Finite Group Databasebeta

← #19134878

Subgroups — #19134878

Order 5504.

374 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 97 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
2#14582779C211yesmaximal, characteristic
3#14582774C212yesmaximal, complemented
4#14582665C212yesmaximal, complemented
5C2×#99×C43C211yesmaximal, characteristic
6C23×Dic43C2211yescharacteristic
7D4×Dic43—22no—
8D4×Dic43—22no—
9#13063284—21no—
10C2×C4⋊Dic43—22no—
11C2×C22⋊Dic43—21no—
12C2×C22⋊Dic43—21no—
13C2×C22⋊Dic43C2211yescharacteristic
14C2×C22⋊Dic43C2212yes—
15C43⋊#95—21no—
16C43⋊#95—22no—
17C22×D4×C43C2211yescharacteristic
18C2×C22⋊C4×C43C2212yes—
19#99×C43C414yescomplemented
20C24×C43D411yescharacteristic
21C24×C43C2311yescharacteristic
22C2×D4×C43—22no—
23C2×D4×C43—22no—
24C2×D4×C43C2×C412yes—
25C2×D4×C43Q812yes—
26C22×C4×C43—22no—
27C22×C4×C43D411yescharacteristic
28C22×Dic43—21no—
29C22×Dic43—21no—
30C22×Dic43—21no—
31C22×Dic43—22no—
32C22×Dic43—21no—
33C22×Dic43—42no—
34C22×Dic43D412yes—
35C22×Dic43D412yes—
36C22⋊C4×C43—22no—
37C22⋊C4×C43C2×C414yescomplemented
38C22⋊Dic43—22no—
39C22⋊Dic43—22no—
40C22⋊Dic43—22no—
41C22⋊Dic43—22no—
42C22⋊Dic43—42no—
43C4⋊Dic43—21no—
44C4⋊Dic43—21no—
45C4⋊Dic43—44no—
46C4×Dic43—22no—
47C23×C43—21no—
48C23×C43—21no—
49C23×C43—41no—
50C23×C43—41no—
51C23×C43—41no—
52C23×C43—41no—
53C23×C43C4⋊C412yescomplemented
54C23×C43C22×C411yescharacteristic
55C23×C43C2×D411yescharacteristic
56C23×C43C2×D412yes—
57C23×C43C2×Q811yescharacteristic
58C23×C43#4112yes—
59D4×C43—24no—
60D4×C43—24no—
61C2×C4×C43—21no—
62C2×C4×C43—21no—
63C2×C4×C43—24no—
64C2×C4×C43—42no—
65C2×C4×C43—42no—
66C2×C4×C43C4⋊C412yescomplemented
67C2×Dic43—24no—
68C2×Dic43—22no—
69C2×Dic43—22no—
70C2×Dic43—22no—
71C2×Dic43—41no—
72C2×Dic43—42no—
73C2×Dic43—41no—
74C2×Dic43—42no—
75C2×Dic43—42no—
76C2×Dic43—41no—
77C2×Dic43—41no—
78C2×Dic43—41no—
79C2×Dic43—81no—
80C2×Dic43—81no—
81C22×C43—21no—
82C22×C43—22no—
83C22×C43—21no—
84C22×C43—22no—
85C22×C43—22no—
86C22×C43—41no—
87C22×C43—41no—
88C22×C43—42no—
89C22×C43—42no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—81no—
93C22×C43C2×C4⋊C411yescharacteristic
94C22×C43C4×D412yes—
95C22×C43#12011yescharacteristic
96C22×C43C22⋊Q812yes—
97C22×C43#12311yescharacteristic
98C4×C43—22no—
99C4×C43—44no—
100Dic43—42no—
101Dic43—42no—
102Dic43—42no—
103Dic43—81no—
104#1867—431nomaximal, Sylow
105C2×C43—21no—
106C2×C43—22no—
107C2×C43—21no—
108C2×C43—22no—
109C2×C43—42no—
110C2×C43#38511yescharacteristic
111C2×C43B(4,𝔽2)11yescharacteristic
112C2×C43#45811yescharacteristic
113#518—431no—
114C2×#99D4311yescharacteristic
115#386—431no—
116#385—432no—
117#342—432no—
118C43#186711yescharacteristic, complemented, Sylow
119C22×D4C2×D4311yescharacteristic
120C23×C4—431no—
121C4×D4—862no—
122C4×D4—862no—
123#117—861no—
124C2×C4⋊C4—862no—
125C2×C22⋊C4—432no—
126C2×C22⋊C4—431no—
127C2×C22⋊C4—861no—
128C2×C22⋊C4—861no—
129C2×C22⋊C4C2×D4312yes—
130#99Dic4314yescomplemented
131#95—862no—
132#95—861no—
133C24D17211yescharacteristic
134C24C22×D4311yescharacteristic
135C2×D4—22no—
136C2×D4—22no—
137C2×D4Dic8612yes—
138C2×D4C2×Dic4312yes—
139C22×C4—22no—
140C22×C4—432no—
141C22×C4—432no—
142C22×C4—861no—
143C22×C4—861no—
144C22×C4—861no—
145C22×C4—862no—
146C22×C4—861no—
147C22×C4—1722no—
148C22×C4D17211yescharacteristic
149C4⋊C4—861no—
150C4⋊C4—861no—
151C4⋊C4—1724no—
152C22⋊C4—22no—
153C22⋊C4—862no—
154C22⋊C4—862no—
155C22⋊C4—862no—
156C22⋊C4—862no—
157C22⋊C4—1722no—
158C22⋊C4C2×Dic4314yescomplemented
159C42—862no—
160C23—21no—
161C23—21no—
162C23—41no—
163C23—41no—
164C23—41no—
165C23—41no—
166C23C4⋊Dic4312yescomplemented
167C23C2×Dic8611yescharacteristic
168C23C2×D17211yescharacteristic
169C23D4×D4312yes—
170C23#1062190012yes—
171C23C22×Dic4311yescharacteristic
172D4—24no—
173D4—24no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—24no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—862no—
180C2×C4—864no—
181C2×C4—862no—
182C2×C4—862no—
183C2×C4—3441no—
184C2×C4—3441no—
185C2×C4—1721no—
186C2×C4—1721no—
187C2×C4—1721no—
188C2×C4—1722no—
189C2×C4—1721no—
190C2×C4—1721no—
191C2×C4—1722no—
192C2×C4—1722no—
193C2×C4C4⋊Dic4312yescomplemented
194C22—22no—
195C22—21no—
196C22—22no—
197C22—21no—
198C22—22no—
199C22—41no—
200C22—42no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22—41no—
205C22—81no—
206C22C2×C4⋊Dic4311yescharacteristic
207C22D4×Dic4312yes—
208C22#1306329511yescharacteristic
209C22#1306330212yes—
210C22#1306330911yescharacteristic
211C4—22no—
212C4—44no—
213C4—3441no—
214C4—1722no—
215C4—1722no—
216C4—1722no—
217C2—22no—
218C2—21no—
219C2—21no—
220C2—22no—
221C2—42no—
222C2#1458277411yescharacteristic
223C2#1458308711yescharacteristic
224C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC23×C43C22×C4
FrattiniC24C22×D43
FittingC2×#99×C43C2
socleC22×C43#120
hypercenterC2×#99D43
hypocenterC43#1867
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
3. #14582774C2semidirect
4. #14582665C2semidirect
19. #99×C43C4semidirect
37. C22⋊C4×C43C2×C4semidirect
53. C23×C43C4⋊C4semidirect
66. C2×C4×C43C4⋊C4semidirect
118. C43#1867semidirect
130. #99Dic43semidirect
158. C22⋊C4C2×Dic43semidirect
166. C23C4⋊Dic43semidirect
193. C2×C4C4⋊Dic43semidirect