Finite Group Databasebeta

← #25101650

Subgroups — #25101650

Order 11008.

1538 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583446C211yesmaximal, characteristic
2C2×#14582950C211yesmaximal, characteristic, complemented
3C4×C4⋊C4×D43C211yesmaximal, characteristic, complemented
4#19135545C212yesmaximal, complemented
5#19135520C212yesmaximal, complemented
6#19134911C212yesmaximal, complemented
7#19134909C212yesmaximal, complemented
8C4×#13063245C211yesmaximal, characteristic, complemented
9C4×#13063247C211yesmaximal, characteristic, complemented
10C4×#13063246C211yesmaximal, characteristic, complemented
11C4×#102×C43C211yesmaximal, characteristic, complemented
12C22×#10621898—21no—
13#14583446—24no—
14#14583446C418yescomplemented
15C2×#13063324C2211yescharacteristic
16C2×#13063321C2211yescharacteristic
17C2×#13063311—21no—
18C2×#13063300C2211yescharacteristic
19C2×#13063298—21no—
20C2×#13063296C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×C22⋊D43—21no—
23C2×C4⋊C4×D43C2212yes—
24C2×C42×D43—21no—
25C2×C42×D43C2211yescharacteristic
26#14582950—24no—
27C2×Dic43⋊C8C2212yes—
28C2×#13063247C2212yes—
29C2×#13063246C2212yes—
30C2×#13063245C2212yes—
31C2×(C2×D43)⋊C8C2212yes—
32C2×C4×C43⋊C8C2211yescharacteristic
33C4⋊C4×Dic43C2212yes—
34C4×Dic43⋊C4—21no—
35C4×C4⋊Dic43C2211yescharacteristic
36#14582750—21no—
37#95×D43—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×D4×C43C2211yescharacteristic
42C2×#102×C43C2212yes—
43C2×C4×C8×C43C2211yescharacteristic
44C4×C4⋊C4×C43C2211yescharacteristic
45C43×#340C2212yes—
46C2×#10621898—28no—
47C2×#10621898—44no—
48C2×#10621898—44no—
49C22×Dic86—21no—
50C22×D172—21no—
51C22×D172C2311yescharacteristic
52C22×C22⋊D43—21no—
53C22×C22⋊D43—21no—
54C22×C22⋊D43—21no—
55C22×C4×D43—22no—
56C22×C4×D43—21no—
57C22×C4×D43D411yescharacteristic
58C22×C4×D43D411yescharacteristic
59C22×C4×D43C2311yescharacteristic
60C22×C43⋊C8C2312yes—
61#13063324—22no—
62#13063324C2×C414yescomplemented
63#13063321—22no—
64#13063321C2×C414yescomplemented
65#13063311—28no—
66#13063300—22no—
67#13063300C2×C414yes—
68#13063298—28no—
69#13063296—22no—
70#13063296C2×C414yes—
71C4×D172—22no—
72C4×D172C2×C414yescomplemented
73C4×C22⋊D43—28no—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×C4⋊Dic43C2312yes—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—21no—
78C4⋊C4×D43—24no—
79C4⋊C4×D43—24no—
80C2×C22⋊Dic43—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—21no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43—44no—
89C42×D43C2×C414yes—
90C42×D43D414yes—
91Dic43⋊C8—24no—
92#13063247—24no—
93#13063246—24no—
94#13063245—24no—
95(C2×D43)⋊C8—24no—
96C4×C43⋊C8—22no—
97C43⋊#95—21no—
98C43⋊#95—22no—
99C22×D4×C43C2311yescharacteristic
100C23×C4×C43—21no—
101C22×C8×C43C2312yes—
102C4×D4×C43—22no—
103C4×D4×C43C2×C414yescomplemented
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C4⋊C4×C43C2312yes—
106C2×C22⋊C4×C43—21no—
107C2×C42×C43—21no—
108C2×C42×C43C2311yescharacteristic
109#102×C43—24no—
110C4×C8×C43—22no—
111#95×C43—21no—
112C24×C43—21no—
113C23×D43—21no—
114C23×D43C2×D411yescharacteristic
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43C22×C412yes—
119C22×C4×C43—24no—
120C22×C4×C43—22no—
121C22×C4×C43—21no—
122C22×C4×C43—42no—
123C22×C4×C43—42no—
124C22×C4×C43C2×D411yescharacteristic
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—24no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—44no—
131C2×C22⋊D43—42no—
132C2×C22⋊D43—42no—
133C2×C22⋊D43—42no—
134C2×C22⋊D43—42no—
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43C2×D411yescharacteristic
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140#10621898—432no—
141C2×D172—21no—
142C2×D172—24no—
143C2×D172—22no—
144C2×D172—22no—
145C2×D172—42no—
146C2×D172—42no—
147C2×D172C22×C412yes—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—28no—
151C2×C4×D43—24no—
152C2×C4×D43—42no—
153C2×C4×D43—44no—
154C2×C4×D43—42no—
155C2×C4×D43—42no—
156C2×C4×D43—44no—
157C2×C4×D43C22⋊C414yes—
158C2×C4×D43C22⋊C414yes—
159C2×C4×D43D814yes—
160C2×C4×D43SD1614yes—
161C2×C4×D43C22×C412yes—
162C2×C4×D43C2×D412yes—
163C2×Dic86—24no—
164C2×Dic86—42no—
165C2×Dic86—42no—
166C2×C8×C43—22no—
167C2×C8×C43—22no—
168C2×C8×C43—22no—
169C4⋊C4×C43—21no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43C22×C412yes—
172C4⋊C4×C43#4114yescomplemented
173C22⋊C4×C43—24no—
174C42×C43—42no—
175C42×C43C22×C412yes—
176C42×C43C2×D412yes—
177C22⋊Dic43—24no—
178(C2×D43)⋊C4—24no—
179(C2×D43)⋊C4—24no—
180C4⋊Dic43—21no—
181C4⋊Dic43—22no—
182C4⋊Dic43C22×C412yes—
183C4⋊Dic43#4114yescomplemented
184Dic43⋊C4—28no—
185Dic43⋊C4—24no—
186C4×Dic43—42no—
187C4×Dic43—44no—
188C4×Dic43C22⋊C414yes—
189C4×Dic43C22⋊C414yes—
190C4×Dic43C22×C412yes—
191C4×Dic43C2×D412yes—
192C2×C43⋊C8—22no—
193C2×C43⋊C8—22no—
194C2×C43⋊C8—22no—
195C23×C43—22no—
196C23×C43—42no—
197C23×C43—41no—
198C23×C43—41no—
199C23×C43—42no—
200C23×C43C22×D411yescharacteristic
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—42no—
205C22×D43—41no—
206C22×D43—41no—
207C22×D43—42no—
208C22×D43C2×C22⋊C412yes—
209C22×D43C2×D812yes—
210C22×D43C2×SD1612yes—
211D4×C43—22no—
212D4×C43—22no—
213D4×C43—42no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—24no—
217C2×C4×C43—42no—
218C2×C4×C43—41no—
219C2×C4×C43—41no—
220C2×C4×C43—42no—
221C2×C4×C43—48no—
222C2×C4×C43C2×C22⋊C412yes—
223C2×C4×C43C2×C22⋊C412yes—
224C2×C4×C43C2×D812yes—
225C2×C4×C43C2×SD1612yes—
226C2×C4×C43C23×C411yescharacteristic
227C2×C4×C43C22×D411yescharacteristic
228C2×C4×C43C2×#4112yes—
229C2×C4×C43C2×#4112yes—
230C22⋊D43—48no—
231C22⋊D43—48no—
232C22⋊D43—48no—
233C2×Dic43—22no—
234C2×Dic43—22no—
235C2×Dic43—22no—
236C2×Dic43—24no—
237C2×Dic43—42no—
238C2×Dic43—41no—
239C2×Dic43—41no—
240C2×Dic43—42no—
241C2×Dic43C2×C22⋊C412yes—
242C2×Dic43C2×C22⋊C412yes—
243C2×Dic43C2×C22⋊C412yes—
244C2×Dic43C2×D812yes—
245C2×Dic43C2×SD1612yes—
246D172—22no—
247D172—22no—
248D172—48no—
249D172—42no—
250C4×D43—22no—
251C4×D43—22no—
252C4×D43—24no—
253C4×D43—44no—
254C4×D43—416no—
255C4×D43—48no—
256C4×D43#102116yescomplemented
257Dic86—48no—
258C8×C43—42no—
259C43⋊C8—42no—
260#21386—431nomaximal, Sylow
261C22×C43—42no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—82no—
265C22×C43—82no—
266C22×C43C22×C22⋊C411yescharacteristic
267C22×C43#52512yes—
268C22×C43C22×D811yescharacteristic
269C22×C43C22×SD1611yescharacteristic
270C22×C43#57512yes—
271C2×D43—24no—
272C2×D43—24no—
273C2×D43—22no—
274C2×D43—22no—
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—82no—
279C2×D43—82no—
280C2×D43C2×#10214yes—
281C4×C43—22no—
282C4×C43—44no—
283C4×C43—42no—
284C4×C43C2×#10214yes—
285C4×C43C4×#4111yescharacteristic
286C4×C43C4×#4111yescharacteristic
287C4×C43#53212yes—
288Dic43—22no—
289Dic43—22no—
290Dic43—44no—
291Dic43—42no—
292Dic43C2×#10214yes—
293C2×#532—431no—
294C2×#431—431no—
295C2×C4×C4⋊C4—431no—
296#1988—432no—
297#1982—432no—
298#1874—432no—
299#1874—432no—
300C4×#102—431no—
301C4×#102—431no—
302C4×#102—431no—
303C4×#102D4311yescharacteristic, complemented
304C2×C43—82no—
305C2×C43#229711yescharacteristic
306C2×C43C22×#10211yescharacteristic
307C2×C43#289611yescharacteristic
308C2×C43#310012yes—
309C2×C43#310312yes—
310D43—24no—
311D43—82no—
312C22×#41—861no—
313#532—438no—
314#532—864no—
315C2×C4⋊Q8—431no—
316C2×#127—431no—
317C2×#124—861no—
318C2×#121—431no—
319C2×#121—431no—
320C2×#121—861no—
321C2×C4×D4—431no—
322C2×C4×D4—861no—
323C2×C4×D4C2×D4311yescharacteristic
324C22×C4⋊C4—432no—
325C22×C42—431no—
326C22×C42—861no—
327#431—864no—
328C2×C4⋊C8—432no—
329C2×#102—432no—
330C2×#102—432no—
331C2×#102—432no—
332C2×#102C2×D4312yes—
333C2×C22⋊C8—432no—
334C2×C4×C8—431no—
335C2×C4×C8C2×D4311yescharacteristic
336C4×C4⋊C4—432no—
337C4×C4⋊C4—431no—
338C4×C4⋊C4—861no—
339C4×C4⋊C4—861no—
340C4×C4⋊C4C2×D4311yescharacteristic
341C2×#95—861no—
342#340—432no—
343#340—432no—
344#340—432no—
345#340C2×D4312yes—
346C43#2138611yescharacteristic, complemented, Sylow
347C2×#41—868no—
348C2×#41—1724no—
349C2×#41—1724no—
350C22×Q8—861no—
351C22×D4—431no—
352C22×D4—861no—
353C22×D4—861no—
354C22×D4—861no—
355C22×D4—861no—
356C22×D4C22×D4311yescharacteristic
357C23×C4—21no—
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—862no—
362C23×C4—861no—
363C22×C8—432no—
364C22×C8C22×D4312yes—
365C4⋊Q8—434no—
366C4⋊Q8—862no—
367#127—434no—
368#127—862no—
369#124—868no—
370#121—434no—
371#121—434no—
372#121—868no—
373#121—862no—
374#121—862no—
375C4×D4—22no—
376C4×D4—434no—
377C4×D4—868no—
378C4×D4—862no—
379C4×D4C4×D4314yescomplemented
380C2×C4⋊C4—432no—
381C2×C4⋊C4—431no—
382C2×C4⋊C4—864no—
383C2×C4⋊C4—862no—
384C2×C4⋊C4—861no—
385C2×C4⋊C4—864no—
386C2×C4⋊C4C22×D4311yescharacteristic
387C2×C4⋊C4C22×D4312yes—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—861no—
390C2×C22⋊C4—861no—
391C2×C22⋊C4—861no—
392C2×C42—21no—
393C2×C42—431no—
394C2×C42—431no—
395C2×C42—431no—
396C2×C42—434no—
397C2×C42—434no—
398C2×C42—862no—
399C2×C42—861no—
400C2×C42—1724no—
401C2×C42C22×D4311yescharacteristic
402C4⋊C8—864no—
403#102—24no—
404#102—864no—
405#102—864no—
406#102—864no—
407C22⋊C8—864no—
408C4×C8—22no—
409C4×C8—862no—
410#95—21no—
411#95—862no—
412#95—861no—
413C24—21no—
414C24—431no—
415C24—861no—
416#41—17232no—
417C2×Q8—864no—
418C2×Q8—1722no—
419C2×Q8—1722no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—432no—
424C2×D4—864no—
425C2×D4—864no—
426C2×D4—864no—
427C2×D4—864no—
428C2×D4—861no—
429C2×D4—862no—
430C2×D4—862no—
431C2×D4—1722no—
432C2×D4—1722no—
433C2×D4—1722no—
434C2×D4—1722no—
435C2×D4—1724no—
436C2×D4—1722no—
437C2×D4—1722no—
438C2×D4C2×C4×D4312yes—
439C22×C4—22no—
440C22×C4—21no—
441C22×C4—24no—
442C22×C4—42no—
443C22×C4—42no—
444C22×C4—431no—
445C22×C4—434no—
446C22×C4—434no—
447C22×C4—434no—
448C22×C4—431no—
449C22×C4—431no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—434no—
453C22×C4—868no—
454C22×C4—862no—
455C22×C4—862no—
456C22×C4—862no—
457C22×C4—861no—
458C22×C4—864no—
459C22×C4—1722no—
460C22×C4—1724no—
461C22×C4—1724no—
462C22×C4—1722no—
463C22×C4—1722no—
464C22×C4D4×D4311yescharacteristic
465C22×C4D4×D4311yescharacteristic
466C22×C4C23×D4311yescharacteristic
467C2×C8—22no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—862no—
471C2×C8—862no—
472C2×C8—862no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—432no—
476C4⋊C4—434no—
477C4⋊C4—864no—
478C4⋊C4—868no—
479C4⋊C4—861no—
480C4⋊C4—862no—
481C4⋊C4C2×C4×D4312yes—
482C4⋊C4#1062189814yescomplemented
483C22⋊C4—24no—
484C22⋊C4—864no—
485C22⋊C4—864no—
486C22⋊C4—864no—
487C42—42no—
488C42—434no—
489C42—434no—
490C42—432no—
491C42—432no—
492C42—1724no—
493C42—1722no—
494C42C2×C4×D4312yes—
495C42D4×D4312yes—
496C23—22no—
497C23—42no—
498C23—41no—
499C23—41no—
500C23—42no—
501C23—432no—
502C23—432no—
503C23—432no—
504C23—862no—
505C23—862no—
506C23—862no—
507C23—1722no—
508C23—1721no—
509C23—1721no—
510C23—1722no—
511C23C2×D4×D4311yescharacteristic
512Q8—1728no—
513D4—22no—
514D4—22no—
515D4—42no—
516D4—862no—
517D4—862no—
518D4—1728no—
519D4—1728no—
520D4—1728no—
521D4—1728no—
522D4—1722no—
523C2×C4—22no—
524C2×C4—22no—
525C2×C4—24no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—48no—
531C2×C4—432no—
532C2×C4—432no—
533C2×C4—432no—
534C2×C4—4316no—
535C2×C4—432no—
536C2×C4—432no—
537C2×C4—862no—
538C2×C4—862no—
539C2×C4—862no—
540C2×C4—862no—
541C2×C4—864no—
542C2×C4—862no—
543C2×C4—864no—
544C2×C4—1724no—
545C2×C4—17216no—
546C2×C4—1722no—
547C2×C4—1721no—
548C2×C4—1721no—
549C2×C4—1722no—
550C2×C4—1728no—
551C2×C4C22⋊C4×D4312yes—
552C2×C4C22⋊C4×D4312yes—
553C2×C4D8×D4312yes—
554C2×C4SD16×D4312yes—
555C2×C4C22×C4×D4311yescharacteristic
556C2×C4C2×D4×D4311yescharacteristic
557C2×C4#41×D4312yes—
558C2×C4C2×#1062189812yes—
559C8—42no—
560C8—1722no—
561C22—42no—
562C22—42no—
563C22—42no—
564C22—82no—
565C22—82no—
566C22—434no—
567C22—862no—
568C22—864no—
569C22—864no—
570C22—862no—
571C22—3442no—
572C22—3442no—
573C22—1722no—
574C22—1722no—
575C22—1722no—
576C22C2×C22⋊C4×D4311yescharacteristic
577C22#1458340812yes—
578C22C2×D8×D4311yescharacteristic
579C22C2×SD16×D4311yescharacteristic
580C22#1458369612yes—
581C4—22no—
582C4—44no—
583C4—42no—
584C4—434no—
585C4—862no—
586C4—862no—
587C4—1724no—
588C4—1722no—
589C4#102×D4314yes—
590C4#1458336711yescharacteristic
591C4C4×#1062189811yescharacteristic
592C4#1458344612yes—
593C2—82no—
594C2—864no—
595C2—3442no—
596C2#1913708111yescharacteristic
597C2C2×#102×D4311yescharacteristic
598C2#1914311011yescharacteristic
599C2#1914459312yes—
600C2#1914462412yes—
subgroupG/H
centerC22×C4D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC4×#102×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583446C2
cosocleC22×C4×C43C24
hypercenterC4×#102D43
hypocenterC43#21386
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C4×#102

Complements

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

NH ≅ G/Ntype
2. C2×#14582950C2semidirect
3. C4×C4⋊C4×D43C2semidirect
4. #19135545C2semidirect
5. #19135520C2semidirect
6. #19134911C2semidirect
7. #19134909C2semidirect
8. C4×#13063245C2semidirect
9. C4×#13063247C2semidirect
10. C4×#13063246C2semidirect
11. C4×#102×C43C2semidirect
14. #14583446C4semidirect
62. #13063324C2×C4semidirect
64. #13063321C2×C4semidirect
72. C4×D172C2×C4semidirect
103. C4×D4×C43C2×C4semidirect
172. C4⋊C4×C43#41semidirect
183. C4⋊Dic43#41semidirect
256. C4×D43#102semidirect
303. C4×#102D43semidirect
346. C43#21386semidirect
379. C4×D4C4×D43semidirect
482. C4⋊C4#10621898semidirect

Maximal subgroups

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

subgroupindex
C2×#145834462
C2×#145829502
C4×C4⋊C4×D432
#191355452
#191355202
#191349112
#191349092
C4×#130632452
C4×#130632472
C4×#130632462
C4×#102×C432
#2138643