Finite Group Databasebeta

← #25960831

Subgroups — #25960831

Order 11008.

2742 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583705C211yesmaximal, characteristic
2#19147804C211yesmaximal, characteristic, complemented
3#19147799C211yesmaximal, characteristic, complemented
4#19143480C211yesmaximal, characteristic, complemented
5#19143473C212yesmaximal, complemented
6#19143449C212yesmaximal, complemented
7#19143438C211yesmaximal, characteristic, complemented
8#19143435C212yesmaximal, complemented
9#19143427C211yesmaximal, characteristic, complemented
10#19143426C212yesmaximal, complemented
11#19143417C212yesmaximal, complemented
12#19143410C211yesmaximal, characteristic, complemented
13#19143400C212yesmaximal, complemented
14#19143399C211yesmaximal, characteristic, complemented
15#19143366C211yesmaximal, characteristic, complemented
16C4×#13063346C212yesmaximal, complemented
17C2×SD16×Dic43C211yesmaximal, characteristic, complemented
18C4×SD16×D43C212yesmaximal, complemented
19#19143187C211yesmaximal, characteristic, complemented
20#19143127C211yesmaximal, characteristic, complemented
21#19143120C211yesmaximal, characteristic, complemented
22#19143017C211yesmaximal, characteristic, complemented
23C43×#2949C211yesmaximal, characteristic, complemented
24C2×#13063373C2211yescharacteristic
25C2×#13063370C2211yescharacteristic
26#14583705C4116yescomplemented
27C2×#13063356C2211yescharacteristic
28C2×#13063354C2212yes—
29C2×#13063352C2212yes—
30C2×#13063351C2211yescharacteristic
31C2×#13063347C2211yescharacteristic
32C2×#13063346C2212yes—
33C2×SD16×D43C2212yes—
34C2×#13063333C2211yescharacteristic
35C2×#13063331C2211yescharacteristic
36#14583381—21no—
37#14583381C2212yescomplemented
38#14583379—22no—
39#14583379C2211yescharacteristic
40#14583379C2211yescharacteristic
41#14583379C2211yescharacteristic
42#14583379C2211yescharacteristic, complemented
43#14583378—21no—
44#14583378C2212yes—
45#14583375—21no—
46#14583375C2212yescomplemented
47#14583372—22no—
48#14583371—21no—
49#14583371C2212yes—
50C4×#10621902—21no—
51C4×#10621902C2212yescomplemented
52#14583367—22no—
53#14583367C2211yescharacteristic
54#14583367C2211yescharacteristic
55#14583367C2211yescharacteristic, complemented
56C4×#10621900—21no—
57C4×#10621900C2212yes—
58C2×Q8×Dic43C2211yescharacteristic, complemented
59C4×Q8×D43—21no—
60C4×Q8×D43C2212yescomplemented
61C2×D4×Dic43C2211yescharacteristic
62C2×(C22⋊D43)⋊C4—22no—
63C4×D4×D43—21no—
64C4×D4×D43C2212yes—
65#14583012C2212yescomplemented
66#14583009C2212yescomplemented
67#14583008C2212yescomplemented
68#14583007C2212yescomplemented
69#14583004C2212yescomplemented
70#14583003C2212yescomplemented
71#14583002C2212yescomplemented
72#14582999C2212yescomplemented
73#14582997C2212yescomplemented
74#14582996C2212yescomplemented
75#14582993C2211yescharacteristic, complemented
76#14582993C2211yescharacteristic, complemented
77C4×#10621885C2212yescomplemented
78#14582991C2212yescomplemented
79#14582990C2212yescomplemented
80C4×#10621873C2212yescomplemented
81C4×#10621873C2212yescomplemented
82SD16×Dic43C2212yescomplemented
83SD16×Dic43C2212yescomplemented
84SD16×Dic43C2212yescomplemented
85SD16×Dic43C2212yescomplemented
86C4×#10621884C2212yescomplemented
87#14582986C2211yescharacteristic, complemented
88#14582986C2211yescharacteristic, complemented
89#14582986C2211yescharacteristic, complemented
90#14582986C2211yescharacteristic, complemented
91C4×#10621883C2212yescomplemented
92#14582984C2212yescomplemented
93#14582981C2211yescharacteristic, complemented
94#14582981C2211yescharacteristic, complemented
95C4×#10621882C2212yescomplemented
96#14582979C2212yescomplemented
97#14582942C2211yescharacteristic, complemented
98#14582942C2211yescharacteristic, complemented
99#14582940C2212yescomplemented
100#14582940C2212yescomplemented
101#14582934C2212yescomplemented
102C2×#13063257C2211yescharacteristic, complemented
103#106×D43C2212yescomplemented
104#14582906C2212yescomplemented
105#14582902C2212yes—
106#14582901C2211yescharacteristic
107#14582901C2211yescharacteristic, complemented
108#14582899C2212yescomplemented
109#14582897C2212yes—
110#14582894C2212yescomplemented
111#14582893C2211yescharacteristic
112#14582893C2211yescharacteristic, complemented
113#14582892C2212yes—
114C2×#13063249C2211yescharacteristic, complemented
115#103×D43C2212yescomplemented
116C2×#13063246C2211yescharacteristic
117#102×D43C2212yes—
118#14582856C2212yescomplemented
119#14582855C2211yescharacteristic, complemented
120#14582853C2212yescomplemented
121#14582851C2212yescomplemented
122M16×Dic43C2211yescharacteristic, complemented
123C2×C8×Dic43C2211yescharacteristic, complemented
124C4×C8×D43C2212yescomplemented
125C22×SD16×C43C2211yescharacteristic
126C43×#519C2211yescharacteristic, complemented
127C43×#518C2211yescharacteristic
128C43×#440C2212yescomplemented
129C43×#440C2212yescomplemented
130C4×SD16×C43C2212yescomplemented
131C4×SD16×C43C2212yescomplemented
132C43×#427C2211yescharacteristic, complemented
133C43×#419C2211yescharacteristic, complemented
134C43×#418C2211yescharacteristic
135C43×#405C2211yescharacteristic, complemented
136#13063373—24no—
137#13063373C2×C418yescomplemented
138#13063370—24no—
139#13063370C2×C418yescomplemented
140C2×#10621902—21no—
141C2×#10621902C2312yes—
142C2×#10621898—22no—
143C2×#10621898C2311yescharacteristic
144C2×#10621898C2311yescharacteristic
145C2×#10621898C2311yescharacteristic
146C2×#10621900—21no—
147C2×#10621900C2312yes—
148C2×Q8×D43—21no—
149C2×Q8×D43C2312yes—
150C22×C22⋊D43—22no—
151C2×D4×D43—21no—
152C2×D4×D43C2312yes—
153C23×Dic43—21no—
154C22×C4×D43—22no—
155#13063356C2×C418yescomplemented
156#13063354C2×C4116yescomplemented
157#13063352C2×C4116yescomplemented
158#13063351C2×C418yescomplemented
159#13063347C2×C418yescomplemented
160#13063346C2×C4116yescomplemented
161C2×Dic172C2311yescharacteristic
162C2×#10621885C2312yes—
163C2×#10621873C2311yescharacteristic
164C2×#10621873C2311yescharacteristic
165C2×#10621883C2312yes—
166C2×#10621884C2312yes—
167SD16×D43C2×C4116yescomplemented
168C2×D344C2311yescharacteristic
169C2×#10621882C2312yes—
170#13063333—24no—
171#13063331C2×C418yescomplemented
172C2×#10621877C2311yescharacteristic
173C2×#10621872C2312yes—
174C2×#10621872C2312yes—
175C22×C43⋊C8C2311yescharacteristic
176C2×C8×D43C2312yes—
177C2×C8×D43C2312yes—
178Q8×Dic43—21no—
179Q8×Dic43—21no—
180Q8×Dic43C2312yes—
181Q8×Dic43C2312yes—
182C4×Dic86—21no—
183C4×Dic86—21no—
184C4×Dic86—22no—
185C4×Dic86—22no—
186C4×Dic86C2312yes—
187C4×Dic86C2312yes—
188#13063290—22no—
189#13063290—22no—
190#13063290D411yescharacteristic
191#13063290D411yescharacteristic
192#13063290C2311yescharacteristic
193#13063290C2311yescharacteristic
194#13063290C2311yescharacteristic
195#13063290C2311yescharacteristic
196C4×D172—21no—
197C4×D172—21no—
198C4×D172—22no—
199C4×D172—22no—
200C4×D172C2312yes—
201C4×D172C2312yes—
202D4×Dic43—21no—
203D4×Dic43—21no—
204D4×Dic43C2312yes—
205D4×Dic43C2312yes—
206#13063287—22no—
207#13063287—22no—
208#13063287D411yescharacteristic
209#13063287D411yescharacteristic
210#13063287C2311yescharacteristic
211#13063287C2311yescharacteristic
212#13063287C2311yescharacteristic
213#13063287C2311yescharacteristic
214C4×C22⋊D43—22no—
215C4×C22⋊D43—22no—
216C4×C22⋊D43—22no—
217C4×C22⋊D43—22no—
218(C22⋊D43)⋊C4—22no—
219(C22⋊D43)⋊C4—22no—
220(C22⋊D43)⋊C4—21no—
221(C22⋊D43)⋊C4—21no—
222(C22⋊D43)⋊C4—21no—
223(C22⋊D43)⋊C4—21no—
224(C22⋊D43)⋊C4—22no—
225(C22⋊D43)⋊C4—22no—
226(C22⋊D43)⋊C4—22no—
227(C22⋊D43)⋊C4—22no—
228(C22⋊D43)⋊C4—22no—
229(C22⋊D43)⋊C4—22no—
230(C22⋊D43)⋊C4D412yes—
231(C22⋊D43)⋊C4D412yes—
232#13063283—21no—
233#13063283—21no—
234#13063283—22no—
235#13063283—22no—
236#13063283C2312yes—
237#13063283C2312yes—
238#13063282—22no—
239#13063282—22no—
240#13063282—21no—
241#13063282—21no—
242#13063282C2312yes—
243#13063281—22no—
244#13063281—22no—
245C2×C4⋊Dic43—21no—
246C2×C4⋊Dic43C2311yescharacteristic
247C2×C4⋊Dic43C2311yescharacteristic
248C2×Dic43⋊C4—22no—
249C4⋊C4×D43—22no—
250C4⋊C4×D43—21no—
251C4⋊C4×D43—21no—
252C4⋊C4×D43—22no—
253C4⋊C4×D43C2312yes—
254C4⋊C4×D43C2312yes—
255C2×C22⋊Dic43—21no—
256C2×(C2×D43)⋊C4—22no—
257C22⋊C4×D43—22no—
258C22⋊C4×D43—22no—
259C2×C4×Dic43—21no—
260C2×C4×Dic43—22no—
261C2×C4×Dic43C2311yescharacteristic
262C42×D43—22no—
263C42×D43—21no—
264C42×D43—22no—
265C42×D43—21no—
266C42×D43C2312yes—
267#13063258C2312yes—
268#13063258C2312yes—
269#13063257C2312yes—
270#13063257C2312yes—
271#13063256C2312yes—
272#13063256C2312yes—
273#13063250C2312yes—
274#13063250C2312yes—
275#13063249C2312yes—
276#13063249C2312yes—
277#13063248C2311yescharacteristic
278#13063248C2311yescharacteristic
279#13063248C2311yescharacteristic
280#13063248C2311yescharacteristic
281#13063247C2312yes—
282#13063247C2312yes—
283#13063246C2312yes—
284#13063246C2312yes—
285#13063245C2311yescharacteristic
286#13063245C2311yescharacteristic
287#13063245C2311yescharacteristic
288#13063245C2311yescharacteristic
289#13063236C2312yes—
290#13063235C2312yes—
291C4×C43⋊C8C2312yes—
292C8×Dic43C2311yescharacteristic
293C8×Dic43C2312yes—
294C8×Dic43C2311yescharacteristic
295C8×Dic43C2311yescharacteristic
296C8×Dic43C2311yescharacteristic
297C22×Q8×C43C2311yescharacteristic
298C22×D4×C43C2311yescharacteristic
299C2×SD16×C43C2×C418yescomplemented
300C2×SD16×C43C2312yes—
301C2×SD16×C43C2312yes—
302C2×M16×C43C2311yescharacteristic
303C22×C8×C43C2311yescharacteristic
304C4×Q8×C43—21no—
305C4×Q8×C43—21no—
306C4×Q8×C43C2312yes—
307C4×Q8×C43C2312yes—
308C4×D4×C43—21no—
309C4×D4×C43—21no—
310C4×D4×C43C2312yes—
311C4×D4×C43C2312yes—
312#117×C43—22no—
313#117×C43C2311yescharacteristic
314#117×C43C2311yescharacteristic
315#117×C43C2311yescharacteristic
316C2×C22⋊C4×C43—22no—
317#107×C43C2311yescharacteristic
318#107×C43C2311yescharacteristic
319#106×C43C2311yescharacteristic
320#106×C43C2311yescharacteristic
321#103×C43C2312yes—
322#103×C43C2312yes—
323#102×C43C2312yes—
324#102×C43C2312yes—
325#97×C43C2312yes—
326C4×C8×C43C2312yes—
327C24×C43—21no—
328C23×D43—22no—
329C2×Q8×C43—21no—
330C2×Q8×C43—22no—
331C2×Q8×C43C22×C414yescomplemented
332C2×Q8×C43C2412yes—
333C2×D4×C43—21no—
334C2×D4×C43—22no—
335C2×D4×C43C22×C414yes—
336C2×D4×C43C2412yes—
337C22×C4×C43—22no—
338C22×C4×C43—22no—
339C22×C4×C43—21no—
340C22×C4×C43C2411yescharacteristic
341C2×C22⋊D43—216no—
342C2×C22⋊D43—22no—
343C2×C22⋊D43—21no—
344C2×C22⋊D43—21no—
345C2×C22⋊D43—22no—
346C2×C22⋊D43C2×D412yes—
347C22×Dic43—22no—
348C22×Dic43—22no—
349C22×Dic43—22no—
350C22×Dic43—21no—
351C22×Dic43—21no—
352C22×Dic43—82no—
353C22×Dic43C2×D411yescharacteristic
354C22×Dic43C2×D411yescharacteristic
355#10621902—28no—
356#10621902—24no—
357#10621902C22×C418yescomplemented
358Q8×D43—24no—
359Q8×D43—28no—
360Q8×D43C22×C418yescomplemented
361#10621900—24no—
362#10621900—28no—
363#10621900C22×C418yes—
364D4×D43—28no—
365D4×D43—24no—
366D4×D43C22×C418yes—
367#10621898—22no—
368#10621898—22no—
369#10621898—216no—
370#10621898C22×C414yes—
371#10621898C22×C414yes—
372#10621898C22×C414yescomplemented
373#10621898#4114yes—
374C2×D172—22no—
375C2×D172C2×D411yescharacteristic
376C2×D172C2411yescharacteristic
377C2×D172C2411yescharacteristic
378C2×C4×D43—21no—
379C2×C4×D43—21no—
380C2×C4×D43—22no—
381C2×C4×D43—21no—
382C2×C4×D43—21no—
383C2×C4×D43—22no—
384C2×C4×D43—22no—
385C2×C4×D43—21no—
386C2×C4×D43—21no—
387C2×C4×D43—22no—
388C2×C4×D43—22no—
389C2×C4×D43—22no—
390C2×C4×D43—84no—
391C2×C4×D43C2×D412yes—
392C2×C4×D43C2×D412yes—
393C2×C4×D43C2412yes—
394C2×Dic86—22no—
395C2×Dic86C2×D411yescharacteristic
396C2×Dic86C2411yescharacteristic
397C2×Dic86C2411yescharacteristic
398SD16×C43C22×C418yescomplemented
399SD16×C43C22×C418yescomplemented
400M16×C43—22no—
401C2×C8×C43C22×C414yescomplemented
402C2×C8×C43C2412yes—
403C2×C8×C43C2411yescharacteristic
404C2×C8×C43C2411yescharacteristic
405C4⋊C4×C43—22no—
406C4⋊C4×C43—22no—
407C4⋊C4×C43C2×D411yescharacteristic
408C4⋊C4×C43C2×D411yescharacteristic
409C4⋊C4×C43C2411yescharacteristic
410C4⋊C4×C43C2411yescharacteristic
411C4⋊C4×C43C2411yescharacteristic
412C4⋊C4×C43C2411yescharacteristic
413C22⋊C4×C43—22no—
414C22⋊C4×C43—22no—
415C22⋊C4×C43—21no—
416C22⋊C4×C43—21no—
417C22⋊C4×C43C2×D412yes—
418C42×C43—22no—
419C42×C43—22no—
420C42×C43—21no—
421C42×C43—21no—
422C42×C43C2412yes—
423C22⋊Dic43—22no—
424C22⋊Dic43—22no—
425#10621885C22×C418yescomplemented
426#10621884C22×C418yescomplemented
427#10621883C22×C418yescomplemented
428#10621882C22×C418yescomplemented
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—21no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4C2×D412yes—
438(C2×D43)⋊C4C2×D412yes—
439C4⋊Dic43—21no—
440C4⋊Dic43—21no—
441C4⋊Dic43—22no—
442C4⋊Dic43—22no—
443C4⋊Dic43C2412yes—
444C4⋊Dic43C2412yes—
445Dic43⋊C4—22no—
446Dic43⋊C4—22no—
447Dic43⋊C4—21no—
448Dic43⋊C4—22no—
449Dic43⋊C4—22no—
450Dic43⋊C4—21no—
451Dic43⋊C4—21no—
452Dic43⋊C4—21no—
453Dic43⋊C4C2×D412yes—
454Dic43⋊C4C2×D412yes—
455C4×Dic43—22no—
456C4×Dic43—22no—
457C4×Dic43—21no—
458C4×Dic43—22no—
459C4×Dic43—21no—
460C4×Dic43—21no—
461C4×Dic43—21no—
462C4×Dic43—22no—
463C4×Dic43—22no—
464C4×Dic43—22no—
465C4×Dic43C2×D411yescharacteristic
466C4×Dic43C2×D412yes—
467C4×Dic43C2×D412yes—
468C4×Dic43C2×D411yescharacteristic
469C4×Dic43C2411yescharacteristic
470C4×Dic43C2411yescharacteristic
471#10621877C22×C414yescomplemented
472C2×C43⋊C8—22no—
473C2×C43⋊C8C2411yescharacteristic
474C2×C43⋊C8C2411yescharacteristic
475C2×C43⋊C8C2412yes—
476Dic172C22×C414yescomplemented
477D344C22×C414yescomplemented
478#10621873C22×C414yescomplemented
479#10621873C22×C414yescomplemented
480#10621872—24no—
481#10621872C22×C418yescomplemented
482C8×D43—24no—
483C8×D43C22×C418yescomplemented
484C23×C43—22no—
485C23×C43—24no—
486C23×C43—81no—
487C23×C43—81no—
488C23×C43C22×D411yescharacteristic
489C22×D43—21no—
490C22×D43—21no—
491C22×D43—28no—
492C22×D43—82no—
493C22×D43—82no—
494C22×D43C22×D412yes—
495Q8×C43—24no—
496Q8×C43—22no—
497Q8×C43C23×C414yes—
498D4×C43—24no—
499D4×C43—22no—
500D4×C43C23×C414yes—
501C2×C4×C43—24no—
502C2×C4×C43—22no—
503C2×C4×C43—21no—
504C2×C4×C43—21no—
505C2×C4×C43—21no—
506C2×C4×C43—21no—
507C2×C4×C43—82no—
508C2×C4×C43—82no—
509C2×C4×C43C23×C412yes—
510C2×C4×C43C22×D412yes—
511C2×C4×C43C22×D412yes—
512C2×C4×C43C22×D411yescharacteristic
513C2×C4×C43C2×#4112yes—
514C2×C4×C43C2511yescharacteristic
515C22⋊D43—24no—
516C22⋊D43—24no—
517C22⋊D43—28no—
518C22⋊D43—28no—
519C22⋊D43C4×D418yes—
520C2×Dic43—21no—
521C2×Dic43—21no—
522C2×Dic43—28no—
523C2×Dic43—22no—
524C2×Dic43—22no—
525C2×Dic43—22no—
526C2×Dic43—41no—
527C2×Dic43—44no—
528C2×Dic43—82no—
529C2×Dic43—81no—
530C2×Dic43—81no—
531C2×Dic43C22×D411yescharacteristic
532C2×Dic43C22×D411yescharacteristic
533C2×Dic43C22×D411yescharacteristic
534C2×Dic43C22×D412yes—
535C2×Dic43C22×D411yescharacteristic
536D172—28no—
537D172—21no—
538D172—21no—
539D172C4×D414yes—
540D172C23×C412yes—
541D172C23×C412yes—
542C4×D43—28no—
543C4×D43—24no—
544C4×D43—24no—
545C4×D43—28no—
546C4×D43—24no—
547C4×D43—42no—
548C4×D43—42no—
549C4×D43—42no—
550C4×D43—81no—
551C4×D43—81no—
552C4×D43—82no—
553C4×D43—82no—
554C4×D43—82no—
555C4×D43—82no—
556C4×D43C23×C414yes—
557C4×D43C2×#4114yes—
558Dic86—21no—
559Dic86—21no—
560Dic86—28no—
561Dic86C4×D414yes—
562Dic86C23×C412yes—
563Dic86C23×C412yes—
564C8×C43—22no—
565C8×C43C23×C412yes—
566C8×C43C23×C412yes—
567C43⋊C8—21no—
568C43⋊C8—21no—
569C43⋊C8C23×C414yes—
570C4×#577—431nomaximal, Sylow
571C22×C43—21no—
572C22×C43—21no—
573C22×C43—24no—
574C22×C43—42no—
575C22×C43—42no—
576C22×C43—84no—
577C22×C43C2×C4×D412yes—
578C22×C43C23×D411yescharacteristic
579C2×D43—22no—
580C2×D43—22no—
581C2×D43—22no—
582C2×D43—22no—
583C2×D43—41no—
584C2×D43—41no—
585C2×D43—41no—
586C2×D43—41no—
587C2×D43—88no—
588C2×D43C2×C4×D414yes—
589C4×C43—22no—
590C4×C43—24no—
591C4×C43—22no—
592C4×C43—41no—
593C4×C43—41no—
594C4×C43—41no—
595C4×C43—41no—
596C4×C43C2×C4×D412yes—
597C4×C43C24×C411yescharacteristic
598C4×C43C22×#4111yescharacteristic
599Dic43—21no—
600Dic43—21no—
601Dic43—22no—
602Dic43—22no—
603Dic43—21no—
604Dic43—42no—
605Dic43—42no—
606Dic43C2×C4×D414yes—
607Dic43#57712yescomplemented
608C2×#577—431no—
609C4×2−1+4—431no—
610C4×H(5,𝔽2)—431no—
611#2952—432no—
612#2952—431no—
613#2949—432no—
614#2949D4311yescharacteristic, complemented
615#2947—432no—
616#2947—431no—
617#2946—432no—
618#2946—431no—
619C4×#137—432no—
620C4×#137—431no—
621C4×AGL(1,ℤ/8)—432no—
622C4×AGL(1,ℤ/8)—431no—
623C4×#135—432no—
624C4×#135—431no—
625C2×C4×SD16—432no—
626C2×C4×SD16—431no—
627#2912—431no—
628#2898—431no—
629#2897—431no—
630C4×#131—431no—
631C2×C43—22no—
632C2×C43—44no—
633C2×C43C22×C4×D411yescharacteristic
634C2×C43C2×#57711yescharacteristic
635C2×C43#358411yescharacteristic
636D43—24no—
637D43—42no—
638D43—42no—
639C2×2−1+4—431no—
640C2×H(5,𝔽2)—431no—
641#577—4316no—
642C2×#137—431no—
643C2×#137—432no—
644C2×AGL(1,ℤ/8)—431no—
645C2×AGL(1,ℤ/8)—432no—
646C2×#135—432no—
647C2×#135—431no—
648C22×SD16—432no—
649C22×SD16C2×D4311yescharacteristic
650C2×#131—431no—
651C2×#131—431no—
652#520—431no—
653#520—431no—
654#520—432no—
655#520—432no—
656#520—431no—
657#520—431no—
658#520—862no—
659#520—861no—
660#520—861no—
661#519—432no—
662#519—861no—
663#519C2×D4311yescharacteristic, complemented
664#518—432no—
665#518—862no—
666#518—861no—
667#518C2×D4311yescharacteristic
668C4×#41—431no—
669C4×#41—432no—
670C4×#41—432no—
671C4×#41—431no—
672C4×#41—431no—
673C4×#41—862no—
674C4×#41—861no—
675C4×#41—861no—
676C2×C4×Q8—431no—
677C2×C4×Q8—432no—
678C2×C4×Q8—861no—
679C2×C4×D4—431no—
680C2×C4×D4—432no—
681C2×C4×D4—862no—
682C2×C4×D4—861no—
683#442—432no—
684#442—432no—
685#442—432no—
686#441—432no—
687#441—432no—
688#441—432no—
689#440—432no—
690#440—432no—
691#440—432no—
692#440—432no—
693#440C2×D4312yescomplemented
694#440C2×D4312yescomplemented
695C4×Q16—432no—
696C4×Q16—431no—
697C4×Q16—431no—
698C4×Q16—432no—
699C4×SD16—432no—
700C4×SD16—432no—
701C4×SD16—432no—
702C4×SD16—432no—
703C4×SD16—432no—
704C4×SD16—432no—
705C4×SD16—431no—
706C4×SD16—431no—
707C4×SD16—431no—
708C4×SD16—431no—
709C4×SD16—432no—
710C4×SD16—432no—
711C4×SD16—432no—
712C4×SD16—432no—
713C4×SD16C2×D4312yescomplemented
714C4×SD16C2×D4312yescomplemented
715C4×D8—432no—
716C4×D8—431no—
717C4×D8—431no—
718C4×D8—432no—
719#428—431no—
720#428—431no—
721#428—432no—
722#428—432no—
723#427—432no—
724#427C2×D4311yescharacteristic, complemented
725C2×#106—431no—
726C2×#106—432no—
727#419—432no—
728#419C2×D4311yescharacteristic, complemented
729#418—432no—
730#418C2×D4311yescharacteristic
731#417—431no—
732#417—431no—
733#417—432no—
734#417—432no—
735#416—431no—
736#416—431no—
737#416—432no—
738#416—432no—
739C2×#103—431no—
740C2×#103—432no—
741C2×#102—431no—
742C2×#102—432no—
743#405—431no—
744#405—432no—
745#405—432no—
746#405C2×D4311yescharacteristic, complemented
747C4×M16—431no—
748C4×M16—432no—
749C2×C4×C8—431no—
750C2×C4×C8—432no—
751C43C4×#57711yescharacteristic, complemented, Sylow
7522−1+4—438no—
7532−1+4—864no—
754H(5,𝔽2)—438no—
755H(5,𝔽2)—864no—
756C2×#41—431no—
757C2×#41—432no—
758C2×#41—432no—
759C2×#41—431no—
760C2×#41—431no—
761C2×#41—862no—
762C2×#41—861no—
763C2×#41—861no—
764C22×Q8—432no—
765C22×Q8—861no—
766C22×Q8C22×D4311yescharacteristic
767C22×D4—432no—
768C22×D4—861no—
769C22×D4—862no—
770C22×D4C22×D4311yescharacteristic
771C23×C4—862no—
772C23×C4—861no—
773#137—438no—
774#137—4316no—
775AGL(1,ℤ/8)—438no—
776AGL(1,ℤ/8)—4316no—
777#135—4316no—
778#135—438no—
779C2×Q16—432no—
780C2×Q16—431no—
781C2×SD16—432no—
782C2×SD16—432no—
783C2×SD16—4316no—
784C2×SD16—431no—
785C2×SD16—431no—
786C2×SD16C4×D4318yescomplemented
787C2×SD16C22×D4312yes—
788C2×SD16C22×D4312yes—
789C2×D8—432no—
790C2×D8—431no—
791#131—438no—
792#131—864no—
793C2×M16—431no—
794C2×M16—432no—
795C2×M16—432no—
796C2×M16C22×D4311yescharacteristic
797C22×C8—432no—
798C22×C8—431no—
799C22×C8—432no—
800C22×C8C22×D4311yescharacteristic
801C4×Q8—21no—
802C4×Q8—21no—
803C4×Q8—431no—
804C4×Q8—431no—
805C4×Q8—432no—
806C4×Q8—432no—
807C4×Q8—431no—
808C4×Q8—431no—
809C4×Q8—431no—
810C4×Q8—431no—
811C4×Q8—432no—
812C4×Q8—432no—
813C4×Q8—862no—
814C4×Q8—862no—
815C4×Q8—861no—
816C4×Q8—861no—
817C4×Q8—862no—
818C4×Q8—861no—
819C4×Q8—861no—
820C4×Q8—862no—
821C4×Q8C22×D4312yes—
822C4×Q8C22×D4312yes—
823C4×D4—21no—
824C4×D4—21no—
825C4×D4—431no—
826C4×D4—431no—
827C4×D4—432no—
828C4×D4—432no—
829C4×D4—432no—
830C4×D4—432no—
831C4×D4—431no—
832C4×D4—431no—
833C4×D4—431no—
834C4×D4—431no—
835C4×D4—432no—
836C4×D4—432no—
837C4×D4—862no—
838C4×D4—862no—
839C4×D4—861no—
840C4×D4—861no—
841C4×D4—862no—
842C4×D4—862no—
843C4×D4—861no—
844C4×D4—861no—
845C4×D4—862no—
846C4×D4—862no—
847C4×D4—861no—
848C4×D4—862no—
849C4×D4—861no—
850C4×D4—861no—
851C4×D4—861no—
852C4×D4—862no—
853C4×D4—862no—
854C4×D4—862no—
855C4×D4—862no—
856C4×D4—862no—
857C4×D4—862no—
858C4×D4—862no—
859C4×D4—862no—
860C4×D4—862no—
861C4×D4C22×D4312yes—
862C4×D4C22×D4312yes—
863#117—22no—
864#117—432no—
865#117—432no—
866#117—432no—
867#117—861no—
868#117—861no—
869#117—862no—
870#117—862no—
871#117—862no—
872#117—862no—
873#117—862no—
874#117—862no—
875#117—861no—
876#117—861no—
877#117C22×D4311yescharacteristic
878#117C22×D4311yescharacteristic
879#117C22×D4311yescharacteristic
880C2×C4⋊C4—431no—
881C2×C4⋊C4—431no—
882C2×C4⋊C4—432no—
883C2×C4⋊C4—432no—
884C2×C4⋊C4—862no—
885C2×C4⋊C4—862no—
886C2×C4⋊C4—862no—
887C2×C4⋊C4—861no—
888C2×C4⋊C4—861no—
889C2×C4⋊C4—861no—
890C2×C22⋊C4—22no—
891C2×C22⋊C4—862no—
892C2×C22⋊C4—862no—
893C2×C22⋊C4—862no—
894C2×C22⋊C4—861no—
895C2×C42—431no—
896C2×C42—432no—
897C2×C42—861no—
898C2×C42—862no—
899C2×C42—861no—
900C2×C42—862no—
901C2×C42—862no—
902C2×C42—861no—
903#107—432no—
904#107—432no—
905#107C22×D4311yescharacteristic
906#107C22×D4311yescharacteristic
907#106—432no—
908#106—432no—
909#106—432no—
910#106—432no—
911#106C22×D4311yescharacteristic
912#106C22×D4311yescharacteristic
913#103—432no—
914#103—432no—
915#103—432no—
916#103—432no—
917#103—431no—
918#103—431no—
919#103—431no—
920#103—431no—
921#103C22×D4312yes—
922#103C22×D4312yes—
923#102—432no—
924#102—432no—
925#102—432no—
926#102—432no—
927#102—431no—
928#102—431no—
929#102—431no—
930#102—431no—
931#102C22×D4312yes—
932#102C22×D4312yes—
933#97—432no—
934#97—432no—
935#97C22×D4312yes—
936C4×C8—431no—
937C4×C8—432no—
938C4×C8—431no—
939C4×C8—431no—
940C4×C8—431no—
941C4×C8—432no—
942C4×C8C22×D4312yes—
943C24—21no—
944C24—862no—
945#41—434no—
946#41—434no—
947#41—438no—
948#41—438no—
949#41—434no—
950#41—434no—
951#41—8616no—
952#41—864no—
953#41—864no—
954#41—868no—
955#41—868no—
956#41—862no—
957#41—862no—
958C2×Q8—21no—
959C2×Q8—22no—
960C2×Q8—431no—
961C2×Q8—438no—
962C2×Q8—431no—
963C2×Q8—431no—
964C2×Q8—862no—
965C2×Q8—864no—
966C2×Q8—868no—
967C2×Q8C2×C4×D4314yescomplemented
968C2×Q8C23×D4312yes—
969C2×D4—21no—
970C2×D4—22no—
971C2×D4—432no—
972C2×D4—438no—
973C2×D4—431no—
974C2×D4—431no—
975C2×D4—431no—
976C2×D4—862no—
977C2×D4—864no—
978C2×D4—862no—
979C2×D4—868no—
980C2×D4—8616no—
981C2×D4—862no—
982C2×D4—861no—
983C2×D4—861no—
984C2×D4C2×C4×D4314yes—
985C2×D4C23×D4312yes—
986C22×C4—21no—
987C22×C4—22no—
988C22×C4—22no—
989C22×C4—432no—
990C22×C4—431no—
991C22×C4—431no—
992C22×C4—432no—
993C22×C4—432no—
994C22×C4—862no—
995C22×C4—861no—
996C22×C4—861no—
997C22×C4—861no—
998C22×C4—861no—
999C22×C4—862no—
1000C22×C4—862no—
1001C22×C4—862no—
1002C22×C4—862no—
1003C22×C4—862no—
1004C22×C4—862no—
1005C22×C4—861no—
1006C22×C4—861no—
1007C22×C4—861no—
1008C22×C4—861no—
1009C22×C4—862no—
1010C22×C4—862no—
1011C22×C4—3444no—
1012C22×C4—3442no—
1013C22×C4C23×D4311yescharacteristic
1014Q16—438no—
1015Q16—434no—
1016SD16—438no—
1017SD16—438no—
1018SD16—434no—
1019SD16—434no—
1020SD16C2×C4×D4318yescomplemented
1021SD16C2×C4×D4318yescomplemented
1022D8—438no—
1023D8—434no—
1024M16—22no—
1025M16—434no—
1026M16—438no—
1027M16—864no—
1028C2×C8—432no—
1029C2×C8—438no—
1030C2×C8—431no—
1031C2×C8—431no—
1032C2×C8—864no—
1033C2×C8—862no—
1034C2×C8C2×C4×D4314yescomplemented
1035C2×C8C23×D4312yes—
1036C2×C8C23×D4311yescharacteristic
1037C2×C8C23×D4311yescharacteristic
1038C4⋊C4—22no—
1039C4⋊C4—22no—
1040C4⋊C4—432no—
1041C4⋊C4—432no—
1042C4⋊C4—432no—
1043C4⋊C4—432no—
1044C4⋊C4—862no—
1045C4⋊C4—862no—
1046C4⋊C4—861no—
1047C4⋊C4—861no—
1048C4⋊C4—862no—
1049C4⋊C4—862no—
1050C4⋊C4—861no—
1051C4⋊C4—861no—
1052C4⋊C4—861no—
1053C4⋊C4—861no—
1054C4⋊C4—862no—
1055C4⋊C4—862no—
1056C4⋊C4D4×D4311yescharacteristic
1057C4⋊C4D4×D4311yescharacteristic
1058C4⋊C4C23×D4311yescharacteristic
1059C4⋊C4C23×D4311yescharacteristic
1060C4⋊C4C23×D4311yescharacteristic
1061C4⋊C4C23×D4311yescharacteristic
1062C22⋊C4—21no—
1063C22⋊C4—21no—
1064C22⋊C4—22no—
1065C22⋊C4—22no—
1066C22⋊C4—432no—
1067C22⋊C4—432no—
1068C22⋊C4—861no—
1069C22⋊C4—861no—
1070C22⋊C4—861no—
1071C22⋊C4—861no—
1072C22⋊C4—862no—
1073C22⋊C4—862no—
1074C22⋊C4—862no—
1075C22⋊C4—862no—
1076C22⋊C4—862no—
1077C22⋊C4—862no—
1078C22⋊C4D4×D4312yes—
1079C42—22no—
1080C42—22no—
1081C42—21no—
1082C42—21no—
1083C42—432no—
1084C42—431no—
1085C42—432no—
1086C42—431no—
1087C42—431no—
1088C42—431no—
1089C42—861no—
1090C42—862no—
1091C42—861no—
1092C42—862no—
1093C42—862no—
1094C42—861no—
1095C42—862no—
1096C42—861no—
1097C42—862no—
1098C42—862no—
1099C42C23×D4312yes—
1100C23—22no—
1101C23—24no—
1102C23—81no—
1103C23—81no—
1104C23—432no—
1105C23—868no—
1106C23—861no—
1107C23—861no—
1108C23—3442no—
1109C23—3442no—
1110C23C2×D4×D4311yescharacteristic
1111Q8—24no—
1112Q8—22no—
1113Q8—434no—
1114Q8—432no—
1115Q8—432no—
1116Q8—868no—
1117Q8—861no—
1118Q8—861no—
1119Q8C22×C4×D4314yes—
1120D4—24no—
1121D4—22no—
1122D4—438no—
1123D4—434no—
1124D4—432no—
1125D4—432no—
1126D4—868no—
1127D4—868no—
1128D4—868no—
1129D4—864no—
1130D4—864no—
1131D4—861no—
1132D4—861no—
1133D4C22×C4×D4314yes—
1134C2×C4—24no—
1135C2×C4—22no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—82no—
1141C2×C4—82no—
1142C2×C4—431no—
1143C2×C4—432no—
1144C2×C4—434no—
1145C2×C4—434no—
1146C2×C4—431no—
1147C2×C4—431no—
1148C2×C4—431no—
1149C2×C4—864no—
1150C2×C4—868no—
1151C2×C4—868no—
1152C2×C4—862no—
1153C2×C4—868no—
1154C2×C4—861no—
1155C2×C4—861no—
1156C2×C4—864no—
1157C2×C4—864no—
1158C2×C4—862no—
1159C2×C4—862no—
1160C2×C4—3442no—
1161C2×C4—3442no—
1162C2×C4—3441no—
1163C2×C4—3441no—
1164C2×C4—3442no—
1165C2×C4—3442no—
1166C2×C4—3442no—
1167C2×C4—3441no—
1168C2×C4—3441no—
1169C2×C4—1722no—
1170C2×C4—1722no—
1171C2×C4—1722no—
1172C2×C4—1724no—
1173C2×C4—1721no—
1174C2×C4C22×C4×D4312yes—
1175C2×C4C2×D4×D4312yes—
1176C2×C4C2×D4×D4312yes—
1177C2×C4C2×D4×D4311yescharacteristic
1178C2×C4#41×D4312yes—
1179C2×C4C24×D4311yescharacteristic
1180C8—22no—
1181C8—434no—
1182C8—861no—
1183C8—861no—
1184C8C22×C4×D4312yes—
1185C8C22×C4×D4312yes—
1186C22—21no—
1187C22—21no—
1188C22—24no—
1189C22—42no—
1190C22—42no—
1191C22—84no—
1192C22—434no—
1193C22—862no—
1194C22—862no—
1195C22—862no—
1196C22—862no—
1197C22—3448no—
1198C22—1721no—
1199C22—1721no—
1200C22—1721no—
1201C22—1721no—
1202C22C4×D4×D4312yes—
1203C22C22×D4×D4311yescharacteristic
1204C4—22no—
1205C4—22no—
1206C4—24no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—432no—
1212C4—434no—
1213C4—861no—
1214C4—861no—
1215C4—861no—
1216C4—862no—
1217C4—862no—
1218C4—1722no—
1219C4—1722no—
1220C4C4×D4×D4312yes—
1221C4C23×C4×D4311yescharacteristic
1222C4C2×#41×D4311yescharacteristic
1223C2—22no—
1224C2—44no—
1225C2—864no—
1226C2—1722no—
1227C2—1722no—
1228C2C2×C4×D4×D4311yescharacteristic
1229C2#577×D4311yescharacteristic
1230C2#1914936711yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC43×#2949C2
socleC22×C43C23×D4
prime radicalC2×#14583705C2
cosocleC2×C4×C43C25
hypercenter#2949D43
hypocenterC43C4×#577
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ #117 ◁ #2949

Complements

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

NH ≅ G/Ntype
2. #19147804C2semidirect
3. #19147799C2semidirect
4. #19143480C2semidirect
5. #19143473C2semidirect
6. #19143449C2semidirect
7. #19143438C2semidirect
8. #19143435C2semidirect
9. #19143427C2semidirect
10. #19143426C2semidirect
11. #19143417C2semidirect
12. #19143410C2semidirect
13. #19143400C2semidirect
14. #19143399C2semidirect
15. #19143366C2semidirect
16. C4×#13063346C2semidirect
17. C2×SD16×Dic43C2semidirect
18. C4×SD16×D43C2semidirect
19. #19143187C2semidirect
20. #19143127C2semidirect
21. #19143120C2semidirect
22. #19143017C2semidirect
23. C43×#2949C2semidirect
26. #14583705C4semidirect
37. #14583381C22semidirect
42. #14583379C22semidirect
46. #14583375C22semidirect
51. C4×#10621902C22semidirect
55. #14583367C22semidirect
58. C2×Q8×Dic43C22semidirect
60. C4×Q8×D43C22semidirect
65. #14583012C22semidirect
66. #14583009C22semidirect
67. #14583008C22semidirect
68. #14583007C22semidirect
69. #14583004C22semidirect
70. #14583003C22semidirect
71. #14583002C22semidirect
72. #14582999C22semidirect
73. #14582997C22semidirect
74. #14582996C22semidirect
75. #14582993C22semidirect
76. #14582993C22semidirect
77. C4×#10621885C22semidirect
78. #14582991C22semidirect
79. #14582990C22semidirect
80. C4×#10621873C22semidirect
81. C4×#10621873C22semidirect
82. SD16×Dic43C22semidirect
83. SD16×Dic43C22semidirect
84. SD16×Dic43C22semidirect
85. SD16×Dic43C22semidirect
86. C4×#10621884C22semidirect
87. #14582986C22semidirect
88. #14582986C22semidirect
89. #14582986C22semidirect
90. #14582986C22semidirect
91. C4×#10621883C22semidirect
92. #14582984C22semidirect
93. #14582981C22semidirect
94. #14582981C22semidirect
95. C4×#10621882C22semidirect
96. #14582979C22semidirect
97. #14582942C22semidirect
98. #14582942C22semidirect
99. #14582940C22semidirect
100. #14582940C22semidirect
101. #14582934C22semidirect
102. C2×#13063257C22semidirect
103. #106×D43C22semidirect
104. #14582906C22semidirect
107. #14582901C22semidirect
108. #14582899C22semidirect
110. #14582894C22semidirect
112. #14582893C22semidirect
114. C2×#13063249C22semidirect
115. #103×D43C22semidirect
118. #14582856C22semidirect
119. #14582855C22semidirect
120. #14582853C22semidirect
121. #14582851C22semidirect
122. M16×Dic43C22semidirect
123. C2×C8×Dic43C22semidirect
124. C4×C8×D43C22semidirect
126. C43×#519C22semidirect
128. C43×#440C22semidirect
129. C43×#440C22semidirect
130. C4×SD16×C43C22semidirect
131. C4×SD16×C43C22semidirect
132. C43×#427C22semidirect
133. C43×#419C22semidirect
135. C43×#405C22semidirect
137. #13063373C2×C4semidirect
139. #13063370C2×C4semidirect
155. #13063356C2×C4semidirect
156. #13063354C2×C4semidirect
157. #13063352C2×C4semidirect
158. #13063351C2×C4semidirect
159. #13063347C2×C4semidirect
160. #13063346C2×C4semidirect
167. SD16×D43C2×C4semidirect
171. #13063331C2×C4semidirect
299. C2×SD16×C43C2×C4semidirect
331. C2×Q8×C43C22×C4semidirect
357. #10621902C22×C4semidirect
360. Q8×D43C22×C4semidirect
372. #10621898C22×C4semidirect
398. SD16×C43C22×C4semidirect
399. SD16×C43C22×C4semidirect
401. C2×C8×C43C22×C4semidirect
425. #10621885C22×C4semidirect
426. #10621884C22×C4semidirect
427. #10621883C22×C4semidirect
428. #10621882C22×C4semidirect
471. #10621877C22×C4semidirect
476. Dic172C22×C4semidirect
477. D344C22×C4semidirect
478. #10621873C22×C4semidirect
479. #10621873C22×C4semidirect
481. #10621872C22×C4semidirect
483. C8×D43C22×C4semidirect
607. Dic43#577semidirect
614. #2949D43semidirect
663. #519C2×D43semidirect
693. #440C2×D43semidirect
694. #440C2×D43semidirect
713. C4×SD16C2×D43semidirect
714. C4×SD16C2×D43semidirect
724. #427C2×D43semidirect
728. #419C2×D43semidirect
746. #405C2×D43semidirect
751. C43C4×#577semidirect
786. C2×SD16C4×D43semidirect
967. C2×Q8C2×C4×D43semidirect
1020. SD16C2×C4×D43semidirect
1021. SD16C2×C4×D43semidirect
1034. C2×C8C2×C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145837052
#191478042
#191477992
#191434802
#191434732
#191434492
#191434382
#191434352
#191434272
#191434262
#191434172
#191434102
#191434002
#191433992
#191433662
C4×#130633462
C2×SD16×Dic432
C4×SD16×D432
#191431872
#191431272
#191431202
#191430172
C43×#29492
C4×#57743