Finite Group Databasebeta

← #26005187

Subgroups — #26005187

Order 11008.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148518C214yesmaximal, complemented
2#19148507C214yesmaximal, complemented
3#19148494C212yesmaximal, complemented
4#19148492C212yesmaximal, complemented
5#19148479C211yesmaximal, characteristic, complemented
6#19148472C211yesmaximal, characteristic, complemented
7#19148471C211yesmaximal, characteristic, complemented
8#19148461C214yesmaximal, complemented
9#19148448C214yesmaximal, complemented
10#19148435C218yesmaximal, complemented
11#19148195C214yesmaximal, complemented
12#19148187C214yesmaximal, complemented
13#19148160C218yesmaximal, complemented
14#19147986C214yesmaximal, complemented
15#19147927C212yesmaximal, complemented
16#19147892C214yesmaximal, complemented
17#533×D43C211yesmaximal, characteristic, complemented
18C2×#14583450C211yesmaximal, characteristic, complemented
19#19147797C212yesmaximal, complemented
20C4×#41×D43C211yesmaximal, characteristic, complemented
21C43×#3509C211yesmaximal, characteristic, complemented
22C22×#10621902C2212yes—
23C2×#41×D43C2211yescharacteristic
24#14583634C2214yescomplemented
25#14583634C2218yescomplemented
26#14583634C2214yescomplemented
27#14583631C2218yescomplemented
28#14583624C2214yescomplemented
29#14583623C2214yescomplemented
30#14583623C2218yescomplemented
31#14583621C2218yescomplemented
32#14583621C2218yescomplemented
33#14583612C2218yescomplemented
34#14583605C2218yescomplemented
35#14583602C2218yescomplemented
36#14583602C22116yescomplemented
37#14583600C22116yescomplemented
38#14583600C22116yescomplemented
39#14583593C2218yescomplemented
40#14583584C2218yescomplemented
41#14583581C22116yescomplemented
42#14583573C22116yescomplemented
43#14583572C22116yescomplemented
44#14583571C2214yescomplemented
45#14583570C2214yescomplemented
46#14583561C2218yescomplemented
47#14583559C2218yescomplemented
48#14583551C2218yescomplemented
49#14583545C2218yescomplemented
50#14583540C2218yescomplemented
51#14583522C2218yescomplemented
52#14583521C2218yescomplemented
53#14583510C2214yescomplemented
54#14583505C2214yescomplemented
55#14583504C2214yescomplemented
56#14583497C22116yescomplemented
57#14583488C22116yescomplemented
58#14583479C2218yescomplemented
59#14583474C2214yescomplemented
60#14583473C2212yes—
61#14583468C2212yes—
62#14583467C2214yescomplemented
63#14583463C2212yes—
64#14583460C2218yes—
65#14583456C2211yescharacteristic, complemented
66#14583455C2212yescomplemented
67#14583454C2212yescomplemented
68#14583454C2214yescomplemented
69#14583453C2214yescomplemented
70#14583452C2212yescomplemented
71#14583451C2214yescomplemented
72#14583450C2212yes—
73#14583450C2214yes—
74#14583450C2212yes—
75#14583450C2214yescomplemented
76#14583450C2212yescomplemented
77#14583450C2212yescomplemented
78#14583450C2214yescomplemented
79#14583450C2214yescomplemented
80#14583449C2214yescomplemented
81#14583448C2214yescomplemented
82C4⋊Q8×D43C2212yescomplemented
83C2×#13063322C2211yescharacteristic, complemented
84#14583436C2218yescomplemented
85#14583436C2218yescomplemented
86#14583435C2218yescomplemented
87#14583435C2218yescomplemented
88#14583434C2218yescomplemented
89#14583434C2218yescomplemented
90#14583434C22116yescomplemented
91#14583432C22116yescomplemented
92#125×D43C2212yescomplemented
93C2×#13063314C2212yescomplemented
94#14583412C2218yescomplemented
95#14583412C2218yescomplemented
96#14583411C2218yescomplemented
97#14583407C2218yes—
98C22⋊Q8×D43C2214yes—
99C2×#13063300C2214yes—
100#14583381C2218yescomplemented
101#14583381C2218yescomplemented
102#14583377C2212yescomplemented
103#14583373C2218yes—
104#14583373C2212yescomplemented
105#14583373C2212yescomplemented
106#41×Dic43C2211yescharacteristic
107C4×#10621902C2218yescomplemented
108C4×#10621902C2218yescomplemented
109C4×#10621902C2218yescomplemented
110C4×#10621902C2212yescomplemented
111C4×#10621898C2211yescharacteristic
112C4×#10621898C2212yescomplemented
113#14583367C2211yescharacteristic
114#14583367C2218yescomplemented
115#14583367C2212yescomplemented
116C4×#10621900C2214yes—
117C4×#10621900C2212yescomplemented
118C4×Q8×D43C2214yescomplemented
119C4×Q8×D43C2212yescomplemented
120C2×#13063287C2214yescomplemented
121C4×D4×D43C2214yes—
122C4×D4×D43C2212yescomplemented
123#117×D43C2211yescharacteristic
124#117×D43C2212yes—
125#117×D43C2218yescomplemented
126#117×D43C2212yescomplemented
127C2×C42×D43C2211yescharacteristic
128C2×C42×D43C2212yescomplemented
129C43×#557C2214yescomplemented
130C43×#556C2214yescomplemented
131C43×#552C2218yescomplemented
132C43×#541C2214yescomplemented
133C43×#536C2212yes—
134C43×#533C2211yescharacteristic, complemented
135C43×#533C2214yescomplemented
136C2×C4⋊Q8×C43C2211yescharacteristic, complemented
137C43×#519C2212yescomplemented
138C4×#41×C43C2211yescharacteristic
139C2×#10621902—216no—
140C2×#10621902C2314yes—
141C2×#10621902C2314yes—
142C2×#10621902C2311yescharacteristic
143C2×#10621902C2314yes—
144C2×#10621902C2314yes—
145C2×#10621902C2318yes—
146C2×#10621898C2311yescharacteristic
147C2×#10621898C2312yes—
148C2×#10621898C2318yes—
149C2×#10621900C2312yes—
150C2×#10621900C2311yescharacteristic
151#41×D43—28no—
152C2×Q8×D43C2311yescharacteristic
153C2×Q8×D43C2314yes—
154C22×D172C2314yes—
155C22×D172C2312yes—
156C22×D172C2314yes—
157C2×D4×D43C2312yes—
158C2×D4×D43C2311yescharacteristic
159C22×C4×D43C2312yes—
160C22×C4×D43C2314yes—
161C22×C4×D43C2312yes—
162C22×C4×D43C2314yes—
163C22×C4×D43C2311yescharacteristic
164#13063325C2312yes—
165#13063324C2314yes—
166#13063324C2314yes—
167#13063323C2314yes—
168#13063323C2314yes—
169#13063322C2314yes—
170#13063322C2314yes—
171#13063322C2312yes—
172#13063322C2312yes—
173#13063321C2314yes—
174#13063320C23116yes—
175#13063320C23116yes—
176#13063320C23116yes—
177#13063320C23116yes—
178#13063319C23116yes—
179#13063317C2312yes—
180#13063316C2318yes—
181#13063316C2314yes—
182#13063315C2318yes—
183#13063315C23116yes—
184#13063314C2318yes—
185#13063314C2318yes—
186#13063314C2314yes—
187#13063314C2314yes—
188#13063314C2314yes—
189#13063314C2314yes—
190#13063313C23116yes—
191#13063313C2318yes—
192#13063313C2314yes—
193#13063311C23116yes—
194#13063310C23116yes—
195#13063310C23116yes—
196#13063310C23116yes—
197#13063310C23116yes—
198#13063310C23116yes—
199#13063309C23116yes—
200#13063308C2318yes—
201#13063307C23116yes—
202#13063305C23116yes—
203#13063305C2318yes—
204#13063305C2314yes—
205#13063304C2314yes—
206#13063303C23116yes—
207#13063303C23116yes—
208#13063303C2318yes—
209#13063302C2318yes—
210#13063301C2314yes—
211#13063301C2318yes—
212#13063300C2318yes—
213#13063300C23116yes—
214#13063300C23116yes—
215#13063300C2318yes—
216#13063300C2318yes—
217#13063300C2318yes—
218#13063300C2318yes—
219#13063300C2318yes—
220#13063299C2318yes—
221#13063299C2318yes—
222#13063298C23116yes—
223#13063298C23116yes—
224#13063298C23116yes—
225#13063295C2318yes—
226#13063295C23116yes—
227#13063293C2318yes—
228Q8×Dic43C2312yes—
229Q8×Dic43C2314yes—
230Q8×Dic43C2318yes—
231Q8×Dic43C2318yes—
232C4×Dic86C2314yes—
233C4×Dic86C2314yes—
234C4×Dic86C2318yes—
235C4×Dic86C2312yes—
236#13063290C2318yes—
237#13063290C2314yes—
238#13063290C2312yes—
239#13063290C2314yes—
240#13063290C2318yes—
241C4×D172C2314yes—
242C4×D172C23116yes—
243C4×D172C2312yes—
244C4×D172C2318yes—
245C4×D172C23116yes—
246C4×D172C2318yes—
247C4×D172C23116yes—
248C4×D172C2318yes—
249D4×Dic43C2314yes—
250D4×Dic43C2312yes—
251#13063287C23116yes—
252#13063287C2318yes—
253#13063287C2318yes—
254#13063287C2318yes—
255#13063287C2314yes—
256#13063287C2318yes—
257#13063287C2312yes—
258#13063287C2318yes—
259#13063287C2318yes—
260#13063287C23116yes—
261#13063287C2318yes—
262#13063287C23116yes—
263C4×C22⋊D43C2314yes—
264C4×C22⋊D43C2314yes—
265C4×C22⋊D43C2314yes—
266(C22⋊D43)⋊C4C23116yes—
267(C22⋊D43)⋊C4C2314yes—
268(C22⋊D43)⋊C4C2314yes—
269(C22⋊D43)⋊C4C2314yes—
270(C22⋊D43)⋊C4C23116yes—
271#13063284C2318yes—
272#13063284C2311yescharacteristic
273#13063284C2312yes—
274#13063284C2312yes—
275#13063283C23116yes—
276#13063283C2318yes—
277#13063283C2312yes—
278#13063283C2314yes—
279#13063283C2314yes—
280#13063283C23116yes—
281#13063282C23116yes—
282#13063282C23116yes—
283#13063282C2312yes—
284#13063282C2314yes—
285#13063282C2312yes—
286#13063282C2312yes—
287#13063281C2312yes—
288#13063281C2314yes—
289#13063281C2314yes—
290C4⋊C4×D43C23116yes—
291C4⋊C4×D43C2314yes—
292C4⋊C4×D43C2318yes—
293C4⋊C4×D43C2312yes—
294C4⋊C4×D43C2314yes—
295C4⋊C4×D43C2314yes—
296C2×(C2×D43)⋊C4C2318yes—
297C22⋊C4×D43C2318yes—
298C22⋊C4×D43C2318yes—
299C22⋊C4×D43C2312yes—
300C22⋊C4×D43C2314yes—
301C22⋊C4×D43C2314yes—
302C2×C4×Dic43C2312yes—
303C2×C4×Dic43C2311yescharacteristic
304C2×C4×Dic43C2314yes—
305C2×C4×Dic43C2312yes—
306C42×D43C2311yescharacteristic
307C42×D43C2311yescharacteristic
308C42×D43C2312yes—
309C42×D43C2312yes—
310C42×D43C2311yescharacteristic
311C42×D43C2311yescharacteristic
312C42×D43C2312yes—
313C42×D43C2314yes—
314C42×D43C2314yes—
315C42×D43C2312yes—
316C42×D43C2312yes—
317C42×D43C2314yes—
318C42×D43C23116yes—
319C2×#41×C43C2311yescharacteristic
320C22×Q8×C43C2312yes—
321C4⋊Q8×C43C2312yes—
322C4⋊Q8×C43C2312yes—
323C4⋊Q8×C43C2314yes—
324C4⋊Q8×C43C2312yes—
325C4⋊Q8×C43C2314yes—
326#126×C43C23116yes—
327#125×C43C23116yes—
328#125×C43C2312yes—
329#125×C43C2318yes—
330#124×C43C2314yes—
331#123×C43C2318yes—
332C22⋊Q8×C43C2318yes—
333C22⋊Q8×C43C2318yes—
334C22⋊Q8×C43C2314yes—
335C4×Q8×C43C2318yes—
336C4×Q8×C43C2314yes—
337C4×Q8×C43C2312yes—
338C4×Q8×C43C2318yes—
339C4×Q8×C43C2318yes—
340C4×D4×C43C2312yes—
341C4×D4×C43C2314yes—
342#117×C43C2311yescharacteristic
343#117×C43C2312yes—
344#117×C43C2318yes—
345#117×C43C2312yes—
346#117×C43C2318yes—
347C2×C4⋊C4×C43C2314yes—
348C2×C42×C43C2311yescharacteristic
349C2×C42×C43C2312yes—
350C23×D43C2414yes—
351C23×D43C2412yes—
352C23×D43C2411yescharacteristic
353#41×C43—24no—
354C2×Q8×C43—28no—
355C2×Q8×C43C2414yes—
356C2×Q8×C43C2414yes—
357C2×Q8×C43C2414yes—
358C2×Q8×C43C2411yescharacteristic
359C2×D4×C43C2412yes—
360C2×D4×C43C2411yescharacteristic
361C22×C4×C43C2412yes—
362C22×C4×C43C2414yes—
363C22×C4×C43C2412yes—
364C22×C4×C43C2414yes—
365C22×C4×C43C2411yescharacteristic
366C2×C22⋊D43C2412yes—
367C2×C22⋊D43C2412yes—
368C2×C22⋊D43C2412yes—
369C2×C22⋊D43C24116yes—
370C22×Dic43C2412yes—
371C22×Dic43C2412yes—
372C22×Dic43C2414yes—
373C22×Dic43C2411yescharacteristic
374#10621902—24no—
375#10621902—216no—
376#10621902—216no—
377#10621902—216no—
378#10621902—216no—
379#10621902—416no—
380Q8×D43—24no—
381Q8×D43—48no—
382#10621900—28no—
383#10621900—24no—
384D4×D43—24no—
385D4×D43—28no—
386#10621898—24no—
387#10621898—28no—
388#10621898—416no—
389C2×D172—28no—
390C2×D172—216no—
391C2×D172—48no—
392C2×D172C2418yes—
393C2×D172C2418yes—
394C2×D172C2418yes—
395C2×D172C2414yes—
396C2×D172C2412yes—
397C2×D172C2414yes—
398C2×D172C2411yescharacteristic
399C2×D172C2418yes—
400C2×D172C24116yes—
401C2×C4×D43—216no—
402C2×C4×D43—28no—
403C2×C4×D43—44no—
404C2×C4×D43—48no—
405C2×C4×D43#4118yescomplemented
406C2×C4×D43C2412yes—
407C2×C4×D43C2412yes—
408C2×C4×D43C2412yes—
409C2×C4×D43C2412yes—
410C2×C4×D43C2418yes—
411C2×C4×D43C2414yes—
412C2×C4×D43C2412yes—
413C2×C4×D43C2418yes—
414C2×C4×D43C2414yes—
415C2×C4×D43C2412yes—
416C2×C4×D43C2412yes—
417C2×C4×D43C2414yes—
418C2×C4×D43C2418yes—
419C2×C4×D43C24116yes—
420C2×C4×D43C24116yes—
421C2×C4×D43C2411yescharacteristic
422C2×C4×D43C2411yescharacteristic
423C2×C4×D43C2411yescharacteristic
424C2×C4×D43C2411yescharacteristic
425C2×Dic86C2414yes—
426C2×Dic86C2412yes—
427C2×Dic86C2411yescharacteristic
428C2×Dic86C2418yes—
429C4⋊C4×C43C2418yes—
430C4⋊C4×C43C2418yes—
431C4⋊C4×C43C2414yes—
432C4⋊C4×C43C2412yes—
433C4⋊C4×C43C2414yes—
434C4⋊C4×C43C2414yes—
435C4⋊C4×C43C24116yes—
436C4⋊C4×C43C24116yes—
437C4⋊C4×C43C2418yes—
438C22⋊C4×C43C2412yes—
439C22⋊C4×C43C2414yes—
440C22⋊C4×C43C2414yes—
441C22⋊C4×C43C24116yes—
442C42×C43C2411yescharacteristic
443C42×C43C2412yes—
444C42×C43C2411yescharacteristic
445C42×C43C2414yes—
446C42×C43C2412yes—
447C42×C43C24116yes—
448C42×C43C2414yes—
449C22⋊Dic43C2412yes—
450C22⋊Dic43C2414yes—
451C22⋊Dic43C2414yes—
452(C2×D43)⋊C4C2414yes—
453(C2×D43)⋊C4C2414yes—
454(C2×D43)⋊C4C2414yes—
455(C2×D43)⋊C4C2418yes—
456(C2×D43)⋊C4C24116yes—
457(C2×D43)⋊C4C24116yes—
458(C2×D43)⋊C4C24116yes—
459(C2×D43)⋊C4C24116yes—
460(C2×D43)⋊C4C24116yes—
461(C2×D43)⋊C4C24116yes—
462(C2×D43)⋊C4C24116yes—
463C4⋊Dic43C2414yes—
464C4⋊Dic43C2418yes—
465C4⋊Dic43C2412yes—
466C4⋊Dic43C2414yes—
467C4⋊Dic43C2414yes—
468C4⋊Dic43C24116yes—
469Dic43⋊C4C2414yes—
470Dic43⋊C4C2418yes—
471Dic43⋊C4C2414yes—
472Dic43⋊C4C2414yes—
473Dic43⋊C4C2418yes—
474Dic43⋊C4C2418yes—
475Dic43⋊C4C2418yes—
476Dic43⋊C4C24116yes—
477C4×Dic43C2414yes—
478C4×Dic43C2412yes—
479C4×Dic43C2411yescharacteristic
480C4×Dic43C2418yes—
481C4×Dic43C2412yes—
482C4×Dic43C2414yes—
483C4×Dic43C2412yes—
484C4×Dic43C2411yescharacteristic
485C4×Dic43C2414yes—
486C4×Dic43C2412yes—
487C4×Dic43C2412yes—
488C4×Dic43C2414yes—
489C4×Dic43C2412yes—
490C4×Dic43C24116yes—
491C4×Dic43C2414yes—
492C23×C43C2512yes—
493C23×C43C2511yescharacteristic
494C22×D43—28no—
495C22×D43—24no—
496C22×D43—42no—
497C22×D43—44no—
498C22×D43—48no—
499C22×D43C2×#4114yes—
500C22×D43C2518yes—
501C22×D43C2512yes—
502C22×D43C2511yescharacteristic
503C22×D43C2511yescharacteristic
504Q8×C43—22no—
505Q8×C43—28no—
506Q8×C43—28no—
507Q8×C43—28no—
508D4×C43—24no—
509D4×C43—22no—
510C2×C4×C43—28no—
511C2×C4×C43—24no—
512C2×C4×C43—24no—
513C2×C4×C43—28no—
514C2×C4×C43C2×#4114yes—
515C2×C4×C43C2512yes—
516C2×C4×C43C2518yes—
517C2×C4×C43C2514yes—
518C2×C4×C43C2512yes—
519C2×C4×C43C2518yes—
520C2×C4×C43C2511yescharacteristic
521C2×C4×C43C2511yescharacteristic
522C2×C4×C43C2512yes—
523C22⋊D43—24no—
524C22⋊D43—24no—
525C22⋊D43—24no—
526C22⋊D43—416no—
527C2×Dic43—24no—
528C2×Dic43—42no—
529C2×Dic43—44no—
530C2×Dic43C2×#4114yes—
531C2×Dic43C2512yes—
532C2×Dic43C2514yes—
533C2×Dic43C2512yes—
534C2×Dic43C2518yes—
535C2×Dic43C2512yes—
536C2×Dic43C2511yescharacteristic
537C2×Dic43C2511yescharacteristic
538D172—216no—
539D172—216no—
540D172—24no—
541D172—28no—
542D172—28no—
543D172—22no—
544D172—216no—
545D172—48no—
546D172—416no—
547C4×D43—24no—
548C4×D43—24no—
549C4×D43—24no—
550C4×D43—24no—
551C4×D43—28no—
552C4×D43—24no—
553C4×D43—216no—
554C4×D43—216no—
555C4×D43—42no—
556C4×D43—44no—
557C4×D43—44no—
558C4×D43—42no—
559C4×D43—416no—
560C4×D43—48no—
561C4×D43—416no—
562C4×D43C2×#4114yes—
563C4×D43C2×#4114yes—
564C4×D43C2×#4114yes—
565C4×D43C2×#4114yes—
566Dic86—22no—
567Dic86—28no—
568Dic86—24no—
569Dic86—48no—
570#62815—431nomaximal, Sylow
571C22×C43—22no—
572C22×C43—22no—
573C22×C43—24no—
574C22×C43C22×#4112yes—
575C22×C43C2611yescharacteristic
576C2×D43—22no—
577C2×D43—22no—
578C2×D43—28no—
579C2×D43—22no—
580C2×D43—24no—
581C2×D43—216no—
582C2×D43—44no—
583C2×D43—48no—
584C2×D43—88no—
585C2×D43C22×#4112yes—
586C2×D43C22×#4112yes—
587C4×C43—22no—
588C4×C43—28no—
589C4×C43—28no—
590C4×C43—24no—
591C4×C43—22no—
592C4×C43C22×#4112yes—
593C4×C43C22×#4112yes—
594C4×C43#58514yes—
595Dic43—22no—
596Dic43—28no—
597Dic43—22no—
598Dic43—24no—
599Dic43—22no—
600Dic43C22×#4112yes—
601Dic43C22×#4112yes—
602#3512—434no—
603#3511—434no—
604#3510—432no—
605#3510—432no—
606#3509—431no—
607#3509D4311yescharacteristic, complemented
608#3508—431no—
609#3508—431no—
610#3507—434no—
611#3506—434no—
612#3505—438no—
613#3480—434no—
614#3480—434no—
615#3475—438no—
616#3455—434no—
617#3449—432no—
618#3444—434no—
619C2×#533—431no—
620C2×#532—431no—
621#3428—432no—
622C2×C4×#41—431no—
623C2×C43—22no—
624C2×C43—42no—
625C2×C43C23×#4111yescharacteristic
626C2×C43C2×#58512yes—
627D43—22no—
628D43—22no—
629D43—42no—
630D43—48no—
631C22×#41—431no—
632C22×#41—432no—
633#559—438no—
634#559—438no—
635#559—434no—
636#559—434no—
637#557—434no—
638#557C2×D4314yescomplemented
639#556—434no—
640#556—438no—
641#556—438no—
642#556—438no—
643#556C2×D4314yescomplemented
644#555—438no—
645#554—438no—
646#553—4316no—
647#553—4316no—
648#553—438no—
649#553—4316no—
650#553—438no—
651#552—4316no—
652#552—438no—
653#552C2×D4318yescomplemented
654#551—4316no—
655#551—4316no—
656#550—434no—
657#550—434no—
658#548—438no—
659#548—438no—
660#547—438no—
661#546—438no—
662#546—438no—
663#542—438no—
664#542—438no—
665#541—434no—
666#541C2×D4314yescomplemented
667#540—434no—
668#540—434no—
669#539—4316no—
670#538—4316no—
671#537—438no—
672#536—432no—
673#536—434no—
674#536C2×D4312yes—
675#535—432no—
676#535—434no—
677#535—432no—
678#534—438no—
679#533—432no—
680#533—434no—
681#533—432no—
682#533—434no—
683#533—434no—
684#533—432no—
685#533—431no—
686#533C2×D4311yescharacteristic, complemented
687#533C2×D4314yescomplemented
688#532—432no—
689#532—432no—
690#532—434no—
691#532—434no—
692#532—432no—
693#532—432no—
694#532—434no—
695#532—434no—
696#532—434no—
697#532—434no—
698C2×C4⋊Q8—432no—
699C2×C4⋊Q8C2×D4311yescharacteristic, complemented
700C2×#127—431no—
701#529—4316no—
702#529—438no—
703#529—438no—
704#529—4316no—
705#529—438no—
706#529—438no—
707#529—438no—
708#529—438no—
709C2×#125—432no—
710C2×#124—432no—
711#525—438no—
712#525—438no—
713#525—438no—
714#525—438no—
715C2×C22⋊Q8—434no—
716C2×#121—434no—
717#520—438no—
718#520—438no—
719#519—432no—
720#519C2×D4312yescomplemented
721#518—438no—
722#518—432no—
723#518—432no—
724C4×#41—431no—
725C4×#41—432no—
726C4×#41—438no—
727C4×#41—438no—
728C4×#41—438no—
729C4×#41—434no—
730C4×#41—432no—
731C4×#41—431no—
732C4×#41—432no—
733C4×#41—438no—
734C4×#41—431no—
735C4×#41—432no—
736C4×#41C2×D4311yescharacteristic
737C2×C4×Q8—432no—
738C2×C4×Q8—434no—
739C2×C4×D4—434no—
740C2×C4×D4—432no—
741C2×C4×D4—434no—
742C2×#117—431no—
743C2×#117—432no—
744C2×#117—432no—
745C2×#117—438no—
746C22×C42—431no—
747C22×C42—432no—
748C43#6281511yescharacteristic, complemented, Sylow
749C2×#41—434no—
750C2×#41—431no—
751C2×#41—434no—
752C2×#41—434no—
753C2×#41—434no—
754C2×#41—438no—
755C2×#41—432no—
756C2×#41—431no—
757C2×#41—431no—
758C2×#41—432no—
759C2×#41—438no—
760C2×#41—8616no—
761C2×#41—868no—
762C2×#41C22×D4311yescharacteristic
763C22×Q8—431no—
764C22×Q8—434no—
765C22×Q8C22×D4312yes—
766C22×D4—432no—
767C22×D4—431no—
768C22×D4—434no—
769C22×D4—432no—
770C22×D4—434no—
771C23×C4—431no—
772C23×C4—434no—
773C23×C4—432no—
774C23×C4—432no—
775C23×C4—434no—
776C4⋊Q8—434no—
777C4⋊Q8—434no—
778C4⋊Q8—434no—
779C4⋊Q8—434no—
780C4⋊Q8—432no—
781C4⋊Q8C22×D4312yes—
782C4⋊Q8C22×D4312yes—
783C4⋊Q8C22×D4312yes—
784C4⋊Q8C22×D4314yes—
785C4⋊Q8C22×D4314yes—
786#127—434no—
787#127—432no—
788#127—432no—
789#127—434no—
790#127—434no—
791#126—4316no—
792#126—4316no—
793#126—4316no—
794#126—4316no—
795#126—4316no—
796#126C22×D43116yes—
797#125—434no—
798#125—438no—
799#125—438no—
800#125—4316no—
801#125—432no—
802#125C22×D4312yes—
803#125C22×D4318yes—
804#125C22×D43116yes—
805#124—434no—
806#124—434no—
807#124—438no—
808#124—438no—
809#124—434no—
810#124—434no—
811#124—4316no—
812#124—438no—
813#124—4316no—
814#124—434no—
815#124C22×D4314yes—
816#123—438no—
817#123—4316no—
818#123—4316no—
819#123—4316no—
820#123—4316no—
821#123—4316no—
822#123—4316no—
823#123—4316no—
824#123C22×D4318yes—
825C22⋊Q8—434no—
826C22⋊Q8—438no—
827C22⋊Q8—434no—
828C22⋊Q8—434no—
829C22⋊Q8—438no—
830C22⋊Q8—438no—
831C22⋊Q8—4316no—
832C22⋊Q8—4316no—
833C22⋊Q8—4316no—
834C22⋊Q8—438no—
835C22⋊Q8C22×D4314yes—
836C22⋊Q8C22×D4318yes—
837C22⋊Q8C22×D4318yes—
838#121—438no—
839#121—438no—
840#121—438no—
841#121—438no—
842#121—438no—
843#121—438no—
844#121—438no—
845#121—438no—
846#121—4316no—
847#121—4316no—
848#121—4316no—
849#121—4316no—
850#121—4316no—
851#120—438no—
852#120—4316no—
853#120—438no—
854C4×Q8—434no—
855C4×Q8—432no—
856C4×Q8—438no—
857C4×Q8—438no—
858C4×Q8—434no—
859C4×Q8—434no—
860C4×Q8—432no—
861C4×Q8—438no—
862C4×Q8—438no—
863C4×Q8—434no—
864C4×Q8—432no—
865C4×Q8—434no—
866C4×Q8—438no—
867C4×Q8C22×D4312yes—
868C4×Q8C22×D4314yes—
869C4×Q8C22×D4318yes—
870C4×Q8C22×D4318yes—
871C4×Q8C22×D4318yes—
872C4×D4—434no—
873C4×D4—432no—
874C4×D4—434no—
875C4×D4—434no—
876C4×D4—434no—
877C4×D4—438no—
878C4×D4—434no—
879C4×D4—432no—
880C4×D4—438no—
881C4×D4—438no—
882C4×D4—438no—
883C4×D4—4316no—
884C4×D4—438no—
885C4×D4—4316no—
886C4×D4—438no—
887C4×D4—4316no—
888C4×D4—438no—
889C4×D4—434no—
890C4×D4—434no—
891C4×D4—434no—
892C4×D4—4316no—
893C4×D4—4316no—
894C4×D4—434no—
895C4×D4—432no—
896C4×D4—4316no—
897C4×D4—438no—
898C4×D4—4316no—
899C4×D4—438no—
900C4×D4—4316no—
901C4×D4—438no—
902C4×D4C22×D4314yes—
903C4×D4C22×D4312yes—
904#117—431no—
905#117—432no—
906#117—432no—
907#117—438no—
908#117—432no—
909#117—434no—
910#117—434no—
911#117—4316no—
912#117—438no—
913#117—4316no—
914#117—432no—
915#117—434no—
916#117—434no—
917#117—432no—
918#117—432no—
919#117—432no—
920#117—434no—
921#117—4316no—
922#117—4316no—
923#117C22×D4311yescharacteristic
924#117C22×D4312yes—
925#117C22×D4312yes—
926#117C22×D4318yes—
927#117C22×D4318yes—
928C2×C4⋊C4—432no—
929C2×C4⋊C4—434no—
930C2×C4⋊C4—434no—
931C2×C4⋊C4—4316no—
932C2×C4⋊C4—438no—
933C2×C4⋊C4—434no—
934C2×C4⋊C4C22×D4314yes—
935C2×C22⋊C4—438no—
936C2×C22⋊C4—432no—
937C2×C22⋊C4—434no—
938C2×C22⋊C4—434no—
939C2×C22⋊C4—438no—
940C2×C22⋊C4—438no—
941C2×C42—432no—
942C2×C42—434no—
943C2×C42—431no—
944C2×C42—432no—
945C2×C42—432no—
946C2×C42—431no—
947C2×C42—434no—
948C2×C42—4316no—
949C2×C42—434no—
950C2×C42—432no—
951C2×C42—432no—
952C2×C42—434no—
953C2×C42—431no—
954C2×C42—432no—
955C2×C42—431no—
956C2×C42—432no—
957C2×C42—431no—
958C2×C42C22×D4311yescharacteristic
959C2×C42C22×D4312yes—
960C24—431no—
961C24—434no—
962C24—432no—
963#41—24no—
964#41—868no—
965#41—868no—
966#41—864no—
967#41—8616no—
968#41—8616no—
969#41—8616no—
970#41—8616no—
971#41—864no—
972#41—864no—
973#41—17216no—
974#41—17216no—
975C2×Q8—28no—
976C2×Q8—432no—
977C2×Q8—434no—
978C2×Q8—431no—
979C2×Q8—438no—
980C2×Q8—864no—
981C2×Q8—1728no—
982C2×Q8C23×D4314yes—
983C2×Q8C23×D4311yescharacteristic
984C2×Q8C23×D4314yes—
985C2×Q8C23×D4314yes—
986C2×D4—432no—
987C2×D4—432no—
988C2×D4—432no—
989C2×D4—4316no—
990C2×D4—438no—
991C2×D4—432no—
992C2×D4—438no—
993C2×D4—434no—
994C2×D4—438no—
995C2×D4—431no—
996C2×D4—434no—
997C2×D4—4316no—
998C2×D4—438no—
999C2×D4—8616no—
1000C2×D4—864no—
1001C2×D4—868no—
1002C2×D4—868no—
1003C2×D4—1728no—
1004C2×D4C23×D4312yes—
1005C2×D4C23×D4311yescharacteristic
1006C22×C4—431no—
1007C22×C4—438no—
1008C22×C4—431no—
1009C22×C4—431no—
1010C22×C4—431no—
1011C22×C4—431no—
1012C22×C4—432no—
1013C22×C4—432no—
1014C22×C4—434no—
1015C22×C4—432no—
1016C22×C4—432no—
1017C22×C4—432no—
1018C22×C4—432no—
1019C22×C4—438no—
1020C22×C4—434no—
1021C22×C4—432no—
1022C22×C4—438no—
1023C22×C4—434no—
1024C22×C4—432no—
1025C22×C4—432no—
1026C22×C4—434no—
1027C22×C4—438no—
1028C22×C4—4316no—
1029C22×C4—4316no—
1030C22×C4—8616no—
1031C22×C4—868no—
1032C22×C4—1724no—
1033C22×C4—1728no—
1034C22×C4C23×D4312yes—
1035C22×C4C23×D4312yes—
1036C22×C4C23×D4314yes—
1037C22×C4C23×D4314yes—
1038C22×C4C23×D4311yescharacteristic
1039C4⋊C4—434no—
1040C4⋊C4—438no—
1041C4⋊C4—432no—
1042C4⋊C4—434no—
1043C4⋊C4—434no—
1044C4⋊C4—434no—
1045C4⋊C4—434no—
1046C4⋊C4—438no—
1047C4⋊C4—4316no—
1048C4⋊C4—438no—
1049C4⋊C4—434no—
1050C4⋊C4—438no—
1051C4⋊C4—438no—
1052C4⋊C4—4316no—
1053C4⋊C4C23×D4312yes—
1054C4⋊C4C23×D4314yes—
1055C4⋊C4C23×D43116yes—
1056C4⋊C4C23×D4314yes—
1057C4⋊C4C23×D4314yes—
1058C4⋊C4C23×D4318yes—
1059C4⋊C4C23×D4318yes—
1060C4⋊C4C23×D4318yes—
1061C4⋊C4C23×D43116yes—
1062C22⋊C4—432no—
1063C22⋊C4—434no—
1064C22⋊C4—434no—
1065C22⋊C4—434no—
1066C22⋊C4—438no—
1067C22⋊C4—434no—
1068C22⋊C4—4316no—
1069C22⋊C4—4316no—
1070C22⋊C4—4316no—
1071C22⋊C4—434no—
1072C22⋊C4—4316no—
1073C22⋊C4—4316no—
1074C22⋊C4—4316no—
1075C22⋊C4—4316no—
1076C22⋊C4C23×D4312yes—
1077C22⋊C4C23×D4314yes—
1078C22⋊C4C23×D4314yes—
1079C22⋊C4C23×D43116yes—
1080C42—434no—
1081C42—432no—
1082C42—431no—
1083C42—432no—
1084C42—438no—
1085C42—432no—
1086C42—434no—
1087C42—434no—
1088C42—431no—
1089C42—432no—
1090C42—432no—
1091C42—434no—
1092C42—432no—
1093C42—4316no—
1094C42—434no—
1095C42C23×D4311yescharacteristic
1096C42C23×D4312yes—
1097C42C23×D4311yescharacteristic
1098C42C23×D4314yes—
1099C42C23×D4312yes—
1100C42C23×D43116yes—
1101C42C23×D4314yes—
1102C23—431no—
1103C23—431no—
1104C23—434no—
1105C23—432no—
1106C23—438no—
1107C23—864no—
1108C23—868no—
1109C23—1728no—
1110C23—1722no—
1111C23—1724no—
1112C23C24×D4312yes—
1113C23C24×D4311yescharacteristic
1114Q8—28no—
1115Q8—28no—
1116Q8—22no—
1117Q8—28no—
1118Q8—864no—
1119Q8—862no—
1120Q8—868no—
1121Q8—1728no—
1122D4—24no—
1123D4—22no—
1124D4—864no—
1125D4—8616no—
1126D4—8616no—
1127D4—864no—
1128D4—864no—
1129D4—864no—
1130D4—868no—
1131D4—862no—
1132D4—868no—
1133D4—8616no—
1134D4—1728no—
1135D4—17216no—
1136D4—17216no—
1137C2×C4—28no—
1138C2×C4—24no—
1139C2×C4—24no—
1140C2×C4—28no—
1141C2×C4—434no—
1142C2×C4—431no—
1143C2×C4—431no—
1144C2×C4—434no—
1145C2×C4—434no—
1146C2×C4—434no—
1147C2×C4—434no—
1148C2×C4—434no—
1149C2×C4—432no—
1150C2×C4—432no—
1151C2×C4—432no—
1152C2×C4—438no—
1153C2×C4—864no—
1154C2×C4—8616no—
1155C2×C4—8616no—
1156C2×C4—864no—
1157C2×C4—864no—
1158C2×C4—864no—
1159C2×C4—864no—
1160C2×C4—864no—
1161C2×C4—868no—
1162C2×C4—1724no—
1163C2×C4—1724no—
1164C2×C4—1722no—
1165C2×C4—1722no—
1166C2×C4—1728no—
1167C2×C4—17216no—
1168C2×C4—17216no—
1169C2×C4—1724no—
1170C2×C4—1722no—
1171C2×C4#41×D4314yes—
1172C2×C4C24×D4314yes—
1173C2×C4C24×D4312yes—
1174C2×C4C24×D4318yes—
1175C2×C4C24×D4312yes—
1176C2×C4C24×D4318yes—
1177C2×C4C24×D4311yescharacteristic
1178C2×C4C24×D4311yescharacteristic
1179C2×C4C24×D4312yes—
1180C22—22no—
1181C22—22no—
1182C22—24no—
1183C22—432no—
1184C22—432no—
1185C22—862no—
1186C22—862no—
1187C22—868no—
1188C22—862no—
1189C22—864no—
1190C22—8616no—
1191C22—3448no—
1192C22—1724no—
1193C22—1728no—
1194C22C2×#41×D4312yes—
1195C22C25×D4311yescharacteristic
1196C4—22no—
1197C4—28no—
1198C4—24no—
1199C4—22no—
1200C4—28no—
1201C4—432no—
1202C4—432no—
1203C4—862no—
1204C4—862no—
1205C4—864no—
1206C4—862no—
1207C4—868no—
1208C4C2×#41×D4312yes—
1209C4C2×#41×D4312yes—
1210C4#1458373614yes—
1211C2—22no—
1212C2—42no—
1213C2—862no—
1214C2—862no—
1215C2—1728no—
1216C2—1722no—
1217C2C22×#41×D4311yescharacteristic
1218C2C2×#1458373612yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3509C2
hypercenter#3509D43
hypocenterC43#62815
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #19148518C2semidirect
2. #19148507C2semidirect
3. #19148494C2semidirect
4. #19148492C2semidirect
5. #19148479C2semidirect
6. #19148472C2semidirect
7. #19148471C2semidirect
8. #19148461C2semidirect
9. #19148448C2semidirect
10. #19148435C2semidirect
11. #19148195C2semidirect
12. #19148187C2semidirect
13. #19148160C2semidirect
14. #19147986C2semidirect
15. #19147927C2semidirect
16. #19147892C2semidirect
17. #533×D43C2semidirect
18. C2×#14583450C2semidirect
19. #19147797C2semidirect
20. C4×#41×D43C2semidirect
21. C43×#3509C2semidirect
24. #14583634C22semidirect
25. #14583634C22semidirect
26. #14583634C22semidirect
27. #14583631C22semidirect
28. #14583624C22semidirect
29. #14583623C22semidirect
30. #14583623C22semidirect
31. #14583621C22semidirect
32. #14583621C22semidirect
33. #14583612C22semidirect
34. #14583605C22semidirect
35. #14583602C22semidirect
36. #14583602C22semidirect
37. #14583600C22semidirect
38. #14583600C22semidirect
39. #14583593C22semidirect
40. #14583584C22semidirect
41. #14583581C22semidirect
42. #14583573C22semidirect
43. #14583572C22semidirect
44. #14583571C22semidirect
45. #14583570C22semidirect
46. #14583561C22semidirect
47. #14583559C22semidirect
48. #14583551C22semidirect
49. #14583545C22semidirect
50. #14583540C22semidirect
51. #14583522C22semidirect
52. #14583521C22semidirect
53. #14583510C22semidirect
54. #14583505C22semidirect
55. #14583504C22semidirect
56. #14583497C22semidirect
57. #14583488C22semidirect
58. #14583479C22semidirect
59. #14583474C22semidirect
62. #14583467C22semidirect
65. #14583456C22semidirect
66. #14583455C22semidirect
67. #14583454C22semidirect
68. #14583454C22semidirect
69. #14583453C22semidirect
70. #14583452C22semidirect
71. #14583451C22semidirect
75. #14583450C22semidirect
76. #14583450C22semidirect
77. #14583450C22semidirect
78. #14583450C22semidirect
79. #14583450C22semidirect
80. #14583449C22semidirect
81. #14583448C22semidirect
82. C4⋊Q8×D43C22semidirect
83. C2×#13063322C22semidirect
84. #14583436C22semidirect
85. #14583436C22semidirect
86. #14583435C22semidirect
87. #14583435C22semidirect
88. #14583434C22semidirect
89. #14583434C22semidirect
90. #14583434C22semidirect
91. #14583432C22semidirect
92. #125×D43C22semidirect
93. C2×#13063314C22semidirect
94. #14583412C22semidirect
95. #14583412C22semidirect
96. #14583411C22semidirect
100. #14583381C22semidirect
101. #14583381C22semidirect
102. #14583377C22semidirect
104. #14583373C22semidirect
105. #14583373C22semidirect
107. C4×#10621902C22semidirect
108. C4×#10621902C22semidirect
109. C4×#10621902C22semidirect
110. C4×#10621902C22semidirect
112. C4×#10621898C22semidirect
114. #14583367C22semidirect
115. #14583367C22semidirect
117. C4×#10621900C22semidirect
118. C4×Q8×D43C22semidirect
119. C4×Q8×D43C22semidirect
120. C2×#13063287C22semidirect
122. C4×D4×D43C22semidirect
125. #117×D43C22semidirect
126. #117×D43C22semidirect
128. C2×C42×D43C22semidirect
129. C43×#557C22semidirect
130. C43×#556C22semidirect
131. C43×#552C22semidirect
132. C43×#541C22semidirect
134. C43×#533C22semidirect
135. C43×#533C22semidirect
136. C2×C4⋊Q8×C43C22semidirect
137. C43×#519C22semidirect
405. C2×C4×D43#41semidirect
607. #3509D43semidirect
638. #557C2×D43semidirect
643. #556C2×D43semidirect
653. #552C2×D43semidirect
666. #541C2×D43semidirect
686. #533C2×D43semidirect
687. #533C2×D43semidirect
699. C2×C4⋊Q8C2×D43semidirect
720. #519C2×D43semidirect
748. C43#62815semidirect

Maximal subgroups

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

subgroupindex
#191485182
#191485072
#191484942
#191484922
#191484792
#191484722
#191484712
#191484612
#191484482
#191484352
#191481952
#191481872
#191481602
#191479862
#191479272
#191478922
#533×D432
C2×#145834502
#191477972
C4×#41×D432
C43×#35092
#6281543