Finite Group Databasebeta

← #19133191

Subgroups — #19133191

Order 5504.

264 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 61 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#124×D43C211yesmaximal, characteristic
2#14582954C211yesmaximal, characteristic, complemented
3#14582851C211yesmaximal, characteristic, complemented
4#14582639C211yesmaximal, characteristic, complemented
5#14582638C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic, complemented
7C43×#329C211yesmaximal, characteristic, complemented
8C2×Q8×D43C411yescharacteristic
9C2×D4×D43C411yescharacteristic
10C2×#10621872—21no—
11#13063314C411yescharacteristic
12#13063313C2211yescharacteristic
13#13063312C411yescharacteristic
14#13063311—21no—
15#13063311—21no—
16C22⋊C4×D43—21no—
17C22⋊C4×D43—21no—
18C42×D43C2211yescharacteristic
19Dic43⋊C8—21no—
20(C2×D43)⋊C8—21no—
21#13063236C2211yescharacteristic, complemented
22#13063236C2211yescharacteristic, complemented
23C8×Dic43—21no—
24#124×C43C2211yescharacteristic
25#97×C43C2211yescharacteristic, complemented
26#97×C43C2211yescharacteristic, complemented
27C23×D43—21no—
28C2×Q8×C43C2×C411yescharacteristic
29C2×D4×C43C2×C411yescharacteristic
30C2×C22⋊D43—21no—
31Q8×D43—42no—
32D4×D43—42no—
33C2×D172C2×C411yescharacteristic
34C2×C4×D43—21no—
35C2×C4×D43C2×C411yescharacteristic
36C2×C4×D43D411yescharacteristic
37C2×C4×D43D411yescharacteristic
38C2×Dic86—21no—
39C2×Dic86C2×C411yescharacteristic
40C2×C8×C43—21no—
41C2×C8×C43—21no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43—21no—
44C42×C43C2311yescharacteristic
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51C4×Dic43C2×C411yescharacteristic
52C4×Dic43D411yescharacteristic
53C4×Dic43D411yescharacteristic
54C2×C43⋊C8—21no—
55C2×C43⋊C8—21no—
56#10621872—24no—
57C23×C43—21no—
58C22×D43—21no—
59C22×D43—42no—
60C22×D43—42no—
61C22×D43—42no—
62C22×D43C22⋊C411yescharacteristic
63Q8×C43—41no—
64D4×C43—41no—
65C2×C4×C43—21no—
66C2×C4×C43C22×C411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C22⋊D43—42no—
70C2×Dic43—21no—
71C2×Dic43C22⋊C411yescharacteristic
72C2×Dic43C22⋊C411yescharacteristic
73C2×Dic43C22⋊C411yescharacteristic
74D172—41no—
75C4×D43—22no—
76C4×D43—22no—
77C4×D43—41no—
78C4×D43—42no—
79Dic86—42no—
80Dic86—41no—
81C8×C43—22no—
82C8×C43—41no—
83C43⋊C8—22no—
84C43⋊C8—41no—
85C22×C43—41no—
86C22×C43—41no—
87C22×C43—41no—
88C22×C43C2×C22⋊C411yescharacteristic
89C2×D43—21no—
90C2×D43—21no—
91C2×D43—41no—
92C2×D43—41no—
93C2×D43—41no—
94C2×D43—84no—
95C2×D43#10412yes—
96C4×C43—21no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—41no—
100Dic43—21no—
101Dic43—21no—
102Dic43—41no—
103Dic43#10012yes—
104#1527—431nomaximal, Sylow
105C2×C43—81no—
106C2×C43C2×#10011yescharacteristic
107C2×C43C2×#10411yescharacteristic
108C2×C43#42111yescharacteristic
109D43—22no—
110D43—81no—
111C2×#124—431no—
112#432—431no—
113C4×M16—431no—
114#329—431no—
115#329—431no—
116#329—431no—
117#329D4311yescharacteristic, complemented
118C43#152711yescharacteristic, complemented, Sylow
119C22×Q8—431no—
120C22×D4—431no—
121C2×M16—861no—
122#124—431no—
123#124—431no—
124#124—431no—
125#124—861no—
126#124—861no—
127#124C2×D4311yescharacteristic
128C2×C22⋊C4—861no—
129C2×C22⋊C4—861no—
130C2×C42—431no—
131C4⋊C8—861no—
132C22⋊C8—861no—
133#97—431no—
134#97—431no—
135#97C2×D4311yescharacteristic, complemented
136#97C2×D4311yescharacteristic, complemented
137C4×C8—861no—
138C24—861no—
139C2×Q8—431no—
140C2×Q8—861no—
141C2×Q8—1722no—
142C2×Q8C4×D4311yescharacteristic
143C2×D4—431no—
144C2×D4—861no—
145C2×D4—1722no—
146C2×D4C4×D4311yescharacteristic
147C22×C4—431no—
148C22×C4—431no—
149C22×C4—431no—
150C22×C4—861no—
151M16—864no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—861no—
155C2×C8—861no—
156C22⋊C4—21no—
157C22⋊C4—21no—
158C22⋊C4—861no—
159C22⋊C4—861no—
160C22⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C42—431no—
165C42—431no—
166C42—431no—
167C42C22×D4311yescharacteristic
168C23—21no—
169C23—431no—
170C23—861no—
171C23—1722no—
172C23—1722no—
173C23—1722no—
174Q8—41no—
175Q8—1721no—
176Q8—1722no—
177D4—41no—
178D4—1721no—
179D4—1722no—
180C2×C4—21no—
181C2×C4—431no—
182C2×C4—431no—
183C2×C4—431no—
184C2×C4—862no—
185C2×C4—862no—
186C2×C4—861no—
187C2×C4—1721no—
188C2×C4—1722no—
189C2×C4C2×C4×D4311yescharacteristic
190C2×C4D4×D4311yescharacteristic
191C2×C4D4×D4311yescharacteristic
192C8—22no—
193C8—41no—
194C8—862no—
195C8—1721no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—432no—
200C22—861no—
201C22—861no—
202C22—3444no—
203C22—1721no—
204C22—1721no—
205C22—1721no—
206C22C22⋊C4×D4311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—41no—
211C4—432no—
212C4—861no—
213C4—861no—
214C4—1721no—
215C2—81no—
216C2—862no—
217C2—3441no—
218C2#100×D4311yescharacteristic
219C2#104×D4311yescharacteristic
220C2#1458291411yescharacteristic
subgroupG/H
centerC22C22⋊C4×D43
commutatorC2×C4×C43C22×C4
FrattiniC42C22×D43
FittingC43×#329C2
socleC22×C43C2×C22⋊C4
hypercenter#329D43
hypocenterC43#1527
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14582954C2semidirect
3. #14582851C2semidirect
4. #14582639C2semidirect
5. #14582638C2semidirect
6. #14582638C2semidirect
7. C43×#329C2semidirect
21. #13063236C22semidirect
22. #13063236C22semidirect
25. #97×C43C22semidirect
26. #97×C43C22semidirect
117. #329D43semidirect
118. C43#1527semidirect
135. #97C2×D43semidirect
136. #97C2×D43semidirect