Finite Group Databasebeta

← #25062509

Subgroups — #25062509

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583378C211yesmaximal, characteristic
2#19143622C212yesmaximal, complemented
3#19132937C212yesmaximal, complemented
4#19132933C211yesmaximal, characteristic, complemented
5#19132926C212yesmaximal, complemented
6#19132924C212yesmaximal, complemented
7#19132910C212yesmaximal, complemented
8#324×D43C212yesmaximal, complemented
9C43×#1465C211yesmaximal, characteristic, complemented
10C22×#10621900C411yescharacteristic
11#14583378—24no—
12#14583378—24no—
13C2×C4×Dic86C411yescharacteristic
14C2×#13063290C2211yescharacteristic
15C2×D4×Dic43C411yescharacteristic
16C2×C4×C22⋊D43C411yescharacteristic
17C2×C4×C22⋊D43C2211yescharacteristic
18C2×(C22⋊D43)⋊C4C411yescharacteristic
19C2×(C22⋊D43)⋊C4C2211yescharacteristic
20C2×#13063282C411yescharacteristic
21C2×#13063281C411yescharacteristic
22C2×#13063281C2211yescharacteristic
23C22×Dic43⋊C4C411yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C2×C4⋊C4×D43C2211yescharacteristic
26#14582973—24no—
27#14582968—24no—
28#14582953C2214yes—
29#14582863C2212yes—
30C22⋊C8×D43C2214yes—
31#14582625C2212yes—
32#14582624C2214yes—
33#14582624C2214yes—
34#14582623C2212yes—
35C2×C4×D4×C43C2211yescharacteristic
36C43×#407C2212yes—
37C43×#324C2212yes—
38C43×#323C2212yes—
39C2×#10621900—24no—
40C2×#10621900—24no—
41C2×#10621900—24no—
42C22×Dic86C2×C411yescharacteristic
43C22×C22⋊D43C2×C411yescharacteristic
44C22×C22⋊D43C2×C411yescharacteristic
45C23×Dic43C2×C411yescharacteristic
46C23×Dic43C2×C411yescharacteristic
47C23×Dic43C2×C411yescharacteristic
48C23×Dic43C2×C411yescharacteristic
49C22×C4×D43C2×C411yescharacteristic
50C22×C4×D43C2×C411yescharacteristic
51C22×C4×D43C2311yescharacteristic
52C2×#10621877—22no—
53C2×C8×D43—24no—
54C4×Dic86—22no—
55C4×Dic86—22no—
56#13063290—24no—
57D4×Dic43—24no—
58C4×C22⋊D43—22no—
59C4×C22⋊D43—22no—
60C4×C22⋊D43D414yes—
61C4×C22⋊D43D414yes—
62(C22⋊D43)⋊C4—24no—
63(C22⋊D43)⋊C4—24no—
64#13063282—22no—
65#13063282—22no—
66#13063281—24no—
67#13063281—24no—
68C2×C4⋊Dic43C2×C411yescharacteristic
69C2×Dic43⋊C4—22no—
70C2×Dic43⋊C4—22no—
71C2×Dic43⋊C4—22no—
72C2×Dic43⋊C4—22no—
73C2×Dic43⋊C4C2×C411yescharacteristic
74C2×Dic43⋊C4C2×C411yescharacteristic
75C2×Dic43⋊C4C2×C411yescharacteristic
76C2×Dic43⋊C4C2×C411yescharacteristic
77C2×Dic43⋊C4C2×C411yescharacteristic
78C2×Dic43⋊C4C2×C411yescharacteristic
79C2×Dic43⋊C4C2311yescharacteristic
80C2×Dic43⋊C4C2311yescharacteristic
81C4⋊C4×D43—24no—
82C2×C22⋊Dic43C2×C411yescharacteristic
83C2×C22⋊Dic43C2×C411yescharacteristic
84C2×(C2×D43)⋊C4C2×C411yescharacteristic
85C2×(C2×D43)⋊C4C2×C411yescharacteristic
86C2×C4×Dic43C2×C411yescharacteristic
87C2×C4×Dic43C2×C411yescharacteristic
88C2×C4×Dic43C2×C411yescharacteristic
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2311yescharacteristic
91Dic43⋊C8—24no—
92C22⋊(C43⋊C8)—22no—
93C22⋊(C43⋊C8)C2314yes—
94(C2×D43)⋊C8—24no—
95#13063235—24no—
96C22×D4×C43C2×C411yescharacteristic
97C23×C4×C43C2×C411yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C2×M16×C43—22no—
100C4×D4×C43—22no—
101C4×D4×C43—22no—
102C2×C4⋊C4×C43C2311yescharacteristic
103C2×C22⋊C4×C43C2×C411yescharacteristic
104C2×C22⋊C4×C43C2311yescharacteristic
105C2×C42×C43C2×C411yescharacteristic
106C22⋊C8×C43—22no—
107C22⋊C8×C43C2314yes—
108C24×C43C22×C411yescharacteristic
109C24×C43C22×C411yescharacteristic
110C23×D43C22×C411yescharacteristic
111C2×D4×C43—22no—
112C2×D4×C43—22no—
113C2×D4×C43—22no—
114C22×C4×C43—21no—
115C22×C4×C43—21no—
116C22×C4×C43—81no—
117C22×C4×C43—81no—
118C22×C4×C43C22×C411yescharacteristic
119C22×C4×C43C22×C411yescharacteristic
120C22×C4×C43C22×C411yescharacteristic
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43C2411yescharacteristic
125C2×C22⋊D43—22no—
126C2×C22⋊D43—22no—
127C2×C22⋊D43—22no—
128C2×C22⋊D43—22no—
129C2×C22⋊D43C22⋊C414yes—
130C2×C22⋊D43M1614yescomplemented
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—22no—
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—81no—
140C22×Dic43—81no—
141C22×Dic43C22×C411yescharacteristic
142C22×Dic43C22×C411yescharacteristic
143C22×Dic43C22×C411yescharacteristic
144C22×Dic43C22×C411yescharacteristic
145C22×Dic43C22×C411yescharacteristic
146C22×Dic43C22×C411yescharacteristic
147C22×Dic43C22×C411yescharacteristic
148#10621900—232no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—81no—
153C2×C4×D43—81no—
154C2×C4×D43M1614yescomplemented
155C2×C4×D43C2×D414yes—
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—22no—
159M16×C43—82no—
160C2×C8×C43—24no—
161C4⋊C4×C43—22no—
162C22⋊C4×C43—22no—
163C22⋊C4×C43—22no—
164C42×C43—21no—
165C42×C43—21no—
166C22⋊Dic43—22no—
167C22⋊Dic43C22⋊C414yes—
168(C2×D43)⋊C4—22no—
169(C2×D43)⋊C4C22⋊C412yes—
170(C2×D43)⋊C4C22⋊C412yes—
171C4⋊Dic43—22no—
172Dic43⋊C4—21no—
173Dic43⋊C4—21no—
174Dic43⋊C4—21no—
175Dic43⋊C4—21no—
176Dic43⋊C4—22no—
177Dic43⋊C4—22no—
178Dic43⋊C4—22no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4C22⋊C412yes—
182Dic43⋊C4C22⋊C412yes—
183C4×Dic43—22no—
184C4×Dic43—22no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43C2×D414yes—
188#10621877—82no—
189C2×C43⋊C8—24no—
190C8×D43—84no—
191C23×C43—21no—
192C23×C43—21no—
193C23×C43—21no—
194C23×C43—21no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43C2×C22⋊C412yes—
200C23×C43C2×M1612yes—
201C23×C43C23×C411yescharacteristic
202C22×D43—41no—
203C22×D43—41no—
204C22×D43C2×C22⋊C412yes—
205C22×D43C2×M1612yes—
206C22×D43C2×M1612yes—
207D4×C43—28no—
208C2×C4×C43—21no—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—41no—
215C2×C4×C43—41no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—81no—
219C2×C4×C43—81no—
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—28no—
227C2×Dic43—28no—
228C2×Dic43—21no—
229C2×Dic43—21no—
230C2×Dic43—21no—
231C2×Dic43—21no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—82no—
241C2×Dic43—82no—
242C2×Dic43C2×C22⋊C412yes—
243C2×Dic43C2×C22⋊C412yes—
244C2×Dic43C2×C22⋊C412yes—
245C2×Dic43C2×M1612yes—
246C2×Dic43C2×M1612yes—
247C4×D43—28no—
248C4×D43—44no—
249C4×D43—82no—
250Dic86—28no—
251C8×C43—44no—
252C43⋊C8—44no—
253#17368—431nomaximal, Sylow
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—22no—
257C22×C43—22no—
258C22×C43—22no—
259C22×C43—22no—
260C22×C43—42no—
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—41no—
265C22×C43—41no—
266C22×C43C22×C22⋊C411yescharacteristic
267C22×C43C22×M1611yescharacteristic
268C22×C43C22×M1611yescharacteristic
269C2×D43—22no—
270C2×D43—22no—
271C2×D43—42no—
272C2×D43—42no—
273C2×D43#40714yes—
274C4×C43—22no—
275C4×C43—22no—
276C4×C43—21no—
277C4×C43—21no—
278C4×C43—41no—
279C4×C43—41no—
280Dic43—22no—
281Dic43—22no—
282Dic43—22no—
283Dic43—22no—
284Dic43—22no—
285Dic43—41no—
286Dic43—41no—
287C2×#520—431no—
288#2973—432no—
289#1467—432no—
290#1465—431no—
291#1465D4311yescharacteristic, complemented
292#1464—432no—
293#1463—432no—
294#1459—432no—
295C2×#324—432no—
296C2×C43—21no—
297C2×C43—21no—
298C2×C43—42no—
299C2×C43—42no—
300C2×C43C2×#40711yescharacteristic
301C2×C43#288311yescharacteristic
302C2×C43#288911yescharacteristic
303D43—24no—
304C22×#41—431no—
305#520—864no—
306#520—864no—
307C2×C4×Q8—431no—
308C2×C4×Q8—431no—
309C2×C4×D4—431no—
310C2×C4×D4—431no—
311C2×C4×D4—431no—
312C2×C4×D4—431no—
313C2×C4×D4—431no—
314C2×C4×D4C2×D4311yescharacteristic
315C2×#117—431no—
316C2×#117—431no—
317C2×#117—431no—
318C22×C4⋊C4—431no—
319C22×C4⋊C4—431no—
320C22×C4⋊C4—431no—
321#435—864no—
322#435—864no—
323#432—434no—
324#407—432no—
325#407C2×D4312yes—
326C2×C22⋊C8—434no—
327#324—432no—
328#324—434no—
329#324—434no—
330#324C2×D4312yes—
331#323—432no—
332#323C2×D4312yes—
333C43#1736811yescharacteristic, complemented, Sylow
334C2×#41—864no—
335C2×#41—864no—
336C2×#41—864no—
337C22×Q8—431no—
338C22×D4—431no—
339C22×D4—431no—
340C22×D4C4×D4311yescharacteristic
341C23×C4—431no—
342C23×C4—431no—
343C23×C4—431no—
344C23×C4—431no—
345C23×C4—431no—
346C23×C4—431no—
347C23×C4—431no—
348C23×C4C4×D4311yescharacteristic
349C23×C4C22×D4311yescharacteristic
350C2×M16—22no—
351C2×M16—862no—
352C22×C8—864no—
353C4×Q8—862no—
354C4×Q8—862no—
355C4×Q8—864no—
356C4×D4—22no—
357C4×D4—22no—
358C4×D4—434no—
359C4×D4—434no—
360C4×D4—864no—
361C4×D4—864no—
362C4×D4—862no—
363C4×D4—862no—
364C4×D4—864no—
365#117—862no—
366#117—862no—
367#117—864no—
368#117—864no—
369C2×C4⋊C4—431no—
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—862no—
380C2×C4⋊C4—862no—
381C2×C4⋊C4—862no—
382C2×C4⋊C4—862no—
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×C42—431no—
395C2×C42C4×D4311yescharacteristic
396C4⋊C8—864no—
397C22⋊C8—22no—
398C22⋊C8—434no—
399C22⋊C8—864no—
400C22⋊C8—862no—
401C22⋊C8C22×D4314yes—
402#97—864no—
403C24—431no—
404C24C2×C4×D4311yescharacteristic
405C24C2×C4×D4311yescharacteristic
406#41—8632no—
407C2×Q8—862no—
408C2×Q8—862no—
409C2×Q8—862no—
410C2×D4—22no—
411C2×D4—22no—
412C2×D4—22no—
413C2×D4—434no—
414C2×D4—434no—
415C2×D4—862no—
416C2×D4—862no—
417C2×D4—862no—
418C2×D4—862no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—434no—
429C22×C4—434no—
430C22×C4—431no—
431C22×C4—431no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—862no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—3441no—
444C22×C4—3441no—
445C22×C4—3441no—
446C22×C4—3441no—
447C22×C4C2×C4×D4311yescharacteristic
448C22×C4C2×C4×D4311yescharacteristic
449C22×C4C2×C4×D4311yescharacteristic
450C22×C4C2×C4×D4311yescharacteristic
451C22×C4D4×D4312yes—
452C22×C4D4×D4312yes—
453C22×C4C23×D4311yescharacteristic
454M16—82no—
455M16—3442no—
456C2×C8—24no—
457C2×C8—864no—
458C2×C8—3444no—
459C4⋊C4—22no—
460C4⋊C4—432no—
461C4⋊C4—432no—
462C4⋊C4—862no—
463C4⋊C4—862no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—861no—
467C4⋊C4—861no—
468C4⋊C4—861no—
469C4⋊C4—861no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—434no—
475C22⋊C4—432no—
476C22⋊C4—432no—
477C22⋊C4—862no—
478C22⋊C4—862no—
479C42—21no—
480C42—21no—
481C42—434no—
482C42—862no—
483C42—862no—
484C42—862no—
485C42—862no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—432no—
495C23—432no—
496C23—432no—
497C23—1721no—
498C23—1721no—
499C23C22⋊C4×D4312yes—
500C23M16×D4312yes—
501C23C22×C4×D4311yescharacteristic
502Q8—868no—
503D4—28no—
504D4—868no—
505D4—868no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—81no—
517C2×C4—81no—
518C2×C4—432no—
519C2×C4—432no—
520C2×C4—432no—
521C2×C4—432no—
522C2×C4—432no—
523C2×C4—868no—
524C2×C4—868no—
525C2×C4—868no—
526C2×C4—861no—
527C2×C4—861no—
528C2×C4—861no—
529C2×C4—861no—
530C2×C4—861no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—3442no—
535C2×C4—3442no—
536C2×C4—3442no—
537C2×C4—1724no—
538C2×C4—1721no—
539C2×C4—1721no—
540C2×C4—1721no—
541C2×C4—1721no—
542C2×C4C22⋊C4×D4311yescharacteristic
543C2×C4C22⋊C4×D4311yescharacteristic
544C2×C4M16×D4312yes—
545C2×C4C2×D4×D4312yes—
546C8—44no—
547C8—1724no—
548C22—21no—
549C22—21no—
550C22—22no—
551C22—22no—
552C22—22no—
553C22—22no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—42no—
558C22—41no—
559C22—41no—
560C22—434no—
561C22—862no—
562C22—862no—
563C22—1722no—
564C22—1722no—
565C22C2×C22⋊C4×D4311yescharacteristic
566C22C2×M16×D4311yescharacteristic
567C22C2×M16×D4311yescharacteristic
568C4—22no—
569C4—22no—
570C4—21no—
571C4—21no—
572C4—41no—
573C4—41no—
574C4—862no—
575C4—862no—
576C4—862no—
577C4—862no—
578C4—862no—
579C4—1721no—
580C4—1721no—
581C2—21no—
582C2—21no—
583C2—42no—
584C2—42no—
585C2—864no—
586C2#407×D4311yescharacteristic
587C2#1914305311yescharacteristic
588C2#1914307611yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1465C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621900C4
cosocleC22×C4×C43C24
hypercenter#1465D43
hypocenterC43#17368
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
2. #19143622C2semidirect
3. #19132937C2semidirect
4. #19132933C2semidirect
5. #19132926C2semidirect
6. #19132924C2semidirect
7. #19132910C2semidirect
8. #324×D43C2semidirect
9. C43×#1465C2semidirect
130. C2×C22⋊D43M16semidirect
154. C2×C4×D43M16semidirect
291. #1465D43semidirect
333. C43#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#145833782
#191436222
#191329372
#191329332
#191329262
#191329242
#191329102
#324×D432
C43×#14652
#1736843