Finite Group Databasebeta

← #26004887

Subgroups — #26004887

Order 11008.

7190 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148698C216yesmaximal, complemented
2#19148696C212yesmaximal, complemented
3#19148612C211yesmaximal, characteristic, complemented
4#19148610C213yesmaximal, complemented
5#19148593C213yesmaximal, complemented
6#19148445C213yesmaximal, complemented
7#19148439C213yesmaximal, complemented
8#19148399C211yesmaximal, characteristic, complemented
9#19148360C211yesmaximal, characteristic, complemented
10#19148311C216yesmaximal, complemented
11#19148248C212yesmaximal, complemented
12#19148218C211yesmaximal, characteristic, complemented
13#19148218C213yesmaximal, complemented
14#19148215C211yesmaximal, characteristic, complemented
15#19148207C213yesmaximal, complemented
16#19148194C212yesmaximal, complemented
17#19148189C216yesmaximal, complemented
18#19148010C216yesmaximal, complemented
19#19147890C213yesmaximal, complemented
20#19147889C213yesmaximal, complemented
21#19147806C212yesmaximal, complemented
22C4×#41×D43C211yesmaximal, characteristic, complemented
23C43×#3517C211yesmaximal, characteristic, complemented
24C2×#13063372C2212yes—
25C2×#41×D43C2211yescharacteristic
26#14583635C2216yescomplemented
27#14583633C22112yescomplemented
28#14583632C2216yescomplemented
29Q8×Dic86C2213yescomplemented
30Q8×Dic86C2211yescharacteristic, complemented
31#14583628C2212yescomplemented
32#14583626C2216yescomplemented
33#14583624C2213yescomplemented
34#14583622C2213yescomplemented
35#14583620C2216yescomplemented
36#14583619C2216yescomplemented
37#14583619C2213yescomplemented
38#14583617C2216yescomplemented
39#14583616C22112yescomplemented
40#14583614C2216yescomplemented
41#14583614C2213yescomplemented
42#14583614C2213yescomplemented
43#14583613C2216yescomplemented
44#14583613C22112yescomplemented
45#14583613C2216yescomplemented
46#14583598C22112yescomplemented
47#14583597C2216yescomplemented
48#14583596C2216yescomplemented
49#14583596C2216yescomplemented
50#14583592C22112yescomplemented
51#14583587C2216yescomplemented
52#14583586C22112yescomplemented
53#14583584C2216yescomplemented
54#14583569C2216yes—
55#14583569C2213yescomplemented
56#14583569C2213yescomplemented
57#14583568C2212yes—
58#14583568C2216yescomplemented
59#14583567C2216yes—
60Q8×D172C2211yescharacteristic, complemented
61D4×Dic86C2213yescomplemented
62#14583561C2212yes—
63#14583558C2216yes—
64#14583556C2212yes—
65#14583556C2212yescomplemented
66#14583555C2216yes—
67#14583555C2216yescomplemented
68#14583552C2213yescomplemented
69#14583548C2216yescomplemented
70#14583529C2216yes—
71#14583520C2216yescomplemented
72#14583517C22112yescomplemented
73#14583514C2216yescomplemented
74#14583500C2216yescomplemented
75#14583499C22112yescomplemented
76#14583485C22112yes—
77#14583481C22112yes—
78#14583478C2216yes—
79#14583465C2216yes—
80#14583462C2216yes—
81#14583456C2213yescomplemented
82#14583455C2213yescomplemented
83#14583454C2213yes—
84#14583454C2213yescomplemented
85#14583453C2213yes—
86#14583451C2213yescomplemented
87#14583448C2213yescomplemented
88#14583447C2213yes—
89#14583447C2213yescomplemented
90#14583447C2216yescomplemented
91#14583446C2213yes—
92#14583444C2213yescomplemented
93#14583444C2216yescomplemented
94#14583444C22112yescomplemented
95#14583434C2211yescharacteristic
96#14583434C2216yescomplemented
97#14583433C2213yescomplemented
98#14583432C2216yes—
99#14583432C2216yescomplemented
100#14583431C2216yes—
101#14583431C2216yescomplemented
102#14583430C2216yescomplemented
103#14583430C2216yescomplemented
104#14583430C2216yescomplemented
105#14583428C2213yes—
106#14583428C2216yescomplemented
107#14583427C2216yescomplemented
108#14583426C2216yescomplemented
109#14583426C22112yescomplemented
110#14583412C2213yes—
111#14583409C2216yes—
112#14583409C2213yes—
113#14583409C2216yes—
114#14583408C2216yes—
115#14583407C2216yes—
116#14583406C2216yes—
117#14583380C2216yes—
118#14583378C2216yes—
119#14583378C2216yescomplemented
120#14583376C2216yescomplemented
121#14583375C2212yes—
122#14583375C2212yescomplemented
123#41×Dic43C2211yescharacteristic
124#41×Dic43C2212yescomplemented
125#41×Dic43C2216yescomplemented
126C4×#10621902C2211yescharacteristic
127C4×#10621902C2211yescharacteristic
128C4×#10621902C2213yescomplemented
129C4×#10621898C2213yes—
130#14583367C2216yes—
131#14583367C2213yes—
132C4×#10621900C2216yes—
133C4×#10621900C2213yes—
134C4×#10621900C2213yes—
135C4×#10621900C2216yescomplemented
136C4×#10621900C2216yescomplemented
137C4×#10621900C2213yescomplemented
138C4×#10621900C2216yescomplemented
139C2×#13063290C2216yescomplemented
140C4×Q8×D43C2211yescharacteristic
141C4×Q8×D43C2211yescharacteristic
142C4×Q8×D43C2212yescomplemented
143C4×D4×D43C2213yes—
144C4×D4×D43C2213yes—
145#117×D43C2213yes—
146C2×C42×D43C2213yes—
147C43×#557C2211yescharacteristic, complemented
148C43×#553C2216yescomplemented
149C43×#550C2212yes—
150C43×#550C2211yescharacteristic, complemented
151C43×#550C2213yescomplemented
152C43×#547C2213yescomplemented
153C43×#540C2216yescomplemented
154C43×#532C2213yescomplemented
155C43×#529C2213yescomplemented
156C43×#520C2212yescomplemented
157C4×#41×C43C2211yescharacteristic
158#13063372—216no—
159C2×#10621902C2311yescharacteristic
160C2×#10621902C2313yes—
161C2×#10621898C2313yes—
162C2×#10621898C2316yes—
163C2×#10621900C2313yes—
164C2×#10621900C2316yes—
165C2×#10621900C2316yes—
166C2×#10621900C2313yes—
167C2×#10621900C2316yes—
168C2×#10621900C2316yes—
169#41×D43—28no—
170C22×Dic86C2316yes—
171C2×Q8×D43C2312yes—
172C2×Q8×D43C2311yescharacteristic
173C2×D4×D43C2313yes—
174C22×C4×D43C2313yes—
175C22×C4×D43C2313yes—
176C22×C4×D43C2313yes—
177#13063325C2313yes—
178#13063325C2313yes—
179#13063325C2316yes—
180#13063324C2313yes—
181#13063324C2313yes—
182#13063324C23112yes—
183#13063324C2316yes—
184#13063323C2313yes—
185#13063321C2316yes—
186#13063321C23112yes—
187#13063321C2313yes—
188#13063320C23112yes—
189#13063320C23112yes—
190#13063320C2312yes—
191#13063319C2316yes—
192#13063318C23112yes—
193#13063318C23112yes—
194#13063318C23112yes—
195#13063318C2316yes—
196#13063317C2313yes—
197#13063316C2316yes—
198#13063316C2316yes—
199#13063316C2316yes—
200#13063315C2316yes—
201#13063315C23112yes—
202#13063315C2316yes—
203#13063313C2316yes—
204#13063313C2311yescharacteristic
205#13063312C2316yes—
206#13063312C2316yes—
207#13063312C2316yes—
208#13063312C23112yes—
209#13063311C23112yes—
210#13063311C2316yes—
211#13063311C2316yes—
212#13063311C23112yes—
213#13063311C23112yes—
214#13063311C23112yes—
215#13063310C23112yes—
216#13063310C2316yes—
217#13063310C2312yes—
218#13063308C23112yes—
219#13063308C2316yes—
220#13063307C2316yes—
221#13063307C2316yes—
222#13063307C23112yes—
223#13063306C23112yes—
224#13063306C23112yes—
225#13063305C2316yes—
226#13063305C2316yes—
227#13063305C2311yescharacteristic
228#13063305C2316yes—
229#13063304C2316yes—
230#13063304C2316yes—
231#13063304C2313yes—
232#13063304C2316yes—
233#13063303C2316yes—
234#13063303C2316yes—
235#13063303C2316yes—
236#13063302C2316yes—
237#13063302C23112yes—
238#13063301C2316yes—
239#13063301C2313yes—
240#13063300C2316yes—
241#13063300C2311yescharacteristic
242#13063299C2316yes—
243#13063299C2313yes—
244#13063299C23112yes—
245#13063298C2316yes—
246#13063298C2316yes—
247#13063298C2316yes—
248#13063297C23112yes—
249#13063297C23112yes—
250#13063297C23112yes—
251#13063297C2316yes—
252#13063297C23112yes—
253#13063296C2316yes—
254#13063296C2316yes—
255#13063296C2316yes—
256#13063296C2316yes—
257#13063296C23112yes—
258#13063296C2313yes—
259#13063296C2316yes—
260#13063295C2316yes—
261#13063293C23112yes—
262#13063293C2316yes—
263Q8×Dic43C2312yes—
264Q8×Dic43C2311yescharacteristic
265Q8×Dic43C2316yes—
266Q8×Dic43C2311yescharacteristic
267Q8×Dic43C2313yes—
268C4×Dic86C2316yes—
269C4×Dic86C2313yes—
270C4×Dic86C2313yes—
271C4×Dic86C2316yes—
272C4×Dic86C2316yes—
273C4×Dic86C2313yes—
274C4×Dic86C2316yes—
275C4×Dic86C2316yes—
276#13063290C2316yes—
277#13063290C2313yes—
278#13063290C2316yes—
279#13063290C23112yes—
280#13063290C2316yes—
281#13063290C2313yes—
282#13063290C2316yes—
283#13063290C2316yes—
284#13063290C2311yescharacteristic
285#13063290C2316yes—
286#13063290C2316yes—
287C4×D172C2313yes—
288C4×D172C2313yes—
289C4×D172C2316yes—
290C4×D172C2313yes—
291D4×Dic43C23112yes—
292D4×Dic43C2316yes—
293D4×Dic43C2316yes—
294D4×Dic43C2316yes—
295D4×Dic43C2316yes—
296D4×Dic43C2313yes—
297D4×Dic43C2313yes—
298D4×Dic43C2316yes—
299D4×Dic43C2313yes—
300D4×Dic43C23112yes—
301#13063287C2313yes—
302#13063287C2313yes—
303#13063287C2312yes—
304#13063287C2316yes—
305#13063287C2311yescharacteristic
306#13063287C2316yes—
307C4×C22⋊D43C2316yes—
308C4×C22⋊D43C2316yes—
309C4×C22⋊D43C2316yes—
310C4×C22⋊D43C23112yes—
311C4×C22⋊D43C2316yes—
312C4×C22⋊D43C23112yes—
313C4×C22⋊D43C2316yes—
314C4×C22⋊D43C23112yes—
315(C22⋊D43)⋊C4C23112yes—
316(C22⋊D43)⋊C4C2316yes—
317(C22⋊D43)⋊C4C2316yes—
318(C22⋊D43)⋊C4C2316yes—
319(C22⋊D43)⋊C4C2316yes—
320(C22⋊D43)⋊C4C2316yes—
321(C22⋊D43)⋊C4C2316yes—
322(C22⋊D43)⋊C4C2316yes—
323(C22⋊D43)⋊C4C2316yes—
324(C22⋊D43)⋊C4C2316yes—
325#13063284C23112yes—
326#13063284C2313yes—
327#13063284C2316yes—
328#13063284C2316yes—
329#13063283C2313yes—
330#13063283C2313yes—
331#13063283C2316yes—
332#13063283C2316yes—
333#13063283C2313yes—
334#13063283C2313yes—
335#13063283C2316yes—
336#13063283C2312yes—
337#13063283C2316yes—
338#13063282C2316yes—
339#13063282C2316yes—
340#13063282C2316yes—
341#13063281C2316yes—
342#13063281C2316yes—
343#13063281C23112yes—
344#13063281C23112yes—
345#13063281C2316yes—
346#13063281C2316yes—
347C2×Dic43⋊C4C23112yes—
348C4⋊C4×D43C2316yes—
349C4⋊C4×D43C2313yes—
350C4⋊C4×D43C2313yes—
351C22⋊C4×D43C2316yes—
352C2×C4×Dic43C2313yes—
353C2×C4×Dic43C2313yes—
354C2×C4×Dic43C2313yes—
355C2×C4×Dic43C23112yes—
356C2×C4×Dic43C2316yes—
357C42×D43C2311yescharacteristic
358C42×D43C2313yes—
359C42×D43C2313yes—
360C42×D43C2313yes—
361C42×D43C2313yes—
362C42×D43C2313yes—
363C42×D43C2313yes—
364C42×D43C2313yes—
365C42×D43C2316yes—
366C2×#41×C43C2311yescharacteristic
367C2×#41×C43C2312yes—
368C2×#41×C43C2316yes—
369C4⋊Q8×C43C2313yes—
370#127×C43C2316yes—
371#127×C43C2313yes—
372#126×C43C2316yes—
373#125×C43C2311yescharacteristic
374#125×C43C2316yes—
375#124×C43C2313yes—
376#123×C43C2316yes—
377#123×C43C23112yes—
378C22⋊Q8×C43C2313yes—
379#121×C43C2316yes—
380#121×C43C2316yes—
381#121×C43C2316yes—
382#121×C43C2313yes—
383#121×C43C2316yes—
384#121×C43C23112yes—
385C4×Q8×C43C2312yes—
386C4×Q8×C43C2311yescharacteristic
387C4×Q8×C43C2311yescharacteristic
388C4×Q8×C43C2313yes—
389C4×D4×C43C2316yes—
390C4×D4×C43C2313yes—
391C4×D4×C43C2313yes—
392C4×D4×C43C2313yes—
393C4×D4×C43C2316yes—
394C4×D4×C43C2316yes—
395C4×D4×C43C2316yes—
396#117×C43C2313yes—
397#117×C43C2316yes—
398C2×C4⋊C4×C43C2316yes—
399C2×C42×C43C2313yes—
400C23×D43C2413yes—
401#41×C43—24no—
402#41×C43—28no—
403#41×C43—412no—
404C2×Q8×C43C2413yes—
405C2×Q8×C43C2411yescharacteristic
406C2×D4×C43C2413yes—
407C2×D4×C43C2416yes—
408C2×D4×C43C2413yes—
409C2×D4×C43C2416yes—
410C2×D4×C43C2416yes—
411C2×D4×C43C24112yes—
412C22×C4×C43C2413yes—
413C22×C4×C43C2413yes—
414C22×C4×C43C2416yes—
415C22×C4×C43C2413yes—
416C22×C4×C43C24112yes—
417C2×C22⋊D43C2416yes—
418C2×C22⋊D43C2416yes—
419C2×C22⋊D43C2416yes—
420C2×C22⋊D43C24112yes—
421C2×C22⋊D43C2416yes—
422C2×C22⋊D43C2416yes—
423C2×C22⋊D43C2416yes—
424C22×Dic43C2416yes—
425C22×Dic43C2413yes—
426C22×Dic43C2413yes—
427C22×Dic43C24112yes—
428C22×Dic43C2413yes—
429C22×Dic43C2416yes—
430#10621902—24no—
431#10621902—46no—
432Q8×D43—28no—
433Q8×D43#4118yescomplemented
434#10621900—224no—
435#10621900—212no—
436#10621900—224no—
437#10621900—46no—
438#10621900—412no—
439#10621900—412no—
440D4×D43—212no—
441#10621898—224no—
442#10621898—212no—
443C2×D172C2412yes—
444C2×D172C2413yes—
445C2×D172C2411yescharacteristic
446C2×D172C2416yes—
447C2×C4×D43—212no—
448C2×C4×D43—46no—
449C2×C4×D43—46no—
450C2×C4×D43C2411yescharacteristic
451C2×C4×D43C2411yescharacteristic
452C2×C4×D43C2411yescharacteristic
453C2×C4×D43C2412yes—
454C2×C4×D43C2413yes—
455C2×C4×D43C2413yes—
456C2×C4×D43C2413yes—
457C2×C4×D43C2413yes—
458C2×C4×D43C2416yes—
459C2×C4×D43C2413yes—
460C2×C4×D43C2413yes—
461C2×C4×D43C2413yes—
462C2×C4×D43C2413yes—
463C2×C4×D43C2416yes—
464C2×C4×D43C2413yes—
465C2×Dic86—224no—
466C2×Dic86C2416yes—
467C2×Dic86C2416yes—
468C2×Dic86C2411yescharacteristic
469C2×Dic86C2416yes—
470C2×Dic86C2416yes—
471C2×Dic86C2413yes—
472C4⋊C4×C43C2413yes—
473C4⋊C4×C43C2416yes—
474C4⋊C4×C43C2416yes—
475C4⋊C4×C43C2412yes—
476C4⋊C4×C43C2413yes—
477C4⋊C4×C43C2411yescharacteristic
478C4⋊C4×C43C2412yes—
479C4⋊C4×C43C2416yes—
480C4⋊C4×C43C2411yescharacteristic
481C4⋊C4×C43C2416yes—
482C22⋊C4×C43C2416yes—
483C22⋊C4×C43C2416yes—
484C22⋊C4×C43C2416yes—
485C22⋊C4×C43C2416yes—
486C22⋊C4×C43C2416yes—
487C22⋊C4×C43C2416yes—
488C42×C43C2411yescharacteristic
489C42×C43C2413yes—
490C42×C43C2413yes—
491C42×C43C2413yes—
492C42×C43C2416yes—
493C22⋊Dic43C2416yes—
494C22⋊Dic43C24112yes—
495C22⋊Dic43C2416yes—
496C22⋊Dic43C2416yes—
497C22⋊Dic43C2416yes—
498C22⋊Dic43C24112yes—
499C22⋊Dic43C24112yes—
500(C2×D43)⋊C4C2416yes—
501(C2×D43)⋊C4C2416yes—
502(C2×D43)⋊C4C2412yes—
503(C2×D43)⋊C4C2412yes—
504(C2×D43)⋊C4C2416yes—
505(C2×D43)⋊C4C2416yes—
506(C2×D43)⋊C4C2412yes—
507(C2×D43)⋊C4C2412yes—
508(C2×D43)⋊C4C2412yes—
509(C2×D43)⋊C4C24112yes—
510(C2×D43)⋊C4C2416yes—
511(C2×D43)⋊C4C2416yes—
512(C2×D43)⋊C4C2416yes—
513C4⋊Dic43C2413yes—
514C4⋊Dic43C2413yes—
515C4⋊Dic43C2416yes—
516C4⋊Dic43C2413yes—
517C4⋊Dic43C2416yes—
518C4⋊Dic43C2413yes—
519C4⋊Dic43C2412yes—
520C4⋊Dic43C2416yes—
521C4⋊Dic43C24112yes—
522Dic43⋊C4C2416yes—
523Dic43⋊C4C24112yes—
524Dic43⋊C4C2416yes—
525Dic43⋊C4C2416yes—
526Dic43⋊C4C2416yes—
527Dic43⋊C4C2412yes—
528Dic43⋊C4C2416yes—
529Dic43⋊C4C2416yes—
530Dic43⋊C4C2416yes—
531Dic43⋊C4C2416yes—
532Dic43⋊C4C2416yes—
533Dic43⋊C4C2416yes—
534Dic43⋊C4C2416yes—
535C4×Dic43C2411yescharacteristic
536C4×Dic43C2413yes—
537C4×Dic43C2411yescharacteristic
538C4×Dic43C2411yescharacteristic
539C4×Dic43C2413yes—
540C4×Dic43C2413yes—
541C4×Dic43C2413yes—
542C4×Dic43C2413yes—
543C4×Dic43C2413yes—
544C4×Dic43C2413yes—
545C4×Dic43C2413yes—
546C4×Dic43C2413yes—
547C4×Dic43C2416yes—
548C4×Dic43C2416yes—
549C4×Dic43C2412yes—
550C4×Dic43C2416yes—
551C4×Dic43C24112yes—
552C4×Dic43C24112yes—
553C4×Dic43C2416yes—
554C23×C43C2513yes—
555C23×C43C2516yes—
556C22×D43—26no—
557C22×D43—43no—
558C22×D43—43no—
559C22×D43C2513yes—
560C22×D43C2512yes—
561C22×D43C2511yescharacteristic
562Q8×C43—26no—
563Q8×C43C2×#4114yes—
564D4×C43—26no—
565D4×C43—212no—
566D4×C43—26no—
567D4×C43—46no—
568D4×C43—46no—
569D4×C43—412no—
570C2×C4×C43—212no—
571C2×C4×C43—26no—
572C2×C4×C43—26no—
573C2×C4×C43—43no—
574C2×C4×C43—412no—
575C2×C4×C43C2513yes—
576C2×C4×C43C2511yescharacteristic
577C2×C4×C43C2511yescharacteristic
578C2×C4×C43C2512yes—
579C2×C4×C43C2516yes—
580C2×C4×C43C2512yes—
581C2×C4×C43C2513yes—
582C2×C4×C43C2513yes—
583C2×C4×C43C2511yescharacteristic
584C22⋊D43—212no—
585C22⋊D43—212no—
586C22⋊D43—212no—
587C22⋊D43—46no—
588C22⋊D43—412no—
589C22⋊D43—46no—
590C22⋊D43—46no—
591C2×Dic43—224no—
592C2×Dic43—26no—
593C2×Dic43—26no—
594C2×Dic43—212no—
595C2×Dic43—43no—
596C2×Dic43—46no—
597C2×Dic43C2511yescharacteristic
598C2×Dic43C2513yes—
599C2×Dic43C2511yescharacteristic
600C2×Dic43C2516yes—
601C2×Dic43C2512yes—
602C2×Dic43C2513yes—
603C2×Dic43C2516yes—
604C2×Dic43C2513yes—
605C2×Dic43C2511yescharacteristic
606D172—24no—
607D172—26no—
608D172—22no—
609D172—46no—
610C4×D43—22no—
611C4×D43—26no—
612C4×D43—212no—
613C4×D43—22no—
614C4×D43—26no—
615C4×D43—26no—
616C4×D43—22no—
617C4×D43—26no—
618C4×D43—24no—
619C4×D43—43no—
620C4×D43—43no—
621C4×D43—43no—
622C4×D43—43no—
623C4×D43—46no—
624C4×D43C2×#41112yes—
625Dic86—212no—
626Dic86—22no—
627Dic86—212no—
628Dic86—46no—
629Dic86—46no—
630Dic86C2×#41112yes—
631#62793—431nomaximal, Sylow
632C22×C43—23no—
633C22×C43—26no—
634C22×C43—23no—
635C22×C43—23no—
636C22×C43—26no—
637C22×C43—26no—
638C22×C43C2611yescharacteristic
639C2×D43—21no—
640C2×D43—21no—
641C2×D43—23no—
642C2×D43—22no—
643C2×D43—23no—
644C2×D43—23no—
645C2×D43—22no—
646C2×D43—22no—
647C2×D43—412no—
648C2×D43C22×#4112yes—
649C4×C43—22no—
650C4×C43—21no—
651C4×C43—22no—
652C4×C43—23no—
653C4×C43—21no—
654C4×C43—23no—
655C4×C43—26no—
656C4×C43C22×#4116yes—
657C4×C43#58512yes—
658Dic43—26no—
659Dic43—21no—
660Dic43—22no—
661Dic43—26no—
662Dic43—23no—
663Dic43—21no—
664Dic43—23no—
665Dic43C22×#4116yes—
666Dic43#58512yes—
667#3524—436no—
668#3524—432no—
669#3518—433no—
670#3518—431no—
671#3517—433no—
672#3517D4311yescharacteristic, complemented
673#3506—433no—
674#3506—433no—
675#3502—431no—
676#3497—431no—
677#3493—436no—
678#3487—432no—
679#3483—431no—
680#3483—433no—
681#3482—431no—
682#3482—433no—
683#3480—436no—
684#3480—432no—
685#3460—436no—
686#3444—433no—
687#3444—433no—
688C4×2−1+4—432no—
689C2×C4×#41—431no—
690C2×C43—43no—
691C2×C43—46no—
692C2×C43C23×#4111yescharacteristic
693C2×C43C2×#58511yescharacteristic
694C2×C43C2×#58511yescharacteristic
695D43—22no—
696D43—42no—
697D43—43no—
698C2×2−1+4—432no—
699C22×#41—431no—
700#559—436no—
701#559—4312no—
702#559—436no—
703Q82—431no—
704Q82—433no—
705#557—433no—
706#557—436no—
707#557—432no—
708#557C2×D4311yescharacteristic, complemented
709#556—4312no—
710#556—436no—
711#556—433no—
712#556—436no—
713#556—433no—
714#556—436no—
715#555—436no—
716#555—4312no—
717#555—436no—
718#555—436no—
719#555—433no—
720#555—433no—
721#553—4312no—
722#553—436no—
723#553—436no—
724#553—4312no—
725#553—436no—
726#553C2×D4316yescomplemented
727#552—436no—
728#552—4312no—
729#552—436no—
730#550—432no—
731#550—436no—
732#550—436no—
733#550—433no—
734#550—433no—
735#550—436no—
736#550C2×D4312yes—
737#550C2×D4311yescharacteristic, complemented
738#550C2×D4313yescomplemented
739D4×Q8—431no—
740D4×Q8—433no—
741#548—432no—
742#548—432no—
743#548—436no—
744#548—436no—
745#548—432no—
746#548—436no—
747#547—436no—
748#547—433no—
749#547C2×D4313yescomplemented
750#544—436no—
751#542—4312no—
752#542—436no—
753#542—436no—
754#540—4312no—
755#540—436no—
756#540C2×D4316yescomplemented
757#538—4312no—
758#538—4312no—
759#537—436no—
760#535—436no—
761#535—436no—
762#533—433no—
763#533—433no—
764#533—433no—
765#533—433no—
766#533—433no—
767#533—433no—
768#532—433no—
769#532—433no—
770#532—436no—
771#532—433no—
772#532—433no—
773#532—436no—
774#532—4312no—
775#532—433no—
776#532C2×D4313yescomplemented
777#529—436no—
778#529—436no—
779#529—431no—
780#529—436no—
781#529—433no—
782#529—436no—
783#529—436no—
784#529—4312no—
785#529—436no—
786#529—436no—
787#529—436no—
788#529—436no—
789#529—436no—
790#529—436no—
791#529—433no—
792#529C2×D4313yescomplemented
793#525—436no—
794#525—436no—
795#525—433no—
796#525—436no—
797#525—436no—
798#525—433no—
799#525—436no—
800#520—436no—
801#520—436no—
802#520—436no—
803#520C2×D4312yescomplemented
804#519—432no—
805#519—432no—
806#519—436no—
807C4×#41—431no—
808C4×#41—432no—
809C4×#41—436no—
810C4×#41—431no—
811C4×#41—431no—
812C4×#41—433no—
813C4×#41—433no—
814C4×#41—433no—
815C4×#41—436no—
816C4×#41—436no—
817C4×#41—436no—
818C4×#41—436no—
819C4×#41—433no—
820C4×#41—433no—
821C4×#41—436no—
822C4×#41—433no—
823C4×#41C2×D4311yescharacteristic
824C2×C4×Q8—431no—
825C2×C4×Q8—431no—
826C2×C4×Q8—432no—
827C2×C4×Q8—436no—
828C2×C4×D4—433no—
829C2×C4×D4—433no—
830C2×#117—433no—
831C22×C42—433no—
832C43#6279311yescharacteristic, complemented, Sylow
8332−1+4—8616no—
834C2×#41—431no—
835C2×#41—433no—
836C2×#41—433no—
837C2×#41—436no—
838C2×#41—436no—
839C2×#41—436no—
840C2×#41—436no—
841C2×#41—433no—
842C2×#41—433no—
843C2×#41—436no—
844C2×#41—868no—
845C2×#41C22×D4311yescharacteristic
846C2×#41C22×D4312yes—
847C2×#41C22×D4316yes—
848C22×Q8—431no—
849C22×Q8—432no—
850C22×Q8—436no—
851C22×D4—433no—
852C23×C4—433no—
853C23×C4—433no—
854C23×C4—433no—
855C4⋊Q8—433no—
856C4⋊Q8—433no—
857C4⋊Q8—433no—
858C4⋊Q8—4312no—
859C4⋊Q8—436no—
860C4⋊Q8—433no—
861C4⋊Q8—433no—
862C4⋊Q8—436no—
863C4⋊Q8C22×D4313yes—
864#127—433no—
865#127—4312no—
866#127—436no—
867#127C22×D4313yes—
868#127C22×D4316yes—
869#126—432no—
870#126—4312no—
871#126—4312no—
872#126—436no—
873#126—4312no—
874#126—4312no—
875#126—4312no—
876#126—436no—
877#126C22×D4316yes—
878#125—436no—
879#125—436no—
880#125—436no—
881#125—436no—
882#125—4312no—
883#125—436no—
884#125—433no—
885#125C22×D4311yescharacteristic
886#125C22×D4316yes—
887#124—436no—
888#124—436no—
889#124—436no—
890#124—4312no—
891#124—436no—
892#124—436no—
893#124—4312no—
894#124—4312no—
895#124—4312no—
896#124—4312no—
897#124—431no—
898#124—436no—
899#124C22×D4313yes—
900#123—4312no—
901#123—4312no—
902#123—436no—
903#123—4312no—
904#123—432no—
905#123—436no—
906#123—4312no—
907#123—436no—
908#123—4312no—
909#123—436no—
910#123C22×D4316yes—
911#123C22×D43112yes—
912C22⋊Q8—433no—
913C22⋊Q8—436no—
914C22⋊Q8—436no—
915C22⋊Q8—433no—
916C22⋊Q8—436no—
917C22⋊Q8—436no—
918C22⋊Q8—431no—
919C22⋊Q8—436no—
920C22⋊Q8—436no—
921C22⋊Q8—436no—
922C22⋊Q8—436no—
923C22⋊Q8—436no—
924C22⋊Q8—436no—
925C22⋊Q8—436no—
926C22⋊Q8—4312no—
927C22⋊Q8C22×D4313yes—
928#121—433no—
929#121—436no—
930#121—436no—
931#121—436no—
932#121—436no—
933#121—4312no—
934#121—436no—
935#121—4312no—
936#121—436no—
937#121—4312no—
938#121—4312no—
939#121—4312no—
940#121—433no—
941#121—436no—
942#121—4312no—
943#121—431no—
944#121—436no—
945#121—436no—
946#121—436no—
947#121—436no—
948#121C22×D4316yes—
949#121C22×D4316yes—
950#121C22×D4313yes—
951#121C22×D4316yes—
952#121C22×D4316yes—
953#121C22×D43112yes—
954#120—436no—
955#120—4312no—
956#120—436no—
957C4×Q8—431no—
958C4×Q8—431no—
959C4×Q8—433no—
960C4×Q8—432no—
961C4×Q8—436no—
962C4×Q8—433no—
963C4×Q8—436no—
964C4×Q8—436no—
965C4×Q8—433no—
966C4×Q8—436no—
967C4×Q8—4312no—
968C4×Q8—436no—
969C4×Q8—431no—
970C4×Q8—436no—
971C4×Q8—436no—
972C4×Q8—436no—
973C4×Q8—433no—
974C4×Q8—433no—
975C4×Q8—436no—
976C4×Q8—436no—
977C4×Q8—436no—
978C4×Q8—433no—
979C4×Q8—436no—
980C4×Q8—436no—
981C4×Q8C22×D4311yescharacteristic
982C4×Q8C22×D4311yescharacteristic
983C4×Q8C22×D4312yes—
984C4×Q8C22×D4313yes—
985C4×D4—433no—
986C4×D4—433no—
987C4×D4—433no—
988C4×D4—436no—
989C4×D4—436no—
990C4×D4—4312no—
991C4×D4—4312no—
992C4×D4—436no—
993C4×D4—436no—
994C4×D4—436no—
995C4×D4—436no—
996C4×D4—436no—
997C4×D4—4312no—
998C4×D4—4312no—
999C4×D4—436no—
1000C4×D4—436no—
1001C4×D4—4312no—
1002C4×D4—436no—
1003C4×D4—433no—
1004C4×D4—433no—
1005C4×D4—432no—
1006C4×D4—431no—
1007C4×D4—436no—
1008C4×D4—436no—
1009C4×D4—436no—
1010C4×D4—436no—
1011C4×D4—436no—
1012C4×D4—436no—
1013C4×D4—436no—
1014C4×D4—436no—
1015C4×D4—436no—
1016C4×D4—4312no—
1017C4×D4—436no—
1018C4×D4—436no—
1019C4×D4—433no—
1020C4×D4—433no—
1021C4×D4—436no—
1022C4×D4—433no—
1023C4×D4C22×D4313yes—
1024C4×D4C22×D4313yes—
1025C4×D4C22×D4316yes—
1026C4×D4C22×D4316yes—
1027C4×D4C22×D4316yes—
1028C4×D4C22×D4316yes—
1029C4×D4C22×D4313yes—
1030#117—433no—
1031#117—436no—
1032#117—436no—
1033#117—4312no—
1034#117—433no—
1035#117—433no—
1036#117—432no—
1037#117—436no—
1038#117—436no—
1039#117—436no—
1040#117—433no—
1041#117—433no—
1042#117—436no—
1043#117—436no—
1044#117—436no—
1045#117—4312no—
1046#117—4312no—
1047#117—436no—
1048#117—436no—
1049#117—436no—
1050#117—436no—
1051#117—436no—
1052#117C22×D4313yes—
1053#117C22×D4316yes—
1054C2×C4⋊C4—4312no—
1055C2×C4⋊C4—433no—
1056C2×C4⋊C4—433no—
1057C2×C4⋊C4—436no—
1058C2×C4⋊C4C22×D4316yes—
1059C2×C22⋊C4—436no—
1060C2×C42—4312no—
1061C2×C42—436no—
1062C2×C42—433no—
1063C2×C42—433no—
1064C2×C42—433no—
1065C2×C42—433no—
1066C2×C42—433no—
1067C2×C42—433no—
1068C2×C42—436no—
1069C2×C42—433no—
1070C2×C42—433no—
1071C2×C42—433no—
1072C2×C42—433no—
1073C2×C42—431no—
1074C2×C42C22×D4313yes—
1075C24—433no—
1076#41—24no—
1077#41—28no—
1078#41—412no—
1079#41—8624no—
1080#41—8612no—
1081#41—8624no—
1082#41—8612no—
1083#41—8624no—
1084#41—864no—
1085#41—17212no—
1086#41—17212no—
1087#41—1726no—
1088#41—1726no—
1089C2×Q8—438no—
1090C2×Q8—433no—
1091C2×Q8—436no—
1092C2×Q8—436no—
1093C2×Q8—431no—
1094C2×Q8—436no—
1095C2×Q8—436no—
1096C2×Q8—8624no—
1097C2×Q8—868no—
1098C2×Q8C23×D4313yes—
1099C2×Q8C23×D4311yescharacteristic
1100C2×D4—436no—
1101C2×D4—436no—
1102C2×D4—436no—
1103C2×D4—436no—
1104C2×D4—4312no—
1105C2×D4—436no—
1106C2×D4—436no—
1107C2×D4—432no—
1108C2×D4—433no—
1109C2×D4—431no—
1110C2×D4—436no—
1111C2×D4—8612no—
1112C2×D4C23×D4313yes—
1113C2×D4C23×D4313yes—
1114C2×D4C23×D4316yes—
1115C2×D4C23×D43112yes—
1116C2×D4C23×D4316yes—
1117C2×D4C23×D4316yes—
1118C22×C4—433no—
1119C22×C4—436no—
1120C22×C4—433no—
1121C22×C4—433no—
1122C22×C4—4312no—
1123C22×C4—433no—
1124C22×C4—436no—
1125C22×C4—431no—
1126C22×C4—431no—
1127C22×C4—431no—
1128C22×C4—432no—
1129C22×C4—433no—
1130C22×C4—433no—
1131C22×C4—433no—
1132C22×C4—433no—
1133C22×C4—436no—
1134C22×C4—433no—
1135C22×C4—433no—
1136C22×C4—433no—
1137C22×C4—433no—
1138C22×C4—436no—
1139C22×C4—8612no—
1140C22×C4—1726no—
1141C22×C4—1726no—
1142C22×C4C23×D4313yes—
1143C22×C4C23×D4313yes—
1144C22×C4C23×D4316yes—
1145C22×C4C23×D4313yes—
1146C22×C4C23×D43112yes—
1147C4⋊C4—436no—
1148C4⋊C4—433no—
1149C4⋊C4—436no—
1150C4⋊C4—4312no—
1151C4⋊C4—436no—
1152C4⋊C4—436no—
1153C4⋊C4—433no—
1154C4⋊C4—433no—
1155C4⋊C4—432no—
1156C4⋊C4—436no—
1157C4⋊C4—436no—
1158C4⋊C4—436no—
1159C4⋊C4—433no—
1160C4⋊C4—436no—
1161C4⋊C4—436no—
1162C4⋊C4—436no—
1163C4⋊C4—432no—
1164C4⋊C4—436no—
1165C4⋊C4—4312no—
1166C4⋊C4—436no—
1167C4⋊C4—436no—
1168C4⋊C4—436no—
1169C4⋊C4C23×D4313yes—
1170C4⋊C4C23×D4316yes—
1171C4⋊C4C23×D4313yes—
1172C4⋊C4C23×D4316yes—
1173C4⋊C4C23×D4311yescharacteristic
1174C4⋊C4C23×D4311yescharacteristic
1175C4⋊C4C23×D4316yes—
1176C4⋊C4C23×D4312yes—
1177C4⋊C4C23×D4316yes—
1178C4⋊C4C23×D4312yes—
1179C22⋊C4—436no—
1180C22⋊C4—4312no—
1181C22⋊C4—436no—
1182C22⋊C4—436no—
1183C22⋊C4—436no—
1184C22⋊C4—4312no—
1185C22⋊C4—4312no—
1186C22⋊C4—436no—
1187C22⋊C4—436no—
1188C22⋊C4—436no—
1189C22⋊C4—432no—
1190C22⋊C4—432no—
1191C22⋊C4—432no—
1192C22⋊C4—436no—
1193C22⋊C4—432no—
1194C22⋊C4—432no—
1195C22⋊C4—4312no—
1196C22⋊C4—436no—
1197C22⋊C4—436no—
1198C22⋊C4—436no—
1199C22⋊C4C23×D4316yes—
1200C22⋊C4C23×D4316yes—
1201C22⋊C4C23×D4316yes—
1202C22⋊C4C23×D4316yes—
1203C22⋊C4C23×D4316yes—
1204C22⋊C4C23×D4316yes—
1205C42—431no—
1206C42—433no—
1207C42—433no—
1208C42—431no—
1209C42—431no—
1210C42—433no—
1211C42—433no—
1212C42—436no—
1213C42—432no—
1214C42—433no—
1215C42—433no—
1216C42—433no—
1217C42—433no—
1218C42—433no—
1219C42—436no—
1220C42—436no—
1221C42—4312no—
1222C42—4312no—
1223C42—436no—
1224C42C23×D4311yescharacteristic
1225C42C23×D4313yes—
1226C42C23×D4313yes—
1227C42C23×D4313yes—
1228C42C23×D4316yes—
1229C23—431no—
1230C23—433no—
1231C23—432no—
1232C23—866no—
1233C23—1723no—
1234C23—1723no—
1235C23C24×D4313yes—
1236C23C24×D4316yes—
1237Q8—26no—
1238Q8—4312no—
1239Q8—8612no—
1240Q8—8612no—
1241Q8—862no—
1242Q8—1726no—
1243Q8—1726no—
1244Q8#41×D4314yes—
1245D4—26no—
1246D4—212no—
1247D4—26no—
1248D4—412no—
1249D4—46no—
1250D4—46no—
1251D4—864no—
1252D4—8612no—
1253D4—8612no—
1254D4—8612no—
1255D4—866no—
1256D4—862no—
1257D4—1726no—
1258D4—1726no—
1259D4—1726no—
1260D4—17212no—
1261D4—1726no—
1262C2×C4—26no—
1263C2×C4—212no—
1264C2×C4—26no—
1265C2×C4—43no—
1266C2×C4—412no—
1267C2×C4—431no—
1268C2×C4—433no—
1269C2×C4—4312no—
1270C2×C4—431no—
1271C2×C4—431no—
1272C2×C4—433no—
1273C2×C4—436no—
1274C2×C4—436no—
1275C2×C4—433no—
1276C2×C4—432no—
1277C2×C4—866no—
1278C2×C4—862no—
1279C2×C4—866no—
1280C2×C4—864no—
1281C2×C4—862no—
1282C2×C4—866no—
1283C2×C4—866no—
1284C2×C4—8624no—
1285C2×C4—8612no—
1286C2×C4—866no—
1287C2×C4—8612no—
1288C2×C4—862no—
1289C2×C4—866no—
1290C2×C4—1723no—
1291C2×C4—1723no—
1292C2×C4—1723no—
1293C2×C4—1723no—
1294C2×C4—1726no—
1295C2×C4—1723no—
1296C2×C4—1726no—
1297C2×C4C24×D4313yes—
1298C2×C4C24×D4311yescharacteristic
1299C2×C4C24×D4311yescharacteristic
1300C2×C4C24×D4312yes—
1301C2×C4C24×D4312yes—
1302C2×C4C24×D4316yes—
1303C2×C4C24×D4313yes—
1304C2×C4C24×D4313yes—
1305C2×C4C24×D4311yescharacteristic
1306C22—26no—
1307C22—23no—
1308C22—23no—
1309C22—26no—
1310C22—23no—
1311C22—26no—
1312C22—432no—
1313C22—861no—
1314C22—861no—
1315C22—862no—
1316C22—863no—
1317C22—863no—
1318C22—862no—
1319C22—863no—
1320C22—862no—
1321C22—17212no—
1322C22C25×D4311yescharacteristic
1323C4—21no—
1324C4—22no—
1325C4—21no—
1326C4—23no—
1327C4—22no—
1328C4—23no—
1329C4—26no—
1330C4—436no—
1331C4—432no—
1332C4—861no—
1333C4—866no—
1334C4—863no—
1335C4—866no—
1336C4—861no—
1337C4—863no—
1338C4—862no—
1339C4C2×#41×D4316yes—
1340C4#1458373412yes—
1341C2—43no—
1342C2—46no—
1343C2—862no—
1344C2—1723no—
1345C2—1722no—
1346C2C22×#41×D4311yescharacteristic
1347C2#585×D4311yescharacteristic
1348C2C2×#1458373411yescharacteristic
subgroupG/H
center, FrattiniC22C25×D43
commutator, socle, cosocleC22×C43C26
FittingC43×#3517C2
hypercenter#3517D43
hypocenterC43#62793
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ #3517

Complements

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

NH ≅ G/Ntype
1. #19148698C2semidirect
2. #19148696C2semidirect
3. #19148612C2semidirect
4. #19148610C2semidirect
5. #19148593C2semidirect
6. #19148445C2semidirect
7. #19148439C2semidirect
8. #19148399C2semidirect
9. #19148360C2semidirect
10. #19148311C2semidirect
11. #19148248C2semidirect
12. #19148218C2semidirect
13. #19148218C2semidirect
14. #19148215C2semidirect
15. #19148207C2semidirect
16. #19148194C2semidirect
17. #19148189C2semidirect
18. #19148010C2semidirect
19. #19147890C2semidirect
20. #19147889C2semidirect
21. #19147806C2semidirect
22. C4×#41×D43C2semidirect
23. C43×#3517C2semidirect
26. #14583635C22semidirect
27. #14583633C22semidirect
28. #14583632C22semidirect
29. Q8×Dic86C22semidirect
30. Q8×Dic86C22semidirect
31. #14583628C22semidirect
32. #14583626C22semidirect
33. #14583624C22semidirect
34. #14583622C22semidirect
35. #14583620C22semidirect
36. #14583619C22semidirect
37. #14583619C22semidirect
38. #14583617C22semidirect
39. #14583616C22semidirect
40. #14583614C22semidirect
41. #14583614C22semidirect
42. #14583614C22semidirect
43. #14583613C22semidirect
44. #14583613C22semidirect
45. #14583613C22semidirect
46. #14583598C22semidirect
47. #14583597C22semidirect
48. #14583596C22semidirect
49. #14583596C22semidirect
50. #14583592C22semidirect
51. #14583587C22semidirect
52. #14583586C22semidirect
53. #14583584C22semidirect
55. #14583569C22semidirect
56. #14583569C22semidirect
58. #14583568C22semidirect
60. Q8×D172C22semidirect
61. D4×Dic86C22semidirect
65. #14583556C22semidirect
67. #14583555C22semidirect
68. #14583552C22semidirect
69. #14583548C22semidirect
71. #14583520C22semidirect
72. #14583517C22semidirect
73. #14583514C22semidirect
74. #14583500C22semidirect
75. #14583499C22semidirect
81. #14583456C22semidirect
82. #14583455C22semidirect
84. #14583454C22semidirect
86. #14583451C22semidirect
87. #14583448C22semidirect
89. #14583447C22semidirect
90. #14583447C22semidirect
92. #14583444C22semidirect
93. #14583444C22semidirect
94. #14583444C22semidirect
96. #14583434C22semidirect
97. #14583433C22semidirect
99. #14583432C22semidirect
101. #14583431C22semidirect
102. #14583430C22semidirect
103. #14583430C22semidirect
104. #14583430C22semidirect
106. #14583428C22semidirect
107. #14583427C22semidirect
108. #14583426C22semidirect
109. #14583426C22semidirect
119. #14583378C22semidirect
120. #14583376C22semidirect
122. #14583375C22semidirect
124. #41×Dic43C22semidirect
125. #41×Dic43C22semidirect
128. C4×#10621902C22semidirect
135. C4×#10621900C22semidirect
136. C4×#10621900C22semidirect
137. C4×#10621900C22semidirect
138. C4×#10621900C22semidirect
139. C2×#13063290C22semidirect
142. C4×Q8×D43C22semidirect
147. C43×#557C22semidirect
148. C43×#553C22semidirect
150. C43×#550C22semidirect
151. C43×#550C22semidirect
152. C43×#547C22semidirect
153. C43×#540C22semidirect
154. C43×#532C22semidirect
155. C43×#529C22semidirect
156. C43×#520C22semidirect
433. Q8×D43#41semidirect
672. #3517D43semidirect
708. #557C2×D43semidirect
726. #553C2×D43semidirect
737. #550C2×D43semidirect
738. #550C2×D43semidirect
749. #547C2×D43semidirect
756. #540C2×D43semidirect
776. #532C2×D43semidirect
792. #529C2×D43semidirect
803. #520C2×D43semidirect
832. C43#62793semidirect

Maximal subgroups

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

subgroupindex
#191486982
#191486962
#191486122
#191486102
#191485932
#191484452
#191484392
#191483992
#191483602
#191483112
#191482482
#191482182
#191482152
#191482072
#191481942
#191481892
#191480102
#191478902
#191478892
#191478062
C4×#41×D432
C43×#35172
#6279343