Finite Group Databasebeta

← #19135014

Subgroups — #19135014

Order 5504.

342 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 93 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
1#14583666C211yesmaximal, characteristic, complemented
2#14582883C211yesmaximal, characteristic, complemented
3#14582863C212yesmaximal, complemented
4#14582669C212yesmaximal, complemented
5C43×#525C211yesmaximal, characteristic
6#13063332—24no—
7C2×#10621877—22no—
8C2×#10621877C2212yes—
9C2×#10621877C2212yes—
10#13063244—21no—
11#13063242—21no—
12C22⋊(C43⋊C8)—24no—
13C2×#41×C43C2211yescharacteristic
14C23×C4×C43C2211yescharacteristic
15#123×C43C412yes—
16C22⋊Q8×C43—21no—
17#121×C43—21no—
18#120×C43C412yes—
19C4×D4×C43—22no—
20#117×C43C2211yescharacteristic
21C24×C43C2×C411yescharacteristic
22#41×C43—22no—
23#41×C43—22no—
24C2×Q8×C43D411yescharacteristic
25C2×D4×C43—22no—
26C2×D4×C43C2×C412yes—
27C2×D4×C43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43—21no—
30C22×C4×C43—22no—
31C22×C4×C43—22no—
32C22×C4×C43C2×C411yescharacteristic
33C22×C4×C43D412yes—
34C22×C4×C43C2311yescharacteristic
35C4⋊C4×C43—22no—
36C4⋊C4×C43—21no—
37C22⋊C4×C43—22no—
38C22⋊C4×C43—22no—
39C22⋊C4×C43C2×C412yes—
40C42×C43—21no—
41#10621877—24no—
42#10621877—22no—
43#10621877—22no—
44#10621877—22no—
45#10621877—22no—
46C2×C43⋊C8—24no—
47C2×C43⋊C8—22no—
48C2×C43⋊C8D414yescomplemented
49C23×C43—21no—
50C23×C43—22no—
51C23×C43—42no—
52C23×C43C22⋊C412yes—
53C23×C43C22×C411yescharacteristic
54Q8×C43—22no—
55D4×C43—24no—
56D4×C43—22no—
57D4×C43—44no—
58C2×C4×C43—22no—
59C2×C4×C43—22no—
60C2×C4×C43—22no—
61C2×C4×C43—21no—
62C2×C4×C43—22no—
63C2×C4×C43—41no—
64C2×C4×C43—42no—
65C2×C4×C43—41no—
66C2×C4×C43C22⋊C412yes—
67C2×C4×C43C2×D412yes—
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43#4112yes—
71C43⋊C8—24no—
72C43⋊C8—42no—
73C22×C43—24no—
74C22×C43—22no—
75C22×C43—22no—
76C22×C43—41no—
77C22×C43—42no—
78C22×C43—41no—
79C22×C43—42no—
80C22×C43—41no—
81C22×C43C2×C22⋊C411yescharacteristic
82C22×C43C4×D412yes—
83C4×C43—22no—
84C4×C43—42no—
85C4×C43—41no—
86C4×C43#12011yescharacteristic
87C4×C43#12112yes—
88C4×C43#12311yescharacteristic
89#1891—431nomaximal, Sylow
90C2×C43—21no—
91C2×C43—22no—
92C2×C43—42no—
93C2×C43—42no—
94C2×C43#38611yescharacteristic
95#568—431no—
96#525D4311yescharacteristic
97#413—431no—
98#407—432no—
99#344—432no—
100C43#189111yescharacteristic, complemented, Sylow
101C2×#41C2×D4311yescharacteristic
102C23×C4C2×D4311yescharacteristic
103#131—864no—
104C2×M16—432no—
105C2×M16—432no—
106C2×M16—862no—
107#123Dic4312yes—
108C22⋊Q8—21no—
109#121—21no—
110#120Dic4312yes—
111C4×D4—22no—
112#117C2×D4311yescharacteristic
113#101—861no—
114#100—861no—
115C22⋊C8—864no—
116C24C2×Dic4311yescharacteristic
117#41—22no—
118#41—22no—
119C2×Q8C22⋊D4311yescharacteristic
120C2×D4—22no—
121C2×D4C2×Dic4312yes—
122C2×D4C22⋊D4311yescharacteristic
123C22×C4—22no—
124C22×C4—22no—
125C22×C4—21no—
126C22×C4—21no—
127C22×C4C2×Dic4311yescharacteristic
128C22×C4C22⋊D4312yes—
129C22×C4C22×D4311yescharacteristic
130M16—864no—
131M16—862no—
132M16—862no—
133M16—862no—
134M16—862no—
135C2×C8—434no—
136C2×C8—864no—
137C2×C8—862no—
138C4⋊C4—22no—
139C4⋊C4—21no—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4C2×Dic4312yes—
143C42—21no—
144C23—21no—
145C23—22no—
146C23—42no—
147C23C22⋊Dic4312yes—
148C23C22×Dic4311yescharacteristic
149Q8—22no—
150D4—24no—
151D4—22no—
152D4—44no—
153C2×C4—22no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—42no—
160C2×C4—41no—
161C2×C4C22⋊Dic4312yes—
162C2×C4D4×D4312yes—
163C2×C4#1062190012yes—
164C2×C4C2×C22⋊D4311yescharacteristic
165C2×C4C2×C22⋊D4311yescharacteristic
166C8—864no—
167C8—1722no—
168C22—22no—
169C22—24no—
170C22—22no—
171C22—41no—
172C22—42no—
173C22—41no—
174C22—42no—
175C22—41no—
176C22C2×C22⋊Dic4311yescharacteristic
177C22D4×Dic4312yes—
178C4—22no—
179C4—42no—
180C4—41no—
181C4#1306329311yescharacteristic
182C4#1306329712yes—
183C4#1306330611yescharacteristic
184C2—21no—
185C2—22no—
186C2—42no—
187C2—42no—
188C2#1458277911yescharacteristic
subgroupG/H
centerC4#13063293
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#525C2
socleC2×C43#386
hypercenter#525D43
hypocenterC43#1891
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #14583666C2semidirect
2. #14582883C2semidirect
3. #14582863C2semidirect
4. #14582669C2semidirect
48. C2×C43⋊C8D4semidirect
100. C43#1891semidirect