Finite Group Databasebeta

← #28293206

Subgroups — #28293206

Order 13568.

11222 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16811458C212yesmaximal, complemented
2#20288484C212yesmaximal, complemented
3#20288481C212yesmaximal, complemented
4#20288479C211yesmaximal, characteristic, complemented
5#20288476C214yesmaximal, complemented
6#20288474C212yesmaximal, complemented
7#20288472C214yesmaximal, complemented
8#20288389C218yesmaximal, complemented
9#20288386C218yesmaximal, complemented
10#20288378C218yesmaximal, complemented
11#20288375C218yesmaximal, complemented
12#20288042C212yesmaximal, complemented
13#20288041C214yesmaximal, complemented
14C2×#16811200C214yesmaximal, complemented
15#537×D53C212yesmaximal, complemented
16C2×#16811102C211yesmaximal, characteristic, complemented
17C53×#3496C211yesmaximal, characteristic, complemented
18#16811458—232no—
19C2×#13133264C2218yescomplemented
20C2×#13133264C2214yescomplemented
21C2×#13133262C2218yescomplemented
22C2×#13133262C2218yescomplemented
23C2×#13133262C2212yescomplemented
24C22×#11719947C2211yescharacteristic
25C22×#11719947C2218yescomplemented
26C22×#11719947C2218yescomplemented
27C2×#41×D53C2214yescomplemented
28C2×#41×D53C2218yescomplemented
29#16811294C2214yescomplemented
30#16811293C2214yescomplemented
31#16811291C2218yescomplemented
32D4×Dic106C2214yescomplemented
33#16811288C2214yescomplemented
34#16811286C2218yescomplemented
35#16811283C2218yescomplemented
36#16811282C2218yescomplemented
37#16811281C2218yescomplemented
38#16811279C2218yescomplemented
39#16811277C2214yescomplemented
40#16811274C2218yescomplemented
41#16811273C2218yescomplemented
42#16811272C2218yescomplemented
43#16811271C22116yescomplemented
44#16811268C2218yescomplemented
45#16811267C2218yescomplemented
46#16811265C22116yescomplemented
47#16811263C22116yescomplemented
48#16811262C22116yescomplemented
49#16811261C2218yescomplemented
50#16811260C22116yescomplemented
51D4×D212C2214yescomplemented
52#16811257C2218yescomplemented
53D4×C22⋊D53C2218yescomplemented
54D4×C22⋊D53C2218yescomplemented
55#16811255C22116yescomplemented
56#16811204C2212yescomplemented
57#16811203C2218yescomplemented
58#16811202C2218yescomplemented
59#16811201C2214yescomplemented
60#16811200C2218yescomplemented
61#16811200C2214yescomplemented
62#16811200C22116yescomplemented
63#16811200C22116yescomplemented
64#16811200C2218yescomplemented
65#16811200C2218yescomplemented
66#16811200C2214yescomplemented
67#16811198C2214yescomplemented
68#16811195C22116yescomplemented
69#16811193C2214yescomplemented
70#16811191C2214yescomplemented
71#16811188C22116yescomplemented
72#16811186C2214yescomplemented
73#16811185C2214yescomplemented
74#16811182C2218yescomplemented
75#16811181C2214yescomplemented
76#16811181C2214yescomplemented
77#16811173C2212yescomplemented
78#16811169C2214yescomplemented
79#16811168C2218yescomplemented
80#16811168C2218yescomplemented
81#16811132C2218yescomplemented
82#16811132C2218yescomplemented
83#16811131C22116yescomplemented
84#16811129C22116yescomplemented
85C2×#13133195C2218yescomplemented
86C2×#13133194C2218yescomplemented
87C22⋊Q8×D53C2218yescomplemented
88C2×#13133191C2214yescomplemented
89C2×#13133190C2218yescomplemented
90C2×#13133189C2218yescomplemented
91C2×#13133189C2218yescomplemented
92#121×D53C2218yescomplemented
93#121×D53C2218yescomplemented
94#16811102C2218yescomplemented
95#16811102C2218yescomplemented
96C2×C4×Dic106C2211yescharacteristic, complemented
97C2×#13133182C2211yescharacteristic, complemented
98C2×D4×Dic53C2211yescharacteristic, complemented
99C2×C4×C22⋊D53C2212yescomplemented
100C2×#13133177C2212yescomplemented
101C2×#13133174C2211yescharacteristic, complemented
102C2×#13133173C2212yescomplemented
103C22×#11719919C2212yescomplemented
104C2×C4⋊C4×D53C2211yescharacteristic, complemented
105C2×H(5,𝔽2)×C53C2212yescomplemented
106C53×#547C2214yescomplemented
107C53×#546C2218yescomplemented
108D42×C53C2214yescomplemented
109C53×#537C2212yescomplemented
110C53×#534C2214yescomplemented
111C53×#532C2212yescomplemented
112C2×#121×C53C2214yescomplemented
113C2×C4×D4×C53C2211yescharacteristic, complemented
114#13133264—264no—
115#13133264—232no—
116#13133262—216no—
117#13133262—264no—
118#13133262—264no—
119C2×#11719949C2314yes—
120C2×#11719945C23116yes—
121C2×#11719945C2318yes—
122C2×#11719945C2318yes—
123C2×#11719945C2314yes—
124C2×#11719947—264no—
125C2×#11719947—264no—
126C2×#11719947D4116yescomplemented
127C2×#11719947C2318yes—
128C2×#11719947C23116yes—
129C2×#11719947C2318yes—
130C2×#11719947C23116yes—
131C2×#11719947C23116yes—
132C2×#11719947C2314yes—
133C2×#11719947C23116yes—
134C2×#11719947C2318yes—
135C2×#11719947C2318yes—
136#41×D53—264no—
137#41×D53—232no—
138C22×Dic106C2318yes—
139C22×Dic106C2318yes—
140C22×Dic106C2311yescharacteristic
141C2×Q8×D53C2318yes—
142C2×Q8×D53C2314yes—
143C22×D212C2314yes—
144C22×C22⋊D53C2318yes—
145C22×C22⋊D53C2318yes—
146C22×C22⋊D53C23116yes—
147C22×C22⋊D53C2318yes—
148C22×C22⋊D53C2312yes—
149C2×D4×D53C23116yes—
150C2×D4×D53C2318yes—
151C2×D4×D53C2318yes—
152C2×D4×D53C2314yes—
153C2×D4×D53C2318yes—
154C23×Dic53C2318yes—
155C23×Dic53C2312yes—
156C23×Dic53C2312yes—
157C22×C4×D53C2318yes—
158C22×C4×D53C2318yes—
159C22×C4×D53C2312yes—
160C22×C4×D53C2311yescharacteristic
161#13133217C2312yes—
162#13133216C2318yes—
163#13133216C2318yes—
164#13133215C2314yes—
165#13133214C2312yes—
166#13133213C2318yes—
167#13133213C2314yes—
168#13133213C2318yes—
169#13133206C2314yes—
170#13133205C2314yes—
171#13133204C2314yes—
172#13133203C23116yes—
173#13133203C23116yes—
174#13133202C2318yes—
175#13133202C2318yes—
176#13133201C23116yes—
177#13133200C23116yes—
178#13133199C2318yes—
179#13133199C2318yes—
180#13133198C23116yes—
181#13133197C2318yes—
182#13133196C2318yes—
183#13133195C23116yes—
184#13133195C23116yes—
185#13133195C23116yes—
186#13133195C2318yes—
187#13133195C2318yes—
188#13133194C23116yes—
189#13133194C23116yes—
190#13133194C23116yes—
191#13133194C2318yes—
192#13133194C2318yes—
193#13133193C2318yes—
194#13133192C2318yes—
195#13133192C2318yes—
196#13133191C2318yes—
197#13133191C2318yes—
198#13133191C2318yes—
199#13133191C2318yes—
200#13133191C2314yes—
201#13133191C2314yes—
202#13133190C23116yes—
203#13133190C23116yes—
204#13133190C23116yes—
205#13133190C23116yes—
206#13133190C2318yes—
207#13133190C2318yes—
208#13133189C23116yes—
209#13133189C23116yes—
210#13133189C23116yes—
211#13133189C23116yes—
212#13133189C23116yes—
213#13133189C23116yes—
214#13133189C2318yes—
215#13133189C2318yes—
216#13133189C2318yes—
217#13133189C2318yes—
218#13133188C2318yes—
219#13133188C2318yes—
220#13133187C2318yes—
221#13133187C23116yes—
222#13133187C2318yes—
223#13133186C23116yes—
224#13133185C23116yes—
225#13133185C2318yes—
226#13133185C2318yes—
227C4×Dic106C2314yes—
228C4×Dic106C2314yes—
229#13133182C2318yes—
230C4×D212C2314yes—
231C4×D212C2314yes—
232D4×Dic53C2318yes—
233D4×Dic53C2318yes—
234D4×Dic53C2318yes—
235#13133179C2318yes—
236#13133179C2318yes—
237C4×C22⋊D53C2318yes—
238C4×C22⋊D53C2318yes—
239C4×C22⋊D53C2318yes—
240C4×C22⋊D53C2318yes—
241#13133177C23116yes—
242#13133177C23116yes—
243#13133177C23116yes—
244#13133174C2314yes—
245#13133174C2314yes—
246#13133173C23116yes—
247C2×C4⋊Dic53C2314yes—
248C2×C4⋊Dic53C2311yescharacteristic
249C2×#11719919C2318yes—
250C2×#11719919C2312yes—
251C2×#11719919C2311yescharacteristic
252C2×#11719919C2312yes—
253C2×#11719919C2312yes—
254C2×#11719919C2318yes—
255C2×#11719919C2318yes—
256C2×#11719919C2311yescharacteristic
257C4⋊C4×D53C2318yes—
258C4⋊C4×D53C2318yes—
259C2×C22⋊Dic53C2318yes—
260C2×C22⋊Dic53C2312yes—
261C2×#11719921C2318yes—
262C2×#11719921C2318yes—
263C2×#11719921C2311yescharacteristic
264C2×#11719921C2311yescharacteristic
265C22⋊C4×D53C23116yes—
266C2×C4×Dic53C2312yes—
267C2×C4×Dic53C2312yes—
268C2×C4×Dic53C2311yescharacteristic
269H(5,𝔽2)×C53—216no—
270C2×#41×C53C2318yes—
271C2×#41×C53C2314yes—
272C22×D4×C53C2318yes—
273C22×D4×C53C2318yes—
274C22×D4×C53C2314yes—
275C22×D4×C53C2311yescharacteristic
276C23×C4×C53C2312yes—
277C4⋊Q8×C53C2312yes—
278#127×C53C2312yes—
279#124×C53C2314yes—
280#123×C53C23116yes—
281C22⋊Q8×C53C2318yes—
282#121×C53C2318yes—
283#121×C53C2318yes—
284#121×C53C2314yes—
285#121×C53C2318yes—
286#121×C53C2318yes—
287#121×C53C2314yes—
288#120×C53C23116yes—
289C4×D4×C53C2314yes—
290C4×D4×C53C2314yes—
291C4×D4×C53C2314yes—
292C4×D4×C53C2314yes—
293C2×C4⋊C4×C53C2314yes—
294C2×C4⋊C4×C53C2311yescharacteristic
295C2×C22⋊C4×C53C2312yes—
296C2×C22⋊C4×C53C2318yes—
297C2×C42×C53C2311yescharacteristic
298C24×C53C2418yes—
299C24×C53C2412yes—
300C23×D53C2418yes—
301C23×D53C2418yes—
302C23×D53C2411yescharacteristic
303#41×C53—232no—
304#41×C53—216no—
305C2×Q8×C53C2414yes—
306C2×D4×C53—232no—
307C2×D4×C53—232no—
308C2×D4×C53—84no—
309C2×D4×C53C2×D418yescomplemented
310C2×D4×C53C24116yes—
311C2×D4×C53C2418yes—
312C2×D4×C53C2414yes—
313C2×D4×C53C2414yes—
314C2×D4×C53C2414yes—
315C2×D4×C53C2418yes—
316C2×D4×C53C2414yes—
317C22×C4×C53—82no—
318C22×C4×C53C2418yes—
319C22×C4×C53C2418yes—
320C22×C4×C53C2411yescharacteristic
321C22×C4×C53C2411yescharacteristic
322C22×C4×C53C2414yes—
323C22×C4×C53C2412yes—
324C22×C4×C53C2414yes—
325C22×C4×C53C2411yescharacteristic
326C2×C22⋊D53—232no—
327C2×C22⋊D53—264no—
328C2×C22⋊D53—232no—
329C2×C22⋊D53—88no—
330C2×C22⋊D53C2×D4116yescomplemented
331C2×C22⋊D53C2418yes—
332C2×C22⋊D53C24116yes—
333C2×C22⋊D53C2418yes—
334C2×C22⋊D53C2418yes—
335C2×C22⋊D53C24116yes—
336C2×C22⋊D53C2418yes—
337C2×C22⋊D53C24116yes—
338C2×C22⋊D53C2418yes—
339C2×C22⋊D53C2418yes—
340C22×Dic53—232no—
341C22×Dic53—82no—
342C22×Dic53C2×D4116yescomplemented
343C22×Dic53C2418yes—
344C22×Dic53C24116yes—
345C22×Dic53C2418yes—
346C22×Dic53C2411yescharacteristic
347C22×Dic53C2411yescharacteristic
348C22×Dic53C2412yes—
349C22×Dic53C2418yes—
350C22×Dic53C2412yes—
351C22×Dic53C2411yescharacteristic
352C22×Dic53C2418yes—
353#11719949—216no—
354Q8×D53—216no—
355Q8×D53—232no—
356#11719947—232no—
357#11719947—264no—
358#11719947—264no—
359#11719947—232no—
360#11719947—264no—
361#11719947—264no—
362#11719947—216no—
363#11719947—232no—
364#11719947C2×D4164yescomplemented
365D4×D53—232no—
366D4×D53—232no—
367D4×D53—264no—
368D4×D53—216no—
369D4×D53—88no—
370#11719945—216no—
371#11719945—264no—
372#11719945—232no—
373#11719945—232no—
374C2×D212—84no—
375C2×D212C2418yes—
376C2×D212C2414yes—
377C2×D212C2414yes—
378C2×D212C2418yes—
379C2×D212C2414yes—
380C2×C4×D53—232no—
381C2×C4×D53—232no—
382C2×C4×D53—82no—
383C2×C4×D53C2×D418yescomplemented
384C2×C4×D53C2418yes—
385C2×C4×D53C24116yes—
386C2×C4×D53C2418yes—
387C2×C4×D53C2418yes—
388C2×C4×D53C2418yes—
389C2×C4×D53C2414yes—
390C2×Dic106—232no—
391C2×Dic106—232no—
392C2×Dic106C2×D418yescomplemented
393C2×Dic106C2418yes—
394C2×Dic106C24116yes—
395C2×Dic106C2414yes—
396C2×Dic106C2414yes—
397C4⋊C4×C53C2414yes—
398C4⋊C4×C53C2414yes—
399C4⋊C4×C53C2418yes—
400C4⋊C4×C53C2414yes—
401C22⋊C4×C53C2418yes—
402C22⋊C4×C53C2418yes—
403C22⋊C4×C53C24116yes—
404C22⋊C4×C53C2418yes—
405C42×C53C2412yes—
406C42×C53C2412yes—
407C22⋊Dic53C24116yes—
408C22⋊Dic53C2418yes—
409C22⋊Dic53C2418yes—
410C22⋊Dic53C2418yes—
411#11719921C24116yes—
412#11719921C24116yes—
413#11719921C2418yes—
414#11719921C2418yes—
415#11719921C2414yes—
416#11719921C2412yes—
417#11719921C2412yes—
418#11719921C2418yes—
419#11719921C2418yes—
420C4⋊Dic53C2414yes—
421C4⋊Dic53C2418yes—
422C4⋊Dic53C2414yes—
423C4⋊Dic53C2414yes—
424#11719919C2418yes—
425#11719919C24116yes—
426#11719919C2412yes—
427#11719919C2412yes—
428#11719919C2418yes—
429#11719919C2414yes—
430#11719919C2414yes—
431#11719919C2418yes—
432#11719919C2414yes—
433#11719919C2418yes—
434C4×Dic53C2418yes—
435C4×Dic53C2418yes—
436C4×Dic53C2414yes—
437C23×C53—216no—
438C23×C53—42no—
439C23×C53—42no—
440C23×C53—48no—
441C23×C53—48no—
442C23×C53C22×D418yes—
443C23×C53C2518yes—
444C23×C53C2511yescharacteristic
445C23×C53C2514yes—
446C22×D53—216no—
447C22×D53—216no—
448C22×D53—41no—
449C22×D53—41no—
450C22×D53—48no—
451C22×D53—48no—
452C22×D53—48no—
453C22×D53—48no—
454C22×D53C22×D414yes—
455C22×D53C2518yes—
456C22×D53C2512yes—
457Q8×C53—28no—
458D4×C53—232no—
459D4×C53—216no—
460D4×C53—28no—
461D4×C53—48no—
462D4×C53—44no—
463D4×C53—44no—
464D4×C53C22×D4116yes—
465C2×C4×C53—216no—
466C2×C4×C53—216no—
467C2×C4×C53—42no—
468C2×C4×C53—44no—
469C2×C4×C53—41no—
470C2×C4×C53—44no—
471C2×C4×C53—41no—
472C2×C4×C53C22×D414yes—
473C2×C4×C53C2518yes—
474C2×C4×C53C2514yes—
475C2×C4×C53C2511yescharacteristic
476C2×C4×C53C2512yes—
477C2×C4×C53C2511yescharacteristic
478C2×C4×C53C2512yes—
479C22⋊D53—232no—
480C22⋊D53—216no—
481C22⋊D53—216no—
482C22⋊D53—232no—
483C22⋊D53—216no—
484C22⋊D53—416no—
485C22⋊D53—48no—
486C22⋊D53—48no—
487C22⋊D53C22×D4132yes—
488C2×Dic53—216no—
489C2×Dic53—232no—
490C2×Dic53—216no—
491C2×Dic53—42no—
492C2×Dic53—41no—
493C2×Dic53—48no—
494C2×Dic53—41no—
495C2×Dic53C22×D4132yes—
496C2×Dic53C22×D418yes—
497C2×Dic53C22×D414yes—
498C2×Dic53C2518yes—
499C2×Dic53C2514yes—
500C2×Dic53C2512yes—
501C2×Dic53C2512yes—
502C2×Dic53C2514yes—
503C2×Dic53C2512yes—
504D212—216no—
505D212—28no—
506D212—44no—
507D212—48no—
508D212—44no—
509C4×D53—216no—
510C4×D53—216no—
511C4×D53—216no—
512C4×D53—232no—
513C4×D53—48no—
514C4×D53C22×D4116yes—
515Dic106—28no—
516Dic106—232no—
517Dic106—216no—
518Dic106C22×D4116yes—
519#62853—531nomaximal, Sylow
520C22×C53—21no—
521C22×C53—24no—
522C22×C53—21no—
523C22×C53—24no—
524C22×C53—28no—
525C22×C53—28no—
526C22×C53—28no—
527C22×C53—48no—
528C22×C53—816no—
529C22×C53C23×D418yes—
530C22×C53C23×D412yes—
531C22×C53C2611yescharacteristic
532C2×D53—22no—
533C2×D53—22no—
534C2×D53—28no—
535C2×D53—28no—
536C2×D53—28no—
537C2×D53—44no—
538C2×D53—816no—
539C2×D53—816no—
540C2×D53C23×D414yes—
541C4×C53—28no—
542C4×C53—24no—
543C4×C53—21no—
544C4×C53—21no—
545C4×C53—22no—
546C4×C53C23×D414yes—
547Dic53—28no—
548Dic53—24no—
549Dic53—22no—
550Dic53—22no—
551Dic53C23×D418yes—
552Dic53C23×D414yes—
553C2×#585—532no—
554#3497—532no—
555#3497—532no—
556#3496—532no—
557#3496—534no—
558#3496—534no—
559#3496—531no—
560#3496D5311yescharacteristic, complemented
561#3489—538no—
562#3489—538no—
563#3488—538no—
564#3488—538no—
565#3449—534no—
566#3449—532no—
567C2×#537—532no—
568C2×#537—534no—
569C2×#520—531no—
570C2×C53—22no—
571C2×C53—28no—
572C2×C53—48no—
573C2×C53C24×D411yescharacteristic
574C2×C53H(7,𝔽2)11yescharacteristic
575C2×C532−1+611yescharacteristic
576D53—24no—
577D53—48no—
578#585—10632no—
579C2×2−1+4—538no—
580C2×2−1+4—534no—
581C2×H(5,𝔽2)—538no—
582C2×H(5,𝔽2)—538no—
583C2×H(5,𝔽2)—532no—
584C2×H(5,𝔽2)C2×D5312yescomplemented
585C22×#41—534no—
586C22×#41—538no—
587C22×#41—531no—
588C22×#41—538no—
589C22×#41—538no—
590#550—534no—
591#550—538no—
592#550—534no—
593D4×Q8—534no—
594D4×Q8—538no—
595D4×Q8—534no—
596#548—538no—
597#548—538no—
598#548—538no—
599#548—538no—
600#547—538no—
601#547—5316no—
602#547—538no—
603#547—534no—
604#547—538no—
605#547C2×D5314yescomplemented
606#546—538no—
607#546—538no—
608#546—5316no—
609#546—5316no—
610#546—5316no—
611#546—538no—
612#546—5316no—
613#546C2×D5318yescomplemented
614D42—538no—
615D42—538no—
616D42—538no—
617D42—5316no—
618D42—534no—
619D42C2×D5314yescomplemented
620#537—534no—
621#537—538no—
622#537—538no—
623#537—534no—
624#537—5316no—
625#537—5316no—
626#537—538no—
627#537—538no—
628#537—538no—
629#537—534no—
630#537—532no—
631#537C2×D5312yescomplemented
632#536—534no—
633#536—534no—
634#536—5316no—
635#535—534no—
636#535—534no—
637#535—5316no—
638#534—538no—
639#534—534no—
640#534—534no—
641#534—534no—
642#534C2×D5314yescomplemented
643#532—534no—
644#532—538no—
645#532—538no—
646#532—532no—
647#532C2×D5312yescomplemented
648#525—5316no—
649#525—5316no—
650#525—538no—
651#525—538no—
652C2×C22⋊Q8—538no—
653C2×C22⋊Q8—538no—
654C2×C22⋊Q8—538no—
655C2×#121—538no—
656C2×#121—538no—
657C2×#121—534no—
658C2×#121—538no—
659C2×#121—538no—
660C2×#121—538no—
661C2×#121C2×D5314yescomplemented
662#520—538no—
663#520—538no—
664C2×C4×Q8—531no—
665C2×C4×Q8—531no—
666C2×C4×D4—531no—
667C2×C4×D4—532no—
668C2×C4×D4—532no—
669C2×C4×D4C2×D5311yescharacteristic, complemented
670C2×#117—532no—
671C2×#117—531no—
672C22×C4⋊C4—532no—
673C22×C4⋊C4—531no—
674C53#6285311yescharacteristic, complemented, Sylow
6752−1+4—10632no—
6762−1+4—10664no—
677H(5,𝔽2)—216no—
678H(5,𝔽2)—10664no—
679H(5,𝔽2)—10664no—
680H(5,𝔽2)—10616no—
681C2×#41—534no—
682C2×#41—5316no—
683C2×#41—538no—
684C2×#41—5316no—
685C2×#41—5316no—
686C2×#41—5316no—
687C2×#41—534no—
688C2×#41—538no—
689C2×#41—538no—
690C2×#41—5316no—
691C2×#41—538no—
692C2×#41—538no—
693C2×#41—534no—
694C2×#41—5316no—
695C2×#41—538no—
696C2×#41—10664no—
697C2×#41—10632no—
698C2×#41—10664no—
699C2×#41—10664no—
700C2×#41C22×D5314yes—
701C2×#41C22×D5318yes—
702C22×Q8—534no—
703C22×Q8—538no—
704C22×Q8—531no—
705C22×Q8—538no—
706C22×Q8—538no—
707C22×D4—532no—
708C22×D4—538no—
709C22×D4—538no—
710C22×D4—5316no—
711C22×D4—538no—
712C22×D4—538no—
713C22×D4—534no—
714C22×D4—5316no—
715C22×D4—538no—
716C22×D4—538no—
717C22×D4—534no—
718C22×D4C22×D5318yes—
719C22×D4C22×D5318yes—
720C22×D4C22×D5314yes—
721C22×D4C22×D5311yescharacteristic
722C23×C4—532no—
723C23×C4—531no—
724C23×C4—538no—
725C23×C4—532no—
726C23×C4—538no—
727C23×C4—538no—
728C23×C4—532no—
729C23×C4C22×D5312yes—
730C4⋊Q8—534no—
731C4⋊Q8—538no—
732C4⋊Q8—538no—
733C4⋊Q8—532no—
734C4⋊Q8C22×D5312yes—
735#127—538no—
736#127—538no—
737#127—534no—
738#127—532no—
739#127C22×D5312yes—
740#124—534no—
741#124—534no—
742#124—5316no—
743#124—5316no—
744#124—534no—
745#124C22×D5314yes—
746#123—5316no—
747#123—5316no—
748#123—538no—
749#123—538no—
750#123—538no—
751#123—538no—
752#123—5316no—
753#123C22×D53116yes—
754C22⋊Q8—538no—
755C22⋊Q8—538no—
756C22⋊Q8—5316no—
757C22⋊Q8—538no—
758C22⋊Q8—5316no—
759C22⋊Q8—5316no—
760C22⋊Q8—538no—
761C22⋊Q8—538no—
762C22⋊Q8—5316no—
763C22⋊Q8—538no—
764C22⋊Q8—5316no—
765C22⋊Q8—5316no—
766C22⋊Q8—538no—
767C22⋊Q8C22×D5318yes—
768#121—5316no—
769#121—538no—
770#121—538no—
771#121—5316no—
772#121—538no—
773#121—5316no—
774#121—5316no—
775#121—538no—
776#121—5316no—
777#121—5316no—
778#121—538no—
779#121—538no—
780#121—538no—
781#121—534no—
782#121—538no—
783#121—538no—
784#121—538no—
785#121—534no—
786#121—538no—
787#121—538no—
788#121—5316no—
789#121—538no—
790#121—5316no—
791#121—5316no—
792#121—5316no—
793#121—538no—
794#121C22×D5318yes—
795#121C22×D5318yes—
796#121C22×D5314yes—
797#121C22×D5318yes—
798#121C22×D5318yes—
799#121C22×D5314yes—
800#120—5316no—
801#120—538no—
802#120—5316no—
803#120—538no—
804#120—538no—
805#120—5316no—
806#120—538no—
807#120C22×D53116yes—
808C4×Q8—538no—
809C4×Q8—534no—
810C4×Q8—534no—
811C4×D4—538no—
812C4×D4—538no—
813C4×D4—538no—
814C4×D4—538no—
815C4×D4—538no—
816C4×D4—538no—
817C4×D4—538no—
818C4×D4—538no—
819C4×D4—538no—
820C4×D4—5316no—
821C4×D4—5316no—
822C4×D4—5316no—
823C4×D4—534no—
824C4×D4—534no—
825C4×D4C22×D5314yes—
826C4×D4C22×D5314yes—
827C4×D4C22×D5314yes—
828C4×D4C22×D5314yes—
829#117—5316no—
830#117—534no—
831#117—534no—
832C2×C4⋊C4—532no—
833C2×C4⋊C4—531no—
834C2×C4⋊C4—532no—
835C2×C4⋊C4—532no—
836C2×C4⋊C4—531no—
837C2×C4⋊C4—538no—
838C2×C4⋊C4—538no—
839C2×C4⋊C4—531no—
840C2×C4⋊C4—538no—
841C2×C4⋊C4—534no—
842C2×C4⋊C4—538no—
843C2×C4⋊C4—538no—
844C2×C4⋊C4C22×D5311yescharacteristic
845C2×C4⋊C4C22×D5314yes—
846C2×C22⋊C4—532no—
847C2×C22⋊C4—538no—
848C2×C22⋊C4—531no—
849C2×C22⋊C4—531no—
850C2×C22⋊C4—538no—
851C2×C22⋊C4—538no—
852C2×C22⋊C4—5316no—
853C2×C22⋊C4C22×D5312yes—
854C2×C22⋊C4C22×D5318yes—
855C2×C42—532no—
856C2×C42—532no—
857C2×C42—531no—
858C2×C42C22×D5311yescharacteristic
859C24—531no—
860C24—538no—
861C24—538no—
862C24C23×D5318yes—
863C24C23×D5312yes—
864#41—232no—
865#41—216no—
866#41—5364no—
867#41—10632no—
868#41—10664no—
869#41—10632no—
870#41—10632no—
871#41—10664no—
872#41—10616no—
873#41—10664no—
874#41—10664no—
875#41—10616no—
876#41—10664no—
877#41—10632no—
878#41—10632no—
879#41—10616no—
880C2×Q8—538no—
881C2×Q8—534no—
882C2×Q8—538no—
883C2×Q8—5316no—
884C2×Q8—534no—
885C2×Q8—10632no—
886C2×Q8—10632no—
887C2×Q8—10616no—
888C2×Q8—10632no—
889C2×Q8C23×D5314yes—
890C2×D4—232no—
891C2×D4—232no—
892C2×D4—84no—
893C2×D4—5316no—
894C2×D4—538no—
895C2×D4—538no—
896C2×D4—5316no—
897C2×D4—538no—
898C2×D4—538no—
899C2×D4—5316no—
900C2×D4—538no—
901C2×D4—5316no—
902C2×D4—538no—
903C2×D4—538no—
904C2×D4—534no—
905C2×D4—534no—
906C2×D4—538no—
907C2×D4—534no—
908C2×D4—10616no—
909C2×D4—10632no—
910C2×D4—10664no—
911C2×D4—10632no—
912C2×D4—10664no—
913C2×D4—10632no—
914C2×D4—10632no—
915C2×D4—4244no—
916C2×D4—4248no—
917C2×D4—4248no—
918C2×D4D4×D5318yescomplemented
919C2×D4C23×D53116yes—
920C2×D4C23×D5318yes—
921C2×D4C23×D5314yes—
922C2×D4C23×D5314yes—
923C2×D4C23×D5318yes—
924C2×D4C23×D5314yes—
925C2×D4C23×D5314yes—
926C22×C4—82no—
927C22×C4—5316no—
928C22×C4—532no—
929C22×C4—531no—
930C22×C4—538no—
931C22×C4—538no—
932C22×C4—534no—
933C22×C4—538no—
934C22×C4—5316no—
935C22×C4—538no—
936C22×C4—531no—
937C22×C4—531no—
938C22×C4—532no—
939C22×C4—538no—
940C22×C4—538no—
941C22×C4—5316no—
942C22×C4—538no—
943C22×C4—538no—
944C22×C4—538no—
945C22×C4—10632no—
946C22×C4—10632no—
947C22×C4—10632no—
948C22×C4—4242no—
949C22×C4—4242no—
950C22×C4C23×D5318yes—
951C22×C4C23×D5318yes—
952C22×C4C23×D5311yescharacteristic
953C22×C4C23×D5312yes—
954C22×C4C23×D5311yescharacteristic
955C22×C4C23×D5314yes—
956C22×C4C23×D5314yes—
957C22×C4C23×D5311yescharacteristic
958C4⋊C4—538no—
959C4⋊C4—532no—
960C4⋊C4—532no—
961C4⋊C4—538no—
962C4⋊C4—534no—
963C4⋊C4—534no—
964C4⋊C4—534no—
965C4⋊C4—538no—
966C4⋊C4—5316no—
967C4⋊C4—538no—
968C4⋊C4—534no—
969C4⋊C4—534no—
970C4⋊C4—538no—
971C4⋊C4—534no—
972C4⋊C4C23×D5314yes—
973C4⋊C4C23×D5318yes—
974C4⋊C4C23×D5314yes—
975C4⋊C4C23×D5314yes—
976C22⋊C4—538no—
977C22⋊C4—5316no—
978C22⋊C4—538no—
979C22⋊C4—538no—
980C22⋊C4—538no—
981C22⋊C4—5316no—
982C22⋊C4—5316no—
983C22⋊C4—538no—
984C22⋊C4—532no—
985C22⋊C4—532no—
986C22⋊C4—534no—
987C22⋊C4—538no—
988C22⋊C4—538no—
989C22⋊C4C23×D53116yes—
990C22⋊C4C23×D5318yes—
991C22⋊C4C23×D5318yes—
992C22⋊C4C23×D5318yes—
993C42—538no—
994C42—538no—
995C42—534no—
996C42C23×D5312yes—
997C42C23×D5312yes—
998C23—216no—
999C23—42no—
1000C23—42no—
1001C23—48no—
1002C23—48no—
1003C23—532no—
1004C23—534no—
1005C23—538no—
1006C23—10616no—
1007C23—10616no—
1008C23—2128no—
1009C23—2128no—
1010C23—2128no—
1011C23—2128no—
1012C23—2121no—
1013C23—2121no—
1014C23C2×D4×D5318yes—
1015C23C24×D5318yes—
1016C23C24×D5314yes—
1017C23C24×D5311yescharacteristic
1018Q8—28no—
1019Q8—5316no—
1020Q8—10616no—
1021Q8—10632no—
1022Q8—1068no—
1023D4—232no—
1024D4—216no—
1025D4—28no—
1026D4—44no—
1027D4—48no—
1028D4—44no—
1029D4—5332no—
1030D4—10616no—
1031D4—10616no—
1032D4—10632no—
1033D4—10616no—
1034D4—10632no—
1035D4—10616no—
1036D4—1068no—
1037D4—2124no—
1038D4—2124no—
1039D4—2128no—
1040D4—2128no—
1041D4—21216no—
1042D4—2128no—
1043D4C2×D4×D53116yes—
1044C2×C4—216no—
1045C2×C4—216no—
1046C2×C4—41no—
1047C2×C4—42no—
1048C2×C4—44no—
1049C2×C4—44no—
1050C2×C4—41no—
1051C2×C4—534no—
1052C2×C4—5332no—
1053C2×C4—538no—
1054C2×C4—534no—
1055C2×C4—532no—
1056C2×C4—5316no—
1057C2×C4—532no—
1058C2×C4—534no—
1059C2×C4—532no—
1060C2×C4—538no—
1061C2×C4—10616no—
1062C2×C4—10632no—
1063C2×C4—10616no—
1064C2×C4—10616no—
1065C2×C4—10632no—
1066C2×C4—10616no—
1067C2×C4—10616no—
1068C2×C4—2128no—
1069C2×C4—2121no—
1070C2×C4—2122no—
1071C2×C4—2121no—
1072C2×C4—2128no—
1073C2×C4C2×D4×D5314yes—
1074C2×C4C24×D5312yes—
1075C2×C4C24×D5314yes—
1076C2×C4C24×D5311yescharacteristic
1077C2×C4C24×D5311yescharacteristic
1078C2×C4C24×D5318yes—
1079C2×C4C24×D5312yes—
1080C22—21no—
1081C22—24no—
1082C22—21no—
1083C22—24no—
1084C22—28no—
1085C22—28no—
1086C22—28no—
1087C22—48no—
1088C22—816no—
1089C22—534no—
1090C22—1062no—
1091C22—1062no—
1092C22—1068no—
1093C22—1068no—
1094C22—1068no—
1095C22—42416no—
1096C22—42416no—
1097C22—2124no—
1098C22C22×D4×D5318yes—
1099C22C22×D4×D5312yes—
1100C22C25×D5311yescharacteristic
1101C4—28no—
1102C4—21no—
1103C4—21no—
1104C4—24no—
1105C4—22no—
1106C4—534no—
1107C4—538no—
1108C4—1068no—
1109C4—1064no—
1110C4—1062no—
1111C4—1062no—
1112C4C22×D4×D5314yes—
1113C2—22no—
1114C2—28no—
1115C2—48no—
1116C2—1064no—
1117C2—2128no—
1118C2C23×D4×D5311yescharacteristic
1119C2#2028952511yescharacteristic
1120C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3496C2
hypercenter#3496D53
hypocenterC53#62853
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. C2×#16811458C2semidirect
2. #20288484C2semidirect
3. #20288481C2semidirect
4. #20288479C2semidirect
5. #20288476C2semidirect
6. #20288474C2semidirect
7. #20288472C2semidirect
8. #20288389C2semidirect
9. #20288386C2semidirect
10. #20288378C2semidirect
11. #20288375C2semidirect
12. #20288042C2semidirect
13. #20288041C2semidirect
14. C2×#16811200C2semidirect
15. #537×D53C2semidirect
16. C2×#16811102C2semidirect
17. C53×#3496C2semidirect
19. C2×#13133264C22semidirect
20. C2×#13133264C22semidirect
21. C2×#13133262C22semidirect
22. C2×#13133262C22semidirect
23. C2×#13133262C22semidirect
25. C22×#11719947C22semidirect
26. C22×#11719947C22semidirect
27. C2×#41×D53C22semidirect
28. C2×#41×D53C22semidirect
29. #16811294C22semidirect
30. #16811293C22semidirect
31. #16811291C22semidirect
32. D4×Dic106C22semidirect
33. #16811288C22semidirect
34. #16811286C22semidirect
35. #16811283C22semidirect
36. #16811282C22semidirect
37. #16811281C22semidirect
38. #16811279C22semidirect
39. #16811277C22semidirect
40. #16811274C22semidirect
41. #16811273C22semidirect
42. #16811272C22semidirect
43. #16811271C22semidirect
44. #16811268C22semidirect
45. #16811267C22semidirect
46. #16811265C22semidirect
47. #16811263C22semidirect
48. #16811262C22semidirect
49. #16811261C22semidirect
50. #16811260C22semidirect
51. D4×D212C22semidirect
52. #16811257C22semidirect
53. D4×C22⋊D53C22semidirect
54. D4×C22⋊D53C22semidirect
55. #16811255C22semidirect
56. #16811204C22semidirect
57. #16811203C22semidirect
58. #16811202C22semidirect
59. #16811201C22semidirect
60. #16811200C22semidirect
61. #16811200C22semidirect
62. #16811200C22semidirect
63. #16811200C22semidirect
64. #16811200C22semidirect
65. #16811200C22semidirect
66. #16811200C22semidirect
67. #16811198C22semidirect
68. #16811195C22semidirect
69. #16811193C22semidirect
70. #16811191C22semidirect
71. #16811188C22semidirect
72. #16811186C22semidirect
73. #16811185C22semidirect
74. #16811182C22semidirect
75. #16811181C22semidirect
76. #16811181C22semidirect
77. #16811173C22semidirect
78. #16811169C22semidirect
79. #16811168C22semidirect
80. #16811168C22semidirect
81. #16811132C22semidirect
82. #16811132C22semidirect
83. #16811131C22semidirect
84. #16811129C22semidirect
85. C2×#13133195C22semidirect
86. C2×#13133194C22semidirect
87. C22⋊Q8×D53C22semidirect
88. C2×#13133191C22semidirect
89. C2×#13133190C22semidirect
90. C2×#13133189C22semidirect
91. C2×#13133189C22semidirect
92. #121×D53C22semidirect
93. #121×D53C22semidirect
94. #16811102C22semidirect
95. #16811102C22semidirect
96. C2×C4×Dic106C22semidirect
97. C2×#13133182C22semidirect
98. C2×D4×Dic53C22semidirect
99. C2×C4×C22⋊D53C22semidirect
100. C2×#13133177C22semidirect
101. C2×#13133174C22semidirect
102. C2×#13133173C22semidirect
103. C22×#11719919C22semidirect
104. C2×C4⋊C4×D53C22semidirect
105. C2×H(5,𝔽2)×C53C22semidirect
106. C53×#547C22semidirect
107. C53×#546C22semidirect
108. D42×C53C22semidirect
109. C53×#537C22semidirect
110. C53×#534C22semidirect
111. C53×#532C22semidirect
112. C2×#121×C53C22semidirect
113. C2×C4×D4×C53C22semidirect
126. C2×#11719947D4semidirect
309. C2×D4×C53C2×D4semidirect
330. C2×C22⋊D53C2×D4semidirect
342. C22×Dic53C2×D4semidirect
364. #11719947C2×D4semidirect
383. C2×C4×D53C2×D4semidirect
392. C2×Dic106C2×D4semidirect
560. #3496D53semidirect
584. C2×H(5,𝔽2)C2×D53semidirect
605. #547C2×D53semidirect
613. #546C2×D53semidirect
619. D42C2×D53semidirect
631. #537C2×D53semidirect
642. #534C2×D53semidirect
647. #532C2×D53semidirect
661. C2×#121C2×D53semidirect
669. C2×C4×D4C2×D53semidirect
674. C53#62853semidirect
918. C2×D4D4×D53semidirect

Maximal subgroups

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

subgroupindex
C2×#168114582
#202884842
#202884812
#202884792
#202884762
#202884742
#202884722
#202883892
#202883862
#202883782
#202883752
#202880422
#202880412
C2×#168112002
#537×D532
C2×#168111022
C53×#34962
#6285353