Finite Group Databasebeta

← #28292914

Subgroups — #28292914

Order 13568.

6636 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289396C218yesmaximal, complemented
2#20289336C214yesmaximal, complemented
3#20289272C214yesmaximal, complemented
4#20289223C212yesmaximal, complemented
5#20289144C212yesmaximal, complemented
6#20288954C211yesmaximal, characteristic, complemented
7#20288944C212yesmaximal, complemented
8#20288709C214yesmaximal, complemented
9#20288690C214yesmaximal, complemented
10#20288677C214yesmaximal, complemented
11#20288660C214yesmaximal, complemented
12#20288642C218yesmaximal, complemented
13#20288638C212yesmaximal, complemented
14#20288614C212yesmaximal, complemented
15#20288436C214yesmaximal, complemented
16#20288409C214yesmaximal, complemented
17#20288007C211yesmaximal, characteristic, complemented
18C2×#16811159C212yesmaximal, complemented
19C53×#3538C211yesmaximal, characteristic, complemented
20#16811377C2218yescomplemented
21#16811372C2214yescomplemented
22#16811369C2218yescomplemented
23#16811363C2214yes—
24#16811363C2214yescomplemented
25#16811358C2214yescomplemented
26#16811355C2218yescomplemented
27#16811349C2214yescomplemented
28#16811347C2218yescomplemented
29#16811347C2218yescomplemented
30#16811347C2214yescomplemented
31#16811339C2218yescomplemented
32#16811339C2214yescomplemented
33#16811331C2218yescomplemented
34#16811331C2214yescomplemented
35#16811329C2214yescomplemented
36#16811326C2218yescomplemented
37#16811326C2218yescomplemented
38#16811324C2218yescomplemented
39#16811324C2218yescomplemented
40#16811319C2214yes—
41#16811319C2218yescomplemented
42#16811317C2214yescomplemented
43#16811311C2218yescomplemented
44#16811311C2218yescomplemented
45#16811309C2218yescomplemented
46#16811307C2218yescomplemented
47#16811307C2214yescomplemented
48#16811306C2218yescomplemented
49#16811305C2218yescomplemented
50#16811301C2214yescomplemented
51#16811300C2218yescomplemented
52#16811300C2218yescomplemented
53#16811298C2218yescomplemented
54#16811297C2218yescomplemented
55#16811296C2218yescomplemented
56#16811296C2218yescomplemented
57#16811284C2214yescomplemented
58#16811284C2214yescomplemented
59#16811274C2214yescomplemented
60#16811271C2218yescomplemented
61#16811268C2218yescomplemented
62#16811265C2218yescomplemented
63#16811264C2214yescomplemented
64#16811264C2214yescomplemented
65#16811263C2218yescomplemented
66D4×D212C2214yes—
67#16811255C2214yes—
68#16811248C2214yescomplemented
69#16811247C2218yescomplemented
70#16811246C2214yescomplemented
71#16811246C2214yescomplemented
72#16811246C2218yescomplemented
73#16811239C2218yescomplemented
74#16811234C2218yescomplemented
75#16811234C2212yescomplemented
76#16811232C2218yescomplemented
77#16811229C2212yescomplemented
78#16811228C2212yes—
79#16811225C2218yescomplemented
80#16811221C2218yescomplemented
81#16811220C2214yescomplemented
82#16811217C2218yescomplemented
83#16811214C2218yescomplemented
84#16811214C2218yescomplemented
85#16811213C2214yes—
86#16811213C2218yescomplemented
87#16811213C2218yescomplemented
88#16811213C2214yescomplemented
89#16811212C2218yescomplemented
90#16811207C2218yescomplemented
91#16811204C2214yescomplemented
92#16811203C2214yescomplemented
93#16811187C2212yes—
94#16811181C2214yes—
95#16811176C2211yescharacteristic, complemented
96#16811176C2212yescomplemented
97#16811175C2212yescomplemented
98#16811174C2212yescomplemented
99#16811169C2211yescharacteristic, complemented
100#16811168C2212yescomplemented
101#16811160C2214yescomplemented
102#16811159C2212yescomplemented
103#16811159C2214yescomplemented
104#16811159C2214yescomplemented
105#16811159C2214yescomplemented
106#16811159C2214yescomplemented
107#16811159C2214yescomplemented
108#16811159C2214yescomplemented
109#16811159C2218yescomplemented
110#16811159C2214yescomplemented
111#16811159C2214yescomplemented
112#16811159C2214yescomplemented
113#16811154C2212yescomplemented
114#16811153C2214yescomplemented
115#16811153C2218yescomplemented
116#16811150C2214yescomplemented
117C2×#13133212C2214yescomplemented
118C2×#13133208C2212yescomplemented
119#125×D53C2212yescomplemented
120C2×#13133206C2212yescomplemented
121C2×#13133206C2212yescomplemented
122#16811135C2218yescomplemented
123#16811134C2211yescharacteristic, complemented
124#16811129C2214yescomplemented
125C2×#13133201C2214yescomplemented
126#123×D53C2218yescomplemented
127C2×#13133191C2212yes—
128#16811105C2214yescomplemented
129#16811103C2218yescomplemented
130#16811101C2212yescomplemented
131#16811097C2212yescomplemented
132#16811095C2218yescomplemented
133#41×Dic53C2211yescharacteristic, complemented
134#16811091C2211yescharacteristic, complemented
135C4×#11719947C2214yescomplemented
136C2×Q8×Dic53C2212yescomplemented
137C2×#13133179C2212yescomplemented
138C2×#13133177C2214yescomplemented
139C2×#13133175C2214yescomplemented
140C22×C4×Dic53C2211yescharacteristic, complemented
141C53×#563C2214yescomplemented
142C53×#552C2214yescomplemented
143C53×#551C2214yescomplemented
144D4×Q8×C53C2214yescomplemented
145C53×#544C2214yescomplemented
146C53×#541C2212yescomplemented
147C53×#539C2214yescomplemented
148C53×#536C2212yescomplemented
149C53×#525C2211yescharacteristic
150C2×C22⋊Q8×C53C2212yescomplemented
151C2×#11719949C2314yes—
152C2×#11719945C2318yes—
153C2×#11719945C2311yescharacteristic
154C2×#11719947C2314yes—
155C22×D212C2312yes—
156C22×D212C2312yes—
157C22×C22⋊D53C2314yes—
158C2×D4×D53C2318yes—
159C23×Dic53C2312yes—
160C22×C4×D53C2314yes—
161#13133216C2318yes—
162#13133216C2314yes—
163#13133216C2312yes—
164#13133215C2311yescharacteristic
165#13133214C2312yes—
166#13133213C2314yes—
167#13133213C2311yescharacteristic
168#13133212C2318yes—
169#13133212C2318yes—
170#13133212C2318yes—
171#13133212C2318yes—
172#13133212C2318yes—
173#13133212C2318yes—
174#13133212C2318yes—
175#13133212C2318yes—
176#13133212C2318yes—
177#13133212C2314yes—
178#13133212C2318yes—
179#13133212C2318yes—
180#13133212C2318yes—
181#13133211C2318yes—
182#13133210C2314yes—
183#13133210C2318yes—
184#13133209C2318yes—
185#13133209C2312yes—
186#13133208C2318yes—
187#13133208C2314yes—
188#13133208C2314yes—
189#13133208C2312yes—
190#13133208C2314yes—
191#13133208C2314yes—
192#13133207C2318yes—
193#13133207C2318yes—
194#13133207C2318yes—
195#13133207C2318yes—
196#13133207C2314yes—
197#13133206C2314yes—
198#13133206C2314yes—
199#13133206C2318yes—
200#13133206C2318yes—
201#13133206C2314yes—
202#13133206C2318yes—
203#13133206C2311yescharacteristic
204#13133206C2314yes—
205#13133206C2314yes—
206#13133206C2314yes—
207#13133205C2318yes—
208#13133204C2311yescharacteristic
209#13133203C2318yes—
210#13133203C2318yes—
211#13133203C2314yes—
212#13133202C2318yes—
213#13133202C2318yes—
214#13133202C2318yes—
215#13133202C2318yes—
216#13133202C2318yes—
217#13133202C2318yes—
218#13133202C2318yes—
219#13133202C2318yes—
220#13133201C2318yes—
221#13133201C2318yes—
222#13133201C2318yes—
223#13133201C2318yes—
224#13133201C2318yes—
225#13133201C2314yes—
226#13133200C2318yes—
227#13133200C2312yes—
228#13133199C2318yes—
229#13133199C2318yes—
230#13133199C2318yes—
231#13133199C2318yes—
232#13133199C2318yes—
233#13133198C2314yes—
234#13133197C2318yes—
235#13133197C2318yes—
236#13133197C2318yes—
237#13133197C2318yes—
238#13133197C2318yes—
239#13133196C2312yes—
240#13133195C2318yes—
241#13133195C2318yes—
242#13133195C2318yes—
243#13133195C2318yes—
244#13133194C2318yes—
245#13133194C2314yes—
246#13133194C2318yes—
247#13133194C2314yes—
248#13133193C2314yes—
249#13133193C2318yes—
250#13133193C2318yes—
251#13133192C2314yes—
252#13133192C2318yes—
253#13133192C2318yes—
254#13133192C2318yes—
255#13133192C2318yes—
256#13133192C2318yes—
257#13133192C2318yes—
258#13133191C2318yes—
259#13133191C2318yes—
260#13133191C2314yes—
261#13133191C2314yes—
262#13133191C2314yes—
263#13133191C2314yes—
264#13133191C2314yes—
265#13133191C2312yes—
266#13133190C2318yes—
267#13133190C2318yes—
268#13133190C2318yes—
269#13133190C2318yes—
270#13133189C2314yes—
271#13133189C2318yes—
272#13133189C2314yes—
273#13133187C2318yes—
274#13133187C2318yes—
275#13133187C2318yes—
276#13133187C2318yes—
277#13133186C2312yes—
278#13133185C2314yes—
279#13133185C2314yes—
280Q8×Dic53C2314yes—
281Q8×Dic53C2314yes—
282Q8×Dic53C2314yes—
283Q8×Dic53C2318yes—
284Q8×Dic53C2314yes—
285Q8×Dic53C2314yes—
286Q8×Dic53C2312yes—
287C4×Dic106C2318yes—
288C4×Dic106C2318yes—
289C4×Dic106C2314yes—
290#13133182C2312yes—
291#13133182C2314yes—
292C4×D212C2318yes—
293C4×D212C2318yes—
294C4×D212C2318yes—
295C4×D212C2318yes—
296C4×D212C2314yes—
297C4×D212C2318yes—
298D4×Dic53C2312yes—
299D4×Dic53C2314yes—
300D4×Dic53C2314yes—
301#13133179C2314yes—
302#13133179C2314yes—
303#13133179C2318yes—
304#13133179C2314yes—
305#13133179C2318yes—
306#13133179C2312yes—
307#13133179C2314yes—
308#13133179C2314yes—
309C4×C22⋊D53C2314yes—
310C4×C22⋊D53C2314yes—
311C4×C22⋊D53C2318yes—
312C4×C22⋊D53C2318yes—
313#13133177C2318yes—
314#13133177C2318yes—
315#13133177C2318yes—
316#13133177C2318yes—
317#13133177C2318yes—
318#13133177C2314yes—
319#13133177C2318yes—
320#13133177C2318yes—
321#13133177C2314yes—
322#13133177C2314yes—
323#13133176C2318yes—
324#13133176C2312yes—
325#13133176C2312yes—
326#13133176C2311yescharacteristic
327#13133175C2318yes—
328#13133175C2318yes—
329#13133175C2318yes—
330#13133175C2318yes—
331#13133175C2318yes—
332#13133175C2318yes—
333#13133175C2318yes—
334#13133175C2314yes—
335#13133174C2318yes—
336#13133174C2318yes—
337#13133174C2312yes—
338#13133173C2314yes—
339#13133173C2314yes—
340C2×C4⋊Dic53C2312yes—
341C2×C4⋊Dic53C2314yes—
342C2×C4⋊Dic53C2314yes—
343C2×#11719919C2314yes—
344C4⋊C4×D53C2318yes—
345C4⋊C4×D53C2314yes—
346C4⋊C4×D53C2318yes—
347C4⋊C4×D53C2318yes—
348C2×#11719921C2314yes—
349C2×#11719921C2314yes—
350C2×#11719921C2318yes—
351C2×#11719921C2314yes—
352C2×#11719921C2314yes—
353C22⋊C4×D53C2318yes—
354C22⋊C4×D53C2318yes—
355C22⋊C4×D53C2318yes—
356C2×C4×Dic53C2312yes—
357C2×C4×Dic53C2312yes—
358C2×C4×Dic53C2312yes—
359C2×C4×Dic53C2311yescharacteristic
360C2×C4×Dic53C2312yes—
361C2×C4×Dic53C2312yes—
362C2×C4×Dic53C2311yescharacteristic
363C2×C4×Dic53C2314yes—
364C2×C4×Dic53C2312yes—
365C42×D53C2312yes—
366C2×#41×C53C2311yescharacteristic
367C22×Q8×C53C2312yes—
368C22×Q8×C53C2312yes—
369C23×C4×C53C2311yescharacteristic
370C4⋊Q8×C53C2314yes—
371C4⋊Q8×C53C2312yes—
372C4⋊Q8×C53C2318yes—
373#126×C53C2318yes—
374#126×C53C2318yes—
375#125×C53C2318yes—
376#125×C53C2318yes—
377#125×C53C2312yes—
378#124×C53C2314yes—
379#123×C53C2318yes—
380#123×C53C2314yes—
381#123×C53C2314yes—
382#123×C53C2312yes—
383C22⋊Q8×C53C2314yes—
384C22⋊Q8×C53C2314yes—
385C22⋊Q8×C53C2318yes—
386C22⋊Q8×C53C2318yes—
387C22⋊Q8×C53C2314yes—
388C22⋊Q8×C53C2314yes—
389C22⋊Q8×C53C2314yes—
390C22⋊Q8×C53C2312yes—
391#121×C53C2312yes—
392#120×C53C2312yes—
393C4×Q8×C53C2314yes—
394C4×D4×C53C2318yes—
395C4×D4×C53C2314yes—
396#117×C53C2318yes—
397#117×C53C2311yescharacteristic
398#117×C53C2312yes—
399C2×C4⋊C4×C53C2312yes—
400C2×C4⋊C4×C53C2314yes—
401C2×C22⋊C4×C53C2314yes—
402C24×C53C2411yescharacteristic
403C23×D53C2414yes—
404C23×D53C2414yes—
405#41×C53—42no—
406C2×Q8×C53—44no—
407C2×Q8×C53—44no—
408C2×Q8×C53C2414yes—
409C2×Q8×C53C2414yes—
410C2×Q8×C53C2414yes—
411C2×Q8×C53C2411yescharacteristic
412C2×D4×C53C2414yes—
413C2×D4×C53C2412yes—
414C2×D4×C53C2411yescharacteristic
415C22×C4×C53—42no—
416C22×C4×C53C2414yes—
417C22×C4×C53C2412yes—
418C22×C4×C53C2412yes—
419C22×C4×C53C2411yescharacteristic
420C22×C4×C53C2414yes—
421C22×C4×C53C2412yes—
422C22×C4×C53C2414yes—
423C22×C4×C53C2411yescharacteristic
424C2×C22⋊D53—48no—
425C2×C22⋊D53C2414yes—
426C2×C22⋊D53C2418yes—
427C2×C22⋊D53C2418yes—
428C2×C22⋊D53C2412yes—
429C2×C22⋊D53C2418yes—
430C2×C22⋊D53C2414yes—
431C22×Dic53—44no—
432C22×Dic53C2412yes—
433C22×Dic53C2412yes—
434C22×Dic53C2412yes—
435C22×Dic53C2412yes—
436C22×Dic53C2412yes—
437C22×Dic53C2412yes—
438C22×Dic53C2414yes—
439C22×Dic53C2414yes—
440#11719949—48no—
441#11719947—48no—
442D4×D53—416no—
443#11719945—42no—
444#11719945—416no—
445C2×D212—44no—
446C2×D212—44no—
447C2×D212C2414yes—
448C2×D212C2414yes—
449C2×D212C2411yescharacteristic
450C2×D212C2418yes—
451C2×D212C2418yes—
452C2×D212C2418yes—
453C2×D212C2414yes—
454C2×C4×D53—48no—
455C2×C4×D53C2412yes—
456C2×C4×D53C2414yes—
457C2×C4×D53C2418yes—
458C2×C4×D53C2418yes—
459C2×C4×D53C2418yes—
460C2×C4×D53C2418yes—
461C2×C4×D53C2418yes—
462C2×C4×D53C2418yes—
463C2×Dic106C2411yescharacteristic
464C2×Dic106C2414yes—
465C2×Dic106C2418yes—
466C4⋊C4×C53C2414yes—
467C4⋊C4×C53C2418yes—
468C4⋊C4×C53C2418yes—
469C4⋊C4×C53C2414yes—
470C4⋊C4×C53C2412yes—
471C4⋊C4×C53C2418yes—
472C4⋊C4×C53C2418yes—
473C4⋊C4×C53C2418yes—
474C4⋊C4×C53C2414yes—
475C4⋊C4×C53C2418yes—
476C22⋊C4×C53C2418yes—
477C22⋊C4×C53C2418yes—
478C22⋊C4×C53C2414yes—
479C22⋊C4×C53C2412yes—
480C22⋊C4×C53C2414yes—
481C22⋊C4×C53C2414yes—
482C22⋊C4×C53C2418yes—
483C42×C53C2414yes—
484C42×C53C2412yes—
485C42×C53C2418yes—
486C22⋊Dic53C2414yes—
487C22⋊Dic53C2414yes—
488C22⋊Dic53C2414yes—
489C22⋊Dic53C2414yes—
490C22⋊Dic53C2412yes—
491#11719921C2418yes—
492#11719921C2418yes—
493#11719921C2418yes—
494#11719921C2418yes—
495#11719921C2418yes—
496#11719921C2418yes—
497#11719921C2418yes—
498#11719921C2418yes—
499#11719921C2418yes—
500#11719921C2418yes—
501#11719921C2418yes—
502#11719921C2418yes—
503#11719921C2414yes—
504#11719921C2418yes—
505#11719921C2414yes—
506#11719921C2414yes—
507#11719921C2418yes—
508#11719921C2418yes—
509C4⋊Dic53C2418yes—
510C4⋊Dic53C2418yes—
511C4⋊Dic53C2414yes—
512C4⋊Dic53C2418yes—
513C4⋊Dic53C2414yes—
514C4⋊Dic53C2418yes—
515C4⋊Dic53C2414yes—
516C4⋊Dic53C2414yes—
517C4⋊Dic53C2412yes—
518C4⋊Dic53C2418yes—
519#11719919C2414yes—
520#11719919C2414yes—
521#11719919C2418yes—
522#11719919C2418yes—
523#11719919C2418yes—
524#11719919C2418yes—
525#11719919C2418yes—
526#11719919C2414yes—
527#11719919C2414yes—
528#11719919C2414yes—
529#11719919C2418yes—
530C4×Dic53C2411yescharacteristic
531C4×Dic53C2414yes—
532C4×Dic53C2412yes—
533C4×Dic53C2411yescharacteristic
534C4×Dic53C2411yescharacteristic
535C4×Dic53C2412yes—
536C4×Dic53C2412yes—
537C4×Dic53C2412yes—
538C4×Dic53C2412yes—
539C4×Dic53C2412yes—
540C4×Dic53C2411yescharacteristic
541C4×Dic53C2414yes—
542C4×Dic53C2418yes—
543C4×Dic53C2418yes—
544C4×Dic53C2412yes—
545C4×Dic53C2418yes—
546C4×Dic53C2414yes—
547C23×C53—24no—
548C23×C53—41no—
549C23×C53C2511yescharacteristic
550C23×C53C2512yes—
551C23×C53C2512yes—
552C22×D53—28no—
553C22×D53—44no—
554C22×D53—44no—
555C22×D53—44no—
556C22×D53—48no—
557C22×D53C2512yes—
558C22×D53C2518yes—
559Q8×C53—28no—
560Q8×C53—44no—
561Q8×C53—44no—
562Q8×C53—41no—
563D4×C53—28no—
564D4×C53—41no—
565D4×C53—42no—
566C2×C4×C53—28no—
567C2×C4×C53—24no—
568C2×C4×C53—24no—
569C2×C4×C53—22no—
570C2×C4×C53—42no—
571C2×C4×C53—41no—
572C2×C4×C53—44no—
573C2×C4×C53—44no—
574C2×C4×C53C2518yes—
575C2×C4×C53C2514yes—
576C2×C4×C53C2511yescharacteristic
577C2×C4×C53C2518yes—
578C2×C4×C53C2512yes—
579C2×C4×C53C2512yes—
580C2×C4×C53C2511yescharacteristic
581C22⋊D53—28no—
582C22⋊D53—216no—
583C22⋊D53—42no—
584C22⋊D53—48no—
585C22⋊D53—44no—
586C22⋊D53—48no—
587C2×Dic53—24no—
588C2×Dic53—24no—
589C2×Dic53—44no—
590C2×Dic53—42no—
591C2×Dic53—42no—
592C2×Dic53—42no—
593C2×Dic53—42no—
594C2×Dic53—44no—
595C2×Dic53C2514yes—
596C2×Dic53C2512yes—
597C2×Dic53C2512yes—
598C2×Dic53C2518yes—
599C2×Dic53C2512yes—
600C2×Dic53C2512yes—
601C2×Dic53C2512yes—
602D212—28no—
603D212—44no—
604D212—44no—
605D212—48no—
606D212—41no—
607D212—48no—
608D212—48no—
609C4×D53—24no—
610C4×D53—48no—
611C4×D53—48no—
612C4×D53—48no—
613C4×D53—48no—
614C4×D53—48no—
615C4×D53—44no—
616C4×D53—48no—
617Dic106—48no—
618Dic106—41no—
619Dic106—44no—
620#62829—531nomaximal, Sylow
621C22×C53—22no—
622C22×C53—22no—
623C22×C53—22no—
624C22×C53—24no—
625C22×C53—21no—
626C22×C53—22no—
627C22×C53—44no—
628C22×C53#58514yes—
629C22×C53C2611yescharacteristic
630C2×D53—22no—
631C2×D53—24no—
632C2×D53—28no—
633C2×D53—28no—
634C2×D53—28no—
635C2×D53—88no—
636C2×D53—164no—
637C4×C53—28no—
638C4×C53—24no—
639C4×C53—21no—
640C4×C53—28no—
641C4×C53—22no—
642C4×C53—22no—
643C4×C53#58512yes—
644Dic53—24no—
645Dic53—22no—
646Dic53—22no—
647Dic53—28no—
648Dic53—22no—
649Dic53—22no—
650Dic53—22no—
651#3566—538no—
652#3564—534no—
653#3560—534no—
654#3557—532no—
655#3551—532no—
656#3538D5311yescharacteristic, complemented
657#3537—531no—
658#3536—532no—
659#3516—534no—
660#3515—534no—
661#3514—534no—
662#3513—534no—
663#3513—538no—
664#3512—532no—
665#3510—532no—
666#3493—534no—
667#3491—534no—
668#3444—531no—
669C2×#529—532no—
670C2×C53—24no—
671C2×C53—42no—
672C2×C53—41no—
673C2×C53C2×#58511yescharacteristic
674C2×C53C2×#58512yes—
675D53—42no—
676D53—48no—
677#563—534no—
678#563—538no—
679#563C2×D5314yescomplemented
680#562—538no—
681#560—534no—
682#560—534no—
683#559—538no—
684#559—534no—
685#557—534no—
686#556—538no—
687#556—538no—
688#556—534no—
689#555—534no—
690#555—538no—
691#554—534no—
692#554—538no—
693#554—534no—
694#553—538no—
695#553—538no—
696#553—538no—
697#553—538no—
698#553—534no—
699#553—538no—
700#553—534no—
701#552—538no—
702#552—538no—
703#552—538no—
704#552—538no—
705#552—538no—
706#552—534no—
707#552—538no—
708#552C2×D5314yescomplemented
709#551—538no—
710#551—538no—
711#551—538no—
712#551—534no—
713#551—538no—
714#551—538no—
715#551—538no—
716#551C2×D5314yescomplemented
717D4×Q8C2×D5314yescomplemented
718#548—534no—
719#548—534no—
720#547—538no—
721#547—534no—
722#546—538no—
723#546—534no—
724#546—534no—
725#546—538no—
726#546—538no—
727D42—534no—
728D42—534no—
729#544C2×D5314yescomplemented
730#543—534no—
731#542—538no—
732#542—538no—
733#542—534no—
734#542—534no—
735#542—538no—
736#541—532no—
737#541—538no—
738#541—538no—
739#541C2×D5312yescomplemented
740#540—532no—
741#540—538no—
742#540—532no—
743#539—538no—
744#539—538no—
745#539—538no—
746#539—538no—
747#539—534no—
748#539C2×D5314yescomplemented
749#538—538no—
750#538—538no—
751#538—538no—
752#538—534no—
753#538—534no—
754#538—538no—
755#537—534no—
756#537—534no—
757#536C2×D5312yescomplemented
758#535—532no—
759#534—534no—
760#533—532no—
761#533—531no—
762#533—532no—
763#532—531no—
764#532—532no—
765#532—532no—
766#529—534no—
767#529—534no—
768#529—534no—
769#529—534no—
770#529—534no—
771#529—534no—
772#529—534no—
773#529—534no—
774#529—534no—
775#529—532no—
776#529—538no—
777#529—534no—
778#529—532no—
779#529—534no—
780#529—534no—
781#529—538no—
782C2×#126—534no—
783C2×#125—532no—
784C2×#125—532no—
785C2×#124—532no—
786C2×#124—532no—
787#525—531no—
788#525—534no—
789#525—538no—
790#525C2×D5311yescharacteristic
791C2×#123—538no—
792C2×#123—534no—
793C2×C22⋊Q8C2×D5312yescomplemented
794C2×#121—532no—
795#520—534no—
796#520—538no—
797#519—532no—
798#518—538no—
799#518—532no—
800C4×#41—531no—
801C4×#41—534no—
802C4×#41—531no—
803C2×C4×Q8—532no—
804C2×C4×D4—532no—
805C2×C4×D4—534no—
806C2×#117—534no—
807C22×C42—531no—
808C53#6282911yescharacteristic, complemented, Sylow
809C2×#41—534no—
810C2×#41—534no—
811C2×#41—531no—
812C2×#41—538no—
813C2×#41C22×D5311yescharacteristic
814C22×Q8C22×D5312yes—
815C22×Q8C22×D5312yes—
816C22×D4—534no—
817C22×D4—538no—
818C22×D4—532no—
819C22×D4—532no—
820C23×C4—532no—
821C23×C4—534no—
822C23×C4C22×D5311yescharacteristic
823C4⋊Q8—531no—
824C4⋊Q8—532no—
825C4⋊Q8—534no—
826C4⋊Q8—538no—
827C4⋊Q8C22×D5312yes—
828C4⋊Q8C22×D5314yes—
829C4⋊Q8C22×D5318yes—
830#127—531no—
831#127—534no—
832#127—532no—
833#126—538no—
834#126—538no—
835#126—538no—
836#126—538no—
837#126—534no—
838#126—538no—
839#126—538no—
840#126—538no—
841#126—538no—
842#126—538no—
843#126—538no—
844#126—538no—
845#126—538no—
846#126—534no—
847#126—538no—
848#126—538no—
849#126C22×D5318yes—
850#126C22×D5318yes—
851#125—534no—
852#125—534no—
853#125—534no—
854#125—534no—
855#125—538no—
856#125—534no—
857#125—532no—
858#125—538no—
859#125—538no—
860#125—538no—
861#125—538no—
862#125—532no—
863#125—538no—
864#125C22×D5312yes—
865#125C22×D5318yes—
866#125C22×D5318yes—
867#124—534no—
868#124—534no—
869#124—534no—
870#124—534no—
871#124—538no—
872#124—534no—
873#124—531no—
874#124—538no—
875#124—534no—
876#124—538no—
877#124—531no—
878#124—534no—
879#124—538no—
880#124—538no—
881#124—538no—
882#124C22×D5314yes—
883#123—534no—
884#123—538no—
885#123—532no—
886#123—538no—
887#123—538no—
888#123—538no—
889#123—538no—
890#123—538no—
891#123—538no—
892#123—538no—
893#123—538no—
894#123—538no—
895#123—538no—
896#123—538no—
897#123—538no—
898#123—538no—
899#123—538no—
900#123—534no—
901#123—538no—
902#123—538no—
903#123—538no—
904#123—538no—
905#123C22×D5318yes—
906#123C22×D5312yes—
907#123C22×D5314yes—
908#123C22×D5314yes—
909C22⋊Q8—534no—
910C22⋊Q8—538no—
911C22⋊Q8—538no—
912C22⋊Q8—532no—
913C22⋊Q8—538no—
914C22⋊Q8—538no—
915C22⋊Q8—538no—
916C22⋊Q8—538no—
917C22⋊Q8—538no—
918C22⋊Q8—538no—
919C22⋊Q8—538no—
920C22⋊Q8—538no—
921C22⋊Q8—538no—
922C22⋊Q8—534no—
923C22⋊Q8—534no—
924C22⋊Q8—538no—
925C22⋊Q8—538no—
926C22⋊Q8C22×D5314yes—
927C22⋊Q8C22×D5314yes—
928C22⋊Q8C22×D5314yes—
929C22⋊Q8C22×D5314yes—
930C22⋊Q8C22×D5312yes—
931C22⋊Q8C22×D5314yes—
932C22⋊Q8C22×D5318yes—
933C22⋊Q8C22×D5318yes—
934#121—534no—
935#121—534no—
936#121—538no—
937#121—534no—
938#121—534no—
939#121—534no—
940#121—534no—
941#121—532no—
942#121—534no—
943#121—538no—
944#121—538no—
945#121—538no—
946#121—538no—
947#121—534no—
948#121—538no—
949#121—538no—
950#121—538no—
951#121—538no—
952#121—538no—
953#121—538no—
954#121—538no—
955#121—538no—
956#121C22×D5312yes—
957#120—532no—
958#120—534no—
959#120—534no—
960#120—538no—
961#120—538no—
962#120—538no—
963#120—538no—
964#120C22×D5312yes—
965C4×Q8—534no—
966C4×Q8—534no—
967C4×Q8—534no—
968C4×Q8—534no—
969C4×Q8—532no—
970C4×Q8—538no—
971C4×Q8—534no—
972C4×Q8—534no—
973C4×Q8—532no—
974C4×Q8—534no—
975C4×Q8—538no—
976C4×Q8—538no—
977C4×Q8C22×D5314yes—
978C4×D4—534no—
979C4×D4—534no—
980C4×D4—532no—
981C4×D4—534no—
982C4×D4—534no—
983C4×D4—538no—
984C4×D4—538no—
985C4×D4—534no—
986C4×D4—534no—
987C4×D4—534no—
988C4×D4—534no—
989C4×D4—532no—
990C4×D4—534no—
991C4×D4—538no—
992C4×D4—538no—
993C4×D4—538no—
994C4×D4—538no—
995C4×D4—538no—
996C4×D4—538no—
997C4×D4—534no—
998C4×D4—534no—
999C4×D4—534no—
1000C4×D4—538no—
1001C4×D4—538no—
1002C4×D4—538no—
1003C4×D4—538no—
1004C4×D4—538no—
1005C4×D4—538no—
1006C4×D4—538no—
1007C4×D4—538no—
1008C4×D4—534no—
1009C4×D4C22×D5314yes—
1010C4×D4C22×D5318yes—
1011#117—532no—
1012#117—531no—
1013#117—538no—
1014#117—532no—
1015#117—538no—
1016#117—538no—
1017#117—538no—
1018#117—538no—
1019#117—534no—
1020#117—538no—
1021#117—538no—
1022#117—538no—
1023#117—534no—
1024#117—534no—
1025#117—532no—
1026#117—538no—
1027#117—538no—
1028#117C22×D5311yescharacteristic
1029#117C22×D5312yes—
1030#117C22×D5318yes—
1031C2×C4⋊C4—534no—
1032C2×C4⋊C4—534no—
1033C2×C4⋊C4—532no—
1034C2×C4⋊C4—534no—
1035C2×C4⋊C4—538no—
1036C2×C4⋊C4—538no—
1037C2×C4⋊C4—534no—
1038C2×C4⋊C4—538no—
1039C2×C4⋊C4C22×D5314yes—
1040C2×C4⋊C4C22×D5312yes—
1041C2×C22⋊C4—534no—
1042C2×C22⋊C4—534no—
1043C2×C22⋊C4—534no—
1044C2×C22⋊C4—534no—
1045C2×C22⋊C4—538no—
1046C2×C22⋊C4—538no—
1047C2×C22⋊C4—538no—
1048C2×C22⋊C4—538no—
1049C2×C22⋊C4C22×D5314yes—
1050C2×C42—532no—
1051C2×C42—534no—
1052C2×C42—532no—
1053C2×C42—532no—
1054C2×C42—532no—
1055C2×C42—531no—
1056C2×C42—532no—
1057C2×C42—532no—
1058C2×C42—531no—
1059C2×C42—532no—
1060C24—534no—
1061C24—534no—
1062C24C23×D5311yescharacteristic
1063#41—42no—
1064#41—2122no—
1065#41—21216no—
1066#41—2128no—
1067#41—2128no—
1068C2×Q8—44no—
1069C2×Q8—44no—
1070C2×Q8—531no—
1071C2×Q8—538no—
1072C2×Q8—534no—
1073C2×Q8C23×D5314yes—
1074C2×Q8C23×D5314yes—
1075C2×Q8C23×D5314yes—
1076C2×Q8C23×D5311yescharacteristic
1077C2×D4—534no—
1078C2×D4—538no—
1079C2×D4—534no—
1080C2×D4—538no—
1081C2×D4—532no—
1082C2×D4—538no—
1083C2×D4—534no—
1084C2×D4—538no—
1085C2×D4—538no—
1086C2×D4—534no—
1087C2×D4—538no—
1088C2×D4—534no—
1089C2×D4—531no—
1090C2×D4—2124no—
1091C2×D4—2124no—
1092C2×D4—21216no—
1093C2×D4—2128no—
1094C2×D4C23×D5314yes—
1095C2×D4C23×D5311yescharacteristic
1096C2×D4C23×D5312yes—
1097C22×C4—42no—
1098C22×C4—532no—
1099C22×C4—532no—
1100C22×C4—532no—
1101C22×C4—532no—
1102C22×C4—532no—
1103C22×C4—532no—
1104C22×C4—534no—
1105C22×C4—534no—
1106C22×C4—532no—
1107C22×C4—534no—
1108C22×C4—538no—
1109C22×C4—538no—
1110C22×C4—538no—
1111C22×C4—538no—
1112C22×C4—538no—
1113C22×C4—538no—
1114C22×C4—2128no—
1115C22×C4—2124no—
1116C22×C4C23×D5312yes—
1117C22×C4C23×D5311yescharacteristic
1118C22×C4C23×D5312yes—
1119C22×C4C23×D5314yes—
1120C22×C4C23×D5312yes—
1121C22×C4C23×D5311yescharacteristic
1122C22×C4C23×D5314yes—
1123C22×C4C23×D5314yes—
1124C4⋊C4—534no—
1125C4⋊C4—538no—
1126C4⋊C4—538no—
1127C4⋊C4—538no—
1128C4⋊C4—534no—
1129C4⋊C4—534no—
1130C4⋊C4—538no—
1131C4⋊C4—538no—
1132C4⋊C4—538no—
1133C4⋊C4—538no—
1134C4⋊C4—538no—
1135C4⋊C4—534no—
1136C4⋊C4—538no—
1137C4⋊C4—534no—
1138C4⋊C4—534no—
1139C4⋊C4—538no—
1140C4⋊C4—532no—
1141C4⋊C4—534no—
1142C4⋊C4—534no—
1143C4⋊C4—534no—
1144C4⋊C4—538no—
1145C4⋊C4C23×D5318yes—
1146C4⋊C4C23×D5314yes—
1147C4⋊C4C23×D5318yes—
1148C4⋊C4C23×D5318yes—
1149C4⋊C4C23×D5318yes—
1150C4⋊C4C23×D5314yes—
1151C4⋊C4C23×D5318yes—
1152C4⋊C4C23×D5318yes—
1153C4⋊C4C23×D5314yes—
1154C4⋊C4C23×D5312yes—
1155C22⋊C4—534no—
1156C22⋊C4—534no—
1157C22⋊C4—534no—
1158C22⋊C4—534no—
1159C22⋊C4—532no—
1160C22⋊C4—538no—
1161C22⋊C4—538no—
1162C22⋊C4—538no—
1163C22⋊C4—538no—
1164C22⋊C4—538no—
1165C22⋊C4—538no—
1166C22⋊C4—538no—
1167C22⋊C4—538no—
1168C22⋊C4—538no—
1169C22⋊C4—538no—
1170C22⋊C4—538no—
1171C22⋊C4—538no—
1172C22⋊C4—534no—
1173C22⋊C4—534no—
1174C22⋊C4—538no—
1175C22⋊C4—538no—
1176C22⋊C4—538no—
1177C22⋊C4—534no—
1178C22⋊C4C23×D5314yes—
1179C22⋊C4C23×D5318yes—
1180C22⋊C4C23×D5318yes—
1181C22⋊C4C23×D5318yes—
1182C22⋊C4C23×D5314yes—
1183C22⋊C4C23×D5314yes—
1184C22⋊C4C23×D5312yes—
1185C42—531no—
1186C42—531no—
1187C42—532no—
1188C42—531no—
1189C42—532no—
1190C42—532no—
1191C42—532no—
1192C42—532no—
1193C42—532no—
1194C42—531no—
1195C42—534no—
1196C42—538no—
1197C42—538no—
1198C42—534no—
1199C42—532no—
1200C42—538no—
1201C42—534no—
1202C42C23×D5312yes—
1203C42C23×D5318yes—
1204C42C23×D5314yes—
1205C23—24no—
1206C23—41no—
1207C23—538no—
1208C23—532no—
1209C23—1068no—
1210C23—2124no—
1211C23—2128no—
1212C23—2124no—
1213C23—2124no—
1214C23C24×D5312yes—
1215C23C24×D5311yescharacteristic
1216C23C24×D5312yes—
1217Q8—28no—
1218Q8—44no—
1219Q8—44no—
1220Q8—41no—
1221Q8—2121no—
1222Q8—2128no—
1223Q8—2124no—
1224D4—28no—
1225D4—41no—
1226D4—42no—
1227D4—10616no—
1228D4—1068no—
1229D4—1068no—
1230D4—2124no—
1231D4—2124no—
1232D4—2128no—
1233D4—2121no—
1234D4—2128no—
1235D4—2128no—
1236D4—2128no—
1237D4—2128no—
1238D4—2122no—
1239D4—2124no—
1240C2×C4—28no—
1241C2×C4—24no—
1242C2×C4—22no—
1243C2×C4—24no—
1244C2×C4—42no—
1245C2×C4—41no—
1246C2×C4—44no—
1247C2×C4—44no—
1248C2×C4—532no—
1249C2×C4—532no—
1250C2×C4—532no—
1251C2×C4—534no—
1252C2×C4—532no—
1253C2×C4—538no—
1254C2×C4—532no—
1255C2×C4—1064no—
1256C2×C4—1064no—
1257C2×C4—1064no—
1258C2×C4—2128no—
1259C2×C4—2128no—
1260C2×C4—2128no—
1261C2×C4—2128no—
1262C2×C4—2128no—
1263C2×C4—2128no—
1264C2×C4—2124no—
1265C2×C4—2122no—
1266C2×C4—2122no—
1267C2×C4—2122no—
1268C2×C4—2122no—
1269C2×C4—2124no—
1270C2×C4—2124no—
1271C2×C4C24×D5312yes—
1272C2×C4C24×D5311yescharacteristic
1273C2×C4C24×D5312yes—
1274C2×C4C24×D5318yes—
1275C2×C4C24×D5314yes—
1276C2×C4C24×D5318yes—
1277C2×C4C24×D5311yescharacteristic
1278C22—22no—
1279C22—22no—
1280C22—22no—
1281C22—21no—
1282C22—22no—
1283C22—24no—
1284C22—44no—
1285C22—8484no—
1286C22—1062no—
1287C22—1068no—
1288C22—1064no—
1289C22—1068no—
1290C22—1068no—
1291C22—4248no—
1292C22#1681146014yes—
1293C22C25×D5311yescharacteristic
1294C4—21no—
1295C4—22no—
1296C4—22no—
1297C4—28no—
1298C4—28no—
1299C4—24no—
1300C4—1062no—
1301C4—1062no—
1302C4—1062no—
1303C4—1062no—
1304C4—1062no—
1305C4—1068no—
1306C4—1064no—
1307C4#1681145812yes—
1308C2—24no—
1309C2—41no—
1310C2—42no—
1311C2—2128no—
1312C2—2122no—
1313C2C2×#1681145811yescharacteristic
1314C2C2×#1681146012yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3538C2
hypercenter#3538D53
hypocenterC53#62829
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3538

Complements

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

NH ≅ G/Ntype
1. #20289396C2semidirect
2. #20289336C2semidirect
3. #20289272C2semidirect
4. #20289223C2semidirect
5. #20289144C2semidirect
6. #20288954C2semidirect
7. #20288944C2semidirect
8. #20288709C2semidirect
9. #20288690C2semidirect
10. #20288677C2semidirect
11. #20288660C2semidirect
12. #20288642C2semidirect
13. #20288638C2semidirect
14. #20288614C2semidirect
15. #20288436C2semidirect
16. #20288409C2semidirect
17. #20288007C2semidirect
18. C2×#16811159C2semidirect
19. C53×#3538C2semidirect
20. #16811377C22semidirect
21. #16811372C22semidirect
22. #16811369C22semidirect
24. #16811363C22semidirect
25. #16811358C22semidirect
26. #16811355C22semidirect
27. #16811349C22semidirect
28. #16811347C22semidirect
29. #16811347C22semidirect
30. #16811347C22semidirect
31. #16811339C22semidirect
32. #16811339C22semidirect
33. #16811331C22semidirect
34. #16811331C22semidirect
35. #16811329C22semidirect
36. #16811326C22semidirect
37. #16811326C22semidirect
38. #16811324C22semidirect
39. #16811324C22semidirect
41. #16811319C22semidirect
42. #16811317C22semidirect
43. #16811311C22semidirect
44. #16811311C22semidirect
45. #16811309C22semidirect
46. #16811307C22semidirect
47. #16811307C22semidirect
48. #16811306C22semidirect
49. #16811305C22semidirect
50. #16811301C22semidirect
51. #16811300C22semidirect
52. #16811300C22semidirect
53. #16811298C22semidirect
54. #16811297C22semidirect
55. #16811296C22semidirect
56. #16811296C22semidirect
57. #16811284C22semidirect
58. #16811284C22semidirect
59. #16811274C22semidirect
60. #16811271C22semidirect
61. #16811268C22semidirect
62. #16811265C22semidirect
63. #16811264C22semidirect
64. #16811264C22semidirect
65. #16811263C22semidirect
68. #16811248C22semidirect
69. #16811247C22semidirect
70. #16811246C22semidirect
71. #16811246C22semidirect
72. #16811246C22semidirect
73. #16811239C22semidirect
74. #16811234C22semidirect
75. #16811234C22semidirect
76. #16811232C22semidirect
77. #16811229C22semidirect
79. #16811225C22semidirect
80. #16811221C22semidirect
81. #16811220C22semidirect
82. #16811217C22semidirect
83. #16811214C22semidirect
84. #16811214C22semidirect
86. #16811213C22semidirect
87. #16811213C22semidirect
88. #16811213C22semidirect
89. #16811212C22semidirect
90. #16811207C22semidirect
91. #16811204C22semidirect
92. #16811203C22semidirect
95. #16811176C22semidirect
96. #16811176C22semidirect
97. #16811175C22semidirect
98. #16811174C22semidirect
99. #16811169C22semidirect
100. #16811168C22semidirect
101. #16811160C22semidirect
102. #16811159C22semidirect
103. #16811159C22semidirect
104. #16811159C22semidirect
105. #16811159C22semidirect
106. #16811159C22semidirect
107. #16811159C22semidirect
108. #16811159C22semidirect
109. #16811159C22semidirect
110. #16811159C22semidirect
111. #16811159C22semidirect
112. #16811159C22semidirect
113. #16811154C22semidirect
114. #16811153C22semidirect
115. #16811153C22semidirect
116. #16811150C22semidirect
117. C2×#13133212C22semidirect
118. C2×#13133208C22semidirect
119. #125×D53C22semidirect
120. C2×#13133206C22semidirect
121. C2×#13133206C22semidirect
122. #16811135C22semidirect
123. #16811134C22semidirect
124. #16811129C22semidirect
125. C2×#13133201C22semidirect
126. #123×D53C22semidirect
128. #16811105C22semidirect
129. #16811103C22semidirect
130. #16811101C22semidirect
131. #16811097C22semidirect
132. #16811095C22semidirect
133. #41×Dic53C22semidirect
134. #16811091C22semidirect
135. C4×#11719947C22semidirect
136. C2×Q8×Dic53C22semidirect
137. C2×#13133179C22semidirect
138. C2×#13133177C22semidirect
139. C2×#13133175C22semidirect
140. C22×C4×Dic53C22semidirect
141. C53×#563C22semidirect
142. C53×#552C22semidirect
143. C53×#551C22semidirect
144. D4×Q8×C53C22semidirect
145. C53×#544C22semidirect
146. C53×#541C22semidirect
147. C53×#539C22semidirect
148. C53×#536C22semidirect
150. C2×C22⋊Q8×C53C22semidirect
656. #3538D53semidirect
679. #563C2×D53semidirect
708. #552C2×D53semidirect
716. #551C2×D53semidirect
717. D4×Q8C2×D53semidirect
729. #544C2×D53semidirect
739. #541C2×D53semidirect
748. #539C2×D53semidirect
757. #536C2×D53semidirect
793. C2×C22⋊Q8C2×D53semidirect
808. C53#62829semidirect

Maximal subgroups

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

subgroupindex
#202893962
#202893362
#202892722
#202892232
#202891442
#202889542
#202889442
#202887092
#202886902
#202886772
#202886602
#202886422
#202886382
#202886142
#202884362
#202884092
#202880072
C2×#168111592
C53×#35382
#6282953