Finite Group Databasebeta

← #25062507

Subgroups — #25062507

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583379C211yesmaximal, characteristic
2#19143623C212yesmaximal, complemented
3#19132938C212yesmaximal, complemented
4#19132930C212yesmaximal, complemented
5#19132929C211yesmaximal, characteristic, complemented
6#19132923C212yesmaximal, complemented
7#19132910C212yesmaximal, complemented
8#324×D43C212yesmaximal, complemented
9C43×#1464C211yesmaximal, characteristic, complemented
10C22×#10621898C411yescharacteristic
11#14583379—24no—
12#14583379—24no—
13C2×C4×Dic86C411yescharacteristic
14C2×C4×Dic86C2211yescharacteristic
15C2×C4×D172C411yescharacteristic
16C2×C4×D172C2211yescharacteristic
17C2×(C22⋊D43)⋊C4C411yescharacteristic
18C2×(C22⋊D43)⋊C4C411yescharacteristic
19C2×(C22⋊D43)⋊C4C2211yescharacteristic
20C2×(C22⋊D43)⋊C4C2211yescharacteristic
21C2×#13063283C411yescharacteristic
22C2×#13063283C411yescharacteristic
23C22×C4⋊Dic43C411yescharacteristic
24C2×C4⋊C4×D43C2211yescharacteristic
25C2×C4⋊C4×D43C2211yescharacteristic
26#14582972—24no—
27#14582969—24no—
28#14582956C2212yes—
29#14582861C2214yes—
30C22⋊C8×D43C2214yes—
31#14582625C2212yes—
32#14582624C2214yes—
33#14582624C2214yes—
34#14582623C2212yes—
35C2×#117×C43C2211yescharacteristic
36C43×#432C2212yes—
37C43×#324C2212yes—
38C43×#323C2212yes—
39C2×#10621898—24no—
40C2×#10621898—22no—
41C2×#10621898—22no—
42C2×#10621898—24no—
43C22×Dic86C2×C411yescharacteristic
44C22×D172C2×C411yescharacteristic
45C22×C22⋊D43C2×C411yescharacteristic
46C22×C22⋊D43C2×C411yescharacteristic
47C23×Dic43C2×C411yescharacteristic
48C23×Dic43C2×C411yescharacteristic
49C22×C4×D43C2×C411yescharacteristic
50C22×C4×D43C2×C411yescharacteristic
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2×C411yescharacteristic
53C22×C4×D43C2311yescharacteristic
54C22×C4×D43C2311yescharacteristic
55C2×#10621872—24no—
56C2×C8×D43—24no—
57C4×Dic86—22no—
58C4×Dic86—22no—
59C4×Dic86—22no—
60C4×Dic86—22no—
61C4×D172—22no—
62C4×D172—22no—
63C4×D172D414yes—
64C4×D172D414yes—
65(C22⋊D43)⋊C4—24no—
66(C22⋊D43)⋊C4—24no—
67(C22⋊D43)⋊C4—24no—
68(C22⋊D43)⋊C4—24no—
69#13063283—24no—
70#13063283—24no—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43—22no—
73C2×C4⋊Dic43C2×C411yescharacteristic
74C2×C4⋊Dic43C2×C411yescharacteristic
75C2×C4⋊Dic43C2×C411yescharacteristic
76C2×C4⋊Dic43C2×C411yescharacteristic
77C2×Dic43⋊C4C2×C411yescharacteristic
78C2×Dic43⋊C4C2×C411yescharacteristic
79C2×Dic43⋊C4C2311yescharacteristic
80C2×Dic43⋊C4C2311yescharacteristic
81C4⋊C4×D43—24no—
82C4⋊C4×D43—24no—
83C2×(C2×D43)⋊C4C2×C411yescharacteristic
84C2×(C2×D43)⋊C4C2×C411yescharacteristic
85C2×(C2×D43)⋊C4C2×C411yescharacteristic
86C2×(C2×D43)⋊C4C2×C411yescharacteristic
87C2×C4×Dic43C2×C411yescharacteristic
88C2×C4×Dic43C2×C411yescharacteristic
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2×C411yescharacteristic
91C4⋊(C43⋊C8)—22no—
92C22⋊(C43⋊C8)C2314yes—
93(C2×D43)⋊C8—24no—
94(C2×D43)⋊C8—24no—
95#13063236—22no—
96C23×C4×C43C2×C411yescharacteristic
97#117×C43—22no—
98#117×C43—22no—
99C2×C4⋊C4×C43C2×C411yescharacteristic
100C2×C4⋊C4×C43C2311yescharacteristic
101C2×C22⋊C4×C43C2×C411yescharacteristic
102C2×C22⋊C4×C43C2311yescharacteristic
103C2×C42×C43C2×C411yescharacteristic
104C2×C42×C43C2311yescharacteristic
105C4⋊C8×C43—22no—
106C22⋊C8×C43C2314yes—
107#97×C43—22no—
108C24×C43C22×C411yescharacteristic
109C23×D43C22×C411yescharacteristic
110C23×D43C22×C411yescharacteristic
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—22no—
114C22×C4×C43—22no—
115C22×C4×C43C22×C411yescharacteristic
116C22×C4×C43C22×C411yescharacteristic
117C22×C4×C43C22×C411yescharacteristic
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C2411yescharacteristic
121C2×C22⋊D43—22no—
122C2×C22⋊D43—22no—
123C2×C22⋊D43—22no—
124C2×C22⋊D43—22no—
125C2×C22⋊D43—22no—
126C2×C22⋊D43M1614yescomplemented
127C22×Dic43—22no—
128C22×Dic43—22no—
129C22×Dic43—81no—
130C22×Dic43—81no—
131C22×Dic43C22×C411yescharacteristic
132C22×Dic43C22×C411yescharacteristic
133C22×Dic43C22×C411yescharacteristic
134C22×Dic43C22×C411yescharacteristic
135C22×Dic43C22×C411yescharacteristic
136C22×Dic43C22×C411yescharacteristic
137#10621898—216no—
138#10621898—216no—
139C2×D172—22no—
140C2×D172—22no—
141C2×D172C22⋊C412yes—
142C2×D172C22⋊C412yes—
143C2×C4×D43—22no—
144C2×C4×D43—22no—
145C2×C4×D43—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—81no—
151C2×C4×D43—81no—
152C2×C4×D43—81no—
153C2×C4×D43—81no—
154C2×C4×D43M1614yescomplemented
155C2×C4×D43C2×D414yes—
156C2×C4×D43C2×D414yes—
157C2×Dic86—21no—
158C2×Dic86—21no—
159C2×Dic86—22no—
160C2×Dic86—22no—
161C2×C8×C43—24no—
162C4⋊C4×C43—22no—
163C4⋊C4×C43—22no—
164C22⋊C4×C43—22no—
165C22⋊C4×C43—22no—
166C42×C43—21no—
167C42×C43—21no—
168C42×C43C2×D412yes—
169C42×C43C2×D412yes—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—22no—
172(C2×D43)⋊C4C22⋊C414yes—
173(C2×D43)⋊C4C22⋊C414yes—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—22no—
177C4⋊Dic43—22no—
178C4⋊Dic43C22⋊C412yes—
179C4⋊Dic43C22⋊C412yes—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184C4×Dic43—22no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C2×C43⋊C8—24no—
189#10621872—84no—
190C8×D43—84no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43C2×M1612yes—
196C23×C43C23×C411yescharacteristic
197C22×D43—21no—
198C22×D43—21no—
199C22×D43—41no—
200C22×D43—41no—
201C22×D43—41no—
202C22×D43—41no—
203C22×D43C2×C22⋊C412yes—
204C22×D43C2×C22⋊C412yes—
205C22×D43C2×M1612yes—
206C22×D43C2×M1612yes—
207C2×C4×C43—24no—
208C2×C4×C43—24no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—41no—
219C2×C4×C43C2×C22⋊C412yes—
220C2×C4×C43C2×C22⋊C411yescharacteristic
221C2×C4×C43C2×C22⋊C411yescharacteristic
222C2×C4×C43C2×M1612yes—
223C2×C4×C43C22×D412yes—
224C22⋊D43—28no—
225C22⋊D43—28no—
226C2×Dic43—21no—
227C2×Dic43—21no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—41no—
233C2×Dic43—41no—
234C2×Dic43—41no—
235C2×Dic43—41no—
236C2×Dic43—82no—
237C2×Dic43—82no—
238C2×Dic43C2×C22⋊C412yes—
239C2×Dic43C2×C22⋊C412yes—
240C2×Dic43C2×M1612yes—
241C2×Dic43C2×M1612yes—
242D172—24no—
243D172—24no—
244C4×D43—28no—
245C4×D43—28no—
246C4×D43—44no—
247C4×D43—44no—
248C4×D43—82no—
249C4×D43—82no—
250Dic86—24no—
251Dic86—24no—
252C8×C43—44no—
253C43⋊C8—44no—
254#17368—431nomaximal, Sylow
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—22no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—41no—
261C22×C43—41no—
262C22×C43C22×C22⋊C411yescharacteristic
263C22×C43C22×M1611yescharacteristic
264C22×C43C22×M1611yescharacteristic
265C2×D43—22no—
266C2×D43—22no—
267C2×D43—22no—
268C2×D43—22no—
269C2×D43—22no—
270C2×D43—42no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43—42no—
274C2×D43#40714yes—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—22no—
278C4×C43—22no—
279C4×C43—22no—
280C4×C43—41no—
281C4×C43—41no—
282Dic43—22no—
283Dic43—22no—
284Dic43—22no—
285Dic43—22no—
286Dic43—41no—
287Dic43—41no—
288C2×#520—431no—
289#2973—432no—
290#1467—432no—
291#1465—432no—
292#1464—431no—
293#1464D4311yescharacteristic, complemented
294#1463—432no—
295#1459—432no—
296C2×#324—432no—
297C2×C43—21no—
298C2×C43—21no—
299C2×C43—42no—
300C2×C43C2×#40711yescharacteristic
301C2×C43#288311yescharacteristic
302C2×C43#288911yescharacteristic
303D43—24no—
304D43—42no—
305C22×#41—431no—
306#520—864no—
307#520—864no—
308C2×C4×Q8—431no—
309C2×C4×Q8—431no—
310C2×C4×D4—431no—
311C2×C4×D4—431no—
312C2×C4×D4—431no—
313C2×C4×D4—431no—
314C2×C4×D4—431no—
315C2×C4×D4—431no—
316C2×#117—431no—
317C2×#117—431no—
318C2×#117C2×D4311yescharacteristic
319C22×C4⋊C4—431no—
320C22×C4⋊C4—431no—
321C22×C4⋊C4—431no—
322#435—864no—
323#435—864no—
324#432—432no—
325#432C2×D4312yes—
326#407—434no—
327C2×C22⋊C8—434no—
328#324—432no—
329#324—434no—
330#324—434no—
331#324C2×D4312yes—
332#323—432no—
333#323C2×D4312yes—
334C43#1736811yescharacteristic, complemented, Sylow
335C2×#41—864no—
336C2×#41—862no—
337C2×#41—862no—
338C2×#41—864no—
339C22×Q8—431no—
340C22×D4—431no—
341C22×D4—431no—
342C22×D4—431no—
343C23×C4—431no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—431no—
348C23×C4—431no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4C4×D4311yescharacteristic
352C2×M16—864no—
353C22×C8—864no—
354C4×Q8—862no—
355C4×Q8—862no—
356C4×Q8—862no—
357C4×Q8—862no—
358C4×D4—434no—
359C4×D4—434no—
360C4×D4—862no—
361C4×D4—862no—
362C4×D4—864no—
363C4×D4—864no—
364C4×D4—864no—
365C4×D4—864no—
366#117—22no—
367#117—22no—
368#117—864no—
369#117—864no—
370C2×C4⋊C4—431no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—864no—
379C2×C4⋊C4—864no—
380C2×C4⋊C4—862no—
381C2×C4⋊C4—862no—
382C2×C4⋊C4C4×D4311yescharacteristic
383C2×C4⋊C4C22×D4311yescharacteristic
384C2×C22⋊C4—431no—
385C2×C22⋊C4—431no—
386C2×C22⋊C4—431no—
387C2×C22⋊C4—431no—
388C2×C22⋊C4C4×D4311yescharacteristic
389C2×C22⋊C4C22×D4311yescharacteristic
390C2×C42—431no—
391C2×C42—431no—
392C2×C42—431no—
393C2×C42—431no—
394C2×C42C4×D4311yescharacteristic
395C2×C42C22×D4311yescharacteristic
396C4⋊C8—22no—
397C4⋊C8—862no—
398C22⋊C8—434no—
399C22⋊C8—864no—
400C22⋊C8—864no—
401C22⋊C8C22×D4314yes—
402#97—22no—
403#97—862no—
404C24—431no—
405C24—431no—
406C24C2×C4×D4311yescharacteristic
407#41—8616no—
408#41—8616no—
409C2×Q8—862no—
410C2×Q8—862no—
411C2×Q8—861no—
412C2×Q8—861no—
413C2×D4—434no—
414C2×D4—432no—
415C2×D4—432no—
416C2×D4—862no—
417C2×D4—862no—
418C2×D4—862no—
419C2×D4—862no—
420C2×D4—862no—
421C2×D4—862no—
422C2×D4—862no—
423C22×C4—22no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—434no—
432C22×C4—434no—
433C22×C4—434no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—3441no—
446C22×C4—3441no—
447C22×C4—3441no—
448C22×C4—3441no—
449C22×C4—3441no—
450C22×C4—3441no—
451C22×C4C2×C4×D4311yescharacteristic
452C22×C4C2×C4×D4311yescharacteristic
453C22×C4C2×C4×D4311yescharacteristic
454C22×C4C2×C4×D4311yescharacteristic
455C22×C4C2×C4×D4311yescharacteristic
456C22×C4C23×D4311yescharacteristic
457M16—3444no—
458C2×C8—24no—
459C2×C8—864no—
460C2×C8—3444no—
461C4⋊C4—22no—
462C4⋊C4—22no—
463C4⋊C4—432no—
464C4⋊C4—432no—
465C4⋊C4—862no—
466C4⋊C4—862no—
467C4⋊C4—862no—
468C4⋊C4—862no—
469C4⋊C4—861no—
470C4⋊C4—861no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—434no—
476C22⋊C4—434no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C42—21no—
480C42—21no—
481C42—862no—
482C42—862no—
483C42—862no—
484C42—862no—
485C42D4×D4312yes—
486C42D4×D4312yes—
487C23—21no—
488C23—21no—
489C23—41no—
490C23—41no—
491C23—432no—
492C23—432no—
493C23—432no—
494C23—432no—
495C23—861no—
496C23—861no—
497C23—1721no—
498C23—1721no—
499C23—1721no—
500C23—1721no—
501C23M16×D4312yes—
502C23C22×C4×D4311yescharacteristic
503Q8—864no—
504Q8—864no—
505D4—864no—
506D4—864no—
507D4—868no—
508D4—868no—
509C2×C4—24no—
510C2×C4—24no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—432no—
524C2×C4—432no—
525C2×C4—868no—
526C2×C4—868no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—3442no—
534C2×C4—3442no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—1724no—
538C2×C4—1724no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4—1721no—
543C2×C4C22⋊C4×D4311yescharacteristic
544C2×C4C22⋊C4×D4311yescharacteristic
545C2×C4C22⋊C4×D4312yes—
546C2×C4M16×D4312yes—
547C2×C4C2×D4×D4312yes—
548C8—44no—
549C8—1724no—
550C22—21no—
551C22—21no—
552C22—22no—
553C22—42no—
554C22—42no—
555C22—41no—
556C22—41no—
557C22—434no—
558C22—862no—
559C22—862no—
560C22—862no—
561C22—862no—
562C22—862no—
563C22—1722no—
564C22—1722no—
565C22—1722no—
566C22—1722no—
567C22C2×C22⋊C4×D4311yescharacteristic
568C22C2×M16×D4311yescharacteristic
569C22C2×M16×D4311yescharacteristic
570C4—22no—
571C4—21no—
572C4—21no—
573C4—22no—
574C4—22no—
575C4—41no—
576C4—41no—
577C4—862no—
578C4—862no—
579C4—862no—
580C4—862no—
581C4—1721no—
582C4—1721no—
583C2—21no—
584C2—21no—
585C2—42no—
586C2—864no—
587C2—1722no—
588C2#407×D4311yescharacteristic
589C2#1914305411yescharacteristic
590C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1464C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C4
cosocleC22×C4×C43C24
hypercenter#1464D43
hypocenterC43#17368
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1464

Complements

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

NH ≅ G/Ntype
2. #19143623C2semidirect
3. #19132938C2semidirect
4. #19132930C2semidirect
5. #19132929C2semidirect
6. #19132923C2semidirect
7. #19132910C2semidirect
8. #324×D43C2semidirect
9. C43×#1464C2semidirect
126. C2×C22⋊D43M16semidirect
154. C2×C4×D43M16semidirect
293. #1464D43semidirect
334. C43#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#145833792
#191436232
#191329382
#191329302
#191329292
#191329232
#191329102
#324×D432
C43×#14642
#1736843