Finite Group Databasebeta

← #25112726

Subgroups — #25112726

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
2C22⋊C4×C22⋊D43C212yesmaximal, complemented
3#19135578C212yesmaximal, complemented
4#19135048C212yesmaximal, complemented
5#19135047C212yesmaximal, complemented
6#19134669C211yesmaximal, characteristic, complemented
7#19134668C211yesmaximal, characteristic, complemented
8#19134582C211yesmaximal, characteristic, complemented
9#19134382C211yesmaximal, characteristic, complemented
10#342×D43C211yesmaximal, characteristic, complemented
11C2×C43×#342C211yesmaximal, 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⋊D43—22no—
28C2×C4×C22⋊D43C411yescharacteristic, complemented
29C2×(C22⋊D43)⋊C4C2211yescharacteristic
30C2×C22⋊C4×D43C2211yescharacteristic
31C2×C22⋊C4×D43C2212yes—
32C2×#13063239C2212yes—
33C2×#13063239C2212yes—
34#14582799—22no—
35#14582778—22no—
36#14582775—22no—
37#14582757C2212yes—
38#14582755C2212yes—
39#14582754C2212yes—
40C22⋊C4×Dic43C2212yes—
41#14582666C2212yes—
42#14582666C2211yescharacteristic
43#14582666C2211yescharacteristic
44#14582665C2212yes—
45#14582665C2212yes—
46C22×C22⋊C4×C43C2211yescharacteristic
47C22×C22⋊C4×C43C2212yes—
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×Dic43C2311yescharacteristic
73C22×C4×D43—22no—
74C22×C4×D43C2×C411yescharacteristic, complemented
75C22×C4×D43C2×C411yescharacteristic, complemented
76C22×C4×D43C2×C411yescharacteristic, complemented
77#13063311—22no—
78#13063311—22no—
79#13063308—22no—
80#13063308—22no—
81#13063307—22no—
82#13063307—22no—
83#13063302—22no—
84#13063302—22no—
85#13063299—22no—
86#13063299—22no—
87#13063298—22no—
88#13063298—22no—
89#13063298—22no—
90#13063298—22no—
91#13063295—22no—
92#13063295—22no—
93#13063294—22no—
94#13063294—22no—
95C4×C22⋊D43—21no—
96C4×C22⋊D43—21no—
97C4×C22⋊D43—21no—
98C4×C22⋊D43—21no—
99C4×C22⋊D43—48no—
100(C22⋊D43)⋊C4—22no—
101(C22⋊D43)⋊C4—22no—
102C2×C4⋊Dic43C2×C411yescharacteristic, complemented
103C2×Dic43⋊C4—22no—
104C2×Dic43⋊C4C2×C411yescharacteristic, complemented
105C2×Dic43⋊C4C2×C411yescharacteristic, complemented
106C2×Dic43⋊C4C2×C411yescharacteristic, complemented
107C2×C22⋊Dic43—22no—
108C2×C22⋊Dic43—22no—
109C2×C22⋊Dic43C2×C411yescharacteristic, complemented
110C2×C22⋊Dic43C2×C411yescharacteristic, complemented
111C2×C22⋊Dic43C2312yes—
112C2×C22⋊Dic43C2312yes—
113C2×C22⋊Dic43C2311yescharacteristic
114C2×(C2×D43)⋊C4—22no—
115C2×(C2×D43)⋊C4—22no—
116C2×(C2×D43)⋊C4—22no—
117C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
118C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
119C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
120C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
121C2×(C2×D43)⋊C4C2×C411yescharacteristic, complemented
122C22⋊C4×D43—22no—
123C22⋊C4×D43—22no—
124C22⋊C4×D43—24no—
125C22⋊C4×D43—42no—
126C2×C4×Dic43—22no—
127C2×C4×Dic43C2×C411yescharacteristic, complemented
128#13063239—24no—
129#13063239—42no—
130C43⋊#95—22no—
131C43⋊#95—22no—
132C25×C43C2311yescharacteristic
133C23×C4×C43—22no—
134C23×C4×C43C2×C411yescharacteristic, complemented
135C23×C4×C43C2×C411yescharacteristic, complemented
136C2×C22⋊C4×C43—22no—
137C2×C22⋊C4×C43—22no—
138C2×C22⋊C4×C43—24no—
139C2×C22⋊C4×C43—22no—
140C2×C22⋊C4×C43—42no—
141C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
142C2×C22⋊C4×C43C2×C411yescharacteristic, complemented
143C2×C22⋊C4×C43C2312yes—
144C2×C22⋊C4×C43C2311yescharacteristic
145C2×C22⋊C4×C43C2311yescharacteristic
146C2×C22⋊C4×C43C2312yes—
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—44no—
174C22×C4×C43—42no—
175C22×C4×C43—44no—
176C22×C4×C43—81no—
177C22×C4×C43—82no—
178C22×C4×C43C22×C411yescharacteristic
179C22×C4×C43C22×C411yescharacteristic
180C22×C4×C43C22×C411yescharacteristic
181C22×C4×C43C22×C411yescharacteristic
182C2×C22⋊D43—28no—
183C2×C22⋊D43—24no—
184C2×C22⋊D43—21no—
185C2×C22⋊D43—21no—
186C2×C22⋊D43—22no—
187C2×C22⋊D43—22no—
188C2×C22⋊D43—22no—
189C2×C22⋊D43—21no—
190C2×C22⋊D43—21no—
191C2×C22⋊D43—42no—
192C2×C22⋊D43—44no—
193C2×C22⋊D43—42no—
194C2×C22⋊D43—44no—
195C2×C22⋊D43—42no—
196C2×C22⋊D43—42no—
197C2×C22⋊D43—44no—
198C2×C22⋊D43—81no—
199C2×C22⋊D43C22⋊C411yescharacteristic
200C2×C22⋊D43C22⋊C411yescharacteristic
201C2×C22⋊D43C22⋊C411yescharacteristic
202C2×C22⋊D43C22⋊C412yes—
203C2×C22⋊D43C22⋊C412yes—
204C2×C22⋊D43C22⋊C412yes—
205C2×C22⋊D43C22⋊C412yes—
206C2×C22⋊D43C22⋊C412yes—
207C2×C22⋊D43C22⋊C412yes—
208C2×C22⋊D43C22⋊C411yescharacteristic
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—42no—
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—44no—
251C22⋊C4×C43#4114yescomplemented
252C22⋊Dic43—21no—
253C22⋊Dic43—21no—
254C22⋊Dic43—22no—
255C22⋊Dic43—22no—
256C22⋊Dic43—22no—
257C22⋊Dic43—22no—
258C22⋊Dic43—22no—
259C22⋊Dic43—22no—
260C22⋊Dic43—44no—
261C22⋊Dic43—82no—
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—41no—
292C23×C43—42no—
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—24no—
341C2×C4×C43—42no—
342C2×C4×C43—42no—
343C2×C4×C43—42no—
344C2×C4×C43—42no—
345C2×C4×C43—41no—
346C2×C4×C43—41no—
347C2×C4×C43—41no—
348C2×C4×C43—41no—
349C2×C4×C43—42no—
350C2×C4×C43—42no—
351C2×C4×C43—42no—
352C2×C4×C43—81no—
353C2×C4×C43—81no—
354C2×C4×C43—88no—
355C22⋊D43—22no—
356C22⋊D43—24no—
357C22⋊D43—22no—
358C22⋊D43—24no—
359C22⋊D43—22no—
360C22⋊D43—24no—
361C22⋊D43—42no—
362C22⋊D43—42no—
363C22⋊D43—42no—
364C22⋊D43—42no—
365C22⋊D43—42no—
366C22⋊D43—42no—
367C22⋊D43—42no—
368C22⋊D43—82no—
369C22⋊D43#9914yescomplemented
370C2×Dic43—24no—
371C2×Dic43—22no—
372C2×Dic43—21no—
373C2×Dic43—21no—
374C2×Dic43—21no—
375C2×Dic43—21no—
376C2×Dic43—21no—
377C2×Dic43—41no—
378C2×Dic43—42no—
379C2×Dic43—41no—
380C2×Dic43—41no—
381C2×Dic43—42no—
382C2×Dic43—42no—
383C2×Dic43—42no—
384C2×Dic43—42no—
385C2×Dic43—42no—
386C2×Dic43—42no—
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—44no—
455C4×C43—41no—
456C4×C43—41no—
457C4×C43—41no—
458C4×C43—41no—
459C4×C43—82no—
460Dic43—21no—
461Dic43—22no—
462Dic43—41no—
463Dic43—41no—
464Dic43—41no—
465Dic43—82no—
466Dic43—82no—
467Dic43C2×#9912yes—
468C2×#546—431no—
469D4×C22⋊C4—432no—
470#1996—432no—
471#1898—432no—
472#1898—432no—
473#1819—431no—
474#1819—431no—
475#1799—431no—
476C4×#99—431no—
477C2×#342—431no—
478C2×#342D4311yescharacteristic, complemented
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⋊C4C2×D4311yescharacteristic
514C22×C22⋊C4C2×D4312yes—
515C2×#99—432no—
516C2×#99—432no—
517#390—862no—
518#386—862no—
519#386—862no—
520#380—432no—
521#379—432no—
522#379—432no—
523C4×C22⋊C4—432no—
524#342—431no—
525#342—431no—
526#342—432no—
527#342—432no—
528#342—432no—
529#342C2×D4311yescharacteristic
530#342C2×D4312yes—
531#342C2×D4311yescharacteristic
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—22no—
556C23×C4—431no—
557C23×C4—431no—
558C23×C4—431no—
559C23×C4—431no—
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—24no—
596C2×C22⋊C4—22no—
597C2×C22⋊C4—42no—
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—432no—
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—862no—
616C2×C22⋊C4—1722no—
617C2×C22⋊C4C4×D4311yescharacteristic, complemented
618C2×C22⋊C4C4×D4311yescharacteristic, complemented
619C2×C22⋊C4C22×D4312yes—
620C2×C22⋊C4C22×D4311yescharacteristic
621C2×C22⋊C4C22×D4311yescharacteristic
622C2×C22⋊C4C22×D4312yes—
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—22no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—44no—
695C22×C4—42no—
696C22×C4—44no—
697C22×C4—82no—
698C22×C4—81no—
699C22×C4—431no—
700C22×C4—432no—
701C22×C4—431no—
702C22×C4—432no—
703C22×C4—431no—
704C22×C4—431no—
705C22×C4—431no—
706C22×C4—861no—
707C22×C4—861no—
708C22×C4—861no—
709C22×C4—861no—
710C22×C4—861no—
711C22×C4—861no—
712C22×C4—862no—
713C22×C4—862no—
714C22×C4—3442no—
715C22×C4—3441no—
716C22×C4—1724no—
717C22×C4—1722no—
718C22×C4—1724no—
719C22×C4—1722no—
720C22×C4—1722no—
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—44no—
739C22⋊C4—862no—
740C22⋊C4—862no—
741C22⋊C4—862no—
742C22⋊C4—861no—
743C22⋊C4—861no—
744C22⋊C4—862no—
745C22⋊C4—861no—
746C22⋊C4—861no—
747C22⋊C4—862no—
748C22⋊C4—862no—
749C22⋊C4—862no—
750C22⋊C4—862no—
751C22⋊C4—862no—
752C22⋊C4—862no—
753C22⋊C4—3442no—
754C22⋊C4—3442no—
755C22⋊C4—1724no—
756C22⋊C4—1724no—
757C22⋊C4—1724no—
758C22⋊C4#1062189814yescomplemented
759C42—861no—
760C42—861no—
761C42—1724no—
762C23—21no—
763C23—24no—
764C23—22no—
765C23—21no—
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—
815C23C2×#1062189812yes—
816C23#1306337011yescharacteristic
817C23#1306337311yescharacteristic
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—24no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—81no—
855C2×C4—81no—
856C2×C4—88no—
857C2×C4—431no—
858C2×C4—431no—
859C2×C4—432no—
860C2×C4—864no—
861C2×C4—862no—
862C2×C4—861no—
863C2×C4—861no—
864C2×C4—861no—
865C2×C4—861no—
866C2×C4—861no—
867C2×C4—3448no—
868C2×C4—3441no—
869C2×C4—3441no—
870C2×C4—1722no—
871C2×C4—1722no—
872C2×C4—1722no—
873C2×C4—1722no—
874C2×C4—1722no—
875C2×C4—1721no—
876C2×C4—1722no—
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—22no—
887C22—21no—
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—861no—
913C22—862no—
914C22—862no—
915C22—861no—
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
931C22C4×#1062189811yescharacteristic
932C22#1458338011yescharacteristic
933C22#1458353912yes—
934C22#1458355012yes—
935C4—44no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—82no—
941C4—432no—
942C4—861no—
943C4—862no—
944C4—3442no—
945C4—3442no—
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#1913742211yescharacteristic
961C2C2×#99×D4311yescharacteristic
962C2#1914305311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC22×C43C22×C22⋊C4
prime radicalC2×#14583539C2
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43#22476
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C22⋊D43C2semidirect
3. #19135578C2semidirect
4. #19135048C2semidirect
5. #19135047C2semidirect
6. #19134669C2semidirect
7. #19134668C2semidirect
8. #19134582C2semidirect
9. #19134382C2semidirect
10. #342×D43C2semidirect
11. C2×C43×#342C2semidirect
12. C22×#10621898C4semidirect
18. C2×#13063311C4semidirect
19. C2×#13063308C4semidirect
20. C2×#13063307C4semidirect
22. C2×#13063299C4semidirect
23. C2×#13063298C4semidirect
24. C2×#13063298C4semidirect
28. 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
74. C22×C4×D43C2×C4semidirect
75. C22×C4×D43C2×C4semidirect
76. C22×C4×D43C2×C4semidirect
102. C2×C4⋊Dic43C2×C4semidirect
104. C2×Dic43⋊C4C2×C4semidirect
105. C2×Dic43⋊C4C2×C4semidirect
106. C2×Dic43⋊C4C2×C4semidirect
109. C2×C22⋊Dic43C2×C4semidirect
110. C2×C22⋊Dic43C2×C4semidirect
117. C2×(C2×D43)⋊C4C2×C4semidirect
118. C2×(C2×D43)⋊C4C2×C4semidirect
119. C2×(C2×D43)⋊C4C2×C4semidirect
120. C2×(C2×D43)⋊C4C2×C4semidirect
121. C2×(C2×D43)⋊C4C2×C4semidirect
127. C2×C4×Dic43C2×C4semidirect
134. C23×C4×C43C2×C4semidirect
135. C23×C4×C43C2×C4semidirect
141. C2×C22⋊C4×C43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
251. C22⋊C4×C43#41semidirect
369. C22⋊D43#99semidirect
478. C2×#342D43semidirect
532. C43#22476semidirect
561. C23×C4C4×D43semidirect
562. C23×C4C4×D43semidirect
617. C2×C22⋊C4C4×D43semidirect
618. C2×C22⋊C4C4×D43semidirect
758. C22⋊C4#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145835392
C22⋊C4×C22⋊D432
#191355782
#191350482
#191350472
#191346692
#191346682
#191345822
#191343822
#342×D432
C2×C43×#3422
#2247643