Finite Group Databasebeta

← #25062508

Subgroups — #25062508

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583378C211yesmaximal, characteristic
2#19143624C211yesmaximal, characteristic, complemented
3#19132938C212yesmaximal, complemented
4#19132931C212yesmaximal, complemented
5#19132927C212yesmaximal, complemented
6#19132924C212yesmaximal, complemented
7#19132911C212yesmaximal, complemented
8C2×#14582624C212yesmaximal, complemented
9C43×#2973C211yesmaximal, characteristic, complemented
10C22×#10621900C411yescharacteristic
11#14583378—24no—
12#14583378—24no—
13C2×C4×Dic86C2211yescharacteristic
14C2×#13063290C411yescharacteristic
15C2×D4×Dic43C411yescharacteristic
16C2×C4×C22⋊D43C2211yescharacteristic
17C2×C4×C22⋊D43C2211yescharacteristic
18C2×(C22⋊D43)⋊C4C411yescharacteristic
19C2×(C22⋊D43)⋊C4C411yescharacteristic
20C2×#13063282C2211yescharacteristic
21C2×#13063281C411yescharacteristic
22C2×#13063281C411yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C2×C4⋊C4×D43C411yescharacteristic
26#14582971—24no—
27#14582956C2212yes—
28#14582863C2212yes—
29C2×C22⋊(C43⋊C8)C2212yes—
30#14582624C2214yes—
31#14582624C2214yes—
32#14582624C2214yes—
33#14582622C2214yes—
34C2×C4×D4×C43C2211yescharacteristic
35C43×#435—24no—
36C43×#432C2212yes—
37C43×#407C2212yes—
38C2×C22⋊C8×C43C2212yes—
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×D43C2×C411yescharacteristic
52C2×#10621877—22no—
53C22×C43⋊C8—22no—
54C4×Dic86—22no—
55C4×Dic86—22no—
56#13063290—24no—
57D4×Dic43—24no—
58C4×C22⋊D43—22no—
59C4×C22⋊D43—22no—
60C4×C22⋊D43—22no—
61C4×C22⋊D43—22no—
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⋊C4C2311yescharacteristic
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)⋊C4C2311yescharacteristic
86C2×C4×Dic43C2×C411yescharacteristic
87C2×C4×Dic43C2×C411yescharacteristic
88C2×C4×Dic43C2×C411yescharacteristic
89C2×C4×Dic43C2×C411yescharacteristic
90C2×C4×Dic43C2×C411yescharacteristic
91C4⋊(C43⋊C8)—22no—
92C22⋊(C43⋊C8)—22no—
93C22⋊(C43⋊C8)—22no—
94C22⋊(C43⋊C8)C2314yes—
95#13063236—22no—
96C22×D4×C43C2×C411yescharacteristic
97C23×C4×C43C2311yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C2×M16×C43—22no—
100C22×C8×C43—22no—
101C4×D4×C43D414yes—
102C4×D4×C43D414yes—
103C2×C4⋊C4×C43C2×C411yescharacteristic
104C2×C22⋊C4×C43C2×C411yescharacteristic
105C2×C22⋊C4×C43C2×C411yescharacteristic
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—22no—
108C22⋊C8×C43—22no—
109C22⋊C8×C43—22no—
110C22⋊C8×C43C2314yes—
111#97×C43—22no—
112C24×C43C22×C411yescharacteristic
113C24×C43C22×C411yescharacteristic
114C23×D43C22×C411yescharacteristic
115C2×D4×C43—22no—
116C2×D4×C43—22no—
117C2×D4×C43C22⋊C414yes—
118C22×C4×C43—81no—
119C22×C4×C43—81no—
120C22×C4×C43C22×C411yescharacteristic
121C22×C4×C43C22×C411yescharacteristic
122C22×C4×C43C22×C411yescharacteristic
123C22×C4×C43C22×C411yescharacteristic
124C22×C4×C43C2×D412yes—
125C22×C4×C43C2×D412yes—
126C22×C4×C43C2×D412yes—
127C22×C4×C43C2×D412yes—
128C22×C4×C43C2411yescharacteristic
129C2×C22⋊D43—22no—
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43—22no—
133C2×C22⋊D43—22no—
134C2×C22⋊D43M1614yescomplemented
135C22×Dic43—22no—
136C22×Dic43—22no—
137C22×Dic43—22no—
138C22×Dic43—22no—
139C22×Dic43—22no—
140C22×Dic43—22no—
141C22×Dic43—22no—
142C22×Dic43—81no—
143C22×Dic43—81no—
144C22×Dic43M1614yescomplemented
145C22×Dic43C22×C411yescharacteristic
146C22×Dic43C22×C411yescharacteristic
147C22×Dic43C22×C411yescharacteristic
148C22×Dic43C22×C411yescharacteristic
149C22×Dic43C22×C411yescharacteristic
150C22×Dic43C22×C411yescharacteristic
151C22×Dic43C22×C411yescharacteristic
152#10621900—232no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—81no—
159C2×C4×D43—81no—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163M16×C43—82no—
164C2×C8×C43—24no—
165C2×C8×C43—82no—
166C4⋊C4×C43C22⋊C414yes—
167C22⋊C4×C43C22⋊C414yes—
168C22⋊C4×C43C22⋊C414yes—
169C42×C43C2×D412yes—
170C42×C43C2×D412yes—
171C22⋊Dic43—22no—
172C22⋊Dic43—22no—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—21no—
175(C2×D43)⋊C4—21no—
176C4⋊Dic43—22no—
177Dic43⋊C4—22no—
178Dic43⋊C4—22no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—21no—
183Dic43⋊C4—21no—
184Dic43⋊C4—21no—
185Dic43⋊C4—21no—
186Dic43⋊C4—21no—
187Dic43⋊C4—21no—
188C4×Dic43—22no—
189C4×Dic43—22no—
190C4×Dic43—22no—
191C4×Dic43—22no—
192C4×Dic43—22no—
193#10621877—82no—
194C2×C43⋊C8—24no—
195C2×C43⋊C8—82no—
196C23×C43—21no—
197C23×C43—21no—
198C23×C43—41no—
199C23×C43—41no—
200C23×C43—41no—
201C23×C43—41no—
202C23×C43C2×C22⋊C412yes—
203C23×C43C2×C22⋊C412yes—
204C23×C43C2×M1612yes—
205C23×C43C2×M1612yes—
206C23×C43C23×C411yescharacteristic
207C22×D43—21no—
208C22×D43—21no—
209C22×D43—41no—
210C22×D43—41no—
211C22×D43C2×M1612yes—
212D4×C43—28no—
213C2×C4×C43—21no—
214C2×C4×C43—21no—
215C2×C4×C43—42no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—41no—
220C2×C4×C43—41no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43C2×C22⋊C412yes—
224C2×C4×C43C2×C22⋊C412yes—
225C2×C4×C43C2×C22⋊C412yes—
226C2×C4×C43C2×C22⋊C412yes—
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C22×D411yescharacteristic
229C22⋊D43—28no—
230C22⋊D43—28no—
231C2×Dic43—28no—
232C2×Dic43—21no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—28no—
239C2×Dic43—21no—
240C2×Dic43—21no—
241C2×Dic43—21no—
242C2×Dic43—21no—
243C2×Dic43—41no—
244C2×Dic43—41no—
245C2×Dic43—41no—
246C2×Dic43—41no—
247C2×Dic43—82no—
248C2×Dic43—82no—
249C2×Dic43C2×M1612yes—
250C2×Dic43C2×M1612yes—
251C2×Dic43C2×M1612yes—
252C4×D43—28no—
253C4×D43—82no—
254C4×D43—82no—
255Dic86—28no—
256C8×C43—44no—
257C43⋊C8—44no—
258#17368—431nomaximal, Sylow
259C22×C43—21no—
260C22×C43—22no—
261C22×C43—21no—
262C22×C43—22no—
263C22×C43—22no—
264C22×C43—22no—
265C22×C43—22no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—42no—
270C22×C43#40714yes—
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43C22×M1611yescharacteristic
273C22×C43C22×M1611yescharacteristic
274C2×D43—22no—
275C2×D43—42no—
276C2×D43—41no—
277C2×D43—41no—
278C2×D43—42no—
279C4×C43—22no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—22no—
285Dic43—22no—
286Dic43—22no—
287Dic43—22no—
288Dic43—41no—
289Dic43—41no—
290Dic43—41no—
291Dic43—41no—
292C2×#520—431no—
293#2973—431no—
294#2973D4311yescharacteristic, complemented
295#1467—432no—
296#1465—432no—
297#1464—432no—
298#1463—432no—
299#1459—432no—
300C2×#324—432no—
301C2×C43—21no—
302C2×C43—21no—
303C2×C43—24no—
304C2×C43—42no—
305C2×C43C2×#40711yescharacteristic
306C2×C43#288311yescharacteristic
307C2×C43#288911yescharacteristic
308D43—42no—
309C22×#41—431no—
310#520—864no—
311#520—864no—
312C2×C4×Q8—431no—
313C2×C4×Q8—431no—
314C2×C4×D4—431no—
315C2×C4×D4—431no—
316C2×C4×D4—431no—
317C2×C4×D4—431no—
318C2×C4×D4—431no—
319C2×C4×D4C2×D4311yescharacteristic
320C2×#117—431no—
321C2×#117—431no—
322C2×#117—431no—
323C22×C4⋊C4—431no—
324C22×C4⋊C4—431no—
325C22×C4⋊C4—431no—
326#435—24no—
327#435—864no—
328#432—432no—
329#432C2×D4312yes—
330#407—432no—
331#407C2×D4312yes—
332C2×C22⋊C8—432no—
333C2×C22⋊C8C2×D4312yes—
334#324—434no—
335#324—434no—
336#324—434no—
337#323—434no—
338C43#1736811yescharacteristic, complemented, Sylow
339C2×#41—864no—
340C2×#41—864no—
341C2×#41—864no—
342C22×Q8—431no—
343C22×D4—431no—
344C22×D4—431no—
345C22×D4C4×D4311yescharacteristic
346C23×C4—431no—
347C23×C4—431no—
348C23×C4—431no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—431no—
352C23×C4—431no—
353C23×C4C22×D4311yescharacteristic
354C23×C4C22×D4311yescharacteristic
355C2×M16—22no—
356C2×M16—862no—
357C22×C8—22no—
358C22×C8—862no—
359C4×Q8—864no—
360C4×Q8—862no—
361C4×Q8—862no—
362C4×D4—864no—
363C4×D4—862no—
364C4×D4—862no—
365C4×D4—862no—
366C4×D4—862no—
367C4×D4—864no—
368C4×D4—864no—
369C4×D4D17214yes—
370C4×D4C22⋊D4314yes—
371#117—864no—
372#117—864no—
373#117—862no—
374#117—862no—
375C2×C4⋊C4—431no—
376C2×C4⋊C4—431no—
377C2×C4⋊C4—431no—
378C2×C4⋊C4—431no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—862no—
385C2×C4⋊C4—862no—
386C2×C4⋊C4—862no—
387C2×C4⋊C4—862no—
388C2×C4⋊C4—864no—
389C2×C4⋊C4C4×D4311yescharacteristic
390C2×C22⋊C4—431no—
391C2×C22⋊C4—431no—
392C2×C22⋊C4—431no—
393C2×C22⋊C4—431no—
394C2×C22⋊C4C4×D4311yescharacteristic
395C2×C22⋊C4C4×D4311yescharacteristic
396C2×C42—431no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42C22×D4311yescharacteristic
402C4⋊C8—22no—
403C4⋊C8—862no—
404C22⋊C8—22no—
405C22⋊C8—22no—
406C22⋊C8—434no—
407C22⋊C8—862no—
408C22⋊C8—862no—
409C22⋊C8C22×D4314yes—
410#97—22no—
411#97—862no—
412C24—431no—
413C24C2×C4×D4311yescharacteristic
414C24C2×C4×D4311yescharacteristic
415#41—8632no—
416C2×Q8—862no—
417C2×Q8—862no—
418C2×Q8—862no—
419C2×D4—22no—
420C2×D4—22no—
421C2×D4—434no—
422C2×D4—862no—
423C2×D4—862no—
424C2×D4—862no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4(C2×D43)⋊C414yes—
428C22×C4—81no—
429C22×C4—81no—
430C22×C4—434no—
431C22×C4—431no—
432C22×C4—431no—
433C22×C4—431no—
434C22×C4—431no—
435C22×C4—431no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—862no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—3441no—
451C22×C4—3441no—
452C22×C4—3441no—
453C22×C4—3441no—
454C22×C4C2×C4×D4311yescharacteristic
455C22×C4C2×C4×D4311yescharacteristic
456C22×C4C2×C4×D4311yescharacteristic
457C22×C4C2×C4×D4311yescharacteristic
458C22×C4C2×D17212yes—
459C22×C4C2×D17212yes—
460C22×C4C2×C22⋊D4312yes—
461C22×C4C2×C22⋊D4312yes—
462C22×C4C23×D4311yescharacteristic
463M16—82no—
464M16—3442no—
465C2×C8—24no—
466C2×C8—82no—
467C2×C8—864no—
468C2×C8—3442no—
469C4⋊C4—862no—
470C4⋊C4—862no—
471C4⋊C4—862no—
472C4⋊C4—862no—
473C4⋊C4—862no—
474C4⋊C4—862no—
475C4⋊C4—861no—
476C4⋊C4—861no—
477C4⋊C4—861no—
478C4⋊C4—861no—
479C4⋊C4—861no—
480C4⋊C4—861no—
481C4⋊C4(C2×D43)⋊C414yes—
482C22⋊C4—862no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4(C2×D43)⋊C414yes—
488C22⋊C4(C2×D43)⋊C414yes—
489C42—862no—
490C42—862no—
491C42—862no—
492C42—862no—
493C42—862no—
494C42C2×D17212yes—
495C42C2×C22⋊D4312yes—
496C23—21no—
497C23—21no—
498C23—41no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—432no—
503C23—861no—
504C23—861no—
505C23—1721no—
506C23—1721no—
507C23C2×(C2×D43)⋊C412yes—
508C23C2×(C2×D43)⋊C412yes—
509C23M16×D4312yes—
510C23M16×D4312yes—
511C23C22×C4×D4311yescharacteristic
512Q8—868no—
513D4—28no—
514D4—868no—
515D4—868no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—432no—
527C2×C4—432no—
528C2×C4—432no—
529C2×C4—868no—
530C2×C4—868no—
531C2×C4—861no—
532C2×C4—861no—
533C2×C4—861no—
534C2×C4—868no—
535C2×C4—861no—
536C2×C4—861no—
537C2×C4—861no—
538C2×C4—861no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—3442no—
543C2×C4—3442no—
544C2×C4—3442no—
545C2×C4—3442no—
546C2×C4—1721no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1721no—
550C2×C4C2×(C2×D43)⋊C412yes—
551C2×C4C2×(C2×D43)⋊C412yes—
552C2×C4C2×(C2×D43)⋊C412yes—
553C2×C4C2×(C2×D43)⋊C412yes—
554C2×C4C22×C22⋊D4311yescharacteristic
555C2×C4C22×D17211yescharacteristic
556C8—44no—
557C8—1724no—
558C22—21no—
559C22—22no—
560C22—21no—
561C22—22no—
562C22—22no—
563C22—22no—
564C22—22no—
565C22—42no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—862no—
570C22—1722no—
571C22—1722no—
572C22—1721no—
573C22—1721no—
574C22#1458286214yes—
575C22C22×(C2×D43)⋊C411yescharacteristic
576C22C2×M16×D4311yescharacteristic
577C22C2×M16×D4311yescharacteristic
578C4—22no—
579C4—21no—
580C4—21no—
581C4—22no—
582C4—22no—
583C4—22no—
584C4—862no—
585C4—862no—
586C4—862no—
587C4—1721no—
588C4—1721no—
589C4—1721no—
590C4—1721no—
591C2—21no—
592C2—21no—
593C2—24no—
594C2—42no—
595C2—1722no—
596C2C2×#1458286211yescharacteristic
597C2#1914305511yescharacteristic
598C2#1914307711yescharacteristic
subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#2973C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621900C4
cosocleC22×C4×C43C24
hypercenter#2973D43
hypocenterC43#17368
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #2973

Complements

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

NH ≅ G/Ntype
2. #19143624C2semidirect
3. #19132938C2semidirect
4. #19132931C2semidirect
5. #19132927C2semidirect
6. #19132924C2semidirect
7. #19132911C2semidirect
8. C2×#14582624C2semidirect
9. C43×#2973C2semidirect
134. C2×C22⋊D43M16semidirect
144. C22×Dic43M16semidirect
294. #2973D43semidirect
338. C43#17368semidirect

Maximal subgroups

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

subgroupindex
C2×#145833782
#191436242
#191329382
#191329312
#191329272
#191329242
#191329112
C2×#145826242
C43×#29732
#1736843