Finite Group Databasebeta

← D43×#1495 #25063223

Subgroups — D43×#1495 #25063223

Order 11008.

1066 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#529×D43C211yesmaximal, characteristic
2#431×D43C211yesmaximal, characteristic, complemented
3#423×D43C211yesmaximal, characteristic, complemented
4#19133061C211yesmaximal, characteristic, complemented
5#19133060C211yesmaximal, characteristic, complemented
6#19133059C212yesmaximal, complemented
7#19133058C211yesmaximal, characteristic, complemented
8#19133057C212yesmaximal, complemented
9Q8⋊C8×D43C212yesmaximal, complemented
10D4⋊C8×D43C212yesmaximal, complemented
11C43×#1495C211yesmaximal, characteristic, complemented
12C2×M16×D43—21no—
13#14583436C2211yescharacteristic
14#14583435C411yescharacteristic
15#14583434C411yescharacteristic
16#14583433C2211yescharacteristic
17#14583432—21no—
18#14583431C2211yescharacteristic
19#14583430C411yescharacteristic
20#14583429—21no—
21#14583428C411yescharacteristic
22#14583427—21no—
23#14583426—21no—
24#126×D43—21no—
25#125×D43C411yescharacteristic
26#124×D43C411yescharacteristic
27#123×D43—21no—
28C22⋊Q8×D43C411yescharacteristic
29#121×D43C411yescharacteristic
30C4×Q8×D43C2211yescharacteristic
31C4×D4×D43—21no—
32C4×D4×D43C2211yescharacteristic
33#117×D43—21no—
34C2×C42×D43C2211yescharacteristic
35#14582952C2211yescharacteristic, complemented
36#14582951—21no—
37#14582950C2212yescomplemented
38#14582949—21no—
39#14582923C2211yescharacteristic, complemented
40#14582922—21no—
41#14582921—21no—
42#14582921C2212yescomplemented
43C4⋊C8×D43—21no—
44C4⋊C8×D43—21no—
45C4⋊C8×D43C2212yes—
46C22⋊C8×D43—21no—
47C4×C8×D43C2212yes—
48#14582631C2212yescomplemented
49Q8⋊(C43⋊C8)C2212yescomplemented
50#14582629C2212yescomplemented
51#14582628C2212yescomplemented
52D4⋊(C43⋊C8)C2212yescomplemented
53#14582626C2212yescomplemented
54C43×#529C2211yescharacteristic
55C43×#431C2211yescharacteristic, complemented
56C43×#423C2211yescharacteristic, complemented
57C43×Q8⋊C8C2212yescomplemented
58C43×D4⋊C8C2212yescomplemented
59C2×Q8×D43C2×C411yescharacteristic
60C2×D4×D43—21no—
61C2×D4×D43C2×C411yescharacteristic
62C22×C4×D43—21no—
63C22×C4×D43C2×C411yescharacteristic
64C22×C4×D43D411yescharacteristic
65C22×C4×D43D411yescharacteristic
66C2×#10621877—21no—
67C2×#10621872—22no—
68M16×D43—44no—
69C2×C8×D43—22no—
70C2×C8×D43—22no—
71#13063320—21no—
72#13063320—21no—
73#13063320—21no—
74#13063319—21no—
75#13063318—21no—
76#13063318—21no—
77#13063318—21no—
78#13063317C2×C411yescharacteristic
79#13063316C2×C411yescharacteristic
80#13063316C2×C411yescharacteristic
81#13063315—21no—
82#13063315—21no—
83#13063314C2×C411yescharacteristic
84#13063313C2×C411yescharacteristic
85#13063312C2×C411yescharacteristic
86#13063311—21no—
87#13063311—21no—
88#13063310—21no—
89#13063310—21no—
90#13063309—21no—
91#13063308—21no—
92#13063307—21no—
93#13063307—21no—
94#13063306—21no—
95#13063305C2×C411yescharacteristic
96#13063304C2×C411yescharacteristic
97#13063303—21no—
98#13063302—21no—
99#13063301C2×C411yescharacteristic
100#13063300C2×C411yescharacteristic
101#13063299C2×C411yescharacteristic
102#13063298—21no—
103#13063297—21no—
104#13063296C2×C411yescharacteristic
105Q8×Dic43C2×C411yescharacteristic
106C4×Dic86—21no—
107C4×Dic86C2311yescharacteristic
108#13063290—21no—
109#13063290C2×C411yescharacteristic
110C4×D172—21no—
111C4×D172C2311yescharacteristic
112D4×Dic43—21no—
113D4×Dic43C2×C411yescharacteristic
114#13063287—21no—
115#13063287C2×C411yescharacteristic
116C4×C22⋊D43—21no—
117C4×C22⋊D43—21no—
118C4×C22⋊D43—21no—
119(C22⋊D43)⋊C4—21no—
120(C22⋊D43)⋊C4—21no—
121(C22⋊D43)⋊C4—21no—
122#13063284—21no—
123#13063283—21no—
124#13063283—21no—
125#13063282—21no—
126#13063282—21no—
127#13063281—21no—
128#13063281—21no—
129C4⋊C4×D43—21no—
130C4⋊C4×D43—21no—
131C4⋊C4×D43—21no—
132C4⋊C4×D43—21no—
133C4⋊C4×D43C2×C411yescharacteristic
134C4⋊C4×D43C2×C411yescharacteristic
135C22⋊C4×D43—21no—
136C22⋊C4×D43—21no—
137C22⋊C4×D43—21no—
138C22⋊C4×D43—21no—
139C22⋊C4×D43—21no—
140C2×C4×Dic43C2×C411yescharacteristic
141C2×C4×Dic43D411yescharacteristic
142C2×C4×Dic43D411yescharacteristic
143C42×D43—21no—
144C42×D43C2×C411yescharacteristic
145C42×D43C2×C411yescharacteristic
146C42×D43D411yescharacteristic
147C42×D43D411yescharacteristic
148C42×D43D411yescharacteristic
149C42×D43D411yescharacteristic
150C42×D43C2311yescharacteristic
151C42×D43C2311yescharacteristic
152C4⋊(C43⋊C8)—21no—
153C4⋊(C43⋊C8)—21no—
154C4⋊(C43⋊C8)C2312yes—
155Dic43⋊C8—22no—
156Dic43⋊C8—22no—
157Dic43⋊C8—22no—
158C22⋊(C43⋊C8)—21no—
159(C2×D43)⋊C8—22no—
160C4×C43⋊C8C2312yes—
161C8×Dic43—22no—
162C2×M16×C43—21no—
163#126×C43—21no—
164#125×C43C2×C411yescharacteristic
165#124×C43C2×C411yescharacteristic
166#123×C43—21no—
167C22⋊Q8×C43C2×C411yescharacteristic
168#121×C43C2×C411yescharacteristic
169C4×Q8×C43C2311yescharacteristic
170C4×D4×C43—21no—
171C4×D4×C43C2311yescharacteristic
172#117×C43—21no—
173C2×C42×C43C2311yescharacteristic
174C4⋊C8×C43—21no—
175C4⋊C8×C43—21no—
176C4⋊C8×C43C2312yes—
177C22⋊C8×C43—21no—
178C4×C8×C43C2312yes—
179C23×D43—21no—
180C23×D43C22⋊C411yescharacteristic
181C2×Q8×C43C22×C411yescharacteristic
182C2×D4×C43—21no—
183C2×D4×C43C22×C411yescharacteristic
184C22×C4×C43—21no—
185C22×C4×C43C22×C411yescharacteristic
186C22×C4×C43C2×D411yescharacteristic
187C22×C4×C43C2×D411yescharacteristic
188C2×C22⋊D43—21no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C22×Dic43—21no—
192C22×Dic43C22⋊C411yescharacteristic
193C22×Dic43C22⋊C411yescharacteristic
194C22×Dic43C22⋊C411yescharacteristic
195Q8×D43—24no—
196D4×D43—24no—
197D4×D43—44no—
198C2×D172—21no—
199C2×D172C22×C411yescharacteristic
200C2×C4×D43—24no—
201C2×C4×D43—22no—
202C2×C4×D43—22no—
203C2×C4×D43—21no—
204C2×C4×D43—21no—
205C2×C4×D43—21no—
206C2×C4×D43—21no—
207C2×C4×D43—21no—
208C2×C4×D43—42no—
209C2×C4×D43—42no—
210C2×C4×D43—42no—
211C2×C4×D43C22⋊C411yescharacteristic
212C2×C4×D43C22⋊C411yescharacteristic
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×D43C2×D411yescharacteristic
220C2×C4×D43C2×D411yescharacteristic
221C2×C4×D43C2×D411yescharacteristic
222C2×C4×D43C2×D411yescharacteristic
223C2×Dic86—21no—
224C2×Dic86C22×C411yescharacteristic
225M16×C43—42no—
226C2×C8×C43—22no—
227C2×C8×C43—22no—
228C4⋊C4×C43—21no—
229C4⋊C4×C43—21no—
230C4⋊C4×C43—21no—
231C4⋊C4×C43—21no—
232C4⋊C4×C43C22×C411yescharacteristic
233C4⋊C4×C43C22×C411yescharacteristic
234C22⋊C4×C43—21no—
235C22⋊C4×C43—21no—
236C22⋊C4×C43—21no—
237C22⋊C4×C43—21no—
238C22⋊C4×C43—21no—
239C42×C43—21no—
240C42×C43C22×C411yescharacteristic
241C42×C43C2×D411yescharacteristic
242C42×C43C2×D411yescharacteristic
243C42×C43C2411yescharacteristic
244C22⋊Dic43—21no—
245C22⋊Dic43—21no—
246C22⋊Dic43—21no—
247C22⋊Dic43—21no—
248C22⋊Dic43—21no—
249(C2×D43)⋊C4—21no—
250(C2×D43)⋊C4—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—
259C4⋊Dic43—21no—
260C4⋊Dic43—21no—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43C22×C411yescharacteristic
264C4⋊Dic43C22×C411yescharacteristic
265Dic43⋊C4—21no—
266Dic43⋊C4—21no—
267Dic43⋊C4—21no—
268Dic43⋊C4—21no—
269Dic43⋊C4—21no—
270Dic43⋊C4—21no—
271Dic43⋊C4—21no—
272Dic43⋊C4—21no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275C4×Dic43—21no—
276C4×Dic43—21no—
277C4×Dic43—21no—
278C4×Dic43C22⋊C411yescharacteristic
279C4×Dic43C22⋊C411yescharacteristic
280C4×Dic43C22⋊C411yescharacteristic
281C4×Dic43C22⋊C411yescharacteristic
282C4×Dic43C22⋊C411yescharacteristic
283C4×Dic43C22⋊C411yescharacteristic
284C4×Dic43C22×C411yescharacteristic
285C4×Dic43C22×C411yescharacteristic
286C4×Dic43C2×D411yescharacteristic
287C4×Dic43C2×D411yescharacteristic
288C4×Dic43C2×D411yescharacteristic
289C4×Dic43C2×D411yescharacteristic
290#10621877—42no—
291C2×C43⋊C8—22no—
292C2×C43⋊C8—22no—
293#10621872—44no—
294C8×D43—44no—
295C8×D43—44no—
296C23×C43—21no—
297C23×C43C2×C22⋊C411yescharacteristic
298C22×D43—22no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—21no—
302C22×D43—42no—
303C22×D43—42no—
304C22×D43—42no—
305C22×D43C2×C22⋊C411yescharacteristic
306C22×D43C2×C22⋊C411yescharacteristic
307Q8×C43—22no—
308D4×C43—22no—
309D4×C43—42no—
310C2×C4×C43—22no—
311C2×C4×C43—21no—
312C2×C4×C43—21no—
313C2×C4×C43—21no—
314C2×C4×C43—21no—
315C2×C4×C43—21no—
316C2×C4×C43—41no—
317C2×C4×C43—41no—
318C2×C4×C43—41no—
319C2×C4×C43C2×C22⋊C411yescharacteristic
320C2×C4×C43C2×C22⋊C411yescharacteristic
321C2×C4×C43C2×C22⋊C411yescharacteristic
322C2×C4×C43C23×C411yescharacteristic
323C2×C4×C43C22×D411yescharacteristic
324C2×C4×C43C22×D411yescharacteristic
325C22⋊D43—42no—
326C22⋊D43—42no—
327C22⋊D43—42no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C2×Dic43—41no—
334C2×Dic43—42no—
335C2×Dic43C2×C22⋊C411yescharacteristic
336C2×Dic43C2×C22⋊C411yescharacteristic
337C2×Dic43C2×C22⋊C411yescharacteristic
338C2×Dic43C2×C22⋊C411yescharacteristic
339C2×Dic43C2×C22⋊C411yescharacteristic
340C2×Dic43C2×C22⋊C411yescharacteristic
341D172—22no—
342D172—42no—
343C4×D43—22no—
344C4×D43—22no—
345C4×D43—22no—
346C4×D43—22no—
347C4×D43—22no—
348C4×D43—21no—
349C4×D43—21no—
350C4×D43—22no—
351C4×D43—22no—
352C4×D43—41no—
353C4×D43—41no—
354C4×D43—42no—
355C4×D43—42no—
356C4×D43—42no—
357C4×D43—41no—
358C4×D43—41no—
359C4×D43—42no—
360C4×D43#13114yes—
361C4×D43AGL(1,ℤ/8)12yes—
362C4×D43#13712yes—
363Dic86—22no—
364Dic86—42no—
365C8×C43—42no—
366C8×C43—42no—
367C43⋊C8—42no—
368C43⋊C8—42no—
369C2×#1495—431nomaximal, Sylow
370C22×C43—21no—
371C22×C43—21no—
372C22×C43—21no—
373C22×C43—41no—
374C22×C43—41no—
375C22×C43—41no—
376C22×C43C22×C22⋊C411yescharacteristic
377C2×D43—21no—
378C2×D43—21no—
379C2×D43—21no—
380C2×D43—44no—
381C2×D43—41no—
382C2×D43—41no—
383C2×D43—41no—
384C2×D43—84no—
385C2×D43#40812yes—
386C2×D43#41712yes—
387C2×D43#42112yes—
388C4×C43—21no—
389C4×C43—21no—
390C4×C43—21no—
391C4×C43—21no—
392C4×C43—41no—
393C4×C43—41no—
394C4×C43—41no—
395C4×C43C2×#13112yes—
396C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
397C4×C43C2×#13711yescharacteristic
398Dic43—21no—
399Dic43—21no—
400Dic43—21no—
401Dic43—21no—
402Dic43—41no—
403Dic43—41no—
404Dic43—41no—
405Dic43#40812yes—
406Dic43#41712yes—
407C2×#529—431no—
408C2×#431—431no—
409C2×#423—431no—
410#1495—431no—
411#1495—431no—
412#1495—432no—
413#1495—432no—
414#1495—431no—
415#1495D4311yescharacteristic, direct product factor
416C2×Q8⋊C8—432no—
417C2×D4⋊C8—432no—
418C2×C43—41no—
419C2×C43—81no—
420C2×C43C2×#40811yescharacteristic
421C2×C43C2×#41711yescharacteristic
422C2×C43C2×#42111yescharacteristic
423D43—41no—
424D43—81no—
425D43#149514yesdirect product factor
426C22×M16—861no—
427#529—431no—
428#529—431no—
429#529—431no—
430#529—431no—
431#529—431no—
432#529—431no—
433#529—431no—
434#529—861no—
435#529—861no—
436#529—861no—
437#529—861no—
438#529C2×D4311yescharacteristic
439C2×#126—861no—
440C2×#125—431no—
441C2×#124—431no—
442C2×#123—861no—
443C2×C22⋊Q8—431no—
444C2×#121—431no—
445C2×C4×Q8—431no—
446C2×C4×D4—431no—
447C2×C4×D4—861no—
448C2×#117—861no—
449C22×C42—431no—
450#431—431no—
451#431—432no—
452#431—861no—
453#431—861no—
454#431C2×D4311yescharacteristic, complemented
455#423—431no—
456#423—432no—
457#423—861no—
458#423—861no—
459#423C2×D4311yescharacteristic, complemented
460C2×C4⋊C8—432no—
461C2×C4⋊C8—861no—
462C2×C4⋊C8—861no—
463C2×C22⋊C8—861no—
464C2×C4×C8—432no—
465Q8⋊C8—432no—
466Q8⋊C8—432no—
467Q8⋊C8—432no—
468Q8⋊C8C2×D4312yescomplemented
469D4⋊C8—432no—
470D4⋊C8—432no—
471D4⋊C8—432no—
472D4⋊C8C2×D4312yescomplemented
473C43C2×#149511yescharacteristic, complemented, Sylow
474C22×Q8—431no—
475C22×D4—431no—
476C22×D4—861no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—431no—
480C23×C4—861no—
481C2×M16—21no—
482C2×M16—862no—
483C2×M16—861no—
484C2×M16—1724no—
485C22×C8—862no—
486C22×C8—862no—
487#126—21no—
488#126—861no—
489#126—861no—
490#126—861no—
491#126—861no—
492#126—861no—
493#126—861no—
494#126—861no—
495#125—431no—
496#125—431no—
497#125—431no—
498#125—861no—
499#125—861no—
500#125C4×D4311yescharacteristic
501#124—431no—
502#124—431no—
503#124—431no—
504#124—861no—
505#124—861no—
506#124C4×D4311yescharacteristic
507#123—21no—
508#123—861no—
509#123—861no—
510#123—861no—
511#123—861no—
512#123—861no—
513#123—861no—
514#123—861no—
515C22⋊Q8—431no—
516C22⋊Q8—431no—
517C22⋊Q8—431no—
518C22⋊Q8—861no—
519C22⋊Q8—861no—
520C22⋊Q8C4×D4311yescharacteristic
521#121—431no—
522#121—431no—
523#121—431no—
524#121—861no—
525#121—861no—
526#121C4×D4311yescharacteristic
527C4×Q8—431no—
528C4×Q8—431no—
529C4×Q8—431no—
530C4×Q8—861no—
531C4×Q8—861no—
532C4×Q8C22×D4311yescharacteristic
533C4×D4—21no—
534C4×D4—431no—
535C4×D4—431no—
536C4×D4—431no—
537C4×D4—861no—
538C4×D4—861no—
539C4×D4—861no—
540C4×D4—861no—
541C4×D4—861no—
542C4×D4—861no—
543C4×D4—861no—
544C4×D4—861no—
545C4×D4—861no—
546C4×D4C22×D4311yescharacteristic
547#117—21no—
548#117—861no—
549#117—861no—
550#117—861no—
551#117—861no—
552#117—861no—
553#117—861no—
554#117—861no—
555C2×C4⋊C4—431no—
556C2×C4⋊C4—431no—
557C2×C4⋊C4—861no—
558C2×C4⋊C4—861no—
559C2×C4⋊C4—861no—
560C2×C4⋊C4—861no—
561C2×C22⋊C4—861no—
562C2×C22⋊C4—861no—
563C2×C22⋊C4—861no—
564C2×C22⋊C4—861no—
565C2×C22⋊C4—861no—
566C2×C42—431no—
567C2×C42—431no—
568C2×C42—431no—
569C2×C42—431no—
570C2×C42—431no—
571C2×C42—431no—
572C2×C42—431no—
573C2×C42—431no—
574C2×C42—431no—
575C2×C42—431no—
576C2×C42—431no—
577C2×C42—861no—
578C2×C42C22×D4311yescharacteristic
579C4⋊C8—21no—
580C4⋊C8—21no—
581C4⋊C8—432no—
582C4⋊C8—862no—
583C4⋊C8—862no—
584C4⋊C8—862no—
585C4⋊C8—861no—
586C4⋊C8—861no—
587C4⋊C8C22×D4312yes—
588C22⋊C8—21no—
589C22⋊C8—862no—
590C22⋊C8—861no—
591C4×C8—432no—
592C4×C8—862no—
593C4×C8C22×D4312yes—
594C24—431no—
595C24—861no—
596C2×Q8—431no—
597C2×Q8—861no—
598C2×Q8—864no—
599C2×Q8C2×C4×D4311yescharacteristic
600C2×D4—21no—
601C2×D4—431no—
602C2×D4—861no—
603C2×D4—864no—
604C2×D4—861no—
605C2×D4—861no—
606C2×D4—861no—
607C2×D4—1724no—
608C2×D4C2×C4×D4311yescharacteristic
609C22×C4—21no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—431no—
619C22×C4—431no—
620C22×C4—431no—
621C22×C4—431no—
622C22×C4—431no—
623C22×C4—431no—
624C22×C4—431no—
625C22×C4—862no—
626C22×C4—864no—
627C22×C4—862no—
628C22×C4—861no—
629C22×C4—861no—
630C22×C4—861no—
631C22×C4—861no—
632C22×C4—861no—
633C22×C4—861no—
634C22×C4—1722no—
635C22×C4—1722no—
636C22×C4—1722no—
637C22×C4C2×C4×D4311yescharacteristic
638C22×C4D4×D4311yescharacteristic
639C22×C4D4×D4311yescharacteristic
640M16—42no—
641M16—1724no—
642M16—1722no—
643C2×C8—22no—
644C2×C8—22no—
645C2×C8—862no—
646C2×C8—862no—
647C2×C8—1724no—
648C2×C8—1724no—
649C4⋊C4—21no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—431no—
654C4⋊C4—431no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—861no—
658C4⋊C4—861no—
659C4⋊C4—861no—
660C4⋊C4—861no—
661C4⋊C4—861no—
662C4⋊C4—861no—
663C4⋊C4—861no—
664C4⋊C4—861no—
665C4⋊C4—861no—
666C4⋊C4—861no—
667C4⋊C4—861no—
668C4⋊C4—861no—
669C4⋊C4C2×C4×D4311yescharacteristic
670C4⋊C4C2×C4×D4311yescharacteristic
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—21no—
674C22⋊C4—21no—
675C22⋊C4—21no—
676C22⋊C4—861no—
677C22⋊C4—861no—
678C22⋊C4—861no—
679C22⋊C4—861no—
680C22⋊C4—861no—
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—
691C42—21no—
692C42—431no—
693C42—431no—
694C42—431no—
695C42—431no—
696C42—431no—
697C42—431no—
698C42—431no—
699C42—431no—
700C42—431no—
701C42—431no—
702C42—431no—
703C42—431no—
704C42—861no—
705C42—861no—
706C42—861no—
707C42C2×C4×D4311yescharacteristic
708C42D4×D4311yescharacteristic
709C42D4×D4311yescharacteristic
710C42C23×D4311yescharacteristic
711C23—21no—
712C23—431no—
713C23—431no—
714C23—862no—
715C23—862no—
716C23—862no—
717C23—861no—
718C23—1722no—
719C23—1722no—
720C23—1722no—
721C23C22⋊C4×D4311yescharacteristic
722Q8—22no—
723Q8—862no—
724Q8—1722no—
725D4—22no—
726D4—42no—
727D4—862no—
728D4—1722no—
729D4—1722no—
730D4—1722no—
731D4—1722no—
732C2×C4—22no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—21no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—431no—
742C2×C4—431no—
743C2×C4—434no—
744C2×C4—432no—
745C2×C4—432no—
746C2×C4—431no—
747C2×C4—431no—
748C2×C4—431no—
749C2×C4—431no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—861no—
760C2×C4—861no—
761C2×C4—861no—
762C2×C4—861no—
763C2×C4—861no—
764C2×C4—1721no—
765C2×C4—1721no—
766C2×C4—1722no—
767C2×C4—1722no—
768C2×C4—1722no—
769C2×C4—1722no—
770C2×C4—1722no—
771C2×C4—1721no—
772C2×C4—1721no—
773C2×C4—1721no—
774C2×C4C22⋊C4×D4311yescharacteristic
775C2×C4C22⋊C4×D4311yescharacteristic
776C2×C4C22⋊C4×D4311yescharacteristic
777C2×C4C22×C4×D4311yescharacteristic
778C2×C4C2×D4×D4311yescharacteristic
779C2×C4C2×D4×D4311yescharacteristic
780C8—42no—
781C8—42no—
782C8—1722no—
783C8—1722no—
784C22—21no—
785C22—21no—
786C22—21no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—432no—
791C22—432no—
792C22—432no—
793C22—861no—
794C22—861no—
795C22—861no—
796C22—3444no—
797C22—1724no—
798C22—1721no—
799C22—1721no—
800C22—1721no—
801C22C2×C22⋊C4×D4311yescharacteristic
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—432no—
810C4—432no—
811C4—861no—
812C4—861no—
813C4—861no—
814C4—861no—
815C4—1721no—
816C4—1721no—
817C4—1721no—
818C4#131×D4312yes—
819C4AGL(1,ℤ/8)×D4311yescharacteristic
820C4#137×D4311yescharacteristic
821C2—41no—
822C2—81no—
823C2—434no—
824C2—3441no—
825C2—1721no—
826C2#408×D4311yescharacteristic
827C2#417×D4311yescharacteristic
828C2#421×D4311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC43×#1495C2
socleC22×C43C22×C22⋊C4
prime radical#121×D43C4
cosocleC42×C43C24
hypercenter#1495D43
hypocenterC43C2×#1495
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #431×D43C2semidirect
3. #423×D43C2semidirect
4. #19133061C2semidirect
5. #19133060C2semidirect
6. #19133059C2semidirect
7. #19133058C2semidirect
8. #19133057C2semidirect
9. Q8⋊C8×D43C2semidirect
10. D4⋊C8×D43C2semidirect
11. C43×#1495C2semidirect
35. #14582952C22semidirect
37. #14582950C22semidirect
39. #14582923C22semidirect
42. #14582921C22semidirect
48. #14582631C22semidirect
49. Q8⋊(C43⋊C8)C22semidirect
50. #14582629C22semidirect
51. #14582628C22semidirect
52. D4⋊(C43⋊C8)C22semidirect
53. #14582626C22semidirect
55. C43×#431C22semidirect
56. C43×#423C22semidirect
57. C43×Q8⋊C8C22semidirect
58. C43×D4⋊C8C22semidirect
415. #1495D43direct (N × H)
425. D43#1495direct (N × H)
454. #431C2×D43semidirect
459. #423C2×D43semidirect
468. Q8⋊C8C2×D43semidirect
472. D4⋊C8C2×D43semidirect
473. C43C2×#1495semidirect

Maximal subgroups

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

subgroupindex
#529×D432
#431×D432
#423×D432
#191330612
#191330602
#191330592
#191330582
#191330572
Q8⋊C8×D432
D4⋊C8×D432
C43×#14952
C2×#149543