Finite Group Databasebeta

← C2×#19127843 #24916661

Subgroups — C2×#19127843 #24916661

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×#13050578C211yesmaximal, characteristic, complemented
3C2×#14581763C211yesmaximal, characteristic, complemented
4#19127843C218yesmaximal, direct product factor
5C2×#14581717C211yesmaximal, characteristic, complemented
6C2×#14581713C211yesmaximal, characteristic, complemented
7C2×(C2×D83)⋊C8C211yesmaximal, characteristic, complemented
8C22×D8×C83C211yesmaximal, characteristic, complemented
9C2×#13050589—24no—
10C2×#13050589—22no—
11C2×#13050589—24no—
12C2×#13050589C2214yescomplemented
13C22×Dic166C2211yescharacteristic
14C22×C22⋊D83—21no—
15C22×C22⋊D83—21no—
16C23×Dic83—21no—
17C22×C4×D83C2211yescharacteristic
18C2×#13050578—24no—
19C2×#13050578C2214yescomplemented
20C22×C83⋊C8C2211yescharacteristic
21#14581763—22no—
22#14581763C2214yescomplemented
23C2×C4⋊Dic83C2211yescharacteristic
24C2×C22⋊Dic83—21no—
25#14581717C2214yescomplemented
26#14581713C2214yescomplemented
27(C2×D83)⋊C8C2214yescomplemented
28C22×D4×C83C2211yescharacteristic
29C22×D4×C83C2211yescharacteristic
30C2×D8×C83—24no—
31C2×D8×C83C2214yescomplemented
32C22×C8×C83C2211yescharacteristic
33C23×D83D411yescharacteristic
34#13050589—216no—
35#13050589—28no—
36#13050589—28no—
37C2×Dic166—21no—
38C2×Dic166—22no—
39C2×Dic166D414yescomplemented
40C2×Dic166C2312yes—
41C2×C22⋊D83—28no—
42C2×C22⋊D83—24no—
43C2×C22⋊D83—24no—
44C2×C22⋊D83—44no—
45C22×Dic83—28no—
46C22×Dic83—21no—
47C22×Dic83—24no—
48C22×Dic83—21no—
49C22×Dic83D411yescharacteristic
50C2×C4×D83—22no—
51C2×C4×D83—22no—
52C2×C4×D83D412yes—
53C2×C4×D83C2312yes—
54#13050578—28no—
55C2×C83⋊C8—22no—
56C2×C83⋊C8C2312yes—
57C4⋊Dic83—21no—
58C4⋊Dic83C2312yes—
59C22⋊Dic83—24no—
60C24×C83—21no—
61C24×C83—21no—
62C2×D4×C83—21no—
63C2×D4×C83—22no—
64C2×D4×C83—22no—
65C2×D4×C83—22no—
66C2×D4×C83—21no—
67C2×D4×C83D414yescomplemented
68C2×D4×C83C2312yes—
69C2×D4×C83C2312yes—
70C22×C4×C83C2311yescharacteristic
71D8×C83—28no—
72C2×C8×C83—22no—
73C2×C8×C83C2312yes—
74C23×C83—24no—
75C23×C83—22no—
76C23×C83—22no—
77C23×C83—42no—
78C23×C83—42no—
79C23×C83—42no—
80C23×C83—42no—
81C23×C83—42no—
82C23×C83C2×D411yescharacteristic
83C22×D83—22no—
84C22×D83—22no—
85C22×D83—22no—
86C22×D83C2×D412yes—
87D4×C83—24no—
88D4×C83—22no—
89D4×C83—22no—
90D4×C83—22no—
91D4×C83—42no—
92D4×C83C2×D414yescomplemented
93C2×C4×C83C2×D411yescharacteristic
94C2×C4×C83C2×D412yes—
95C2×C4×C83C2×D412yes—
96C2×C4×C83C2411yescharacteristic
97C22⋊D83—216no—
98C22⋊D83—48no—
99C2×Dic83—216no—
100C2×Dic83—22no—
101C2×Dic83—24no—
102C2×Dic83—22no—
103C2×Dic83—22no—
104C2×Dic83—42no—
105C2×Dic83C2×D412yes—
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—42no—
119C22×C83—42no—
120C22×C83—42no—
121C22×C83—84no—
122C22×C83#12012yes—
123C22×C83#13512yes—
124C22×C83AGL(1,ℤ/8)12yes—
125C22×C83C22×D411yescharacteristic
126C2×D83—22no—
127C2×D83—22no—
128C2×D83—22no—
129C2×D83—44no—
130C4×C83#12012yes—
131C4×C83C22×D411yescharacteristic
132C4×C83C22×D411yescharacteristic
133Dic83—24no—
134Dic83—22no—
135Dic83—42no—
136C2×C83—44no—
137C2×C83—82no—
138C2×C83#44914yescomplemented
139C2×C83C2×#12011yescharacteristic
140C2×C83C2×#13511yescharacteristic
141C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
142D83—42no—
143C2×#449—831nomaximal, Sylow
144C83C2×#44911yescharacteristic, complemented, Sylow
145C22×#41—831no—
146C22×SD16—831no—
147C22×D8D8311yescharacteristic, complemented
148C2×#121—831no—
149#449—838no—
150C2×#103—831no—
151C2×#102—831no—
152C2×C22⋊C8—831no—
153C2×#41—834no—
154C2×#41—1662no—
155C2×#41—1664no—
156C2×#41—1664no—
157C22×Q8—831no—
158C22×D4—1661no—
159C22×D4—1661no—
160C22×D4C2×D8311yescharacteristic
161C22×D4C2×D8311yescharacteristic
162C23×C4—831no—
163C23×C4—1661no—
164C2×SD16—834no—
165C2×SD16—1664no—
166C2×D8—24no—
167C2×D8C2×D8314yescomplemented
168C22×C8—831no—
169C22×C8C2×D8311yescharacteristic
170#121—834no—
171#121—1662no—
172C2×C4⋊C4—831no—
173C2×C22⋊C4—1661no—
174#103—834no—
175#102—834no—
176C22⋊C8—834no—
177C24—21no—
178C24—21no—
179C24—831no—
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—22no—
190C2×D4—21no—
191C2×D4—22no—
192C2×D4—3324no—
193C2×D4—1664no—
194C2×D4—1664no—
195C2×D4—1668no—
196C2×D4C22⋊D8314yescomplemented
197C2×D4C22×D8312yes—
198C2×D4C22×D8312yes—
199C22×C4—831no—
200C22×C4—832no—
201C22×C4—832no—
202C22×C4—1661no—
203C22×C4—1664no—
204C22×C4—1668no—
205C22×C4—1661no—
206C22×C4—1662no—
207C22×C4—1662no—
208C22×C4C22×D8311yescharacteristic
209SD16—1668no—
210D8—28no—
211C2×C8—22no—
212C2×C8—832no—
213C2×C8—1662no—
214C2×C8C22×D8312yes—
215C4⋊C4—832no—
216C4⋊C4—1661no—
217C22⋊C4—1664no—
218C23—24no—
219C23—22no—
220C23—22no—
221C23—42no—
222C23—42no—
223C23—42no—
224C23—42no—
225C23—42no—
226C23—832no—
227C23—1662no—
228C23—1662no—
229C23—1662no—
230C23D4×D8311yescharacteristic
231Q8—834no—
232Q8—1664no—
233Q8—1662no—
234D4—24no—
235D4—22no—
236D4—22no—
237D4—22no—
238D4—42no—
239D4—3328no—
240D4—16616no—
241D4C2×C22⋊D8314yescomplemented
242C2×C4—3322no—
243C2×C4—832no—
244C2×C4—1662no—
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×C22⋊D8312yes—
255C2×C4C23×D8311yescharacteristic
256C8—22no—
257C8—1662no—
258C22—24no—
259C22—48no—
260C22—42no—
261C22—42no—
262C22—42no—
263C22—42no—
264C22—42no—
265C22—84no—
266C22—3324no—
267C22—1662no—
268C22—1662no—
269C22—1662no—
270C22#1458176012yes—
271C22#1458181112yes—
272C22#1458181612yes—
273C22C2×D4×D8311yescharacteristic
274C4—3322no—
275C4—1662no—
276C4—1664no—
277C4#1458176012yes—
278C4C2×D4×D8311yescharacteristic
279C4C22×C22⋊D8311yescharacteristic
280C2—44no—
281C2—82no—
282C2—3322no—
283C2#1912784314yesdirect product factor
284C2C2×#1458176011yescharacteristic
285C2C2×#1458181111yescharacteristic
286C2C2×#1458181611yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×D8×C83C2
socleC23×C83C2×D4
hypercenterC22×D8D83
hypocenterC83C2×#449
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D8

Complements

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

NH ≅ G/Ntype
1. C22×#13050589C2semidirect
2. C22×#13050578C2semidirect
3. C2×#14581763C2semidirect
4. #19127843C2direct (N × H)
5. C2×#14581717C2semidirect
6. C2×#14581713C2semidirect
7. C2×(C2×D83)⋊C8C2semidirect
8. C22×D8×C83C2semidirect
12. C2×#13050589C22semidirect
19. C2×#13050578C22semidirect
22. #14581763C22semidirect
25. #14581717C22semidirect
26. #14581713C22semidirect
27. (C2×D83)⋊C8C22semidirect
31. C2×D8×C83C22semidirect
39. C2×Dic166D4semidirect
67. C2×D4×C83D4semidirect
92. D4×C83C2×D4semidirect
111. Dic166C2×D4semidirect
138. C2×C83#449semidirect
144. C83C2×#449semidirect
147. C22×D8D83semidirect
167. C2×D8C2×D83semidirect
196. C2×D4C22⋊D83semidirect
241. D4C2×C22⋊D83semidirect
283. C2#19127843direct (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×#130505782
C2×#145817632
#191278432
C2×#145817172
C2×#145817132
C2×(C2×D83)⋊C82
C22×D8×C832
C2×#44983