Finite Group Databasebeta

← #25062506

Subgroups — #25062506

Order 11008.

1210 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583380C211yesmaximal, characteristic
2#19143621C212yesmaximal, complemented
3#19132937C212yesmaximal, complemented
4#19132932C212yesmaximal, complemented
5#19132928C212yesmaximal, complemented
6#19132923C212yesmaximal, complemented
7#19132911C212yesmaximal, complemented
8C2×#14582625C211yesmaximal, characteristic, complemented
9C2×C43×#324C211yesmaximal, characteristic, complemented
10C22×#10621898C411yescharacteristic
11#14583380—24no—
12#14583380—24no—
13C2×#13063290C411yescharacteristic
14C2×#13063290C2211yescharacteristic
15C2×#13063287C411yescharacteristic
16C2×#13063287C2211yescharacteristic
17C2×C4×C22⋊D43C411yescharacteristic
18C2×C4×C22⋊D43C411yescharacteristic
19C2×C4×C22⋊D43C2211yescharacteristic
20C2×C4×C22⋊D43C2211yescharacteristic
21C2×#13063284C411yescharacteristic
22C2×#13063283C411yescharacteristic
23C2×#13063283C2211yescharacteristic
24C2×C4⋊C4×D43C411yescharacteristic
25C2×C4⋊C4×D43C2211yescharacteristic
26#14582970—24no—
27#14582967—24no—
28#14582953C2214yes—
29#14582861C2214yes—
30C2×C22⋊(C43⋊C8)C2212yes—
31#14582625C2212yes—
32#14582625C2212yes—
33#14582624C2214yes—
34#14582622C2214yes—
35C22×C4⋊C4×C43C2211yescharacteristic
36C2×C22⋊C8×C43C2212yes—
37C43×#324C2212yes—
38C43×#324C2212yes—
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
47C22×C4×D43C2×C411yescharacteristic
48C22×C4×D43C2×C411yescharacteristic
49C22×C4×D43C2×C411yescharacteristic
50C22×C4×D43C2×C411yescharacteristic
51C22×C4×D43C2×C411yescharacteristic
52C22×C4×D43C2311yescharacteristic
53C2×#10621872—24no—
54C22×C43⋊C8—22no—
55#13063290—24no—
56#13063290—24no—
57#13063287—24no—
58#13063287—24no—
59C4×C22⋊D43—22no—
60C4×C22⋊D43—22no—
61C4×C22⋊D43—22no—
62C4×C22⋊D43—22no—
63C4×C22⋊D43—22no—
64C4×C22⋊D43—22no—
65C4×C22⋊D43D414yes—
66C4×C22⋊D43D414yes—
67#13063284—22no—
68#13063284—22no—
69#13063283—24no—
70#13063283—24no—
71C2×C4⋊Dic43C2×C411yescharacteristic
72C2×C4⋊Dic43C2×C411yescharacteristic
73C2×Dic43⋊C4C2×C411yescharacteristic
74C2×Dic43⋊C4C2×C411yescharacteristic
75C2×Dic43⋊C4C2×C411yescharacteristic
76C2×Dic43⋊C4C2311yescharacteristic
77C4⋊C4×D43—24no—
78C4⋊C4×D43—24no—
79C2×C22⋊Dic43C2×C411yescharacteristic
80C2×C22⋊Dic43C2×C411yescharacteristic
81C2×(C2×D43)⋊C4C2×C411yescharacteristic
82C2×(C2×D43)⋊C4C2×C411yescharacteristic
83C2×(C2×D43)⋊C4C2×C411yescharacteristic
84C2×(C2×D43)⋊C4C2311yescharacteristic
85C2×C4×Dic43C2×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—
96C23×C4×C43C2×C411yescharacteristic
97C23×C4×C43C2×C411yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C22×C8×C43—22no—
100C2×C4⋊C4×C43—22no—
101C2×C4⋊C4×C43—22no—
102C2×C4⋊C4×C43C2×C411yescharacteristic
103C2×C4⋊C4×C43C2×C411yescharacteristic
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2311yescharacteristic
106C22⋊C8×C43—22no—
107C22⋊C8×C43C2314yes—
108C24×C43C22×C411yescharacteristic
109C23×D43C22×C411yescharacteristic
110C23×D43C22×C411yescharacteristic
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—21no—
114C22×C4×C43—21no—
115C22×C4×C43—22no—
116C22×C4×C43—81no—
117C22×C4×C43—81no—
118C22×C4×C43M1614yescomplemented
119C22×C4×C43C22×C411yescharacteristic
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×C43C2411yescharacteristic
127C2×C22⋊D43—21no—
128C2×C22⋊D43—21no—
129C2×C22⋊D43—22no—
130C2×C22⋊D43—22no—
131C2×C22⋊D43—22no—
132C2×C22⋊D43C22⋊C412yes—
133C2×C22⋊D43C22⋊C412yes—
134C2×C22⋊D43M1614yescomplemented
135C22×Dic43C22×C411yescharacteristic
136C22×Dic43C22×C411yescharacteristic
137C22×Dic43C22×C411yescharacteristic
138C22×Dic43C22×C411yescharacteristic
139C22×Dic43C22×C411yescharacteristic
140C22×Dic43C22×C411yescharacteristic
141#10621898—216no—
142#10621898—216no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—22no—
146C2×C4×D43—22no—
147C2×C4×D43—22no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—22no—
153C2×C4×D43—22no—
154C2×C4×D43—22no—
155C2×C4×D43—81no—
156C2×C4×D43—81no—
157C2×C4×D43—81no—
158C2×C4×D43—81no—
159C2×C4×D43C2×D414yes—
160C2×Dic86—22no—
161C2×Dic86—22no—
162C2×Dic86—22no—
163C2×C8×C43—24no—
164C2×C8×C43—82no—
165C4⋊C4×C43—22no—
166C4⋊C4×C43—22no—
167C4⋊C4×C43—22no—
168C4⋊C4×C43—22no—
169C22⋊Dic43—21no—
170C22⋊Dic43—21no—
171C22⋊Dic43C22⋊C412yes—
172C22⋊Dic43C22⋊C412yes—
173(C2×D43)⋊C4—22no—
174(C2×D43)⋊C4—22no—
175(C2×D43)⋊C4—22no—
176(C2×D43)⋊C4C22⋊C414yes—
177C4⋊Dic43—22no—
178C4⋊Dic43—22no—
179Dic43⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4C22⋊C414yes—
183C4×Dic43—22no—
184C4×Dic43—22no—
185C4×Dic43—22no—
186C4×Dic43—22no—
187C4×Dic43—22no—
188C4×Dic43C2×D414yes—
189C2×C43⋊C8—24no—
190C2×C43⋊C8—82no—
191#10621872—84no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43C2×C22⋊C411yescharacteristic
195C23×C43C2×C22⋊C411yescharacteristic
196C23×C43C2×M1612yes—
197C23×C43C2×M1612yes—
198C23×C43C23×C411yescharacteristic
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—21no—
202C22×D43—21no—
203C22×D43—41no—
204C22×D43—41no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43C2×C22⋊C412yes—
208C22×D43C2×M1612yes—
209C2×C4×C43—21no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—21no—
213C2×C4×C43—24no—
214C2×C4×C43—24no—
215C2×C4×C43—21no—
216C2×C4×C43—21no—
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×C43—81no—
224C2×C4×C43—81no—
225C2×C4×C43C2×C22⋊C412yes—
226C2×C4×C43C2×M1612yes—
227C2×C4×C43C2×M1612yes—
228C2×C4×C43C22×D412yes—
229C22⋊D43—24no—
230C22⋊D43—24no—
231C22⋊D43—24no—
232C22⋊D43—24no—
233C2×Dic43—21no—
234C2×Dic43—21no—
235C2×Dic43—21no—
236C2×Dic43—21no—
237C2×Dic43—21no—
238C2×Dic43—21no—
239C2×Dic43—41no—
240C2×Dic43—41no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243C2×Dic43C2×C22⋊C412yes—
244C2×Dic43C2×C22⋊C412yes—
245C2×Dic43C2×C22⋊C412yes—
246C2×Dic43C2×M1612yes—
247D172—28no—
248C4×D43—28no—
249C4×D43—28no—
250C4×D43—44no—
251C4×D43—82no—
252C4×D43—82no—
253C4×D43—82no—
254Dic86—28no—
255C8×C43—44no—
256C43⋊C8—44no—
257#17368—431nomaximal, Sylow
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—21no—
263C22×C43—21no—
264C22×C43—42no—
265C22×C43—42no—
266C22×C43#40712yes—
267C22×C43#40712yes—
268C22×C43C22×C22⋊C411yescharacteristic
269C22×C43C22×M1611yescharacteristic
270C22×C43C22×M1611yescharacteristic
271C2×D43—22no—
272C2×D43—22no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—41no—
279C2×D43—41no—
280C2×D43—42no—
281C4×C43—22no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—22no—
285C4×C43—41no—
286C4×C43—41no—
287Dic43—22no—
288Dic43—22no—
289Dic43—22no—
290Dic43—22no—
291Dic43—41no—
292Dic43—41no—
293C2×#520—431no—
294#2973—432no—
295#1467—432no—
296#1465—432no—
297#1464—432no—
298#1463—432no—
299#1459—432no—
300C2×#324—431no—
301C2×#324D4311yescharacteristic, complemented
302C2×C43—21no—
303C2×C43—21no—
304C2×C43—22no—
305C2×C43—22no—
306C2×C43C2×#40711yescharacteristic
307C2×C43#288311yescharacteristic
308C2×C43#288911yescharacteristic
309D43—42no—
310D43—42no—
311C22×#41—431no—
312#520—864no—
313#520—864no—
314C2×C4×Q8—431no—
315C2×C4×Q8—431no—
316C2×C4×D4—431no—
317C2×C4×D4—431no—
318C2×C4×D4—431no—
319C2×C4×D4—431no—
320C2×C4×D4—431no—
321C2×C4×D4—431no—
322C2×#117—431no—
323C2×#117—431no—
324C2×#117—431no—
325C22×C4⋊C4—431no—
326C22×C4⋊C4—431no—
327C22×C4⋊C4C2×D4311yescharacteristic
328#435—864no—
329#435—864no—
330#432—434no—
331#407—434no—
332C2×C22⋊C8—432no—
333C2×C22⋊C8C2×D4312yes—
334#324—432no—
335#324—432no—
336#324—434no—
337#324C2×D4312yes—
338#324C2×D4312yes—
339#323—434no—
340C43#1736811yescharacteristic, complemented, Sylow
341C2×#41—862no—
342C2×#41—862no—
343C2×#41—864no—
344C2×#41—864no—
345C22×Q8—431no—
346C22×D4—431no—
347C22×D4—431no—
348C22×D4—431no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—431no—
352C23×C4—431no—
353C23×C4—431no—
354C23×C4—431no—
355C23×C4C4×D4311yescharacteristic
356C23×C4C4×D4311yescharacteristic
357C23×C4C22×D4311yescharacteristic
358C2×M16—864no—
359C22×C8—22no—
360C22×C8—862no—
361C4×Q8—864no—
362C4×Q8—864no—
363C4×D4—434no—
364C4×D4—434no—
365C4×D4—864no—
366C4×D4—862no—
367C4×D4—862no—
368C4×D4—864no—
369C4×D4—862no—
370C4×D4—862no—
371C4×D4—862no—
372C4×D4—862no—
373#117—864no—
374#117—864no—
375#117—862no—
376#117—862no—
377C2×C4⋊C4—22no—
378C2×C4⋊C4—22no—
379C2×C4⋊C4—431no—
380C2×C4⋊C4—431no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—431no—
383C2×C4⋊C4—431no—
384C2×C4⋊C4—431no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4—864no—
387C2×C4⋊C4C4×D4311yescharacteristic
388C2×C4⋊C4C4×D4311yescharacteristic
389C2×C4⋊C4C22×D4311yescharacteristic
390C2×C4⋊C4C22×D4311yescharacteristic
391C2×C22⋊C4—431no—
392C2×C22⋊C4—431no—
393C2×C22⋊C4—431no—
394C2×C22⋊C4—431no—
395C2×C22⋊C4—431no—
396C2×C22⋊C4—431no—
397C2×C42—431no—
398C2×C42—431no—
399C2×C42—431no—
400C2×C42—431no—
401C2×C42—431no—
402C2×C42—431no—
403C4⋊C8—864no—
404C22⋊C8—22no—
405C22⋊C8—434no—
406C22⋊C8—864no—
407C22⋊C8—862no—
408C22⋊C8C22×D4314yes—
409#97—864no—
410C24—431no—
411C24—431no—
412C24C2×C4×D4311yescharacteristic
413#41—8616no—
414#41—8616no—
415C2×Q8—862no—
416C2×Q8—862no—
417C2×Q8—862no—
418C2×D4—432no—
419C2×D4—432no—
420C2×D4—434no—
421C2×D4—862no—
422C2×D4—862no—
423C2×D4—861no—
424C2×D4—861no—
425C2×D4—862no—
426C2×D4—862no—
427C2×D4—862no—
428C2×D4—862no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—22no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—81no—
435C22×C4—81no—
436C22×C4—431no—
437C22×C4—431no—
438C22×C4—431no—
439C22×C4—431no—
440C22×C4—434no—
441C22×C4—431no—
442C22×C4—431no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—862no—
446C22×C4—862no—
447C22×C4—862no—
448C22×C4—862no—
449C22×C4—862no—
450C22×C4—862no—
451C22×C4—862no—
452C22×C4—3441no—
453C22×C4—3441no—
454C22×C4—3441no—
455C22×C4—3441no—
456C22×C4#1062187214yescomplemented
457C22×C4C2×C4×D4311yescharacteristic
458C22×C4C2×C4×D4311yescharacteristic
459C22×C4C2×C4×D4311yescharacteristic
460C22×C4C2×C4×D4311yescharacteristic
461C22×C4C2×C4×D4311yescharacteristic
462C22×C4D4×D4312yes—
463C22×C4D4×D4312yes—
464C22×C4C23×D4311yescharacteristic
465M16—3444no—
466C2×C8—24no—
467C2×C8—82no—
468C2×C8—864no—
469C2×C8—3442no—
470C4⋊C4—22no—
471C4⋊C4—22no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—434no—
475C4⋊C4—862no—
476C4⋊C4—862no—
477C4⋊C4—862no—
478C4⋊C4—862no—
479C4⋊C4—862no—
480C22⋊C4—432no—
481C22⋊C4—432no—
482C22⋊C4—434no—
483C22⋊C4—862no—
484C22⋊C4—862no—
485C22⋊C4—861no—
486C22⋊C4—861no—
487C22⋊C4—862no—
488C42—434no—
489C42—862no—
490C42—862no—
491C42—862no—
492C42—862no—
493C42—862no—
494C23—41no—
495C23—41no—
496C23—432no—
497C23—432no—
498C23—861no—
499C23—861no—
500C23—861no—
501C23—861no—
502C23—1721no—
503C23—1721no—
504C23—1721no—
505C23—1721no—
506C23C22⋊C4×D4311yescharacteristic
507C23C22⋊C4×D4311yescharacteristic
508C23M16×D4312yes—
509C23C2×#1062187212yes—
510C23C22×C4×D4311yescharacteristic
511Q8—868no—
512D4—868no—
513D4—864no—
514D4—864no—
515D4—864no—
516D4—864no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—24no—
520C2×C4—24no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—81no—
532C2×C4—81no—
533C2×C4—432no—
534C2×C4—432no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—868no—
538C2×C4—868no—
539C2×C4—861no—
540C2×C4—861no—
541C2×C4—861no—
542C2×C4—861no—
543C2×C4—861no—
544C2×C4—861no—
545C2×C4—3442no—
546C2×C4—3442no—
547C2×C4—3442no—
548C2×C4—1724no—
549C2×C4—1721no—
550C2×C4—1721no—
551C2×C4—1721no—
552C2×C4—1721no—
553C2×C4C22⋊C4×D4312yes—
554C2×C4C2×#1062187212yes—
555C2×C4C2×#1062187212yes—
556C2×C4C2×D4×D4312yes—
557C8—44no—
558C8—1724no—
559C22—21no—
560C22—21no—
561C22—21no—
562C22—21no—
563C22—21no—
564C22—21no—
565C22—42no—
566C22—42no—
567C22—862no—
568C22—862no—
569C22—862no—
570C22—862no—
571C22—1722no—
572C22—1722no—
573C22—1722no—
574C22—1722no—
575C22—1721no—
576C22—1721no—
577C22#1458286112yes—
578C22#1458286112yes—
579C22C2×C22⋊C4×D4311yescharacteristic
580C22C2×M16×D4311yescharacteristic
581C22C22×#1062187211yescharacteristic
582C4—22no—
583C4—22no—
584C4—22no—
585C4—22no—
586C4—41no—
587C4—41no—
588C4—862no—
589C4—862no—
590C4—862no—
591C4—862no—
592C4—1721no—
593C4—1721no—
594C2—21no—
595C2—21no—
596C2—22no—
597C2—22no—
598C2—1722no—
599C2—1722no—
600C2C2×#1458286111yescharacteristic
601C2#1914305311yescharacteristic
602C2#1914307511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C4
cosocleC22×C4×C43C24
hypercenterC2×#324D43
hypocenterC43#17368
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #19143621C2semidirect
3. #19132937C2semidirect
4. #19132932C2semidirect
5. #19132928C2semidirect
6. #19132923C2semidirect
7. #19132911C2semidirect
8. C2×#14582625C2semidirect
9. C2×C43×#324C2semidirect
118. C22×C4×C43M16semidirect
134. C2×C22⋊D43M16semidirect
301. C2×#324D43semidirect
340. C43#17368semidirect
456. C22×C4#10621872semidirect

Maximal subgroups

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

subgroupindex
C2×#145833802
#191436212
#191329372
#191329322
#191329282
#191329232
#191329112
C2×#145826252
C2×C43×#3242
#1736843