Finite Group Databasebeta

← #25968861

Subgroups — #25968861

Order 11008.

2006 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
3#19145829C212yesmaximal, complemented
4#19145824C212yesmaximal, complemented
5#19145820C212yesmaximal, complemented
6#19145815C212yesmaximal, complemented
7#19145745C212yesmaximal, complemented
8#19145738C212yesmaximal, complemented
9#19145722C212yesmaximal, complemented
10#19145715C212yesmaximal, complemented
11#19145139C212yesmaximal, complemented
12#19144986C212yesmaximal, complemented
13#19144521C212yesmaximal, complemented
14#19144516C212yesmaximal, complemented
15#19144411C211yesmaximal, characteristic, complemented
16#19144410C211yesmaximal, characteristic, complemented
17#19144404C211yesmaximal, characteristic, complemented
18#19143227C211yesmaximal, characteristic, complemented
19C43×#3079C211yesmaximal, characteristic, complemented
20C22×Q8×D43—21no—
21#14583453C2211yescharacteristic
22#14583453C2211yescharacteristic
23#14583452C2211yescharacteristic
24#14583446C2211yescharacteristic
25#14583446C2211yescharacteristic
26#14583445C2211yescharacteristic
27C2×#13063325C2211yescharacteristic
28C2×#13063324—21no—
29C2×#13063324C2212yes—
30C2×#13063323—21no—
31C4⋊Q8×D43—21no—
32C4⋊Q8×D43—21no—
33C4⋊Q8×D43—21no—
34C4⋊Q8×D43—21no—
35C4⋊Q8×D43C2212yes—
36C4⋊Q8×D43C2212yes—
37C4⋊Q8×D43C2212yes—
38C4⋊Q8×D43C2212yes—
39#14583436C2211yescharacteristic
40#14583436C2211yescharacteristic
41#14583431C2211yescharacteristic
42#14583431C2211yescharacteristic
43#14583429—21no—
44#14583429—21no—
45#14583427—21no—
46#14583427—21no—
47#14583411C2211yescharacteristic
48#14583408—21no—
49#14583408—21no—
50#14583406C2211yescharacteristic
51C4×#10621898—21no—
52C4×#10621898—21no—
53C4×#10621898C2211yescharacteristic
54C2×C4⋊C4×D43—21no—
55C2×C4⋊C4×D43C2212yes—
56C2×C42×D43C2211yescharacteristic
57#14583307C2214yescomplemented
58#14583306C2214yescomplemented
59#14583303C2214yescomplemented
60#14583296C2214yescomplemented
61#14583260C2214yescomplemented
62#14583257C2214yescomplemented
63#14583248C2214yescomplemented
64#14583244C2214yescomplemented
65#14583236C2214yes—
66#14583233C2214yes—
67#14583231C2214yes—
68#14583228C2214yes—
69#14583219C2214yes—
70#14583216C2214yes—
71#14583214C2214yes—
72#14583211C2214yes—
73#14583195C2212yescomplemented
74#14583194C2212yescomplemented
75#14583191C2212yescomplemented
76#14583190C2212yescomplemented
77#14583189C2212yescomplemented
78#14583186C2212yescomplemented
79#14583185C2212yescomplemented
80#14583184C2212yescomplemented
81#14583181C2212yescomplemented
82#14583180C2212yescomplemented
83#14583179C2212yescomplemented
84#14583176C2212yescomplemented
85#14582955C2212yes—
86#14582955C2212yes—
87#14582951C2212yes—
88#14582951C2212yes—
89#14582942C2212yes—
90#14582941C2212yes—
91#14582939C2212yes—
92#14582923C2211yescharacteristic
93#14582901C2212yes—
94#14582900C2212yes—
95#14582898C2212yes—
96#14582862C2212yes—
97M16×Dic43C2212yes—
98C2×C4⋊Q8×C43C2211yescharacteristic
99C4×#41×C43C2211yescharacteristic
100C43×#477C2212yescomplemented
101C43×#476C2212yescomplemented
102C43×#475C2212yescomplemented
103C43×#474C2212yescomplemented
104C43×#428C2212yes—
105C43×#423C2211yescharacteristic
106C43×#417C2212yes—
107C2×#10621898—21no—
108C2×#10621898—21no—
109C2×#10621898C2311yescharacteristic
110C22×Dic86—21no—
111C22×Dic86—22no—
112C2×Q8×D43—22no—
113C2×Q8×D43—22no—
114C2×Q8×D43—22no—
115C2×Q8×D43—22no—
116C2×Q8×D43—48no—
117C22×C4×D43—22no—
118C22×C4×D43D411yescharacteristic
119C22×C4×D43D411yescharacteristic
120C22×C4×D43C2311yescharacteristic
121C2×#10621877C2312yes—
122#13063325—21no—
123#13063325—21no—
124#13063325C2312yes—
125#13063325C2312yes—
126#13063324—22no—
127#13063324—22no—
128#13063324—22no—
129#13063324—22no—
130#13063324—22no—
131#13063324—22no—
132#13063324C2311yescharacteristic
133#13063324C2314yes—
134#13063324C2311yescharacteristic
135#13063324C2314yes—
136#13063323—22no—
137#13063323—22no—
138#13063323—22no—
139#13063323—22no—
140#13063323C2311yescharacteristic
141#13063321C2311yescharacteristic
142#13063320—21no—
143#13063320—21no—
144#13063318—21no—
145#13063318—21no—
146#13063316C2311yescharacteristic
147#13063316C2311yescharacteristic
148#13063315—21no—
149#13063315—21no—
150#13063314C2311yescharacteristic
151#13063312C2311yescharacteristic
152#13063311—21no—
153#13063311—21no—
154#13063310—21no—
155#13063310—21no—
156#13063309—21no—
157#13063307—21no—
158#13063307—21no—
159#13063306—21no—
160#13063305C2311yescharacteristic
161#13063305C2311yescharacteristic
162#13063303—21no—
163#13063303—21no—
164#13063302—21no—
165#13063302—21no—
166#13063301C2311yescharacteristic
167#13063301C2311yescharacteristic
168#13063300C2311yescharacteristic
169#13063300C2311yescharacteristic
170#13063298—21no—
171#13063298—21no—
172#13063297—21no—
173#13063297—21no—
174#13063296C2311yescharacteristic
175#13063296C2311yescharacteristic
176#13063295—21no—
177#13063293—21no—
178C4×Dic86—21no—
179C4×Dic86—21no—
180C4×Dic86—21no—
181C4×Dic86—21no—
182C4×Dic86C2311yescharacteristic
183C4×Dic86C2311yescharacteristic
184C4×D172—21no—
185C4×D172—21no—
186C4×D172—21no—
187C4×D172—21no—
188C4×D172C2311yescharacteristic
189C4×D172C2311yescharacteristic
190C4×C22⋊D43—21no—
191C4×C22⋊D43—21no—
192C4×C22⋊D43—21no—
193C4×C22⋊D43—21no—
194C4×C22⋊D43—21no—
195C4×C22⋊D43—21no—
196C4×C22⋊D43—21no—
197C4×C22⋊D43—21no—
198C4×C22⋊D43—21no—
199C4×C22⋊D43—21no—
200#13063284—21no—
201#13063284—21no—
202#13063284C2311yescharacteristic
203#13063282—21no—
204#13063282—21no—
205#13063282—21no—
206#13063282—21no—
207#13063282—21no—
208C2×C4⋊Dic43—21no—
209C2×C4⋊Dic43C2312yes—
210C2×Dic43⋊C4—22no—
211C2×Dic43⋊C4—22no—
212C4⋊C4×D43—22no—
213C4⋊C4×D43—22no—
214C4⋊C4×D43—22no—
215C4⋊C4×D43—22no—
216C4⋊C4×D43—22no—
217C4⋊C4×D43—22no—
218C4⋊C4×D43C2314yes—
219C4⋊C4×D43C2314yes—
220C2×C4×Dic43D411yescharacteristic
221C2×C4×Dic43D411yescharacteristic
222C2×C4×Dic43C2311yescharacteristic
223C42×D43—21no—
224C42×D43D411yescharacteristic
225C42×D43D411yescharacteristic
226C42×D43D411yescharacteristic
227C42×D43D411yescharacteristic
228C42×D43C2311yescharacteristic
229C42×D43C2311yescharacteristic
230C42×D43C2311yescharacteristic
231C42×D43C2311yescharacteristic
232#13063259C2314yes—
233#13063258C2314yes—
234#13063258C2314yes—
235#13063257C2314yes—
236#13063256C2314yes—
237#13063256C2314yes—
238C4⋊(C43⋊C8)C2312yes—
239C4⋊(C43⋊C8)C2312yes—
240#13063250C2314yes—
241#13063249C2314yes—
242#13063248C2314yes—
243#13063247C2314yes—
244#13063246C2314yes—
245#13063245C2314yes—
246(C2×D43)⋊C8C2314yes—
247(C2×D43)⋊C8C2314yes—
248#13063235C2314yes—
249C8×Dic43C2314yes—
250C2×#41×C43C2311yescharacteristic
251C22×Q8×C43—21no—
252C2×M16×C43C2312yes—
253C4⋊Q8×C43—21no—
254C4⋊Q8×C43—21no—
255C4⋊Q8×C43C2312yes—
256C4⋊Q8×C43C2312yes—
257C4×Q8×C43C2311yescharacteristic
258C4×Q8×C43C2311yescharacteristic
259C4×D4×C43—21no—
260C4×D4×C43—21no—
261C4×D4×C43C2311yescharacteristic
262C4×D4×C43C2311yescharacteristic
263#117×C43—21no—
264#117×C43C2311yescharacteristic
265C2×C4⋊C4×C43—21no—
266C2×C4⋊C4×C43C2312yes—
267C2×C42×C43—21no—
268C2×C42×C43C2311yescharacteristic
269#107×C43C2314yes—
270#106×C43C2314yes—
271C4⋊C8×C43C2312yes—
272C4⋊C8×C43C2312yes—
273#103×C43C2314yes—
274#102×C43C2314yes—
275C23×D43C2×D411yescharacteristic
276#41×C43—22no—
277#41×C43—22no—
278C2×Q8×C43—22no—
279C2×Q8×C43—22no—
280C2×Q8×C43—44no—
281C2×Q8×C43C2411yescharacteristic
282C2×D4×C43—21no—
283C2×D4×C43C2411yescharacteristic
284C22×C4×C43—21no—
285C22×C4×C43—21no—
286C22×C4×C43—21no—
287C22×C4×C43—22no—
288C22×C4×C43C2×D411yescharacteristic
289C22×C4×C43C2×D411yescharacteristic
290C22×C4×C43C2411yescharacteristic
291C2×C22⋊D43—21no—
292C2×C22⋊D43—21no—
293C2×C22⋊D43—21no—
294C2×C22⋊D43—21no—
295C2×C22⋊D43—21no—
296C22×Dic43—22no—
297C22×Dic43C2×D411yescharacteristic
298C22×Dic43C2×D411yescharacteristic
299C22×Dic43C2×D411yescharacteristic
300Q8×D43—48no—
301Q8×D43—48no—
302Q8×D43—48no—
303Q8×D43—48no—
304#10621898—22no—
305#10621898—22no—
306#10621898—44no—
307#10621898—44no—
308C2×D172—21no—
309C2×D172—21no—
310C2×D172C2411yescharacteristic
311C2×C4×D43—22no—
312C2×C4×D43—22no—
313C2×C4×D43—24no—
314C2×C4×D43—24no—
315C2×C4×D43—21no—
316C2×C4×D43—21no—
317C2×C4×D43—21no—
318C2×C4×D43—24no—
319C2×C4×D43—24no—
320C2×C4×D43—48no—
321C2×C4×D43C2×D411yescharacteristic
322C2×C4×D43C2×D411yescharacteristic
323C2×C4×D43C2×D411yescharacteristic
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2×D411yescharacteristic
328C2×C4×D43C2×D411yescharacteristic
329C2×C4×D43C2×D411yescharacteristic
330C2×C4×D43C2×D411yescharacteristic
331C2×C4×D43C2411yescharacteristic
332C2×C4×D43C2411yescharacteristic
333C2×Dic86—22no—
334C2×Dic86—22no—
335C2×Dic86—21no—
336C2×Dic86—21no—
337C2×Dic86—24no—
338C2×Dic86—24no—
339C2×Dic86—48no—
340C2×Dic86—44no—
341C2×Dic86C2411yescharacteristic
342M16×C43—24no—
343C2×C8×C43C2414yes—
344C4⋊C4×C43—22no—
345C4⋊C4×C43—22no—
346C4⋊C4×C43—22no—
347C4⋊C4×C43—21no—
348C4⋊C4×C43—21no—
349C4⋊C4×C43C2414yes—
350C4⋊C4×C43C2411yescharacteristic
351C4⋊C4×C43C2411yescharacteristic
352C22⋊C4×C43—21no—
353C22⋊C4×C43—21no—
354C22⋊C4×C43—21no—
355C42×C43—21no—
356C42×C43—21no—
357C42×C43—21no—
358C42×C43C2×D411yescharacteristic
359C42×C43C2×D411yescharacteristic
360C42×C43C2411yescharacteristic
361C42×C43C2411yescharacteristic
362C22⋊Dic43—21no—
363C22⋊Dic43—21no—
364C22⋊Dic43—21no—
365C22⋊Dic43—21no—
366C22⋊Dic43—21no—
367(C2×D43)⋊C4—21no—
368(C2×D43)⋊C4—21no—
369(C2×D43)⋊C4—21no—
370(C2×D43)⋊C4—21no—
371(C2×D43)⋊C4—21no—
372(C2×D43)⋊C4—21no—
373(C2×D43)⋊C4—21no—
374(C2×D43)⋊C4—21no—
375(C2×D43)⋊C4—21no—
376(C2×D43)⋊C4—21no—
377C4⋊Dic43—22no—
378C4⋊Dic43—22no—
379C4⋊Dic43—22no—
380C4⋊Dic43—21no—
381C4⋊Dic43—21no—
382C4⋊Dic43—21no—
383C4⋊Dic43—21no—
384C4⋊Dic43C2414yes—
385C4⋊Dic43C2411yescharacteristic
386C4⋊Dic43C2411yescharacteristic
387Dic43⋊C4—21no—
388Dic43⋊C4—21no—
389Dic43⋊C4—24no—
390Dic43⋊C4—24no—
391Dic43⋊C4—24no—
392Dic43⋊C4—24no—
393Dic43⋊C4—21no—
394Dic43⋊C4—21no—
395Dic43⋊C4—21no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—21no—
400Dic43⋊C4—21no—
401C4×Dic43—21no—
402C4×Dic43—21no—
403C4×Dic43—21no—
404C4×Dic43C2×D411yescharacteristic
405C4×Dic43C2×D411yescharacteristic
406C4×Dic43C2×D411yescharacteristic
407C4×Dic43C2×D411yescharacteristic
408C4×Dic43C2×D411yescharacteristic
409C4×Dic43C2×D411yescharacteristic
410C4×Dic43C2×D411yescharacteristic
411C4×Dic43C2×D411yescharacteristic
412C4×Dic43C2×D411yescharacteristic
413C4×Dic43C2×D411yescharacteristic
414C4×Dic43C2411yescharacteristic
415C4×Dic43C2411yescharacteristic
416#10621877—24no—
417C2×C43⋊C8C2414yes—
418C23×C43—21no—
419C23×C43C22×D411yescharacteristic
420C22×D43—22no—
421C22×D43—22no—
422C22×D43—22no—
423C22×D43—21no—
424C22×D43C22×D411yescharacteristic
425C22×D43C22×D411yescharacteristic
426Q8×C43—21no—
427Q8×C43—21no—
428Q8×C43—44no—
429Q8×C43—44no—
430D4×C43—21no—
431D4×C43—21no—
432D4×C43—42no—
433C2×C4×C43—22no—
434C2×C4×C43—22no—
435C2×C4×C43—21no—
436C2×C4×C43—24no—
437C2×C4×C43—21no—
438C2×C4×C43—21no—
439C2×C4×C43—44no—
440C2×C4×C43—42no—
441C2×C4×C43—42no—
442C2×C4×C43—42no—
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C22×D411yescharacteristic
445C2×C4×C43C22×D411yescharacteristic
446C2×C4×C43C22×D411yescharacteristic
447C2×C4×C43C22×D411yescharacteristic
448C2×C4×C432−1+412yes—
449C2×C4×C432−1+412yes—
450C2×C4×C43C2511yescharacteristic
451C22⋊D43—42no—
452C22⋊D43—42no—
453C22⋊D43—42no—
454C22⋊D43—42no—
455C22⋊D43—42no—
456C2×Dic43—22no—
457C2×Dic43—22no—
458C2×Dic43—22no—
459C2×Dic43—21no—
460C2×Dic43—21no—
461C2×Dic43—21no—
462C2×Dic43—24no—
463C2×Dic43—44no—
464C2×Dic43C22×D411yescharacteristic
465C2×Dic43C22×D411yescharacteristic
466C2×Dic43C22×D411yescharacteristic
467C2×Dic43C22×D411yescharacteristic
468C2×Dic43C22×D411yescharacteristic
469C2×Dic43C22×D411yescharacteristic
470D172—21no—
471D172—21no—
472D172—42no—
473D172—42no—
474C4×D43—22no—
475C4×D43—22no—
476C4×D43—22no—
477C4×D43—22no—
478C4×D43—22no—
479C4×D43—22no—
480C4×D43—21no—
481C4×D43—21no—
482C4×D43—21no—
483C4×D43—21no—
484C4×D43—22no—
485C4×D43—22no—
486C4×D43—48no—
487C4×D43—48no—
488C4×D43—42no—
489C4×D43—42no—
490C4×D43—42no—
491C4×D43AGL(1,ℤ/8)14yes—
492C4×D43#13714yes—
493Dic86—21no—
494Dic86—21no—
495Dic86—48no—
496Dic86—44no—
497Dic86—44no—
498Dic86—48no—
499Dic86—42no—
500Dic86—42no—
501C8×C43—24no—
502C43⋊C8—24no—
503#60860—431nomaximal, Sylow
504C22×C43—21no—
505C22×C43—21no—
506C22×C43—41no—
507C22×C43—41no—
508C22×C43—41no—
509C22×C43#53612yes—
510C22×C43C23×D411yescharacteristic
511C2×D43—28no—
512C2×D43—21no—
513C2×D43—21no—
514C2×D43—21no—
515C2×D43—21no—
516C2×D43—41no—
517C2×D43—41no—
518C2×D43—41no—
519C2×D43C2×AGL(1,ℤ/8)12yes—
520C2×D43C2×#13712yes—
521C4×C43—21no—
522C4×C43—21no—
523C4×C43—41no—
524C4×C43—44no—
525C4×C43—41no—
526C4×C43—41no—
527C4×C43#53612yes—
528C4×C43C2×AGL(1,ℤ/8)12yes—
529C4×C43C2×#13712yes—
530C4×C43C2×2−1+411yescharacteristic
531C4×C43C2×2−1+411yescharacteristic
532Dic43—21no—
533Dic43—21no—
534Dic43—21no—
535Dic43—21no—
536Dic43—41no—
537Dic43—44no—
538Dic43—41no—
539Dic43—41no—
540Dic43C2×AGL(1,ℤ/8)12yes—
541Dic43C2×#13712yes—
542#3444—431no—
543C22×C4⋊Q8—431no—
544#3239—432no—
545#3239—432no—
546#3238—432no—
547#3238—432no—
548#3230—432no—
549#3229—432no—
550#3227—432no—
551#3226—432no—
552#3165—432no—
553#3141—432no—
554#3092—432no—
555#3092—432no—
556#3079—431no—
557#3079—431no—
558#3079—431no—
559#3079D4311yescharacteristic, complemented
560#2920—431no—
561C2×C43—22no—
562C2×C43—81no—
563C2×C43C2×#53611yescharacteristic
564C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
565C2×C43C22×#13711yescharacteristic
566D43—22no—
567D43—22no—
568D43—81no—
569C23×Q8—861no—
570#533—431no—
571#533—431no—
572#533—431no—
573#532—431no—
574#532—431no—
575#532—431no—
576C2×C4⋊Q8—432no—
577C2×C4⋊Q8—432no—
578C2×C4⋊Q8—432no—
579C2×C4⋊Q8—432no—
580C2×C4⋊Q8—432no—
581C2×C4⋊Q8—431no—
582C2×C4⋊Q8—861no—
583C2×C4⋊Q8—861no—
584C2×C4⋊Q8—861no—
585C2×C4⋊Q8—861no—
586C2×C4⋊Q8—861no—
587C2×C4⋊Q8—861no—
588C2×C4⋊Q8C2×D4311yescharacteristic
589#529—431no—
590#529—431no—
591#529—431no—
592#529—431no—
593#529—861no—
594#529—861no—
595#529—861no—
596#529—861no—
597#525—431no—
598#525—431no—
599#525—861no—
600#525—861no—
601C4×#41—431no—
602C4×#41—861no—
603C4×#41—861no—
604C4×#41C2×D4311yescharacteristic
605C22×C4⋊C4—432no—
606C22×C4⋊C4—861no—
607C22×C42—431no—
608#501—434no—
609#501—434no—
610#500—434no—
611#498—434no—
612#489—434no—
613#489—434no—
614#487—434no—
615#486—434no—
616#484—434no—
617#484—434no—
618#483—434no—
619#483—434no—
620#481—434no—
621#481—434no—
622#480—434no—
623#480—434no—
624#477—432no—
625#477—432no—
626#477—432no—
627#477C2×D4312yescomplemented
628#476—432no—
629#476—432no—
630#476—432no—
631#476C2×D4312yescomplemented
632#475—432no—
633#475—432no—
634#475—432no—
635#475C2×D4312yescomplemented
636#474—432no—
637#474—432no—
638#474—432no—
639#474C2×D4312yescomplemented
640#432—432no—
641#432—432no—
642#431—432no—
643#431—432no—
644#428—432no—
645#428—432no—
646#428—432no—
647#428C2×D4312yes—
648#423—431no—
649#423C2×D4311yescharacteristic
650#417—432no—
651#417—432no—
652#417—432no—
653#417C2×D4312yes—
654#407—432no—
655C4×M16—432no—
656C43#6086011yescharacteristic, complemented, Sylow
657C2×#41—431no—
658C2×#41—861no—
659C2×#41—861no—
660C2×#41C22×D4311yescharacteristic
661C22×Q8—21no—
662C22×Q8—862no—
663C22×Q8—862no—
664C22×Q8—862no—
665C22×Q8—862no—
666C22×Q8—862no—
667C22×Q8—861no—
668C22×Q8—1728no—
669C23×C4—431no—
670C23×C4—431no—
671C23×C4—431no—
672C23×C4—862no—
673C2×M16—432no—
674C2×M16C22×D4312yes—
675C4⋊Q8—21no—
676C4⋊Q8—21no—
677C4⋊Q8—434no—
678C4⋊Q8—434no—
679C4⋊Q8—431no—
680C4⋊Q8—431no—
681C4⋊Q8—431no—
682C4⋊Q8—432no—
683C4⋊Q8—432no—
684C4⋊Q8—862no—
685C4⋊Q8—862no—
686C4⋊Q8—862no—
687C4⋊Q8—862no—
688C4⋊Q8—862no—
689C4⋊Q8—862no—
690C4⋊Q8—862no—
691C4⋊Q8—862no—
692C4⋊Q8—862no—
693C4⋊Q8—862no—
694C4⋊Q8—861no—
695C4⋊Q8—861no—
696C4⋊Q8C22×D4312yes—
697C4⋊Q8C22×D4312yes—
698#127—431no—
699#126—861no—
700#126—861no—
701#126—861no—
702#126—861no—
703#125—431no—
704#125—431no—
705#125—861no—
706#125—861no—
707#124—431no—
708#124—431no—
709#124—861no—
710#124—861no—
711#123—861no—
712#123—861no—
713#123—861no—
714#123—861no—
715#123—861no—
716#123—861no—
717C22⋊Q8—431no—
718C22⋊Q8—431no—
719C22⋊Q8—431no—
720C22⋊Q8—431no—
721C22⋊Q8—861no—
722C22⋊Q8—861no—
723C22⋊Q8—861no—
724C22⋊Q8—861no—
725#121—431no—
726#121—431no—
727#121—431no—
728#121—431no—
729#121—861no—
730#121—861no—
731#121—861no—
732#121—861no—
733#120—861no—
734#120—861no—
735C4×Q8—431no—
736C4×Q8—431no—
737C4×Q8—861no—
738C4×Q8—861no—
739C4×Q8—861no—
740C4×Q8—861no—
741C4×Q8C22×D4311yescharacteristic
742C4×Q8C22×D4311yescharacteristic
743C4×D4—21no—
744C4×D4—21no—
745C4×D4—431no—
746C4×D4—431no—
747C4×D4—861no—
748C4×D4—861no—
749C4×D4—861no—
750C4×D4—861no—
751C4×D4—861no—
752C4×D4—861no—
753C4×D4—861no—
754C4×D4—861no—
755C4×D4—861no—
756C4×D4—861no—
757C4×D4—861no—
758C4×D4—861no—
759C4×D4—861no—
760C4×D4—861no—
761C4×D4C22×D4311yescharacteristic
762C4×D4C22×D4311yescharacteristic
763#117—21no—
764#117—431no—
765#117—861no—
766#117—861no—
767#117—861no—
768#117—861no—
769#117—861no—
770#117—861no—
771#117—861no—
772#117C22×D4311yescharacteristic
773C2×C4⋊C4—21no—
774C2×C4⋊C4—432no—
775C2×C4⋊C4—434no—
776C2×C4⋊C4—434no—
777C2×C4⋊C4—862no—
778C2×C4⋊C4—862no—
779C2×C4⋊C4—862no—
780C2×C4⋊C4—862no—
781C2×C4⋊C4—862no—
782C2×C4⋊C4—862no—
783C2×C4⋊C4—862no—
784C2×C4⋊C4—862no—
785C2×C4⋊C4—861no—
786C2×C4⋊C4C22×D4312yes—
787C2×C42—21no—
788C2×C42—431no—
789C2×C42—431no—
790C2×C42—431no—
791C2×C42—431no—
792C2×C42—431no—
793C2×C42—431no—
794C2×C42—431no—
795C2×C42—431no—
796C2×C42—431no—
797C2×C42—431no—
798C2×C42—431no—
799C2×C42—861no—
800C2×C42C22×D4311yescharacteristic
801#107—434no—
802#107—434no—
803#107—434no—
804#107C22×D4314yes—
805#106—434no—
806#106—434no—
807#106—434no—
808#106C22×D4314yes—
809C4⋊C8—432no—
810C4⋊C8—432no—
811C4⋊C8C22×D4312yes—
812C4⋊C8C22×D4312yes—
813#103—434no—
814#103—434no—
815#103—434no—
816#103C22×D4314yes—
817#102—434no—
818#102—434no—
819#102—434no—
820#102C22×D4314yes—
821C22⋊C8—434no—
822C22⋊C8—434no—
823#97—434no—
824C4×C8—434no—
825C24—431no—
826#41—22no—
827#41—22no—
828#41—862no—
829#41—862no—
830#41—1724no—
831#41—1724no—
832C2×Q8—22no—
833C2×Q8—22no—
834C2×Q8—44no—
835C2×Q8—431no—
836C2×Q8—861no—
837C2×Q8—861no—
838C2×Q8—864no—
839C2×Q8—864no—
840C2×Q8—862no—
841C2×Q8—862no—
842C2×Q8—1724no—
843C2×Q8—1728no—
844C2×Q8—1728no—
845C2×Q8—1728no—
846C2×Q8—1728no—
847C2×Q8—1728no—
848C2×Q8C23×D4311yescharacteristic
849C2×D4—21no—
850C2×D4—431no—
851C2×D4—861no—
852C2×D4—861no—
853C2×D4—861no—
854C2×D4—861no—
855C2×D4—861no—
856C2×D4—861no—
857C2×D4—861no—
858C2×D4C23×D4311yescharacteristic
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—431no—
864C22×C4—431no—
865C22×C4—431no—
866C22×C4—431no—
867C22×C4—431no—
868C22×C4—431no—
869C22×C4—431no—
870C22×C4—431no—
871C22×C4—431no—
872C22×C4—431no—
873C22×C4—431no—
874C22×C4—431no—
875C22×C4—431no—
876C22×C4—431no—
877C22×C4—431no—
878C22×C4—864no—
879C22×C4—864no—
880C22×C4—864no—
881C22×C4—864no—
882C22×C4—862no—
883C22×C4—862no—
884C22×C4—862no—
885C22×C4—861no—
886C22×C4—861no—
887C22×C4—861no—
888C22×C4—1728no—
889C22×C4D4×D4311yescharacteristic
890C22×C4D4×D4311yescharacteristic
891C22×C4C23×D4311yescharacteristic
892M16—24no—
893M16—864no—
894C2×C8—434no—
895C2×C8C23×D4314yes—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—434no—
902C4⋊C4—431no—
903C4⋊C4—431no—
904C4⋊C4—864no—
905C4⋊C4—864no—
906C4⋊C4—864no—
907C4⋊C4—864no—
908C4⋊C4—861no—
909C4⋊C4—861no—
910C4⋊C4—861no—
911C4⋊C4—861no—
912C4⋊C4—861no—
913C4⋊C4—861no—
914C4⋊C4—861no—
915C4⋊C4—861no—
916C4⋊C4—861no—
917C4⋊C4—861no—
918C4⋊C4—861no—
919C4⋊C4—861no—
920C4⋊C4—862no—
921C4⋊C4—862no—
922C4⋊C4—862no—
923C4⋊C4—861no—
924C4⋊C4—861no—
925C4⋊C4C23×D4314yes—
926C4⋊C4C23×D4311yescharacteristic
927C4⋊C4C23×D4311yescharacteristic
928C22⋊C4—21no—
929C22⋊C4—21no—
930C22⋊C4—21no—
931C22⋊C4—861no—
932C22⋊C4—861no—
933C22⋊C4—861no—
934C22⋊C4—861no—
935C22⋊C4—861no—
936C22⋊C4—861no—
937C22⋊C4—861no—
938C22⋊C4—861no—
939C22⋊C4—861no—
940C22⋊C4—861no—
941C22⋊C4—861no—
942C22⋊C4—861no—
943C22⋊C4—861no—
944C22⋊C4—861no—
945C22⋊C4—861no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—431no—
950C42—431no—
951C42—431no—
952C42—431no—
953C42—431no—
954C42—431no—
955C42—431no—
956C42—431no—
957C42—431no—
958C42—431no—
959C42—431no—
960C42—431no—
961C42—861no—
962C42—861no—
963C42—861no—
964C42D4×D4311yescharacteristic
965C42D4×D4311yescharacteristic
966C42C23×D4311yescharacteristic
967C42C23×D4311yescharacteristic
968C23—21no—
969C23—431no—
970C23—431no—
971C23—862no—
972C23—862no—
973C23—862no—
974C23—861no—
975C23C2×D4×D4311yescharacteristic
976Q8—21no—
977Q8—21no—
978Q8—44no—
979Q8—44no—
980Q8—861no—
981Q8—861no—
982Q8—1724no—
983Q8—1728no—
984Q8—1722no—
985Q8—1722no—
986Q8—1728no—
987Q8—1724no—
988D4—21no—
989D4—21no—
990D4—42no—
991D4—861no—
992D4—861no—
993D4—1722no—
994D4—1722no—
995D4—1722no—
996D4—1722no—
997D4—1722no—
998D4—1722no—
999D4—1722no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—24no—
1006C2×C4—44no—
1007C2×C4—42no—
1008C2×C4—42no—
1009C2×C4—42no—
1010C2×C4—431no—
1011C2×C4—431no—
1012C2×C4—434no—
1013C2×C4—434no—
1014C2×C4—431no—
1015C2×C4—431no—
1016C2×C4—431no—
1017C2×C4—431no—
1018C2×C4—862no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—862no—
1027C2×C4—862no—
1028C2×C4—862no—
1029C2×C4—861no—
1030C2×C4—861no—
1031C2×C4—861no—
1032C2×C4—861no—
1033C2×C4—861no—
1034C2×C4—861no—
1035C2×C4—861no—
1036C2×C4—864no—
1037C2×C4—1728no—
1038C2×C4—1728no—
1039C2×C4—1724no—
1040C2×C4—1722no—
1041C2×C4—1722no—
1042C2×C4—1722no—
1043C2×C4C2×D4×D4311yescharacteristic
1044C2×C4C2×D4×D4311yescharacteristic
1045C2×C4C2×D4×D4311yescharacteristic
1046C2×C4C2×D4×D4311yescharacteristic
1047C2×C4C2×D4×D4311yescharacteristic
1048C2×C4#1306337212yes—
1049C2×C4#1306337312yes—
1050C2×C4C24×D4311yescharacteristic
1051C8—24no—
1052C8—864no—
1053C22—21no—
1054C22—21no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—432no—
1059C22—432no—
1060C22—868no—
1061C22—861no—
1062C22—861no—
1063C22—861no—
1064C22—861no—
1065C22—1721no—
1066C22—1721no—
1067C22—1721no—
1068C22#1458347212yes—
1069C22C22×D4×D4311yescharacteristic
1070C4—21no—
1071C4—21no—
1072C4—44no—
1073C4—41no—
1074C4—41no—
1075C4—41no—
1076C4—432no—
1077C4—432no—
1078C4—861no—
1079C4—861no—
1080C4—861no—
1081C4—861no—
1082C4—1724no—
1083C4—1721no—
1084C4—1721no—
1085C4—1721no—
1086C4#1458347212yes—
1087C4AGL(1,ℤ/8)×D4312yes—
1088C4#137×D4312yes—
1089C4C2×#1306337211yescharacteristic
1090C4C2×#1306337311yescharacteristic
1091C2—22no—
1092C2—81no—
1093C2—862no—
1094C2—862no—
1095C2—3441no—
1096C2C2×#1458347211yescharacteristic
1097C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1098C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3079C2
socleC22×C43C23×D4
prime radical#19147888C2
hypercenter#3079D43
hypocenterC43#60860
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊Q8×D43C2semidirect
3. #19145829C2semidirect
4. #19145824C2semidirect
5. #19145820C2semidirect
6. #19145815C2semidirect
7. #19145745C2semidirect
8. #19145738C2semidirect
9. #19145722C2semidirect
10. #19145715C2semidirect
11. #19145139C2semidirect
12. #19144986C2semidirect
13. #19144521C2semidirect
14. #19144516C2semidirect
15. #19144411C2semidirect
16. #19144410C2semidirect
17. #19144404C2semidirect
18. #19143227C2semidirect
19. C43×#3079C2semidirect
57. #14583307C22semidirect
58. #14583306C22semidirect
59. #14583303C22semidirect
60. #14583296C22semidirect
61. #14583260C22semidirect
62. #14583257C22semidirect
63. #14583248C22semidirect
64. #14583244C22semidirect
73. #14583195C22semidirect
74. #14583194C22semidirect
75. #14583191C22semidirect
76. #14583190C22semidirect
77. #14583189C22semidirect
78. #14583186C22semidirect
79. #14583185C22semidirect
80. #14583184C22semidirect
81. #14583181C22semidirect
82. #14583180C22semidirect
83. #14583179C22semidirect
84. #14583176C22semidirect
100. C43×#477C22semidirect
101. C43×#476C22semidirect
102. C43×#475C22semidirect
103. C43×#474C22semidirect
559. #3079D43semidirect
627. #477C2×D43semidirect
631. #476C2×D43semidirect
635. #475C2×D43semidirect
639. #474C2×D43semidirect
656. C43#60860semidirect

Maximal subgroups

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

subgroupindex
#191478882
C2×C4⋊Q8×D432
#191458292
#191458242
#191458202
#191458152
#191457452
#191457382
#191457222
#191457152
#191451392
#191449862
#191445212
#191445162
#191444112
#191444102
#191444042
#191432272
C43×#30792
#6086043