Finite Group Databasebeta

← C2×#19127944 #24917048

Subgroups — C2×#19127944 #24917048

Order 10624.

544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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×#13050573C211yesmaximal, characteristic, complemented
2C2×#14581768C211yesmaximal, characteristic, complemented
3C2×#14581763C211yesmaximal, characteristic
4#19127944C218yesmaximal, direct product factor
5C2×#14581726C211yesmaximal, characteristic, complemented
6C2×#14581716C211yesmaximal, characteristic, complemented
7C2×#14581713C211yesmaximal, characteristic, complemented
8C22×SD16×C83C211yesmaximal, characteristic, complemented
9C22×C22⋊D83—21no—
10C22×C4×D83C2211yescharacteristic
11C2×#13050573—24no—
12C2×#13050573C2214yescomplemented
13C22×C83⋊C8C2211yescharacteristic
14#14581768—22no—
15#14581768C2214yescomplemented
16#14581763—22no—
17#14581763C2214yes—
18C2×C4⋊Dic83C2211yescharacteristic
19C2×C4⋊Dic83C2211yescharacteristic
20C2×Dic83⋊C4—21no—
21C2×C22⋊Dic83—21no—
22C2×(C2×D83)⋊C4—21no—
23#14581726C2214yescomplemented
24#14581716C2214yescomplemented
25#14581713C2214yescomplemented
26C22×Q8×C83C2211yescharacteristic
27C22×D4×C83C2211yescharacteristic
28C2×SD16×C83—24no—
29C2×SD16×C83C2214yescomplemented
30C22×C8×C83C2211yescharacteristic
31C23×D83D411yescharacteristic
32C2×C22⋊D83—24no—
33C2×C22⋊D83—44no—
34C22×Dic83—21no—
35C22×Dic83—21no—
36C22×Dic83D411yescharacteristic
37C2×C4×D83—22no—
38C2×C4×D83—22no—
39C2×C4×D83D412yes—
40C2×C4×D83C2312yes—
41#13050573—28no—
42C2×C83⋊C8—22no—
43C2×C83⋊C8C2312yes—
44C4⋊Dic83—21no—
45C4⋊Dic83—21no—
46C4⋊Dic83C2312yes—
47C4⋊Dic83C2312yes—
48Dic83⋊C4—24no—
49C22⋊Dic83—24no—
50(C2×D83)⋊C4—24no—
51C24×C83—21no—
52C2×Q8×C83—21no—
53C2×Q8×C83—22no—
54C2×Q8×C83—22no—
55C2×Q8×C83C2312yes—
56C2×D4×C83—22no—
57C2×D4×C83—21no—
58C2×D4×C83—22no—
59C2×D4×C83C2312yes—
60C22×C4×C83—21no—
61C22×C4×C83C2311yescharacteristic
62SD16×C83—28no—
63C2×C8×C83D414yescomplemented
64C2×C8×C83C2312yes—
65C23×C83—22no—
66C23×C83—42no—
67C23×C83—42no—
68C23×C83—42no—
69C23×C83C2×D411yescharacteristic
70C22×D83—22no—
71C22×D83—22no—
72C22×D83—22no—
73C22×D83C2×D412yes—
74Q8×C83—22no—
75Q8×C83—22no—
76Q8×C83—42no—
77D4×C83—22no—
78D4×C83—22no—
79D4×C83—42no—
80C2×C4×C83—22no—
81C2×C4×C83—42no—
82C2×C4×C83C2×D411yescharacteristic
83C2×C4×C83C2×D412yes—
84C2×C4×C83#4112yes—
85C2×C4×C83C2411yescharacteristic
86C22⋊D83—48no—
87C2×Dic83—22no—
88C2×Dic83—22no—
89C2×Dic83—22no—
90C2×Dic83—42no—
91C2×Dic83—42no—
92C2×Dic83C2×D412yes—
93C4×D83—24no—
94C4×D83—22no—
95C4×D83—22no—
96C8×C83C2×D414yescomplemented
97C83⋊C8—22no—
98C22×C83—42no—
99C22×C83—42no—
100C22×C83—42no—
101C22×C83—84no—
102C22×C83#12112yes—
103C22×C83AGL(1,ℤ/8)12yes—
104C22×C83#13712yes—
105C22×C83C22×D411yescharacteristic
106C2×D83—22no—
107C2×D83—22no—
108C2×D83—22no—
109C2×D83—44no—
110C4×C83—42no—
111C4×C83#12112yes—
112C4×C83C22×D411yescharacteristic
113C4×C83C2×#4111yescharacteristic
114Dic83—22no—
115Dic83—42no—
116Dic83—42no—
117C2×C83—82no—
118C2×C83#46814yescomplemented
119C2×C83C2×#12111yescharacteristic
120C2×C83C2×AGL(1,ℤ/8)11yescharacteristic
121C2×C83C2×#13711yescharacteristic
122D83—42no—
123C2×#468—831nomaximal, Sylow
124C83C2×#46811yescharacteristic, complemented, Sylow
125C22×SD16D8311yescharacteristic, complemented
126C22×M16—831no—
127C2×C22⋊Q8—831no—
128C2×#121—831no—
129#468—838no—
130C2×#107—831no—
131C2×#103—831no—
132C2×#102—831no—
133C22×Q8C2×D8311yescharacteristic
134C22×D4—1661no—
135C22×D4C2×D8311yescharacteristic
136C23×C4—831no—
137C2×SD16—24no—
138C2×SD16C2×D8314yescomplemented
139C2×M16—834no—
140C2×M16—1664no—
141C22×C8—831no—
142C22×C8C2×D8311yescharacteristic
143C22⋊Q8—834no—
144C22⋊Q8—1662no—
145#121—834no—
146#121—1662no—
147C2×C4⋊C4—831no—
148C2×C4⋊C4—831no—
149C2×C4⋊C4—1661no—
150C2×C22⋊C4—1661no—
151C2×C22⋊C4—1661no—
152#107—834no—
153#103—834no—
154#102—834no—
155C24—21no—
156C24—831no—
157C2×Q8—21no—
158C2×Q8—22no—
159C2×Q8—22no—
160C2×Q8C22×D8312yes—
161C2×D4—21no—
162C2×D4—22no—
163C2×D4—22no—
164C2×D4—3324no—
165C2×D4—1664no—
166C2×D4C22×D8312yes—
167C22×C4—21no—
168C22×C4—831no—
169C22×C4—832no—
170C22×C4—832no—
171C22×C4—1661no—
172C22×C4—1661no—
173C22×C4—1662no—
174C22×C4—1662no—
175C22×C4C22×D8311yescharacteristic
176SD16—28no—
177M16—1668no—
178C2×C8—832no—
179C2×C8—1662no—
180C2×C8C22⋊D8314yescomplemented
181C2×C8C22×D8312yes—
182C4⋊C4—832no—
183C4⋊C4—832no—
184C4⋊C4—1664no—
185C4⋊C4—1661no—
186C4⋊C4—1661no—
187C22⋊C4—1664no—
188C22⋊C4—1664no—
189C23—22no—
190C23—42no—
191C23—42no—
192C23—42no—
193C23—832no—
194C23—1662no—
195C23—1662no—
196C23—1662no—
197C23D4×D8311yescharacteristic
198Q8—22no—
199Q8—22no—
200Q8—42no—
201D4—22no—
202D4—22no—
203D4—42no—
204D4—3328no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—3322no—
208C2×C4—3322no—
209C2×C4—832no—
210C2×C4—1662no—
211C2×C4—1662no—
212C2×C4—1662no—
213C2×C4—1664no—
214C2×C4—1662no—
215C2×C4—1662no—
216C2×C4D4×D8311yescharacteristic
217C2×C4C2×C22⋊D8312yes—
218C2×C4#1305058912yes—
219C2×C4C23×D8311yescharacteristic
220C8—1662no—
221C8C2×C22⋊D8314yescomplemented
222C22—42no—
223C22—42no—
224C22—42no—
225C22—84no—
226C22—3324no—
227C22—1662no—
228C22—1662no—
229C22—1662no—
230C22#1458176312yes—
231C22#1458181912yes—
232C22#1458182112yes—
233C22C2×D4×D8311yescharacteristic
234C4—42no—
235C4—3322no—
236C4—3322no—
237C4—1662no—
238C4#1458176312yes—
239C4C22×C22⋊D8311yescharacteristic
240C4C2×#1305058911yescharacteristic
241C2—82no—
242C2—3322no—
243C2#1912794414yesdirect product factor
244C2C2×#1458176311yescharacteristic
245C2C2×#1458181911yescharacteristic
246C2C2×#1458182111yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC22×SD16×C83C2
socleC23×C83C2×D4
prime radicalC2×#14581763C2
hypercenterC22×SD16D83
hypocenterC83C2×#468
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C22×#13050573C2semidirect
2. C2×#14581768C2semidirect
4. #19127944C2direct (N × H)
5. C2×#14581726C2semidirect
6. C2×#14581716C2semidirect
7. C2×#14581713C2semidirect
8. C22×SD16×C83C2semidirect
12. C2×#13050573C22semidirect
15. #14581768C22semidirect
23. #14581726C22semidirect
24. #14581716C22semidirect
25. #14581713C22semidirect
29. C2×SD16×C83C22semidirect
63. C2×C8×C83D4semidirect
96. C8×C83C2×D4semidirect
118. C2×C83#468semidirect
124. C83C2×#468semidirect
125. C22×SD16D83semidirect
138. C2×SD16C2×D83semidirect
180. C2×C8C22⋊D83semidirect
221. C8C2×C22⋊D83semidirect
243. C2#19127944direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130505732
C2×#145817682
C2×#145817632
#191279442
C2×#145817262
C2×#145817162
C2×#145817132
C22×SD16×C832
C2×#46883