Finite Group Databasebeta

← #19140542

Subgroups — #19140542

Order 5504.

416 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063324C211yesmaximal, characteristic
2C2×#13063315C211yesmaximal, characteristic
3#14582841C212yesmaximal
4#14582840C212yesmaximal
5#14582839C211yesmaximal, characteristic
6#14582838C211yesmaximal, characteristic
7#14582837C211yesmaximal, characteristic
8#14582803C212yesmaximal
9#14582803C212yesmaximal
10#14582744C211yesmaximal, characteristic
11C43×#400C211yesmaximal, characteristic
12C22×Dic86C2212yes—
13#13063324—24no—
14#13063315—24no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2211yescharacteristic
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2212yes—
22C2×C4×Dic43C2212yes—
23C2×C4×Dic43C2211yescharacteristic
24C43⋊#95C2212yes—
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2212yes—
30C43⋊#95C2211yescharacteristic
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C22×C4×C43C2312yes—
38C22×C4×C43C2311yescharacteristic
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×Dic43C2312yes—
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×Dic86—24no—
49C2×Dic86—28no—
50C4⋊C4×C43—22no—
51C4⋊C4×C43—22no—
52C4⋊Dic43—22no—
53C4⋊Dic43—22no—
54Dic43⋊C4—22no—
55Dic43⋊C4—22no—
56Dic43⋊C4—22no—
57Dic43⋊C4—22no—
58Dic43⋊C4—24no—
59C4×Dic43—24no—
60C4×Dic43D414yes—
61C23×C43C2411yescharacteristic
62C2×C4×C43—22no—
63C2×C4×C43—21no—
64C2×C4×C43—21no—
65C2×C4×C43—22no—
66C2×C4×C43—22no—
67C2×C4×C43—24no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—22no—
71C2×C4×C43—22no—
72C2×C4×C43—21no—
73C2×C4×C43C2×D412yes—
74C2×Dic43—21no—
75C2×Dic43—21no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—22no—
79C2×Dic43—22no—
80C2×Dic43—24no—
81C2×Dic43—22no—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43—21no—
85C2×Dic43—22no—
86C2×Dic43C2×D412yes—
87C2×Dic43C2×D412yes—
88C2×Dic43#4114yes—
89Dic86—48no—
90C22×C43C22×D411yescharacteristic
91C22×C43C2×#4112yes—
92C22×C432−1+412yes—
93C22×C432−1+411yescharacteristic
94C22×C432−1+411yescharacteristic
95C4×C43—22no—
96C4×C43—42no—
97C4×C43—41no—
98C4×C43—41no—
99C4×C43—42no—
100Dic43—22no—
101Dic43—42no—
102Dic43—41no—
103Dic43—41no—
104Dic43—42no—
105Dic43#12414yes—
106#2642—431nomaximal, Sylow
107C2×C43C2×#12411yescharacteristic
108C2×C43#53611yescharacteristic
109C2×C43#53611yescharacteristic
110C2×C43#54112yes—
111C2×C43#54112yes—
112C2×C4⋊Q8—431no—
113C2×#125—431no—
114#400—431no—
115#400—431no—
116#400—431no—
117#400—432no—
118#400—432no—
119#400D4311yescharacteristic
120#391—432no—
121#391—432no—
122#376—431no—
123C43#264211yescharacteristic, complemented, Sylow
124C22×Q8—432no—
125C4⋊Q8—864no—
126#125—864no—
127C2×C4⋊C4—431no—
128C2×C4⋊C4—431no—
129C2×C4⋊C4—431no—
130C2×C4⋊C4—431no—
131C2×C4⋊C4—431no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—431no—
134C2×C4⋊C4C2×D4311yescharacteristic
135C2×C4⋊C4C2×D4311yescharacteristic
136C2×C42—431no—
137C2×C42—432no—
138#95—432no—
139#95—431no—
140#95—432no—
141#95—432no—
142#95—432no—
143#95—432no—
144#95—432no—
145#95—432no—
146#95C2×D4311yescharacteristic
147#95C2×D4312yes—
148#95C2×D4312yes—
149C2×Q8—864no—
150C2×Q8—868no—
151C22×C4—431no—
152C22×C4—431no—
153C22×C4—432no—
154C22×C4—431no—
155C22×C4—431no—
156C22×C4—432no—
157C22×C4C22×D4312yes—
158C22×C4C22×D4311yescharacteristic
159C22×C4C22×D4311yescharacteristic
160C22×C4C22×D4312yes—
161C22×C4C22×D4311yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—862no—
165C4⋊C4—862no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—864no—
169C4⋊C4—862no—
170C4⋊C4—862no—
171C42—434no—
172C42—864no—
173C23C23×D4311yescharacteristic
174Q8—1728no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—22no—
182C2×C4—21no—
183C2×C4—22no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—432no—
187C2×C4—434no—
188C2×C4—432no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—864no—
196C2×C4—862no—
197C2×C4—861no—
198C2×C4—862no—
199C2×C4—861no—
200C2×C4—862no—
201C2×C4D4×D4312yes—
202C22C2×D4×D4311yescharacteristic
203C22#41×D4312yes—
204C22#1306337212yes—
205C22#1306337211yescharacteristic
206C22#1306337311yescharacteristic
207C4—22no—
208C4—42no—
209C4—41no—
210C4—41no—
211C4—42no—
212C4—434no—
213C4—862no—
214C4—1722no—
215C4—1721no—
216C4—1721no—
217C4—1722no—
218C2#124×D4311yescharacteristic
219C2#1458347111yescharacteristic
220C2#1458347211yescharacteristic
221C2#1458350612yes—
222C2#1458350812yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2642
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
123. C43#2642semidirect