Finite Group Databasebeta

← #25969625

Subgroups — #25969625

Order 11008.

1888 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19147888C211yesmaximal, characteristic
2C2×#14583454C211yesmaximal, characteristic, complemented
3#19145987C212yesmaximal, complemented
4#19145979C212yesmaximal, complemented
5#19145966C212yesmaximal, complemented
6#19145964C212yesmaximal, complemented
7#19145938C212yesmaximal, complemented
8#19145930C212yesmaximal, complemented
9#19145928C212yesmaximal, complemented
10#19145908C212yesmaximal, complemented
11#19144411C211yesmaximal, characteristic, complemented
12#19144410C211yesmaximal, characteristic, complemented
13#19144397C212yesmaximal, complemented
14#19144223C212yesmaximal, complemented
15#19144219C212yesmaximal, complemented
16#19144078C211yesmaximal, characteristic, complemented
17#19144064C212yesmaximal, complemented
18#423×D43C211yesmaximal, characteristic, complemented
19C43×#3039C211yesmaximal, characteristic, complemented
20C2×#13063356C2212yes—
21C2×M16×D43C2212yes—
22#14583454—21no—
23#14583454—21no—
24#14583454—21no—
25#14583454—21no—
26#14583454C2212yes—
27#14583454C2212yes—
28#14583454C2212yes—
29#14583454C2212yes—
30#14583453C2211yescharacteristic
31#14583453C2211yescharacteristic
32#14583452C2211yescharacteristic
33#14583446C2211yescharacteristic
34#14583446C2211yescharacteristic
35#14583445C2211yescharacteristic
36C2×#13063325C2211yescharacteristic
37#14583436C2211yescharacteristic
38#14583436C2211yescharacteristic
39#14583431C2211yescharacteristic
40#14583431C2211yescharacteristic
41#14583429—21no—
42#14583429—21no—
43#14583427—21no—
44#14583427—21no—
45C2×#13063316—21no—
46#14583411C2211yescharacteristic
47#14583408—21no—
48#14583408—21no—
49#14583406C2211yescharacteristic
50C2×#13063305—21no—
51C2×#13063301C2212yes—
52C4×#10621898—21no—
53C4×#10621898—21no—
54C4×#10621898C2211yescharacteristic
55C2×Q8×Dic43C2212yes—
56C2×#13063290—21no—
57C2×#13063283—21no—
58C2×C42×D43C2211yescharacteristic
59#14583208C2214yescomplemented
60#14583204C2214yescomplemented
61#14583195C2212yescomplemented
62#14583194C2212yescomplemented
63#14583192C2214yescomplemented
64#14583190C2212yescomplemented
65#14583189C2212yescomplemented
66#14583185C2212yescomplemented
67#14583184C2212yescomplemented
68#14583182C2214yescomplemented
69#14583180C2212yescomplemented
70#14583179C2212yescomplemented
71#14583156C2214yes—
72#14583154C2214yes—
73#14583148C2214yes—
74#14583142C2214yes—
75#14583139C2214yes—
76#14583137C2214yes—
77#14583131C2214yes—
78#14583125C2214yes—
79#14583123C2214yescomplemented
80#14583119C2214yescomplemented
81#14583107C2214yescomplemented
82#14583106C2212yescomplemented
83#14583106C2212yescomplemented
84#14583101C2212yescomplemented
85#14583101C2212yescomplemented
86#14583097C2214yescomplemented
87#14582942C2212yes—
88#14582941C2212yes—
89#14582923C2211yescharacteristic
90#14582922C2212yes—
91#14582921C2212yes—
92#14582921C2212yes—
93C4⋊C8×D43C2212yes—
94C4⋊C8×D43C2212yes—
95#14582908C2212yes—
96#14582901C2212yes—
97#14582900C2212yes—
98C2×#137×C43C2212yes—
99C2×C4⋊Q8×C43C2211yescharacteristic
100C4×#41×C43C2211yescharacteristic
101C43×#462C2212yescomplemented
102C43×#462C2212yescomplemented
103C43×#461C2212yescomplemented
104C43×#461C2212yescomplemented
105C43×#423C2211yescharacteristic
106C43×#419C2212yes—
107C2×#10621898—21no—
108C2×#10621898—21no—
109C2×#10621898C2311yescharacteristic
110C22×Dic86—21no—
111C22×C4×D43D411yescharacteristic
112C22×C4×D43D411yescharacteristic
113C22×C4×D43C2311yescharacteristic
114#13063356—44no—
115C2×#10621885C2314yes—
116C2×#10621884C2314yes—
117C2×#10621877C2312yes—
118C2×#10621872C2314yes—
119M16×D43—44no—
120C2×C8×D43C2314yes—
121#13063325—21no—
122#13063325—21no—
123#13063325C2312yes—
124#13063325C2312yes—
125#13063324C2311yescharacteristic
126#13063324C2311yescharacteristic
127#13063323C2311yescharacteristic
128#13063321C2311yescharacteristic
129#13063320—21no—
130#13063320—21no—
131#13063318—21no—
132#13063318—21no—
133#13063316—22no—
134#13063316—22no—
135#13063316—22no—
136#13063316—22no—
137#13063316C2311yescharacteristic
138#13063316C2311yescharacteristic
139#13063315—21no—
140#13063315—21no—
141#13063314C2311yescharacteristic
142#13063312C2311yescharacteristic
143#13063311—21no—
144#13063311—21no—
145#13063310—21no—
146#13063310—21no—
147#13063309—21no—
148#13063307—21no—
149#13063307—21no—
150#13063306—21no—
151#13063305—22no—
152#13063305—22no—
153#13063305—22no—
154#13063305—22no—
155#13063305C2311yescharacteristic
156#13063305C2311yescharacteristic
157#13063303—21no—
158#13063303—21no—
159#13063302—21no—
160#13063302—21no—
161#13063301—22no—
162#13063301—22no—
163#13063301C2314yes—
164#13063301C2311yescharacteristic
165#13063301C2314yes—
166#13063301C2311yescharacteristic
167#13063300C2311yescharacteristic
168#13063300C2311yescharacteristic
169#13063298—21no—
170#13063298—21no—
171#13063297—21no—
172#13063297—21no—
173#13063296C2311yescharacteristic
174#13063296C2311yescharacteristic
175#13063295—21no—
176#13063293—21no—
177Q8×Dic43—22no—
178Q8×Dic43—22no—
179Q8×Dic43C2314yes—
180Q8×Dic43C2314yes—
181C4×Dic86—21no—
182C4×Dic86—21no—
183C4×Dic86—21no—
184C4×Dic86—21no—
185C4×Dic86C2311yescharacteristic
186C4×Dic86C2311yescharacteristic
187#13063290—22no—
188#13063290—22no—
189#13063290—22no—
190#13063290—22no—
191C4×D172—21no—
192C4×D172—21no—
193C4×D172—21no—
194C4×D172—21no—
195C4×D172C2311yescharacteristic
196C4×D172C2311yescharacteristic
197C4×C22⋊D43—21no—
198C4×C22⋊D43—21no—
199C4×C22⋊D43—21no—
200C4×C22⋊D43—21no—
201C4×C22⋊D43—21no—
202C4×C22⋊D43—21no—
203C4×C22⋊D43—21no—
204C4×C22⋊D43—21no—
205C4×C22⋊D43—21no—
206C4×C22⋊D43—21no—
207#13063284—21no—
208#13063284—21no—
209#13063284C2311yescharacteristic
210#13063283—22no—
211#13063283—22no—
212#13063283—22no—
213#13063283—22no—
214#13063282—21no—
215#13063282—21no—
216#13063282—21no—
217#13063282—21no—
218#13063282—21no—
219C2×C4⋊Dic43—21no—
220C2×C4⋊Dic43—22no—
221C2×C4⋊Dic43C2312yes—
222C2×Dic43⋊C4—22no—
223C2×(C2×D43)⋊C4—22no—
224C2×C4×Dic43—22no—
225C2×C4×Dic43D411yescharacteristic
226C2×C4×Dic43D411yescharacteristic
227C2×C4×Dic43C2311yescharacteristic
228C42×D43—21no—
229C42×D43D411yescharacteristic
230C42×D43D411yescharacteristic
231C42×D43D411yescharacteristic
232C42×D43D411yescharacteristic
233C42×D43C2311yescharacteristic
234C42×D43C2311yescharacteristic
235C42×D43C2311yescharacteristic
236C42×D43C2311yescharacteristic
237#13063259C2314yes—
238#13063258C2314yes—
239#13063257C2314yes—
240#13063256C2314yes—
241C4⋊(C43⋊C8)C2312yes—
242C4⋊(C43⋊C8)C2312yes—
243Dic43⋊C8C2314yes—
244Dic43⋊C8C2314yes—
245#13063250C2314yes—
246#13063249C2314yes—
247#13063249C2314yes—
248#13063249C2314yes—
249#13063247C2314yes—
250#13063246C2314yes—
251C2×#41×C43C2311yescharacteristic
252C22×Q8×C43C2312yes—
253#137×C43—44no—
254C2×Q16×C43C2314yes—
255C2×SD16×C43C2314yes—
256C2×M16×C43C2312yes—
257C4⋊Q8×C43—21no—
258C4⋊Q8×C43—21no—
259C4⋊Q8×C43C2312yes—
260C4⋊Q8×C43C2312yes—
261C4×Q8×C43C2311yescharacteristic
262C4×Q8×C43C2311yescharacteristic
263C4×D4×C43—21no—
264C4×D4×C43—21no—
265C4×D4×C43C2311yescharacteristic
266C4×D4×C43C2311yescharacteristic
267#117×C43—21no—
268#117×C43C2311yescharacteristic
269C2×C4⋊C4×C43—21no—
270C2×C4⋊C4×C43—21no—
271C2×C42×C43—21no—
272C2×C42×C43C2311yescharacteristic
273C4⋊C8×C43C2312yes—
274C4⋊C8×C43C2312yes—
275#103×C43C2314yes—
276#103×C43C2314yes—
277C23×D43C2×D411yescharacteristic
278#41×C43—22no—
279#41×C43—22no—
280C2×Q8×C43—22no—
281C2×Q8×C43—24no—
282C2×Q8×C43—24no—
283C2×Q8×C43C2414yes—
284C2×Q8×C43C2411yescharacteristic
285C2×D4×C43—21no—
286C2×D4×C43C2411yescharacteristic
287C22×C4×C43—21no—
288C22×C4×C43—21no—
289C22×C4×C43—21no—
290C22×C4×C43—22no—
291C22×C4×C43C2×D411yescharacteristic
292C22×C4×C43C2×D411yescharacteristic
293C22×C4×C43C2411yescharacteristic
294C2×C22⋊D43—21no—
295C2×C22⋊D43—21no—
296C2×C22⋊D43—21no—
297C2×C22⋊D43—21no—
298C2×C22⋊D43—21no—
299C22×Dic43—22no—
300C22×Dic43C2×D411yescharacteristic
301C22×Dic43C2×D411yescharacteristic
302C22×Dic43C2×D411yescharacteristic
303#10621898—22no—
304#10621898—22no—
305#10621898—44no—
306#10621898—44no—
307C2×D172—21no—
308C2×D172—21no—
309C2×D172C2411yescharacteristic
310C2×C4×D43—22no—
311C2×C4×D43—22no—
312C2×C4×D43—24no—
313C2×C4×D43—21no—
314C2×C4×D43—21no—
315C2×C4×D43—21no—
316C2×C4×D43—42no—
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—21no—
333C2×Dic86—44no—
334C2×Dic86C2411yescharacteristic
335Q16×C43—44no—
336SD16×C43—44no—
337M16×C43—24no—
338C2×C8×C43C2414yes—
339C4⋊C4×C43—22no—
340C4⋊C4×C43—22no—
341C4⋊C4×C43—22no—
342C4⋊C4×C43—22no—
343C4⋊C4×C43—21no—
344C4⋊C4×C43—21no—
345C4⋊C4×C43C2411yescharacteristic
346C4⋊C4×C43C2411yescharacteristic
347C22⋊C4×C43—21no—
348C22⋊C4×C43—21no—
349C22⋊C4×C43—21no—
350C42×C43—21no—
351C42×C43—21no—
352C42×C43—21no—
353C42×C43C2×D411yescharacteristic
354C42×C43C2×D411yescharacteristic
355C42×C43C2411yescharacteristic
356C42×C43C2411yescharacteristic
357C22⋊Dic43—21no—
358C22⋊Dic43—21no—
359C22⋊Dic43—21no—
360C22⋊Dic43—21no—
361C22⋊Dic43—21no—
362#10621885—44no—
363#10621884—44no—
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—24no—
371(C2×D43)⋊C4—24no—
372(C2×D43)⋊C4—21no—
373(C2×D43)⋊C4—21no—
374(C2×D43)⋊C4—21no—
375(C2×D43)⋊C4—21no—
376C4⋊Dic43—22no—
377C4⋊Dic43—22no—
378C4⋊Dic43—22no—
379C4⋊Dic43—24no—
380C4⋊Dic43—24no—
381C4⋊Dic43—21no—
382C4⋊Dic43—21no—
383C4⋊Dic43—21no—
384C4⋊Dic43—21no—
385C4⋊Dic43C2414yes—
386C4⋊Dic43C2411yescharacteristic
387C4⋊Dic43C2411yescharacteristic
388Dic43⋊C4—21no—
389Dic43⋊C4—21no—
390Dic43⋊C4—24no—
391Dic43⋊C4—24no—
392Dic43⋊C4—21no—
393Dic43⋊C4—21no—
394Dic43⋊C4—21no—
395Dic43⋊C4—21no—
396Dic43⋊C4—21no—
397Dic43⋊C4—21no—
398Dic43⋊C4—21no—
399Dic43⋊C4—21no—
400C4×Dic43—21no—
401C4×Dic43—21no—
402C4×Dic43—21no—
403C4×Dic43—24no—
404C4×Dic43—24no—
405C4×Dic43C2×D411yescharacteristic
406C4×Dic43C2×D411yescharacteristic
407C4×Dic43C2×D411yescharacteristic
408C4×Dic43C2×D411yescharacteristic
409C4×Dic43C2×D411yescharacteristic
410C4×Dic43C2×D411yescharacteristic
411C4×Dic43C2×D411yescharacteristic
412C4×Dic43C2×D411yescharacteristic
413C4×Dic43C2×D411yescharacteristic
414C4×Dic43C2×D411yescharacteristic
415C4×Dic43C2411yescharacteristic
416C4×Dic43C2411yescharacteristic
417#10621877—24no—
418C2×C43⋊C8C2414yes—
419#10621872—44no—
420C8×D43—44no—
421C23×C43—21no—
422C23×C43C22×D411yescharacteristic
423C22×D43—22no—
424C22×D43—22no—
425C22×D43—21no—
426C22×D43—41no—
427C22×D43C22×D411yescharacteristic
428C22×D43C22×D411yescharacteristic
429Q8×C43—24no—
430Q8×C43—21no—
431Q8×C43—24no—
432Q8×C43—21no—
433Q8×C43—44no—
434D4×C43—21no—
435D4×C43—21no—
436D4×C43—42no—
437C2×C4×C43—22no—
438C2×C4×C43—22no—
439C2×C4×C43—24no—
440C2×C4×C43—21no—
441C2×C4×C43—21no—
442C2×C4×C43—21no—
443C2×C4×C43—44no—
444C2×C4×C43—42no—
445C2×C4×C43—42no—
446C2×C4×C43—42no—
447C2×C4×C43C22×D411yescharacteristic
448C2×C4×C43C22×D411yescharacteristic
449C2×C4×C43C22×D411yescharacteristic
450C2×C4×C43C22×D411yescharacteristic
451C2×C4×C43C22×D411yescharacteristic
452C2×C4×C43H(5,𝔽2)12yes—
453C2×C4×C432−1+412yes—
454C2×C4×C43C2511yescharacteristic
455C22⋊D43—42no—
456C22⋊D43—42no—
457C22⋊D43—42no—
458C22⋊D43—42no—
459C22⋊D43—42no—
460C2×Dic43—22no—
461C2×Dic43—22no—
462C2×Dic43—21no—
463C2×Dic43—21no—
464C2×Dic43—21no—
465C2×Dic43—24no—
466C2×Dic43—41no—
467C2×Dic43—44no—
468C2×Dic43C22×D411yescharacteristic
469C2×Dic43C22×D411yescharacteristic
470C2×Dic43C22×D411yescharacteristic
471C2×Dic43C22×D411yescharacteristic
472C2×Dic43C22×D411yescharacteristic
473C2×Dic43C22×D411yescharacteristic
474D172—21no—
475D172—21no—
476D172—42no—
477D172—42no—
478C4×D43—22no—
479C4×D43—22no—
480C4×D43—22no—
481C4×D43—22no—
482C4×D43—22no—
483C4×D43—22no—
484C4×D43—21no—
485C4×D43—21no—
486C4×D43—21no—
487C4×D43—21no—
488C4×D43—22no—
489C4×D43—41no—
490C4×D43—41no—
491C4×D43—42no—
492C4×D43—42no—
493C4×D43—42no—
494C4×D43#13714yescomplemented
495Dic86—21no—
496Dic86—21no—
497Dic86—42no—
498Dic86—44no—
499Dic86—44no—
500Dic86—42no—
501C8×C43—24no—
502C43⋊C8—24no—
503#60918—431nomaximal, Sylow
504C22×C43—21no—
505C22×C43—21no—
506C22×C43—41no—
507C22×C43—41no—
508C22×C43—41no—
509C22×C43#53712yes—
510C22×C43C23×D411yescharacteristic
511C2×D43—21no—
512C2×D43—21no—
513C2×D43—21no—
514C2×D43—21no—
515C2×D43—21no—
516C2×D43—44no—
517C2×D43—41no—
518C2×D43—41no—
519C2×D43—41no—
520C2×D43C2×#13712yes—
521C4×C43—21no—
522C4×C43—21no—
523C4×C43—41no—
524C4×C43—44no—
525C4×C43—41no—
526C4×C43—41no—
527C4×C43#53712yes—
528C4×C43C2×#13712yes—
529C4×C43#57512yes—
530C4×C43C2×H(5,𝔽2)11yescharacteristic
531C4×C43C2×2−1+411yescharacteristic
532Dic43—21no—
533Dic43—21no—
534Dic43—21no—
535Dic43—21no—
536Dic43—21no—
537Dic43—41no—
538Dic43—41no—
539Dic43—44no—
540Dic43—41no—
541Dic43C2×#13712yes—
542#3444—431no—
543C2×#533—431no—
544#3255—432no—
545#3254—432no—
546#3252—432no—
547#3252—432no—
548#3249—432no—
549#3248—432no—
550#3248—432no—
551#3246—432no—
552#3079—431no—
553#3079—431no—
554#3078—432no—
555#3056—432no—
556#3056—432no—
557#3039—431no—
558#3039D4311yescharacteristic, complemented
559#3037—432no—
560C2×#423—431no—
561C2×C43—22no—
562C2×C43—81no—
563C2×C43C2×#53711yescharacteristic
564C2×C43C22×#13711yescharacteristic
565C2×C43C2×#57511yescharacteristic
566D43—22no—
567D43—41no—
568D43—81no—
569C2×#137—432no—
570C2×#137C2×D4312yes—
571C22×M16—432no—
572#533—431no—
573#533—432no—
574#533—432no—
575#533—432no—
576#533—432no—
577#533—431no—
578#533—431no—
579#533—861no—
580#533—861no—
581#533—861no—
582#533—861no—
583#532—431no—
584#532—431no—
585#532—431no—
586C2×C4⋊Q8—431no—
587C2×C4⋊Q8C2×D4311yescharacteristic
588#529—431no—
589#529—431no—
590#529—431no—
591#529—431no—
592#529—861no—
593#529—861no—
594#529—861no—
595#529—861no—
596C2×#125—861no—
597#525—431no—
598#525—431no—
599#525—861no—
600#525—861no—
601C2×C22⋊Q8—432no—
602C2×C22⋊Q8—861no—
603C4×#41—431no—
604C4×#41—861no—
605C4×#41—861no—
606C4×#41C2×D4311yescharacteristic
607C2×C4×Q8—432no—
608C2×C4×Q8—861no—
609C2×#117—861no—
610C22×C42—431no—
611#479—434no—
612#479—434no—
613#477—432no—
614#477—432no—
615#477—434no—
616#476—432no—
617#476—432no—
618#475—432no—
619#475—432no—
620#475—434no—
621#474—432no—
622#474—432no—
623#470—434no—
624#470—434no—
625#468—434no—
626#468—434no—
627#467—434no—
628#467—434no—
629#465—434no—
630#465—434no—
631#464—434no—
632#464—434no—
633#462—434no—
634#462—432no—
635#462—432no—
636#462C2×D4312yescomplemented
637#462C2×D4312yescomplemented
638#461—432no—
639#461—432no—
640#461C2×D4312yescomplemented
641#461C2×D4312yescomplemented
642#460—434no—
643#428—432no—
644#428—432no—
645#423—432no—
646#423—431no—
647#423—432no—
648#423—432no—
649#423C2×D4311yescharacteristic
650C2×C4⋊C8—432no—
651C2×C4⋊C8—432no—
652#419—432no—
653#419C2×D4312yes—
654#417—432no—
655#417—432no—
656C43#6091811yescharacteristic, complemented, Sylow
657C2×#41—431no—
658C2×#41—861no—
659C2×#41—861no—
660C2×#41C22×D4311yescharacteristic
661C22×Q8—861no—
662C22×Q8C22×D4312yes—
663C23×C4—431no—
664C23×C4—431no—
665C23×C4—431no—
666#137—44no—
667#137—1724no—
668C2×Q16—434no—
669C2×Q16C22×D4314yes—
670C2×SD16—434no—
671C2×SD16C22×D4314yes—
672C2×M16—432no—
673C2×M16—434no—
674C2×M16—1724no—
675C2×M16C22×D4312yes—
676C22×C8—434no—
677C4⋊Q8—21no—
678C4⋊Q8—21no—
679C4⋊Q8—431no—
680C4⋊Q8—431no—
681C4⋊Q8—431no—
682C4⋊Q8—432no—
683C4⋊Q8—432no—
684C4⋊Q8—861no—
685C4⋊Q8—861no—
686C4⋊Q8C22×D4312yes—
687C4⋊Q8C22×D4312yes—
688#127—431no—
689#126—861no—
690#126—861no—
691#126—861no—
692#126—861no—
693#125—431no—
694#125—431no—
695#125—862no—
696#125—862no—
697#125—862no—
698#125—862no—
699#125—861no—
700#125—861no—
701#124—431no—
702#124—431no—
703#124—861no—
704#124—861no—
705#123—861no—
706#123—861no—
707#123—861no—
708#123—861no—
709#123—861no—
710#123—861no—
711C22⋊Q8—434no—
712C22⋊Q8—434no—
713C22⋊Q8—431no—
714C22⋊Q8—431no—
715C22⋊Q8—431no—
716C22⋊Q8—431no—
717C22⋊Q8—861no—
718C22⋊Q8—861no—
719C22⋊Q8—862no—
720C22⋊Q8—862no—
721C22⋊Q8—862no—
722C22⋊Q8—862no—
723C22⋊Q8—861no—
724C22⋊Q8—861no—
725C22⋊Q8—862no—
726C22⋊Q8—862no—
727#121—431no—
728#121—431no—
729#121—431no—
730#121—431no—
731#121—861no—
732#121—861no—
733#121—861no—
734#121—861no—
735#120—861no—
736#120—861no—
737C4×Q8—434no—
738C4×Q8—434no—
739C4×Q8—431no—
740C4×Q8—431no—
741C4×Q8—861no—
742C4×Q8—861no—
743C4×Q8—861no—
744C4×Q8—861no—
745C4×Q8—862no—
746C4×Q8—862no—
747C4×Q8—862no—
748C4×Q8—862no—
749C4×Q8—862no—
750C4×Q8—862no—
751C4×Q8C22×D4311yescharacteristic
752C4×Q8C22×D4311yescharacteristic
753C4×D4—21no—
754C4×D4—21no—
755C4×D4—431no—
756C4×D4—431no—
757C4×D4—861no—
758C4×D4—861no—
759C4×D4—861no—
760C4×D4—861no—
761C4×D4—861no—
762C4×D4—861no—
763C4×D4—861no—
764C4×D4—861no—
765C4×D4—861no—
766C4×D4—861no—
767C4×D4—861no—
768C4×D4—861no—
769C4×D4—861no—
770C4×D4—861no—
771C4×D4C22×D4311yescharacteristic
772C4×D4C22×D4311yescharacteristic
773#117—21no—
774#117—431no—
775#117—861no—
776#117—861no—
777#117—861no—
778#117—861no—
779#117—861no—
780#117—861no—
781#117—862no—
782#117—862no—
783#117—862no—
784#117—862no—
785#117—861no—
786#117C22×D4311yescharacteristic
787C2×C4⋊C4—21no—
788C2×C4⋊C4—21no—
789C2×C4⋊C4—432no—
790C2×C4⋊C4—862no—
791C2×C4⋊C4—862no—
792C2×C4⋊C4—861no—
793C2×C22⋊C4—862no—
794C2×C42—21no—
795C2×C42—431no—
796C2×C42—431no—
797C2×C42—431no—
798C2×C42—431no—
799C2×C42—431no—
800C2×C42—431no—
801C2×C42—431no—
802C2×C42—431no—
803C2×C42—431no—
804C2×C42—431no—
805C2×C42—431no—
806C2×C42—862no—
807C2×C42—861no—
808C2×C42C22×D4311yescharacteristic
809#107—434no—
810#107—434no—
811#106—434no—
812#106—434no—
813C4⋊C8—434no—
814C4⋊C8—434no—
815C4⋊C8—432no—
816C4⋊C8—432no—
817C4⋊C8C22×D4312yes—
818C4⋊C8C22×D4312yes—
819#103—434no—
820#103—434no—
821#103—434no—
822#103—434no—
823#103C22×D4314yes—
824#103C22×D4314yes—
825#102—434no—
826#102—434no—
827C24—431no—
828#41—22no—
829#41—22no—
830#41—862no—
831#41—862no—
832#41—1724no—
833#41—1724no—
834C2×Q8—22no—
835C2×Q8—24no—
836C2×Q8—24no—
837C2×Q8—431no—
838C2×Q8—861no—
839C2×Q8—861no—
840C2×Q8—862no—
841C2×Q8—862no—
842C2×Q8—1724no—
843C2×Q8C23×D4311yescharacteristic
844C2×Q8C23×D4314yes—
845C2×D4—21no—
846C2×D4—431no—
847C2×D4—861no—
848C2×D4—861no—
849C2×D4—861no—
850C2×D4—861no—
851C2×D4—861no—
852C2×D4—861no—
853C2×D4—861no—
854C2×D4C23×D4311yescharacteristic
855C22×C4—22no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—431no—
860C22×C4—431no—
861C22×C4—431no—
862C22×C4—431no—
863C22×C4—431no—
864C22×C4—431no—
865C22×C4—431no—
866C22×C4—431no—
867C22×C4—431no—
868C22×C4—431no—
869C22×C4—431no—
870C22×C4—431no—
871C22×C4—431no—
872C22×C4—431no—
873C22×C4—431no—
874C22×C4—864no—
875C22×C4—862no—
876C22×C4—862no—
877C22×C4—862no—
878C22×C4—861no—
879C22×C4—861no—
880C22×C4—861no—
881C22×C4—1722no—
882C22×C4D4×D4311yescharacteristic
883C22×C4D4×D4311yescharacteristic
884C22×C4C23×D4311yescharacteristic
885Q16—44no—
886Q16—1724no—
887SD16—44no—
888SD16—1724no—
889M16—24no—
890M16—864no—
891M16—1724no—
892C2×C8—434no—
893C2×C8—1724no—
894C2×C8C23×D4314yes—
895C4⋊C4—22no—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—434no—
902C4⋊C4—431no—
903C4⋊C4—431no—
904C4⋊C4—864no—
905C4⋊C4—864no—
906C4⋊C4—864no—
907C4⋊C4—864no—
908C4⋊C4—861no—
909C4⋊C4—861no—
910C4⋊C4—861no—
911C4⋊C4—861no—
912C4⋊C4—861no—
913C4⋊C4—861no—
914C4⋊C4—861no—
915C4⋊C4—861no—
916C4⋊C4—861no—
917C4⋊C4—861no—
918C4⋊C4—861no—
919C4⋊C4—861no—
920C4⋊C4—862no—
921C4⋊C4—862no—
922C4⋊C4—862no—
923C4⋊C4—861no—
924C4⋊C4—861no—
925C4⋊C4C23×D4311yescharacteristic
926C4⋊C4C23×D4311yescharacteristic
927C22⋊C4—21no—
928C22⋊C4—21no—
929C22⋊C4—21no—
930C22⋊C4—861no—
931C22⋊C4—861no—
932C22⋊C4—861no—
933C22⋊C4—861no—
934C22⋊C4—864no—
935C22⋊C4—864no—
936C22⋊C4—861no—
937C22⋊C4—861no—
938C22⋊C4—861no—
939C22⋊C4—861no—
940C22⋊C4—861no—
941C22⋊C4—861no—
942C22⋊C4—861no—
943C22⋊C4—861no—
944C22⋊C4—861no—
945C22⋊C4—861no—
946C22⋊C4—861no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—431no—
951C42—431no—
952C42—431no—
953C42—431no—
954C42—431no—
955C42—431no—
956C42—431no—
957C42—431no—
958C42—431no—
959C42—431no—
960C42—431no—
961C42—431no—
962C42—864no—
963C42—864no—
964C42—861no—
965C42—861no—
966C42—861no—
967C42D4×D4311yescharacteristic
968C42D4×D4311yescharacteristic
969C42C23×D4311yescharacteristic
970C42C23×D4311yescharacteristic
971C23—21no—
972C23—431no—
973C23—431no—
974C23—862no—
975C23—862no—
976C23—861no—
977C23—1721no—
978C23C2×D4×D4311yescharacteristic
979Q8—24no—
980Q8—21no—
981Q8—24no—
982Q8—21no—
983Q8—44no—
984Q8—861no—
985Q8—861no—
986Q8—1724no—
987Q8—1722no—
988Q8—1722no—
989Q8—1724no—
990D4—21no—
991D4—21no—
992D4—42no—
993D4—861no—
994D4—861no—
995D4—1722no—
996D4—1722no—
997D4—1722no—
998D4—1722no—
999D4—1722no—
1000D4—1722no—
1001D4—1722no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—24no—
1008C2×C4—44no—
1009C2×C4—42no—
1010C2×C4—42no—
1011C2×C4—42no—
1012C2×C4—431no—
1013C2×C4—434no—
1014C2×C4—431no—
1015C2×C4—431no—
1016C2×C4—431no—
1017C2×C4—431no—
1018C2×C4—431no—
1019C2×C4—862no—
1020C2×C4—862no—
1021C2×C4—862no—
1022C2×C4—862no—
1023C2×C4—862no—
1024C2×C4—862no—
1025C2×C4—862no—
1026C2×C4—861no—
1027C2×C4—861no—
1028C2×C4—861no—
1029C2×C4—861no—
1030C2×C4—862no—
1031C2×C4—862no—
1032C2×C4—861no—
1033C2×C4—861no—
1034C2×C4—861no—
1035C2×C4—864no—
1036C2×C4—1721no—
1037C2×C4—1721no—
1038C2×C4—1721no—
1039C2×C4—1724no—
1040C2×C4—1722no—
1041C2×C4—1722no—
1042C2×C4—1722no—
1043C2×C4C2×D4×D4311yescharacteristic
1044C2×C4C2×D4×D4311yescharacteristic
1045C2×C4C2×D4×D4311yescharacteristic
1046C2×C4C2×D4×D4311yescharacteristic
1047C2×C4C2×D4×D4311yescharacteristic
1048C2×C4#1306337012yes—
1049C2×C4#1306337212yes—
1050C2×C4C24×D4311yescharacteristic
1051C8—24no—
1052C8—864no—
1053C22—21no—
1054C22—21no—
1055C22—41no—
1056C22—41no—
1057C22—41no—
1058C22—432no—
1059C22—861no—
1060C22—861no—
1061C22—861no—
1062C22—861no—
1063C22—861no—
1064C22—1724no—
1065C22—1721no—
1066C22—1721no—
1067C22—1721no—
1068C22#1458347812yes—
1069C22C22×D4×D4311yescharacteristic
1070C4—21no—
1071C4—21no—
1072C4—41no—
1073C4—41no—
1074C4—41no—
1075C4—44no—
1076C4—432no—
1077C4—861no—
1078C4—861no—
1079C4—861no—
1080C4—861no—
1081C4—861no—
1082C4—1721no—
1083C4—1721no—
1084C4—1724no—
1085C4—1721no—
1086C4#1458347812yes—
1087C4#137×D4312yes—
1088C4#1458369812yes—
1089C4C2×#1306337011yescharacteristic
1090C4C2×#1306337211yescharacteristic
1091C2—22no—
1092C2—81no—
1093C2—862no—
1094C2—3441no—
1095C2—1721no—
1096C2C2×#1458347811yescharacteristic
1097C2C2×#137×D4311yescharacteristic
1098C2C2×#1458369811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3039C2
socleC22×C43C23×D4
prime radical#19147888C2
hypercenter#3039D43
hypocenterC43#60918
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
2. C2×#14583454C2semidirect
3. #19145987C2semidirect
4. #19145979C2semidirect
5. #19145966C2semidirect
6. #19145964C2semidirect
7. #19145938C2semidirect
8. #19145930C2semidirect
9. #19145928C2semidirect
10. #19145908C2semidirect
11. #19144411C2semidirect
12. #19144410C2semidirect
13. #19144397C2semidirect
14. #19144223C2semidirect
15. #19144219C2semidirect
16. #19144078C2semidirect
17. #19144064C2semidirect
18. #423×D43C2semidirect
19. C43×#3039C2semidirect
59. #14583208C22semidirect
60. #14583204C22semidirect
61. #14583195C22semidirect
62. #14583194C22semidirect
63. #14583192C22semidirect
64. #14583190C22semidirect
65. #14583189C22semidirect
66. #14583185C22semidirect
67. #14583184C22semidirect
68. #14583182C22semidirect
69. #14583180C22semidirect
70. #14583179C22semidirect
79. #14583123C22semidirect
80. #14583119C22semidirect
81. #14583107C22semidirect
82. #14583106C22semidirect
83. #14583106C22semidirect
84. #14583101C22semidirect
85. #14583101C22semidirect
86. #14583097C22semidirect
101. C43×#462C22semidirect
102. C43×#462C22semidirect
103. C43×#461C22semidirect
104. C43×#461C22semidirect
494. C4×D43#137semidirect
558. #3039D43semidirect
636. #462C2×D43semidirect
637. #462C2×D43semidirect
640. #461C2×D43semidirect
641. #461C2×D43semidirect
656. C43#60918semidirect

Maximal subgroups

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

subgroupindex
#191478882
C2×#145834542
#191459872
#191459792
#191459662
#191459642
#191459382
#191459302
#191459282
#191459082
#191444112
#191444102
#191443972
#191442232
#191442192
#191440782
#191440642
#423×D432
C43×#30392
#6091843