Finite Group Databasebeta

← D43×#3231 #25968659

Subgroups — D43×#3231 #25968659

Order 11008.

1778 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#533×D43C211yesmaximal, characteristic
2#533×D43C211yesmaximal, characteristic
3#19145757C211yesmaximal, characteristic, complemented
4#19145756C211yesmaximal, characteristic, complemented
5#19145755C211yesmaximal, characteristic, complemented
6#19145754C211yesmaximal, characteristic, complemented
7#19145753C214yesmaximal, complemented
8#19145752C214yesmaximal, complemented
9#19145751C211yesmaximal, characteristic, complemented
10#19145750C211yesmaximal, characteristic, complemented
11#19145749C211yesmaximal, characteristic, complemented
12#500×D43C211yesmaximal, characteristic, complemented
13#498×D43C211yesmaximal, characteristic, complemented
14#487×D43C211yesmaximal, characteristic, complemented
15#487×D43C211yesmaximal, characteristic, complemented
16#485×D43C214yesmaximal
17#479×D43C214yesmaximal, complemented
18#431×D43C211yesmaximal, characteristic
19C43×#3231C211yesmaximal, characteristic, complemented
20#14583456C2211yescharacteristic
21#14583456C2211yescharacteristic
22#14583455—21no—
23#14583455C2212yes—
24#14583454C2211yescharacteristic
25#14583454C2211yescharacteristic
26#14583454C2211yescharacteristic
27#14583454C2211yescharacteristic
28#14583453—21no—
29#14583453—21no—
30#14583453—21no—
31#14583453C2212yes—
32#14583452—21no—
33#14583452C2212yes—
34#14583451—21no—
35#14583451—21no—
36#14583451—21no—
37#14583451C2212yes—
38C4⋊Q8×D43C2211yescharacteristic
39C4⋊Q8×D43C2211yescharacteristic
40C4⋊Q8×D43C2211yescharacteristic
41C4⋊Q8×D43C2211yescharacteristic
42#125×D43—21no—
43#125×D43C2212yes—
44C22⋊Q8×D43—21no—
45C22⋊Q8×D43—21no—
46C22⋊Q8×D43—21no—
47C22⋊Q8×D43C2212yes—
48C4×Q8×D43—21no—
49C4×Q8×D43—21no—
50C4×Q8×D43—21no—
51C4×Q8×D43C2212yes—
52#117×D43—21no—
53#117×D43C2212yes—
54C2×C42×D43C2211yescharacteristic
55#14583304C2211yescharacteristic, complemented
56#14583303C2214yescomplemented
57#14583302C2211yescharacteristic, complemented
58#14583302C2211yescharacteristic, complemented
59#14583297C2211yescharacteristic, complemented
60#14583296C2214yescomplemented
61#14583295C2211yescharacteristic, complemented
62#14583295C2211yescharacteristic, complemented
63#14583251C2211yescharacteristic, complemented
64#14583251C2211yescharacteristic, complemented
65#14583250C2211yescharacteristic, complemented
66#14583250C2211yescharacteristic, complemented
67#14583249C2211yescharacteristic, complemented
68#14583249C2211yescharacteristic, complemented
69#14583248C2214yescomplemented
70#14583248C2214yescomplemented
71#14583243C2214yes—
72#14583242C2214yes—
73#14583241C2214yes—
74#14583240C2214yes—
75#14583239C2214yes—
76#14583238C2214yes—
77#14583237C2214yes—
78#14583209C2214yescomplemented
79#14583208C2214yescomplemented
80#14583207C2214yescomplemented
81#14583206C2214yescomplemented
82#14583205C2214yescomplemented
83#14583204C2214yescomplemented
84#14583203C2214yescomplemented
85#14582952C2211yescharacteristic
86#14582951C2212yes—
87#14582950C2211yescharacteristic
88#14582950C2211yescharacteristic
89#14582949C2212yes—
90#107×D43C2214yes—
91#106×D43C2214yes—
92C4⋊C8×D43C2212yes—
93#103×D43C2214yes—
94#103×D43C2214yes—
95C22⋊C8×D43C2212yes—
96C4×C8×D43C2211yescharacteristic
97C4×C8×D43C2211yescharacteristic
98C43×#533C2211yescharacteristic
99C43×#533C2211yescharacteristic
100C43×#500C2211yescharacteristic, complemented
101C43×#498C2211yescharacteristic, complemented
102C43×#487C2211yescharacteristic, complemented
103C43×#487C2211yescharacteristic, complemented
104C43×#485C2214yes—
105C43×#479C2214yescomplemented
106C43×#431C2211yescharacteristic
107C2×Q8×D43—21no—
108C2×Q8×D43—21no—
109C2×Q8×D43—21no—
110C2×Q8×D43C2312yes—
111C22×C4×D43D411yescharacteristic
112C22×C4×D43D411yescharacteristic
113C22×C4×D43C2311yescharacteristic
114C2×C8×D43C2312yes—
115C2×C8×D43C2312yes—
116#13063325C2311yescharacteristic
117#13063325C2311yescharacteristic
118#13063325C2311yescharacteristic
119#13063325C2311yescharacteristic
120#13063324—21no—
121#13063324—21no—
122#13063324—21no—
123#13063324—21no—
124#13063324—21no—
125#13063324C2312yes—
126#13063324C2312yes—
127#13063324C2312yes—
128#13063323—21no—
129#13063323—21no—
130#13063323—21no—
131#13063323C2312yes—
132#13063317—21no—
133#13063317C2312yes—
134#13063316—21no—
135#13063316—21no—
136#13063316C2312yes—
137#13063316C2312yes—
138#13063315—22no—
139#13063315—22no—
140#13063315—22no—
141#13063315—22no—
142#13063305—21no—
143#13063305—21no—
144#13063305—21no—
145#13063305C2312yes—
146#13063304—21no—
147#13063304—21no—
148#13063304—21no—
149#13063304C2312yes—
150#13063303—22no—
151#13063303—22no—
152#13063303—22no—
153#13063303—22no—
154#13063302—22no—
155#13063302—22no—
156#13063302—22no—
157#13063302—22no—
158#13063301—21no—
159#13063301—21no—
160#13063301—21no—
161#13063301C2312yes—
162Q8×Dic43—21no—
163Q8×Dic43—21no—
164Q8×Dic43—21no—
165Q8×Dic43C2312yes—
166C4×Dic86—21no—
167C4×Dic86—21no—
168C4×Dic86—21no—
169C4×Dic86—22no—
170C4×Dic86—22no—
171C4×Dic86—22no—
172C4×Dic86—22no—
173C4×Dic86C2312yes—
174#13063290—21no—
175#13063290—21no—
176#13063290—21no—
177#13063290—22no—
178#13063290—22no—
179#13063290—22no—
180#13063290—22no—
181#13063290C2312yes—
182#13063284—21no—
183#13063284C2312yes—
184#13063283—21no—
185#13063283—21no—
186#13063283C2312yes—
187#13063283C2312yes—
188#13063282—22no—
189#13063282—22no—
190#13063281—22no—
191#13063281—22no—
192C4⋊C4×D43—21no—
193C4⋊C4×D43—21no—
194C4⋊C4×D43—22no—
195C4⋊C4×D43—22no—
196C4⋊C4×D43—21no—
197C4⋊C4×D43—21no—
198C4⋊C4×D43—21no—
199C4⋊C4×D43—22no—
200C4⋊C4×D43—22no—
201C4⋊C4×D43C2312yes—
202C4⋊C4×D43C2312yes—
203C4⋊C4×D43C2312yes—
204C22⋊C4×D43—22no—
205C22⋊C4×D43—22no—
206C2×C4×Dic43D411yescharacteristic
207C2×C4×Dic43D411yescharacteristic
208C2×C4×Dic43C2311yescharacteristic
209C42×D43—22no—
210C42×D43—22no—
211C42×D43D411yescharacteristic
212C42×D43D411yescharacteristic
213C42×D43D411yescharacteristic
214C42×D43D411yescharacteristic
215C42×D43C2311yescharacteristic
216C42×D43C2311yescharacteristic
217C42×D43C2311yescharacteristic
218C42×D43C2311yescharacteristic
219#13063259C2314yes—
220#13063258C2314yes—
221#13063258C2314yes—
222#13063257C2314yes—
223#13063256C2314yes—
224#13063256C2314yes—
225C4⋊(C43⋊C8)C2312yes—
226Dic43⋊C8C2312yes—
227Dic43⋊C8C2312yes—
228#13063250C2314yes—
229#13063250C2314yes—
230#13063249C2314yes—
231#13063249C2314yes—
232#13063248C2314yes—
233#13063248C2314yes—
234C22⋊(C43⋊C8)C2312yes—
235(C2×D43)⋊C8C2312yes—
236(C2×D43)⋊C8C2312yes—
237C4×C43⋊C8C2311yescharacteristic
238C4×C43⋊C8C2311yescharacteristic
239C8×Dic43C2312yes—
240C8×Dic43C2312yes—
241C4⋊Q8×C43C2311yescharacteristic
242C4⋊Q8×C43C2311yescharacteristic
243C4⋊Q8×C43C2311yescharacteristic
244C4⋊Q8×C43C2311yescharacteristic
245#125×C43—21no—
246#125×C43C2312yes—
247C22⋊Q8×C43—21no—
248C22⋊Q8×C43—21no—
249C22⋊Q8×C43—21no—
250C22⋊Q8×C43C2312yes—
251C4×Q8×C43—21no—
252C4×Q8×C43—21no—
253C4×Q8×C43—21no—
254C4×Q8×C43C2312yes—
255#117×C43—21no—
256#117×C43C2312yes—
257C2×C42×C43C2311yescharacteristic
258#107×C43C2314yes—
259#106×C43C2314yes—
260C4⋊C8×C43C2312yes—
261#103×C43C2314yes—
262#103×C43C2314yes—
263C22⋊C8×C43C2312yes—
264C4×C8×C43C2311yescharacteristic
265C4×C8×C43C2311yescharacteristic
266C23×D43C2×D411yescharacteristic
267C2×Q8×C43—21no—
268C2×Q8×C43—21no—
269C2×Q8×C43—21no—
270C2×Q8×C43C2412yes—
271C22×C4×C43C2×D411yescharacteristic
272C22×C4×C43C2×D411yescharacteristic
273C22×C4×C43C2411yescharacteristic
274C22×Dic43C2×D411yescharacteristic
275C22×Dic43C2×D411yescharacteristic
276C22×Dic43C2×D411yescharacteristic
277Q8×D43—28no—
278Q8×D43—44no—
279Q8×D43—44no—
280Q8×D43—44no—
281C2×C4×D43—24no—
282C2×C4×D43—24no—
283C2×C4×D43—24no—
284C2×C4×D43—22no—
285C2×C4×D43—22no—
286C2×C4×D43—22no—
287C2×C4×D43—22no—
288C2×C4×D43C2×D411yescharacteristic
289C2×C4×D43C2×D411yescharacteristic
290C2×C4×D43C2×D411yescharacteristic
291C2×C4×D43C2×D411yescharacteristic
292C2×C4×D43C2×D411yescharacteristic
293C2×C4×D43C2×D411yescharacteristic
294C2×C4×D43C2×D411yescharacteristic
295C2×C4×D43C2×D411yescharacteristic
296C2×C4×D43C2×D411yescharacteristic
297C2×C4×D43C2×D411yescharacteristic
298C2×C4×D43C2411yescharacteristic
299C2×C4×D43C2411yescharacteristic
300C2×Dic86—21no—
301C2×Dic86—21no—
302C2×Dic86—21no—
303C2×Dic86—22no—
304C2×Dic86—22no—
305C2×Dic86—22no—
306C2×Dic86—22no—
307C2×Dic86C2412yes—
308C2×C8×C43C2412yes—
309C2×C8×C43C2412yes—
310C4⋊C4×C43—21no—
311C4⋊C4×C43—21no—
312C4⋊C4×C43—22no—
313C4⋊C4×C43—22no—
314C4⋊C4×C43—21no—
315C4⋊C4×C43—21no—
316C4⋊C4×C43—21no—
317C4⋊C4×C43—22no—
318C4⋊C4×C43—22no—
319C4⋊C4×C43C2412yes—
320C4⋊C4×C43C2412yes—
321C4⋊C4×C43C2412yes—
322C22⋊C4×C43—22no—
323C22⋊C4×C43—22no—
324C42×C43—22no—
325C42×C43—22no—
326C42×C43C2×D411yescharacteristic
327C42×C43C2×D411yescharacteristic
328C42×C43C2411yescharacteristic
329C42×C43C2411yescharacteristic
330C22⋊Dic43—22no—
331C22⋊Dic43—22no—
332(C2×D43)⋊C4—22no—
333(C2×D43)⋊C4—22no—
334(C2×D43)⋊C4—22no—
335(C2×D43)⋊C4—22no—
336C4⋊Dic43—21no—
337C4⋊Dic43—21no—
338C4⋊Dic43—21no—
339C4⋊Dic43—21no—
340C4⋊Dic43—21no—
341C4⋊Dic43—22no—
342C4⋊Dic43—22no—
343C4⋊Dic43—22no—
344C4⋊Dic43—22no—
345C4⋊Dic43C2412yes—
346C4⋊Dic43C2412yes—
347C4⋊Dic43C2412yes—
348Dic43⋊C4—22no—
349Dic43⋊C4—22no—
350Dic43⋊C4—22no—
351Dic43⋊C4—22no—
352Dic43⋊C4—22no—
353Dic43⋊C4—22no—
354Dic43⋊C4—22no—
355Dic43⋊C4—22no—
356Dic43⋊C4—22no—
357Dic43⋊C4—22no—
358Dic43⋊C4—22no—
359Dic43⋊C4—22no—
360Dic43⋊C4—22no—
361Dic43⋊C4—22no—
362Dic43⋊C4—22no—
363Dic43⋊C4—22no—
364C4×Dic43—22no—
365C4×Dic43—22no—
366C4×Dic43—22no—
367C4×Dic43—22no—
368C4×Dic43—22no—
369C4×Dic43—22no—
370C4×Dic43C2×D411yescharacteristic
371C4×Dic43C2×D411yescharacteristic
372C4×Dic43C2×D411yescharacteristic
373C4×Dic43C2×D411yescharacteristic
374C4×Dic43C2×D411yescharacteristic
375C4×Dic43C2×D411yescharacteristic
376C4×Dic43C2×D411yescharacteristic
377C4×Dic43C2×D411yescharacteristic
378C4×Dic43C2×D411yescharacteristic
379C4×Dic43C2×D411yescharacteristic
380C4×Dic43C2411yescharacteristic
381C4×Dic43C2411yescharacteristic
382C2×C43⋊C8C2412yes—
383C2×C43⋊C8C2412yes—
384C8×D43—24no—
385C8×D43—24no—
386C23×C43C22×D411yescharacteristic
387C22×D43—22no—
388C22×D43—22no—
389C22×D43—22no—
390C22×D43C22×D411yescharacteristic
391C22×D43C22×D411yescharacteristic
392Q8×C43—24no—
393Q8×C43—42no—
394Q8×C43—42no—
395Q8×C43—42no—
396C2×C4×C43—22no—
397C2×C4×C43—22no—
398C2×C4×C43—22no—
399C2×C4×C43—22no—
400C2×C4×C43—22no—
401C2×C4×C43—22no—
402C2×C4×C43—22no—
403C2×C4×C43C22×D411yescharacteristic
404C2×C4×C43C22×D411yescharacteristic
405C2×C4×C43C22×D411yescharacteristic
406C2×C4×C43C22×D411yescharacteristic
407C2×C4×C43C22×D411yescharacteristic
408C2×C4×C43C2511yescharacteristic
409C2×Dic43—22no—
410C2×Dic43—22no—
411C2×Dic43—22no—
412C2×Dic43—22no—
413C2×Dic43—22no—
414C2×Dic43—22no—
415C2×Dic43—22no—
416C2×Dic43C22×D411yescharacteristic
417C2×Dic43C22×D411yescharacteristic
418C2×Dic43C22×D411yescharacteristic
419C2×Dic43C22×D411yescharacteristic
420C2×Dic43C22×D411yescharacteristic
421C2×Dic43C22×D411yescharacteristic
422C4×D43—22no—
423C4×D43—22no—
424C4×D43—22no—
425C4×D43—22no—
426C4×D43—22no—
427C4×D43—22no—
428C4×D43—22no—
429C4×D43—22no—
430C4×D43—22no—
431C4×D43—44no—
432C4×D43—44no—
433C4×D43—44no—
434C4×D43—44no—
435C4×D43#13514yes—
436C4×D43#13714yes—
437C4×D432−1+414yes—
438Dic86—24no—
439Dic86—42no—
440Dic86—42no—
441Dic86—42no—
442Dic86—44no—
443Dic86—44no—
444Dic86—44no—
445Dic86—44no—
446C8×C43—22no—
447C8×C43—22no—
448C43⋊C8—22no—
449C43⋊C8—22no—
450C2×#3231—431nomaximal, Sylow
451C22×C43—21no—
452C22×C43—21no—
453C22×C43—21no—
454C22×C43C23×D411yescharacteristic
455C2×D43—21no—
456C2×D43—21no—
457C2×D43—21no—
458C2×D43—44no—
459C2×D43#53612yes—
460C2×D43C2×#13512yes—
461C2×D43C2×#13712yes—
462C4×C43—21no—
463C4×C43—21no—
464C4×C43—21no—
465C4×C43—42no—
466C4×C43—42no—
467C4×C43—42no—
468C4×C43—42no—
469C4×C43C2×#13512yes—
470C4×C43C2×#13712yes—
471C4×C43C2×2−1+412yes—
472Dic43—21no—
473Dic43—21no—
474Dic43—21no—
475Dic43—42no—
476Dic43—42no—
477Dic43—42no—
478Dic43—42no—
479Dic43#53612yes—
480Dic43C2×#13512yes—
481Dic43C2×#13712yes—
482C2×#533—431no—
483C2×#533—431no—
484#3231—431no—
485#3231—431no—
486#3231—431no—
487#3231—431no—
488#3231—434no—
489#3231—434no—
490#3231—431no—
491#3231—431no—
492#3231—431no—
493#3231D4311yescharacteristic, direct product factor
494C2×#500—431no—
495C2×#498—431no—
496C2×#487—431no—
497C2×#487—431no—
498C2×#485—434no—
499C2×#479—434no—
500C2×#431—431no—
501C2×C43—41no—
502C2×C43C2×#53611yescharacteristic
503C2×C43C22×#13511yescharacteristic
504C2×C43C22×#13711yescharacteristic
505D43—41no—
506D43#323114yesdirect product factor
507#533—431no—
508#533—431no—
509#533—432no—
510#533—432no—
511#533—431no—
512#533—431no—
513#533—432no—
514#533—432no—
515#533—431no—
516#533—431no—
517#533—861no—
518#533—861no—
519#533—861no—
520#533—861no—
521#533—861no—
522#533—861no—
523#533—861no—
524#533—861no—
525#533C2×D4311yescharacteristic
526#533C2×D4311yescharacteristic
527C2×C4⋊Q8—431no—
528C2×C4⋊Q8—431no—
529C2×C4⋊Q8—431no—
530C2×C4⋊Q8—431no—
531C2×#125—432no—
532C2×#125—861no—
533C2×C22⋊Q8—432no—
534C2×C22⋊Q8—861no—
535C2×C22⋊Q8—861no—
536C2×C22⋊Q8—861no—
537C2×C4×Q8—432no—
538C2×C4×Q8—861no—
539C2×C4×Q8—861no—
540C2×C4×Q8—861no—
541C2×#117—432no—
542C2×#117—861no—
543C22×C42—431no—
544#500—431no—
545#500—431no—
546#500—434no—
547#500—431no—
548#500C2×D4311yescharacteristic, complemented
549#498—431no—
550#498—431no—
551#498—434no—
552#498—431no—
553#498C2×D4311yescharacteristic, complemented
554#487—431no—
555#487—431no—
556#487—431no—
557#487—431no—
558#487—434no—
559#487—434no—
560#487—431no—
561#487—431no—
562#487C2×D4311yescharacteristic, complemented
563#487C2×D4311yescharacteristic, complemented
564#485—434no—
565#485—434no—
566#485—434no—
567#485—434no—
568#485—434no—
569#485—434no—
570#485—434no—
571#485C2×D4314yes—
572#479—434no—
573#479—434no—
574#479—434no—
575#479—434no—
576#479—434no—
577#479—434no—
578#479—434no—
579#479C2×D4314yescomplemented
580#431—431no—
581#431—432no—
582#431—432no—
583#431—431no—
584#431—431no—
585#431C2×D4311yescharacteristic
586C2×#107—434no—
587C2×#106—434no—
588C2×C4⋊C8—432no—
589C2×#103—434no—
590C2×#103—434no—
591C2×C22⋊C8—432no—
592C2×C4×C8—431no—
593C2×C4×C8—431no—
594C43C2×#323111yescharacteristic, complemented, Sylow
595C22×Q8—432no—
596C22×Q8—861no—
597C22×Q8—861no—
598C22×Q8—861no—
599C23×C4—431no—
600C23×C4—431no—
601C23×C4—431no—
602C22×C8—432no—
603C22×C8—432no—
604C4⋊Q8—432no—
605C4⋊Q8—432no—
606C4⋊Q8—432no—
607C4⋊Q8—432no—
608C4⋊Q8—431no—
609C4⋊Q8—431no—
610C4⋊Q8—431no—
611C4⋊Q8—431no—
612C4⋊Q8—861no—
613C4⋊Q8—861no—
614C4⋊Q8—861no—
615C4⋊Q8—861no—
616C4⋊Q8—861no—
617C4⋊Q8—861no—
618C4⋊Q8—861no—
619C4⋊Q8—861no—
620C4⋊Q8C22×D4311yescharacteristic
621C4⋊Q8C22×D4311yescharacteristic
622C4⋊Q8C22×D4311yescharacteristic
623C4⋊Q8C22×D4311yescharacteristic
624#125—21no—
625#125—432no—
626#125—432no—
627#125—432no—
628#125—862no—
629#125—862no—
630#125—862no—
631#125—862no—
632#125—861no—
633#125—861no—
634#125—861no—
635#125C22×D4312yes—
636C22⋊Q8—21no—
637C22⋊Q8—21no—
638C22⋊Q8—21no—
639C22⋊Q8—432no—
640C22⋊Q8—432no—
641C22⋊Q8—432no—
642C22⋊Q8—862no—
643C22⋊Q8—862no—
644C22⋊Q8—862no—
645C22⋊Q8—862no—
646C22⋊Q8—862no—
647C22⋊Q8—862no—
648C22⋊Q8—862no—
649C22⋊Q8—862no—
650C22⋊Q8—861no—
651C22⋊Q8—861no—
652C22⋊Q8—861no—
653C22⋊Q8—861no—
654C22⋊Q8—861no—
655C22⋊Q8—861no—
656C22⋊Q8—861no—
657C22⋊Q8—861no—
658C22⋊Q8—861no—
659C22⋊Q8C22×D4312yes—
660C4×Q8—21no—
661C4×Q8—21no—
662C4×Q8—21no—
663C4×Q8—432no—
664C4×Q8—432no—
665C4×Q8—432no—
666C4×Q8—862no—
667C4×Q8—862no—
668C4×Q8—862no—
669C4×Q8—862no—
670C4×Q8—862no—
671C4×Q8—862no—
672C4×Q8—861no—
673C4×Q8—861no—
674C4×Q8—862no—
675C4×Q8—862no—
676C4×Q8—861no—
677C4×Q8—861no—
678C4×Q8—861no—
679C4×Q8—861no—
680C4×Q8—861no—
681C4×Q8—861no—
682C4×Q8—861no—
683C4×Q8C22×D4312yes—
684#117—21no—
685#117—432no—
686#117—432no—
687#117—432no—
688#117—862no—
689#117—862no—
690#117—862no—
691#117—862no—
692#117—861no—
693#117—861no—
694#117—861no—
695#117C22×D4312yes—
696C2×C4⋊C4—432no—
697C2×C4⋊C4—432no—
698C2×C4⋊C4—432no—
699C2×C4⋊C4—861no—
700C2×C4⋊C4—861no—
701C2×C4⋊C4—862no—
702C2×C4⋊C4—862no—
703C2×C4⋊C4—862no—
704C2×C4⋊C4—862no—
705C2×C4⋊C4—861no—
706C2×C4⋊C4—861no—
707C2×C4⋊C4—861no—
708C2×C22⋊C4—862no—
709C2×C22⋊C4—862no—
710C2×C42—431no—
711C2×C42—431no—
712C2×C42—431no—
713C2×C42—431no—
714C2×C42—431no—
715C2×C42—431no—
716C2×C42—431no—
717C2×C42—431no—
718C2×C42—431no—
719C2×C42—431no—
720C2×C42—431no—
721C2×C42—862no—
722C2×C42—862no—
723C2×C42C22×D4311yescharacteristic
724#107—434no—
725#107—434no—
726#107—434no—
727#107C22×D4314yes—
728#106—434no—
729#106—434no—
730#106—434no—
731#106C22×D4314yes—
732C4⋊C8—432no—
733C4⋊C8—432no—
734C4⋊C8—432no—
735C4⋊C8C22×D4312yes—
736#103—434no—
737#103—434no—
738#103—434no—
739#103—434no—
740#103—434no—
741#103—434no—
742#103C22×D4314yes—
743#103C22×D4314yes—
744C22⋊C8—432no—
745C22⋊C8—432no—
746C22⋊C8—432no—
747C22⋊C8C22×D4312yes—
748C4×C8—432no—
749C4×C8—432no—
750C4×C8—431no—
751C4×C8—431no—
752C4×C8C22×D4311yescharacteristic
753C4×C8C22×D4311yescharacteristic
754C24—431no—
755C2×Q8—21no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—432no—
759C2×Q8—862no—
760C2×Q8—862no—
761C2×Q8—862no—
762C2×Q8—862no—
763C2×Q8—868no—
764C2×Q8—861no—
765C2×Q8—861no—
766C2×Q8—861no—
767C2×Q8—1724no—
768C2×Q8—1724no—
769C2×Q8—1724no—
770C2×Q8C23×D4312yes—
771C22×C4—431no—
772C22×C4—431no—
773C22×C4—431no—
774C22×C4—431no—
775C22×C4—431no—
776C22×C4—431no—
777C22×C4—431no—
778C22×C4—431no—
779C22×C4—431no—
780C22×C4—431no—
781C22×C4—431no—
782C22×C4—431no—
783C22×C4—431no—
784C22×C4—431no—
785C22×C4—431no—
786C22×C4—864no—
787C22×C4—864no—
788C22×C4—864no—
789C22×C4—862no—
790C22×C4—862no—
791C22×C4—862no—
792C22×C4—862no—
793C22×C4D4×D4311yescharacteristic
794C22×C4D4×D4311yescharacteristic
795C22×C4C23×D4311yescharacteristic
796C2×C8—432no—
797C2×C8—432no—
798C2×C8—864no—
799C2×C8—864no—
800C2×C8C23×D4312yes—
801C2×C8C23×D4312yes—
802C4⋊C4—21no—
803C4⋊C4—21no—
804C4⋊C4—22no—
805C4⋊C4—22no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—22no—
810C4⋊C4—22no—
811C4⋊C4—432no—
812C4⋊C4—432no—
813C4⋊C4—432no—
814C4⋊C4—862no—
815C4⋊C4—862no—
816C4⋊C4—862no—
817C4⋊C4—862no—
818C4⋊C4—862no—
819C4⋊C4—862no—
820C4⋊C4—862no—
821C4⋊C4—862no—
822C4⋊C4—862no—
823C4⋊C4—862no—
824C4⋊C4—862no—
825C4⋊C4—862no—
826C4⋊C4—862no—
827C4⋊C4—862no—
828C4⋊C4—862no—
829C4⋊C4—862no—
830C4⋊C4—861no—
831C4⋊C4—861no—
832C4⋊C4—862no—
833C4⋊C4—862no—
834C4⋊C4—862no—
835C4⋊C4—862no—
836C4⋊C4—861no—
837C4⋊C4—861no—
838C4⋊C4—861no—
839C4⋊C4C23×D4312yes—
840C4⋊C4C23×D4312yes—
841C4⋊C4C23×D4312yes—
842C22⋊C4—22no—
843C22⋊C4—22no—
844C22⋊C4—862no—
845C22⋊C4—862no—
846C22⋊C4—862no—
847C22⋊C4—862no—
848C22⋊C4—862no—
849C22⋊C4—862no—
850C42—22no—
851C42—22no—
852C42—431no—
853C42—431no—
854C42—431no—
855C42—431no—
856C42—431no—
857C42—431no—
858C42—431no—
859C42—431no—
860C42—431no—
861C42—431no—
862C42—431no—
863C42—431no—
864C42—862no—
865C42—862no—
866C42—862no—
867C42—862no—
868C42—862no—
869C42—862no—
870C42D4×D4311yescharacteristic
871C42D4×D4311yescharacteristic
872C42C23×D4311yescharacteristic
873C42C23×D4311yescharacteristic
874C23—431no—
875C23—431no—
876C23—862no—
877C23—862no—
878C23—862no—
879C23C2×D4×D4311yescharacteristic
880Q8—24no—
881Q8—42no—
882Q8—42no—
883Q8—42no—
884Q8—864no—
885Q8—1724no—
886Q8—1724no—
887Q8—1724no—
888Q8—1724no—
889Q8—1722no—
890Q8—1722no—
891Q8—1722no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—431no—
900C2×C4—431no—
901C2×C4—431no—
902C2×C4—434no—
903C2×C4—434no—
904C2×C4—434no—
905C2×C4—431no—
906C2×C4—431no—
907C2×C4—431no—
908C2×C4—862no—
909C2×C4—862no—
910C2×C4—862no—
911C2×C4—862no—
912C2×C4—862no—
913C2×C4—862no—
914C2×C4—862no—
915C2×C4—862no—
916C2×C4—862no—
917C2×C4—862no—
918C2×C4—862no—
919C2×C4—862no—
920C2×C4—862no—
921C2×C4—862no—
922C2×C4—862no—
923C2×C4—862no—
924C2×C4—1724no—
925C2×C4—1724no—
926C2×C4—1724no—
927C2×C4—1724no—
928C2×C4C2×D4×D4311yescharacteristic
929C2×C4C2×D4×D4311yescharacteristic
930C2×C4C2×D4×D4311yescharacteristic
931C2×C4C2×D4×D4311yescharacteristic
932C2×C4C2×D4×D4311yescharacteristic
933C2×C4C24×D4311yescharacteristic
934C8—22no—
935C8—22no—
936C8—862no—
937C8—862no—
938C22—21no—
939C22—21no—
940C22—21no—
941C22—432no—
942C22—432no—
943C22—432no—
944C22—861no—
945C22—861no—
946C22—861no—
947C22—1724no—
948C22C22×D4×D4311yescharacteristic
949C4—21no—
950C4—21no—
951C4—21no—
952C4—42no—
953C4—42no—
954C4—42no—
955C4—42no—
956C4—432no—
957C4—432no—
958C4—432no—
959C4—861no—
960C4—861no—
961C4—861no—
962C4—1722no—
963C4—1722no—
964C4—1722no—
965C4—1722no—
966C4#135×D4312yes—
967C4#137×D4312yes—
968C42−1+4×D4312yes—
969C2—41no—
970C2—434no—
971C2—1721no—
972C2#536×D4311yescharacteristic
973C2C2×#135×D4311yescharacteristic
974C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3231C2
socleC22×C43C23×D4
prime radicalC23×D43C2×D4
hypercenter#3231D43
hypocenterC43C2×#3231
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3231

Complements

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

NH ≅ G/Ntype
3. #19145757C2semidirect
4. #19145756C2semidirect
5. #19145755C2semidirect
6. #19145754C2semidirect
7. #19145753C2semidirect
8. #19145752C2semidirect
9. #19145751C2semidirect
10. #19145750C2semidirect
11. #19145749C2semidirect
12. #500×D43C2semidirect
13. #498×D43C2semidirect
14. #487×D43C2semidirect
15. #487×D43C2semidirect
17. #479×D43C2semidirect
19. C43×#3231C2semidirect
55. #14583304C22semidirect
56. #14583303C22semidirect
57. #14583302C22semidirect
58. #14583302C22semidirect
59. #14583297C22semidirect
60. #14583296C22semidirect
61. #14583295C22semidirect
62. #14583295C22semidirect
63. #14583251C22semidirect
64. #14583251C22semidirect
65. #14583250C22semidirect
66. #14583250C22semidirect
67. #14583249C22semidirect
68. #14583249C22semidirect
69. #14583248C22semidirect
70. #14583248C22semidirect
78. #14583209C22semidirect
79. #14583208C22semidirect
80. #14583207C22semidirect
81. #14583206C22semidirect
82. #14583205C22semidirect
83. #14583204C22semidirect
84. #14583203C22semidirect
100. C43×#500C22semidirect
101. C43×#498C22semidirect
102. C43×#487C22semidirect
103. C43×#487C22semidirect
105. C43×#479C22semidirect
493. #3231D43direct (N × H)
506. D43#3231direct (N × H)
548. #500C2×D43semidirect
553. #498C2×D43semidirect
562. #487C2×D43semidirect
563. #487C2×D43semidirect
579. #479C2×D43semidirect
594. C43C2×#3231semidirect

Maximal subgroups

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

subgroupindex
#533×D432
#191457572
#191457562
#191457552
#191457542
#191457532
#191457522
#191457512
#191457502
#191457492
#500×D432
#498×D432
#487×D432
#485×D432
#479×D432
#431×D432
C43×#32312
C2×#323143