Finite Group Databasebeta

← #28293099

Subgroups — #28293099

Order 13568.

6624 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289412C218yesmaximal, complemented
2#20289126C212yesmaximal, complemented
3#20289120C211yesmaximal, characteristic, complemented
4#20288992C214yesmaximal, complemented
5#20288987C218yesmaximal, complemented
6#20288733C214yesmaximal, complemented
7#20288729C214yesmaximal, complemented
8#20288727C214yesmaximal, complemented
9#20288679C214yesmaximal, complemented
10#20288677C214yesmaximal, complemented
11#20288675C214yesmaximal, complemented
12#20288614C214yesmaximal, complemented
13#20288607C218yesmaximal, complemented
14#20288012C212yesmaximal, complemented
15#20288010C211yesmaximal, characteristic, complemented
16C53×#3550C211yesmaximal, characteristic, complemented
17#16811377C2218yescomplemented
18#16811365C2214yescomplemented
19#16811365C2218yescomplemented
20#16811363C2218yescomplemented
21#16811358C2214yescomplemented
22#16811357C2218yescomplemented
23#16811355C22116yescomplemented
24Q8×Dic106C2214yescomplemented
25#16811347C22116yescomplemented
26#16811347C2214yescomplemented
27#16811347C2218yescomplemented
28#16811346C2214yescomplemented
29#16811346C2218yescomplemented
30#16811344C22116yescomplemented
31#16811344C2218yescomplemented
32#16811340C22116yescomplemented
33#16811339C2212yescomplemented
34#16811339C2218yescomplemented
35#16811338C2214yescomplemented
36#16811338C2218yescomplemented
37#16811336C2218yescomplemented
38#16811303C2218yescomplemented
39#16811300C22116yescomplemented
40#16811298C22116yescomplemented
41#16811296C22116yescomplemented
42#16811296C22116yescomplemented
43Q8×D212C2214yescomplemented
44#16811288C2214yescomplemented
45#16811285C2218yescomplemented
46#16811284C2218yescomplemented
47#16811281C2218yescomplemented
48#16811268C2218yescomplemented
49#16811266C2218yescomplemented
50#16811264C2218yescomplemented
51D4×D212C2214yescomplemented
52#16811258C2212yescomplemented
53#16811247C2218yescomplemented
54#16811247C22116yescomplemented
55#16811246C2218yescomplemented
56#16811246C2218yescomplemented
57#16811246C22116yescomplemented
58#16811244C2218yescomplemented
59#16811242C2218yescomplemented
60#16811239C22116yescomplemented
61#16811213C22116yescomplemented
62#16811212C22116yescomplemented
63#16811209C22116yescomplemented
64#16811196C2218yescomplemented
65#16811189C2218yes—
66#16811187C2214yes—
67#16811180C2211yescharacteristic, complemented
68#16811178C2212yescomplemented
69#16811178C2212yescomplemented
70#16811178C2212yescomplemented
71#16811178C2218yescomplemented
72#16811176C2214yescomplemented
73#16811174C2212yes—
74#16811174C2212yes—
75#16811173C2212yes—
76#16811171C2212yes—
77#16811160C2214yescomplemented
78#16811160C2214yescomplemented
79#16811160C2218yescomplemented
80#16811159C2214yescomplemented
81#16811159C2214yescomplemented
82#16811159C2218yescomplemented
83#16811158C2214yescomplemented
84#16811158C2214yescomplemented
85#16811155C2214yescomplemented
86#16811155C2218yescomplemented
87#16811154C2214yescomplemented
88#16811152C2214yescomplemented
89C2×#13133206C2214yescomplemented
90#124×D53C2218yescomplemented
91#16811136C2214yescomplemented
92#16811136C2214yescomplemented
93#16811135C2214yescomplemented
94#16811133C2214yescomplemented
95#16811130C2212yescomplemented
96#16811101C2214yescomplemented
97#16811099C2218yescomplemented
98#16811097C2214yescomplemented
99#16811095C2218yescomplemented
100#41×Dic53C2212yescomplemented
101C4×#11719949C2214yescomplemented
102C4×#11719949C2214yescomplemented
103#16811091C2214yescomplemented
104C4×#11719947C2214yescomplemented
105C2×C42×D53C2211yescharacteristic, complemented
106C53×#563C2214yescomplemented
107C53×#559C2212yescomplemented
108Q82×C53C2212yescomplemented
109C53×#556C2214yescomplemented
110D4×Q8×C53C2214yescomplemented
111C53×#542C2218yescomplemented
112C53×#536C2214yescomplemented
113C53×#533C2212yescomplemented
114C53×#532C2211yescharacteristic
115C2×#11719949C2314yes—
116C2×#11719949C2314yes—
117C2×#11719945C2314yes—
118C2×#11719947C2314yes—
119C2×Q8×D53C2318yes—
120C22×D212C2314yes—
121C2×D4×D53C2318yes—
122C22×C4×D53C2311yescharacteristic
123C22×C4×D53C2312yes—
124#13133217C2312yes—
125#13133217C2318yes—
126#13133217C2312yes—
127#13133216C2318yes—
128#13133216C23116yes—
129#13133214C2312yes—
130#13133213C2318yes—
131#13133212C2318yes—
132#13133212C23116yes—
133#13133212C23116yes—
134#13133212C23116yes—
135#13133212C2318yes—
136#13133212C23116yes—
137#13133212C23116yes—
138#13133210C2318yes—
139#13133210C23116yes—
140#13133209C2312yes—
141#13133208C2314yes—
142#13133208C2314yes—
143#13133208C2314yes—
144#13133206C2318yes—
145#13133206C23116yes—
146#13133206C23116yes—
147#13133206C2318yes—
148#13133206C2314yes—
149#13133206C2314yes—
150#13133205C2318yes—
151#13133205C23116yes—
152#13133205C2314yes—
153#13133204C2314yes—
154#13133203C23116yes—
155#13133203C23116yes—
156#13133203C23116yes—
157#13133203C23116yes—
158#13133203C23116yes—
159#13133202C23116yes—
160#13133202C23116yes—
161#13133202C2318yes—
162#13133202C2318yes—
163#13133201C23116yes—
164#13133201C2318yes—
165#13133199C23116yes—
166#13133199C23116yes—
167#13133199C2318yes—
168#13133198C2314yes—
169#13133197C2318yes—
170#13133197C2314yes—
171#13133197C23116yes—
172#13133197C23116yes—
173#13133197C2314yes—
174#13133197C2314yes—
175#13133196C2314yes—
176#13133195C23116yes—
177#13133194C23116yes—
178#13133193C2318yes—
179#13133193C2314yes—
180#13133193C2314yes—
181#13133193C23116yes—
182#13133193C2314yes—
183#13133192C2314yes—
184#13133192C23116yes—
185#13133192C2314yes—
186#13133192C2318yes—
187#13133192C2314yes—
188#13133192C2314yes—
189#13133191C23116yes—
190#13133191C2318yes—
191#13133191C2314yes—
192#13133191C2314yes—
193#13133190C23116yes—
194#13133188C2314yes—
195#13133188C2318yes—
196#13133188C2314yes—
197#13133187C23116yes—
198#13133187C23116yes—
199#13133187C2318yes—
200#13133185C2318yes—
201#13133185C2318yes—
202#13133185C2314yes—
203Q8×Dic53C2318yes—
204Q8×Dic53C23116yes—
205Q8×Dic53C2314yes—
206Q8×Dic53C2314yes—
207Q8×Dic53C2314yes—
208C4×Dic106C2318yes—
209C4×Dic106C2314yes—
210C4×Dic106C23116yes—
211#13133182C2314yes—
212#13133182C23116yes—
213#13133182C2314yes—
214#13133182C2314yes—
215C4×D212C2318yes—
216C4×D212C2318yes—
217C4×D212C2318yes—
218C4×D212C23116yes—
219C4×D212C2314yes—
220C4×D212C2314yes—
221D4×Dic53C2314yes—
222D4×Dic53C2318yes—
223D4×Dic53C2314yes—
224#13133179C2318yes—
225#13133179C2314yes—
226#13133179C2314yes—
227#13133179C2314yes—
228#13133179C2314yes—
229#13133179C2318yes—
230#13133179C2318yes—
231C4×C22⋊D53C2318yes—
232C4×C22⋊D53C23116yes—
233#13133177C23116yes—
234#13133177C2318yes—
235#13133177C2318yes—
236#13133177C2318yes—
237#13133176C23116yes—
238#13133176C2314yes—
239#13133176C2314yes—
240#13133176C2312yes—
241#13133175C2318yes—
242#13133175C23116yes—
243#13133175C2318yes—
244#13133175C2314yes—
245#13133175C2314yes—
246#13133175C2318yes—
247#13133175C2318yes—
248#13133175C2314yes—
249#13133174C23116yes—
250#13133174C2318yes—
251#13133173C2318yes—
252C2×#11719921C23116yes—
253C22⋊C4×D53C23116yes—
254C22⋊C4×D53C23116yes—
255C2×C4×Dic53C2312yes—
256C2×C4×Dic53C2311yescharacteristic
257C2×C4×Dic53C2314yes—
258C42×D53C2312yes—
259C42×D53C2312yes—
260C42×D53C2312yes—
261C42×D53C2312yes—
262C42×D53C2318yes—
263C2×#41×C53C2312yes—
264C22×Q8×C53C2314yes—
265C4⋊Q8×C53C2312yes—
266C4⋊Q8×C53C2311yescharacteristic
267C4⋊Q8×C53C2312yes—
268C4⋊Q8×C53C2318yes—
269C4⋊Q8×C53C2318yes—
270#127×C53C2311yescharacteristic
271#126×C53C23116yes—
272#125×C53C2314yes—
273#124×C53C2318yes—
274#124×C53C2318yes—
275#124×C53C2312yes—
276#123×C53C2318yes—
277#123×C53C2318yes—
278C22⋊Q8×C53C2318yes—
279C22⋊Q8×C53C23116yes—
280C22⋊Q8×C53C2314yes—
281C22⋊Q8×C53C2314yes—
282#121×C53C2314yes—
283C4×Q8×C53C2318yes—
284C4×Q8×C53C2314yes—
285C4×Q8×C53C2314yes—
286C4×D4×C53C2318yes—
287C4×D4×C53C2314yes—
288#117×C53C2314yes—
289#117×C53C2314yes—
290C2×C42×C53C2311yescharacteristic
291C23×D53C2418yes—
292C23×D53C2411yescharacteristic
293#41×C53—44no—
294C2×Q8×C53—48no—
295C2×Q8×C53C2414yes—
296C2×Q8×C53C2414yes—
297C2×Q8×C53C2418yes—
298C2×Q8×C53C2412yes—
299C2×D4×C53C2414yes—
300C2×D4×C53C2414yes—
301C2×D4×C53C2412yes—
302C22×C4×C53C2412yes—
303C22×C4×C53C2411yescharacteristic
304C22×C4×C53C2414yes—
305C22×C4×C53C2418yes—
306C2×C22⋊D53C2418yes—
307C2×C22⋊D53C2418yes—
308C2×C22⋊D53C24116yes—
309C22×Dic53C2411yescharacteristic
310C22×Dic53C2412yes—
311C22×Dic53C2418yes—
312#11719949—48no—
313#11719949—48no—
314Q8×D53—416no—
315#11719947—48no—
316D4×D53—416no—
317#11719945—48no—
318C2×D212—48no—
319C2×D212C2414yes—
320C2×D212C2414yes—
321C2×D212C2414yes—
322C2×D212C2418yes—
323C2×D212C2418yes—
324C2×D212C2418yes—
325C2×C4×D53—44no—
326C2×C4×D53—42no—
327C2×C4×D53C2412yes—
328C2×C4×D53C2412yes—
329C2×C4×D53C2412yes—
330C2×C4×D53C2418yes—
331C2×C4×D53C2412yes—
332C2×C4×D53C2412yes—
333C2×C4×D53C2412yes—
334C2×C4×D53C2418yes—
335C2×C4×D53C2418yes—
336C2×C4×D53C24116yes—
337C2×Dic106C2414yes—
338C2×Dic106C2414yes—
339C2×Dic106C24116yes—
340C4⋊C4×C53C2414yes—
341C4⋊C4×C53C2414yes—
342C4⋊C4×C53C2414yes—
343C4⋊C4×C53C2414yes—
344C4⋊C4×C53C2414yes—
345C4⋊C4×C53C2418yes—
346C4⋊C4×C53C24116yes—
347C4⋊C4×C53C2418yes—
348C22⋊C4×C53C2418yes—
349C22⋊C4×C53C2418yes—
350C22⋊C4×C53C2418yes—
351C22⋊C4×C53C24116yes—
352C42×C53C2412yes—
353C42×C53C2411yescharacteristic
354C42×C53C2411yescharacteristic
355C42×C53C2418yes—
356C42×C53C2418yes—
357C22⋊Dic53C2418yes—
358C22⋊Dic53C2418yes—
359C22⋊Dic53C2418yes—
360C22⋊Dic53C2414yes—
361#11719921C2418yes—
362#11719921C2418yes—
363#11719921C24116yes—
364#11719921C24116yes—
365#11719921C2418yes—
366#11719921C2418yes—
367#11719921C24116yes—
368#11719921C24116yes—
369#11719921C2418yes—
370#11719921C2418yes—
371#11719921C2418yes—
372#11719921C2418yes—
373#11719921C2418yes—
374C4⋊Dic53C2414yes—
375C4⋊Dic53C2414yes—
376C4⋊Dic53C2418yes—
377C4⋊Dic53C2414yes—
378C4⋊Dic53C2418yes—
379C4⋊Dic53C2418yes—
380C4⋊Dic53C2414yes—
381C4⋊Dic53C24116yes—
382#11719919C2418yes—
383#11719919C2418yes—
384#11719919C2418yes—
385#11719919C2418yes—
386#11719919C24116yes—
387C4×Dic53C2412yes—
388C4×Dic53C2411yescharacteristic
389C4×Dic53C2412yes—
390C4×Dic53C2412yes—
391C4×Dic53C2412yes—
392C4×Dic53C2412yes—
393C4×Dic53C2411yescharacteristic
394C4×Dic53C2418yes—
395C4×Dic53C2418yes—
396C4×Dic53C2418yes—
397C4×Dic53C2414yes—
398C4×Dic53C24116yes—
399C4×Dic53C2418yes—
400C23×C53C2511yescharacteristic
401C23×C53C2514yes—
402C22×D53—41no—
403C22×D53—42no—
404C22×D53—48no—
405C22×D53—416no—
406C22×D53C2512yes—
407C22×D53C2518yes—
408Q8×C53—28no—
409Q8×C53—28no—
410Q8×C53—48no—
411Q8×C53—42no—
412D4×C53—28no—
413D4×C53—42no—
414D4×C53—44no—
415C2×C4×C53—24no—
416C2×C4×C53—22no—
417C2×C4×C53—28no—
418C2×C4×C53—48no—
419C2×C4×C53C2518yes—
420C2×C4×C53C2512yes—
421C2×C4×C53C2511yescharacteristic
422C2×C4×C53C2518yes—
423C2×C4×C53C2514yes—
424C2×C4×C53C2512yes—
425C2×C4×C53C2511yescharacteristic
426C22⋊D53—48no—
427C22⋊D53—416no—
428C22⋊D53—48no—
429C2×Dic53—41no—
430C2×Dic53—42no—
431C2×Dic53—48no—
432C2×Dic53C2518yes—
433C2×Dic53C2518yes—
434C2×Dic53C2512yes—
435C2×Dic53C2512yes—
436C2×Dic53C2512yes—
437D212—28no—
438D212—28no—
439D212—48no—
440D212—44no—
441D212—48no—
442D212—48no—
443C4×D53—24no—
444C4×D53—24no—
445C4×D53—24no—
446C4×D53—216no—
447C4×D53—42no—
448C4×D53—42no—
449C4×D53—42no—
450C4×D53—416no—
451C4×D53—48no—
452C4×D53—48no—
453Dic106—28no—
454Dic106—44no—
455Dic106—416no—
456#62841—531nomaximal, Sylow
457C22×C53—22no—
458C22×C53—28no—
459C22×C53—21no—
460C22×C53—24no—
461C22×C53C2611yescharacteristic
462C2×D53—28no—
463C2×D53—22no—
464C2×D53—22no—
465C2×D53—22no—
466C2×D53—28no—
467C2×D53—28no—
468C2×D53—44no—
469C2×D53—168no—
470C4×C53—28no—
471C4×C53—22no—
472C4×C53—21no—
473C4×C53—28no—
474C4×C53—24no—
475C4×C53#58512yes—
476C4×C53#58514yes—
477Dic53—28no—
478Dic53—28no—
479Dic53—22no—
480Dic53—22no—
481Dic53—22no—
482#3568—538no—
483#3550—532no—
484#3550D5311yescharacteristic, complemented
485#3549—531no—
486#3540—538no—
487#3540—534no—
488#3518—534no—
489#3518—534no—
490#3518—534no—
491#3514—534no—
492#3514—534no—
493#3514—534no—
494#3510—538no—
495#3510—534no—
496#3444—532no—
497#3444—531no—
498C2×C53—41no—
499C2×C53—44no—
500C2×C53C2×#58511yescharacteristic
501C2×C53C2×#58512yes—
502D53—42no—
503D53—48no—
504#563—538no—
505#563C2×D5314yescomplemented
506H(3,𝔽4)—538no—
507H(3,𝔽4)—534no—
508#560—538no—
509#559—5316no—
510#559—538no—
511#559—534no—
512#559C2×D5312yescomplemented
513Q82—534no—
514Q82C2×D5312yescomplemented
515#556—5316no—
516#556—534no—
517#556—538no—
518#556—5316no—
519#556—5316no—
520#556—538no—
521#556—534no—
522#556—538no—
523#556C2×D5314yescomplemented
524#555—538no—
525#555—532no—
526#555—538no—
527#555—534no—
528#555—538no—
529#551—5316no—
530#551—538no—
531#551—5316no—
532#551—5316no—
533#551—5316no—
534D4×Q8—534no—
535D4×Q8—534no—
536D4×Q8C2×D5314yescomplemented
537#548—538no—
538#548—538no—
539#548—538no—
540#546—538no—
541#546—538no—
542#546—538no—
543D42—532no—
544D42—534no—
545#542—538no—
546#542—5316no—
547#542—5316no—
548#542—538no—
549#542—538no—
550#542—538no—
551#542—5316no—
552#542—538no—
553#542C2×D5318yescomplemented
554#538—5316no—
555#538—5316no—
556#538—5316no—
557#536—538no—
558#536C2×D5314yescomplemented
559#535—534no—
560#535—538no—
561#533—532no—
562#533—532no—
563#533—532no—
564#533—538no—
565#533—534no—
566#533—531no—
567#533C2×D5312yescomplemented
568#532—532no—
569#532—532no—
570#532—532no—
571#532—532no—
572#532C2×D5311yescharacteristic
573#529—534no—
574#529—534no—
575#529—534no—
576#529—534no—
577#529—534no—
578#529—538no—
579#529—534no—
580#529—534no—
581#529—534no—
582#529—538no—
583#529—534no—
584#529—538no—
585C2×#124—534no—
586C2×#124—538no—
587#525—532no—
588#525—534no—
589#525—534no—
590#525—534no—
591#525—534no—
592#519—534no—
593#519—538no—
594#518—538no—
595#518—534no—
596C4×#41—532no—
597C4×#41—534no—
598C4×#41—534no—
599C4×#41—534no—
600C4×#41—534no—
601C22×C42—531no—
602C53#6284111yescharacteristic, complemented, Sylow
603C2×#41—534no—
604C2×#41—534no—
605C2×#41—534no—
606C2×#41—534no—
607C2×#41C22×D5312yes—
608C22×Q8—538no—
609C22×Q8C22×D5314yes—
610C22×D4—538no—
611C22×D4—534no—
612C23×C4—531no—
613C23×C4—532no—
614C4⋊Q8—538no—
615C4⋊Q8—5316no—
616C4⋊Q8—532no—
617C4⋊Q8—532no—
618C4⋊Q8—538no—
619C4⋊Q8C22×D5312yes—
620C4⋊Q8C22×D5312yes—
621C4⋊Q8C22×D5311yescharacteristic
622C4⋊Q8C22×D5318yes—
623C4⋊Q8C22×D5318yes—
624#127—538no—
625#127—532no—
626#127C22×D5311yescharacteristic
627#126—538no—
628#126—538no—
629#126—5316no—
630#126—5316no—
631#126—5316no—
632#126—5316no—
633#126—5316no—
634#126—538no—
635#126—5316no—
636#126C22×D53116yes—
637#125—534no—
638#125—534no—
639#125—534no—
640#125—532no—
641#125C22×D5314yes—
642#124—534no—
643#124—534no—
644#124—5316no—
645#124—538no—
646#124—538no—
647#124—5316no—
648#124—534no—
649#124—5316no—
650#124—5316no—
651#124—5316no—
652#124—5316no—
653#124—5316no—
654#124—538no—
655#124—534no—
656#124—5316no—
657#124C22×D5318yes—
658#124C22×D5312yes—
659#124C22×D5318yes—
660#123—534no—
661#123—538no—
662#123—538no—
663#123—5316no—
664#123—5316no—
665#123—538no—
666#123—538no—
667#123—5316no—
668#123—5316no—
669#123—5316no—
670#123C22×D5318yes—
671#123C22×D5318yes—
672C22⋊Q8—534no—
673C22⋊Q8—534no—
674C22⋊Q8—534no—
675C22⋊Q8—538no—
676C22⋊Q8—5316no—
677C22⋊Q8—534no—
678C22⋊Q8—534no—
679C22⋊Q8—534no—
680C22⋊Q8—534no—
681C22⋊Q8—538no—
682C22⋊Q8—5316no—
683C22⋊Q8—5316no—
684C22⋊Q8—5316no—
685C22⋊Q8—5316no—
686C22⋊Q8C22×D5314yes—
687C22⋊Q8C22×D5314yes—
688C22⋊Q8C22×D5318yes—
689C22⋊Q8C22×D53116yes—
690#121—534no—
691#121—534no—
692#121—538no—
693#121—534no—
694#121—534no—
695#121—538no—
696#121—5316no—
697#121—534no—
698#121—534no—
699#121—534no—
700#121—534no—
701#121—538no—
702#121—5316no—
703#121—5316no—
704#121C22×D5314yes—
705#120—534no—
706#120—538no—
707#120—538no—
708#120—538no—
709#120—5316no—
710#120—5316no—
711C4×Q8—534no—
712C4×Q8—534no—
713C4×Q8—534no—
714C4×Q8—538no—
715C4×Q8—5316no—
716C4×Q8—534no—
717C4×Q8—534no—
718C4×Q8—534no—
719C4×Q8—5316no—
720C4×Q8—534no—
721C4×Q8—538no—
722C4×Q8—5316no—
723C4×Q8C22×D5314yes—
724C4×Q8C22×D5314yes—
725C4×Q8C22×D5318yes—
726C4×D4—534no—
727C4×D4—538no—
728C4×D4—534no—
729C4×D4—538no—
730C4×D4—5316no—
731C4×D4—534no—
732C4×D4—534no—
733C4×D4—538no—
734C4×D4—538no—
735C4×D4—534no—
736C4×D4—534no—
737C4×D4—538no—
738C4×D4—538no—
739C4×D4—538no—
740C4×D4—538no—
741C4×D4—5316no—
742C4×D4—538no—
743C4×D4—538no—
744C4×D4—534no—
745C4×D4—534no—
746C4×D4—5316no—
747C4×D4—538no—
748C4×D4C22×D5314yes—
749C4×D4C22×D5318yes—
750#117—534no—
751#117—532no—
752#117—5316no—
753#117—534no—
754#117—534no—
755#117—534no—
756#117—534no—
757#117—538no—
758#117—538no—
759#117—538no—
760#117—5316no—
761#117—538no—
762#117—538no—
763#117—538no—
764#117—5316no—
765#117C22×D5314yes—
766#117C22×D5314yes—
767C2×C22⋊C4—5316no—
768C2×C22⋊C4—5316no—
769C2×C22⋊C4—5316no—
770C2×C42—534no—
771C2×C42—531no—
772C2×C42—532no—
773C2×C42—538no—
774C2×C42—532no—
775C2×C42—532no—
776C2×C42—532no—
777C2×C42—532no—
778C2×C42C22×D5311yescharacteristic
779C24—538no—
780C24—531no—
781#41—44no—
782#41—2128no—
783#41—2128no—
784#41—2128no—
785#41—2128no—
786C2×Q8—48no—
787C2×Q8—534no—
788C2×Q8—5316no—
789C2×Q8—534no—
790C2×Q8—21216no—
791C2×Q8C23×D5314yes—
792C2×Q8C23×D5314yes—
793C2×Q8C23×D5318yes—
794C2×Q8C23×D5312yes—
795C2×D4—538no—
796C2×D4—538no—
797C2×D4—5316no—
798C2×D4—534no—
799C2×D4—534no—
800C2×D4—534no—
801C2×D4—538no—
802C2×D4—538no—
803C2×D4—538no—
804C2×D4—2128no—
805C2×D4—21216no—
806C2×D4C23×D5314yes—
807C2×D4C23×D5312yes—
808C2×D4C23×D5314yes—
809C22×C4—531no—
810C22×C4—532no—
811C22×C4—538no—
812C22×C4—532no—
813C22×C4—532no—
814C22×C4—532no—
815C22×C4—538no—
816C22×C4—532no—
817C22×C4—532no—
818C22×C4—532no—
819C22×C4—538no—
820C22×C4—538no—
821C22×C4—5316no—
822C22×C4—2122no—
823C22×C4—2124no—
824C22×C4C23×D5311yescharacteristic
825C22×C4C23×D5312yes—
826C22×C4C23×D5314yes—
827C22×C4C23×D5318yes—
828C4⋊C4—534no—
829C4⋊C4—534no—
830C4⋊C4—534no—
831C4⋊C4—538no—
832C4⋊C4—538no—
833C4⋊C4—538no—
834C4⋊C4—538no—
835C4⋊C4—538no—
836C4⋊C4—538no—
837C4⋊C4—534no—
838C4⋊C4—538no—
839C4⋊C4—5316no—
840C4⋊C4—5316no—
841C4⋊C4C23×D5314yes—
842C4⋊C4C23×D5314yes—
843C4⋊C4C23×D5314yes—
844C4⋊C4C23×D5318yes—
845C4⋊C4C23×D5318yes—
846C4⋊C4C23×D53116yes—
847C4⋊C4C23×D5314yes—
848C4⋊C4C23×D5314yes—
849C22⋊C4—538no—
850C22⋊C4—538no—
851C22⋊C4—538no—
852C22⋊C4—534no—
853C22⋊C4—538no—
854C22⋊C4—538no—
855C22⋊C4—538no—
856C22⋊C4—538no—
857C22⋊C4—5316no—
858C22⋊C4—5316no—
859C22⋊C4—5316no—
860C22⋊C4—5316no—
861C22⋊C4—538no—
862C22⋊C4—538no—
863C22⋊C4—538no—
864C22⋊C4—538no—
865C22⋊C4—538no—
866C22⋊C4C23×D5318yes—
867C22⋊C4C23×D53116yes—
868C22⋊C4C23×D5318yes—
869C22⋊C4C23×D5318yes—
870C42—531no—
871C42—532no—
872C42—531no—
873C42—532no—
874C42—532no—
875C42—532no—
876C42—532no—
877C42—538no—
878C42—538no—
879C42—538no—
880C42—534no—
881C42—5316no—
882C42—538no—
883C42C23×D5311yescharacteristic
884C42C23×D5312yes—
885C42C23×D5311yescharacteristic
886C42C23×D5318yes—
887C42C23×D5318yes—
888C23—538no—
889C23—532no—
890C23—2128no—
891C23—21216no—
892C23—2121no—
893C23—2122no—
894C23C24×D5314yes—
895C23C24×D5311yescharacteristic
896Q8—28no—
897Q8—28no—
898Q8—48no—
899Q8—42no—
900Q8—1068no—
901Q8—21216no—
902Q8—2124no—
903D4—28no—
904D4—42no—
905D4—44no—
906D4—1068no—
907D4—1068no—
908D4—2128no—
909D4—2128no—
910D4—2124no—
911D4—2128no—
912D4—21216no—
913D4—2128no—
914D4—2128no—
915C2×C4—22no—
916C2×C4—28no—
917C2×C4—24no—
918C2×C4—48no—
919C2×C4—532no—
920C2×C4—532no—
921C2×C4—532no—
922C2×C4—538no—
923C2×C4—538no—
924C2×C4—1064no—
925C2×C4—1064no—
926C2×C4—1064no—
927C2×C4—10616no—
928C2×C4—2122no—
929C2×C4—2122no—
930C2×C4—2122no—
931C2×C4—21216no—
932C2×C4—2128no—
933C2×C4—2128no—
934C2×C4—2121no—
935C2×C4—2122no—
936C2×C4—2128no—
937C2×C4C24×D5314yes—
938C2×C4C24×D5318yes—
939C2×C4C24×D5311yescharacteristic
940C2×C4C24×D5312yes—
941C2×C4C24×D5318yes—
942C2×C4C24×D5311yescharacteristic
943C2×C4C24×D5312yes—
944C22—24no—
945C22—21no—
946C22—22no—
947C22—28no—
948C22—8488no—
949C22—1062no—
950C22—1068no—
951C22—1068no—
952C22—1062no—
953C22—1062no—
954C22—1068no—
955C22—2124no—
956C22C25×D5311yescharacteristic
957C4—21no—
958C4—24no—
959C4—28no—
960C4—22no—
961C4—28no—
962C4—1062no—
963C4—1062no—
964C4—1062no—
965C4—1068no—
966C4—1068no—
967C4#1681145812yes—
968C4#1681146014yes—
969C2—44no—
970C2—41no—
971C2—2128no—
972C2—2122no—
973C2C2×#1681145811yescharacteristic
974C2C2×#1681146012yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3550C2
hypercenter#3550D53
hypocenterC53#62841
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #20289412C2semidirect
2. #20289126C2semidirect
3. #20289120C2semidirect
4. #20288992C2semidirect
5. #20288987C2semidirect
6. #20288733C2semidirect
7. #20288729C2semidirect
8. #20288727C2semidirect
9. #20288679C2semidirect
10. #20288677C2semidirect
11. #20288675C2semidirect
12. #20288614C2semidirect
13. #20288607C2semidirect
14. #20288012C2semidirect
15. #20288010C2semidirect
16. C53×#3550C2semidirect
17. #16811377C22semidirect
18. #16811365C22semidirect
19. #16811365C22semidirect
20. #16811363C22semidirect
21. #16811358C22semidirect
22. #16811357C22semidirect
23. #16811355C22semidirect
24. Q8×Dic106C22semidirect
25. #16811347C22semidirect
26. #16811347C22semidirect
27. #16811347C22semidirect
28. #16811346C22semidirect
29. #16811346C22semidirect
30. #16811344C22semidirect
31. #16811344C22semidirect
32. #16811340C22semidirect
33. #16811339C22semidirect
34. #16811339C22semidirect
35. #16811338C22semidirect
36. #16811338C22semidirect
37. #16811336C22semidirect
38. #16811303C22semidirect
39. #16811300C22semidirect
40. #16811298C22semidirect
41. #16811296C22semidirect
42. #16811296C22semidirect
43. Q8×D212C22semidirect
44. #16811288C22semidirect
45. #16811285C22semidirect
46. #16811284C22semidirect
47. #16811281C22semidirect
48. #16811268C22semidirect
49. #16811266C22semidirect
50. #16811264C22semidirect
51. D4×D212C22semidirect
52. #16811258C22semidirect
53. #16811247C22semidirect
54. #16811247C22semidirect
55. #16811246C22semidirect
56. #16811246C22semidirect
57. #16811246C22semidirect
58. #16811244C22semidirect
59. #16811242C22semidirect
60. #16811239C22semidirect
61. #16811213C22semidirect
62. #16811212C22semidirect
63. #16811209C22semidirect
64. #16811196C22semidirect
67. #16811180C22semidirect
68. #16811178C22semidirect
69. #16811178C22semidirect
70. #16811178C22semidirect
71. #16811178C22semidirect
72. #16811176C22semidirect
77. #16811160C22semidirect
78. #16811160C22semidirect
79. #16811160C22semidirect
80. #16811159C22semidirect
81. #16811159C22semidirect
82. #16811159C22semidirect
83. #16811158C22semidirect
84. #16811158C22semidirect
85. #16811155C22semidirect
86. #16811155C22semidirect
87. #16811154C22semidirect
88. #16811152C22semidirect
89. C2×#13133206C22semidirect
90. #124×D53C22semidirect
91. #16811136C22semidirect
92. #16811136C22semidirect
93. #16811135C22semidirect
94. #16811133C22semidirect
95. #16811130C22semidirect
96. #16811101C22semidirect
97. #16811099C22semidirect
98. #16811097C22semidirect
99. #16811095C22semidirect
100. #41×Dic53C22semidirect
101. C4×#11719949C22semidirect
102. C4×#11719949C22semidirect
103. #16811091C22semidirect
104. C4×#11719947C22semidirect
105. C2×C42×D53C22semidirect
106. C53×#563C22semidirect
107. C53×#559C22semidirect
108. Q82×C53C22semidirect
109. C53×#556C22semidirect
110. D4×Q8×C53C22semidirect
111. C53×#542C22semidirect
112. C53×#536C22semidirect
113. C53×#533C22semidirect
484. #3550D53semidirect
505. #563C2×D53semidirect
512. #559C2×D53semidirect
514. Q82C2×D53semidirect
523. #556C2×D53semidirect
536. D4×Q8C2×D53semidirect
553. #542C2×D53semidirect
558. #536C2×D53semidirect
567. #533C2×D53semidirect
602. C53#62841semidirect

Maximal subgroups

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

subgroupindex
#202894122
#202891262
#202891202
#202889922
#202889872
#202887332
#202887292
#202887272
#202886792
#202886772
#202886752
#202886142
#202886072
#202880122
#202880102
C53×#35502
#6284153