Finite Group Databasebeta

← #28292642

Subgroups — #28292642

Order 13568.

11346 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C212yesmaximal, complemented
2#20288507C214yesmaximal, complemented
3#20288504C214yesmaximal, complemented
4#20288497C214yesmaximal, complemented
5#20288490C214yesmaximal, complemented
6#20288484C214yesmaximal, complemented
7#20288478C214yesmaximal, complemented
8#20288476C218yesmaximal, complemented
9#20288198C2116yesmaximal, complemented
10#20288048C211yesmaximal, characteristic, complemented
11#20288042C214yesmaximal, complemented
12C2×#16811169C212yesmaximal, complemented
13#532×D53C214yesmaximal, complemented
14C2×#16811091C211yesmaximal, characteristic, complemented
15C53×#3449C211yesmaximal, characteristic, complemented
16#16811459—232no—
17C2×#13133265C2214yescomplemented
18C2×#13133264C2214yescomplemented
19C2×#13133264C2214yescomplemented
20C2×#13133263C2214yescomplemented
21C2×#13133263C2214yescomplemented
22C2×#13133262C2218yescomplemented
23C2×#13133262C2214yescomplemented
24C22×#11719945C2211yescharacteristic
25C22×#11719945C2212yescomplemented
26C22×#11719945C2218yescomplemented
27C2×#41×D53C2218yescomplemented
28C2×#41×D53C2218yescomplemented
29#16811291C22116yescomplemented
30#16811286C22116yescomplemented
31#16811283C22116yescomplemented
32#16811279C22116yescomplemented
33#16811275C22116yescomplemented
34#16811271C22132yescomplemented
35#16811270C22116yescomplemented
36#16811265C22132yescomplemented
37#16811264C22116yescomplemented
38#16811260C22132yescomplemented
39#16811257C22116yescomplemented
40#16811255C22132yescomplemented
41#16811204C2214yescomplemented
42#16811200C22116yescomplemented
43#16811199C2214yescomplemented
44#16811198C2218yescomplemented
45#16811193C2218yescomplemented
46#16811192C2214yescomplemented
47#16811191C2218yescomplemented
48#16811186C2218yescomplemented
49#16811185C2214yescomplemented
50#16811181C22116yescomplemented
51#16811174C2214yescomplemented
52#16811173C2214yescomplemented
53#16811172C2218yescomplemented
54#16811171C2214yescomplemented
55#16811170C22116yescomplemented
56#16811169C2214yescomplemented
57#16811169C2218yescomplemented
58#16811169C2218yescomplemented
59#16811169C2214yescomplemented
60#16811169C2214yescomplemented
61#16811169C2214yescomplemented
62#16811168C22116yescomplemented
63C2×#13133215C2212yescomplemented
64C4⋊Q8×D53C2214yescomplemented
65C2×#13133213C2212yescomplemented
66#127×D53C2214yescomplemented
67C2×#13133206C2212yescomplemented
68C2×#13133204C2212yescomplemented
69#124×D53C2218yescomplemented
70#16811135C2218yescomplemented
71#16811132C22132yescomplemented
72C2×#13133189C2218yescomplemented
73#121×D53C22116yescomplemented
74#16811091C2218yescomplemented
75#16811091C2214yescomplemented
76#16811091C2214yescomplemented
77C2×#13133182C2212yescomplemented
78C2×#13133179C2212yescomplemented
79C2×C4×C22⋊D53C2218yescomplemented
80C2×#13133177C2214yescomplemented
81C4×D4×D53C22116yescomplemented
82C2×#13133174C2212yescomplemented
83C22×C4×Dic53C2211yescharacteristic, complemented
84C2×C42×D53C2212yescomplemented
85C22×#41×C53C2212yescomplemented
86C53×#537C2214yescomplemented
87C53×#536C2214yescomplemented
88C53×#535C2214yescomplemented
89C53×#534C2214yescomplemented
90C53×#532C2214yescomplemented
91C53×#525C2218yescomplemented
92C2×#117×C53C2211yescharacteristic, complemented
93#13133265—232no—
94#13133264—232no—
95#13133264—232no—
96#13133263—232no—
97#13133263—232no—
98#13133262—264no—
99#13133262—232no—
100C2×#11719949C2318yes—
101C2×#11719949C2318yes—
102C2×#11719945—216no—
103C2×#11719945—264no—
104C2×#11719945D4116yescomplemented
105C2×#11719945C23116yes—
106C2×#11719945C2318yes—
107C2×#11719945C2318yes—
108C2×#11719945C23116yes—
109C2×#11719945C2314yes—
110C2×#11719945C2314yes—
111C2×#11719945C2314yes—
112C2×#11719945C2314yes—
113C2×#11719945C2314yes—
114C2×#11719945C2314yes—
115C2×#11719947C23116yes—
116C2×#11719947C2318yes—
117C2×#11719947C23116yes—
118C2×#11719947C2318yes—
119#41×D53—264no—
120#41×D53—264no—
121C22×Dic106C2318yes—
122C22×Dic106C2312yes—
123C22×Dic106C2311yescharacteristic
124C2×Q8×D53C2318yes—
125C2×Q8×D53C2318yes—
126C22×D212C2318yes—
127C22×D212C2312yes—
128C22×D212C2311yescharacteristic
129C22×C22⋊D53C2314yes—
130C22×C22⋊D53C23116yes—
131C22×C22⋊D53C2318yes—
132C22×C22⋊D53C2312yes—
133C2×D4×D53C23116yes—
134C2×D4×D53C2318yes—
135C2×D4×D53C23116yes—
136C2×D4×D53C2318yes—
137C2×D4×D53C23116yes—
138C23×Dic53C2312yes—
139C22×C4×D53C23116yes—
140C22×C4×D53C2314yes—
141C22×C4×D53C2314yes—
142C22×C4×D53C2312yes—
143#13133217C2314yes—
144#13133216C23116yes—
145#13133215C2318yes—
146#13133215C2314yes—
147#13133215C2314yes—
148#13133214C2314yes—
149#13133213C23116yes—
150#13133213C2318yes—
151#13133213C2314yes—
152#13133213C2314yes—
153#13133206C2318yes—
154#13133206C2314yes—
155#13133206C2314yes—
156#13133205C2318yes—
157#13133204C2318yes—
158#13133204C2314yes—
159#13133204C2314yes—
160#13133203C23132yes—
161#13133202C23132yes—
162#13133201C23116yes—
163#13133199C23132yes—
164#13133197C23116yes—
165#13133195C23132yes—
166#13133194C23132yes—
167#13133192C23116yes—
168#13133192C23116yes—
169#13133191C23116yes—
170#13133190C23132yes—
171#13133190C23132yes—
172#13133189C23116yes—
173#13133189C23116yes—
174#13133189C23132yes—
175#13133189C23116yes—
176#13133189C23116yes—
177#13133188C23116yes—
178#13133187C23132yes—
179#13133187C23116yes—
180#13133185C23132yes—
181#13133182C2318yes—
182#13133182C2318yes—
183C4×D212C23116yes—
184D4×Dic53C23116yes—
185#13133179C2318yes—
186#13133179C23116yes—
187#13133179C2318yes—
188C4×C22⋊D53C23116yes—
189C4×C22⋊D53C23116yes—
190C4×C22⋊D53C23116yes—
191C4×C22⋊D53C23116yes—
192#13133177C23116yes—
193#13133177C23116yes—
194#13133177C23132yes—
195#13133174C2318yes—
196#13133174C2318yes—
197C2×#11719919C2318yes—
198C2×#11719919C2314yes—
199C4⋊C4×D53C23116yes—
200C2×C22⋊Dic53C2318yes—
201C2×#11719921C2318yes—
202C2×#11719921C2314yes—
203C22⋊C4×D53C23132yes—
204C2×C4×Dic53C2311yescharacteristic
205C2×C4×Dic53C2314yes—
206C2×C4×Dic53C2311yescharacteristic
207C2×C4×Dic53C2314yes—
208C2×C4×Dic53C2312yes—
209C2×C4×Dic53C2312yes—
210C2×C4×Dic53C2312yes—
211C42×D53C2318yes—
212C42×D53C2314yes—
213C42×D53C2314yes—
214C2×#41×C53—216no—
215C2×#41×C53C2314yes—
216C2×#41×C53C2314yes—
217C2×#41×C53C2314yes—
218C2×#41×C53C2314yes—
219C22×Q8×C53C2312yes—
220C22×D4×C53C2314yes—
221C22×D4×C53C2312yes—
222C23×C4×C53C2314yes—
223C23×C4×C53C2311yescharacteristic
224C4⋊Q8×C53C2314yes—
225#127×C53C2314yes—
226#124×C53C2318yes—
227#123×C53C23116yes—
228C22⋊Q8×C53C23116yes—
229#121×C53C23116yes—
230#121×C53C23116yes—
231#120×C53C23116yes—
232C4×D4×C53C23116yes—
233#117×C53C2314yes—
234#117×C53C2314yes—
235C2×C4⋊C4×C53C2312yes—
236C2×C22⋊C4×C53C2312yes—
237C2×C42×C53C2312yes—
238C24×C53C2414yes—
239C24×C53C2411yescharacteristic
240C23×D53C24116yes—
241C23×D53C2414yes—
242C23×D53C2412yes—
243#41×C53—216no—
244#41×C53—216no—
245#41×C53—216no—
246#41×C53—216no—
247C2×Q8×C53—28no—
248C2×Q8×C53C2414yes—
249C2×Q8×C53C2414yes—
250C2×D4×C53—216no—
251C2×D4×C53—28no—
252C2×D4×C53C2418yes—
253C2×D4×C53C2418yes—
254C2×D4×C53C2414yes—
255C2×D4×C53C2414yes—
256C2×D4×C53C24116yes—
257C22×C4×C53—216no—
258C22×C4×C53C2×D418yescomplemented
259C22×C4×C53C2418yes—
260C22×C4×C53C2418yes—
261C22×C4×C53C2414yes—
262C22×C4×C53C2414yes—
263C22×C4×C53C2411yescharacteristic
264C22×C4×C53C2411yescharacteristic
265C22×C4×C53C2412yes—
266C22×C4×C53C2412yes—
267C2×C22⋊D53—216no—
268C2×C22⋊D53—264no—
269C2×C22⋊D53—416no—
270C2×C22⋊D53C2×D4116yescomplemented
271C2×C22⋊D53C24116yes—
272C2×C22⋊D53C24116yes—
273C2×C22⋊D53C2418yes—
274C2×C22⋊D53C2418yes—
275C2×C22⋊D53C24116yes—
276C2×C22⋊D53C24116yes—
277C2×C22⋊D53C2418yes—
278C22×Dic53—44no—
279C22×Dic53C2412yes—
280C22×Dic53C2414yes—
281C22×Dic53C2414yes—
282C22×Dic53C24116yes—
283C22×Dic53C2414yes—
284C22×Dic53C2412yes—
285C22×Dic53C2412yes—
286#11719949—232no—
287#11719949—232no—
288Q8×D53—232no—
289Q8×D53—232no—
290#11719947—264no—
291#11719947—264no—
292#11719947—232no—
293#11719947—232no—
294D4×D53—264no—
295D4×D53—264no—
296D4×D53—232no—
297D4×D53—232no—
298D4×D53—432no—
299#11719945—216no—
300#11719945—216no—
301#11719945—216no—
302#11719945—216no—
303#11719945—264no—
304#11719945—232no—
305#11719945—264no—
306#11719945—232no—
307#11719945C2×D4132yescomplemented
308#11719945C2×D4132yescomplemented
309C2×D212—28no—
310C2×D212—232no—
311C2×D212C2×D418yescomplemented
312C2×D212C24116yes—
313C2×D212C2414yes—
314C2×D212C2414yes—
315C2×D212C24116yes—
316C2×D212C2414yes—
317C2×C4×D53—216no—
318C2×C4×D53—264no—
319C2×C4×D53—48no—
320C2×C4×D53C2×D4116yescomplemented
321C2×C4×D53C2418yes—
322C2×C4×D53C24116yes—
323C2×C4×D53C24116yes—
324C2×C4×D53C2418yes—
325C2×C4×D53C2418yes—
326C2×C4×D53C2418yes—
327C2×C4×D53C2414yes—
328C2×C4×D53C2414yes—
329C2×Dic106—28no—
330C2×Dic106—232no—
331C2×Dic106C2×D418yescomplemented
332C2×Dic106C24116yes—
333C2×Dic106C2414yes—
334C2×Dic106C2414yes—
335C2×Dic106C2414yes—
336C4⋊C4×C53C2418yes—
337C4⋊C4×C53C24116yes—
338C22⋊C4×C53C2418yes—
339C22⋊C4×C53C24132yes—
340C42×C53C2414yes—
341C42×C53C2414yes—
342C22⋊Dic53C24116yes—
343C22⋊Dic53C24116yes—
344#11719921C24116yes—
345#11719921C24132yes—
346#11719921C24116yes—
347#11719921C24116yes—
348C4⋊Dic53C24116yes—
349#11719919C24116yes—
350#11719919C24116yes—
351#11719919C24116yes—
352C4×Dic53C2412yes—
353C4×Dic53C2411yescharacteristic
354C4×Dic53C2411yescharacteristic
355C4×Dic53C2418yes—
356C4×Dic53C2418yes—
357C4×Dic53C2412yes—
358C4×Dic53C2412yes—
359C4×Dic53C2414yes—
360C4×Dic53C2414yes—
361C23×C53—28no—
362C23×C53—42no—
363C23×C53—48no—
364C23×C53C22×D414yes—
365C23×C53C2518yes—
366C23×C53C2511yescharacteristic
367C23×C53C2512yes—
368C22×D53—28no—
369C22×D53—232no—
370C22×D53—44no—
371C22×D53—432no—
372C22×D53—48no—
373C22×D53C22×D418yes—
374C22×D53C2518yes—
375C22×D53C2514yes—
376Q8×C53—28no—
377Q8×C53—28no—
378D4×C53—216no—
379D4×C53—216no—
380D4×C53—28no—
381D4×C53—28no—
382D4×C53—416no—
383C2×C4×C53—28no—
384C2×C4×C53—216no—
385C2×C4×C53—216no—
386C2×C4×C53—44no—
387C2×C4×C53C22×D418yes—
388C2×C4×C53C22×D414yes—
389C2×C4×C53C22×D418yes—
390C2×C4×C53C22×D414yes—
391C2×C4×C53C2518yes—
392C2×C4×C53C2518yes—
393C2×C4×C53C2512yes—
394C2×C4×C53C2511yescharacteristic
395C2×C4×C53C2511yescharacteristic
396C22⋊D53—216no—
397C22⋊D53—216no—
398C22⋊D53—232no—
399C22⋊D53—232no—
400C22⋊D53—232no—
401C22⋊D53—416no—
402C22⋊D53C22×D4132yes—
403C2×Dic53—28no—
404C2×Dic53—232no—
405C2×Dic53—24no—
406C2×Dic53—28no—
407C2×Dic53—44no—
408C2×Dic53—42no—
409C2×Dic53C22×D418yes—
410C2×Dic53C2518yes—
411C2×Dic53C2512yes—
412C2×Dic53C2514yes—
413C2×Dic53C2514yes—
414C2×Dic53C2512yes—
415D212—232no—
416D212—28no—
417D212—28no—
418D212—416no—
419D212C22×D4116yes—
420C4×D53—232no—
421C4×D53—216no—
422C4×D53—216no—
423C4×D53—232no—
424C4×D53—216no—
425C4×D53—48no—
426C4×D53C22×D4116yes—
427C4×D53C22×D4116yes—
428Dic106—28no—
429Dic106—28no—
430Dic106—232no—
431Dic106C22×D4116yes—
432#62812—531nomaximal, Sylow
433C22×C53—22no—
434C22×C53—24no—
435C22×C53—28no—
436C22×C53—216no—
437C22×C53—44no—
438C22×C53—88no—
439C22×C53C23×D414yes—
440C22×C53C23×D412yes—
441C22×C53C2611yescharacteristic
442C2×D53—28no—
443C2×D53—28no—
444C2×D53—216no—
445C2×D53—48no—
446C2×D53—832no—
447C2×D53—88no—
448C2×D53C23×D418yes—
449C4×C53—28no—
450C4×C53—28no—
451C4×C53C23×D412yes—
452C4×C53C23×D414yes—
453C4×C53C23×D412yes—
454Dic53—28no—
455Dic53—22no—
456Dic53—24no—
457Dic53C23×D418yes—
458Dic53#58514yescomplemented
459C2×#585—532no—
460#3500—534no—
461#3500—534no—
462#3499—534no—
463#3498—534no—
464#3497—534no—
465#3496—534no—
466#3496—538no—
467D4×#41—5316no—
468#3449—534no—
469#3449—531no—
470#3449D5311yescharacteristic, complemented
471C2×#532—532no—
472C2×#532—534no—
473C2×C4×#41—531no—
474C2×C53—22no—
475C2×C53—24no—
476C2×C53—48no—
477C2×C53C24×D411yescharacteristic
478C2×C53C2×#58512yes—
479D53—28no—
480D53—48no—
481#585—10632no—
482C2×2−1+4—534no—
483C2×2−1+4—534no—
484C2×2−1+4—534no—
485C2×H(5,𝔽2)—534no—
486C2×H(5,𝔽2)—534no—
487C2×H(5,𝔽2)—538no—
488C2×H(5,𝔽2)—534no—
489C22×#41—538no—
490C22×#41—538no—
491C22×#41—531no—
492C22×#41—532no—
493C22×#41—538no—
494C22×#41C2×D5312yescomplemented
495#550—5316no—
496D4×Q8—5316no—
497#548—5316no—
498#548—5316no—
499#547—5332no—
500#547—5316no—
501#546—5332no—
502#546—5316no—
503#546—5316no—
504#546—5332no—
505D42—5316no—
506D42—5332no—
507#537—5316no—
508#537—534no—
509#537C2×D5314yescomplemented
510#536—538no—
511#536—538no—
512#536—534no—
513#536C2×D5314yescomplemented
514#535—538no—
515#535—538no—
516#535—534no—
517#535C2×D5314yescomplemented
518#534—5316no—
519#534—534no—
520#534C2×D5314yescomplemented
521#532—534no—
522#532—534no—
523#532—538no—
524#532—538no—
525#532—534no—
526#532—534no—
527#532—534no—
528#532—534no—
529#532—538no—
530#532—5316no—
531#532—5316no—
532#532—534no—
533#532C2×D5314yescomplemented
534C2×C4⋊Q8—532no—
535C2×C4⋊Q8—534no—
536C2×#127—532no—
537C2×#127—534no—
538C2×#124—532no—
539C2×#124—532no—
540C2×#124—538no—
541#525—5332no—
542#525—538no—
543#525C2×D5318yescomplemented
544C2×#121—538no—
545C2×#121—5316no—
546C4×#41—538no—
547C4×#41—534no—
548C4×#41—534no—
549C2×C4×Q8—532no—
550C2×C4×D4—538no—
551C2×C4×D4—5316no—
552C2×C4×D4—532no—
553C2×C4×D4—534no—
554C2×#117—532no—
555C2×#117C2×D5311yescharacteristic, complemented
556C22×C42—531no—
557C22×C42—532no—
558C53#6281211yescharacteristic, complemented, Sylow
5592−1+4—10632no—
5602−1+4—10632no—
5612−1+4—10632no—
562H(5,𝔽2)—10664no—
563H(5,𝔽2)—10632no—
564H(5,𝔽2)—10632no—
565H(5,𝔽2)—10632no—
566C2×#41—216no—
567C2×#41—538no—
568C2×#41—538no—
569C2×#41—538no—
570C2×#41—5316no—
571C2×#41—5316no—
572C2×#41—538no—
573C2×#41—5316no—
574C2×#41—534no—
575C2×#41—534no—
576C2×#41—5316no—
577C2×#41—534no—
578C2×#41—534no—
579C2×#41—534no—
580C2×#41—534no—
581C2×#41—538no—
582C2×#41—5316no—
583C2×#41—538no—
584C2×#41—10664no—
585C2×#41—10664no—
586C2×#41—10664no—
587C2×#41—10616no—
588C2×#41C22×D5314yes—
589C2×#41C22×D5314yes—
590C2×#41C22×D5314yes—
591C2×#41C22×D5314yes—
592C22×Q8—538no—
593C22×Q8—538no—
594C22×Q8—531no—
595C22×Q8—532no—
596C22×Q8—538no—
597C22×Q8C22×D5312yes—
598C22×D4—532no—
599C22×D4—534no—
600C22×D4—5316no—
601C22×D4—538no—
602C22×D4—5316no—
603C22×D4—538no—
604C22×D4—5316no—
605C22×D4—538no—
606C22×D4—5316no—
607C22×D4—531no—
608C22×D4—532no—
609C22×D4—538no—
610C22×D4C22×D5314yes—
611C22×D4C22×D5312yes—
612C23×C4—532no—
613C23×C4—532no—
614C23×C4—5316no—
615C23×C4—534no—
616C23×C4—534no—
617C23×C4C22×D5314yes—
618C23×C4C22×D5311yescharacteristic
619C4⋊Q8—534no—
620C4⋊Q8—534no—
621C4⋊Q8—538no—
622C4⋊Q8—5316no—
623C4⋊Q8—534no—
624C4⋊Q8C22×D5314yes—
625#127—534no—
626#127—534no—
627#127—5316no—
628#127—538no—
629#127—534no—
630#127C22×D5314yes—
631#124—534no—
632#124—534no—
633#124—538no—
634#124—534no—
635#124—534no—
636#124—538no—
637#124—5332no—
638#124—538no—
639#124C22×D5318yes—
640#123—5332no—
641#123—5332no—
642#123—5316no—
643#123C22×D53116yes—
644C22⋊Q8—5332no—
645C22⋊Q8—5316no—
646C22⋊Q8—5332no—
647C22⋊Q8C22×D53116yes—
648#121—5316no—
649#121—5316no—
650#121—5316no—
651#121—5316no—
652#121—5316no—
653#121—5332no—
654#121—5316no—
655#121—5316no—
656#121—5316no—
657#121—5332no—
658#121—5332no—
659#121C22×D53116yes—
660#121C22×D53116yes—
661#120—5332no—
662#120—5332no—
663#120—5316no—
664#120C22×D53116yes—
665C4×Q8—538no—
666C4×Q8—538no—
667C4×D4—5316no—
668C4×D4—5316no—
669C4×D4—5316no—
670C4×D4—5316no—
671C4×D4—5316no—
672C4×D4—538no—
673C4×D4—538no—
674C4×D4—5316no—
675C4×D4—5316no—
676C4×D4—5316no—
677C4×D4—5332no—
678C4×D4—5316no—
679C4×D4C22×D53116yes—
680#117—538no—
681#117—538no—
682#117C22×D5314yes—
683#117C22×D5314yes—
684C2×C4⋊C4—534no—
685C2×C4⋊C4—538no—
686C2×C4⋊C4—5316no—
687C2×C4⋊C4C22×D5312yes—
688C2×C22⋊C4—538no—
689C2×C22⋊C4—534no—
690C2×C22⋊C4—538no—
691C2×C22⋊C4—5332no—
692C2×C22⋊C4C22×D5312yes—
693C2×C42—531no—
694C2×C42—534no—
695C2×C42—534no—
696C2×C42—532no—
697C2×C42—532no—
698C2×C42—532no—
699C2×C42—531no—
700C2×C42—538no—
701C2×C42—534no—
702C2×C42—534no—
703C2×C42C22×D5312yes—
704C24—532no—
705C24—5316no—
706C24—534no—
707C24C23×D5314yes—
708C24C23×D5311yescharacteristic
709#41—216no—
710#41—216no—
711#41—216no—
712#41—216no—
713#41—5332no—
714#41—5332no—
715#41—10664no—
716#41—10664no—
717#41—10632no—
718#41—10632no—
719#41—10664no—
720#41—10632no—
721#41—10632no—
722#41—10664no—
723#41—10632no—
724#41—10632no—
725#41—10616no—
726#41—10616no—
727#41—10616no—
728#41—10616no—
729C2×Q8—28no—
730C2×Q8—538no—
731C2×Q8—534no—
732C2×Q8—5316no—
733C2×Q8—534no—
734C2×Q8—534no—
735C2×Q8—10632no—
736C2×Q8—10632no—
737C2×Q8—10632no—
738C2×Q8—1068no—
739C2×Q8C23×D5314yes—
740C2×Q8C23×D5314yes—
741C2×D4—216no—
742C2×D4—28no—
743C2×D4—5316no—
744C2×D4—538no—
745C2×D4—5316no—
746C2×D4—5316no—
747C2×D4—538no—
748C2×D4—538no—
749C2×D4—5316no—
750C2×D4—5316no—
751C2×D4—538no—
752C2×D4—534no—
753C2×D4—5316no—
754C2×D4—534no—
755C2×D4—534no—
756C2×D4—5316no—
757C2×D4—10632no—
758C2×D4—10632no—
759C2×D4—10664no—
760C2×D4—10632no—
761C2×D4—10664no—
762C2×D4—10664no—
763C2×D4—10616no—
764C2×D4—1068no—
765C2×D4—21232no—
766C2×D4—21216no—
767C2×D4C23×D5318yes—
768C2×D4C23×D5318yes—
769C2×D4C23×D5314yes—
770C2×D4C23×D5314yes—
771C2×D4C23×D53116yes—
772C22×C4—216no—
773C22×C4—532no—
774C22×C4—5316no—
775C22×C4—534no—
776C22×C4—534no—
777C22×C4—532no—
778C22×C4—534no—
779C22×C4—534no—
780C22×C4—5316no—
781C22×C4—534no—
782C22×C4—532no—
783C22×C4—538no—
784C22×C4—5316no—
785C22×C4—5316no—
786C22×C4—538no—
787C22×C4—538no—
788C22×C4—538no—
789C22×C4—10664no—
790C22×C4—10616no—
791C22×C4—2128no—
792C22×C4—2124no—
793C22×C4D4×D5318yescomplemented
794C22×C4C23×D5314yes—
795C22×C4C23×D5318yes—
796C22×C4C23×D5318yes—
797C22×C4C23×D5314yes—
798C22×C4C23×D5311yescharacteristic
799C22×C4C23×D5312yes—
800C22×C4C23×D5311yescharacteristic
801C22×C4C23×D5312yes—
802C4⋊C4—5316no—
803C4⋊C4—5316no—
804C4⋊C4—5316no—
805C4⋊C4—5316no—
806C4⋊C4C23×D53116yes—
807C4⋊C4C23×D5318yes—
808C22⋊C4—5316no—
809C22⋊C4—5316no—
810C22⋊C4—5316no—
811C22⋊C4—5316no—
812C22⋊C4—5316no—
813C22⋊C4—5332no—
814C22⋊C4C23×D53132yes—
815C22⋊C4C23×D5318yes—
816C42—531no—
817C42—531no—
818C42—532no—
819C42—538no—
820C42—534no—
821C42—538no—
822C42—534no—
823C42—532no—
824C42—532no—
825C42C23×D5314yes—
826C42C23×D5314yes—
827C23—28no—
828C23—42no—
829C23—48no—
830C23—534no—
831C23—538no—
832C23—538no—
833C23—10632no—
834C23—1068no—
835C23—2128no—
836C23—21232no—
837C23—2124no—
838C23C2×D4×D5314yes—
839C23C24×D5318yes—
840C23C24×D5312yes—
841C23C24×D5311yescharacteristic
842Q8—28no—
843Q8—28no—
844Q8—5316no—
845Q8—10632no—
846Q8—1068no—
847Q8—1068no—
848D4—216no—
849D4—216no—
850D4—28no—
851D4—28no—
852D4—416no—
853D4—5332no—
854D4—5316no—
855D4—10632no—
856D4—10632no—
857D4—10632no—
858D4—10632no—
859D4—10616no—
860D4—10616no—
861D4—1068no—
862D4—1068no—
863D4—21216no—
864D4—21216no—
865C2×C4—28no—
866C2×C4—216no—
867C2×C4—216no—
868C2×C4—44no—
869C2×C4—538no—
870C2×C4—532no—
871C2×C4—534no—
872C2×C4—5316no—
873C2×C4—5316no—
874C2×C4—532no—
875C2×C4—534no—
876C2×C4—538no—
877C2×C4—10632no—
878C2×C4—10616no—
879C2×C4—10632no—
880C2×C4—10632no—
881C2×C4—1064no—
882C2×C4—1068no—
883C2×C4—1068no—
884C2×C4—10616no—
885C2×C4—10616no—
886C2×C4—2128no—
887C2×C4—2124no—
888C2×C4—2122no—
889C2×C4C2×D4×D5318yes—
890C2×C4C2×D4×D5314yes—
891C2×C4C2×D4×D5318yes—
892C2×C4C2×D4×D5314yes—
893C2×C4C24×D5318yes—
894C2×C4C24×D5318yes—
895C2×C4C24×D5311yescharacteristic
896C2×C4C24×D5312yes—
897C2×C4C24×D5311yescharacteristic
898C22—22no—
899C22—24no—
900C22—28no—
901C22—216no—
902C22—44no—
903C22—88no—
904C22—538no—
905C22—1068no—
906C22—1068no—
907C22—10616no—
908C22—4248no—
909C22—42432no—
910C22—2128no—
911C22C22×D4×D5314yes—
912C22C22×D4×D5312yes—
913C22C25×D5311yescharacteristic
914C4—28no—
915C4—28no—
916C4—538no—
917C4—534no—
918C4—1068no—
919C4—1062no—
920C4—1064no—
921C4C22×D4×D5312yes—
922C4C22×D4×D5314yes—
923C4C22×D4×D5312yes—
924C2—24no—
925C2—22no—
926C2—48no—
927C2—1068no—
928C2—2128no—
929C2C23×D4×D5311yescharacteristic
930C2#585×D5312yes—
subgroupG/H
centerC2×C4C24×D53
commutator, socle, cosocleC22×C53C26
FrattiniC22C25×D53
FittingC53×#3449C2
hypercenter#3449D53
hypocenterC53#62812
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16811459C2semidirect
2. #20288507C2semidirect
3. #20288504C2semidirect
4. #20288497C2semidirect
5. #20288490C2semidirect
6. #20288484C2semidirect
7. #20288478C2semidirect
8. #20288476C2semidirect
9. #20288198C2semidirect
10. #20288048C2semidirect
11. #20288042C2semidirect
12. C2×#16811169C2semidirect
13. #532×D53C2semidirect
14. C2×#16811091C2semidirect
15. C53×#3449C2semidirect
17. C2×#13133265C22semidirect
18. C2×#13133264C22semidirect
19. C2×#13133264C22semidirect
20. C2×#13133263C22semidirect
21. C2×#13133263C22semidirect
22. C2×#13133262C22semidirect
23. C2×#13133262C22semidirect
25. C22×#11719945C22semidirect
26. C22×#11719945C22semidirect
27. C2×#41×D53C22semidirect
28. C2×#41×D53C22semidirect
29. #16811291C22semidirect
30. #16811286C22semidirect
31. #16811283C22semidirect
32. #16811279C22semidirect
33. #16811275C22semidirect
34. #16811271C22semidirect
35. #16811270C22semidirect
36. #16811265C22semidirect
37. #16811264C22semidirect
38. #16811260C22semidirect
39. #16811257C22semidirect
40. #16811255C22semidirect
41. #16811204C22semidirect
42. #16811200C22semidirect
43. #16811199C22semidirect
44. #16811198C22semidirect
45. #16811193C22semidirect
46. #16811192C22semidirect
47. #16811191C22semidirect
48. #16811186C22semidirect
49. #16811185C22semidirect
50. #16811181C22semidirect
51. #16811174C22semidirect
52. #16811173C22semidirect
53. #16811172C22semidirect
54. #16811171C22semidirect
55. #16811170C22semidirect
56. #16811169C22semidirect
57. #16811169C22semidirect
58. #16811169C22semidirect
59. #16811169C22semidirect
60. #16811169C22semidirect
61. #16811169C22semidirect
62. #16811168C22semidirect
63. C2×#13133215C22semidirect
64. C4⋊Q8×D53C22semidirect
65. C2×#13133213C22semidirect
66. #127×D53C22semidirect
67. C2×#13133206C22semidirect
68. C2×#13133204C22semidirect
69. #124×D53C22semidirect
70. #16811135C22semidirect
71. #16811132C22semidirect
72. C2×#13133189C22semidirect
73. #121×D53C22semidirect
74. #16811091C22semidirect
75. #16811091C22semidirect
76. #16811091C22semidirect
77. C2×#13133182C22semidirect
78. C2×#13133179C22semidirect
79. C2×C4×C22⋊D53C22semidirect
80. C2×#13133177C22semidirect
81. C4×D4×D53C22semidirect
82. C2×#13133174C22semidirect
83. C22×C4×Dic53C22semidirect
84. C2×C42×D53C22semidirect
85. C22×#41×C53C22semidirect
86. C53×#537C22semidirect
87. C53×#536C22semidirect
88. C53×#535C22semidirect
89. C53×#534C22semidirect
90. C53×#532C22semidirect
91. C53×#525C22semidirect
92. C2×#117×C53C22semidirect
104. C2×#11719945D4semidirect
258. C22×C4×C53C2×D4semidirect
270. C2×C22⋊D53C2×D4semidirect
307. #11719945C2×D4semidirect
308. #11719945C2×D4semidirect
311. C2×D212C2×D4semidirect
320. C2×C4×D53C2×D4semidirect
331. C2×Dic106C2×D4semidirect
458. Dic53#585semidirect
470. #3449D53semidirect
494. C22×#41C2×D53semidirect
509. #537C2×D53semidirect
513. #536C2×D53semidirect
517. #535C2×D53semidirect
520. #534C2×D53semidirect
533. #532C2×D53semidirect
543. #525C2×D53semidirect
555. C2×#117C2×D53semidirect
558. C53#62812semidirect
793. C22×C4D4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114592
#202885072
#202885042
#202884972
#202884902
#202884842
#202884782
#202884762
#202881982
#202880482
#202880422
C2×#168111692
#532×D532
C2×#168110912
C53×#34492
#6281253