Finite Group Databasebeta

← D43×#3080 #25964130

Subgroups — D43×#3080 #25964130

Order 11008.

2142 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#125×D43C211yesmaximal, characteristic, complemented
2C4×#41×D43C211yesmaximal, characteristic
3#19144418C211yesmaximal, characteristic, complemented
4#19144417C211yesmaximal, characteristic, complemented
5#19144416C212yesmaximal, complemented
6#19144415C212yesmaximal, complemented
7#19144414C214yesmaximal, complemented
8#19144413C211yesmaximal, characteristic, complemented
9#19144412C214yesmaximal, complemented
10#479×D43C214yesmaximal, complemented
11#478×D43C214yesmaximal, complemented
12#428×D43C212yesmaximal, complemented
13#423×D43C211yesmaximal, characteristic, complemented
14#417×D43C212yesmaximal
15C43×#3080C211yesmaximal, characteristic, complemented
16C2×#41×D43C2211yescharacteristic
17C2×M16×D43C2212yes—
18C2×#13063317C2211yescharacteristic, complemented
19C2×#13063316C2212yescomplemented
20C2×#13063315—22no—
21#125×D43—21no—
22#125×D43—21no—
23#125×D43—21no—
24#125×D43—21no—
25#125×D43C2214yes—
26#125×D43C2214yescomplemented
27#41×Dic43C2211yescharacteristic
28C4×#10621902C2212yes—
29C4×#10621898—21no—
30C4×#10621898C2211yescharacteristic
31#14583367—21no—
32#14583367C2211yescharacteristic
33C4×#10621900—22no—
34C4×#10621900C2212yes—
35C4×Q8×D43C2212yes—
36C4×D4×D43—22no—
37C4×D4×D43C2212yes—
38#117×D43—21no—
39#117×D43C2211yescharacteristic
40C2×C4⋊C4×D43—22no—
41C2×C4⋊C4×D43C2212yes—
42C2×C42×D43—21no—
43C2×C42×D43C2211yescharacteristic
44#14583209C2214yescomplemented
45#14583208C2214yescomplemented
46#14583207C2214yescomplemented
47#14583206C2214yescomplemented
48#14583205C2214yescomplemented
49#14583204C2214yescomplemented
50#14583203C2214yescomplemented
51#14583202C2214yescomplemented
52#14583201C2214yescomplemented
53#14583200C2214yescomplemented
54#14583199C2214yescomplemented
55#14583198C2214yescomplemented
56#14583197C2214yescomplemented
57#14583196C2214yescomplemented
58#14582942C2212yescomplemented
59#14582941C2212yescomplemented
60#14582940C2214yescomplemented
61#14582939C2212yescomplemented
62#14582938C2214yescomplemented
63#107×D43C2214yes—
64#106×D43C2214yes—
65#14582923C2211yescharacteristic, complemented
66#14582922C2212yescomplemented
67#14582921C2214yescomplemented
68C4⋊C8×D43C2214yes—
69#14582901C2212yes—
70#14582900C2212yes—
71#14582899C2214yes—
72#14582898C2212yes—
73#14582897C2214yes—
74#103×D43C2214yes—
75#102×D43C2214yes—
76C2×#125×C43C2211yescharacteristic, complemented
77C4×#41×C43C2211yescharacteristic
78C43×#479C2214yescomplemented
79C43×#478C2214yescomplemented
80C43×#428C2212yescomplemented
81C43×#423C2211yescharacteristic, complemented
82C43×#417C2212yes—
83C2×#10621902C2311yescharacteristic
84C2×#10621898—21no—
85C2×#10621898C2311yescharacteristic
86C2×#10621900—21no—
87C2×#10621900C2311yescharacteristic
88#41×D43—24no—
89#41×D43Q818yes—
90C2×Q8×D43C2311yescharacteristic
91C2×D4×D43—21no—
92C2×D4×D43C2311yescharacteristic
93C22×C4×D43—21no—
94C22×C4×D43—22no—
95C22×C4×D43—22no—
96C22×C4×D43D412yes—
97C22×C4×D43C2311yescharacteristic
98C2×#10621877C2312yes—
99C2×#10621872C2314yes—
100M16×D43—28no—
101C2×C8×D43C2314yes—
102#13063317—21no—
103#13063317—21no—
104#13063317C2314yes—
105#13063316—22no—
106#13063316—22no—
107#13063316C2314yes—
108#13063316C2314yes—
109#13063315—24no—
110#13063315—24no—
111#13063315—24no—
112#13063315—24no—
113Q8×Dic43C2312yes—
114C4×Dic86—22no—
115C4×Dic86C2312yes—
116#13063290—22no—
117#13063290C2312yes—
118C4×D172—22no—
119C4×D172C2312yes—
120D4×Dic43—22no—
121D4×Dic43C2312yes—
122#13063287—22no—
123#13063287C2312yes—
124C4×C22⋊D43—22no—
125C4×C22⋊D43—22no—
126C4×C22⋊D43—22no—
127(C22⋊D43)⋊C4—22no—
128(C22⋊D43)⋊C4—22no—
129(C22⋊D43)⋊C4—22no—
130#13063284—21no—
131#13063284C2311yescharacteristic
132#13063283—22no—
133#13063283C2312yes—
134#13063282—21no—
135#13063282—21no—
136#13063282—21no—
137#13063281—21no—
138#13063281—22no—
139C2×C4⋊Dic43—22no—
140C2×C4⋊Dic43C2312yes—
141C2×Dic43⋊C4—22no—
142C2×Dic43⋊C4—22no—
143C2×Dic43⋊C4—22no—
144C4⋊C4×D43—24no—
145C4⋊C4×D43—24no—
146C4⋊C4×D43—24no—
147C4⋊C4×D43—24no—
148C4⋊C4×D43—22no—
149C4⋊C4×D43—22no—
150C4⋊C4×D43—22no—
151C4⋊C4×D43C2314yes—
152C4⋊C4×D43C2314yes—
153C4⋊C4×D43C2312yes—
154C22⋊C4×D43—21no—
155C22⋊C4×D43—22no—
156C2×C4×Dic43—22no—
157C2×C4×Dic43—21no—
158C2×C4×Dic43D412yes—
159C2×C4×Dic43C2311yescharacteristic
160C42×D43—21no—
161C42×D43—22no—
162C42×D43—21no—
163C42×D43—22no—
164C42×D43—21no—
165C42×D43D411yescharacteristic
166C42×D43D411yescharacteristic
167C42×D43D411yescharacteristic
168C42×D43D411yescharacteristic
169C42×D43C2312yes—
170C42×D43C2312yes—
171#13063259C2314yes—
172#13063258C2314yes—
173#13063258C2314yes—
174#13063257C2314yes—
175#13063256C2314yes—
176#13063256C2314yes—
177C4⋊(C43⋊C8)C2314yes—
178Dic43⋊C8C2314yes—
179Dic43⋊C8C2314yes—
180#13063250C2314yes—
181#13063249C2314yes—
182#13063248C2314yes—
183#13063247C2314yes—
184#13063246C2314yes—
185#13063245C2314yes—
186C2×#41×C43C2311yescharacteristic
187C2×M16×C43C2312yes—
188#125×C43—21no—
189#125×C43—21no—
190#125×C43C2314yes—
191C4×Q8×C43C2312yes—
192C4×D4×C43—22no—
193C4×D4×C43C2312yes—
194#117×C43—21no—
195#117×C43C2311yescharacteristic
196C2×C4⋊C4×C43—22no—
197C2×C4⋊C4×C43C2312yes—
198C2×C42×C43—21no—
199C2×C42×C43C2311yescharacteristic
200#107×C43C2314yes—
201#106×C43C2314yes—
202C4⋊C8×C43C2314yes—
203#103×C43C2314yes—
204#102×C43C2314yes—
205C23×D43—21no—
206C23×D43C2×D411yescharacteristic
207#41×C43—22no—
208#41×C43C2×Q814yes—
209C2×Q8×C43C2411yescharacteristic
210C2×D4×C43—21no—
211C2×D4×C43C2411yescharacteristic
212C22×C4×C43—21no—
213C22×C4×C43—22no—
214C22×C4×C43—22no—
215C22×C4×C43C2×D412yes—
216C22×C4×C43C2411yescharacteristic
217C2×C22⋊D43—21no—
218C2×C22⋊D43—21no—
219C2×C22⋊D43—21no—
220C22×Dic43—21no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43C2×D412yes—
224C22×Dic43C2×D411yescharacteristic
225#10621902—22no—
226#10621902C2×Q814yes—
227Q8×D43—22no—
228Q8×D43C2×Q814yes—
229#10621900—28no—
230#10621900—22no—
231#10621900C2×Q814yes—
232D4×D43—22no—
233D4×D43—28no—
234D4×D43C2×Q814yes—
235#10621898—22no—
236#10621898—28no—
237#10621898C2×Q814yes—
238C2×D172—21no—
239C2×D172C2411yescharacteristic
240C2×C4×D43—21no—
241C2×C4×D43—21no—
242C2×C4×D43—28no—
243C2×C4×D43—22no—
244C2×C4×D43—22no—
245C2×C4×D43—21no—
246C2×C4×D43—22no—
247C2×C4×D43—24no—
248C2×C4×D43—24no—
249C2×C4×D43—44no—
250C2×C4×D43—48no—
251C2×C4×D43—48no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2×D412yes—
254C2×C4×D43C2×D412yes—
255C2×C4×D43C2×D412yes—
256C2×C4×D43C2×D411yescharacteristic
257C2×C4×D43C2×D411yescharacteristic
258C2×C4×D43C2×Q814yes—
259C2×C4×D43#4114yes—
260C2×C4×D43C2411yescharacteristic
261C2×C4×D43C2411yescharacteristic
262C2×Dic86—21no—
263C2×Dic86C2411yescharacteristic
264M16×C43—24no—
265C2×C8×C43C2414yes—
266C4⋊C4×C43—24no—
267C4⋊C4×C43—24no—
268C4⋊C4×C43—22no—
269C4⋊C4×C43—22no—
270C4⋊C4×C43C2414yes—
271C4⋊C4×C43C2412yes—
272C22⋊C4×C43—22no—
273C22⋊C4×C43—21no—
274C42×C43—21no—
275C42×C43—22no—
276C42×C43C2×D411yescharacteristic
277C42×C43C2×D411yescharacteristic
278C42×C43C2412yes—
279C22⋊Dic43—22no—
280C22⋊Dic43—21no—
281(C2×D43)⋊C4—22no—
282(C2×D43)⋊C4—22no—
283(C2×D43)⋊C4—22no—
284C4⋊Dic43—22no—
285C4⋊Dic43—24no—
286C4⋊Dic43—24no—
287C4⋊Dic43—22no—
288C4⋊Dic43C2414yes—
289C4⋊Dic43C2412yes—
290Dic43⋊C4—24no—
291Dic43⋊C4—24no—
292Dic43⋊C4—22no—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296Dic43⋊C4—24no—
297Dic43⋊C4—22no—
298Dic43⋊C4—22no—
299C4×Dic43—21no—
300C4×Dic43—22no—
301C4×Dic43—22no—
302C4×Dic43—22no—
303C4×Dic43—22no—
304C4×Dic43C2×D411yescharacteristic
305C4×Dic43C2×D412yes—
306C4×Dic43C2×D411yescharacteristic
307C4×Dic43C2×D412yes—
308C4×Dic43C2×D412yes—
309C4×Dic43C2×D412yes—
310C4×Dic43C2412yes—
311#10621877—24no—
312C2×C43⋊C8C2414yes—
313#10621872—28no—
314C8×D43—28no—
315C23×C43—21no—
316C23×C43C22×D411yescharacteristic
317C22×D43—24no—
318C22×D43—21no—
319C22×D43—24no—
320C22×D43—44no—
321C22×D43C22⋊Q814yes—
322C22×D43C22×D411yescharacteristic
323C22×D43C22×D411yescharacteristic
324Q8×C43—21no—
325Q8×C43C22×Q812yes—
326D4×C43—24no—
327D4×C43—21no—
328D4×C43C22×Q812yes—
329C2×C4×C43—21no—
330C2×C4×C43—24no—
331C2×C4×C43—22no—
332C2×C4×C43—24no—
333C2×C4×C43—42no—
334C2×C4×C43—44no—
335C2×C4×C43—44no—
336C2×C4×C43C22×D412yes—
337C2×C4×C43C22×D412yes—
338C2×C4×C43C22×D411yescharacteristic
339C2×C4×C43C22×Q812yes—
340C2×C4×C43C2×#4112yes—
341C2×C4×C43C2511yescharacteristic
342C22⋊D43—24no—
343C22⋊D43—24no—
344C22⋊D43—24no—
345C2×Dic43—21no—
346C2×Dic43—24no—
347C2×Dic43—22no—
348C2×Dic43—24no—
349C2×Dic43—42no—
350C2×Dic43—44no—
351C2×Dic43—44no—
352C2×Dic43C22⋊Q814yes—
353C2×Dic43C22×D412yes—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D411yescharacteristic
356C2×Dic43C22×D411yescharacteristic
357D172—24no—
358D172—21no—
359D172C22×Q812yes—
360C4×D43—24no—
361C4×D43—24no—
362C4×D43—24no—
363C4×D43—24no—
364C4×D43—24no—
365C4×D43—42no—
366C4×D43—42no—
367C4×D43—44no—
368C4×D43—44no—
369C4×D43—48no—
370C4×D43—44no—
371C4×D43—48no—
372C4×D43C22⋊Q814yes—
373C4×D43C22⋊Q814yes—
374C4×D43C22×Q812yes—
375C4×D43C22×Q812yes—
376C4×D43C2×#4112yes—
377C4×D43C2×#4112yes—
378Dic86—21no—
379Dic86—24no—
380Dic86C22×Q812yes—
381C8×C43—24no—
382C43⋊C8—24no—
383C2×#3080—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—42no—
387C22×C43C2×C22⋊Q812yes—
388C22×C43C23×D411yescharacteristic
389C2×D43—22no—
390C2×D43—28no—
391C2×D43—22no—
392C2×D43—42no—
393C2×D43—48no—
394C2×D43C2×C22⋊Q812yes—
395C2×D43C2×C22⋊Q812yes—
396C2×D43#57514yes—
397C4×C43—22no—
398C4×C43—22no—
399C4×C43—22no—
400C4×C43—42no—
401C4×C43—44no—
402C4×C43C2×C22⋊Q812yes—
403C4×C43C23×Q811yescharacteristic
404C4×C43C22×#4111yescharacteristic
405Dic43—22no—
406Dic43—22no—
407Dic43—22no—
408Dic43—42no—
409Dic43—44no—
410Dic43C2×C22⋊Q812yes—
411Dic43C2×C22⋊Q812yes—
412C22×#125—431no—
413C2×C4×#41—431no—
414#3080—434no—
415#3080—434no—
416#3080—432no—
417#3080—431no—
418#3080—432no—
419#3080—431no—
420#3080—431no—
421#3080D4311yescharacteristic, direct product factor
422C2×#479—434no—
423C2×#478—434no—
424C2×#428—432no—
425C2×#423—431no—
426C2×#417—432no—
427C2×C43—22no—
428C2×C43—42no—
429C2×C43C22×C22⋊Q811yescharacteristic
430C2×C43C2×#57512yes—
431D43—22no—
432D43—42no—
433D43#308014yesdirect product factor
434C22×#41—431no—
435C22×M16—432no—
436C2×#125—434no—
437C2×#125—434no—
438C2×#125—432no—
439C2×#125—431no—
440C2×#125—862no—
441C2×#125—861no—
442C2×#125—861no—
443C2×#125—861no—
444C2×#125—861no—
445C2×#125C2×D4311yescharacteristic, complemented
446C4×#41—431no—
447C4×#41—432no—
448C4×#41—432no—
449C4×#41—431no—
450C4×#41—431no—
451C4×#41—861no—
452C4×#41—861no—
453C4×#41—862no—
454C4×#41C2×D4311yescharacteristic
455C2×C4×Q8—432no—
456C2×C4×D4—432no—
457C2×C4×D4—862no—
458C2×#117—431no—
459C2×#117—861no—
460C22×C4⋊C4—432no—
461C22×C4⋊C4—862no—
462C22×C42—431no—
463C22×C42—861no—
464#479—434no—
465#479—434no—
466#479—434no—
467#479—434no—
468#479—434no—
469#479—434no—
470#479—434no—
471#479C2×D4314yescomplemented
472#478—434no—
473#478—434no—
474#478—434no—
475#478—434no—
476#478—434no—
477#478—434no—
478#478—434no—
479#478C2×D4314yescomplemented
480#428—432no—
481#428—432no—
482#428—432no—
483#428—434no—
484#428—434no—
485#428C2×D4312yescomplemented
486C2×#107—434no—
487C2×#106—434no—
488#423—432no—
489#423—431no—
490#423—434no—
491#423C2×D4311yescharacteristic, complemented
492C2×C4⋊C8—434no—
493#417—432no—
494#417—432no—
495#417—432no—
496#417—434no—
497#417—434no—
498#417C2×D4312yes—
499C2×#103—434no—
500C2×#102—434no—
501C43C2×#308011yescharacteristic, complemented, Sylow
502C2×#41—438no—
503C2×#41—431no—
504C2×#41—431no—
505C2×#41—431no—
506C2×#41—861no—
507C2×#41—861no—
508C2×#41—864no—
509C2×#41C22×D4311yescharacteristic
510C22×Q8—431no—
511C22×D4—431no—
512C22×D4—861no—
513C23×C4—431no—
514C23×C4—432no—
515C23×C4—861no—
516C23×C4—862no—
517C23×C4—862no—
518C2×M16—432no—
519C2×M16—434no—
520C2×M16—868no—
521C2×M16C22×D4312yes—
522C22×C8—434no—
523#125—21no—
524#125—21no—
525#125—434no—
526#125—434no—
527#125—434no—
528#125—864no—
529#125—864no—
530#125—864no—
531#125—864no—
532#125—862no—
533#125—862no—
534#125—861no—
535#125—861no—
536#125C22×D4314yes—
537C4×Q8—432no—
538C4×Q8—432no—
539C4×Q8—432no—
540C4×Q8—862no—
541C4×Q8—862no—
542C4×Q8C22×D4312yes—
543C4×D4—22no—
544C4×D4—432no—
545C4×D4—432no—
546C4×D4—432no—
547C4×D4—862no—
548C4×D4—862no—
549C4×D4—862no—
550C4×D4—862no—
551C4×D4—862no—
552C4×D4—862no—
553C4×D4—862no—
554C4×D4—862no—
555C4×D4—862no—
556C4×D4C22×D4312yes—
557#117—21no—
558#117—431no—
559#117—432no—
560#117—861no—
561#117—861no—
562#117—862no—
563#117—862no—
564#117—861no—
565#117—861no—
566#117—861no—
567#117C22×D4311yescharacteristic
568C2×C4⋊C4—22no—
569C2×C4⋊C4—432no—
570C2×C4⋊C4—434no—
571C2×C4⋊C4—434no—
572C2×C4⋊C4—432no—
573C2×C4⋊C4—862no—
574C2×C4⋊C4—862no—
575C2×C4⋊C4—864no—
576C2×C4⋊C4—864no—
577C2×C4⋊C4—864no—
578C2×C4⋊C4—864no—
579C2×C4⋊C4—862no—
580C2×C4⋊C4—862no—
581C2×C4⋊C4—862no—
582C2×C4⋊C4—862no—
583C2×C4⋊C4—862no—
584C2×C4⋊C4C22×D4312yes—
585C2×C22⋊C4—862no—
586C2×C22⋊C4—861no—
587C2×C42—21no—
588C2×C42—432no—
589C2×C42—431no—
590C2×C42—431no—
591C2×C42—431no—
592C2×C42—431no—
593C2×C42—431no—
594C2×C42—432no—
595C2×C42—432no—
596C2×C42—861no—
597C2×C42—862no—
598C2×C42—861no—
599C2×C42—862no—
600C2×C42—862no—
601C2×C42—861no—
602C2×C42—861no—
603C2×C42C22×D4311yescharacteristic
604#107—434no—
605#107—434no—
606#107—434no—
607#107C22×D4314yes—
608#106—434no—
609#106—434no—
610#106—434no—
611#106C22×D4314yes—
612C4⋊C8—434no—
613C4⋊C8—434no—
614C4⋊C8—434no—
615C4⋊C8C22×D4314yes—
616#103—434no—
617#103—434no—
618#103—434no—
619#103C22×D4314yes—
620#102—434no—
621#102—434no—
622#102—434no—
623#102C22×D4314yes—
624C24—431no—
625C24—861no—
626#41—22no—
627#41—434no—
628#41—434no—
629#41—434no—
630#41—868no—
631#41—868no—
632#41—862no—
633#41—862no—
634#41—862no—
635#41Q8×D4314yes—
636C2×Q8—434no—
637C2×Q8—431no—
638C2×Q8—861no—
639C2×Q8—862no—
640C2×Q8C23×D4311yescharacteristic
641C2×D4—21no—
642C2×D4—434no—
643C2×D4—431no—
644C2×D4—861no—
645C2×D4—862no—
646C2×D4—861no—
647C2×D4—868no—
648C2×D4—861no—
649C2×D4—861no—
650C2×D4C23×D4311yescharacteristic
651C22×C4—21no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—431no—
655C22×C4—431no—
656C22×C4—431no—
657C22×C4—434no—
658C22×C4—434no—
659C22×C4—431no—
660C22×C4—431no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—432no—
666C22×C4—861no—
667C22×C4—868no—
668C22×C4—862no—
669C22×C4—861no—
670C22×C4—862no—
671C22×C4—864no—
672C22×C4—864no—
673C22×C4—861no—
674C22×C4—862no—
675C22×C4—861no—
676C22×C4—862no—
677C22×C4—862no—
678C22×C4—1724no—
679C22×C4—1728no—
680C22×C4—1728no—
681C22×C4D4×D4312yes—
682C22×C4C23×D4311yescharacteristic
683M16—24no—
684M16—868no—
685M16—864no—
686C2×C8—434no—
687C2×C8—868no—
688C2×C8C23×D4314yes—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—434no—
694C4⋊C4—432no—
695C4⋊C4—864no—
696C4⋊C4—864no—
697C4⋊C4—862no—
698C4⋊C4—864no—
699C4⋊C4—864no—
700C4⋊C4—864no—
701C4⋊C4—864no—
702C4⋊C4—862no—
703C4⋊C4—862no—
704C4⋊C4—862no—
705C4⋊C4—864no—
706C4⋊C4—864no—
707C4⋊C4—862no—
708C4⋊C4C23×D4314yes—
709C4⋊C4C23×D4312yes—
710C22⋊C4—21no—
711C22⋊C4—22no—
712C22⋊C4—862no—
713C22⋊C4—862no—
714C22⋊C4—862no—
715C22⋊C4—861no—
716C22⋊C4—862no—
717C42—21no—
718C42—22no—
719C42—432no—
720C42—431no—
721C42—432no—
722C42—431no—
723C42—432no—
724C42—432no—
725C42—432no—
726C42—862no—
727C42—862no—
728C42—862no—
729C42—861no—
730C42—862no—
731C42D4×D4311yescharacteristic
732C42D4×D4311yescharacteristic
733C42C23×D4312yes—
734C23—21no—
735C23—431no—
736C23—434no—
737C23—431no—
738C23—864no—
739C23—864no—
740C23—861no—
741C23—1724no—
742C23C2×D4×D4311yescharacteristic
743Q8—21no—
744Q8—432no—
745Q8—864no—
746Q8—861no—
747Q8C2×Q8×D4312yes—
748D4—24no—
749D4—21no—
750D4—432no—
751D4—864no—
752D4—864no—
753D4—864no—
754D4—864no—
755D4—861no—
756D4C2×Q8×D4312yes—
757C2×C4—21no—
758C2×C4—24no—
759C2×C4—22no—
760C2×C4—24no—
761C2×C4—42no—
762C2×C4—44no—
763C2×C4—44no—
764C2×C4—434no—
765C2×C4—431no—
766C2×C4—431no—
767C2×C4—434no—
768C2×C4—434no—
769C2×C4—432no—
770C2×C4—432no—
771C2×C4—432no—
772C2×C4—432no—
773C2×C4—432no—
774C2×C4—432no—
775C2×C4—864no—
776C2×C4—864no—
777C2×C4—864no—
778C2×C4—864no—
779C2×C4—864no—
780C2×C4—861no—
781C2×C4—864no—
782C2×C4—862no—
783C2×C4—864no—
784C2×C4—1722no—
785C2×C4—1722no—
786C2×C4—1724no—
787C2×C4—1724no—
788C2×C4—1724no—
789C2×C4—1728no—
790C2×C4—1728no—
791C2×C4—1722no—
792C2×C4—1724no—
793C2×C4—1724no—
794C2×C4C2×D4×D4312yes—
795C2×C4C2×D4×D4312yes—
796C2×C4C2×D4×D4311yescharacteristic
797C2×C4C2×Q8×D4312yes—
798C2×C4#41×D4312yes—
799C2×C4C24×D4311yescharacteristic
800C8—24no—
801C8—864no—
802C22—22no—
803C22—22no—
804C22—42no—
805C22—434no—
806C22—432no—
807C22—432no—
808C22—868no—
809C22—862no—
810C22—862no—
811C22—1728no—
812C22—1722no—
813C22C22⋊Q8×D4312yes—
814C22C22×D4×D4311yescharacteristic
815C4—22no—
816C4—22no—
817C4—22no—
818C4—42no—
819C4—44no—
820C4—432no—
821C4—432no—
822C4—862no—
823C4—862no—
824C4—862no—
825C4—1722no—
826C4—1724no—
827C4C22⋊Q8×D4312yes—
828C4C22×Q8×D4311yescharacteristic
829C4C2×#41×D4311yescharacteristic
830C2—22no—
831C2—42no—
832C2—434no—
833C2—862no—
834C2—1722no—
835C2C2×C22⋊Q8×D4311yescharacteristic
836C2#575×D4312yes—
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3080C2
socleC22×C43C23×D4
prime radicalC2×#41×D43C22
hypercenter#3080D43
hypocenterC43C2×#3080
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. C2×#125×D43C2semidirect
3. #19144418C2semidirect
4. #19144417C2semidirect
5. #19144416C2semidirect
6. #19144415C2semidirect
7. #19144414C2semidirect
8. #19144413C2semidirect
9. #19144412C2semidirect
10. #479×D43C2semidirect
11. #478×D43C2semidirect
12. #428×D43C2semidirect
13. #423×D43C2semidirect
15. C43×#3080C2semidirect
18. C2×#13063317C22semidirect
19. C2×#13063316C22semidirect
26. #125×D43C22semidirect
44. #14583209C22semidirect
45. #14583208C22semidirect
46. #14583207C22semidirect
47. #14583206C22semidirect
48. #14583205C22semidirect
49. #14583204C22semidirect
50. #14583203C22semidirect
51. #14583202C22semidirect
52. #14583201C22semidirect
53. #14583200C22semidirect
54. #14583199C22semidirect
55. #14583198C22semidirect
56. #14583197C22semidirect
57. #14583196C22semidirect
58. #14582942C22semidirect
59. #14582941C22semidirect
60. #14582940C22semidirect
61. #14582939C22semidirect
62. #14582938C22semidirect
65. #14582923C22semidirect
66. #14582922C22semidirect
67. #14582921C22semidirect
76. C2×#125×C43C22semidirect
78. C43×#479C22semidirect
79. C43×#478C22semidirect
80. C43×#428C22semidirect
81. C43×#423C22semidirect
421. #3080D43direct (N × H)
433. D43#3080direct (N × H)
445. C2×#125C2×D43semidirect
471. #479C2×D43semidirect
479. #478C2×D43semidirect
485. #428C2×D43semidirect
491. #423C2×D43semidirect
501. C43C2×#3080semidirect

Maximal subgroups

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

subgroupindex
C2×#125×D432
C4×#41×D432
#191444182
#191444172
#191444162
#191444152
#191444142
#191444132
#191444122
#479×D432
#478×D432
#428×D432
#423×D432
#417×D432
C43×#30802
C2×#308043