Finite Group Databasebeta

← #19137885

Subgroups — #19137885

Order 5504.

504 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 167 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×Q8×Dic43C211yesmaximal, characteristic
2C2×#13063290C211yesmaximal, characteristic
3#14582832C212yesmaximal
4#14582831C211yesmaximal, characteristic
5#14582829C211yesmaximal, characteristic
6#14582820C212yesmaximal
7#14582818C211yesmaximal, characteristic
8C4⋊C4×Dic43C212yesmaximal
9#14582750C212yesmaximal
10#14582744C211yesmaximal, characteristic
11C43×#395C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13Q8×Dic43—24no—
14#13063290—24no—
15C2×C4⋊Dic43C2212yes—
16C2×C4⋊Dic43C2212yes—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×Dic43⋊C4C2211yescharacteristic
19C2×Dic43⋊C4C2212yes—
20C2×Dic43⋊C4C2212yes—
21C2×Dic43⋊C4C2211yescharacteristic
22C2×C4×Dic43C2211yescharacteristic
23C2×C4×Dic43C2211yescharacteristic
24C2×C4×Dic43C2212yes—
25C2×C4×Dic43C2211yescharacteristic
26C2×C4×Dic43C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C22×Q8×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34C2×C4⋊C4×C43C2212yes—
35#95×C43C2212yes—
36#95×C43C2211yescharacteristic
37C2×Q8×C43—22no—
38C2×Q8×C43—24no—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2312yes—
42C22×C4×C43C2311yescharacteristic
43C22×C4×C43C2312yes—
44C22×Dic43C2311yescharacteristic
45C22×Dic43C2312yes—
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2312yes—
48C22×Dic43C2311yescharacteristic
49C22×Dic43C2311yescharacteristic
50C2×Dic86—22no—
51C2×Dic86—22no—
52C2×Dic86—22no—
53C4⋊C4×C43—22no—
54C4⋊C4×C43—24no—
55C4⋊Dic43—22no—
56C4⋊Dic43—24no—
57C4⋊Dic43—24no—
58Dic43⋊C4—22no—
59Dic43⋊C4—24no—
60Dic43⋊C4—24no—
61Dic43⋊C4—22no—
62C4×Dic43—22no—
63C4×Dic43—22no—
64C4×Dic43—24no—
65C4×Dic43D414yes—
66C4×Dic43Q818yescomplemented
67C23×C43C2411yescharacteristic
68Q8×C43—28no—
69C2×C4×C43—22no—
70C2×C4×C43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—22no—
73C2×C4×C43—21no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—21no—
77C2×C4×C43—22no—
78C2×C4×C43C2×D412yes—
79C2×C4×C43C2×Q814yes—
80C2×C4×C43#4114yes—
81C2×C4×C43#4112yes—
82C2×Dic43—21no—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—21no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43C2×D412yes—
94C2×Dic43C2×D412yes—
95C2×Dic43C2×Q814yes—
96C2×Dic43C2×Q814yes—
97C2×Dic43#4112yes—
98Dic86—28no—
99C22×C43C22×D411yescharacteristic
100C22×C43C22×Q812yes—
101C22×C43C2×#4111yescharacteristic
102C22×C43C2×#4112yes—
103C22×C43C2×#4111yescharacteristic
104C4×C43—22no—
105C4×C43—22no—
106C4×C43—24no—
107C4×C43—24no—
108C4×C43—41no—
109Dic43—22no—
110Dic43—22no—
111Dic43—24no—
112Dic43—41no—
113Dic43—42no—
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#398—431no—
126#395—431no—
127#395—432no—
128#395D4311yescharacteristic
129C4×C4⋊C4—432no—
130C4×C4⋊C4—432no—
131#376—431no—
132C43#239911yescharacteristic, complemented, Sylow
133C22×Q8—431no—
134C22×Q8C2×D4311yescharacteristic
135C4×Q8—864no—
136C4×Q8—864no—
137C2×C4⋊C4—431no—
138C2×C4⋊C4—431no—
139C2×C4⋊C4—432no—
140C2×C4⋊C4—431no—
141C2×C4⋊C4—432no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—432no—
144C2×C4⋊C4C2×D4311yescharacteristic
145C2×C4⋊C4C2×D4312yes—
146C2×C42—431no—
147C2×C42—432no—
148C2×C42—431no—
149C2×C42—432no—
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—22no—
159C2×Q8—24no—
160C2×Q8—862no—
161C2×Q8—862no—
162C2×Q8—862no—
163C22×C4—431no—
164C22×C4—432no—
165C22×C4—431no—
166C22×C4—431no—
167C22×C4—432no—
168C22×C4—431no—
169C22×C4C22×D4311yescharacteristic
170C22×C4C22×D4311yescharacteristic
171C22×C4C22×D4312yes—
172C22×C4C22×D4312yes—
173C22×C4C22×D4311yescharacteristic
174C4⋊C4—22no—
175C4⋊C4—24no—
176C4⋊C4—862no—
177C4⋊C4—864no—
178C4⋊C4—864no—
179C4⋊C4—862no—
180C4⋊C4—862no—
181C4⋊C4—864no—
182C4⋊C4—864no—
183C42—434no—
184C42—438no—
185C42—862no—
186C42—864no—
187C42—862no—
188C23C23×D4311yescharacteristic
189Q8—28no—
190Q8—868no—
191C2×C4—21no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—22no—
198C2×C4—21no—
199C2×C4—22no—
200C2×C4—432no—
201C2×C4—434no—
202C2×C4—432no—
203C2×C4—434no—
204C2×C4—432no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—862no—
208C2×C4—862no—
209C2×C4—861no—
210C2×C4—861no—
211C2×C4—861no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4D4×D4312yes—
217C2×C4#1062190014yes—
218C2×C4Q8×D4314yes—
219C2×C4#1062190212yes—
220C22C2×D4×D4311yescharacteristic
221C22C2×Q8×D4312yes—
222C22#41×D4311yescharacteristic
223C22C2×#1062190012yes—
224C22C2×#1062190211yescharacteristic
225C4—22no—
226C4—24no—
227C4—22no—
228C4—24no—
229C4—41no—
230C4—434no—
231C4—862no—
232C4—862no—
233C4—864no—
234C4—1721no—
235C4—1722no—
236C2#1458340511yescharacteristic
237C2#1458341211yescharacteristic
238C2C4⋊Q8×D4311yescharacteristic
239C2#1458345112yes—
240C2#1458345412yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#395C2
hypercenter#395D43
hypocenterC43#2399
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #395

Complements

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

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