Finite Group Databasebeta

← #25106342

Subgroups — #25106342

Order 11008.

1118 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583428C211yesmaximal, characteristic
2C2×#14582954C211yesmaximal, characteristic, complemented
3#19137000C211yesmaximal, characteristic, complemented
4#19135564C211yesmaximal, characteristic, complemented
5#19135563C211yesmaximal, characteristic, complemented
6#19135412C211yesmaximal, characteristic, complemented
7#19134914C212yesmaximal
8#19134904C212yesmaximal, complemented
9#19134608C212yesmaximal, complemented
10#19134603C212yesmaximal, complemented
11C43×#1959C211yesmaximal, characteristic, complemented
12#14583428—24no—
13#14583428C418yescomplemented
14C2×#13063318—21no—
15C2×#13063317C2211yescharacteristic
16C2×#13063307—21no—
17C2×#13063301C2211yescharacteristic
18C2×#13063296C2211yescharacteristic
19C2×Q8×Dic43C2211yescharacteristic
20C2×D4×Dic43C2211yescharacteristic
21C2×(C22⋊D43)⋊C4—21no—
22C2×#13063283C2212yes—
23C2×#13063281—21no—
24C2×C42×D43C2211yescharacteristic
25#14582954—24no—
26C2×Dic43⋊C8C2212yes—
27C2×#13063249C2212yes—
28C2×#13063246C2212yes—
29C2×(C2×D43)⋊C8C2212yes—
30C2×#13063236C2211yescharacteristic
31#14582769C2211yescharacteristic
32#14582764C2212yes—
33#14582756—21no—
34#14582756—21no—
35C4⋊C4×Dic43—21no—
36C4⋊C4×Dic43—21no—
37#14582662C2212yes—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×#124×C43C2211yescharacteristic
42C2×#103×C43C2212yes—
43C2×#102×C43C2212yes—
44C2×#97×C43C2211yescharacteristic
45C43×#384C2211yescharacteristic
46C22×C22⋊D43—21no—
47C23×Dic43—21no—
48C22×C4×D43D411yescharacteristic
49C22×C4×D43D411yescharacteristic
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063318—28no—
53#13063317—22no—
54#13063317C2×C414yes—
55#13063307—28no—
56#13063301—22no—
57#13063301C2×C414yes—
58#13063296—22no—
59#13063296C2×C414yes—
60Q8×Dic43—22no—
61Q8×Dic43C2×C414yes—
62D4×Dic43—22no—
63D4×Dic43C2×C414yes—
64(C22⋊D43)⋊C4—28no—
65#13063283—42no—
66#13063283—42no—
67#13063281—28no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2312yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×C22⋊Dic43—21no—
78C2×C22⋊Dic43—21no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—22no—
81C2×C4×Dic43—21no—
82C2×C4×Dic43—22no—
83C2×C4×Dic43D411yescharacteristic
84C2×C4×Dic43D411yescharacteristic
85C2×C4×Dic43C2311yescharacteristic
86C42×D43C2×C414yes—
87C42×D43D414yes—
88Dic43⋊C8—24no—
89#13063249—42no—
90#13063246—42no—
91(C2×D43)⋊C8—24no—
92#13063236—22no—
93C43⋊#95—22no—
94C43⋊#95—22no—
95C22×Q8×C43C2311yescharacteristic
96C22×D4×C43C2311yescharacteristic
97C22×C8×C43C2312yes—
98#124×C43—22no—
99#124×C43C2×C414yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43C2312yes—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—21no—
105C2×C42×C43C2311yescharacteristic
106#103×C43—42no—
107#102×C43—42no—
108#97×C43—22no—
109C24×C43—21no—
110C23×D43C2×D411yescharacteristic
111C2×Q8×C43—21no—
112C2×Q8×C43—22no—
113C2×Q8×C43—22no—
114C2×Q8×C43C22×C412yes—
115C2×D4×C43—21no—
116C2×D4×C43—22no—
117C2×D4×C43—22no—
118C2×D4×C43C22×C412yes—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2×D411yescharacteristic
123C22×C4×C43C2411yescharacteristic
124C2×C22⋊D43—24no—
125C2×C22⋊D43—42no—
126C2×C22⋊D43—42no—
127C22×Dic43—24no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—22no—
131C22×Dic43—42no—
132C22×Dic43—42no—
133C22×Dic43C2×D411yescharacteristic
134C22×Dic43C2×D411yescharacteristic
135C22×Dic43C2×D411yescharacteristic
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—41no—
139C2×C4×D43—41no—
140C2×C4×D43—41no—
141C2×C4×D43—41no—
142C2×C4×D43C22⋊C414yes—
143C2×C4×D43C22⋊C414yes—
144C2×C4×D43C22×C412yes—
145C2×C4×D43C2×D412yes—
146C2×C8×C43—22no—
147C2×C8×C43—22no—
148C2×C8×C43—22no—
149C4⋊C4×C43—22no—
150C4⋊C4×C43—22no—
151C4⋊C4×C43—42no—
152C4⋊C4×C43—42no—
153C22⋊C4×C43—24no—
154C22⋊C4×C43—24no—
155C42×C43C22×C412yes—
156C42×C43C2×D412yes—
157C22⋊Dic43—24no—
158C22⋊Dic43—24no—
159(C2×D43)⋊C4—24no—
160(C2×D43)⋊C4—44no—
161C4⋊Dic43—21no—
162C4⋊Dic43—21no—
163C4⋊Dic43—24no—
164C4⋊Dic43—22no—
165C4⋊Dic43—22no—
166C4⋊Dic43—42no—
167C4⋊Dic43—42no—
168C4⋊Dic43C22×C412yes—
169C4⋊Dic43C22×C412yes—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—24no—
173C4×Dic43—24no—
174C4×Dic43—44no—
175C4×Dic43C22⋊C414yes—
176C4×Dic43C22⋊C414yes—
177C4×Dic43C22×C412yes—
178C4×Dic43C2×D412yes—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—22no—
182C23×C43—22no—
183C23×C43—41no—
184C23×C43—41no—
185C23×C43—41no—
186C23×C43—41no—
187C23×C43—41no—
188C23×C43—41no—
189C23×C43C22×D411yescharacteristic
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43—21no—
194C22×D43—21no—
195C22×D43—21no—
196C22×D43C2×C22⋊C412yes—
197Q8×C43—24no—
198Q8×C43—42no—
199D4×C43—24no—
200D4×C43—42no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—22no—
206C2×C4×C43—41no—
207C2×C4×C43—41no—
208C2×C4×C43—42no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43C2×C22⋊C412yes—
212C2×C4×C43C2×C22⋊C412yes—
213C2×C4×C43C23×C411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43H(5,𝔽2)12yes—
216C2×C4×C432−1+412yes—
217C22⋊D43—48no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—48no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231C2×Dic43—42no—
232C2×Dic43—42no—
233C2×Dic43—42no—
234C2×Dic43C2×C22⋊C412yes—
235C2×Dic43C2×C22⋊C412yes—
236C2×Dic43C2×C22⋊C412yes—
237C4×D43—24no—
238C4×D43—24no—
239C4×D43—44no—
240C4×D43—44no—
241C8×C43—42no—
242C43⋊C8—42no—
243#21868—431nomaximal, Sylow
244C22×C43—42no—
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—81no—
248C22×C43—81no—
249C22×C43—81no—
250C22×C43—81no—
251C22×C43C22×C22⋊C411yescharacteristic
252C22×C43#53511yescharacteristic
253C22×C43#53611yescharacteristic
254C22×C43#57511yescharacteristic
255C22×C43#57511yescharacteristic
256C22×C43#57511yescharacteristic
257C22×C43#57511yescharacteristic
258C2×D43—22no—
259C2×D43—22no—
260C2×D43—22no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—82no—
269C4×C43#52012yes—
270C4×C43#53712yes—
271Dic43—22no—
272Dic43—22no—
273Dic43—22no—
274Dic43—42no—
275Dic43—42no—
276Dic43—82no—
277C2×#529—431no—
278C2×#432—431no—
279#2285—431no—
280#1992—431no—
281#1992—431no—
282#1959—431no—
283#1959D4311yescharacteristic, complemented
284#1875—432no—
285#1873—432no—
286#1805—432no—
287#1804—432no—
288C2×C43—82no—
289C2×C43#231111yescharacteristic
290C2×C43#289611yescharacteristic
291C2×C43#289611yescharacteristic
292C2×C43#321911yescharacteristic
293C2×C43#321911yescharacteristic
294C2×C43#324011yescharacteristic
295C2×C43#324011yescharacteristic
296D43—42no—
297#529—438no—
298#529—864no—
299C2×#126—861no—
300C2×#125—431no—
301C2×#124C2×D4311yescharacteristic
302C2×#123—861no—
303C2×C22⋊Q8—431no—
304C2×#121—431no—
305C2×C4×Q8—431no—
306C2×C4×D4—431no—
307C2×C4×D4—861no—
308C2×#117—432no—
309C2×#117—861no—
310C22×C42—431no—
311#432—864no—
312C2×C4⋊C8—432no—
313C2×#103—432no—
314C2×#103C2×D4312yes—
315C2×#102—432no—
316C2×#102C2×D4312yes—
317C2×C22⋊C8—432no—
318C2×#97—431no—
319C2×#97C2×D4311yescharacteristic
320#384—431no—
321#384C2×D4311yescharacteristic
322#382—432no—
323#380—861no—
324#380—861no—
325C4×C4⋊C4—861no—
326C4×C4⋊C4—861no—
327#340—432no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2186811yescharacteristic, complemented, Sylow
332C22×Q8C22×D4311yescharacteristic
333C22×D4—861no—
334C22×D4C22×D4311yescharacteristic
335C23×C4—431no—
336C23×C4—431no—
337C23×C4—431no—
338C23×C4—861no—
339C22×C8—432no—
340C22×C8C22×D4312yes—
341#126—868no—
342#125—434no—
343#125—862no—
344#124—22no—
345#124C4×D4314yes—
346#123—868no—
347C22⋊Q8—434no—
348C22⋊Q8—862no—
349#121—434no—
350#121—862no—
351C4×Q8—434no—
352C4×Q8—862no—
353C4×D4—434no—
354C4×D4—862no—
355C4×D4—868no—
356#117—868no—
357#117—1722no—
358#117—1722no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—431no—
362C2×C4⋊C4—431no—
363C2×C4⋊C4—432no—
364C2×C4⋊C4—861no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4C22×D4312yes—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—861no—
374C2×C22⋊C4—861no—
375C2×C22⋊C4—861no—
376C2×C22⋊C4—862no—
377C2×C42—431no—
378C2×C42—431no—
379C2×C42—431no—
380C2×C42—434no—
381C2×C42—434no—
382C2×C42—861no—
383C2×C42—862no—
384C2×C42C22×D4311yescharacteristic
385C4⋊C8—864no—
386#103—42no—
387#103—1722no—
388#102—42no—
389#102—1722no—
390C22⋊C8—864no—
391#97—22no—
392#97—862no—
393#95—862no—
394#95—862no—
395C24—21no—
396C24—431no—
397C2×Q8—21no—
398C2×Q8—22no—
399C2×Q8—22no—
400C2×Q8C2×C4×D4312yes—
401C2×D4—21no—
402C2×D4—22no—
403C2×D4—22no—
404C2×D4—864no—
405C2×D4—1722no—
406C2×D4—1722no—
407C2×D4C2×C4×D4312yes—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—431no—
411C22×C4—431no—
412C22×C4—431no—
413C22×C4—432no—
414C22×C4—432no—
415C22×C4—434no—
416C22×C4—434no—
417C22×C4—864no—
418C22×C4—862no—
419C22×C4—862no—
420C22×C4—861no—
421C22×C4—861no—
422C22×C4—862no—
423C22×C4—1721no—
424C22×C4—1721no—
425C22×C4—1721no—
426C22×C4—1721no—
427C22×C4—1722no—
428C22×C4—1722no—
429C22×C4D4×D4311yescharacteristic
430C22×C4D4×D4311yescharacteristic
431C22×C4C23×D4311yescharacteristic
432C2×C8—22no—
433C2×C8—22no—
434C2×C8—22no—
435C2×C8—862no—
436C2×C8—862no—
437C2×C8—862no—
438C4⋊C4—22no—
439C4⋊C4—22no—
440C4⋊C4—42no—
441C4⋊C4—42no—
442C4⋊C4—432no—
443C4⋊C4—432no—
444C4⋊C4—864no—
445C4⋊C4—864no—
446C4⋊C4—864no—
447C4⋊C4—864no—
448C4⋊C4—861no—
449C4⋊C4—861no—
450C4⋊C4—862no—
451C4⋊C4—862no—
452C4⋊C4—1722no—
453C4⋊C4—1722no—
454C22⋊C4—24no—
455C22⋊C4—24no—
456C22⋊C4—864no—
457C22⋊C4—864no—
458C22⋊C4—864no—
459C22⋊C4—1724no—
460C42—434no—
461C42—434no—
462C42—432no—
463C42—432no—
464C42—864no—
465C42—1724no—
466C42C2×C4×D4312yes—
467C42D4×D4312yes—
468C23—22no—
469C23—41no—
470C23—41no—
471C23—41no—
472C23—41no—
473C23—41no—
474C23—41no—
475C23—432no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—861no—
480C23—861no—
481C23—861no—
482C23C2×D4×D4311yescharacteristic
483Q8—24no—
484Q8—42no—
485D4—24no—
486D4—42no—
487D4—1728no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—42no—
497C2×C4—42no—
498C2×C4—432no—
499C2×C4—432no—
500C2×C4—432no—
501C2×C4—861no—
502C2×C4—861no—
503C2×C4—861no—
504C2×C4—861no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—864no—
508C2×C4—864no—
509C2×C4—862no—
510C2×C4—862no—
511C2×C4—1724no—
512C2×C4—1724no—
513C2×C4—1728no—
514C2×C4—1722no—
515C2×C4—1722no—
516C2×C4—1722no—
517C2×C4—1721no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4C22⋊C4×D4312yes—
522C2×C4C22⋊C4×D4312yes—
523C2×C4C22×C4×D4311yescharacteristic
524C2×C4C2×D4×D4311yescharacteristic
525C2×C4#1306337012yes—
526C2×C4#1306337212yes—
527C8—42no—
528C8—1722no—
529C22—42no—
530C22—42no—
531C22—42no—
532C22—81no—
533C22—81no—
534C22—81no—
535C22—81no—
536C22—862no—
537C22—862no—
538C22—862no—
539C22—1721no—
540C22—1721no—
541C22—1721no—
542C22—1721no—
543C22C2×C22⋊C4×D4311yescharacteristic
544C22#1458346211yescharacteristic
545C22#1458346911yescharacteristic
546C22#1458369511yescharacteristic
547C22#1458369511yescharacteristic
548C22#1458369811yescharacteristic
549C22#1458369811yescharacteristic
550C4—22no—
551C4—22no—
552C4—42no—
553C4—82no—
554C4—862no—
555C4—862no—
556C4—862no—
557C4—3442no—
558C4—1722no—
559C4—1722no—
560C4#1458337812yes—
561C4#1458347812yes—
562C2—82no—
563C2—1722no—
564C2#1913718511yescharacteristic
565C2#1914311111yescharacteristic
566C2#1914311111yescharacteristic
567C2#1914562711yescharacteristic
568C2#1914562911yescharacteristic
569C2#1914583011yescharacteristic
570C2#1914583211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1959C2
socleC23×C43C22×D4
prime radicalC2×#13063296C22
cosocleC22×C4×C43C24
hypercenter#1959D43
hypocenterC43#21868
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1959

Complements

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

NH ≅ G/Ntype
2. C2×#14582954C2semidirect
3. #19137000C2semidirect
4. #19135564C2semidirect
5. #19135563C2semidirect
6. #19135412C2semidirect
8. #19134904C2semidirect
9. #19134608C2semidirect
10. #19134603C2semidirect
11. C43×#1959C2semidirect
13. #14583428C4semidirect
283. #1959D43semidirect
331. C43#21868semidirect

Maximal subgroups

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

subgroupindex
C2×#145834282
C2×#145829542
#191370002
#191355642
#191355632
#191354122
#191349142
#191349042
#191346082
#191346032
C43×#19592
#2186843