Finite Group Databasebeta

← #25130537

Subgroups — #25130537

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×#14583552C211yesmaximal, characteristic
2C2×#14583181C211yesmaximal, characteristic, complemented
3C2×C4×#10621873C211yesmaximal, characteristic, complemented
4#19139518C211yesmaximal, characteristic, complemented
5#19135787C212yesmaximal, complemented
6#19135601C212yesmaximal, complemented
7#19135389C211yesmaximal, characteristic, complemented
8#19134901C212yesmaximal, complemented
9#19134789C212yesmaximal, complemented
10#19134592C211yesmaximal, characteristic, complemented
11C43×#1990C211yesmaximal, characteristic, complemented
12C22×#10621902—21no—
13C22×#10621873C2211yescharacteristic
14#14583552—24no—
15#14583552—24no—
16C2×#13063310—22no—
17C2×#13063305C2212yes—
18C2×#13063301—21no—
19C2×#13063300C2212yes—
20C2×C4×Dic86C2211yescharacteristic
21C2×C4×D172C2211yescharacteristic
22C2×C4×D172C2211yescharacteristic
23C2×C4⋊C4×D43C2212yes—
24#14583181—24no—
25C4×#10621873—24no—
26C2×#13063257C2211yescharacteristic
27C2×#13063256C2212yes—
28C2×C4⋊(C43⋊C8)C2211yescharacteristic
29C2×#13063250C2211yescharacteristic
30C2×#13063248C2212yes—
31C2×#13063247C2211yescharacteristic
32C2×#13063245C2212yes—
33C2×(C2×D43)⋊C8C2212yes—
34C2×(C2×D43)⋊C8C2212yes—
35#14582821—22no—
36#14582800—21no—
37#14582798—21no—
38#14582756C2212yes—
39#14582661C2212yes—
40C2×C4⋊Q8×C43C2211yescharacteristic
41C2×C4×C8×C43C2211yescharacteristic
42C43×#384C2211yescharacteristic
43C43×#340C2212yes—
44C43×#340C2212yes—
45C2×#10621902—28no—
46C2×#10621902—44no—
47C2×#10621902—44no—
48C22×Dic86C2311yescharacteristic
49C22×D172—22no—
50C22×D172D411yescharacteristic
51C22×D172C2311yescharacteristic
52C22×C4×D43—22no—
53C22×C4×D43—21no—
54C22×C4×D43C2312yes—
55C2×#10621873—22no—
56C2×#10621873—22no—
57C2×#10621873—22no—
58C22×C43⋊C8C2312yes—
59#13063310—216no—
60#13063305—24no—
61#13063305—42no—
62#13063301—28no—
63#13063300—24no—
64#13063300—24no—
65C4×Dic86—22no—
66C4×Dic86—22no—
67C4×D172—22no—
68C4×D172—22no—
69C4×D172—22no—
70C4×D172D414yes—
71C2×C4⋊Dic43—22no—
72C2×C4⋊Dic43D411yescharacteristic
73C2×C4⋊Dic43C2311yescharacteristic
74C2×C4⋊Dic43C2311yescharacteristic
75C2×Dic43⋊C4—22no—
76C2×Dic43⋊C4—21no—
77C4⋊C4×D43—24no—
78C4⋊C4×D43—24no—
79C2×(C2×D43)⋊C4—21no—
80C2×(C2×D43)⋊C4—22no—
81C2×(C2×D43)⋊C4—22no—
82C2×(C2×D43)⋊C4—22no—
83C2×(C2×D43)⋊C4D412yes—
84C2×C4×Dic43—21no—
85#13063257—22no—
86#13063256—24no—
87C4⋊(C43⋊C8)—22no—
88#13063250—22no—
89#13063248—24no—
90#13063247—22no—
91#13063245—42no—
92(C2×D43)⋊C8—24no—
93(C2×D43)⋊C8—42no—
94C43⋊#95—22no—
95C22×Q8×C43—21no—
96C22×C8×C43C2311yescharacteristic
97C22×C8×C43C2311yescharacteristic
98C4⋊Q8×C43—22no—
99C4⋊Q8×C43D414yes—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43C2312yes—
104C2×C4⋊C4×C43C2312yes—
105C2×C42×C43C2311yescharacteristic
106C4×C8×C43—22no—
107C23×D43—21no—
108C23×D43C2×D412yes—
109C2×Q8×C43—24no—
110C2×Q8×C43—42no—
111C2×Q8×C43—42no—
112C22×C4×C43—22no—
113C22×C4×C43—22no—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43C2411yescharacteristic
117C22×Dic43—21no—
118C22×Dic43—21no—
119C22×Dic43—21no—
120C22×Dic43C2×D412yes—
121#10621902—432no—
122C2×D172—22no—
123C2×D172—22no—
124C2×D172—28no—
125C2×D172—21no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—21no—
129C2×D172—21no—
130C2×D172—44no—
131C2×D172—44no—
132C2×D172SD1614yescomplemented
133C2×D172C2×D412yes—
134C2×C4×D43—28no—
135C2×C4×D43—24no—
136C2×C4×D43—22no—
137C2×C4×D43—22no—
138C2×C4×D43—22no—
139C2×C4×D43—22no—
140C2×C4×D43—22no—
141C2×C4×D43—22no—
142C2×C4×D43—44no—
143C2×C4×D43—42no—
144C2×C4×D43—42no—
145C2×C4×D43—44no—
146C2×Dic86—21no—
147C2×Dic86—21no—
148C2×Dic86—21no—
149C2×Dic86—21no—
150C2×Dic86—21no—
151C2×Dic86#4112yescomplemented
152C2×C8×C43—21no—
153C2×C8×C43—21no—
154C2×C8×C43—21no—
155C2×C8×C43—21no—
156C2×C8×C43—21no—
157C2×C8×C43#4112yescomplemented
158C4⋊C4×C43—24no—
159C4⋊C4×C43—22no—
160C4⋊C4×C43—22no—
161C4⋊C4×C43—22no—
162C4⋊C4×C43—42no—
163C4⋊C4×C43—81no—
164C4⋊C4×C43C2×D414yes—
165C42×C43C2×D412yes—
166C42×C43C2×D412yes—
167(C2×D43)⋊C4—28no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170(C2×D43)⋊C4—44no—
171(C2×D43)⋊C4—82no—
172C4⋊Dic43—22no—
173C4⋊Dic43—21no—
174C4⋊Dic43—21no—
175C4⋊Dic43—21no—
176C4⋊Dic43—44no—
177C4⋊Dic43C2×D412yes—
178Dic43⋊C4—28no—
179Dic43⋊C4—42no—
180C4×Dic43—42no—
181C2×C43⋊C8—22no—
182C2×C43⋊C8—22no—
183C2×C43⋊C8—22no—
184#10621873—28no—
185C23×C43C22×D411yescharacteristic
186C22×D43—22no—
187C22×D43—22no—
188C22×D43—22no—
189C22×D43—22no—
190C22×D43—22no—
191C22×D43—22no—
192C22×D43—22no—
193C22×D43—41no—
194C22×D43—41no—
195C22×D43—41no—
196C22×D43—41no—
197C22×D43—41no—
198C22×D43—41no—
199C22×D43C2×SD1614yes—
200Q8×C43—48no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—24no—
204C2×C4×C43—42no—
205C2×C4×C43—42no—
206C2×C4×C43—42no—
207C2×C4×C43—42no—
208C2×C4×C43—42no—
209C2×C4×C43#12012yes—
210C2×C4×C43#12012yes—
211C2×C4×C43C2×SD1612yes—
212C2×C4×C43AGL(1,ℤ/8)12yes—
213C2×C4×C43C22×D411yescharacteristic
214C2×C4×C43C22×D411yescharacteristic
215C2×C4×C43C2×#4111yescharacteristic
216C2×C4×C43C2×#4111yescharacteristic
217C2×C4×C43H(5,𝔽2)11yescharacteristic
218C2×C4×C432−1+411yescharacteristic
219C2×Dic43—22no—
220C2×Dic43—22no—
221C2×Dic43—22no—
222C2×Dic43—22no—
223C2×Dic43—22no—
224C2×Dic43—41no—
225C2×Dic43—41no—
226C2×Dic43—41no—
227C2×Dic43—41no—
228C2×Dic43—41no—
229C2×Dic43—41no—
230C2×Dic43—41no—
231D172—22no—
232D172—22no—
233D172—28no—
234D172—416no—
235D172—41no—
236D172—41no—
237C4×D43—416no—
238C4×D43—42no—
239C4×D43—42no—
240C4×D43—42no—
241C4×D43—42no—
242C4×D43—48no—
243Dic86—22no—
244Dic86—22no—
245Dic86—41no—
246Dic86—41no—
247C8×C43—22no—
248C8×C43—41no—
249C43⋊C8—42no—
250#24120—431nomaximal, Sylow
251C22×C43C2×#12011yescharacteristic
252C22×C43#54611yescharacteristic
253C22×C43#54711yescharacteristic
254C22×C43C22×SD1611yescharacteristic
255C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
256C22×C43#57711yescharacteristic
257C22×C43#57811yescharacteristic
258C2×D43—24no—
259C2×D43—24no—
260C2×D43—24no—
261C2×D43—42no—
262C2×D43—42no—
263C2×D43—42no—
264C2×D43—42no—
265C2×D43—42no—
266C2×D43—42no—
267C2×D43—42no—
268C2×D43—81no—
269C2×D43—81no—
270C2×D43—81no—
271C2×D43—81no—
272C4×C43—22no—
273C4×C43—44no—
274C4×C43—82no—
275C4×C43#45014yes—
276C4×C43#52511yescharacteristic
277C4×C43#53711yescharacteristic
278C4×C43#54811yescharacteristic
279C4×C43#55011yescharacteristic
280Dic43—42no—
281Dic43—42no—
282Dic43—42no—
283Dic43—81no—
284C2×#547—431no—
285C2×#475—431no—
286C2×C4×SD16—431no—
287#2538—431no—
288#2034—432no—
289#2000—432no—
290#1990D4311yescharacteristic, complemented
291#1954—431no—
292#1872—432no—
293#1853—432no—
294#1802—431no—
295C2×C43#240711yescharacteristic
296C2×C43C2×#45011yescharacteristic
297C2×C43#301311yescharacteristic
298C2×C43#329811yescharacteristic
299C2×C43#333211yescharacteristic
300C2×C43#333511yescharacteristic
301C2×C43#335311yescharacteristic
302D43—44no—
303D43—82no—
304C22×#41—861no—
305C22×SD16—431no—
306#547—864no—
307#547—864no—
308C2×C4⋊Q8C2×D4311yescharacteristic
309C2×#123—862no—
310C2×C22⋊Q8—432no—
311C2×C22⋊Q8—861no—
312C2×#121—432no—
313C2×C4×Q8—431no—
314C2×C4×D4—431no—
315C2×C4×D4—431no—
316C22×C4⋊C4—432no—
317#475—864no—
318C4×SD16—864no—
319C2×#106—431no—
320C2×#106—432no—
321C2×C4⋊C8—431no—
322C2×#103—431no—
323C2×#103—432no—
324C2×#102—431no—
325C2×#102—432no—
326C2×C22⋊C8—432no—
327C2×C22⋊C8—432no—
328C2×C4×C8C2×D4311yescharacteristic
329#396—862no—
330#390—861no—
331#389—861no—
332#384C2×D4311yescharacteristic
333#380—432no—
334#340—432no—
335#340C2×D4312yes—
336#340C2×D4312yes—
337C43#2412011yescharacteristic, complemented, Sylow
338C2×#41—868no—
339C2×#41—1724no—
340C2×#41—1724no—
341C22×Q8—21no—
342C22×Q8—431no—
343C22×D4—431no—
344C22×D4—431no—
345C22×D4—862no—
346C23×C4—432no—
347C23×C4—862no—
348C23×C4—861no—
349C2×SD16—862no—
350C2×SD16—862no—
351C2×SD16—862no—
352C22×C8—432no—
353C22×C8C22×D4311yescharacteristic
354C22×C8C22×D4311yescharacteristic
355C4⋊Q8—22no—
356C4⋊Q8D17214yes—
357#123—8616no—
358C22⋊Q8—868no—
359C22⋊Q8—864no—
360C22⋊Q8—1722no—
361#121—864no—
362#121—864no—
363C4×Q8—862no—
364C4×Q8—862no—
365C4×D4—434no—
366C4×D4—862no—
367C4×D4—862no—
368C4×D4—862no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—431no—
373C2×C4⋊C4—431no—
374C2×C4⋊C4—431no—
375C2×C4⋊C4—864no—
376C2×C4⋊C4—862no—
377C2×C4⋊C4—864no—
378C2×C4⋊C4—862no—
379C2×C4⋊C4—861no—
380C2×C4⋊C4C22×D4312yes—
381C2×C4⋊C4C22×D4312yes—
382C2×C22⋊C4—432no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—862no—
386C2×C22⋊C4—862no—
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—22no—
399#95—862no—
400C24—432no—
401C24—861no—
402#41—17232no—
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—434no—
413C2×D4—432no—
414C2×D4—868no—
415C2×D4—862no—
416C2×D4—862no—
417C2×D4—861no—
418C2×D4—861no—
419C2×D4—861no—
420C2×D4—861no—
421C2×D4—861no—
422C2×D4—1724no—
423C2×D4—1724no—
424C22×C4—22no—
425C22×C4—22no—
426C22×C4—432no—
427C22×C4—868no—
428C22×C4—861no—
429C22×C4—861no—
430C22×C4—864no—
431C22×C4—862no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—862no—
437C22×C4—861no—
438C22×C4—1724no—
439C22×C4—1724no—
440C22×C4—1722no—
441C22×C4—1722no—
442C22×C4D4×D4311yescharacteristic
443C22×C4D4×D4311yescharacteristic
444C22×C4C23×D4311yescharacteristic
445SD16—868no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—862no—
452C2×C8—862no—
453C2×C8—862no—
454C2×C8#1062190212yescomplemented
455C4⋊C4—24no—
456C4⋊C4—22no—
457C4⋊C4—22no—
458C4⋊C4—22no—
459C4⋊C4—42no—
460C4⋊C4—81no—
461C4⋊C4—432no—
462C4⋊C4—868no—
463C4⋊C4—862no—
464C4⋊C4—861no—
465C4⋊C4—861no—
466C4⋊C4—861no—
467C4⋊C4—1724no—
468C4⋊C4—1722no—
469C4⋊C4C2×D17214yes—
470C22⋊C4—868no—
471C22⋊C4—864no—
472C22⋊C4—864no—
473C22⋊C4—3442no—
474C22⋊C4—1724no—
475C42—1722no—
476C42C2×D17212yes—
477C42D4×D4312yes—
478C23—434no—
479C23—862no—
480C23—862no—
481C23—862no—
482C23—862no—
483C23—862no—
484C23—862no—
485C23—862no—
486C23—1721no—
487C23—1721no—
488C23—1721no—
489C23—1721no—
490C23—1721no—
491C23—1721no—
492C23C2×D4×D4311yescharacteristic
493Q8—48no—
494Q8—862no—
495Q8—862no—
496Q8—1721no—
497Q8—1721no—
498D4—868no—
499D4—862no—
500D4—862no—
501D4—17216no—
502D4—1721no—
503D4—1721no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—24no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—862no—
513C2×C4—862no—
514C2×C4—862no—
515C2×C4—862no—
516C2×C4—862no—
517C2×C4—17216no—
518C2×C4—1721no—
519C2×C4—1721no—
520C2×C4—1721no—
521C2×C4—1721no—
522C2×C4—1721no—
523C2×C4—1721no—
524C2×C4—1721no—
525C2×C4—1722no—
526C2×C4—1728no—
527C2×C4—1722no—
528C2×C4—1722no—
529C2×C4—1722no—
530C2×C4#1306329512yes—
531C2×C4#1306329512yes—
532C2×C4SD16×D4312yes—
533C2×C4#1306334912yes—
534C2×C4C2×D4×D4311yescharacteristic
535C2×C4C22×D17211yescharacteristic
536C2×C4#41×D4311yescharacteristic
537C2×C4C2×#1062190211yescharacteristic
538C2×C4#1306337111yescharacteristic
539C2×C4#1306337311yescharacteristic
540C8—22no—
541C8—41no—
542C8—1722no—
543C22—864no—
544C22—864no—
545C22—864no—
546C22—3441no—
547C22—3441no—
548C22—3441no—
549C22—3441no—
550C22—1722no—
551C22—1722no—
552C22—1722no—
553C22—1722no—
554C22—1722no—
555C22—1722no—
556C22—1722no—
557C22C2×#1306329511yescharacteristic
558C22#1458354211yescharacteristic
559C22#1458355211yescharacteristic
560C22C2×SD16×D4311yescharacteristic
561C22C2×#1306334911yescharacteristic
562C22#1458370511yescharacteristic
563C22#1458371211yescharacteristic
564C4—22no—
565C4—44no—
566C4—82no—
567C4—3441no—
568C4—1722no—
569C4—1722no—
570C4—1722no—
571C4#1458305114yes—
572C4#1458341211yescharacteristic
573C4#1458347911yescharacteristic
574C4#1458356111yescharacteristic
575C4#1458357111yescharacteristic
576C2—3442no—
577C2—1724no—
578C2#1913794311yescharacteristic
579C2C2×#1458305111yescharacteristic
580C2#1914391511yescharacteristic
581C2#1914645911yescharacteristic
582C2#1914692111yescharacteristic
583C2#1914695111yescharacteristic
584C2#1914717811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC43×#1990C2
socleC23×C43C22×D4
prime radicalC2×#14583552C2
hypercenter#1990D43
hypocenterC43#24120
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
2. C2×#14583181C2semidirect
3. C2×C4×#10621873C2semidirect
4. #19139518C2semidirect
5. #19135787C2semidirect
6. #19135601C2semidirect
7. #19135389C2semidirect
8. #19134901C2semidirect
9. #19134789C2semidirect
10. #19134592C2semidirect
11. C43×#1990C2semidirect
132. C2×D172SD16semidirect
151. C2×Dic86#41semidirect
157. C2×C8×C43#41semidirect
290. #1990D43semidirect
337. C43#24120semidirect
454. C2×C8#10621902semidirect

Maximal subgroups

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

subgroupindex
C2×#145835522
C2×#145831812
C2×C4×#106218732
#191395182
#191357872
#191356012
#191353892
#191349012
#191347892
#191345922
C43×#19902
#2412043