1144C42—538no—
1145C42—534no—
1146C42C23×D5318yes—
1147C42C23×D5314yes—
1148C42C23×D5314yes—
1149C23—24no—
1150C23—42no—
1151C23—44no—
1152C23—534no—
1153C23—1064no—
1154C23—2124no—
1155C23#41×D5314yes—
1156C23C24×D5314yes—
1157C23C24×D5312yes—
1158C23C24×D5311yescharacteristic
1159Q8—44no—
1160Q8—1064no—
1161Q8—1064no—
1162Q8—1068no—
1163Q8—1068no—
1164Q8—1064no—
1165Q8—1064no—
1166Q8—1068no—
1167Q8—1068no—
1168Q8—2128no—
1169Q8—2124no—
1170D4—28no—
1171D4—28no—
1172D4—44no—
1173D4—1068no—
1174D4—1068no—
1175D4—1068no—
1176D4—1068no—
1177D4—2124no—
1178D4—2128no—
1179C2×C4—28no—
1180C2×C4—22no—
1181C2×C4—22no—
1182C2×C4—24no—
1183C2×C4—42no—
1184C2×C4—48no—
1185C2×C4—44no—
1186C2×C4—42no—
1187C2×C4—538no—
1188C2×C4—538no—
1189C2×C4—534no—
1190C2×C4—534no—
1191C2×C4—531no—
1192C2×C4—532no—
1193C2×C4—531no—
1194C2×C4—534no—
1195C2×C4—534no—
1196C2×C4—538no—
1197C2×C4—532no—
1198C2×C4—532no—
1199C2×C4—534no—
1200C2×C4—1068no—
1201C2×C4—1068no—
1202C2×C4—1068no—
1203C2×C4—1068no—
1204C2×C4—1064no—
1205C2×C4—1068no—
1206C2×C4—1062no—
1207C2×C4—1062no—
1208C2×C4—2128no—
1209C2×C4—2128no—
1210C2×C4—2122no—
1211C2×C4—2128no—
1212C2×C4—2124no—
1213C2×C4—2122no—
1214C2×C4C24×D5314yes—
1215C2×C4C24×D5314yes—
1216C2×C4C24×D5312yes—
1217C2×C4C24×D5318yes—
1218C2×C4C24×D5314yes—
1219C2×C4C24×D5312yes—
1220C22—22no—
1221C22—24no—
1222C22—24no—
1223C22—28no—
1224C22—44no—
1225C22—84no—
1226C22—1064no—
1227C22—1068no—
1228C22—4244no—
1229C22C2×#41×D5314yes—
1230C22C2×#41×D5312yes—
1231C22C25×D5311yescharacteristic
1232C4—22no—
1233C4—22no—
1234C4—24no—
1235C4—24no—
1236C4—28no—
1237C4—24no—
1238C4—532no—
1239C4—534no—
1240C4—532no—
1241C4—1064no—
1242C4—1062no—
1243C4—1062no—
1244C4—1064no—
1245C4—1068no—
1246C4—1064no—
1247C2—24no—
1248C2—22no—
1249C2—44no—
1250C2—2124no—
1251C2C22×#41×D5311yescharacteristic
1252C2#2028952812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3491C2
prime radical#20288041C2
hypercenter#3491D53
hypocenterC53#62860
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3491

Complements

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

NH ≅ G/Ntype
1. #20288603C2semidirect
2. #20288593C2semidirect
3. #20288575C2semidirect
4. #20288571C2semidirect
5. #20288458C2semidirect
6. #20288454C2semidirect
7. #20288414C2semidirect
8. #20288413C2semidirect
9. #20288412C2semidirect
10. #20288411C2semidirect
11. #20288408C2semidirect
12. #20288145C2semidirect
13. #20288144C2semidirect
14. #20288117C2semidirect
16. C2×#16811195C2semidirect
17. #20287913C2semidirect
18. C2×#16811100C2semidirect
19. C53×#3491C2semidirect
22. #16811357C22semidirect
23. #16811356C22semidirect
24. #16811355C22semidirect
25. #16811350C22semidirect
26. #16811350C22semidirect
27. #16811349C22semidirect
28. #16811345C22semidirect
29. #16811344C22semidirect
30. #16811342C22semidirect
31. #16811341C22semidirect
32. #16811340C22semidirect
33. #16811340C22semidirect
34. #16811340C22semidirect
35. #16811332C22semidirect
36. #16811329C22semidirect
37. #16811327C22semidirect
38. #16811315C22semidirect
39. #16811313C22semidirect
40. #16811310C22semidirect
41. #16811310C22semidirect
42. #16811310C22semidirect
43. #16811309C22semidirect
44. #16811308C22semidirect
45. #16811306C22semidirect
46. #16811306C22semidirect
47. #16811306C22semidirect
48. #16811305C22semidirect
49. #16811304C22semidirect
50. #16811302C22semidirect
51. #16811300C22semidirect
52. #16811299C22semidirect
53. #16811299C22semidirect
54. #16811297C22semidirect
55. #16811296C22semidirect
56. #16811252C22semidirect
57. #16811252C22semidirect
60. #16811243C22semidirect
61. #16811241C22semidirect
62. #16811239C22semidirect
63. #16811237C22semidirect
64. #16811232C22semidirect
65. #16811232C22semidirect
66. #16811230C22semidirect
67. #16811230C22semidirect
68. #16811222C22semidirect
69. #16811220C22semidirect
70. #16811218C22semidirect
71. #16811217C22semidirect
72. #16811215C22semidirect
77. #16811195C22semidirect
78. #16811195C22semidirect
79. #16811195C22semidirect
80. #16811195C22semidirect
84. #16811179C22semidirect
85. #16811177C22semidirect
86. #16811176C22semidirect
87. #16811175C22semidirect
88. #16811175C22semidirect
89. #16811175C22semidirect
91. C2×#13133216C22semidirect
92. #16811159C22semidirect
93. #16811157C22semidirect
94. #16811156C22semidirect
95. #16811154C22semidirect
96. #16811153C22semidirect
97. #16811153C22semidirect
98. #16811151C22semidirect
99. #16811150C22semidirect
100. #16811150C22semidirect
101. C2×#13133203C22semidirect
107. C2×#13133195C22semidirect
108. C2×#13133194C22semidirect
110. #16811102C22semidirect
111. #16811100C22semidirect
112. #16811100C22semidirect
113. #16811100C22semidirect
117. #16811096C22semidirect
119. C4×#11719947C22semidirect
120. C2×C4×Dic106C22semidirect
121. C2×C4×Dic106C22semidirect
122. C2×#13133182C22semidirect
123. C2×#13133182C22semidirect
130. C2×#13133173C22semidirect
131. #117×D53C22semidirect
132. C53×#552C22semidirect
133. C53×#551C22semidirect
135. C53×#539C22semidirect
137. C53×#529C22semidirect
632. #3491D53semidirect
675. #552C2×D53semidirect
683. #551C2×D53semidirect
702. #539C2×D53semidirect
732. #529C2×D53semidirect
767. C53#62860semidirect

Maximal subgroups

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

subgroupindex
#202886032
#202885932
#202885752
#202885712
#202884582
#202884542
#202884142
#202884132
#202884122
#202884112
#202884082
#202881452
#202881442
#202881172
#202880412
C2×#168111952
#202879132
C2×#168111002
C53×#34912
#6286053