Finite Group Databasebeta

← #19139620

Subgroups — #19139620

Order 5504.

556 conjugacy classes of subgroups; only the 181 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 181 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×#13063324C212yesmaximal
2C2×#13063323C212yesmaximal
3#14582820C212yesmaximal
4#14582819C211yesmaximal, characteristic
5#14582796C212yesmaximal
6#14582794C212yesmaximal
7#14582768C211yesmaximal, characteristic
8#14582750C212yesmaximal
9C43×#395C211yesmaximal, characteristic
10C22×Dic86C2211yescharacteristic
11C22×Dic86C2212yes—
12#13063324—28no—
13#13063323—28no—
14C2×C4⋊Dic43C2212yes—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×Dic43⋊C4C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2212yes—
22C2×C4×Dic43C2212yes—
23C2×C4×Dic43C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C43⋊#95C2211yescharacteristic
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C22×Q8×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2212yes—
30C2×C4⋊C4×C43C2211yescharacteristic
31#95×C43C2211yescharacteristic
32#95×C43C2212yes—
33C2×Q8×C43—24no—
34C2×Q8×C43—41no—
35C22×C4×C43C2311yescharacteristic
36C22×C4×C43C2311yescharacteristic
37C22×C4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2312yes—
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C22×Dic43C2312yes—
44C2×Dic86—24no—
45C2×Dic86—24no—
46C2×Dic86—24no—
47C2×Dic86—41no—
48C2×Dic86—42no—
49C4⋊C4×C43—24no—
50C4⋊C4×C43—41no—
51C4⋊Dic43—24no—
52C4⋊Dic43—41no—
53Dic43⋊C4—24no—
54Dic43⋊C4—24no—
55Dic43⋊C4—24no—
56Dic43⋊C4—24no—
57Dic43⋊C4D418yes—
58Dic43⋊C4Q818yescomplemented
59C4×Dic43—24no—
60C4×Dic43—24no—
61C4×Dic43Q814yescomplemented
62C23×C43C2411yescharacteristic
63Q8×C43—44no—
64C2×C4×C43—22no—
65C2×C4×C43—22no—
66C2×C4×C43—21no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43C2×D414yes—
75C2×C4×C43C2×Q812yes—
76C2×C4×C43C2×Q814yes—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—22no—
81C2×Dic43—22no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43C2×D414yes—
85C2×Dic43C2×D414yes—
86C2×Dic43C2×Q814yes—
87C2×Dic43C2×Q814yes—
88C2×Dic43C2×Q814yes—
89Dic86—44no—
90Dic86—48no—
91C22×C43C22×D412yes—
92C22×C43C22×Q811yescharacteristic
93C22×C43C22×Q812yes—
94C22×C43H(5,𝔽2)11yescharacteristic
95C22×C432−1+411yescharacteristic
96C4×C43—22no—
97C4×C43—24no—
98C4×C43—24no—
99C4×C43—41no—
100C4×C43—41no—
101Dic43—24no—
102Dic43—24no—
103Dic43—42no—
104Dic43C4⋊Q818yescomplemented
105#2551—431nomaximal, Sylow
106C2×C43C2×C4⋊Q812yes—
107C2×C43#54411yescharacteristic
108C2×C43D4211yescharacteristic
109C2×C43D4×Q812yes—
110C2×C43Q8211yescharacteristic
111C2×C4⋊Q8—432no—
112C2×C4⋊Q8—432no—
113#395—431no—
114#395—432no—
115#395D4311yescharacteristic
116#389—432no—
117#389—432no—
118#384—431no—
119C4×C4⋊C4—432no—
120C43#255111yescharacteristic, complemented, Sylow
121C22×Q8—431no—
122C22×Q8—432no—
123C22×Q8C2×D4311yescharacteristic
124C4⋊Q8—868no—
125C4⋊Q8—868no—
126C2×C4⋊C4—432no—
127C2×C4⋊C4—432no—
128C2×C4⋊C4—432no—
129C2×C4⋊C4—432no—
130C2×C4⋊C4—432no—
131C2×C4⋊C4—432no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4C2×D4312yes—
135C2×C4⋊C4C2×D4311yescharacteristic
136C2×C42—431no—
137C2×C42—432no—
138C2×C42—432no—
139#95—432no—
140#95—431no—
141#95—432no—
142#95C2×D4312yes—
143#95C2×D4311yescharacteristic
144C2×Q8—24no—
145C2×Q8—41no—
146C2×Q8—864no—
147C2×Q8—864no—
148C2×Q8—864no—
149C2×Q8—1722no—
150C2×Q8—1721no—
151C22×C4—432no—
152C22×C4—432no—
153C22×C4—432no—
154C22×C4—432no—
155C22×C4C22×D4311yescharacteristic
156C22×C4C22×D4311yescharacteristic
157C22×C4C22×D4312yes—
158C22×C4C22×D4311yescharacteristic
159C22×C4C22×D4312yes—
160C4⋊C4—24no—
161C4⋊C4—41no—
162C4⋊C4—438no—
163C4⋊C4—438no—
164C4⋊C4—864no—
165C4⋊C4—864no—
166C4⋊C4—864no—
167C4⋊C4—864no—
168C4⋊C4—864no—
169C4⋊C4—1721no—
170C42—434no—
171C42—864no—
172C42—864no—
173C23C23×D4311yescharacteristic
174Q8—44no—
175Q8—1728no—
176Q8—1724no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—434no—
188C2×C4—434no—
189C2×C4—434no—
190C2×C4—434no—
191C2×C4—434no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—862no—
199C2×C4D4×D4314yes—
200C2×C4Q8×D4312yes—
201C2×C4Q8×D4314yes—
202C22C2×D4×D4312yes—
203C22C2×Q8×D4312yes—
204C22C2×Q8×D4311yescharacteristic
205C22#1306337011yescharacteristic
206C22#1306337211yescharacteristic
207C4—24no—
208C4—22no—
209C4—24no—
210C4—41no—
211C4—41no—
212C4—438no—
213C4—864no—
214C4—864no—
215C4—1722no—
216C2C4⋊Q8×D4312yes—
217C2#1458352811yescharacteristic
218C2#1458353111yescharacteristic
219C2#1458356212yes—
220C2#1458362911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2551
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

NH ≅ G/Ntype
58. Dic43⋊C4Q8semidirect
61. C4×Dic43Q8semidirect
104. Dic43C4⋊Q8semidirect
120. C43#2551semidirect