Finite Group Databasebeta

← #25130528

Subgroups — #25130528

Order 11008.

1350 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583181C211yesmaximal, characteristic, complemented
2C2×C4×#10621883C211yesmaximal, characteristic, complemented
3#19139517C211yesmaximal, characteristic, complemented
4#19135781C212yesmaximal, complemented
5#19135598C212yesmaximal, complemented
6#19135557C211yesmaximal, characteristic, complemented
7#19135390C211yesmaximal, characteristic, complemented
8#19134902C212yesmaximal, complemented
9#19134788C212yesmaximal, complemented
10#19134595C211yesmaximal, characteristic, complemented
11C2×C43×#547C211yesmaximal, characteristic
12C22×#10621883C2211yescharacteristic
13C2×#13063304C2212yes—
14C2×C4×Dic86C2211yescharacteristic
15#14583181—24no—
16C4×#10621883—24no—
17C2×#13063256C2212yes—
18C2×#13063256C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic
20C2×#13063248C2212yes—
21C2×#13063248C2211yescharacteristic
22C2×#13063246C2211yescharacteristic
23C2×#13063246C2212yes—
24C2×C22⋊(C43⋊C8)C2212yes—
25C2×C22⋊(C43⋊C8)C2212yes—
26C2×C4×C43⋊C8C2211yescharacteristic
27#14582822—22no—
28#14582802—21no—
29#14582795—21no—
30#14582769C2211yescharacteristic
31#14582759C2212yes—
32#14582661C2212yes—
33#14582661C2212yes—
34#14582661C2212yes—
35C22×#41×C43—21no—
36C43×#547—24no—
37C43×#547—24no—
38C2×C4⋊Q8×C43C2211yescharacteristic
39C2×#123×C43—22no—
40C2×C22⋊Q8×C43—21no—
41C2×#121×C43C2212yes—
42C2×C4×D4×C43C2211yescharacteristic
43C2×C4×D4×C43C2211yescharacteristic
44C22×C4⋊C4×C43C2212yes—
45C22×Dic86C2311yescharacteristic
46C2×#10621883—22no—
47C2×#10621883—22no—
48C2×#10621883—22no—
49C22×C43⋊C8C2311yescharacteristic
50C22×C43⋊C8C2312yes—
51C22×C43⋊C8C2311yescharacteristic
52#13063304—24no—
53#13063304—42no—
54C4×Dic86—22no—
55C4×Dic86—22no—
56C2×C4⋊Dic43—21no—
57C2×C4⋊Dic43—21no—
58C2×C4⋊Dic43C2311yescharacteristic
59C2×C4⋊Dic43C2312yes—
60C2×Dic43⋊C4—22no—
61C2×Dic43⋊C4—21no—
62C2×C22⋊Dic43—22no—
63C2×C22⋊Dic43—22no—
64C2×C4×Dic43—21no—
65#13063256—24no—
66#13063256—22no—
67C4⋊(C43⋊C8)—22no—
68#13063248—24no—
69#13063248—22no—
70#13063246—22no—
71#13063246—42no—
72C22⋊(C43⋊C8)—24no—
73C22⋊(C43⋊C8)—42no—
74C4×C43⋊C8—22no—
75C43⋊#95—22no—
76C2×#41×C43—28no—
77C2×#41×C43—44no—
78C2×#41×C43—44no—
79C22×Q8×C43—21no—
80C22×D4×C43—22no—
81C22×D4×C43D411yescharacteristic
82C22×D4×C43C2311yescharacteristic
83C23×C4×C43—22no—
84C23×C4×C43—21no—
85C23×C4×C43C2312yes—
86C4⋊Q8×C43—22no—
87C4⋊Q8×C43D414yes—
88#123×C43—216no—
89C22⋊Q8×C43—28no—
90#121×C43—24no—
91#121×C43—24no—
92C4×D4×C43—22no—
93C4×D4×C43—22no—
94C4×D4×C43—22no—
95C4×D4×C43D414yes—
96C2×C4⋊C4×C43—22no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—24no—
99C2×C4⋊C4×C43—24no—
100C2×C4⋊C4×C43D411yescharacteristic
101C2×C4⋊C4×C43C2311yescharacteristic
102C2×C4⋊C4×C43C2312yes—
103C2×C22⋊C4×C43—21no—
104C2×C22⋊C4×C43—22no—
105C2×C22⋊C4×C43D412yes—
106C2×C42×C43C2311yescharacteristic
107C24×C43—21no—
108C24×C43C2×D412yes—
109#41×C43—432no—
110C2×Q8×C43—24no—
111C2×Q8×C43—42no—
112C2×Q8×C43—42no—
113C2×D4×C43—28no—
114C2×D4×C43—22no—
115C2×D4×C43—22no—
116C2×D4×C43—21no—
117C2×D4×C43—21no—
118C2×D4×C43—21no—
119C2×D4×C43—21no—
120C2×D4×C43—21no—
121C2×D4×C43—44no—
122C2×D4×C43—44no—
123C2×D4×C43SD1614yescomplemented
124C2×D4×C43C2×D412yes—
125C22×C4×C43—28no—
126C22×C4×C43—24no—
127C22×C4×C43—22no—
128C22×C4×C43—22no—
129C22×C4×C43—22no—
130C22×C4×C43—22no—
131C22×C4×C43—22no—
132C22×C4×C43—22no—
133C22×C4×C43—21no—
134C22×C4×C43—22no—
135C22×C4×C43—44no—
136C22×C4×C43—42no—
137C22×C4×C43—42no—
138C22×C4×C43—44no—
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D411yescharacteristic
142C22×C4×C43C2411yescharacteristic
143C22×Dic43—21no—
144C22×Dic43—21no—
145C22×Dic43—22no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86#4112yescomplemented
152C4⋊C4×C43—28no—
153C4⋊C4×C43—24no—
154C4⋊C4×C43—22no—
155C4⋊C4×C43—21no—
156C4⋊C4×C43—22no—
157C4⋊C4×C43C2×D412yes—
158C4⋊C4×C43C2×D414yes—
159C22⋊C4×C43—28no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C42×C43C2×D412yes—
163C42×C43C2×D412yes—
164C22⋊Dic43—44no—
165C22⋊Dic43—82no—
166#10621883—28no—
167C4⋊Dic43—21no—
168C4⋊Dic43—21no—
169C4⋊Dic43—22no—
170C4⋊Dic43—22no—
171C4⋊Dic43—42no—
172C4⋊Dic43—81no—
173Dic43⋊C4—44no—
174Dic43⋊C4—42no—
175C4×Dic43—42no—
176C2×C43⋊C8—21no—
177C2×C43⋊C8—21no—
178C2×C43⋊C8—21no—
179C2×C43⋊C8—22no—
180C2×C43⋊C8—22no—
181C2×C43⋊C8—21no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—21no—
184C2×C43⋊C8#4112yescomplemented
185C23×C43—22no—
186C23×C43—22no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—41no—
193C23×C43—41no—
194C23×C43—41no—
195C23×C43—41no—
196C23×C43—41no—
197C23×C43—41no—
198C23×C43C2×SD1614yes—
199C23×C43C22×D411yescharacteristic
200Q8×C43—48no—
201D4×C43—22no—
202D4×C43—22no—
203D4×C43—28no—
204D4×C43—416no—
205D4×C43—41no—
206D4×C43—41no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—22no—
210C2×C4×C43—22no—
211C2×C4×C43—24no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—416no—
215C2×C4×C43—41no—
216C2×C4×C43—42no—
217C2×C4×C43—41no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—42no—
223C2×C4×C43—48no—
224C2×C4×C43#12012yes—
225C2×C4×C43#12012yes—
226C2×C4×C43C2×SD1612yes—
227C2×C4×C43AGL(1,ℤ/8)12yes—
228C2×C4×C43C22×D411yescharacteristic
229C2×C4×C43C22×D411yescharacteristic
230C2×C4×C43C2×#4111yescharacteristic
231C2×C4×C43C2×#4111yescharacteristic
232C2×C4×C43H(5,𝔽2)11yescharacteristic
233C2×C4×C432−1+411yescharacteristic
234C2×Dic43—22no—
235C2×Dic43—41no—
236C2×Dic43—41no—
237C2×Dic43—41no—
238C2×Dic43—42no—
239C2×Dic43—42no—
240C2×Dic43—42no—
241C2×Dic43—41no—
242C2×Dic43—41no—
243Dic86—22no—
244Dic86—22no—
245Dic86—41no—
246Dic86—41no—
247C43⋊C8—22no—
248C43⋊C8—41no—
249C43⋊C8—42no—
250#24120—431nomaximal, Sylow
251C22×C43—24no—
252C22×C43—24no—
253C22×C43—24no—
254C22×C43—42no—
255C22×C43—42no—
256C22×C43—42no—
257C22×C43—42no—
258C22×C43—42no—
259C22×C43—42no—
260C22×C43—42no—
261C22×C43—81no—
262C22×C43—81no—
263C22×C43—81no—
264C22×C43—81no—
265C22×C43C2×#12011yescharacteristic
266C22×C43#54611yescharacteristic
267C22×C43#54711yescharacteristic
268C22×C43C22×SD1611yescharacteristic
269C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
270C22×C43#57711yescharacteristic
271C22×C43#57811yescharacteristic
272C4×C43—22no—
273C4×C43—42no—
274C4×C43—42no—
275C4×C43—44no—
276C4×C43#45014yes—
277C4×C43#52511yescharacteristic
278C4×C43#53711yescharacteristic
279C4×C43#54811yescharacteristic
280C4×C43#55011yescharacteristic
281Dic43—42no—
282Dic43—82no—
283Dic43—81no—
284C2×#547D4311yescharacteristic
285C2×#475—431no—
286C2×C4×SD16—431no—
287#2538—431no—
288#2034—432no—
289#2000—432no—
290#1990—431no—
291#1954—431no—
292#1872—432no—
293#1853—432no—
294#1802—431no—
295C2×C43—44no—
296C2×C43—82no—
297C2×C43#240711yescharacteristic
298C2×C43C2×#45011yescharacteristic
299C2×C43#301311yescharacteristic
300C2×C43#329811yescharacteristic
301C2×C43#333211yescharacteristic
302C2×C43#333511yescharacteristic
303C2×C43#335311yescharacteristic
304C22×#41—21no—
305C22×SD16—431no—
306#547—24no—
307#547—24no—
308C2×C4⋊Q8C2×D4311yescharacteristic
309C2×#123—22no—
310C2×C22⋊Q8—21no—
311C2×C22⋊Q8—432no—
312C2×#121C2×D4312yes—
313C2×C4×Q8—431no—
314C2×C4×D4C2×D4311yescharacteristic
315C2×C4×D4C2×D4311yescharacteristic
316C22×C4⋊C4C2×D4312yes—
317#475—864no—
318C4×SD16—864no—
319C2×#106—432no—
320C2×#106—431no—
321C2×C4⋊C8—431no—
322C2×#103—432no—
323C2×#103—431no—
324C2×#102—431no—
325C2×#102—432no—
326C2×C22⋊C8—432no—
327C2×C22⋊C8—432no—
328C2×C4×C8—431no—
329#396—862no—
330#390—861no—
331#389—861no—
332#384—431no—
333#380—432no—
334#340—432no—
335#340—432no—
336#340—432no—
337C43#2412011yescharacteristic, complemented, Sylow
338C2×#41—28no—
339C2×#41—44no—
340C2×#41—44no—
341C22×Q8—21no—
342C22×Q8—431no—
343C22×D4—22no—
344C22×D4C22⋊D4311yescharacteristic
345C22×D4C22×D4311yescharacteristic
346C23×C4—22no—
347C23×C4—21no—
348C23×C4C22×D4312yes—
349C2×SD16—862no—
350C2×SD16—862no—
351C2×SD16—862no—
352C22×C8—431no—
353C22×C8—431no—
354C22×C8—432no—
355C4⋊Q8—22no—
356C4⋊Q8C22⋊D4314yes—
357#123—216no—
358C22⋊Q8—28no—
359C22⋊Q8—864no—
360C22⋊Q8—1722no—
361#121—24no—
362#121—24no—
363C4×Q8—862no—
364C4×Q8—862no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—22no—
368C4×D4C22⋊D4314yes—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—24no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—432no—
375C2×C4⋊C4—861no—
376C2×C4⋊C4—861no—
377C2×C4⋊C4—862no—
378C2×C4⋊C4—861no—
379C2×C4⋊C4C22⋊D4311yescharacteristic
380C2×C4⋊C4C22×D4311yescharacteristic
381C2×C4⋊C4C22×D4312yes—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—862no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4C22⋊D4312yes—
387C2×C42—861no—
388C2×C42C22×D4311yescharacteristic
389#106—862no—
390#106—864no—
391C4⋊C8—862no—
392#103—862no—
393#103—864no—
394#102—862no—
395#102—1722no—
396C22⋊C8—864no—
397C22⋊C8—1722no—
398C4×C8—862no—
399#95—862no—
400C24—21no—
401C24C2×C22⋊D4312yes—
402#41—432no—
403C2×Q8—24no—
404C2×Q8—42no—
405C2×Q8—42no—
406C2×Q8—432no—
407C2×Q8—861no—
408C2×Q8—861no—
409C2×Q8—861no—
410C2×Q8—861no—
411C2×Q8—861no—
412C2×D4—28no—
413C2×D4—22no—
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4—44no—
421C2×D4—44no—
422C2×D4#1062188314yescomplemented
423C2×D4C2×C22⋊D4312yes—
424C22×C4—28no—
425C22×C4—21no—
426C22×C4—22no—
427C22×C4—24no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—22no—
434C22×C4—44no—
435C22×C4—44no—
436C22×C4—42no—
437C22×C4—42no—
438C22×C4—861no—
439C22×C4—861no—
440C22×C4—862no—
441C22×C4C2×C22⋊D4312yes—
442C22×C4C2×C22⋊D4311yescharacteristic
443C22×C4C2×C22⋊D4311yescharacteristic
444C22×C4C23×D4311yescharacteristic
445SD16—868no—
446C2×C8—432no—
447C2×C8—861no—
448C2×C8—861no—
449C2×C8—861no—
450C2×C8—862no—
451C2×C8—862no—
452C2×C8—861no—
453C2×C8—862no—
454C2×C8—861no—
455C4⋊C4—28no—
456C4⋊C4—24no—
457C4⋊C4—22no—
458C4⋊C4—21no—
459C4⋊C4—22no—
460C4⋊C4—861no—
461C4⋊C4—861no—
462C4⋊C4—862no—
463C4⋊C4—862no—
464C4⋊C4—3441no—
465C4⋊C4—1724no—
466C4⋊C4—1722no—
467C4⋊C4—1722no—
468C4⋊C4C2×C22⋊D4312yes—
469C4⋊C4C2×C22⋊D4314yes—
470C22⋊C4—28no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—3442no—
474C22⋊C4—1724no—
475C42—1722no—
476C42C2×C22⋊D4312yes—
477C42C2×C22⋊D4312yes—
478C23—22no—
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23—41no—
491C23C2×#1062188314yes—
492C23C22×C22⋊D4311yescharacteristic
493Q8—48no—
494Q8—862no—
495Q8—862no—
496Q8—1721no—
497Q8—1721no—
498D4—28no—
499D4—22no—
500D4—22no—
501D4—416no—
502D4—41no—
503D4—41no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—22no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—416no—
512C2×C4—41no—
513C2×C4—42no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—48no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—862no—
522C2×C4—1721no—
523C2×C4—1722no—
524C2×C4—1721no—
525C2×C4—1722no—
526C2×C4—1721no—
527C2×C4—1722no—
528C2×C4—1721no—
529C2×C4—1721no—
530C2×C4#1306329412yes—
531C2×C4#1306329412yes—
532C2×C4C2×#1062188312yes—
533C2×C4#1306335112yes—
534C2×C4C22×C22⋊D4311yescharacteristic
535C2×C4C22×C22⋊D4311yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C2×C4#41×D4311yescharacteristic
538C2×C4#1306337111yescharacteristic
539C2×C4#1306337211yescharacteristic
540C8—862no—
541C8—1722no—
542C8—1721no—
543C22—24no—
544C22—24no—
545C22—24no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—42no—
550C22—42no—
551C22—42no—
552C22—42no—
553C22—81no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22C2×#1306329411yescharacteristic
558C22#1458353711yescharacteristic
559C22#1458354811yescharacteristic
560C22C22×#1062188311yescharacteristic
561C22C2×#1306335111yescharacteristic
562C22#1458370711yescharacteristic
563C22#1458371411yescharacteristic
564C4—22no—
565C4—42no—
566C4—44no—
567C4—42no—
568C4—3442no—
569C4—3441no—
570C4—1722no—
571C4#1458305014yes—
572C4#1458340611yescharacteristic
573C4#1458347711yescharacteristic
574C4#1458355611yescharacteristic
575C4#1458356811yescharacteristic
576C2—44no—
577C2—82no—
578C2#1913793411yescharacteristic
579C2C2×#1458305011yescharacteristic
580C2#1914391011yescharacteristic
581C2#1914645411yescharacteristic
582C2#1914691611yescharacteristic
583C2#1914695211yescharacteristic
584C2#1914717911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#547C2
socleC23×C43C22×D4
hypercenterC2×#547D43
hypocenterC43#24120
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#14583181C2semidirect
2. C2×C4×#10621883C2semidirect
3. #19139517C2semidirect
4. #19135781C2semidirect
5. #19135598C2semidirect
6. #19135557C2semidirect
7. #19135390C2semidirect
8. #19134902C2semidirect
9. #19134788C2semidirect
10. #19134595C2semidirect
123. C2×D4×C43SD16semidirect
151. C2×Dic86#41semidirect
184. C2×C43⋊C8#41semidirect
337. C43#24120semidirect
422. C2×D4#10621883semidirect

Maximal subgroups

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

subgroupindex
C2×#145831812
C2×C4×#106218832
#191395172
#191357812
#191355982
#191355572
#191353902
#191349022
#191347882
#191345952
C2×C43×#5472
#2412043