Finite Group Databasebeta

← #28293241

Subgroups — #28293241

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288637C214yesmaximal, complemented
2#20288632C214yesmaximal, complemented
3#20288626C214yesmaximal, complemented
4#20288618C214yesmaximal, complemented
5#20288545C218yesmaximal, complemented
6#20288467C214yesmaximal, complemented
7#20288457C214yesmaximal, complemented
8#20288450C214yesmaximal, complemented
9#20288440C214yesmaximal, complemented
10#20288428C214yesmaximal, complemented
11#20288418C214yesmaximal, complemented
12#20288142C214yesmaximal, complemented
13#20288131C214yesmaximal, complemented
14C2×#16811251C211yesmaximal, characteristic, complemented
15#20288048C211yesmaximal, characteristic, complemented
16#20288044C211yesmaximal, characteristic, complemented
17C2×#16811201C211yesmaximal, characteristic, complemented
18#20287916C211yesmaximal, characteristic, complemented
19C2×#16811103C211yesmaximal, characteristic, complemented
20C53×#3428C211yesmaximal, characteristic, complemented
21C22×#11719945C2211yescharacteristic
22C22×#11719945C2211yescharacteristic
23#16811346C2218yescomplemented
24#16811341C2218yescomplemented
25#16811338C2218yescomplemented
26#16811336C2218yescomplemented
27#16811333C2218yescomplemented
28#16811328C2218yescomplemented
29#16811323C2218yescomplemented
30#16811323C2218yescomplemented
31#16811322C22116yescomplemented
32#16811322C22116yescomplemented
33#16811321C2218yescomplemented
34#16811319C22116yescomplemented
35#16811317C2218yescomplemented
36#16811314C2218yescomplemented
37#16811314C2218yescomplemented
38#16811312C2218yescomplemented
39#16811308C2218yescomplemented
40#16811306C22116yescomplemented
41#16811299C22116yescomplemented
42#16811297C22116yescomplemented
43#16811282C22116yescomplemented
44#16811278C2218yescomplemented
45#16811274C2218yescomplemented
46#16811263C22116yescomplemented
47#16811251C2214yescomplemented
48#16811251C2214yescomplemented
49#16811251C2214yescomplemented
50#16811251C2214yescomplemented
51#16811245C2218yescomplemented
52#16811244C2218yescomplemented
53#16811244C2218yescomplemented
54#16811238C2218yescomplemented
55#16811235C2218yescomplemented
56#16811231C2218yescomplemented
57#16811228C2218yescomplemented
58#16811224C2218yescomplemented
59#16811215C22116yescomplemented
60#16811206C22116yescomplemented
61#16811204C2212yescomplemented
62#16811204C2212yescomplemented
63#16811201C2214yes—
64#16811201C2214yes—
65#16811201C2214yescomplemented
66#16811201C2214yescomplemented
67#16811201C2212yescomplemented
68#16811201C2212yescomplemented
69#16811199C2212yes—
70#16811199C2212yescomplemented
71#16811197C2212yes—
72#16811194C2212yescomplemented
73#16811192C2212yes—
74#16811192C2212yescomplemented
75#16811190C2212yes—
76#16811187C2212yescomplemented
77#16811185C2214yes—
78#16811182C2214yes—
79#16811180C2218yescomplemented
80#16811177C2218yescomplemented
81#16811173C2214yescomplemented
82#16811173C2218yescomplemented
83#16811170C2218yescomplemented
84#16811169C2214yescomplemented
85C2×#13133217C2212yescomplemented
86C2×#13133216C2212yescomplemented
87#16811160C2218yescomplemented
88#16811157C2218yescomplemented
89#16811157C2218yescomplemented
90#16811155C2218yescomplemented
91#16811153C22116yescomplemented
92C2×#13133209C2212yescomplemented
93C2×#13133208C2212yescomplemented
94#16811135C2214yes—
95#16811135C2214yescomplemented
96#16811134C2214yes—
97#16811132C22116yescomplemented
98#16811130C2214yescomplemented
99C2×#13133196C2212yescomplemented
100C2×#13133194C2214yes—
101C2×#13133193C2212yescomplemented
102C2×#13133191C2212yescomplemented
103C2×#13133189C2214yes—
104C2×#13133188C2212yescomplemented
105#16811104C2212yescomplemented
106#16811104C2212yescomplemented
107#16811103C2214yes—
108#16811103C2214yes—
109#16811103C2214yescomplemented
110#16811103C2212yescomplemented
111#16811103C2214yescomplemented
112#16811103C2212yescomplemented
113#16811100C2212yescomplemented
114#16811097C2212yescomplemented
115#16811096C2214yes—
116C4×#11719945C2214yescomplemented
117#16811091C2214yescomplemented
118C2×C4×Dic106C2212yescomplemented
119C2×C4×D212C2212yescomplemented
120C2×#13133177C2214yes—
121C2×#13133176C2211yescharacteristic
122C2×#13133175C2212yescomplemented
123#117×D53C2214yescomplemented
124C22×C4⋊Dic53C2211yescharacteristic
125C2×C4⋊C4×D53C2212yescomplemented
126C22×#41×C53C2211yescharacteristic
127C53×#520C2212yescomplemented
128C53×#520C2212yescomplemented
129C53×#520C2212yescomplemented
130C53×#520C2212yescomplemented
131C53×#519C2212yescomplemented
132C53×#518C2214yes—
133C53×#518C2212yescomplemented
134C4×#41×C53C2214yescomplemented
135C4×#41×C53C2214yescomplemented
136C2×#117×C53C2211yescharacteristic
137C2×#117×C53C2211yescharacteristic
138C2×#117×C53C2214yescomplemented
139C2×#11719945—28no—
140C2×#11719945—28no—
141C2×#11719945C2312yes—
142C2×#11719945C2312yes—
143C2×#11719945C2312yes—
144C2×#11719945C2312yes—
145C2×#11719945C2312yes—
146C2×#11719945C2312yes—
147C2×#11719945C2312yes—
148C2×#11719945C2312yes—
149C2×#11719945C23116yes—
150C22×Dic106C2311yescharacteristic
151C22×Dic106C2311yescharacteristic
152C22×Dic106C2314yes—
153C22×D212C2311yescharacteristic
154C22×D212C2311yescharacteristic
155C22×C22⋊D53C2312yes—
156C22×C22⋊D53C2312yes—
157C22×C22⋊D53C2314yes—
158C23×Dic53C2312yes—
159C22×C4×D53C2312yes—
160C22×C4×D53C2312yes—
161C22×C4×D53C2314yes—
162#13133217C2318yes—
163#13133217C2318yes—
164#13133217C2314yes—
165#13133216C2318yes—
166#13133216C2318yes—
167#13133215C2314yes—
168#13133214C2314yes—
169#13133213C2314yes—
170#13133212C23116yes—
171#13133212C23116yes—
172#13133211C23116yes—
173#13133211C23116yes—
174#13133210C23116yes—
175#13133210C23116yes—
176#13133209C23116yes—
177#13133209C2318yes—
178#13133209C2318yes—
179#13133208C2318yes—
180#13133208C2318yes—
181#13133207C23116yes—
182#13133207C23116yes—
183#13133206C2314yes—
184#13133205C23116yes—
185#13133205C2314yes—
186#13133205C2314yes—
187#13133204C2314yes—
188#13133203C23116yes—
189#13133203C23116yes—
190#13133202C23116yes—
191#13133202C23116yes—
192#13133201C2318yes—
193#13133201C2318yes—
194#13133200C23116yes—
195#13133200C2318yes—
196#13133200C23116yes—
197#13133199C23116yes—
198#13133199C23116yes—
199#13133198C2318yes—
200#13133197C2314yes—
201#13133197C2314yes—
202#13133197C2314yes—
203#13133197C2314yes—
204#13133196C23116yes—
205#13133196C2318yes—
206#13133196C2318yes—
207#13133196C2314yes—
208#13133196C2314yes—
209#13133195C23116yes—
210#13133195C23116yes—
211#13133194C23116yes—
212#13133194C23116yes—
213#13133193C2314yes—
214#13133193C2318yes—
215#13133193C2314yes—
216#13133193C2318yes—
217#13133192C2314yes—
218#13133192C2314yes—
219#13133192C2314yes—
220#13133192C2314yes—
221#13133191C2318yes—
222#13133191C2318yes—
223#13133191C2318yes—
224#13133191C23116yes—
225#13133191C2318yes—
226#13133191C2314yes—
227#13133191C2314yes—
228#13133190C23116yes—
229#13133190C23116yes—
230#13133189C2318yes—
231#13133189C23116yes—
232#13133189C2318yes—
233#13133189C23116yes—
234#13133188C2314yes—
235#13133188C2318yes—
236#13133188C2314yes—
237#13133188C2318yes—
238#13133187C2318yes—
239#13133187C2318yes—
240#13133186C2318yes—
241#13133185C2318yes—
242C4×Dic106C23116yes—
243C4×Dic106C2318yes—
244C4×Dic106C2318yes—
245C4×Dic106C2314yes—
246C4×Dic106C2314yes—
247#13133182C2314yes—
248#13133182C2314yes—
249C4×D212C2318yes—
250C4×D212C23116yes—
251C4×D212C2318yes—
252C4×D212C2318yes—
253C4×D212C2318yes—
254C4×D212C2314yes—
255C4×D212C2314yes—
256#13133179C2314yes—
257#13133179C2314yes—
258C4×C22⋊D53C2318yes—
259C4×C22⋊D53C23116yes—
260C4×C22⋊D53C2318yes—
261C4×C22⋊D53C23116yes—
262C4×C22⋊D53C2318yes—
263C4×C22⋊D53C2318yes—
264#13133177C2318yes—
265#13133177C23116yes—
266#13133177C23116yes—
267#13133177C2318yes—
268#13133176C23116yes—
269#13133176C2312yes—
270#13133176C2312yes—
271#13133176C2312yes—
272#13133176C2312yes—
273#13133175C2318yes—
274#13133175C2314yes—
275#13133175C2318yes—
276#13133175C2314yes—
277#13133174C23116yes—
278#13133174C23116yes—
279#13133174C2318yes—
280#13133173C2318yes—
281C2×C4⋊Dic53C2314yes—
282C2×C4⋊Dic53C2312yes—
283C2×C4⋊Dic53C2312yes—
284C2×C4⋊Dic53C2312yes—
285C2×C4⋊Dic53C2312yes—
286C2×C4⋊Dic53C2312yes—
287C2×C4⋊Dic53C2312yes—
288C2×C4⋊Dic53C2311yescharacteristic
289C2×C4⋊Dic53C2311yescharacteristic
290C2×#11719919C2314yes—
291C2×#11719919C2314yes—
292C2×#11719919C2314yes—
293C2×#11719919C2314yes—
294C4⋊C4×D53C2318yes—
295C4⋊C4×D53C2314yes—
296C4⋊C4×D53C2318yes—
297C4⋊C4×D53C2314yes—
298C2×C22⋊Dic53C2314yes—
299C2×C22⋊Dic53C2312yes—
300C2×#11719921C2314yes—
301C2×#11719921C2314yes—
302C22⋊C4×D53C2318yes—
303C2×C4×Dic53C2314yes—
304C2×C4×Dic53C2312yes—
305C42×D53C2318yes—
306C2×#41×C53—28no—
307C2×#41×C53C2312yes—
308C2×#41×C53C2312yes—
309C2×#41×C53C2312yes—
310C2×#41×C53C2312yes—
311C22×Q8×C53C2311yescharacteristic
312C22×D4×C53C2312yes—
313C22×D4×C53C2311yescharacteristic
314C23×C4×C53C2312yes—
315C23×C4×C53C2311yescharacteristic
316C4×Q8×C53C2314yes—
317C4×Q8×C53C2314yes—
318C4×Q8×C53C2314yes—
319C4×Q8×C53C2314yes—
320C4×D4×C53C2314yes—
321C4×D4×C53C2318yes—
322C4×D4×C53C2318yes—
323C4×D4×C53C2318yes—
324C4×D4×C53C2318yes—
325C4×D4×C53C2314yes—
326C4×D4×C53C2314yes—
327C4×D4×C53C2314yes—
328#117×C53C2312yes—
329#117×C53C2312yes—
330#117×C53C2312yes—
331#117×C53C2312yes—
332#117×C53C2312yes—
333#117×C53C2312yes—
334#117×C53C2312yes—
335#117×C53C2312yes—
336#117×C53C2318yes—
337#117×C53C2318yes—
338#117×C53C2314yes—
339#117×C53C2314yes—
340C2×C4⋊C4×C53C2314yes—
341C2×C4⋊C4×C53C2311yescharacteristic
342C2×C4⋊C4×C53C2311yescharacteristic
343C2×C4⋊C4×C53C2311yescharacteristic
344C2×C4⋊C4×C53C2311yescharacteristic
345C2×C4⋊C4×C53C2314yes—
346C2×C22⋊C4×C53C2312yes—
347C2×C22⋊C4×C53C2312yes—
348C2×C22⋊C4×C53C2318yes—
349C2×C42×C53C2312yes—
350C2×C42×C53C2312yes—
351C2×C42×C53C2318yes—
352C24×C53C2412yes—
353C24×C53C2411yescharacteristic
354C23×D53C2412yes—
355C23×D53C2412yes—
356#41×C53—28no—
357#41×C53—28no—
358#41×C53—28no—
359#41×C53—28no—
360C2×Q8×C53—24no—
361C2×Q8×C53C2412yes—
362C2×Q8×C53C2412yes—
363C2×D4×C53—28no—
364C2×D4×C53—24no—
365C2×D4×C53C2414yes—
366C2×D4×C53C2412yes—
367C2×D4×C53C2412yes—
368C2×D4×C53C2414yes—
369C22×C4×C53—28no—
370C22×C4×C53#4118yescomplemented
371C22×C4×C53C2414yes—
372C22×C4×C53C2414yes—
373C22×C4×C53C2412yes—
374C22×C4×C53C2412yes—
375C22×C4×C53C2412yes—
376C22×C4×C53C2412yes—
377C22×C4×C53C2412yes—
378C22×C4×C53C2418yes—
379C22×C4×C53C2418yes—
380C22×C4×C53C2411yescharacteristic
381C22×C4×C53C2411yescharacteristic
382C22×C4×C53C2411yescharacteristic
383C22×C4×C53C2411yescharacteristic
384C22×C4×C53C2411yescharacteristic
385C22×C4×C53C2411yescharacteristic
386C2×C22⋊D53—28no—
387C2×C22⋊D53—28no—
388C2×C22⋊D53—84no—
389C2×C22⋊D53C2414yes—
390C2×C22⋊D53C2414yes—
391C2×C22⋊D53C2414yes—
392C2×C22⋊D53C2414yes—
393C2×C22⋊D53C2418yes—
394C2×C22⋊D53C2418yes—
395C2×C22⋊D53C24116yes—
396C22×Dic53—82no—
397C22×Dic53C2412yes—
398C22×Dic53C2412yes—
399C22×Dic53C2414yes—
400C22×Dic53C2412yes—
401C22×Dic53C2412yes—
402C22×Dic53C2414yes—
403C22×Dic53C2414yes—
404#11719945—28no—
405#11719945—28no—
406#11719945—28no—
407#11719945—28no—
408#11719945—28no—
409#11719945—28no—
410#11719945—28no—
411#11719945—28no—
412#11719945—816no—
413C2×D212—24no—
414C2×D212—24no—
415C2×D212C2412yes—
416C2×D212C2412yes—
417C2×D212C2412yes—
418C2×D212C2412yes—
419C2×D212C2418yes—
420C2×D212C2418yes—
421C2×C4×D53—28no—
422C2×C4×D53—28no—
423C2×C4×D53—84no—
424C2×C4×D53C2414yes—
425C2×C4×D53C2414yes—
426C2×C4×D53C2414yes—
427C2×C4×D53C2414yes—
428C2×C4×D53C2418yes—
429C2×C4×D53C2418yes—
430C2×C4×D53C24116yes—
431C2×Dic106—24no—
432C2×Dic106—24no—
433C2×Dic106—84no—
434C2×Dic106C2412yes—
435C2×Dic106C2412yes—
436C2×Dic106C2412yes—
437C2×Dic106C2412yes—
438C2×Dic106C24116yes—
439C4⋊C4×C53C2412yes—
440C4⋊C4×C53C2412yes—
441C4⋊C4×C53C2412yes—
442C4⋊C4×C53C2412yes—
443C4⋊C4×C53C2412yes—
444C4⋊C4×C53C2412yes—
445C4⋊C4×C53C2412yes—
446C4⋊C4×C53C2412yes—
447C4⋊C4×C53C2418yes—
448C4⋊C4×C53C2418yes—
449C22⋊C4×C53C2414yes—
450C22⋊C4×C53C2414yes—
451C22⋊C4×C53C2414yes—
452C22⋊C4×C53C2414yes—
453C22⋊C4×C53C2418yes—
454C22⋊C4×C53C2418yes—
455C42×C53C2414yes—
456C42×C53C2414yes—
457C42×C53C2414yes—
458C42×C53C2418yes—
459C42×C53C2418yes—
460C42×C53C2414yes—
461C22⋊Dic53C2414yes—
462C22⋊Dic53C2414yes—
463C22⋊Dic53C24116yes—
464C22⋊Dic53C2418yes—
465C22⋊Dic53C2418yes—
466#11719921C2418yes—
467#11719921C2418yes—
468#11719921C24116yes—
469#11719921C24116yes—
470#11719921C2418yes—
471#11719921C2418yes—
472#11719921C2418yes—
473#11719921C2418yes—
474#11719921C2418yes—
475#11719921C2418yes—
476C4⋊Dic53C2414yes—
477C4⋊Dic53C2414yes—
478C4⋊Dic53C2412yes—
479C4⋊Dic53C2412yes—
480C4⋊Dic53C2414yes—
481C4⋊Dic53C2414yes—
482C4⋊Dic53C2412yes—
483C4⋊Dic53C2412yes—
484C4⋊Dic53C24116yes—
485C4⋊Dic53C2418yes—
486C4⋊Dic53C2418yes—
487#11719919C24116yes—
488#11719919C2418yes—
489#11719919C2418yes—
490#11719919C24116yes—
491#11719919C24116yes—
492#11719919C24116yes—
493#11719919C2418yes—
494#11719919C2418yes—
495C4×Dic53C2414yes—
496C4×Dic53C2418yes—
497C4×Dic53C2418yes—
498C4×Dic53C24116yes—
499C4×Dic53C2414yes—
500C23×C53—24no—
501C23×C53—41no—
502C23×C53—41no—
503C23×C53—42no—
504C23×C53—42no—
505C23×C53C2×#4114yes—
506C23×C53C2514yes—
507C23×C53C2511yescharacteristic
508C23×C53C2511yescharacteristic
509C23×C53C2511yescharacteristic
510C22×D53—24no—
511C22×D53—24no—
512C22×D53—42no—
513C22×D53—42no—
514C22×D53—42no—
515C22×D53—42no—
516C22×D53C2514yes—
517C22×D53C2514yes—
518Q8×C53—24no—
519Q8×C53—24no—
520D4×C53—28no—
521D4×C53—28no—
522D4×C53—24no—
523D4×C53—24no—
524C2×C4×C53—24no—
525C2×C4×C53—28no—
526C2×C4×C53—28no—
527C2×C4×C53—42no—
528C2×C4×C53—42no—
529C2×C4×C53—48no—
530C2×C4×C53—42no—
531C2×C4×C53—48no—
532C2×C4×C53—42no—
533C2×C4×C53C2×#4114yes—
534C2×C4×C53C2×#4114yes—
535C2×C4×C53C2×#4114yes—
536C2×C4×C53C2×#4114yes—
537C2×C4×C53C2×#4114yes—
538C2×C4×C53C2×#4114yes—
539C2×C4×C53C2514yes—
540C2×C4×C53C2514yes—
541C2×C4×C53C2514yes—
542C2×C4×C53C2514yes—
543C2×C4×C53C2514yes—
544C2×C4×C53C2511yescharacteristic
545C2×C4×C53C2511yescharacteristic
546C2×C4×C53C2511yescharacteristic
547C2×C4×C53C2511yescharacteristic
548C22⋊D53—28no—
549C22⋊D53—28no—
550C22⋊D53—28no—
551C22⋊D53—28no—
552C22⋊D53—48no—
553C22⋊D53—416no—
554C22⋊D53—48no—
555C2×Dic53—24no—
556C2×Dic53—24no—
557C2×Dic53—42no—
558C2×Dic53—44no—
559C2×Dic53—44no—
560C2×Dic53—44no—
561C2×Dic53—42no—
562C2×Dic53C2514yes—
563C2×Dic53C2518yes—
564C2×Dic53C2514yes—
565C2×Dic53C2514yes—
566C2×Dic53C2514yes—
567D212—24no—
568D212—24no—
569D212—24no—
570D212—24no—
571D212—48no—
572D212—48no—
573C4×D53—28no—
574C4×D53—28no—
575C4×D53—28no—
576C4×D53—28no—
577C4×D53—416no—
578C4×D53—48no—
579C4×D53—48no—
580Dic106—24no—
581Dic106—24no—
582Dic106—24no—
583Dic106—24no—
584Dic106—416no—
585#62856—531nomaximal, Sylow
586C22×C53—21no—
587C22×C53—21no—
588C22×C53—21no—
589C22×C53—21no—
590C22×C53—21no—
591C22×C53—21no—
592C22×C53—24no—
593C22×C53—24no—
594C22×C53—24no—
595C22×C53—44no—
596C22×C53—84no—
597C22×C53C22×#4112yes—
598C22×C53C22×#4112yes—
599C22×C53C22×#4112yes—
600C22×C53C2611yescharacteristic
601C2×D53—24no—
602C2×D53—24no—
603C2×D53—24no—
604C2×D53—24no—
605C2×D53—24no—
606C2×D53—24no—
607C2×D53—48no—
608C2×D53—84no—
609C4×C53—24no—
610C4×C53—24no—
611C4×C53—24no—
612C4×C53—24no—
613C4×C53—24no—
614C4×C53C22×#4112yes—
615C4×C53C22×#4112yes—
616C4×C53C22×#4112yes—
617C4×C53C22×#4112yes—
618Dic53—24no—
619Dic53—24no—
620Dic53—24no—
621Dic53—28no—
622Dic53—24no—
623#3512—534no—
624#3512—534no—
625#3511—534no—
626#3511—534no—
627#3505—538no—
628#3495—534no—
629#3495—534no—
630#3494—534no—
631#3494—534no—
632#3493—534no—
633#3492—534no—
634#3461—534no—
635#3460—534no—
636C2×#544—531no—
637#3449—531no—
638#3449—531no—
639C2×#537—531no—
640#3428—531no—
641#3428D5311yescharacteristic, complemented
642C2×#520—531no—
643C2×C53—22no—
644C2×C53—22no—
645C2×C53—22no—
646C2×C53—44no—
647C2×C53C23×#4111yescharacteristic
648C2×C53H(7,𝔽2)11yescharacteristic
649C2×C532−1+611yescharacteristic
650D53—44no—
651D53—44no—
652C22×#41—531no—
653C22×#41—531no—
654C22×#41C2×D5311yescharacteristic
655#556—538no—
656#556—538no—
657#555—538no—
658#555—538no—
659#554—538no—
660#554—538no—
661#553—5316no—
662#553—5316no—
663#553—5316no—
664#553—538no—
665#553—538no—
666#553—538no—
667#553—538no—
668#552—538no—
669#552—538no—
670#552—5316no—
671#552—538no—
672#552—538no—
673#551—5316no—
674#551—5316no—
675#548—5316no—
676#547—538no—
677#547—538no—
678#546—5316no—
679#544—534no—
680#544—534no—
681#544—534no—
682#544—534no—
683#542—538no—
684#542—538no—
685#542—538no—
686#542—538no—
687#541—538no—
688#541—538no—
689#540—538no—
690#540—538no—
691#539—5316no—
692#538—5316no—
693#537—534no—
694#537—534no—
695#537—534no—
696#537—534no—
697#537—532no—
698#537—532no—
699#537—532no—
700#537—532no—
701#536—532no—
702#536—532no—
703#536—532no—
704#536—532no—
705#535—532no—
706#535—532no—
707#535—532no—
708#535—532no—
709#534—534no—
710#534—534no—
711#533—538no—
712#533—538no—
713#532—534no—
714#532—538no—
715#532—534no—
716#532—538no—
717C2×C4⋊Q8—532no—
718C2×C4⋊Q8—532no—
719#529—538no—
720#529—5316no—
721#529—538no—
722#529—538no—
723#529—538no—
724C2×#125—532no—
725C2×#125—532no—
726#525—534no—
727#525—534no—
728#525—5316no—
729#525—534no—
730#525—534no—
731C2×C22⋊Q8—532no—
732C2×C22⋊Q8—532no—
733C2×C22⋊Q8—534no—
734C2×#121—532no—
735C2×#121—534no—
736C2×#121—532no—
737#520—534no—
738#520—534no—
739#520—534no—
740#520—534no—
741#520—532no—
742#520—532no—
743#520—532no—
744#520—532no—
745#520C2×D5312yescomplemented
746#520C2×D5312yescomplemented
747#520C2×D5312yescomplemented
748#520C2×D5312yescomplemented
749#519—532no—
750#519C2×D5312yescomplemented
751#518—532no—
752#518—534no—
753#518C2×D5314yes—
754#518C2×D5312yescomplemented
755C4×#41—534no—
756C4×#41—534no—
757C4×#41C2×D5314yescomplemented
758C4×#41C2×D5314yescomplemented
759C2×C4×Q8—532no—
760C2×C4×D4—534no—
761C2×C4×D4—532no—
762C2×#117—531no—
763C2×#117—534no—
764C2×#117—532no—
765C2×#117C2×D5311yescharacteristic
766C2×#117C2×D5311yescharacteristic
767C2×#117C2×D5314yescomplemented
768C22×C4⋊C4—531no—
769C22×C4⋊C4—532no—
770C53#6285611yescharacteristic, complemented, Sylow
771C2×#41—28no—
772C2×#41—532no—
773C2×#41—532no—
774C2×#41—532no—
775C2×#41—532no—
776C2×#41—532no—
777C2×#41—532no—
778C2×#41—532no—
779C2×#41—532no—
780C2×#41—5316no—
781C2×#41—1068no—
782C2×#41—1068no—
783C2×#41C22×D5312yes—
784C2×#41C22×D5312yes—
785C2×#41C22×D5312yes—
786C2×#41C22×D5312yes—
787C22×Q8—531no—
788C22×Q8—531no—
789C22×Q8—534no—
790C22×Q8C22×D5311yescharacteristic
791C22×D4—532no—
792C22×D4—532no—
793C22×D4—534no—
794C22×D4—531no—
795C22×D4—531no—
796C22×D4C22×D5312yes—
797C22×D4C22×D5311yescharacteristic
798C23×C4—532no—
799C23×C4—532no—
800C23×C4—532no—
801C23×C4—534no—
802C23×C4C22×D5312yes—
803C23×C4C22×D5311yescharacteristic
804C4⋊Q8—534no—
805C4⋊Q8—538no—
806C4⋊Q8—538no—
807C4⋊Q8—538no—
808C4⋊Q8—538no—
809C4⋊Q8—534no—
810#127—534no—
811#127—534no—
812#126—5316no—
813#126—5316no—
814#126—5316no—
815#126—5316no—
816#126—5316no—
817#126—5316no—
818#125—538no—
819#125—538no—
820#125—5316no—
821#125—5316no—
822#125—538no—
823#125—538no—
824#125—5316no—
825#124—534no—
826#124—534no—
827#124—5316no—
828#124—5316no—
829#124—534no—
830#124—534no—
831#124—5316no—
832#123—538no—
833#123—538no—
834#123—5316no—
835#123—5316no—
836#123—5316no—
837#123—5316no—
838#123—538no—
839#123—538no—
840#123—5316no—
841#123—5316no—
842C22⋊Q8—538no—
843C22⋊Q8—538no—
844C22⋊Q8—534no—
845C22⋊Q8—534no—
846C22⋊Q8—538no—
847C22⋊Q8—538no—
848C22⋊Q8—534no—
849C22⋊Q8—534no—
850C22⋊Q8—5316no—
851C22⋊Q8—534no—
852C22⋊Q8—534no—
853C22⋊Q8—534no—
854C22⋊Q8—534no—
855C22⋊Q8—5316no—
856C22⋊Q8—5316no—
857C22⋊Q8—5316no—
858C22⋊Q8—5316no—
859#121—5316no—
860#121—538no—
861#121—538no—
862#121—5316no—
863#121—534no—
864#121—534no—
865#121—538no—
866#121—538no—
867#121—538no—
868#121—538no—
869#121—534no—
870#121—534no—
871#121—538no—
872#121—538no—
873#121—5316no—
874#121—534no—
875#121—534no—
876#121—534no—
877#121—534no—
878#121—5316no—
879#121—5316no—
880#120—538no—
881#120—538no—
882#120—538no—
883#120—538no—
884C4×Q8—534no—
885C4×Q8—534no—
886C4×Q8—538no—
887C4×Q8—538no—
888C4×Q8—534no—
889C4×Q8—534no—
890C4×Q8—5316no—
891C4×Q8C22×D5314yes—
892C4×Q8C22×D5314yes—
893C4×Q8C22×D5314yes—
894C4×Q8C22×D5314yes—
895C4×D4—538no—
896C4×D4—538no—
897C4×D4—538no—
898C4×D4—538no—
899C4×D4—5316no—
900C4×D4—5316no—
901C4×D4—534no—
902C4×D4—534no—
903C4×D4—5316no—
904C4×D4—5316no—
905C4×D4—538no—
906C4×D4—538no—
907C4×D4—538no—
908C4×D4—538no—
909C4×D4—534no—
910C4×D4—534no—
911C4×D4—538no—
912C4×D4—538no—
913C4×D4—5316no—
914C4×D4C22×D5318yes—
915C4×D4C22×D5318yes—
916C4×D4C22×D5318yes—
917C4×D4C22×D5318yes—
918C4×D4C22×D5314yes—
919C4×D4C22×D5314yes—
920C4×D4C22×D5314yes—
921C4×D4C22×D5314yes—
922#117—532no—
923#117—532no—
924#117—532no—
925#117—532no—
926#117—5316no—
927#117—534no—
928#117—538no—
929#117—538no—
930#117—534no—
931#117—538no—
932#117—538no—
933#117—5316no—
934#117—5316no—
935#117C22×D5312yes—
936#117C22×D5312yes—
937#117C22×D5312yes—
938#117C22×D5312yes—
939#117C22×D5312yes—
940#117C22×D5312yes—
941#117C22×D5312yes—
942#117C22×D5312yes—
943#117C22×D5318yes—
944#117C22×D5318yes—
945#117C22×D5314yes—
946#117C22×D5314yes—
947C2×C4⋊C4—532no—
948C2×C4⋊C4—532no—
949C2×C4⋊C4—534no—
950C2×C4⋊C4—532no—
951C2×C4⋊C4—532no—
952C2×C4⋊C4—532no—
953C2×C4⋊C4—532no—
954C2×C4⋊C4—531no—
955C2×C4⋊C4—531no—
956C2×C4⋊C4—534no—
957C2×C4⋊C4—534no—
958C2×C4⋊C4—534no—
959C2×C4⋊C4—534no—
960C2×C4⋊C4—538no—
961C2×C4⋊C4—538no—
962C2×C4⋊C4—534no—
963C2×C4⋊C4—534no—
964C2×C4⋊C4C22×D5311yescharacteristic
965C2×C4⋊C4C22×D5311yescharacteristic
966C2×C4⋊C4C22×D5311yescharacteristic
967C2×C4⋊C4C22×D5311yescharacteristic
968C2×C4⋊C4C22×D5314yes—
969C2×C4⋊C4C22×D5314yes—
970C2×C22⋊C4—532no—
971C2×C22⋊C4—534no—
972C2×C22⋊C4—534no—
973C2×C22⋊C4—534no—
974C2×C22⋊C4—538no—
975C2×C22⋊C4C22×D5312yes—
976C2×C22⋊C4C22×D5312yes—
977C2×C22⋊C4C22×D5318yes—
978C2×C42—534no—
979C2×C42—532no—
980C2×C42—538no—
981C2×C42C22×D5312yes—
982C2×C42C22×D5312yes—
983C2×C42C22×D5318yes—
984C24—532no—
985C24—532no—
986C24C23×D5312yes—
987C24C23×D5311yescharacteristic
988#41—28no—
989#41—28no—
990#41—28no—
991#41—28no—
992#41—1068no—
993#41—1068no—
994#41—1068no—
995#41—1068no—
996#41—1068no—
997#41—1068no—
998#41—1068no—
999#41—1068no—
1000#41—42416no—
1001C2×Q8—24no—
1002C2×Q8—532no—
1003C2×Q8—532no—
1004C2×Q8—532no—
1005C2×Q8—532no—
1006C2×Q8—5316no—
1007C2×Q8—1064no—
1008C2×Q8—1064no—
1009C2×Q8—4244no—
1010C2×Q8C23×D5312yes—
1011C2×Q8C23×D5312yes—
1012C2×D4—28no—
1013C2×D4—24no—
1014C2×D4—534no—
1015C2×D4—534no—
1016C2×D4—534no—
1017C2×D4—534no—
1018C2×D4—538no—
1019C2×D4—538no—
1020C2×D4—5316no—
1021C2×D4—532no—
1022C2×D4—532no—
1023C2×D4—532no—
1024C2×D4—532no—
1025C2×D4—538no—
1026C2×D4—538no—
1027C2×D4—1068no—
1028C2×D4—1068no—
1029C2×D4—1064no—
1030C2×D4—1064no—
1031C2×D4—4244no—
1032C2×D4C23×D5314yes—
1033C2×D4C23×D5314yes—
1034C2×D4C23×D5312yes—
1035C2×D4C23×D5312yes—
1036C22×C4—28no—
1037C22×C4—532no—
1038C22×C4—532no—
1039C22×C4—532no—
1040C22×C4—532no—
1041C22×C4—534no—
1042C22×C4—534no—
1043C22×C4—534no—
1044C22×C4—534no—
1045C22×C4—534no—
1046C22×C4—534no—
1047C22×C4—534no—
1048C22×C4—538no—
1049C22×C4—538no—
1050C22×C4—5316no—
1051C22×C4—1068no—
1052C22×C4—1068no—
1053C22×C4—4244no—
1054C22×C4—4242no—
1055C22×C4#1171994518yescomplemented
1056C22×C4C23×D5314yes—
1057C22×C4C23×D5312yes—
1058C22×C4C23×D5314yes—
1059C22×C4C23×D5312yes—
1060C22×C4C23×D5312yes—
1061C22×C4C23×D5312yes—
1062C22×C4C23×D5312yes—
1063C22×C4C23×D5318yes—
1064C22×C4C23×D5318yes—
1065C22×C4C23×D5311yescharacteristic
1066C22×C4C23×D5311yescharacteristic
1067C22×C4C23×D5311yescharacteristic
1068C22×C4C23×D5311yescharacteristic
1069C22×C4C23×D5311yescharacteristic
1070C22×C4C23×D5311yescharacteristic
1071C4⋊C4—534no—
1072C4⋊C4—534no—
1073C4⋊C4—532no—
1074C4⋊C4—532no—
1075C4⋊C4—534no—
1076C4⋊C4—534no—
1077C4⋊C4—5316no—
1078C4⋊C4—532no—
1079C4⋊C4—532no—
1080C4⋊C4—538no—
1081C4⋊C4—538no—
1082C4⋊C4—5316no—
1083C4⋊C4—5316no—
1084C4⋊C4—5316no—
1085C4⋊C4—5316no—
1086C4⋊C4—538no—
1087C4⋊C4—538no—
1088C4⋊C4—538no—
1089C4⋊C4—538no—
1090C4⋊C4C23×D5312yes—
1091C4⋊C4C23×D5312yes—
1092C4⋊C4C23×D5312yes—
1093C4⋊C4C23×D5312yes—
1094C4⋊C4C23×D5312yes—
1095C4⋊C4C23×D5312yes—
1096C4⋊C4C23×D5312yes—
1097C4⋊C4C23×D5312yes—
1098C4⋊C4C23×D5318yes—
1099C4⋊C4C23×D5318yes—
1100C22⋊C4—534no—
1101C22⋊C4—534no—
1102C22⋊C4—5316no—
1103C22⋊C4—538no—
1104C22⋊C4—538no—
1105C22⋊C4—538no—
1106C22⋊C4—5316no—
1107C22⋊C4—538no—
1108C22⋊C4—5316no—
1109C22⋊C4—538no—
1110C22⋊C4—538no—
1111C22⋊C4—538no—
1112C22⋊C4—538no—
1113C22⋊C4—538no—
1114C22⋊C4—538no—
1115C22⋊C4C23×D5314yes—
1116C22⋊C4C23×D5314yes—
1117C22⋊C4C23×D5314yes—
1118C22⋊C4C23×D5314yes—
1119C22⋊C4C23×D5318yes—
1120C22⋊C4C23×D5318yes—
1121C42—534no—
1122C42—538no—
1123C42—5316no—
1124C42—538no—
1125C42—534no—
1126C42C23×D5314yes—
1127C42C23×D5314yes—
1128C42C23×D5314yes—
1129C42C23×D5318yes—
1130C42C23×D5318yes—
1131C42C23×D5314yes—
1132C23—24no—
1133C23—41no—
1134C23—41no—
1135C23—42no—
1136C23—42no—
1137C23—534no—
1138C23—534no—
1139C23—1064no—
1140C23—1064no—
1141C23—2122no—
1142C23—2122no—
1143C23—2122no—
1144C23—2122no—
1145C23C2×#1171994514yes—
1146C23C24×D5314yes—
1147C23C24×D5311yescharacteristic
1148C23C24×D5311yescharacteristic
1149C23C24×D5311yescharacteristic
1150Q8—24no—
1151Q8—24no—
1152Q8—1064no—
1153Q8—1064no—
1154Q8—1064no—
1155Q8—1064no—
1156Q8—21216no—
1157D4—28no—
1158D4—28no—
1159D4—24no—
1160D4—24no—
1161D4—1068no—
1162D4—1068no—
1163D4—1068no—
1164D4—1068no—
1165D4—1064no—
1166D4—1064no—
1167D4—1064no—
1168D4—1064no—
1169D4—2128no—
1170D4—2128no—
1171D4—2128no—
1172D4—21216no—
1173D4—2128no—
1174C2×C4—24no—
1175C2×C4—28no—
1176C2×C4—28no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—48no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—48no—
1183C2×C4—534no—
1184C2×C4—534no—
1185C2×C4—534no—
1186C2×C4—534no—
1187C2×C4—538no—
1188C2×C4—1064no—
1189C2×C4—1064no—
1190C2×C4—1068no—
1191C2×C4—1068no—
1192C2×C4—1068no—
1193C2×C4—1068no—
1194C2×C4—2128no—
1195C2×C4—21216no—
1196C2×C4—2128no—
1197C2×C4—2122no—
1198C2×C4—2124no—
1199C2×C4—2124no—
1200C2×C4—2124no—
1201C2×C4—2122no—
1202C2×C4C2×#1171994514yes—
1203C2×C4C2×#1171994514yes—
1204C2×C4C2×#1171994514yes—
1205C2×C4C2×#1171994514yes—
1206C2×C4C2×#1171994514yes—
1207C2×C4C2×#1171994514yes—
1208C2×C4C24×D5314yes—
1209C2×C4C24×D5314yes—
1210C2×C4C24×D5314yes—
1211C2×C4C24×D5314yes—
1212C2×C4C24×D5314yes—
1213C2×C4C24×D5311yescharacteristic
1214C2×C4C24×D5311yescharacteristic
1215C2×C4C24×D5311yescharacteristic
1216C2×C4C24×D5311yescharacteristic
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—44no—
1227C22—84no—
1228C22—1064no—
1229C22—1064no—
1230C22—1064no—
1231C22—1064no—
1232C22—1064no—
1233C22—1064no—
1234C22—4244no—
1235C22—2128no—
1236C22C22×#1171994512yes—
1237C22C22×#1171994512yes—
1238C22C22×#1171994512yes—
1239C22C25×D5311yescharacteristic
1240C4—24no—
1241C4—24no—
1242C4—24no—
1243C4—24no—
1244C4—24no—
1245C4—1064no—
1246C4—1064no—
1247C4—1068no—
1248C4—1064no—
1249C4—1064no—
1250C4C22×#1171994512yes—
1251C4C22×#1171994512yes—
1252C4C22×#1171994512yes—
1253C4C22×#1171994512yes—
1254C2—22no—
1255C2—22no—
1256C2—22no—
1257C2—44no—
1258C2—2124no—
1259C2—2124no—
1260C2C23×#1171994511yescharacteristic
1261C2#2028952611yescharacteristic
1262C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3428C2
hypercenter#3428D53
hypocenterC53#62856
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #20288637C2semidirect
2. #20288632C2semidirect
3. #20288626C2semidirect
4. #20288618C2semidirect
5. #20288545C2semidirect
6. #20288467C2semidirect
7. #20288457C2semidirect
8. #20288450C2semidirect
9. #20288440C2semidirect
10. #20288428C2semidirect
11. #20288418C2semidirect
12. #20288142C2semidirect
13. #20288131C2semidirect
14. C2×#16811251C2semidirect
15. #20288048C2semidirect
16. #20288044C2semidirect
17. C2×#16811201C2semidirect
18. #20287916C2semidirect
19. C2×#16811103C2semidirect
20. C53×#3428C2semidirect
23. #16811346C22semidirect
24. #16811341C22semidirect
25. #16811338C22semidirect
26. #16811336C22semidirect
27. #16811333C22semidirect
28. #16811328C22semidirect
29. #16811323C22semidirect
30. #16811323C22semidirect
31. #16811322C22semidirect
32. #16811322C22semidirect
33. #16811321C22semidirect
34. #16811319C22semidirect
35. #16811317C22semidirect
36. #16811314C22semidirect
37. #16811314C22semidirect
38. #16811312C22semidirect
39. #16811308C22semidirect
40. #16811306C22semidirect
41. #16811299C22semidirect
42. #16811297C22semidirect
43. #16811282C22semidirect
44. #16811278C22semidirect
45. #16811274C22semidirect
46. #16811263C22semidirect
47. #16811251C22semidirect
48. #16811251C22semidirect
49. #16811251C22semidirect
50. #16811251C22semidirect
51. #16811245C22semidirect
52. #16811244C22semidirect
53. #16811244C22semidirect
54. #16811238C22semidirect
55. #16811235C22semidirect
56. #16811231C22semidirect
57. #16811228C22semidirect
58. #16811224C22semidirect
59. #16811215C22semidirect
60. #16811206C22semidirect
61. #16811204C22semidirect
62. #16811204C22semidirect
65. #16811201C22semidirect
66. #16811201C22semidirect
67. #16811201C22semidirect
68. #16811201C22semidirect
70. #16811199C22semidirect
72. #16811194C22semidirect
74. #16811192C22semidirect
76. #16811187C22semidirect
79. #16811180C22semidirect
80. #16811177C22semidirect
81. #16811173C22semidirect
82. #16811173C22semidirect
83. #16811170C22semidirect
84. #16811169C22semidirect
85. C2×#13133217C22semidirect
86. C2×#13133216C22semidirect
87. #16811160C22semidirect
88. #16811157C22semidirect
89. #16811157C22semidirect
90. #16811155C22semidirect
91. #16811153C22semidirect
92. C2×#13133209C22semidirect
93. C2×#13133208C22semidirect
95. #16811135C22semidirect
97. #16811132C22semidirect
98. #16811130C22semidirect
99. C2×#13133196C22semidirect
101. C2×#13133193C22semidirect
102. C2×#13133191C22semidirect
104. C2×#13133188C22semidirect
105. #16811104C22semidirect
106. #16811104C22semidirect
109. #16811103C22semidirect
110. #16811103C22semidirect
111. #16811103C22semidirect
112. #16811103C22semidirect
113. #16811100C22semidirect
114. #16811097C22semidirect
116. C4×#11719945C22semidirect
117. #16811091C22semidirect
118. C2×C4×Dic106C22semidirect
119. C2×C4×D212C22semidirect
122. C2×#13133175C22semidirect
123. #117×D53C22semidirect
125. C2×C4⋊C4×D53C22semidirect
127. C53×#520C22semidirect
128. C53×#520C22semidirect
129. C53×#520C22semidirect
130. C53×#520C22semidirect
131. C53×#519C22semidirect
133. C53×#518C22semidirect
134. C4×#41×C53C22semidirect
135. C4×#41×C53C22semidirect
138. C2×#117×C53C22semidirect
370. C22×C4×C53#41semidirect
641. #3428D53semidirect
745. #520C2×D53semidirect
746. #520C2×D53semidirect
747. #520C2×D53semidirect
748. #520C2×D53semidirect
750. #519C2×D53semidirect
754. #518C2×D53semidirect
757. C4×#41C2×D53semidirect
758. C4×#41C2×D53semidirect
767. C2×#117C2×D53semidirect
770. C53#62856semidirect
1055. C22×C4#11719945semidirect

Maximal subgroups

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

subgroupindex
#202886372
#202886322
#202886262
#202886182
#202885452
#202884672
#202884572
#202884502
#202884402
#202884282
#202884182
#202881422
#202881312
C2×#168112512
#202880482
#202880442
C2×#168112012
#202879162
C2×#168111032
C53×#34282
#6285653