Finite Group Databasebeta

← #25101010

Subgroups — #25101010

Order 11008.

722 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#13063345C211yesmaximal, characteristic
2#19143247C211yesmaximal, characteristic, complemented
3#19143246C211yesmaximal, characteristic, complemented
4#19135485C212yesmaximal
5#19135347C212yesmaximal, complemented
6#19135300C212yesmaximal, complemented
7#19135296C212yesmaximal, complemented
8C4×#13063260C211yesmaximal, characteristic, complemented
9#19134406C211yesmaximal, characteristic, complemented
10#19134282C211yesmaximal, characteristic, complemented
11C43×#1759C211yesmaximal, characteristic, complemented
12C2×#13063345C2211yescharacteristic
13C4×#10621898C2211yescharacteristic
14C4×#10621885C412yescomplemented
15C4×#10621884C412yescomplemented
16C4×#10621883C412yescomplemented
17C4×#10621882C412yescomplemented
18#14582960—22no—
19#14582958—22no—
20#14582956—22no—
21#14582954—22no—
22C2×#13063260C2212yes—
23#14582935C2211yescharacteristic
24#14582927C2212yes—
25#14582926C2212yes—
26C2×#13063253C2212yes—
27#14582895C2211yescharacteristic
28#14582893C2211yescharacteristic
29#14582867C2212yes—
30#14582866C2212yes—
31C4×#10621877C2211yescharacteristic
32C2×#13063236C2212yes—
33C2×#13063236C2211yescharacteristic
34C2×C4×C43⋊C8C2212yes—
35C2×C4×C43⋊C8C2211yescharacteristic
36#14582663C2212yes—
37#14582659C2212yes—
38C4×#41×C43C2211yescharacteristic
39C2×#104×C43C2212yes—
40C4×M16×C43C2211yescharacteristic
41C43×#376C2211yescharacteristic
42C43×#339C2212yes—
43C2×#10621898C2311yescharacteristic
44#13063345—24no—
45C2×#10621885C2×C411yescharacteristic
46C2×#10621883C2×C411yescharacteristic
47C2×#10621884C2×C411yescharacteristic
48C2×#10621882C2×C411yescharacteristic
49C2×#10621877C2312yes—
50C22×C43⋊C8C2311yescharacteristic
51C22×C43⋊C8C2312yes—
52C22×C43⋊C8C2311yescharacteristic
53C4×Dic86C2×C412yes—
54C4×D172C2×C412yes—
55C4×C22⋊D43—22no—
56#13063284C2311yescharacteristic
57#13063282—21no—
58C42×D43—21no—
59#13063260—24no—
60#13063258C2×C412yes—
61#13063256C2×C412yes—
62C4⋊(C43⋊C8)—24no—
63Dic43⋊C8—24no—
64#13063253—24no—
65#13063249C2×C412yes—
66#13063248C2×C412yes—
67#13063246C2×C412yes—
68#13063245C2×C412yes—
69C22⋊(C43⋊C8)—24no—
70(C2×D43)⋊C8—24no—
71#13063236—21no—
72#13063236—24no—
73#13063236D412yes—
74#13063236D412yes—
75C4×C43⋊C8—21no—
76C4×C43⋊C8—24no—
77C4×C43⋊C8C2×C412yes—
78C4×C43⋊C8C2×C412yes—
79C2×#41×C43C2311yescharacteristic
80C2×M16×C43C2312yes—
81C4×Q8×C43C2×C412yes—
82C4×D4×C43—22no—
83C4×D4×C43C2×C412yes—
84#117×C43—21no—
85#117×C43C2311yescharacteristic
86C2×C42×C43—21no—
87C2×C42×C43C2312yes—
88C2×C42×C43C2311yescharacteristic
89#104×C43—24no—
90#97×C43—21no—
91C4×C8×C43—21no—
92#95×C43—22no—
93#41×C43—22no—
94#41×C43—22no—
95C2×Q8×C43C22×C411yescharacteristic
96C2×D4×C43—21no—
97C2×D4×C43C22×C411yescharacteristic
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—22no—
101C22×C4×C43#4112yes—
102C22×C4×C43C2411yescharacteristic
103C2×C22⋊D43—21no—
104#10621898—22no—
105#10621898—22no—
106C2×D172C22×C411yescharacteristic
107C2×C4×D43—21no—
108C2×C4×D43—22no—
109C2×Dic86C22×C411yescharacteristic
110M16×C43—22no—
111M16×C43—22no—
112C2×C8×C43—22no—
113C4⋊C4×C43—22no—
114C4⋊C4×C43C22×C412yes—
115C22⋊C4×C43—22no—
116C22⋊C4×C43—21no—
117C42×C43—22no—
118C42×C43—21no—
119C42×C43—22no—
120C42×C43C22×C412yes—
121C42×C43C2×D411yescharacteristic
122C42×C43C2×D411yescharacteristic
123C42×C43#4114yes—
124C22⋊Dic43—21no—
125#10621885—22no—
126#10621884—22no—
127#10621883—22no—
128#10621882—22no—
129(C2×D43)⋊C4—22no—
130C4⋊Dic43C22×C412yes—
131Dic43⋊C4—22no—
132C4×Dic43—22no—
133C4×Dic43—21no—
134#10621877—22no—
135#10621877—22no—
136C2×C43⋊C8—22no—
137C2×C43⋊C8—22no—
138C2×C43⋊C8—22no—
139C2×C43⋊C8—22no—
140C2×C43⋊C8C22×C412yes—
141C2×C43⋊C8C22×C411yescharacteristic
142C2×C43⋊C8C22×C411yescharacteristic
143C2×C43⋊C8C2×D414yes—
144C2×C43⋊C8#4114yes—
145C23×C43—21no—
146C23×C43C2×#4111yescharacteristic
147C22×D43—21no—
148Q8×C43—21no—
149Q8×C43—21no—
150D4×C43—21no—
151D4×C43—21no—
152D4×C43—42no—
153C2×C4×C43—22no—
154C2×C4×C43—21no—
155C2×C4×C43—24no—
156C2×C4×C43—42no—
157C2×C4×C43—44no—
158C2×C4×C43—42no—
159C2×C4×C43—82no—
160C2×C4×C43C4×D412yes—
161C2×C4×C43C4×D412yes—
162C2×C4×C43C23×C411yescharacteristic
163C2×C4×C43C22×D411yescharacteristic
164C2×C4×C43C2×#4112yes—
165C2×C4×C43C2×#4112yes—
166C22⋊D43—42no—
167C2×Dic43—21no—
168C2×Dic43—22no—
169D172—21no—
170D172—21no—
171C4×D43—42no—
172C4×D43—82no—
173Dic86—21no—
174Dic86—21no—
175C8×C43—42no—
176C43⋊C8—22no—
177C43⋊C8—24no—
178C43⋊C8—42no—
179C43⋊C8#11712yes—
180C43⋊C8#11712yes—
181#21295—431nomaximal, Sylow
182C22×C43—22no—
183C22×C43—42no—
184C22×C43—41no—
185C22×C43C2×C4×D411yescharacteristic
186C22×C43#52912yes—
187C2×D43—42no—
188C2×D43—41no—
189C4×C43—22no—
190C4×C43—22no—
191C4×C43—44no—
192C4×C43—42no—
193C4×C43—41no—
194C4×C43C2×#11711yescharacteristic
195C4×C43C4×#4111yescharacteristic
196C4×C43#53212yes—
197Dic43—42no—
198Dic43—41no—
199C4×#135—431no—
200#2923—431no—
201#2923—431no—
202#1975—432no—
203#1946—432no—
204#1937—432no—
205#1937—432no—
206C4×#108—431no—
207#1759—431no—
208#1759D4311yescharacteristic, complemented
209#1726—431no—
210C2×C43—22no—
211C2×C43—81no—
212C2×C43#229311yescharacteristic
213C2×C43#295712yes—
214D43—81no—
215C2×#135—431no—
216C4×#41—431no—
217C4×#41C2×D4311yescharacteristic
218C4×Q16—432no—
219C4×SD16—432no—
220C4×SD16—432no—
221C4×D8—432no—
222#433—862no—
223#433—862no—
224#432—862no—
225#432—862no—
226C2×#108—432no—
227#427—431no—
228#424—432no—
229#424—432no—
230C2×#104—432no—
231C2×#104C2×D4312yes—
232#416—431no—
233#416—431no—
234#408—432no—
235#408—432no—
236C4×M16—431no—
237C4×M16C2×D4311yescharacteristic
238C2×#97—431no—
239C2×#97—432no—
240C2×C4×C8—431no—
241C2×C4×C8—432no—
242#376C2×D4311yescharacteristic
243#341—432no—
244#339—432no—
245#339C2×D4312yes—
246C43#2129511yescharacteristic, complemented, Sylow
247C2×#41—431no—
248C2×#41C22×D4311yescharacteristic
249#135—864no—
250C2×Q16—431no—
251C2×SD16—431no—
252C2×SD16—431no—
253C2×D8—431no—
254C2×M16—432no—
255C2×M16C22×D4312yes—
256C22×C8—431no—
257C22×C8—431no—
258C22×C8—432no—
259C4×Q8—432no—
260C4×Q8C4×D4312yes—
261C4×D4—22no—
262C4×D4—432no—
263C4×D4—862no—
264C4×D4C4×D4312yes—
265#117—21no—
266#117—431no—
267#117—861no—
268#117C22×D4311yescharacteristic
269C2×C42—21no—
270C2×C42—861no—
271C2×C42C22×D4312yes—
272C2×C42C22×D4311yescharacteristic
273#108—864no—
274#107—432no—
275#106—432no—
276C4⋊C8—864no—
277C4⋊C8—864no—
278#104—24no—
279#104—864no—
280#103—432no—
281#103—432no—
282#102—432no—
283#102—432no—
284C22⋊C8—864no—
285C22⋊C8—864no—
286#97—21no—
287#97—432no—
288#97—432no—
289#97—864no—
290#97—861no—
291C4×C8—21no—
292C4×C8—432no—
293C4×C8—432no—
294C4×C8—864no—
295C4×C8—861no—
296#95—22no—
297#41—22no—
298#41—22no—
299#41—862no—
300#41—862no—
301C2×Q8—431no—
302C2×Q8C2×C4×D4311yescharacteristic
303C2×D4—21no—
304C2×D4—431no—
305C2×D4—861no—
306C2×D4C2×C4×D4311yescharacteristic
307C22×C4—22no—
308C22×C4—21no—
309C22×C4—22no—
310C22×C4—862no—
311C22×C4—861no—
312C22×C4#1062190012yes—
313C22×C4C23×D4311yescharacteristic
314Q16—862no—
315SD16—862no—
316SD16—862no—
317D8—862no—
318M16—22no—
319M16—22no—
320M16—862no—
321M16—862no—
322C2×C8—22no—
323C2×C8—431no—
324C2×C8—431no—
325C2×C8—434no—
326C2×C8—432no—
327C2×C8—434no—
328C2×C8—862no—
329C2×C8—862no—
330C2×C8—862no—
331C2×C8—862no—
332C4⋊C4—22no—
333C4⋊C4—432no—
334C4⋊C4—862no—
335C4⋊C4C2×C4×D4312yes—
336C22⋊C4—21no—
337C22⋊C4—22no—
338C22⋊C4—861no—
339C22⋊C4—862no—
340C42—22no—
341C42—21no—
342C42—22no—
343C42—862no—
344C42—861no—
345C42C2×C4×D4312yes—
346C42#1062189814yes—
347C42D4×D4311yescharacteristic
348C42D4×D4311yescharacteristic
349C23—21no—
350C23—861no—
351C23C2×#1062190011yescharacteristic
352Q8—21no—
353Q8—21no—
354Q8—861no—
355Q8—861no—
356D4—21no—
357D4—21no—
358D4—42no—
359D4—861no—
360D4—861no—
361D4—1722no—
362C2×C4—22no—
363C2×C4—21no—
364C2×C4—24no—
365C2×C4—42no—
366C2×C4—44no—
367C2×C4—42no—
368C2×C4—82no—
369C2×C4—862no—
370C2×C4—861no—
371C2×C4—3442no—
372C2×C4—1722no—
373C2×C4(C22⋊D43)⋊C412yes—
374C2×C4(C22⋊D43)⋊C412yes—
375C2×C4C22×C4×D4311yescharacteristic
376C2×C4C2×D4×D4311yescharacteristic
377C2×C4#41×D4312yes—
378C2×C4C2×#1062189812yes—
379C8—42no—
380C8—432no—
381C8—432no—
382C8—862no—
383C8—864no—
384C8—1722no—
385C22—22no—
386C22—41no—
387C22—42no—
388C22—1721no—
389C22—1722no—
390C22C2×(C22⋊D43)⋊C411yescharacteristic
391C22#1458342912yes—
392C4—22no—
393C4—22no—
394C4—44no—
395C4—41no—
396C4—42no—
397C4—1721no—
398C4—1722no—
399C4#117×D4311yescharacteristic
400C4C4×#1062189811yescharacteristic
401C4#1458344612yes—
402C2—22no—
403C2—81no—
404C2—3441no—
405C2#1913705811yescharacteristic
406C2#1914350812yes—
subgroupG/H
centerC2×C4C2×D4×D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1759C2
socleC22×C43C2×C4×D4
prime radicalC2×#13063345C22
cosocleC22×C4×C43C24
hypercenter#1759D43
hypocenterC43#21295
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1759

Complements

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

NH ≅ G/Ntype
2. #19143247C2semidirect
3. #19143246C2semidirect
5. #19135347C2semidirect
6. #19135300C2semidirect
7. #19135296C2semidirect
8. C4×#13063260C2semidirect
9. #19134406C2semidirect
10. #19134282C2semidirect
11. C43×#1759C2semidirect
14. C4×#10621885C4semidirect
15. C4×#10621884C4semidirect
16. C4×#10621883C4semidirect
17. C4×#10621882C4semidirect
208. #1759D43semidirect
246. C43#21295semidirect

Maximal subgroups

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

subgroupindex
C4×#130633452
#191432472
#191432462
#191354852
#191353472
#191353002
#191352962
C4×#130632602
#191344062
#191342822
C43×#17592
#2129543