Finite Group Databasebeta

← #19136282

Subgroups — #19136282

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#14583473C211yesmaximal, characteristic
2C2×#13063244C211yesmaximal, characteristic, complemented
3#14582697C212yesmaximal, complemented
4#14582695C212yesmaximal, complemented
5C2×#101×C43C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic
7C2×#10621877—21no—
8#13063323C411yescharacteristic
9#13063323C2211yescharacteristic
10#13063314C411yescharacteristic
11#13063314C2211yescharacteristic
12#13063308—21no—
13#13063308—21no—
14#13063301—21no—
15#13063301—21no—
16#13063284C411yescharacteristic
17#13063244—21no—
18#13063244C2212yes—
19C22×Q8×C43C2211yescharacteristic
20C2×M16×C43—21no—
21#101×C43—21no—
22#101×C43C2212yes—
23C2×Q8×C43—41no—
24C2×Q8×C43—41no—
25C2×Q8×C43C2×C411yescharacteristic
26C2×Q8×C43D411yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C2×Q8×C43C2311yescharacteristic
29C22×C4×C43C2×C411yescharacteristic
30C22×C4×C43D411yescharacteristic
31C22×C4×C43D411yescharacteristic
32C2×C22⋊D43—21no—
33#10621898—41no—
34#10621898—41no—
35C2×D172C2×C411yescharacteristic
36C2×C4×D43—21no—
37C2×Dic86C2×C411yescharacteristic
38M16×C43—22no—
39M16×C43—41no—
40C2×C8×C43—41no—
41C22⋊Dic43—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45(C2×D43)⋊C4—21no—
46C4⋊Dic43—21no—
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51C4×Dic43C2×C411yescharacteristic
52C4×Dic43C2×C411yescharacteristic
53#10621877—22no—
54#10621877—41no—
55C2×C43⋊C8—41no—
56C23×C43C22⋊C411yescharacteristic
57C22×D43—21no—
58Q8×C43—41no—
59Q8×C43—41no—
60Q8×C43—41no—
61Q8×C43—41no—
62C2×C4×C43—21no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43C22⋊C411yescharacteristic
69C2×C4×C43C22⋊C411yescharacteristic
70C2×C4×C43C22⋊C411yescharacteristic
71C2×C4×C43C22×C411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C22⋊D43—41no—
75C22⋊D43—41no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79D172—41no—
80C4×D43—42no—
81Dic86—41no—
82C8×C43—42no—
83C43⋊C8—42no—
84C22×C43—41no—
85C22×C43#9911yescharacteristic
86C22×C43#9911yescharacteristic
87C22×C43C2×C22⋊C411yescharacteristic
88C2×D43—42no—
89C2×D43—41no—
90C4×C43—21no—
91C4×C43—21no—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—21no—
96Dic43—41no—
97Dic43—41no—
98Dic43—41no—
99#2133—431nomaximal, Sylow
100C2×C43—21no—
101C2×C43—21no—
102C2×C43—21no—
103C2×C43C2×#9911yescharacteristic
104D43—81no—
105#536—431no—
106C2×#101—431no—
107C2×#101D4311yescharacteristic, complemented
108#356—432no—
109#355—432no—
110C43#213311yescharacteristic, complemented, Sylow
111C2×#41—431no—
112C22×Q8C2×D4311yescharacteristic
113C2×M16—21no—
114C2×M16—861no—
115C4⋊Q8—431no—
116C4⋊Q8—431no—
117#124—431no—
118#124—431no—
119#123—861no—
120#123—861no—
121C22⋊Q8—861no—
122C22⋊Q8—861no—
123#117—431no—
124#101—21no—
125#101—432no—
126#101—861no—
127#101C2×D4312yes—
128#41—1721no—
129#41—1721no—
130C2×Q8—41no—
131C2×Q8—41no—
132C2×Q8—431no—
133C2×Q8C4×D4311yescharacteristic
134C2×Q8D17211yescharacteristic
135C2×Q8C22⋊D4311yescharacteristic
136C2×Q8C22×D4311yescharacteristic
137C2×D4—431no—
138C2×D4—861no—
139C22×C4—861no—
140C22×C4C4×D4311yescharacteristic
141C22×C4D17211yescharacteristic
142C22×C4C22⋊D4311yescharacteristic
143M16—22no—
144M16—41no—
145M16—862no—
146M16—1721no—
147C2×C8—41no—
148C2×C8—1721no—
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—861no—
152C4⋊C4—861no—
153C4⋊C4—861no—
154C22⋊C4—861no—
155C22⋊C4—861no—
156C22⋊C4—861no—
157C22⋊C4—861no—
158C22⋊C4—861no—
159C42—431no—
160C42—431no—
161C23—861no—
162C23(C2×D43)⋊C411yescharacteristic
163Q8—41no—
164Q8—41no—
165Q8—41no—
166Q8—41no—
167Q8—1721no—
168D4—1721no—
169D4—1721no—
170D4—1721no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—861no—
178C2×C4—861no—
179C2×C4—861no—
180C2×C4—1722no—
181C2×C4(C2×D43)⋊C411yescharacteristic
182C2×C4(C2×D43)⋊C411yescharacteristic
183C2×C4(C2×D43)⋊C411yescharacteristic
184C2×C4C2×C4×D4311yescharacteristic
185C2×C4C2×D17211yescharacteristic
186C2×C4C2×C22⋊D4311yescharacteristic
187C8—42no—
188C8—1722no—
189C22—41no—
190C22—1722no—
191C22—1721no—
192C22#1306323911yescharacteristic
193C22#1306323911yescharacteristic
194C22C2×(C2×D43)⋊C411yescharacteristic
195C4—21no—
196C4—21no—
197C4—21no—
198C4—21no—
199C4—21no—
200C4—21no—
201C4—1721no—
202C4—1721no—
203C4—1721no—
204C2—21no—
205C2—21no—
206C2—21no—
207C2—3441no—
208C2C2×#1306323911yescharacteristic
subgroupG/H
centerC2C2×#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC2×#101×C43C2
socleC2×C43C2×#99
hypercenterC2×#101D43
hypocenterC43#2133
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C23 ◁ C22×Q8 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#13063244C2semidirect
3. #14582697C2semidirect
4. #14582695C2semidirect
5. C2×#101×C43C2semidirect
107. C2×#101D43semidirect
110. C43#2133semidirect