Finite Group Databasebeta

← C2×#19127847 #24916665

Subgroups — C2×#19127847 #24916665

Order 10624.

812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.

normal subgroups only

This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13050589C211yesmaximal, characteristic, complemented
2C22×#13050579C211yesmaximal, characteristic, complemented
3C22×#13050575C211yesmaximal, characteristic, complemented
4C2×#14581767C211yesmaximal, characteristic, complemented
5#19127847C218yesmaximal, direct product factor
6C2×#14581715C211yesmaximal, characteristic, complemented
7C2×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
8C2×#102×C83C211yesmaximal, characteristic, complemented
9C2×#13050589—24no—
10C2×#13050589—22no—
11C2×#13050589—24no—
12C2×#13050589C2214yescomplemented
13C22×Dic166C2211yescharacteristic
14C22×D332—21no—
15C22×D332C2211yescharacteristic
16C22×C22⋊D83—21no—
17C23×Dic83—21no—
18C22×C4×D83C2211yescharacteristic
19C2×#13050579—24no—
20C2×#13050579C2214yescomplemented
21C2×#13050575—24no—
22C2×#13050575C2214yescomplemented
23C22×C83⋊C8C2211yescharacteristic
24#14581767—22no—
25#14581767C2214yescomplemented
26C2×(C2×D83)⋊C4—21no—
27#14581715C2214yescomplemented
28(C2×D83)⋊C8C2214yescomplemented
29C22×D4×C83C2211yescharacteristic
30C22×C8×C83C2211yescharacteristic
31C2×C4⋊C4×C83C2211yescharacteristic
32#102×C83C2214yescomplemented
33C23×D83—21no—
34C23×D83D411yescharacteristic
35#13050589—216no—
36#13050589—28no—
37#13050589—28no—
38C2×Dic166—21no—
39C2×Dic166—22no—
40C2×Dic166D414yescomplemented
41C2×Dic166C2312yes—
42C2×D332—22no—
43C2×D332—22no—
44C2×D332—24no—
45C2×D332—21no—
46C2×D332—44no—
47C2×D332C2312yes—
48C2×C22⋊D83—28no—
49C2×C22⋊D83—24no—
50C22×Dic83—28no—
51C22×Dic83—21no—
52C22×Dic83—24no—
53C22×Dic83D411yescharacteristic
54C2×C4×D83—22no—
55C2×C4×D83—22no—
56C2×C4×D83D412yes—
57C2×C4×D83C2312yes—
58#13050579—28no—
59#13050575—28no—
60C2×C83⋊C8—22no—
61C2×C83⋊C8C2312yes—
62(C2×D83)⋊C4—24no—
63C24×C83—21no—
64C2×D4×C83—21no—
65C2×D4×C83—22no—
66C2×D4×C83D414yescomplemented
67C2×D4×C83C2312yes—
68C22×C4×C83—21no—
69C22×C4×C83C2311yescharacteristic
70C2×C8×C83—22no—
71C2×C8×C83C2312yes—
72C4⋊C4×C83—21no—
73C4⋊C4×C83C2312yes—
74C23×C83—24no—
75C23×C83—22no—
76C23×C83—42no—
77C23×C83—42no—
78C23×C83C2×D411yescharacteristic
79C22×D83—22no—
80C22×D83—22no—
81C22×D83—22no—
82C22×D83—22no—
83C22×D83—42no—
84C22×D83—42no—
85C22×D83—42no—
86C22×D83C2×D412yes—
87D4×C83—24no—
88D4×C83—22no—
89D4×C83C2×D414yescomplemented
90C2×C4×C83—22no—
91C2×C4×C83—42no—
92C2×C4×C83C2×D411yescharacteristic
93C2×C4×C83C2×D412yes—
94C2×C4×C83C2×D412yes—
95C2×C4×C83C2411yescharacteristic
96C22⋊D83—216no—
97C2×Dic83—216no—
98C2×Dic83—22no—
99C2×Dic83—24no—
100C2×Dic83—22no—
101C2×Dic83C2×D412yes—
102D332—22no—
103D332—22no—
104D332—48no—
105D332—42no—
106C4×D83—24no—
107C4×D83—22no—
108C4×D83—22no—
109Dic166—24no—
110Dic166—22no—
111Dic166C2×D414yescomplemented
112C8×C83—22no—
113C83⋊C8—22no—
114C22×C83—24no—
115C22×C83—42no—
116C22×C83—42no—
117C22×C83—48no—
118C22×C83#12012yes—
119C22×C83#13512yes—
120C22×C83AGL(1,ℤ/8)12yes—
121C22×C83C22×D411yescharacteristic
122C2×D83—22no—
123C2×D83—22no—
124C2×D83—22no—
125C2×D83—44no—
126C2×D83—42no—
127C2×D83—42no—
128C2×D83—42no—
129C2×D83—84no—
130C4×C83—42no—
131C4×C83#12012yes—
132C4×C83C22×D411yescharacteristic
133C4×C83C22×D411yescharacteristic
134Dic83—24no—
135Dic83—22no—
136C2×C83—44no—
137C2×C83#44914yescomplemented
138C2×C83C2×#12011yescharacteristic
139C2×C83C2×#13511yescharacteristic
140C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
141D83—42no—
142D83—82no—
143C2×#449—831nomaximal, Sylow
144C83C2×#44911yescharacteristic, complemented, Sylow
145C22×#41—831no—
146C22×SD16—831no—
147C22×D8—831no—
148C2×#121—831no—
149#449—838no—
150C2×#103—831no—
151C2×#102D8311yescharacteristic, complemented
152C2×C22⋊C8—831no—
153C2×#41—834no—
154C2×#41—1662no—
155C2×#41—1664no—
156C2×#41—1664no—
157C22×Q8—831no—
158C22×D4—831no—
159C22×D4—1661no—
160C22×D4—1661no—
161C22×D4C2×D8311yescharacteristic
162C23×C4—831no—
163C23×C4—1661no—
164C2×SD16—834no—
165C2×SD16—1664no—
166C2×D8—834no—
167C2×D8—1664no—
168C22×C8—831no—
169C22×C8C2×D8311yescharacteristic
170#121—834no—
171#121—1662no—
172C2×C4⋊C4C2×D8311yescharacteristic
173C2×C22⋊C4—1661no—
174#103—834no—
175#102C2×D8314yescomplemented
176C22⋊C8—834no—
177C24—21no—
178C24—831no—
179C24—1661no—
180#41—1668no—
181#41—16616no—
182#41—1668no—
183C2×Q8—834no—
184C2×Q8—832no—
185C2×Q8—1661no—
186C2×Q8—1662no—
187C2×D4—21no—
188C2×D4—22no—
189C2×D4—3324no—
190C2×D4—832no—
191C2×D4—1664no—
192C2×D4—1664no—
193C2×D4—1668no—
194C2×D4—1661no—
195C2×D4—1662no—
196C2×D4—1662no—
197C2×D4D33214yescomplemented
198C2×D4C22×D8312yes—
199C22×C4—21no—
200C22×C4—831no—
201C22×C4—832no—
202C22×C4—832no—
203C22×C4—1664no—
204C22×C4—1668no—
205C22×C4—1661no—
206C22×C4—1662no—
207C22×C4—1662no—
208C22×C4C22×D8311yescharacteristic
209SD16—1668no—
210D8—1668no—
211C2×C8—22no—
212C2×C8—832no—
213C2×C8—1662no—
214C2×C8C22×D8312yes—
215C4⋊C4—21no—
216C4⋊C4C22×D8312yes—
217C22⋊C4—1664no—
218C23—24no—
219C23—22no—
220C23—42no—
221C23—42no—
222C23—3322no—
223C23—3322no—
224C23—3322no—
225C23—832no—
226C23—1662no—
227C23—1662no—
228C23—1662no—
229C23—1662no—
230C23D4×D8311yescharacteristic
231Q8—834no—
232Q8—1664no—
233Q8—1662no—
234D4—24no—
235D4—22no—
236D4—3328no—
237D4—3322no—
238D4—16616no—
239D4—1662no—
240D4—1662no—
241D4C2×D33214yescomplemented
242C2×C4—22no—
243C2×C4—42no—
244C2×C4—832no—
245C2×C4—16616no—
246C2×C4—1662no—
247C2×C4—1664no—
248C2×C4—1662no—
249C2×C4—1664no—
250C2×C4—1662no—
251C2×C4—1662no—
252C2×C4D4×D8311yescharacteristic
253C2×C4D4×D8312yes—
254C2×C4C2×D33212yes—
255C2×C4C23×D8311yescharacteristic
256C8—22no—
257C8—1662no—
258C22—24no—
259C22—48no—
260C22—42no—
261C22—42no—
262C22—3324no—
263C22—3322no—
264C22—3322no—
265C22—3322no—
266C22—6644no—
267C22—1662no—
268C22—1662no—
269C22—1662no—
270C22#1458176212yes—
271C22#1458181312yes—
272C22#1458181612yes—
273C22C2×D4×D8311yescharacteristic
274C4—42no—
275C4—1662no—
276C4—1664no—
277C4#1458176212yes—
278C4C2×D4×D8311yescharacteristic
279C4C22×D33211yescharacteristic
280C2—44no—
281C2—3322no—
282C2—6642no—
283C2#1912784714yesdirect product factor
284C2C2×#1458176211yescharacteristic
285C2C2×#1458181311yescharacteristic
286C2C2×#1458181611yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#102×C83C2
socleC23×C83C2×D4
hypercenterC2×#102D83
hypocenterC83C2×#449
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C22×#13050589C2semidirect
2. C22×#13050579C2semidirect
3. C22×#13050575C2semidirect
4. C2×#14581767C2semidirect
5. #19127847C2direct (N × H)
6. C2×#14581715C2semidirect
7. C2×(C2×D83)⋊C8C2semidirect
8. C2×#102×C83C2semidirect
12. C2×#13050589C22semidirect
20. C2×#13050579C22semidirect
22. C2×#13050575C22semidirect
25. #14581767C22semidirect
27. #14581715C22semidirect
28. (C2×D83)⋊C8C22semidirect
32. #102×C83C22semidirect
40. C2×Dic166D4semidirect
66. C2×D4×C83D4semidirect
89. D4×C83C2×D4semidirect
111. Dic166C2×D4semidirect
137. C2×C83#449semidirect
144. C83C2×#449semidirect
151. C2×#102D83semidirect
175. #102C2×D83semidirect
197. C2×D4D332semidirect
241. D4C2×D332semidirect
283. C2#19127847direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130505892
C22×#130505792
C22×#130505752
C2×#145817672
#191278472
C2×#145817152
C2×(C2×D83)⋊C82
C2×#102×C832
C2×#44983