Finite Group Databasebeta

← #28292773

Subgroups — #28292773

Order 13568.

7274 conjugacy classes of subgroups.

The subgroup lattice has 1458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289265C218yesmaximal, complemented
2#20289245C214yesmaximal, complemented
3#20289233C214yesmaximal, complemented
4#20289064C214yesmaximal, complemented
5#20289055C212yesmaximal, complemented
6#20289048C211yesmaximal, characteristic, complemented
7#20288797C212yesmaximal, complemented
8#20288795C212yesmaximal, complemented
9#20288746C212yesmaximal, complemented
10#20288738C212yesmaximal, complemented
11#20288656C214yesmaximal, complemented
12#20288640C214yesmaximal, complemented
13#20288542C214yesmaximal, complemented
14#20288471C214yesmaximal, complemented
15#20288447C214yesmaximal, complemented
16#20288442C214yesmaximal, complemented
17#20288356C214yesmaximal, complemented
18C2×#16811171C211yesmaximal, characteristic, complemented
19#529×D53C212yesmaximal, complemented
20C53×#3543C211yesmaximal, characteristic, complemented
21C2×#13133262C2214yescomplemented
22C22×#11719947C2212yescomplemented
23#16811376C2214yescomplemented
24#16811375C2218yescomplemented
25#16811368C2218yescomplemented
26#16811366C2214yescomplemented
27#16811360C2214yescomplemented
28#16811359C2211yescharacteristic, complemented
29#16811359C2214yescomplemented
30#16811355C2214yescomplemented
31Q8×Dic106C2212yescomplemented
32#16811338C2212yescomplemented
33#16811337C2218yescomplemented
34#16811333C2212yescomplemented
35#16811332C2214yescomplemented
36#16811330C2212yescomplemented
37#16811330C2214yescomplemented
38#16811325C2218yescomplemented
39#16811325C2214yescomplemented
40#16811323C2214yescomplemented
41#16811320C2218yescomplemented
42#16811320C2214yescomplemented
43#16811320C2214yescomplemented
44#16811318C2218yescomplemented
45#16811316C2218yescomplemented
46#16811315C2214yescomplemented
47#16811313C2214yescomplemented
48#16811304C2218yescomplemented
49#16811304C2214yescomplemented
50#16811304C2218yescomplemented
51#16811301C2214yescomplemented
52#16811299C2218yescomplemented
53#16811296C2218yescomplemented
54#16811293C2212yescomplemented
55#16811281C2214yescomplemented
56#16811280C2214yescomplemented
57#16811278C2214yescomplemented
58#16811277C2214yescomplemented
59#16811273C2218yescomplemented
60#16811273C2214yescomplemented
61#16811273C2214yescomplemented
62#16811273C2218yescomplemented
63#16811271C2218yescomplemented
64#16811271C2218yescomplemented
65#16811270C2218yescomplemented
66#16811267C2214yescomplemented
67#16811267C2218yescomplemented
68#16811267C2214yescomplemented
69#16811262C2218yescomplemented
70#16811262C2218yescomplemented
71#16811261C2214yescomplemented
72#16811260C2218yescomplemented
73#16811260C2218yescomplemented
74#16811260C2218yescomplemented
75#16811260C2218yescomplemented
76#16811258C2211yescharacteristic, complemented
77#16811258C2214yescomplemented
78D4×C22⋊D53C2214yescomplemented
79D4×C22⋊D53C2214yescomplemented
80#16811253C2214yescomplemented
81#16811251C2214yescomplemented
82#16811244C2214yescomplemented
83#16811242C2214yescomplemented
84#16811242C2214yescomplemented
85#16811241C2218yescomplemented
86#16811240C2218yescomplemented
87#16811240C2214yescomplemented
88#16811227C2214yescomplemented
89#16811227C2214yescomplemented
90#16811226C2214yescomplemented
91#16811218C2218yescomplemented
92#16811217C2218yescomplemented
93#16811216C2218yescomplemented
94#16811210C2218yescomplemented
95#16811208C2218yescomplemented
96#16811208C2218yescomplemented
97#16811205C2218yescomplemented
98#16811205C2218yescomplemented
99#16811202C2218yescomplemented
100#16811195C2218yescomplemented
101#16811186C2214yescomplemented
102#16811183C2218yescomplemented
103#16811183C2218yescomplemented
104#16811182C2214yescomplemented
105#16811171C2214yescomplemented
106#16811171C2212yescomplemented
107#16811171C2212yescomplemented
108#16811171C2214yescomplemented
109#16811171C2214yescomplemented
110#16811171C2214yescomplemented
111#16811170C2214yescomplemented
112C2×#13133217C2211yescharacteristic, complemented
113#16811160C2212yescomplemented
114#16811159C2212yescomplemented
115#16811158C2212yescomplemented
116#16811157C2212yescomplemented
117#16811156C2214yescomplemented
118#16811155C2214yescomplemented
119#16811155C2212yescomplemented
120#16811154C2212yescomplemented
121#16811153C2214yescomplemented
122#16811152C2214yescomplemented
123#16811152C2212yescomplemented
124#16811151C2214yescomplemented
125#16811150C2214yescomplemented
126#126×D53C2214yescomplemented
127#125×D53C2212yescomplemented
128C2×#13133204C2212yescomplemented
129#124×D53C2212yescomplemented
130#16811133C2214yescomplemented
131#16811130C2214yescomplemented
132#16811129C2218yescomplemented
133C2×#13133201C2214yescomplemented
134C2×#13133198C2214yescomplemented
135#123×D53C2214yescomplemented
136C22⋊Q8×D53C2212yescomplemented
137C2×#13133188C2214yescomplemented
138C2×#13133188C2214yescomplemented
139#121×D53C2212yes—
140#121×D53C2214yescomplemented
141#16811106C2214yescomplemented
142#16811102C2214yescomplemented
143#16811098C2214yescomplemented
144#16811096C2214yescomplemented
145#16811095C2214yescomplemented
146C4×Q8×D53C2212yescomplemented
147C2×D4×Dic53C2214yescomplemented
148C4×D4×D53C2214yescomplemented
149C4×D4×D53C2212yescomplemented
150#117×D53C2214yescomplemented
151C2×C42×D53C2211yescharacteristic, complemented
152C53×#560C2214yescomplemented
153C53×#559C2211yescharacteristic, complemented
154C53×#550C2212yescomplemented
155C53×#546C2214yescomplemented
156D42×C53C2214yescomplemented
157D42×C53C2211yescharacteristic, complemented
158C53×#540C2214yescomplemented
159C53×#535C2214yescomplemented
160C53×#534C2214yescomplemented
161C2×#127×C53C2211yescharacteristic, complemented
162C53×#529C2212yescomplemented
163#13133262—416no—
164C2×#11719945C2318yes—
165C2×#11719947—48no—
166C2×#11719947C2314yes—
167C2×#11719947C2318yes—
168C2×#11719947C2314yes—
169C2×#11719947C2318yes—
170C2×#11719947C2318yes—
171C2×#11719947C2314yes—
172C22×Dic106C2312yes—
173C2×Q8×D53C2312yes—
174C22×C22⋊D53C2314yes—
175C22×C22⋊D53C2318yes—
176C22×C22⋊D53C2314yes—
177C2×D4×D53C2314yes—
178C2×D4×D53C2318yes—
179C2×D4×D53C2312yes—
180C2×D4×D53C2314yes—
181C23×Dic53C2314yes—
182C22×C4×D53C2311yescharacteristic
183C22×C4×D53C2312yes—
184C22×C4×D53C2314yes—
185#13133217C2314yes—
186#13133217C2312yes—
187#13133217C2312yes—
188#13133217C2314yes—
189#13133216C2318yes—
190#13133216C2318yes—
191#13133216C2314yes—
192#13133213C2314yes—
193#13133212C2314yes—
194#13133212C2318yes—
195#13133212C2314yes—
196#13133212C2314yes—
197#13133211C2314yes—
198#13133210C2318yes—
199#13133210C2318yes—
200#13133210C2318yes—
201#13133210C2314yes—
202#13133210C2318yes—
203#13133210C2318yes—
204#13133210C2314yes—
205#13133210C2314yes—
206#13133209C2314yes—
207#13133209C2312yes—
208#13133208C2318yes—
209#13133208C2314yes—
210#13133208C2312yes—
211#13133208C2312yes—
212#13133207C2318yes—
213#13133207C2314yes—
214#13133207C2314yes—
215#13133206C2312yes—
216#13133205C2312yes—
217#13133204C2312yes—
218#13133204C2318yes—
219#13133204C2314yes—
220#13133204C2318yes—
221#13133204C2314yes—
222#13133204C2314yes—
223#13133204C2314yes—
224#13133204C2314yes—
225#13133203C2318yes—
226#13133203C2318yes—
227#13133203C2318yes—
228#13133203C2318yes—
229#13133203C2314yes—
230#13133203C2314yes—
231#13133202C2314yes—
232#13133202C2314yes—
233#13133201C2318yes—
234#13133201C2318yes—
235#13133201C2318yes—
236#13133201C2318yes—
237#13133201C2314yes—
238#13133200C2318yes—
239#13133200C2314yes—
240#13133199C2318yes—
241#13133199C2318yes—
242#13133199C2318yes—
243#13133199C2314yes—
244#13133199C2314yes—
245#13133199C2318yes—
246#13133199C2318yes—
247#13133198C2318yes—
248#13133198C2318yes—
249#13133198C2318yes—
250#13133198C2318yes—
251#13133198C2314yes—
252#13133198C2314yes—
253#13133198C2318yes—
254#13133198C2318yes—
255#13133198C2318yes—
256#13133198C2314yes—
257#13133197C2318yes—
258#13133197C2312yes—
259#13133196C2312yes—
260#13133196C2318yes—
261#13133196C2314yes—
262#13133196C2318yes—
263#13133195C2318yes—
264#13133195C2318yes—
265#13133195C2314yes—
266#13133194C2318yes—
267#13133194C2318yes—
268#13133194C2318yes—
269#13133194C2318yes—
270#13133194C2318yes—
271#13133194C2318yes—
272#13133194C2318yes—
273#13133194C2314yes—
274#13133193C2314yes—
275#13133193C2312yes—
276#13133192C2312yes—
277#13133191C2312yes—
278#13133191C2314yes—
279#13133190C2318yes—
280#13133190C2318yes—
281#13133190C2314yes—
282#13133189C2314yes—
283#13133189C2318yes—
284#13133189C2318yes—
285#13133189C2318yes—
286#13133189C2318yes—
287#13133189C2318yes—
288#13133189C2318yes—
289#13133189C2318yes—
290#13133189C2318yes—
291#13133188C2314yes—
292#13133188C2314yes—
293#13133188C2318yes—
294#13133188C2318yes—
295#13133188C2318yes—
296#13133188C2318yes—
297#13133188C2314yes—
298#13133188C2318yes—
299#13133188C2314yes—
300#13133188C2314yes—
301#13133188C2312yes—
302#13133188C2314yes—
303#13133188C2314yes—
304#13133188C2318yes—
305#13133186C2318yes—
306#13133186C2318yes—
307#13133185C2318yes—
308#13133185C2318yes—
309#13133185C2314yes—
310#13133185C2314yes—
311#13133185C2318yes—
312#13133185C2318yes—
313Q8×Dic53C2314yes—
314Q8×Dic53C2312yes—
315C4×Dic106C2314yes—
316C4×Dic106C2312yes—
317C4×Dic106C2314yes—
318#13133182C2312yes—
319#13133182C2314yes—
320C4×D212C2314yes—
321C4×D212C2314yes—
322C4×D212C2312yes—
323D4×Dic53C2314yes—
324D4×Dic53C2314yes—
325D4×Dic53C2314yes—
326D4×Dic53C2318yes—
327D4×Dic53C2318yes—
328D4×Dic53C2314yes—
329D4×Dic53C2314yes—
330D4×Dic53C2318yes—
331D4×Dic53C2318yes—
332D4×Dic53C2318yes—
333D4×Dic53C2314yes—
334D4×Dic53C2312yes—
335D4×Dic53C2314yes—
336D4×Dic53C2314yes—
337D4×Dic53C2318yes—
338#13133179C2314yes—
339#13133179C2312yes—
340C4×C22⋊D53C2318yes—
341C4×C22⋊D53C2314yes—
342C4×C22⋊D53C2314yes—
343C4×C22⋊D53C2318yes—
344C4×C22⋊D53C2314yes—
345C4×C22⋊D53C2318yes—
346C4×C22⋊D53C2318yes—
347#13133177C2318yes—
348#13133177C2318yes—
349#13133177C2318yes—
350#13133177C2318yes—
351#13133177C2314yes—
352#13133177C2314yes—
353#13133177C2314yes—
354#13133176C2318yes—
355#13133176C2314yes—
356#13133176C2314yes—
357#13133175C2314yes—
358#13133175C2314yes—
359#13133175C2314yes—
360#13133174C2314yes—
361#13133174C2314yes—
362#13133173C2318yes—
363#13133173C2314yes—
364#13133173C2318yes—
365#13133173C2314yes—
366C2×C4⋊Dic53C2318yes—
367C2×C4⋊Dic53C2314yes—
368C2×C4⋊Dic53C2314yes—
369C2×#11719919C2318yes—
370C4⋊C4×D53C2314yes—
371C4⋊C4×D53C2314yes—
372C4⋊C4×D53C2312yes—
373C4⋊C4×D53C2314yes—
374C4⋊C4×D53C2314yes—
375C4⋊C4×D53C2312yes—
376C4⋊C4×D53C2314yes—
377C2×C22⋊Dic53C2314yes—
378C2×C22⋊Dic53C2318yes—
379C2×C22⋊Dic53C2318yes—
380C2×C22⋊Dic53C2318yes—
381C2×#11719921C2318yes—
382C22⋊C4×D53C2314yes—
383C22⋊C4×D53C2318yes—
384C22⋊C4×D53C2314yes—
385C22⋊C4×D53C2314yes—
386C22⋊C4×D53C2314yes—
387C22⋊C4×D53C2314yes—
388C2×C4×Dic53C2312yes—
389C2×C4×Dic53C2311yescharacteristic
390C42×D53C2312yes—
391C42×D53C2312yes—
392C42×D53C2312yes—
393C42×D53C2312yes—
394C42×D53C2314yes—
395C2×#41×C53C2314yes—
396C22×D4×C53C2314yes—
397C22×D4×C53C2314yes—
398C22×D4×C53C2314yes—
399C22×D4×C53C2312yes—
400#127×C53C2311yescharacteristic
401#127×C53C2314yes—
402#127×C53C2311yescharacteristic
403#127×C53C2312yes—
404#127×C53C2314yes—
405#126×C53C2314yes—
406#125×C53C2312yes—
407#124×C53C2314yes—
408#124×C53C2312yes—
409#123×C53C2314yes—
410#123×C53C2314yes—
411#123×C53C2318yes—
412#123×C53C2314yes—
413C22⋊Q8×C53C2312yes—
414#121×C53C2318yes—
415#121×C53C2312yes—
416#121×C53C2318yes—
417#121×C53C2318yes—
418#121×C53C2314yes—
419#121×C53C2318yes—
420#121×C53C2314yes—
421#120×C53C2314yes—
422#120×C53C2318yes—
423#120×C53C2318yes—
424#120×C53C2314yes—
425C4×Q8×C53C2312yes—
426C4×D4×C53C2314yes—
427C4×D4×C53C2314yes—
428C4×D4×C53C2312yes—
429C4×D4×C53C2314yes—
430#117×C53C2314yes—
431C2×C22⋊C4×C53C2314yes—
432C2×C42×C53C2311yescharacteristic
433C24×C53C2414yes—
434C24×C53C2414yes—
435C23×D53C2414yes—
436C23×D53C2414yes—
437C23×D53C2411yescharacteristic
438#41×C53—48no—
439C2×Q8×C53C2412yes—
440C2×D4×C53—48no—
441C2×D4×C53—48no—
442C2×D4×C53—44no—
443C2×D4×C53—48no—
444C2×D4×C53C2414yes—
445C2×D4×C53C2412yes—
446C2×D4×C53C2414yes—
447C2×D4×C53C2414yes—
448C2×D4×C53C2418yes—
449C2×D4×C53C2418yes—
450C2×D4×C53C2412yes—
451C2×D4×C53C2418yes—
452C2×D4×C53C2418yes—
453C2×D4×C53C2414yes—
454C2×D4×C53C2412yes—
455C22×C4×C53C2412yes—
456C22×C4×C53C2411yescharacteristic
457C22×C4×C53C2414yes—
458C22×C4×C53C2418yes—
459C22×C4×C53C2414yes—
460C2×C22⋊D53—216no—
461C2×C22⋊D53—416no—
462C2×C22⋊D53—48no—
463C2×C22⋊D53C2418yes—
464C2×C22⋊D53C2414yes—
465C2×C22⋊D53C2414yes—
466C2×C22⋊D53C2418yes—
467C2×C22⋊D53C2418yes—
468C2×C22⋊D53C2414yes—
469C2×C22⋊D53C2418yes—
470C2×C22⋊D53C2418yes—
471C2×C22⋊D53C2418yes—
472C22×Dic53—48no—
473C22×Dic53C2411yescharacteristic
474C22×Dic53C2414yes—
475C22×Dic53C2412yes—
476C22×Dic53C2418yes—
477C22×Dic53C2418yes—
478C22×Dic53C2414yes—
479C22×Dic53C2418yes—
480C22×Dic53C2418yes—
481C22×Dic53C2414yes—
482Q8×D53—44no—
483#11719947—48no—
484#11719947—48no—
485#11719947—416no—
486#11719947—48no—
487#11719947—416no—
488#11719947—416no—
489D4×D53—216no—
490D4×D53—48no—
491D4×D53—44no—
492D4×D53—416no—
493#11719945—416no—
494C2×D212C2412yes—
495C2×D212C2414yes—
496C2×C4×D53—24no—
497C2×C4×D53—48no—
498C2×C4×D53—44no—
499C2×C4×D53C2412yes—
500C2×C4×D53C2412yes—
501C2×C4×D53C2412yes—
502C2×C4×D53C2412yes—
503C2×C4×D53C2414yes—
504C2×C4×D53C2414yes—
505C2×C4×D53C2412yes—
506C2×C4×D53C2412yes—
507C2×C4×D53C2414yes—
508C2×C4×D53C2414yes—
509C2×C4×D53C2414yes—
510C2×C4×D53C2418yes—
511C2×Dic106—44no—
512C2×Dic106C2412yes—
513C2×Dic106C2414yes—
514C2×Dic106C2418yes—
515C2×Dic106C2414yes—
516C2×Dic106C2414yes—
517C4⋊C4×C53C2414yes—
518C4⋊C4×C53C2414yes—
519C4⋊C4×C53C2412yes—
520C4⋊C4×C53C2412yes—
521C4⋊C4×C53C2414yes—
522C4⋊C4×C53C2414yes—
523C22⋊C4×C53C2414yes—
524C22⋊C4×C53C2414yes—
525C22⋊C4×C53C2414yes—
526C22⋊C4×C53C2414yes—
527C22⋊C4×C53C2414yes—
528C22⋊C4×C53C2414yes—
529C22⋊C4×C53C2414yes—
530C22⋊C4×C53C2418yes—
531C22⋊C4×C53C2418yes—
532C42×C53C2412yes—
533C42×C53C2411yescharacteristic
534C42×C53C2411yescharacteristic
535C42×C53C2414yes—
536C22⋊Dic53C2414yes—
537C22⋊Dic53C2414yes—
538C22⋊Dic53C2414yes—
539C22⋊Dic53C2414yes—
540C22⋊Dic53C2418yes—
541C22⋊Dic53C2414yes—
542C22⋊Dic53C2418yes—
543C22⋊Dic53C2418yes—
544C22⋊Dic53C2414yes—
545C22⋊Dic53C2414yes—
546C22⋊Dic53C2418yes—
547C22⋊Dic53C2418yes—
548C22⋊Dic53C2418yes—
549C22⋊Dic53C2418yes—
550C22⋊Dic53C2418yes—
551#11719921C2414yes—
552#11719921C2414yes—
553#11719921C2414yes—
554#11719921C2418yes—
555#11719921C2414yes—
556#11719921C2414yes—
557#11719921C2414yes—
558#11719921C2414yes—
559#11719921C2414yes—
560#11719921C2414yes—
561#11719921C2414yes—
562#11719921C2418yes—
563C4⋊Dic53C2414yes—
564C4⋊Dic53C2412yes—
565C4⋊Dic53C2414yes—
566C4⋊Dic53C2414yes—
567C4⋊Dic53C2414yes—
568C4⋊Dic53C2412yes—
569C4⋊Dic53C2414yes—
570C4⋊Dic53C2414yes—
571C4⋊Dic53C2418yes—
572C4⋊Dic53C2418yes—
573C4⋊Dic53C2418yes—
574#11719919C2414yes—
575#11719919C2414yes—
576#11719919C2418yes—
577#11719919C2414yes—
578#11719919C2414yes—
579#11719919C2414yes—
580#11719919C2414yes—
581#11719919C2414yes—
582#11719919C2414yes—
583#11719919C2414yes—
584#11719919C2414yes—
585#11719919C2418yes—
586#11719919C2418yes—
587#11719919C2418yes—
588C4×Dic53C2411yescharacteristic
589C4×Dic53C2412yes—
590C4×Dic53C2412yes—
591C4×Dic53C2412yes—
592C4×Dic53C2412yes—
593C4×Dic53C2412yes—
594C4×Dic53C2411yescharacteristic
595C4×Dic53C2414yes—
596C4×Dic53C2414yes—
597C4×Dic53C2414yes—
598C4×Dic53C2418yes—
599C4×Dic53C2418yes—
600C23×C53—28no—
601C23×C53—48no—
602C23×C53—44no—
603C23×C53—48no—
604C23×C53C2514yes—
605C23×C53C2514yes—
606C23×C53C2514yes—
607C23×C53C2511yescharacteristic
608C22×D53—28no—
609C22×D53—42no—
610C22×D53—44no—
611C22×D53—44no—
612C22×D53—44no—
613C22×D53—48no—
614C22×D53H(5,𝔽2)14yes—
615C22×D53C2514yes—
616C22×D53C2512yes—
617Q8×C53—24no—
618D4×C53—28no—
619D4×C53—24no—
620D4×C53—28no—
621D4×C53—28no—
622D4×C53—48no—
623D4×C53—42no—
624D4×C53—44no—
625D4×C53—42no—
626D4×C53—48no—
627D4×C53—48no—
628D4×C53—48no—
629C2×C4×C53—22no—
630C2×C4×C53—24no—
631C2×C4×C53—28no—
632C2×C4×C53—44no—
633C2×C4×C53—48no—
634C2×C4×C53C2511yescharacteristic
635C2×C4×C53C2511yescharacteristic
636C2×C4×C53C2514yes—
637C2×C4×C53C2514yes—
638C2×C4×C53C2514yes—
639C2×C4×C53C2512yes—
640C2×C4×C53C2512yes—
641C22⋊D53—28no—
642C22⋊D53—216no—
643C22⋊D53—28no—
644C22⋊D53—216no—
645C22⋊D53—48no—
646C22⋊D53—48no—
647C22⋊D53—44no—
648C22⋊D53—48no—
649C22⋊D53—48no—
650C2×Dic53—28no—
651C2×Dic53—22no—
652C2×Dic53—42no—
653C2×Dic53—44no—
654C2×Dic53—48no—
655C2×Dic53—48no—
656C2×Dic53—48no—
657C2×Dic53—44no—
658C2×Dic53—48no—
659C2×Dic53C2518yes—
660C2×Dic53C2512yes—
661C2×Dic53C2514yes—
662C2×Dic53C2514yes—
663C2×Dic53C2512yes—
664C2×Dic53C2512yes—
665C2×Dic53C2514yes—
666D212—28no—
667D212—24no—
668C4×D53—24no—
669C4×D53—24no—
670C4×D53—28no—
671C4×D53—24no—
672C4×D53—28no—
673C4×D53—24no—
674C4×D53—42no—
675C4×D53—44no—
676C4×D53—42no—
677C4×D53—44no—
678C4×D53—48no—
679C4×D53—44no—
680Dic106—24no—
681Dic106—44no—
682Dic106—44no—
683Dic106—48no—
684Dic106—44no—
685#62822—531nomaximal, Sylow
686C22×C53—22no—
687C22×C53—24no—
688C22×C53—24no—
689C22×C53—24no—
690C22×C53—28no—
691C22×C53—24no—
692C22×C53—28no—
693C22×C53—24no—
694C22×C53—88no—
695C22×C53—164no—
696C22×C53C2×H(5,𝔽2)12yes—
697C22×C53C2611yescharacteristic
698C2×D53—22no—
699C2×D53—22no—
700C2×D53—24no—
701C2×D53—24no—
702C2×D53—24no—
703C2×D53—44no—
704C2×D53—88no—
705C2×D53—164no—
706C2×D53C2×H(5,𝔽2)14yes—
707C4×C53—21no—
708C4×C53—21no—
709C4×C53—24no—
710C4×C53—24no—
711C4×C53—24no—
712C4×C53—22no—
713C4×C53#58514yes—
714Dic53—28no—
715Dic53—24no—
716Dic53—22no—
717Dic53—24no—
718Dic53—22no—
719Dic53—22no—
720Dic53—24no—
721#3560—538no—
722#3559—534no—
723#3558—534no—
724#3545—534no—
725#3544—532no—
726#3543—531no—
727#3543D5311yescharacteristic, complemented
728#3522—532no—
729#3522—532no—
730#3519—532no—
731#3519—532no—
732#3513—534no—
733#3513—534no—
734#3505—534no—
735#3496—534no—
736#3494—534no—
737#3494—534no—
738#3485—534no—
739C2×#532—531no—
740C2×#529—532no—
741C2×C53—22no—
742C2×C53—44no—
743C2×C53—44no—
744C2×C53—44no—
745C2×C53C22×H(5,𝔽2)11yescharacteristic
746C2×C53C2×#58512yes—
747D53—24no—
748D53—44no—
749C2×H(5,𝔽2)—534no—
750C22×#41—532no—
751#563—538no—
752#563—534no—
753#562—538no—
754H(3,𝔽4)—534no—
755#560—534no—
756#560C2×D5314yescomplemented
757#559—534no—
758#559—531no—
759#559—534no—
760#559C2×D5311yescharacteristic, complemented
761Q82—532no—
762#555—538no—
763#555—532no—
764#554—532no—
765#554—534no—
766#554—532no—
767#554—534no—
768#553—538no—
769#553—538no—
770#553—538no—
771#553—534no—
772#553—534no—
773#553—538no—
774#553—534no—
775#553—534no—
776#552—534no—
777#552—534no—
778#551—538no—
779#551—534no—
780#551—534no—
781#551—538no—
782#551—538no—
783#551—538no—
784#550—532no—
785#550C2×D5312yescomplemented
786#548—534no—
787#548—534no—
788#547—538no—
789#547—538no—
790#547—538no—
791#547—538no—
792#547—534no—
793#547—534no—
794#547—534no—
795#547—534no—
796#546—534no—
797#546—538no—
798#546—534no—
799#546—534no—
800#546—538no—
801#546—538no—
802#546—538no—
803#546—538no—
804#546—538no—
805#546—538no—
806#546—538no—
807#546C2×D5314yescomplemented
808D42—534no—
809D42—534no—
810D42—534no—
811D42—531no—
812D42C2×D5314yescomplemented
813D42C2×D5311yescharacteristic, complemented
814#544—534no—
815#544—534no—
816#542—534no—
817#542—534no—
818#542—538no—
819#542—534no—
820#542—538no—
821#542—534no—
822#540—534no—
823#540—534no—
824#540—534no—
825#540C2×D5314yescomplemented
826#539—538no—
827#539—538no—
828#539—538no—
829#538—538no—
830#538—538no—
831#538—538no—
832#538—538no—
833#538—538no—
834#537—538no—
835#536—538no—
836#535—534no—
837#535C2×D5314yescomplemented
838#534—534no—
839#534—538no—
840#534—538no—
841#534C2×D5314yescomplemented
842#532—534no—
843#532—532no—
844#532—532no—
845#532—534no—
846#532—534no—
847#532—534no—
848#532—534no—
849C2×C4⋊Q8—531no—
850C2×#127C2×D5311yescharacteristic, complemented
851#529—534no—
852#529—532no—
853#529—532no—
854#529—534no—
855#529—534no—
856#529—532no—
857#529—532no—
858#529—532no—
859#529—534no—
860#529—532no—
861#529—534no—
862#529—534no—
863#529—532no—
864#529C2×D5312yescomplemented
865C2×#126—534no—
866C2×#125—532no—
867C2×#124—532no—
868C2×#124—532no—
869#525—534no—
870#525—534no—
871#525—538no—
872C2×#123—534no—
873C2×#123—534no—
874C2×#123—534no—
875C2×C22⋊Q8—532no—
876C2×#121—534no—
877C2×#121—534no—
878C2×#121—532no—
879C2×#121—534no—
880#520—534no—
881#520—534no—
882#518—534no—
883#518—534no—
884#518—534no—
885C2×C4×Q8—532no—
886C2×C4×D4—534no—
887C2×C4×D4—534no—
888C2×C4×D4—532no—
889C2×#117—534no—
890C22×C42—531no—
891C53#6282211yescharacteristic, complemented, Sylow
892H(5,𝔽2)—21216no—
893C2×#41—534no—
894C2×#41—538no—
895C2×#41—534no—
896C2×#41—538no—
897C2×#41—534no—
898C2×#41—538no—
899C2×#41—538no—
900C2×#41—2128no—
901C2×#41C22×D5314yes—
902C22×Q8—532no—
903C22×Q8—532no—
904C22×D4—534no—
905C22×D4—538no—
906C22×D4—534no—
907C22×D4—534no—
908C22×D4—532no—
909C22×D4—534no—
910C22×D4—538no—
911C22×D4C22×D5314yes—
912C22×D4C22×D5314yes—
913C22×D4C22×D5314yes—
914C22×D4C22×D5312yes—
915C23×C4—534no—
916C23×C4—531no—
917C23×C4—534no—
918C23×C4—532no—
919C4⋊Q8—534no—
920C4⋊Q8—538no—
921C4⋊Q8—538no—
922C4⋊Q8—534no—
923C4⋊Q8—532no—
924C4⋊Q8—532no—
925C4⋊Q8—534no—
926#127—534no—
927#127C22×D5314yes—
928#127C22×D5311yescharacteristic
929#127C22×D5311yescharacteristic
930#127C22×D5312yes—
931#127C22×D5314yes—
932#126—534no—
933#126—534no—
934#126—534no—
935#126—538no—
936#126—534no—
937#126—534no—
938#126—534no—
939#126—538no—
940#126—538no—
941#126—538no—
942#126—538no—
943#126—538no—
944#126—534no—
945#126C22×D5314yes—
946#125—534no—
947#125—532no—
948#125—532no—
949#125—534no—
950#125—534no—
951#125—538no—
952#125—538no—
953#125—532no—
954#125—534no—
955#125C22×D5312yes—
956#124—532no—
957#124—532no—
958#124—534no—
959#124—534no—
960#124—534no—
961#124—534no—
962#124—534no—
963#124—538no—
964#124—538no—
965#124—534no—
966#124—534no—
967#124—538no—
968#124—538no—
969#124—538no—
970#124—538no—
971#124—532no—
972#124C22×D5312yes—
973#124C22×D5314yes—
974#123—534no—
975#123—538no—
976#123—538no—
977#123—538no—
978#123—538no—
979#123—538no—
980#123—534no—
981#123—534no—
982#123—538no—
983#123—538no—
984#123—534no—
985#123—538no—
986#123—534no—
987#123—534no—
988#123—534no—
989#123—534no—
990#123—534no—
991#123—538no—
992#123—538no—
993#123—538no—
994#123—538no—
995#123—538no—
996#123—538no—
997#123—538no—
998#123—538no—
999#123—538no—
1000#123C22×D5314yes—
1001#123C22×D5314yes—
1002#123C22×D5314yes—
1003#123C22×D5318yes—
1004C22⋊Q8—532no—
1005C22⋊Q8—534no—
1006C22⋊Q8—532no—
1007C22⋊Q8—534no—
1008C22⋊Q8—538no—
1009C22⋊Q8—538no—
1010C22⋊Q8—532no—
1011C22⋊Q8—534no—
1012C22⋊Q8—538no—
1013C22⋊Q8—538no—
1014C22⋊Q8—538no—
1015C22⋊Q8—534no—
1016C22⋊Q8—538no—
1017C22⋊Q8—538no—
1018C22⋊Q8—538no—
1019C22⋊Q8—538no—
1020C22⋊Q8—538no—
1021C22⋊Q8—538no—
1022C22⋊Q8—538no—
1023C22⋊Q8C22×D5312yes—
1024#121—532no—
1025#121—534no—
1026#121—534no—
1027#121—534no—
1028#121—538no—
1029#121—534no—
1030#121—534no—
1031#121—538no—
1032#121—538no—
1033#121—538no—
1034#121—538no—
1035#121—534no—
1036#121—534no—
1037#121—538no—
1038#121—538no—
1039#121—534no—
1040#121—538no—
1041#121—538no—
1042#121—538no—
1043#121—538no—
1044#121—538no—
1045#121—538no—
1046#121—538no—
1047#121—532no—
1048#121—534no—
1049#121—532no—
1050#121—534no—
1051#121—538no—
1052#121—538no—
1053#121C22×D5312yes—
1054#121C22×D5314yes—
1055#121C22×D5314yes—
1056#121C22×D5318yes—
1057#121C22×D5318yes—
1058#121C22×D5318yes—
1059#121C22×D5318yes—
1060#120—538no—
1061#120—538no—
1062#120—538no—
1063#120—538no—
1064#120—534no—
1065#120—538no—
1066#120—534no—
1067#120—538no—
1068#120C22×D5318yes—
1069#120C22×D5318yes—
1070#120C22×D5314yes—
1071#120C22×D5314yes—
1072C4×Q8—532no—
1073C4×Q8—534no—
1074C4×Q8—532no—
1075C4×Q8—534no—
1076C4×Q8—532no—
1077C4×Q8—534no—
1078C4×Q8—534no—
1079C4×Q8C22×D5312yes—
1080C4×D4—532no—
1081C4×D4—534no—
1082C4×D4—534no—
1083C4×D4—534no—
1084C4×D4—538no—
1085C4×D4—534no—
1086C4×D4—534no—
1087C4×D4—538no—
1088C4×D4—538no—
1089C4×D4—538no—
1090C4×D4—534no—
1091C4×D4—534no—
1092C4×D4—538no—
1093C4×D4—534no—
1094C4×D4—538no—
1095C4×D4—534no—
1096C4×D4—534no—
1097C4×D4—534no—
1098C4×D4—538no—
1099C4×D4—538no—
1100C4×D4—538no—
1101C4×D4—538no—
1102C4×D4—532no—
1103C4×D4—534no—
1104C4×D4—534no—
1105C4×D4—534no—
1106C4×D4—534no—
1107C4×D4—538no—
1108C4×D4—538no—
1109C4×D4—538no—
1110C4×D4—538no—
1111C4×D4—534no—
1112C4×D4—532no—
1113C4×D4—534no—
1114C4×D4C22×D5314yes—
1115C4×D4C22×D5312yes—
1116C4×D4C22×D5314yes—
1117C4×D4C22×D5314yes—
1118#117—534no—
1119#117—534no—
1120#117—538no—
1121#117—534no—
1122#117—534no—
1123#117—534no—
1124#117—534no—
1125#117—534no—
1126#117—538no—
1127#117—538no—
1128#117—534no—
1129#117—534no—
1130#117C22×D5314yes—
1131C2×C4⋊C4—534no—
1132C2×C4⋊C4—534no—
1133C2×C4⋊C4—538no—
1134C2×C4⋊C4—538no—
1135C2×C4⋊C4—534no—
1136C2×C4⋊C4—534no—
1137C2×C4⋊C4—532no—
1138C2×C4⋊C4—534no—
1139C2×C4⋊C4—532no—
1140C2×C4⋊C4—534no—
1141C2×C4⋊C4—534no—
1142C2×C22⋊C4—538no—
1143C2×C22⋊C4—538no—
1144C2×C22⋊C4—534no—
1145C2×C22⋊C4—538no—
1146C2×C22⋊C4—538no—
1147C2×C22⋊C4—534no—
1148C2×C22⋊C4—534no—
1149C2×C22⋊C4—534no—
1150C2×C22⋊C4—534no—
1151C2×C22⋊C4—534no—
1152C2×C22⋊C4—538no—
1153C2×C22⋊C4C22×D5314yes—
1154C2×C42—532no—
1155C2×C42—531no—
1156C2×C42—532no—
1157C2×C42—534no—
1158C2×C42—532no—
1159C2×C42—532no—
1160C2×C42—532no—
1161C2×C42C22×D5311yescharacteristic
1162C24—531no—
1163C24—534no—
1164C24—534no—
1165C24C23×D5314yes—
1166C24C23×D5314yes—
1167#41—48no—
1168#41—21216no—
1169#41—21216no—
1170#41—2128no—
1171#41—2128no—
1172#41—21216no—
1173#41—2128no—
1174#41—21216no—
1175C2×Q8—532no—
1176C2×Q8—534no—
1177C2×Q8—538no—
1178C2×Q8—534no—
1179C2×Q8—534no—
1180C2×Q8—2124no—
1181C2×Q8—2124no—
1182C2×Q8C23×D5312yes—
1183C2×D4—48no—
1184C2×D4—48no—
1185C2×D4—44no—
1186C2×D4—48no—
1187C2×D4—534no—
1188C2×D4—538no—
1189C2×D4—538no—
1190C2×D4—534no—
1191C2×D4—538no—
1192C2×D4—534no—
1193C2×D4—538no—
1194C2×D4—538no—
1195C2×D4—538no—
1196C2×D4—532no—
1197C2×D4—534no—
1198C2×D4—10616no—
1199C2×D4—10616no—
1200C2×D4—2124no—
1201C2×D4—2128no—
1202C2×D4—21216no—
1203C2×D4—2128no—
1204C2×D4—21216no—
1205C2×D4C23×D5312yes—
1206C2×D4C23×D5314yes—
1207C2×D4C23×D5314yes—
1208C2×D4C23×D5314yes—
1209C2×D4C23×D5318yes—
1210C2×D4C23×D5318yes—
1211C2×D4C23×D5318yes—
1212C2×D4C23×D5312yes—
1213C2×D4C23×D5314yes—
1214C2×D4C23×D5312yes—
1215C2×D4C23×D5318yes—
1216C22×C4—531no—
1217C22×C4—534no—
1218C22×C4—532no—
1219C22×C4—538no—
1220C22×C4—534no—
1221C22×C4—538no—
1222C22×C4—538no—
1223C22×C4—538no—
1224C22×C4—534no—
1225C22×C4—532no—
1226C22×C4—532no—
1227C22×C4—532no—
1228C22×C4—532no—
1229C22×C4—534no—
1230C22×C4—534no—
1231C22×C4—532no—
1232C22×C4—532no—
1233C22×C4—534no—
1234C22×C4—534no—
1235C22×C4—534no—
1236C22×C4—538no—
1237C22×C4—1064no—
1238C22×C4—2124no—
1239C22×C4—2128no—
1240C22×C4—2128no—
1241C22×C4C23×D5312yes—
1242C22×C4C23×D5311yescharacteristic
1243C22×C4C23×D5314yes—
1244C22×C4C23×D5318yes—
1245C22×C4C23×D5314yes—
1246C4⋊C4—534no—
1247C4⋊C4—534no—
1248C4⋊C4—532no—
1249C4⋊C4—534no—
1250C4⋊C4—534no—
1251C4⋊C4—534no—
1252C4⋊C4—534no—
1253C4⋊C4—538no—
1254C4⋊C4—538no—
1255C4⋊C4—534no—
1256C4⋊C4—534no—
1257C4⋊C4—532no—
1258C4⋊C4—534no—
1259C4⋊C4—534no—
1260C4⋊C4—534no—
1261C4⋊C4—534no—
1262C4⋊C4—534no—
1263C4⋊C4—538no—
1264C4⋊C4—534no—
1265C4⋊C4—538no—
1266C4⋊C4—538no—
1267C4⋊C4—534no—
1268C4⋊C4—534no—
1269C4⋊C4—538no—
1270C4⋊C4—538no—
1271C4⋊C4C23×D5312yes—
1272C4⋊C4C23×D5312yes—
1273C4⋊C4C23×D5314yes—
1274C4⋊C4C23×D5314yes—
1275C4⋊C4C23×D5314yes—
1276C4⋊C4C23×D5314yes—
1277C22⋊C4—534no—
1278C22⋊C4—534no—
1279C22⋊C4—534no—
1280C22⋊C4—534no—
1281C22⋊C4—538no—
1282C22⋊C4—538no—
1283C22⋊C4—538no—
1284C22⋊C4—538no—
1285C22⋊C4—534no—
1286C22⋊C4—538no—
1287C22⋊C4—538no—
1288C22⋊C4—538no—
1289C22⋊C4—534no—
1290C22⋊C4—534no—
1291C22⋊C4—538no—
1292C22⋊C4—534no—
1293C22⋊C4—534no—
1294C22⋊C4—534no—
1295C22⋊C4—538no—
1296C22⋊C4—534no—
1297C22⋊C4—534no—
1298C22⋊C4—534no—
1299C22⋊C4—534no—
1300C22⋊C4—534no—
1301C22⋊C4—534no—
1302C22⋊C4—538no—
1303C22⋊C4—534no—
1304C22⋊C4C23×D5314yes—
1305C22⋊C4C23×D5314yes—
1306C22⋊C4C23×D5314yes—
1307C22⋊C4C23×D5314yes—
1308C22⋊C4C23×D5314yes—
1309C22⋊C4C23×D5318yes—
1310C22⋊C4C23×D5314yes—
1311C22⋊C4C23×D5314yes—
1312C22⋊C4C23×D5318yes—
1313C42—531no—
1314C42—532no—
1315C42—532no—
1316C42—532no—
1317C42—532no—
1318C42—532no—
1319C42—531no—
1320C42—534no—
1321C42—534no—
1322C42—534no—
1323C42—538no—
1324C42—538no—
1325C42C23×D5312yes—
1326C42C23×D5311yescharacteristic
1327C42C23×D5311yescharacteristic
1328C42C23×D5314yes—
1329C23—28no—
1330C23—48no—
1331C23—44no—
1332C23—48no—
1333C23—532no—
1334C23—534no—
1335C23—534no—
1336C23—1068no—
1337C23—2124no—
1338C23—2128no—
1339C23—2124no—
1340C23—2124no—
1341C23—2122no—
1342C23C24×D5314yes—
1343C23C24×D5314yes—
1344C23C24×D5314yes—
1345C23C24×D5311yescharacteristic
1346Q8—24no—
1347Q8—1064no—
1348Q8—2124no—
1349Q8—2124no—
1350Q8—2124no—
1351Q8—2128no—
1352D4—28no—
1353D4—24no—
1354D4—28no—
1355D4—28no—
1356D4—48no—
1357D4—48no—
1358D4—48no—
1359D4—42no—
1360D4—44no—
1361D4—42no—
1362D4—48no—
1363D4—1068no—
1364D4—1068no—
1365D4—10616no—
1366D4—10616no—
1367D4—1068no—
1368D4—1064no—
1369D4—2128no—
1370D4—2124no—
1371D4—2128no—
1372D4—2128no—
1373D4—2128no—
1374C2×C4—22no—
1375C2×C4—24no—
1376C2×C4—28no—
1377C2×C4—44no—
1378C2×C4—48no—
1379C2×C4—532no—
1380C2×C4—532no—
1381C2×C4—534no—
1382C2×C4—532no—
1383C2×C4—534no—
1384C2×C4—538no—
1385C2×C4—534no—
1386C2×C4—1064no—
1387C2×C4—1064no—
1388C2×C4—1068no—
1389C2×C4—1062no—
1390C2×C4—1068no—
1391C2×C4—1064no—
1392C2×C4—1064no—
1393C2×C4—1068no—
1394C2×C4—2124no—
1395C2×C4—2124no—
1396C2×C4—2122no—
1397C2×C4—2122no—
1398C2×C4—2128no—
1399C2×C4—2124no—
1400C2×C4—2124no—
1401C2×C4—2122no—
1402C2×C4—2128no—
1403C2×C4—2128no—
1404C2×C4—2124no—
1405C2×C4—2128no—
1406C2×C4—2128no—
1407C2×C4C24×D5314yes—
1408C2×C4C24×D5312yes—
1409C2×C4C24×D5311yescharacteristic
1410C2×C4C24×D5311yescharacteristic
1411C2×C4C24×D5314yes—
1412C2×C4C24×D5314yes—
1413C2×C4C24×D5312yes—
1414C22—22no—
1415C22—24no—
1416C22—24no—
1417C22—24no—
1418C22—24no—
1419C22—28no—
1420C22—28no—
1421C22—24no—
1422C22—88no—
1423C22—164no—
1424C22—534no—
1425C22—8484no—
1426C22—1062no—
1427C22—1062no—
1428C22—1064no—
1429C22—1064no—
1430C22—1064no—
1431C22—4248no—
1432C22—2124no—
1433C22H(5,𝔽2)×D5312yes—
1434C22C25×D5311yescharacteristic
1435C4—21no—
1436C4—21no—
1437C4—24no—
1438C4—24no—
1439C4—22no—
1440C4—24no—
1441C4—1062no—
1442C4—1064no—
1443C4—1068no—
1444C4—1062no—
1445C4—1064no—
1446C4—1062no—
1447C4—1064no—
1448C4#1681145814yes—
1449C2—22no—
1450C2—44no—
1451C2—44no—
1452C2—44no—
1453C2—1064no—
1454C2—2124no—
1455C2C2×H(5,𝔽2)×D5311yescharacteristic
1456C2C2×#1681145812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3543C2
hypercenter#3543D53
hypocenterC53#62822
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3543

Complements

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

NH ≅ G/Ntype
1. #20289265C2semidirect
2. #20289245C2semidirect
3. #20289233C2semidirect
4. #20289064C2semidirect
5. #20289055C2semidirect
6. #20289048C2semidirect
7. #20288797C2semidirect
8. #20288795C2semidirect
9. #20288746C2semidirect
10. #20288738C2semidirect
11. #20288656C2semidirect
12. #20288640C2semidirect
13. #20288542C2semidirect
14. #20288471C2semidirect
15. #20288447C2semidirect
16. #20288442C2semidirect
17. #20288356C2semidirect
18. C2×#16811171C2semidirect
19. #529×D53C2semidirect
20. C53×#3543C2semidirect
21. C2×#13133262C22semidirect
22. C22×#11719947C22semidirect
23. #16811376C22semidirect
24. #16811375C22semidirect
25. #16811368C22semidirect
26. #16811366C22semidirect
27. #16811360C22semidirect
28. #16811359C22semidirect
29. #16811359C22semidirect
30. #16811355C22semidirect
31. Q8×Dic106C22semidirect
32. #16811338C22semidirect
33. #16811337C22semidirect
34. #16811333C22semidirect
35. #16811332C22semidirect
36. #16811330C22semidirect
37. #16811330C22semidirect
38. #16811325C22semidirect
39. #16811325C22semidirect
40. #16811323C22semidirect
41. #16811320C22semidirect
42. #16811320C22semidirect
43. #16811320C22semidirect
44. #16811318C22semidirect
45. #16811316C22semidirect
46. #16811315C22semidirect
47. #16811313C22semidirect
48. #16811304C22semidirect
49. #16811304C22semidirect
50. #16811304C22semidirect
51. #16811301C22semidirect
52. #16811299C22semidirect
53. #16811296C22semidirect
54. #16811293C22semidirect
55. #16811281C22semidirect
56. #16811280C22semidirect
57. #16811278C22semidirect
58. #16811277C22semidirect
59. #16811273C22semidirect
60. #16811273C22semidirect
61. #16811273C22semidirect
62. #16811273C22semidirect
63. #16811271C22semidirect
64. #16811271C22semidirect
65. #16811270C22semidirect
66. #16811267C22semidirect
67. #16811267C22semidirect
68. #16811267C22semidirect
69. #16811262C22semidirect
70. #16811262C22semidirect
71. #16811261C22semidirect
72. #16811260C22semidirect
73. #16811260C22semidirect
74. #16811260C22semidirect
75. #16811260C22semidirect
76. #16811258C22semidirect
77. #16811258C22semidirect
78. D4×C22⋊D53C22semidirect
79. D4×C22⋊D53C22semidirect
80. #16811253C22semidirect
81. #16811251C22semidirect
82. #16811244C22semidirect
83. #16811242C22semidirect
84. #16811242C22semidirect
85. #16811241C22semidirect
86. #16811240C22semidirect
87. #16811240C22semidirect
88. #16811227C22semidirect
89. #16811227C22semidirect
90. #16811226C22semidirect
91. #16811218C22semidirect
92. #16811217C22semidirect
93. #16811216C22semidirect
94. #16811210C22semidirect
95. #16811208C22semidirect
96. #16811208C22semidirect
97. #16811205C22semidirect
98. #16811205C22semidirect
99. #16811202C22semidirect
100. #16811195C22semidirect
101. #16811186C22semidirect
102. #16811183C22semidirect
103. #16811183C22semidirect
104. #16811182C22semidirect
105. #16811171C22semidirect
106. #16811171C22semidirect
107. #16811171C22semidirect
108. #16811171C22semidirect
109. #16811171C22semidirect
110. #16811171C22semidirect
111. #16811170C22semidirect
112. C2×#13133217C22semidirect
113. #16811160C22semidirect
114. #16811159C22semidirect
115. #16811158C22semidirect
116. #16811157C22semidirect
117. #16811156C22semidirect
118. #16811155C22semidirect
119. #16811155C22semidirect
120. #16811154C22semidirect
121. #16811153C22semidirect
122. #16811152C22semidirect
123. #16811152C22semidirect
124. #16811151C22semidirect
125. #16811150C22semidirect
126. #126×D53C22semidirect
127. #125×D53C22semidirect
128. C2×#13133204C22semidirect
129. #124×D53C22semidirect
130. #16811133C22semidirect
131. #16811130C22semidirect
132. #16811129C22semidirect
133. C2×#13133201C22semidirect
134. C2×#13133198C22semidirect
135. #123×D53C22semidirect
136. C22⋊Q8×D53C22semidirect
137. C2×#13133188C22semidirect
138. C2×#13133188C22semidirect
140. #121×D53C22semidirect
141. #16811106C22semidirect
142. #16811102C22semidirect
143. #16811098C22semidirect
144. #16811096C22semidirect
145. #16811095C22semidirect
146. C4×Q8×D53C22semidirect
147. C2×D4×Dic53C22semidirect
148. C4×D4×D53C22semidirect
149. C4×D4×D53C22semidirect
150. #117×D53C22semidirect
151. C2×C42×D53C22semidirect
152. C53×#560C22semidirect
153. C53×#559C22semidirect
154. C53×#550C22semidirect
155. C53×#546C22semidirect
156. D42×C53C22semidirect
157. D42×C53C22semidirect
158. C53×#540C22semidirect
159. C53×#535C22semidirect
160. C53×#534C22semidirect
161. C2×#127×C53C22semidirect
162. C53×#529C22semidirect
727. #3543D53semidirect
756. #560C2×D53semidirect
760. #559C2×D53semidirect
785. #550C2×D53semidirect
807. #546C2×D53semidirect
812. D42C2×D53semidirect
813. D42C2×D53semidirect
825. #540C2×D53semidirect
837. #535C2×D53semidirect
841. #534C2×D53semidirect
850. C2×#127C2×D53semidirect
864. #529C2×D53semidirect
891. C53#62822semidirect

Maximal subgroups

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

subgroupindex
#202892652
#202892452
#202892332
#202890642
#202890552
#202890482
#202887972
#202887952
#202887462
#202887382
#202886562
#202886402
#202885422
#202884712
#202884472
#202884422
#202883562
C2×#168111712
#529×D532
C53×#35432
#6282253