Finite Group Databasebeta

← C2×#19136496 #25250041

Subgroups — C2×#19136496 #25250041

Order 11008.

710 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583335C211yesmaximal, characteristic
2C2×#14583020C211yesmaximal, characteristic, complemented
3C2×#14583011C211yesmaximal, characteristic, complemented
4#19136496C218yesmaximal, direct product factor
5C2×#14582723C211yesmaximal, characteristic, complemented
6C2×#14582710C211yesmaximal, characteristic, complemented
7C2×#14582676C211yesmaximal, characteristic, complemented
8C2×C43×#361C211yesmaximal, characteristic, complemented
9C2×#13063347C2211yescharacteristic
10C2×#13063333—21no—
11C2×D4×Dic43—21no—
12#14583335C414yescomplemented
13#14583335C2214yes—
14C2×#13063269C412yescomplemented
15C2×#13063266C412yescomplemented
16C2×#13063265C2211yescharacteristic
17#14583020—22no—
18#14583020C2214yescomplemented
19#14583011—22no—
20#14583011C2214yescomplemented
21C2×#13063257C2211yescharacteristic
22C2×#13063251—21no—
23C2×#13063246—21no—
24C2×#13063235C2211yescharacteristic
25#14582723C2214yescomplemented
26#14582710C2214yescomplemented
27#14582676C2214yescomplemented
28C22×D8×C43C2211yescharacteristic
29C2×M32×C43C2211yescharacteristic
30C2×#108×C43C2211yescharacteristic
31C43×#361C2214yescomplemented
32C2×#10621898—21no—
33C23×Dic43—41no—
34#13063347—21no—
35#13063347—21no—
36#13063347C2×C412yescomplemented
37#13063347C2312yes—
38C2×Dic172C2×C411yescharacteristic, complemented
39C2×#10621873—21no—
40C2×D344C2×C411yescharacteristic, complemented
41#13063333—24no—
42#13063333—42no—
43C2×#10621872—41no—
44C22×C43⋊C8D411yescharacteristic
45C2×C8×D43—41no—
46D4×Dic43—24no—
47D4×Dic43—42no—
48C2×C4⋊Dic43—21no—
49C2×C22⋊Dic43—41no—
50C2×C4×Dic43D411yescharacteristic
51#13063269C2×C418yescomplemented
52#13063266C2×C418yescomplemented
53#13063265C2×C412yescomplemented
54#13063265C2312yes—
55C2×C43⋊C16C2×C412yescomplemented
56#13063257—21no—
57#13063257C2312yes—
58#13063251—24no—
59#13063246—24no—
60#13063235D412yes—
61#13063235C2312yes—
62C22×D4×C43—21no—
63C2×D8×C43—21no—
64C2×D8×C43—21no—
65C2×D8×C43—21no—
66C2×D8×C43C2×C412yes—
67C2×D8×C43C2×C412yes—
68C2×D8×C43C2312yes—
69C2×M16×C43—21no—
70C22×C8×C43C2311yescharacteristic
71M32×C43—21no—
72M32×C43C2312yes—
73C2×C16×C43—21no—
74#108×C43—21no—
75#108×C43C2312yes—
76C24×C43—41no—
77C2×D4×C43—22no—
78C2×D4×C43—22no—
79C2×D4×C43—22no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C22×C4×C43C2×D411yescharacteristic
84C2×C22⋊D43—41no—
85C22×Dic43—21no—
86C22×Dic43—44no—
87C22×Dic43—41no—
88C22×Dic43—84no—
89#10621898—22no—
90#10621898—22no—
91#10621898—41no—
92#10621898—41no—
93C2×D172—21no—
94C2×C4×D43—41no—
95C2×Dic86—21no—
96D8×C43—22no—
97D8×C43—22no—
98D8×C43—22no—
99D8×C43C22×C414yes—
100M16×C43—22no—
101M16×C43—41no—
102C2×C8×C43—41no—
103C2×C8×C43C22×C411yescharacteristic
104C2×C8×C43C22×C411yescharacteristic
105C2×C8×C43C2×D411yescharacteristic
106C2×C8×C43#4111yescharacteristic
107C2×C8×C43#4111yescharacteristic
108C2×C8×C43C2411yescharacteristic
109C22⋊Dic43—44no—
110C4⋊Dic43—22no—
111C4⋊Dic43—41no—
112C4×Dic43—21no—
113C4×Dic43C2×D412yes—
114C2×C43⋊C8—21no—
115C2×C43⋊C8—21no—
116C2×C43⋊C8C2×D412yes—
117Dic172—21no—
118Dic172C22×C412yescomplemented
119D344—21no—
120D344C22×C412yescomplemented
121#10621873—22no—
122#10621873—22no—
123#10621872—44no—
124C8×D43—44no—
125C16×C43—22no—
126C43⋊C16C22×C414yescomplemented
127C23×C43—42no—
128C23×C43—42no—
129C23×C43—42no—
130C23×C43—82no—
131C23×C43—82no—
132C23×C43AGL(1,ℤ/8)11yescharacteristic
133C22×D43—41no—
134D4×C43—24no—
135D4×C43—42no—
136D4×C43—42no—
137D4×C43—42no—
138C2×C4×C43C4×D411yescharacteristic
139C2×C4×C43C4×D411yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43C22×D411yescharacteristic
144C22⋊D43—42no—
145C22⋊D43—42no—
146C2×Dic43—22no—
147C2×Dic43—42no—
148C2×Dic43—41no—
149C2×Dic43—42no—
150C2×Dic43—88no—
151C2×Dic43—82no—
152D172—22no—
153D172—41no—
154C4×D43—42no—
155C4×D43—42no—
156Dic86—22no—
157Dic86—41no—
158C8×C43—42no—
159C8×C43C4×D411yescharacteristic
160C8×C43C4×D411yescharacteristic
161C8×C43C23×C411yescharacteristic
162C8×C43C2×#4111yescharacteristic
163C43⋊C8—22no—
164C2×AGL(1,ℤ/16)—431nomaximal, Sylow
165C22×C43—22no—
166C22×C43—44no—
167C22×C43—82no—
168C22×C43—84no—
169C22×C43—82no—
170C22×C43—84no—
171C22×C43#44211yescharacteristic
172C22×C43#44211yescharacteristic
173C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
174C2×D43—42no—
175C2×D43—82no—
176C4×C43#44211yescharacteristic
177C4×C43#44211yescharacteristic
178C4×C43C2×C4×D411yescharacteristic
179C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
180Dic43—42no—
181Dic43—42no—
182Dic43—82no—
183C2×#509—431no—
184C2×#444—431no—
185C2×#442—431no—
186AGL(1,ℤ/16)—438no—
187C2×#365—431no—
188C2×#361D4311yescharacteristic, complemented
189C2×#360—431no—
190C2×#347—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43—84no—
194C2×C43AGL(1,ℤ/16)12yescomplemented
195C2×C43C2×#44211yescharacteristic
196D43—82no—
197C2×#135—431no—
198C22×D8C2×D4311yescharacteristic
199C2×#131—861no—
200C2×C4×D4—861no—
201#509—434no—
202#509—434no—
203C2×SD32—432no—
204C2×D16—432no—
205C2×M32—431no—
206C2×M32C2×D4311yescharacteristic
207#444—434no—
208#444—862no—
209#442—434no—
210#442—862no—
211C2×#108C2×D4311yescharacteristic
212C2×#106—431no—
213C2×#104—861no—
214C2×#102—861no—
215C2×#97—431no—
216#365—434no—
217#361C2×D4314yescomplemented
218#360—434no—
219#347—434no—
220C43C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
221C2×#41—861no—
222C22×D4—21no—
223C23×C4—1721no—
224#135—432no—
225#135—432no—
226#135—861no—
227#135—861no—
228C2×Q16—431no—
229C2×SD16—861no—
230C2×D8—21no—
231C2×D8—21no—
232C2×D8—21no—
233C2×D8—431no—
234C2×D8C4×D4312yes—
235C2×D8C4×D4312yes—
236C2×D8C22×D4312yes—
237#131—864no—
238#131—1722no—
239C2×M16—21no—
240C2×M16—1721no—
241C22×C8—431no—
242C22×C8—1721no—
243C22×C8C22×D4311yescharacteristic
244C4×D4—864no—
245C4×D4—1722no—
246C2×C4⋊C4—861no—
247C2×C22⋊C4—1721no—
248C2×C42—431no—
249SD32—438no—
250D16—438no—
251M32—21no—
252M32—432no—
253M32—432no—
254M32C22×D4312yes—
255C2×C16—21no—
256C2×C16—432no—
257#108—21no—
258#108C22×D4312yes—
259#106—432no—
260#106—861no—
261#104—864no—
262#102—864no—
263#97—432no—
264#97—432no—
265C24—41no—
266#41—862no—
267#41—862no—
268#41—1721no—
269#41—1721no—
270C2×Q8—861no—
271C2×D4—22no—
272C2×D4—22no—
273C2×D4—22no—
274C2×D4—41no—
275C2×D4—41no—
276C2×D4—41no—
277C2×D4—861no—
278C2×D4—1721no—
279C22×C4—861no—
280C22×C4—3444no—
281C22×C4—1724no—
282C22×C4—1721no—
283C22×C4—1721no—
284C22×C4D4×D4311yescharacteristic
285Q16—432no—
286Q16—861no—
287SD16—862no—
288SD16—862no—
289D8—22no—
290D8—22no—
291D8—22no—
292D8—432no—
293D8—861no—
294D8C2×C4×D4314yes—
295M16—22no—
296M16—41no—
297M16—1724no—
298C2×C8—41no—
299C2×C8—432no—
300C2×C8—861no—
301C2×C8—861no—
302C2×C8—1724no—
303C2×C8C2×C4×D4311yescharacteristic
304C2×C8C2×C4×D4311yescharacteristic
305C2×C8D4×D4311yescharacteristic
306C2×C8#1062190011yescharacteristic
307C2×C8#1062190011yescharacteristic
308C2×C8C23×D4311yescharacteristic
309C4⋊C4—862no—
310C4⋊C4—1721no—
311C22⋊C4—1724no—
312C42—432no—
313C42—861no—
314C16—22no—
315C16—434no—
316C23—42no—
317C23—42no—
318C23—42no—
319C23—82no—
320C23—82no—
321C23—1721no—
322C23#1306335211yescharacteristic
323Q8—862no—
324Q8—1721no—
325D4—24no—
326D4—42no—
327D4—42no—
328D4—42no—
329D4—862no—
330D4—1722no—
331D4—1722no—
332D4—1721no—
333C2×C4—862no—
334C2×C4—3442no—
335C2×C4—3448no—
336C2×C4—1722no—
337C2×C4—1722no—
338C2×C4—1721no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4(C22⋊D43)⋊C411yescharacteristic
342C2×C4(C22⋊D43)⋊C411yescharacteristic
343C2×C4#1306334911yescharacteristic
344C2×C4#1306334911yescharacteristic
345C2×C4#1306335211yescharacteristic
346C2×C4C2×D4×D4311yescharacteristic
347C8—42no—
348C8—862no—
349C8(C22⋊D43)⋊C411yescharacteristic
350C8(C22⋊D43)⋊C411yescharacteristic
351C8C22×C4×D4311yescharacteristic
352C8C2×#1062190011yescharacteristic
353C22—22no—
354C22—44no—
355C22—82no—
356C22—82no—
357C22—84no—
358C22—84no—
359C22—3442no—
360C22—1722no—
361C22#1458300811yescharacteristic
362C22#1458300811yescharacteristic
363C22C2×#1306335211yescharacteristic
364C4—3442no—
365C4—1722no—
366C4—1722no—
367C4#1458300811yescharacteristic
368C4#1458300811yescharacteristic
369C4C2×(C22⋊D43)⋊C411yescharacteristic
370C4C2×#1306334911yescharacteristic
371C2—21no—
372C2—21no—
373C2—84no—
374C2—3442no—
375C2#1913649612yesdirect product factor
376C2C2×#1458300811yescharacteristic
subgroupG/H
centerC22#14583008
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#361C2
socleC22×C43#442
prime radicalC2×#14583335C2
cosocleC2×C8×C43C24
hypercenterC2×#361D43
hypocenterC43C2×AGL(1,ℤ/16)
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#14583020C2semidirect
3. C2×#14583011C2semidirect
4. #19136496C2direct (N × H)
5. C2×#14582723C2semidirect
6. C2×#14582710C2semidirect
7. C2×#14582676C2semidirect
8. C2×C43×#361C2semidirect
12. #14583335C4semidirect
14. C2×#13063269C4semidirect
15. C2×#13063266C4semidirect
18. #14583020C22semidirect
20. #14583011C22semidirect
25. #14582723C22semidirect
26. #14582710C22semidirect
27. #14582676C22semidirect
31. C43×#361C22semidirect
36. #13063347C2×C4semidirect
38. C2×Dic172C2×C4semidirect
40. C2×D344C2×C4semidirect
51. #13063269C2×C4semidirect
52. #13063266C2×C4semidirect
53. #13063265C2×C4semidirect
55. C2×C43⋊C16C2×C4semidirect
118. Dic172C22×C4semidirect
120. D344C22×C4semidirect
126. C43⋊C16C22×C4semidirect
188. C2×#361D43semidirect
194. C2×C43AGL(1,ℤ/16)semidirect
217. #361C2×D43semidirect
220. C43C2×AGL(1,ℤ/16)semidirect
375. C2#19136496direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833352
C2×#145830202
C2×#145830112
#191364962
C2×#145827232
C2×#145827102
C2×#145826762
C2×C43×#3612
C2×AGL(1,ℤ/16)43