Finite Group Databasebeta

← #25149962

Subgroups — #25149962

Order 11008.

1126 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583590C211yesmaximal, characteristic
2C2×#14583267C211yesmaximal, characteristic, complemented
3#19139549C211yesmaximal, characteristic
4#19135602C212yesmaximal, complemented
5#19135602C212yesmaximal, complemented
6#19135550C211yesmaximal, characteristic, complemented
7#19135392C211yesmaximal, characteristic
8#19134904C212yesmaximal, complemented
9#19134899C212yesmaximal, complemented
10#19134425C211yesmaximal, characteristic, complemented
11C2×C43×#462C211yesmaximal, characteristic, complemented
12#14583590—24no—
13#14583590—24no—
14C2×#13063319—21no—
15C2×#13063317C2211yescharacteristic
16C2×#13063315—21no—
17C2×#13063310—21no—
18C2×#13063301C2211yescharacteristic
19C2×#13063301C2211yescharacteristic
20C2×#13063301C2212yes—
21C2×#13063301C2212yes—
22C2×C4×D172C2211yescharacteristic
23C2×#13063283C2211yescharacteristic
24C2×#13063282—21no—
25C2×C4⋊C4×D43C2211yescharacteristic
26#14583267—24no—
27C2×#13063249C2212yes—
28C2×#13063249C2212yes—
29C2×#13063249C2212yes—
30C2×(C2×D43)⋊C8C2212yes—
31C2×(C2×D43)⋊C8C2212yes—
32C2×#13063236C2211yescharacteristic
33#14582834—21no—
34#14582834—21no—
35#14582800—21no—
36#14582768—21no—
37C4×C4⋊Dic43C2211yescharacteristic
38#14582662C2212yes—
39#14582662C2212yes—
40#14582661C2212yes—
41C22×Q16×C43C2212yes—
42C2×C4⋊Q8×C43C2211yescharacteristic
43C2×C4×Q8×C43C2211yescharacteristic
44C43×#462—24no—
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×#103×C43C2212yes—
47C22×D172D411yescharacteristic
48C22×C4×D43—21no—
49C22×C4×D43C2311yescharacteristic
50C22×C4×D43C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52#13063319—28no—
53#13063317—22no—
54#13063317D414yes—
55#13063315—28no—
56#13063310—28no—
57#13063301—22no—
58#13063301—22no—
59#13063301—22no—
60#13063301—22no—
61#13063301—24no—
62#13063301—24no—
63#13063301—42no—
64#13063301—42no—
65C4×D172—22no—
66C4×D172—22no—
67#13063283—22no—
68#13063283—22no—
69#13063282—28no—
70C2×C4⋊Dic43D411yescharacteristic
71C2×C4⋊Dic43C2311yescharacteristic
72C2×C4⋊Dic43C2311yescharacteristic
73C2×C4⋊Dic43C2312yes—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—21no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4—22no—
80C2×Dic43⋊C4—22no—
81C4⋊C4×D43—22no—
82C4⋊C4×D43—22no—
83C2×(C2×D43)⋊C4—21no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—22no—
88C2×(C2×D43)⋊C4D411yescharacteristic
89C2×(C2×D43)⋊C4D411yescharacteristic
90C2×C4×Dic43—21no—
91C2×C4×Dic43—21no—
92#13063249—24no—
93#13063249—24no—
94#13063249—24no—
95(C2×D43)⋊C8—42no—
96(C2×D43)⋊C8—42no—
97#13063236—22no—
98C43⋊#95—21no—
99C22×Q8×C43C2312yes—
100C22×Q8×C43C2311yescharacteristic
101C2×Q16×C43—24no—
102C2×Q16×C43—42no—
103C2×Q16×C43—42no—
104C22×C8×C43C2312yes—
105C4⋊Q8×C43—22no—
106C4⋊Q8×C43—22no—
107C4×Q8×C43—22no—
108C4×Q8×C43D414yes—
109C2×C4⋊C4×C43—21no—
110C2×C4⋊C4×C43—21no—
111C2×C4⋊C4×C43—21no—
112C2×C4⋊C4×C43C2311yescharacteristic
113C2×C42×C43—21no—
114C2×C42×C43C2311yescharacteristic
115C4⋊C8×C43—22no—
116#103×C43—24no—
117C23×D43C2×D411yescharacteristic
118C23×D43C2×D411yescharacteristic
119C2×Q8×C43—21no—
120C2×Q8×C43—22no—
121C2×Q8×C43—22no—
122C2×Q8×C43—22no—
123C2×Q8×C43—22no—
124C2×Q8×C43—22no—
125C2×Q8×C43—22no—
126C2×Q8×C43—22no—
127C2×Q8×C43—22no—
128C2×Q8×C43C2×D412yes—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—22no—
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2411yescharacteristic
135C22×Dic43—22no—
136C22×Dic43—21no—
137C22×Dic43—21no—
138C22×Dic43C2×D411yescharacteristic
139C22×Dic43C2×D411yescharacteristic
140C2×D172—22no—
141C2×D172—22no—
142C2×D172—41no—
143C2×C4×D43—24no—
144C2×C4×D43—21no—
145C2×C4×D43—21no—
146C2×C4×D43—21no—
147C2×C4×D43—21no—
148C2×C4×D43—22no—
149C2×C4×D43—22no—
150C2×C4×D43—22no—
151C2×C4×D43—22no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154Q16×C43—48no—
155C2×C8×C43—22no—
156C2×C8×C43—22no—
157C2×C8×C43—22no—
158C4⋊C4×C43—24no—
159C4⋊C4×C43—21no—
160C4⋊C4×C43—42no—
161C4⋊C4×C43—42no—
162C4⋊C4×C43C2×D412yes—
163C42×C43—24no—
164C42×C43C2×D412yes—
165C42×C43C2×D412yes—
166(C2×D43)⋊C4—24no—
167(C2×D43)⋊C4—24no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—22no—
170(C2×D43)⋊C4—22no—
171(C2×D43)⋊C4—44no—
172(C2×D43)⋊C4—44no—
173C4⋊Dic43—22no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—22no—
177C4⋊Dic43C2×D412yes—
178C4⋊Dic43C2×D412yes—
179C4⋊Dic43#4114yes—
180Dic43⋊C4—24no—
181Dic43⋊C4—24no—
182Dic43⋊C4—24no—
183Dic43⋊C4—24no—
184Dic43⋊C4—24no—
185Dic43⋊C4—44no—
186Dic43⋊C4—44no—
187C4×Dic43—24no—
188C4×Dic43—42no—
189C2×C43⋊C8—22no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C23×C43C22×D411yescharacteristic
193C22×D43—21no—
194C22×D43—22no—
195C22×D43—21no—
196C22×D43—22no—
197C22×D43—21no—
198C22×D43—22no—
199C22×D43—21no—
200C22×D43—21no—
201C22×D43—22no—
202C22×D43#13712yes—
203Q8×C43—22no—
204Q8×C43—22no—
205Q8×C43—42no—
206Q8×C43—42no—
207Q8×C43—42no—
208Q8×C43—42no—
209Q8×C43—42no—
210C2×C4×C43—21no—
211C2×C4×C43—21no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43#12012yes—
222C2×C4×C43#12012yes—
223C2×C4×C43C22×D411yescharacteristic
224C2×C4×C43C22×D411yescharacteristic
225C2×C4×C43C2×#4112yes—
226C2×C4×C43H(5,𝔽2)12yes—
227C2×Dic43—21no—
228C2×Dic43—22no—
229C2×Dic43—21no—
230C2×Dic43—22no—
231C2×Dic43—24no—
232C2×Dic43—22no—
233C2×Dic43—22no—
234C2×Dic43—41no—
235C2×Dic43—42no—
236C2×Dic43—41no—
237C2×Dic43—42no—
238C2×Dic43—42no—
239D172—44no—
240C4×D43—48no—
241C4×D43—41no—
242C4×D43—41no—
243C4×D43—41no—
244C4×D43—41no—
245C4×D43—42no—
246C4×D43—42no—
247C8×C43—42no—
248C43⋊C8—42no—
249#25584—431nomaximal, Sylow
250C22×C43C2×#12011yescharacteristic
251C22×C43#54612yes—
252C22×C43C2×#13711yescharacteristic
253C22×C43#57511yescharacteristic
254C22×C43#57812yes—
255C2×D43—22no—
256C2×D43—24no—
257C2×D43—41no—
258C2×D43—41no—
259C2×D43—42no—
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—42no—
264C2×D43—42no—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—42no—
268C4×C43—42no—
269C4×C43—82no—
270C4×C43#53211yescharacteristic
271C4×C43#53511yescharacteristic
272C4×C43#55012yes—
273Dic43—41no—
274Dic43—41no—
275Dic43—42no—
276Dic43—42no—
277Dic43—44no—
278C2×#552—431no—
279C2×#491—431no—
280C2×#462D4311yescharacteristic, complemented
281#2542—431no—
282#2001—432no—
283#2001—432no—
284#1989—431no—
285#1955—431no—
286#1873—432no—
287#1872—432no—
288#1763—431no—
289C2×C43#243111yescharacteristic
290C2×C43#300711yescharacteristic
291C2×C43#301111yescharacteristic
292C2×C43#331212yes—
293C2×C43#331512yes—
294D43—42no—
295D43—81no—
296C22×Q16C2×D4312yes—
297#552—864no—
298#552—864no—
299C2×C4⋊Q8C2×D4311yescharacteristic
300C2×#126—861no—
301C2×#125—431no—
302C2×#125—861no—
303C2×#123—861no—
304C2×C22⋊Q8—431no—
305C2×C22⋊Q8—431no—
306C2×C22⋊Q8—432no—
307C2×C22⋊Q8—432no—
308C2×C4×Q8C2×D4311yescharacteristic
309C2×C4×D4—431no—
310C2×#117—431no—
311C2×#117—861no—
312C22×C4⋊C4—431no—
313#491—864no—
314#462—24no—
315C2×C4⋊C8C2×D4311yescharacteristic
316C2×#103—432no—
317C2×#103—432no—
318C2×#103—432no—
319C2×#103C2×D4312yes—
320C2×C22⋊C8—432no—
321C2×C22⋊C8—432no—
322C2×#97—431no—
323#399—861no—
324#399—861no—
325#390—861no—
326#384—861no—
327C4×C4⋊C4—431no—
328#340—432no—
329#340—432no—
330#340—432no—
331C43#2558411yescharacteristic, complemented, Sylow
332C22×Q8C22×D4312yes—
333C22×Q8C22×D4311yescharacteristic
334C22×D4—431no—
335C23×C4—431no—
336C23×C4—431no—
337C23×C4—861no—
338C2×Q16—24no—
339C2×Q16—42no—
340C2×Q16—42no—
341C22×C8—432no—
342C22×C8C22×D4312yes—
343C4⋊Q8—22no—
344C4⋊Q8—22no—
345#126—868no—
346#125—434no—
347#125—868no—
348#125—862no—
349#123—868no—
350C22⋊Q8—862no—
351C22⋊Q8—862no—
352C22⋊Q8—862no—
353C22⋊Q8—862no—
354C22⋊Q8—864no—
355C22⋊Q8—864no—
356C22⋊Q8—1722no—
357C22⋊Q8—1722no—
358C4×Q8—22no—
359C4×Q8C22⋊D4314yes—
360C4×D4—862no—
361C4×D4—862no—
362#117—868no—
363#117—862no—
364#117—862no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—431no—
369C2×C4⋊C4—431no—
370C2×C4⋊C4—432no—
371C2×C4⋊C4—431no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—861no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4—862no—
380C2×C4⋊C4—862no—
381C2×C4⋊C4C22×D4311yescharacteristic
382C2×C22⋊C4—431no—
383C2×C22⋊C4—431no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—862no—
388C2×C22⋊C4—862no—
389C2×C42—21no—
390C2×C42—861no—
391C2×C42—861no—
392C2×C42C22×D4311yescharacteristic
393C4⋊C8—22no—
394#103—24no—
395#103—864no—
396#103—864no—
397#103—864no—
398C22⋊C8—1722no—
399C22⋊C8—1722no—
400#97—862no—
401#95—861no—
402C24—431no—
403C24—431no—
404C2×Q8—21no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8C2×C22⋊D4312yes—
414C2×D4—862no—
415C2×D4—862no—
416C2×D4—1721no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—431no—
421C22×C4—431no—
422C22×C4—864no—
423C22×C4—862no—
424C22×C4—861no—
425C22×C4—861no—
426C22×C4—861no—
427C22×C4—861no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—862no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—1722no—
435C22×C4—1722no—
436C22×C4D4×D4311yescharacteristic
437C22×C4D4×D4311yescharacteristic
438C22×C4C23×D4311yescharacteristic
439Q16—48no—
440C2×C8—22no—
441C2×C8—22no—
442C2×C8—22no—
443C2×C8—862no—
444C2×C8—862no—
445C2×C8—862no—
446C4⋊C4—24no—
447C4⋊C4—21no—
448C4⋊C4—42no—
449C4⋊C4—42no—
450C4⋊C4—432no—
451C4⋊C4—432no—
452C4⋊C4—434no—
453C4⋊C4—864no—
454C4⋊C4—864no—
455C4⋊C4—864no—
456C4⋊C4—862no—
457C4⋊C4—864no—
458C4⋊C4—864no—
459C4⋊C4—861no—
460C4⋊C4—861no—
461C4⋊C4—862no—
462C4⋊C4—1724no—
463C4⋊C4—1724no—
464C4⋊C4C2×C22⋊D4312yes—
465C22⋊C4—864no—
466C22⋊C4—864no—
467C22⋊C4—864no—
468C22⋊C4—862no—
469C22⋊C4—862no—
470C22⋊C4—1724no—
471C22⋊C4—1724no—
472C42—24no—
473C42—864no—
474C42—1722no—
475C42D4×D4312yes—
476C42C2×C22⋊D4312yes—
477C23—432no—
478C23—861no—
479C23—861no—
480C23—862no—
481C23—862no—
482C23—861no—
483C23—861no—
484C23—861no—
485C23—862no—
486C23—862no—
487C23C2×D4×D4311yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—42no—
491Q8—42no—
492Q8—42no—
493Q8—42no—
494Q8—42no—
495D4—1724no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—861no—
508C2×C4—862no—
509C2×C4—862no—
510C2×C4—861no—
511C2×C4—864no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—1728no—
515C2×C4—1721no—
516C2×C4—1722no—
517C2×C4—1721no—
518C2×C4—1722no—
519C2×C4—1722no—
520C2×C4—1722no—
521C2×C4—1722no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1721no—
526C2×C4#1306329312yes—
527C2×C4#1306329312yes—
528C2×C4C2×D4×D4311yescharacteristic
529C2×C4C22×C22⋊D4311yescharacteristic
530C2×C4#41×D4312yes—
531C2×C4#1306337012yes—
532C8—42no—
533C8—1722no—
534C22—864no—
535C22—862no—
536C22—1722no—
537C22—1721no—
538C22—1721no—
539C22—1722no—
540C22—1721no—
541C22—1721no—
542C22—1722no—
543C22—1721no—
544C22C2×#1306329311yescharacteristic
545C22#1458354612yes—
546C22#137×D4311yescharacteristic
547C22#1458369811yescharacteristic
548C22#1458371212yes—
549C4—22no—
550C4—22no—
551C4—42no—
552C4—42no—
553C4—82no—
554C4—1721no—
555C4—1721no—
556C4—1722no—
557C4—1724no—
558C4—1722no—
559C4#1458344511yescharacteristic
560C4#1458346611yescharacteristic
561C4#1458356712yes—
562C2—3441no—
563C2—1722no—
564C2#1913821511yescharacteristic
565C2#1914385111yescharacteristic
566C2#1914388611yescharacteristic
567C2#1914665312yes—
568C2#1914669812yes—
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#462C2
socleC23×C43C22×D4
prime radicalC22×D172D4
hypercenterC2×#462D43
hypocenterC43#25584
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
2. C2×#14583267C2semidirect
4. #19135602C2semidirect
5. #19135602C2semidirect
6. #19135550C2semidirect
8. #19134904C2semidirect
9. #19134899C2semidirect
10. #19134425C2semidirect
11. C2×C43×#462C2semidirect
280. C2×#462D43semidirect
331. C43#25584semidirect

Maximal subgroups

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

subgroupindex
C2×#145835902
C2×#145832672
#191395492
#191356022
#191355502
#191353922
#191349042
#191348992
#191344252
C2×C43×#4622
#2558443