Finite Group Databasebeta

← #19135044

Subgroups — #19135044

Order 5504.

358 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13063284C211yesmaximal, characteristic, complemented
2C2×#13063252C212yesmaximal, complemented
3#14582863C211yesmaximal, characteristic, complemented
4#14582658C212yesmaximal, complemented
5C43×#525C211yesmaximal, characteristic
6C2×#10621877C2212yes—
7#13063284—24no—
8C2×C4⋊Dic43—21no—
9C2×C22⋊Dic43—21no—
10C2×C4×Dic43C2212yes—
11#13063252—24no—
12C22⋊(C43⋊C8)—22no—
13C2×#41×C43C2211yescharacteristic
14C23×C4×C43C2211yescharacteristic
15#123×C43—21no—
16C22⋊Q8×C43C412yescomplemented
17#121×C43C412yescomplemented
18#120×C43—21no—
19C4×D4×C43—22no—
20#117×C43C2211yescharacteristic
21C24×C43D411yescharacteristic
22#41×C43—22no—
23#41×C43—22no—
24C2×Q8×C43C2×C411yescharacteristic
25C2×D4×C43—22no—
26C2×D4×C43—21no—
27C2×D4×C43C2×C411yescharacteristic
28C22×C4×C43—22no—
29C22×C4×C43—22no—
30C22×C4×C43—21no—
31C22×C4×C43C2×C412yes—
32C22×C4×C43D412yes—
33C22×C4×C43D411yescharacteristic
34C22×C4×C43C2311yescharacteristic
35C22×Dic43—22no—
36C4⋊C4×C43—22no—
37C4⋊C4×C43C2×C412yes—
38C22⋊C4×C43—22no—
39C22⋊C4×C43—22no—
40C22⋊C4×C43—21no—
41C42×C43—21no—
42C22⋊Dic43—24no—
43C4⋊Dic43—24no—
44C4×Dic43—22no—
45C4×Dic43D414yescomplemented
46#10621877—22no—
47#10621877—22no—
48C2×C43⋊C8—22no—
49C23×C43—21no—
50C23×C43—21no—
51C23×C43—21no—
52C23×C43—42no—
53C23×C43C22⋊C412yes—
54C23×C43C2×D411yescharacteristic
55Q8×C43—22no—
56D4×C43—22no—
57D4×C43—44no—
58D4×C43—41no—
59D4×C43—41no—
60C2×C4×C43—21no—
61C2×C4×C43—21no—
62C2×C4×C43—24no—
63C2×C4×C43—24no—
64C2×C4×C43—22no—
65C2×C4×C43—21no—
66C2×C4×C43—42no—
67C2×C4×C43C22⋊C412yes—
68C2×C4×C43C22×C411yescharacteristic
69C2×C4×C43C2×D412yes—
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43#4112yes—
72C2×Dic43—24no—
73C2×Dic43—44no—
74C43⋊C8—42no—
75C22×C43—22no—
76C22×C43—22no—
77C22×C43—22no—
78C22×C43—22no—
79C22×C43—42no—
80C22×C43—42no—
81C22×C43—41no—
82C22×C43—42no—
83C22×C43C2×C22⋊C411yescharacteristic
84C22×C43#12011yescharacteristic
85C22×C43#12311yescharacteristic
86C4×C43—22no—
87C4×C43—41no—
88C4×C43—42no—
89C4×C43C4×D412yes—
90C4×C43#12112yes—
91Dic43—44no—
92#1897—431nomaximal, Sylow
93C2×C43—21no—
94C2×C43—21no—
95C2×C43—42no—
96C2×C43—81no—
97C2×C43#38611yescharacteristic
98C2×C43#42112yes—
99#525D4311yescharacteristic
100C2×#117—431no—
101C2×#104—432no—
102#407—431no—
103#339—432no—
104C43#189711yescharacteristic, complemented, Sylow
105C2×#41C2×D4311yescharacteristic
106C23×C4C2×D4311yescharacteristic
107C2×M16—432no—
108#123—21no—
109C22⋊Q8Dic4312yescomplemented
110#121Dic4312yescomplemented
111#120—21no—
112C4×D4—22no—
113#117—864no—
114#117C2×D4311yescharacteristic
115C2×C4⋊C4—861no—
116C2×C22⋊C4—861no—
117C2×C42—432no—
118#104—864no—
119C22⋊C8—862no—
120C24C22⋊D4311yescharacteristic
121#41—22no—
122#41—22no—
123C2×Q8C2×Dic4311yescharacteristic
124C2×D4—22no—
125C2×D4—21no—
126C2×D4C2×Dic4311yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—862no—
131C22×C4C2×Dic4312yes—
132C22×C4C22⋊D4311yescharacteristic
133C22×C4C22⋊D4312yes—
134C22×C4C22×D4311yescharacteristic
135M16—862no—
136M16—862no—
137C2×C8—862no—
138C4⋊C4—22no—
139C4⋊C4—864no—
140C4⋊C4C2×Dic4312yes—
141C22⋊C4—22no—
142C22⋊C4—21no—
143C22⋊C4—22no—
144C22⋊C4—864no—
145C42—21no—
146C42—434no—
147C42—862no—
148C23—21no—
149C23—21no—
150C23—21no—
151C23—42no—
152C23C22⋊Dic4312yes—
153C23C2×C22⋊D4311yescharacteristic
154Q8—22no—
155D4—22no—
156D4—44no—
157D4—41no—
158D4—41no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—21no—
165C2×C4—42no—
166C2×C4—864no—
167C2×C4—1724no—
168C2×C4C22⋊Dic4312yes—
169C2×C4D4×D4312yes—
170C2×C4#1062190012yes—
171C2×C4C22×Dic4311yescharacteristic
172C2×C4C2×C22⋊D4311yescharacteristic
173C8—1722no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—42no—
181C22—41no—
182C22C2×C22⋊Dic4311yescharacteristic
183C22#1306329311yescharacteristic
184C22#1306330611yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—1724no—
189C4D4×Dic4312yes—
190C4#1306329712yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—81no—
195C2#1458277911yescharacteristic
196C2#1458291612yes—
subgroupG/H
centerC2×C4C2×C22⋊D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#525C2
socleC22×C43C2×C22⋊C4
hypercenter#525D43
hypocenterC43#1897
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. C2×#13063284C2semidirect
2. C2×#13063252C2semidirect
3. #14582863C2semidirect
4. #14582658C2semidirect
16. C22⋊Q8×C43C4semidirect
17. #121×C43C4semidirect
45. C4×Dic43D4semidirect
104. C43#1897semidirect
109. C22⋊Q8Dic43semidirect
110. #121Dic43semidirect