Finite Group Databasebeta

← #28293031

Subgroups — #28293031

Order 13568.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289303C218yesmaximal, complemented
2#20289186C214yesmaximal, complemented
3#20289087C214yesmaximal, complemented
4#20289031C218yesmaximal, complemented
5#20288719C214yesmaximal, complemented
6#20288678C214yesmaximal, complemented
7#20288659C218yesmaximal, complemented
8#20288626C214yesmaximal, complemented
9#20288613C212yesmaximal, complemented
10#20288601C211yesmaximal, characteristic, complemented
11#20288591C211yesmaximal, characteristic, complemented
12#20288591C214yesmaximal, complemented
13#20288502C212yesmaximal, complemented
14#20288500C211yesmaximal, characteristic, complemented
15#20288493C211yesmaximal, characteristic, complemented
16#20288369C212yesmaximal, complemented
17#20288357C212yesmaximal, complemented
18#20288011C211yesmaximal, characteristic, complemented
19C2×#16811173C211yesmaximal, characteristic, complemented
20C53×#3444C211yesmaximal, characteristic, complemented
21C2×#13133264C2212yescomplemented
22C2×#13133263C2212yes—
23C22×#11719945C2212yescomplemented
24#16811369C22116yescomplemented
25#16811361C22116yescomplemented
26#16811358C2218yescomplemented
27#16811358C2218yescomplemented
28#16811358C2214yescomplemented
29#16811351C2214yescomplemented
30#16811346C2218yescomplemented
31#16811343C2214yescomplemented
32#16811338C2218yescomplemented
33#16811333C2218yescomplemented
34#16811324C22116yescomplemented
35#16811319C2218yescomplemented
36#16811319C2218yescomplemented
37#16811313C2218yescomplemented
38#16811300C22116yescomplemented
39#16811298C22116yescomplemented
40#16811295C2214yescomplemented
41#16811294C2218yescomplemented
42#16811294C2218yescomplemented
43#16811294C2214yescomplemented
44#16811291C2218yescomplemented
45Q8×D212C2214yescomplemented
46#16811283C2218yescomplemented
47#16811282C2218yescomplemented
48#16811282C2218yescomplemented
49#16811278C2218yescomplemented
50#16811277C2218yescomplemented
51#16811277C2214yescomplemented
52#16811275C2218yescomplemented
53#16811270C2218yescomplemented
54#16811269C2218yescomplemented
55#16811269C2218yescomplemented
56#16811269C2218yescomplemented
57#16811269C2218yescomplemented
58#16811269C2218yescomplemented
59#16811262C22116yescomplemented
60D4×D212C2218yes—
61D4×D212C2214yescomplemented
62#16811247C2218yescomplemented
63#16811244C2218yescomplemented
64#16811244C2218yescomplemented
65#16811235C2214yescomplemented
66#16811228C2218yescomplemented
67#16811228C2214yescomplemented
68#16811228C2218yescomplemented
69#16811225C22116yescomplemented
70#16811221C22116yescomplemented
71#16811209C22116yescomplemented
72#16811207C22116yescomplemented
73#16811201C2218yescomplemented
74#16811199C2214yescomplemented
75#16811199C2212yescomplemented
76#16811198C2214yescomplemented
77#16811194C2212yes—
78#16811192C2212yes—
79#16811192C2214yescomplemented
80#16811188C2218yescomplemented
81#16811187C2218yescomplemented
82#16811187C2212yescomplemented
83#16811186C2214yescomplemented
84#16811183C2218yescomplemented
85#16811180C2211yescharacteristic, complemented
86#16811180C2212yescomplemented
87#16811180C2214yescomplemented
88#16811173C2211yescharacteristic
89#16811173C2212yescomplemented
90#16811173C2214yescomplemented
91#16811173C2214yescomplemented
92#16811173C2214yescomplemented
93#16811173C2212yescomplemented
94#16811173C2214yescomplemented
95#16811173C2212yescomplemented
96#16811173C2214yescomplemented
97#16811172C2214yescomplemented
98C2×#13133217C2211yescharacteristic, complemented
99C2×#13133217C2212yescomplemented
100C2×#13133214C2211yescharacteristic
101C2×#13133214C2212yescomplemented
102#16811158C2218yescomplemented
103#16811157C2214yescomplemented
104#16811157C2214yescomplemented
105#16811157C2214yescomplemented
106C2×#13133205C2212yescomplemented
107#124×D53C2214yescomplemented
108#16811134C2214yescomplemented
109#16811134C2212yescomplemented
110#16811131C2218yescomplemented
111#123×D53C2218yescomplemented
112C2×#13133191C2214yescomplemented
113#16811103C2218yescomplemented
114#16811100C2212yescomplemented
115#16811097C2212yescomplemented
116#16811097C2218yescomplemented
117C4×#11719945C2212yescomplemented
118C4×#11719945C2214yescomplemented
119C2×C4×D212C2214yescomplemented
120C53×#533C2211yescharacteristic, complemented
121C53×#533C2212yescomplemented
122C53×#532C2211yescharacteristic
123C53×#532C2212yescomplemented
124C53×#529C2214yescomplemented
125C53×#529C2214yescomplemented
126C53×#529C2212yescomplemented
127C53×#529C2212yescomplemented
128C53×#525C2211yescharacteristic
129C53×#525C2214yescomplemented
130C53×#525C2211yescharacteristic, complemented
131C4×#41×C53C2211yescharacteristic
132C4×#41×C53C2214yescomplemented
133C4×#41×C53C2211yescharacteristic, complemented
134C22×C42×C53C2211yescharacteristic, complemented
135#13133264—48no—
136#13133263—48no—
137C2×#11719949C2314yes—
138C2×#11719945—48no—
139C2×#11719945C2312yes—
140C2×#11719945C2314yes—
141C2×#11719945C2318yes—
142C2×#11719945C2314yes—
143C2×#11719945C2318yes—
144C2×#11719945C2318yes—
145C2×#11719945C2314yes—
146C2×#11719947C2314yes—
147C2×#11719947C2318yes—
148C22×Dic106C2312yes—
149C22×Dic106C2314yes—
150C2×Q8×D53C2314yes—
151C22×D212C2312yes—
152C22×D212C2314yes—
153C22×D212C2314yes—
154C22×D212C2318yes—
155C22×C22⋊D53C2314yes—
156C2×D4×D53C2314yes—
157C2×D4×D53C2318yes—
158C22×C4×D53C2314yes—
159#13133217C2318yes—
160#13133217C2314yes—
161#13133217C2314yes—
162#13133217C2311yescharacteristic
163#13133217C2312yes—
164#13133217C2312yes—
165#13133217C2312yes—
166#13133215C2314yes—
167#13133214C2314yes—
168#13133214C2314yes—
169#13133214C2318yes—
170#13133214C2312yes—
171#13133214C2312yes—
172#13133214C2311yescharacteristic
173#13133213C2314yes—
174#13133213C23116yes—
175#13133212C23116yes—
176#13133212C23116yes—
177#13133211C2318yes—
178#13133210C23116yes—
179#13133209C2318yes—
180#13133209C2314yes—
181#13133209C2312yes—
182#13133207C23116yes—
183#13133206C2314yes—
184#13133206C23116yes—
185#13133205C2314yes—
186#13133205C2314yes—
187#13133205C2318yes—
188#13133205C2318yes—
189#13133205C2314yes—
190#13133205C2314yes—
191#13133205C2314yes—
192#13133205C2312yes—
193#13133204C2314yes—
194#13133203C23116yes—
195#13133203C23116yes—
196#13133202C23116yes—
197#13133202C23116yes—
198#13133202C23116yes—
199#13133202C23116yes—
200#13133202C23116yes—
201#13133201C2318yes—
202#13133201C23116yes—
203#13133200C2318yes—
204#13133200C2314yes—
205#13133199C23116yes—
206#13133199C23116yes—
207#13133198C2318yes—
208#13133197C2318yes—
209#13133197C23116yes—
210#13133196C2318yes—
211#13133196C2314yes—
212#13133196C2318yes—
213#13133196C2314yes—
214#13133196C2314yes—
215#13133195C23116yes—
216#13133195C23116yes—
217#13133193C23116yes—
218#13133192C2318yes—
219#13133192C23116yes—
220#13133191C2314yes—
221#13133191C2318yes—
222#13133191C2318yes—
223#13133191C2318yes—
224#13133191C2318yes—
225#13133191C2314yes—
226#13133191C2318yes—
227#13133191C2318yes—
228#13133191C2318yes—
229#13133191C2318yes—
230#13133191C2314yes—
231#13133190C23116yes—
232#13133190C23116yes—
233#13133190C23116yes—
234#13133190C23116yes—
235#13133190C23116yes—
236#13133189C23116yes—
237#13133189C23116yes—
238#13133188C23116yes—
239#13133187C23116yes—
240#13133187C2318yes—
241#13133186C2314yes—
242#13133185C23116yes—
243#13133185C23116yes—
244#13133185C2318yes—
245C4×Dic106C2314yes—
246C4×Dic106C2318yes—
247C4×Dic106C2318yes—
248C4×Dic106C2314yes—
249C4×Dic106C2314yes—
250#13133182C2318yes—
251C4×D212C2314yes—
252C4×D212C2318yes—
253C4×D212C2318yes—
254C4×D212C2318yes—
255C4×D212C2318yes—
256C4×D212C2314yes—
257C4×D212C2318yes—
258C4×D212C2318yes—
259C4×D212C2318yes—
260C4×D212C2318yes—
261C4×D212C2314yes—
262#13133179C2318yes—
263#13133179C23116yes—
264#13133179C23116yes—
265C4×C22⋊D53C2318yes—
266C4×C22⋊D53C2318yes—
267C4×C22⋊D53C2318yes—
268#13133177C23116yes—
269#13133177C23116yes—
270#13133176C2318yes—
271#13133176C2314yes—
272#13133176C2312yes—
273#13133175C23116yes—
274#13133174C2318yes—
275#13133174C2314yes—
276#13133173C2318yes—
277C2×C4⋊Dic53C2314yes—
278C2×C4⋊Dic53C2318yes—
279C4⋊C4×D53C23116yes—
280C2×#11719921C2318yes—
281C22⋊C4×D53C23116yes—
282C22⋊C4×D53C23116yes—
283C22⋊C4×D53C2318yes—
284C42×D53C2314yes—
285C2×#41×C53C2311yescharacteristic
286C2×#41×C53C2311yescharacteristic
287C2×#41×C53C2314yes—
288C23×C4×C53C2311yescharacteristic
289C23×C4×C53C2312yes—
290C4⋊Q8×C53C2311yescharacteristic
291C4⋊Q8×C53C2312yes—
292#127×C53C2311yescharacteristic
293#126×C53C2314yes—
294#126×C53C2314yes—
295#125×C53C2312yes—
296#125×C53C2314yes—
297#124×C53C2311yescharacteristic
298#124×C53C2311yescharacteristic
299#124×C53C2314yes—
300#123×C53C2312yes—
301#123×C53C2312yes—
302#123×C53C2314yes—
303#123×C53C2314yes—
304C22⋊Q8×C53C2312yes—
305C22⋊Q8×C53C2312yes—
306C22⋊Q8×C53C2314yes—
307C22⋊Q8×C53C2314yes—
308#121×C53C2312yes—
309#121×C53C2312yes—
310#121×C53C2314yes—
311#121×C53C2314yes—
312#120×C53C2312yes—
313#120×C53C2312yes—
314C4×Q8×C53C2312yes—
315C4×Q8×C53C2312yes—
316C4×Q8×C53C2314yes—
317C4×Q8×C53C2314yes—
318C4×D4×C53C2314yes—
319C4×D4×C53C2314yes—
320C4×D4×C53C2314yes—
321C4×D4×C53C2314yes—
322C4×D4×C53C2314yes—
323C4×D4×C53C2312yes—
324C4×D4×C53C2314yes—
325C4×D4×C53C2314yes—
326C4×D4×C53C2314yes—
327C4×D4×C53C2312yes—
328#117×C53C2311yescharacteristic
329#117×C53C2312yes—
330#117×C53C2311yescharacteristic
331#117×C53C2314yes—
332#117×C53C2314yes—
333#117×C53C2314yes—
334#117×C53C2312yes—
335C2×C42×C53C2311yescharacteristic
336C2×C42×C53C2312yes—
337C2×C42×C53C2312yes—
338C2×C42×C53C2312yes—
339C2×C42×C53C2312yes—
340C2×C42×C53C2311yescharacteristic
341C2×C42×C53C2312yes—
342C2×C42×C53C2312yes—
343C2×C42×C53C2312yes—
344C24×C53C2411yescharacteristic
345C23×D53C2414yes—
346C23×D53C2418yes—
347#41×C53—24no—
348#41×C53—24no—
349#41×C53—48no—
350C2×Q8×C53C2411yescharacteristic
351C2×Q8×C53C2411yescharacteristic
352C2×Q8×C53C2414yes—
353C2×D4×C53C2412yes—
354C2×D4×C53C2412yes—
355C2×D4×C53C2411yescharacteristic
356C2×D4×C53C2411yescharacteristic
357C2×D4×C53C2414yes—
358C2×D4×C53C2414yes—
359C2×D4×C53C2414yes—
360C22×C4×C53—24no—
361C22×C4×C53—44no—
362C22×C4×C53C2412yes—
363C22×C4×C53C2412yes—
364C22×C4×C53C2412yes—
365C22×C4×C53C2412yes—
366C22×C4×C53C2412yes—
367C22×C4×C53C2411yescharacteristic
368C22×C4×C53C2414yes—
369C22×C4×C53C2414yes—
370C22×C4×C53C2412yes—
371C22×C4×C53C2412yes—
372C22×C4×C53C2412yes—
373C22×C4×C53C2412yes—
374C22×C4×C53C2412yes—
375C22×C4×C53C2411yescharacteristic
376C2×C22⋊D53—48no—
377C2×C22⋊D53C2414yes—
378C2×C22⋊D53C24116yes—
379C2×C22⋊D53C2418yes—
380C2×C22⋊D53C2418yes—
381C2×C22⋊D53C24116yes—
382C2×C22⋊D53C2418yes—
383C22×Dic53C2414yes—
384C22×Dic53C2418yes—
385#11719949—48no—
386Q8×D53—48no—
387#11719947—48no—
388#11719947—416no—
389D4×D53—48no—
390D4×D53—416no—
391#11719945—28no—
392#11719945—416no—
393#11719945—416no—
394#11719945—48no—
395#11719945—416no—
396#11719945—48no—
397#11719945—48no—
398C2×D212—28no—
399C2×D212—48no—
400C2×D212—416no—
401C2×D212—48no—
402C2×D212C2414yes—
403C2×D212C2414yes—
404C2×D212C2418yes—
405C2×D212C2414yes—
406C2×D212C2412yes—
407C2×D212C24116yes—
408C2×D212C2418yes—
409C2×D212C2418yes—
410C2×C4×D53—48no—
411C2×C4×D53C2414yes—
412C2×C4×D53C2418yes—
413C2×C4×D53C24116yes—
414C2×C4×D53C2418yes—
415C2×C4×D53C24116yes—
416C2×C4×D53C2418yes—
417C2×Dic106—28no—
418C2×Dic106—48no—
419C2×Dic106C2414yes—
420C2×Dic106C2414yes—
421C2×Dic106C2414yes—
422C2×Dic106C2412yes—
423C2×Dic106C2418yes—
424C4⋊C4×C53C2412yes—
425C4⋊C4×C53C2412yes—
426C4⋊C4×C53C2414yes—
427C4⋊C4×C53C2414yes—
428C4⋊C4×C53C2414yes—
429C4⋊C4×C53C2414yes—
430C4⋊C4×C53C2414yes—
431C4⋊C4×C53C2414yes—
432C4⋊C4×C53C2414yes—
433C4⋊C4×C53C2414yes—
434C22⋊C4×C53C2412yes—
435C22⋊C4×C53C2412yes—
436C22⋊C4×C53C2414yes—
437C22⋊C4×C53C2414yes—
438C22⋊C4×C53C2414yes—
439C22⋊C4×C53C2414yes—
440C22⋊C4×C53C2414yes—
441C22⋊C4×C53C2414yes—
442C22⋊C4×C53C2414yes—
443C22⋊C4×C53C2414yes—
444C42×C53C2411yescharacteristic
445C42×C53C2412yes—
446C42×C53C2411yescharacteristic
447C42×C53C2412yes—
448C42×C53C2412yes—
449C42×C53C2412yes—
450C42×C53C2411yescharacteristic
451C42×C53C2412yes—
452C42×C53C2412yes—
453C42×C53C2411yescharacteristic
454C42×C53C2414yes—
455C42×C53C2412yes—
456C42×C53C2414yes—
457C42×C53C2412yes—
458C22⋊Dic53C2414yes—
459C22⋊Dic53C24116yes—
460C22⋊Dic53C2418yes—
461#11719921C2418yes—
462#11719921C24116yes—
463#11719921C24116yes—
464#11719921C24116yes—
465#11719921C24116yes—
466#11719921C24116yes—
467#11719921C2418yes—
468#11719921C2418yes—
469#11719921C24116yes—
470C4⋊Dic53C24116yes—
471C4⋊Dic53C2418yes—
472C4⋊Dic53C2414yes—
473C4⋊Dic53C2418yes—
474C4⋊Dic53C2414yes—
475C4⋊Dic53C2414yes—
476#11719919C2418yes—
477#11719919C24116yes—
478#11719919C24116yes—
479#11719919C2418yes—
480#11719919C2418yes—
481C4×Dic53C2418yes—
482C4×Dic53C2414yes—
483C4×Dic53C24116yes—
484C23×C53—22no—
485C23×C53—42no—
486C23×C53C2512yes—
487C23×C53C2512yes—
488C23×C53C2512yes—
489C23×C53C2511yescharacteristic
490C22×D53—28no—
491C22×D53—48no—
492C22×D53—48no—
493C22×D53—416no—
494C22×D53C2514yes—
495C22×D53C2518yes—
496Q8×C53—22no—
497Q8×C53—22no—
498Q8×C53—44no—
499D4×C53—24no—
500D4×C53—24no—
501D4×C53—22no—
502D4×C53—22no—
503D4×C53—44no—
504D4×C53—44no—
505D4×C53—44no—
506C2×C4×C53—22no—
507C2×C4×C53—24no—
508C2×C4×C53—24no—
509C2×C4×C53—24no—
510C2×C4×C53—24no—
511C2×C4×C53—24no—
512C2×C4×C53—28no—
513C2×C4×C53—24no—
514C2×C4×C53—28no—
515C2×C4×C53—24no—
516C2×C4×C53—42no—
517C2×C4×C53—42no—
518C2×C4×C53—42no—
519C2×C4×C53H(5,𝔽2)14yes—
520C2×C4×C53C2512yes—
521C2×C4×C53C2512yes—
522C2×C4×C53C2512yes—
523C2×C4×C53C2512yes—
524C2×C4×C53C2514yes—
525C2×C4×C53C2512yes—
526C2×C4×C53C2514yes—
527C2×C4×C53C2512yes—
528C2×C4×C53C2511yescharacteristic
529C2×C4×C53C2511yescharacteristic
530C2×C4×C53C2512yes—
531C22⋊D53—28no—
532C22⋊D53—416no—
533C22⋊D53—48no—
534C22⋊D53—48no—
535C22⋊D53—48no—
536C22⋊D53—416no—
537C2×Dic53—28no—
538C2×Dic53—48no—
539C2×Dic53C2518yes—
540C2×Dic53C2514yes—
541C2×Dic53C2518yes—
542D212—28no—
543D212—28no—
544D212—24no—
545D212—216no—
546D212—28no—
547D212—48no—
548D212—416no—
549D212—48no—
550C4×D53—28no—
551C4×D53—416no—
552C4×D53—48no—
553C4×D53—416no—
554C4×D53—48no—
555C4×D53—48no—
556Dic106—28no—
557Dic106—28no—
558Dic106—24no—
559Dic106—28no—
560Dic106—48no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—22no—
564C22×C53—22no—
565C22×C53—22no—
566C22×C53—22no—
567C22×C53—24no—
568C22×C53—22no—
569C22×C53—24no—
570C22×C53—44no—
571C22×C53C2×H(5,𝔽2)12yes—
572C22×C53C2611yescharacteristic
573C2×D53—24no—
574C2×D53—28no—
575C2×D53—216no—
576C2×D53—28no—
577C2×D53—88no—
578C2×D53—168no—
579C4×C53—22no—
580C4×C53—22no—
581C4×C53—22no—
582C4×C53—22no—
583C4×C53—24no—
584C4×C53—22no—
585C4×C53—24no—
586C4×C53—22no—
587C4×C53C2×H(5,𝔽2)12yes—
588C4×C53C2×H(5,𝔽2)12yes—
589C4×C53#58514yes—
590Dic53—28no—
591Dic53—24no—
592Dic53—28no—
593#3562—538no—
594#3554—534no—
595#3546—534no—
596#3542—538no—
597#3517—534no—
598#3514—534no—
599#3513—538no—
600#3511—534no—
601#3510—532no—
602#3509—531no—
603#3508—531no—
604#3508—534no—
605#3500—532no—
606#3499—531no—
607#3498—531no—
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444D5311yescharacteristic, complemented
612C2×#532—531no—
613C2×C53—22no—
614C2×C53—42no—
615C2×C53—42no—
616C2×C53—42no—
617C2×C53C22×H(5,𝔽2)11yescharacteristic
618C2×C53C2×#58512yes—
619D53—48no—
620D53—44no—
621C2×2−1+4—532no—
622C2×H(5,𝔽2)—532no—
623C22×#41—532no—
624#562—5316no—
625#560—5316no—
626#559—538no—
627#559—538no—
628#559—534no—
629#557—534no—
630#556—538no—
631#556—534no—
632#555—538no—
633#554—538no—
634#553—5316no—
635#553—538no—
636#553—538no—
637#552—538no—
638#551—5316no—
639#551—5316no—
640#550—538no—
641#550—534no—
642#550—538no—
643#550—538no—
644#550—534no—
645D4×Q8—534no—
646#548—538no—
647#548—538no—
648#548—538no—
649#547—538no—
650#547—538no—
651#547—534no—
652#547—538no—
653#546—538no—
654#546—5316no—
655#546—538no—
656#546—538no—
657#546—538no—
658#546—538no—
659#546—538no—
660D42—538no—
661D42—534no—
662#542—538no—
663#542—538no—
664#542—538no—
665#541—534no—
666#540—5316no—
667#540—538no—
668#540—538no—
669#540—534no—
670#539—5316no—
671#538—5316no—
672#538—5316no—
673#537—538no—
674#536—532no—
675#536—534no—
676#536—532no—
677#536—534no—
678#535—532no—
679#535—538no—
680#535—534no—
681#535—538no—
682#535—532no—
683#535—534no—
684#534—538no—
685#533—531no—
686#533—532no—
687#533—534no—
688#533C2×D5311yescharacteristic, complemented
689#533C2×D5312yescomplemented
690#532—534no—
691#532—534no—
692#532—534no—
693#532—534no—
694#532—534no—
695#532—531no—
696#532—532no—
697#532—532no—
698#532—532no—
699#532—534no—
700#532C2×D5311yescharacteristic
701#532C2×D5312yescomplemented
702C2×C4⋊Q8—531no—
703C2×C4⋊Q8—532no—
704C2×#127—531no—
705C2×#127—532no—
706#529—538no—
707#529—534no—
708#529—534no—
709#529—534no—
710#529C2×D5314yescomplemented
711#529C2×D5312yescomplemented
712#529C2×D5312yescomplemented
713#529C2×D5314yescomplemented
714C2×#124—534no—
715C2×#124—532no—
716#525—532no—
717#525—534no—
718#525—538no—
719#525C2×D5311yescharacteristic
720#525C2×D5311yescharacteristic, complemented
721#525C2×D5314yescomplemented
722C2×#123—538no—
723C2×#121—534no—
724#520—538no—
725#519—532no—
726#518—532no—
727#518—538no—
728C4×#41—532no—
729C4×#41—534no—
730C4×#41C2×D5311yescharacteristic
731C4×#41C2×D5311yescharacteristic, complemented
732C4×#41C2×D5314yescomplemented
733C2×C4×D4—534no—
734C22×C42C2×D5311yescharacteristic, complemented
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—2128no—
737H(5,𝔽2)—2128no—
738C2×#41—534no—
739C2×#41—538no—
740C2×#41—534no—
741C2×#41—532no—
742C2×#41—534no—
743C2×#41—538no—
744C2×#41—538no—
745C2×#41—538no—
746C2×#41—534no—
747C2×#41—534no—
748C2×#41—2128no—
749C2×#41C22×D5311yescharacteristic
750C2×#41C22×D5311yescharacteristic
751C2×#41C22×D5314yes—
752C22×Q8—534no—
753C22×Q8—532no—
754C22×Q8—534no—
755C22×D4—534no—
756C22×D4—538no—
757C22×D4—534no—
758C22×D4—532no—
759C22×D4—534no—
760C22×D4—538no—
761C22×D4—534no—
762C23×C4—534no—
763C23×C4C22×D5311yescharacteristic
764C23×C4C22×D5312yes—
765C4⋊Q8—534no—
766C4⋊Q8—532no—
767C4⋊Q8—531no—
768C4⋊Q8—532no—
769C4⋊Q8—534no—
770C4⋊Q8—534no—
771C4⋊Q8—538no—
772C4⋊Q8—532no—
773C4⋊Q8C22×D5311yescharacteristic
774C4⋊Q8C22×D5312yes—
775#127—534no—
776#127—5316no—
777#127—532no—
778#127—531no—
779#127—532no—
780#127—534no—
781#127—534no—
782#127—538no—
783#127C22×D5311yescharacteristic
784#126—5316no—
785#126—5316no—
786#126—5316no—
787#126—538no—
788#126C22×D5314yes—
789#126C22×D5314yes—
790#125—5316no—
791#125—532no—
792#125—534no—
793#125—538no—
794#125C22×D5312yes—
795#125C22×D5314yes—
796#124—534no—
797#124—5316no—
798#124—534no—
799#124—5316no—
800#124—5316no—
801#124—534no—
802#124—534no—
803#124—538no—
804#124—532no—
805#124—534no—
806#124—534no—
807#124—534no—
808#124—538no—
809#124C22×D5311yescharacteristic
810#124C22×D5311yescharacteristic
811#124C22×D5314yes—
812#123—538no—
813#123—534no—
814#123—538no—
815#123—5316no—
816#123—5316no—
817#123—5316no—
818#123—5316no—
819#123—5316no—
820#123—538no—
821#123—5316no—
822#123—5316no—
823#123—5316no—
824#123C22×D5312yes—
825#123C22×D5312yes—
826#123C22×D5314yes—
827#123C22×D5314yes—
828C22⋊Q8—5316no—
829C22⋊Q8—534no—
830C22⋊Q8—534no—
831C22⋊Q8—534no—
832C22⋊Q8—538no—
833C22⋊Q8—538no—
834C22⋊Q8—5316no—
835C22⋊Q8—538no—
836C22⋊Q8—5316no—
837C22⋊Q8—5316no—
838C22⋊Q8C22×D5312yes—
839C22⋊Q8C22×D5312yes—
840C22⋊Q8C22×D5314yes—
841C22⋊Q8C22×D5314yes—
842#121—5316no—
843#121—5316no—
844#121—5316no—
845#121—538no—
846#121—538no—
847#121—538no—
848#121—538no—
849#121—534no—
850#121—534no—
851#121—534no—
852#121—538no—
853#121—538no—
854#121—538no—
855#121—538no—
856#121—538no—
857#121—5316no—
858#121—5316no—
859#121—5316no—
860#121—5316no—
861#121—5316no—
862#121—5316no—
863#121C22×D5312yes—
864#121C22×D5314yes—
865#121C22×D5312yes—
866#121C22×D5314yes—
867#120—534no—
868#120—538no—
869#120—5316no—
870#120—5316no—
871#120—538no—
872#120—5316no—
873#120C22×D5312yes—
874#120C22×D5312yes—
875C4×Q8—538no—
876C4×Q8—534no—
877C4×Q8—534no—
878C4×Q8—534no—
879C4×Q8—538no—
880C4×Q8—538no—
881C4×Q8C22×D5312yes—
882C4×Q8C22×D5312yes—
883C4×Q8C22×D5314yes—
884C4×Q8C22×D5314yes—
885C4×D4—538no—
886C4×D4—538no—
887C4×D4—538no—
888C4×D4—5316no—
889C4×D4—5316no—
890C4×D4—538no—
891C4×D4—5316no—
892C4×D4—5316no—
893C4×D4—538no—
894C4×D4—538no—
895C4×D4—538no—
896C4×D4—538no—
897C4×D4—534no—
898C4×D4—534no—
899C4×D4—534no—
900C4×D4—538no—
901C4×D4—538no—
902C4×D4—538no—
903C4×D4—538no—
904C4×D4C22×D5314yes—
905C4×D4C22×D5312yes—
906C4×D4C22×D5314yes—
907C4×D4C22×D5314yes—
908C4×D4C22×D5314yes—
909C4×D4C22×D5314yes—
910C4×D4C22×D5314yes—
911C4×D4C22×D5314yes—
912C4×D4C22×D5314yes—
913C4×D4C22×D5312yes—
914#117—532no—
915#117—534no—
916#117—538no—
917#117—5316no—
918#117—538no—
919#117—534no—
920#117—538no—
921#117C22×D5311yescharacteristic
922#117C22×D5312yes—
923#117C22×D5311yescharacteristic
924#117C22×D5314yes—
925#117C22×D5314yes—
926#117C22×D5314yes—
927#117C22×D5312yes—
928C2×C4⋊C4—534no—
929C2×C4⋊C4—538no—
930C2×C4⋊C4—5316no—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—538no—
933C2×C22⋊C4—5316no—
934C2×C22⋊C4—5316no—
935C2×C42—534no—
936C2×C42C22×D5312yes—
937C2×C42C22×D5311yescharacteristic
938C2×C42C22×D5312yes—
939C2×C42C22×D5312yes—
940C2×C42C22×D5311yescharacteristic
941C2×C42C22×D5312yes—
942C2×C42C22×D5312yes—
943C2×C42C22×D5312yes—
944C2×C42C22×D5312yes—
945C24—534no—
946C24—538no—
947C24C23×D5311yescharacteristic
948#41—24no—
949#41—24no—
950#41—48no—
951#41—1068no—
952#41—2128no—
953#41—21216no—
954#41—21216no—
955#41—21216no—
956#41—2128no—
957#41—2128no—
958#41—21216no—
959#41—2128no—
960#41—2128no—
961C2×Q8—534no—
962C2×Q8—534no—
963C2×Q8—534no—
964C2×Q8—532no—
965C2×Q8—538no—
966C2×Q8—1068no—
967C2×Q8—2128no—
968C2×Q8—2128no—
969C2×Q8C23×D5311yescharacteristic
970C2×Q8C23×D5311yescharacteristic
971C2×Q8C23×D5314yes—
972C2×D4—534no—
973C2×D4—538no—
974C2×D4—5316no—
975C2×D4—538no—
976C2×D4—538no—
977C2×D4—5316no—
978C2×D4—538no—
979C2×D4—534no—
980C2×D4—534no—
981C2×D4—534no—
982C2×D4—532no—
983C2×D4—538no—
984C2×D4—5316no—
985C2×D4—538no—
986C2×D4—1068no—
987C2×D4—2128no—
988C2×D4—21216no—
989C2×D4—2128no—
990C2×D4—2128no—
991C2×D4—2128no—
992C2×D4—21216no—
993C2×D4C23×D5312yes—
994C2×D4C23×D5312yes—
995C2×D4C23×D5311yescharacteristic
996C2×D4C23×D5311yescharacteristic
997C2×D4C23×D5314yes—
998C2×D4C23×D5314yes—
999C2×D4C23×D5314yes—
1000C22×C4—24no—
1001C22×C4—44no—
1002C22×C4—534no—
1003C22×C4—538no—
1004C22×C4—534no—
1005C22×C4—538no—
1006C22×C4—5316no—
1007C22×C4—538no—
1008C22×C4—5316no—
1009C22×C4—538no—
1010C22×C4—2128no—
1011C22×C4C23×D5312yes—
1012C22×C4C23×D5312yes—
1013C22×C4C23×D5312yes—
1014C22×C4C23×D5312yes—
1015C22×C4C23×D5312yes—
1016C22×C4C23×D5311yescharacteristic
1017C22×C4C23×D5314yes—
1018C22×C4C23×D5314yes—
1019C22×C4C23×D5312yes—
1020C22×C4C23×D5312yes—
1021C22×C4C23×D5312yes—
1022C22×C4C23×D5312yes—
1023C22×C4C23×D5312yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—538no—
1026C4⋊C4—534no—
1027C4⋊C4—538no—
1028C4⋊C4—5316no—
1029C4⋊C4—538no—
1030C4⋊C4—5316no—
1031C4⋊C4—534no—
1032C4⋊C4—534no—
1033C4⋊C4—538no—
1034C4⋊C4—538no—
1035C4⋊C4—5316no—
1036C4⋊C4C23×D5314yes—
1037C4⋊C4C23×D5314yes—
1038C4⋊C4C23×D5312yes—
1039C4⋊C4C23×D5314yes—
1040C4⋊C4C23×D5314yes—
1041C4⋊C4C23×D5312yes—
1042C4⋊C4C23×D5314yes—
1043C4⋊C4C23×D5314yes—
1044C4⋊C4C23×D5314yes—
1045C4⋊C4C23×D5314yes—
1046C22⋊C4—534no—
1047C22⋊C4—5316no—
1048C22⋊C4—538no—
1049C22⋊C4—538no—
1050C22⋊C4—5316no—
1051C22⋊C4—5316no—
1052C22⋊C4—5316no—
1053C22⋊C4—5316no—
1054C22⋊C4—5316no—
1055C22⋊C4—5316no—
1056C22⋊C4—538no—
1057C22⋊C4—538no—
1058C22⋊C4C23×D5312yes—
1059C22⋊C4C23×D5314yes—
1060C22⋊C4C23×D5314yes—
1061C22⋊C4C23×D5312yes—
1062C22⋊C4C23×D5314yes—
1063C22⋊C4C23×D5314yes—
1064C22⋊C4C23×D5314yes—
1065C22⋊C4C23×D5314yes—
1066C22⋊C4C23×D5314yes—
1067C22⋊C4C23×D5314yes—
1068C42—538no—
1069C42—534no—
1070C42—5316no—
1071C42C23×D5311yescharacteristic
1072C42C23×D5311yescharacteristic
1073C42C23×D5312yes—
1074C42C23×D5311yescharacteristic
1075C42C23×D5312yes—
1076C42C23×D5311yescharacteristic
1077C42C23×D5312yes—
1078C42C23×D5312yes—
1079C42C23×D5312yes—
1080C42C23×D5312yes—
1081C42C23×D5312yes—
1082C42C23×D5314yes—
1083C42C23×D5314yes—
1084C42C23×D5312yes—
1085C23—22no—
1086C23—42no—
1087C23—534no—
1088C23—538no—
1089C23—1068no—
1090C23—2128no—
1091C23—21216no—
1092C23—2128no—
1093C23C24×D5312yes—
1094C23C24×D5312yes—
1095C23C24×D5312yes—
1096C23C24×D5311yescharacteristic
1097Q8—22no—
1098Q8—22no—
1099Q8—44no—
1100Q8—1068no—
1101Q8—1068no—
1102Q8—1064no—
1103Q8—1068no—
1104Q8—2128no—
1105D4—24no—
1106D4—24no—
1107D4—22no—
1108D4—22no—
1109D4—44no—
1110D4—44no—
1111D4—44no—
1112D4—1068no—
1113D4—1068no—
1114D4—1068no—
1115D4—1064no—
1116D4—1068no—
1117D4—10616no—
1118D4—2128no—
1119D4—21216no—
1120D4—2128no—
1121D4—2128no—
1122D4—21216no—
1123D4—2128no—
1124D4—21216no—
1125D4—2128no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—24no—
1134C2×C4—28no—
1135C2×C4—28no—
1136C2×C4—42no—
1137C2×C4—42no—
1138C2×C4—42no—
1139C2×C4—538no—
1140C2×C4—534no—
1141C2×C4—538no—
1142C2×C4—1068no—
1143C2×C4—1068no—
1144C2×C4—21216no—
1145C2×C4—2128no—
1146C2×C4—2128no—
1147C2×C4—2128no—
1148C2×C4—21216no—
1149C2×C4—2128no—
1150C2×C4#1313326314yes—
1151C2×C4C24×D5312yes—
1152C2×C4C24×D5314yes—
1153C2×C4C24×D5312yes—
1154C2×C4C24×D5312yes—
1155C2×C4C24×D5312yes—
1156C2×C4C24×D5314yes—
1157C2×C4C24×D5312yes—
1158C2×C4C24×D5312yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—22no—
1167C22—22no—
1168C22—24no—
1169C22—24no—
1170C22—44no—
1171C22—8488no—
1172C22—1064no—
1173C22—1068no—
1174C22—1068no—
1175C22—10616no—
1176C22—4248no—
1177C22C2×#1313326312yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—22no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—22no—
1185C4—24no—
1186C4—24no—
1187C4—1064no—
1188C4—1068no—
1189C4—1068no—
1190C4C2×#1313326312yes—
1191C4C2×#1313326312yes—
1192C4#1681145914yes—
1193C2—22no—
1194C2—42no—
1195C2—42no—
1196C2—42no—
1197C2—2124no—
1198C2—2128no—
1199C2C22×#1313326311yescharacteristic
1200C2C2×#1681145912yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3444C2
hypercenter#3444D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #20289303C2semidirect
2. #20289186C2semidirect
3. #20289087C2semidirect
4. #20289031C2semidirect
5. #20288719C2semidirect
6. #20288678C2semidirect
7. #20288659C2semidirect
8. #20288626C2semidirect
9. #20288613C2semidirect
10. #20288601C2semidirect
11. #20288591C2semidirect
12. #20288591C2semidirect
13. #20288502C2semidirect
14. #20288500C2semidirect
15. #20288493C2semidirect
16. #20288369C2semidirect
17. #20288357C2semidirect
18. #20288011C2semidirect
19. C2×#16811173C2semidirect
20. C53×#3444C2semidirect
21. C2×#13133264C22semidirect
23. C22×#11719945C22semidirect
24. #16811369C22semidirect
25. #16811361C22semidirect
26. #16811358C22semidirect
27. #16811358C22semidirect
28. #16811358C22semidirect
29. #16811351C22semidirect
30. #16811346C22semidirect
31. #16811343C22semidirect
32. #16811338C22semidirect
33. #16811333C22semidirect
34. #16811324C22semidirect
35. #16811319C22semidirect
36. #16811319C22semidirect
37. #16811313C22semidirect
38. #16811300C22semidirect
39. #16811298C22semidirect
40. #16811295C22semidirect
41. #16811294C22semidirect
42. #16811294C22semidirect
43. #16811294C22semidirect
44. #16811291C22semidirect
45. Q8×D212C22semidirect
46. #16811283C22semidirect
47. #16811282C22semidirect
48. #16811282C22semidirect
49. #16811278C22semidirect
50. #16811277C22semidirect
51. #16811277C22semidirect
52. #16811275C22semidirect
53. #16811270C22semidirect
54. #16811269C22semidirect
55. #16811269C22semidirect
56. #16811269C22semidirect
57. #16811269C22semidirect
58. #16811269C22semidirect
59. #16811262C22semidirect
61. D4×D212C22semidirect
62. #16811247C22semidirect
63. #16811244C22semidirect
64. #16811244C22semidirect
65. #16811235C22semidirect
66. #16811228C22semidirect
67. #16811228C22semidirect
68. #16811228C22semidirect
69. #16811225C22semidirect
70. #16811221C22semidirect
71. #16811209C22semidirect
72. #16811207C22semidirect
73. #16811201C22semidirect
74. #16811199C22semidirect
75. #16811199C22semidirect
76. #16811198C22semidirect
79. #16811192C22semidirect
80. #16811188C22semidirect
81. #16811187C22semidirect
82. #16811187C22semidirect
83. #16811186C22semidirect
84. #16811183C22semidirect
85. #16811180C22semidirect
86. #16811180C22semidirect
87. #16811180C22semidirect
89. #16811173C22semidirect
90. #16811173C22semidirect
91. #16811173C22semidirect
92. #16811173C22semidirect
93. #16811173C22semidirect
94. #16811173C22semidirect
95. #16811173C22semidirect
96. #16811173C22semidirect
97. #16811172C22semidirect
98. C2×#13133217C22semidirect
99. C2×#13133217C22semidirect
101. C2×#13133214C22semidirect
102. #16811158C22semidirect
103. #16811157C22semidirect
104. #16811157C22semidirect
105. #16811157C22semidirect
106. C2×#13133205C22semidirect
107. #124×D53C22semidirect
108. #16811134C22semidirect
109. #16811134C22semidirect
110. #16811131C22semidirect
111. #123×D53C22semidirect
112. C2×#13133191C22semidirect
113. #16811103C22semidirect
114. #16811100C22semidirect
115. #16811097C22semidirect
116. #16811097C22semidirect
117. C4×#11719945C22semidirect
118. C4×#11719945C22semidirect
119. C2×C4×D212C22semidirect
120. C53×#533C22semidirect
121. C53×#533C22semidirect
123. C53×#532C22semidirect
124. C53×#529C22semidirect
125. C53×#529C22semidirect
126. C53×#529C22semidirect
127. C53×#529C22semidirect
129. C53×#525C22semidirect
130. C53×#525C22semidirect
132. C4×#41×C53C22semidirect
133. C4×#41×C53C22semidirect
134. C22×C42×C53C22semidirect
611. #3444D53semidirect
688. #533C2×D53semidirect
689. #533C2×D53semidirect
701. #532C2×D53semidirect
710. #529C2×D53semidirect
711. #529C2×D53semidirect
712. #529C2×D53semidirect
713. #529C2×D53semidirect
720. #525C2×D53semidirect
721. #525C2×D53semidirect
731. C4×#41C2×D53semidirect
732. C4×#41C2×D53semidirect
734. C22×C42C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202893032
#202891862
#202890872
#202890312
#202887192
#202886782
#202886592
#202886262
#202886132
#202886012
#202885912
#202885022
#202885002
#202884932
#202883692
#202883572
#202880112
C2×#168111732
C53×#34442
#6283653