Finite Group Databasebeta

← #26005326

Subgroups — #26005326

Order 11008.

6530 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19149197C214yesmaximal, complemented
2#19149191C214yesmaximal, complemented
3#19149130C214yesmaximal, complemented
4#19149128C214yesmaximal, complemented
5#19149047C218yesmaximal, complemented
6#19148576C214yesmaximal, complemented
7#19148572C214yesmaximal, complemented
8#19148568C214yesmaximal, complemented
9#19148567C214yesmaximal, complemented
10#19148519C211yesmaximal, characteristic, complemented
11#19148517C211yesmaximal, characteristic, complemented
12#19148512C212yesmaximal, complemented
13#19148418C212yesmaximal, complemented
14#19148416C211yesmaximal, characteristic, complemented
15#19148305C212yesmaximal, complemented
16#19148303C218yesmaximal, complemented
17#19148298C212yesmaximal, complemented
18#19147892C211yesmaximal, characteristic, complemented
19#19147888C211yesmaximal, characteristic, complemented
20C2×#125×D43C211yesmaximal, characteristic, complemented
21C43×#3504C211yesmaximal, characteristic, complemented
22C43⋊#564C2218yescomplemented
23#14583650C2218yescomplemented
24#14583648C2218yescomplemented
25#14583645C2218yescomplemented
26#14583627C2214yescomplemented
27#14583626C2214yescomplemented
28#14583624C2214yescomplemented
29#14583610C2214yes—
30#14583610C2214yes—
31#14583610C2214yescomplemented
32#14583609C2214yes—
33#14583609C2214yescomplemented
34#14583607C2218yes—
35#14583605C2214yescomplemented
36#14583604C2214yes—
37#14583603C2218yes—
38#14583603C2218yes—
39#14583602C2214yes—
40#14583602C2214yes—
41#14583602C2214yescomplemented
42#14583599C2214yes—
43#14583599C2214yescomplemented
44#14583598C2218yes—
45#14583598C2218yes—
46#14583597C2218yes—
47#14583597C2214yescomplemented
48#14583595C2218yes—
49#14583593C2214yes—
50#14583593C2214yescomplemented
51#14583590C2214yes—
52#14583590C2218yes—
53#14583590C2218yescomplemented
54#14583590C2214yescomplemented
55#14583588C2214yes—
56#14583588C2214yescomplemented
57#14583587C2214yes—
58#14583587C2214yes—
59#14583587C2214yescomplemented
60#14583584C2218yescomplemented
61#14583584C2214yescomplemented
62#14583583C2218yes—
63#14583583C2218yescomplemented
64#14583581C2218yes—
65#14583581C2218yes—
66#14583581C2218yescomplemented
67#14583554C2214yes—
68#14583552C2218yes—
69#14583552C2214yes—
70#14583552C2214yes—
71#14583551C2218yes—
72#14583551C2218yes—
73#14583550C2214yes—
74#14583550C2218yes—
75#14583529C2214yescomplemented
76#14583527C2212yes—
77#14583526C2218yes—
78#14583526C2214yescomplemented
79#14583526C2214yescomplemented
80#14583512C2212yescomplemented
81#14583511C2212yescomplemented
82#14583510C2218yescomplemented
83#14583509C2218yescomplemented
84#14583508C2218yescomplemented
85#14583507C2218yescomplemented
86#14583507C2214yescomplemented
87#14583505C2212yescomplemented
88#14583504C2212yescomplemented
89#14583500C2214yescomplemented
90#14583498C2218yes—
91#14583497C2218yes—
92#14583497C2218yes—
93#14583497C2218yescomplemented
94#14583496C2218yescomplemented
95#14583495C2218yes—
96#14583495C2218yes—
97#14583495C2218yescomplemented
98#14583495C2218yescomplemented
99#14583491C2218yes—
100#14583480C2212yes—
101#14583479C2218yes—
102#14583477C2212yes—
103#14583455C2212yescomplemented
104#14583454C2212yes—
105#14583454C2214yescomplemented
106#14583453C2212yes—
107#14583452C2211yescharacteristic
108#14583450C2212yes—
109#14583449C2211yescharacteristic
110#14583446C2212yes—
111#14583445C2211yescharacteristic
112#14583436C2212yes—
113#14583436C2214yes—
114#14583436C2214yescomplemented
115#14583435C2214yes—
116#14583434C2212yes—
117#14583434C2212yes—
118#14583434C2214yescomplemented
119#14583433C2214yescomplemented
120#14583431C2212yes—
121#14583431C2214yescomplemented
122#14583429C2214yes—
123#14583427C2214yes—
124C2×#13063317C2211yescharacteristic
125C2×#13063316C2212yes—
126C2×#13063315C2214yes—
127#125×D43C2214yes—
128#125×D43C2214yes—
129#125×D43C2214yes—
130#125×D43C2214yes—
131#125×D43C2212yescomplemented
132#125×D43C2214yescomplemented
133#14583412C2218yes—
134#14583412C2214yes—
135#14583411C2212yes—
136#14583411C2211yescharacteristic
137#14583408C2218yes—
138#14583408C2214yes—
139#14583406C2211yescharacteristic
140#14583381C2218yes—
141#14583380C2212yes—
142#14583380C2218yes—
143#14583379C2212yes—
144#14583379C2212yes—
145C4×#10621902C2214yes—
146C4×#10621898C2214yes—
147C4×#10621898C2211yescharacteristic
148#14583367C2212yes—
149C2×C4⋊C4×D43C2212yes—
150C2×C4⋊C4×D43C2214yes—
151C2×C42×D43C2211yescharacteristic
152C43×#557C2214yescomplemented
153C43×#554C2218yes—
154C43×#554C2214yescomplemented
155C43×#544C2212yes—
156C43×#544C2214yescomplemented
157C43×#533C2211yescharacteristic
158C43×#533C2212yescomplemented
159C2×#125×C43C2211yescharacteristic
160C2×#125×C43C2212yescomplemented
161C43×#520C2212yes—
162C4×#41×C43C2211yescharacteristic
163C2×#10621902C2318yes—
164C2×#10621902C2314yes—
165C2×#10621898C2312yes—
166C2×#10621898C2311yescharacteristic
167C2×#10621898C2318yes—
168C2×#10621898C2314yes—
169C22×C4×D43C2311yescharacteristic
170C22×C4×D43C2312yes—
171C22×C4×D43C2314yes—
172#13063325C2314yes—
173#13063325C2311yescharacteristic
174#13063324C2314yes—
175#13063324C2318yes—
176#13063324C2312yes—
177#13063323C2318yes—
178#13063323C2318yes—
179#13063323C2311yescharacteristic
180#13063322C2311yescharacteristic
181#13063321C2311yescharacteristic
182#13063320C2318yes—
183#13063320C2318yes—
184#13063320C2318yes—
185#13063320C2318yes—
186#13063320C2318yes—
187#13063320C2318yes—
188#13063320C2314yes—
189#13063320C2314yes—
190#13063320C2314yes—
191#13063319C2318yes—
192#13063319C2318yes—
193#13063319C2318yes—
194#13063318C2318yes—
195#13063318C2318yes—
196#13063318C2318yes—
197#13063318C2314yes—
198#13063317C2318yes—
199#13063317C2318yes—
200#13063317C2314yes—
201#13063317C2314yes—
202#13063317C2312yes—
203#13063317C2312yes—
204#13063316C2318yes—
205#13063316C2318yes—
206#13063316C2318yes—
207#13063316C2314yes—
208#13063316C2314yes—
209#13063316C2314yes—
210#13063316C2314yes—
211#13063316C2314yes—
212#13063316C2314yes—
213#13063316C2312yes—
214#13063315C2318yes—
215#13063315C2318yes—
216#13063315C2318yes—
217#13063315C2318yes—
218#13063315C2318yes—
219#13063315C2318yes—
220#13063315C2318yes—
221#13063315C2318yes—
222#13063315C2318yes—
223#13063315C2318yes—
224#13063315C2318yes—
225#13063315C2314yes—
226#13063315C2318yes—
227#13063315C2318yes—
228#13063314C2314yes—
229#13063314C2311yescharacteristic
230#13063313C2312yes—
231#13063312C2311yescharacteristic
232#13063311C2314yes—
233#13063310C2314yes—
234#13063310C2318yes—
235#13063310C2318yes—
236#13063310C2318yes—
237#13063310C2318yes—
238#13063310C2318yes—
239#13063310C2318yes—
240#13063310C2318yes—
241#13063310C2314yes—
242#13063310C2318yes—
243#13063310C2314yes—
244#13063310C2318yes—
245#13063309C2312yes—
246#13063309C2314yes—
247#13063308C2318yes—
248#13063308C2318yes—
249#13063308C2318yes—
250#13063307C2318yes—
251#13063307C2318yes—
252#13063307C2314yes—
253#13063307C2318yes—
254#13063307C2318yes—
255#13063306C2312yes—
256#13063305C2314yes—
257#13063305C2318yes—
258#13063305C2312yes—
259#13063305C2312yes—
260#13063305C2314yes—
261#13063305C2312yes—
262#13063305C2318yes—
263#13063304C2318yes—
264#13063304C2314yes—
265#13063303C2318yes—
266#13063303C2318yes—
267#13063303C2318yes—
268#13063303C2318yes—
269#13063303C2318yes—
270#13063303C2318yes—
271#13063303C2314yes—
272#13063302C2318yes—
273#13063302C2314yes—
274#13063301C2318yes—
275#13063301C2318yes—
276#13063301C2318yes—
277#13063301C2318yes—
278#13063301C2318yes—
279#13063301C2312yes—
280#13063301C2314yes—
281#13063301C2318yes—
282#13063301C2314yes—
283#13063300C2312yes—
284#13063300C2312yes—
285#13063300C2314yes—
286#13063300C2318yes—
287#13063300C2318yes—
288#13063300C2314yes—
289#13063300C2312yes—
290#13063300C2314yes—
291#13063299C2314yes—
292#13063299C2318yes—
293#13063299C2318yes—
294#13063299C2314yes—
295#13063298C2318yes—
296#13063298C2318yes—
297#13063298C2318yes—
298#13063298C2314yes—
299#13063297C2314yes—
300#13063297C2318yes—
301#13063296C2312yes—
302#13063296C2314yes—
303#13063295C2314yes—
304#13063295C2312yes—
305#13063293C2312yes—
306Q8×Dic43C2318yes—
307Q8×Dic43C2314yes—
308C4×Dic86C2314yes—
309C4×Dic86C2314yes—
310C4×Dic86C2312yes—
311C4×Dic86C2314yes—
312C4×Dic86C2314yes—
313#13063290C2318yes—
314#13063290C2318yes—
315#13063290C2312yes—
316#13063290C2314yes—
317#13063290C2312yes—
318C4×D172C2314yes—
319C4×D172C2314yes—
320C4×D172C2318yes—
321C4×D172C2318yes—
322C4×D172C2314yes—
323C4×D172C2314yes—
324C4×D172C2314yes—
325C4×D172C2314yes—
326C4×D172C2312yes—
327C4×D172C2314yes—
328#13063287C2318yes—
329#13063287C2318yes—
330#13063287C2318yes—
331#13063287C2314yes—
332#13063287C2312yes—
333#13063287C2312yes—
334#13063287C2314yes—
335#13063287C2314yes—
336#13063287C2314yes—
337C4×C22⋊D43C2318yes—
338C4×C22⋊D43C2318yes—
339C4×C22⋊D43C2314yes—
340C4×C22⋊D43C2318yes—
341C4×C22⋊D43C2314yes—
342C4×C22⋊D43C2314yes—
343C4×C22⋊D43C2318yes—
344C4×C22⋊D43C2314yes—
345C4×C22⋊D43C2314yes—
346(C22⋊D43)⋊C4C2314yes—
347(C22⋊D43)⋊C4C2318yes—
348(C22⋊D43)⋊C4C2318yes—
349(C22⋊D43)⋊C4C2314yes—
350#13063284C2318yes—
351#13063284C2314yes—
352#13063284C2311yescharacteristic
353#13063283C2314yes—
354#13063283C2318yes—
355#13063283C2314yes—
356#13063283C2314yes—
357#13063283C2318yes—
358#13063283C2314yes—
359#13063283C2314yes—
360#13063283C2314yes—
361#13063282C2314yes—
362#13063282C2318yes—
363#13063282C2318yes—
364#13063282C2318yes—
365#13063282C2314yes—
366#13063282C2314yes—
367#13063282C2312yes—
368C2×C4⋊Dic43C2314yes—
369C2×C4⋊Dic43C2312yes—
370C2×Dic43⋊C4C2314yes—
371C2×Dic43⋊C4C2314yes—
372C2×Dic43⋊C4C2314yes—
373C4⋊C4×D43C2314yes—
374C4⋊C4×D43C2318yes—
375C4⋊C4×D43C2318yes—
376C4⋊C4×D43C2314yes—
377C4⋊C4×D43C2314yes—
378C4⋊C4×D43C2314yes—
379C4⋊C4×D43C2314yes—
380C4⋊C4×D43C2318yes—
381C4⋊C4×D43C2318yes—
382C4⋊C4×D43C2318yes—
383C4⋊C4×D43C2314yes—
384C4⋊C4×D43C2314yes—
385C4⋊C4×D43C2318yes—
386C4⋊C4×D43C2318yes—
387C2×C4×Dic43C2311yescharacteristic
388C2×C4×Dic43C2312yes—
389C42×D43C2312yes—
390C42×D43C2312yes—
391C42×D43C2312yes—
392C42×D43C2312yes—
393C42×D43C2314yes—
394C42×D43C2312yes—
395C2×#41×C43C2311yescharacteristic
396C4⋊Q8×C43C2314yes—
397C4⋊Q8×C43C2314yes—
398C4⋊Q8×C43C2318yes—
399C4⋊Q8×C43C2312yes—
400#125×C43C2318yes—
401#125×C43C2318yes—
402#125×C43C2312yes—
403#125×C43C2314yes—
404#125×C43C2312yes—
405#125×C43C2311yescharacteristic
406#125×C43C2314yes—
407#125×C43C2314yes—
408#125×C43C2311yescharacteristic
409C22⋊Q8×C43C2318yes—
410C22⋊Q8×C43C2318yes—
411C22⋊Q8×C43C2314yes—
412C22⋊Q8×C43C2318yes—
413C22⋊Q8×C43C2318yes—
414C4×Q8×C43C2312yes—
415C4×Q8×C43C2314yes—
416C4×Q8×C43C2314yes—
417C4×Q8×C43C2318yes—
418C4×D4×C43C2314yes—
419C4×D4×C43C2314yes—
420C4×D4×C43C2312yes—
421C4×D4×C43C2318yes—
422#117×C43C2311yescharacteristic
423#117×C43C2312yes—
424#117×C43C2312yes—
425#117×C43C2314yes—
426C2×C4⋊C4×C43C2312yes—
427C2×C4⋊C4×C43C2314yes—
428C2×C4⋊C4×C43C2314yes—
429C2×C4⋊C4×C43C2318yes—
430C2×C42×C43C2311yescharacteristic
431C2×C42×C43C2312yes—
432C23×D43C2411yescharacteristic
433#41×C43—24no—
434C2×Q8×C43C2411yescharacteristic
435C2×Q8×C43C2418yes—
436C2×Q8×C43C2414yes—
437C2×D4×C43C2412yes—
438C2×D4×C43C2411yescharacteristic
439C22×C4×C43C2412yes—
440C22×C4×C43C2412yes—
441C22×C4×C43C2414yes—
442C22×C4×C43C2414yes—
443C22×C4×C43C2418yes—
444C22×C4×C43C2411yescharacteristic
445C2×C22⋊D43C2414yes—
446C2×C22⋊D43C2412yes—
447C2×C22⋊D43C2414yes—
448C2×C22⋊D43C2418yes—
449C2×C22⋊D43C2414yes—
450C22×Dic43C2411yescharacteristic
451C22×Dic43C2412yes—
452C22×Dic43C2414yes—
453#10621902—416no—
454#10621902—48no—
455#10621898—28no—
456#10621898—24no—
457#10621898—48no—
458#10621898—416no—
459C2×D172C2412yes—
460C2×D172C2414yes—
461C2×D172C2414yes—
462C2×D172C2414yes—
463C2×D172C2411yescharacteristic
464C2×D172C2414yes—
465C2×D172C2418yes—
466C2×C4×D43—24no—
467C2×C4×D43—44no—
468C2×C4×D43—48no—
469C2×C4×D43C2412yes—
470C2×C4×D43C2412yes—
471C2×C4×D43C2412yes—
472C2×C4×D43C2412yes—
473C2×C4×D43C2412yes—
474C2×C4×D43C2414yes—
475C2×C4×D43C2418yes—
476C2×C4×D43C2412yes—
477C2×C4×D43C2412yes—
478C2×C4×D43C2414yes—
479C2×C4×D43C2414yes—
480C2×C4×D43C2414yes—
481C2×C4×D43C2418yes—
482C2×C4×D43C2418yes—
483C2×C4×D43C2418yes—
484C2×C4×D43C2418yes—
485C2×Dic86C2412yes—
486C2×Dic86C2411yescharacteristic
487C2×Dic86C2418yes—
488C2×Dic86C2414yes—
489C4⋊C4×C43C2414yes—
490C4⋊C4×C43C2412yes—
491C4⋊C4×C43C2418yes—
492C4⋊C4×C43C2414yes—
493C4⋊C4×C43C2414yes—
494C4⋊C4×C43C2418yes—
495C4⋊C4×C43C2418yes—
496C4⋊C4×C43C2418yes—
497C4⋊C4×C43C2418yes—
498C4⋊C4×C43C2412yes—
499C4⋊C4×C43C2412yes—
500C4⋊C4×C43C2414yes—
501C4⋊C4×C43C2414yes—
502C4⋊C4×C43C2418yes—
503C4⋊C4×C43C2414yes—
504C22⋊C4×C43C2414yes—
505C22⋊C4×C43C2412yes—
506C22⋊C4×C43C2414yes—
507C22⋊C4×C43C2418yes—
508C42×C43C2411yescharacteristic
509C42×C43C2411yescharacteristic
510C42×C43C2412yes—
511C42×C43C2412yes—
512C42×C43C2414yes—
513C42×C43C2414yes—
514C42×C43C2418yes—
515C22⋊Dic43C2414yes—
516C22⋊Dic43C2412yes—
517C22⋊Dic43C2418yes—
518C22⋊Dic43C2414yes—
519(C2×D43)⋊C4C2414yes—
520(C2×D43)⋊C4C2414yes—
521(C2×D43)⋊C4C2414yes—
522(C2×D43)⋊C4C2414yes—
523(C2×D43)⋊C4C2414yes—
524(C2×D43)⋊C4C2414yes—
525(C2×D43)⋊C4C2414yes—
526(C2×D43)⋊C4C2414yes—
527(C2×D43)⋊C4C2414yes—
528(C2×D43)⋊C4C2418yes—
529(C2×D43)⋊C4C2418yes—
530(C2×D43)⋊C4C2414yes—
531(C2×D43)⋊C4C2414yes—
532(C2×D43)⋊C4C2418yes—
533(C2×D43)⋊C4C2418yes—
534(C2×D43)⋊C4C2418yes—
535(C2×D43)⋊C4C2418yes—
536(C2×D43)⋊C4C2414yes—
537(C2×D43)⋊C4C2414yes—
538C4⋊Dic43C2414yes—
539C4⋊Dic43C2414yes—
540C4⋊Dic43C2418yes—
541C4⋊Dic43C2418yes—
542C4⋊Dic43C2412yes—
543C4⋊Dic43C2414yes—
544C4⋊Dic43C2418yes—
545C4⋊Dic43C2418yes—
546C4⋊Dic43C2414yes—
547C4⋊Dic43C2414yes—
548C4⋊Dic43C2414yes—
549C4⋊Dic43C2414yes—
550Dic43⋊C4C2418yes—
551Dic43⋊C4C2418yes—
552Dic43⋊C4C2418yes—
553Dic43⋊C4C2418yes—
554Dic43⋊C4C2418yes—
555Dic43⋊C4C2418yes—
556Dic43⋊C4C2414yes—
557Dic43⋊C4C2418yes—
558Dic43⋊C4C2418yes—
559Dic43⋊C4C2418yes—
560Dic43⋊C4C2418yes—
561Dic43⋊C4C2418yes—
562Dic43⋊C4C2418yes—
563Dic43⋊C4C2414yes—
564Dic43⋊C4C2414yes—
565Dic43⋊C4C2414yes—
566Dic43⋊C4C2414yes—
567Dic43⋊C4C2414yes—
568Dic43⋊C4C2414yes—
569C4×Dic43C2411yescharacteristic
570C4×Dic43C2411yescharacteristic
571C4×Dic43C2412yes—
572C4×Dic43C2412yes—
573C4×Dic43C2412yes—
574C4×Dic43C2412yes—
575C4×Dic43C2412yes—
576C4×Dic43C2414yes—
577C4×Dic43C2414yes—
578C4×Dic43C2412yes—
579C4×Dic43C2414yes—
580C4×Dic43C2418yes—
581C4×Dic43C2418yes—
582C4×Dic43C2418yes—
583C23×C43C2512yes—
584C23×C43C2511yescharacteristic
585C22×D43—22no—
586C22×D43—24no—
587C22×D43C2514yes—
588C22×D43C2512yes—
589C22×D43C2512yes—
590Q8×C43—22no—
591Q8×C43—44no—
592Q8×C43—48no—
593D4×C43—24no—
594D4×C43—22no—
595C2×C4×C43—24no—
596C2×C4×C43—42no—
597C2×C4×C43—44no—
598C2×C4×C43—48no—
599C2×C4×C43—44no—
600C2×C4×C432−1+414yes—
601C2×C4×C43C2512yes—
602C2×C4×C43C2514yes—
603C2×C4×C43C2512yes—
604C2×C4×C43C2514yes—
605C2×C4×C43C2514yes—
606C2×C4×C43C2518yes—
607C2×C4×C43C2512yes—
608C2×C4×C43C2511yescharacteristic
609C2×C4×C43C2511yescharacteristic
610C22⋊D43—28no—
611C22⋊D43—24no—
612C22⋊D43—28no—
613C22⋊D43—44no—
614C22⋊D43—48no—
615C2×Dic43—22no—
616C2×Dic43—42no—
617C2×Dic43—44no—
618C2×Dic43C2512yes—
619C2×Dic43C2514yes—
620C2×Dic43C2512yes—
621C2×Dic43C2512yes—
622C2×Dic43C2512yes—
623C2×Dic43C2514yes—
624C2×Dic43C2518yes—
625D172—28no—
626D172—28no—
627D172—28no—
628D172—24no—
629D172—22no—
630D172—48no—
631D172—44no—
632C4×D43—24no—
633C4×D43—216no—
634C4×D43—24no—
635C4×D43—24no—
636C4×D43—24no—
637C4×D43—24no—
638C4×D43—28no—
639C4×D43—42no—
640C4×D43—48no—
641C4×D43—42no—
642C4×D43—44no—
643C4×D43—48no—
644C4×D43—48no—
645C4×D43—48no—
646C4×D43—44no—
647C4×D43—44no—
648Dic86—24no—
649Dic86—22no—
650Dic86—44no—
651Dic86—48no—
652#62825—431nomaximal, Sylow
653C22×C43—22no—
654C22×C43—22no—
655C22×C43—24no—
656C22×C43C2×2−1+412yes—
657C22×C43C2611yescharacteristic
658C2×D43—28no—
659C2×D43—22no—
660C2×D43—22no—
661C2×D43—24no—
662C2×D43—22no—
663C2×D43—24no—
664C2×D43—24no—
665C2×D43—24no—
666C2×D43#58514yes—
667C4×C43—22no—
668C4×C43—24no—
669C4×C43—24no—
670C4×C43—22no—
671C4×C43—28no—
672C4×C43—22no—
673C4×C43—24no—
674C4×C43C2×2−1+412yes—
675C4×C43C2×2−1+412yes—
676Dic43—24no—
677Dic43—22no—
678Dic43—22no—
679Dic43—24no—
680Dic43—22no—
681Dic43—28no—
682Dic43—22no—
683#3563—434no—
684#3563—434no—
685#3559—434no—
686#3559—434no—
687#3553—438no—
688#3515—434no—
689#3515—434no—
690#3515—434no—
691#3515—434no—
692#3512—431no—
693#3512—432no—
694#3512—431no—
695#3504—432no—
696#3504—431no—
697#3504D4311yescharacteristic, complemented
698#3492—438no—
699#3492—432no—
700#3492—432no—
701#3444—431no—
702#3444—431no—
703C22×#125—431no—
704C2×C43—22no—
705C2×C43—42no—
706C2×C43C22×2−1+411yescharacteristic
707C2×C43C2×#58512yes—
708D43—24no—
709D43—44no—
710D43—42no—
711#564—438no—
712#563—438no—
713#563—438no—
714#562—438no—
715#557—434no—
716#557—434no—
717#557—434no—
718#557C2×D4314yescomplemented
719#554—434no—
720#554—434no—
721#554—434no—
722#554—434no—
723#554—438no—
724#554—438no—
725#554—438no—
726#554—434no—
727#554—434no—
728#554—434no—
729#554C2×D4318yes—
730#554C2×D4314yescomplemented
731#553—434no—
732#553—434no—
733#553—434no—
734#553—438no—
735#553—438no—
736#553—438no—
737#553—434no—
738#553—434no—
739#553—434no—
740#553—434no—
741#553—438no—
742#553—434no—
743#552—438no—
744#552—438no—
745#552—438no—
746#552—434no—
747#552—434no—
748#552—434no—
749#552—438no—
750#552—438no—
751#552—438no—
752#552—434no—
753#552—434no—
754#552—438no—
755#552—434no—
756#552—434no—
757#552—434no—
758#552—438no—
759#547—438no—
760#547—434no—
761#547—434no—
762#547—438no—
763#547—438no—
764#547—434no—
765#547—438no—
766#547—434no—
767#544—438no—
768#544—434no—
769#544—434no—
770#544—434no—
771#544—432no—
772#544C2×D4312yes—
773#544C2×D4314yescomplemented
774#541—438no—
775#541—432no—
776#541—438no—
777#541—438no—
778#541—434no—
779#541—438no—
780#541—432no—
781#540—432no—
782#540—434no—
783#540—432no—
784#539—438no—
785#539—438no—
786#539—438no—
787#539—438no—
788#539—438no—
789#539—438no—
790#539—438no—
791#539—438no—
792#539—438no—
793#539—438no—
794#537—432no—
795#537—438no—
796#537—432no—
797#533—432no—
798#533—434no—
799#533—432no—
800#533—432no—
801#533—431no—
802#533C2×D4311yescharacteristic
803#533C2×D4312yescomplemented
804#532—431no—
805#532—432no—
806#532—432no—
807#532—431no—
808#529—432no—
809#529—432no—
810#529—434no—
811#529—434no—
812#529—432no—
813#529—434no—
814#529—434no—
815#529—434no—
816#529—432no—
817#529—434no—
818#529—434no—
819#529—434no—
820C2×#125—434no—
821C2×#125—434no—
822C2×#125—434no—
823C2×#125—434no—
824C2×#125—434no—
825C2×#125—432no—
826C2×#125—434no—
827C2×#125—432no—
828C2×#125—431no—
829C2×#125C2×D4311yescharacteristic
830C2×#125C2×D4312yescomplemented
831#525—431no—
832#525—434no—
833#525—438no—
834#525—434no—
835#525—438no—
836#525—432no—
837#525—431no—
838#520—438no—
839#520—432no—
840#520—432no—
841#520—432no—
842#520—438no—
843#520C2×D4312yes—
844C4×#41—434no—
845C4×#41—432no—
846C4×#41—431no—
847C4×#41—434no—
848C4×#41C2×D4311yescharacteristic
849C22×C4⋊C4—432no—
850C22×C4⋊C4—434no—
851C22×C42—431no—
852C43#6282511yescharacteristic, complemented, Sylow
853C2×#41—434no—
854C2×#41—438no—
855C2×#41—432no—
856C2×#41—431no—
857C2×#41—434no—
858C2×#41—438no—
859C2×#41C22×D4311yescharacteristic
860C23×C4—431no—
861C23×C4—434no—
862C23×C4—432no—
863C4⋊Q8—431no—
864C4⋊Q8—438no—
865C4⋊Q8—438no—
866C4⋊Q8—432no—
867C4⋊Q8—434no—
868C4⋊Q8—438no—
869C4⋊Q8—431no—
870C4⋊Q8—434no—
871C4⋊Q8C22×D4312yes—
872C4⋊Q8C22×D4314yes—
873C4⋊Q8C22×D4314yes—
874C4⋊Q8C22×D4318yes—
875#127—431no—
876#127—431no—
877#126—434no—
878#126—434no—
879#126—434no—
880#126—438no—
881#126—438no—
882#126—438no—
883#126—438no—
884#126—438no—
885#126—438no—
886#126—434no—
887#126—438no—
888#126—438no—
889#126—438no—
890#126—438no—
891#126—438no—
892#126—438no—
893#125—434no—
894#125—438no—
895#125—438no—
896#125—434no—
897#125—438no—
898#125—434no—
899#125—434no—
900#125—438no—
901#125—432no—
902#125—438no—
903#125—438no—
904#125—438no—
905#125—434no—
906#125—434no—
907#125—434no—
908#125—438no—
909#125—438no—
910#125—438no—
911#125—438no—
912#125—438no—
913#125—438no—
914#125—438no—
915#125—438no—
916#125—438no—
917#125—432no—
918#125—432no—
919#125—434no—
920#125—434no—
921#125—438no—
922#125—438no—
923#125C22×D4312yes—
924#125C22×D4312yes—
925#125C22×D4314yes—
926#125C22×D4311yescharacteristic
927#125C22×D4314yes—
928#125C22×D4311yescharacteristic
929#125C22×D4318yes—
930#125C22×D4314yes—
931#125C22×D4318yes—
932#124—431no—
933#124—434no—
934#124—431no—
935#124—434no—
936#124—432no—
937#123—432no—
938#123—438no—
939#123—438no—
940#123—438no—
941#123—434no—
942#123—434no—
943#123—434no—
944#123—438no—
945#123—438no—
946#123—438no—
947#123—438no—
948#123—438no—
949#123—438no—
950#123—438no—
951#123—438no—
952#123—438no—
953#123—434no—
954#123—432no—
955#123—434no—
956#123—438no—
957#123—438no—
958#123—438no—
959#123—438no—
960C22⋊Q8—434no—
961C22⋊Q8—432no—
962C22⋊Q8—438no—
963C22⋊Q8—434no—
964C22⋊Q8—438no—
965C22⋊Q8—438no—
966C22⋊Q8—438no—
967C22⋊Q8—438no—
968C22⋊Q8—438no—
969C22⋊Q8—434no—
970C22⋊Q8—438no—
971C22⋊Q8—434no—
972C22⋊Q8—432no—
973C22⋊Q8—432no—
974C22⋊Q8—432no—
975C22⋊Q8—438no—
976C22⋊Q8—434no—
977C22⋊Q8—434no—
978C22⋊Q8—438no—
979C22⋊Q8—438no—
980C22⋊Q8—438no—
981C22⋊Q8—438no—
982C22⋊Q8—438no—
983C22⋊Q8—438no—
984C22⋊Q8—438no—
985C22⋊Q8—434no—
986C22⋊Q8—438no—
987C22⋊Q8C22×D4314yes—
988C22⋊Q8C22×D4318yes—
989C22⋊Q8C22×D4318yes—
990C22⋊Q8C22×D4318yes—
991C22⋊Q8C22×D4318yes—
992#121—432no—
993#121—434no—
994#121—438no—
995#121—434no—
996#121—434no—
997#121—438no—
998#121—434no—
999#121—438no—
1000#121—434no—
1001#121—432no—
1002#121—432no—
1003#121—432no—
1004#121—438no—
1005#121—434no—
1006#121—434no—
1007#121—438no—
1008#121—434no—
1009#121—438no—
1010#121—438no—
1011#121—438no—
1012#120—432no—
1013#120—434no—
1014#120—432no—
1015C4×Q8—434no—
1016C4×Q8—438no—
1017C4×Q8—432no—
1018C4×Q8—432no—
1019C4×Q8—434no—
1020C4×Q8—438no—
1021C4×Q8—438no—
1022C4×Q8—434no—
1023C4×Q8—432no—
1024C4×Q8—434no—
1025C4×Q8—434no—
1026C4×Q8—434no—
1027C4×Q8C22×D4314yes—
1028C4×Q8C22×D4312yes—
1029C4×Q8C22×D4318yes—
1030C4×Q8C22×D4314yes—
1031C4×D4—434no—
1032C4×D4—434no—
1033C4×D4—434no—
1034C4×D4—434no—
1035C4×D4—434no—
1036C4×D4—438no—
1037C4×D4—438no—
1038C4×D4—438no—
1039C4×D4—438no—
1040C4×D4—434no—
1041C4×D4—434no—
1042C4×D4—434no—
1043C4×D4—432no—
1044C4×D4—432no—
1045C4×D4—438no—
1046C4×D4—438no—
1047C4×D4—438no—
1048C4×D4—434no—
1049C4×D4—434no—
1050C4×D4—434no—
1051C4×D4—438no—
1052C4×D4—438no—
1053C4×D4—434no—
1054C4×D4—434no—
1055C4×D4—434no—
1056C4×D4—434no—
1057C4×D4—434no—
1058C4×D4—432no—
1059C4×D4—438no—
1060C4×D4—438no—
1061C4×D4—434no—
1062C4×D4—434no—
1063C4×D4C22×D4314yes—
1064C4×D4C22×D4312yes—
1065C4×D4C22×D4318yes—
1066C4×D4C22×D4314yes—
1067#117—431no—
1068#117—434no—
1069#117—438no—
1070#117—434no—
1071#117—434no—
1072#117—434no—
1073#117—438no—
1074#117—438no—
1075#117—434no—
1076#117—434no—
1077#117—434no—
1078#117—434no—
1079#117—434no—
1080#117—432no—
1081#117—434no—
1082#117—438no—
1083#117—438no—
1084#117—438no—
1085#117C22×D4312yes—
1086#117C22×D4311yescharacteristic
1087#117C22×D4312yes—
1088#117C22×D4314yes—
1089C2×C4⋊C4—432no—
1090C2×C4⋊C4—434no—
1091C2×C4⋊C4—434no—
1092C2×C4⋊C4—434no—
1093C2×C4⋊C4—434no—
1094C2×C4⋊C4—438no—
1095C2×C4⋊C4—438no—
1096C2×C4⋊C4—434no—
1097C2×C4⋊C4—434no—
1098C2×C4⋊C4—438no—
1099C2×C4⋊C4—438no—
1100C2×C4⋊C4—434no—
1101C2×C4⋊C4—434no—
1102C2×C4⋊C4—438no—
1103C2×C4⋊C4—438no—
1104C2×C4⋊C4—438no—
1105C2×C4⋊C4—434no—
1106C2×C4⋊C4—434no—
1107C2×C4⋊C4—434no—
1108C2×C4⋊C4C22×D4312yes—
1109C2×C4⋊C4C22×D4314yes—
1110C2×C4⋊C4C22×D4318yes—
1111C2×C4⋊C4C22×D4314yes—
1112C2×C42—431no—
1113C2×C42—432no—
1114C2×C42—434no—
1115C2×C42—432no—
1116C2×C42—432no—
1117C2×C42—432no—
1118C2×C42—432no—
1119C2×C42—432no—
1120C2×C42C22×D4312yes—
1121C2×C42C22×D4311yescharacteristic
1122C24—431no—
1123#41—24no—
1124#41—864no—
1125#41—868no—
1126#41—1728no—
1127#41—17216no—
1128#41—1728no—
1129#41—17216no—
1130C2×Q8—432no—
1131C2×Q8—431no—
1132C2×Q8—438no—
1133C2×Q8—434no—
1134C2×Q8C23×D4311yescharacteristic
1135C2×Q8C23×D4318yes—
1136C2×Q8C23×D4314yes—
1137C2×D4—432no—
1138C2×D4—434no—
1139C2×D4—434no—
1140C2×D4—438no—
1141C2×D4—434no—
1142C2×D4—432no—
1143C2×D4—431no—
1144C2×D4—434no—
1145C2×D4—434no—
1146C2×D4—434no—
1147C2×D4—438no—
1148C2×D4—434no—
1149C2×D4C23×D4312yes—
1150C2×D4C23×D4311yescharacteristic
1151C22×C4—431no—
1152C22×C4—432no—
1153C22×C4—434no—
1154C22×C4—432no—
1155C22×C4—432no—
1156C22×C4—432no—
1157C22×C4—432no—
1158C22×C4—432no—
1159C22×C4—434no—
1160C22×C4—438no—
1161C22×C4—432no—
1162C22×C4—432no—
1163C22×C4—434no—
1164C22×C4—434no—
1165C22×C4—434no—
1166C22×C4—438no—
1167C22×C4—438no—
1168C22×C4—438no—
1169C22×C4—438no—
1170C22×C4—864no—
1171C22×C4—1728no—
1172C22×C4—1724no—
1173C22×C4C23×D4312yes—
1174C22×C4C23×D4312yes—
1175C22×C4C23×D4314yes—
1176C22×C4C23×D4314yes—
1177C22×C4C23×D4318yes—
1178C22×C4C23×D4311yescharacteristic
1179C4⋊C4—434no—
1180C4⋊C4—434no—
1181C4⋊C4—438no—
1182C4⋊C4—438no—
1183C4⋊C4—438no—
1184C4⋊C4—438no—
1185C4⋊C4—438no—
1186C4⋊C4—438no—
1187C4⋊C4—438no—
1188C4⋊C4—438no—
1189C4⋊C4—432no—
1190C4⋊C4—434no—
1191C4⋊C4—434no—
1192C4⋊C4—438no—
1193C4⋊C4—438no—
1194C4⋊C4—438no—
1195C4⋊C4—438no—
1196C4⋊C4—438no—
1197C4⋊C4—438no—
1198C4⋊C4—438no—
1199C4⋊C4—438no—
1200C4⋊C4—434no—
1201C4⋊C4—434no—
1202C4⋊C4—434no—
1203C4⋊C4—434no—
1204C4⋊C4—434no—
1205C4⋊C4—434no—
1206C4⋊C4—434no—
1207C4⋊C4—434no—
1208C4⋊C4—434no—
1209C4⋊C4—434no—
1210C4⋊C4C23×D4314yes—
1211C4⋊C4C23×D4318yes—
1212C4⋊C4C23×D4314yes—
1213C4⋊C4C23×D4318yes—
1214C4⋊C4C23×D4312yes—
1215C4⋊C4C23×D4314yes—
1216C4⋊C4C23×D4312yes—
1217C4⋊C4C23×D4318yes—
1218C4⋊C4C23×D4318yes—
1219C4⋊C4C23×D4312yes—
1220C4⋊C4C23×D4314yes—
1221C4⋊C4C23×D4318yes—
1222C4⋊C4C23×D4318yes—
1223C4⋊C4C23×D4314yes—
1224C4⋊C4C23×D4314yes—
1225C22⋊C4—434no—
1226C22⋊C4—432no—
1227C22⋊C4—438no—
1228C22⋊C4—434no—
1229C22⋊C4—434no—
1230C22⋊C4—434no—
1231C22⋊C4—434no—
1232C22⋊C4—434no—
1233C22⋊C4—434no—
1234C22⋊C4—434no—
1235C22⋊C4—434no—
1236C22⋊C4—434no—
1237C22⋊C4—434no—
1238C22⋊C4—434no—
1239C22⋊C4—438no—
1240C22⋊C4—438no—
1241C22⋊C4—438no—
1242C22⋊C4—438no—
1243C22⋊C4—438no—
1244C22⋊C4—438no—
1245C22⋊C4—434no—
1246C22⋊C4—434no—
1247C22⋊C4—434no—
1248C22⋊C4C23×D4314yes—
1249C22⋊C4C23×D4312yes—
1250C22⋊C4C23×D4314yes—
1251C22⋊C4C23×D4318yes—
1252C42—431no—
1253C42—432no—
1254C42—431no—
1255C42—432no—
1256C42—432no—
1257C42—432no—
1258C42—432no—
1259C42—434no—
1260C42—434no—
1261C42—434no—
1262C42—432no—
1263C42—438no—
1264C42—438no—
1265C42—438no—
1266C42C23×D4311yescharacteristic
1267C42C23×D4311yescharacteristic
1268C42C23×D4312yes—
1269C42C23×D4314yes—
1270C42C23×D4314yes—
1271C42C23×D4312yes—
1272C42C23×D4318yes—
1273C23—432no—
1274C23—434no—
1275C23—432no—
1276C23—864no—
1277C23—862no—
1278C23C24×D4312yes—
1279C23C24×D4311yescharacteristic
1280Q8—22no—
1281Q8—48no—
1282Q8—44no—
1283Q8—864no—
1284Q8—862no—
1285Q8—1728no—
1286Q8—1724no—
1287D4—24no—
1288D4—22no—
1289D4—868no—
1290D4—868no—
1291D4—868no—
1292D4—868no—
1293D4—864no—
1294D4—868no—
1295D4—864no—
1296D4—862no—
1297D4—1728no—
1298D4—1724no—
1299D4—1728no—
1300D4—1724no—
1301C2×C4—24no—
1302C2×C4—42no—
1303C2×C4—44no—
1304C2×C4—44no—
1305C2×C4—48no—
1306C2×C4—432no—
1307C2×C4—432no—
1308C2×C4—434no—
1309C2×C4—432no—
1310C2×C4—434no—
1311C2×C4—432no—
1312C2×C4—438no—
1313C2×C4—864no—
1314C2×C4—8616no—
1315C2×C4—864no—
1316C2×C4—862no—
1317C2×C4—864no—
1318C2×C4—864no—
1319C2×C4—864no—
1320C2×C4—868no—
1321C2×C4—1722no—
1322C2×C4—1728no—
1323C2×C4—1722no—
1324C2×C4—1724no—
1325C2×C4—1728no—
1326C2×C4—1724no—
1327C2×C4—1728no—
1328C2×C4—1724no—
1329C2×C4—1728no—
1330C2×C4—1722no—
1331C2×C4—1724no—
1332C2×C4#1306337314yes—
1333C2×C4C24×D4312yes—
1334C2×C4C24×D4314yes—
1335C2×C4C24×D4314yes—
1336C2×C4C24×D4312yes—
1337C2×C4C24×D4314yes—
1338C2×C4C24×D4318yes—
1339C2×C4C24×D4312yes—
1340C2×C4C24×D4311yescharacteristic
1341C2×C4C24×D4311yescharacteristic
1342C22—22no—
1343C22—22no—
1344C22—24no—
1345C22—434no—
1346C22—868no—
1347C22—862no—
1348C22—862no—
1349C22—862no—
1350C22—864no—
1351C22—864no—
1352C22—864no—
1353C22—864no—
1354C22C2×#1306337312yes—
1355C22C25×D4311yescharacteristic
1356C4—22no—
1357C4—22no—
1358C4—28no—
1359C4—24no—
1360C4—22no—
1361C4—24no—
1362C4—24no—
1363C4—862no—
1364C4—862no—
1365C4—864no—
1366C4—862no—
1367C4—868no—
1368C4—862no—
1369C4—864no—
1370C4C2×#1306337312yes—
1371C4C2×#1306337312yes—
1372C2—22no—
1373C2—42no—
1374C2—864no—
1375C2—1724no—
1376C2—1722no—
1377C2C22×#1306337311yescharacteristic
1378C2#585×D4312yes—
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3504C2
hypercenter#3504D43
hypocenterC43#62825
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3504

Complements

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

NH ≅ G/Ntype
1. #19149197C2semidirect
2. #19149191C2semidirect
3. #19149130C2semidirect
4. #19149128C2semidirect
5. #19149047C2semidirect
6. #19148576C2semidirect
7. #19148572C2semidirect
8. #19148568C2semidirect
9. #19148567C2semidirect
10. #19148519C2semidirect
11. #19148517C2semidirect
12. #19148512C2semidirect
13. #19148418C2semidirect
14. #19148416C2semidirect
15. #19148305C2semidirect
16. #19148303C2semidirect
17. #19148298C2semidirect
18. #19147892C2semidirect
19. #19147888C2semidirect
20. C2×#125×D43C2semidirect
21. C43×#3504C2semidirect
22. C43⋊#564C22semidirect
23. #14583650C22semidirect
24. #14583648C22semidirect
25. #14583645C22semidirect
26. #14583627C22semidirect
27. #14583626C22semidirect
28. #14583624C22semidirect
31. #14583610C22semidirect
33. #14583609C22semidirect
35. #14583605C22semidirect
41. #14583602C22semidirect
43. #14583599C22semidirect
47. #14583597C22semidirect
50. #14583593C22semidirect
53. #14583590C22semidirect
54. #14583590C22semidirect
56. #14583588C22semidirect
59. #14583587C22semidirect
60. #14583584C22semidirect
61. #14583584C22semidirect
63. #14583583C22semidirect
66. #14583581C22semidirect
75. #14583529C22semidirect
78. #14583526C22semidirect
79. #14583526C22semidirect
80. #14583512C22semidirect
81. #14583511C22semidirect
82. #14583510C22semidirect
83. #14583509C22semidirect
84. #14583508C22semidirect
85. #14583507C22semidirect
86. #14583507C22semidirect
87. #14583505C22semidirect
88. #14583504C22semidirect
89. #14583500C22semidirect
93. #14583497C22semidirect
94. #14583496C22semidirect
97. #14583495C22semidirect
98. #14583495C22semidirect
103. #14583455C22semidirect
105. #14583454C22semidirect
114. #14583436C22semidirect
118. #14583434C22semidirect
119. #14583433C22semidirect
121. #14583431C22semidirect
131. #125×D43C22semidirect
132. #125×D43C22semidirect
152. C43×#557C22semidirect
154. C43×#554C22semidirect
156. C43×#544C22semidirect
158. C43×#533C22semidirect
160. C2×#125×C43C22semidirect
697. #3504D43semidirect
718. #557C2×D43semidirect
730. #554C2×D43semidirect
773. #544C2×D43semidirect
803. #533C2×D43semidirect
830. C2×#125C2×D43semidirect
852. C43#62825semidirect

Maximal subgroups

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

subgroupindex
#191491972
#191491912
#191491302
#191491282
#191490472
#191485762
#191485722
#191485682
#191485672
#191485192
#191485172
#191485122
#191484182
#191484162
#191483052
#191483032
#191482982
#191478922
#191478882
C2×#125×D432
C43×#35042
#6282543