Finite Group Databasebeta

← #19133080

Subgroups — #19133080

Order 5504.

238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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#14583435C211yesmaximal, characteristic
2#14582949C211yesmaximal, characteristic, complemented
3#14582744C211yesmaximal, characteristic, complemented
4#14582636C211yesmaximal, characteristic, complemented
5#14582634C211yesmaximal, characteristic
6#14582632C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic, complemented
8#13063320—21no—
9#13063316C411yescharacteristic, complemented
10#13063314C411yescharacteristic, complemented
11#13063309—21no—
12#13063299C2211yescharacteristic
13Q8×Dic43C411yescharacteristic, complemented
14#13063287C411yescharacteristic, complemented
15(C22⋊D43)⋊C4—21no—
16#13063283—21no—
17C2×C4×Dic43—21no—
18C2×C4×Dic43C2211yescharacteristic
19Dic43⋊C8—21no—
20C22⋊(C43⋊C8)C2211yescharacteristic
21C8×Dic43—21no—
22C43⋊#95—21no—
23C43⋊#95C2211yescharacteristic
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×Q8×C43C2×C411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31C22×Dic43—21no—
32C22×Dic43D411yescharacteristic
33C22×Dic43D411yescharacteristic
34C2×D172C2×C411yescharacteristic
35C2×C4×D43—21no—
36C2×C8×C43—21no—
37C4⋊C4×C43—21no—
38C4⋊C4×C43C2×C411yescharacteristic
39C22⋊C4×C43—21no—
40(C2×D43)⋊C4—21no—
41(C2×D43)⋊C4—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43C2×C411yescharacteristic
47Dic43⋊C4—21no—
48C4×Dic43—24no—
49C4×Dic43—21no—
50C4×Dic43C2×C411yescharacteristic
51C4×Dic43C2×C411yescharacteristic
52C4×Dic43D411yescharacteristic
53C4×Dic43D411yescharacteristic
54C2×C43⋊C8—21no—
55C23×C43C2×D411yescharacteristic
56C22×D43—21no—
57Q8×C43—41no—
58C2×C4×C43—22no—
59C2×C4×C43—21no—
60C2×C4×C43—21no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43—41no—
64C2×C4×C43C22×C411yescharacteristic
65C2×C4×C43C2×D411yescharacteristic
66C22⋊D43—41no—
67C22⋊D43—41no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—22no—
71C2×Dic43—22no—
72C2×Dic43—21no—
73C2×Dic43—41no—
74C2×Dic43—41no—
75C2×Dic43C22⋊C411yescharacteristic
76C2×Dic43C22⋊C411yescharacteristic
77C2×Dic43C22⋊C411yescharacteristic
78C2×Dic43C22⋊C411yescharacteristic
79D172—41no—
80C4×D43—42no—
81C8×C43—41no—
82C43⋊C8—41no—
83C22×C43—21no—
84C22×C43—21no—
85C22×C43C2×C22⋊C411yescharacteristic
86C22×C43#13511yescharacteristic
87C22×C43#13511yescharacteristic
88C2×D43—41no—
89C2×D43—41no—
90C2×D43—41no—
91C4×C43—21no—
92C4×C43—21no—
93C4×C43—42no—
94C4×C43—41no—
95C4×C43—41no—
96Dic43—21no—
97Dic43—21no—
98Dic43—21no—
99Dic43—42no—
100Dic43—41no—
101Dic43#10412yes—
102#1500—431nomaximal, Sylow
103C2×C43—21no—
104C2×C43—21no—
105C2×C43#41011yescharacteristic
106C2×C43#41611yescharacteristic
107C2×C43C2×#10411yescharacteristic
108D43—81no—
109#529—431no—
110#431—431no—
111#376—431no—
112#328—431no—
113#328D4311yescharacteristic, complemented
114#327—431no—
115#327—431no—
116C43#150011yescharacteristic, complemented, Sylow
117#126—861no—
118#125—431no—
119#124—431no—
120#123—861no—
121C22⋊Q8C2×D4311yescharacteristic
122#121—431no—
123C4×Q8—431no—
124C4×D4—431no—
125C4×D4—861no—
126#117—861no—
127C2×C42—431no—
128C2×C42—861no—
129C4⋊C8—861no—
130C22⋊C8—431no—
131C22⋊C8C2×D4311yescharacteristic
132C4×C8—861no—
133#95—431no—
134#95—861no—
135#95C2×D4311yescharacteristic
136C2×Q8C4×D4311yescharacteristic
137C2×D4—431no—
138C2×D4—861no—
139C22×C4—21no—
140C22×C4—431no—
141C22×C4—431no—
142C22×C4—861no—
143C22×C4—861no—
144C22×C4C22×D4311yescharacteristic
145C2×C8—21no—
146C2×C8—861no—
147C4⋊C4—21no—
148C4⋊C4—431no—
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—861no—
152C4⋊C4C4×D4311yescharacteristic
153C22⋊C4—21no—
154C22⋊C4—861no—
155C22⋊C4—861no—
156C22⋊C4—861no—
157C22⋊C4—861no—
158C42—431no—
159C42—431no—
160C42—431no—
161C42—431no—
162C42—861no—
163C42—864no—
164C23—861no—
165C23D4×D4311yescharacteristic
166Q8—41no—
167D4—1721no—
168D4—1721no—
169D4—1721no—
170C2×C4—22no—
171C2×C4—21no—
172C2×C4—21no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—431no—
177C2×C4—431no—
178C2×C4—431no—
179C2×C4—431no—
180C2×C4—862no—
181C2×C4—861no—
182C2×C4—861no—
183C2×C4—862no—
184C2×C4—861no—
185C2×C4—1722no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4C2×C4×D4311yescharacteristic
189C2×C4D4×D4311yescharacteristic
190C8—41no—
191C8—1721no—
192C22—21no—
193C22—21no—
194C22—1721no—
195C22—1721no—
196C22—1721no—
197C22C22⋊C4×D4311yescharacteristic
198C22#1306334611yescharacteristic
199C22#1306334811yescharacteristic
200C4—21no—
201C4—21no—
202C4—42no—
203C4—41no—
204C4—41no—
205C4—432no—
206C4—861no—
207C4—861no—
208C4—861no—
209C4—1722no—
210C4—1721no—
211C2—21no—
212C2—21no—
213C2—3441no—
214C2#1458287111yescharacteristic
215C2#1458289411yescharacteristic
216C2#104×D4311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43C2×C22⋊C4
hypercenter#328D43
hypocenterC43#1500
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #14582949C2semidirect
3. #14582744C2semidirect
4. #14582636C2semidirect
7. C43×#328C2semidirect
9. #13063316C4semidirect
10. #13063314C4semidirect
13. Q8×Dic43C4semidirect
14. #13063287C4semidirect
113. #328D43semidirect
116. C43#1500semidirect