Finite Group Databasebeta

← #25106356

Subgroups — #25106356

Order 11008.

1086 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2C2×#14582955C211yesmaximal, characteristic
3#19137000C211yesmaximal, characteristic
4#19135566C212yesmaximal, complemented
5#19135413C212yesmaximal, complemented
6#19134906C212yesmaximal
7#19134904C212yesmaximal
8#19134601C211yesmaximal, characteristic, complemented
9#19134600C211yesmaximal, characteristic, complemented
10#19134597C211yesmaximal, characteristic, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12#14583453—24no—
13#14583453C418yescomplemented
14C2×#13063324C2211yescharacteristic
15C2×#13063323C2211yescharacteristic
16C2×#13063315—21no—
17C2×#13063305C2211yescharacteristic
18C2×#13063303—21no—
19C2×#13063301C2211yescharacteristic
20C2×C4×Dic86—21no—
21C2×C4×Dic86C2211yescharacteristic
22C2×#13063283C2212yes—
23C2×#13063282—21no—
24C2×C42×D43C2211yescharacteristic
25#14582955—24no—
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×#13063250C2212yes—
28C2×#13063249C2212yes—
29C2×#13063248C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×#13063235C2212yes—
32#14582769C2211yescharacteristic
33#14582764C2212yes—
34#14582756—21no—
35#14582756—21no—
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43—21no—
38#14582662C2212yes—
39#14582661C2212yes—
40#14582661C2212yes—
41C2×C4×Q8×C43C2211yescharacteristic
42C2×C4⋊C8×C43C2211yescharacteristic
43C2×#103×C43C2212yes—
44C43×#384C2211yescharacteristic
45C43×#340C2212yes—
46C22×Dic86—21no—
47C22×Dic86C2311yescharacteristic
48C22×C4×D43D411yescharacteristic
49C22×C4×D43D411yescharacteristic
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063324—22no—
53#13063324C2×C414yes—
54#13063323—22no—
55#13063323C2×C414yes—
56#13063315—28no—
57#13063305—22no—
58#13063305C2×C414yes—
59#13063303—28no—
60#13063301—22no—
61#13063301C2×C414yes—
62C4×Dic86—22no—
63C4×Dic86—28no—
64C4×Dic86C2×C414yes—
65#13063283—42no—
66#13063283—42no—
67#13063282—28no—
68C2×C4⋊Dic43—21no—
69C2×C4⋊Dic43—21no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43C2312yes—
72C2×C4⋊Dic43C2311yescharacteristic
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×(C2×D43)⋊C4—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—
88C4⋊(C43⋊C8)—22no—
89#13063250—42no—
90#13063249—42no—
91#13063248—42no—
92(C2×D43)⋊C8—24no—
93#13063235—24no—
94C43⋊#95—22no—
95C43⋊#95—22no—
96C22×Q8×C43C2311yescharacteristic
97C22×C8×C43C2312yes—
98C4×Q8×C43—22no—
99C4×Q8×C43C2×C414yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2311yescharacteristic
105C2×C42×C43—21no—
106C2×C42×C43C2311yescharacteristic
107C4⋊C8×C43—22no—
108#103×C43—42no—
109C23×D43C2×D411yescharacteristic
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43C22×C412yes—
116C22×C4×C43—21no—
117C22×C4×C43—21no—
118C22×C4×C43—22no—
119C22×C4×C43C2×D411yescharacteristic
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2411yescharacteristic
122C22×Dic43—21no—
123C22×Dic43—21no—
124C22×Dic43—22no—
125C22×Dic43C2×D411yescharacteristic
126C22×Dic43C2×D411yescharacteristic
127C22×Dic43C2×D411yescharacteristic
128C2×C4×D43—22no—
129C2×C4×D43—22no—
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—21no—
134C2×C4×D43—41no—
135C2×C4×D43—41no—
136C2×C4×D43C22⋊C414yes—
137C2×C4×D43C22⋊C414yes—
138C2×C4×D43C22×C412yes—
139C2×C4×D43C2×D412yes—
140C2×Dic86—21no—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—24no—
146C2×Dic86—42no—
147C2×Dic86—42no—
148C2×Dic86C22×C412yes—
149C2×C8×C43—22no—
150C2×C8×C43—22no—
151C2×C8×C43—22no—
152C4⋊C4×C43—24no—
153C4⋊C4×C43—21no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—42no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43C22×C412yes—
159C42×C43—24no—
160C42×C43C22×C412yes—
161C42×C43C2×D412yes—
162(C2×D43)⋊C4—24no—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—44no—
165C4⋊Dic43—21no—
166C4⋊Dic43—24no—
167C4⋊Dic43—22no—
168C4⋊Dic43—22no—
169C4⋊Dic43—42no—
170C4⋊Dic43—42no—
171C4⋊Dic43C22×C412yes—
172Dic43⋊C4—24no—
173Dic43⋊C4—24no—
174Dic43⋊C4—24no—
175Dic43⋊C4—24no—
176Dic43⋊C4—24no—
177C4×Dic43—24no—
178C4×Dic43—44no—
179C4×Dic43C22⋊C414yes—
180C4×Dic43C22⋊C414yes—
181C4×Dic43C22×C412yes—
182C4×Dic43C2×D412yes—
183C2×C43⋊C8—22no—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C23×C43C22×D411yescharacteristic
187C22×D43—21no—
188C22×D43—21no—
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43C2×C22⋊C412yes—
194Q8×C43—22no—
195Q8×C43—22no—
196Q8×C43—41no—
197Q8×C43—41no—
198C2×C4×C43—21no—
199C2×C4×C43—21no—
200C2×C4×C43—22no—
201C2×C4×C43—22no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43C2×C22⋊C412yes—
210C2×C4×C43C2×C22⋊C412yes—
211C2×C4×C43#13712yes—
212C2×C4×C43#13712yes—
213C2×C4×C43C23×C411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43H(5,𝔽2)11yescharacteristic
216C2×C4×C43H(5,𝔽2)11yescharacteristic
217C2×C4×C432−1+411yescharacteristic
218C2×C4×C432−1+411yescharacteristic
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43—21no—
222C2×Dic43—21no—
223C2×Dic43—21no—
224C2×Dic43—21no—
225C2×Dic43—22no—
226C2×Dic43—22no—
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—22no—
238C4×D43—22no—
239C4×D43—22no—
240C4×D43—22no—
241C4×D43—28no—
242C4×D43—44no—
243Dic86—22no—
244Dic86—22no—
245Dic86—48no—
246Dic86—41no—
247Dic86—41no—
248C8×C43—42no—
249C43⋊C8—42no—
250#21870—431nomaximal, Sylow
251C22×C43C22×C22⋊C411yescharacteristic
252C22×C43#53511yescharacteristic
253C22×C43#53611yescharacteristic
254C22×C43C2×#13711yescharacteristic
255C22×C43C2×#13711yescharacteristic
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—42no—
267C4×C43—42no—
268C4×C43—82no—
269C4×C43#41914yes—
270C4×C43#52011yescharacteristic
271C4×C43#52011yescharacteristic
272C4×C43#53711yescharacteristic
273C4×C43#53711yescharacteristic
274Dic43—22no—
275Dic43—22no—
276Dic43—22no—
277Dic43—42no—
278Dic43—42no—
279Dic43—82no—
280C2×#533—431no—
281C2×#432—431no—
282#2285—431no—
283#1993—432no—
284#1960—432no—
285#1873—432no—
286#1873—432no—
287#1803—431no—
288#1803—431no—
289#1803—431no—
290#1803D4311yescharacteristic, complemented
291C2×C43#231111yescharacteristic
292C2×C43C2×#41911yescharacteristic
293C2×C43#289611yescharacteristic
294C2×C43#321611yescharacteristic
295C2×C43#321611yescharacteristic
296C2×C43#323711yescharacteristic
297C2×C43#323711yescharacteristic
298D43—42no—
299#533—438no—
300#533—864no—
301C2×C4⋊Q8—431no—
302C2×C4⋊Q8—431no—
303C2×#125—861no—
304C2×C22⋊Q8—431no—
305C2×C22⋊Q8—431no—
306C2×C22⋊Q8—861no—
307C2×C4×Q8—431no—
308C2×C4×Q8—861no—
309C2×C4×Q8C2×D4311yescharacteristic
310C2×#117—432no—
311C2×#117—861no—
312C22×C42—431no—
313#432—864no—
314C2×C4⋊C8—431no—
315C2×C4⋊C8C2×D4311yescharacteristic
316C2×#103—432no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#103C2×D4312yes—
320C2×C22⋊C8—432no—
321C2×#97—432no—
322#384—431no—
323#384C2×D4311yescharacteristic
324#382—432no—
325#380—861no—
326#380—861no—
327C4×C4⋊C4—861no—
328C4×C4⋊C4—861no—
329#340—432no—
330#340—432no—
331#340—432no—
332#340C2×D4312yes—
333C43#2187011yescharacteristic, complemented, Sylow
334C22×Q8—431no—
335C22×Q8—861no—
336C22×Q8C22×D4311yescharacteristic
337C23×C4—431no—
338C23×C4—431no—
339C23×C4—431no—
340C22×C8—432no—
341C22×C8C22×D4312yes—
342C4⋊Q8—434no—
343C4⋊Q8—434no—
344C4⋊Q8—862no—
345C4⋊Q8—862no—
346#125—868no—
347C22⋊Q8—434no—
348C22⋊Q8—434no—
349C22⋊Q8—862no—
350C22⋊Q8—868no—
351C22⋊Q8—862no—
352C4×Q8—22no—
353C4×Q8—434no—
354C4×Q8—868no—
355C4×Q8—862no—
356C4×Q8C4×D4314yes—
357#117—868no—
358#117—1722no—
359#117—1722no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—431no—
364C2×C4⋊C4—432no—
365C2×C4⋊C4—861no—
366C2×C4⋊C4—861no—
367C2×C4⋊C4—861no—
368C2×C4⋊C4—861no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4C22×D4312yes—
374C2×C4⋊C4C22×D4311yescharacteristic
375C2×C22⋊C4—861no—
376C2×C22⋊C4—861no—
377C2×C22⋊C4—862no—
378C2×C42—21no—
379C2×C42—431no—
380C2×C42—431no—
381C2×C42—431no—
382C2×C42—434no—
383C2×C42—434no—
384C2×C42—861no—
385C2×C42—862no—
386C2×C42C22×D4311yescharacteristic
387C4⋊C8—22no—
388C4⋊C8—862no—
389#103—42no—
390#103—1722no—
391#103—1722no—
392#103—1722no—
393C22⋊C8—864no—
394#97—864no—
395#95—862no—
396#95—862no—
397C24—431no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—432no—
404C2×Q8—864no—
405C2×Q8—861no—
406C2×Q8—861no—
407C2×Q8—861no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—1722no—
411C2×Q8—1722no—
412C2×Q8C2×C4×D4312yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—22no—
416C22×C4—431no—
417C22×C4—431no—
418C22×C4—431no—
419C22×C4—434no—
420C22×C4—432no—
421C22×C4—432no—
422C22×C4—434no—
423C22×C4—862no—
424C22×C4—862no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—862no—
432C22×C4—1721no—
433C22×C4—1721no—
434C22×C4D4×D4311yescharacteristic
435C22×C4D4×D4311yescharacteristic
436C22×C4C23×D4311yescharacteristic
437C2×C8—22no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—862no—
441C2×C8—862no—
442C2×C8—862no—
443C4⋊C4—24no—
444C4⋊C4—21no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—432no—
450C4⋊C4—864no—
451C4⋊C4—864no—
452C4⋊C4—864no—
453C4⋊C4—864no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4—861no—
457C4⋊C4—862no—
458C4⋊C4—862no—
459C4⋊C4—1722no—
460C4⋊C4—1722no—
461C4⋊C4C2×C4×D4312yes—
462C22⋊C4—864no—
463C22⋊C4—864no—
464C22⋊C4—1724no—
465C42—24no—
466C42—434no—
467C42—434no—
468C42—432no—
469C42—432no—
470C42—864no—
471C42—1724no—
472C42C2×C4×D4312yes—
473C42D4×D4312yes—
474C23—432no—
475C23—861no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23—861no—
480C23—861no—
481C23C2×D4×D4311yescharacteristic
482Q8—22no—
483Q8—22no—
484Q8—41no—
485Q8—41no—
486Q8—862no—
487Q8—862no—
488Q8—1728no—
489Q8—1721no—
490Q8—1721no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—432no—
503C2×C4—432no—
504C2×C4—432no—
505C2×C4—861no—
506C2×C4—861no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—862no—
512C2×C4—862no—
513C2×C4—868no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—1724no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4C22⋊C4×D4312yes—
527C2×C4C22⋊C4×D4312yes—
528C2×C4#1306335412yes—
529C2×C4#1306335712yes—
530C2×C4C22×C4×D4311yescharacteristic
531C2×C4C2×D4×D4311yescharacteristic
532C2×C4#1306337011yescharacteristic
533C2×C4#1306337111yescharacteristic
534C2×C4#1306337211yescharacteristic
535C2×C4#1306337311yescharacteristic
536C8—42no—
537C8—1722no—
538C22—862no—
539C22—862no—
540C22—862no—
541C22—1721no—
542C22—1721no—
543C22—1721no—
544C22—1721no—
545C22C2×C22⋊C4×D4311yescharacteristic
546C22#1458346511yescharacteristic
547C22#1458347211yescharacteristic
548C22C2×#1306335411yescharacteristic
549C22C2×#1306335711yescharacteristic
550C22#1458369511yescharacteristic
551C22#1458369811yescharacteristic
552C4—22no—
553C4—42no—
554C4—42no—
555C4—82no—
556C4—862no—
557C4—862no—
558C4—862no—
559C4—3442no—
560C4—1722no—
561C4—1722no—
562C4#1458290614yes—
563C4#1458337911yescharacteristic
564C4#1458338011yescharacteristic
565C4#1458347811yescharacteristic
566C4#1458347911yescharacteristic
567C2—1722no—
568C2#1913718411yescharacteristic
569C2C2×#1458290611yescharacteristic
570C2#1914311111yescharacteristic
571C2#1914560411yescharacteristic
572C2#1914560511yescharacteristic
573C2#1914580711yescharacteristic
574C2#1914580811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1803C2
socleC23×C43C22×D4
prime radicalC23×D43C2×D4
cosocleC22×C4×C43C24
hypercenter#1803D43
hypocenterC43#21870
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1803

Complements

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

NH ≅ G/Ntype
4. #19135566C2semidirect
5. #19135413C2semidirect
8. #19134601C2semidirect
9. #19134600C2semidirect
10. #19134597C2semidirect
11. C43×#1803C2semidirect
13. #14583453C4semidirect
290. #1803D43semidirect
333. C43#21870semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×#145829552
#191370002
#191355662
#191354132
#191349062
#191349042
#191346012
#191346002
#191345972
C43×#18032
#2187043