Finite Group Databasebeta

← #25147005

Subgroups — #25147005

Order 11008.

732 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144991C211yesmaximal, characteristic
2#19144067C211yesmaximal, characteristic
3#19143338C211yesmaximal, characteristic
4#19136041C212yesmaximal, complemented
5#19135895C212yesmaximal, complemented
6#19135585C211yesmaximal, characteristic, complemented
7#19135371C211yesmaximal, characteristic, complemented
8#19135113C212yesmaximal, complemented
9#19134655C212yesmaximal, complemented
10C4×#13063244C211yesmaximal, characteristic, complemented
11C2×C43×#475C211yesmaximal, characteristic, complemented
12C2×#13063356C2212yes—
13C2×#13063331C2212yes—
14#14583449C2211yescharacteristic
15#14583261—22no—
16#14583251—21no—
17#14583247—21no—
18#14583121—22no—
19#14583109—21no—
20#14583099—21no—
21#14582976—21no—
22#14582969—22no—
23#14582964—21no—
24C2×#13063261C2212yes—
25#14582923C2211yescharacteristic
26#14582898C2212yes—
27#14582898C2212yes—
28#14582898C2212yes—
29C2×#13063244C2211yescharacteristic
30C2×#13063244C2211yescharacteristic
31#14582865C2212yes—
32C4×#10621877C2211yescharacteristic
33C4×#10621877C2211yescharacteristic
34#14582668C2211yescharacteristic
35#14582668C2212yes—
36#14582668C2212yes—
37#14582668C2211yescharacteristic
38#14582664C2212yes—
39C2×C4⋊Q8×C43C2211yescharacteristic
40C2×C4×Q8×C43C2211yescharacteristic
41C43×#475—21no—
42C43×#475—22no—
43C43×#475—21no—
44C2×#106×C43C2212yes—
45C2×C4⋊C8×C43C2211yescharacteristic
46C2×#103×C43C2212yes—
47C2×#10621898C2312yes—
48#13063356—24no—
49#13063356—42no—
50C2×#10621885—22no—
51C2×#10621884—22no—
52#13063331—24no—
53#13063331—42no—
54C2×#10621877C2311yescharacteristic
55C2×#10621877C2311yescharacteristic
56C2×#10621877C2311yescharacteristic
57C2×#10621877C2312yes—
58C2×#10621877C2311yescharacteristic
59C2×#10621872—22no—
60C2×C8×D43—22no—
61#13063325D411yescharacteristic
62#13063322D411yescharacteristic
63#13063313D412yes—
64#13063299—21no—
65#13063299—21no—
66C4×D172—21no—
67C4×D172—21no—
68#13063261—42no—
69C4⋊(C43⋊C8)—21no—
70C4⋊(C43⋊C8)—21no—
71#13063248—22no—
72#13063248—22no—
73#13063248—22no—
74#13063245—22no—
75#13063245—22no—
76#13063245—22no—
77#13063244—22no—
78#13063244—22no—
79(C2×D43)⋊C8—22no—
80(C2×D43)⋊C8—22no—
81#13063236—21no—
82#13063236—21no—
83C4×C43⋊C8—21no—
84C4×C43⋊C8—21no—
85C22×Q8×C43—21no—
86C22×Q8×C43C2311yescharacteristic
87C22×C8×C43C2312yes—
88C4⋊Q8×C43—21no—
89C4⋊Q8×C43—21no—
90C4⋊Q8×C43—21no—
91C4⋊Q8×C43—21no—
92C4×Q8×C43—21no—
93C4×Q8×C43—21no—
94C4×Q8×C43—21no—
95C4×Q8×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43C2311yescharacteristic
99C2×C4⋊C4×C43C2312yes—
100C2×C42×C43—21no—
101C2×C42×C43C2311yescharacteristic
102#106×C43—22no—
103#106×C43—22no—
104C4⋊C8×C43D411yescharacteristic
105C4⋊C8×C43D412yes—
106C4⋊C8×C43D411yescharacteristic
107#103×C43—22no—
108#103×C43—22no—
109C2×Q8×C43—21no—
110C2×Q8×C43—21no—
111C2×Q8×C43—21no—
112C2×Q8×C43—21no—
113C2×Q8×C43—21no—
114C2×Q8×C43—41no—
115C2×Q8×C43—41no—
116C2×Q8×C43—82no—
117C2×Q8×C43#4112yes—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—22no—
121C22×C4×C43#4111yescharacteristic
122C22×C4×C43#4111yescharacteristic
123C22×C4×C43C2411yescharacteristic
124C2×C22⋊D43—22no—
125#10621898—22no—
126#10621898—22no—
127#10621898—22no—
128#10621898—22no—
129C2×D172—21no—
130C2×D172—21no—
131C2×D172C2×D412yes—
132C2×C4×D43—22no—
133C2×Dic86C2×D412yes—
134C2×C8×C43—22no—
135C2×C8×C43—22no—
136C2×C8×C43C2×D412yes—
137C2×C8×C43C2×D412yes—
138C4⋊C4×C43—22no—
139C4⋊C4×C43—21no—
140C4⋊C4×C43—21no—
141C4⋊C4×C43—22no—
142C4⋊C4×C43—41no—
143C4⋊C4×C43—41no—
144C4⋊C4×C43—41no—
145C4⋊C4×C43—41no—
146C42×C43—41no—
147C42×C43—41no—
148C42×C43C2×D411yescharacteristic
149C42×C43C2×D411yescharacteristic
150C42×C43C2×D411yescharacteristic
151C42×C43C2×D411yescharacteristic
152#10621885—44no—
153#10621884—44no—
154(C2×D43)⋊C4—22no—
155(C2×D43)⋊C4—22no—
156C4⋊Dic43—21no—
157C4⋊Dic43—21no—
158#10621877—21no—
159#10621877—21no—
160#10621877—21no—
161#10621877—21no—
162#10621877—22no—
163#10621877—21no—
164#10621877—22no—
165#10621877—21no—
166#10621877—21no—
167#10621877#4112yes—
168C2×C43⋊C8—21no—
169C2×C43⋊C8—21no—
170C2×C43⋊C8—21no—
171C2×C43⋊C8—21no—
172C2×C43⋊C8—22no—
173#10621872—44no—
174C8×D43—44no—
175C23×C43C2×#4111yescharacteristic
176C22×D43—22no—
177Q8×C43—22no—
178Q8×C43—22no—
179Q8×C43—41no—
180Q8×C43—41no—
181Q8×C43—82no—
182Q8×C43—82no—
183C2×C4×C43—22no—
184C2×C4×C43—22no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—42no—
190C2×C4×C43—81no—
191C2×C4×C43—82no—
192C2×C4×C43#12111yescharacteristic
193C2×C4×C43#12111yescharacteristic
194C2×C4×C43#12111yescharacteristic
195C2×C4×C43#12111yescharacteristic
196C2×C4×C43C22×D411yescharacteristic
197C2×C4×C43C22×D411yescharacteristic
198C2×C4×C43C2×#4111yescharacteristic
199C2×C4×C43C2×#4111yescharacteristic
200C2×C4×C43H(5,𝔽2)11yescharacteristic
201C2×C4×C432−1+411yescharacteristic
202C22⋊D43—42no—
203C22⋊D43—42no—
204C2×Dic43—22no—
205D172—22no—
206D172—22no—
207D172—42no—
208D172—81no—
209C4×D43—42no—
210C4×D43—42no—
211Dic86—22no—
212Dic86—22no—
213C8×C43—22no—
214C8×C43—22no—
215C43⋊C8—22no—
216C43⋊C8—41no—
217C43⋊C8—42no—
218C43⋊C8—41no—
219C43⋊C8—41no—
220#25361—431nomaximal, Sylow
221C22×C43—21no—
222C22×C43—21no—
223C22×C43C2×#12111yescharacteristic
224C22×C43#52911yescharacteristic
225C22×C43#54211yescharacteristic
226C2×D43—42no—
227C2×D43—42no—
228C2×D43—42no—
229C4×C43—21no—
230C4×C43—21no—
231C4×C43—21no—
232C4×C43—42no—
233C4×C43—82no—
234C4×C43—81no—
235C4×C43#47112yes—
236C4×C43#54611yescharacteristic
237C4×C43#54611yescharacteristic
238C4×C43#54711yescharacteristic
239C4×C43#54811yescharacteristic
240Dic43—42no—
241#3141—431no—
242C2×#475D4311yescharacteristic, complemented
243#3037—431no—
244#2935—431no—
245#2079—432no—
246#2052—432no—
247#1997—431no—
248#1950—431no—
249#1908—432no—
250#1815—432no—
251C4×#101—431no—
252C2×C43—21no—
253C2×C43—21no—
254C2×C43#242711yescharacteristic
255C2×C43C2×#47111yescharacteristic
256C2×C43#306911yescharacteristic
257D43—82no—
258C2×#137—432no—
259C2×#131—432no—
260#532—431no—
261C2×C4⋊Q8C2×D4311yescharacteristic
262C2×C4×Q8C2×D4311yescharacteristic
263#489—862no—
264#487—861no—
265#486—861no—
266#475—21no—
267#475—22no—
268#475—21no—
269#464—862no—
270#462—861no—
271#460—861no—
272#436—861no—
273#435—862no—
274C8×D4—861no—
275C2×#108—432no—
276C2×#106C2×D4312yes—
277#423—431no—
278C2×C4⋊C8C2×D4311yescharacteristic
279#417—432no—
280#417—432no—
281#417—432no—
282C2×#103C2×D4312yes—
283C2×#101—431no—
284C2×#101—431no—
285#408—432no—
286C4×M16—431no—
287C4×M16—431no—
288#343—432no—
289#343—431no—
290#343—432no—
291#343—431no—
292#341—432no—
293C43#2536111yescharacteristic, complemented, Sylow
294C2×#41—432no—
295C22×Q8—21no—
296C22×Q8C22×D4311yescharacteristic
297#137—864no—
298#137—1722no—
299C2×Q16—862no—
300C2×SD16—862no—
301#131—864no—
302#131—1722no—
303C2×M16—431no—
304C2×M16—432no—
305C2×M16—431no—
306C2×M16—431no—
307C2×M16—431no—
308C2×M16—862no—
309C22×C8—862no—
310C22×C8C22×D4312yes—
311C4⋊Q8—21no—
312C4⋊Q8—21no—
313C4⋊Q8—21no—
314C4⋊Q8—21no—
315C4⋊Q8—431no—
316#127—431no—
317#124—432no—
318#121—861no—
319#121—861no—
320C4×Q8—21no—
321C4×Q8—21no—
322C4×Q8—21no—
323C4×Q8—21no—
324C4×D4—861no—
325C4×D4—861no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—21no—
328C2×C4⋊C4C22×D4311yescharacteristic
329C2×C4⋊C4C22×D4312yes—
330C2×C42—21no—
331C2×C42C22×D4311yescharacteristic
332#108—1722no—
333#106—22no—
334#106—22no—
335C4⋊C8—861no—
336C4⋊C8—861no—
337C4⋊C8C22⋊D4311yescharacteristic
338C4⋊C8C22⋊D4312yes—
339C4⋊C8C22⋊D4311yescharacteristic
340#103—22no—
341#103—22no—
342#103—862no—
343#103—862no—
344#103—862no—
345#102—862no—
346#102—862no—
347#102—862no—
348#101—862no—
349#101—862no—
350C22⋊C8—862no—
351C22⋊C8—862no—
352#97—861no—
353#97—861no—
354C4×C8—861no—
355C4×C8—861no—
356#41—862no—
357#41—862no—
358#41—862no—
359#41—862no—
360C2×Q8—21no—
361C2×Q8—21no—
362C2×Q8—21no—
363C2×Q8—21no—
364C2×Q8—21no—
365C2×Q8—41no—
366C2×Q8—41no—
367C2×Q8—82no—
368C2×Q8—432no—
369C2×Q8#1062190212yes—
370C2×D4—432no—
371C2×D4—862no—
372C2×D4—861no—
373C2×D4—861no—
374C22×C4—21no—
375C22×C4—21no—
376C22×C4—22no—
377C22×C4—862no—
378C22×C4#1062190011yescharacteristic
379C22×C4#1062190011yescharacteristic
380C22×C4C23×D4311yescharacteristic
381Q16—1724no—
382SD16—1724no—
383M16—432no—
384M16—861no—
385M16—861no—
386M16—861no—
387M16—861no—
388M16—862no—
389M16—861no—
390M16—862no—
391M16—861no—
392M16—861no—
393M16—1724no—
394C2×C8—22no—
395C2×C8—22no—
396C2×C8—861no—
397C2×C8—861no—
398C2×C8—861no—
399C2×C8—862no—
400C2×C8—861no—
401C2×C8—1724no—
402C2×C8C2×C22⋊D4312yes—
403C2×C8C2×C22⋊D4312yes—
404C4⋊C4—21no—
405C4⋊C4—22no—
406C4⋊C4—22no—
407C4⋊C4—21no—
408C4⋊C4—41no—
409C4⋊C4—41no—
410C4⋊C4—41no—
411C4⋊C4—41no—
412C4⋊C4—861no—
413C4⋊C4—861no—
414C22⋊C4—862no—
415C22⋊C4—862no—
416C42—41no—
417C42—41no—
418C42D4×D4311yescharacteristic
419C42D4×D4311yescharacteristic
420C42C2×C22⋊D4311yescharacteristic
421C42C2×C22⋊D4311yescharacteristic
422C23—862no—
423C23C2×#1062190011yescharacteristic
424Q8—22no—
425Q8—22no—
426Q8—41no—
427Q8—41no—
428Q8—82no—
429Q8—82no—
430Q8—862no—
431Q8—862no—
432D4—862no—
433D4—862no—
434D4—3441no—
435D4—1722no—
436D4—1722no—
437D4—1722no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—42no—
445C2×C4—82no—
446C2×C4—81no—
447C2×C4—862no—
448C2×C4—1722no—
449C2×C4—1722no—
450C2×C4#1306329611yescharacteristic
451C2×C4#1306329611yescharacteristic
452C2×C4#1306329611yescharacteristic
453C2×C4#1306329611yescharacteristic
454C2×C4C2×D4×D4311yescharacteristic
455C2×C4C22×C22⋊D4311yescharacteristic
456C2×C4#41×D4311yescharacteristic
457C2×C4C2×#1062190211yescharacteristic
458C2×C4#1306337111yescharacteristic
459C2×C4#1306337311yescharacteristic
460C8—22no—
461C8—22no—
462C8—862no—
463C8—1721no—
464C8—1722no—
465C8—1721no—
466C8—1721no—
467C22—21no—
468C22—21no—
469C22—1722no—
470C22—1722no—
471C22—1722no—
472C22C2×#1306329611yescharacteristic
473C22#1458343511yescharacteristic
474C22#1458352211yescharacteristic
475C4—21no—
476C4—21no—
477C4—21no—
478C4—42no—
479C4—82no—
480C4—81no—
481C4—1722no—
482C4#1458315912yes—
483C4#1458353711yescharacteristic
484C4#1458354011yescharacteristic
485C4#1458355111yescharacteristic
486C4#1458356011yescharacteristic
487C2—21no—
488C2—21no—
489C2—3442no—
490C2#1913816811yescharacteristic
491C2C2×#1458315911yescharacteristic
492C2#1914432811yescharacteristic
subgroupG/H
centerC22C2×#13063296
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#475C2
socleC22×C43C2×#121
prime radical#14583449C22
hypercenterC2×#475D43
hypocenterC43#25361
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
4. #19136041C2semidirect
5. #19135895C2semidirect
6. #19135585C2semidirect
7. #19135371C2semidirect
8. #19135113C2semidirect
9. #19134655C2semidirect
10. C4×#13063244C2semidirect
11. C2×C43×#475C2semidirect
242. C2×#475D43semidirect
293. C43#25361semidirect

Maximal subgroups

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

subgroupindex
#191449912
#191440672
#191433382
#191360412
#191358952
#191355852
#191353712
#191351132
#191346552
C4×#130632442
C2×C43×#4752
#2536143