Finite Group Databasebeta

← D43×#3238 #25968714

Subgroups — D43×#3238 #25968714

Order 11008.

2018 conjugacy classes of subgroups.

The subgroup lattice has 1078 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊Q8×D43C211yesmaximal, characteristic, complemented
2#529×D43C211yesmaximal, characteristic
3#19145820C212yesmaximal, complemented
4#19145819C212yesmaximal, complemented
5#19145818C211yesmaximal, characteristic, complemented
6#19145817C212yesmaximal, complemented
7#19145816C211yesmaximal, characteristic, complemented
8#19145815C212yesmaximal, complemented
9#19145814C212yesmaximal, complemented
10#19145813C211yesmaximal, characteristic, complemented
11#19145812C212yesmaximal, complemented
12#501×D43C212yesmaximal, complemented
13#489×D43C212yesmaximal, complemented
14#483×D43C212yesmaximal, complemented
15#480×D43C212yesmaximal
16#477×D43C212yesmaximal, complemented
17#476×D43C212yesmaximal, complemented
18#432×D43C211yesmaximal, characteristic, complemented
19C43×#3238C211yesmaximal, characteristic, complemented
20C22×Q8×D43—21no—
21C2×#13063325C2211yescharacteristic, complemented
22C2×#13063324—21no—
23C2×#13063324C2212yescomplemented
24C2×#13063323—21no—
25C4⋊Q8×D43—21no—
26C4⋊Q8×D43—21no—
27C4⋊Q8×D43—21no—
28C4⋊Q8×D43—21no—
29C4⋊Q8×D43C2212yes—
30C4⋊Q8×D43C2212yes—
31C4⋊Q8×D43C2212yescomplemented
32C4⋊Q8×D43C2212yescomplemented
33#14583436C2211yescharacteristic
34#14583435C2211yescharacteristic
35#14583434C2211yescharacteristic
36#14583433C2211yescharacteristic
37#14583432—21no—
38#14583431C2211yescharacteristic
39#14583430C2211yescharacteristic
40#14583429—21no—
41#14583428C2211yescharacteristic
42#14583427—21no—
43#14583426—21no—
44#126×D43—21no—
45#125×D43C2211yescharacteristic
46#124×D43C2211yescharacteristic
47#123×D43—21no—
48C22⋊Q8×D43C2211yescharacteristic
49#121×D43C2211yescharacteristic
50C4×Q8×D43C2211yescharacteristic
51C4×D4×D43—21no—
52C4×D4×D43C2211yescharacteristic
53#117×D43—21no—
54C2×C4⋊C4×D43—21no—
55C2×C4⋊C4×D43C2212yes—
56C2×C42×D43C2211yescharacteristic
57#14583309C2212yescomplemented
58#14583308C2212yescomplemented
59#14583307C2214yescomplemented
60#14583306C2214yescomplemented
61#14583305C2212yescomplemented
62#14583261C2212yescomplemented
63#14583260C2214yescomplemented
64#14583259C2212yescomplemented
65#14583258C2212yescomplemented
66#14583257C2214yescomplemented
67#14583231C2214yescomplemented
68#14583230C2212yescomplemented
69#14583229C2212yescomplemented
70#14583228C2214yescomplemented
71#14583227C2212yescomplemented
72#14583214C2214yes—
73#14583213C2212yes—
74#14583212C2212yes—
75#14583211C2214yes—
76#14583210C2212yes—
77#14583195C2212yescomplemented
78#14583194C2212yescomplemented
79#14583193C2214yescomplemented
80#14583192C2214yescomplemented
81#14583191C2212yescomplemented
82#14583190C2212yescomplemented
83#14583189C2212yescomplemented
84#14583188C2214yescomplemented
85#14583187C2214yescomplemented
86#14583186C2212yescomplemented
87#14582956C2211yescharacteristic, complemented
88#14582955C2212yescomplemented
89#14582954C2212yescomplemented
90#14582953C2212yescomplemented
91#107×D43C2214yes—
92#106×D43C2214yes—
93C4⋊C8×D43C2212yes—
94#103×D43C2214yes—
95#102×D43C2214yes—
96C22⋊C8×D43C2212yes—
97#97×D43C2212yes—
98C2×C4⋊Q8×C43C2211yescharacteristic, complemented
99C43×#529C2211yescharacteristic
100C43×#501C2212yescomplemented
101C43×#489C2212yescomplemented
102C43×#483C2212yescomplemented
103C43×#480C2212yes—
104C43×#477C2212yescomplemented
105C43×#476C2212yescomplemented
106C43×#432C2211yescharacteristic, complemented
107C22×Dic86—21no—
108C22×Dic86—22no—
109C2×Q8×D43—22no—
110C2×Q8×D43—22no—
111C2×Q8×D43—22no—
112C2×Q8×D43—22no—
113C2×Q8×D43—48no—
114C2×Q8×D43C2311yescharacteristic
115C2×D4×D43—21no—
116C2×D4×D43C2311yescharacteristic
117C22×C4×D43—22no—
118C22×C4×D43—21no—
119C22×C4×D43D411yescharacteristic
120C22×C4×D43D411yescharacteristic
121C22×C4×D43C2311yescharacteristic
122C2×C8×D43C2314yes—
123#13063325—21no—
124#13063325—21no—
125#13063325C2312yes—
126#13063325C2312yes—
127#13063324—22no—
128#13063324—22no—
129#13063324—22no—
130#13063324—22no—
131#13063324—22no—
132#13063324—22no—
133#13063324C2314yes—
134#13063324C2314yes—
135#13063323—22no—
136#13063323—22no—
137#13063323—22no—
138#13063323—22no—
139#13063320—21no—
140#13063320—21no—
141#13063320—21no—
142#13063319—21no—
143#13063318—21no—
144#13063318—21no—
145#13063318—21no—
146#13063317C2311yescharacteristic
147#13063316C2311yescharacteristic
148#13063316C2311yescharacteristic
149#13063315—21no—
150#13063315—21no—
151#13063314C2311yescharacteristic
152#13063313C2311yescharacteristic
153#13063312C2311yescharacteristic
154#13063311—21no—
155#13063311—21no—
156#13063310—21no—
157#13063310—21no—
158#13063309—21no—
159#13063308—21no—
160#13063307—21no—
161#13063307—21no—
162#13063306—21no—
163#13063305C2311yescharacteristic
164#13063304C2311yescharacteristic
165#13063303—21no—
166#13063302—21no—
167#13063301C2311yescharacteristic
168#13063300C2311yescharacteristic
169#13063299C2311yescharacteristic
170#13063298—21no—
171#13063297—21no—
172#13063296C2311yescharacteristic
173Q8×Dic43C2311yescharacteristic
174C4×Dic86—21no—
175C4×Dic86C2311yescharacteristic
176#13063290—21no—
177#13063290C2311yescharacteristic
178C4×D172—21no—
179C4×D172C2311yescharacteristic
180D4×Dic43—21no—
181D4×Dic43C2311yescharacteristic
182#13063287—21no—
183#13063287C2311yescharacteristic
184C4×C22⋊D43—21no—
185C4×C22⋊D43—21no—
186C4×C22⋊D43—21no—
187(C22⋊D43)⋊C4—21no—
188(C22⋊D43)⋊C4—21no—
189(C22⋊D43)⋊C4—21no—
190#13063284—21no—
191#13063283—21no—
192#13063283—21no—
193#13063282—21no—
194#13063282—21no—
195#13063281—21no—
196#13063281—21no—
197C2×C4⋊Dic43—21no—
198C2×C4⋊Dic43C2312yes—
199C2×Dic43⋊C4—22no—
200C2×Dic43⋊C4—22no—
201C4⋊C4×D43—22no—
202C4⋊C4×D43—22no—
203C4⋊C4×D43—22no—
204C4⋊C4×D43—22no—
205C4⋊C4×D43—22no—
206C4⋊C4×D43—22no—
207C4⋊C4×D43—21no—
208C4⋊C4×D43—21no—
209C4⋊C4×D43—21no—
210C4⋊C4×D43—21no—
211C4⋊C4×D43C2314yes—
212C4⋊C4×D43C2314yes—
213C4⋊C4×D43C2311yescharacteristic
214C4⋊C4×D43C2311yescharacteristic
215C22⋊C4×D43—21no—
216C22⋊C4×D43—21no—
217C22⋊C4×D43—21no—
218C22⋊C4×D43—21no—
219C22⋊C4×D43—21no—
220C2×C4×Dic43D411yescharacteristic
221C2×C4×Dic43D411yescharacteristic
222C2×C4×Dic43C2311yescharacteristic
223C42×D43—21no—
224C42×D43D411yescharacteristic
225C42×D43D411yescharacteristic
226C42×D43D411yescharacteristic
227C42×D43D411yescharacteristic
228C42×D43C2311yescharacteristic
229C42×D43C2311yescharacteristic
230C42×D43C2311yescharacteristic
231C42×D43C2311yescharacteristic
232#13063259C2314yes—
233#13063258C2314yes—
234#13063258C2314yes—
235#13063257C2314yes—
236#13063256C2314yes—
237#13063256C2314yes—
238C4⋊(C43⋊C8)C2312yes—
239Dic43⋊C8C2314yes—
240#13063250C2314yes—
241#13063249C2314yes—
242#13063248C2314yes—
243#13063247C2314yes—
244#13063246C2314yes—
245#13063245C2314yes—
246C22⋊(C43⋊C8)C2312yes—
247(C2×D43)⋊C8C2314yes—
248#13063236C2312yes—
249#13063235C2314yes—
250C22×Q8×C43—21no—
251C4⋊Q8×C43—21no—
252C4⋊Q8×C43—21no—
253C4⋊Q8×C43C2312yes—
254C4⋊Q8×C43C2312yes—
255#126×C43—21no—
256#125×C43C2311yescharacteristic
257#124×C43C2311yescharacteristic
258#123×C43—21no—
259C22⋊Q8×C43C2311yescharacteristic
260#121×C43C2311yescharacteristic
261C4×Q8×C43C2311yescharacteristic
262C4×D4×C43—21no—
263C4×D4×C43C2311yescharacteristic
264#117×C43—21no—
265C2×C4⋊C4×C43—21no—
266C2×C4⋊C4×C43C2312yes—
267C2×C42×C43C2311yescharacteristic
268#107×C43C2314yes—
269#106×C43C2314yes—
270C4⋊C8×C43C2312yes—
271#103×C43C2314yes—
272#102×C43C2314yes—
273C22⋊C8×C43C2312yes—
274#97×C43C2312yes—
275C23×D43—21no—
276C23×D43C2×D411yescharacteristic
277C2×Q8×C43—22no—
278C2×Q8×C43—22no—
279C2×Q8×C43—44no—
280C2×Q8×C43C2411yescharacteristic
281C2×D4×C43—21no—
282C2×D4×C43C2411yescharacteristic
283C22×C4×C43—21no—
284C22×C4×C43—22no—
285C22×C4×C43C2×D411yescharacteristic
286C22×C4×C43C2×D411yescharacteristic
287C22×C4×C43C2411yescharacteristic
288C2×C22⋊D43—21no—
289C2×C22⋊D43—21no—
290C2×C22⋊D43—21no—
291C22×Dic43—21no—
292C22×Dic43—22no—
293C22×Dic43C2×D411yescharacteristic
294C22×Dic43C2×D411yescharacteristic
295C22×Dic43C2×D411yescharacteristic
296Q8×D43—24no—
297Q8×D43—48no—
298Q8×D43—48no—
299Q8×D43—48no—
300Q8×D43—48no—
301D4×D43—24no—
302D4×D43—44no—
303C2×D172—21no—
304C2×D172C2411yescharacteristic
305C2×C4×D43—24no—
306C2×C4×D43—24no—
307C2×C4×D43—21no—
308C2×C4×D43—21no—
309C2×C4×D43—24no—
310C2×C4×D43—21no—
311C2×C4×D43—21no—
312C2×C4×D43—21no—
313C2×C4×D43—24no—
314C2×C4×D43—24no—
315C2×C4×D43—44no—
316C2×C4×D43—48no—
317C2×C4×D43C2×D411yescharacteristic
318C2×C4×D43C2×D411yescharacteristic
319C2×C4×D43C2×D411yescharacteristic
320C2×C4×D43C2×D411yescharacteristic
321C2×C4×D43C2×D411yescharacteristic
322C2×C4×D43C2×D411yescharacteristic
323C2×C4×D43C2×D411yescharacteristic
324C2×C4×D43C2×D411yescharacteristic
325C2×C4×D43C2×D411yescharacteristic
326C2×C4×D43C2×D411yescharacteristic
327C2×C4×D43C2411yescharacteristic
328C2×C4×D43C2411yescharacteristic
329C2×Dic86—22no—
330C2×Dic86—22no—
331C2×Dic86—21no—
332C2×Dic86—24no—
333C2×Dic86—24no—
334C2×Dic86—48no—
335C2×Dic86—44no—
336C2×Dic86C2411yescharacteristic
337C2×C8×C43C2414yes—
338C4⋊C4×C43—22no—
339C4⋊C4×C43—22no—
340C4⋊C4×C43—22no—
341C4⋊C4×C43—21no—
342C4⋊C4×C43—21no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43C2414yes—
346C4⋊C4×C43C2411yescharacteristic
347C4⋊C4×C43C2411yescharacteristic
348C22⋊C4×C43—21no—
349C22⋊C4×C43—21no—
350C22⋊C4×C43—21no—
351C22⋊C4×C43—21no—
352C22⋊C4×C43—21no—
353C42×C43—21no—
354C42×C43C2×D411yescharacteristic
355C42×C43C2×D411yescharacteristic
356C42×C43C2411yescharacteristic
357C42×C43C2411yescharacteristic
358C22⋊Dic43—21no—
359C22⋊Dic43—21no—
360C22⋊Dic43—21no—
361C22⋊Dic43—21no—
362C22⋊Dic43—21no—
363(C2×D43)⋊C4—21no—
364(C2×D43)⋊C4—21no—
365(C2×D43)⋊C4—21no—
366(C2×D43)⋊C4—21no—
367(C2×D43)⋊C4—21no—
368(C2×D43)⋊C4—21no—
369(C2×D43)⋊C4—21no—
370(C2×D43)⋊C4—21no—
371(C2×D43)⋊C4—21no—
372(C2×D43)⋊C4—21no—
373C4⋊Dic43—22no—
374C4⋊Dic43—22no—
375C4⋊Dic43—22no—
376C4⋊Dic43—21no—
377C4⋊Dic43—21no—
378C4⋊Dic43—21no—
379C4⋊Dic43—21no—
380C4⋊Dic43C2414yes—
381C4⋊Dic43C2411yescharacteristic
382C4⋊Dic43C2411yescharacteristic
383Dic43⋊C4—21no—
384Dic43⋊C4—21no—
385Dic43⋊C4—21no—
386Dic43⋊C4—21no—
387Dic43⋊C4—24no—
388Dic43⋊C4—24no—
389Dic43⋊C4—24no—
390Dic43⋊C4—24no—
391Dic43⋊C4—21no—
392Dic43⋊C4—21no—
393Dic43⋊C4—21no—
394Dic43⋊C4—21no—
395Dic43⋊C4—21no—
396Dic43⋊C4—21no—
397C4×Dic43—21no—
398C4×Dic43—21no—
399C4×Dic43—21no—
400C4×Dic43C2×D411yescharacteristic
401C4×Dic43C2×D411yescharacteristic
402C4×Dic43C2×D411yescharacteristic
403C4×Dic43C2×D411yescharacteristic
404C4×Dic43C2×D411yescharacteristic
405C4×Dic43C2×D411yescharacteristic
406C4×Dic43C2×D411yescharacteristic
407C4×Dic43C2×D411yescharacteristic
408C4×Dic43C2×D411yescharacteristic
409C4×Dic43C2×D411yescharacteristic
410C4×Dic43C2411yescharacteristic
411C4×Dic43C2411yescharacteristic
412C2×C43⋊C8C2414yes—
413C8×D43—28no—
414C23×C43—21no—
415C23×C43C22×D411yescharacteristic
416C22×D43—22no—
417C22×D43—22no—
418C22×D43—21no—
419C22×D43—42no—
420C22×D43—42no—
421C22×D43—42no—
422C22×D43AGL(1,ℤ/8)14yes—
423C22×D43C22×D411yescharacteristic
424C22×D43C22×D411yescharacteristic
425Q8×C43—22no—
426Q8×C43—44no—
427Q8×C43—44no—
428D4×C43—22no—
429D4×C43—42no—
430C2×C4×C43—22no—
431C2×C4×C43—22no—
432C2×C4×C43—22no—
433C2×C4×C43—21no—
434C2×C4×C43—21no—
435C2×C4×C43—24no—
436C2×C4×C43—21no—
437C2×C4×C43—44no—
438C2×C4×C43—42no—
439C2×C4×C43C22×D411yescharacteristic
440C2×C4×C43C22×D411yescharacteristic
441C2×C4×C43C22×D411yescharacteristic
442C2×C4×C43C22×D411yescharacteristic
443C2×C4×C43C22×D411yescharacteristic
444C2×C4×C43C2511yescharacteristic
445C22⋊D43—42no—
446C22⋊D43—42no—
447C22⋊D43—42no—
448C2×Dic43—22no—
449C2×Dic43—22no—
450C2×Dic43—22no—
451C2×Dic43—21no—
452C2×Dic43—21no—
453C2×Dic43—21no—
454C2×Dic43—24no—
455C2×Dic43—44no—
456C2×Dic43—42no—
457C2×Dic43C22×D411yescharacteristic
458C2×Dic43C22×D411yescharacteristic
459C2×Dic43C22×D411yescharacteristic
460C2×Dic43C22×D411yescharacteristic
461C2×Dic43C22×D411yescharacteristic
462C2×Dic43C22×D411yescharacteristic
463D172—22no—
464D172—42no—
465C4×D43—22no—
466C4×D43—22no—
467C4×D43—22no—
468C4×D43—22no—
469C4×D43—22no—
470C4×D43—22no—
471C4×D43—22no—
472C4×D43—22no—
473C4×D43—22no—
474C4×D43—22no—
475C4×D43—42no—
476C4×D43—48no—
477C4×D43—48no—
478C4×D43—42no—
479C4×D43—42no—
480C4×D43—42no—
481C4×D43—42no—
482C4×D43#13714yes—
483C4×D432−1+414yes—
484Dic86—22no—
485Dic86—48no—
486Dic86—48no—
487Dic86—44no—
488Dic86—44no—
489Dic86—42no—
490C8×C43—24no—
491C43⋊C8—24no—
492C2×#3238—431nomaximal, Sylow
493C22×C43—21no—
494C22×C43—21no—
495C22×C43—41no—
496C22×C43—41no—
497C22×C43—41no—
498C22×C43C2×AGL(1,ℤ/8)12yes—
499C22×C43C23×D411yescharacteristic
500C2×D43—21no—
501C2×D43—21no—
502C2×D43—28no—
503C2×D43—41no—
504C2×D43—41no—
505C2×D43—41no—
506C2×D43—84no—
507C2×D43#53612yes—
508C2×D43C2×AGL(1,ℤ/8)12yes—
509C2×D43C2×AGL(1,ℤ/8)12yes—
510C2×D43C2×#13712yes—
511C4×C43—21no—
512C4×C43—21no—
513C4×C43—21no—
514C4×C43—21no—
515C4×C43—41no—
516C4×C43—44no—
517C4×C43—41no—
518C4×C43—41no—
519C4×C43C2×#13712yes—
520C4×C43C2×2−1+412yes—
521Dic43—21no—
522Dic43—21no—
523Dic43—21no—
524Dic43—21no—
525Dic43—41no—
526Dic43—44no—
527Dic43—41no—
528Dic43—41no—
529Dic43#53612yes—
530Dic43C2×#13712yes—
531C22×C4⋊Q8—431no—
532C2×#529—431no—
533#3238—432no—
534#3238—432no—
535#3238—432no—
536#3238—432no—
537#3238—432no—
538#3238—432no—
539#3238—431no—
540#3238—431no—
541#3238—431no—
542#3238D4311yescharacteristic, direct product factor
543C2×#501—432no—
544C2×#489—432no—
545C2×#483—432no—
546C2×#480—432no—
547C2×#477—432no—
548C2×#476—432no—
549C2×#432—431no—
550C2×C43—22no—
551C2×C43—81no—
552C2×C43C2×#53611yescharacteristic
553C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
554C2×C43C22×#13711yescharacteristic
555D43—22no—
556D43—81no—
557D43#323814yesdirect product factor
558C23×Q8—861no—
559C2×C4⋊Q8—432no—
560C2×C4⋊Q8—432no—
561C2×C4⋊Q8—432no—
562C2×C4⋊Q8—432no—
563C2×C4⋊Q8—432no—
564C2×C4⋊Q8—431no—
565C2×C4⋊Q8—861no—
566C2×C4⋊Q8—861no—
567C2×C4⋊Q8—861no—
568C2×C4⋊Q8—861no—
569C2×C4⋊Q8—861no—
570C2×C4⋊Q8—861no—
571C2×C4⋊Q8C2×D4311yescharacteristic, complemented
572#529—431no—
573#529—431no—
574#529—431no—
575#529—431no—
576#529—431no—
577#529—431no—
578#529—431no—
579#529—861no—
580#529—861no—
581#529—861no—
582#529—861no—
583#529C2×D4311yescharacteristic
584C2×#126—861no—
585C2×#125—431no—
586C2×#124—431no—
587C2×#123—861no—
588C2×C22⋊Q8—431no—
589C2×#121—431no—
590C2×C4×Q8—431no—
591C2×C4×D4—431no—
592C2×C4×D4—861no—
593C2×#117—861no—
594C22×C4⋊C4—432no—
595C22×C4⋊C4—861no—
596C22×C42—431no—
597#501—432no—
598#501—432no—
599#501—434no—
600#501—434no—
601#501—432no—
602#501C2×D4312yescomplemented
603#489—432no—
604#489—432no—
605#489—434no—
606#489—434no—
607#489—432no—
608#489C2×D4312yescomplemented
609#483—432no—
610#483—432no—
611#483—434no—
612#483—434no—
613#483—432no—
614#483C2×D4312yescomplemented
615#480—432no—
616#480—432no—
617#480—434no—
618#480—434no—
619#480—432no—
620#480C2×D4312yes—
621#477—432no—
622#477—432no—
623#477—434no—
624#477—432no—
625#477—434no—
626#477C2×D4312yescomplemented
627#476—432no—
628#476—432no—
629#476—434no—
630#476—432no—
631#476—434no—
632#476C2×D4312yescomplemented
633#432—431no—
634#432—432no—
635#432—432no—
636#432—432no—
637#432C2×D4311yescharacteristic, complemented
638C2×#107—434no—
639C2×#106—434no—
640C2×C4⋊C8—432no—
641C2×#103—434no—
642C2×#102—434no—
643C2×C22⋊C8—432no—
644C2×#97—432no—
645C43C2×#323811yescharacteristic, complemented, Sylow
646C22×Q8—21no—
647C22×Q8—431no—
648C22×Q8—862no—
649C22×Q8—862no—
650C22×Q8—862no—
651C22×Q8—862no—
652C22×Q8—862no—
653C22×Q8—861no—
654C22×Q8—1728no—
655C22×D4—431no—
656C22×D4—861no—
657C23×C4—431no—
658C23×C4—431no—
659C23×C4—431no—
660C23×C4—861no—
661C23×C4—862no—
662C22×C8—434no—
663C4⋊Q8—21no—
664C4⋊Q8—21no—
665C4⋊Q8—434no—
666C4⋊Q8—434no—
667C4⋊Q8—432no—
668C4⋊Q8—432no—
669C4⋊Q8—862no—
670C4⋊Q8—862no—
671C4⋊Q8—862no—
672C4⋊Q8—862no—
673C4⋊Q8—862no—
674C4⋊Q8—862no—
675C4⋊Q8—862no—
676C4⋊Q8—862no—
677C4⋊Q8—862no—
678C4⋊Q8—862no—
679C4⋊Q8—861no—
680C4⋊Q8—861no—
681C4⋊Q8C22×D4312yes—
682C4⋊Q8C22×D4312yes—
683#126—21no—
684#126—861no—
685#126—861no—
686#126—861no—
687#126—861no—
688#126—861no—
689#126—861no—
690#126—861no—
691#125—431no—
692#125—431no—
693#125—431no—
694#125—861no—
695#125—861no—
696#125C22×D4311yescharacteristic
697#124—431no—
698#124—431no—
699#124—431no—
700#124—861no—
701#124—861no—
702#124C22×D4311yescharacteristic
703#123—21no—
704#123—861no—
705#123—861no—
706#123—861no—
707#123—861no—
708#123—861no—
709#123—861no—
710#123—861no—
711C22⋊Q8—431no—
712C22⋊Q8—431no—
713C22⋊Q8—431no—
714C22⋊Q8—861no—
715C22⋊Q8—861no—
716C22⋊Q8C22×D4311yescharacteristic
717#121—431no—
718#121—431no—
719#121—431no—
720#121—861no—
721#121—861no—
722#121C22×D4311yescharacteristic
723C4×Q8—431no—
724C4×Q8—431no—
725C4×Q8—431no—
726C4×Q8—861no—
727C4×Q8—861no—
728C4×Q8C22×D4311yescharacteristic
729C4×D4—21no—
730C4×D4—431no—
731C4×D4—431no—
732C4×D4—431no—
733C4×D4—861no—
734C4×D4—861no—
735C4×D4—861no—
736C4×D4—861no—
737C4×D4—861no—
738C4×D4—861no—
739C4×D4—861no—
740C4×D4—861no—
741C4×D4—861no—
742C4×D4C22×D4311yescharacteristic
743#117—21no—
744#117—861no—
745#117—861no—
746#117—861no—
747#117—861no—
748#117—861no—
749#117—861no—
750#117—861no—
751C2×C4⋊C4—21no—
752C2×C4⋊C4—432no—
753C2×C4⋊C4—434no—
754C2×C4⋊C4—434no—
755C2×C4⋊C4—431no—
756C2×C4⋊C4—431no—
757C2×C4⋊C4—862no—
758C2×C4⋊C4—862no—
759C2×C4⋊C4—862no—
760C2×C4⋊C4—862no—
761C2×C4⋊C4—862no—
762C2×C4⋊C4—862no—
763C2×C4⋊C4—861no—
764C2×C4⋊C4—861no—
765C2×C4⋊C4—861no—
766C2×C4⋊C4—861no—
767C2×C4⋊C4—862no—
768C2×C4⋊C4—862no—
769C2×C4⋊C4—861no—
770C2×C4⋊C4C22×D4312yes—
771C2×C22⋊C4—861no—
772C2×C22⋊C4—861no—
773C2×C22⋊C4—861no—
774C2×C22⋊C4—861no—
775C2×C22⋊C4—861no—
776C2×C42—431no—
777C2×C42—431no—
778C2×C42—431no—
779C2×C42—431no—
780C2×C42—431no—
781C2×C42—431no—
782C2×C42—431no—
783C2×C42—431no—
784C2×C42—431no—
785C2×C42—431no—
786C2×C42—431no—
787C2×C42—861no—
788C2×C42C22×D4311yescharacteristic
789#107—434no—
790#107—434no—
791#107—434no—
792#107C22×D4314yes—
793#106—434no—
794#106—434no—
795#106—434no—
796#106C22×D4314yes—
797C4⋊C8—434no—
798C4⋊C8—432no—
799C4⋊C8C22×D4312yes—
800#103—434no—
801#103—434no—
802#103—434no—
803#103C22×D4314yes—
804#102—434no—
805#102—434no—
806#102—434no—
807#102C22×D4314yes—
808C22⋊C8—432no—
809C22⋊C8—434no—
810C22⋊C8C22×D4312yes—
811#97—434no—
812#97—432no—
813#97C22×D4312yes—
814C24—431no—
815C24—861no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—44no—
819C2×Q8—431no—
820C2×Q8—861no—
821C2×Q8—864no—
822C2×Q8—864no—
823C2×Q8—864no—
824C2×Q8—862no—
825C2×Q8—862no—
826C2×Q8—1724no—
827C2×Q8—1728no—
828C2×Q8—1728no—
829C2×Q8—1728no—
830C2×Q8—1728no—
831C2×Q8—1728no—
832C2×Q8C23×D4311yescharacteristic
833C2×D4—21no—
834C2×D4—431no—
835C2×D4—861no—
836C2×D4—864no—
837C2×D4—861no—
838C2×D4—861no—
839C2×D4—861no—
840C2×D4—1724no—
841C2×D4C23×D4311yescharacteristic
842C22×C4—22no—
843C22×C4—21no—
844C22×C4—431no—
845C22×C4—431no—
846C22×C4—431no—
847C22×C4—431no—
848C22×C4—431no—
849C22×C4—431no—
850C22×C4—431no—
851C22×C4—431no—
852C22×C4—431no—
853C22×C4—431no—
854C22×C4—431no—
855C22×C4—431no—
856C22×C4—431no—
857C22×C4—431no—
858C22×C4—431no—
859C22×C4—864no—
860C22×C4—864no—
861C22×C4—861no—
862C22×C4—864no—
863C22×C4—861no—
864C22×C4—861no—
865C22×C4—861no—
866C22×C4—864no—
867C22×C4—864no—
868C22×C4—861no—
869C22×C4—862no—
870C22×C4—861no—
871C22×C4—1724no—
872C22×C4—1728no—
873C22×C4D4×D4311yescharacteristic
874C22×C4D4×D4311yescharacteristic
875C22×C4C23×D4311yescharacteristic
876C2×C8—434no—
877C2×C8—868no—
878C2×C8C23×D4314yes—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—434no—
887C4⋊C4—431no—
888C4⋊C4—431no—
889C4⋊C4—864no—
890C4⋊C4—864no—
891C4⋊C4—861no—
892C4⋊C4—861no—
893C4⋊C4—864no—
894C4⋊C4—864no—
895C4⋊C4—861no—
896C4⋊C4—861no—
897C4⋊C4—861no—
898C4⋊C4—861no—
899C4⋊C4—861no—
900C4⋊C4—861no—
901C4⋊C4—861no—
902C4⋊C4—861no—
903C4⋊C4—862no—
904C4⋊C4—862no—
905C4⋊C4—862no—
906C4⋊C4—861no—
907C4⋊C4—861no—
908C4⋊C4—861no—
909C4⋊C4—861no—
910C4⋊C4C23×D4314yes—
911C4⋊C4C23×D4311yescharacteristic
912C4⋊C4C23×D4311yescharacteristic
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—861no—
919C22⋊C4—861no—
920C22⋊C4—861no—
921C22⋊C4—861no—
922C22⋊C4—861no—
923C22⋊C4—861no—
924C22⋊C4—861no—
925C22⋊C4—861no—
926C22⋊C4—861no—
927C22⋊C4—861no—
928C22⋊C4—861no—
929C22⋊C4—861no—
930C22⋊C4—861no—
931C22⋊C4—861no—
932C22⋊C4—861no—
933C42—21no—
934C42—431no—
935C42—431no—
936C42—431no—
937C42—431no—
938C42—431no—
939C42—431no—
940C42—431no—
941C42—431no—
942C42—431no—
943C42—431no—
944C42—431no—
945C42—431no—
946C42—861no—
947C42—861no—
948C42—861no—
949C42D4×D4311yescharacteristic
950C42D4×D4311yescharacteristic
951C42C23×D4311yescharacteristic
952C42C23×D4311yescharacteristic
953C23—21no—
954C23—431no—
955C23—434no—
956C23—431no—
957C23—862no—
958C23—862no—
959C23—861no—
960C23—1722no—
961C23—1722no—
962C23—1722no—
963C23C2×D4×D4311yescharacteristic
964Q8—22no—
965Q8—44no—
966Q8—44no—
967Q8—862no—
968Q8—1724no—
969Q8—1724no—
970Q8—1722no—
971Q8—1728no—
972Q8—1728no—
973D4—22no—
974D4—42no—
975D4—862no—
976D4—1722no—
977D4—1722no—
978D4—1722no—
979D4—1722no—
980C2×C4—22no—
981C2×C4—22no—
982C2×C4—22no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—24no—
987C2×C4—44no—
988C2×C4—42no—
989C2×C4—431no—
990C2×C4—431no—
991C2×C4—434no—
992C2×C4—434no—
993C2×C4—431no—
994C2×C4—431no—
995C2×C4—431no—
996C2×C4—431no—
997C2×C4—862no—
998C2×C4—862no—
999C2×C4—862no—
1000C2×C4—862no—
1001C2×C4—862no—
1002C2×C4—862no—
1003C2×C4—862no—
1004C2×C4—862no—
1005C2×C4—862no—
1006C2×C4—862no—
1007C2×C4—862no—
1008C2×C4—862no—
1009C2×C4—862no—
1010C2×C4—861no—
1011C2×C4—861no—
1012C2×C4—861no—
1013C2×C4—864no—
1014C2×C4—1722no—
1015C2×C4—1728no—
1016C2×C4—1728no—
1017C2×C4—1722no—
1018C2×C4—1722no—
1019C2×C4—1722no—
1020C2×C4—1722no—
1021C2×C4—1724no—
1022C2×C4—1722no—
1023C2×C4C2×D4×D4311yescharacteristic
1024C2×C4C2×D4×D4311yescharacteristic
1025C2×C4C2×D4×D4311yescharacteristic
1026C2×C4C2×D4×D4311yescharacteristic
1027C2×C4C2×D4×D4311yescharacteristic
1028C2×C4C24×D4311yescharacteristic
1029C8—24no—
1030C8—864no—
1031C22—21no—
1032C22—21no—
1033C22—41no—
1034C22—41no—
1035C22—41no—
1036C22—432no—
1037C22—432no—
1038C22—432no—
1039C22—432no—
1040C22—868no—
1041C22—861no—
1042C22—861no—
1043C22—3444no—
1044C22—1721no—
1045C22—1721no—
1046C22—1721no—
1047C22AGL(1,ℤ/8)×D4312yes—
1048C22C22×D4×D4311yescharacteristic
1049C4—21no—
1050C4—21no—
1051C4—21no—
1052C4—21no—
1053C4—44no—
1054C4—41no—
1055C4—41no—
1056C4—41no—
1057C4—432no—
1058C4—432no—
1059C4—861no—
1060C4—861no—
1061C4—861no—
1062C4—861no—
1063C4—1724no—
1064C4—1721no—
1065C4—1721no—
1066C4—1721no—
1067C4#137×D4312yes—
1068C42−1+4×D4312yes—
1069C2—22no—
1070C2—81no—
1071C2—434no—
1072C2—862no—
1073C2—3441no—
1074C2#536×D4311yescharacteristic
1075C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
1076C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3238C2
socleC22×C43C23×D4
prime radical#121×D43C22
hypercenter#3238D43
hypocenterC43C2×#3238
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3238

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊Q8×D43C2semidirect
3. #19145820C2semidirect
4. #19145819C2semidirect
5. #19145818C2semidirect
6. #19145817C2semidirect
7. #19145816C2semidirect
8. #19145815C2semidirect
9. #19145814C2semidirect
10. #19145813C2semidirect
11. #19145812C2semidirect
12. #501×D43C2semidirect
13. #489×D43C2semidirect
14. #483×D43C2semidirect
16. #477×D43C2semidirect
17. #476×D43C2semidirect
18. #432×D43C2semidirect
19. C43×#3238C2semidirect
21. C2×#13063325C22semidirect
23. C2×#13063324C22semidirect
31. C4⋊Q8×D43C22semidirect
32. C4⋊Q8×D43C22semidirect
57. #14583309C22semidirect
58. #14583308C22semidirect
59. #14583307C22semidirect
60. #14583306C22semidirect
61. #14583305C22semidirect
62. #14583261C22semidirect
63. #14583260C22semidirect
64. #14583259C22semidirect
65. #14583258C22semidirect
66. #14583257C22semidirect
67. #14583231C22semidirect
68. #14583230C22semidirect
69. #14583229C22semidirect
70. #14583228C22semidirect
71. #14583227C22semidirect
77. #14583195C22semidirect
78. #14583194C22semidirect
79. #14583193C22semidirect
80. #14583192C22semidirect
81. #14583191C22semidirect
82. #14583190C22semidirect
83. #14583189C22semidirect
84. #14583188C22semidirect
85. #14583187C22semidirect
86. #14583186C22semidirect
87. #14582956C22semidirect
88. #14582955C22semidirect
89. #14582954C22semidirect
90. #14582953C22semidirect
98. C2×C4⋊Q8×C43C22semidirect
100. C43×#501C22semidirect
101. C43×#489C22semidirect
102. C43×#483C22semidirect
104. C43×#477C22semidirect
105. C43×#476C22semidirect
106. C43×#432C22semidirect
542. #3238D43direct (N × H)
557. D43#3238direct (N × H)
571. C2×C4⋊Q8C2×D43semidirect
602. #501C2×D43semidirect
608. #489C2×D43semidirect
614. #483C2×D43semidirect
626. #477C2×D43semidirect
632. #476C2×D43semidirect
637. #432C2×D43semidirect
645. C43C2×#3238semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×D432
#529×D432
#191458202
#191458192
#191458182
#191458172
#191458162
#191458152
#191458142
#191458132
#191458122
#501×D432
#489×D432
#483×D432
#480×D432
#477×D432
#476×D432
#432×D432
C43×#32382
C2×#323843