Finite Group Databasebeta

← #19134997

Subgroups — #19134997

Order 5504.

344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13063313C211yesmaximal, characteristic
2#14583376C211yesmaximal, characteristic, complemented
3#14582905C211yesmaximal, characteristic
4#14582903C211yesmaximal, characteristic
5C2×#13063243C211yesmaximal, characteristic, complemented
6#14582659C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C22×Dic86C2211yescharacteristic
9C22×D172C2211yescharacteristic
10C2×#10621877C2211yescharacteristic
11#13063313—22no—
12#13063313C414yescomplemented
13C4×Dic86—22no—
14#13063290—22no—
15#13063284C2211yescharacteristic
16#13063281—22no—
17C2×(C2×D43)⋊C4—22no—
18#13063247—22no—
19#13063245—22no—
20#13063243—22no—
21C2×M16×C43C2211yescharacteristic
22#117×C43C2211yescharacteristic
23C2×C42×C43C2211yescharacteristic
24C23×D43—21no—
25C22×C4×C43—21no—
26C22×C4×C43C2311yescharacteristic
27C22×Dic43D412yes—
28C2×D172—21no—
29C2×D172—21no—
30C2×D172—21no—
31C2×D172—21no—
32C2×D172—21no—
33C2×D172C2×C412yes—
34C2×Dic86—21no—
35C2×Dic86—21no—
36C2×Dic86—21no—
37C2×Dic86—21no—
38C2×Dic86C2×C412yes—
39C2×Dic86D412yes—
40M16×C43—21no—
41M16×C43—21no—
42C2×C8×C43—21no—
43C4⋊C4×C43D412yes—
44C22⋊C4×C43—21no—
45C42×C43—21no—
46C42×C43—21no—
47C42×C43C2×C412yes—
48C22⋊Dic43—21no—
49(C2×D43)⋊C4—28no—
50C4⋊Dic43D412yes—
51Dic43⋊C4—24no—
52C4×Dic43—24no—
53C4×Dic43—21no—
54#10621877—21no—
55#10621877—21no—
56C2×C43⋊C8—21no—
57C23×C43C2×D411yescharacteristic
58C22×D43—22no—
59C22×D43—44no—
60C22×D43—41no—
61C22×D43—41no—
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—42no—
65C2×C4×C43C22×C411yescharacteristic
66C2×C4×C43C2×D411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43#4111yescharacteristic
70C2×C4×C43#4111yescharacteristic
71C2×Dic43—22no—
72C2×Dic43—22no—
73C2×Dic43—22no—
74C2×Dic43C22⋊C414yes—
75D172—22no—
76D172—22no—
77D172—41no—
78D172—41no—
79Dic86—22no—
80Dic86—22no—
81Dic86—22no—
82Dic86—22no—
83C8×C43—41no—
84C43⋊C8—41no—
85C22×C43—22no—
86C22×C43C2×C22⋊C411yescharacteristic
87C22×C43#12011yescharacteristic
88C22×C43#12311yescharacteristic
89C2×D43—44no—
90C2×D43—42no—
91C2×D43—82no—
92C2×D43—82no—
93C4×C43—42no—
94C4×C43—42no—
95C4×C43C4×D411yescharacteristic
96C4×C43C4×D411yescharacteristic
97C4×C43#12111yescharacteristic
98C4×C43#12111yescharacteristic
99Dic43—24no—
100Dic43—42no—
101#1888—431nomaximal, Sylow
102C2×C43—21no—
103C2×C43—21no—
104C2×C43#38611yescharacteristic
105C2×C43#45412yes—
106D43—82no—
107C2×#124—431no—
108#519—431no—
109#418—431no—
110#418—431no—
111C2×#101—431no—
112#339—431no—
113#339D4311yescharacteristic, complemented
114C43#188811yescharacteristic, complemented, Sylow
115C22×Q8—431no—
116C22×D4—431no—
117C2×M16—431no—
118C2×M16C2×D4311yescharacteristic
119#124—434no—
120#124—862no—
121C4×Q8—862no—
122C4×Q8—862no—
123#117—431no—
124#117—862no—
125#117C2×D4311yescharacteristic
126C2×C22⋊C4—862no—
127C2×C42C2×D4311yescharacteristic
128#102—862no—
129#102—862no—
130#101—862no—
131C24—861no—
132C2×Q8—432no—
133C2×Q8—432no—
134C2×Q8—861no—
135C2×Q8—861no—
136C2×Q8—861no—
137C2×Q8—861no—
138C2×D4—432no—
139C2×D4—861no—
140C2×D4—861no—
141C2×D4—861no—
142C2×D4—861no—
143C2×D4—861no—
144C22×C4—21no—
145C22×C4—432no—
146C22×C4C22×D4311yescharacteristic
147M16—21no—
148M16—21no—
149M16—861no—
150M16—861no—
151C2×C8—21no—
152C2×C8—861no—
153C4⋊C4—432no—
154C4⋊C4—864no—
155C4⋊C4D17212yes—
156C22⋊C4—21no—
157C22⋊C4—868no—
158C22⋊C4—861no—
159C42—21no—
160C42—21no—
161C42—864no—
162C42—861no—
163C42C4×D4312yes—
164C23—862no—
165C23—1724no—
166C23—1721no—
167C23—1721no—
168C23D4×D4311yescharacteristic
169Q8—862no—
170Q8—862no—
171Q8—862no—
172Q8—862no—
173D4—862no—
174D4—862no—
175D4—1721no—
176D4—1721no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—434no—
181C2×C4—862no—
182C2×C4—862no—
183C2×C4—862no—
184C2×C4C2×C4×D4311yescharacteristic
185C2×C4C2×D17211yescharacteristic
186C2×C4#1062189811yescharacteristic
187C2×C4D4×D4311yescharacteristic
188C2×C4D4×D4311yescharacteristic
189C2×C4#1062190211yescharacteristic
190C8—41no—
191C8—1721no—
192C22—22no—
193C22—3442no—
194C22—3442no—
195C22—1724no—
196C22—1722no—
197C22C22⋊C4×D4311yescharacteristic
198C22#1306329511yescharacteristic
199C22#1306331011yescharacteristic
200C4—42no—
201C4—42no—
202C4—864no—
203C4—1722no—
204C4#1306328711yescharacteristic
205C4C4×D17211yescharacteristic
206C4#1306329811yescharacteristic
207C4#1306330011yescharacteristic
208C2—21no—
209C2—21no—
210C2—3442no—
211C2#1458277711yescharacteristic
212C2#1458307312yes—
subgroupG/H
centerC22#13063295
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC22×C43#120
hypercenter#339D43
hypocenterC43#1888
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14583376C2semidirect
5. C2×#13063243C2semidirect
6. #14582659C2semidirect
7. C43×#339C2semidirect
12. #13063313C4semidirect
113. #339D43semidirect
114. C43#1888semidirect