Finite Group Databasebeta

← #25106481

Subgroups — #25106481

Order 11008.

1162 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583453C211yesmaximal, characteristic
2C2×C4⋊C8×D43C211yesmaximal, characteristic
3#19137000C211yesmaximal, characteristic
4#19135541C212yesmaximal, complemented
5#19135516C212yesmaximal, complemented
6#19135017C212yesmaximal
7#19135015C212yesmaximal
8#19134601C211yesmaximal, characteristic, complemented
9#19134600C211yesmaximal, characteristic, complemented
10#19134597C211yesmaximal, characteristic, complemented
11C43×#1803C211yesmaximal, characteristic, complemented
12C22×C8×D43C2212yes—
13#14583453—24no—
14#14583453C418yescomplemented
15C2×#13063324C2211yescharacteristic
16C2×#13063323C2211yescharacteristic
17C2×#13063315—21no—
18C2×#13063305C2211yescharacteristic
19C2×#13063303—21no—
20C2×#13063301C2211yescharacteristic
21C2×C4×Dic86—21no—
22C2×C4×Dic86C2211yescharacteristic
23C2×#13063283—21no—
24C2×#13063282—21no—
25C2×C42×D43C2211yescharacteristic
26C2×C4⋊(C43⋊C8)C2211yescharacteristic
27C2×Dic43⋊C8C2212yes—
28C4⋊C8×D43—24no—
29C2×#13063250C2212yes—
30C2×#13063249C2212yes—
31C2×#13063248C2212yes—
32#14582769C2211yescharacteristic
33#14582764—21no—
34#14582756—21no—
35#14582756C2212yes—
36C4⋊C4×Dic43—21no—
37C4⋊C4×Dic43C2212yes—
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—
52C2×C8×D43—24no—
53C2×C8×D43—42no—
54C2×C8×D43—42no—
55#13063324—22no—
56#13063324C2×C414yes—
57#13063323—22no—
58#13063323C2×C414yes—
59#13063315—28no—
60#13063305—22no—
61#13063305C2×C414yes—
62#13063303—28no—
63#13063301—22no—
64#13063301C2×C414yes—
65C4×Dic86—22no—
66C4×Dic86—28no—
67C4×Dic86C2×C414yes—
68#13063283—44no—
69#13063282—28no—
70C2×C4⋊Dic43—21no—
71C2×C4⋊Dic43—21no—
72C2×C4⋊Dic43—21no—
73C2×C4⋊Dic43C2312yes—
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—21no—
80C2×(C2×D43)⋊C4—21no—
81C2×(C2×D43)⋊C4—21no—
82C2×(C2×D43)⋊C4—22no—
83C2×C4×Dic43—21no—
84C2×C4×Dic43—22no—
85C2×C4×Dic43D411yescharacteristic
86C2×C4×Dic43D411yescharacteristic
87C2×C4×Dic43C2311yescharacteristic
88C42×D43C2×C414yes—
89C42×D43D414yes—
90C4⋊(C43⋊C8)—22no—
91Dic43⋊C8—24no—
92#13063250—42no—
93#13063249—42no—
94#13063248—42no—
95C43⋊#95—22no—
96C43⋊#95—22no—
97C22×Q8×C43C2311yescharacteristic
98C22×C8×C43C2312yes—
99C4×Q8×C43—22no—
100C4×Q8×C43C2×C414yes—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43C2312yes—
105C2×C4⋊C4×C43C2311yescharacteristic
106C2×C42×C43—21no—
107C2×C42×C43C2311yescharacteristic
108C4⋊C8×C43—22no—
109#103×C43—42no—
110C23×D43C2×D411yescharacteristic
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—21no—
115C2×Q8×C43—21no—
116C2×Q8×C43C22×C412yes—
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—22no—
120C22×C4×C43C2×D411yescharacteristic
121C22×C4×C43C2×D411yescharacteristic
122C22×C4×C43C2411yescharacteristic
123C22×Dic43—21no—
124C22×Dic43—21no—
125C22×Dic43—22no—
126C22×Dic43C2×D411yescharacteristic
127C22×Dic43C2×D411yescharacteristic
128C22×Dic43C2×D411yescharacteristic
129C2×C4×D43—21no—
130C2×C4×D43—21no—
131C2×C4×D43—21no—
132C2×C4×D43—21no—
133C2×C4×D43—41no—
134C2×C4×D43—41no—
135C2×C4×D43C22⋊C414yes—
136C2×C4×D43C22⋊C414yes—
137C2×C4×D43SD1614yes—
138C2×C4×D43Q1614yes—
139C2×C4×D43C22×C412yes—
140C2×C4×D43C2×D412yes—
141C2×Dic86—21no—
142C2×Dic86—21no—
143C2×Dic86—21no—
144C2×Dic86—21no—
145C2×Dic86—21no—
146C2×Dic86—24no—
147C2×Dic86—42no—
148C2×Dic86—42no—
149C2×Dic86C22×C412yes—
150C2×C8×C43—22no—
151C2×C8×C43—22no—
152C2×C8×C43—22no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—21no—
155C4⋊C4×C43—22no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43—42no—
158C4⋊C4×C43—42no—
159C4⋊C4×C43C22×C412yes—
160C42×C43—24no—
161C42×C43C22×C412yes—
162C42×C43C2×D412yes—
163(C2×D43)⋊C4—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—44no—
166C4⋊Dic43—21no—
167C4⋊Dic43—24no—
168C4⋊Dic43—22no—
169C4⋊Dic43—22no—
170C4⋊Dic43—42no—
171C4⋊Dic43—42no—
172C4⋊Dic43C22×C412yes—
173Dic43⋊C4—24no—
174Dic43⋊C4—24no—
175Dic43⋊C4—24no—
176Dic43⋊C4—24no—
177Dic43⋊C4—24no—
178C4×Dic43—24no—
179C4×Dic43—44no—
180C4×Dic43C22⋊C414yes—
181C4×Dic43C22⋊C414yes—
182C4×Dic43C22×C412yes—
183C4×Dic43C2×D412yes—
184C2×C43⋊C8—22no—
185C2×C43⋊C8—22no—
186C2×C43⋊C8—22no—
187C8×D43—48no—
188C23×C43C22×D411yescharacteristic
189C22×D43—21no—
190C22×D43—21no—
191C22×D43—21no—
192C22×D43—21no—
193C22×D43C2×C22⋊C412yes—
194C22×D43C2×SD1612yes—
195C22×D43C2×Q1612yes—
196Q8×C43—22no—
197Q8×C43—22no—
198Q8×C43—41no—
199Q8×C43—41no—
200C2×C4×C43—21no—
201C2×C4×C43—21no—
202C2×C4×C43—22no—
203C2×C4×C43—22no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
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×C43C2×SD1612yes—
214C2×C4×C43C2×Q1612yes—
215C2×C4×C43C23×C411yescharacteristic
216C2×C4×C43C22×D411yescharacteristic
217C2×C4×C43H(5,𝔽2)11yescharacteristic
218C2×C4×C43H(5,𝔽2)11yescharacteristic
219C2×C4×C432−1+411yescharacteristic
220C2×C4×C432−1+411yescharacteristic
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—
237C2×Dic43C2×SD1612yes—
238C2×Dic43C2×Q1612yes—
239C4×D43—22no—
240C4×D43—22no—
241C4×D43—22no—
242C4×D43—22no—
243C4×D43—44no—
244C4×D43#103116yescomplemented
245Dic86—22no—
246Dic86—22no—
247Dic86—48no—
248Dic86—41no—
249Dic86—41no—
250C8×C43—42no—
251C43⋊C8—42no—
252#21885—431nomaximal, Sylow
253C22×C43C22×C22⋊C411yescharacteristic
254C22×C43#53711yescharacteristic
255C22×C43#53711yescharacteristic
256C22×C43C22×SD1611yescharacteristic
257C22×C43C22×Q1611yescharacteristic
258C22×C43#57511yescharacteristic
259C22×C43#57511yescharacteristic
260C2×D43—22no—
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
264C2×D43—22no—
265C2×D43—22no—
266C2×D43C2×#10314yes—
267C4×C43—22no—
268C4×C43—42no—
269C4×C43—42no—
270C4×C43—82no—
271C4×C43C2×#10314yes—
272C4×C43#52011yescharacteristic
273C4×C43#52011yescharacteristic
274C4×C43#53511yescharacteristic
275C4×C43#53611yescharacteristic
276Dic43—22no—
277Dic43—22no—
278Dic43—42no—
279Dic43—42no—
280Dic43—82no—
281Dic43C2×#10314yes—
282C2×#533—431no—
283C22×C4⋊C8—431no—
284#2285—431no—
285#1987—432no—
286#1981—432no—
287#1892—432no—
288#1892—432no—
289#1803—431no—
290#1803—431no—
291#1803—431no—
292#1803D4311yescharacteristic, complemented
293C2×C43#231111yescharacteristic
294C2×C43C22×#10311yescharacteristic
295C2×C43#289611yescharacteristic
296C2×C43#324611yescharacteristic
297C2×C43#324611yescharacteristic
298C2×C43#324911yescharacteristic
299C2×C43#324911yescharacteristic
300D43—24no—
301C23×C8—432no—
302#533—438no—
303#533—864no—
304C2×C4⋊Q8—431no—
305C2×C4⋊Q8—431no—
306C2×#125—861no—
307C2×C22⋊Q8—431no—
308C2×C22⋊Q8—431no—
309C2×C22⋊Q8—861no—
310C2×C4×Q8—431no—
311C2×C4×Q8—861no—
312C2×C4×Q8C2×D4311yescharacteristic
313C2×#117—861no—
314C2×#117—861no—
315C22×C42—431no—
316C2×C4⋊C8—432no—
317C2×C4⋊C8—431no—
318C2×C4⋊C8—864no—
319C2×C4⋊C8C2×D4311yescharacteristic
320C2×#103—432no—
321C2×#103—432no—
322C2×#103—432no—
323C2×#103C2×D4312yes—
324#384—431no—
325#384C2×D4311yescharacteristic
326#382—861no—
327#380—432no—
328#380—861no—
329C4×C4⋊C4—432no—
330C4×C4⋊C4—861no—
331#340—432no—
332#340—432no—
333#340—432no—
334#340C2×D4312yes—
335C43#2188511yescharacteristic, complemented, Sylow
336C22×Q8—431no—
337C22×Q8—861no—
338C22×Q8C22×D4311yescharacteristic
339C23×C4—431no—
340C23×C4—431no—
341C23×C4—431no—
342C22×C8—432no—
343C22×C8—864no—
344C22×C8—1722no—
345C22×C8—1722no—
346C22×C8C22×D4312yes—
347C4⋊Q8—434no—
348C4⋊Q8—434no—
349C4⋊Q8—862no—
350C4⋊Q8—862no—
351#125—868no—
352C22⋊Q8—434no—
353C22⋊Q8—434no—
354C22⋊Q8—862no—
355C22⋊Q8—868no—
356C22⋊Q8—862no—
357C4×Q8—22no—
358C4×Q8—434no—
359C4×Q8—868no—
360C4×Q8—862no—
361C4×Q8C4×D4314yes—
362#117—868no—
363#117—1724no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—431no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—861no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4C22×D4312yes—
378C2×C4⋊C4C22×D4311yescharacteristic
379C2×C22⋊C4—861no—
380C2×C22⋊C4—861no—
381C2×C22⋊C4—862no—
382C2×C42—21no—
383C2×C42—431no—
384C2×C42—431no—
385C2×C42—431no—
386C2×C42—434no—
387C2×C42—434no—
388C2×C42—861no—
389C2×C42—862no—
390C2×C42C22×D4311yescharacteristic
391C4⋊C8—22no—
392C4⋊C8—864no—
393C4⋊C8—862no—
394#103—42no—
395#103—1722no—
396#103—1722no—
397#103—1722no—
398#95—862no—
399#95—862no—
400C24—431no—
401C2×Q8—21no—
402C2×Q8—21no—
403C2×Q8—21no—
404C2×Q8—21no—
405C2×Q8—21no—
406C2×Q8—432no—
407C2×Q8—864no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×Q8—861no—
413C2×Q8—1722no—
414C2×Q8—1722no—
415C2×Q8C2×C4×D4312yes—
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—22no—
419C22×C4—431no—
420C22×C4—434no—
421C22×C4—434no—
422C22×C4—434no—
423C22×C4—431no—
424C22×C4—431no—
425C22×C4—432no—
426C22×C4—432no—
427C22×C4—434no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—862no—
435C22×C4—1721no—
436C22×C4—1721no—
437C22×C4D4×D4311yescharacteristic
438C22×C4D4×D4311yescharacteristic
439C22×C4C23×D4311yescharacteristic
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—862no—
446C2×C8—1728no—
447C4⋊C4—24no—
448C4⋊C4—21no—
449C4⋊C4—22no—
450C4⋊C4—22no—
451C4⋊C4—42no—
452C4⋊C4—42no—
453C4⋊C4—432no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4—864no—
457C4⋊C4—864no—
458C4⋊C4—864no—
459C4⋊C4—864no—
460C4⋊C4—861no—
461C4⋊C4—862no—
462C4⋊C4—862no—
463C4⋊C4—1722no—
464C4⋊C4—1722no—
465C4⋊C4C2×C4×D4312yes—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C22⋊C4—1724no—
469C42—24no—
470C42—434no—
471C42—434no—
472C42—432no—
473C42—432no—
474C42—864no—
475C42—1724no—
476C42C2×C4×D4312yes—
477C42D4×D4312yes—
478C23—432no—
479C23—432no—
480C23—432no—
481C23—861no—
482C23—861no—
483C23—861no—
484C23—861no—
485C23C2×D4×D4311yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—41no—
489Q8—41no—
490Q8—862no—
491Q8—862no—
492Q8—1728no—
493Q8—1721no—
494Q8—1721no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—432no—
507C2×C4—432no—
508C2×C4—432no—
509C2×C4—4316no—
510C2×C4—432no—
511C2×C4—432no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—862no—
517C2×C4—862no—
518C2×C4—862no—
519C2×C4—862no—
520C2×C4—862no—
521C2×C4—862no—
522C2×C4—1724no—
523C2×C4—1722no—
524C2×C4—1722no—
525C2×C4—1722no—
526C2×C4—1721no—
527C2×C4—1721no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4C22⋊C4×D4312yes—
531C2×C4C22⋊C4×D4312yes—
532C2×C4SD16×D4312yes—
533C2×C4Q16×D4312yes—
534C2×C4C22×C4×D4311yescharacteristic
535C2×C4C2×D4×D4311yescharacteristic
536C2×C4#1306337011yescharacteristic
537C2×C4#1306337111yescharacteristic
538C2×C4#1306337211yescharacteristic
539C2×C4#1306337311yescharacteristic
540C8—42no—
541C8—1722no—
542C22—434no—
543C22—862no—
544C22—862no—
545C22—862no—
546C22—862no—
547C22—862no—
548C22—862no—
549C22C2×C22⋊C4×D4311yescharacteristic
550C22#1458347811yescharacteristic
551C22#1458347911yescharacteristic
552C22C2×SD16×D4311yescharacteristic
553C22C2×Q16×D4311yescharacteristic
554C22#1458369511yescharacteristic
555C22#1458369811yescharacteristic
556C4—22no—
557C4—42no—
558C4—42no—
559C4—82no—
560C4—434no—
561C4—862no—
562C4—862no—
563C4—3442no—
564C4—1722no—
565C4—1722no—
566C4#103×D4314yes—
567C4#1458337911yescharacteristic
568C4#1458338011yescharacteristic
569C4#1458346511yescharacteristic
570C4#1458347211yescharacteristic
571C2—864no—
572C2#1913718411yescharacteristic
573C2C2×#103×D4311yescharacteristic
574C2#1914311111yescharacteristic
575C2#1914590911yescharacteristic
576C2#1914591011yescharacteristic
577C2#1914593811yescharacteristic
578C2#1914593911yescharacteristic
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#21885
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. #19135541C2semidirect
5. #19135516C2semidirect
8. #19134601C2semidirect
9. #19134600C2semidirect
10. #19134597C2semidirect
11. C43×#1803C2semidirect
14. #14583453C4semidirect
244. C4×D43#103semidirect
292. #1803D43semidirect
335. C43#21885semidirect

Maximal subgroups

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

subgroupindex
C2×#145834532
C2×C4⋊C8×D432
#191370002
#191355412
#191355162
#191350172
#191350152
#191346012
#191346002
#191345972
C43×#18032
#2188543