Finite Group Databasebeta

← D43×#3236 #25968705

Subgroups — D43×#3236 #25968705

Order 11008.

1770 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2C2×#125×D43C211yesmaximal, characteristic
3#19145803C211yesmaximal, characteristic, complemented
4#19145802C212yesmaximal, complemented
5#19145801C211yesmaximal, characteristic, complemented
6#19145800C212yesmaximal, complemented
7#19145799C214yesmaximal, complemented
8#19145798C212yesmaximal, complemented
9#19145797C211yesmaximal, characteristic, complemented
10#19145796C212yesmaximal, complemented
11#501×D43C212yesmaximal, complemented
12#491×D43C212yesmaximal, complemented
13#484×D43C212yesmaximal
14#483×D43C212yesmaximal
15#479×D43C214yesmaximal, complemented
16#432×D43C211yesmaximal, characteristic
17C43×#3236C211yesmaximal, characteristic, complemented
18#14583456C2211yescharacteristic
19#14583455—21no—
20#14583454C2211yescharacteristic
21#14583454C2211yescharacteristic
22#14583453—21no—
23#14583453C2212yes—
24#14583452—21no—
25#14583451—21no—
26#14583451C2212yes—
27C4⋊Q8×D43C2211yescharacteristic
28C4⋊Q8×D43C2211yescharacteristic
29C2×#13063317C2211yescharacteristic
30C2×#13063316C2211yescharacteristic
31C2×#13063316C2211yescharacteristic
32C2×#13063315—21no—
33C2×#13063315—21no—
34#125×D43—21no—
35#125×D43—21no—
36#125×D43—21no—
37#125×D43—21no—
38#125×D43—21no—
39#125×D43C2212yes—
40#125×D43C2212yes—
41#125×D43C2212yes—
42#125×D43C2212yes—
43C22⋊Q8×D43—21no—
44C22⋊Q8×D43C2212yes—
45C4×Q8×D43—21no—
46C4×Q8×D43C2212yes—
47#117×D43—21no—
48C2×C4⋊C4×D43—21no—
49C2×C4⋊C4×D43—21no—
50C2×C4⋊C4×D43C2211yescharacteristic
51C2×C4⋊C4×D43C2211yescharacteristic
52C2×C42×D43C2211yescharacteristic
53#14583309C2212yescomplemented
54#14583308C2212yescomplemented
55#14583307C2214yescomplemented
56#14583306C2214yescomplemented
57#14583305C2212yescomplemented
58#14583269C2212yescomplemented
59#14583268C2212yescomplemented
60#14583267C2212yescomplemented
61#14583266C2214yescomplemented
62#14583266C2214yescomplemented
63#14583236C2214yes—
64#14583235C2212yes—
65#14583234C2212yes—
66#14583233C2214yes—
67#14583232C2212yes—
68#14583231C2214yes—
69#14583230C2212yes—
70#14583229C2212yes—
71#14583228C2214yes—
72#14583227C2212yes—
73#14583209C2214yescomplemented
74#14583208C2214yescomplemented
75#14583207C2214yescomplemented
76#14583206C2214yescomplemented
77#14583205C2214yescomplemented
78#14583204C2214yescomplemented
79#14583203C2214yescomplemented
80#14582956C2211yescharacteristic
81#14582955C2212yes—
82#14582954C2212yes—
83#14582953C2212yes—
84#107×D43C2214yes—
85#106×D43C2214yes—
86C4⋊C8×D43C2212yes—
87#103×D43C2214yes—
88#103×D43C2214yes—
89C22⋊C8×D43C2212yes—
90#97×D43C2212yes—
91C43×#533C2211yescharacteristic
92C2×#125×C43C2211yescharacteristic
93C43×#501C2212yescomplemented
94C43×#491C2212yescomplemented
95C43×#484C2212yes—
96C43×#483C2212yes—
97C43×#479C2214yescomplemented
98C43×#432C2211yescharacteristic
99C2×Q8×D43—21no—
100C2×Q8×D43C2312yes—
101C22×C4×D43—21no—
102C22×C4×D43—21no—
103C22×C4×D43D411yescharacteristic
104C22×C4×D43D411yescharacteristic
105C22×C4×D43C2311yescharacteristic
106C2×C8×D43C2314yes—
107#13063325C2311yescharacteristic
108#13063325C2311yescharacteristic
109#13063324—21no—
110#13063324—21no—
111#13063324—21no—
112#13063324C2312yes—
113#13063323—21no—
114#13063323C2312yes—
115#13063317—21no—
116#13063317—21no—
117#13063317—21no—
118#13063317C2312yes—
119#13063317C2312yes—
120#13063316—21no—
121#13063316—21no—
122#13063316—21no—
123#13063316—21no—
124#13063316—21no—
125#13063316—21no—
126#13063316C2312yes—
127#13063316C2312yes—
128#13063316C2312yes—
129#13063316C2312yes—
130#13063315—22no—
131#13063315—22no—
132#13063315—22no—
133#13063315—22no—
134#13063315—22no—
135#13063315—22no—
136#13063315—22no—
137#13063315—22no—
138#13063315—22no—
139#13063315—22no—
140#13063305—21no—
141#13063305C2312yes—
142#13063304—21no—
143#13063304C2312yes—
144#13063303—22no—
145#13063303—22no—
146#13063302—22no—
147#13063302—22no—
148#13063301—21no—
149#13063301C2312yes—
150Q8×Dic43—21no—
151Q8×Dic43C2312yes—
152C4×Dic86—21no—
153C4×Dic86—22no—
154C4×Dic86—22no—
155C4×Dic86C2312yes—
156#13063290—21no—
157#13063290—22no—
158#13063290—22no—
159#13063290C2312yes—
160#13063284—21no—
161#13063283—21no—
162#13063283—21no—
163#13063282—22no—
164#13063281—22no—
165C2×C4⋊Dic43—21no—
166C2×C4⋊Dic43—21no—
167C2×C4⋊Dic43C2311yescharacteristic
168C2×C4⋊Dic43C2311yescharacteristic
169C2×Dic43⋊C4—21no—
170C2×Dic43⋊C4—21no—
171C2×Dic43⋊C4—21no—
172C2×Dic43⋊C4—21no—
173C2×Dic43⋊C4—21no—
174C2×Dic43⋊C4—21no—
175C4⋊C4×D43—22no—
176C4⋊C4×D43—22no—
177C4⋊C4×D43—22no—
178C4⋊C4×D43—22no—
179C4⋊C4×D43—22no—
180C4⋊C4×D43—22no—
181C4⋊C4×D43—22no—
182C4⋊C4×D43—22no—
183C4⋊C4×D43—21no—
184C4⋊C4×D43—21no—
185C4⋊C4×D43—21no—
186C4⋊C4×D43—21no—
187C4⋊C4×D43—21no—
188C4⋊C4×D43—21no—
189C4⋊C4×D43—21no—
190C4⋊C4×D43—22no—
191C4⋊C4×D43—22no—
192C4⋊C4×D43C2312yes—
193C4⋊C4×D43C2312yes—
194C4⋊C4×D43C2312yes—
195C4⋊C4×D43C2312yes—
196C4⋊C4×D43C2312yes—
197C22⋊C4×D43—22no—
198C2×C4×Dic43D411yescharacteristic
199C2×C4×Dic43D411yescharacteristic
200C2×C4×Dic43C2311yescharacteristic
201C42×D43—22no—
202C42×D43D411yescharacteristic
203C42×D43D411yescharacteristic
204C42×D43D411yescharacteristic
205C42×D43D411yescharacteristic
206C42×D43C2311yescharacteristic
207C42×D43C2311yescharacteristic
208C42×D43C2311yescharacteristic
209C42×D43C2311yescharacteristic
210#13063259C2314yes—
211#13063258C2314yes—
212#13063258C2314yes—
213#13063257C2314yes—
214#13063256C2314yes—
215#13063256C2314yes—
216C4⋊(C43⋊C8)C2312yes—
217Dic43⋊C8C2314yes—
218#13063250C2314yes—
219#13063250C2314yes—
220#13063249C2314yes—
221#13063249C2314yes—
222#13063248C2314yes—
223#13063248C2314yes—
224C22⋊(C43⋊C8)C2312yes—
225(C2×D43)⋊C8C2314yes—
226#13063236C2312yes—
227#13063235C2314yes—
228C4⋊Q8×C43C2311yescharacteristic
229C4⋊Q8×C43C2311yescharacteristic
230#125×C43—21no—
231#125×C43—21no—
232#125×C43—21no—
233#125×C43C2312yes—
234#125×C43C2312yes—
235C22⋊Q8×C43—21no—
236C22⋊Q8×C43C2312yes—
237C4×Q8×C43—21no—
238C4×Q8×C43C2312yes—
239#117×C43—21no—
240C2×C4⋊C4×C43—21no—
241C2×C4⋊C4×C43—21no—
242C2×C4⋊C4×C43C2311yescharacteristic
243C2×C4⋊C4×C43C2311yescharacteristic
244C2×C42×C43C2311yescharacteristic
245#107×C43C2314yes—
246#106×C43C2314yes—
247C4⋊C8×C43C2312yes—
248#103×C43C2314yes—
249#103×C43C2314yes—
250C22⋊C8×C43C2312yes—
251#97×C43C2312yes—
252C23×D43C2×D411yescharacteristic
253C2×Q8×C43—21no—
254C2×Q8×C43C2412yes—
255C22×C4×C43—21no—
256C22×C4×C43—21no—
257C22×C4×C43C2×D411yescharacteristic
258C22×C4×C43C2×D411yescharacteristic
259C22×C4×C43C2411yescharacteristic
260C22×Dic43—21no—
261C22×Dic43—21no—
262C22×Dic43C2×D411yescharacteristic
263C22×Dic43C2×D411yescharacteristic
264C22×Dic43C2×D411yescharacteristic
265Q8×D43—28no—
266Q8×D43—44no—
267C2×C4×D43—24no—
268C2×C4×D43—24no—
269C2×C4×D43—22no—
270C2×C4×D43—22no—
271C2×C4×D43—22no—
272C2×C4×D43—22no—
273C2×C4×D43—22no—
274C2×C4×D43—22no—
275C2×C4×D43—42no—
276C2×C4×D43—44no—
277C2×C4×D43—44no—
278C2×C4×D43C2×D411yescharacteristic
279C2×C4×D43C2×D411yescharacteristic
280C2×C4×D43C2×D411yescharacteristic
281C2×C4×D43C2×D411yescharacteristic
282C2×C4×D43C2×D411yescharacteristic
283C2×C4×D43C2×D411yescharacteristic
284C2×C4×D43C2×D411yescharacteristic
285C2×C4×D43C2×D411yescharacteristic
286C2×C4×D43C2×D411yescharacteristic
287C2×C4×D43C2×D411yescharacteristic
288C2×C4×D43C2411yescharacteristic
289C2×C4×D43C2411yescharacteristic
290C2×Dic86—21no—
291C2×Dic86—22no—
292C2×Dic86—22no—
293C2×Dic86C2412yes—
294C2×C8×C43C2414yes—
295C4⋊C4×C43—22no—
296C4⋊C4×C43—22no—
297C4⋊C4×C43—22no—
298C4⋊C4×C43—22no—
299C4⋊C4×C43—21no—
300C4⋊C4×C43—21no—
301C4⋊C4×C43—21no—
302C4⋊C4×C43—21no—
303C4⋊C4×C43—21no—
304C4⋊C4×C43—22no—
305C4⋊C4×C43—22no—
306C4⋊C4×C43C2412yes—
307C4⋊C4×C43C2412yes—
308C4⋊C4×C43C2412yes—
309C22⋊C4×C43—22no—
310C42×C43—22no—
311C42×C43C2×D411yescharacteristic
312C42×C43C2×D411yescharacteristic
313C42×C43C2411yescharacteristic
314C42×C43C2411yescharacteristic
315C22⋊Dic43—22no—
316(C2×D43)⋊C4—22no—
317(C2×D43)⋊C4—22no—
318C4⋊Dic43—21no—
319C4⋊Dic43—21no—
320C4⋊Dic43—21no—
321C4⋊Dic43—21no—
322C4⋊Dic43—21no—
323C4⋊Dic43—22no—
324C4⋊Dic43—22no—
325C4⋊Dic43—22no—
326C4⋊Dic43—22no—
327C4⋊Dic43—22no—
328C4⋊Dic43—22no—
329C4⋊Dic43C2412yes—
330C4⋊Dic43C2412yes—
331C4⋊Dic43C2412yes—
332Dic43⋊C4—22no—
333Dic43⋊C4—22no—
334Dic43⋊C4—22no—
335Dic43⋊C4—22no—
336Dic43⋊C4—22no—
337Dic43⋊C4—22no—
338Dic43⋊C4—22no—
339Dic43⋊C4—22no—
340Dic43⋊C4—22no—
341Dic43⋊C4—22no—
342Dic43⋊C4—22no—
343Dic43⋊C4—22no—
344Dic43⋊C4—22no—
345Dic43⋊C4—22no—
346Dic43⋊C4—22no—
347Dic43⋊C4—22no—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351Dic43⋊C4—22no—
352C4×Dic43—22no—
353C4×Dic43—22no—
354C4×Dic43—22no—
355C4×Dic43C2×D411yescharacteristic
356C4×Dic43C2×D411yescharacteristic
357C4×Dic43C2×D411yescharacteristic
358C4×Dic43C2×D411yescharacteristic
359C4×Dic43C2×D411yescharacteristic
360C4×Dic43C2×D411yescharacteristic
361C4×Dic43C2×D411yescharacteristic
362C4×Dic43C2×D411yescharacteristic
363C4×Dic43C2×D411yescharacteristic
364C4×Dic43C2×D411yescharacteristic
365C4×Dic43C2411yescharacteristic
366C4×Dic43C2411yescharacteristic
367C2×C43⋊C8C2414yes—
368C8×D43—28no—
369C23×C43C22×D411yescharacteristic
370C22×D43—22no—
371C22×D43—22no—
372C22×D43#13714yes—
373C22×D43C22×D411yescharacteristic
374C22×D43C22×D411yescharacteristic
375Q8×C43—24no—
376Q8×C43—42no—
377C2×C4×C43—22no—
378C2×C4×C43—22no—
379C2×C4×C43—22no—
380C2×C4×C43—22no—
381C2×C4×C43—22no—
382C2×C4×C43—22no—
383C2×C4×C43—41no—
384C2×C4×C43—42no—
385C2×C4×C43—42no—
386C2×C4×C43C22×D411yescharacteristic
387C2×C4×C43C22×D411yescharacteristic
388C2×C4×C43C22×D411yescharacteristic
389C2×C4×C43C22×D411yescharacteristic
390C2×C4×C43C22×D411yescharacteristic
391C2×C4×C43C2511yescharacteristic
392C2×Dic43—22no—
393C2×Dic43—22no—
394C2×Dic43—22no—
395C2×Dic43—22no—
396C2×Dic43—22no—
397C2×Dic43—22no—
398C2×Dic43—41no—
399C2×Dic43—42no—
400C2×Dic43—42no—
401C2×Dic43C22×D411yescharacteristic
402C2×Dic43C22×D411yescharacteristic
403C2×Dic43C22×D411yescharacteristic
404C2×Dic43C22×D411yescharacteristic
405C2×Dic43C22×D411yescharacteristic
406C2×Dic43C22×D411yescharacteristic
407C4×D43—22no—
408C4×D43—22no—
409C4×D43—22no—
410C4×D43—22no—
411C4×D43—22no—
412C4×D43—22no—
413C4×D43—22no—
414C4×D43—22no—
415C4×D43—22no—
416C4×D43—41no—
417C4×D43—41no—
418C4×D43—44no—
419C4×D43—44no—
420C4×D43—44no—
421C4×D43—44no—
422C4×D43—44no—
423C4×D43—44no—
424C4×D432−1+414yes—
425Dic86—24no—
426Dic86—44no—
427Dic86—42no—
428Dic86—44no—
429C8×C43—24no—
430C43⋊C8—24no—
431C2×#3236—431nomaximal, Sylow
432C22×C43—21no—
433C22×C43—21no—
434C22×C43C2×#13712yes—
435C22×C43C23×D411yescharacteristic
436C2×D43—21no—
437C2×D43—21no—
438C2×D43—28no—
439C2×D43#53612yes—
440C2×D43C2×#13712yes—
441C2×D43C2×#13712yes—
442C2×D43#57512yes—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—21no—
446C4×C43—21no—
447C4×C43—21no—
448C4×C43—42no—
449C4×C43—42no—
450C4×C43—42no—
451C4×C43—42no—
452C4×C43C2×2−1+412yes—
453Dic43—21no—
454Dic43—21no—
455Dic43—21no—
456Dic43—21no—
457Dic43—21no—
458Dic43—42no—
459Dic43—42no—
460Dic43—42no—
461Dic43—42no—
462Dic43#53612yes—
463C2×#533—431no—
464C22×#125—431no—
465#3236—432no—
466#3236—432no—
467#3236—432no—
468#3236—432no—
469#3236—434no—
470#3236—431no—
471#3236—431no—
472#3236—431no—
473#3236D4311yescharacteristic, direct product factor
474C2×#501—432no—
475C2×#491—432no—
476C2×#484—432no—
477C2×#483—432no—
478C2×#479—434no—
479C2×#432—431no—
480C2×C43—22no—
481C2×C43C2×#53611yescharacteristic
482C2×C43C22×#13711yescharacteristic
483C2×C43C2×#57511yescharacteristic
484D43—22no—
485D43#323614yesdirect product factor
486#533—431no—
487#533—431no—
488#533—432no—
489#533—432no—
490#533—431no—
491#533—861no—
492#533—861no—
493#533—861no—
494#533—861no—
495#533C2×D4311yescharacteristic
496C2×C4⋊Q8—431no—
497C2×C4⋊Q8—431no—
498C2×#125—432no—
499C2×#125—432no—
500C2×#125—432no—
501C2×#125—432no—
502C2×#125—431no—
503C2×#125—431no—
504C2×#125—431no—
505C2×#125—861no—
506C2×#125—861no—
507C2×#125—861no—
508C2×#125—861no—
509C2×#125—861no—
510C2×#125—861no—
511C2×#125—861no—
512C2×#125C2×D4311yescharacteristic
513C2×C22⋊Q8—432no—
514C2×C22⋊Q8—861no—
515C2×C4×Q8—432no—
516C2×C4×Q8—861no—
517C2×#117—861no—
518C22×C4⋊C4—431no—
519C22×C4⋊C4—431no—
520C22×C4⋊C4—861no—
521C22×C4⋊C4—861no—
522C22×C42—431no—
523#501—432no—
524#501—432no—
525#501—434no—
526#501—434no—
527#501—432no—
528#501C2×D4312yescomplemented
529#491—432no—
530#491—432no—
531#491—434no—
532#491—434no—
533#491—432no—
534#491C2×D4312yescomplemented
535#484—432no—
536#484—432no—
537#484—434no—
538#484—434no—
539#484—432no—
540#484C2×D4312yes—
541#483—432no—
542#483—432no—
543#483—434no—
544#483—434no—
545#483—432no—
546#483C2×D4312yes—
547#479—434no—
548#479—434no—
549#479—434no—
550#479—434no—
551#479—434no—
552#479—434no—
553#479—434no—
554#479C2×D4314yescomplemented
555#432—431no—
556#432—432no—
557#432—432no—
558#432—432no—
559#432C2×D4311yescharacteristic
560C2×#107—434no—
561C2×#106—434no—
562C2×C4⋊C8—432no—
563C2×#103—434no—
564C2×#103—434no—
565C2×C22⋊C8—432no—
566C2×#97—432no—
567C43C2×#323611yescharacteristic, complemented, Sylow
568C22×Q8—432no—
569C22×Q8—861no—
570C23×C4—431no—
571C23×C4—431no—
572C23×C4—431no—
573C23×C4—861no—
574C23×C4—861no—
575C22×C8—434no—
576C4⋊Q8—432no—
577C4⋊Q8—432no—
578C4⋊Q8—431no—
579C4⋊Q8—431no—
580C4⋊Q8—861no—
581C4⋊Q8—861no—
582C4⋊Q8—861no—
583C4⋊Q8—861no—
584C4⋊Q8C22×D4311yescharacteristic
585C4⋊Q8C22×D4311yescharacteristic
586#125—21no—
587#125—21no—
588#125—21no—
589#125—432no—
590#125—432no—
591#125—432no—
592#125—432no—
593#125—432no—
594#125—432no—
595#125—862no—
596#125—862no—
597#125—862no—
598#125—862no—
599#125—862no—
600#125—862no—
601#125—862no—
602#125—862no—
603#125—861no—
604#125—861no—
605#125—861no—
606#125—861no—
607#125—862no—
608#125—862no—
609#125—861no—
610#125—861no—
611#125—861no—
612#125—861no—
613#125—861no—
614#125C22×D4312yes—
615#125C22×D4312yes—
616C22⋊Q8—21no—
617C22⋊Q8—432no—
618C22⋊Q8—432no—
619C22⋊Q8—432no—
620C22⋊Q8—862no—
621C22⋊Q8—862no—
622C22⋊Q8—862no—
623C22⋊Q8—862no—
624C22⋊Q8—861no—
625C22⋊Q8—861no—
626C22⋊Q8—861no—
627C22⋊Q8C22×D4312yes—
628C4×Q8—21no—
629C4×Q8—432no—
630C4×Q8—432no—
631C4×Q8—432no—
632C4×Q8—862no—
633C4×Q8—862no—
634C4×Q8—862no—
635C4×Q8—861no—
636C4×Q8—862no—
637C4×Q8—861no—
638C4×Q8—861no—
639C4×Q8C22×D4312yes—
640#117—21no—
641#117—862no—
642#117—862no—
643#117—861no—
644#117—861no—
645#117—861no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—431no—
649C2×C4⋊C4—431no—
650C2×C4⋊C4—432no—
651C2×C4⋊C4—432no—
652C2×C4⋊C4—432no—
653C2×C4⋊C4—432no—
654C2×C4⋊C4—432no—
655C2×C4⋊C4—861no—
656C2×C4⋊C4—861no—
657C2×C4⋊C4—861no—
658C2×C4⋊C4—861no—
659C2×C4⋊C4—862no—
660C2×C4⋊C4—862no—
661C2×C4⋊C4—862no—
662C2×C4⋊C4—862no—
663C2×C4⋊C4—862no—
664C2×C4⋊C4—862no—
665C2×C4⋊C4—862no—
666C2×C4⋊C4—862no—
667C2×C4⋊C4—861no—
668C2×C4⋊C4—861no—
669C2×C4⋊C4—862no—
670C2×C4⋊C4—862no—
671C2×C4⋊C4—861no—
672C2×C4⋊C4—861no—
673C2×C4⋊C4—861no—
674C2×C4⋊C4—861no—
675C2×C4⋊C4—861no—
676C2×C4⋊C4—861no—
677C2×C4⋊C4—861no—
678C2×C4⋊C4—861no—
679C2×C4⋊C4—861no—
680C2×C4⋊C4C22×D4311yescharacteristic
681C2×C4⋊C4C22×D4311yescharacteristic
682C2×C22⋊C4—862no—
683C2×C42—431no—
684C2×C42—431no—
685C2×C42—431no—
686C2×C42—431no—
687C2×C42—431no—
688C2×C42—431no—
689C2×C42—431no—
690C2×C42—431no—
691C2×C42—431no—
692C2×C42—431no—
693C2×C42—431no—
694C2×C42—862no—
695C2×C42C22×D4311yescharacteristic
696#107—434no—
697#107—434no—
698#107—434no—
699#107C22×D4314yes—
700#106—434no—
701#106—434no—
702#106—434no—
703#106C22×D4314yes—
704C4⋊C8—434no—
705C4⋊C8—432no—
706C4⋊C8C22×D4312yes—
707#103—434no—
708#103—434no—
709#103—434no—
710#103—434no—
711#103—434no—
712#103—434no—
713#103C22×D4314yes—
714#103C22×D4314yes—
715C22⋊C8—432no—
716C22⋊C8—434no—
717C22⋊C8C22×D4312yes—
718#97—434no—
719#97—432no—
720#97C22×D4312yes—
721C24—431no—
722C2×Q8—21no—
723C2×Q8—432no—
724C2×Q8—862no—
725C2×Q8—862no—
726C2×Q8—868no—
727C2×Q8—861no—
728C2×Q8—1724no—
729C2×Q8C23×D4312yes—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—431no—
733C22×C4—431no—
734C22×C4—431no—
735C22×C4—431no—
736C22×C4—431no—
737C22×C4—431no—
738C22×C4—431no—
739C22×C4—431no—
740C22×C4—431no—
741C22×C4—431no—
742C22×C4—431no—
743C22×C4—431no—
744C22×C4—431no—
745C22×C4—431no—
746C22×C4—431no—
747C22×C4—864no—
748C22×C4—864no—
749C22×C4—862no—
750C22×C4—862no—
751C22×C4—862no—
752C22×C4—862no—
753C22×C4—862no—
754C22×C4—862no—
755C22×C4—861no—
756C22×C4—861no—
757C22×C4—1722no—
758C22×C4—1724no—
759C22×C4—1724no—
760C22×C4D4×D4311yescharacteristic
761C22×C4D4×D4311yescharacteristic
762C22×C4C23×D4311yescharacteristic
763C2×C8—434no—
764C2×C8—868no—
765C2×C8C23×D4314yes—
766C4⋊C4—22no—
767C4⋊C4—22no—
768C4⋊C4—22no—
769C4⋊C4—22no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—21no—
775C4⋊C4—22no—
776C4⋊C4—22no—
777C4⋊C4—432no—
778C4⋊C4—432no—
779C4⋊C4—432no—
780C4⋊C4—862no—
781C4⋊C4—862no—
782C4⋊C4—862no—
783C4⋊C4—862no—
784C4⋊C4—862no—
785C4⋊C4—862no—
786C4⋊C4—862no—
787C4⋊C4—862no—
788C4⋊C4—862no—
789C4⋊C4—862no—
790C4⋊C4—862no—
791C4⋊C4—862no—
792C4⋊C4—862no—
793C4⋊C4—862no—
794C4⋊C4—862no—
795C4⋊C4—862no—
796C4⋊C4—862no—
797C4⋊C4—862no—
798C4⋊C4—862no—
799C4⋊C4—862no—
800C4⋊C4—861no—
801C4⋊C4—861no—
802C4⋊C4—862no—
803C4⋊C4—862no—
804C4⋊C4—862no—
805C4⋊C4—862no—
806C4⋊C4—861no—
807C4⋊C4—861no—
808C4⋊C4—862no—
809C4⋊C4—862no—
810C4⋊C4—861no—
811C4⋊C4C23×D4312yes—
812C4⋊C4C23×D4312yes—
813C4⋊C4C23×D4312yes—
814C22⋊C4—22no—
815C22⋊C4—862no—
816C22⋊C4—862no—
817C22⋊C4—862no—
818C42—22no—
819C42—431no—
820C42—431no—
821C42—431no—
822C42—431no—
823C42—431no—
824C42—431no—
825C42—431no—
826C42—431no—
827C42—431no—
828C42—431no—
829C42—431no—
830C42—431no—
831C42—862no—
832C42—862no—
833C42—862no—
834C42D4×D4311yescharacteristic
835C42D4×D4311yescharacteristic
836C42C23×D4311yescharacteristic
837C42C23×D4311yescharacteristic
838C23—431no—
839C23—434no—
840C23—431no—
841C23—862no—
842C23—862no—
843C23C2×D4×D4311yescharacteristic
844Q8—24no—
845Q8—42no—
846Q8—864no—
847Q8—1722no—
848Q8—1724no—
849Q8—1724no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—431no—
860C2×C4—434no—
861C2×C4—431no—
862C2×C4—431no—
863C2×C4—431no—
864C2×C4—431no—
865C2×C4—431no—
866C2×C4—862no—
867C2×C4—862no—
868C2×C4—862no—
869C2×C4—862no—
870C2×C4—862no—
871C2×C4—862no—
872C2×C4—862no—
873C2×C4—862no—
874C2×C4—862no—
875C2×C4—862no—
876C2×C4—862no—
877C2×C4—862no—
878C2×C4—862no—
879C2×C4—862no—
880C2×C4—862no—
881C2×C4—1721no—
882C2×C4—1721no—
883C2×C4—1724no—
884C2×C4—1724no—
885C2×C4—1724no—
886C2×C4—1724no—
887C2×C4—1724no—
888C2×C4—1724no—
889C2×C4—1721no—
890C2×C4—1722no—
891C2×C4—1722no—
892C2×C4C2×D4×D4311yescharacteristic
893C2×C4C2×D4×D4311yescharacteristic
894C2×C4C2×D4×D4311yescharacteristic
895C2×C4C2×D4×D4311yescharacteristic
896C2×C4C2×D4×D4311yescharacteristic
897C2×C4C24×D4311yescharacteristic
898C8—24no—
899C8—864no—
900C22—21no—
901C22—21no—
902C22—432no—
903C22—432no—
904C22—432no—
905C22—432no—
906C22—868no—
907C22—861no—
908C22—861no—
909C22#137×D4312yes—
910C22C22×D4×D4311yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—42no—
917C4—42no—
918C4—42no—
919C4—42no—
920C4—432no—
921C4—861no—
922C4—861no—
923C4—861no—
924C4—861no—
925C4—861no—
926C4—1722no—
927C4—1722no—
928C4—1722no—
929C4—1722no—
930C42−1+4×D4312yes—
931C2—22no—
932C2—434no—
933C2—862no—
934C2#536×D4311yescharacteristic
935C2C2×#137×D4311yescharacteristic
936C2#575×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3236C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3236D43
hypocenterC43C2×#3236
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3236

Complements

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

NH ≅ G/Ntype
3. #19145803C2semidirect
4. #19145802C2semidirect
5. #19145801C2semidirect
6. #19145800C2semidirect
7. #19145799C2semidirect
8. #19145798C2semidirect
9. #19145797C2semidirect
10. #19145796C2semidirect
11. #501×D43C2semidirect
12. #491×D43C2semidirect
15. #479×D43C2semidirect
17. C43×#3236C2semidirect
53. #14583309C22semidirect
54. #14583308C22semidirect
55. #14583307C22semidirect
56. #14583306C22semidirect
57. #14583305C22semidirect
58. #14583269C22semidirect
59. #14583268C22semidirect
60. #14583267C22semidirect
61. #14583266C22semidirect
62. #14583266C22semidirect
73. #14583209C22semidirect
74. #14583208C22semidirect
75. #14583207C22semidirect
76. #14583206C22semidirect
77. #14583205C22semidirect
78. #14583204C22semidirect
79. #14583203C22semidirect
93. C43×#501C22semidirect
94. C43×#491C22semidirect
97. C43×#479C22semidirect
473. #3236D43direct (N × H)
485. D43#3236direct (N × H)
528. #501C2×D43semidirect
534. #491C2×D43semidirect
554. #479C2×D43semidirect
567. C43C2×#3236semidirect

Maximal subgroups

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

subgroupindex
#533×D432
C2×#125×D432
#191458032
#191458022
#191458012
#191458002
#191457992
#191457982
#191457972
#191457962
#501×D432
#491×D432
#484×D432
#483×D432
#479×D432
#432×D432
C43×#32362
C2×#323643