Finite Group Databasebeta

← #28293207

Subgroups — #28293207

Order 13568.

11222 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C212yesmaximal, complemented
2#20288484C214yesmaximal, complemented
3#20288478C214yesmaximal, complemented
4#20288472C218yesmaximal, complemented
5#20288391C218yesmaximal, complemented
6#20288390C218yesmaximal, complemented
7#20288380C218yesmaximal, complemented
8#20288379C218yesmaximal, complemented
9#20288044C212yesmaximal, complemented
10#20288043C214yesmaximal, complemented
11C2×#16811204C211yesmaximal, characteristic, complemented
12#537×D53C214yesmaximal, complemented
13C2×#16811104C211yesmaximal, characteristic, complemented
14C2×C53×#537C211yesmaximal, characteristic, complemented
15#16811459—232no—
16C2×#13133265C2214yescomplemented
17C2×#13133264C2214yescomplemented
18C2×#13133264C2214yescomplemented
19C2×#13133263C2214yescomplemented
20C2×#13133263C2214yescomplemented
21C2×#13133262C2214yescomplemented
22C2×#13133262C2218yescomplemented
23C22×#11719945C2211yescharacteristic
24C22×#11719945C2212yescomplemented
25C22×#11719945C2218yescomplemented
26C2×#41×D53C2218yescomplemented
27C2×#41×D53C2218yescomplemented
28#16811291C22116yescomplemented
29#16811286C22116yescomplemented
30#16811283C22116yescomplemented
31#16811279C22116yescomplemented
32#16811275C22116yescomplemented
33#16811274C22116yescomplemented
34#16811273C22116yescomplemented
35#16811270C22116yescomplemented
36#16811264C22116yescomplemented
37#16811263C22132yescomplemented
38#16811262C22132yescomplemented
39#16811257C22116yescomplemented
40#16811257C22116yescomplemented
41D4×C22⋊D53C22116yescomplemented
42#16811204C2214yescomplemented
43#16811204C2218yescomplemented
44#16811204C2214yescomplemented
45#16811203C22116yescomplemented
46#16811202C22116yescomplemented
47#16811201C2214yescomplemented
48#16811201C2214yescomplemented
49#16811200C22116yescomplemented
50#16811197C2214yescomplemented
51#16811196C22116yescomplemented
52#16811194C2214yescomplemented
53#16811190C2214yescomplemented
54#16811189C22116yescomplemented
55#16811187C2214yescomplemented
56#16811182C2218yescomplemented
57#16811181C22116yescomplemented
58#16811169C2218yescomplemented
59#16811168C22116yescomplemented
60#16811136C22116yescomplemented
61#16811134C2218yescomplemented
62#16811133C22116yescomplemented
63#16811130C2218yescomplemented
64C2×#13133197C2214yescomplemented
65C22⋊Q8×D53C22116yescomplemented
66C2×#13133192C2214yescomplemented
67C2×#13133191C2214yescomplemented
68#121×D53C22116yescomplemented
69#121×D53C22116yescomplemented
70#16811104C2218yescomplemented
71#16811104C2218yescomplemented
72C2×#13133182C2212yescomplemented
73C2×#13133179C2212yescomplemented
74C2×C4×C22⋊D53C2214yescomplemented
75C2×#13133176C2211yescharacteristic, complemented
76C2×#13133175C2212yescomplemented
77C2×C4⋊C4×D53C2212yescomplemented
78C22×#41×C53C2212yescomplemented
79C53×#537C2214yescomplemented
80C53×#537C2218yescomplemented
81C53×#537C2214yescomplemented
82C2×C22⋊Q8×C53C2214yescomplemented
83C2×#121×C53C2214yescomplemented
84C2×#121×C53C2214yescomplemented
85C22×C4⋊C4×C53C2211yescharacteristic, complemented
86#13133265—232no—
87#13133264—232no—
88#13133264—232no—
89#13133263—232no—
90#13133263—232no—
91#13133262—264no—
92#13133262—232no—
93C2×#11719949C2318yes—
94C2×#11719949C2318yes—
95C2×#11719945—216no—
96C2×#11719945—264no—
97C2×#11719945D4116yescomplemented
98C2×#11719945C2318yes—
99C2×#11719945C23116yes—
100C2×#11719945C2318yes—
101C2×#11719945C2314yes—
102C2×#11719945C2314yes—
103C2×#11719945C23116yes—
104C2×#11719945C2314yes—
105C2×#11719945C2314yes—
106C2×#11719945C2314yes—
107C2×#11719945C2314yes—
108C2×#11719947C23116yes—
109C2×#11719947C2318yes—
110C2×#11719947C2318yes—
111C2×#11719947C23116yes—
112#41×D53—264no—
113#41×D53—264no—
114C22×Dic106C2318yes—
115C22×Dic106C2312yes—
116C22×Dic106C2311yescharacteristic
117C2×Q8×D53C2318yes—
118C2×Q8×D53C2318yes—
119C22×D212C2318yes—
120C22×D212C2312yes—
121C22×D212C2314yes—
122C22×D212C2311yescharacteristic
123C22×C22⋊D53C2314yes—
124C22×C22⋊D53C23116yes—
125C22×C22⋊D53C2312yes—
126C2×D4×D53C2318yes—
127C2×D4×D53C23116yes—
128C2×D4×D53C2318yes—
129C2×D4×D53C23116yes—
130C2×D4×D53C23116yes—
131C22×C4×D53C23116yes—
132C22×C4×D53C2314yes—
133C22×C4×D53C2314yes—
134C22×C4×D53C2312yes—
135#13133216C23116yes—
136#13133215C2318yes—
137#13133213C23116yes—
138#13133213C2318yes—
139#13133206C2318yes—
140#13133204C2318yes—
141#13133203C23132yes—
142#13133202C23132yes—
143#13133200C23116yes—
144#13133199C23132yes—
145#13133198C23116yes—
146#13133197C23116yes—
147#13133197C23116yes—
148#13133196C2318yes—
149#13133196C2318yes—
150#13133195C23132yes—
151#13133194C23132yes—
152#13133193C2318yes—
153#13133193C2318yes—
154#13133192C23116yes—
155#13133192C23116yes—
156#13133192C23116yes—
157#13133191C23116yes—
158#13133191C2318yes—
159#13133191C23116yes—
160#13133191C2318yes—
161#13133190C23132yes—
162#13133190C23132yes—
163#13133189C23132yes—
164#13133189C23116yes—
165#13133189C23116yes—
166#13133188C23116yes—
167#13133188C2318yes—
168#13133188C2318yes—
169#13133187C23132yes—
170#13133186C23116yes—
171#13133185C23132yes—
172#13133185C23116yes—
173#13133182C23116yes—
174D4×Dic53C23116yes—
175#13133179C23116yes—
176#13133179C23116yes—
177C4×C22⋊D53C23116yes—
178C4×C22⋊D53C23116yes—
179C4×C22⋊D53C23116yes—
180C4×C22⋊D53C23116yes—
181#13133177C23132yes—
182#13133176C2314yes—
183#13133176C2314yes—
184#13133175C23116yes—
185C2×C4⋊Dic53C2314yes—
186C2×C4⋊Dic53C2311yescharacteristic
187C2×C4⋊Dic53C2311yescharacteristic
188C2×#11719919C2314yes—
189C4⋊C4×D53C23116yes—
190C4⋊C4×D53C23116yes—
191C2×C22⋊Dic53C2312yes—
192C2×#11719921C2314yes—
193C2×#11719921C2318yes—
194C22⋊C4×D53C23132yes—
195C2×C4×Dic53C2314yes—
196C2×C4×Dic53C2312yes—
197C2×#41×C53—216no—
198C2×#41×C53C2314yes—
199C2×#41×C53C2314yes—
200C2×#41×C53C2314yes—
201C2×#41×C53C2314yes—
202C22×Q8×C53C2312yes—
203C22×D4×C53C2314yes—
204C22×D4×C53C2312yes—
205C22×D4×C53C2314yes—
206C23×C4×C53C2314yes—
207C23×C4×C53C2312yes—
208C23×C4×C53C2311yescharacteristic
209C22⋊Q8×C53C23116yes—
210C22⋊Q8×C53C23116yes—
211#121×C53C23116yes—
212#121×C53C23116yes—
213#121×C53C23116yes—
214#121×C53C23116yes—
215C2×C4⋊C4×C53C2314yes—
216C2×C4⋊C4×C53C2314yes—
217C2×C4⋊C4×C53C2312yes—
218C2×C4⋊C4×C53C2312yes—
219C2×C4⋊C4×C53C2314yes—
220C2×C22⋊C4×C53C2318yes—
221C24×C53C2414yes—
222C24×C53C2411yescharacteristic
223C23×D53C24116yes—
224C23×D53C2414yes—
225C23×D53C2412yes—
226#41×C53—216no—
227#41×C53—216no—
228#41×C53—216no—
229#41×C53—216no—
230C2×Q8×C53—28no—
231C2×Q8×C53C2414yes—
232C2×Q8×C53C2414yes—
233C2×D4×C53—216no—
234C2×D4×C53—28no—
235C2×D4×C53—84no—
236C2×D4×C53C2418yes—
237C2×D4×C53C2414yes—
238C2×D4×C53C2418yes—
239C2×D4×C53C2414yes—
240C2×D4×C53C24116yes—
241C22×C4×C53—216no—
242C22×C4×C53—82no—
243C22×C4×C53C2×D418yescomplemented
244C22×C4×C53C2414yes—
245C22×C4×C53C2418yes—
246C22×C4×C53C2418yes—
247C22×C4×C53C2414yes—
248C22×C4×C53C2414yes—
249C22×C4×C53C2414yes—
250C22×C4×C53C2412yes—
251C22×C4×C53C2411yescharacteristic
252C22×C4×C53C2411yescharacteristic
253C22×C4×C53C2412yes—
254C2×C22⋊D53—216no—
255C2×C22⋊D53—264no—
256C2×C22⋊D53C2×D4116yescomplemented
257C2×C22⋊D53C24116yes—
258C2×C22⋊D53C2418yes—
259C2×C22⋊D53C2418yes—
260C2×C22⋊D53C24116yes—
261C2×C22⋊D53C24116yes—
262C2×C22⋊D53C24116yes—
263C2×C22⋊D53C2414yes—
264C2×C22⋊D53C2414yes—
265C22×Dic53C2414yes—
266C22×Dic53C24116yes—
267C22×Dic53C2412yes—
268C22×Dic53C2412yes—
269C22×Dic53C2412yes—
270#11719949—232no—
271#11719949—232no—
272Q8×D53—232no—
273Q8×D53—232no—
274#11719947—264no—
275#11719947—264no—
276#11719947—232no—
277#11719947—232no—
278D4×D53—264no—
279D4×D53—264no—
280D4×D53—232no—
281D4×D53—232no—
282D4×D53—816no—
283#11719945—216no—
284#11719945—216no—
285#11719945—216no—
286#11719945—216no—
287#11719945—264no—
288#11719945—232no—
289#11719945—264no—
290#11719945—232no—
291#11719945C2×D4132yescomplemented
292#11719945C2×D4132yescomplemented
293C2×D212—28no—
294C2×D212—232no—
295C2×D212—84no—
296C2×D212C2×D418yescomplemented
297C2×D212C24116yes—
298C2×D212C2414yes—
299C2×D212C2414yes—
300C2×D212C24116yes—
301C2×D212C2414yes—
302C2×C4×D53—216no—
303C2×C4×D53—264no—
304C2×C4×D53—84no—
305C2×C4×D53C2×D4116yescomplemented
306C2×C4×D53C24116yes—
307C2×C4×D53C24116yes—
308C2×C4×D53C2418yes—
309C2×C4×D53C2418yes—
310C2×C4×D53C24116yes—
311C2×C4×D53C2418yes—
312C2×Dic106—28no—
313C2×Dic106—232no—
314C2×Dic106C2×D418yescomplemented
315C2×Dic106C24116yes—
316C2×Dic106C2414yes—
317C2×Dic106C2414yes—
318C2×Dic106C2414yes—
319C4⋊C4×C53C2418yes—
320C4⋊C4×C53C2418yes—
321C4⋊C4×C53C24116yes—
322C22⋊C4×C53C24132yes—
323C22⋊Dic53C24116yes—
324C22⋊Dic53C2414yes—
325C22⋊Dic53C2414yes—
326C22⋊Dic53C24116yes—
327#11719921C24116yes—
328#11719921C24132yes—
329#11719921C24116yes—
330#11719921C24116yes—
331C4⋊Dic53C2414yes—
332C4⋊Dic53C24116yes—
333C4⋊Dic53C2414yes—
334#11719919C24116yes—
335#11719919C24116yes—
336#11719919C24116yes—
337C4×Dic53C24116yes—
338C4×Dic53C2418yes—
339C23×C53—28no—
340C23×C53—41no—
341C23×C53—41no—
342C23×C53—44no—
343C23×C53—44no—
344C23×C53C22×D414yes—
345C23×C53C2518yes—
346C23×C53C2511yescharacteristic
347C23×C53C2511yescharacteristic
348C23×C53C2511yescharacteristic
349C22×D53—28no—
350C22×D53—232no—
351C22×D53—42no—
352C22×D53—42no—
353C22×D53—44no—
354C22×D53—416no—
355C22×D53—416no—
356C22×D53—44no—
357C22×D53C22×D418yes—
358C22×D53C2518yes—
359C22×D53C2514yes—
360Q8×C53—28no—
361Q8×C53—28no—
362D4×C53—216no—
363D4×C53—216no—
364D4×C53—28no—
365D4×C53—28no—
366D4×C53—416no—
367C2×C4×C53—28no—
368C2×C4×C53—216no—
369C2×C4×C53—216no—
370C2×C4×C53—44no—
371C2×C4×C53—44no—
372C2×C4×C53—44no—
373C2×C4×C53C22×D418yes—
374C2×C4×C53C22×D414yes—
375C2×C4×C53C22×D414yes—
376C2×C4×C53C22×D418yes—
377C2×C4×C53C2518yes—
378C2×C4×C53C2518yes—
379C2×C4×C53C2512yes—
380C2×C4×C53C2512yes—
381C22⋊D53—216no—
382C22⋊D53—216no—
383C22⋊D53—232no—
384C22⋊D53—232no—
385C22⋊D53—416no—
386C22⋊D53—416no—
387C22⋊D53C22×D4116yes—
388C22⋊D53C22×D4116yes—
389C2×Dic53—28no—
390C2×Dic53—232no—
391C2×Dic53—42no—
392C2×Dic53—42no—
393C2×Dic53C22×D418yes—
394C2×Dic53C2518yes—
395C2×Dic53C2514yes—
396C2×Dic53C2514yes—
397C2×Dic53C2514yes—
398D212—232no—
399D212—28no—
400D212—28no—
401D212—416no—
402D212C22×D4116yes—
403C4×D53—232no—
404C4×D53—216no—
405C4×D53—216no—
406C4×D53—232no—
407C4×D53—416no—
408C4×D53C22×D4132yes—
409Dic106—28no—
410Dic106—28no—
411Dic106—232no—
412Dic106C22×D4116yes—
413#62853—531nomaximal, Sylow
414C22×C53—21no—
415C22×C53—21no—
416C22×C53—21no—
417C22×C53—21no—
418C22×C53—21no—
419C22×C53—21no—
420C22×C53—28no—
421C22×C53—28no—
422C22×C53—28no—
423C22×C53—44no—
424C22×C53—88no—
425C22×C53C23×D412yes—
426C22×C53C23×D412yes—
427C22×C53C23×D412yes—
428C22×C53C2611yescharacteristic
429C2×D53—24no—
430C2×D53—24no—
431C2×D53—28no—
432C2×D53—28no—
433C2×D53—28no—
434C2×D53—48no—
435C2×D53—832no—
436C2×D53—88no—
437C2×D53C23×D418yes—
438C4×C53—28no—
439C4×C53—28no—
440C4×C53C23×D414yes—
441C4×C53C23×D414yes—
442Dic53—28no—
443Dic53—24no—
444Dic53—24no—
445Dic53C23×D418yes—
446C2×#585—532no—
447#3497—534no—
448#3496—534no—
449#3496—538no—
450#3489—538no—
451#3489—538no—
452#3488—538no—
453#3488—538no—
454#3449—532no—
455#3449—534no—
456C2×#537—534no—
457C2×#537—531no—
458C2×#537D5311yescharacteristic, complemented
459C2×#520—531no—
460C2×C53—22no—
461C2×C53—22no—
462C2×C53—22no—
463C2×C53—48no—
464C2×C53C24×D411yescharacteristic
465C2×C53H(7,𝔽2)11yescharacteristic
466C2×C532−1+611yescharacteristic
467D53—28no—
468D53—48no—
469#585—10632no—
470C2×2−1+4—534no—
471C2×2−1+4—534no—
472C2×2−1+4—534no—
473C2×H(5,𝔽2)—534no—
474C2×H(5,𝔽2)—534no—
475C2×H(5,𝔽2)—534no—
476C2×H(5,𝔽2)—538no—
477C22×#41—538no—
478C22×#41—538no—
479C22×#41—531no—
480C22×#41—532no—
481C22×#41—538no—
482C22×#41C2×D5312yescomplemented
483#550—5316no—
484D4×Q8—5316no—
485#548—5316no—
486#548—5316no—
487#547—5316no—
488#547—5316no—
489#547—5316no—
490#546—5316no—
491#546—5316no—
492#546—5332no—
493#546—5332no—
494D42—5316no—
495D42—5316no—
496D42—5316no—
497#537—534no—
498#537—534no—
499#537—5316no—
500#537—5316no—
501#537—5316no—
502#537—534no—
503#537—538no—
504#537—534no—
505#537C2×D5314yescomplemented
506#537C2×D5318yescomplemented
507#537C2×D5314yescomplemented
508#536—534no—
509#536—534no—
510#536—5316no—
511#535—534no—
512#535—534no—
513#535—5316no—
514#534—538no—
515#534—5316no—
516#532—538no—
517#532—5316no—
518#525—538no—
519#525—538no—
520#525—5316no—
521#525—5316no—
522C2×C22⋊Q8—5316no—
523C2×C22⋊Q8—534no—
524C2×C22⋊Q8C2×D5314yescomplemented
525C2×#121—534no—
526C2×#121—5316no—
527C2×#121—5316no—
528C2×#121—534no—
529C2×#121C2×D5314yescomplemented
530C2×#121C2×D5314yescomplemented
531#520—538no—
532#520—538no—
533C2×C4×Q8—532no—
534C2×C4×D4—534no—
535C2×C4×D4—532no—
536C2×#117—531no—
537C2×#117—532no—
538C22×C4⋊C4—532no—
539C22×C4⋊C4C2×D5311yescharacteristic, complemented
540C53#6285311yescharacteristic, complemented, Sylow
5412−1+4—10632no—
5422−1+4—10632no—
5432−1+4—10632no—
544H(5,𝔽2)—10664no—
545H(5,𝔽2)—10632no—
546H(5,𝔽2)—10632no—
547H(5,𝔽2)—10632no—
548C2×#41—216no—
549C2×#41—538no—
550C2×#41—538no—
551C2×#41—538no—
552C2×#41—5316no—
553C2×#41—5316no—
554C2×#41—538no—
555C2×#41—5316no—
556C2×#41—534no—
557C2×#41—534no—
558C2×#41—534no—
559C2×#41—534no—
560C2×#41—5316no—
561C2×#41—534no—
562C2×#41—534no—
563C2×#41—538no—
564C2×#41—5316no—
565C2×#41—538no—
566C2×#41—10664no—
567C2×#41—10664no—
568C2×#41—10664no—
569C2×#41—10616no—
570C2×#41C22×D5314yes—
571C2×#41C22×D5314yes—
572C2×#41C22×D5314yes—
573C2×#41C22×D5314yes—
574C22×Q8—538no—
575C22×Q8—538no—
576C22×Q8—531no—
577C22×Q8—532no—
578C22×Q8—538no—
579C22×Q8C22×D5312yes—
580C22×D4—532no—
581C22×D4—534no—
582C22×D4—5316no—
583C22×D4—5316no—
584C22×D4—538no—
585C22×D4—5316no—
586C22×D4—538no—
587C22×D4—5316no—
588C22×D4—531no—
589C22×D4—532no—
590C22×D4—538no—
591C22×D4—534no—
592C22×D4C22×D5314yes—
593C22×D4C22×D5312yes—
594C22×D4C22×D5314yes—
595C23×C4—532no—
596C23×C4—5316no—
597C23×C4—534no—
598C23×C4—534no—
599C23×C4C22×D5314yes—
600C23×C4C22×D5312yes—
601C23×C4C22×D5311yescharacteristic
602C4⋊Q8—538no—
603C4⋊Q8—5316no—
604#127—5316no—
605#127—538no—
606#124—538no—
607#124—538no—
608#124—5332no—
609#123—5316no—
610#123—5316no—
611#123—5332no—
612#123—5332no—
613C22⋊Q8—538no—
614C22⋊Q8—538no—
615C22⋊Q8—538no—
616C22⋊Q8—538no—
617C22⋊Q8—5316no—
618C22⋊Q8—5332no—
619C22⋊Q8—5316no—
620C22⋊Q8—5332no—
621C22⋊Q8C22×D53116yes—
622C22⋊Q8C22×D53116yes—
623#121—538no—
624#121—5316no—
625#121—5316no—
626#121—5332no—
627#121—538no—
628#121—5316no—
629#121—538no—
630#121—5316no—
631#121—5316no—
632#121—538no—
633#121—5316no—
634#121—5316no—
635#121—5316no—
636#121—5332no—
637#121—5332no—
638#121C22×D53116yes—
639#121C22×D53116yes—
640#121C22×D53116yes—
641#121C22×D53116yes—
642#120—5316no—
643#120—5316no—
644#120—5332no—
645#120—5332no—
646C4×Q8—5316no—
647C4×D4—5316no—
648C4×D4—5316no—
649C4×D4—5316no—
650C4×D4—5316no—
651C4×D4—5316no—
652C4×D4—5316no—
653C4×D4—5316no—
654C4×D4—5332no—
655#117—534no—
656#117—534no—
657#117—5316no—
658C2×C4⋊C4—531no—
659C2×C4⋊C4—534no—
660C2×C4⋊C4—531no—
661C2×C4⋊C4—534no—
662C2×C4⋊C4—5316no—
663C2×C4⋊C4—5316no—
664C2×C4⋊C4C22×D5312yes—
665C2×C4⋊C4C22×D5312yes—
666C2×C4⋊C4C22×D5314yes—
667C2×C4⋊C4C22×D5314yes—
668C2×C4⋊C4C22×D5314yes—
669C2×C22⋊C4—532no—
670C2×C22⋊C4—534no—
671C2×C22⋊C4—538no—
672C2×C22⋊C4—5332no—
673C2×C22⋊C4C22×D5318yes—
674C2×C42—534no—
675C2×C42—532no—
676C24—532no—
677C24—5316no—
678C24—534no—
679C24C23×D5314yes—
680C24C23×D5311yescharacteristic
681#41—216no—
682#41—216no—
683#41—216no—
684#41—216no—
685#41—5332no—
686#41—5332no—
687#41—10664no—
688#41—10664no—
689#41—10632no—
690#41—10632no—
691#41—10664no—
692#41—10632no—
693#41—10632no—
694#41—10664no—
695#41—10632no—
696#41—10632no—
697#41—10616no—
698#41—10616no—
699#41—10616no—
700#41—10616no—
701C2×Q8—28no—
702C2×Q8—538no—
703C2×Q8—534no—
704C2×Q8—534no—
705C2×Q8—5316no—
706C2×Q8—534no—
707C2×Q8—10632no—
708C2×Q8—10632no—
709C2×Q8—10632no—
710C2×Q8—1068no—
711C2×Q8C23×D5314yes—
712C2×Q8C23×D5314yes—
713C2×D4—216no—
714C2×D4—28no—
715C2×D4—84no—
716C2×D4—5316no—
717C2×D4—534no—
718C2×D4—534no—
719C2×D4—5316no—
720C2×D4—538no—
721C2×D4—538no—
722C2×D4—5316no—
723C2×D4—5316no—
724C2×D4—5316no—
725C2×D4—538no—
726C2×D4—534no—
727C2×D4—5316no—
728C2×D4—534no—
729C2×D4—534no—
730C2×D4—5316no—
731C2×D4—10632no—
732C2×D4—10632no—
733C2×D4—10664no—
734C2×D4—10632no—
735C2×D4—10664no—
736C2×D4—10664no—
737C2×D4—10616no—
738C2×D4—1068no—
739C2×D4—4244no—
740C2×D4—42416no—
741C2×D4C23×D5318yes—
742C2×D4C23×D5318yes—
743C2×D4C23×D5314yes—
744C2×D4C23×D5314yes—
745C2×D4C23×D53116yes—
746C22×C4—216no—
747C22×C4—82no—
748C22×C4—532no—
749C22×C4—5316no—
750C22×C4—538no—
751C22×C4—534no—
752C22×C4—5316no—
753C22×C4—532no—
754C22×C4—532no—
755C22×C4—5316no—
756C22×C4—5316no—
757C22×C4—538no—
758C22×C4—538no—
759C22×C4—5316no—
760C22×C4—10664no—
761C22×C4—10616no—
762C22×C4—4244no—
763C22×C4D4×D5318yescomplemented
764C22×C4C23×D5314yes—
765C22×C4C23×D5318yes—
766C22×C4C23×D5318yes—
767C22×C4C23×D5314yes—
768C22×C4C23×D5314yes—
769C22×C4C23×D5314yes—
770C22×C4C23×D5311yescharacteristic
771C22×C4C23×D5311yescharacteristic
772C22×C4C23×D5312yes—
773C22×C4C23×D5312yes—
774C4⋊C4—534no—
775C4⋊C4—5316no—
776C4⋊C4—5316no—
777C4⋊C4—5316no—
778C4⋊C4—534no—
779C4⋊C4—5316no—
780C4⋊C4C23×D5318yes—
781C4⋊C4C23×D53116yes—
782C4⋊C4C23×D5318yes—
783C22⋊C4—5316no—
784C22⋊C4—534no—
785C22⋊C4—534no—
786C22⋊C4—5316no—
787C22⋊C4—5316no—
788C22⋊C4—5332no—
789C22⋊C4—5316no—
790C22⋊C4—5316no—
791C22⋊C4C23×D53132yes—
792C42—5316no—
793C42—538no—
794C23—28no—
795C23—41no—
796C23—41no—
797C23—44no—
798C23—44no—
799C23—534no—
800C23—538no—
801C23—538no—
802C23—10632no—
803C23—1068no—
804C23—2124no—
805C23—21216no—
806C23—2124no—
807C23—21216no—
808C23—2122no—
809C23—2122no—
810C23C2×D4×D5314yes—
811C23C24×D5318yes—
812C23C24×D5311yescharacteristic
813C23C24×D5311yescharacteristic
814C23C24×D5311yescharacteristic
815Q8—28no—
816Q8—28no—
817Q8—5316no—
818Q8—10632no—
819Q8—1068no—
820Q8—1068no—
821D4—216no—
822D4—216no—
823D4—28no—
824D4—28no—
825D4—416no—
826D4—5316no—
827D4—5316no—
828D4—5316no—
829D4—10632no—
830D4—10632no—
831D4—10632no—
832D4—10616no—
833D4—10616no—
834D4—1068no—
835D4—1068no—
836D4—21216no—
837D4—21216no—
838D4—21216no—
839C2×C4—28no—
840C2×C4—216no—
841C2×C4—216no—
842C2×C4—44no—
843C2×C4—44no—
844C2×C4—44no—
845C2×C4—538no—
846C2×C4—534no—
847C2×C4—5332no—
848C2×C4—534no—
849C2×C4—534no—
850C2×C4—538no—
851C2×C4—10632no—
852C2×C4—10632no—
853C2×C4—10632no—
854C2×C4—1068no—
855C2×C4—10616no—
856C2×C4—10616no—
857C2×C4—21216no—
858C2×C4—2122no—
859C2×C4—2122no—
860C2×C4C2×D4×D5318yes—
861C2×C4C2×D4×D5314yes—
862C2×C4C2×D4×D5318yes—
863C2×C4C2×D4×D5314yes—
864C2×C4C24×D5318yes—
865C2×C4C24×D5318yes—
866C2×C4C24×D5312yes—
867C2×C4C24×D5312yes—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—28no—
875C22—28no—
876C22—28no—
877C22—44no—
878C22—88no—
879C22—538no—
880C22—1064no—
881C22—1064no—
882C22—1068no—
883C22—1068no—
884C22—1068no—
885C22—4248no—
886C22—42432no—
887C22—2128no—
888C22C22×D4×D5312yes—
889C22C22×D4×D5312yes—
890C22C22×D4×D5312yes—
891C22C25×D5311yescharacteristic
892C4—28no—
893C4—28no—
894C4—538no—
895C4—1068no—
896C4—1064no—
897C4—1064no—
898C4C22×D4×D5314yes—
899C4C22×D4×D5314yes—
900C2—22no—
901C2—22no—
902C2—22no—
903C2—48no—
904C2—1068no—
905C2—2128no—
906C2C23×D4×D5311yescharacteristic
907C2#2028952511yescharacteristic
908C2#2028952711yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC2×C53×#537C2
hypercenterC2×#537D53
hypocenterC53#62853
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#16811459C2semidirect
2. #20288484C2semidirect
3. #20288478C2semidirect
4. #20288472C2semidirect
5. #20288391C2semidirect
6. #20288390C2semidirect
7. #20288380C2semidirect
8. #20288379C2semidirect
9. #20288044C2semidirect
10. #20288043C2semidirect
11. C2×#16811204C2semidirect
12. #537×D53C2semidirect
13. C2×#16811104C2semidirect
14. C2×C53×#537C2semidirect
16. C2×#13133265C22semidirect
17. C2×#13133264C22semidirect
18. C2×#13133264C22semidirect
19. C2×#13133263C22semidirect
20. C2×#13133263C22semidirect
21. C2×#13133262C22semidirect
22. C2×#13133262C22semidirect
24. C22×#11719945C22semidirect
25. C22×#11719945C22semidirect
26. C2×#41×D53C22semidirect
27. C2×#41×D53C22semidirect
28. #16811291C22semidirect
29. #16811286C22semidirect
30. #16811283C22semidirect
31. #16811279C22semidirect
32. #16811275C22semidirect
33. #16811274C22semidirect
34. #16811273C22semidirect
35. #16811270C22semidirect
36. #16811264C22semidirect
37. #16811263C22semidirect
38. #16811262C22semidirect
39. #16811257C22semidirect
40. #16811257C22semidirect
41. D4×C22⋊D53C22semidirect
42. #16811204C22semidirect
43. #16811204C22semidirect
44. #16811204C22semidirect
45. #16811203C22semidirect
46. #16811202C22semidirect
47. #16811201C22semidirect
48. #16811201C22semidirect
49. #16811200C22semidirect
50. #16811197C22semidirect
51. #16811196C22semidirect
52. #16811194C22semidirect
53. #16811190C22semidirect
54. #16811189C22semidirect
55. #16811187C22semidirect
56. #16811182C22semidirect
57. #16811181C22semidirect
58. #16811169C22semidirect
59. #16811168C22semidirect
60. #16811136C22semidirect
61. #16811134C22semidirect
62. #16811133C22semidirect
63. #16811130C22semidirect
64. C2×#13133197C22semidirect
65. C22⋊Q8×D53C22semidirect
66. C2×#13133192C22semidirect
67. C2×#13133191C22semidirect
68. #121×D53C22semidirect
69. #121×D53C22semidirect
70. #16811104C22semidirect
71. #16811104C22semidirect
72. C2×#13133182C22semidirect
73. C2×#13133179C22semidirect
74. C2×C4×C22⋊D53C22semidirect
75. C2×#13133176C22semidirect
76. C2×#13133175C22semidirect
77. C2×C4⋊C4×D53C22semidirect
78. C22×#41×C53C22semidirect
79. C53×#537C22semidirect
80. C53×#537C22semidirect
81. C53×#537C22semidirect
82. C2×C22⋊Q8×C53C22semidirect
83. C2×#121×C53C22semidirect
84. C2×#121×C53C22semidirect
85. C22×C4⋊C4×C53C22semidirect
97. C2×#11719945D4semidirect
243. C22×C4×C53C2×D4semidirect
256. C2×C22⋊D53C2×D4semidirect
291. #11719945C2×D4semidirect
292. #11719945C2×D4semidirect
296. C2×D212C2×D4semidirect
305. C2×C4×D53C2×D4semidirect
314. C2×Dic106C2×D4semidirect
458. C2×#537D53semidirect
482. C22×#41C2×D53semidirect
505. #537C2×D53semidirect
506. #537C2×D53semidirect
507. #537C2×D53semidirect
524. C2×C22⋊Q8C2×D53semidirect
529. C2×#121C2×D53semidirect
530. C2×#121C2×D53semidirect
539. C22×C4⋊C4C2×D53semidirect
540. C53#62853semidirect
763. 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
#202884842
#202884782
#202884722
#202883912
#202883902
#202883802
#202883792
#202880442
#202880432
C2×#168112042
#537×D532
C2×#168111042
C2×C53×#5372
#6285353