Finite Group Databasebeta

← #28292653

Subgroups — #28292653

Order 13568.

7286 conjugacy classes of subgroups.

The subgroup lattice has 1312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288454C218yesmaximal, complemented
2#20288437C218yesmaximal, complemented
3#20288430C214yesmaximal, complemented
4#20288416C214yesmaximal, complemented
5#20288414C211yesmaximal, characteristic, complemented
6#20288412C211yesmaximal, characteristic, complemented
7#20288408C212yesmaximal, complemented
8#20288404C211yesmaximal, characteristic, complemented
9#20288402C212yesmaximal, complemented
10#20288270C218yesmaximal, complemented
11#20288266C218yesmaximal, complemented
12#20288117C211yesmaximal, characteristic, complemented
13#20288097C214yesmaximal, complemented
14#20288041C211yesmaximal, characteristic, complemented
15#20288007C214yesmaximal, complemented
16C2×#16811129C212yesmaximal, complemented
17#20287913C212yesmaximal, complemented
18C22×#13133173C211yesmaximal, characteristic, complemented
19C53×#3490C211yesmaximal, characteristic, complemented
20C22×#11719947C2212yes—
21C24×Dic53C2211yescharacteristic
22#16811342C2218yescomplemented
23#16811340C2218yescomplemented
24#16811337C2218yescomplemented
25#16811335C2218yescomplemented
26#16811332C2218yescomplemented
27#16811327C2218yescomplemented
28#16811322C2218yescomplemented
29#16811318C2218yescomplemented
30#16811316C2218yescomplemented
31#16811316C2218yescomplemented
32#16811315C2218yescomplemented
33#16811313C2218yescomplemented
34#16811310C2218yescomplemented
35#16811310C2218yescomplemented
36#16811310C2218yescomplemented
37#16811309C2218yescomplemented
38#16811306C2218yescomplemented
39#16811306C2218yescomplemented
40#16811304C2218yescomplemented
41#16811304C2218yescomplemented
42#16811302C2218yescomplemented
43#16811300C2218yescomplemented
44#16811299C2218yescomplemented
45#16811299C2218yescomplemented
46#16811299C2218yescomplemented
47#16811272C2218yescomplemented
48#16811271C2218yescomplemented
49#16811267C2218yescomplemented
50#16811263C2218yescomplemented
51#16811260C2218yescomplemented
52#16811252C2214yescomplemented
53#16811252C2218yescomplemented
54#16811249C2212yes—
55#16811249C2211yescharacteristic
56#16811241C2218yescomplemented
57#16811237C2218yescomplemented
58#16811230C2218yescomplemented
59#16811223C2218yescomplemented
60#16811222C2214yescomplemented
61#16811218C2214yescomplemented
62#16811215C2218yescomplemented
63#16811211C2214yescomplemented
64#16811208C2218yescomplemented
65#16811200C2214yescomplemented
66#16811195C2214yescomplemented
67#16811188C2214yescomplemented
68#16811185C2211yescharacteristic
69#16811182C2212yes—
70#16811176C2214yescomplemented
71#16811175C2214yescomplemented
72#16811175C2214yescomplemented
73#16811175C2218yescomplemented
74#16811169C2214yescomplemented
75#16811168C2214yescomplemented
76#16811168C2214yescomplemented
77#16811159C2214yescomplemented
78#16811159C2214yescomplemented
79#16811156C2218yescomplemented
80#16811154C2214yescomplemented
81#16811154C2214yescomplemented
82#16811154C2218yescomplemented
83#16811153C2218yescomplemented
84#16811153C2218yescomplemented
85#16811152C2218yescomplemented
86#16811150C2218yescomplemented
87#16811150C2218yescomplemented
88#16811150C2218yescomplemented
89#16811134C2214yescomplemented
90#16811131C2214yescomplemented
91#16811129C2218yes—
92#16811129C2218yes—
93#16811129C2214yescomplemented
94#16811129C2218yescomplemented
95#16811129C2214yescomplemented
96#16811129C2214yescomplemented
97#16811129C2214yescomplemented
98#16811129C2214yescomplemented
99C2×#13133201C2212yes—
100C2×#13133198C2212yes—
101C2×#13133194C2214yescomplemented
102C2×#13133189C2214yescomplemented
103C2×#13133186C2212yes—
104#16811102C2218yescomplemented
105#16811102C2218yescomplemented
106#16811100C2214yescomplemented
107#16811098C2212yes—
108#16811096C2212yes—
109#16811096C2212yes—
110#16811096C2214yescomplemented
111#41×Dic53C2214yescomplemented
112#16811091C2214yescomplemented
113C4×#11719947C2218yescomplemented
114C4×#11719947C2218yescomplemented
115C4×#11719947C2218yescomplemented
116C2×D4×Dic53C2214yescomplemented
117C2×#13133177C2214yescomplemented
118C2×#13133173C2211yescharacteristic
119C2×#13133173C2212yes—
120C2×#13133173C2211yescharacteristic
121C2×#13133173C2211yescharacteristic
122C2×#13133173C2211yescharacteristic
123C2×#13133173C2218yescomplemented
124C2×#13133173C2212yescomplemented
125C2×#13133173C2212yescomplemented
126C2×#13133173C2218yescomplemented
127C2×#13133173C2214yescomplemented
128#117×D53C2214yescomplemented
129C22×#11719919C2212yescomplemented
130C22×C22⋊Dic53C2211yescharacteristic
131C22×C4×Dic53C2212yescomplemented
132C53×#551C2218yescomplemented
133C53×#546C2218yescomplemented
134C53×#543C2211yescharacteristic
135C53×#538C2214yescomplemented
136C53×#534C2211yescharacteristic
137C53×#525C2214yescomplemented
138C2×#120×C53C2212yes—
139C53×#518C2212yes—
140C22×C22⋊C4×C53C2211yescharacteristic
141C2×#11719945C2314yes—
142C2×#11719947—216no—
143C2×#11719947C2314yes—
144C2×#11719947C2314yes—
145C2×#11719947C2314yes—
146C2×#11719947C2314yes—
147C2×#11719947C2318yes—
148C22×Dic106C2312yes—
149C22×C22⋊D53C2312yes—
150C22×C22⋊D53C2312yes—
151C22×C22⋊D53C2314yes—
152C23×Dic53—28no—
153C23×Dic53C2311yescharacteristic
154C23×Dic53C2311yescharacteristic
155C23×Dic53C2311yescharacteristic
156C23×Dic53C2314yes—
157C23×Dic53C2312yes—
158C23×Dic53C2314yes—
159C23×Dic53C2311yescharacteristic
160C23×Dic53C2311yescharacteristic
161C23×Dic53C2312yes—
162C23×Dic53C2311yescharacteristic
163C22×C4×D53C2312yes—
164#13133216C2318yescomplemented
165#13133216C2314yescomplemented
166#13133216C2314yescomplemented
167#13133215C2318yescomplemented
168#13133215C2314yescomplemented
169#13133213C2314yescomplemented
170#13133212C2318yescomplemented
171#13133212C2318yescomplemented
172#13133212C2318yescomplemented
173#13133211C2318yescomplemented
174#13133210C2318yes—
175#13133210C2318yes—
176#13133210C2318yes—
177#13133210C2318yescomplemented
178#13133210C2318yescomplemented
179#13133210C2318yescomplemented
180#13133210C2318yescomplemented
181#13133209C2318yescomplemented
182#13133208C2314yescomplemented
183#13133208C2314yescomplemented
184#13133208C2318yescomplemented
185#13133207C2318yescomplemented
186#13133207C2318yescomplemented
187#13133207C2318yescomplemented
188#13133207C2318yescomplemented
189#13133207C2318yescomplemented
190#13133207C2318yescomplemented
191#13133206C2314yescomplemented
192#13133204C2318yes—
193#13133204C2314yescomplemented
194#13133203C2318yes—
195#13133203C2318yes—
196#13133203C2318yescomplemented
197#13133203C2318yescomplemented
198#13133202C2318yescomplemented
199#13133201C2318yes—
200#13133201C2314yes—
201#13133201C2318yes—
202#13133201C2314yes—
203#13133201C2314yes—
204#13133200C2318yes—
205#13133200C2314yes—
206#13133200C2318yescomplemented
207#13133199C2318yes—
208#13133199C2318yes—
209#13133199C2318yescomplemented
210#13133198C2318yes—
211#13133198C2318yes—
212#13133198C2318yes—
213#13133198C2314yes—
214#13133198C2314yes—
215#13133198C2314yes—
216#13133198C2318yescomplemented
217#13133196C2318yes—
218#13133196C2314yes—
219#13133196C2314yes—
220#13133196C2318yescomplemented
221#13133195C2318yescomplemented
222#13133195C2318yescomplemented
223#13133194C2318yes—
224#13133194C2318yes—
225#13133194C2318yes—
226#13133194C2318yes—
227#13133194C2318yes—
228#13133194C2318yes—
229#13133194C2318yes—
230#13133194C2318yes—
231#13133194C2318yescomplemented
232#13133194C2318yescomplemented
233#13133193C2318yescomplemented
234#13133191C2314yes—
235#13133191C2314yes—
236#13133190C2318yes—
237#13133190C2318yescomplemented
238#13133189C2318yes—
239#13133189C2318yes—
240#13133189C2318yes—
241#13133189C2318yes—
242#13133189C2318yes—
243#13133189C2318yes—
244#13133189C2318yes—
245#13133189C2318yescomplemented
246#13133188C2318yes—
247#13133187C2314yes—
248#13133186C2314yes—
249#13133186C2318yes—
250#13133186C2314yes—
251#13133186C2314yes—
252#13133185C2314yes—
253Q8×Dic53C2314yescomplemented
254Q8×Dic53C2314yescomplemented
255C4×Dic106C2318yescomplemented
256C4×Dic106C2318yescomplemented
257C4×Dic106C2318yescomplemented
258#13133182C2318yescomplemented
259#13133182C2314yescomplemented
260#13133182C2318yescomplemented
261#13133182C2318yescomplemented
262#13133182C2314yescomplemented
263D4×Dic53C2318yes—
264D4×Dic53C2318yes—
265D4×Dic53C2318yes—
266D4×Dic53C2318yes—
267D4×Dic53C2318yes—
268D4×Dic53C2318yes—
269D4×Dic53C2318yes—
270D4×Dic53C2314yescomplemented
271D4×Dic53C2314yescomplemented
272#13133179C2314yescomplemented
273#13133179C2314yescomplemented
274C4×C22⋊D53C2318yes—
275C4×C22⋊D53C2318yes—
276C4×C22⋊D53C2318yes—
277C4×C22⋊D53C2318yescomplemented
278C4×C22⋊D53C2318yescomplemented
279C4×C22⋊D53C2318yescomplemented
280#13133177C2318yes—
281#13133177C2318yes—
282#13133177C2318yes—
283#13133177C2318yes—
284#13133177C2318yes—
285#13133177C2318yes—
286#13133177C2318yes—
287#13133177C2318yescomplemented
288#13133177C2318yescomplemented
289#13133177C2318yescomplemented
290#13133176C2314yes—
291#13133176C2314yes—
292#13133176C2318yescomplemented
293#13133175C2318yescomplemented
294#13133175C2318yescomplemented
295#13133174C2318yescomplemented
296#13133174C2318yescomplemented
297#13133173C2314yes—
298#13133173C2318yes—
299#13133173C2318yes—
300#13133173C2318yes—
301#13133173C2314yes—
302#13133173C2318yes—
303#13133173C2318yes—
304#13133173C2314yes—
305#13133173C2314yes—
306#13133173C2314yes—
307#13133173C2314yes—
308#13133173C2314yes—
309#13133173C2314yes—
310#13133173C2314yes—
311#13133173C2314yes—
312#13133173C2318yes—
313#13133173C2318yes—
314#13133173C2318yescomplemented
315#13133173C2318yescomplemented
316#13133173C2318yescomplemented
317C2×C4⋊Dic53C2314yes—
318C2×#11719919C2318yes—
319C2×#11719919C2314yes—
320C2×#11719919C2318yes—
321C2×#11719919C2312yes—
322C2×#11719919C2312yes—
323C2×#11719919C2312yes—
324C2×#11719919C2312yes—
325C2×#11719919C2314yes—
326C2×#11719919C2318yescomplemented
327C4⋊C4×D53C2318yescomplemented
328C2×C22⋊Dic53C2314yes—
329C2×C22⋊Dic53C2318yes—
330C2×C22⋊Dic53C2314yes—
331C2×C22⋊Dic53C2314yes—
332C2×C22⋊Dic53C2311yescharacteristic
333C2×C22⋊Dic53C2311yescharacteristic
334C2×C22⋊Dic53C2312yes—
335C2×C22⋊Dic53C2312yes—
336C2×#11719921C2314yes—
337C22⋊C4×D53C2314yes—
338C22⋊C4×D53C2314yes—
339C2×C4×Dic53C2312yes—
340C2×C4×Dic53C2312yes—
341C2×C4×Dic53C2312yes—
342C2×C4×Dic53C2312yes—
343C2×C4×Dic53C2314yes—
344C2×C4×Dic53C2314yes—
345C2×C4×Dic53C2314yes—
346C2×C4×Dic53C2314yes—
347C2×C4×Dic53C2314yes—
348C2×C4×Dic53C2318yescomplemented
349C42×D53C2318yescomplemented
350C25×C53C2311yescharacteristic
351C2×#41×C53C2314yes—
352C22×D4×C53C2312yes—
353C22×D4×C53C2314yes—
354C23×C4×C53C2312yes—
355#126×C53C2318yes—
356#124×C53C2318yes—
357#123×C53C2318yes—
358#123×C53C2314yes—
359#123×C53C2318yes—
360C22⋊Q8×C53C2318yes—
361C22⋊Q8×C53C2314yes—
362C22⋊Q8×C53C2314yes—
363#121×C53C2314yes—
364#121×C53C2314yes—
365#121×C53C2318yes—
366#120×C53C2314yes—
367#120×C53C2318yes—
368#120×C53C2314yes—
369#120×C53C2314yes—
370C4×D4×C53C2318yes—
371C4×D4×C53C2318yes—
372C4×D4×C53C2318yes—
373#117×C53C2314yes—
374#117×C53C2314yes—
375C2×C22⋊C4×C53C2311yescharacteristic
376C2×C22⋊C4×C53C2318yes—
377C2×C22⋊C4×C53C2311yescharacteristic
378C2×C22⋊C4×C53C2312yes—
379C2×C22⋊C4×C53C2314yes—
380C2×C22⋊C4×C53C2312yes—
381C2×C22⋊C4×C53C2314yes—
382C24×C53—24no—
383C24×C53—44no—
384C24×C53C2411yescharacteristic
385C24×C53C2414yes—
386C24×C53C2411yescharacteristic
387C24×C53C2412yes—
388C24×C53C2411yescharacteristic
389C23×D53C2412yes—
390#41×C53—48no—
391C2×Q8×C53C2414yes—
392C2×D4×C53—28no—
393C2×D4×C53—48no—
394C2×D4×C53C2414yes—
395C2×D4×C53C2414yes—
396C2×D4×C53C2418yes—
397C2×D4×C53C2414yes—
398C2×D4×C53C2418yes—
399C22×C4×C53—44no—
400C22×C4×C53C2412yes—
401C22×C4×C53C2414yes—
402C22×C4×C53C2412yes—
403C22×C4×C53C2414yes—
404C22×C4×C53C2414yes—
405C22×C4×C53C2412yes—
406C22×C4×C53C2418yes—
407C2×C22⋊D53—28no—
408C2×C22⋊D53—28no—
409C2×C22⋊D53—48no—
410C2×C22⋊D53C2418yes—
411C2×C22⋊D53C2414yes—
412C2×C22⋊D53C2414yes—
413C2×C22⋊D53C2414yes—
414C2×C22⋊D53C2414yes—
415C2×C22⋊D53C2418yes—
416C2×C22⋊D53C2418yes—
417C22×Dic53—24no—
418C22×Dic53—216no—
419C22×Dic53—216no—
420C22×Dic53—24no—
421C22×Dic53—24no—
422C22×Dic53—24no—
423C22×Dic53—24no—
424C22×Dic53—28no—
425C22×Dic53—44no—
426C22×Dic53#4118yescomplemented
427C22×Dic53C2412yes—
428C22×Dic53C2412yes—
429C22×Dic53C2411yescharacteristic
430C22×Dic53C2414yes—
431C22×Dic53C2414yes—
432C22×Dic53C2414yes—
433C22×Dic53C2412yes—
434C22×Dic53C2414yes—
435C22×Dic53C2411yescharacteristic
436C22×Dic53C2414yes—
437C22×Dic53C2412yes—
438C22×Dic53C2414yes—
439C22×Dic53C2412yes—
440C22×Dic53C2412yes—
441C22×Dic53C2414yes—
442C22×Dic53C2412yes—
443C22×Dic53C2414yes—
444C22×Dic53C2418yes—
445C22×Dic53C2411yescharacteristic
446C22×Dic53C2412yes—
447C22×Dic53C2411yescharacteristic
448C22×Dic53C2412yes—
449#11719947—216no—
450#11719947—216no—
451#11719947—216no—
452#11719947—216no—
453#11719947—416no—
454#11719945—48no—
455C2×D212C2414yes—
456C2×C4×D53—28no—
457C2×C4×D53C2414yes—
458C2×C4×D53C2414yes—
459C2×C4×D53C2418yes—
460C2×C4×D53C2418yes—
461C2×Dic106—28no—
462C2×Dic106C2414yes—
463C2×Dic106C2414yes—
464C2×Dic106C2414yes—
465C2×Dic106C2418yes—
466C4⋊C4×C53C2418yes—
467C4⋊C4×C53C2414yes—
468C4⋊C4×C53C2414yes—
469C4⋊C4×C53C2418yes—
470C22⋊C4×C53C2414yes—
471C22⋊C4×C53C2414yes—
472C22⋊C4×C53C2418yes—
473C22⋊C4×C53C2414yes—
474C22⋊C4×C53C2418yes—
475C22⋊C4×C53C2414yes—
476C22⋊C4×C53C2418yes—
477C22⋊C4×C53C2418yes—
478C22⋊C4×C53C2418yes—
479C42×C53C2418yes—
480C22⋊Dic53C2414yes—
481C22⋊Dic53C2414yes—
482C22⋊Dic53C2414yes—
483C22⋊Dic53C2418yes—
484C22⋊Dic53C2414yes—
485C22⋊Dic53C2418yes—
486C22⋊Dic53C2418yes—
487C22⋊Dic53C2418yes—
488C22⋊Dic53C2418yes—
489C22⋊Dic53C2418yes—
490C22⋊Dic53C2418yes—
491#11719921C2418yes—
492#11719921C2418yes—
493#11719921C2418yes—
494#11719921C2418yes—
495#11719921C2418yes—
496#11719921C2418yes—
497C4⋊Dic53C2418yes—
498C4⋊Dic53C2418yes—
499C4⋊Dic53C2418yes—
500C4⋊Dic53C2414yes—
501C4⋊Dic53C2414yes—
502C4⋊Dic53C2418yes—
503#11719919C2418yes—
504#11719919C2418yes—
505#11719919C2418yes—
506#11719919C2418yes—
507#11719919C2418yes—
508#11719919C2418yes—
509#11719919C2418yes—
510#11719919C2418yes—
511#11719919C2418yes—
512#11719919C2418yes—
513#11719919C2418yes—
514#11719919C2418yes—
515#11719919C2418yes—
516#11719919C2418yes—
517C4×Dic53C2414yes—
518C4×Dic53C2418yes—
519C4×Dic53C2418yes—
520C4×Dic53C2414yes—
521C4×Dic53C2414yes—
522C4×Dic53C2414yes—
523C4×Dic53C2414yes—
524C4×Dic53C2414yes—
525C4×Dic53C2414yes—
526C4×Dic53C2414yes—
527C4×Dic53C2418yes—
528C4×Dic53C2418yes—
529C4×Dic53C2418yes—
530C23×C53—22no—
531C23×C53—24no—
532C23×C53—28no—
533C23×C53—22no—
534C23×C53—28no—
535C23×C53—24no—
536C23×C53—42no—
537C23×C53—44no—
538C23×C53—42no—
539C23×C53—44no—
540C23×C53—416no—
541C23×C53C2×#4114yes—
542C23×C53C2514yes—
543C23×C53C2512yes—
544C23×C53C2511yescharacteristic
545C23×C53C2512yes—
546C23×C53C2512yes—
547C22×D53—24no—
548C22×D53—44no—
549C22×D53C2514yes—
550Q8×C53—44no—
551D4×C53—28no—
552D4×C53—28no—
553D4×C53—216no—
554D4×C53—48no—
555D4×C53—44no—
556C2×C4×C53—24no—
557C2×C4×C53—28no—
558C2×C4×C53—42no—
559C2×C4×C53—44no—
560C2×C4×C53—42no—
561C2×C4×C53—44no—
562C2×C4×C53—48no—
563C2×C4×C53C2514yes—
564C2×C4×C53C2518yes—
565C2×C4×C53C2514yes—
566C2×C4×C53C2514yes—
567C22⋊D53—28no—
568C22⋊D53—28no—
569C22⋊D53—216no—
570C22⋊D53—28no—
571C22⋊D53—28no—
572C22⋊D53—48no—
573C22⋊D53—48no—
574C2×Dic53—24no—
575C2×Dic53—28no—
576C2×Dic53—22no—
577C2×Dic53—22no—
578C2×Dic53—28no—
579C2×Dic53—28no—
580C2×Dic53—28no—
581C2×Dic53—24no—
582C2×Dic53—24no—
583C2×Dic53—28no—
584C2×Dic53—28no—
585C2×Dic53—24no—
586C2×Dic53—24no—
587C2×Dic53—48no—
588C2×Dic53—42no—
589C2×Dic53—44no—
590C2×Dic53—42no—
591C2×Dic53—44no—
592C2×Dic53C2×#4118yes—
593C2×Dic53C2×#4118yes—
594C2×Dic53C2×#4114yes—
595C2×Dic53C2×#4114yes—
596C2×Dic53C2518yes—
597C2×Dic53C2514yes—
598C2×Dic53C2514yes—
599C2×Dic53C2514yes—
600C2×Dic53C2512yes—
601C2×Dic53C2512yes—
602C2×Dic53C2511yescharacteristic
603C2×Dic53C2512yes—
604C2×Dic53C2511yescharacteristic
605D212—44no—
606C4×D53—28no—
607C4×D53—28no—
608C4×D53—48no—
609C4×D53—48no—
610Dic106—28no—
611Dic106—28no—
612Dic106—44no—
613Dic106—48no—
614#62814—531nomaximal, Sylow
615C22×C53—28no—
616C22×C53—22no—
617C22×C53—22no—
618C22×C53—22no—
619C22×C53—24no—
620C22×C53—22no—
621C22×C53—24no—
622C22×C53—28no—
623C22×C53—24no—
624C22×C53—44no—
625C22×C53—416no—
626C22×C53—44no—
627C22×C53—84no—
628C22×C53C22×#4114yes—
629C22×C53C22×#4112yes—
630C22×C53#58514yes—
631C22×C53C2611yescharacteristic
632C2×D53—24no—
633C2×D53—28no—
634C2×D53—84no—
635C4×C53—24no—
636C4×C53—28no—
637C4×C53—24no—
638C4×C53—24no—
639Dic53—24no—
640Dic53—22no—
641Dic53—22no—
642Dic53—28no—
643Dic53—24no—
644Dic53—24no—
645Dic53C22×#4112yes—
646Dic53C22×#4114yes—
647Dic53C22×#4112yes—
648#3495—538no—
649#3494—538no—
650#3493—534no—
651#3492—534no—
652#3491—531no—
653#3491—531no—
654#3491—532no—
655#3490—532no—
656#3490—531no—
657#3490D5311yescharacteristic, complemented
658#3475—538no—
659#3475—538no—
660#3458—531no—
661#3455—534no—
662#3449—531no—
663#3444—534no—
664C2×#525—532no—
665#3428—532no—
666C22×#117—531no—
667C2×C53—24no—
668C2×C53—22no—
669C2×C53—24no—
670C2×C53—42no—
671C2×C53—44no—
672C2×C53C23×#4111yescharacteristic
673C2×C53C2×#58512yes—
674D53—44no—
675C22×#41—532no—
676C24×C4—531no—
677#556—538no—
678#556—538no—
679#555—538no—
680#555—538no—
681#554—538no—
682#554—538no—
683#553—538no—
684#553—538no—
685#553—538no—
686#553—538no—
687#552—538no—
688#552—538no—
689#552—538no—
690#552—538no—
691#552—538no—
692#552—538no—
693#552—538no—
694#552—538no—
695#551—538no—
696#551—538no—
697#551—538no—
698#551—538no—
699#551—538no—
700#551—538no—
701#551—538no—
702#551C2×D5318yescomplemented
703#547—538no—
704#547—538no—
705#546—538no—
706#546—538no—
707#546—538no—
708#546C2×D5318yescomplemented
709#544—534no—
710#544—538no—
711#543—532no—
712#543—531no—
713#543C2×D5311yescharacteristic
714#542—538no—
715#542—538no—
716#541—538no—
717#540—538no—
718#539—534no—
719#539—534no—
720#539—538no—
721#538—538no—
722#538—534no—
723#538C2×D5314yescomplemented
724#537—534no—
725#536—534no—
726#535—534no—
727#534—532no—
728#534—531no—
729#534C2×D5311yescharacteristic
730#533—534no—
731#533—534no—
732#533—538no—
733#533—534no—
734#532—534no—
735#532—534no—
736#532—534no—
737#529—538no—
738#529—538no—
739#529—538no—
740#529—538no—
741#529—538no—
742#529—534no—
743#529—534no—
744#529—534no—
745#529—534no—
746#529—538no—
747#529—538no—
748#529—538no—
749#525—534no—
750#525—534no—
751#525—534no—
752#525—538no—
753#525—538no—
754#525—534no—
755#525—534no—
756#525—534no—
757#525—538no—
758#525—534no—
759#525C2×D5314yescomplemented
760C2×#123—532no—
761C2×#123—532no—
762C2×C22⋊Q8—534no—
763C2×#121—534no—
764C2×#120—532no—
765C2×#120C2×D5312yes—
766#520—538no—
767#520—538no—
768#519—534no—
769#518—532no—
770#518—532no—
771#518—532no—
772#518—534no—
773#518C2×D5312yes—
774C4×#41—534no—
775C4×#41—538no—
776C4×#41—538no—
777C4×#41—538no—
778C4×#41—534no—
779C2×C4×D4—534no—
780C2×C4×D4—534no—
781C2×#117—534no—
782C2×#117—531no—
783C2×#117—531no—
784C2×#117—531no—
785C2×#117—531no—
786C2×#117—532no—
787C2×#117—532no—
788C2×#117—538no—
789C2×#117—532no—
790C2×#117—538no—
791C2×#117—534no—
792C22×C4⋊C4—532no—
793C22×C22⋊C4—531no—
794C22×C22⋊C4C2×D5311yescharacteristic
795C22×C42—532no—
796C53#6281411yescharacteristic, complemented, Sylow
797C25C22×D5311yescharacteristic
798C2×#41—534no—
799C2×#41—534no—
800C2×#41—534no—
801C2×#41—534no—
802C2×#41—538no—
803C2×#41—534no—
804C2×#41—10616no—
805C2×#41C22×D5314yes—
806C22×Q8—532no—
807C22×D4—532no—
808C22×D4—532no—
809C22×D4—534no—
810C22×D4C22×D5312yes—
811C22×D4C22×D5314yes—
812C23×C4—531no—
813C23×C4—531no—
814C23×C4—534no—
815C23×C4—532no—
816C23×C4—534no—
817C23×C4—531no—
818C23×C4—531no—
819C23×C4—531no—
820C23×C4—531no—
821C23×C4—532no—
822C23×C4—532no—
823C23×C4—1068no—
824C23×C4C22×D5312yes—
825C4⋊Q8—534no—
826C4⋊Q8—538no—
827C4⋊Q8—534no—
828C4⋊Q8—534no—
829C4⋊Q8—538no—
830#127—534no—
831#126—538no—
832#126—538no—
833#126—538no—
834#126—538no—
835#126—538no—
836#126—538no—
837#126—538no—
838#126—538no—
839#126—538no—
840#126—538no—
841#126—538no—
842#126C22×D5318yes—
843#125—538no—
844#125—538no—
845#125—534no—
846#125—534no—
847#125—538no—
848#125—538no—
849#125—538no—
850#125—538no—
851#125—538no—
852#125—538no—
853#124—534no—
854#124—534no—
855#124—538no—
856#124—538no—
857#124—538no—
858#124—538no—
859#124—538no—
860#124C22×D5318yes—
861#123—534no—
862#123—534no—
863#123—538no—
864#123—538no—
865#123—534no—
866#123—538no—
867#123—538no—
868#123—538no—
869#123—534no—
870#123—538no—
871#123—538no—
872#123—534no—
873#123—534no—
874#123—538no—
875#123—538no—
876#123—534no—
877#123—538no—
878#123—538no—
879#123—538no—
880#123C22×D5314yes—
881#123C22×D5318yes—
882#123C22×D5318yes—
883C22⋊Q8—538no—
884C22⋊Q8—534no—
885C22⋊Q8—534no—
886C22⋊Q8—538no—
887C22⋊Q8—538no—
888C22⋊Q8—538no—
889C22⋊Q8—538no—
890C22⋊Q8—538no—
891C22⋊Q8—538no—
892C22⋊Q8—538no—
893C22⋊Q8—538no—
894C22⋊Q8—538no—
895C22⋊Q8—538no—
896C22⋊Q8—538no—
897C22⋊Q8—538no—
898C22⋊Q8—538no—
899C22⋊Q8—538no—
900C22⋊Q8C22×D5314yes—
901C22⋊Q8C22×D5314yes—
902C22⋊Q8C22×D5318yes—
903#121—538no—
904#121—538no—
905#121—538no—
906#121—538no—
907#121—538no—
908#121—538no—
909#121—538no—
910#121—538no—
911#121—538no—
912#121—534no—
913#121—534no—
914#121—538no—
915#121—538no—
916#121C22×D5314yes—
917#121C22×D5314yes—
918#121C22×D5318yes—
919#120—534no—
920#120—534no—
921#120—538no—
922#120—534no—
923#120—534no—
924#120—534no—
925#120C22×D5314yes—
926#120C22×D5314yes—
927#120C22×D5318yes—
928#120C22×D5314yes—
929C4×Q8—534no—
930C4×Q8—534no—
931C4×Q8—538no—
932C4×Q8—538no—
933C4×Q8—538no—
934C4×Q8—534no—
935C4×Q8—534no—
936C4×Q8—538no—
937C4×Q8—538no—
938C4×Q8—538no—
939C4×D4—538no—
940C4×D4—538no—
941C4×D4—538no—
942C4×D4—538no—
943C4×D4—538no—
944C4×D4—538no—
945C4×D4—534no—
946C4×D4—538no—
947C4×D4—534no—
948C4×D4—538no—
949C4×D4—538no—
950C4×D4—538no—
951C4×D4—538no—
952C4×D4—538no—
953C4×D4—538no—
954C4×D4—534no—
955C4×D4—534no—
956C4×D4—538no—
957C4×D4—538no—
958C4×D4—538no—
959C4×D4—538no—
960C4×D4—538no—
961C4×D4—538no—
962C4×D4—538no—
963C4×D4—538no—
964C4×D4—538no—
965C4×D4—538no—
966C4×D4C22×D5318yes—
967C4×D4C22×D5318yes—
968C4×D4C22×D5318yes—
969#117—534no—
970#117—534no—
971#117—538no—
972#117—538no—
973#117—538no—
974#117—534no—
975#117—534no—
976#117—534no—
977#117—534no—
978#117—538no—
979#117—534no—
980#117—538no—
981#117—538no—
982#117—538no—
983#117—538no—
984#117—538no—
985#117—534no—
986#117—538no—
987#117—534no—
988#117—534no—
989#117—534no—
990#117—534no—
991#117—538no—
992#117—538no—
993#117—538no—
994#117—538no—
995#117—538no—
996#117C22×D5314yes—
997#117C22×D5314yes—
998C2×C4⋊C4—532no—
999C2×C4⋊C4—532no—
1000C2×C4⋊C4—532no—
1001C2×C4⋊C4—532no—
1002C2×C4⋊C4—538no—
1003C2×C4⋊C4—538no—
1004C2×C4⋊C4—534no—
1005C2×C4⋊C4—538no—
1006C2×C4⋊C4—534no—
1007C2×C4⋊C4—534no—
1008C2×C4⋊C4—538no—
1009C2×C22⋊C4—531no—
1010C2×C22⋊C4—531no—
1011C2×C22⋊C4—532no—
1012C2×C22⋊C4—538no—
1013C2×C22⋊C4—532no—
1014C2×C22⋊C4—534no—
1015C2×C22⋊C4—534no—
1016C2×C22⋊C4—534no—
1017C2×C22⋊C4—534no—
1018C2×C22⋊C4—534no—
1019C2×C22⋊C4—534no—
1020C2×C22⋊C4C22×D5311yescharacteristic
1021C2×C22⋊C4C22×D5311yescharacteristic
1022C2×C22⋊C4C22×D5312yes—
1023C2×C22⋊C4C22×D5318yes—
1024C2×C22⋊C4C22×D5312yes—
1025C2×C22⋊C4C22×D5314yes—
1026C2×C22⋊C4C22×D5314yes—
1027C2×C42—532no—
1028C2×C42—534no—
1029C2×C42—534no—
1030C2×C42—532no—
1031C2×C42—532no—
1032C2×C42—534no—
1033C2×C42—534no—
1034C2×C42—532no—
1035C2×C42—534no—
1036C2×C42—538no—
1037C2×C42—538no—
1038C24—24no—
1039C24—44no—
1040C24—532no—
1041C24C23×D5311yescharacteristic
1042C24C23×D5314yes—
1043C24C23×D5312yes—
1044C24C23×D5311yescharacteristic
1045C24C23×D5311yescharacteristic
1046#41—48no—
1047#41—10616no—
1048#41—10616no—
1049#41—10616no—
1050#41—10616no—
1051#41—2128no—
1052#41—21216no—
1053C2×Q8—534no—
1054C2×Q8—534no—
1055C2×Q8—534no—
1056C2×Q8—538no—
1057C2×Q8—1068no—
1058C2×Q8C23×D5314yes—
1059C2×D4—28no—
1060C2×D4—48no—
1061C2×D4—534no—
1062C2×D4—534no—
1063C2×D4—538no—
1064C2×D4—534no—
1065C2×D4—534no—
1066C2×D4—538no—
1067C2×D4—538no—
1068C2×D4—534no—
1069C2×D4—1068no—
1070C2×D4—1068no—
1071C2×D4—2128no—
1072C2×D4C23×D5318yes—
1073C2×D4C23×D5314yes—
1074C2×D4C23×D5314yes—
1075C2×D4C23×D5318yes—
1076C2×D4C23×D5314yes—
1077C22×C4—44no—
1078C22×C4—538no—
1079C22×C4—531no—
1080C22×C4—532no—
1081C22×C4—531no—
1082C22×C4—532no—
1083C22×C4—532no—
1084C22×C4—532no—
1085C22×C4—531no—
1086C22×C4—534no—
1087C22×C4—534no—
1088C22×C4—534no—
1089C22×C4—532no—
1090C22×C4—534no—
1091C22×C4—531no—
1092C22×C4—534no—
1093C22×C4—532no—
1094C22×C4—534no—
1095C22×C4—532no—
1096C22×C4—532no—
1097C22×C4—534no—
1098C22×C4—532no—
1099C22×C4—534no—
1100C22×C4—538no—
1101C22×C4—534no—
1102C22×C4—534no—
1103C22×C4—538no—
1104C22×C4—538no—
1105C22×C4—1068no—
1106C22×C4—10616no—
1107C22×C4—10616no—
1108C22×C4—1064no—
1109C22×C4—1064no—
1110C22×C4—1064no—
1111C22×C4—1064no—
1112C22×C4—1068no—
1113C22×C4—1064no—
1114C22×C4—2124no—
1115C22×C4C23×D5314yes—
1116C22×C4C23×D5312yes—
1117C22×C4C23×D5312yes—
1118C22×C4C23×D5314yes—
1119C22×C4C23×D5312yes—
1120C22×C4C23×D5314yes—
1121C22×C4C23×D5318yes—
1122C4⋊C4—538no—
1123C4⋊C4—538no—
1124C4⋊C4—538no—
1125C4⋊C4—538no—
1126C4⋊C4—538no—
1127C4⋊C4—538no—
1128C4⋊C4—538no—
1129C4⋊C4—538no—
1130C4⋊C4—538no—
1131C4⋊C4—538no—
1132C4⋊C4—538no—
1133C4⋊C4—538no—
1134C4⋊C4—538no—
1135C4⋊C4—538no—
1136C4⋊C4—538no—
1137C4⋊C4—538no—
1138C4⋊C4—538no—
1139C4⋊C4—534no—
1140C4⋊C4—534no—
1141C4⋊C4—538no—
1142C4⋊C4C23×D5318yes—
1143C4⋊C4C23×D5318yes—
1144C4⋊C4C23×D5314yes—
1145C4⋊C4C23×D5314yes—
1146C22⋊C4—534no—
1147C22⋊C4—534no—
1148C22⋊C4—534no—
1149C22⋊C4—538no—
1150C22⋊C4—534no—
1151C22⋊C4—538no—
1152C22⋊C4—538no—
1153C22⋊C4—538no—
1154C22⋊C4—538no—
1155C22⋊C4—538no—
1156C22⋊C4—538no—
1157C22⋊C4—538no—
1158C22⋊C4—538no—
1159C22⋊C4—538no—
1160C22⋊C4—538no—
1161C22⋊C4—538no—
1162C22⋊C4—538no—
1163C22⋊C4C23×D5314yes—
1164C22⋊C4C23×D5314yes—
1165C22⋊C4C23×D5314yes—
1166C22⋊C4C23×D5318yes—
1167C22⋊C4C23×D5314yes—
1168C22⋊C4C23×D5318yes—
1169C22⋊C4C23×D5318yes—
1170C22⋊C4C23×D5318yes—
1171C22⋊C4C23×D5318yes—
1172C42—534no—
1173C42—534no—
1174C42—534no—
1175C42—534no—
1176C42—538no—
1177C42—534no—
1178C42—534no—
1179C42—534no—
1180C42—534no—
1181C42—538no—
1182C42—538no—
1183C42—538no—
1184C42—538no—
1185C42C23×D5318yes—
1186C23—22no—
1187C23—24no—
1188C23—28no—
1189C23—22no—
1190C23—28no—
1191C23—24no—
1192C23—42no—
1193C23—44no—
1194C23—42no—
1195C23—44no—
1196C23—416no—
1197C23—534no—
1198C23—1064no—
1199C23—2124no—
1200C23#41×D5314yes—
1201C23C24×D5312yes—
1202C23C24×D5314yes—
1203C23C24×D5312yes—
1204C23C24×D5311yescharacteristic
1205C23C24×D5312yes—
1206Q8—44no—
1207Q8—1068no—
1208Q8—1068no—
1209Q8—2124no—
1210Q8—2128no—
1211D4—28no—
1212D4—28no—
1213D4—216no—
1214D4—48no—
1215D4—44no—
1216D4—1068no—
1217D4—1068no—
1218D4—1068no—
1219D4—1068no—
1220D4—10616no—
1221D4—2124no—
1222D4—2128no—
1223D4—2128no—
1224C2×C4—24no—
1225C2×C4—28no—
1226C2×C4—42no—
1227C2×C4—44no—
1228C2×C4—42no—
1229C2×C4—44no—
1230C2×C4—48no—
1231C2×C4—538no—
1232C2×C4—538no—
1233C2×C4—534no—
1234C2×C4—534no—
1235C2×C4—531no—
1236C2×C4—531no—
1237C2×C4—532no—
1238C2×C4—532no—
1239C2×C4—534no—
1240C2×C4—534no—
1241C2×C4—534no—
1242C2×C4—538no—
1243C2×C4—532no—
1244C2×C4—1068no—
1245C2×C4—1068no—
1246C2×C4—1064no—
1247C2×C4—1064no—
1248C2×C4—1068no—
1249C2×C4—1068no—
1250C2×C4—1064no—
1251C2×C4—1064no—
1252C2×C4—1068no—
1253C2×C4—1068no—
1254C2×C4—1068no—
1255C2×C4—1062no—
1256C2×C4—1062no—
1257C2×C4—1064no—
1258C2×C4—1068no—
1259C2×C4—2128no—
1260C2×C4—2128no—
1261C2×C4—2122no—
1262C2×C4—2124no—
1263C2×C4—2122no—
1264C2×C4—2124no—
1265C2×C4—2128no—
1266C2×C4C24×D5314yes—
1267C2×C4C24×D5314yes—
1268C2×C4C24×D5318yes—
1269C2×C4C24×D5314yes—
1270C22—28no—
1271C22—22no—
1272C22—22no—
1273C22—22no—
1274C22—24no—
1275C22—22no—
1276C22—24no—
1277C22—28no—
1278C22—24no—
1279C22—44no—
1280C22—416no—
1281C22—44no—
1282C22—84no—
1283C22—1064no—
1284C22—1068no—
1285C22—4244no—
1286C22C2×#41×D5314yes—
1287C22C2×#41×D5312yes—
1288C22#1681145814yes—
1289C22C25×D5311yescharacteristic
1290C4—24no—
1291C4—24no—
1292C4—24no—
1293C4—28no—
1294C4—532no—
1295C4—534no—
1296C4—532no—
1297C4—1062no—
1298C4—1062no—
1299C4—1064no—
1300C4—1064no—
1301C4—1064no—
1302C4—1068no—
1303C2—22no—
1304C2—24no—
1305C2—24no—
1306C2—42no—
1307C2—44no—
1308C2—2124no—
1309C2C22×#41×D5311yescharacteristic
1310C2C2×#1681145812yes—
subgroupG/H
center, FrattiniC22C25×D53
commutator, socle, cosocleC22×C53C26
FittingC53×#3490C2
hypercenter#3490D53
hypocenterC53#62814
LCSG ▷ C22×C53 ▷ C53
UCSC1 ◁ C22 ◁ #3490

Complements

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

NH ≅ G/Ntype
1. #20288454C2semidirect
2. #20288437C2semidirect
3. #20288430C2semidirect
4. #20288416C2semidirect
5. #20288414C2semidirect
6. #20288412C2semidirect
7. #20288408C2semidirect
8. #20288404C2semidirect
9. #20288402C2semidirect
10. #20288270C2semidirect
11. #20288266C2semidirect
12. #20288117C2semidirect
13. #20288097C2semidirect
14. #20288041C2semidirect
15. #20288007C2semidirect
16. C2×#16811129C2semidirect
17. #20287913C2semidirect
18. C22×#13133173C2semidirect
19. C53×#3490C2semidirect
22. #16811342C22semidirect
23. #16811340C22semidirect
24. #16811337C22semidirect
25. #16811335C22semidirect
26. #16811332C22semidirect
27. #16811327C22semidirect
28. #16811322C22semidirect
29. #16811318C22semidirect
30. #16811316C22semidirect
31. #16811316C22semidirect
32. #16811315C22semidirect
33. #16811313C22semidirect
34. #16811310C22semidirect
35. #16811310C22semidirect
36. #16811310C22semidirect
37. #16811309C22semidirect
38. #16811306C22semidirect
39. #16811306C22semidirect
40. #16811304C22semidirect
41. #16811304C22semidirect
42. #16811302C22semidirect
43. #16811300C22semidirect
44. #16811299C22semidirect
45. #16811299C22semidirect
46. #16811299C22semidirect
47. #16811272C22semidirect
48. #16811271C22semidirect
49. #16811267C22semidirect
50. #16811263C22semidirect
51. #16811260C22semidirect
52. #16811252C22semidirect
53. #16811252C22semidirect
56. #16811241C22semidirect
57. #16811237C22semidirect
58. #16811230C22semidirect
59. #16811223C22semidirect
60. #16811222C22semidirect
61. #16811218C22semidirect
62. #16811215C22semidirect
63. #16811211C22semidirect
64. #16811208C22semidirect
65. #16811200C22semidirect
66. #16811195C22semidirect
67. #16811188C22semidirect
70. #16811176C22semidirect
71. #16811175C22semidirect
72. #16811175C22semidirect
73. #16811175C22semidirect
74. #16811169C22semidirect
75. #16811168C22semidirect
76. #16811168C22semidirect
77. #16811159C22semidirect
78. #16811159C22semidirect
79. #16811156C22semidirect
80. #16811154C22semidirect
81. #16811154C22semidirect
82. #16811154C22semidirect
83. #16811153C22semidirect
84. #16811153C22semidirect
85. #16811152C22semidirect
86. #16811150C22semidirect
87. #16811150C22semidirect
88. #16811150C22semidirect
89. #16811134C22semidirect
90. #16811131C22semidirect
93. #16811129C22semidirect
94. #16811129C22semidirect
95. #16811129C22semidirect
96. #16811129C22semidirect
97. #16811129C22semidirect
98. #16811129C22semidirect
101. C2×#13133194C22semidirect
102. C2×#13133189C22semidirect
104. #16811102C22semidirect
105. #16811102C22semidirect
106. #16811100C22semidirect
110. #16811096C22semidirect
111. #41×Dic53C22semidirect
112. #16811091C22semidirect
113. C4×#11719947C22semidirect
114. C4×#11719947C22semidirect
115. C4×#11719947C22semidirect
116. C2×D4×Dic53C22semidirect
117. C2×#13133177C22semidirect
123. C2×#13133173C22semidirect
124. C2×#13133173C22semidirect
125. C2×#13133173C22semidirect
126. C2×#13133173C22semidirect
127. C2×#13133173C22semidirect
128. #117×D53C22semidirect
129. C22×#11719919C22semidirect
131. C22×C4×Dic53C22semidirect
132. C53×#551C22semidirect
133. C53×#546C22semidirect
135. C53×#538C22semidirect
137. C53×#525C22semidirect
164. #13133216C23semidirect
165. #13133216C23semidirect
166. #13133216C23semidirect
167. #13133215C23semidirect
168. #13133215C23semidirect
169. #13133213C23semidirect
170. #13133212C23semidirect
171. #13133212C23semidirect
172. #13133212C23semidirect
173. #13133211C23semidirect
177. #13133210C23semidirect
178. #13133210C23semidirect
179. #13133210C23semidirect
180. #13133210C23semidirect
181. #13133209C23semidirect
182. #13133208C23semidirect
183. #13133208C23semidirect
184. #13133208C23semidirect
185. #13133207C23semidirect
186. #13133207C23semidirect
187. #13133207C23semidirect
188. #13133207C23semidirect
189. #13133207C23semidirect
190. #13133207C23semidirect
191. #13133206C23semidirect
193. #13133204C23semidirect
196. #13133203C23semidirect
197. #13133203C23semidirect
198. #13133202C23semidirect
206. #13133200C23semidirect
209. #13133199C23semidirect
216. #13133198C23semidirect
220. #13133196C23semidirect
221. #13133195C23semidirect
222. #13133195C23semidirect
231. #13133194C23semidirect
232. #13133194C23semidirect
233. #13133193C23semidirect
237. #13133190C23semidirect
245. #13133189C23semidirect
253. Q8×Dic53C23semidirect
254. Q8×Dic53C23semidirect
255. C4×Dic106C23semidirect
256. C4×Dic106C23semidirect
257. C4×Dic106C23semidirect
258. #13133182C23semidirect
259. #13133182C23semidirect
260. #13133182C23semidirect
261. #13133182C23semidirect
262. #13133182C23semidirect
270. D4×Dic53C23semidirect
271. D4×Dic53C23semidirect
272. #13133179C23semidirect
273. #13133179C23semidirect
277. C4×C22⋊D53C23semidirect
278. C4×C22⋊D53C23semidirect
279. C4×C22⋊D53C23semidirect
287. #13133177C23semidirect
288. #13133177C23semidirect
289. #13133177C23semidirect
292. #13133176C23semidirect
293. #13133175C23semidirect
294. #13133175C23semidirect
295. #13133174C23semidirect
296. #13133174C23semidirect
314. #13133173C23semidirect
315. #13133173C23semidirect
316. #13133173C23semidirect
326. C2×#11719919C23semidirect
327. C4⋊C4×D53C23semidirect
348. C2×C4×Dic53C23semidirect
349. C42×D53C23semidirect
426. C22×Dic53#41semidirect
657. #3490D53semidirect
702. #551C2×D53semidirect
708. #546C2×D53semidirect
723. #538C2×D53semidirect
759. #525C2×D53semidirect
796. C53#62814semidirect

Maximal subgroups

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

subgroupindex
#202884542
#202884372
#202884302
#202884162
#202884142
#202884122
#202884082
#202884042
#202884022
#202882702
#202882662
#202881172
#202880972
#202880412
#202880072
C2×#168111292
#202879132
C22×#131331732
C53×#34902
#6281453