Finite Group Databasebeta

← #19135138

Subgroups — #19135138

Order 5504.

380 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 93 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#14583374C211yesmaximal, characteristic, complemented
2C2×#13063240C212yesmaximal, complemented
3C2×#13063240C211yesmaximal, characteristic, complemented
4#14582665C212yesmaximal, complemented
5C43×#534C211yesmaximal, characteristic
6D4×Dic43—24no—
7#13063284—21no—
8C2×C22⋊Dic43—21no—
9C2×C22⋊Dic43C2212yes—
10C2×C22⋊Dic43C2212yes—
11#13063240—22no—
12#13063240—24no—
13C22×D4×C43C2211yescharacteristic
14C22×D4×C43C2211yescharacteristic
15#123×C43—21no—
16#123×C43C412yescomplemented
17#121×C43—22no—
18#120×C43—21no—
19#120×C43C412yescomplemented
20C2×C22⋊C4×C43C2211yescharacteristic
21C24×C43C2×C411yescharacteristic, complemented
22C24×C43D411yescharacteristic
23C24×C43C2311yescharacteristic
24C2×D4×C43—22no—
25C2×D4×C43—22no—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—22no—
29C2×D4×C43—22no—
30C2×D4×C43—22no—
31C2×D4×C43C2×C412yes—
32C2×D4×C43D412yes—
33C22×C4×C43—21no—
34C22×C4×C43C2×C411yescharacteristic, complemented
35C22×C4×C43D411yescharacteristic
36C22×Dic43—22no—
37C22×Dic43—22no—
38C22×Dic43—22no—
39C4⋊C4×C43—22no—
40C22⋊C4×C43—22no—
41C22⋊C4×C43—22no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43C2×C412yescomplemented
44C22⋊Dic43—22no—
45C22⋊Dic43—22no—
46C22⋊Dic43—22no—
47C22⋊Dic43—22no—
48C22⋊Dic43D414yescomplemented
49C4⋊Dic43—22no—
50C4×Dic43—22no—
51C23×C43—21no—
52C23×C43—21no—
53C23×C43—21no—
54C23×C43—22no—
55C23×C43—81no—
56C23×C43—81no—
57C23×C43—81no—
58C23×C43C22⋊C412yes—
59C23×C43C22×C411yescharacteristic
60C23×C43C2×D412yes—
61C23×C43C2×D411yescharacteristic
62C23×C43C2×D411yescharacteristic
63C23×C43#4112yes—
64D4×C43—24no—
65D4×C43—24no—
66D4×C43—41no—
67D4×C43—42no—
68D4×C43—41no—
69D4×C43—82no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—81no—
76C2×C4×C43C22⋊C412yes—
77C2×Dic43—24no—
78C2×Dic43—42no—
79C2×Dic43—82no—
80C2×Dic43—82no—
81C2×Dic43—82no—
82C22×C43—22no—
83C22×C43—41no—
84C22×C43—41no—
85C22×C43—42no—
86C22×C43—41no—
87C22×C43—42no—
88C22×C43—42no—
89C22×C43—42no—
90C22×C43—42no—
91C22×C43—41no—
92C22×C43—81no—
93C22×C43—82no—
94C22×C43C2×C22⋊C411yescharacteristic
95C22×C43C4×D412yes—
96C22×C43#12011yescharacteristic
97C22×C43#12112yes—
98C22×C43#12311yescharacteristic
99C4×C43—22no—
100C4×C43—42no—
101C4×C43—41no—
102Dic43—44no—
103Dic43—82no—
104#1913—431nomaximal, Sylow
105C2×C43—21no—
106C2×C43—22no—
107C2×C43—21no—
108C2×C43—22no—
109C2×C43—21no—
110C2×C43—42no—
111C2×C43—81no—
112C2×C43#38611yescharacteristic
113#534D4311yescharacteristic
114#518—431no—
115C2×#99—432no—
116C2×#99—431no—
117#342—432no—
118C43#191311yescharacteristic, complemented, Sylow
119C22×D4C2×D4311yescharacteristic
120C22×D4C2×D4311yescharacteristic
121#123—21no—
122#123Dic4312yescomplemented
123#121—22no—
124#120—21no—
125#120Dic4312yescomplemented
126C4×D4—864no—
127#117—861no—
128C2×C22⋊C4—432no—
129C2×C22⋊C4—432no—
130C2×C22⋊C4—861no—
131C2×C22⋊C4C2×D4311yescharacteristic
132#99—864no—
133#99—862no—
134C24C2×Dic4311yescharacteristic, complemented
135C24C22⋊D4311yescharacteristic
136C24C22×D4311yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—22no—
140C2×D4—22no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—22no—
144C2×D4C2×Dic4312yes—
145C2×D4C22⋊D4312yes—
146C22×C4—21no—
147C22×C4—862no—
148C22×C4—862no—
149C22×C4—862no—
150C22×C4C2×Dic4311yescharacteristic, complemented
151C22×C4C22⋊D4311yescharacteristic
152C4⋊C4—22no—
153C4⋊C4—862no—
154C22⋊C4—22no—
155C22⋊C4—21no—
156C22⋊C4—22no—
157C22⋊C4—434no—
158C22⋊C4—862no—
159C22⋊C4—862no—
160C22⋊C4—862no—
161C22⋊C4—862no—
162C22⋊C4C2×Dic4312yescomplemented
163C42—862no—
164C23—21no—
165C23—21no—
166C23—21no—
167C23—22no—
168C23—81no—
169C23—81no—
170C23—81no—
171C23C22⋊Dic4312yes—
172C23D4×D4312yes—
173C23#1062190012yes—
174C23C22×Dic4311yescharacteristic
175C23C2×C22⋊D4311yescharacteristic
176C23C2×C22⋊D4311yescharacteristic
177D4—24no—
178D4—24no—
179D4—41no—
180D4—42no—
181D4—41no—
182D4—82no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—81no—
189C2×C4—864no—
190C2×C4—3442no—
191C2×C4—3442no—
192C2×C4—3442no—
193C2×C4—1722no—
194C2×C4C22⋊Dic4312yes—
195C22—22no—
196C22—41no—
197C22—42no—
198C22—42no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—41no—
205C22—81no—
206C22—82no—
207C22C2×C22⋊Dic4311yescharacteristic
208C22D4×Dic4312yes—
209C22#1306329311yescharacteristic
210C22#1306329712yes—
211C22#1306330611yescharacteristic
212C4—22no—
213C4—42no—
214C4—41no—
215C4—3442no—
216C4—1724no—
217C2—21no—
218C2—22no—
219C2—21no—
220C2—22no—
221C2—21no—
222C2—42no—
223C2—81no—
224C2#1458277911yescharacteristic
subgroupG/H
centerC2#14582779
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC43×#534C2
socleC2×C43#386
hypercenter#534D43
hypocenterC43#1913
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C24 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14583374C2semidirect
2. C2×#13063240C2semidirect
3. C2×#13063240C2semidirect
4. #14582665C2semidirect
16. #123×C43C4semidirect
19. #120×C43C4semidirect
21. C24×C43C2×C4semidirect
34. C22×C4×C43C2×C4semidirect
43. C22⋊C4×C43C2×C4semidirect
48. C22⋊Dic43D4semidirect
118. C43#1913semidirect
122. #123Dic43semidirect
125. #120Dic43semidirect
134. C24C2×Dic43semidirect
150. C22×C4C2×Dic43semidirect
162. C22⋊C4C2×Dic43semidirect