Finite Group Databasebeta

← #25112723

Subgroups — #25112723

Order 11008.

1696 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583539C211yesmaximal, characteristic
2#19137411C212yesmaximal, complemented
3#19135578C212yesmaximal, complemented
4#19135047C212yesmaximal, complemented
5#19135046C212yesmaximal, complemented
6#19134668C211yesmaximal, characteristic, complemented
7#19134582C211yesmaximal, characteristic, complemented
8#19134382C211yesmaximal, characteristic, complemented
9C2×#14582666C211yesmaximal, characteristic, complemented
10#342×D43C211yesmaximal, characteristic, complemented
11C43×#1819C211yesmaximal, characteristic, complemented
12C22×#10621898C411yescharacteristic, complemented
13C23×C22⋊D43C2211yescharacteristic
14#14583539—22no—
15#14583539—22no—
16#14583539—22no—
17#14583539—22no—
18C2×#13063311C411yescharacteristic, complemented
19C2×#13063308C411yescharacteristic, complemented
20C2×#13063307C411yescharacteristic, complemented
21C2×#13063302C2211yescharacteristic
22C2×#13063299C411yescharacteristic, complemented
23C2×#13063298C411yescharacteristic, complemented
24C2×#13063298C411yescharacteristic, complemented
25C2×#13063295C2211yescharacteristic
26C2×#13063294C2211yescharacteristic
27C2×C4×C22⋊D43C411yescharacteristic, complemented
28C2×(C22⋊D43)⋊C4—22no—
29C2×(C22⋊D43)⋊C4C2211yescharacteristic
30C22×C22⋊Dic43C2212yes—
31C2×C22⋊C4×D43C2211yescharacteristic
32C2×C22⋊C4×D43C2212yes—
33C2×#13063239C2212yes—
34C2×#13063239C2212yes—
35#14582799—22no—
36#14582776—22no—
37#14582775—22no—
38#14582757C2212yes—
39#14582754C2212yes—
40C22⋊C4×Dic43C2212yes—
41#14582666C2212yes—
42#14582666C2211yescharacteristic
43#14582666C2211yescharacteristic
44#14582665C2212yes—
45#14582665C2212yes—
46C22×C22⋊C4×C43C2211yescharacteristic
47C43×#379C2212yes—
48C43×#342C2212yes—
49C43×#342C2211yescharacteristic
50C43×#342C2211yescharacteristic
51C24×D43C2311yescharacteristic
52C2×#10621898—21no—
53C2×#10621898—21no—
54C2×#10621898—21no—
55C2×#10621898—21no—
56C2×#10621898—44no—
57C22×Dic86C2×C411yescharacteristic, complemented
58C22×D172C2×C411yescharacteristic, complemented
59C22×D172C2×C411yescharacteristic, complemented
60C22×C22⋊D43—44no—
61C22×C22⋊D43C2×C411yescharacteristic
62C22×C22⋊D43C2×C411yescharacteristic
63C22×C22⋊D43C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic, complemented
66C22×C22⋊D43C2×C411yescharacteristic, complemented
67C22×C22⋊D43D412yes—
68C22×C22⋊D43D412yes—
69C22×C22⋊D43D412yes—
70C22×C22⋊D43D412yes—
71C22×C22⋊D43C2311yescharacteristic
72C23×Dic43—22no—
73C23×Dic43C2311yescharacteristic
74C22×C4×D43—22no—
75C22×C4×D43C2×C411yescharacteristic, complemented
76C22×C4×D43C2×C411yescharacteristic, complemented
77C22×C4×D43C2×C411yescharacteristic, complemented
78#13063311—22no—
79#13063311—22no—
80#13063308—22no—
81#13063308—22no—
82#13063307—22no—
83#13063307—22no—
84#13063302—22no—
85#13063302—22no—
86#13063299—22no—
87#13063299—22no—
88#13063298—22no—
89#13063298—22no—
90#13063298—22no—
91#13063298—22no—
92#13063295—22no—
93#13063295—22no—
94#13063294—22no—
95#13063294—22no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—21no—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102(C22⋊D43)⋊C4—48no—
103C2×C4⋊Dic43C2×C411yescharacteristic, complemented
104C2×Dic43⋊C4—22no—
105C2×Dic43⋊C4C2×C411yescharacteristic, complemented
106C2×Dic43⋊C4C2×C411yescharacteristic, complemented
107C2×Dic43⋊C4C2×C411yescharacteristic, complemented
108C2×C22⋊Dic43—24no—
109C2×C22⋊Dic43—22no—
110C2×C22⋊Dic43—42no—
111C2×C22⋊Dic43C2×C411yescharacteristic, complemented
112C2×C22⋊Dic43C2×C411yescharacteristic, complemented
113C2×C22⋊Dic43C2312yes—
114C2×C22⋊Dic43C2311yescharacteristic
115C2×C22⋊Dic43C2312yes—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4—22no—
118C2×(C2×D43)⋊C4—22no—
119C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
120C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
121C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
122C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
123C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
124C22⋊C4×D43—22no—
125C22⋊C4×D43—22no—
126C22⋊C4×D43—24no—
127C22⋊C4×D43—42no—
128C2×C4×Dic43—22no—
129C2×C4×Dic43C2×C411yescharacteristic, complemented
130#13063239—24no—
131#13063239—42no—
132C43⋊#95—22no—
133C43⋊#95—22no—
134C25×C43C2311yescharacteristic
135C23×C4×C43C2×C411yescharacteristic, complemented
136C23×C4×C43C2×C411yescharacteristic, complemented
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—22no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—22no—
141C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
142C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
143C2×C22⋊C4×C43C2312yes—
144C2×C22⋊C4×C43C2312yes—
145C2×C22⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43C2311yescharacteristic
147C24×C43—22no—
148C24×C43—21no—
149C24×C43—21no—
150C24×C43—42no—
151C24×C43—81no—
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C24×C43C2×D412yes—
155C24×C43C2×D412yes—
156C24×C43C2411yescharacteristic
157C23×D43—22no—
158C23×D43—21no—
159C23×D43—21no—
160C23×D43—42no—
161C23×D43—81no—
162C23×D43C22×C411yescharacteristic
163C23×D43C22×C411yescharacteristic
164C23×D43C22×C411yescharacteristic
165C23×D43C2×D412yes—
166C23×D43C2×D412yes—
167C22×C4×C43—21no—
168C22×C4×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—42no—
174C22×C4×C43—81no—
175C22×C4×C43C22×C411yescharacteristic
176C22×C4×C43C22×C411yescharacteristic
177C22×C4×C43C22×C411yescharacteristic
178C22×C4×C43C22×C411yescharacteristic
179C2×C22⋊D43—28no—
180C2×C22⋊D43—24no—
181C2×C22⋊D43—21no—
182C2×C22⋊D43—21no—
183C2×C22⋊D43—22no—
184C2×C22⋊D43—22no—
185C2×C22⋊D43—22no—
186C2×C22⋊D43—21no—
187C2×C22⋊D43—21no—
188C2×C22⋊D43—42no—
189C2×C22⋊D43—44no—
190C2×C22⋊D43—42no—
191C2×C22⋊D43—44no—
192C2×C22⋊D43—42no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—44no—
195C2×C22⋊D43—81no—
196C2×C22⋊D43C22⋊C411yescharacteristic
197C2×C22⋊D43C22⋊C411yescharacteristic
198C2×C22⋊D43C22⋊C411yescharacteristic
199C2×C22⋊D43C22⋊C412yes—
200C2×C22⋊D43C22⋊C412yes—
201C2×C22⋊D43C22⋊C412yes—
202C2×C22⋊D43C22⋊C412yes—
203C2×C22⋊D43C22⋊C412yes—
204C2×C22⋊D43C22⋊C412yes—
205C2×C22⋊D43C22⋊C411yescharacteristic
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—44no—
209C22×Dic43—44no—
210C22×Dic43—42no—
211C22×Dic43—82no—
212C22×Dic43C22×C411yescharacteristic
213C22×Dic43C22×C411yescharacteristic
214C22×Dic43C22×C411yescharacteristic
215C22×Dic43C22×C411yescharacteristic
216C22×Dic43C22×C411yescharacteristic
217C22×Dic43C2×D412yes—
218C22×Dic43C2×D412yes—
219#10621898—44no—
220#10621898—44no—
221#10621898—44no—
222#10621898—44no—
223C2×D172—21no—
224C2×D172—21no—
225C2×D172—22no—
226C2×D172—42no—
227C2×D172—81no—
228C2×C4×D43—21no—
229C2×C4×D43—21no—
230C2×C4×D43—21no—
231C2×C4×D43—21no—
232C2×C4×D43—21no—
233C2×C4×D43—21no—
234C2×C4×D43—42no—
235C2×C4×D43—44no—
236C2×C4×D43—44no—
237C2×C4×D43—42no—
238C2×C4×D43—82no—
239C2×C4×D43—81no—
240C2×Dic86—21no—
241C2×Dic86—21no—
242C2×Dic86—42no—
243C22⋊C4×C43—22no—
244C22⋊C4×C43—22no—
245C22⋊C4×C43—22no—
246C22⋊C4×C43—22no—
247C22⋊C4×C43—22no—
248C22⋊C4×C43—22no—
249C22⋊C4×C43—22no—
250C22⋊C4×C43—22no—
251C22⋊C4×C43—44no—
252C22⋊C4×C43—82no—
253C22⋊Dic43—21no—
254C22⋊Dic43—21no—
255C22⋊Dic43—22no—
256C22⋊Dic43—22no—
257C22⋊Dic43—22no—
258C22⋊Dic43—22no—
259C22⋊Dic43—22no—
260C22⋊Dic43—44no—
261C22⋊Dic43#4114yescomplemented
262(C2×D43)⋊C4—22no—
263(C2×D43)⋊C4—22no—
264(C2×D43)⋊C4—22no—
265(C2×D43)⋊C4—21no—
266(C2×D43)⋊C4—21no—
267(C2×D43)⋊C4—22no—
268(C2×D43)⋊C4—44no—
269(C2×D43)⋊C4—44no—
270(C2×D43)⋊C4—82no—
271C4⋊Dic43—22no—
272Dic43⋊C4—22no—
273Dic43⋊C4—21no—
274Dic43⋊C4—21no—
275Dic43⋊C4—22no—
276Dic43⋊C4—44no—
277C4×Dic43—21no—
278C4×Dic43—21no—
279C4×Dic43—44no—
280C23×C43—21no—
281C23×C43—21no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—24no—
285C23×C43—22no—
286C23×C43—21no—
287C23×C43—21no—
288C23×C43—22no—
289C23×C43—22no—
290C23×C43—41no—
291C23×C43—42no—
292C23×C43—41no—
293C23×C43—41no—
294C23×C43—42no—
295C23×C43—41no—
296C23×C43—42no—
297C23×C43—41no—
298C23×C43—84no—
299C23×C43—82no—
300C23×C43—82no—
301C23×C43C2×C22⋊C412yes—
302C23×C43C2×C22⋊C411yescharacteristic
303C23×C43C2×C22⋊C411yescharacteristic
304C23×C43C23×C411yescharacteristic
305C23×C43C22×D412yes—
306C23×C43C2×#4112yes—
307C23×C43H(5,𝔽2)11yescharacteristic
308C23×C432−1+411yescharacteristic
309C22×D43—21no—
310C22×D43—21no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—21no—
314C22×D43—21no—
315C22×D43—22no—
316C22×D43—22no—
317C22×D43—24no—
318C22×D43—22no—
319C22×D43—21no—
320C22×D43—21no—
321C22×D43—21no—
322C22×D43—41no—
323C22×D43—42no—
324C22×D43—42no—
325C22×D43—41no—
326C22×D43—41no—
327C22×D43—42no—
328C22×D43—41no—
329C22×D43—41no—
330C22×D43—82no—
331C22×D43—84no—
332C22×D43—82no—
333C22×D43C2×C22⋊C412yes—
334C22×D43C2×C22⋊C411yescharacteristic
335C22×D43C2×C22⋊C411yescharacteristic
336C2×C4×C43—21no—
337C2×C4×C43—21no—
338C2×C4×C43—21no—
339C2×C4×C43—21no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43—41no—
343C2×C4×C43—41no—
344C2×C4×C43—41no—
345C2×C4×C43—41no—
346C2×C4×C43—42no—
347C2×C4×C43—42no—
348C2×C4×C43—42no—
349C2×C4×C43—42no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43—81no—
353C2×C4×C43—81no—
354C22⋊D43—22no—
355C22⋊D43—24no—
356C22⋊D43—22no—
357C22⋊D43—24no—
358C22⋊D43—22no—
359C22⋊D43—24no—
360C22⋊D43—42no—
361C22⋊D43—42no—
362C22⋊D43—42no—
363C22⋊D43—42no—
364C22⋊D43—42no—
365C22⋊D43—42no—
366C22⋊D43—42no—
367C22⋊D43—82no—
368C22⋊D43#9914yescomplemented
369C2×Dic43—24no—
370C2×Dic43—22no—
371C2×Dic43—21no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—24no—
377C2×Dic43—41no—
378C2×Dic43—42no—
379C2×Dic43—42no—
380C2×Dic43—42no—
381C2×Dic43—41no—
382C2×Dic43—41no—
383C2×Dic43—42no—
384C2×Dic43—42no—
385C2×Dic43—42no—
386C2×Dic43—88no—
387C2×Dic43C2×C22⋊C411yescharacteristic
388C2×Dic43C2×C22⋊C412yes—
389C2×Dic43C2×C22⋊C411yescharacteristic
390D172—42no—
391D172—42no—
392D172—82no—
393C4×D43—42no—
394C4×D43—42no—
395C4×D43—42no—
396C4×D43—42no—
397C4×D43—81no—
398C4×D43—81no—
399C4×D43—88no—
400Dic86—42no—
401Dic86—42no—
402#22476—431nomaximal, Sylow
403C22×C43—21no—
404C22×C43—21no—
405C22×C43—22no—
406C22×C43—21no—
407C22×C43—22no—
408C22×C43—21no—
409C22×C43—21no—
410C22×C43—22no—
411C22×C43—22no—
412C22×C43—21no—
413C22×C43—22no—
414C22×C43—21no—
415C22×C43—42no—
416C22×C43—41no—
417C22×C43—41no—
418C22×C43—44no—
419C22×C43—42no—
420C22×C43—42no—
421C22×C43—44no—
422C22×C43—82no—
423C22×C43—82no—
424C22×C43—81no—
425C22×C43—81no—
426C22×C43C2×#9912yes—
427C22×C43C22×C22⋊C411yescharacteristic
428C22×C43C4×#4111yescharacteristic
429C22×C43#52011yescharacteristic
430C22×C43#54612yes—
431C22×C43#54712yes—
432C2×D43—21no—
433C2×D43—21no—
434C2×D43—21no—
435C2×D43—22no—
436C2×D43—21no—
437C2×D43—22no—
438C2×D43—21no—
439C2×D43—22no—
440C2×D43—44no—
441C2×D43—42no—
442C2×D43—42no—
443C2×D43—44no—
444C2×D43—41no—
445C2×D43—41no—
446C2×D43—41no—
447C2×D43—82no—
448C2×D43—82no—
449C2×D43—81no—
450C2×D43—81no—
451C2×D43—81no—
452C2×D43—81no—
453C2×D43C2×#9912yes—
454C4×C43—41no—
455C4×C43—41no—
456C4×C43—41no—
457C4×C43—41no—
458C4×C43—82no—
459C4×C43—82no—
460Dic43—21no—
461Dic43—22no—
462Dic43—44no—
463Dic43—41no—
464Dic43—41no—
465Dic43—41no—
466Dic43—82no—
467Dic43C2×#9912yes—
468C2×#546—431no—
469D4×C22⋊C4—432no—
470#1996—432no—
471#1898—432no—
472#1898—432no—
473#1819—431no—
474#1819D4311yescharacteristic, complemented
475#1799—431no—
476C4×#99—431no—
477C2×#342—431no—
478C2×#342—431no—
479C2×C43—22no—
480C2×C43—22no—
481C2×C43—21no—
482C2×C43—21no—
483C2×C43—22no—
484C2×C43—42no—
485C2×C43—41no—
486C2×C43#233911yescharacteristic
487C2×C43C22×#9911yescharacteristic
488C2×C43#288311yescharacteristic
489D43—22no—
490D43—41no—
491D43—42no—
492D43—81no—
493C22×#41—431no—
494C23×D4—431no—
495#546—862no—
496#546—862no—
497#546—862no—
498#546—862no—
499C2×#124—431no—
500C2×#123—431no—
501C2×#123—431no—
502C2×C22⋊Q8—431no—
503C2×#121—431no—
504C2×#121—431no—
505C2×#121—431no—
506C2×#120—431no—
507C2×#120—431no—
508C2×C4×D4—431no—
509C2×C4×D4—431no—
510C2×C4×D4—862no—
511C22×C22⋊C4—431no—
512C22×C22⋊C4—432no—
513C22×C22⋊C4—432no—
514C22×C22⋊C4C2×D4311yescharacteristic
515C2×#99—432no—
516C2×#99—432no—
517#390—862no—
518#386—862no—
519#386—862no—
520#380—432no—
521#379—432no—
522#379C2×D4312yes—
523C4×C22⋊C4—432no—
524#342—431no—
525#342—432no—
526#342—432no—
527#342—432no—
528#342—431no—
529#342C2×D4311yescharacteristic
530#342C2×D4311yescharacteristic
531#342C2×D4312yes—
532C43#2247611yescharacteristic, complemented, Sylow
533C25—431no—
534C25C22×D4311yescharacteristic
535C2×#41—861no—
536C2×#41—861no—
537C2×#41—861no—
538C2×#41—861no—
539C2×#41—1724no—
540C22×Q8—431no—
541C22×D4—431no—
542C22×D4—432no—
543C22×D4—431no—
544C22×D4—431no—
545C22×D4—431no—
546C22×D4—432no—
547C22×D4—432no—
548C22×D4—432no—
549C22×D4—431no—
550C22×D4—431no—
551C22×D4—431no—
552C22×D4—431no—
553C22×D4—431no—
554C22×D4—1724no—
555C23×C4—431no—
556C23×C4—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—862no—
560C23×C4—862no—
561C23×C4C4×D4311yescharacteristic, complemented
562C23×C4C4×D4311yescharacteristic, complemented
563#124—862no—
564#124—862no—
565#123—862no—
566#123—862no—
567#123—862no—
568#123—862no—
569C22⋊Q8—862no—
570C22⋊Q8—862no—
571#121—862no—
572#121—862no—
573#121—862no—
574#121—862no—
575#121—862no—
576#121—862no—
577#120—862no—
578#120—862no—
579#120—862no—
580#120—862no—
581C4×D4—862no—
582C4×D4—862no—
583C4×D4—861no—
584C4×D4—861no—
585C4×D4—861no—
586C4×D4—861no—
587C4×D4—1728no—
588C2×C4⋊C4—431no—
589C2×C4⋊C4—431no—
590C2×C4⋊C4—431no—
591C2×C4⋊C4—431no—
592C2×C4⋊C4—862no—
593C2×C22⋊C4—22no—
594C2×C22⋊C4—22no—
595C2×C22⋊C4—22no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—432no—
598C2×C22⋊C4—431no—
599C2×C22⋊C4—431no—
600C2×C22⋊C4—431no—
601C2×C22⋊C4—431no—
602C2×C22⋊C4—431no—
603C2×C22⋊C4—431no—
604C2×C22⋊C4—431no—
605C2×C22⋊C4—431no—
606C2×C22⋊C4—432no—
607C2×C22⋊C4—864no—
608C2×C22⋊C4—862no—
609C2×C22⋊C4—862no—
610C2×C22⋊C4—864no—
611C2×C22⋊C4—862no—
612C2×C22⋊C4—862no—
613C2×C22⋊C4—862no—
614C2×C22⋊C4—862no—
615C2×C22⋊C4—1722no—
616C2×C22⋊C4—1722no—
617C2×C22⋊C4C4×D4311yescharacteristic, complemented
618C2×C22⋊C4C4×D4311yescharacteristic, complemented
619C2×C22⋊C4C22×D4312yes—
620C2×C22⋊C4C22×D4312yes—
621C2×C22⋊C4C22×D4311yescharacteristic
622C2×C22⋊C4C22×D4311yescharacteristic
623C2×C42—431no—
624C2×C42—862no—
625#99—864no—
626#99—1722no—
627#95—862no—
628#95—862no—
629C24—22no—
630C24—21no—
631C24—21no—
632C24—42no—
633C24—81no—
634C24—431no—
635C24—432no—
636C24—431no—
637C24—432no—
638C24—431no—
639C24—862no—
640C24—861no—
641C24—861no—
642C24—3441no—
643C24—1722no—
644C24C2×C4×D4311yescharacteristic
645C24C2×C4×D4311yescharacteristic
646C24D4×D4312yes—
647C24D4×D4312yes—
648C24C23×D4311yescharacteristic
649#41—1724no—
650#41—1724no—
651#41—1724no—
652#41—1724no—
653C2×Q8—861no—
654C2×Q8—861no—
655C2×Q8—1722no—
656C2×D4—431no—
657C2×D4—431no—
658C2×D4—431no—
659C2×D4—431no—
660C2×D4—432no—
661C2×D4—432no—
662C2×D4—432no—
663C2×D4—432no—
664C2×D4—432no—
665C2×D4—432no—
666C2×D4—862no—
667C2×D4—861no—
668C2×D4—861no—
669C2×D4—868no—
670C2×D4—864no—
671C2×D4—862no—
672C2×D4—861no—
673C2×D4—861no—
674C2×D4—862no—
675C2×D4—862no—
676C2×D4—861no—
677C2×D4—861no—
678C2×D4—3441no—
679C2×D4—3441no—
680C2×D4—1722no—
681C2×D4—1724no—
682C2×D4—1722no—
683C2×D4—1724no—
684C2×D4—1722no—
685C2×D4—1724no—
686C2×D4—1722no—
687C2×D4—1722no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—42no—
695C22×C4—81no—
696C22×C4—431no—
697C22×C4—432no—
698C22×C4—431no—
699C22×C4—432no—
700C22×C4—431no—
701C22×C4—431no—
702C22×C4—431no—
703C22×C4—861no—
704C22×C4—861no—
705C22×C4—861no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—862no—
710C22×C4—862no—
711C22×C4—3442no—
712C22×C4—3441no—
713C22×C4—3442no—
714C22×C4—1724no—
715C22×C4—1722no—
716C22×C4—1724no—
717C22×C4—1722no—
718C22×C4—1722no—
719C22×C4—1724no—
720C22×C4—1724no—
721C22×C4C2×C4×D4311yescharacteristic
722C22×C4C2×C4×D4311yescharacteristic
723C22×C4C2×C4×D4311yescharacteristic
724C22×C4C2×C4×D4311yescharacteristic
725C4⋊C4—861no—
726C4⋊C4—861no—
727C4⋊C4—862no—
728C4⋊C4—862no—
729C4⋊C4—862no—
730C4⋊C4—1724no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—44no—
740C22⋊C4—82no—
741C22⋊C4—434no—
742C22⋊C4—862no—
743C22⋊C4—862no—
744C22⋊C4—862no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—862no—
748C22⋊C4—861no—
749C22⋊C4—861no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C22⋊C4—862no—
753C22⋊C4—862no—
754C22⋊C4—862no—
755C22⋊C4—3442no—
756C22⋊C4—1724no—
757C22⋊C4—1724no—
758C22⋊C4—1724no—
759C42—861no—
760C42—861no—
761C42—1724no—
762C23—21no—
763C23—21no—
764C23—24no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—41no—
773C23—42no—
774C23—41no—
775C23—41no—
776C23—42no—
777C23—41no—
778C23—41no—
779C23—42no—
780C23—84no—
781C23—82no—
782C23—82no—
783C23—431no—
784C23—432no—
785C23—431no—
786C23—864no—
787C23—862no—
788C23—861no—
789C23—861no—
790C23—862no—
791C23—862no—
792C23—861no—
793C23—861no—
794C23—862no—
795C23—862no—
796C23—861no—
797C23—861no—
798C23—861no—
799C23—3444no—
800C23—3442no—
801C23—3442no—
802C23—1722no—
803C23—1721no—
804C23—1722no—
805C23—1721no—
806C23—1722no—
807C23—1721no—
808C23—1721no—
809C23—1721no—
810C23C22⋊C4×D4312yes—
811C23C22⋊C4×D4311yescharacteristic
812C23C22⋊C4×D4311yescharacteristic
813C23C22×C4×D4311yescharacteristic
814C23C2×D4×D4312yes—
815C23#41×D4312yes—
816C23#1306337111yescharacteristic
817C23#1306337211yescharacteristic
818Q8—1722no—
819Q8—1722no—
820D4—434no—
821D4—862no—
822D4—864no—
823D4—862no—
824D4—864no—
825D4—862no—
826D4—864no—
827D4—3442no—
828D4—3442no—
829D4—1722no—
830D4—1722no—
831D4—1722no—
832D4—1722no—
833D4—1722no—
834D4—1722no—
835D4—1722no—
836D4—1722no—
837D4—1722no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—431no—
857C2×C4—431no—
858C2×C4—432no—
859C2×C4—864no—
860C2×C4—862no—
861C2×C4—861no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—864no—
867C2×C4—3441no—
868C2×C4—3441no—
869C2×C4—3448no—
870C2×C4—3448no—
871C2×C4—1722no—
872C2×C4—1722no—
873C2×C4—1722no—
874C2×C4—1722no—
875C2×C4—1722no—
876C2×C4—1721no—
877C2×C4—1722no—
878C2×C4—1722no—
879C2×C4—1722no—
880C2×C4—1722no—
881C2×C4—1722no—
882C2×C4—1721no—
883C2×C4—1721no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—22no—
892C22—21no—
893C22—22no—
894C22—21no—
895C22—22no—
896C22—42no—
897C22—41no—
898C22—41no—
899C22—44no—
900C22—44no—
901C22—42no—
902C22—42no—
903C22—82no—
904C22—82no—
905C22—81no—
906C22—81no—
907C22—432no—
908C22—861no—
909C22—861no—
910C22—861no—
911C22—862no—
912C22—862no—
913C22—861no—
914C22—861no—
915C22—862no—
916C22—3441no—
917C22—3441no—
918C22—3442no—
919C22—3442no—
920C22—3441no—
921C22—3441no—
922C22—1724no—
923C22—1724no—
924C22—1722no—
925C22—1722no—
926C22—1721no—
927C22—1721no—
928C22—1721no—
929C22#99×D4312yes—
930C22C2×C22⋊C4×D4311yescharacteristic
931C22#1458336711yescharacteristic
932C22#1458337911yescharacteristic
933C22#1458354112yes—
934C22#1458354712yes—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—82no—
940C4—82no—
941C4—432no—
942C4—861no—
943C4—862no—
944C4—3442no—
945C4—1724no—
946C4—1721no—
947C4—1721no—
948C4—1721no—
949C2—22no—
950C2—22no—
951C2—22no—
952C2—21no—
953C2—21no—
954C2—41no—
955C2—42no—
956C2—862no—
957C2—3441no—
958C2—1721no—
959C2—1722no—
960C2#1913741911yescharacteristic
961C2C2×#99×D4311yescharacteristic
962C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC43×#1819C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583539C2
cosocleC24×C43C24
hypercenter#1819D43
hypocenterC43#22476
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ #1819

Complements

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

NH ≅ G/Ntype
2. #19137411C2semidirect
3. #19135578C2semidirect
4. #19135047C2semidirect
5. #19135046C2semidirect
6. #19134668C2semidirect
7. #19134582C2semidirect
8. #19134382C2semidirect
9. C2×#14582666C2semidirect
10. #342×D43C2semidirect
11. C43×#1819C2semidirect
12. C22×#10621898C4semidirect
18. C2×#13063311C4semidirect
19. C2×#13063308C4semidirect
20. C2×#13063307C4semidirect
22. C2×#13063299C4semidirect
23. C2×#13063298C4semidirect
24. C2×#13063298C4semidirect
27. C2×C4×C22⋊D43C4semidirect
57. C22×Dic86C2×C4semidirect
58. C22×D172C2×C4semidirect
59. C22×D172C2×C4semidirect
65. C22×C22⋊D43C2×C4semidirect
66. C22×C22⋊D43C2×C4semidirect
75. C22×C4×D43C2×C4semidirect
76. C22×C4×D43C2×C4semidirect
77. C22×C4×D43C2×C4semidirect
103. C2×C4⋊Dic43C2×C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
106. C2×Dic43⋊C4C2×C4semidirect
107. C2×Dic43⋊C4C2×C4semidirect
111. C2×C22⋊Dic43C2×C4semidirect
112. C2×C22⋊Dic43C2×C4semidirect
119. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×(C2×D43)⋊C4C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
122. C2×(C2×D43)⋊C4C2×C4semidirect
123. C2×(C2×D43)⋊C4C2×C4semidirect
129. C2×C4×Dic43C2×C4semidirect
135. C23×C4×C43C2×C4semidirect
136. C23×C4×C43C2×C4semidirect
141. C2×C22⋊C4×C43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
261. C22⋊Dic43#41semidirect
368. C22⋊D43#99semidirect
474. #1819D43semidirect
532. C43#22476semidirect
561. C23×C4C4×D43semidirect
562. C23×C4C4×D43semidirect
617. C2×C22⋊C4C4×D43semidirect
618. C2×C22⋊C4C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145835392
#191374112
#191355782
#191350472
#191350462
#191346682
#191345822
#191343822
C2×#145826662
#342×D432
C43×#18192
#2247643