Finite Group Databasebeta

← #19137178

Subgroups — #19137178

Order 5504.

784 conjugacy classes of subgroups; only the 229 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 229 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
1C22×Q8×D43C211yesmaximal, characteristic
2C2×#13063283C211yesmaximal, characteristic
3C2×#13063282C211yesmaximal, characteristic
4#14582806C211yesmaximal, characteristic, complemented
5#14582805C211yesmaximal, characteristic, complemented
6#14582804C211yesmaximal, characteristic, complemented
7#14582803C214yesmaximal, complemented
8#14582761C214yesmaximal
9C43×#391C211yesmaximal, characteristic, complemented
10C22×Dic86C2212yes—
11C22×Dic86C2211yescharacteristic
12C2×Q8×D43—24no—
13C2×Q8×D43—24no—
14C2×Q8×D43C418yescomplemented
15C22×C4×D43C2212yes—
16C22×C4×D43C2211yescharacteristic
17#13063283—24no—
18#13063282—24no—
19C2×C4⋊Dic43C2211yescharacteristic
20C2×Dic43⋊C4C2212yes—
21C2×(C2×D43)⋊C4C2212yes—
22C2×(C2×D43)⋊C4C2212yes—
23C2×C4×Dic43C2212yes—
24C2×C4×Dic43C2211yescharacteristic
25C43⋊#95C2214yes—
26C43⋊#95C2214yes—
27C43⋊#95C2214yes—
28C22×Q8×C43C2211yescharacteristic
29C2×C4⋊C4×C43C2211yescharacteristic
30C2×C42×C43C2211yescharacteristic
31#95×C43C2214yes—
32C23×D43C2311yescharacteristic
33C2×Q8×C43—22no—
34C2×Q8×C43—22no—
35C2×Q8×C43C2×C414yes—
36C22×C4×C43C2312yes—
37C22×C4×C43C2312yes—
38C22×C4×C43C2312yes—
39C22×C4×C43C2311yescharacteristic
40C22×Dic43C2312yes—
41C22×Dic43C2312yes—
42C22×Dic43C2312yes—
43C22×Dic43C2311yescharacteristic
44Q8×D43—232no—
45C2×C4×D43—24no—
46C2×C4×D43—24no—
47C2×C4×D43C2×C418yes—
48C2×C4×D43C2×C414yes—
49C2×C4×D43D414yes—
50C2×C4×D43D414yes—
51C2×Dic86—22no—
52C2×Dic86—22no—
53C2×Dic86—24no—
54C2×Dic86—24no—
55C2×Dic86C2×C414yes—
56C2×Dic86C2×C418yes—
57C4⋊C4×C43—22no—
58C42×C43—22no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61C4⋊Dic43—22no—
62Dic43⋊C4—24no—
63C4×Dic43—22no—
64C4×Dic43—24no—
65C23×C43C2411yescharacteristic
66C22×D43—22no—
67C22×D43—22no—
68C22×D43C22×C412yes—
69C22×D43C2×D412yes—
70C22×D43C2×D412yes—
71Q8×C43—28no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—24no—
78C2×C4×C43—22no—
79C2×C4×C43C22×C414yes—
80C2×C4×C43C22×C412yes—
81C2×C4×C43C2×D412yes—
82C2×C4×C43C2×D412yes—
83C2×Dic43—22no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—24no—
90C2×Dic43C22×C414yes—
91C2×Dic43C22×C412yes—
92C2×Dic43C2×D412yes—
93C2×Dic43C2×D412yes—
94C4×D43—216no—
95C4×D43C22⋊C4116yes—
96Dic86—28no—
97Dic86—216no—
98C22×C43C23×C411yescharacteristic
99C22×C43C22×D411yescharacteristic
100C22×C43C22×D411yescharacteristic
101C22×C432−1+412yes—
102C22×C432−1+412yes—
103C2×D43—24no—
104C2×D43—22no—
105C2×D43—24no—
106C2×D43—22no—
107C2×D43C2×C22⋊C414yes—
108C4×C43—24no—
109C4×C43—42no—
110C4×C43—42no—
111C4×C43C2×C22⋊C414yes—
112Dic43—24no—
113Dic43—42no—
114Dic43—42no—
115Dic43C2×C22⋊C414yes—
116#2310—431nomaximal, Sylow
117C2×C43C22×C22⋊C411yescharacteristic
118C2×C43#51912yes—
119C2×C43#53611yescharacteristic
120C2×C43#53612yes—
121C2×C43#53611yescharacteristic
122D43—24no—
123C23×Q8—431no—
124C2×#117—431no—
125C2×#117—431no—
126#391—431no—
127#391—431no—
128#391—431no—
129#391—434no—
130#391D4311yescharacteristic, complemented
131#381—434no—
132C43#231011yescharacteristic, complemented, Sylow
133C22×Q8—438no—
134C22×Q8—432no—
135C22×Q8—431no—
136C22×Q8—864no—
137C22×Q8—864no—
138C22×Q8C2×D4311yescharacteristic
139C23×C4—431no—
140C23×C4—432no—
141#117—864no—
142#117—864no—
143C2×C4⋊C4—432no—
144C2×C4⋊C4—431no—
145C2×C4⋊C4C2×D4311yescharacteristic
146C2×C22⋊C4—432no—
147C2×C22⋊C4—432no—
148C2×C42—432no—
149C2×C42—431no—
150C2×C42C2×D4311yescharacteristic
151#95—434no—
152#95—434no—
153#95—434no—
154#95C2×D4314yes—
155C24—431no—
156C2×Q8—22no—
157C2×Q8—22no—
158C2×Q8—438no—
159C2×Q8—434no—
160C2×Q8—864no—
161C2×Q8—864no—
162C2×Q8—8632no—
163C2×Q8—862no—
164C2×Q8—862no—
165C2×Q8C4×D4314yes—
166C22×C4—431no—
167C22×C4—434no—
168C22×C4—434no—
169C22×C4—434no—
170C22×C4—432no—
171C22×C4—438no—
172C22×C4—432no—
173C22×C4—432no—
174C22×C4—864no—
175C22×C4—864no—
176C22×C4C22×D4312yes—
177C22×C4C22×D4312yes—
178C22×C4C22×D4312yes—
179C22×C4C22×D4311yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—864no—
182C4⋊C4—862no—
183C22⋊C4—864no—
184C22⋊C4—864no—
185C42—22no—
186C42—864no—
187C42—862no—
188C23—432no—
189C23—432no—
190C23—432no—
191C23—862no—
192C23—862no—
193C23C23×D4311yescharacteristic
194Q8—28no—
195Q8—8616no—
196Q8—868no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—24no—
202C2×C4—22no—
203C2×C4—22no—
204C2×C4—432no—
205C2×C4—432no—
206C2×C4—432no—
207C2×C4—4316no—
208C2×C4—434no—
209C2×C4—8616no—
210C2×C4—862no—
211C2×C4—862no—
212C2×C4—862no—
213C2×C4—862no—
214C2×C4—862no—
215C2×C4—862no—
216C2×C4—864no—
217C2×C4C2×C4×D4314yes—
218C2×C4C2×C4×D4312yes—
219C2×C4D4×D4312yes—
220C2×C4D4×D4312yes—
221C22—434no—
222C22—864no—
223C22—862no—
224C22—864no—
225C22—862no—
226C22C22×C4×D4311yescharacteristic
227C22C2×D4×D4311yescharacteristic
228C22C2×D4×D4311yescharacteristic
229C22#1306337212yes—
230C22#1306337312yes—
231C4—24no—
232C4—42no—
233C4—42no—
234C4—434no—
235C4—864no—
236C4—1722no—
237C4—1722no—
238C4C22⋊C4×D4314yes—
239C2—864no—
240C2C2×C22⋊C4×D4311yescharacteristic
241C2#1458337512yes—
242C2#1458346911yescharacteristic
243C2#1458347212yes—
244C2#1458347411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutatorC22×C43C23×C4
FittingC43×#391C2
socleC23×C43C24
hypercenter#391D43
hypocenterC43#2310
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
4. #14582806C2semidirect
5. #14582805C2semidirect
6. #14582804C2semidirect
7. #14582803C2semidirect
9. C43×#391C2semidirect
14. C2×Q8×D43C4semidirect
130. #391D43semidirect
132. C43#2310semidirect