Finite Group Databasebeta

← #28293098

Subgroups — #28293098

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#20289411C218yesmaximal, complemented
2#20289129C211yesmaximal, characteristic, complemented
3#20289126C212yesmaximal, complemented
4#20289120C211yesmaximal, characteristic, complemented
5#20288990C214yesmaximal, complemented
6#20288983C218yesmaximal, complemented
7#20288732C214yesmaximal, complemented
8#20288730C214yesmaximal, complemented
9#20288724C214yesmaximal, complemented
10#20288678C214yesmaximal, complemented
11#20288676C214yesmaximal, complemented
12#20288671C214yesmaximal, complemented
13#20288611C214yesmaximal, complemented
14#20288604C218yesmaximal, complemented
15#20288011C212yesmaximal, complemented
16C53×#3444C211yesmaximal, characteristic, complemented
17#16811377C2218yescomplemented
18#16811373C2214yescomplemented
19#16811366C2218yescomplemented
20#16811365C2214yescomplemented
21#16811362C2218yescomplemented
22#16811359C2212yescomplemented
23#16811358C2214yescomplemented
24#16811357C2218yescomplemented
25#16811356C22116yescomplemented
26Q8×Dic106C2214yescomplemented
27#16811353C2212yescomplemented
28#16811347C2214yescomplemented
29#16811346C2214yescomplemented
30#16811345C22116yescomplemented
31#16811344C2218yescomplemented
32#16811343C2214yescomplemented
33#16811343C2218yescomplemented
34#16811341C22116yescomplemented
35#16811341C2218yescomplemented
36#16811340C22116yescomplemented
37#16811339C2212yescomplemented
38#16811338C2214yescomplemented
39#16811338C2218yescomplemented
40#16811337C2218yescomplemented
41#16811336C2218yescomplemented
42#16811302C22116yescomplemented
43#16811302C22116yescomplemented
44#16811301C2218yescomplemented
45#16811298C22116yescomplemented
46#16811297C22116yescomplemented
47Q8×D212C2214yescomplemented
48D4×Dic106C2214yescomplemented
49#16811288C2214yescomplemented
50#16811283C2218yescomplemented
51#16811282C2218yescomplemented
52#16811280C2218yescomplemented
53#16811270C2218yescomplemented
54#16811269C2218yescomplemented
55#16811261C2218yescomplemented
56D4×D212C2214yescomplemented
57#16811258C2212yescomplemented
58#16811246C2218yescomplemented
59#16811245C2218yescomplemented
60#16811244C2218yescomplemented
61#16811244C2218yescomplemented
62#16811243C22116yescomplemented
63#16811241C22116yescomplemented
64#16811240C2218yescomplemented
65#16811238C2218yescomplemented
66#16811238C22116yescomplemented
67#16811209C22116yescomplemented
68#16811206C22116yescomplemented
69#16811205C22116yescomplemented
70#16811196C2218yescomplemented
71#16811194C2214yescomplemented
72#16811189C2218yes—
73#16811187C2214yes—
74#16811180C2212yescomplemented
75#16811180C2212yescomplemented
76#16811180C2212yescomplemented
77#16811180C2214yescomplemented
78#16811179C2218yescomplemented
79#16811173C2212yes—
80#16811173C2212yes—
81#16811173C2212yes—
82#16811158C2218yescomplemented
83#16811157C2214yescomplemented
84#16811157C2214yescomplemented
85#16811157C2214yescomplemented
86#16811157C2214yescomplemented
87#16811157C2214yescomplemented
88#16811157C2214yescomplemented
89#16811157C2218yescomplemented
90#16811152C2218yescomplemented
91C2×#13133205C2214yescomplemented
92#124×D53C2218yescomplemented
93#16811134C2214yescomplemented
94#16811134C2214yescomplemented
95#16811134C2214yescomplemented
96#16811100C2214yescomplemented
97#16811099C2218yescomplemented
98#16811097C2214yescomplemented
99#16811095C2218yescomplemented
100C4×#11719945C2214yescomplemented
101C4×#11719945C2214yescomplemented
102C4×#11719945C2214yescomplemented
103C53×#533C2211yescharacteristic, complemented
104C53×#533C2212yescomplemented
105C53×#532C2211yescharacteristic
106C53×#532C2212yes—
107C53×#529C2214yescomplemented
108C53×#529C2214yescomplemented
109C53×#529C2214yescomplemented
110C53×#525C2214yescomplemented
111C53×#525C2212yescomplemented
112C4×#41×C53C2212yescomplemented
113C4×#41×C53C2214yescomplemented
114C22×C42×C53C2211yescharacteristic, complemented
115C2×#11719945C2314yes—
116C2×#11719945C2314yes—
117C2×#11719945C2314yes—
118C22×Dic106C2314yes—
119C2×Q8×D53C2318yes—
120C22×D212C2314yes—
121C2×D4×D53C2318yes—
122#13133217C2312yes—
123#13133217C2312yes—
124#13133217C2318yes—
125#13133217C2312yes—
126#13133216C2318yes—
127#13133216C2318yes—
128#13133216C23116yes—
129#13133215C2318yes—
130#13133214C2312yes—
131#13133213C2318yes—
132#13133212C23116yes—
133#13133212C23116yes—
134#13133212C23116yes—
135#13133211C2318yes—
136#13133211C2318yes—
137#13133211C23116yes—
138#13133210C23116yes—
139#13133210C23116yes—
140#13133210C23116yes—
141#13133209C2314yes—
142#13133209C2314yes—
143#13133209C2314yes—
144#13133206C2318yes—
145#13133206C2318yes—
146#13133205C2318yes—
147#13133205C23116yes—
148#13133205C2314yes—
149#13133205C2314yes—
150#13133205C2314yes—
151#13133204C2318yes—
152#13133204C23116yes—
153#13133204C2318yes—
154#13133203C23116yes—
155#13133203C23116yes—
156#13133203C23116yes—
157#13133203C23116yes—
158#13133203C23116yes—
159#13133203C23116yes—
160#13133202C23116yes—
161#13133202C23116yes—
162#13133200C23116yes—
163#13133200C2318yes—
164#13133200C2318yes—
165#13133200C2318yes—
166#13133199C23116yes—
167#13133199C23116yes—
168#13133198C2318yes—
169#13133198C2318yes—
170#13133197C2318yes—
171#13133197C23116yes—
172#13133196C2318yes—
173#13133196C2314yes—
174#13133196C23116yes—
175#13133196C2314yes—
176#13133196C2314yes—
177#13133196C2314yes—
178#13133196C2314yes—
179#13133196C2314yes—
180#13133195C23116yes—
181#13133195C23116yes—
182#13133195C23116yes—
183#13133194C23116yes—
184#13133193C2318yes—
185#13133192C2318yes—
186#13133191C2314yes—
187#13133191C2318yes—
188#13133191C2314yes—
189#13133191C2314yes—
190#13133191C2314yes—
191#13133191C2314yes—
192#13133191C2314yes—
193#13133190C23116yes—
194#13133189C23116yes—
195#13133188C23116yes—
196#13133188C2318yes—
197#13133187C23116yes—
198#13133186C2318yes—
199#13133185C23116yes—
200#13133185C2318yes—
201#13133185C2318yes—
202Q8×Dic53C2318yes—
203C4×Dic106C2318yes—
204C4×Dic106C2314yes—
205C4×Dic106C2314yes—
206C4×Dic106C2314yes—
207C4×Dic106C2314yes—
208C4×Dic106C23116yes—
209C4×Dic106C2314yes—
210C4×Dic106C2314yes—
211#13133182C2318yes—
212#13133182C23116yes—
213#13133182C23116yes—
214C4×D212C2318yes—
215C4×D212C2314yes—
216C4×D212C2314yes—
217C4×D212C2314yes—
218C4×D212C2314yes—
219C4×D212C2314yes—
220C4×D212C2314yes—
221D4×Dic53C2318yes—
222#13133179C2318yes—
223#13133179C23116yes—
224C4×C22⋊D53C2318yes—
225C4×C22⋊D53C23116yes—
226C4×C22⋊D53C2318yes—
227C4×C22⋊D53C2318yes—
228C4×C22⋊D53C2318yes—
229C4×C22⋊D53C2318yes—
230C4×C22⋊D53C2318yes—
231#13133177C23116yes—
232#13133176C2314yes—
233#13133176C2314yes—
234#13133176C2314yes—
235#13133176C2314yes—
236#13133176C2314yes—
237#13133175C23116yes—
238#13133175C2318yes—
239#13133175C2318yes—
240#13133174C23116yes—
241#13133174C2318yes—
242#13133174C2318yes—
243#13133174C2318yes—
244#13133173C23116yes—
245C2×#11719921C23116yes—
246C22⋊C4×D53C23116yes—
247C22⋊C4×D53C23116yes—
248C42×D53C2318yes—
249C2×#41×C53C2314yes—
250C2×#41×C53C2312yes—
251C23×C4×C53C2312yes—
252C23×C4×C53C2311yescharacteristic
253C4⋊Q8×C53C2312yes—
254C4⋊Q8×C53C2311yescharacteristic
255#127×C53C2311yescharacteristic
256#126×C53C2318yes—
257#125×C53C2312yes—
258#125×C53C2314yes—
259#124×C53C2312yes—
260#124×C53C2314yes—
261#123×C53C2314yes—
262#123×C53C2318yes—
263C22⋊Q8×C53C2314yes—
264C22⋊Q8×C53C2314yes—
265C22⋊Q8×C53C2314yes—
266#121×C53C2314yes—
267#121×C53C2314yes—
268#121×C53C2314yes—
269#120×C53C2314yes—
270C4×Q8×C53C2314yes—
271C4×Q8×C53C2314yes—
272C4×Q8×C53C2314yes—
273C4×D4×C53C2318yes—
274C4×D4×C53C2314yes—
275C4×D4×C53C2314yes—
276C4×D4×C53C2318yes—
277C4×D4×C53C2318yes—
278C4×D4×C53C2314yes—
279#117×C53C2318yes—
280#117×C53C2314yes—
281#117×C53C2312yes—
282#117×C53C2314yes—
283C2×C42×C53C2311yescharacteristic
284C2×C42×C53C2312yes—
285C2×C42×C53C2312yes—
286C2×C42×C53C2312yes—
287C2×C42×C53C2312yes—
288C2×C42×C53C2312yes—
289C2×C42×C53C2311yescharacteristic
290C2×C42×C53C2314yes—
291C24×C53C2411yescharacteristic
292C23×D53C2418yes—
293#41×C53—44no—
294#41×C53—48no—
295C2×Q8×C53C2414yes—
296C2×Q8×C53C2412yes—
297C2×D4×C53C2414yes—
298C2×D4×C53C2418yes—
299C2×D4×C53C2414yes—
300C2×D4×C53C2412yes—
301C22×C4×C53—44no—
302C22×C4×C53—42no—
303C22×C4×C53C2412yes—
304C22×C4×C53C2411yescharacteristic
305C22×C4×C53C2412yes—
306C22×C4×C53C2412yes—
307C22×C4×C53C2412yes—
308C22×C4×C53C2414yes—
309C22×C4×C53C2412yes—
310C22×C4×C53C2412yes—
311C22×C4×C53C2412yes—
312C22×C4×C53C2411yescharacteristic
313C22×C4×C53C2412yes—
314C22×C4×C53C2418yes—
315C2×C22⋊D53C24116yes—
316C2×C22⋊D53C2418yes—
317C2×C22⋊D53C2418yes—
318C2×C22⋊D53C2418yes—
319C22×Dic53C2418yes—
320Q8×D53—416no—
321D4×D53—416no—
322#11719945—48no—
323#11719945—48no—
324#11719945—48no—
325C2×D212—48no—
326C2×D212C2414yes—
327C2×D212C2414yes—
328C2×D212C2418yes—
329C2×D212C2414yes—
330C2×C4×D53C2418yes—
331C2×C4×D53C2418yes—
332C2×C4×D53C2418yes—
333C2×C4×D53C24116yes—
334C2×Dic106—48no—
335C2×Dic106C2414yes—
336C2×Dic106C2414yes—
337C2×Dic106C2418yes—
338C2×Dic106C24116yes—
339C2×Dic106C2414yes—
340C4⋊C4×C53C2414yes—
341C4⋊C4×C53C2414yes—
342C4⋊C4×C53C2414yes—
343C4⋊C4×C53C2418yes—
344C4⋊C4×C53C2418yes—
345C4⋊C4×C53C2418yes—
346C22⋊C4×C53C2418yes—
347C22⋊C4×C53C2414yes—
348C22⋊C4×C53C2418yes—
349C22⋊C4×C53C2418yes—
350C22⋊C4×C53C2418yes—
351C42×C53C2411yescharacteristic
352C42×C53C2411yescharacteristic
353C42×C53C2412yes—
354C42×C53C2412yes—
355C42×C53C2412yes—
356C42×C53C2412yes—
357C42×C53C2412yes—
358C42×C53C2411yescharacteristic
359C42×C53C2412yes—
360C42×C53C2411yescharacteristic
361C42×C53C2418yes—
362C42×C53C2414yes—
363C22⋊Dic53C2418yes—
364C22⋊Dic53C24116yes—
365C22⋊Dic53C2418yes—
366C22⋊Dic53C2418yes—
367C22⋊Dic53C2418yes—
368C22⋊Dic53C2418yes—
369#11719921C2418yes—
370#11719921C2418yes—
371#11719921C24116yes—
372#11719921C24116yes—
373#11719921C2418yes—
374#11719921C2418yes—
375#11719921C24116yes—
376#11719921C24116yes—
377#11719921C2418yes—
378#11719921C2418yes—
379C4⋊Dic53C2414yes—
380C4⋊Dic53C2414yes—
381C4⋊Dic53C24116yes—
382C4⋊Dic53C2414yes—
383C4⋊Dic53C2414yes—
384C4⋊Dic53C2414yes—
385C4⋊Dic53C2414yes—
386#11719919C2418yes—
387#11719919C24116yes—
388#11719919C2418yes—
389#11719919C2418yes—
390#11719919C2418yes—
391#11719919C2418yes—
392#11719919C2418yes—
393#11719919C24116yes—
394C4×Dic53C2418yes—
395C4×Dic53C2418yes—
396C4×Dic53C2418yes—
397C4×Dic53C24116yes—
398C4×Dic53C2418yes—
399C4×Dic53C2418yes—
400C23×C53—42no—
401C23×C53—41no—
402C23×C53C2514yes—
403C23×C53C2512yes—
404C23×C53C2511yescharacteristic
405C22×D53—48no—
406C22×D53—416no—
407C22×D53C2518yes—
408Q8×C53—28no—
409Q8×C53—42no—
410D4×C53—28no—
411D4×C53—48no—
412D4×C53—44no—
413D4×C53—42no—
414C2×C4×C53—28no—
415C2×C4×C53—24no—
416C2×C4×C53—24no—
417C2×C4×C53—24no—
418C2×C4×C53—24no—
419C2×C4×C53—22no—
420C2×C4×C53—42no—
421C2×C4×C53—42no—
422C2×C4×C53—41no—
423C2×C4×C53—42no—
424C2×C4×C53—42no—
425C2×C4×C53—48no—
426C2×C4×C53C2518yes—
427C2×C4×C53C2512yes—
428C2×C4×C53C2514yes—
429C2×C4×C53C2512yes—
430C2×C4×C53C2512yes—
431C2×C4×C53C2512yes—
432C2×C4×C53C2511yescharacteristic
433C2×C4×C53C2511yescharacteristic
434C2×C4×C53C2512yes—
435C22⋊D53—48no—
436C22⋊D53—48no—
437C22⋊D53—48no—
438C22⋊D53—416no—
439C2×Dic53—48no—
440C2×Dic53C2518yes—
441C2×Dic53C2518yes—
442C2×Dic53C2518yes—
443D212—28no—
444D212—28no—
445D212—48no—
446D212—44no—
447C4×D53—216no—
448C4×D53—48no—
449C4×D53—48no—
450C4×D53—416no—
451Dic106—28no—
452Dic106—28no—
453Dic106—48no—
454Dic106—44no—
455Dic106—416no—
456#62841—531nomaximal, Sylow
457C22×C53—24no—
458C22×C53—22no—
459C22×C53—22no—
460C22×C53—22no—
461C22×C53—28no—
462C22×C53—22no—
463C22×C53—21no—
464C22×C53—44no—
465C22×C53C2611yescharacteristic
466C2×D53—28no—
467C2×D53—28no—
468C2×D53—28no—
469C2×D53—168no—
470C4×C53—28no—
471C4×C53—22no—
472C4×C53—24no—
473C4×C53—22no—
474C4×C53—22no—
475C4×C53—22no—
476C4×C53—21no—
477C4×C53#58512yes—
478C4×C53#58514yes—
479Dic53—28no—
480Dic53—28no—
481Dic53—28no—
482#3568—538no—
483#3550—532no—
484#3550—531no—
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#3444D5311yescharacteristic, complemented
498C2×C53—44no—
499C2×C53—42no—
500C2×C53—41no—
501C2×C53C2×#58512yes—
502C2×C53C2×#58511yescharacteristic
503D53—48no—
504#563—538no—
505#563—534no—
506H(3,𝔽4)—534no—
507H(3,𝔽4)—538no—
508#560—538no—
509#559—532no—
510#559—538no—
511#559—534no—
512#559—5316no—
513Q82—532no—
514Q82—534no—
515#556—534no—
516#556—5316no—
517#556—538no—
518#556—5316no—
519#556—534no—
520#556—534no—
521#556—538no—
522#556—5316no—
523#556—538no—
524#555—532no—
525#555—538no—
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×Q8—534no—
537#548—538no—
538#548—538no—
539#548—538no—
540#546—538no—
541#546—538no—
542#546—538no—
543D42—532no—
544D42—534no—
545#542—5316no—
546#542—538no—
547#542—5316no—
548#542—538no—
549#542—538no—
550#542—538no—
551#542—5316no—
552#542—538no—
553#542—538no—
554#538—5316no—
555#538—5316no—
556#538—5316no—
557#536—534no—
558#536—538no—
559#535—534no—
560#535—538no—
561#533—538no—
562#533—532no—
563#533—532no—
564#533—532no—
565#533—534no—
566#533C2×D5312yescomplemented
567#533C2×D5311yescharacteristic, complemented
568#532—532no—
569#532—532no—
570#532—532no—
571#532C2×D5312yes—
572#532C2×D5311yescharacteristic
573#529—538no—
574#529—538no—
575#529—534no—
576#529—534no—
577#529—534no—
578#529—534no—
579#529—534no—
580#529—534no—
581#529—538no—
582#529C2×D5314yescomplemented
583#529C2×D5314yescomplemented
584#529C2×D5314yescomplemented
585C2×#124—538no—
586C2×#124—534no—
587#525—534no—
588#525—534no—
589#525—534no—
590#525C2×D5312yescomplemented
591#525C2×D5314yescomplemented
592#519—538no—
593#519—534no—
594#518—538no—
595#518—534no—
596C4×#41—534no—
597C4×#41—534no—
598C4×#41—534no—
599C4×#41C2×D5312yescomplemented
600C4×#41C2×D5314yescomplemented
601C22×C42C2×D5311yescharacteristic, complemented
602C53#6284111yescharacteristic, complemented, Sylow
603C2×#41—534no—
604C2×#41—534no—
605C2×#41—534no—
606C2×#41C22×D5312yes—
607C2×#41C22×D5314yes—
608C22×Q8—538no—
609C22×Q8—534no—
610C22×D4—538no—
611C22×D4—534no—
612C23×C4C22×D5312yes—
613C23×C4C22×D5311yescharacteristic
614C4⋊Q8—538no—
615C4⋊Q8—538no—
616C4⋊Q8—538no—
617C4⋊Q8—5316no—
618C4⋊Q8—532no—
619C4⋊Q8—532no—
620C4⋊Q8—532no—
621C4⋊Q8—538no—
622C4⋊Q8C22×D5312yes—
623C4⋊Q8C22×D5311yescharacteristic
624#127—538no—
625#127—532no—
626#127C22×D5311yescharacteristic
627#126—5316no—
628#126—5316no—
629#126—5316no—
630#126—5316no—
631#126—5316no—
632#126—5316no—
633#126—538no—
634#126—538no—
635#126—5316no—
636#126C22×D5318yes—
637#125—534no—
638#125—534no—
639#125—534no—
640#125C22×D5314yes—
641#125C22×D5312yes—
642#124—538no—
643#124—538no—
644#124—538no—
645#124—538no—
646#124—5316no—
647#124—5316no—
648#124—5316no—
649#124—5316no—
650#124—5316no—
651#124—5316no—
652#124—5316no—
653#124—534no—
654#124—534no—
655#124—5316no—
656#124—538no—
657#124—534no—
658#124C22×D5314yes—
659#124C22×D5312yes—
660#123—538no—
661#123—538no—
662#123—538no—
663#123—538no—
664#123—538no—
665#123—5316no—
666#123—5316no—
667#123—5316no—
668#123—5316no—
669#123—5316no—
670#123C22×D5318yes—
671#123C22×D5314yes—
672C22⋊Q8—538no—
673C22⋊Q8—534no—
674C22⋊Q8—534no—
675C22⋊Q8—534no—
676C22⋊Q8—534no—
677C22⋊Q8—534no—
678C22⋊Q8—534no—
679C22⋊Q8—538no—
680C22⋊Q8—5316no—
681C22⋊Q8—538no—
682C22⋊Q8—5316no—
683C22⋊Q8—5316no—
684C22⋊Q8—5316no—
685C22⋊Q8—5316no—
686C22⋊Q8—5316no—
687C22⋊Q8C22×D5314yes—
688C22⋊Q8C22×D5314yes—
689C22⋊Q8C22×D5314yes—
690#121—538no—
691#121—5316no—
692#121—5316no—
693#121—534no—
694#121—534no—
695#121—534no—
696#121—534no—
697#121—534no—
698#121—534no—
699#121—538no—
700#121—538no—
701#121—5316no—
702#121C22×D5314yes—
703#121C22×D5314yes—
704#121C22×D5314yes—
705#120—538no—
706#120—538no—
707#120—538no—
708#120—5316no—
709#120—5316no—
710#120C22×D5314yes—
711C4×Q8—538no—
712C4×Q8—538no—
713C4×Q8—5316no—
714C4×Q8—5316no—
715C4×Q8—534no—
716C4×Q8—534no—
717C4×Q8—534no—
718C4×Q8—534no—
719C4×Q8—534no—
720C4×Q8—534no—
721C4×Q8—538no—
722C4×Q8—5316no—
723C4×Q8C22×D5314yes—
724C4×Q8C22×D5314yes—
725C4×Q8C22×D5314yes—
726C4×D4—538no—
727C4×D4—538no—
728C4×D4—538no—
729C4×D4—538no—
730C4×D4—538no—
731C4×D4—538no—
732C4×D4—538no—
733C4×D4—5316no—
734C4×D4—5316no—
735C4×D4—538no—
736C4×D4—5316no—
737C4×D4—534no—
738C4×D4—534no—
739C4×D4—534no—
740C4×D4—534no—
741C4×D4—534no—
742C4×D4—534no—
743C4×D4—538no—
744C4×D4C22×D5314yes—
745C4×D4C22×D5318yes—
746C4×D4C22×D5318yes—
747C4×D4C22×D5318yes—
748C4×D4C22×D5314yes—
749C4×D4C22×D5314yes—
750#117—534no—
751#117—534no—
752#117—534no—
753#117—534no—
754#117—534no—
755#117—538no—
756#117—5316no—
757#117—538no—
758#117—5316no—
759#117—538no—
760#117—538no—
761#117—538no—
762#117—5316no—
763#117C22×D5314yes—
764#117C22×D5312yes—
765#117C22×D5314yes—
766#117C22×D5318yes—
767C2×C22⋊C4—5316no—
768C2×C22⋊C4—5316no—
769C2×C22⋊C4—5316no—
770C2×C42—538no—
771C2×C42C22×D5312yes—
772C2×C42C22×D5312yes—
773C2×C42C22×D5312yes—
774C2×C42C22×D5314yes—
775C2×C42C22×D5311yescharacteristic
776C2×C42C22×D5312yes—
777C2×C42C22×D5312yes—
778C2×C42C22×D5311yescharacteristic
779C24—538no—
780C24C23×D5311yescharacteristic
781#41—44no—
782#41—48no—
783#41—2128no—
784#41—2128no—
785#41—2128no—
786C2×Q8—534no—
787C2×Q8—534no—
788C2×Q8—5316no—
789C2×Q8—538no—
790C2×Q8—534no—
791C2×Q8—2128no—
792C2×Q8—21216no—
793C2×Q8C23×D5314yes—
794C2×Q8C23×D5312yes—
795C2×D4—538no—
796C2×D4—538no—
797C2×D4—538no—
798C2×D4—5316no—
799C2×D4—534no—
800C2×D4—534no—
801C2×D4—534no—
802C2×D4—538no—
803C2×D4—2128no—
804C2×D4—21216no—
805C2×D4C23×D5314yes—
806C2×D4C23×D5312yes—
807C2×D4C23×D5318yes—
808C2×D4C23×D5314yes—
809C22×C4—44no—
810C22×C4—42no—
811C22×C4—538no—
812C22×C4—538no—
813C22×C4—538no—
814C22×C4—538no—
815C22×C4—5316no—
816C22×C4C23×D5312yes—
817C22×C4C23×D5312yes—
818C22×C4C23×D5312yes—
819C22×C4C23×D5312yes—
820C22×C4C23×D5311yescharacteristic
821C22×C4C23×D5314yes—
822C22×C4C23×D5311yescharacteristic
823C22×C4C23×D5312yes—
824C22×C4C23×D5312yes—
825C22×C4C23×D5312yes—
826C22×C4C23×D5312yes—
827C22×C4C23×D5318yes—
828C4⋊C4—534no—
829C4⋊C4—534no—
830C4⋊C4—534no—
831C4⋊C4—534no—
832C4⋊C4—538no—
833C4⋊C4—538no—
834C4⋊C4—538no—
835C4⋊C4—538no—
836C4⋊C4—534no—
837C4⋊C4—534no—
838C4⋊C4—538no—
839C4⋊C4—538no—
840C4⋊C4—5316no—
841C4⋊C4—5316no—
842C4⋊C4—5316no—
843C4⋊C4C23×D5314yes—
844C4⋊C4C23×D5314yes—
845C4⋊C4C23×D5318yes—
846C4⋊C4C23×D5318yes—
847C4⋊C4C23×D5314yes—
848C4⋊C4C23×D5318yes—
849C22⋊C4—538no—
850C22⋊C4—5316no—
851C22⋊C4—538no—
852C22⋊C4—538no—
853C22⋊C4—538no—
854C22⋊C4—538no—
855C22⋊C4—538no—
856C22⋊C4—538no—
857C22⋊C4—538no—
858C22⋊C4—538no—
859C22⋊C4—5316no—
860C22⋊C4—5316no—
861C22⋊C4—5316no—
862C22⋊C4—5316no—
863C22⋊C4—538no—
864C22⋊C4—538no—
865C22⋊C4C23×D5318yes—
866C22⋊C4C23×D5318yes—
867C22⋊C4C23×D5318yes—
868C22⋊C4C23×D5318yes—
869C22⋊C4C23×D5314yes—
870C42—538no—
871C42—538no—
872C42—538no—
873C42—5316no—
874C42—538no—
875C42—538no—
876C42C23×D5312yes—
877C42C23×D5311yescharacteristic
878C42C23×D5312yes—
879C42C23×D5312yes—
880C42C23×D5312yes—
881C42C23×D5311yescharacteristic
882C42C23×D5312yes—
883C42C23×D5311yescharacteristic
884C42C23×D5312yes—
885C42C23×D5311yescharacteristic
886C42C23×D5318yes—
887C42C23×D5314yes—
888C23—42no—
889C23—41no—
890C23—538no—
891C23—2128no—
892C23—21216no—
893C23C24×D5314yes—
894C23C24×D5312yes—
895C23C24×D5311yescharacteristic
896Q8—28no—
897Q8—42no—
898Q8—1068no—
899Q8—1068no—
900Q8—2128no—
901Q8—21216no—
902Q8—2124no—
903D4—28no—
904D4—42no—
905D4—44no—
906D4—48no—
907D4—1068no—
908D4—1068no—
909D4—2128no—
910D4—2124no—
911D4—21216no—
912D4—2128no—
913D4—2128no—
914D4—2128no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—48no—
927C2×C4—538no—
928C2×C4—538no—
929C2×C4—538no—
930C2×C4—10616no—
931C2×C4—21216no—
932C2×C4—2128no—
933C2×C4—2128no—
934C2×C4—2128no—
935C2×C4C24×D5312yes—
936C2×C4C24×D5312yes—
937C2×C4C24×D5314yes—
938C2×C4C24×D5318yes—
939C2×C4C24×D5312yes—
940C2×C4C24×D5311yescharacteristic
941C2×C4C24×D5312yes—
942C2×C4C24×D5312yes—
943C2×C4C24×D5311yescharacteristic
944C22—22no—
945C22—21no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—24no—
950C22—28no—
951C22—44no—
952C22—8488no—
953C22—1068no—
954C22—1068no—
955C22—1068no—
956C22C25×D5311yescharacteristic
957C4—22no—
958C4—22no—
959C4—22no—
960C4—21no—
961C4—22no—
962C4—24no—
963C4—28no—
964C4—1068no—
965C4—1068no—
966C4—1068no—
967C4#1681145912yes—
968C4#1681145914yes—
969C2—42no—
970C2—41no—
971C2—44no—
972C2—2128no—
973C2C2×#1681145912yes—
974C2C2×#1681145911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62841
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289411C2semidirect
2. #20289129C2semidirect
3. #20289126C2semidirect
4. #20289120C2semidirect
5. #20288990C2semidirect
6. #20288983C2semidirect
7. #20288732C2semidirect
8. #20288730C2semidirect
9. #20288724C2semidirect
10. #20288678C2semidirect
11. #20288676C2semidirect
12. #20288671C2semidirect
13. #20288611C2semidirect
14. #20288604C2semidirect
15. #20288011C2semidirect
16. C53×#3444C2semidirect
17. #16811377C22semidirect
18. #16811373C22semidirect
19. #16811366C22semidirect
20. #16811365C22semidirect
21. #16811362C22semidirect
22. #16811359C22semidirect
23. #16811358C22semidirect
24. #16811357C22semidirect
25. #16811356C22semidirect
26. Q8×Dic106C22semidirect
27. #16811353C22semidirect
28. #16811347C22semidirect
29. #16811346C22semidirect
30. #16811345C22semidirect
31. #16811344C22semidirect
32. #16811343C22semidirect
33. #16811343C22semidirect
34. #16811341C22semidirect
35. #16811341C22semidirect
36. #16811340C22semidirect
37. #16811339C22semidirect
38. #16811338C22semidirect
39. #16811338C22semidirect
40. #16811337C22semidirect
41. #16811336C22semidirect
42. #16811302C22semidirect
43. #16811302C22semidirect
44. #16811301C22semidirect
45. #16811298C22semidirect
46. #16811297C22semidirect
47. Q8×D212C22semidirect
48. D4×Dic106C22semidirect
49. #16811288C22semidirect
50. #16811283C22semidirect
51. #16811282C22semidirect
52. #16811280C22semidirect
53. #16811270C22semidirect
54. #16811269C22semidirect
55. #16811261C22semidirect
56. D4×D212C22semidirect
57. #16811258C22semidirect
58. #16811246C22semidirect
59. #16811245C22semidirect
60. #16811244C22semidirect
61. #16811244C22semidirect
62. #16811243C22semidirect
63. #16811241C22semidirect
64. #16811240C22semidirect
65. #16811238C22semidirect
66. #16811238C22semidirect
67. #16811209C22semidirect
68. #16811206C22semidirect
69. #16811205C22semidirect
70. #16811196C22semidirect
71. #16811194C22semidirect
74. #16811180C22semidirect
75. #16811180C22semidirect
76. #16811180C22semidirect
77. #16811180C22semidirect
78. #16811179C22semidirect
82. #16811158C22semidirect
83. #16811157C22semidirect
84. #16811157C22semidirect
85. #16811157C22semidirect
86. #16811157C22semidirect
87. #16811157C22semidirect
88. #16811157C22semidirect
89. #16811157C22semidirect
90. #16811152C22semidirect
91. C2×#13133205C22semidirect
92. #124×D53C22semidirect
93. #16811134C22semidirect
94. #16811134C22semidirect
95. #16811134C22semidirect
96. #16811100C22semidirect
97. #16811099C22semidirect
98. #16811097C22semidirect
99. #16811095C22semidirect
100. C4×#11719945C22semidirect
101. C4×#11719945C22semidirect
102. C4×#11719945C22semidirect
103. C53×#533C22semidirect
104. C53×#533C22semidirect
107. C53×#529C22semidirect
108. C53×#529C22semidirect
109. C53×#529C22semidirect
110. C53×#525C22semidirect
111. C53×#525C22semidirect
112. C4×#41×C53C22semidirect
113. C4×#41×C53C22semidirect
114. C22×C42×C53C22semidirect
497. #3444D53semidirect
566. #533C2×D53semidirect
567. #533C2×D53semidirect
582. #529C2×D53semidirect
583. #529C2×D53semidirect
584. #529C2×D53semidirect
590. #525C2×D53semidirect
591. #525C2×D53semidirect
599. C4×#41C2×D53semidirect
600. C4×#41C2×D53semidirect
601. C22×C42C2×D53semidirect
602. C53#62841semidirect

Maximal subgroups

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

subgroupindex
#202894112
#202891292
#202891262
#202891202
#202889902
#202889832
#202887322
#202887302
#202887242
#202886782
#202886762
#202886712
#202886112
#202886042
#202880112
C53×#34442
#6284153