Finite Group Databasebeta

← #28292821

Subgroups — #28292821

Order 13568.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289317C214yesmaximal, complemented
2#20289311C214yesmaximal, complemented
3#20289250C214yesmaximal, complemented
4#20289248C214yesmaximal, complemented
5#20289167C218yesmaximal, complemented
6#20288696C214yesmaximal, complemented
7#20288692C214yesmaximal, complemented
8#20288688C214yesmaximal, complemented
9#20288687C214yesmaximal, complemented
10#20288639C211yesmaximal, characteristic, complemented
11#20288637C211yesmaximal, characteristic, complemented
12#20288632C212yesmaximal, complemented
13#20288538C212yesmaximal, complemented
14#20288536C211yesmaximal, characteristic, complemented
15#20288425C212yesmaximal, complemented
16#20288423C218yesmaximal, complemented
17#20288418C212yesmaximal, complemented
18#20288012C211yesmaximal, characteristic, complemented
19#20288008C211yesmaximal, characteristic, complemented
20C2×#125×D53C211yesmaximal, characteristic, complemented
21C53×#3504C211yesmaximal, characteristic, complemented
22C53⋊#564C2218yescomplemented
23#16811374C2218yescomplemented
24#16811372C2218yescomplemented
25#16811369C2218yescomplemented
26#16811351C2214yescomplemented
27#16811350C2214yescomplemented
28#16811348C2214yescomplemented
29#16811334C2214yes—
30#16811334C2214yes—
31#16811334C2214yescomplemented
32#16811333C2214yes—
33#16811333C2214yescomplemented
34#16811331C2218yes—
35#16811329C2214yescomplemented
36#16811328C2214yes—
37#16811327C2218yes—
38#16811327C2218yes—
39#16811326C2214yes—
40#16811326C2214yes—
41#16811326C2214yescomplemented
42#16811323C2214yes—
43#16811323C2214yescomplemented
44#16811322C2218yes—
45#16811322C2218yes—
46#16811321C2218yes—
47#16811321C2214yescomplemented
48#16811319C2218yes—
49#16811317C2214yes—
50#16811317C2214yescomplemented
51#16811314C2214yes—
52#16811314C2218yes—
53#16811314C2214yescomplemented
54#16811314C2218yescomplemented
55#16811312C2214yes—
56#16811312C2214yescomplemented
57#16811311C2214yes—
58#16811311C2214yes—
59#16811311C2214yescomplemented
60#16811308C2214yescomplemented
61#16811308C2218yescomplemented
62#16811307C2218yes—
63#16811307C2218yescomplemented
64#16811305C2218yes—
65#16811305C2218yes—
66#16811305C2218yescomplemented
67#16811278C2214yes—
68#16811276C2218yes—
69#16811276C2214yes—
70#16811276C2214yes—
71#16811275C2218yes—
72#16811275C2218yes—
73#16811274C2214yes—
74#16811274C2218yes—
75#16811253C2214yescomplemented
76#16811251C2212yes—
77#16811250C2218yes—
78#16811250C2214yescomplemented
79#16811250C2214yescomplemented
80#16811236C2212yescomplemented
81#16811235C2212yescomplemented
82#16811234C2218yescomplemented
83#16811233C2218yescomplemented
84#16811232C2218yescomplemented
85#16811231C2214yescomplemented
86#16811231C2218yescomplemented
87#16811229C2212yescomplemented
88#16811228C2212yescomplemented
89#16811224C2214yescomplemented
90#16811222C2218yes—
91#16811221C2218yes—
92#16811221C2218yes—
93#16811221C2218yescomplemented
94#16811220C2218yescomplemented
95#16811219C2218yes—
96#16811219C2218yes—
97#16811219C2218yescomplemented
98#16811219C2218yescomplemented
99#16811215C2218yes—
100#16811204C2212yes—
101#16811203C2218yes—
102#16811201C2212yes—
103#16811179C2212yescomplemented
104#16811178C2212yes—
105#16811178C2214yescomplemented
106#16811177C2212yes—
107#16811176C2211yescharacteristic
108#16811174C2212yes—
109#16811173C2211yescharacteristic
110#16811170C2212yes—
111#16811169C2211yescharacteristic
112#16811160C2212yes—
113#16811160C2214yes—
114#16811160C2214yescomplemented
115#16811159C2214yes—
116#16811158C2212yes—
117#16811158C2212yes—
118#16811158C2214yescomplemented
119#16811157C2214yescomplemented
120#16811155C2212yes—
121#16811155C2214yescomplemented
122#16811153C2214yes—
123#16811151C2214yes—
124C2×#13133209C2211yescharacteristic
125C2×#13133208C2212yes—
126C2×#13133207C2214yes—
127#125×D53C2214yes—
128#125×D53C2214yes—
129#125×D53C2214yes—
130#125×D53C2214yes—
131#125×D53C2212yescomplemented
132#125×D53C2214yescomplemented
133#16811136C2214yes—
134#16811136C2218yes—
135#16811135C2211yescharacteristic
136#16811135C2212yes—
137#16811132C2214yes—
138#16811132C2218yes—
139#16811130C2211yescharacteristic
140#16811105C2218yes—
141#16811104C2212yes—
142#16811104C2218yes—
143#16811103C2212yes—
144#16811103C2212yes—
145C4×#11719949C2214yes—
146C4×#11719945C2211yescharacteristic
147C4×#11719945C2214yes—
148#16811091C2212yes—
149C2×C4⋊C4×D53C2212yes—
150C2×C4⋊C4×D53C2214yes—
151C2×C42×D53C2211yescharacteristic
152C53×#557C2214yescomplemented
153C53×#554C2218yes—
154C53×#554C2214yescomplemented
155C53×#544C2212yes—
156C53×#544C2214yescomplemented
157C53×#533C2211yescharacteristic
158C53×#533C2212yescomplemented
159C2×#125×C53C2211yescharacteristic
160C2×#125×C53C2212yescomplemented
161C53×#520C2212yes—
162C4×#41×C53C2211yescharacteristic
163C2×#11719949C2314yes—
164C2×#11719949C2318yes—
165C2×#11719945C2312yes—
166C2×#11719945C2311yescharacteristic
167C2×#11719945C2314yes—
168C2×#11719945C2318yes—
169C22×C4×D53C2311yescharacteristic
170C22×C4×D53C2312yes—
171C22×C4×D53C2314yes—
172#13133217C2314yes—
173#13133217C2311yescharacteristic
174#13133216C2314yes—
175#13133216C2318yes—
176#13133216C2312yes—
177#13133215C2318yes—
178#13133215C2318yes—
179#13133215C2311yescharacteristic
180#13133214C2311yescharacteristic
181#13133213C2311yescharacteristic
182#13133212C2318yes—
183#13133212C2318yes—
184#13133212C2318yes—
185#13133212C2318yes—
186#13133212C2318yes—
187#13133212C2318yes—
188#13133212C2314yes—
189#13133212C2314yes—
190#13133212C2314yes—
191#13133211C2318yes—
192#13133211C2318yes—
193#13133211C2318yes—
194#13133210C2318yes—
195#13133210C2318yes—
196#13133210C2318yes—
197#13133210C2314yes—
198#13133209C2318yes—
199#13133209C2318yes—
200#13133209C2314yes—
201#13133209C2314yes—
202#13133209C2312yes—
203#13133209C2312yes—
204#13133208C2318yes—
205#13133208C2318yes—
206#13133208C2318yes—
207#13133208C2314yes—
208#13133208C2314yes—
209#13133208C2314yes—
210#13133208C2314yes—
211#13133208C2314yes—
212#13133208C2314yes—
213#13133208C2312yes—
214#13133207C2318yes—
215#13133207C2318yes—
216#13133207C2318yes—
217#13133207C2318yes—
218#13133207C2318yes—
219#13133207C2318yes—
220#13133207C2318yes—
221#13133207C2318yes—
222#13133207C2318yes—
223#13133207C2318yes—
224#13133207C2318yes—
225#13133207C2314yes—
226#13133207C2318yes—
227#13133207C2318yes—
228#13133206C2314yes—
229#13133206C2311yescharacteristic
230#13133205C2312yes—
231#13133204C2311yescharacteristic
232#13133203C2314yes—
233#13133202C2314yes—
234#13133202C2318yes—
235#13133202C2318yes—
236#13133202C2314yes—
237#13133202C2318yes—
238#13133202C2318yes—
239#13133202C2318yes—
240#13133202C2314yes—
241#13133202C2318yes—
242#13133202C2318yes—
243#13133202C2318yes—
244#13133202C2318yes—
245#13133201C2312yes—
246#13133201C2314yes—
247#13133200C2318yes—
248#13133200C2318yes—
249#13133200C2318yes—
250#13133199C2314yes—
251#13133199C2318yes—
252#13133199C2318yes—
253#13133199C2318yes—
254#13133199C2318yes—
255#13133198C2312yes—
256#13133197C2318yes—
257#13133197C2318yes—
258#13133197C2314yes—
259#13133197C2312yes—
260#13133197C2312yes—
261#13133197C2314yes—
262#13133197C2312yes—
263#13133196C2318yes—
264#13133196C2314yes—
265#13133195C2318yes—
266#13133195C2318yes—
267#13133195C2318yes—
268#13133195C2318yes—
269#13133195C2318yes—
270#13133195C2318yes—
271#13133195C2314yes—
272#13133194C2318yes—
273#13133194C2314yes—
274#13133193C2318yes—
275#13133193C2318yes—
276#13133193C2318yes—
277#13133193C2318yes—
278#13133193C2318yes—
279#13133193C2312yes—
280#13133193C2314yes—
281#13133193C2318yes—
282#13133193C2314yes—
283#13133192C2312yes—
284#13133192C2318yes—
285#13133192C2312yes—
286#13133192C2312yes—
287#13133192C2314yes—
288#13133192C2318yes—
289#13133192C2314yes—
290#13133192C2314yes—
291#13133191C2314yes—
292#13133191C2318yes—
293#13133191C2318yes—
294#13133191C2314yes—
295#13133190C2318yes—
296#13133190C2318yes—
297#13133190C2318yes—
298#13133190C2314yes—
299#13133189C2314yes—
300#13133189C2318yes—
301#13133188C2312yes—
302#13133188C2314yes—
303#13133187C2314yes—
304#13133187C2312yes—
305#13133185C2312yes—
306Q8×Dic53C2318yes—
307Q8×Dic53C2314yes—
308C4×Dic106C2314yes—
309C4×Dic106C2314yes—
310C4×Dic106C2312yes—
311C4×Dic106C2314yes—
312C4×Dic106C2314yes—
313#13133182C2318yes—
314#13133182C2318yes—
315#13133182C2312yes—
316#13133182C2314yes—
317#13133182C2312yes—
318C4×D212C2314yes—
319C4×D212C2314yes—
320C4×D212C2318yes—
321C4×D212C2318yes—
322C4×D212C2314yes—
323C4×D212C2314yes—
324C4×D212C2314yes—
325C4×D212C2314yes—
326C4×D212C2312yes—
327C4×D212C2314yes—
328#13133179C2318yes—
329#13133179C2314yes—
330#13133179C2318yes—
331#13133179C2318yes—
332#13133179C2312yes—
333#13133179C2312yes—
334#13133179C2314yes—
335#13133179C2314yes—
336#13133179C2314yes—
337C4×C22⋊D53C2318yes—
338C4×C22⋊D53C2314yes—
339C4×C22⋊D53C2318yes—
340C4×C22⋊D53C2318yes—
341C4×C22⋊D53C2314yes—
342C4×C22⋊D53C2314yes—
343C4×C22⋊D53C2318yes—
344C4×C22⋊D53C2314yes—
345C4×C22⋊D53C2314yes—
346#13133177C2314yes—
347#13133177C2318yes—
348#13133177C2318yes—
349#13133177C2314yes—
350#13133176C2318yes—
351#13133176C2314yes—
352#13133176C2311yescharacteristic
353#13133175C2314yes—
354#13133175C2318yes—
355#13133175C2314yes—
356#13133175C2314yes—
357#13133175C2318yes—
358#13133175C2314yes—
359#13133175C2314yes—
360#13133175C2314yes—
361#13133174C2314yes—
362#13133174C2318yes—
363#13133174C2318yes—
364#13133174C2318yes—
365#13133174C2314yes—
366#13133174C2314yes—
367#13133174C2312yes—
368C2×C4⋊Dic53C2314yes—
369C2×C4⋊Dic53C2312yes—
370C2×#11719919C2314yes—
371C2×#11719919C2314yes—
372C2×#11719919C2314yes—
373C4⋊C4×D53C2318yes—
374C4⋊C4×D53C2314yes—
375C4⋊C4×D53C2318yes—
376C4⋊C4×D53C2318yes—
377C4⋊C4×D53C2318yes—
378C4⋊C4×D53C2314yes—
379C4⋊C4×D53C2318yes—
380C4⋊C4×D53C2314yes—
381C4⋊C4×D53C2314yes—
382C4⋊C4×D53C2314yes—
383C4⋊C4×D53C2314yes—
384C4⋊C4×D53C2314yes—
385C4⋊C4×D53C2318yes—
386C4⋊C4×D53C2318yes—
387C2×C4×Dic53C2311yescharacteristic
388C2×C4×Dic53C2312yes—
389C42×D53C2312yes—
390C42×D53C2312yes—
391C42×D53C2312yes—
392C42×D53C2312yes—
393C42×D53C2314yes—
394C42×D53C2312yes—
395C2×#41×C53C2311yescharacteristic
396C4⋊Q8×C53C2314yes—
397C4⋊Q8×C53C2314yes—
398C4⋊Q8×C53C2318yes—
399C4⋊Q8×C53C2312yes—
400#125×C53C2318yes—
401#125×C53C2318yes—
402#125×C53C2312yes—
403#125×C53C2314yes—
404#125×C53C2312yes—
405#125×C53C2311yescharacteristic
406#125×C53C2314yes—
407#125×C53C2314yes—
408#125×C53C2311yescharacteristic
409C22⋊Q8×C53C2318yes—
410C22⋊Q8×C53C2318yes—
411C22⋊Q8×C53C2318yes—
412C22⋊Q8×C53C2314yes—
413C22⋊Q8×C53C2318yes—
414C4×Q8×C53C2312yes—
415C4×Q8×C53C2314yes—
416C4×Q8×C53C2314yes—
417C4×Q8×C53C2318yes—
418C4×D4×C53C2314yes—
419C4×D4×C53C2314yes—
420C4×D4×C53C2312yes—
421C4×D4×C53C2318yes—
422#117×C53C2311yescharacteristic
423#117×C53C2312yes—
424#117×C53C2312yes—
425#117×C53C2314yes—
426C2×C4⋊C4×C53C2314yes—
427C2×C4⋊C4×C53C2318yes—
428C2×C4⋊C4×C53C2312yes—
429C2×C4⋊C4×C53C2314yes—
430C2×C42×C53C2311yescharacteristic
431C2×C42×C53C2312yes—
432C23×D53C2411yescharacteristic
433#41×C53—24no—
434C2×Q8×C53C2411yescharacteristic
435C2×Q8×C53C2418yes—
436C2×Q8×C53C2414yes—
437C2×D4×C53C2412yes—
438C2×D4×C53C2411yescharacteristic
439C22×C4×C53C2412yes—
440C22×C4×C53C2412yes—
441C22×C4×C53C2414yes—
442C22×C4×C53C2414yes—
443C22×C4×C53C2418yes—
444C22×C4×C53C2411yescharacteristic
445C2×C22⋊D53C2414yes—
446C2×C22⋊D53C2412yes—
447C2×C22⋊D53C2414yes—
448C2×C22⋊D53C2418yes—
449C2×C22⋊D53C2414yes—
450C22×Dic53C2411yescharacteristic
451C22×Dic53C2412yes—
452C22×Dic53C2414yes—
453#11719949—416no—
454#11719949—48no—
455#11719945—28no—
456#11719945—24no—
457#11719945—48no—
458#11719945—416no—
459C2×D212C2412yes—
460C2×D212C2414yes—
461C2×D212C2414yes—
462C2×D212C2414yes—
463C2×D212C2411yescharacteristic
464C2×D212C2414yes—
465C2×D212C2418yes—
466C2×C4×D53—24no—
467C2×C4×D53—44no—
468C2×C4×D53—48no—
469C2×C4×D53C2412yes—
470C2×C4×D53C2412yes—
471C2×C4×D53C2412yes—
472C2×C4×D53C2412yes—
473C2×C4×D53C2412yes—
474C2×C4×D53C2414yes—
475C2×C4×D53C2418yes—
476C2×C4×D53C2412yes—
477C2×C4×D53C2412yes—
478C2×C4×D53C2414yes—
479C2×C4×D53C2414yes—
480C2×C4×D53C2414yes—
481C2×C4×D53C2418yes—
482C2×C4×D53C2418yes—
483C2×C4×D53C2418yes—
484C2×C4×D53C2418yes—
485C2×Dic106C2412yes—
486C2×Dic106C2411yescharacteristic
487C2×Dic106C2418yes—
488C2×Dic106C2414yes—
489C4⋊C4×C53C2414yes—
490C4⋊C4×C53C2412yes—
491C4⋊C4×C53C2418yes—
492C4⋊C4×C53C2414yes—
493C4⋊C4×C53C2414yes—
494C4⋊C4×C53C2418yes—
495C4⋊C4×C53C2418yes—
496C4⋊C4×C53C2418yes—
497C4⋊C4×C53C2418yes—
498C4⋊C4×C53C2412yes—
499C4⋊C4×C53C2412yes—
500C4⋊C4×C53C2414yes—
501C4⋊C4×C53C2414yes—
502C4⋊C4×C53C2418yes—
503C4⋊C4×C53C2414yes—
504C22⋊C4×C53C2414yes—
505C22⋊C4×C53C2412yes—
506C22⋊C4×C53C2414yes—
507C22⋊C4×C53C2418yes—
508C42×C53C2411yescharacteristic
509C42×C53C2411yescharacteristic
510C42×C53C2412yes—
511C42×C53C2412yes—
512C42×C53C2414yes—
513C42×C53C2414yes—
514C42×C53C2418yes—
515C22⋊Dic53C2414yes—
516C22⋊Dic53C2412yes—
517C22⋊Dic53C2418yes—
518C22⋊Dic53C2414yes—
519#11719921C2414yes—
520#11719921C2414yes—
521#11719921C2414yes—
522#11719921C2414yes—
523#11719921C2414yes—
524#11719921C2414yes—
525#11719921C2414yes—
526#11719921C2414yes—
527#11719921C2414yes—
528#11719921C2418yes—
529#11719921C2418yes—
530#11719921C2414yes—
531#11719921C2414yes—
532#11719921C2418yes—
533#11719921C2418yes—
534#11719921C2418yes—
535#11719921C2418yes—
536#11719921C2414yes—
537#11719921C2414yes—
538C4⋊Dic53C2414yes—
539C4⋊Dic53C2414yes—
540C4⋊Dic53C2418yes—
541C4⋊Dic53C2418yes—
542C4⋊Dic53C2412yes—
543C4⋊Dic53C2414yes—
544C4⋊Dic53C2418yes—
545C4⋊Dic53C2418yes—
546C4⋊Dic53C2414yes—
547C4⋊Dic53C2414yes—
548C4⋊Dic53C2414yes—
549C4⋊Dic53C2414yes—
550#11719919C2418yes—
551#11719919C2418yes—
552#11719919C2418yes—
553#11719919C2418yes—
554#11719919C2418yes—
555#11719919C2418yes—
556#11719919C2414yes—
557#11719919C2418yes—
558#11719919C2418yes—
559#11719919C2418yes—
560#11719919C2418yes—
561#11719919C2418yes—
562#11719919C2418yes—
563#11719919C2414yes—
564#11719919C2414yes—
565#11719919C2414yes—
566#11719919C2414yes—
567#11719919C2414yes—
568#11719919C2414yes—
569C4×Dic53C2411yescharacteristic
570C4×Dic53C2411yescharacteristic
571C4×Dic53C2412yes—
572C4×Dic53C2412yes—
573C4×Dic53C2412yes—
574C4×Dic53C2412yes—
575C4×Dic53C2412yes—
576C4×Dic53C2414yes—
577C4×Dic53C2414yes—
578C4×Dic53C2412yes—
579C4×Dic53C2414yes—
580C4×Dic53C2418yes—
581C4×Dic53C2418yes—
582C4×Dic53C2418yes—
583C23×C53C2512yes—
584C23×C53C2511yescharacteristic
585C22×D53—22no—
586C22×D53—24no—
587C22×D53C2514yes—
588C22×D53C2512yes—
589C22×D53C2512yes—
590Q8×C53—22no—
591Q8×C53—44no—
592Q8×C53—48no—
593D4×C53—24no—
594D4×C53—22no—
595C2×C4×C53—24no—
596C2×C4×C53—42no—
597C2×C4×C53—44no—
598C2×C4×C53—48no—
599C2×C4×C53—44no—
600C2×C4×C532−1+414yes—
601C2×C4×C53C2514yes—
602C2×C4×C53C2514yes—
603C2×C4×C53C2512yes—
604C2×C4×C53C2518yes—
605C2×C4×C53C2514yes—
606C2×C4×C53C2512yes—
607C2×C4×C53C2512yes—
608C2×C4×C53C2511yescharacteristic
609C2×C4×C53C2511yescharacteristic
610C22⋊D53—28no—
611C22⋊D53—24no—
612C22⋊D53—28no—
613C22⋊D53—44no—
614C22⋊D53—48no—
615C2×Dic53—22no—
616C2×Dic53—42no—
617C2×Dic53—44no—
618C2×Dic53C2514yes—
619C2×Dic53C2512yes—
620C2×Dic53C2518yes—
621C2×Dic53C2514yes—
622C2×Dic53C2512yes—
623C2×Dic53C2512yes—
624C2×Dic53C2512yes—
625D212—28no—
626D212—28no—
627D212—28no—
628D212—24no—
629D212—22no—
630D212—48no—
631D212—44no—
632C4×D53—24no—
633C4×D53—216no—
634C4×D53—24no—
635C4×D53—24no—
636C4×D53—24no—
637C4×D53—24no—
638C4×D53—28no—
639C4×D53—42no—
640C4×D53—48no—
641C4×D53—42no—
642C4×D53—44no—
643C4×D53—48no—
644C4×D53—48no—
645C4×D53—48no—
646C4×D53—44no—
647C4×D53—44no—
648Dic106—24no—
649Dic106—22no—
650Dic106—44no—
651Dic106—48no—
652#62825—531nomaximal, Sylow
653C22×C53—22no—
654C22×C53—22no—
655C22×C53—24no—
656C22×C53C2×2−1+412yes—
657C22×C53C2611yescharacteristic
658C2×D53—28no—
659C2×D53—22no—
660C2×D53—22no—
661C2×D53—24no—
662C2×D53—22no—
663C2×D53—24no—
664C2×D53—24no—
665C2×D53—24no—
666C2×D53#58514yes—
667C4×C53—22no—
668C4×C53—24no—
669C4×C53—24no—
670C4×C53—22no—
671C4×C53—28no—
672C4×C53—22no—
673C4×C53—24no—
674C4×C53C2×2−1+412yes—
675C4×C53C2×2−1+412yes—
676Dic53—24no—
677Dic53—22no—
678Dic53—22no—
679Dic53—24no—
680Dic53—22no—
681Dic53—28no—
682Dic53—22no—
683#3563—534no—
684#3563—534no—
685#3559—534no—
686#3559—534no—
687#3553—538no—
688#3515—534no—
689#3515—534no—
690#3515—534no—
691#3515—534no—
692#3512—531no—
693#3512—532no—
694#3512—531no—
695#3504—532no—
696#3504—531no—
697#3504D5311yescharacteristic, complemented
698#3492—538no—
699#3492—532no—
700#3492—532no—
701#3444—531no—
702#3444—531no—
703C22×#125—531no—
704C2×C53—22no—
705C2×C53—42no—
706C2×C53C22×2−1+411yescharacteristic
707C2×C53C2×#58512yes—
708D53—24no—
709D53—44no—
710D53—42no—
711#564—538no—
712#563—538no—
713#563—538no—
714#562—538no—
715#557—534no—
716#557—534no—
717#557—534no—
718#557C2×D5314yescomplemented
719#554—534no—
720#554—534no—
721#554—534no—
722#554—534no—
723#554—538no—
724#554—538no—
725#554—538no—
726#554—534no—
727#554—534no—
728#554—534no—
729#554C2×D5318yes—
730#554C2×D5314yescomplemented
731#553—534no—
732#553—534no—
733#553—534no—
734#553—538no—
735#553—538no—
736#553—538no—
737#553—534no—
738#553—534no—
739#553—534no—
740#553—534no—
741#553—538no—
742#553—534no—
743#552—538no—
744#552—538no—
745#552—538no—
746#552—534no—
747#552—534no—
748#552—534no—
749#552—538no—
750#552—538no—
751#552—538no—
752#552—534no—
753#552—534no—
754#552—538no—
755#552—534no—
756#552—534no—
757#552—534no—
758#552—538no—
759#547—538no—
760#547—534no—
761#547—534no—
762#547—538no—
763#547—538no—
764#547—534no—
765#547—538no—
766#547—534no—
767#544—538no—
768#544—534no—
769#544—534no—
770#544—534no—
771#544—532no—
772#544C2×D5312yes—
773#544C2×D5314yescomplemented
774#541—538no—
775#541—532no—
776#541—538no—
777#541—538no—
778#541—534no—
779#541—538no—
780#541—532no—
781#540—532no—
782#540—534no—
783#540—532no—
784#539—538no—
785#539—538no—
786#539—538no—
787#539—538no—
788#539—538no—
789#539—538no—
790#539—538no—
791#539—538no—
792#539—538no—
793#539—538no—
794#537—532no—
795#537—538no—
796#537—532no—
797#533—532no—
798#533—534no—
799#533—532no—
800#533—532no—
801#533—531no—
802#533C2×D5311yescharacteristic
803#533C2×D5312yescomplemented
804#532—531no—
805#532—532no—
806#532—532no—
807#532—531no—
808#529—532no—
809#529—532no—
810#529—534no—
811#529—534no—
812#529—532no—
813#529—534no—
814#529—534no—
815#529—534no—
816#529—532no—
817#529—534no—
818#529—534no—
819#529—534no—
820C2×#125—534no—
821C2×#125—534no—
822C2×#125—534no—
823C2×#125—534no—
824C2×#125—534no—
825C2×#125—532no—
826C2×#125—534no—
827C2×#125—532no—
828C2×#125—531no—
829C2×#125C2×D5311yescharacteristic
830C2×#125C2×D5312yescomplemented
831#525—531no—
832#525—534no—
833#525—538no—
834#525—534no—
835#525—538no—
836#525—532no—
837#525—531no—
838#520—538no—
839#520—532no—
840#520—532no—
841#520—532no—
842#520—538no—
843#520C2×D5312yes—
844C4×#41—534no—
845C4×#41—532no—
846C4×#41—531no—
847C4×#41—534no—
848C4×#41C2×D5311yescharacteristic
849C22×C4⋊C4—532no—
850C22×C4⋊C4—534no—
851C22×C42—531no—
852C53#6282511yescharacteristic, complemented, Sylow
853C2×#41—534no—
854C2×#41—538no—
855C2×#41—532no—
856C2×#41—531no—
857C2×#41—534no—
858C2×#41—538no—
859C2×#41C22×D5311yescharacteristic
860C23×C4—531no—
861C23×C4—534no—
862C23×C4—532no—
863C4⋊Q8—531no—
864C4⋊Q8—538no—
865C4⋊Q8—538no—
866C4⋊Q8—532no—
867C4⋊Q8—534no—
868C4⋊Q8—538no—
869C4⋊Q8—531no—
870C4⋊Q8—534no—
871C4⋊Q8C22×D5312yes—
872C4⋊Q8C22×D5314yes—
873C4⋊Q8C22×D5314yes—
874C4⋊Q8C22×D5318yes—
875#127—531no—
876#127—531no—
877#126—534no—
878#126—534no—
879#126—534no—
880#126—538no—
881#126—538no—
882#126—538no—
883#126—538no—
884#126—538no—
885#126—538no—
886#126—534no—
887#126—538no—
888#126—538no—
889#126—538no—
890#126—538no—
891#126—538no—
892#126—538no—
893#125—534no—
894#125—538no—
895#125—538no—
896#125—534no—
897#125—538no—
898#125—534no—
899#125—534no—
900#125—538no—
901#125—532no—
902#125—538no—
903#125—538no—
904#125—538no—
905#125—534no—
906#125—534no—
907#125—534no—
908#125—538no—
909#125—538no—
910#125—538no—
911#125—538no—
912#125—538no—
913#125—538no—
914#125—538no—
915#125—538no—
916#125—538no—
917#125—532no—
918#125—532no—
919#125—534no—
920#125—534no—
921#125—538no—
922#125—538no—
923#125C22×D5312yes—
924#125C22×D5312yes—
925#125C22×D5314yes—
926#125C22×D5311yescharacteristic
927#125C22×D5314yes—
928#125C22×D5311yescharacteristic
929#125C22×D5318yes—
930#125C22×D5314yes—
931#125C22×D5318yes—
932#124—531no—
933#124—534no—
934#124—531no—
935#124—534no—
936#124—532no—
937#123—532no—
938#123—538no—
939#123—538no—
940#123—538no—
941#123—534no—
942#123—534no—
943#123—534no—
944#123—538no—
945#123—538no—
946#123—538no—
947#123—538no—
948#123—538no—
949#123—538no—
950#123—538no—
951#123—538no—
952#123—538no—
953#123—534no—
954#123—532no—
955#123—534no—
956#123—538no—
957#123—538no—
958#123—538no—
959#123—538no—
960C22⋊Q8—534no—
961C22⋊Q8—532no—
962C22⋊Q8—538no—
963C22⋊Q8—534no—
964C22⋊Q8—538no—
965C22⋊Q8—538no—
966C22⋊Q8—538no—
967C22⋊Q8—538no—
968C22⋊Q8—538no—
969C22⋊Q8—534no—
970C22⋊Q8—538no—
971C22⋊Q8—534no—
972C22⋊Q8—532no—
973C22⋊Q8—532no—
974C22⋊Q8—532no—
975C22⋊Q8—538no—
976C22⋊Q8—534no—
977C22⋊Q8—534no—
978C22⋊Q8—538no—
979C22⋊Q8—538no—
980C22⋊Q8—538no—
981C22⋊Q8—538no—
982C22⋊Q8—538no—
983C22⋊Q8—538no—
984C22⋊Q8—538no—
985C22⋊Q8—534no—
986C22⋊Q8—538no—
987C22⋊Q8C22×D5314yes—
988C22⋊Q8C22×D5318yes—
989C22⋊Q8C22×D5318yes—
990C22⋊Q8C22×D5318yes—
991C22⋊Q8C22×D5318yes—
992#121—532no—
993#121—534no—
994#121—538no—
995#121—534no—
996#121—534no—
997#121—538no—
998#121—534no—
999#121—538no—
1000#121—534no—
1001#121—532no—
1002#121—532no—
1003#121—532no—
1004#121—538no—
1005#121—534no—
1006#121—534no—
1007#121—538no—
1008#121—534no—
1009#121—538no—
1010#121—538no—
1011#121—538no—
1012#120—532no—
1013#120—534no—
1014#120—532no—
1015C4×Q8—534no—
1016C4×Q8—538no—
1017C4×Q8—532no—
1018C4×Q8—532no—
1019C4×Q8—534no—
1020C4×Q8—538no—
1021C4×Q8—538no—
1022C4×Q8—534no—
1023C4×Q8—532no—
1024C4×Q8—534no—
1025C4×Q8—534no—
1026C4×Q8—534no—
1027C4×Q8C22×D5314yes—
1028C4×Q8C22×D5312yes—
1029C4×Q8C22×D5318yes—
1030C4×Q8C22×D5314yes—
1031C4×D4—534no—
1032C4×D4—534no—
1033C4×D4—534no—
1034C4×D4—534no—
1035C4×D4—534no—
1036C4×D4—538no—
1037C4×D4—538no—
1038C4×D4—538no—
1039C4×D4—538no—
1040C4×D4—534no—
1041C4×D4—534no—
1042C4×D4—534no—
1043C4×D4—532no—
1044C4×D4—532no—
1045C4×D4—538no—
1046C4×D4—538no—
1047C4×D4—538no—
1048C4×D4—534no—
1049C4×D4—534no—
1050C4×D4—534no—
1051C4×D4—538no—
1052C4×D4—538no—
1053C4×D4—534no—
1054C4×D4—534no—
1055C4×D4—534no—
1056C4×D4—534no—
1057C4×D4—534no—
1058C4×D4—532no—
1059C4×D4—538no—
1060C4×D4—538no—
1061C4×D4—534no—
1062C4×D4—534no—
1063C4×D4C22×D5314yes—
1064C4×D4C22×D5312yes—
1065C4×D4C22×D5318yes—
1066C4×D4C22×D5314yes—
1067#117—531no—
1068#117—534no—
1069#117—538no—
1070#117—534no—
1071#117—534no—
1072#117—534no—
1073#117—538no—
1074#117—538no—
1075#117—534no—
1076#117—534no—
1077#117—534no—
1078#117—534no—
1079#117—534no—
1080#117—532no—
1081#117—534no—
1082#117—538no—
1083#117—538no—
1084#117—538no—
1085#117C22×D5312yes—
1086#117C22×D5311yescharacteristic
1087#117C22×D5312yes—
1088#117C22×D5314yes—
1089C2×C4⋊C4—532no—
1090C2×C4⋊C4—534no—
1091C2×C4⋊C4—534no—
1092C2×C4⋊C4—534no—
1093C2×C4⋊C4—534no—
1094C2×C4⋊C4—538no—
1095C2×C4⋊C4—538no—
1096C2×C4⋊C4—534no—
1097C2×C4⋊C4—534no—
1098C2×C4⋊C4—538no—
1099C2×C4⋊C4—538no—
1100C2×C4⋊C4—534no—
1101C2×C4⋊C4—534no—
1102C2×C4⋊C4—538no—
1103C2×C4⋊C4—538no—
1104C2×C4⋊C4—538no—
1105C2×C4⋊C4—534no—
1106C2×C4⋊C4—534no—
1107C2×C4⋊C4—534no—
1108C2×C4⋊C4C22×D5312yes—
1109C2×C4⋊C4C22×D5314yes—
1110C2×C4⋊C4C22×D5318yes—
1111C2×C4⋊C4C22×D5314yes—
1112C2×C42—531no—
1113C2×C42—532no—
1114C2×C42—534no—
1115C2×C42—532no—
1116C2×C42—532no—
1117C2×C42—532no—
1118C2×C42—532no—
1119C2×C42—532no—
1120C2×C42C22×D5312yes—
1121C2×C42C22×D5311yescharacteristic
1122C24—531no—
1123#41—24no—
1124#41—1064no—
1125#41—1068no—
1126#41—2128no—
1127#41—21216no—
1128#41—2128no—
1129#41—21216no—
1130C2×Q8—532no—
1131C2×Q8—531no—
1132C2×Q8—538no—
1133C2×Q8—534no—
1134C2×Q8C23×D5311yescharacteristic
1135C2×Q8C23×D5318yes—
1136C2×Q8C23×D5314yes—
1137C2×D4—532no—
1138C2×D4—534no—
1139C2×D4—534no—
1140C2×D4—538no—
1141C2×D4—534no—
1142C2×D4—532no—
1143C2×D4—531no—
1144C2×D4—534no—
1145C2×D4—534no—
1146C2×D4—534no—
1147C2×D4—538no—
1148C2×D4—534no—
1149C2×D4C23×D5312yes—
1150C2×D4C23×D5311yescharacteristic
1151C22×C4—531no—
1152C22×C4—532no—
1153C22×C4—534no—
1154C22×C4—532no—
1155C22×C4—532no—
1156C22×C4—532no—
1157C22×C4—532no—
1158C22×C4—532no—
1159C22×C4—534no—
1160C22×C4—538no—
1161C22×C4—532no—
1162C22×C4—532no—
1163C22×C4—534no—
1164C22×C4—534no—
1165C22×C4—534no—
1166C22×C4—538no—
1167C22×C4—538no—
1168C22×C4—538no—
1169C22×C4—538no—
1170C22×C4—1064no—
1171C22×C4—2128no—
1172C22×C4—2124no—
1173C22×C4C23×D5312yes—
1174C22×C4C23×D5312yes—
1175C22×C4C23×D5314yes—
1176C22×C4C23×D5314yes—
1177C22×C4C23×D5318yes—
1178C22×C4C23×D5311yescharacteristic
1179C4⋊C4—534no—
1180C4⋊C4—534no—
1181C4⋊C4—538no—
1182C4⋊C4—538no—
1183C4⋊C4—538no—
1184C4⋊C4—538no—
1185C4⋊C4—538no—
1186C4⋊C4—538no—
1187C4⋊C4—538no—
1188C4⋊C4—538no—
1189C4⋊C4—532no—
1190C4⋊C4—534no—
1191C4⋊C4—534no—
1192C4⋊C4—538no—
1193C4⋊C4—538no—
1194C4⋊C4—538no—
1195C4⋊C4—538no—
1196C4⋊C4—538no—
1197C4⋊C4—538no—
1198C4⋊C4—538no—
1199C4⋊C4—538no—
1200C4⋊C4—534no—
1201C4⋊C4—534no—
1202C4⋊C4—534no—
1203C4⋊C4—534no—
1204C4⋊C4—534no—
1205C4⋊C4—534no—
1206C4⋊C4—534no—
1207C4⋊C4—534no—
1208C4⋊C4—534no—
1209C4⋊C4—534no—
1210C4⋊C4C23×D5314yes—
1211C4⋊C4C23×D5318yes—
1212C4⋊C4C23×D5314yes—
1213C4⋊C4C23×D5318yes—
1214C4⋊C4C23×D5312yes—
1215C4⋊C4C23×D5314yes—
1216C4⋊C4C23×D5312yes—
1217C4⋊C4C23×D5318yes—
1218C4⋊C4C23×D5318yes—
1219C4⋊C4C23×D5312yes—
1220C4⋊C4C23×D5314yes—
1221C4⋊C4C23×D5318yes—
1222C4⋊C4C23×D5318yes—
1223C4⋊C4C23×D5314yes—
1224C4⋊C4C23×D5314yes—
1225C22⋊C4—534no—
1226C22⋊C4—532no—
1227C22⋊C4—538no—
1228C22⋊C4—534no—
1229C22⋊C4—534no—
1230C22⋊C4—534no—
1231C22⋊C4—534no—
1232C22⋊C4—534no—
1233C22⋊C4—534no—
1234C22⋊C4—534no—
1235C22⋊C4—534no—
1236C22⋊C4—534no—
1237C22⋊C4—534no—
1238C22⋊C4—534no—
1239C22⋊C4—538no—
1240C22⋊C4—538no—
1241C22⋊C4—538no—
1242C22⋊C4—538no—
1243C22⋊C4—538no—
1244C22⋊C4—538no—
1245C22⋊C4—534no—
1246C22⋊C4—534no—
1247C22⋊C4—534no—
1248C22⋊C4C23×D5314yes—
1249C22⋊C4C23×D5312yes—
1250C22⋊C4C23×D5314yes—
1251C22⋊C4C23×D5318yes—
1252C42—531no—
1253C42—532no—
1254C42—531no—
1255C42—532no—
1256C42—532no—
1257C42—532no—
1258C42—532no—
1259C42—534no—
1260C42—534no—
1261C42—534no—
1262C42—532no—
1263C42—538no—
1264C42—538no—
1265C42—538no—
1266C42C23×D5311yescharacteristic
1267C42C23×D5311yescharacteristic
1268C42C23×D5312yes—
1269C42C23×D5314yes—
1270C42C23×D5314yes—
1271C42C23×D5312yes—
1272C42C23×D5318yes—
1273C23—532no—
1274C23—534no—
1275C23—532no—
1276C23—1064no—
1277C23—1062no—
1278C23C24×D5312yes—
1279C23C24×D5311yescharacteristic
1280Q8—22no—
1281Q8—48no—
1282Q8—44no—
1283Q8—1064no—
1284Q8—1062no—
1285Q8—2128no—
1286Q8—2124no—
1287D4—24no—
1288D4—22no—
1289D4—1068no—
1290D4—1068no—
1291D4—1068no—
1292D4—1068no—
1293D4—1064no—
1294D4—1068no—
1295D4—1064no—
1296D4—1062no—
1297D4—2128no—
1298D4—2124no—
1299D4—2128no—
1300D4—2124no—
1301C2×C4—24no—
1302C2×C4—42no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—532no—
1307C2×C4—532no—
1308C2×C4—534no—
1309C2×C4—532no—
1310C2×C4—534no—
1311C2×C4—532no—
1312C2×C4—538no—
1313C2×C4—1064no—
1314C2×C4—10616no—
1315C2×C4—1064no—
1316C2×C4—1062no—
1317C2×C4—1064no—
1318C2×C4—1064no—
1319C2×C4—1064no—
1320C2×C4—1068no—
1321C2×C4—2122no—
1322C2×C4—2128no—
1323C2×C4—2122no—
1324C2×C4—2124no—
1325C2×C4—2128no—
1326C2×C4—2124no—
1327C2×C4—2128no—
1328C2×C4—2124no—
1329C2×C4—2128no—
1330C2×C4—2122no—
1331C2×C4—2124no—
1332C2×C4#1313326514yes—
1333C2×C4C24×D5312yes—
1334C2×C4C24×D5314yes—
1335C2×C4C24×D5314yes—
1336C2×C4C24×D5312yes—
1337C2×C4C24×D5314yes—
1338C2×C4C24×D5318yes—
1339C2×C4C24×D5312yes—
1340C2×C4C24×D5311yescharacteristic
1341C2×C4C24×D5311yescharacteristic
1342C22—22no—
1343C22—22no—
1344C22—24no—
1345C22—534no—
1346C22—1068no—
1347C22—1062no—
1348C22—1062no—
1349C22—1062no—
1350C22—1064no—
1351C22—1064no—
1352C22—1064no—
1353C22—1064no—
1354C22C2×#1313326512yes—
1355C22C25×D5311yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—28no—
1359C4—24no—
1360C4—22no—
1361C4—24no—
1362C4—24no—
1363C4—1062no—
1364C4—1062no—
1365C4—1064no—
1366C4—1062no—
1367C4—1068no—
1368C4—1062no—
1369C4—1064no—
1370C4C2×#1313326512yes—
1371C4C2×#1313326512yes—
1372C2—22no—
1373C2—42no—
1374C2—1064no—
1375C2—2124no—
1376C2—2122no—
1377C2C22×#1313326511yescharacteristic
1378C2#585×D5312yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3504C2
hypercenter#3504D53
hypocenterC53#62825
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #20289317C2semidirect
2. #20289311C2semidirect
3. #20289250C2semidirect
4. #20289248C2semidirect
5. #20289167C2semidirect
6. #20288696C2semidirect
7. #20288692C2semidirect
8. #20288688C2semidirect
9. #20288687C2semidirect
10. #20288639C2semidirect
11. #20288637C2semidirect
12. #20288632C2semidirect
13. #20288538C2semidirect
14. #20288536C2semidirect
15. #20288425C2semidirect
16. #20288423C2semidirect
17. #20288418C2semidirect
18. #20288012C2semidirect
19. #20288008C2semidirect
20. C2×#125×D53C2semidirect
21. C53×#3504C2semidirect
22. C53⋊#564C22semidirect
23. #16811374C22semidirect
24. #16811372C22semidirect
25. #16811369C22semidirect
26. #16811351C22semidirect
27. #16811350C22semidirect
28. #16811348C22semidirect
31. #16811334C22semidirect
33. #16811333C22semidirect
35. #16811329C22semidirect
41. #16811326C22semidirect
43. #16811323C22semidirect
47. #16811321C22semidirect
50. #16811317C22semidirect
53. #16811314C22semidirect
54. #16811314C22semidirect
56. #16811312C22semidirect
59. #16811311C22semidirect
60. #16811308C22semidirect
61. #16811308C22semidirect
63. #16811307C22semidirect
66. #16811305C22semidirect
75. #16811253C22semidirect
78. #16811250C22semidirect
79. #16811250C22semidirect
80. #16811236C22semidirect
81. #16811235C22semidirect
82. #16811234C22semidirect
83. #16811233C22semidirect
84. #16811232C22semidirect
85. #16811231C22semidirect
86. #16811231C22semidirect
87. #16811229C22semidirect
88. #16811228C22semidirect
89. #16811224C22semidirect
93. #16811221C22semidirect
94. #16811220C22semidirect
97. #16811219C22semidirect
98. #16811219C22semidirect
103. #16811179C22semidirect
105. #16811178C22semidirect
114. #16811160C22semidirect
118. #16811158C22semidirect
119. #16811157C22semidirect
121. #16811155C22semidirect
131. #125×D53C22semidirect
132. #125×D53C22semidirect
152. C53×#557C22semidirect
154. C53×#554C22semidirect
156. C53×#544C22semidirect
158. C53×#533C22semidirect
160. C2×#125×C53C22semidirect
697. #3504D53semidirect
718. #557C2×D53semidirect
730. #554C2×D53semidirect
773. #544C2×D53semidirect
803. #533C2×D53semidirect
830. C2×#125C2×D53semidirect
852. C53#62825semidirect

Maximal subgroups

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

subgroupindex
#202893172
#202893112
#202892502
#202892482
#202891672
#202886962
#202886922
#202886882
#202886872
#202886392
#202886372
#202886322
#202885382
#202885362
#202884252
#202884232
#202884182
#202880122
#202880082
C2×#125×D532
C53×#35042
#6282553