Finite Group Databasebeta

← #28293243

Subgroups — #28293243

Order 13568.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288636C214yesmaximal, complemented
2#20288635C214yesmaximal, complemented
3#20288624C214yesmaximal, complemented
4#20288622C214yesmaximal, complemented
5#20288552C218yesmaximal, complemented
6#20288469C214yesmaximal, complemented
7#20288464C214yesmaximal, complemented
8#20288452C214yesmaximal, complemented
9#20288447C214yesmaximal, complemented
10#20288432C214yesmaximal, complemented
11#20288421C214yesmaximal, complemented
12#20288139C214yesmaximal, complemented
13#20288128C214yesmaximal, complemented
14C2×#16811251C211yesmaximal, characteristic, complemented
15#20288044C211yesmaximal, characteristic, complemented
16C2×#16811201C211yesmaximal, characteristic, complemented
17#20287918C211yesmaximal, characteristic, complemented
18#20287916C211yesmaximal, characteristic, complemented
19C2×#16811106C211yesmaximal, characteristic, complemented
20C53×#3449C211yesmaximal, characteristic, complemented
21C22×#11719945C2211yescharacteristic
22#16811344C2218yescomplemented
23#16811343C2218yescomplemented
24#16811338C2218yescomplemented
25#16811337C2218yescomplemented
26#16811331C2218yescomplemented
27#16811330C2218yescomplemented
28#16811325C22116yescomplemented
29#16811325C2218yescomplemented
30#16811320C2218yescomplemented
31#16811319C2218yescomplemented
32#16811319C2218yescomplemented
33#16811316C22116yescomplemented
34#16811316C22116yescomplemented
35#16811315C2218yescomplemented
36#16811313C2218yescomplemented
37#16811313C2218yescomplemented
38#16811310C22116yescomplemented
39#16811307C2218yescomplemented
40#16811304C22116yescomplemented
41#16811296C22116yescomplemented
42#16811279C22116yescomplemented
43#16811277C2218yescomplemented
44#16811273C2218yescomplemented
45#16811260C22116yescomplemented
46#16811251C2214yescomplemented
47#16811251C2214yescomplemented
48#16811251C2214yescomplemented
49#16811251C2214yescomplemented
50#16811246C2218yescomplemented
51#16811242C2218yescomplemented
52#16811242C2218yescomplemented
53#16811240C2218yescomplemented
54#16811234C2218yescomplemented
55#16811233C2218yescomplemented
56#16811227C2218yescomplemented
57#16811226C2218yescomplemented
58#16811217C22116yescomplemented
59#16811208C22116yescomplemented
60#16811201C2214yes—
61#16811201C2214yes—
62#16811201C2214yescomplemented
63#16811201C2214yescomplemented
64#16811201C2212yescomplemented
65#16811201C2212yescomplemented
66#16811197C2212yescomplemented
67#16811194C2212yes—
68#16811190C2212yescomplemented
69#16811187C2212yes—
70#16811182C2214yes—
71#16811178C2218yescomplemented
72#16811175C2218yescomplemented
73#16811171C2218yescomplemented
74#16811169C2214yescomplemented
75#16811168C2218yescomplemented
76C2×#13133217C2212yescomplemented
77C2×#13133216C2212yescomplemented
78#16811159C2218yescomplemented
79#16811154C2218yescomplemented
80#16811152C2218yescomplemented
81#16811152C2218yescomplemented
82#16811150C22116yescomplemented
83C2×#13133209C2212yescomplemented
84C2×#13133208C2212yescomplemented
85#16811134C2214yescomplemented
86#16811130C2214yes—
87#16811129C22116yescomplemented
88C2×#13133196C2212yescomplemented
89C2×#13133194C2214yes—
90C2×#13133193C2212yescomplemented
91C2×#13133191C2212yescomplemented
92C2×#13133189C2214yes—
93C2×#13133188C2212yescomplemented
94#16811106C2214yes—
95#16811106C2214yes—
96#16811106C2212yescomplemented
97#16811106C2214yescomplemented
98#16811106C2214yescomplemented
99#16811106C2212yescomplemented
100#16811106C2212yescomplemented
101#16811106C2212yescomplemented
102#16811104C2212yescomplemented
103#16811104C2212yescomplemented
104#16811103C2212yescomplemented
105#16811103C2212yescomplemented
106#16811101C2212yescomplemented
107#16811100C2212yescomplemented
108#16811098C2214yes—
109#16811098C2212yescomplemented
110#16811097C2212yescomplemented
111#16811096C2214yes—
112#41×Dic53C2214yescomplemented
113#41×Dic53C2214yescomplemented
114C4×#11719945C2214yescomplemented
115#16811091C2214yescomplemented
116C2×Q8×Dic53C2212yescomplemented
117C2×D4×Dic53C2214yes—
118C2×D4×Dic53C2212yescomplemented
119C2×#13133176C2211yescharacteristic
120C2×#13133176C2211yescharacteristic
121C2×#13133176C2212yescomplemented
122C2×#13133176C2214yescomplemented
123#117×D53C2214yescomplemented
124C22×C4⋊Dic53C2211yescharacteristic
125C22×C4⋊Dic53C2212yescomplemented
126C22×#41×C53C2211yescharacteristic
127C22×#41×C53C2211yescharacteristic
128C53×#537C2212yescomplemented
129C53×#537C2212yescomplemented
130C53×#536C2212yes—
131C53×#536C2212yescomplemented
132C53×#535C2212yes—
133C53×#535C2212yescomplemented
134C53×#534C2214yes—
135C53×#532C2214yescomplemented
136C53×#525C2214yes—
137C53×#525C2214yescomplemented
138C2×#117×C53C2211yescharacteristic
139C2×#11719945—28no—
140C2×#11719945C2312yes—
141C2×#11719945C2312yes—
142C2×#11719945C2312yes—
143C2×#11719945C2312yes—
144C2×#11719947C23116yes—
145C22×Dic106C2311yescharacteristic
146C22×Dic106C2314yes—
147C22×D212C2311yescharacteristic
148C22×C22⋊D53C2312yes—
149C22×C22⋊D53C2314yes—
150C23×Dic53C2312yes—
151C23×Dic53C2314yes—
152C22×C4×D53C2312yes—
153#13133217C2318yes—
154#13133217C2318yes—
155#13133216C2318yes—
156#13133216C2318yes—
157#13133215C2314yes—
158#13133213C2314yes—
159#13133212C23116yes—
160#13133212C23116yes—
161#13133210C23116yes—
162#13133210C23116yes—
163#13133210C23116yes—
164#13133210C23116yes—
165#13133209C2318yes—
166#13133209C2318yes—
167#13133208C2318yes—
168#13133208C23116yes—
169#13133208C2318yes—
170#13133207C23116yes—
171#13133207C23116yes—
172#13133206C2314yes—
173#13133204C23116yes—
174#13133204C2314yes—
175#13133203C23116yes—
176#13133203C23116yes—
177#13133201C23116yes—
178#13133201C23116yes—
179#13133200C2318yes—
180#13133199C23116yes—
181#13133199C23116yes—
182#13133198C23116yes—
183#13133198C2318yes—
184#13133198C23116yes—
185#13133197C23116yes—
186#13133196C2314yes—
187#13133196C2318yes—
188#13133196C2314yes—
189#13133196C2318yes—
190#13133194C23116yes—
191#13133194C23116yes—
192#13133194C23116yes—
193#13133194C23116yes—
194#13133193C2318yes—
195#13133193C2318yes—
196#13133193C2314yes—
197#13133193C2314yes—
198#13133191C2314yes—
199#13133191C2318yes—
200#13133191C2314yes—
201#13133191C2318yes—
202#13133189C2318yes—
203#13133189C23116yes—
204#13133189C2318yes—
205#13133189C23116yes—
206#13133189C23116yes—
207#13133189C23116yes—
208#13133188C2318yes—
209#13133188C23116yes—
210#13133188C2318yes—
211#13133188C2314yes—
212#13133188C2314yes—
213#13133186C2318yes—
214#13133185C2318yes—
215Q8×Dic53C2314yes—
216Q8×Dic53C2314yes—
217Q8×Dic53C2318yes—
218Q8×Dic53C2318yes—
219Q8×Dic53C2314yes—
220Q8×Dic53C2314yes—
221C4×Dic106C2314yes—
222C4×Dic106C2314yes—
223#13133182C23116yes—
224#13133182C2314yes—
225#13133182C2314yes—
226C4×D212C2314yes—
227C4×D212C2314yes—
228D4×Dic53C2314yes—
229D4×Dic53C2318yes—
230D4×Dic53C23116yes—
231D4×Dic53C23116yes—
232D4×Dic53C23116yes—
233D4×Dic53C2318yes—
234D4×Dic53C2314yes—
235D4×Dic53C2318yes—
236D4×Dic53C2318yes—
237D4×Dic53C2318yes—
238D4×Dic53C2318yes—
239D4×Dic53C2314yes—
240D4×Dic53C2314yes—
241#13133179C2314yes—
242#13133179C2314yes—
243C4×C22⋊D53C2318yes—
244C4×C22⋊D53C2318yes—
245C4×C22⋊D53C2318yes—
246C4×C22⋊D53C2318yes—
247#13133177C23116yes—
248#13133177C23116yes—
249#13133177C2318yes—
250#13133177C2318yes—
251#13133176C2318yes—
252#13133176C2318yes—
253#13133176C2314yes—
254#13133176C2318yes—
255#13133176C2312yes—
256#13133176C2312yes—
257#13133176C2312yes—
258#13133176C2312yes—
259#13133176C2312yes—
260#13133176C2312yes—
261#13133176C2312yes—
262#13133176C2312yes—
263#13133176C2314yes—
264#13133176C2318yes—
265#13133175C23116yes—
266#13133175C2314yes—
267#13133175C2314yes—
268#13133174C2318yes—
269#13133173C2318yes—
270#13133173C23116yes—
271#13133173C23116yes—
272C2×C4⋊Dic53C2318yes—
273C2×C4⋊Dic53C2314yes—
274C2×C4⋊Dic53C2318yes—
275C2×C4⋊Dic53C2314yes—
276C2×C4⋊Dic53C2314yes—
277C2×C4⋊Dic53C2312yes—
278C2×C4⋊Dic53C2312yes—
279C2×C4⋊Dic53C2312yes—
280C2×C4⋊Dic53C2312yes—
281C2×C4⋊Dic53C2312yes—
282C2×C4⋊Dic53C2312yes—
283C2×C4⋊Dic53C2311yescharacteristic
284C2×C4⋊Dic53C2314yes—
285C2×C4⋊Dic53C2311yescharacteristic
286C2×C4⋊Dic53C2311yescharacteristic
287C2×C4⋊Dic53C2311yescharacteristic
288C2×#11719919C2314yes—
289C2×#11719919C2314yes—
290C2×#11719919C2314yes—
291C4⋊C4×D53C2314yes—
292C4⋊C4×D53C2314yes—
293C2×C22⋊Dic53C2314yes—
294C2×C22⋊Dic53C2318yes—
295C2×C22⋊Dic53C2312yes—
296C2×C22⋊Dic53C2312yes—
297C2×C22⋊Dic53C2314yes—
298C2×#11719921C2314yes—
299C22⋊C4×D53C2318yes—
300C2×C4×Dic53C2312yes—
301C2×C4×Dic53C2312yes—
302C2×C4×Dic53C2314yes—
303C2×C4×Dic53C2318yes—
304C42×D53C2318yes—
305C2×#41×C53—28no—
306C2×#41×C53—28no—
307C2×#41×C53C2312yes—
308C2×#41×C53C2312yes—
309C2×#41×C53C2312yes—
310C2×#41×C53C2312yes—
311C2×#41×C53C2312yes—
312C2×#41×C53C2312yes—
313C2×#41×C53C2312yes—
314C2×#41×C53C2312yes—
315C22×Q8×C53C2311yescharacteristic
316C22×Q8×C53C2311yescharacteristic
317C22×D4×C53C2312yes—
318C22×D4×C53C2312yes—
319C22×D4×C53C2311yescharacteristic
320C22×D4×C53C2311yescharacteristic
321C23×C4×C53C2312yes—
322C23×C4×C53C2312yes—
323C23×C4×C53C2311yescharacteristic
324C4⋊Q8×C53C2314yes—
325#127×C53C2314yes—
326#124×C53C2314yes—
327#124×C53C2314yes—
328#123×C53C2318yes—
329#123×C53C2318yes—
330C22⋊Q8×C53C2314yes—
331C22⋊Q8×C53C2314yes—
332C22⋊Q8×C53C2314yes—
333C22⋊Q8×C53C2314yes—
334#121×C53C2314yes—
335#121×C53C2318yes—
336#121×C53C2314yes—
337#121×C53C2314yes—
338#121×C53C2314yes—
339#121×C53C2318yes—
340#120×C53C2318yes—
341#120×C53C2318yes—
342C4×D4×C53C2318yes—
343C4×D4×C53C2318yes—
344#117×C53C2312yes—
345#117×C53C2312yes—
346#117×C53C2312yes—
347#117×C53C2312yes—
348C2×C4⋊C4×C53C2311yescharacteristic
349C2×C4⋊C4×C53C2311yescharacteristic
350C2×C22⋊C4×C53C2312yes—
351C2×C42×C53C2312yes—
352C24×C53C2412yes—
353C24×C53C2412yes—
354C24×C53C2411yescharacteristic
355C23×D53C2412yes—
356#41×C53—28no—
357#41×C53—28no—
358#41×C53—28no—
359#41×C53—28no—
360#41×C53—28no—
361#41×C53—28no—
362#41×C53—28no—
363#41×C53—28no—
364C2×Q8×C53—24no—
365C2×Q8×C53—24no—
366C2×Q8×C53C2412yes—
367C2×Q8×C53C2412yes—
368C2×Q8×C53C2412yes—
369C2×Q8×C53C2412yes—
370C2×D4×C53—28no—
371C2×D4×C53—28no—
372C2×D4×C53—24no—
373C2×D4×C53—24no—
374C2×D4×C53C2414yes—
375C2×D4×C53C2414yes—
376C2×D4×C53C2412yes—
377C2×D4×C53C2414yes—
378C2×D4×C53C2414yes—
379C2×D4×C53C2412yes—
380C2×D4×C53C2412yes—
381C2×D4×C53C2412yes—
382C2×D4×C53C2418yes—
383C2×D4×C53C2418yes—
384C22×C4×C53—28no—
385C22×C4×C53—28no—
386C22×C4×C53#4118yescomplemented
387C22×C4×C53C2414yes—
388C22×C4×C53C2414yes—
389C22×C4×C53C2414yes—
390C22×C4×C53C2414yes—
391C22×C4×C53C2412yes—
392C22×C4×C53C2412yes—
393C22×C4×C53C2412yes—
394C22×C4×C53C2412yes—
395C22×C4×C53C2411yescharacteristic
396C22×C4×C53C2411yescharacteristic
397C22×C4×C53C2411yescharacteristic
398C22×C4×C53C2411yescharacteristic
399C22×C4×C53C2411yescharacteristic
400C22×C4×C53C2411yescharacteristic
401C2×C22⋊D53—28no—
402C2×C22⋊D53—84no—
403C2×C22⋊D53C2414yes—
404C2×C22⋊D53C2414yes—
405C2×C22⋊D53C2418yes—
406C2×C22⋊D53C24116yes—
407C2×C22⋊D53C2418yes—
408C22×Dic53—82no—
409C22×Dic53—84no—
410C22×Dic53C2412yes—
411C22×Dic53C2412yes—
412C22×Dic53C2412yes—
413C22×Dic53C2412yes—
414C22×Dic53C2412yes—
415C22×Dic53C2414yes—
416C22×Dic53C2418yes—
417C22×Dic53C2418yes—
418C22×Dic53C2414yes—
419C22×Dic53C2414yes—
420C22×Dic53C24116yes—
421#11719947—816no—
422#11719945—28no—
423#11719945—28no—
424#11719945—28no—
425#11719945—28no—
426C2×D212—24no—
427C2×D212C2412yes—
428C2×D212C2412yes—
429C2×C4×D53—28no—
430C2×C4×D53C2414yes—
431C2×C4×D53C2414yes—
432C2×C4×D53C2418yes—
433C2×C4×D53C2418yes—
434C2×Dic106—24no—
435C2×Dic106—84no—
436C2×Dic106C2412yes—
437C2×Dic106C2412yes—
438C2×Dic106C24116yes—
439C4⋊C4×C53C2412yes—
440C4⋊C4×C53C2412yes—
441C4⋊C4×C53C2412yes—
442C4⋊C4×C53C2412yes—
443C4⋊C4×C53C2418yes—
444C4⋊C4×C53C2418yes—
445C22⋊C4×C53C2414yes—
446C22⋊C4×C53C2414yes—
447C22⋊C4×C53C2418yes—
448C22⋊C4×C53C2418yes—
449C22⋊C4×C53C2418yes—
450C22⋊C4×C53C2418yes—
451C42×C53C2414yes—
452C42×C53C2414yes—
453C22⋊Dic53C2414yes—
454C22⋊Dic53C2414yes—
455C22⋊Dic53C24116yes—
456C22⋊Dic53C2414yes—
457C22⋊Dic53C2414yes—
458C22⋊Dic53C2418yes—
459C22⋊Dic53C24116yes—
460C22⋊Dic53C2418yes—
461C22⋊Dic53C2418yes—
462C22⋊Dic53C2418yes—
463#11719921C2418yes—
464#11719921C2418yes—
465#11719921C24116yes—
466#11719921C2418yes—
467#11719921C2418yes—
468C4⋊Dic53C2412yes—
469C4⋊Dic53C2412yes—
470C4⋊Dic53C2412yes—
471C4⋊Dic53C2414yes—
472C4⋊Dic53C2414yes—
473C4⋊Dic53C2412yes—
474C4⋊Dic53C2412yes—
475C4⋊Dic53C2412yes—
476C4⋊Dic53C2414yes—
477C4⋊Dic53C2414yes—
478C4⋊Dic53C24116yes—
479C4⋊Dic53C24116yes—
480C4⋊Dic53C2412yes—
481C4⋊Dic53C2412yes—
482C4⋊Dic53C2418yes—
483C4⋊Dic53C2418yes—
484#11719919C2418yes—
485#11719919C2418yes—
486#11719919C24116yes—
487#11719919C24116yes—
488#11719919C24116yes—
489#11719919C2418yes—
490#11719919C2418yes—
491C4×Dic53C2414yes—
492C4×Dic53C2418yes—
493C4×Dic53C2418yes—
494C4×Dic53C2414yes—
495C4×Dic53C2414yes—
496C4×Dic53C2418yes—
497C4×Dic53C24116yes—
498C4×Dic53C2418yes—
499C4×Dic53C2414yes—
500C23×C53—24no—
501C23×C53—24no—
502C23×C53—41no—
503C23×C53—42no—
504C23×C53—41no—
505C23×C53—42no—
506C23×C53—42no—
507C23×C53—42no—
508C23×C53C2×#4114yes—
509C23×C53C2514yes—
510C23×C53C2514yes—
511C23×C53C2511yescharacteristic
512C23×C53C2511yescharacteristic
513C23×C53C2511yescharacteristic
514C22×D53—24no—
515C22×D53—42no—
516C22×D53—42no—
517C22×D53C2514yes—
518Q8×C53—24no—
519Q8×C53—24no—
520Q8×C53—24no—
521Q8×C53—24no—
522D4×C53—28no—
523D4×C53—28no—
524D4×C53—28no—
525D4×C53—28no—
526D4×C53—24no—
527D4×C53—24no—
528D4×C53—24no—
529D4×C53—24no—
530D4×C53—48no—
531D4×C53—48no—
532C2×C4×C53—24no—
533C2×C4×C53—24no—
534C2×C4×C53—28no—
535C2×C4×C53—28no—
536C2×C4×C53—28no—
537C2×C4×C53—28no—
538C2×C4×C53—42no—
539C2×C4×C53—42no—
540C2×C4×C53C2×#4114yes—
541C2×C4×C53C2×#4114yes—
542C2×C4×C53C2×#4114yes—
543C2×C4×C53C2×#4114yes—
544C2×C4×C53C2×#4114yes—
545C2×C4×C53C2×#4114yes—
546C2×C4×C53C2514yes—
547C2×C4×C53C2514yes—
548C2×C4×C53C2514yes—
549C2×C4×C53C2514yes—
550C2×C4×C53C2511yescharacteristic
551C2×C4×C53C2511yescharacteristic
552C2×C4×C53C2511yescharacteristic
553C2×C4×C53C2511yescharacteristic
554C22⋊D53—28no—
555C22⋊D53—28no—
556C22⋊D53—48no—
557C22⋊D53—416no—
558C22⋊D53—48no—
559C2×Dic53—24no—
560C2×Dic53—42no—
561C2×Dic53—44no—
562C2×Dic53—48no—
563C2×Dic53—416no—
564C2×Dic53—44no—
565C2×Dic53—42no—
566C2×Dic53—44no—
567C2×Dic53—42no—
568C2×Dic53—48no—
569C2×Dic53—42no—
570C2×Dic53C2514yes—
571C2×Dic53C2514yes—
572C2×Dic53C2518yes—
573C2×Dic53C2514yes—
574C2×Dic53C2514yes—
575C2×Dic53C2514yes—
576D212—24no—
577D212—24no—
578C4×D53—28no—
579C4×D53—28no—
580C4×D53—48no—
581C4×D53—48no—
582Dic106—24no—
583Dic106—24no—
584Dic106—416no—
585#62856—531nomaximal, Sylow
586C22×C53—21no—
587C22×C53—21no—
588C22×C53—21no—
589C22×C53—21no—
590C22×C53—21no—
591C22×C53—21no—
592C22×C53—24no—
593C22×C53—24no—
594C22×C53—24no—
595C22×C53—24no—
596C22×C53—24no—
597C22×C53—24no—
598C22×C53—44no—
599C22×C53—48no—
600C22×C53—84no—
601C22×C53C22×#4112yes—
602C22×C53C22×#4112yes—
603C22×C53C22×#4112yes—
604C22×C53C2611yescharacteristic
605C2×D53—24no—
606C2×D53—24no—
607C2×D53—24no—
608C2×D53—84no—
609C4×C53—24no—
610C4×C53—24no—
611C4×C53—24no—
612C4×C53—24no—
613C4×C53C22×#4112yes—
614C4×C53C22×#4112yes—
615C4×C53C22×#4112yes—
616C4×C53C22×#4112yes—
617Dic53—24no—
618Dic53—24no—
619Dic53—28no—
620Dic53—24no—
621Dic53—24no—
622Dic53—24no—
623#3512—534no—
624#3512—534no—
625#3511—534no—
626#3511—534no—
627#3505—538no—
628#3495—534no—
629#3495—534no—
630#3494—534no—
631#3494—534no—
632#3493—534no—
633#3492—534no—
634#3461—534no—
635#3460—534no—
636C2×#544—531no—
637#3449—531no—
638#3449D5311yescharacteristic, complemented
639C2×#537—531no—
640#3428—531no—
641#3428—531no—
642C2×#520—531no—
643C2×C53—22no—
644C2×C53—22no—
645C2×C53—22no—
646C2×C53—44no—
647C2×C53—44no—
648C2×C53C23×#4111yescharacteristic
649C2×C53H(7,𝔽2)11yescharacteristic
650C2×C532−1+611yescharacteristic
651D53—44no—
652C22×#41—531no—
653C22×#41C2×D5311yescharacteristic
654C22×#41C2×D5311yescharacteristic
655#556—538no—
656#556—538no—
657#555—538no—
658#555—538no—
659#554—538no—
660#554—538no—
661#553—5316no—
662#553—5316no—
663#553—538no—
664#553—538no—
665#553—5316no—
666#553—538no—
667#553—538no—
668#552—5316no—
669#552—538no—
670#552—538no—
671#552—538no—
672#552—538no—
673#551—5316no—
674#551—5316no—
675#548—5316no—
676#547—538no—
677#547—538no—
678#546—5316no—
679#544—534no—
680#544—534no—
681#544—534no—
682#544—534no—
683#542—538no—
684#542—538no—
685#542—538no—
686#542—538no—
687#541—538no—
688#541—538no—
689#540—538no—
690#540—538no—
691#539—5316no—
692#538—5316no—
693#537—534no—
694#537—534no—
695#537—534no—
696#537—534no—
697#537—532no—
698#537—532no—
699#537C2×D5312yescomplemented
700#537C2×D5312yescomplemented
701#536—532no—
702#536—532no—
703#536C2×D5312yes—
704#536C2×D5312yescomplemented
705#535—532no—
706#535—532no—
707#535C2×D5312yes—
708#535C2×D5312yescomplemented
709#534—534no—
710#534C2×D5314yes—
711#533—538no—
712#533—538no—
713#532—534no—
714#532—538no—
715#532—538no—
716#532C2×D5314yescomplemented
717C2×C4⋊Q8—532no—
718C2×C4⋊Q8—532no—
719#529—538no—
720#529—538no—
721#529—5316no—
722#529—538no—
723#529—538no—
724C2×#125—532no—
725C2×#125—532no—
726#525—534no—
727#525—534no—
728#525—5316no—
729#525C2×D5314yes—
730#525C2×D5314yescomplemented
731C2×C22⋊Q8—532no—
732C2×C22⋊Q8—532no—
733C2×C22⋊Q8—534no—
734C2×#121—532no—
735C2×#121—534no—
736C2×#121—532no—
737#520—534no—
738#520—534no—
739#520—534no—
740#520—534no—
741#520—532no—
742#520—532no—
743#520—532no—
744#520—532no—
745#520—532no—
746#520—532no—
747#520—532no—
748#520—532no—
749#519—532no—
750#519—532no—
751#518—534no—
752#518—532no—
753#518—532no—
754#518—534no—
755C4×#41—534no—
756C4×#41—534no—
757C4×#41—534no—
758C4×#41—534no—
759C2×C4×Q8—532no—
760C2×C4×D4—534no—
761C2×C4×D4—532no—
762C2×#117—531no—
763C2×#117—531no—
764C2×#117—532no—
765C2×#117—534no—
766C2×#117—534no—
767C2×#117C2×D5311yescharacteristic
768C22×C4⋊C4—531no—
769C22×C4⋊C4—532no—
770C53#6285611yescharacteristic, complemented, Sylow
771C2×#41—28no—
772C2×#41—28no—
773C2×#41—5316no—
774C2×#41—532no—
775C2×#41—532no—
776C2×#41—532no—
777C2×#41—532no—
778C2×#41—1068no—
779C2×#41C22×D5312yes—
780C2×#41C22×D5312yes—
781C2×#41C22×D5312yes—
782C2×#41C22×D5312yes—
783C2×#41C22×D5312yes—
784C2×#41C22×D5312yes—
785C2×#41C22×D5312yes—
786C2×#41C22×D5312yes—
787C22×Q8—531no—
788C22×Q8—534no—
789C22×Q8C22×D5311yescharacteristic
790C22×Q8C22×D5311yescharacteristic
791C22×D4—532no—
792C22×D4—534no—
793C22×D4—531no—
794C22×D4C22×D5312yes—
795C22×D4C22×D5311yescharacteristic
796C22×D4C22×D5312yes—
797C22×D4C22×D5311yescharacteristic
798C23×C4—532no—
799C23×C4—534no—
800C23×C4—532no—
801C23×C4C22×D5312yes—
802C23×C4C22×D5312yes—
803C23×C4C22×D5311yescharacteristic
804C4⋊Q8—534no—
805C4⋊Q8—538no—
806C4⋊Q8—538no—
807C4⋊Q8—538no—
808C4⋊Q8—538no—
809C4⋊Q8C22×D5314yes—
810#127—534no—
811#127C22×D5314yes—
812#126—5316no—
813#126—5316no—
814#126—5316no—
815#126—5316no—
816#126—5316no—
817#126—5316no—
818#125—538no—
819#125—538no—
820#125—5316no—
821#125—5316no—
822#125—5316no—
823#125—538no—
824#125—538no—
825#124—534no—
826#124—534no—
827#124—5316no—
828#124—5316no—
829#124—5316no—
830#124C22×D5314yes—
831#124C22×D5314yes—
832#123—538no—
833#123—5316no—
834#123—5316no—
835#123—538no—
836#123—5316no—
837#123—5316no—
838#123—5316no—
839#123—5316no—
840#123C22×D5318yes—
841#123C22×D5318yes—
842C22⋊Q8—538no—
843C22⋊Q8—538no—
844C22⋊Q8—534no—
845C22⋊Q8—534no—
846C22⋊Q8—538no—
847C22⋊Q8—538no—
848C22⋊Q8—534no—
849C22⋊Q8—534no—
850C22⋊Q8—5316no—
851C22⋊Q8—5316no—
852C22⋊Q8—5316no—
853C22⋊Q8—5316no—
854C22⋊Q8—5316no—
855C22⋊Q8C22×D5314yes—
856C22⋊Q8C22×D5314yes—
857C22⋊Q8C22×D5314yes—
858C22⋊Q8C22×D5314yes—
859#121—5316no—
860#121—538no—
861#121—538no—
862#121—5316no—
863#121—534no—
864#121—534no—
865#121—5316no—
866#121—538no—
867#121—538no—
868#121—5316no—
869#121—5316no—
870#121—538no—
871#121—538no—
872#121—534no—
873#121—534no—
874#121C22×D5314yes—
875#121C22×D5314yes—
876#121C22×D5314yes—
877#121C22×D5314yes—
878#121C22×D5318yes—
879#121C22×D5318yes—
880#120—538no—
881#120—538no—
882#120C22×D5318yes—
883#120C22×D5318yes—
884C4×Q8—538no—
885C4×Q8—538no—
886C4×Q8—534no—
887C4×Q8—534no—
888C4×Q8—534no—
889C4×Q8—534no—
890C4×Q8—534no—
891C4×Q8—534no—
892C4×Q8—5316no—
893C4×Q8—534no—
894C4×Q8—534no—
895C4×D4—538no—
896C4×D4—538no—
897C4×D4—5316no—
898C4×D4—5316no—
899C4×D4—538no—
900C4×D4—538no—
901C4×D4—534no—
902C4×D4—534no—
903C4×D4—534no—
904C4×D4—538no—
905C4×D4—538no—
906C4×D4—534no—
907C4×D4—5316no—
908C4×D4—538no—
909C4×D4—538no—
910C4×D4—538no—
911C4×D4—538no—
912C4×D4—534no—
913C4×D4—534no—
914C4×D4—538no—
915C4×D4—538no—
916C4×D4—5316no—
917C4×D4—5316no—
918C4×D4—534no—
919C4×D4—534no—
920C4×D4C22×D5318yes—
921C4×D4C22×D5318yes—
922#117—532no—
923#117—532no—
924#117—532no—
925#117—532no—
926#117—532no—
927#117—532no—
928#117—538no—
929#117—532no—
930#117—538no—
931#117—532no—
932#117—534no—
933#117—538no—
934#117—538no—
935#117—534no—
936#117—534no—
937#117—534no—
938#117—5316no—
939#117—538no—
940#117—5316no—
941#117—5316no—
942#117—538no—
943#117C22×D5312yes—
944#117C22×D5312yes—
945#117C22×D5312yes—
946#117C22×D5312yes—
947C2×C4⋊C4—531no—
948C2×C4⋊C4—532no—
949C2×C4⋊C4—532no—
950C2×C4⋊C4—534no—
951C2×C4⋊C4—532no—
952C2×C4⋊C4—532no—
953C2×C4⋊C4—532no—
954C2×C4⋊C4—532no—
955C2×C4⋊C4—538no—
956C2×C4⋊C4—538no—
957C2×C4⋊C4—531no—
958C2×C4⋊C4—531no—
959C2×C4⋊C4—531no—
960C2×C4⋊C4—534no—
961C2×C4⋊C4—534no—
962C2×C4⋊C4—534no—
963C2×C4⋊C4—534no—
964C2×C4⋊C4—534no—
965C2×C4⋊C4—534no—
966C2×C4⋊C4—534no—
967C2×C4⋊C4—534no—
968C2×C4⋊C4C22×D5311yescharacteristic
969C2×C4⋊C4C22×D5311yescharacteristic
970C2×C22⋊C4—532no—
971C2×C22⋊C4—534no—
972C2×C22⋊C4—532no—
973C2×C22⋊C4—538no—
974C2×C22⋊C4—534no—
975C2×C22⋊C4—534no—
976C2×C22⋊C4—538no—
977C2×C22⋊C4C22×D5312yes—
978C2×C42—532no—
979C2×C42—534no—
980C2×C42—532no—
981C2×C42—538no—
982C2×C42—538no—
983C2×C42C22×D5312yes—
984C24—532no—
985C24C23×D5312yes—
986C24C23×D5312yes—
987C24C23×D5311yescharacteristic
988#41—28no—
989#41—28no—
990#41—28no—
991#41—28no—
992#41—28no—
993#41—28no—
994#41—28no—
995#41—28no—
996#41—1068no—
997#41—1068no—
998#41—1068no—
999#41—1068no—
1000#41—42416no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—532no—
1004C2×Q8—532no—
1005C2×Q8—5316no—
1006C2×Q8—1064no—
1007C2×Q8—4244no—
1008C2×Q8C23×D5312yes—
1009C2×Q8C23×D5312yes—
1010C2×Q8C23×D5312yes—
1011C2×Q8C23×D5312yes—
1012C2×D4—28no—
1013C2×D4—28no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—534no—
1017C2×D4—534no—
1018C2×D4—538no—
1019C2×D4—538no—
1020C2×D4—5316no—
1021C2×D4—532no—
1022C2×D4—532no—
1023C2×D4—1068no—
1024C2×D4—1064no—
1025C2×D4—4244no—
1026C2×D4C23×D5314yes—
1027C2×D4C23×D5314yes—
1028C2×D4C23×D5314yes—
1029C2×D4C23×D5314yes—
1030C2×D4C23×D5312yes—
1031C2×D4C23×D5312yes—
1032C2×D4C23×D5312yes—
1033C2×D4C23×D5312yes—
1034C2×D4C23×D5318yes—
1035C2×D4C23×D5318yes—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—532no—
1039C22×C4—532no—
1040C22×C4—532no—
1041C22×C4—532no—
1042C22×C4—532no—
1043C22×C4—534no—
1044C22×C4—538no—
1045C22×C4—538no—
1046C22×C4—534no—
1047C22×C4—534no—
1048C22×C4—5316no—
1049C22×C4—534no—
1050C22×C4—534no—
1051C22×C4—538no—
1052C22×C4—538no—
1053C22×C4—1068no—
1054C22×C4—4242no—
1055C22×C4—4244no—
1056C22×C4#1171994718yescomplemented
1057C22×C4C23×D5312yes—
1058C22×C4C23×D5314yes—
1059C22×C4C23×D5312yes—
1060C22×C4C23×D5314yes—
1061C22×C4C23×D5314yes—
1062C22×C4C23×D5314yes—
1063C22×C4C23×D5312yes—
1064C22×C4C23×D5312yes—
1065C22×C4C23×D5311yescharacteristic
1066C22×C4C23×D5311yescharacteristic
1067C22×C4C23×D5311yescharacteristic
1068C22×C4C23×D5311yescharacteristic
1069C22×C4C23×D5311yescharacteristic
1070C22×C4C23×D5311yescharacteristic
1071C4⋊C4—532no—
1072C4⋊C4—532no—
1073C4⋊C4—534no—
1074C4⋊C4—534no—
1075C4⋊C4—532no—
1076C4⋊C4—532no—
1077C4⋊C4—532no—
1078C4⋊C4—532no—
1079C4⋊C4—534no—
1080C4⋊C4—534no—
1081C4⋊C4—5316no—
1082C4⋊C4—532no—
1083C4⋊C4—532no—
1084C4⋊C4—538no—
1085C4⋊C4—538no—
1086C4⋊C4—538no—
1087C4⋊C4—538no—
1088C4⋊C4—5316no—
1089C4⋊C4—5316no—
1090C4⋊C4—5316no—
1091C4⋊C4—5316no—
1092C4⋊C4—538no—
1093C4⋊C4—538no—
1094C4⋊C4C23×D5312yes—
1095C4⋊C4C23×D5312yes—
1096C4⋊C4C23×D5312yes—
1097C4⋊C4C23×D5312yes—
1098C4⋊C4C23×D5318yes—
1099C4⋊C4C23×D5318yes—
1100C22⋊C4—534no—
1101C22⋊C4—534no—
1102C22⋊C4—534no—
1103C22⋊C4—534no—
1104C22⋊C4—538no—
1105C22⋊C4—5316no—
1106C22⋊C4—538no—
1107C22⋊C4—5316no—
1108C22⋊C4—538no—
1109C22⋊C4—538no—
1110C22⋊C4—538no—
1111C22⋊C4—538no—
1112C22⋊C4—5316no—
1113C22⋊C4—538no—
1114C22⋊C4—538no—
1115C22⋊C4C23×D5314yes—
1116C22⋊C4C23×D5314yes—
1117C22⋊C4C23×D5318yes—
1118C22⋊C4C23×D5318yes—
1119C22⋊C4C23×D5318yes—
1120C22⋊C4C23×D5318yes—
1121C42—534no—
1122C42—534no—
1123C42—534no—
1124C42—538no—
1125C42—538no—
1126C42—5316no—
1127C42—538no—
1128C42—538no—
1129C42—534no—
1130C42C23×D5314yes—
1131C42C23×D5314yes—
1132C23—24no—
1133C23—24no—
1134C23—41no—
1135C23—42no—
1136C23—41no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—534no—
1141C23—1064no—
1142C23—2122no—
1143C23—2122no—
1144C23C2×#1171994714yes—
1145C23C24×D5314yes—
1146C23C24×D5314yes—
1147C23C24×D5311yescharacteristic
1148C23C24×D5311yescharacteristic
1149C23C24×D5311yescharacteristic
1150Q8—24no—
1151Q8—24no—
1152Q8—24no—
1153Q8—24no—
1154Q8—1064no—
1155Q8—1064no—
1156Q8—21216no—
1157D4—28no—
1158D4—28no—
1159D4—28no—
1160D4—28no—
1161D4—24no—
1162D4—24no—
1163D4—24no—
1164D4—24no—
1165D4—48no—
1166D4—48no—
1167D4—1068no—
1168D4—1068no—
1169D4—1064no—
1170D4—1064no—
1171D4—2128no—
1172D4—21216no—
1173D4—2128no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—28no—
1177C2×C4—28no—
1178C2×C4—28no—
1179C2×C4—28no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—534no—
1183C2×C4—534no—
1184C2×C4—534no—
1185C2×C4—534no—
1186C2×C4—534no—
1187C2×C4—538no—
1188C2×C4—1064no—
1189C2×C4—1068no—
1190C2×C4—1068no—
1191C2×C4—2128no—
1192C2×C4—2128no—
1193C2×C4—2122no—
1194C2×C4—2128no—
1195C2×C4—2122no—
1196C2×C4—2122no—
1197C2×C4—2124no—
1198C2×C4—2124no—
1199C2×C4—2124no—
1200C2×C4—21216no—
1201C2×C4—2122no—
1202C2×C4—2128no—
1203C2×C4C2×#1171994714yes—
1204C2×C4C2×#1171994714yes—
1205C2×C4C2×#1171994714yes—
1206C2×C4C2×#1171994714yes—
1207C2×C4C2×#1171994714yes—
1208C2×C4C2×#1171994714yes—
1209C2×C4C24×D5314yes—
1210C2×C4C24×D5314yes—
1211C2×C4C24×D5314yes—
1212C2×C4C24×D5314yes—
1213C2×C4C24×D5311yescharacteristic
1214C2×C4C24×D5311yescharacteristic
1215C2×C4C24×D5311yescharacteristic
1216C2×C4C24×D5311yescharacteristic
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—44no—
1230C22—48no—
1231C22—84no—
1232C22—1064no—
1233C22—1064no—
1234C22—1064no—
1235C22—4244no—
1236C22C22×#1171994712yes—
1237C22C22×#1171994712yes—
1238C22C22×#1171994712yes—
1239C22C25×D5311yescharacteristic
1240C4—24no—
1241C4—24no—
1242C4—24no—
1243C4—24no—
1244C4—1064no—
1245C4—1064no—
1246C4—1068no—
1247C4—1064no—
1248C4—1064no—
1249C4—1064no—
1250C4C22×#1171994712yes—
1251C4C22×#1171994712yes—
1252C4C22×#1171994712yes—
1253C4C22×#1171994712yes—
1254C2—22no—
1255C2—22no—
1256C2—22no—
1257C2—44no—
1258C2—44no—
1259C2—2124no—
1260C2C23×#1171994711yescharacteristic
1261C2#2028952611yescharacteristic
1262C2#2028952811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3449C2
hypercenter#3449D53
hypocenterC53#62856
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #20288636C2semidirect
2. #20288635C2semidirect
3. #20288624C2semidirect
4. #20288622C2semidirect
5. #20288552C2semidirect
6. #20288469C2semidirect
7. #20288464C2semidirect
8. #20288452C2semidirect
9. #20288447C2semidirect
10. #20288432C2semidirect
11. #20288421C2semidirect
12. #20288139C2semidirect
13. #20288128C2semidirect
14. C2×#16811251C2semidirect
15. #20288044C2semidirect
16. C2×#16811201C2semidirect
17. #20287918C2semidirect
18. #20287916C2semidirect
19. C2×#16811106C2semidirect
20. C53×#3449C2semidirect
22. #16811344C22semidirect
23. #16811343C22semidirect
24. #16811338C22semidirect
25. #16811337C22semidirect
26. #16811331C22semidirect
27. #16811330C22semidirect
28. #16811325C22semidirect
29. #16811325C22semidirect
30. #16811320C22semidirect
31. #16811319C22semidirect
32. #16811319C22semidirect
33. #16811316C22semidirect
34. #16811316C22semidirect
35. #16811315C22semidirect
36. #16811313C22semidirect
37. #16811313C22semidirect
38. #16811310C22semidirect
39. #16811307C22semidirect
40. #16811304C22semidirect
41. #16811296C22semidirect
42. #16811279C22semidirect
43. #16811277C22semidirect
44. #16811273C22semidirect
45. #16811260C22semidirect
46. #16811251C22semidirect
47. #16811251C22semidirect
48. #16811251C22semidirect
49. #16811251C22semidirect
50. #16811246C22semidirect
51. #16811242C22semidirect
52. #16811242C22semidirect
53. #16811240C22semidirect
54. #16811234C22semidirect
55. #16811233C22semidirect
56. #16811227C22semidirect
57. #16811226C22semidirect
58. #16811217C22semidirect
59. #16811208C22semidirect
62. #16811201C22semidirect
63. #16811201C22semidirect
64. #16811201C22semidirect
65. #16811201C22semidirect
66. #16811197C22semidirect
68. #16811190C22semidirect
71. #16811178C22semidirect
72. #16811175C22semidirect
73. #16811171C22semidirect
74. #16811169C22semidirect
75. #16811168C22semidirect
76. C2×#13133217C22semidirect
77. C2×#13133216C22semidirect
78. #16811159C22semidirect
79. #16811154C22semidirect
80. #16811152C22semidirect
81. #16811152C22semidirect
82. #16811150C22semidirect
83. C2×#13133209C22semidirect
84. C2×#13133208C22semidirect
85. #16811134C22semidirect
87. #16811129C22semidirect
88. C2×#13133196C22semidirect
90. C2×#13133193C22semidirect
91. C2×#13133191C22semidirect
93. C2×#13133188C22semidirect
96. #16811106C22semidirect
97. #16811106C22semidirect
98. #16811106C22semidirect
99. #16811106C22semidirect
100. #16811106C22semidirect
101. #16811106C22semidirect
102. #16811104C22semidirect
103. #16811104C22semidirect
104. #16811103C22semidirect
105. #16811103C22semidirect
106. #16811101C22semidirect
107. #16811100C22semidirect
109. #16811098C22semidirect
110. #16811097C22semidirect
112. #41×Dic53C22semidirect
113. #41×Dic53C22semidirect
114. C4×#11719945C22semidirect
115. #16811091C22semidirect
116. C2×Q8×Dic53C22semidirect
118. C2×D4×Dic53C22semidirect
121. C2×#13133176C22semidirect
122. C2×#13133176C22semidirect
123. #117×D53C22semidirect
125. C22×C4⋊Dic53C22semidirect
128. C53×#537C22semidirect
129. C53×#537C22semidirect
131. C53×#536C22semidirect
133. C53×#535C22semidirect
135. C53×#532C22semidirect
137. C53×#525C22semidirect
386. C22×C4×C53#41semidirect
638. #3449D53semidirect
699. #537C2×D53semidirect
700. #537C2×D53semidirect
704. #536C2×D53semidirect
708. #535C2×D53semidirect
716. #532C2×D53semidirect
730. #525C2×D53semidirect
770. C53#62856semidirect
1056. C22×C4#11719947semidirect

Maximal subgroups

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

subgroupindex
#202886362
#202886352
#202886242
#202886222
#202885522
#202884692
#202884642
#202884522
#202884472
#202884322
#202884212
#202881392
#202881282
C2×#168112512
#202880442
C2×#168112012
#202879182
#202879162
C2×#168111062
C53×#34492
#6285653