Finite Group Databasebeta

← #25063417

Subgroups — #25063417

Order 11008.

1112 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2#423×D43C211yesmaximal, characteristic, complemented
3C4×M16×D43C211yesmaximal, characteristic, complemented
4#19133048C212yesmaximal, complemented
5#19133044C212yesmaximal, complemented
6#19133035C211yesmaximal, characteristic, complemented
7#19133034C211yesmaximal, characteristic, complemented
8#19133032C211yesmaximal, characteristic, complemented
9#19133007C212yesmaximal, complemented
10#19133005C212yesmaximal, complemented
11C43×#1489C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13C2×M16×D43—21no—
14#14583453C411yescharacteristic
15#14583453C2211yescharacteristic
16#14583452C411yescharacteristic
17#14583446C411yescharacteristic
18#14583446C2211yescharacteristic
19#14583445C411yescharacteristic
20#14583436C411yescharacteristic
21#14583436C2211yescharacteristic
22#14583431C411yescharacteristic
23#14583431C2211yescharacteristic
24#14583429—21no—
25#14583429—21no—
26#14583427—21no—
27#14583427—21no—
28#14583411C411yescharacteristic
29#14583408—21no—
30#14583408—21no—
31#14583406C411yescharacteristic
32C4×#10621898—21no—
33C4×#10621898—21no—
34C4×#10621898C2211yescharacteristic
35C2×C42×D43C2211yescharacteristic
36#14582923C2211yescharacteristic
37#14582922—21no—
38#14582921—21no—
39#14582921C2212yes—
40C4⋊C8×D43—21no—
41C4⋊C8×D43C2212yes—
42C4×#10621877C2211yescharacteristic
43#14582851—21no—
44M16×Dic43—21no—
45C4×#10621872C2212yes—
46#97×D43—21no—
47C4×C8×D43C2212yes—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C4×#41×C43C2211yescharacteristic
55C43×#423C2211yescharacteristic
56C4×M16×C43C2211yescharacteristic
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×#10621898—21no—
60C2×#10621898—21no—
61C2×#10621898C2×C411yescharacteristic
62C22×C4×D43C2×C411yescharacteristic
63C22×C4×D43D411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C2×#10621877—21no—
66C2×#10621877—21no—
67C2×#10621872—22no—
68C2×#10621872—22no—
69M16×D43—28no—
70M16×D43—44no—
71C2×C8×D43—22no—
72C2×C8×D43—22no—
73#13063324C2×C411yescharacteristic
74#13063324C2×C411yescharacteristic
75#13063323C2×C411yescharacteristic
76#13063321C2×C411yescharacteristic
77#13063320—21no—
78#13063320—21no—
79#13063318—21no—
80#13063318—21no—
81#13063316C2×C411yescharacteristic
82#13063316C2×C411yescharacteristic
83#13063315—21no—
84#13063315—21no—
85#13063314C2×C411yescharacteristic
86#13063312C2×C411yescharacteristic
87#13063311—21no—
88#13063311—21no—
89#13063310—21no—
90#13063310—21no—
91#13063309—21no—
92#13063307—21no—
93#13063307—21no—
94#13063306—21no—
95#13063305C2×C411yescharacteristic
96#13063305C2×C411yescharacteristic
97#13063303—21no—
98#13063303—21no—
99#13063302—21no—
100#13063302—21no—
101#13063301C2×C411yescharacteristic
102#13063301C2×C411yescharacteristic
103#13063300C2×C411yescharacteristic
104#13063300C2×C411yescharacteristic
105#13063298—21no—
106#13063298—21no—
107#13063297—21no—
108#13063297—21no—
109#13063296C2×C411yescharacteristic
110#13063296C2×C411yescharacteristic
111#13063295—21no—
112#13063293—21no—
113C4×Dic86—21no—
114C4×Dic86—21no—
115C4×Dic86—21no—
116C4×Dic86—21no—
117C4×Dic86C2×C411yescharacteristic
118C4×Dic86C2311yescharacteristic
119C4×D172—21no—
120C4×D172—21no—
121C4×D172—21no—
122C4×D172—21no—
123C4×D172C2×C411yescharacteristic
124C4×D172C2311yescharacteristic
125C4×C22⋊D43—21no—
126C4×C22⋊D43—21no—
127C4×C22⋊D43—21no—
128C4×C22⋊D43—21no—
129C4×C22⋊D43—21no—
130C4×C22⋊D43—21no—
131C4×C22⋊D43—21no—
132C4×C22⋊D43—21no—
133C4×C22⋊D43—21no—
134C4×C22⋊D43—21no—
135#13063284—21no—
136#13063284—21no—
137#13063284C2×C411yescharacteristic
138#13063282—21no—
139#13063282—21no—
140#13063282—21no—
141#13063282—21no—
142#13063282—21no—
143C2×C4×Dic43C2×C411yescharacteristic
144C2×C4×Dic43D411yescharacteristic
145C2×C4×Dic43D411yescharacteristic
146C42×D43—21no—
147C42×D43C2×C411yescharacteristic
148C42×D43C2×C411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43D411yescharacteristic
151C42×D43D411yescharacteristic
152C42×D43D411yescharacteristic
153C42×D43C2311yescharacteristic
154C42×D43C2311yescharacteristic
155C4⋊(C43⋊C8)—21no—
156C4⋊(C43⋊C8)C2312yes—
157Dic43⋊C8—22no—
158Dic43⋊C8—22no—
159#13063236—21no—
160#13063235—22no—
161C4×C43⋊C8C2312yes—
162C8×Dic43—22no—
163C2×#41×C43C2×C411yescharacteristic
164C2×M16×C43—21no—
165C2×M16×C43—21no—
166C4×Q8×C43C2×C411yescharacteristic
167C4×Q8×C43C2311yescharacteristic
168C4×D4×C43—21no—
169C4×D4×C43—21no—
170C4×D4×C43C2×C411yescharacteristic
171C4×D4×C43C2311yescharacteristic
172#117×C43—21no—
173#117×C43C2×C411yescharacteristic
174C2×C42×C43—21no—
175C2×C42×C43C2311yescharacteristic
176C4⋊C8×C43—21no—
177C4⋊C8×C43C2312yes—
178#97×C43—21no—
179C4×C8×C43C2312yes—
180C23×D43C22⋊C411yescharacteristic
181#41×C43—42no—
182C2×Q8×C43C22×C411yescharacteristic
183C2×D4×C43—21no—
184C2×D4×C43C22×C411yescharacteristic
185C22×C4×C43—21no—
186C22×C4×C43—21no—
187C22×C4×C43—21no—
188C22×C4×C43C22×C411yescharacteristic
189C22×C4×C43C2×D411yescharacteristic
190C22×C4×C43C2×D411yescharacteristic
191C2×C22⋊D43—21no—
192C2×C22⋊D43—21no—
193C2×C22⋊D43—21no—
194C2×C22⋊D43—21no—
195C2×C22⋊D43—21no—
196C22×Dic43C22⋊C411yescharacteristic
197C22×Dic43C22⋊C411yescharacteristic
198C22×Dic43C22⋊C411yescharacteristic
199#10621898—42no—
200#10621898—44no—
201#10621898—42no—
202#10621898—42no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172C22×C411yescharacteristic
206C2×C4×D43—24no—
207C2×C4×D43—22no—
208C2×C4×D43—22no—
209C2×C4×D43—21no—
210C2×C4×D43—21no—
211C2×C4×D43—21no—
212C2×C4×D43—42no—
213C2×C4×D43C22⋊C411yescharacteristic
214C2×C4×D43C22⋊C411yescharacteristic
215C2×C4×D43C22⋊C411yescharacteristic
216C2×C4×D43C22⋊C411yescharacteristic
217C2×C4×D43C22⋊C411yescharacteristic
218C2×C4×D43C22⋊C411yescharacteristic
219C2×C4×D43C22×C411yescharacteristic
220C2×C4×D43C22×C411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×C4×D43C2×D411yescharacteristic
224C2×C4×D43C2×D411yescharacteristic
225C2×Dic86—21no—
226C2×Dic86—21no—
227C2×Dic86C22×C411yescharacteristic
228M16×C43—24no—
229M16×C43—42no—
230C2×C8×C43—22no—
231C2×C8×C43—22no—
232C4⋊C4×C43—21no—
233C4⋊C4×C43—21no—
234C4⋊C4×C43C22×C411yescharacteristic
235C4⋊C4×C43C22×C411yescharacteristic
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43—21no—
241C42×C43—21no—
242C42×C43C22×C411yescharacteristic
243C42×C43C2×D411yescharacteristic
244C42×C43C2×D411yescharacteristic
245C42×C43C2411yescharacteristic
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249C22⋊Dic43—21no—
250C22⋊Dic43—21no—
251(C2×D43)⋊C4—21no—
252(C2×D43)⋊C4—21no—
253(C2×D43)⋊C4—21no—
254(C2×D43)⋊C4—21no—
255(C2×D43)⋊C4—21no—
256(C2×D43)⋊C4—21no—
257(C2×D43)⋊C4—21no—
258(C2×D43)⋊C4—21no—
259(C2×D43)⋊C4—21no—
260(C2×D43)⋊C4—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—21no—
264C4⋊Dic43—21no—
265C4⋊Dic43C22×C411yescharacteristic
266C4⋊Dic43C22×C411yescharacteristic
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—21no—
276Dic43⋊C4—21no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—21no—
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22⋊C411yescharacteristic
285C4×Dic43C22⋊C411yescharacteristic
286C4×Dic43C22×C411yescharacteristic
287C4×Dic43C22×C411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290C4×Dic43C2×D411yescharacteristic
291C4×Dic43C2×D411yescharacteristic
292#10621877—24no—
293#10621877—42no—
294C2×C43⋊C8—22no—
295C2×C43⋊C8—22no—
296#10621872—28no—
297#10621872—44no—
298C8×D43—28no—
299C8×D43—44no—
300C23×C43—21no—
301C23×C43C2×C22⋊C411yescharacteristic
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—21no—
305C22×D43—41no—
306C22×D43C2×C22⋊C411yescharacteristic
307C22×D43C2×C22⋊C411yescharacteristic
308Q8×C43—22no—
309D4×C43—22no—
310D4×C43—42no—
311C2×C4×C43—22no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—22no—
315C2×C4×C43—21no—
316C2×C4×C43—21no—
317C2×C4×C43—21no—
318C2×C4×C43—42no—
319C2×C4×C43—41no—
320C2×C4×C43—41no—
321C2×C4×C43—42no—
322C2×C4×C43C2×C22⋊C411yescharacteristic
323C2×C4×C43C2×C22⋊C411yescharacteristic
324C2×C4×C43C2×C22⋊C411yescharacteristic
325C2×C4×C43C23×C411yescharacteristic
326C2×C4×C43C22×D411yescharacteristic
327C2×C4×C43C22×D411yescharacteristic
328C22⋊D43—42no—
329C22⋊D43—42no—
330C22⋊D43—42no—
331C22⋊D43—42no—
332C22⋊D43—42no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—21no—
336C2×Dic43—21no—
337C2×Dic43—21no—
338C2×Dic43—41no—
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341C2×Dic43C2×C22⋊C411yescharacteristic
342C2×Dic43C2×C22⋊C411yescharacteristic
343C2×Dic43C2×C22⋊C411yescharacteristic
344C2×Dic43C2×C22⋊C411yescharacteristic
345D172—22no—
346D172—42no—
347D172—42no—
348C4×D43—22no—
349C4×D43—22no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—21no—
353C4×D43—21no—
354C4×D43—22no—
355C4×D43—22no—
356C4×D43—22no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—42no—
360C4×D43—41no—
361C4×D43—41no—
362C4×D43—42no—
363C4×D43#10414yes—
364C4×D43AGL(1,ℤ/8)12yes—
365C4×D43#13712yes—
366Dic86—22no—
367Dic86—42no—
368Dic86—42no—
369C8×C43—24no—
370C8×C43—42no—
371C43⋊C8—24no—
372C43⋊C8—42no—
373#17504—431nomaximal, Sylow
374C22×C43—21no—
375C22×C43—21no—
376C22×C43—21no—
377C22×C43—41no—
378C22×C43—41no—
379C22×C43—41no—
380C22×C43C22×C22⋊C411yescharacteristic
381C2×D43—21no—
382C2×D43—21no—
383C2×D43—21no—
384C2×D43—21no—
385C2×D43—44no—
386C2×D43—41no—
387C2×D43—41no—
388C2×D43—41no—
389C2×D43#41712yes—
390C2×D43C2×#10412yes—
391C4×C43—21no—
392C4×C43—21no—
393C4×C43—21no—
394C4×C43—41no—
395C4×C43—41no—
396C4×C43—41no—
397C4×C43C2×#10412yes—
398C4×C43#56812yes—
399C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
400C4×C43C2×#13711yescharacteristic
401Dic43—21no—
402Dic43—21no—
403Dic43—21no—
404Dic43—21no—
405Dic43—41no—
406Dic43—41no—
407Dic43—41no—
408Dic43#41712yes—
409Dic43C2×#10412yes—
410#3444—431no—
411C2×#423—431no—
412C2×C4×M16—431no—
413#1493—432no—
414#1492—432no—
415#1489—431no—
416#1489—431no—
417#1489—431no—
418#1489D4311yescharacteristic, complemented
419#1483—432no—
420#1483—432no—
421C2×C43—41no—
422C2×C43—81no—
423C2×C43#287911yescharacteristic
424C2×C43C2×#41711yescharacteristic
425C2×C43C22×#10411yescharacteristic
426D43—22no—
427D43—22no—
428D43—81no—
429C22×M16—861no—
430C22×M16—861no—
431#533—431no—
432#533—431no—
433#533—431no—
434#532—431no—
435#532—431no—
436#532—431no—
437#529—431no—
438#529—431no—
439#529—431no—
440#529—431no—
441#529—861no—
442#529—861no—
443#529—861no—
444#529—861no—
445#525—431no—
446#525—431no—
447#525—861no—
448#525—861no—
449C4×#41—431no—
450C4×#41—861no—
451C4×#41—861no—
452C4×#41C2×D4311yescharacteristic
453C22×C42—431no—
454#423—431no—
455#423—432no—
456#423—861no—
457#423—861no—
458#423C2×D4311yescharacteristic
459C2×C4⋊C8—432no—
460C2×C4⋊C8—861no—
461C4×M16—431no—
462C4×M16—432no—
463C4×M16—861no—
464C4×M16—861no—
465C4×M16C2×D4311yescharacteristic
466C2×#97—861no—
467C2×C4×C8—432no—
468Q8⋊C8—432no—
469Q8⋊C8—432no—
470Q8⋊C8—432no—
471Q8⋊C8C2×D4312yescomplemented
472D4⋊C8—432no—
473D4⋊C8—432no—
474D4⋊C8—432no—
475D4⋊C8C2×D4312yescomplemented
476C43#1750411yescharacteristic, complemented, Sylow
477C2×#41—431no—
478C2×#41—861no—
479C2×#41—861no—
480C2×#41C4×D4311yescharacteristic
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C2×M16—21no—
485C2×M16—21no—
486C2×M16—862no—
487C2×M16—862no—
488C2×M16—868no—
489C2×M16—861no—
490C2×M16—861no—
491C2×M16—1724no—
492C22×C8—862no—
493C22×C8—862no—
494C4⋊Q8—431no—
495C4⋊Q8—431no—
496C4⋊Q8—431no—
497#127—431no—
498#126—861no—
499#126—861no—
500#126—861no—
501#126—861no—
502#125—431no—
503#125—431no—
504#125—861no—
505#125—861no—
506#124—431no—
507#124—431no—
508#124—861no—
509#124—861no—
510#123—861no—
511#123—861no—
512#123—861no—
513#123—861no—
514#123—861no—
515#123—861no—
516C22⋊Q8—431no—
517C22⋊Q8—431no—
518C22⋊Q8—431no—
519C22⋊Q8—431no—
520C22⋊Q8—861no—
521C22⋊Q8—861no—
522C22⋊Q8—861no—
523C22⋊Q8—861no—
524#121—431no—
525#121—431no—
526#121—431no—
527#121—431no—
528#121—861no—
529#121—861no—
530#121—861no—
531#121—861no—
532#120—861no—
533#120—861no—
534C4×Q8—431no—
535C4×Q8—431no—
536C4×Q8—861no—
537C4×Q8—861no—
538C4×Q8—861no—
539C4×Q8—861no—
540C4×Q8C4×D4311yescharacteristic
541C4×Q8C22×D4311yescharacteristic
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—431no—
545C4×D4—431no—
546C4×D4—861no—
547C4×D4—861no—
548C4×D4—861no—
549C4×D4—861no—
550C4×D4—861no—
551C4×D4—861no—
552C4×D4—861no—
553C4×D4—861no—
554C4×D4—861no—
555C4×D4—861no—
556C4×D4—861no—
557C4×D4—861no—
558C4×D4—861no—
559C4×D4—861no—
560C4×D4C4×D4311yescharacteristic
561C4×D4C22×D4311yescharacteristic
562#117—21no—
563#117—431no—
564#117—861no—
565#117—861no—
566#117—861no—
567#117—861no—
568#117—861no—
569#117—861no—
570#117—861no—
571#117C4×D4311yescharacteristic
572C2×C42—21no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—431no—
578C2×C42—431no—
579C2×C42—431no—
580C2×C42—431no—
581C2×C42—431no—
582C2×C42—431no—
583C2×C42—431no—
584C2×C42—861no—
585C2×C42C22×D4311yescharacteristic
586C4⋊C8—21no—
587C4⋊C8—432no—
588C4⋊C8—862no—
589C4⋊C8—862no—
590C4⋊C8—861no—
591C4⋊C8C22×D4312yes—
592#97—21no—
593#97—862no—
594#97—861no—
595C4×C8—432no—
596C4×C8—862no—
597C4×C8C22×D4312yes—
598C24—431no—
599#41—42no—
600#41—1722no—
601#41—1724no—
602#41—1722no—
603#41—1722no—
604C2×Q8—431no—
605C2×Q8—861no—
606C2×Q8—861no—
607C2×Q8C2×C4×D4311yescharacteristic
608C2×D4—21no—
609C2×D4—431no—
610C2×D4—861no—
611C2×D4—861no—
612C2×D4—861no—
613C2×D4—861no—
614C2×D4—861no—
615C2×D4—861no—
616C2×D4—861no—
617C2×D4C2×C4×D4311yescharacteristic
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—431no—
626C22×C4—431no—
627C22×C4—431no—
628C22×C4—431no—
629C22×C4—431no—
630C22×C4—431no—
631C22×C4—431no—
632C22×C4—431no—
633C22×C4—431no—
634C22×C4—431no—
635C22×C4—431no—
636C22×C4—864no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—861no—
640C22×C4—861no—
641C22×C4—861no—
642C22×C4—1722no—
643C22×C4C2×C4×D4311yescharacteristic
644C22×C4D4×D4311yescharacteristic
645C22×C4D4×D4311yescharacteristic
646M16—24no—
647M16—42no—
648M16—868no—
649M16—864no—
650M16—1724no—
651M16—1722no—
652C2×C8—22no—
653C2×C8—22no—
654C2×C8—868no—
655C2×C8—862no—
656C2×C8—862no—
657C2×C8—1724no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—431no—
661C4⋊C4—431no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4—861no—
670C4⋊C4—861no—
671C4⋊C4—861no—
672C4⋊C4—861no—
673C4⋊C4—861no—
674C4⋊C4—861no—
675C4⋊C4—861no—
676C4⋊C4C2×C4×D4311yescharacteristic
677C4⋊C4C2×C4×D4311yescharacteristic
678C22⋊C4—21no—
679C22⋊C4—21no—
680C22⋊C4—21no—
681C22⋊C4—861no—
682C22⋊C4—861no—
683C22⋊C4—861no—
684C22⋊C4—861no—
685C22⋊C4—861no—
686C22⋊C4—861no—
687C22⋊C4—861no—
688C22⋊C4—861no—
689C22⋊C4—861no—
690C22⋊C4—861no—
691C22⋊C4—861no—
692C22⋊C4—861no—
693C22⋊C4—861no—
694C22⋊C4—861no—
695C22⋊C4—861no—
696C42—21no—
697C42—21no—
698C42—21no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—431no—
704C42—431no—
705C42—431no—
706C42—431no—
707C42—431no—
708C42—431no—
709C42—431no—
710C42—431no—
711C42—861no—
712C42—861no—
713C42—861no—
714C42C2×C4×D4311yescharacteristic
715C42D4×D4311yescharacteristic
716C42D4×D4311yescharacteristic
717C42C23×D4311yescharacteristic
718C23—21no—
719C23—431no—
720C23—431no—
721C23—862no—
722C23—862no—
723C23—861no—
724C23—1721no—
725C23C22⋊C4×D4311yescharacteristic
726Q8—22no—
727Q8—862no—
728Q8—1722no—
729Q8—1722no—
730D4—22no—
731D4—42no—
732D4—862no—
733D4—1722no—
734D4—1722no—
735D4—1722no—
736D4—1722no—
737D4—1722no—
738D4—1722no—
739D4—1722no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—41no—
750C2×C4—41no—
751C2×C4—431no—
752C2×C4—431no—
753C2×C4—434no—
754C2×C4—432no—
755C2×C4—432no—
756C2×C4—431no—
757C2×C4—431no—
758C2×C4—431no—
759C2×C4—431no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—862no—
767C2×C4—862no—
768C2×C4—862no—
769C2×C4—861no—
770C2×C4—861no—
771C2×C4—861no—
772C2×C4—861no—
773C2×C4—861no—
774C2×C4—1721no—
775C2×C4—1721no—
776C2×C4—1722no—
777C2×C4—1721no—
778C2×C4—1722no—
779C2×C4—1721no—
780C2×C4—1721no—
781C2×C4C22⋊C4×D4311yescharacteristic
782C2×C4C22⋊C4×D4311yescharacteristic
783C2×C4C22⋊C4×D4311yescharacteristic
784C2×C4C22×C4×D4311yescharacteristic
785C2×C4C2×D4×D4311yescharacteristic
786C2×C4C2×D4×D4311yescharacteristic
787C8—24no—
788C8—42no—
789C8—864no—
790C8—1722no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—432no—
798C22—432no—
799C22—861no—
800C22—861no—
801C22—861no—
802C22—861no—
803C22—1724no—
804C22—1721no—
805C22—1721no—
806C22—1721no—
807C22C2×C22⋊C4×D4311yescharacteristic
808C4—21no—
809C4—21no—
810C4—21no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—432no—
815C4—432no—
816C4—861no—
817C4—861no—
818C4—861no—
819C4—861no—
820C4—1721no—
821C4—1721no—
822C4—1721no—
823C4#104×D4312yes—
824C4#1458366512yes—
825C4AGL(1,ℤ/8)×D4311yescharacteristic
826C4#137×D4311yescharacteristic
827C2—41no—
828C2—81no—
829C2—862no—
830C2—862no—
831C2—3441no—
832C2#1914303811yescharacteristic
833C2#417×D4311yescharacteristic
834C2C2×#104×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1489C2
socleC22×C43C22×C22⋊C4
prime radical#19147888C2
cosocleC42×C43C24
hypercenter#1489D43
hypocenterC43#17504
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1489

Complements

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

NH ≅ G/Ntype
2. #423×D43C2semidirect
3. C4×M16×D43C2semidirect
4. #19133048C2semidirect
5. #19133044C2semidirect
6. #19133035C2semidirect
7. #19133034C2semidirect
8. #19133032C2semidirect
9. #19133007C2semidirect
10. #19133005C2semidirect
11. C43×#1489C2semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
418. #1489D43semidirect
471. Q8⋊C8C2×D43semidirect
475. D4⋊C8C2×D43semidirect
476. C43#17504semidirect

Maximal subgroups

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

subgroupindex
#191478882
#423×D432
C4×M16×D432
#191330482
#191330442
#191330352
#191330342
#191330322
#191330072
#191330052
C43×#14892
#1750443