Finite Group Databasebeta

← #28293209

Subgroups — #28293209

Order 13568.

11222 conjugacy classes of subgroups.

The subgroup lattice has 922 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811459C212yesmaximal, complemented
2#20288481C214yesmaximal, complemented
3#20288477C214yesmaximal, complemented
4#20288476C218yesmaximal, complemented
5#20288393C218yesmaximal, complemented
6#20288387C218yesmaximal, complemented
7#20288382C218yesmaximal, complemented
8#20288376C218yesmaximal, complemented
9#20288048C211yesmaximal, characteristic, complemented
10#20288043C214yesmaximal, complemented
11C2×#16811201C212yesmaximal, complemented
12#537×D53C214yesmaximal, complemented
13C2×#16811103C211yesmaximal, characteristic, complemented
14C53×#3449C211yesmaximal, 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#16811294C2218yescomplemented
29#16811293C2218yescomplemented
30D4×Dic106C2218yescomplemented
31#16811288C2218yescomplemented
32#16811282C22116yescomplemented
33#16811281C22116yescomplemented
34#16811278C2218yescomplemented
35#16811276C2218yescomplemented
36#16811271C22132yescomplemented
37#16811269C22116yescomplemented
38#16811266C22116yescomplemented
39#16811265C22132yescomplemented
40#16811260C22132yescomplemented
41D4×D212C2218yescomplemented
42#16811258C2218yescomplemented
43#16811255C22132yescomplemented
44#16811204C2212yescomplemented
45#16811204C2212yescomplemented
46#16811203C22116yescomplemented
47#16811202C22116yescomplemented
48#16811201C2218yescomplemented
49#16811201C2218yescomplemented
50#16811201C2218yescomplemented
51#16811201C2218yescomplemented
52#16811200C22116yescomplemented
53#16811199C2214yescomplemented
54#16811196C22116yescomplemented
55#16811192C2214yescomplemented
56#16811189C22116yescomplemented
57#16811185C2214yescomplemented
58#16811181C22116yescomplemented
59#16811173C2214yescomplemented
60#16811168C22116yescomplemented
61#16811136C22116yescomplemented
62#16811135C2218yescomplemented
63#16811133C22116yescomplemented
64C2×#13133196C2214yescomplemented
65C2×#13133193C2214yescomplemented
66C22⋊Q8×D53C22116yescomplemented
67C2×#13133191C2214yescomplemented
68C2×#13133189C2218yescomplemented
69C2×#13133188C2214yescomplemented
70#121×D53C22116yescomplemented
71#121×D53C22116yescomplemented
72#16811103C2218yescomplemented
73#16811103C2218yescomplemented
74C2×C4×Dic106C2212yescomplemented
75C2×C4×D212C2212yescomplemented
76C2×#13133177C2214yescomplemented
77C2×#13133175C2212yescomplemented
78C22×C4⋊Dic53C2211yescharacteristic, complemented
79C2×C4⋊C4×D53C2212yescomplemented
80C22×#41×C53C2212yescomplemented
81C53×#537C2212yescomplemented
82C53×#537C2212yescomplemented
83C53×#536C2214yescomplemented
84C53×#535C2214yescomplemented
85C53×#534C2214yescomplemented
86C53×#532C2214yescomplemented
87C53×#525C2218yescomplemented
88C2×#117×C53C2211yescharacteristic, complemented
89#13133265—232no—
90#13133264—232no—
91#13133264—232no—
92#13133263—232no—
93#13133263—232no—
94#13133262—264no—
95#13133262—232no—
96C2×#11719949C2318yes—
97C2×#11719949C2318yes—
98C2×#11719945—216no—
99C2×#11719945—264no—
100C2×#11719945D4116yescomplemented
101C2×#11719945C23116yes—
102C2×#11719945C2318yes—
103C2×#11719945C2318yes—
104C2×#11719945C2314yes—
105C2×#11719945C2314yes—
106C2×#11719945C23116yes—
107C2×#11719945C2314yes—
108C2×#11719945C2314yes—
109C2×#11719945C2314yes—
110C2×#11719945C2314yes—
111C2×#11719947C23116yes—
112C2×#11719947C2318yes—
113C2×#11719947C2318yes—
114C2×#11719947C23116yes—
115#41×D53—264no—
116#41×D53—264no—
117C22×Dic106C2318yes—
118C22×Dic106C2312yes—
119C22×Dic106C2311yescharacteristic
120C2×Q8×D53C2318yes—
121C2×Q8×D53C2318yes—
122C22×D212C2318yes—
123C22×D212C2312yes—
124C22×D212C2311yescharacteristic
125C22×C22⋊D53C2314yes—
126C22×C22⋊D53C23116yes—
127C22×C22⋊D53C2318yes—
128C22×C22⋊D53C2312yes—
129C2×D4×D53C23116yes—
130C2×D4×D53C2318yes—
131C2×D4×D53C23116yes—
132C2×D4×D53C2318yes—
133C2×D4×D53C23116yes—
134C23×Dic53C2312yes—
135C22×C4×D53C23116yes—
136C22×C4×D53C2314yes—
137C22×C4×D53C2314yes—
138C22×C4×D53C2312yes—
139#13133217C2314yes—
140#13133216C23116yes—
141#13133214C2314yes—
142#13133213C23116yes—
143#13133205C2318yes—
144#13133203C23132yes—
145#13133202C23132yes—
146#13133201C23116yes—
147#13133199C23132yes—
148#13133197C2318yes—
149#13133197C2318yes—
150#13133196C23116yes—
151#13133196C23116yes—
152#13133195C23132yes—
153#13133194C23132yes—
154#13133193C23116yes—
155#13133193C23116yes—
156#13133192C23116yes—
157#13133192C2318yes—
158#13133192C2318yes—
159#13133191C23116yes—
160#13133191C2318yes—
161#13133191C23116yes—
162#13133191C2318yes—
163#13133190C23132yes—
164#13133190C23132yes—
165#13133189C23132yes—
166#13133189C23132yes—
167#13133189C23132yes—
168#13133188C23116yes—
169#13133188C23116yes—
170#13133188C23116yes—
171#13133187C23116yes—
172#13133187C23132yes—
173#13133185C23132yes—
174C4×Dic106C2318yes—
175C4×Dic106C2318yes—
176C4×D212C2318yes—
177C4×D212C2318yes—
178C4×D212C2318yes—
179C4×D212C2318yes—
180D4×Dic53C23116yes—
181#13133179C23116yes—
182#13133177C23132yes—
183#13133177C23132yes—
184#13133175C23116yes—
185C2×C4⋊Dic53C2312yes—
186C2×C4⋊Dic53C2312yes—
187C2×C4⋊Dic53C2314yes—
188C2×C4⋊Dic53C2314yes—
189C2×#11719919C2318yes—
190C2×#11719919C2314yes—
191C4⋊C4×D53C23116yes—
192C4⋊C4×D53C23116yes—
193C2×C22⋊Dic53C2318yes—
194C2×#11719921C2318yes—
195C2×#11719921C2314yes—
196C22⋊C4×D53C23132yes—
197C2×C4×Dic53C2314yes—
198C2×#41×C53—216no—
199C2×#41×C53C2314yes—
200C2×#41×C53C2314yes—
201C2×#41×C53C2314yes—
202C2×#41×C53C2314yes—
203C22×Q8×C53C2312yes—
204C22×D4×C53C2314yes—
205C22×D4×C53C2312yes—
206C23×C4×C53C2314yes—
207C23×C4×C53C2311yescharacteristic
208C4⋊Q8×C53C2314yes—
209#127×C53C2314yes—
210#124×C53C2318yes—
211#123×C53C23116yes—
212C22⋊Q8×C53C2318yes—
213C22⋊Q8×C53C2318yes—
214#121×C53C2318yes—
215#121×C53C2318yes—
216#121×C53C2318yes—
217#121×C53C2318yes—
218#120×C53C23116yes—
219C4×D4×C53C2318yes—
220C4×D4×C53C2318yes—
221#117×C53C2314yes—
222#117×C53C2314yes—
223C2×C4⋊C4×C53C2311yescharacteristic
224C2×C4⋊C4×C53C2311yescharacteristic
225C2×C22⋊C4×C53C2312yes—
226C2×C42×C53C2312yes—
227C24×C53C2414yes—
228C24×C53C2411yescharacteristic
229C23×D53C24116yes—
230C23×D53C2414yes—
231C23×D53C2412yes—
232#41×C53—216no—
233#41×C53—216no—
234#41×C53—216no—
235#41×C53—216no—
236C2×Q8×C53—28no—
237C2×Q8×C53C2414yes—
238C2×Q8×C53C2414yes—
239C2×D4×C53—216no—
240C2×D4×C53—28no—
241C2×D4×C53C2418yes—
242C2×D4×C53C2414yes—
243C2×D4×C53C2418yes—
244C2×D4×C53C2414yes—
245C2×D4×C53C2418yes—
246C2×D4×C53C2418yes—
247C22×C4×C53—216no—
248C22×C4×C53C2×D418yescomplemented
249C22×C4×C53C2418yes—
250C22×C4×C53C2418yes—
251C22×C4×C53C2414yes—
252C22×C4×C53C2412yes—
253C22×C4×C53C2412yes—
254C22×C4×C53C2411yescharacteristic
255C22×C4×C53C2411yescharacteristic
256C22×C4×C53C2412yes—
257C22×C4×C53C2412yes—
258C2×C22⋊D53—216no—
259C2×C22⋊D53—264no—
260C2×C22⋊D53—88no—
261C2×C22⋊D53C2×D4116yescomplemented
262C2×C22⋊D53C24116yes—
263C2×C22⋊D53C2418yes—
264C2×C22⋊D53C2418yes—
265C2×C22⋊D53C24116yes—
266C2×C22⋊D53C24132yes—
267C2×C22⋊D53C2418yes—
268C22×Dic53—82no—
269C22×Dic53C2414yes—
270C22×Dic53C24116yes—
271C22×Dic53C2414yes—
272C22×Dic53C2418yes—
273C22×Dic53C2412yes—
274#11719949—232no—
275#11719949—232no—
276Q8×D53—232no—
277Q8×D53—232no—
278#11719947—264no—
279#11719947—264no—
280#11719947—232no—
281#11719947—232no—
282D4×D53—264no—
283D4×D53—264no—
284D4×D53—232no—
285D4×D53—232no—
286D4×D53—816no—
287#11719945—216no—
288#11719945—216no—
289#11719945—216no—
290#11719945—216no—
291#11719945—264no—
292#11719945—232no—
293#11719945—264no—
294#11719945—232no—
295#11719945C2×D4132yescomplemented
296#11719945C2×D4132yescomplemented
297C2×D212—28no—
298C2×D212—232no—
299C2×D212C2×D418yescomplemented
300C2×D212C24116yes—
301C2×D212C2414yes—
302C2×D212C2414yes—
303C2×D212C2418yes—
304C2×D212C2418yes—
305C2×D212C2412yes—
306C2×D212C2412yes—
307C2×C4×D53—216no—
308C2×C4×D53—264no—
309C2×C4×D53—84no—
310C2×C4×D53C2×D4116yescomplemented
311C2×C4×D53C24116yes—
312C2×C4×D53C24116yes—
313C2×C4×D53C2418yes—
314C2×C4×D53C2418yes—
315C2×C4×D53C24116yes—
316C2×C4×D53C2418yes—
317C2×Dic106—28no—
318C2×Dic106—232no—
319C2×Dic106C2×D418yescomplemented
320C2×Dic106C24116yes—
321C2×Dic106C2414yes—
322C2×Dic106C2414yes—
323C2×Dic106C2412yes—
324C2×Dic106C2412yes—
325C4⋊C4×C53C2414yes—
326C4⋊C4×C53C2414yes—
327C4⋊C4×C53C2418yes—
328C4⋊C4×C53C2418yes—
329C22⋊C4×C53C2418yes—
330C22⋊C4×C53C24116yes—
331C22⋊C4×C53C24116yes—
332C42×C53C2414yes—
333C42×C53C2414yes—
334C22⋊Dic53C24132yes—
335#11719921C24116yes—
336#11719921C24132yes—
337#11719921C24116yes—
338#11719921C24116yes—
339C4⋊Dic53C2418yes—
340C4⋊Dic53C2418yes—
341C4⋊Dic53C2414yes—
342C4⋊Dic53C2414yes—
343C4⋊Dic53C2418yes—
344#11719919C24116yes—
345#11719919C24132yes—
346C4×Dic53C24116yes—
347C23×C53—28no—
348C23×C53—41no—
349C23×C53—41no—
350C23×C53—44no—
351C23×C53—44no—
352C23×C53C22×D414yes—
353C23×C53C2518yes—
354C23×C53C2511yescharacteristic
355C23×C53C2512yes—
356C22×D53—28no—
357C22×D53—232no—
358C22×D53—42no—
359C22×D53—42no—
360C22×D53—416no—
361C22×D53—44no—
362C22×D53—416no—
363C22×D53—44no—
364C22×D53C22×D418yes—
365C22×D53C2518yes—
366C22×D53C2514yes—
367Q8×C53—28no—
368Q8×C53—28no—
369D4×C53—216no—
370D4×C53—216no—
371D4×C53—28no—
372D4×C53—28no—
373D4×C53—48no—
374D4×C53—48no—
375C2×C4×C53—28no—
376C2×C4×C53—216no—
377C2×C4×C53—216no—
378C2×C4×C53—42no—
379C2×C4×C53—42no—
380C2×C4×C53C22×D418yes—
381C2×C4×C53C22×D414yes—
382C2×C4×C53C22×D418yes—
383C2×C4×C53C22×D414yes—
384C2×C4×C53C2518yes—
385C2×C4×C53C2514yes—
386C2×C4×C53C2514yes—
387C2×C4×C53C2511yescharacteristic
388C2×C4×C53C2512yes—
389C2×C4×C53C2511yescharacteristic
390C22⋊D53—216no—
391C22⋊D53—216no—
392C22⋊D53—232no—
393C22⋊D53—232no—
394C22⋊D53—432no—
395C22⋊D53C22×D4132yes—
396C2×Dic53—28no—
397C2×Dic53—232no—
398C2×Dic53—44no—
399C2×Dic53—48no—
400C2×Dic53C22×D418yes—
401C2×Dic53C2518yes—
402C2×Dic53C2518yes—
403C2×Dic53C2514yes—
404D212—232no—
405D212—28no—
406D212—28no—
407D212—48no—
408D212—48no—
409D212C22×D418yes—
410D212C22×D418yes—
411C4×D53—232no—
412C4×D53—216no—
413C4×D53—216no—
414C4×D53—232no—
415C4×D53—416no—
416C4×D53C22×D4132yes—
417Dic106—28no—
418Dic106—28no—
419Dic106—232no—
420Dic106C22×D418yes—
421Dic106C22×D418yes—
422#62853—531nomaximal, Sylow
423C22×C53—21no—
424C22×C53—22no—
425C22×C53—21no—
426C22×C53—22no—
427C22×C53—28no—
428C22×C53—28no—
429C22×C53—28no—
430C22×C53—44no—
431C22×C53—88no—
432C22×C53C23×D414yes—
433C22×C53C23×D412yes—
434C22×C53C2611yescharacteristic
435C2×D53—24no—
436C2×D53—24no—
437C2×D53—28no—
438C2×D53—28no—
439C2×D53—28no—
440C2×D53—48no—
441C2×D53—832no—
442C2×D53—88no—
443C2×D53C23×D418yes—
444C4×C53—28no—
445C4×C53—24no—
446C4×C53—24no—
447C4×C53C23×D412yes—
448C4×C53C23×D414yes—
449C4×C53C23×D412yes—
450Dic53—28no—
451Dic53—28no—
452Dic53C23×D418yes—
453C2×#585—532no—
454#3497—534no—
455#3496—538no—
456#3496—534no—
457#3489—538no—
458#3489—538no—
459#3488—538no—
460#3488—538no—
461#3449—534no—
462#3449—531no—
463#3449D5311yescharacteristic, complemented
464C2×#537—532no—
465C2×#537—534no—
466C2×#520—531no—
467C2×C53—22no—
468C2×C53—24no—
469C2×C53—48no—
470C2×C53C24×D411yescharacteristic
471C2×C53H(7,𝔽2)11yescharacteristic
472C2×C532−1+611yescharacteristic
473D53—28no—
474D53—48no—
475#585—10632no—
476C2×2−1+4—534no—
477C2×2−1+4—534no—
478C2×2−1+4—534no—
479C2×H(5,𝔽2)—534no—
480C2×H(5,𝔽2)—534no—
481C2×H(5,𝔽2)—534no—
482C2×H(5,𝔽2)—538no—
483C22×#41—538no—
484C22×#41—538no—
485C22×#41—531no—
486C22×#41—532no—
487C22×#41—538no—
488C22×#41C2×D5312yescomplemented
489#550—538no—
490#550—538no—
491D4×Q8—538no—
492D4×Q8—538no—
493#548—5316no—
494#548—5316no—
495#547—538no—
496#547—5332no—
497#547—538no—
498#546—5316no—
499#546—5332no—
500#546—5332no—
501#546—5316no—
502D42—538no—
503D42—5332no—
504D42—538no—
505#537—538no—
506#537—538no—
507#537—538no—
508#537—538no—
509#537—5316no—
510#537—5316no—
511#537—5316no—
512#537—532no—
513#537—532no—
514#537C2×D5312yescomplemented
515#537C2×D5312yescomplemented
516#536—5316no—
517#536—534no—
518#536C2×D5314yescomplemented
519#535—5316no—
520#535—534no—
521#535C2×D5314yescomplemented
522#534—5316no—
523#534—534no—
524#534C2×D5314yescomplemented
525#532—5316no—
526#532—534no—
527#532C2×D5314yescomplemented
528#525—5316no—
529#525—5316no—
530#525—538no—
531#525C2×D5318yescomplemented
532C2×C22⋊Q8—534no—
533C2×C22⋊Q8—534no—
534C2×C22⋊Q8—5316no—
535C2×#121—534no—
536C2×#121—538no—
537C2×#121—534no—
538C2×#121—5316no—
539C2×#121—5316no—
540#520—538no—
541#520—538no—
542C2×C4×Q8—532no—
543C2×C4×D4—534no—
544C2×C4×D4—532no—
545C2×#117—532no—
546C2×#117C2×D5311yescharacteristic, complemented
547C22×C4⋊C4—531no—
548C22×C4⋊C4—532no—
549C53#6285311yescharacteristic, complemented, Sylow
5502−1+4—10632no—
5512−1+4—10632no—
5522−1+4—10632no—
553H(5,𝔽2)—10664no—
554H(5,𝔽2)—10632no—
555H(5,𝔽2)—10632no—
556H(5,𝔽2)—10632no—
557C2×#41—216no—
558C2×#41—538no—
559C2×#41—538no—
560C2×#41—538no—
561C2×#41—5316no—
562C2×#41—5316no—
563C2×#41—538no—
564C2×#41—5316no—
565C2×#41—534no—
566C2×#41—534no—
567C2×#41—534no—
568C2×#41—534no—
569C2×#41—5316no—
570C2×#41—534no—
571C2×#41—534no—
572C2×#41—538no—
573C2×#41—5316no—
574C2×#41—538no—
575C2×#41—10664no—
576C2×#41—10664no—
577C2×#41—10664no—
578C2×#41—10616no—
579C2×#41C22×D5314yes—
580C2×#41C22×D5314yes—
581C2×#41C22×D5314yes—
582C2×#41C22×D5314yes—
583C22×Q8—538no—
584C22×Q8—538no—
585C22×Q8—531no—
586C22×Q8—532no—
587C22×Q8—538no—
588C22×Q8C22×D5312yes—
589C22×D4—532no—
590C22×D4—534no—
591C22×D4—5316no—
592C22×D4—538no—
593C22×D4—5316no—
594C22×D4—538no—
595C22×D4—5316no—
596C22×D4—538no—
597C22×D4—5316no—
598C22×D4—531no—
599C22×D4—532no—
600C22×D4—538no—
601C22×D4C22×D5314yes—
602C22×D4C22×D5312yes—
603C23×C4—532no—
604C23×C4—532no—
605C23×C4—5316no—
606C23×C4—534no—
607C23×C4—534no—
608C23×C4C22×D5314yes—
609C23×C4C22×D5311yescharacteristic
610C4⋊Q8—5316no—
611C4⋊Q8—534no—
612C4⋊Q8C22×D5314yes—
613#127—5316no—
614#127—534no—
615#127C22×D5314yes—
616#124—5332no—
617#124—538no—
618#124C22×D5318yes—
619#123—5332no—
620#123—5332no—
621#123—5316no—
622#123C22×D53116yes—
623C22⋊Q8—5316no—
624C22⋊Q8—5316no—
625C22⋊Q8—5316no—
626C22⋊Q8—5316no—
627C22⋊Q8—538no—
628C22⋊Q8—5332no—
629C22⋊Q8—538no—
630C22⋊Q8—5332no—
631C22⋊Q8C22×D5318yes—
632C22⋊Q8C22×D5318yes—
633#121—5316no—
634#121—5332no—
635#121—5316no—
636#121—5332no—
637#121—5316no—
638#121—5332no—
639#121—5316no—
640#121—538no—
641#121—5316no—
642#121—538no—
643#121—538no—
644#121—5316no—
645#121—538no—
646#121—5332no—
647#121—5332no—
648#121C22×D5318yes—
649#121C22×D5318yes—
650#121C22×D5318yes—
651#121C22×D5318yes—
652#120—5332no—
653#120—5332no—
654#120—5316no—
655#120C22×D53116yes—
656C4×Q8—538no—
657C4×Q8—538no—
658C4×D4—5316no—
659C4×D4—5316no—
660C4×D4—5332no—
661C4×D4—5332no—
662C4×D4—538no—
663C4×D4—538no—
664C4×D4—538no—
665C4×D4—538no—
666C4×D4C22×D5318yes—
667C4×D4C22×D5318yes—
668#117—5316no—
669#117C22×D5314yes—
670#117C22×D5314yes—
671C2×C4⋊C4—532no—
672C2×C4⋊C4—534no—
673C2×C4⋊C4—532no—
674C2×C4⋊C4—534no—
675C2×C4⋊C4—534no—
676C2×C4⋊C4—538no—
677C2×C4⋊C4—5316no—
678C2×C4⋊C4—5316no—
679C2×C4⋊C4C22×D5311yescharacteristic
680C2×C4⋊C4C22×D5311yescharacteristic
681C2×C22⋊C4—538no—
682C2×C22⋊C4—534no—
683C2×C22⋊C4—538no—
684C2×C22⋊C4—5332no—
685C2×C22⋊C4C22×D5312yes—
686C2×C42—534no—
687C2×C42C22×D5312yes—
688C24—532no—
689C24—5316no—
690C24—534no—
691C24C23×D5314yes—
692C24C23×D5311yescharacteristic
693#41—216no—
694#41—216no—
695#41—216no—
696#41—216no—
697#41—5332no—
698#41—5332no—
699#41—10664no—
700#41—10664no—
701#41—10632no—
702#41—10632no—
703#41—10664no—
704#41—10632no—
705#41—10632no—
706#41—10664no—
707#41—10632no—
708#41—10632no—
709#41—10616no—
710#41—10616no—
711#41—10616no—
712#41—10616no—
713C2×Q8—28no—
714C2×Q8—538no—
715C2×Q8—532no—
716C2×Q8—532no—
717C2×Q8—534no—
718C2×Q8—5316no—
719C2×Q8—534no—
720C2×Q8—10632no—
721C2×Q8—10632no—
722C2×Q8—10632no—
723C2×Q8—1068no—
724C2×Q8C23×D5314yes—
725C2×Q8C23×D5314yes—
726C2×D4—216no—
727C2×D4—28no—
728C2×D4—5316no—
729C2×D4—538no—
730C2×D4—5316no—
731C2×D4—538no—
732C2×D4—538no—
733C2×D4—5316no—
734C2×D4—5332no—
735C2×D4—538no—
736C2×D4—532no—
737C2×D4—532no—
738C2×D4—5316no—
739C2×D4—534no—
740C2×D4—534no—
741C2×D4—538no—
742C2×D4—538no—
743C2×D4—10632no—
744C2×D4—10632no—
745C2×D4—10664no—
746C2×D4—10632no—
747C2×D4—10664no—
748C2×D4—10664no—
749C2×D4—10616no—
750C2×D4—1068no—
751C2×D4—42416no—
752C2×D4—4248no—
753C2×D4C23×D5318yes—
754C2×D4C23×D5318yes—
755C2×D4C23×D5314yes—
756C2×D4C23×D5314yes—
757C2×D4C23×D5318yes—
758C2×D4C23×D5318yes—
759C22×C4—216no—
760C22×C4—532no—
761C22×C4—5316no—
762C22×C4—538no—
763C22×C4—534no—
764C22×C4—5316no—
765C22×C4—534no—
766C22×C4—538no—
767C22×C4—5316no—
768C22×C4—5316no—
769C22×C4—538no—
770C22×C4—538no—
771C22×C4—5316no—
772C22×C4—10664no—
773C22×C4—10616no—
774C22×C4—4244no—
775C22×C4—4242no—
776C22×C4D4×D5318yescomplemented
777C22×C4C23×D5314yes—
778C22×C4C23×D5318yes—
779C22×C4C23×D5318yes—
780C22×C4C23×D5312yes—
781C22×C4C23×D5312yes—
782C22×C4C23×D5311yescharacteristic
783C22×C4C23×D5311yescharacteristic
784C22×C4C23×D5312yes—
785C22×C4C23×D5312yes—
786C4⋊C4—538no—
787C4⋊C4—5316no—
788C4⋊C4—534no—
789C4⋊C4—534no—
790C4⋊C4—5332no—
791C4⋊C4—538no—
792C4⋊C4—538no—
793C4⋊C4C23×D5314yes—
794C4⋊C4C23×D5318yes—
795C4⋊C4C23×D5314yes—
796C4⋊C4C23×D5318yes—
797C22⋊C4—5332no—
798C22⋊C4—5332no—
799C22⋊C4—5316no—
800C22⋊C4—5316no—
801C22⋊C4—5316no—
802C22⋊C4C23×D53116yes—
803C22⋊C4C23×D5318yes—
804C22⋊C4C23×D53116yes—
805C42—5316no—
806C42C23×D5314yes—
807C42C23×D5314yes—
808C23—28no—
809C23—41no—
810C23—41no—
811C23—44no—
812C23—44no—
813C23—534no—
814C23—538no—
815C23—538no—
816C23—10632no—
817C23—1068no—
818C23—2124no—
819C23—21216no—
820C23—2124no—
821C23—21216no—
822C23—2122no—
823C23—2122no—
824C23C2×D4×D5314yes—
825C23C24×D5318yes—
826C23C24×D5312yes—
827C23C24×D5311yescharacteristic
828Q8—28no—
829Q8—28no—
830Q8—538no—
831Q8—538no—
832Q8—10632no—
833Q8—1068no—
834Q8—1068no—
835D4—216no—
836D4—216no—
837D4—28no—
838D4—28no—
839D4—48no—
840D4—48no—
841D4—5332no—
842D4—538no—
843D4—538no—
844D4—10632no—
845D4—10632no—
846D4—10632no—
847D4—10616no—
848D4—10616no—
849D4—1068no—
850D4—1068no—
851D4—2128no—
852D4—2128no—
853D4—21232no—
854C2×C4—28no—
855C2×C4—216no—
856C2×C4—216no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—538no—
860C2×C4—534no—
861C2×C4—5332no—
862C2×C4—538no—
863C2×C4—538no—
864C2×C4—10632no—
865C2×C4—10632no—
866C2×C4—10632no—
867C2×C4—1068no—
868C2×C4—10616no—
869C2×C4—10616no—
870C2×C4—21216no—
871C2×C4—2124no—
872C2×C4—2128no—
873C2×C4C2×D4×D5318yes—
874C2×C4C2×D4×D5314yes—
875C2×C4C2×D4×D5318yes—
876C2×C4C2×D4×D5314yes—
877C2×C4C24×D5314yes—
878C2×C4C24×D5314yes—
879C2×C4C24×D5318yes—
880C2×C4C24×D5311yescharacteristic
881C2×C4C24×D5311yescharacteristic
882C2×C4C24×D5312yes—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—22no—
887C22—28no—
888C22—28no—
889C22—28no—
890C22—44no—
891C22—88no—
892C22—538no—
893C22—1064no—
894C22—1064no—
895C22—1068no—
896C22—1068no—
897C22—1068no—
898C22—4248no—
899C22—42432no—
900C22—2128no—
901C22C22×D4×D5314yes—
902C22C22×D4×D5312yes—
903C22C25×D5311yescharacteristic
904C4—28no—
905C4—24no—
906C4—24no—
907C4—538no—
908C4—1068no—
909C4—1068no—
910C4C22×D4×D5312yes—
911C4C22×D4×D5314yes—
912C4C22×D4×D5312yes—
913C2—24no—
914C2—22no—
915C2—48no—
916C2—1068no—
917C2—2128no—
918C2C23×D4×D5311yescharacteristic
919C2#2028952611yescharacteristic
920C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3449C2
hypercenter#3449D53
hypocenterC53#62853
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. C2×#16811459C2semidirect
2. #20288481C2semidirect
3. #20288477C2semidirect
4. #20288476C2semidirect
5. #20288393C2semidirect
6. #20288387C2semidirect
7. #20288382C2semidirect
8. #20288376C2semidirect
9. #20288048C2semidirect
10. #20288043C2semidirect
11. C2×#16811201C2semidirect
12. #537×D53C2semidirect
13. C2×#16811103C2semidirect
14. C53×#3449C2semidirect
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. #16811294C22semidirect
29. #16811293C22semidirect
30. D4×Dic106C22semidirect
31. #16811288C22semidirect
32. #16811282C22semidirect
33. #16811281C22semidirect
34. #16811278C22semidirect
35. #16811276C22semidirect
36. #16811271C22semidirect
37. #16811269C22semidirect
38. #16811266C22semidirect
39. #16811265C22semidirect
40. #16811260C22semidirect
41. D4×D212C22semidirect
42. #16811258C22semidirect
43. #16811255C22semidirect
44. #16811204C22semidirect
45. #16811204C22semidirect
46. #16811203C22semidirect
47. #16811202C22semidirect
48. #16811201C22semidirect
49. #16811201C22semidirect
50. #16811201C22semidirect
51. #16811201C22semidirect
52. #16811200C22semidirect
53. #16811199C22semidirect
54. #16811196C22semidirect
55. #16811192C22semidirect
56. #16811189C22semidirect
57. #16811185C22semidirect
58. #16811181C22semidirect
59. #16811173C22semidirect
60. #16811168C22semidirect
61. #16811136C22semidirect
62. #16811135C22semidirect
63. #16811133C22semidirect
64. C2×#13133196C22semidirect
65. C2×#13133193C22semidirect
66. C22⋊Q8×D53C22semidirect
67. C2×#13133191C22semidirect
68. C2×#13133189C22semidirect
69. C2×#13133188C22semidirect
70. #121×D53C22semidirect
71. #121×D53C22semidirect
72. #16811103C22semidirect
73. #16811103C22semidirect
74. C2×C4×Dic106C22semidirect
75. C2×C4×D212C22semidirect
76. C2×#13133177C22semidirect
77. C2×#13133175C22semidirect
78. C22×C4⋊Dic53C22semidirect
79. C2×C4⋊C4×D53C22semidirect
80. C22×#41×C53C22semidirect
81. C53×#537C22semidirect
82. C53×#537C22semidirect
83. C53×#536C22semidirect
84. C53×#535C22semidirect
85. C53×#534C22semidirect
86. C53×#532C22semidirect
87. C53×#525C22semidirect
88. C2×#117×C53C22semidirect
100. C2×#11719945D4semidirect
248. C22×C4×C53C2×D4semidirect
261. C2×C22⋊D53C2×D4semidirect
295. #11719945C2×D4semidirect
296. #11719945C2×D4semidirect
299. C2×D212C2×D4semidirect
310. C2×C4×D53C2×D4semidirect
319. C2×Dic106C2×D4semidirect
463. #3449D53semidirect
488. C22×#41C2×D53semidirect
514. #537C2×D53semidirect
515. #537C2×D53semidirect
518. #536C2×D53semidirect
521. #535C2×D53semidirect
524. #534C2×D53semidirect
527. #532C2×D53semidirect
531. #525C2×D53semidirect
546. C2×#117C2×D53semidirect
549. C53#62853semidirect
776. 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
#202884812
#202884772
#202884762
#202883932
#202883872
#202883822
#202883762
#202880482
#202880432
C2×#168112012
#537×D532
C2×#168111032
C53×#34492
#6285353