Finite Group Databasebeta

← #19135437

Subgroups — #19135437

Order 5504.

292 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 87 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×#13063323C211yesmaximal, characteristic
2#14582922C211yesmaximal, characteristic
3C2×#13063244C211yesmaximal, characteristic
4C2×#13063243C211yesmaximal, characteristic
5C2×#13063243C211yesmaximal, characteristic
6M16×Dic43C211yesmaximal, characteristic
7C2×#101×C43C211yesmaximal, characteristic
8C22×Dic86C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C2×#10621877C2211yescharacteristic
11#13063323—21no—
12#13063323—21no—
13#13063323—22no—
14C2×Dic43⋊C4C414yes—
15C2×C4×Dic43C2211yescharacteristic
16Dic43⋊C8—22no—
17#13063244—22no—
18#13063243—22no—
19#13063243—22no—
20#13063235—21no—
21C8×Dic43—21no—
22C22×Q8×C43C2211yescharacteristic
23C2×M16×C43C2211yescharacteristic
24C2×M16×C43C2211yescharacteristic
25#101×C43—22no—
26C2×Q8×C43—21no—
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43—21no—
31C2×Q8×C43—21no—
32C22×C4×C43C2×C412yes—
33C22×C4×C43C2311yescharacteristic
34C22×Dic43C2×C412yes—
35C22×Dic43C2×C412yes—
36C2×Dic86—21no—
37C2×Dic86—21no—
38C2×Dic86—21no—
39C2×Dic86—21no—
40C2×Dic86—21no—
41C2×Dic86—21no—
42M16×C43—21no—
43M16×C43—21no—
44M16×C43—21no—
45M16×C43D412yes—
46C2×C8×C43—21no—
47C2×C8×C43—21no—
48Dic43⋊C4—24no—
49Dic43⋊C4—24no—
50C4×Dic43D411yescharacteristic
51C4×Dic43D411yescharacteristic
52C4×Dic43D412yes—
53#10621877—21no—
54#10621877—21no—
55#10621877—21no—
56#10621877D412yes—
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59C23×C43C22×C411yescharacteristic
60Q8×C43—41no—
61Q8×C43—41no—
62Q8×C43—41no—
63Q8×C43—41no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43#4111yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C2×Dic43—24no—
74C2×Dic43—22no—
75C2×Dic43—22no—
76C2×Dic43—22no—
77C2×Dic43C22⋊C412yes—
78C2×Dic43C22⋊C412yes—
79Dic86—41no—
80Dic86—41no—
81Dic86—41no—
82Dic86—41no—
83C8×C43—22no—
84C8×C43—41no—
85C43⋊C8—22no—
86C43⋊C8—41no—
87C22×C43—22no—
88C22×C43C2×C22⋊C411yescharacteristic
89C22×C43C4×D411yescharacteristic
90C22×C43C4×D411yescharacteristic
91C4×C43—42no—
92C4×C43#12111yescharacteristic
93C4×C43#12111yescharacteristic
94C4×C43#12411yescharacteristic
95C4×C43#12711yescharacteristic
96Dic43—22no—
97Dic43—42no—
98Dic43#10114yescomplemented
99#1966—431nomaximal, Sylow
100C2×C43—21no—
101C2×C43—21no—
102C2×C43#39011yescharacteristic
103C2×C43C2×#10112yes—
104C2×C4⋊Q8—431no—
105#423—431no—
106C2×#101—431no—
107C2×#101—431no—
108C2×#101—431no—
109C2×#101D4311yescharacteristic
110C4×M16—431no—
111C43#196611yescharacteristic, complemented, Sylow
112C22×Q8—431no—
113C22×Q8C2×D4311yescharacteristic
114C2×M16—431no—
115C2×M16—431no—
116C2×M16C2×D4311yescharacteristic
117C2×M16C2×D4311yescharacteristic
118C4⋊Q8—861no—
119C4⋊Q8—861no—
120C4⋊Q8—862no—
121C2×C4⋊C4—434no—
122C2×C42—431no—
123C4⋊C8—862no—
124#101—22no—
125#101—862no—
126#101—862no—
127#101—862no—
128#97—861no—
129C4×C8—861no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—861no—
137C2×Q8—861no—
138C2×Q8—861no—
139C2×Q8—861no—
140C2×Q8—861no—
141C2×Q8—861no—
142C22×C4—432no—
143C22×C4—432no—
144C22×C4C4×D4312yes—
145C22×C4C22×D4311yescharacteristic
146M16—21no—
147M16—21no—
148M16—21no—
149M16—432no—
150M16—861no—
151M16—861no—
152M16—861no—
153M16C22⋊D4312yes—
154C2×C8—21no—
155C2×C8—21no—
156C2×C8—861no—
157C2×C8—861no—
158C4⋊C4—864no—
159C4⋊C4—864no—
160C42—431no—
161C42—431no—
162C42—432no—
163C23C2×C4×D4311yescharacteristic
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—41no—
168Q8—1721no—
169Q8—1721no—
170Q8—1721no—
171Q8—1721no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—432no—
176C2×C4—432no—
177C2×C4—864no—
178C2×C4—862no—
179C2×C4—862no—
180C2×C4—862no—
181C2×C4#1062189811yescharacteristic
182C2×C4D4×D4311yescharacteristic
183C2×C4D4×D4311yescharacteristic
184C2×C4D4×D4311yescharacteristic
185C2×C4#1062190011yescharacteristic
186C2×C4C2×C22⋊D4311yescharacteristic
187C8—22no—
188C8—41no—
189C8—862no—
190C8—1721no—
191C22—22no—
192C22C22⋊C4×D4311yescharacteristic
193C22(C22⋊D43)⋊C411yescharacteristic
194C22C4×C22⋊D4311yescharacteristic
195C4—42no—
196C4—434no—
197C4—862no—
198C4—1722no—
199C4#1306329711yescharacteristic
200C4#1306329811yescharacteristic
201C4#1306331111yescharacteristic
202C4#1306332111yescharacteristic
203C2—21no—
204C2—21no—
205C2#1458279911yescharacteristic
206C2#101×D4312yes—
subgroupG/H
centerC22C22⋊C4×D43
commutatorC23×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#101×C43C2
socleC22×C43C2×C22⋊C4
hypercenterC2×#101D43
hypocenterC43#1966
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
98. Dic43#101semidirect
111. C43#1966semidirect