Finite Group Databasebeta

← #28293041

Subgroups — #28293041

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#20289291C218yesmaximal, complemented
2#20289187C214yesmaximal, complemented
3#20289088C214yesmaximal, complemented
4#20289032C218yesmaximal, complemented
5#20288720C214yesmaximal, complemented
6#20288677C214yesmaximal, complemented
7#20288650C218yesmaximal, complemented
8#20288628C214yesmaximal, complemented
9#20288614C212yesmaximal, complemented
10#20288599C211yesmaximal, characteristic, complemented
11#20288591C211yesmaximal, characteristic, complemented
12#20288584C214yesmaximal, complemented
13#20288509C212yesmaximal, complemented
14#20288488C211yesmaximal, characteristic, complemented
15#20288370C212yesmaximal, complemented
16#20288358C212yesmaximal, complemented
17#20288010C211yesmaximal, characteristic, complemented
18#20288008C211yesmaximal, characteristic, complemented
19C2×#16811174C211yesmaximal, characteristic, complemented
20C53×#3499C211yesmaximal, characteristic, complemented
21C2×#13133263C2212yes—
22C22×#11719949C2212yescomplemented
23#16811369C22116yescomplemented
24#16811363C22116yescomplemented
25#16811358C2214yescomplemented
26#16811356C2218yescomplemented
27#16811355C2218yescomplemented
28#16811348C2214yescomplemented
29#16811347C2218yescomplemented
30#16811347C2214yescomplemented
31#16811339C2218yescomplemented
32#16811334C2218yescomplemented
33#16811321C2218yescomplemented
34#16811321C2218yescomplemented
35#16811318C22116yescomplemented
36#16811308C2218yescomplemented
37#16811300C22116yescomplemented
38#16811296C22116yescomplemented
39#16811294C2214yescomplemented
40#16811294C2214yescomplemented
41#16811292C2218yescomplemented
42#16811292C2218yescomplemented
43#16811291C2218yescomplemented
44#16811284C2218yescomplemented
45#16811284C2218yescomplemented
46#16811284C2218yescomplemented
47#16811276C2218yescomplemented
48#16811275C2218yescomplemented
49#16811270C2218yescomplemented
50#16811269C2218yescomplemented
51#16811268C2218yescomplemented
52#16811266C2218yescomplemented
53#16811264C2218yescomplemented
54#16811261C22116yescomplemented
55#16811261C2218yescomplemented
56D4×D212C2214yescomplemented
57#16811257C2218yes—
58#16811247C2218yescomplemented
59#16811247C2218yescomplemented
60#16811246C2218yescomplemented
61#16811234C2214yescomplemented
62#16811228C2214yescomplemented
63#16811226C2218yescomplemented
64#16811225C22116yescomplemented
65#16811224C2218yescomplemented
66#16811219C22116yescomplemented
67#16811213C22116yescomplemented
68#16811209C22116yescomplemented
69#16811204C2218yescomplemented
70#16811197C2212yes—
71#16811197C2214yescomplemented
72#16811191C2214yescomplemented
73#16811189C2218yescomplemented
74#16811187C2212yes—
75#16811187C2218yescomplemented
76#16811187C2214yescomplemented
77#16811187C2212yescomplemented
78#16811184C2218yescomplemented
79#16811180C2211yescharacteristic, complemented
80#16811178C2212yescomplemented
81#16811178C2214yescomplemented
82#16811177C2212yescomplemented
83#16811176C2211yescharacteristic, complemented
84#16811174C2214yescomplemented
85#16811174C2214yescomplemented
86#16811174C2214yescomplemented
87#16811174C2212yescomplemented
88#16811174C2214yescomplemented
89#16811173C2214yescomplemented
90#16811171C2212yescomplemented
91#16811170C2212yescomplemented
92#16811169C2211yescharacteristic
93#16811169C2214yescomplemented
94C2×#13133214C2211yescharacteristic
95#127×D53C2212yescomplemented
96#16811160C2212yescomplemented
97#16811159C2218yescomplemented
98#16811155C2212yescomplemented
99#16811155C2214yescomplemented
100#16811154C2214yescomplemented
101#16811153C2214yescomplemented
102#16811152C2214yescomplemented
103#16811151C2214yescomplemented
104C2×#13133206C2212yescomplemented
105C2×#13133206C2214yescomplemented
106#16811135C2211yescharacteristic
107#16811133C2214yescomplemented
108#16811132C2214yescomplemented
109#16811130C2211yescharacteristic, complemented
110#16811130C2212yescomplemented
111#16811130C2218yescomplemented
112#123×D53C2218yescomplemented
113C2×#13133192C2214yescomplemented
114#16811104C2218yescomplemented
115#16811101C2212yescomplemented
116#16811097C2212yescomplemented
117#16811095C2218yescomplemented
118#41×Dic53C2212yescomplemented
119C4×#11719945C2211yescharacteristic
120C4×#11719945C2214yescomplemented
121C4×#11719947C2214yescomplemented
122C2×#13133179C2214yescomplemented
123C2×C42×D53C2211yescharacteristic, complemented
124C2×2−1+4×C53C2212yescomplemented
125D4×Q8×C53C2214yescomplemented
126C53×#547C2218yescomplemented
127C53×#547C2214yescomplemented
128C53×#536C2214yescomplemented
129C53×#536C2212yescomplemented
130C53×#532C2211yescharacteristic
131C53×#532C2212yescomplemented
132C2×C4⋊Q8×C53C2211yescharacteristic, complemented
133C2×C4⋊Q8×C53C2212yescomplemented
134C4×#41×C53C2211yescharacteristic, complemented
135#13133263—48no—
136C2×#11719949—48no—
137C2×#11719949C2318yes—
138C2×#11719949C2318yes—
139C2×#11719949C2314yes—
140C2×#11719945C2311yescharacteristic
141C2×#11719945C2318yes—
142C2×#11719945C2314yes—
143C2×#11719945C2314yes—
144C2×#11719947C2314yes—
145C22×D212C2312yes—
146C22×D212C2314yes—
147C22×D212C2314yes—
148C22×D212C2314yes—
149C2×D4×D53C2314yes—
150C2×D4×D53C2318yes—
151C2×D4×D53C2318yes—
152C22×C4×D53C2311yescharacteristic
153C22×C4×D53C2312yes—
154C22×C4×D53C2314yes—
155#13133217C2312yes—
156#13133216C2312yes—
157#13133215C2314yes—
158#13133215C2311yescharacteristic
159#13133214C2314yes—
160#13133214C2312yes—
161#13133214C2312yes—
162#13133213C23116yes—
163#13133213C2318yes—
164#13133213C2314yes—
165#13133213C2314yes—
166#13133213C2311yescharacteristic
167#13133212C23116yes—
168#13133212C23116yes—
169#13133212C2314yes—
170#13133212C23116yes—
171#13133210C2314yes—
172#13133210C2318yes—
173#13133209C2312yes—
174#13133208C2318yes—
175#13133208C2314yes—
176#13133208C2312yes—
177#13133207C23116yes—
178#13133207C2314yes—
179#13133206C2314yes—
180#13133206C23116yes—
181#13133206C2314yes—
182#13133206C2314yes—
183#13133206C23116yes—
184#13133206C2318yes—
185#13133206C2311yescharacteristic
186#13133206C2314yes—
187#13133206C2314yes—
188#13133205C2318yes—
189#13133204C2314yes—
190#13133204C2311yescharacteristic
191#13133203C23116yes—
192#13133203C2314yes—
193#13133202C23116yes—
194#13133202C23116yes—
195#13133202C23116yes—
196#13133202C2314yes—
197#13133201C23116yes—
198#13133201C2312yes—
199#13133200C2318yes—
200#13133200C23116yes—
201#13133199C23116yes—
202#13133199C23116yes—
203#13133199C2318yes—
204#13133199C2314yes—
205#13133198C2314yes—
206#13133198C2312yes—
207#13133197C2318yes—
208#13133197C2312yes—
209#13133197C23116yes—
210#13133197C2314yes—
211#13133196C2314yes—
212#13133195C2314yes—
213#13133194C2314yes—
214#13133193C2318yes—
215#13133193C2314yes—
216#13133193C2312yes—
217#13133193C23116yes—
218#13133193C23116yes—
219#13133192C2312yes—
220#13133192C23116yes—
221#13133192C2318yes—
222#13133192C2318yes—
223#13133192C2318yes—
224#13133192C2318yes—
225#13133192C2318yes—
226#13133191C23116yes—
227#13133191C2318yes—
228#13133191C2318yes—
229#13133191C2318yes—
230#13133191C23116yes—
231#13133191C23116yes—
232#13133190C23116yes—
233#13133190C23116yes—
234#13133190C23116yes—
235#13133190C2314yes—
236#13133189C23116yes—
237#13133189C2314yes—
238#13133188C2314yes—
239#13133188C23116yes—
240#13133188C2312yes—
241#13133188C2314yes—
242#13133187C23116yes—
243#13133187C23116yes—
244#13133187C2312yes—
245#13133185C2318yes—
246#13133185C23116yes—
247#13133185C2318yes—
248#13133185C2312yes—
249#13133185C2314yes—
250Q8×Dic53C2314yes—
251Q8×Dic53C2318yes—
252Q8×Dic53C2318yes—
253C4×Dic106C2312yes—
254C4×Dic106C2314yes—
255C4×Dic106C2314yes—
256C4×Dic106C2314yes—
257#13133182C2318yes—
258#13133182C2314yes—
259C4×D212C2314yes—
260C4×D212C2318yes—
261C4×D212C2314yes—
262C4×D212C2318yes—
263C4×D212C2312yes—
264D4×Dic53C2318yes—
265D4×Dic53C2314yes—
266D4×Dic53C2314yes—
267#13133179C2318yes—
268#13133179C2318yes—
269#13133179C2318yes—
270#13133179C2318yes—
271#13133179C2318yes—
272#13133179C2318yes—
273C4×C22⋊D53C2318yes—
274C4×C22⋊D53C2314yes—
275C4×C22⋊D53C2314yes—
276C4×C22⋊D53C2314yes—
277C4×C22⋊D53C23116yes—
278C4×C22⋊D53C23116yes—
279C4×C22⋊D53C23116yes—
280C4×C22⋊D53C2314yes—
281C4×C22⋊D53C2314yes—
282#13133177C23116yes—
283#13133177C2318yes—
284#13133176C2318yes—
285#13133176C2311yescharacteristic
286#13133176C2314yes—
287#13133176C2312yes—
288#13133176C2314yes—
289#13133175C23116yes—
290#13133175C2318yes—
291#13133175C2314yes—
292#13133174C2312yes—
293#13133174C2314yes—
294#13133174C2314yes—
295#13133173C2318yes—
296C4⋊C4×D53C23116yes—
297C2×#11719921C23116yes—
298C2×#11719921C2318yes—
299C22⋊C4×D53C23116yes—
300C22⋊C4×D53C2318yes—
301C2×C4×Dic53C2312yes—
302C2×C4×Dic53C2311yescharacteristic
303C2×C4×Dic53C2314yes—
304C42×D53C2312yes—
305C42×D53C2312yes—
306C42×D53C2312yes—
307C42×D53C2312yes—
308C42×D53C2312yes—
3092−1+4×C53—48no—
310C2×#41×C53C2311yescharacteristic
311C2×#41×C53C2312yes—
312C2×#41×C53C2314yes—
313C2×#41×C53C2314yes—
314C2×#41×C53C2318yes—
315C22×Q8×C53C2312yes—
316C22×Q8×C53C2314yes—
317C22×Q8×C53C2314yes—
318C4⋊Q8×C53C2314yes—
319C4⋊Q8×C53C2311yescharacteristic
320C4⋊Q8×C53C2312yes—
321C4⋊Q8×C53C2312yes—
322C4⋊Q8×C53C2318yes—
323C4⋊Q8×C53C2314yes—
324#127×C53C2311yescharacteristic
325#124×C53C2314yes—
326#124×C53C2312yes—
327#123×C53C2318yes—
328#123×C53C23116yes—
329C22⋊Q8×C53C2318yes—
330C22⋊Q8×C53C23116yes—
331#121×C53C2318yes—
332#121×C53C2314yes—
333C4×Q8×C53C2312yes—
334C4×D4×C53C2318yes—
335C4×D4×C53C2314yes—
336C4×D4×C53C2312yes—
337C4×D4×C53C2314yes—
338#117×C53C2311yescharacteristic
339#117×C53C2312yes—
340C2×C4⋊C4×C53C2314yes—
341C2×C4⋊C4×C53C2318yes—
342C2×C42×C53C2311yescharacteristic
343C2×C42×C53C2312yes—
344C23×D53C2414yes—
345C23×D53C2411yescharacteristic
346C23×D53C2418yes—
347#41×C53—24no—
348#41×C53—28no—
349#41×C53—416no—
350#41×C53—48no—
351#41×C53—48no—
352C2×Q8×C53—28no—
353C2×Q8×C53—48no—
354C2×Q8×C53—48no—
355C2×Q8×C53C2411yescharacteristic
356C2×Q8×C53C2414yes—
357C2×Q8×C53C2414yes—
358C2×Q8×C53C2412yes—
359C2×Q8×C53C2418yes—
360C2×D4×C53C2414yes—
361C2×D4×C53C2412yes—
362C2×D4×C53C2411yescharacteristic
363C2×D4×C53C2414yes—
364C2×D4×C53C2412yes—
365C2×D4×C53C2418yes—
366C22×C4×C53C2412yes—
367C22×C4×C53C2414yes—
368C22×C4×C53C2412yes—
369C22×C4×C53C2414yes—
370C22×C4×C53C2414yes—
371C22×C4×C53C2418yes—
372C22×C4×C53C2418yes—
373C22×C4×C53C2411yescharacteristic
374C2×C22⋊D53C2412yes—
375C2×C22⋊D53C2418yes—
376C2×C22⋊D53C24116yes—
377C2×C22⋊D53C2414yes—
378C2×C22⋊D53C24116yes—
379C2×C22⋊D53C2414yes—
380C2×C22⋊D53C2418yes—
381C22×Dic53C2411yescharacteristic
382C22×Dic53C2412yes—
383C22×Dic53C2418yes—
384#11719949—416no—
385#11719949—416no—
386#11719949—48no—
387#11719947—48no—
388D4×D53—416no—
389D4×D53—48no—
390D4×D53—416no—
391#11719945—24no—
392#11719945—416no—
393#11719945—48no—
394#11719945—48no—
395C2×D212—28no—
396C2×D212—48no—
397C2×D212—48no—
398C2×D212—48no—
399C2×D212C2418yes—
400C2×D212C2414yes—
401C2×D212C2414yes—
402C2×D212C2411yescharacteristic
403C2×D212C2418yes—
404C2×D212C2414yes—
405C2×D212C2418yes—
406C2×D212C24116yes—
407C2×C4×D53—24no—
408C2×C4×D53—44no—
409C2×C4×D53—48no—
410C2×C4×D53C2412yes—
411C2×C4×D53C2412yes—
412C2×C4×D53C2412yes—
413C2×C4×D53C2412yes—
414C2×C4×D53C2414yes—
415C2×C4×D53C2412yes—
416C2×C4×D53C2412yes—
417C2×C4×D53C2412yes—
418C2×C4×D53C24116yes—
419C2×C4×D53C24116yes—
420C2×C4×D53C2418yes—
421C2×Dic106C2414yes—
422C2×Dic106C2411yescharacteristic
423C2×Dic106C2414yes—
424C4⋊C4×C53C2418yes—
425C4⋊C4×C53C2414yes—
426C4⋊C4×C53C24116yes—
427C4⋊C4×C53C2418yes—
428C4⋊C4×C53C2412yes—
429C4⋊C4×C53C2414yes—
430C22⋊C4×C53C2412yes—
431C22⋊C4×C53C2414yes—
432C22⋊C4×C53C24116yes—
433C22⋊C4×C53C2418yes—
434C42×C53C2411yescharacteristic
435C42×C53C2411yescharacteristic
436C42×C53C2412yes—
437C42×C53C2412yes—
438C42×C53C2414yes—
439C22⋊Dic53C2418yes—
440C22⋊Dic53C2414yes—
441C22⋊Dic53C2412yes—
442C22⋊Dic53C2414yes—
443C22⋊Dic53C2414yes—
444C22⋊Dic53C2418yes—
445#11719921C2414yes—
446#11719921C24116yes—
447#11719921C24116yes—
448#11719921C2414yes—
449#11719921C24116yes—
450#11719921C24116yes—
451#11719921C24116yes—
452#11719921C2414yes—
453#11719921C2414yes—
454#11719921C2414yes—
455#11719921C2418yes—
456#11719921C24116yes—
457C4⋊Dic53C2414yes—
458C4⋊Dic53C2414yes—
459C4⋊Dic53C2414yes—
460C4⋊Dic53C2414yes—
461C4⋊Dic53C2418yes—
462C4⋊Dic53C2412yes—
463C4⋊Dic53C24116yes—
464#11719919C2418yes—
465#11719919C24116yes—
466#11719919C2418yes—
467#11719919C2414yes—
468#11719919C2414yes—
469#11719919C2414yes—
470#11719919C2414yes—
471#11719919C2414yes—
472C4×Dic53C2411yescharacteristic
473C4×Dic53C2412yes—
474C4×Dic53C2412yes—
475C4×Dic53C2411yescharacteristic
476C4×Dic53C2412yes—
477C4×Dic53C2412yes—
478C4×Dic53C2412yes—
479C4×Dic53C2414yes—
480C4×Dic53C2412yes—
481C4×Dic53C2418yes—
482C4×Dic53C2414yes—
483C4×Dic53C24116yes—
484C23×C53C2514yes—
485C23×C53C2512yes—
486C23×C53C2511yescharacteristic
487C22×D53—22no—
488C22×D53—28no—
489C22×D53—42no—
490C22×D53—48no—
491C22×D53—48no—
492C22×D53—416no—
493C22×D53C2512yes—
494C22×D53C2518yes—
495C22×D53C2512yes—
496Q8×C53—28no—
497Q8×C53—28no—
498Q8×C53—24no—
499Q8×C53—22no—
500Q8×C53—48no—
501D4×C53—28no—
502D4×C53—24no—
503D4×C53—24no—
504D4×C53—22no—
505D4×C53—28no—
506D4×C53—48no—
507C2×C4×C53—28no—
508C2×C4×C53—28no—
509C2×C4×C53—24no—
510C2×C4×C53—24no—
511C2×C4×C53—28no—
512C2×C4×C53—48no—
513C2×C4×C53—48no—
514C2×C4×C53H(5,𝔽2)14yes—
515C2×C4×C53C2514yes—
516C2×C4×C53C2512yes—
517C2×C4×C53C2514yes—
518C2×C4×C53C2518yes—
519C2×C4×C53C2512yes—
520C2×C4×C53C2511yescharacteristic
521C2×C4×C53C2511yescharacteristic
522C2×C4×C53C2512yes—
523C22⋊D53—24no—
524C22⋊D53—48no—
525C22⋊D53—416no—
526C22⋊D53—44no—
527C22⋊D53—44no—
528C22⋊D53—416no—
529C22⋊D53—48no—
530C2×Dic53—22no—
531C2×Dic53—42no—
532C2×Dic53—48no—
533C2×Dic53C2512yes—
534C2×Dic53C2512yes—
535C2×Dic53C2518yes—
536C2×Dic53C2514yes—
537C2×Dic53C2512yes—
538C2×Dic53C2512yes—
539D212—28no—
540D212—28no—
541D212—22no—
542D212—216no—
543D212—48no—
544D212—48no—
545D212—416no—
546D212—44no—
547C4×D53—24no—
548C4×D53—24no—
549C4×D53—24no—
550C4×D53—24no—
551C4×D53—24no—
552C4×D53—28no—
553C4×D53—42no—
554C4×D53—42no—
555C4×D53—416no—
556C4×D53—416no—
557C4×D53—48no—
558Dic106—22no—
559Dic106—28no—
560Dic106—44no—
561#62836—531nomaximal, Sylow
562C22×C53—22no—
563C22×C53—24no—
564C22×C53—22no—
565C22×C53—28no—
566C22×C53—24no—
567C22×C53C2×H(5,𝔽2)12yes—
568C22×C53C2611yescharacteristic
569C2×D53—22no—
570C2×D53—22no—
571C2×D53—28no—
572C2×D53—22no—
573C2×D53—22no—
574C2×D53—24no—
575C2×D53—216no—
576C2×D53—44no—
577C2×D53—88no—
578C2×D53—168no—
579C4×C53—24no—
580C4×C53—28no—
581C4×C53—22no—
582C4×C53—24no—
583C4×C53—22no—
584C4×C53C2×H(5,𝔽2)12yes—
585C4×C53C2×H(5,𝔽2)12yes—
586C4×C53#58514yes—
587Dic53—22no—
588Dic53—22no—
589Dic53—28no—
590Dic53—22no—
591Dic53—24no—
592Dic53—22no—
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—534no—
604#3508—531no—
605#3500—532no—
606#3499D5311yescharacteristic, complemented
607#3498—531no—
608#3487—532no—
609#3485—532no—
610#3444—531no—
611#3444—531no—
612C2×#532—531no—
613C2×C53—22no—
614C2×C53—44no—
615C2×C53—42no—
616C2×C53C22×H(5,𝔽2)11yescharacteristic
617C2×C53C2×#58512yes—
618D53—42no—
619D53—48no—
620D53—42no—
621C2×2−1+4C2×D5312yescomplemented
622C2×H(5,𝔽2)—532no—
623C22×#41—532no—
624#562—5316no—
625#560—5316no—
626#559—538no—
627#559—534no—
628#559—538no—
629#557—534no—
630#556—534no—
631#556—538no—
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—538no—
642#550—538no—
643#550—534no—
644#550—534no—
645D4×Q8C2×D5314yescomplemented
646#548—538no—
647#548—538no—
648#548—538no—
649#547—538no—
650#547—538no—
651#547C2×D5318yescomplemented
652#547C2×D5314yescomplemented
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#536C2×D5312yescomplemented
677#536C2×D5314yescomplemented
678#535—532no—
679#535—532no—
680#535—538no—
681#535—534no—
682#535—534no—
683#535—538no—
684#534—538no—
685#533—532no—
686#533—534no—
687#533—532no—
688#533—531no—
689#533—531no—
690#532—531no—
691#532—534no—
692#532—534no—
693#532—534no—
694#532—534no—
695#532—534no—
696#532—532no—
697#532—532no—
698#532—532no—
699#532—534no—
700#532C2×D5311yescharacteristic
701#532C2×D5312yescomplemented
702C2×C4⋊Q8C2×D5311yescharacteristic, complemented
703C2×C4⋊Q8C2×D5312yescomplemented
704C2×#127—532no—
705C2×#127—531no—
706#529—534no—
707#529—538no—
708#529—534no—
709#529—532no—
710#529—534no—
711#529—532no—
712#529—534no—
713#529—534no—
714C2×#124—532no—
715C2×#124—534no—
716#525—532no—
717#525—531no—
718#525—538no—
719#525—534no—
720#525—534no—
721#525—531no—
722C2×#123—538no—
723C2×#121—534no—
724#520—538no—
725#519—532no—
726#518—538no—
727#518—532no—
728C4×#41—532no—
729C4×#41—534no—
730C4×#41—531no—
731C4×#41—534no—
732C4×#41C2×D5311yescharacteristic, complemented
733C2×C4×D4—534no—
734C22×C42—531no—
735C53#6283611yescharacteristic, complemented, Sylow
7362−1+4—48no—
737H(5,𝔽2)—2128no—
738C2×#41—538no—
739C2×#41—538no—
740C2×#41—534no—
741C2×#41—534no—
742C2×#41—531no—
743C2×#41—534no—
744C2×#41—538no—
745C2×#41—534no—
746C2×#41—2128no—
747C2×#41C22×D5312yes—
748C2×#41C22×D5311yescharacteristic
749C2×#41C22×D5318yes—
750C2×#41C22×D5314yes—
751C2×#41C22×D5314yes—
752C22×Q8C22×D5312yes—
753C22×Q8C22×D5314yes—
754C22×Q8C22×D5314yes—
755C22×D4—538no—
756C22×D4—538no—
757C22×D4—534no—
758C22×D4—532no—
759C22×D4—534no—
760C22×D4—534no—
761C22×D4—534no—
762C23×C4—531no—
763C23×C4—534no—
764C23×C4—532no—
765C4⋊Q8—531no—
766C4⋊Q8—534no—
767C4⋊Q8—532no—
768C4⋊Q8—532no—
769C4⋊Q8C22×D5311yescharacteristic
770C4⋊Q8C22×D5312yes—
771C4⋊Q8C22×D5312yes—
772C4⋊Q8C22×D5314yes—
773C4⋊Q8C22×D5314yes—
774C4⋊Q8C22×D5318yes—
775#127—534no—
776#127—538no—
777#127—531no—
778#127—534no—
779#127—5316no—
780#127—532no—
781#127—532no—
782#127—534no—
783#127C22×D5311yescharacteristic
784#126—534no—
785#126—5316no—
786#126—5316no—
787#126—5316no—
788#126—538no—
789#126—534no—
790#125—532no—
791#125—534no—
792#125—534no—
793#125—538no—
794#125—5316no—
795#125—532no—
796#124—531no—
797#124—534no—
798#124—534no—
799#124—538no—
800#124—534no—
801#124—534no—
802#124—5316no—
803#124—534no—
804#124—5316no—
805#124—531no—
806#124—534no—
807#124—534no—
808#124—5316no—
809#124—538no—
810#124C22×D5312yes—
811#124C22×D5314yes—
812#123—534no—
813#123—532no—
814#123—538no—
815#123—5316no—
816#123—5316no—
817#123—534no—
818#123—5316no—
819#123—5316no—
820#123—532no—
821#123—5316no—
822#123—534no—
823#123—538no—
824#123—5316no—
825#123—5316no—
826#123C22×D5318yes—
827#123C22×D53116yes—
828C22⋊Q8—534no—
829C22⋊Q8—532no—
830C22⋊Q8—5316no—
831C22⋊Q8—538no—
832C22⋊Q8—5316no—
833C22⋊Q8—534no—
834C22⋊Q8—534no—
835C22⋊Q8—532no—
836C22⋊Q8—534no—
837C22⋊Q8—538no—
838C22⋊Q8—5316no—
839C22⋊Q8—534no—
840C22⋊Q8C22×D5318yes—
841C22⋊Q8C22×D53116yes—
842#121—534no—
843#121—534no—
844#121—534no—
845#121—532no—
846#121—5316no—
847#121—5316no—
848#121—538no—
849#121—538no—
850#121—538no—
851#121—5316no—
852#121—5316no—
853#121—5316no—
854#121—538no—
855#121—538no—
856#121—538no—
857#121—538no—
858#121—532no—
859#121—538no—
860#121—5316no—
861#121—534no—
862#121—5316no—
863#121—5316no—
864#121—5316no—
865#121C22×D5314yes—
866#121C22×D5318yes—
867#120—534no—
868#120—532no—
869#120—538no—
870#120—538no—
871#120—5316no—
872#120—532no—
873#120—5316no—
874#120—5316no—
875C4×Q8—534no—
876C4×Q8—538no—
877C4×Q8—538no—
878C4×Q8—534no—
879C4×Q8—538no—
880C4×Q8—532no—
881C4×Q8—534no—
882C4×Q8—534no—
883C4×Q8—534no—
884C4×Q8C22×D5312yes—
885C4×D4—534no—
886C4×D4—538no—
887C4×D4—534no—
888C4×D4—534no—
889C4×D4—538no—
890C4×D4—534no—
891C4×D4—534no—
892C4×D4—534no—
893C4×D4—534no—
894C4×D4—5316no—
895C4×D4—5316no—
896C4×D4—5316no—
897C4×D4—538no—
898C4×D4—538no—
899C4×D4—538no—
900C4×D4—538no—
901C4×D4—538no—
902C4×D4—538no—
903C4×D4—538no—
904C4×D4—5316no—
905C4×D4—534no—
906C4×D4—534no—
907C4×D4—532no—
908C4×D4—538no—
909C4×D4—538no—
910C4×D4C22×D5314yes—
911C4×D4C22×D5314yes—
912C4×D4C22×D5312yes—
913C4×D4C22×D5318yes—
914#117—532no—
915#117—531no—
916#117—534no—
917#117—534no—
918#117—538no—
919#117—534no—
920#117—538no—
921#117—5316no—
922#117—538no—
923#117—534no—
924#117—534no—
925#117—532no—
926#117C22×D5311yescharacteristic
927#117C22×D5312yes—
928C2×C4⋊C4—5316no—
929C2×C4⋊C4C22×D5314yes—
930C2×C4⋊C4C22×D5318yes—
931C2×C22⋊C4—538no—
932C2×C22⋊C4—5316no—
933C2×C22⋊C4—538no—
934C2×C22⋊C4—5316no—
935C2×C42—532no—
936C2×C42—534no—
937C2×C42—531no—
938C2×C42—532no—
939C2×C42—532no—
940C2×C42—532no—
941C2×C42—532no—
942C2×C42—532no—
943C2×C42C22×D5312yes—
944C2×C42C22×D5311yescharacteristic
945C24—534no—
946C24—531no—
947C24—538no—
948#41—28no—
949#41—24no—
950#41—416no—
951#41—48no—
952#41—48no—
953#41—1064no—
954#41—2128no—
955#41—21216no—
956#41—2128no—
957#41—2128no—
958#41—21216no—
959#41—21216no—
960#41—2128no—
961C2×Q8—28no—
962C2×Q8—48no—
963C2×Q8—48no—
964C2×Q8—534no—
965C2×Q8—531no—
966C2×Q8—534no—
967C2×Q8C23×D5314yes—
968C2×Q8C23×D5312yes—
969C2×Q8C23×D5314yes—
970C2×Q8C23×D5311yescharacteristic
971C2×Q8C23×D5318yes—
972C2×D4—532no—
973C2×D4—534no—
974C2×D4—538no—
975C2×D4—5316no—
976C2×D4—5316no—
977C2×D4—534no—
978C2×D4—538no—
979C2×D4—538no—
980C2×D4—531no—
981C2×D4—534no—
982C2×D4—534no—
983C2×D4—534no—
984C2×D4—538no—
985C2×D4—538no—
986C2×D4—5316no—
987C2×D4—1068no—
988C2×D4—2128no—
989C2×D4—2128no—
990C2×D4—2128no—
991C2×D4—21216no—
992C2×D4—2128no—
993C2×D4—21216no—
994C2×D4C23×D5314yes—
995C2×D4C23×D5312yes—
996C2×D4C23×D5314yes—
997C2×D4C23×D5312yes—
998C2×D4C23×D5311yescharacteristic
999C2×D4C23×D5318yes—
1000C22×C4—531no—
1001C22×C4—532no—
1002C22×C4—538no—
1003C22×C4—532no—
1004C22×C4—532no—
1005C22×C4—532no—
1006C22×C4—532no—
1007C22×C4—534no—
1008C22×C4—532no—
1009C22×C4—532no—
1010C22×C4—532no—
1011C22×C4—5316no—
1012C22×C4—5316no—
1013C22×C4—538no—
1014C22×C4—1064no—
1015C22×C4—2124no—
1016C22×C4—2128no—
1017C22×C4C23×D5312yes—
1018C22×C4C23×D5314yes—
1019C22×C4C23×D5314yes—
1020C22×C4C23×D5312yes—
1021C22×C4C23×D5314yes—
1022C22×C4C23×D5318yes—
1023C22×C4C23×D5318yes—
1024C22×C4C23×D5311yescharacteristic
1025C4⋊C4—534no—
1026C4⋊C4—538no—
1027C4⋊C4—5316no—
1028C4⋊C4—534no—
1029C4⋊C4—534no—
1030C4⋊C4—534no—
1031C4⋊C4—534no—
1032C4⋊C4—534no—
1033C4⋊C4—532no—
1034C4⋊C4—534no—
1035C4⋊C4—538no—
1036C4⋊C4—538no—
1037C4⋊C4—534no—
1038C4⋊C4—534no—
1039C4⋊C4—5316no—
1040C4⋊C4C23×D53116yes—
1041C4⋊C4C23×D5318yes—
1042C4⋊C4C23×D5314yes—
1043C4⋊C4C23×D5318yes—
1044C4⋊C4C23×D5312yes—
1045C4⋊C4C23×D5314yes—
1046C22⋊C4—534no—
1047C22⋊C4—538no—
1048C22⋊C4—532no—
1049C22⋊C4—534no—
1050C22⋊C4—534no—
1051C22⋊C4—538no—
1052C22⋊C4—534no—
1053C22⋊C4—534no—
1054C22⋊C4—5316no—
1055C22⋊C4—5316no—
1056C22⋊C4—5316no—
1057C22⋊C4—5316no—
1058C22⋊C4—5316no—
1059C22⋊C4—534no—
1060C22⋊C4—5316no—
1061C22⋊C4—534no—
1062C22⋊C4—538no—
1063C22⋊C4—534no—
1064C22⋊C4C23×D5312yes—
1065C22⋊C4C23×D53116yes—
1066C22⋊C4C23×D5318yes—
1067C22⋊C4C23×D5314yes—
1068C42—531no—
1069C42—532no—
1070C42—532no—
1071C42—531no—
1072C42—532no—
1073C42—532no—
1074C42—532no—
1075C42—538no—
1076C42—534no—
1077C42—534no—
1078C42—532no—
1079C42—5316no—
1080C42C23×D5311yescharacteristic
1081C42C23×D5311yescharacteristic
1082C42C23×D5312yes—
1083C42C23×D5314yes—
1084C42C23×D5312yes—
1085C23—532no—
1086C23—538no—
1087C23—532no—
1088C23—1068no—
1089C23—1062no—
1090C23—2128no—
1091C23—21216no—
1092C23—2128no—
1093C23—2122no—
1094C23C24×D5314yes—
1095C23C24×D5312yes—
1096C23C24×D5311yescharacteristic
1097Q8—28no—
1098Q8—28no—
1099Q8—22no—
1100Q8—24no—
1101Q8—48no—
1102Q8—1062no—
1103Q8—1068no—
1104Q8—2124no—
1105D4—28no—
1106D4—24no—
1107D4—24no—
1108D4—22no—
1109D4—28no—
1110D4—48no—
1111D4—1064no—
1112D4—1068no—
1113D4—1068no—
1114D4—1062no—
1115D4—10616no—
1116D4—2128no—
1117D4—2128no—
1118D4—21216no—
1119D4—2124no—
1120D4—21216no—
1121D4—2128no—
1122D4—2124no—
1123D4—2124no—
1124D4—21216no—
1125D4—2128no—
1126C2×C4—28no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—28no—
1131C2×C4—48no—
1132C2×C4—48no—
1133C2×C4—532no—
1134C2×C4—534no—
1135C2×C4—532no—
1136C2×C4—538no—
1137C2×C4—532no—
1138C2×C4—532no—
1139C2×C4—1062no—
1140C2×C4—1064no—
1141C2×C4—1064no—
1142C2×C4—1064no—
1143C2×C4—1064no—
1144C2×C4—1064no—
1145C2×C4—1068no—
1146C2×C4—2122no—
1147C2×C4—2122no—
1148C2×C4—21216no—
1149C2×C4—2128no—
1150C2×C4—21216no—
1151C2×C4—2122no—
1152C2×C4—2128no—
1153C2×C4#1313326214yes—
1154C2×C4C24×D5312yes—
1155C2×C4C24×D5314yes—
1156C2×C4C24×D5318yes—
1157C2×C4C24×D5312yes—
1158C2×C4C24×D5314yes—
1159C2×C4C24×D5311yescharacteristic
1160C2×C4C24×D5311yescharacteristic
1161C2×C4C24×D5312yes—
1162C22—22no—
1163C22—22no—
1164C22—24no—
1165C22—24no—
1166C22—28no—
1167C22—8488no—
1168C22—1062no—
1169C22—1062no—
1170C22—1068no—
1171C22—1062no—
1172C22—1062no—
1173C22—1064no—
1174C22—10616no—
1175C22—4248no—
1176C22—2124no—
1177C22C2×#1313326212yes—
1178C22C25×D5311yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—28no—
1182C4—24no—
1183C4—22no—
1184C4—1062no—
1185C4—1062no—
1186C4—1062no—
1187C4—1062no—
1188C4—1064no—
1189C4—1068no—
1190C4C2×#1313326212yes—
1191C4C2×#1313326212yes—
1192C4#1681146014yes—
1193C2—22no—
1194C2—44no—
1195C2—42no—
1196C2—2122no—
1197C2—2128no—
1198C2—2122no—
1199C2C22×#1313326211yescharacteristic
1200C2C2×#1681146012yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3499C2
hypercenter#3499D53
hypocenterC53#62836
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #20289291C2semidirect
2. #20289187C2semidirect
3. #20289088C2semidirect
4. #20289032C2semidirect
5. #20288720C2semidirect
6. #20288677C2semidirect
7. #20288650C2semidirect
8. #20288628C2semidirect
9. #20288614C2semidirect
10. #20288599C2semidirect
11. #20288591C2semidirect
12. #20288584C2semidirect
13. #20288509C2semidirect
14. #20288488C2semidirect
15. #20288370C2semidirect
16. #20288358C2semidirect
17. #20288010C2semidirect
18. #20288008C2semidirect
19. C2×#16811174C2semidirect
20. C53×#3499C2semidirect
22. C22×#11719949C22semidirect
23. #16811369C22semidirect
24. #16811363C22semidirect
25. #16811358C22semidirect
26. #16811356C22semidirect
27. #16811355C22semidirect
28. #16811348C22semidirect
29. #16811347C22semidirect
30. #16811347C22semidirect
31. #16811339C22semidirect
32. #16811334C22semidirect
33. #16811321C22semidirect
34. #16811321C22semidirect
35. #16811318C22semidirect
36. #16811308C22semidirect
37. #16811300C22semidirect
38. #16811296C22semidirect
39. #16811294C22semidirect
40. #16811294C22semidirect
41. #16811292C22semidirect
42. #16811292C22semidirect
43. #16811291C22semidirect
44. #16811284C22semidirect
45. #16811284C22semidirect
46. #16811284C22semidirect
47. #16811276C22semidirect
48. #16811275C22semidirect
49. #16811270C22semidirect
50. #16811269C22semidirect
51. #16811268C22semidirect
52. #16811266C22semidirect
53. #16811264C22semidirect
54. #16811261C22semidirect
55. #16811261C22semidirect
56. D4×D212C22semidirect
58. #16811247C22semidirect
59. #16811247C22semidirect
60. #16811246C22semidirect
61. #16811234C22semidirect
62. #16811228C22semidirect
63. #16811226C22semidirect
64. #16811225C22semidirect
65. #16811224C22semidirect
66. #16811219C22semidirect
67. #16811213C22semidirect
68. #16811209C22semidirect
69. #16811204C22semidirect
71. #16811197C22semidirect
72. #16811191C22semidirect
73. #16811189C22semidirect
75. #16811187C22semidirect
76. #16811187C22semidirect
77. #16811187C22semidirect
78. #16811184C22semidirect
79. #16811180C22semidirect
80. #16811178C22semidirect
81. #16811178C22semidirect
82. #16811177C22semidirect
83. #16811176C22semidirect
84. #16811174C22semidirect
85. #16811174C22semidirect
86. #16811174C22semidirect
87. #16811174C22semidirect
88. #16811174C22semidirect
89. #16811173C22semidirect
90. #16811171C22semidirect
91. #16811170C22semidirect
93. #16811169C22semidirect
95. #127×D53C22semidirect
96. #16811160C22semidirect
97. #16811159C22semidirect
98. #16811155C22semidirect
99. #16811155C22semidirect
100. #16811154C22semidirect
101. #16811153C22semidirect
102. #16811152C22semidirect
103. #16811151C22semidirect
104. C2×#13133206C22semidirect
105. C2×#13133206C22semidirect
107. #16811133C22semidirect
108. #16811132C22semidirect
109. #16811130C22semidirect
110. #16811130C22semidirect
111. #16811130C22semidirect
112. #123×D53C22semidirect
113. C2×#13133192C22semidirect
114. #16811104C22semidirect
115. #16811101C22semidirect
116. #16811097C22semidirect
117. #16811095C22semidirect
118. #41×Dic53C22semidirect
120. C4×#11719945C22semidirect
121. C4×#11719947C22semidirect
122. C2×#13133179C22semidirect
123. C2×C42×D53C22semidirect
124. C2×2−1+4×C53C22semidirect
125. D4×Q8×C53C22semidirect
126. C53×#547C22semidirect
127. C53×#547C22semidirect
128. C53×#536C22semidirect
129. C53×#536C22semidirect
131. C53×#532C22semidirect
132. C2×C4⋊Q8×C53C22semidirect
133. C2×C4⋊Q8×C53C22semidirect
134. C4×#41×C53C22semidirect
606. #3499D53semidirect
621. C2×2−1+4C2×D53semidirect
645. D4×Q8C2×D53semidirect
651. #547C2×D53semidirect
652. #547C2×D53semidirect
676. #536C2×D53semidirect
677. #536C2×D53semidirect
701. #532C2×D53semidirect
702. C2×C4⋊Q8C2×D53semidirect
703. C2×C4⋊Q8C2×D53semidirect
732. C4×#41C2×D53semidirect
735. C53#62836semidirect

Maximal subgroups

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

subgroupindex
#202892912
#202891872
#202890882
#202890322
#202887202
#202886772
#202886502
#202886282
#202886142
#202885992
#202885912
#202885842
#202885092
#202884882
#202883702
#202883582
#202880102
#202880082
C2×#168111742
C53×#34992
#6283653