Finite Group Databasebeta

← #19140091

Subgroups — #19140091

Order 5504.

440 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 440 conjugacy classes of subgroups — too many to draw. Only its 129 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#14582838C211yesmaximal, characteristic, complemented
2#14582829C211yesmaximal, characteristic, complemented
3#14582813C212yesmaximal
4#14582793C212yesmaximal, complemented
5#14582793C212yesmaximal, complemented
6#14582792C212yesmaximal, complemented
7#14582792C212yesmaximal, complemented
8C4×Dic43⋊C4C212yesmaximal, complemented
9C43×#390C211yesmaximal, characteristic
10C2×C4⋊Dic43C2211yescharacteristic
11C2×C4⋊Dic43C2211yescharacteristic
12C2×Dic43⋊C4C2212yes—
13C2×Dic43⋊C4C2212yes—
14C2×C22⋊Dic43C2212yes—
15C2×C22⋊Dic43C2212yes—
16C2×C22⋊Dic43C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C4×Dic43C2212yes—
19C2×C4×Dic43C2212yes—
20C43⋊#95C2212yes—
21C43⋊#95C2212yes—
22C43⋊#95C2212yes—
23C43⋊#95C2211yescharacteristic
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C22×D4×C43C2211yescharacteristic
27C2×C4⋊C4×C43C2211yescharacteristic
28C2×C22⋊C4×C43C2212yes—
29C2×C22⋊C4×C43C2212yes—
30C2×C42×C43C2211yescharacteristic
31C24×C43C2312yes—
32C2×D4×C43—22no—
33C2×D4×C43—41no—
34C2×D4×C43—41no—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C22×Dic43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C4⋊C4×C43—41no—
44C22⋊C4×C43—24no—
45C22⋊C4×C43—24no—
46C42×C43—41no—
47C22⋊Dic43—24no—
48C22⋊Dic43—24no—
49C22⋊Dic43—42no—
50C22⋊Dic43—42no—
51C4⋊Dic43—41no—
52C4⋊Dic43—41no—
53Dic43⋊C4—24no—
54Dic43⋊C4—24no—
55C4×Dic43—24no—
56C4×Dic43—42no—
57C23×C43—22no—
58C23×C43—22no—
59C23×C43—22no—
60C23×C43—22no—
61C23×C43—22no—
62C23×C43—22no—
63C23×C43—22no—
64C23×C43C2411yescharacteristic
65D4×C43—44no—
66C2×C4×C43—22no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43#4112yes—
75C2×C4×C43#4114yes—
76C2×Dic43—22no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43#4114yes—
88C22×C43—42no—
89C22×C43—42no—
90C22×C43—42no—
91C22×C43—42no—
92C22×C43—42no—
93C22×C43—42no—
94C22×C43—42no—
95C22×C43C2×#4112yes—
96C22×C43C2×#4112yes—
97C22×C43C2×#4111yescharacteristic
98C22×C43H(5,𝔽2)11yescharacteristic
99C22×C43H(5,𝔽2)11yescharacteristic
100C4×C43—22no—
101C4×C43—24no—
102C4×C43—41no—
103C4×C43—41no—
104Dic43—24no—
105Dic43—42no—
106Dic43—42no—
107Dic43—42no—
108#2593—431nomaximal, Sylow
109C2×C43—82no—
110C2×C43#52912yes—
111C2×C43#53811yescharacteristic
112C2×C43#55312yes—
113C2×C43#55511yescharacteristic
114C2×C43#55911yescharacteristic
115#400—431no—
116#398—431no—
117#394—432no—
118#390D4311yescharacteristic
119#388—432no—
120#388—432no—
121#388—432no—
122#388—432no—
123C4×C4⋊C4—432no—
124C43#259311yescharacteristic, complemented, Sylow
125C22×D4C2×D4311yescharacteristic
126C2×C4⋊C4—432no—
127C2×C4⋊C4—432no—
128C2×C4⋊C4—431no—
129C2×C4⋊C4—431no—
130C2×C4⋊C4C2×D4311yescharacteristic
131C2×C22⋊C4—432no—
132C2×C22⋊C4—432no—
133C2×C22⋊C4—432no—
134C2×C22⋊C4—432no—
135C2×C22⋊C4C2×D4312yes—
136C2×C22⋊C4C2×D4312yes—
137C2×C42—432no—
138C2×C42—432no—
139C2×C42C2×D4311yescharacteristic
140#95—432no—
141#95—432no—
142#95—431no—
143#95—432no—
144#95—432no—
145#95—431no—
146C24C22×D4312yes—
147C2×D4—22no—
148C2×D4—41no—
149C2×D4—41no—
150C22×C4—432no—
151C22×C4—432no—
152C22×C4—432no—
153C22×C4—432no—
154C22×C4C22×D4311yescharacteristic
155C22×C4C22×D4311yescharacteristic
156C22×C4C22×D4311yescharacteristic
157C22×C4C22×D4312yes—
158C4⋊C4—41no—
159C4⋊C4—864no—
160C4⋊C4—864no—
161C4⋊C4—1721no—
162C4⋊C4—1721no—
163C22⋊C4—24no—
164C22⋊C4—24no—
165C22⋊C4—864no—
166C22⋊C4—864no—
167C22⋊C4—1722no—
168C22⋊C4—1722no—
169C42—41no—
170C42—864no—
171C42—1722no—
172C23—22no—
173C23—22no—
174C23—22no—
175C23—22no—
176C23—22no—
177C23—22no—
178C23—22no—
179C23C23×D4311yescharacteristic
180D4—44no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—434no—
190C2×C4—862no—
191C2×C4—862no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4—862no—
200C2×C4—862no—
201C2×C4#1062189812yes—
202C2×C4#1062190014yes—
203C22—42no—
204C22—42no—
205C22—42no—
206C22—42no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22#41×D4312yes—
211C22C2×#1062190012yes—
212C22C2×#1062189811yescharacteristic
213C22#1306337011yescharacteristic
214C22#1306337011yescharacteristic
215C4—24no—
216C4—22no—
217C4—41no—
218C4—41no—
219C4—864no—
220C4—1722no—
221C4—1722no—
222C4—1722no—
223C2—82no—
224C2#1458343112yes—
225C2#1458348711yescharacteristic
226C2#1458359212yes—
227C2#1458361111yescharacteristic
228C2#1458363511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#390C2
hypercenter#390D43
hypocenterC43#2593
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #14582838C2semidirect
2. #14582829C2semidirect
4. #14582793C2semidirect
5. #14582793C2semidirect
6. #14582792C2semidirect
7. #14582792C2semidirect
8. C4×Dic43⋊C4C2semidirect
124. C43#2593semidirect