Finite Group Databasebeta

← C2×#19136492 #25250037

Subgroups — C2×#19136492 #25250037

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×#14583337C211yesmaximal, characteristic
2C2×#14583020C211yesmaximal, characteristic, complemented
3C2×#14583010C211yesmaximal, characteristic, complemented
4#19136492C218yesmaximal, direct product factor
5C2×#14582711C211yesmaximal, characteristic, complemented
6C2×#14582708C211yesmaximal, characteristic, complemented
7C2×#14582676C211yesmaximal, characteristic, complemented
8C2×C43×#365C211yesmaximal, characteristic, complemented
9C2×#13063347C2211yescharacteristic
10C22×D344C2211yescharacteristic
11C2×#13063333—21no—
12C2×#13063287—21no—
13#14583337C414yescomplemented
14#14583337C2214yes—
15C2×#13063270C412yescomplemented
16C2×D688C412yescomplemented
17C2×#13063265C2211yescharacteristic
18#14583020—22no—
19#14583020C2214yescomplemented
20#14583010—22no—
21#14583010C2214yescomplemented
22C2×#13063251—21no—
23C2×#13063245—21no—
24C2×#13063235C2211yescharacteristic
25#14582711C2214yescomplemented
26#14582708C2214yescomplemented
27#14582676C2214yescomplemented
28C2×M32×C43C2211yescharacteristic
29C2×#108×C43C2211yescharacteristic
30C2×#106×C43C2211yescharacteristic
31C43×#365C2214yescomplemented
32C2×#10621898—21no—
33C22×D172—21no—
34C22×C4×D43—41no—
35#13063347—21no—
36#13063347—21no—
37#13063347C2×C412yescomplemented
38#13063347C2312yes—
39C2×Dic172C2×C411yescharacteristic, complemented
40C2×#10621873—21no—
41C2×D344—21no—
42C2×D344—21no—
43C2×D344—21no—
44C2×D344C2×C412yes—
45C2×D344C2×C412yes—
46C2×D344C2×C411yescharacteristic, complemented
47C2×D344C2312yes—
48#13063333—24no—
49#13063333—42no—
50C2×#10621872—41no—
51C22×C43⋊C8D411yescharacteristic
52C2×C8×D43—41no—
53#13063287—24no—
54#13063287—42no—
55C2×(C2×D43)⋊C4—41no—
56C2×C4×Dic43D411yescharacteristic
57#13063270C2×C418yescomplemented
58D688C2×C418yescomplemented
59#13063265—21no—
60#13063265C2312yes—
61C2×C43⋊C16—21no—
62#13063251—24no—
63#13063245—24no—
64#13063235D412yes—
65#13063235C2312yes—
66C2×M16×C43—21no—
67C22×C8×C43C2311yescharacteristic
68C2×C4⋊C4×C43—21no—
69M32×C43C2×C412yescomplemented
70M32×C43C2312yes—
71C2×C16×C43C2×C412yescomplemented
72#108×C43—21no—
73#108×C43C2312yes—
74#106×C43—21no—
75#106×C43C2312yes—
76C23×D43—41no—
77C22×C4×C43—41no—
78C22×C4×C43C2×D411yescharacteristic
79C2×C22⋊D43—41no—
80C22×Dic43—21no—
81#10621898—22no—
82#10621898—22no—
83#10621898—41no—
84#10621898—41no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—21no—
88C2×D172—22no—
89C2×D172—41no—
90C2×D172—41no—
91C2×D172—41no—
92C2×C4×D43—41no—
93C2×C4×D43—44no—
94C2×C4×D43—84no—
95C2×Dic86—21no—
96M16×C43—22no—
97M16×C43—41no—
98C2×C8×C43—41no—
99C2×C8×C43C22×C411yescharacteristic
100C2×C8×C43C22×C411yescharacteristic
101C2×C8×C43C2×D411yescharacteristic
102C2×C8×C43#4111yescharacteristic
103C2×C8×C43#4111yescharacteristic
104C2×C8×C43C2411yescharacteristic
105C4⋊C4×C43—22no—
106C4⋊C4×C43—41no—
107(C2×D43)⋊C4—44no—
108C4×Dic43—21no—
109C4×Dic43C2×D412yes—
110C2×C43⋊C8—21no—
111C2×C43⋊C8—21no—
112C2×C43⋊C8C2×D412yes—
113Dic172—21no—
114Dic172C22×C412yescomplemented
115D344—22no—
116D344—22no—
117D344—21no—
118D344—22no—
119D344C22×C414yes—
120D344C22×C412yescomplemented
121#10621873—22no—
122#10621873—22no—
123#10621872—44no—
124C8×D43—44no—
125C16×C43C22×C414yescomplemented
126C43⋊C16—22no—
127C23×C43AGL(1,ℤ/8)11yescharacteristic
128C22×D43—42no—
129C22×D43—41no—
130C22×D43—42no—
131C22×D43—42no—
132C22×D43—82no—
133C22×D43—82no—
134C2×C4×C43—42no—
135C2×C4×C43—82no—
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
140C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
141C2×C4×C43C22×D411yescharacteristic
142C22⋊D43—42no—
143C22⋊D43—42no—
144C2×Dic43—22no—
145C2×Dic43—42no—
146C2×Dic43—41no—
147D172—22no—
148D172—24no—
149D172—42no—
150D172—42no—
151D172—42no—
152D172—41no—
153C4×D43—42no—
154C4×D43—42no—
155C4×D43—88no—
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#44211yescharacteristic
167C22×C43#44211yescharacteristic
168C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
169C2×D43—44no—
170C2×D43—42no—
171C2×D43—82no—
172C2×D43—84no—
173C2×D43—82no—
174C2×D43—82no—
175C2×D43—84no—
176C4×C43—82no—
177C4×C43#44211yescharacteristic
178C4×C43#44211yescharacteristic
179C4×C43C2×C4×D411yescharacteristic
180C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
181Dic43—42no—
182Dic43—42no—
183C2×#509—431no—
184C2×#444—431no—
185C2×#442—431no—
186AGL(1,ℤ/16)—438no—
187C2×#365D4311yescharacteristic, complemented
188C2×#361—431no—
189C2×#360—431no—
190C2×#347—431no—
191C2×C43—21no—
192C2×C43—21no—
193C2×C43AGL(1,ℤ/16)12yescomplemented
194C2×C43C2×#44211yescharacteristic
195D43—82no—
196D43—84no—
197C2×#135—431no—
198C22×D8—431no—
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×#106C2×D4311yescharacteristic
213C2×#104—861no—
214C2×#102—861no—
215C2×#97—431no—
216#365C2×D4314yescomplemented
217#361—434no—
218#360—434no—
219#347—434no—
220C43C2×AGL(1,ℤ/16)11yescharacteristic, complemented, Sylow
221C2×#41—861no—
222C22×D4—861no—
223C23×C4—1721no—
224#135—432no—
225#135—432no—
226#135—861no—
227#135—861no—
228C2×Q16—431no—
229C2×SD16—861no—
230C2×D8—432no—
231C2×D8—432no—
232C2×D8—431no—
233C2×D8—432no—
234C2×D8—861no—
235C2×D8—861no—
236C2×D8—861no—
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—21no—
247C2×C22⋊C4—1721no—
248C2×C42—431no—
249SD32—438no—
250D16—438no—
251M32—432no—
252M32—861no—
253M32C4×D4312yescomplemented
254M32C22×D4312yes—
255C2×C16—861no—
256C2×C16C4×D4312yescomplemented
257#108—21no—
258#108C22×D4312yes—
259#106—21no—
260#106C22×D4312yes—
261#104—864no—
262#102—864no—
263#97—432no—
264#97—432no—
265C24—1721no—
266#41—862no—
267#41—862no—
268#41—1721no—
269#41—1721no—
270C2×Q8—861no—
271C2×D4—862no—
272C2×D4—862no—
273C2×D4—861no—
274C2×D4—862no—
275C2×D4—1721no—
276C2×D4—1721no—
277C2×D4—1721no—
278C2×D4—1721no—
279C22×C4—41no—
280C22×C4—861no—
281C22×C4—3444no—
282C22×C4—1724no—
283C22×C4—1721no—
284C22×C4D4×D4311yescharacteristic
285Q16—432no—
286Q16—861no—
287SD16—862no—
288SD16—862no—
289D8—432no—
290D8—434no—
291D8—862no—
292D8—862no—
293D8—861no—
294D8—862no—
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#1062190211yescharacteristic
307C2×C8#1062190211yescharacteristic
308C2×C8C23×D4311yescharacteristic
309C4⋊C4—22no—
310C4⋊C4—41no—
311C22⋊C4—1724no—
312C42—432no—
313C42—861no—
314C16—862no—
315C16C2×C4×D4314yescomplemented
316C23—3442no—
317C23—3442no—
318C23—1722no—
319C23—1722no—
320C23—1721no—
321C23—1722no—
322C23#1306335211yescharacteristic
323Q8—862no—
324Q8—1721no—
325D4—864no—
326D4—862no—
327D4—1722no—
328D4—1722no—
329D4—1722no—
330D4—1722no—
331D4—1722no—
332D4—1721no—
333C2×C4—42no—
334C2×C4—82no—
335C2×C4—862no—
336C2×C4—3448no—
337C2×C4—1722no—
338C2×C4—1721no—
339C2×C4—1722no—
340C2×C4—1722no—
341C2×C4#1306328711yescharacteristic
342C2×C4#1306328711yescharacteristic
343C2×C4#1306335211yescharacteristic
344C2×C4#1306335211yescharacteristic
345C2×C4#1306335211yescharacteristic
346C2×C4C2×D4×D4311yescharacteristic
347C8—42no—
348C8—862no—
349C8#1306328711yescharacteristic
350C8#1306328711yescharacteristic
351C8C22×C4×D4311yescharacteristic
352C8C2×#1062190211yescharacteristic
353C22—22no—
354C22—3442no—
355C22—3442no—
356C22—3444no—
357C22—3444no—
358C22—3442no—
359C22—1722no—
360C22—1724no—
361C22#1458301011yescharacteristic
362C22#1458301011yescharacteristic
363C22C2×#1306335211yescharacteristic
364C4—82no—
365C4—1722no—
366C4—1722no—
367C4#1458301011yescharacteristic
368C4#1458301011yescharacteristic
369C4C2×#1306328711yescharacteristic
370C4C2×#1306335211yescharacteristic
371C2—21no—
372C2—21no—
373C2—3444no—
374C2—3442no—
375C2#1913649212yesdirect product factor
376C2C2×#1458301011yescharacteristic
subgroupG/H
centerC22#14583010
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#365C2
socleC22×C43#442
prime radicalC2×#14583337C2
cosocleC2×C8×C43C24
hypercenterC2×#365D43
hypocenterC43C2×AGL(1,ℤ/16)
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. C2×#14583020C2semidirect
3. C2×#14583010C2semidirect
4. #19136492C2direct (N × H)
5. C2×#14582711C2semidirect
6. C2×#14582708C2semidirect
7. C2×#14582676C2semidirect
8. C2×C43×#365C2semidirect
13. #14583337C4semidirect
15. C2×#13063270C4semidirect
16. C2×D688C4semidirect
19. #14583020C22semidirect
21. #14583010C22semidirect
25. #14582711C22semidirect
26. #14582708C22semidirect
27. #14582676C22semidirect
31. C43×#365C22semidirect
37. #13063347C2×C4semidirect
39. C2×Dic172C2×C4semidirect
46. C2×D344C2×C4semidirect
57. #13063270C2×C4semidirect
58. D688C2×C4semidirect
69. M32×C43C2×C4semidirect
71. C2×C16×C43C2×C4semidirect
114. Dic172C22×C4semidirect
120. D344C22×C4semidirect
125. C16×C43C22×C4semidirect
187. C2×#365D43semidirect
193. C2×C43AGL(1,ℤ/16)semidirect
216. #365C2×D43semidirect
220. C43C2×AGL(1,ℤ/16)semidirect
253. M32C4×D43semidirect
256. C2×C16C4×D43semidirect
315. C16C2×C4×D43semidirect
375. C2#19136492direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145833372
C2×#145830202
C2×#145830102
#191364922
C2×#145827112
C2×#145827082
C2×#145826762
C2×C43×#3652
C2×AGL(1,ℤ/16)43