Finite Group Databasebeta

← #19137887

Subgroups — #19137887

Order 5504.

504 conjugacy classes of subgroups; only the 163 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 163 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×#13063290C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic
3#14582833C212yesmaximal
4#14582830C211yesmaximal, characteristic
5#14582820C211yesmaximal, characteristic
6#14582819C211yesmaximal, characteristic
7#14582819C212yesmaximal
8C4⋊C4×Dic43C212yesmaximal
9#14582750C212yesmaximal
10#14582744C211yesmaximal, characteristic
11C43×#398C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13C22×Dic86C2211yescharacteristic
14#13063290—24no—
15#13063290—24no—
16C2×C4⋊Dic43C2212yes—
17C2×Dic43⋊C4C2212yes—
18C2×Dic43⋊C4C2212yes—
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×C4×Dic43C2211yescharacteristic
23C2×C4×Dic43C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2212yes—
29C43⋊#95C2211yescharacteristic
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2212yes—
34C2×C4⋊C4×C43C2211yescharacteristic
35#95×C43C2211yescharacteristic
36#95×C43C2212yes—
37C22×C4×C43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×Dic43C2311yescharacteristic
43C22×Dic43C2311yescharacteristic
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2312yes—
47C22×Dic43C2311yescharacteristic
48C2×Dic86—22no—
49C2×Dic86—22no—
50C2×Dic86—22no—
51C2×Dic86—22no—
52C2×Dic86—24no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—22no—
55C4⋊C4×C43—24no—
56C4⋊Dic43—24no—
57Dic43⋊C4—22no—
58Dic43⋊C4—24no—
59Dic43⋊C4—22no—
60Dic43⋊C4—24no—
61Dic43⋊C4—24no—
62C4×Dic43—22no—
63C4×Dic43—24no—
64C4×Dic43—22no—
65C4×Dic43D414yes—
66C4×Dic43Q818yescomplemented
67C23×C43C2411yescharacteristic
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×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43C2×D412yes—
79C2×C4×C43C2×Q814yes—
80C2×C4×C43#4112yes—
81C2×Dic43—21no—
82C2×Dic43—22no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—21no—
86C2×Dic43—22no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43C2×D412yes—
92C2×Dic43C2×D412yes—
93C2×Dic43C2×Q814yes—
94C2×Dic43C2×Q814yes—
95C2×Dic43#4112yes—
96C2×Dic43#4114yes—
97Dic86—28no—
98Dic86—28no—
99C22×C43C22×D411yescharacteristic
100C22×C43C22×Q812yes—
101C22×C43C2×#4112yes—
102C22×C43C2×#4111yescharacteristic
103C22×C43C2×#4111yescharacteristic
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—24no—
107C4×C43—41no—
108C4×C43—42no—
109Dic43—22no—
110Dic43—24no—
111Dic43—22no—
112Dic43—24no—
113Dic43—41no—
114Dic43C4⋊Q814yes—
115#2399—431nomaximal, Sylow
116C2×C43#52511yescharacteristic
117C2×C43#52511yescharacteristic
118C2×C43C2×C4⋊Q811yescharacteristic
119C2×C43#53312yes—
120C2×C43#53312yes—
121C2×C4×Q8—431no—
122C2×C4×Q8—431no—
123#398—431no—
124#398—432no—
125#398D4311yescharacteristic
126#395—432no—
127#395—431no—
128#395—431no—
129C4×C4⋊C4—432no—
130C4×C4⋊C4—432no—
131#376—431no—
132C43#239911yescharacteristic, complemented, Sylow
133C22×Q8—431no—
134C22×Q8—431no—
135C4×Q8—864no—
136C4×Q8—864no—
137C2×C4⋊C4—432no—
138C2×C4⋊C4—431no—
139C2×C4⋊C4—431no—
140C2×C4⋊C4—432no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4C2×D4311yescharacteristic
144C2×C4⋊C4C2×D4311yescharacteristic
145C2×C4⋊C4C2×D4312yes—
146C2×C42—431no—
147C2×C42—432no—
148C2×C42—432no—
149C2×C42—431no—
150C2×C42—431no—
151#95—431no—
152#95—432no—
153#95—432no—
154#95—432no—
155#95—432no—
156#95C2×D4311yescharacteristic
157#95C2×D4312yes—
158C2×Q8—862no—
159C2×Q8—864no—
160C2×Q8—862no—
161C2×Q8—862no—
162C2×Q8—862no—
163C22×C4—431no—
164C22×C4—432no—
165C22×C4—431no—
166C22×C4—432no—
167C22×C4—431no—
168C22×C4—431no—
169C22×C4C22×D4312yes—
170C22×C4C22×D4311yescharacteristic
171C22×C4C22×D4311yescharacteristic
172C22×C4C22×D4311yescharacteristic
173C22×C4C22×D4312yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—24no—
177C4⋊C4—864no—
178C4⋊C4—862no—
179C4⋊C4—864no—
180C4⋊C4—864no—
181C4⋊C4—864no—
182C4⋊C4—862no—
183C42—434no—
184C42—438no—
185C42—862no—
186C42—862no—
187C42—864no—
188C23C23×D4311yescharacteristic
189Q8—868no—
190Q8—868no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—432no—
202C2×C4—434no—
203C2×C4—432no—
204C2×C4—434no—
205C2×C4—434no—
206C2×C4—432no—
207C2×C4—862no—
208C2×C4—861no—
209C2×C4—862no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—861no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—861no—
216C2×C4—862no—
217C2×C4D4×D4312yes—
218C2×C4#1062190012yes—
219C2×C4Q8×D4314yes—
220C22C2×D4×D4311yescharacteristic
221C22C2×Q8×D4312yes—
222C22#41×D4312yes—
223C22#41×D4311yescharacteristic
224C22C2×#1062190011yescharacteristic
225C4—22no—
226C4—22no—
227C4—24no—
228C4—41no—
229C4—42no—
230C4—434no—
231C4—864no—
232C4—862no—
233C4—862no—
234C4—864no—
235C4—1721no—
236C2#1458340711yescharacteristic
237C2#1458340911yescharacteristic
238C2C4⋊Q8×D4311yescharacteristic
239C2#1458345112yes—
240C2#1458345512yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#398C2
hypercenter#398D43
hypocenterC43#2399
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #398

Complements

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

NH ≅ G/Ntype
66. C4×Dic43Q8semidirect
132. C43#2399semidirect