Finite Group Databasebeta

← #28293373

Subgroups — #28293373

Order 13568.

7150 conjugacy classes of subgroups.

The subgroup lattice has 1324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289272C214yesmaximal, complemented
2#20289267C214yesmaximal, complemented
3#20289251C214yesmaximal, complemented
4#20289249C214yesmaximal, complemented
5#20288944C214yesmaximal, complemented
6#20288939C214yesmaximal, complemented
7#20288922C218yesmaximal, complemented
8#20288910C214yesmaximal, complemented
9#20288909C214yesmaximal, complemented
10#20288903C218yesmaximal, complemented
11#20288556C212yesmaximal, complemented
12#20288554C212yesmaximal, complemented
13#20288479C212yesmaximal, complemented
14#20288472C212yesmaximal, complemented
15#20288353C214yesmaximal, complemented
16C2×#16811220C211yesmaximal, characteristic, complemented
17C2×#16811204C211yesmaximal, characteristic, complemented
18C2×C53×#539C211yesmaximal, characteristic, complemented
19C2×#13133262C2214yescomplemented
20C22×#11719945C2212yescomplemented
21#16811377C2218yescomplemented
22#16811375C2218yescomplemented
23#16811371C2218yescomplemented
24#16811370C2218yescomplemented
25#16811369C2218yescomplemented
26#16811369C2218yescomplemented
27#16811364C2218yescomplemented
28#16811363C2218yescomplemented
29#16811331C2218yescomplemented
30#16811329C2218yescomplemented
31#16811326C2218yescomplemented
32#16811324C2218yescomplemented
33#16811322C2218yescomplemented
34#16811321C2218yescomplemented
35#16811321C2214yescomplemented
36#16811319C2214yescomplemented
37#16811315C2214yescomplemented
38#16811313C2214yescomplemented
39#16811302C2218yescomplemented
40#16811300C2218yescomplemented
41#16811298C2218yescomplemented
42#16811296C2218yescomplemented
43#16811284C2214yescomplemented
44#16811282C2214yescomplemented
45#16811277C2214yescomplemented
46#16811277C2214yescomplemented
47#16811274C2218yescomplemented
48#16811274C2218yescomplemented
49#16811274C2214yescomplemented
50#16811273C2214yescomplemented
51#16811271C2218yescomplemented
52#16811271C2218yescomplemented
53#16811269C2214yescomplemented
54#16811268C2218yescomplemented
55#16811268C2218yescomplemented
56#16811265C2218yescomplemented
57#16811265C2218yescomplemented
58#16811265C2218yescomplemented
59#16811264C2214yescomplemented
60#16811264C2218yescomplemented
61#16811263C2218yescomplemented
62#16811263C2218yescomplemented
63#16811263C2218yescomplemented
64#16811262C2218yescomplemented
65D4×D212C2214yescomplemented
66D4×D212C2214yescomplemented
67#16811257C2214yescomplemented
68D4×C22⋊D53C2214yescomplemented
69#16811253C2218yescomplemented
70#16811248C2218yescomplemented
71#16811246C2218yescomplemented
72#16811239C2218yescomplemented
73#16811229C2218yescomplemented
74#16811225C2218yescomplemented
75#16811222C2214yescomplemented
76#16811221C2218yescomplemented
77#16811221C2218yescomplemented
78#16811220C2214yescomplemented
79#16811220C2218yescomplemented
80#16811220C2214yescomplemented
81#16811220C2214yescomplemented
82#16811217C2218yescomplemented
83#16811214C2218yescomplemented
84#16811213C2214yescomplemented
85#16811213C2218yescomplemented
86#16811212C2218yescomplemented
87#16811212C2218yescomplemented
88#16811211C2214yescomplemented
89#16811209C2218yescomplemented
90#16811204C2214yescomplemented
91#16811204C2214yescomplemented
92#16811204C2214yescomplemented
93#16811204C2214yescomplemented
94#16811204C2214yescomplemented
95#16811203C2218yescomplemented
96#16811200C2214yescomplemented
97#16811195C2218yescomplemented
98#16811185C2214yescomplemented
99#16811185C2214yescomplemented
100#16811184C2218yescomplemented
101#16811184C2218yescomplemented
102#16811182C2214yescomplemented
103#16811181C2214yescomplemented
104#16811173C2214yescomplemented
105#16811168C2214yescomplemented
106#16811159C2214yescomplemented
107#16811157C2214yescomplemented
108C2×#13133212C2212yescomplemented
109C2×#13133207C2212yescomplemented
110#16811136C2214yescomplemented
111#16811134C2214yescomplemented
112#16811131C2218yescomplemented
113C2×#13133202C2212yescomplemented
114C2×#13133200C2212yescomplemented
115#123×D53C2218yescomplemented
116C2×#13133197C2214yescomplemented
117C2×#13133196C2211yescharacteristic, complemented
118C2×#13133195C2212yescomplemented
119C2×#13133192C2214yescomplemented
120C2×#13133191C2211yescharacteristic
121C2×#13133191C2212yescomplemented
122C2×#13133191C2212yescomplemented
123C2×#13133191C2214yescomplemented
124#121×D53C2214yescomplemented
125#16811096C2214yescomplemented
126C2×C4×C22⋊D53C2212yescomplemented
127C53×#539C2218yescomplemented
128C53×#539C2214yescomplemented
129C53×#539C2214yescomplemented
130C2×#126×C53C2212yescomplemented
131C2×#125×C53C2212yescomplemented
132C2×#123×C53C2212yescomplemented
133C2×#123×C53C2212yescomplemented
134C2×C22⋊Q8×C53C2211yescharacteristic, complemented
135C2×C22⋊Q8×C53C2212yescomplemented
136C2×#121×C53C2211yescharacteristic
137C2×C4×D4×C53C2212yescomplemented
138C22×C4⋊C4×C53C2211yescharacteristic, complemented
139#13133262—416no—
140C2×#11719949C2314yes—
141C2×#11719945—48no—
142C2×#11719945C2318yes—
143C2×#11719945C2318yes—
144C2×#11719945C2318yes—
145C2×#11719945C2314yes—
146C2×#11719947C2318yes—
147C2×#11719947C2318yes—
148C22×Dic106C2312yes—
149C22×Dic106C2311yescharacteristic
150C22×D212C2312yes—
151C22×D212C2312yes—
152C22×D212C2314yes—
153C22×D212C2312yes—
154C22×D212C2311yescharacteristic
155C22×C22⋊D53C2312yes—
156C22×C22⋊D53C2314yes—
157C22×C22⋊D53C2318yes—
158C2×D4×D53C2318yes—
159C2×D4×D53C2318yes—
160C2×D4×D53C2314yes—
161C22×C4×D53C2314yes—
162C22×C4×D53C2312yes—
163#13133217C2314yes—
164#13133216C2318yes—
165#13133216C2318yes—
166#13133216C2314yes—
167#13133214C2314yes—
168#13133213C2314yes—
169#13133212C2318yes—
170#13133212C2318yes—
171#13133212C2318yes—
172#13133212C2318yes—
173#13133212C2318yes—
174#13133212C2318yes—
175#13133211C2318yes—
176#13133210C2318yes—
177#13133209C2314yes—
178#13133208C2318yes—
179#13133208C2314yes—
180#13133207C2318yes—
181#13133207C2318yes—
182#13133207C2318yes—
183#13133206C2318yes—
184#13133206C2314yes—
185#13133205C2318yes—
186#13133205C2314yes—
187#13133203C2318yes—
188#13133203C2318yes—
189#13133203C2318yes—
190#13133203C2318yes—
191#13133202C2318yes—
192#13133202C2318yes—
193#13133202C2318yes—
194#13133202C2318yes—
195#13133202C2318yes—
196#13133202C2318yes—
197#13133202C2318yes—
198#13133202C2318yes—
199#13133202C2318yes—
200#13133202C2318yes—
201#13133202C2318yes—
202#13133201C2318yes—
203#13133201C2318yes—
204#13133201C2318yes—
205#13133201C2318yes—
206#13133200C2318yes—
207#13133200C2318yes—
208#13133200C2318yes—
209#13133200C2318yes—
210#13133199C2318yes—
211#13133199C2318yes—
212#13133199C2318yes—
213#13133199C2318yes—
214#13133198C2318yes—
215#13133197C2318yes—
216#13133197C2318yes—
217#13133197C2318yes—
218#13133197C2318yes—
219#13133197C2318yes—
220#13133197C2318yes—
221#13133196C2314yes—
222#13133196C2314yes—
223#13133196C2314yes—
224#13133195C2318yes—
225#13133195C2318yes—
226#13133195C2318yes—
227#13133195C2318yes—
228#13133195C2318yes—
229#13133195C2318yes—
230#13133195C2318yes—
231#13133195C2318yes—
232#13133194C2318yes—
233#13133194C2318yes—
234#13133194C2318yes—
235#13133193C2318yes—
236#13133193C2314yes—
237#13133192C2318yes—
238#13133192C2318yes—
239#13133192C2318yes—
240#13133192C2314yes—
241#13133192C2318yes—
242#13133192C2318yes—
243#13133192C2318yes—
244#13133192C2318yes—
245#13133192C2314yes—
246#13133192C2318yes—
247#13133192C2318yes—
248#13133191C2314yes—
249#13133191C2314yes—
250#13133191C2318yes—
251#13133191C2314yes—
252#13133191C2318yes—
253#13133191C2314yes—
254#13133191C2318yes—
255#13133191C2314yes—
256#13133191C2314yes—
257#13133191C2314yes—
258#13133191C2314yes—
259#13133191C2314yes—
260#13133191C2314yes—
261#13133191C2314yes—
262#13133191C2314yes—
263#13133191C2314yes—
264#13133190C2318yes—
265#13133190C2318yes—
266#13133190C2318yes—
267#13133190C2318yes—
268#13133190C2318yes—
269#13133190C2318yes—
270#13133190C2318yes—
271#13133189C2318yes—
272#13133189C2318yes—
273#13133189C2318yes—
274#13133188C2314yes—
275#13133187C2318yes—
276#13133187C2318yes—
277#13133187C2318yes—
278#13133187C2318yes—
279#13133187C2318yes—
280#13133187C2318yes—
281#13133187C2318yes—
282#13133186C2318yes—
283#13133185C2318yes—
284#13133185C2318yes—
285Q8×Dic53C2314yes—
286C4×Dic106C2314yes—
287C4×D212C2318yes—
288C4×D212C2314yes—
289C4×D212C2314yes—
290C4×D212C2314yes—
291D4×Dic53C2314yes—
292#13133179C2318yes—
293#13133179C2314yes—
294#13133179C2318yes—
295#13133179C2318yes—
296#13133179C2314yes—
297C4×C22⋊D53C2318yes—
298C4×C22⋊D53C2314yes—
299C4×C22⋊D53C2314yes—
300C4×C22⋊D53C2318yes—
301C4×C22⋊D53C2314yes—
302C4×C22⋊D53C2318yes—
303C4×C22⋊D53C2314yes—
304#13133177C2318yes—
305#13133177C2318yes—
306#13133177C2318yes—
307#13133177C2318yes—
308#13133177C2318yes—
309#13133176C2314yes—
310#13133175C2318yes—
311#13133175C2314yes—
312#13133174C2318yes—
313#13133173C2318yes—
314C2×C4⋊Dic53C2312yes—
315C2×C4⋊Dic53C2311yescharacteristic
316C2×C4⋊Dic53C2312yes—
317C2×C4⋊Dic53C2314yes—
318C2×C4⋊Dic53C2311yescharacteristic
319C2×#11719919C2312yes—
320C2×#11719919C2312yes—
321C2×#11719919C2312yes—
322C2×#11719919C2312yes—
323C4⋊C4×D53C2318yes—
324C4⋊C4×D53C2318yes—
325C4⋊C4×D53C2314yes—
326C2×C22⋊Dic53C2312yes—
327C2×#11719921C2312yes—
328C2×#11719921C2312yes—
329C2×#11719921C2318yes—
330C2×#11719921C2312yes—
331C2×#11719921C2314yes—
332C2×#11719921C2314yes—
333C2×#11719921C2312yes—
334C22⋊C4×D53C2318yes—
335C22⋊C4×D53C2318yes—
336C22⋊C4×D53C2318yes—
337C22⋊C4×D53C2318yes—
338C2×C4×Dic53C2312yes—
339C22×Q8×C53C2311yescharacteristic
340C22×D4×C53C2312yes—
341C22×D4×C53C2311yescharacteristic
342C23×C4×C53C2311yescharacteristic
343C23×C4×C53C2311yescharacteristic
344C23×C4×C53C2311yescharacteristic
345C23×C4×C53C2312yes—
346#126×C53C2318yes—
347#126×C53C2318yes—
348#125×C53C2318yes—
349#125×C53C2318yes—
350#123×C53C2318yes—
351#123×C53C2318yes—
352#123×C53C2318yes—
353#123×C53C2318yes—
354C22⋊Q8×C53C2314yes—
355C22⋊Q8×C53C2318yes—
356C22⋊Q8×C53C2314yes—
357C22⋊Q8×C53C2318yes—
358#121×C53C2314yes—
359#121×C53C2314yes—
360C4×D4×C53C2314yes—
361C4×D4×C53C2314yes—
362C4×D4×C53C2314yes—
363C4×D4×C53C2314yes—
364C2×C4⋊C4×C53C2311yescharacteristic
365C2×C4⋊C4×C53C2312yes—
366C2×C4⋊C4×C53C2312yes—
367C2×C4⋊C4×C53C2312yes—
368C2×C4⋊C4×C53C2312yes—
369C2×C4⋊C4×C53C2314yes—
370C2×C4⋊C4×C53C2312yes—
371C2×C4⋊C4×C53C2312yes—
372C2×C4⋊C4×C53C2312yes—
373C2×C4⋊C4×C53C2312yes—
374C2×C4⋊C4×C53C2311yescharacteristic
375C2×C22⋊C4×C53C2312yes—
376C2×C22⋊C4×C53C2312yes—
377C2×C22⋊C4×C53C2312yes—
378C2×C22⋊C4×C53C2312yes—
379C2×C22⋊C4×C53C2312yes—
380C2×C42×C53C2312yes—
381C24×C53C2412yes—
382C24×C53C2411yescharacteristic
383C23×D53C2414yes—
384C23×D53C2412yes—
385C23×D53C2418yes—
386C2×Q8×C53—81no—
387C2×Q8×C53C2414yes—
388C2×D4×C53—28no—
389C2×D4×C53—81no—
390C2×D4×C53C2414yes—
391C2×D4×C53C2414yes—
392C2×D4×C53C2414yes—
393C22×C4×C53—24no—
394C22×C4×C53—81no—
395C22×C4×C53—81no—
396C22×C4×C53—82no—
397C22×C4×C53C2412yes—
398C22×C4×C53C2412yes—
399C22×C4×C53C2412yes—
400C22×C4×C53C2412yes—
401C22×C4×C53C2412yes—
402C22×C4×C53C2412yes—
403C22×C4×C53C2412yes—
404C22×C4×C53C2411yescharacteristic
405C22×C4×C53C2411yescharacteristic
406C22×C4×C53C2411yescharacteristic
407C22×C4×C53C2412yes—
408C22×C4×C53C2411yescharacteristic
409C22×C4×C53C2412yes—
410C22×C4×C53C2412yes—
411C22×C4×C53C2414yes—
412C22×C4×C53C2414yes—
413C2×C22⋊D53—216no—
414C2×C22⋊D53—28no—
415C2×C22⋊D53—416no—
416C2×C22⋊D53C2418yes—
417C2×C22⋊D53C2418yes—
418C2×C22⋊D53C2414yes—
419C2×C22⋊D53C2414yes—
420C2×C22⋊D53C2418yes—
421C2×C22⋊D53C2418yes—
422C2×C22⋊D53C2418yes—
423C2×C22⋊D53C2418yes—
424C22×Dic53C2412yes—
425C22×Dic53C2414yes—
426C22×Dic53C2412yes—
427C22×Dic53C2412yes—
428C22×Dic53C2418yes—
429#11719949—84no—
430#11719947—416no—
431#11719947—416no—
432D4×D53—416no—
433D4×D53—416no—
434D4×D53—84no—
435#11719945—416no—
436#11719945—416no—
437#11719945—416no—
438#11719945—84no—
439C2×D212—44no—
440C2×D212—81no—
441C2×D212—82no—
442C2×D212—84no—
443C2×D212—82no—
444C2×D212C2418yes—
445C2×D212C2418yes—
446C2×D212C2414yes—
447C2×D212C2414yes—
448C2×D212C2414yes—
449C2×D212C2414yes—
450C2×D212C2414yes—
451C2×D212C2418yes—
452C2×D212C2418yes—
453C2×C4×D53—48no—
454C2×C4×D53—82no—
455C2×C4×D53C2418yes—
456C2×C4×D53C2418yes—
457C2×C4×D53C2414yes—
458C2×C4×D53C2418yes—
459C2×C4×D53C2418yes—
460C2×C4×D53C2418yes—
461C2×C4×D53C2418yes—
462C2×C4×D53C2414yes—
463C2×Dic106—44no—
464C2×Dic106—81no—
465C2×Dic106C2414yes—
466C2×Dic106C2418yes—
467C2×Dic106C2418yes—
468C4⋊C4×C53C2414yes—
469C4⋊C4×C53C2414yes—
470C4⋊C4×C53C2414yes—
471C4⋊C4×C53C2414yes—
472C4⋊C4×C53C2414yes—
473C4⋊C4×C53C2414yes—
474C4⋊C4×C53C2414yes—
475C4⋊C4×C53C2418yes—
476C4⋊C4×C53C2418yes—
477C4⋊C4×C53C2414yes—
478C4⋊C4×C53C2418yes—
479C22⋊C4×C53C2414yes—
480C22⋊C4×C53C2414yes—
481C22⋊C4×C53C2414yes—
482C22⋊C4×C53C2414yes—
483C22⋊C4×C53C2418yes—
484C22⋊C4×C53C2418yes—
485C22⋊C4×C53C2418yes—
486C42×C53C2414yes—
487C42×C53C2414yes—
488C22⋊Dic53C2414yes—
489C22⋊Dic53C2418yes—
490C22⋊Dic53C2418yes—
491C22⋊Dic53C2414yes—
492#11719921C2418yes—
493#11719921C2418yes—
494#11719921C2418yes—
495#11719921C2418yes—
496#11719921C2418yes—
497#11719921C2418yes—
498#11719921C2418yes—
499#11719921C2418yes—
500#11719921C2418yes—
501#11719921C2418yes—
502#11719921C2418yes—
503#11719921C2418yes—
504#11719921C2418yes—
505#11719921C2414yes—
506#11719921C2414yes—
507#11719921C2418yes—
508#11719921C2418yes—
509C4⋊Dic53C2414yes—
510C4⋊Dic53C2418yes—
511C4⋊Dic53C2418yes—
512C4⋊Dic53C2414yes—
513C4⋊Dic53C2414yes—
514C4⋊Dic53C2414yes—
515C4⋊Dic53C2414yes—
516C4⋊Dic53C2414yes—
517#11719919C2418yes—
518#11719919C2418yes—
519#11719919C2418yes—
520#11719919C2418yes—
521#11719919C2418yes—
522#11719919C2414yes—
523#11719919C2414yes—
524#11719919C2418yes—
525#11719919C2418yes—
526C4×Dic53C2414yes—
527C4×Dic53C2414yes—
528C4×Dic53C2418yes—
529C4×Dic53C2418yes—
530C23×C53—24no—
531C23×C53—41no—
532C23×C53—41no—
533C23×C53—42no—
534C23×C53—42no—
535C23×C53H(5,𝔽2)14yes—
536C23×C53C2514yes—
537C23×C53C2511yescharacteristic
538C23×C53C2511yescharacteristic
539C23×C53C2511yescharacteristic
540C22×D53—28no—
541C22×D53—24no—
542C22×D53—42no—
543C22×D53—44no—
544C22×D53—44no—
545C22×D53—42no—
546C22×D53—48no—
547C22×D53—48no—
548C22×D53—48no—
549C22×D53C2518yes—
550C22×D53C2514yes—
551Q8×C53—44no—
552D4×C53—28no—
553D4×C53—28no—
554D4×C53—44no—
555C2×C4×C53—24no—
556C2×C4×C53—24no—
557C2×C4×C53—24no—
558C2×C4×C53—24no—
559C2×C4×C53—41no—
560C2×C4×C53—42no—
561C2×C4×C53—42no—
562C2×C4×C53—42no—
563C2×C4×C53—44no—
564C2×C4×C53—41no—
565C2×C4×C53—44no—
566C2×C4×C53—42no—
567C2×C4×C53—41no—
568C2×C4×C53—41no—
569C2×C4×C53—42no—
570C2×C4×C53—42no—
571C2×C4×C53C2514yes—
572C2×C4×C53C2514yes—
573C2×C4×C53C2512yes—
574C2×C4×C53C2512yes—
575C2×C4×C53C2514yes—
576C2×C4×C53C2512yes—
577C2×C4×C53C2514yes—
578C2×C4×C53C2512yes—
579C22⋊D53—216no—
580C22⋊D53—216no—
581C22⋊D53—28no—
582C22⋊D53—28no—
583C22⋊D53—48no—
584C22⋊D53—48no—
585C22⋊D53—48no—
586C22⋊D53—48no—
587C2×Dic53—28no—
588C2×Dic53—24no—
589C2×Dic53—42no—
590C2×Dic53—48no—
591C2×Dic53—42no—
592C2×Dic53C2518yes—
593C2×Dic53C2514yes—
594C2×Dic53C2514yes—
595C2×Dic53C2514yes—
596D212—48no—
597D212—44no—
598D212—44no—
599D212—44no—
600D212—44no—
601D212—48no—
602D212—44no—
603D212—48no—
604D212—48no—
605C4×D53—48no—
606C4×D53—48no—
607C4×D53—44no—
608C4×D53—44no—
609C4×D53—48no—
610C4×D53—48no—
611C4×D53—48no—
612C4×D53—48no—
613Dic106—48no—
614Dic106—44no—
615Dic106—48no—
616#62866—531nomaximal, Sylow
617C22×C53—21no—
618C22×C53—21no—
619C22×C53—21no—
620C22×C53—21no—
621C22×C53—21no—
622C22×C53—21no—
623C22×C53—24no—
624C22×C53—24no—
625C22×C53—24no—
626C22×C53—44no—
627C22×C53—84no—
628C22×C53C2×H(5,𝔽2)12yes—
629C22×C53C2×H(5,𝔽2)12yes—
630C22×C53C2×H(5,𝔽2)12yes—
631C22×C53C2611yescharacteristic
632C2×D53—28no—
633C2×D53—24no—
634C2×D53—24no—
635C2×D53—28no—
636C2×D53—28no—
637C2×D53—24no—
638C2×D53—88no—
639C2×D53—84no—
640C2×D53—168no—
641C4×C53—24no—
642C4×C53—24no—
643C4×C53—22no—
644C4×C53—22no—
645C4×C53—22no—
646C4×C53—24no—
647C4×C53—22no—
648C4×C53—24no—
649Dic53—28no—
650Dic53—24no—
651Dic53—24no—
652Dic53—24no—
653#3560—534no—
654#3560—534no—
655#3559—534no—
656#3559—534no—
657#3536—534no—
658#3536—534no—
659#3535—538no—
660#3534—538no—
661#3534—534no—
662#3534—534no—
663#3505—532no—
664#3505—532no—
665#3496—532no—
666#3496—532no—
667#3485—534no—
668C2×#539—531no—
669C2×#539D5311yescharacteristic, complemented
670C2×#537—531no—
671C2×C53—22no—
672C2×C53—22no—
673C2×C53—22no—
674C2×C53—44no—
675C2×C53C22×H(5,𝔽2)11yescharacteristic
676C2×C53H(7,𝔽2)11yescharacteristic
677C2×C532−1+611yescharacteristic
678D53—48no—
679D53—44no—
680C2×H(5,𝔽2)—534no—
681C22×#41—532no—
682#563—538no—
683#563—538no—
684#562—538no—
685#562—538no—
686#562—538no—
687#562—538no—
688#560—538no—
689#560—538no—
690#554—538no—
691#554—538no—
692#553—538no—
693#553—538no—
694#553—534no—
695#553—538no—
696#553—538no—
697#553—534no—
698#552—534no—
699#552—534no—
700#551—538no—
701#551—538no—
702#551—538no—
703#551—538no—
704#548—534no—
705#548—534no—
706#547—538no—
707#547—538no—
708#547—534no—
709#547—534no—
710#547—534no—
711#547—538no—
712#547—538no—
713#547—534no—
714#546—538no—
715#546—538no—
716#546—538no—
717#546—534no—
718#546—538no—
719#546—538no—
720#546—538no—
721#546—538no—
722#546—534no—
723#546—538no—
724#546—538no—
725#546—538no—
726D42—534no—
727D42—534no—
728D42—534no—
729D42—534no—
730#544—538no—
731#543—538no—
732#542—538no—
733#542—538no—
734#540—538no—
735#540—538no—
736#539—538no—
737#539—538no—
738#539—538no—
739#539—538no—
740#539—534no—
741#539—538no—
742#539—534no—
743#539—534no—
744#539—534no—
745#539C2×D5318yescomplemented
746#539C2×D5314yescomplemented
747#539C2×D5314yescomplemented
748#538—538no—
749#538—538no—
750#538—538no—
751#538—534no—
752#538—538no—
753#538—534no—
754#537—538no—
755#537—534no—
756#537—534no—
757#537—534no—
758#537—534no—
759#537—534no—
760#537—534no—
761#536—538no—
762#534—534no—
763#534—538no—
764#534—538no—
765#534—534no—
766#534—534no—
767#534—534no—
768#532—534no—
769#532—534no—
770#529—534no—
771#529—534no—
772C2×#126—532no—
773C2×#126C2×D5312yescomplemented
774C2×#125—532no—
775C2×#125C2×D5312yescomplemented
776#525—534no—
777#525—538no—
778#525—534no—
779C2×#123—532no—
780C2×#123—538no—
781C2×#123—532no—
782C2×#123C2×D5312yescomplemented
783C2×#123C2×D5312yescomplemented
784C2×C22⋊Q8—531no—
785C2×C22⋊Q8—532no—
786C2×C22⋊Q8—534no—
787C2×C22⋊Q8C2×D5311yescharacteristic, complemented
788C2×C22⋊Q8C2×D5312yescomplemented
789C2×#121—531no—
790C2×#121—532no—
791C2×#121—532no—
792C2×#121—534no—
793C2×#121—534no—
794C2×#121—534no—
795C2×#121C2×D5311yescharacteristic
796#518—534no—
797C2×C4×D4—532no—
798C2×C4×D4C2×D5312yescomplemented
799C22×C4⋊C4C2×D5311yescharacteristic, complemented
800C53#6286611yescharacteristic, complemented, Sylow
801H(5,𝔽2)—21216no—
802C2×#41—534no—
803C2×#41—538no—
804C2×#41—538no—
805C2×#41—534no—
806C2×#41—538no—
807C2×#41—538no—
808C2×#41—538no—
809C2×#41—2128no—
810C22×Q8—531no—
811C22×Q8—532no—
812C22×Q8C22×D5311yescharacteristic
813C22×D4—532no—
814C22×D4—534no—
815C22×D4—538no—
816C22×D4—534no—
817C22×D4—538no—
818C22×D4—538no—
819C22×D4—532no—
820C22×D4—532no—
821C22×D4—531no—
822C22×D4—534no—
823C22×D4—532no—
824C22×D4C22×D5312yes—
825C22×D4C22×D5311yescharacteristic
826C23×C4—532no—
827C23×C4—534no—
828C23×C4C22×D5311yescharacteristic
829C23×C4C22×D5311yescharacteristic
830C23×C4C22×D5311yescharacteristic
831C23×C4C22×D5312yes—
832C4⋊Q8—534no—
833C4⋊Q8—538no—
834C4⋊Q8—538no—
835C4⋊Q8—534no—
836#127—534no—
837#127—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#126C22×D5318yes—
847#126C22×D5318yes—
848#125—538no—
849#125—538no—
850#125—534no—
851#125—538no—
852#125—538no—
853#125—534no—
854#125C22×D5318yes—
855#125C22×D5318yes—
856#124—534no—
857#124—538no—
858#124—538no—
859#124—538no—
860#124—538no—
861#124—538no—
862#124—534no—
863#124—538no—
864#123—538no—
865#123—538no—
866#123—538no—
867#123—538no—
868#123—538no—
869#123—538no—
870#123—538no—
871#123—538no—
872#123—538no—
873#123—538no—
874#123—538no—
875#123—538no—
876#123—538no—
877#123—538no—
878#123—538no—
879#123—538no—
880#123—538no—
881#123—538no—
882#123—538no—
883#123—538no—
884#123—538no—
885#123—538no—
886#123—538no—
887#123—538no—
888#123C22×D5318yes—
889#123C22×D5318yes—
890#123C22×D5318yes—
891#123C22×D5318yes—
892C22⋊Q8—534no—
893C22⋊Q8—538no—
894C22⋊Q8—534no—
895C22⋊Q8—534no—
896C22⋊Q8—534no—
897C22⋊Q8—538no—
898C22⋊Q8—538no—
899C22⋊Q8—538no—
900C22⋊Q8—538no—
901C22⋊Q8—538no—
902C22⋊Q8—538no—
903C22⋊Q8—538no—
904C22⋊Q8—538no—
905C22⋊Q8—538no—
906C22⋊Q8—538no—
907C22⋊Q8—538no—
908C22⋊Q8—538no—
909C22⋊Q8—538no—
910C22⋊Q8—538no—
911C22⋊Q8—538no—
912C22⋊Q8—538no—
913C22⋊Q8—538no—
914C22⋊Q8C22×D5314yes—
915C22⋊Q8C22×D5318yes—
916C22⋊Q8C22×D5314yes—
917C22⋊Q8C22×D5318yes—
918#121—538no—
919#121—534no—
920#121—538no—
921#121—538no—
922#121—534no—
923#121—534no—
924#121—534no—
925#121—534no—
926#121—534no—
927#121—538no—
928#121—534no—
929#121—534no—
930#121—534no—
931#121—534no—
932#121—538no—
933#121—534no—
934#121—534no—
935#121—534no—
936#121—534no—
937#121—538no—
938#121—538no—
939#121—538no—
940#121—538no—
941#121—538no—
942#121—534no—
943#121—534no—
944#121—538no—
945#121—538no—
946#121—538no—
947#121—538no—
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×D5314yes—
957#121C22×D5314yes—
958#120—538no—
959#120—538no—
960#120—538no—
961#120—538no—
962#120—538no—
963#120—538no—
964#120—538no—
965#120—538no—
966#120—538no—
967#120—538no—
968C4×Q8—534no—
969C4×Q8—534no—
970C4×D4—534no—
971C4×D4—534no—
972C4×D4—534no—
973C4×D4—534no—
974C4×D4—534no—
975C4×D4—538no—
976C4×D4—538no—
977C4×D4—538no—
978C4×D4—538no—
979C4×D4—538no—
980C4×D4—538no—
981C4×D4—534no—
982C4×D4—534no—
983C4×D4—538no—
984C4×D4—538no—
985C4×D4—538no—
986C4×D4—538no—
987C4×D4—538no—
988C4×D4—534no—
989C4×D4—538no—
990C4×D4—534no—
991C4×D4—534no—
992C4×D4C22×D5314yes—
993C4×D4C22×D5314yes—
994C4×D4C22×D5314yes—
995C4×D4C22×D5314yes—
996#117—534no—
997#117—534no—
998#117—538no—
999#117—538no—
1000#117—538no—
1001C2×C4⋊C4—532no—
1002C2×C4⋊C4—532no—
1003C2×C4⋊C4—532no—
1004C2×C4⋊C4—531no—
1005C2×C4⋊C4—534no—
1006C2×C4⋊C4—532no—
1007C2×C4⋊C4—532no—
1008C2×C4⋊C4—531no—
1009C2×C4⋊C4—532no—
1010C2×C4⋊C4—534no—
1011C2×C4⋊C4—538no—
1012C2×C4⋊C4—538no—
1013C2×C4⋊C4C22×D5314yes—
1014C2×C4⋊C4C22×D5312yes—
1015C2×C4⋊C4C22×D5312yes—
1016C2×C4⋊C4C22×D5312yes—
1017C2×C4⋊C4C22×D5312yes—
1018C2×C4⋊C4C22×D5312yes—
1019C2×C4⋊C4C22×D5311yescharacteristic
1020C2×C4⋊C4C22×D5312yes—
1021C2×C4⋊C4C22×D5312yes—
1022C2×C4⋊C4C22×D5311yescharacteristic
1023C2×C4⋊C4C22×D5312yes—
1024C2×C22⋊C4—532no—
1025C2×C22⋊C4—532no—
1026C2×C22⋊C4—534no—
1027C2×C22⋊C4—534no—
1028C2×C22⋊C4—532no—
1029C2×C22⋊C4—538no—
1030C2×C22⋊C4—532no—
1031C2×C22⋊C4—532no—
1032C2×C22⋊C4—538no—
1033C2×C22⋊C4—538no—
1034C2×C22⋊C4—538no—
1035C2×C22⋊C4—538no—
1036C2×C22⋊C4C22×D5312yes—
1037C2×C22⋊C4C22×D5312yes—
1038C2×C22⋊C4C22×D5312yes—
1039C2×C22⋊C4C22×D5312yes—
1040C2×C22⋊C4C22×D5312yes—
1041C2×C42—532no—
1042C2×C42C22×D5312yes—
1043C24—532no—
1044C24—534no—
1045C24—538no—
1046C24C23×D5312yes—
1047C24C23×D5311yescharacteristic
1048#41—4244no—
1049#41—4244no—
1050#41—21216no—
1051#41—21216no—
1052#41—21216no—
1053#41—21216no—
1054#41—21216no—
1055C2×Q8—81no—
1056C2×Q8—534no—
1057C2×Q8—538no—
1058C2×Q8—538no—
1059C2×Q8—4241no—
1060C2×Q8—2124no—
1061C2×Q8C23×D5314yes—
1062C2×D4—28no—
1063C2×D4—81no—
1064C2×D4—534no—
1065C2×D4—538no—
1066C2×D4—538no—
1067C2×D4—534no—
1068C2×D4—538no—
1069C2×D4—538no—
1070C2×D4—538no—
1071C2×D4—538no—
1072C2×D4—538no—
1073C2×D4—538no—
1074C2×D4—534no—
1075C2×D4—534no—
1076C2×D4—534no—
1077C2×D4—534no—
1078C2×D4—534no—
1079C2×D4—538no—
1080C2×D4—538no—
1081C2×D4—10616no—
1082C2×D4—1068no—
1083C2×D4—4241no—
1084C2×D4—4244no—
1085C2×D4—4242no—
1086C2×D4—4242no—
1087C2×D4—4244no—
1088C2×D4—2124no—
1089C2×D4—21216no—
1090C2×D4—21216no—
1091C2×D4—21216no—
1092C2×D4C23×D5314yes—
1093C2×D4C23×D5314yes—
1094C2×D4C23×D5314yes—
1095C22×C4—24no—
1096C22×C4—81no—
1097C22×C4—82no—
1098C22×C4—81no—
1099C22×C4—532no—
1100C22×C4—534no—
1101C22×C4—532no—
1102C22×C4—532no—
1103C22×C4—538no—
1104C22×C4—538no—
1105C22×C4—538no—
1106C22×C4—534no—
1107C22×C4—538no—
1108C22×C4—538no—
1109C22×C4—538no—
1110C22×C4—538no—
1111C22×C4—534no—
1112C22×C4—4242no—
1113C22×C4—2128no—
1114C22×C4C23×D5312yes—
1115C22×C4C23×D5312yes—
1116C22×C4C23×D5312yes—
1117C22×C4C23×D5312yes—
1118C22×C4C23×D5312yes—
1119C22×C4C23×D5312yes—
1120C22×C4C23×D5312yes—
1121C22×C4C23×D5312yes—
1122C22×C4C23×D5311yescharacteristic
1123C22×C4C23×D5312yes—
1124C22×C4C23×D5314yes—
1125C22×C4C23×D5312yes—
1126C22×C4C23×D5311yescharacteristic
1127C22×C4C23×D5311yescharacteristic
1128C22×C4C23×D5314yes—
1129C22×C4C23×D5311yescharacteristic
1130C4⋊C4—534no—
1131C4⋊C4—534no—
1132C4⋊C4—534no—
1133C4⋊C4—538no—
1134C4⋊C4—538no—
1135C4⋊C4—538no—
1136C4⋊C4—538no—
1137C4⋊C4—538no—
1138C4⋊C4—534no—
1139C4⋊C4—538no—
1140C4⋊C4—538no—
1141C4⋊C4—534no—
1142C4⋊C4—534no—
1143C4⋊C4—534no—
1144C4⋊C4—534no—
1145C4⋊C4—538no—
1146C4⋊C4—538no—
1147C4⋊C4C23×D5314yes—
1148C4⋊C4C23×D5318yes—
1149C4⋊C4C23×D5318yes—
1150C4⋊C4C23×D5314yes—
1151C4⋊C4C23×D5314yes—
1152C4⋊C4C23×D5314yes—
1153C4⋊C4C23×D5314yes—
1154C4⋊C4C23×D5318yes—
1155C4⋊C4C23×D5314yes—
1156C4⋊C4C23×D5314yes—
1157C4⋊C4C23×D5314yes—
1158C22⋊C4—534no—
1159C22⋊C4—538no—
1160C22⋊C4—538no—
1161C22⋊C4—534no—
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—538no—
1173C22⋊C4—534no—
1174C22⋊C4—534no—
1175C22⋊C4—538no—
1176C22⋊C4—538no—
1177C22⋊C4—538no—
1178C22⋊C4—538no—
1179C22⋊C4C23×D5314yes—
1180C22⋊C4C23×D5318yes—
1181C22⋊C4C23×D5318yes—
1182C22⋊C4C23×D5318yes—
1183C22⋊C4C23×D5314yes—
1184C22⋊C4C23×D5314yes—
1185C22⋊C4C23×D5314yes—
1186C42—534no—
1187C42—534no—
1188C42—538no—
1189C42—538no—
1190C42C23×D5314yes—
1191C42C23×D5314yes—
1192C23—24no—
1193C23—41no—
1194C23—41no—
1195C23—42no—
1196C23—42no—
1197C23—534no—
1198C23—538no—
1199C23—1068no—
1200C23—1064no—
1201C23—2128no—
1202C23—2128no—
1203C23—2128no—
1204C23—2122no—
1205C23—2124no—
1206C23—2122no—
1207C23—2124no—
1208C23#1313326314yes—
1209C23C24×D5314yes—
1210C23C24×D5311yescharacteristic
1211C23C24×D5311yescharacteristic
1212C23C24×D5311yescharacteristic
1213Q8—44no—
1214Q8—2124no—
1215Q8—2128no—
1216Q8—2128no—
1217D4—28no—
1218D4—28no—
1219D4—44no—
1220D4—1068no—
1221D4—1068no—
1222D4—10616no—
1223D4—10616no—
1224D4—2128no—
1225D4—2124no—
1226D4—2124no—
1227D4—2124no—
1228D4—2124no—
1229D4—2128no—
1230D4—2124no—
1231D4—2128no—
1232D4—2128no—
1233D4—2128no—
1234D4—2128no—
1235D4—2128no—
1236D4—2128no—
1237C2×C4—24no—
1238C2×C4—24no—
1239C2×C4—24no—
1240C2×C4—24no—
1241C2×C4—42no—
1242C2×C4—42no—
1243C2×C4—41no—
1244C2×C4—41no—
1245C2×C4—42no—
1246C2×C4—44no—
1247C2×C4—42no—
1248C2×C4—41no—
1249C2×C4—42no—
1250C2×C4—41no—
1251C2×C4—44no—
1252C2×C4—42no—
1253C2×C4—534no—
1254C2×C4—534no—
1255C2×C4—538no—
1256C2×C4—534no—
1257C2×C4—1068no—
1258C2×C4—1064no—
1259C2×C4—2128no—
1260C2×C4—2124no—
1261C2×C4—2124no—
1262C2×C4—2128no—
1263C2×C4—2128no—
1264C2×C4—2128no—
1265C2×C4—2128no—
1266C2×C4—2128no—
1267C2×C4—2122no—
1268C2×C4—2122no—
1269C2×C4—2128no—
1270C2×C4C24×D5314yes—
1271C2×C4C24×D5312yes—
1272C2×C4C24×D5314yes—
1273C2×C4C24×D5312yes—
1274C2×C4C24×D5312yes—
1275C2×C4C24×D5312yes—
1276C2×C4C24×D5314yes—
1277C2×C4C24×D5314yes—
1278C22—21no—
1279C22—21no—
1280C22—21no—
1281C22—21no—
1282C22—21no—
1283C22—21no—
1284C22—24no—
1285C22—24no—
1286C22—24no—
1287C22—44no—
1288C22—84no—
1289C22—8488no—
1290C22—1068no—
1291C22—1064no—
1292C22—1064no—
1293C22—1068no—
1294C22—1068no—
1295C22—1064no—
1296C22—4248no—
1297C22—4244no—
1298C22C2×#1313326312yes—
1299C22C2×#1313326312yes—
1300C22C2×#1313326312yes—
1301C22C25×D5311yescharacteristic
1302C4—24no—
1303C4—24no—
1304C4—22no—
1305C4—22no—
1306C4—22no—
1307C4—22no—
1308C4—24no—
1309C4—24no—
1310C4—1064no—
1311C4—1068no—
1312C4—1064no—
1313C4—1064no—
1314C2—22no—
1315C2—22no—
1316C2—22no—
1317C2—44no—
1318C2—2124no—
1319C2—2128no—
1320C2C22×#1313326311yescharacteristic
1321C2#2028952511yescharacteristic
1322C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#539C2
hypercenterC2×#539D53
hypocenterC53#62866
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. #20289272C2semidirect
2. #20289267C2semidirect
3. #20289251C2semidirect
4. #20289249C2semidirect
5. #20288944C2semidirect
6. #20288939C2semidirect
7. #20288922C2semidirect
8. #20288910C2semidirect
9. #20288909C2semidirect
10. #20288903C2semidirect
11. #20288556C2semidirect
12. #20288554C2semidirect
13. #20288479C2semidirect
14. #20288472C2semidirect
15. #20288353C2semidirect
16. C2×#16811220C2semidirect
17. C2×#16811204C2semidirect
18. C2×C53×#539C2semidirect
19. C2×#13133262C22semidirect
20. C22×#11719945C22semidirect
21. #16811377C22semidirect
22. #16811375C22semidirect
23. #16811371C22semidirect
24. #16811370C22semidirect
25. #16811369C22semidirect
26. #16811369C22semidirect
27. #16811364C22semidirect
28. #16811363C22semidirect
29. #16811331C22semidirect
30. #16811329C22semidirect
31. #16811326C22semidirect
32. #16811324C22semidirect
33. #16811322C22semidirect
34. #16811321C22semidirect
35. #16811321C22semidirect
36. #16811319C22semidirect
37. #16811315C22semidirect
38. #16811313C22semidirect
39. #16811302C22semidirect
40. #16811300C22semidirect
41. #16811298C22semidirect
42. #16811296C22semidirect
43. #16811284C22semidirect
44. #16811282C22semidirect
45. #16811277C22semidirect
46. #16811277C22semidirect
47. #16811274C22semidirect
48. #16811274C22semidirect
49. #16811274C22semidirect
50. #16811273C22semidirect
51. #16811271C22semidirect
52. #16811271C22semidirect
53. #16811269C22semidirect
54. #16811268C22semidirect
55. #16811268C22semidirect
56. #16811265C22semidirect
57. #16811265C22semidirect
58. #16811265C22semidirect
59. #16811264C22semidirect
60. #16811264C22semidirect
61. #16811263C22semidirect
62. #16811263C22semidirect
63. #16811263C22semidirect
64. #16811262C22semidirect
65. D4×D212C22semidirect
66. D4×D212C22semidirect
67. #16811257C22semidirect
68. D4×C22⋊D53C22semidirect
69. #16811253C22semidirect
70. #16811248C22semidirect
71. #16811246C22semidirect
72. #16811239C22semidirect
73. #16811229C22semidirect
74. #16811225C22semidirect
75. #16811222C22semidirect
76. #16811221C22semidirect
77. #16811221C22semidirect
78. #16811220C22semidirect
79. #16811220C22semidirect
80. #16811220C22semidirect
81. #16811220C22semidirect
82. #16811217C22semidirect
83. #16811214C22semidirect
84. #16811213C22semidirect
85. #16811213C22semidirect
86. #16811212C22semidirect
87. #16811212C22semidirect
88. #16811211C22semidirect
89. #16811209C22semidirect
90. #16811204C22semidirect
91. #16811204C22semidirect
92. #16811204C22semidirect
93. #16811204C22semidirect
94. #16811204C22semidirect
95. #16811203C22semidirect
96. #16811200C22semidirect
97. #16811195C22semidirect
98. #16811185C22semidirect
99. #16811185C22semidirect
100. #16811184C22semidirect
101. #16811184C22semidirect
102. #16811182C22semidirect
103. #16811181C22semidirect
104. #16811173C22semidirect
105. #16811168C22semidirect
106. #16811159C22semidirect
107. #16811157C22semidirect
108. C2×#13133212C22semidirect
109. C2×#13133207C22semidirect
110. #16811136C22semidirect
111. #16811134C22semidirect
112. #16811131C22semidirect
113. C2×#13133202C22semidirect
114. C2×#13133200C22semidirect
115. #123×D53C22semidirect
116. C2×#13133197C22semidirect
117. C2×#13133196C22semidirect
118. C2×#13133195C22semidirect
119. C2×#13133192C22semidirect
121. C2×#13133191C22semidirect
122. C2×#13133191C22semidirect
123. C2×#13133191C22semidirect
124. #121×D53C22semidirect
125. #16811096C22semidirect
126. C2×C4×C22⋊D53C22semidirect
127. C53×#539C22semidirect
128. C53×#539C22semidirect
129. C53×#539C22semidirect
130. C2×#126×C53C22semidirect
131. C2×#125×C53C22semidirect
132. C2×#123×C53C22semidirect
133. C2×#123×C53C22semidirect
134. C2×C22⋊Q8×C53C22semidirect
135. C2×C22⋊Q8×C53C22semidirect
137. C2×C4×D4×C53C22semidirect
138. C22×C4⋊C4×C53C22semidirect
669. C2×#539D53semidirect
745. #539C2×D53semidirect
746. #539C2×D53semidirect
747. #539C2×D53semidirect
773. C2×#126C2×D53semidirect
775. C2×#125C2×D53semidirect
782. C2×#123C2×D53semidirect
783. C2×#123C2×D53semidirect
787. C2×C22⋊Q8C2×D53semidirect
788. C2×C22⋊Q8C2×D53semidirect
798. C2×C4×D4C2×D53semidirect
799. C22×C4⋊C4C2×D53semidirect
800. C53#62866semidirect

Maximal subgroups

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

subgroupindex
#202892722
#202892672
#202892512
#202892492
#202889442
#202889392
#202889222
#202889102
#202889092
#202889032
#202885562
#202885542
#202884792
#202884722
#202883532
C2×#168112202
C2×#168112042
C2×C53×#5392
#6286653