Finite Group Databasebeta

← C2×#19143446 #25960724

Subgroups — C2×#19143446 #25960724

Order 11008.

3086 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D344C211yesmaximal, characteristic
2C2×#14583373C212yesmaximal, complemented
3#19143446C2116yesmaximal, direct product factor
4C2×#14583010C214yesmaximal, complemented
5C2×#14582981C214yesmaximal, complemented
6C2×#14582903C212yesmaximal, complemented
7C2×#14582854C211yesmaximal, characteristic, complemented
8C2×C43×#427C211yesmaximal, characteristic, complemented
9C23×D172C2212yes—
10C22×D344C4116yescomplemented
11C22×D344C2218yes—
12C22×D344C2212yes—
13C22×D344C2212yes—
14C22×#10621877C2211yescharacteristic
15#14583373—28no—
16#14583373C22116yescomplemented
17C2×C4×D172—24no—
18C2×#13063287C2218yescomplemented
19C2×#13063284C2211yescharacteristic
20C2×C22⋊C4×D43—24no—
21#14583010C22132yescomplemented
22#14582981C22132yescomplemented
23#14582903C22116yescomplemented
24C2×#13063245C2218yescomplemented
25#14582854C2218yescomplemented
26C2×#13063235C2212yescomplemented
27C2×C8×Dic43C2212yescomplemented
28C23×C8×C43C2211yescharacteristic
29C2×#117×C43C2212yes—
30C43×#427C2218yescomplemented
31C2×#107×C43C2212yescomplemented
32C2×#106×C43C2212yescomplemented
33C24×D43—22no—
34C22×D172—22no—
35C22×D172—24no—
36C22×D172—28no—
37C22×D172C2×C4116yescomplemented
38C22×D172C2314yes—
39C22×D172C2318yes—
40C22×C4×D43—28no—
41C2×D344C2×C4116yescomplemented
42C2×D344C2×C4116yescomplemented
43C2×D344C2×C4164yescomplemented
44C2×D344C2318yes—
45C2×D344C2318yes—
46C2×#10621877—24no—
47C2×#10621877C2314yes—
48C22×C43⋊C8C2312yes—
49C4×D172—232no—
50#13063287—216no—
51#13063287C23132yescomplemented
52#13063284D414yes—
53#13063284C2314yes—
54C2×C4⋊Dic43D412yes—
55C2×C22⋊Dic43D412yes—
56C2×(C2×D43)⋊C4—28no—
57C22⋊C4×D43—232no—
58C2×C4×Dic43C2312yes—
59#13063245C23132yescomplemented
60#13063235C2318yescomplemented
61C8×Dic43C2318yescomplemented
62C23×C4×C43C2311yescharacteristic
63C22×C8×C43C2×C418yescomplemented
64C22×C8×C43C2311yescharacteristic
65C22×C8×C43C2311yescharacteristic
66C22×C8×C43C2314yes—
67#117×C43—24no—
68#117×C43C2318yes—
69C2×C4⋊C4×C43C2314yes—
70C2×C22⋊C4×C43—22no—
71C2×C42×C43—22no—
72#107×C43C2318yescomplemented
73#106×C43C2318yescomplemented
74C24×C43C2×D411yescharacteristic
75C23×D43—24no—
76C23×D43—216no—
77C23×D43—28no—
78C23×D43—88no—
79C22×C4×C43—24no—
80C22×C4×C43C22×C414yes—
81C22×C4×C43C2×D411yescharacteristic
82C22×C4×C43C2×D412yes—
83C22×C4×C43#4114yes—
84C22×C4×C43C2411yescharacteristic
85C22×C4×C43C2412yes—
86C22×Dic43C2×D414yes—
87C2×D172—216no—
88C2×D172—232no—
89C2×D172—24no—
90C2×D172—28no—
91C2×D172—28no—
92C2×D172—216no—
93C2×D172C22×C4116yes—
94C2×D172C22×C4132yescomplemented
95C2×D172C2418yes—
96C2×C4×D43—232no—
97C2×C4×D43—816no—
98C2×C8×C43C22×C414yes—
99C2×C8×C43C22×C414yes—
100C2×C8×C43C22×C4116yescomplemented
101C2×C8×C43C2412yes—
102C2×C8×C43C2412yes—
103C4⋊C4×C43—24no—
104C4⋊C4×C43C2418yes—
105C22⋊C4×C43—28no—
106C42×C43—28no—
107C22⋊Dic43C2×D418yes—
108(C2×D43)⋊C4—232no—
109C4⋊Dic43C2×D418yes—
110C4×Dic43C2×D414yes—
111C4×Dic43C2414yes—
112#10621877—28no—
113C2×C43⋊C8—24no—
114C2×C43⋊C8C2414yes—
115D344C22×C4132yescomplemented
116D344C22×C4132yescomplemented
117C23×C43—24no—
118C23×C43C4×D414yes—
119C23×C43C22×D412yes—
120C23×C43C22×D411yescharacteristic
121C22×D43—216no—
122C22×D43—28no—
123C22×D43—232no—
124C22×D43—416no—
125C22×D43—832no—
126C22×D43—816no—
127C2×C4×C43—28no—
128C2×C4×C43—48no—
129C2×C4×C43C4×D418yes—
130C2×C4×C43C4×D414yes—
131C2×C4×C43C23×C412yes—
132C2×C4×C43C23×C414yes—
133C2×C4×C43C22×D411yescharacteristic
134C2×C4×C43C22×D412yes—
135C2×C4×C43C2×#4112yes—
136C2×C4×C43C2×#4114yes—
137C2×C4×C43C2511yescharacteristic
138C2×Dic43—28no—
139C2×Dic43C22×D418yes—
140D172—216no—
141D172—232no—
142D172—28no—
143D172C23×C4116yes—
144C4×D43—832no—
145C8×C43C23×C414yes—
146C8×C43C23×C414yes—
147C43⋊C8—24no—
148C2×#2948—431nomaximal, Sylow
149C22×C43—28no—
150C22×C43—24no—
151C22×C43C2×C4×D414yes—
152C22×C43C2×C4×D412yes—
153C22×C43#57614yes—
154C22×C43C23×D411yescharacteristic
155C2×D43—216no—
156C2×D43—432no—
157C2×D43—416no—
158C2×D43—832no—
159C4×C43—48no—
160C4×C43C2×C4×D412yes—
161C4×C43C2×C4×D414yes—
162C4×C43C24×C411yescharacteristic
163C4×C43C22×#4111yescharacteristic
164Dic43—28no—
165C23×D8—431no—
166C2×#518—432no—
167#2948—4316no—
168C2×#442—434no—
169C2×C4×D8—434no—
170C2×#427D4311yescharacteristic, complemented
171C2×#418—432no—
172C2×#405—431no—
173C2×C43—24no—
174C2×C43#294814yescomplemented
175C2×C43C22×C4×D411yescharacteristic
176C2×C43C2×#57612yes—
177D43—416no—
178C23×D4—432no—
179C22×D8—432no—
180C22×D8—432no—
181C22×D8—438no—
182C22×D8—4316no—
183C22×M16—431no—
184C23×C8C2×D4311yescharacteristic
185#518—4316no—
186#518—868no—
187C2×C4×D4—438no—
188C2×C4×D4—864no—
189C2×#117—431no—
190C2×#117C2×D4312yes—
191C22×C22⋊C4—864no—
192#442—4332no—
193C4×D8—4332no—
194#427C2×D4318yescomplemented
195C2×#107C2×D4312yescomplemented
196C2×#106C2×D4312yescomplemented
197#418—4316no—
198C2×#102—438no—
199#405—438no—
200C2×#97—432no—
201C2×C4×C8—432no—
202C43C2×#294811yescharacteristic, complemented, Sylow
203C25—862no—
204C22×D4—4316no—
205C22×D4—434no—
206C22×D4—438no—
207C22×D4—862no—
208C22×D4—864no—
209C22×D4—868no—
210C23×C4—868no—
211C23×C4C22×D4311yescharacteristic
212C2×D8—4316no—
213C2×D8—4316no—
214C2×D8—4364no—
215C2×D8—438no—
216C2×D8—438no—
217C2×M16—434no—
218C2×M16—864no—
219C22×C8—432no—
220C22×C8C4×D4318yescomplemented
221C22×C8C22×D4311yescharacteristic
222C22×C8C22×D4311yescharacteristic
223C22×C8C22×D4314yes—
224C4×D4—4332no—
225C4×D4—8632no—
226C4×D4—8616no—
227#117—24no—
228#117—434no—
229#117—434no—
230#117C22×D4318yes—
231C2×C4⋊C4—432no—
232C2×C4⋊C4C22×D4314yes—
233C2×C22⋊C4—22no—
234C2×C22⋊C4—432no—
235C2×C22⋊C4—8632no—
236C2×C22⋊C4—868no—
237C2×C42—22no—
238C2×C42—432no—
239#107C22×D4318yescomplemented
240#106C22×D4318yescomplemented
241#102—4332no—
242#97—438no—
243C4×C8—438no—
244C24—8616no—
245C24—868no—
246C24—864no—
247C24—3448no—
248C24D4×D4311yescharacteristic
249C2×D4—4316no—
250C2×D4—4332no—
251C2×D4—438no—
252C2×D4—8632no—
253C2×D4—8616no—
254C2×D4—868no—
255C2×D4—864no—
256C2×D4—868no—
257C2×D4—8616no—
258C22×C4—24no—
259C22×C4—434no—
260C22×C4—8632no—
261C22×C4—34416no—
262C22×C4C2×C4×D4314yes—
263C22×C4D4×D4312yes—
264C22×C4D4×D4311yescharacteristic
265C22×C4#1062190214yes—
266C22×C4C23×D4312yes—
267C22×C4C23×D4311yescharacteristic
268D8—4332no—
269D8—4332no—
270M16—868no—
271C2×C8—434no—
272C2×C8—864no—
273C2×C8C2×C4×D4314yes—
274C2×C8C2×C4×D4314yes—
275C2×C8C2×C4×D43116yescomplemented
276C2×C8C23×D4312yes—
277C2×C8C23×D4312yes—
278C4⋊C4—24no—
279C4⋊C4—438no—
280C4⋊C4C23×D4318yes—
281C22⋊C4—28no—
282C22⋊C4—438no—
283C22⋊C4—8632no—
284C42—28no—
285C42—434no—
286C42—434no—
287C23—24no—
288C23—8632no—
289C23—8616no—
290C23—868no—
291C23—34432no—
292C23—34416no—
293C23—17216no—
294C23#1306328714yes—
295C23C2×D4×D4312yes—
296C23C2×D4×D4311yescharacteristic
297D4—4316no—
298D4—8616no—
299D4—8632no—
300D4—868no—
301C2×C4—28no—
302C2×C4—48no—
303C2×C4—438no—
304C2×C4—868no—
305C2×C4—34432no—
306C2×C4#1306328718yes—
307C2×C4#1306328714yes—
308C2×C4C22×C4×D4312yes—
309C2×C4C22×C4×D4314yes—
310C2×C4C2×D4×D4312yes—
311C2×C4C2×D4×D4311yescharacteristic
312C2×C4C2×#1062190212yes—
313C2×C4C2×#1062190214yes—
314C2×C4C24×D4311yescharacteristic
315C8—864no—
316C8C22×C4×D4314yes—
317C8C22×C4×D4314yes—
318C22—28no—
319C22—24no—
320C22—8616no—
321C22—34432no—
322C22—17232no—
323C22—17216no—
324C22C2×#1306328714yes—
325C22C2×#1306328712yes—
326C22#1458370114yes—
327C22C22×D4×D4311yescharacteristic
328C4—48no—
329C4—868no—
330C4C2×#1306328712yes—
331C4C2×#1306328714yes—
332C4C23×C4×D4311yescharacteristic
333C4C22×#1062190211yescharacteristic
334C2—24no—
335C2—17216no—
336C2#1914344614yesdirect product factor
337C2C22×#1306328711yescharacteristic
338C2C2×#1458370112yes—
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC2×C43×#427C2
socleC23×C43C22×D4
prime radicalC23×D344C2
cosocleC2×C4×C43C25
hypercenterC2×#427D43
hypocenterC43C2×#2948
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#427

Complements

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

NH ≅ G/Ntype
2. C2×#14583373C2semidirect
3. #19143446C2direct (N × H)
4. C2×#14583010C2semidirect
5. C2×#14582981C2semidirect
6. C2×#14582903C2semidirect
7. C2×#14582854C2semidirect
8. C2×C43×#427C2semidirect
10. C22×D344C4semidirect
16. #14583373C22semidirect
18. C2×#13063287C22semidirect
21. #14583010C22semidirect
22. #14582981C22semidirect
23. #14582903C22semidirect
24. C2×#13063245C22semidirect
25. #14582854C22semidirect
26. C2×#13063235C22semidirect
27. C2×C8×Dic43C22semidirect
30. C43×#427C22semidirect
31. C2×#107×C43C22semidirect
32. C2×#106×C43C22semidirect
37. C22×D172C2×C4semidirect
41. C2×D344C2×C4semidirect
42. C2×D344C2×C4semidirect
43. C2×D344C2×C4semidirect
51. #13063287C23semidirect
59. #13063245C23semidirect
60. #13063235C23semidirect
61. C8×Dic43C23semidirect
63. C22×C8×C43C2×C4semidirect
72. #107×C43C23semidirect
73. #106×C43C23semidirect
94. C2×D172C22×C4semidirect
100. C2×C8×C43C22×C4semidirect
115. D344C22×C4semidirect
116. D344C22×C4semidirect
170. C2×#427D43semidirect
174. C2×C43#2948semidirect
194. #427C2×D43semidirect
195. C2×#107C2×D43semidirect
196. C2×#106C2×D43semidirect
202. C43C2×#2948semidirect
220. C22×C8C4×D43semidirect
239. #107C22×D43semidirect
240. #106C22×D43semidirect
275. C2×C8C2×C4×D43semidirect
336. C2#19143446direct (N × H)

Maximal subgroups

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

subgroupindex
C23×D3442
C2×#145833732
#191434462
C2×#145830102
C2×#145829812
C2×#145829032
C2×#145828542
C2×C43×#4272
C2×#294843