Finite Group Databasebeta

← C2×#19128033 #24917342

Subgroups — C2×#19128033 #24917342

Order 10624.

460 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 149 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
1C2×#14581772C211yesmaximal, characteristic
2C2×C4⋊C4×D83C211yesmaximal, characteristic
3#19128033C218yesmaximal, direct product factor
4C2×#14581723C211yesmaximal, characteristic, complemented
5C2×#14581717C211yesmaximal, characteristic, complemented
6C2×#14581715C211yesmaximal, characteristic, complemented
7C2×(C2×D83)⋊C8C211yesmaximal, characteristic
8C2×#106×C83C211yesmaximal, characteristic, complemented
9C22×Dic166C2211yescharacteristic
10C22×C4×D83—21no—
11C22×C4×D83C2211yescharacteristic
12C22×C83⋊C8C2211yescharacteristic
13#14581772—22no—
14#14581772C2214yes—
15C2×C4⋊Dic83—21no—
16C2×C4⋊Dic83C2211yescharacteristic
17C2×Dic83⋊C4—21no—
18C4⋊C4×D83—22no—
19C4⋊C4×D83C2214yes—
20C2×(C2×D83)⋊C4—21no—
21#14581723C2214yescomplemented
22#14581717C2214yescomplemented
23#14581715C2214yescomplemented
24(C2×D83)⋊C8C2214yes—
25C22×C8×C83C2211yescharacteristic
26C2×C4⋊C4×C83C2211yescharacteristic
27C2×C4⋊C4×C83C2211yescharacteristic
28#106×C83C2214yescomplemented
29C23×D83D411yescharacteristic
30C2×Dic166—22no—
31C2×Dic166—22no—
32C2×Dic166—21no—
33C2×Dic166C2312yes—
34C22×Dic83—21no—
35C22×Dic83—21no—
36C22×Dic83D411yescharacteristic
37C2×C4×D83—22no—
38C2×C4×D83—22no—
39C2×C4×D83—24no—
40C2×C4×D83—44no—
41C2×C4×D83D412yes—
42C2×C4×D83C2312yes—
43C2×C83⋊C8—22no—
44C2×C83⋊C8C2312yes—
45C4⋊Dic83—21no—
46C4⋊Dic83—24no—
47C4⋊Dic83C2312yes—
48Dic83⋊C4—24no—
49(C2×D83)⋊C4—24no—
50C22×C4×C83—21no—
51C22×C4×C83—21no—
52C22×C4×C83C2311yescharacteristic
53C2×C8×C83—22no—
54C2×C8×C83C2312yes—
55C4⋊C4×C83—21no—
56C4⋊C4×C83—21no—
57C4⋊C4×C83C2312yes—
58C4⋊C4×C83C2312yes—
59C23×C83C2×D411yescharacteristic
60C22×D83—22no—
61C22×D83—22no—
62C22×D83SD1614yes—
63C22×D83C2×D412yes—
64C2×C4×C83—22no—
65C2×C4×C83—22no—
66C2×C4×C83—42no—
67C2×C4×C83—42no—
68C2×C4×C83C2×D411yescharacteristic
69C2×C4×C83#4112yes—
70C2×C4×C83#4112yes—
71C2×C4×C83C2411yescharacteristic
72C2×Dic83—22no—
73C2×Dic83—22no—
74C2×Dic83—22no—
75C2×Dic83—42no—
76C2×Dic83—42no—
77C2×Dic83C2×D412yes—
78C4×D83—24no—
79C4×D83—22no—
80C4×D83—22no—
81C4×D83—48no—
82Dic166—22no—
83Dic166—22no—
84Dic166—42no—
85C8×C83—22no—
86C83⋊C8—22no—
87C22×C83#12312yes—
88C22×C83C2×SD1612yes—
89C22×C83#13712yes—
90C22×C83C22×D411yescharacteristic
91C2×D83—22no—
92C2×D83—22no—
93C2×D83—28no—
94C2×D83C2×SD1614yes—
95C4×C83—42no—
96C4×C83—42no—
97C4×C83#12312yes—
98C4×C83C2×#4111yescharacteristic
99C4×C83C2×#4111yescharacteristic
100Dic83—22no—
101Dic83—42no—
102Dic83—42no—
103C2×C83#48314yescomplemented
104C2×C83C2×#12311yescharacteristic
105C2×C83C22×SD1611yescharacteristic
106C2×C83C2×#13711yescharacteristic
107D83—24no—
108C2×#483—831nomaximal, Sylow
109C83C2×#48311yescharacteristic, complemented, Sylow
110C2×C22⋊Q8—831no—
111C22×C4⋊C4—831no—
112#483—838no—
113C2×#106—831no—
114C2×#106D8311yescharacteristic, complemented
115C2×#103—831no—
116C2×#103—831no—
117C2×C22⋊C8—831no—
118C22×Q8—831no—
119C23×C4—831no—
120C23×C4—1661no—
121C22×C8—831no—
122C22×C8C2×D8311yescharacteristic
123C22⋊Q8—834no—
124C22⋊Q8—1662no—
125C2×C4⋊C4—831no—
126C2×C4⋊C4—834no—
127C2×C4⋊C4—1662no—
128C2×C4⋊C4—1661no—
129C2×C4⋊C4—1661no—
130C2×C4⋊C4C2×D8311yescharacteristic
131C2×C4⋊C4C2×D8311yescharacteristic
132C2×C22⋊C4—1661no—
133#106—834no—
134#106C2×D8314yescomplemented
135#103—834no—
136#103—834no—
137C22⋊C8—834no—
138C24—831no—
139C2×Q8—832no—
140C2×Q8—1662no—
141C2×Q8—1662no—
142C2×Q8—1661no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—3324no—
146C22×C4—831no—
147C22×C4—832no—
148C22×C4—832no—
149C22×C4—1664no—
150C22×C4—1661no—
151C22×C4—1661no—
152C22×C4—1662no—
153C22×C4—1662no—
154C22×C4C22×D8311yescharacteristic
155C2×C8—22no—
156C2×C8—832no—
157C2×C8—1662no—
158C2×C8C22×D8312yes—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—832no—
162C4⋊C4—1664no—
163C4⋊C4—1664no—
164C4⋊C4—1661no—
165C4⋊C4C22×D8312yes—
166C4⋊C4C22×D8312yes—
167C22⋊C4—1664no—
168C23—834no—
169C23—832no—
170C23—1662no—
171C23—1662no—
172C23D4×D8311yescharacteristic
173Q8—3322no—
174Q8—1662no—
175Q8—1662no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—3328no—
181C2×C4—3322no—
182C2×C4—3322no—
183C2×C4—832no—
184C2×C4—1662no—
185C2×C4—1662no—
186C2×C4—1662no—
187C2×C4—1664no—
188C2×C4—1662no—
189C2×C4—1662no—
190C2×C4D4×D8311yescharacteristic
191C2×C4#1305059012yes—
192C2×C4#1305059112yes—
193C2×C4C23×D8311yescharacteristic
194C8—22no—
195C8—1662no—
196C22—834no—
197C22—1662no—
198C22—1662no—
199C22—1668no—
200C22#1458177712yes—
201C22SD16×D8312yes—
202C22#1458182112yes—
203C22C2×D4×D8311yescharacteristic
204C4—42no—
205C4—42no—
206C4—3322no—
207C4—3322no—
208C4—1662no—
209C4#1458177712yes—
210C4C2×#1305059011yescharacteristic
211C4C2×#1305059111yescharacteristic
212C2—1664no—
213C2#1912803314yesdirect product factor
214C2C2×#1458177711yescharacteristic
215C2C2×SD16×D8311yescharacteristic
216C2C2×#1458182111yescharacteristic
subgroupG/H
centerC23D4×D83
commutator, cosocleC2×C4×C83C24
FrattiniC2×C4C23×D83
FittingC2×#106×C83C2
socleC23×C83C2×D4
prime radicalC23×D83D4
hypercenterC2×#106D83
hypocenterC83C2×#483
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
3. #19128033C2direct (N × H)
4. C2×#14581723C2semidirect
5. C2×#14581717C2semidirect
6. C2×#14581715C2semidirect
8. C2×#106×C83C2semidirect
21. #14581723C22semidirect
22. #14581717C22semidirect
23. #14581715C22semidirect
28. #106×C83C22semidirect
103. C2×C83#483semidirect
109. C83C2×#483semidirect
114. C2×#106D83semidirect
134. #106C2×D83semidirect
213. C2#19128033direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145817722
C2×C4⋊C4×D832
#191280332
C2×#145817232
C2×#145817172
C2×#145817152
C2×(C2×D83)⋊C82
C2×#106×C832
C2×#48383