Finite Group Databasebeta

← #19136289

Subgroups — #19136289

Order 5504.

230 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 65 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#14583470C211yesmaximal, characteristic
2#14582883C211yesmaximal, characteristic
3#14582697C214yesmaximal, complemented
4C43×#413C211yesmaximal, characteristic
5C22×Dic86C411yescharacteristic
6C2×#10621877—21no—
7#13063323C2212yes—
8#13063312C412yes—
9#13063306—21no—
10#13063306—21no—
11#13063304—21no—
12#13063304—21no—
13#13063284C411yescharacteristic
14#13063244C2212yes—
15#13063242—21no—
16C2×#41×C43C2211yescharacteristic
17C2×M16×C43—21no—
18#101×C43C2212yes—
19#100×C43—21no—
20#41×C43—41no—
21#41×C43—41no—
22C2×Q8×C43C2311yescharacteristic
23C2×D4×C43C2×C411yescharacteristic
24C2×D4×C43D411yescharacteristic
25C2×D4×C43D411yescharacteristic
26C22×C4×C43C2×C411yescharacteristic
27C22×C4×C43D411yescharacteristic
28C22×C4×C43D411yescharacteristic
29C22×Dic43—21no—
30C2×Dic86—21no—
31C2×Dic86—41no—
32C2×Dic86—41no—
33C2×Dic86C2×C412yes—
34M16×C43—22no—
35M16×C43—41no—
36C2×C8×C43—41no—
37C22⋊Dic43—21no—
38C22⋊Dic43—22no—
39C22⋊Dic43—22no—
40C4⋊Dic43—21no—
41Dic43⋊C4—22no—
42Dic43⋊C4—22no—
43C4×Dic43C2×C412yes—
44#10621877—22no—
45#10621877—41no—
46C2×C43⋊C8—41no—
47C23×C43C22⋊C411yescharacteristic
48C23×C43C22⋊C411yescharacteristic
49C23×C43C22⋊C411yescharacteristic
50Q8×C43—41no—
51D4×C43—41no—
52D4×C43—41no—
53D4×C43—41no—
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43C22⋊C411yescharacteristic
61C2×C4×C43C22×C411yescharacteristic
62C2×C4×C43C2×D411yescharacteristic
63C2×C4×C43C2×D411yescharacteristic
64C2×Dic43—22no—
65C2×Dic43—22no—
66C2×Dic43—42no—
67Dic86—41no—
68Dic86—41no—
69Dic86—42no—
70C8×C43—42no—
71C43⋊C8—42no—
72C22×C43—21no—
73C22×C43—21no—
74C22×C43—21no—
75C22×C43—41no—
76C22×C43—41no—
77C22×C43—41no—
78C22×C43C2×C22⋊C411yescharacteristic
79C4×C43—21no—
80C4×C43—21no—
81C4×C43—21no—
82C4×C43#9911yescharacteristic
83C4×C43#9911yescharacteristic
84Dic43—42no—
85Dic43—42no—
86#2135—431nomaximal, Sylow
87C2×C43—21no—
88C2×C43—41no—
89C2×C43—41no—
90C2×C43—41no—
91C2×C43C2×#9911yescharacteristic
92#536—431no—
93#413—431no—
94#413D4311yescharacteristic
95#356—434no—
96C43#213511yescharacteristic, complemented, Sylow
97C2×#41C2×D4311yescharacteristic
98C22×Q8—431no—
99C2×M16—21no—
100C2×M16—861no—
101C4⋊Q8—432no—
102#124—432no—
103#123—861no—
104#123—861no—
105C22⋊Q8—861no—
106C22⋊Q8—861no—
107#117—431no—
108#101—432no—
109#101C2×D4312yes—
110#100—21no—
111#100—861no—
112#41—41no—
113#41—41no—
114C2×Q8—432no—
115C2×Q8—861no—
116C2×Q8—1721no—
117C2×Q8—1721no—
118C2×Q8C22×D4311yescharacteristic
119C2×D4C4×D4311yescharacteristic
120C2×D4D17211yescharacteristic
121C2×D4C22⋊D4311yescharacteristic
122C22×C4—861no—
123C22×C4C4×D4311yescharacteristic
124C22×C4D17211yescharacteristic
125C22×C4C22⋊D4311yescharacteristic
126M16—22no—
127M16—41no—
128M16—862no—
129M16—1721no—
130C2×C8—41no—
131C2×C8—1721no—
132C4⋊C4—861no—
133C4⋊C4—862no—
134C4⋊C4—862no—
135C22⋊C4—861no—
136C22⋊C4—862no—
137C22⋊C4—862no—
138C42—432no—
139C23(C2×D43)⋊C411yescharacteristic
140C23(C2×D43)⋊C411yescharacteristic
141C23(C2×D43)⋊C411yescharacteristic
142Q8—41no—
143Q8—1722no—
144Q8—1721no—
145Q8—1721no—
146D4—41no—
147D4—41no—
148D4—41no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—862no—
156C2×C4—862no—
157C2×C4—1722no—
158C2×C4(C2×D43)⋊C411yescharacteristic
159C2×C4C2×C4×D4311yescharacteristic
160C2×C4C2×D17211yescharacteristic
161C2×C4C2×C22⋊D4311yescharacteristic
162C8—42no—
163C8—1722no—
164C22—21no—
165C22—21no—
166C22—21no—
167C22—41no—
168C22—41no—
169C22—41no—
170C22C2×(C2×D43)⋊C411yescharacteristic
171C4—21no—
172C4—21no—
173C4—21no—
174C4—1722no—
175C4—1722no—
176C4#1306323911yescharacteristic
177C4#1306323911yescharacteristic
178C2—21no—
179C2—41no—
180C2—41no—
181C2—41no—
182C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC43×#413C2
socleC2×C43C2×#99
hypercenter#413D43
hypocenterC43#2135
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
3. #14582697C2semidirect
96. C43#2135semidirect