Finite Group Databasebeta

← #19140409

Subgroups — #19140409

Order 5504.

508 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 508 conjugacy classes of subgroups — too many to draw. Only its 143 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×#13063305C211yesmaximal, characteristic
2C2×C4⋊C4×D43C211yesmaximal, characteristic
3#14582837C211yesmaximal, characteristic, complemented
4#14582833C212yesmaximal, complemented
5#14582831C212yesmaximal, complemented
6#14582820C211yesmaximal, characteristic, complemented
7#14582819C211yesmaximal, characteristic, complemented
8#14582773C212yesmaximal
9#14582761C212yesmaximal
10#14582758C211yesmaximal, characteristic
11C43×#400C211yesmaximal, characteristic, complemented
12C22×Dic86C2211yescharacteristic
13C22×C4×D43C2211yescharacteristic
14C22×C4×D43C2211yescharacteristic
15C22×C4×D43C2211yescharacteristic
16#13063305—24no—
17C2×C4⋊Dic43C2211yescharacteristic
18C2×C4⋊Dic43C2212yes—
19C2×C4⋊Dic43C2212yes—
20C2×Dic43⋊C4C2211yescharacteristic
21C2×Dic43⋊C4C2211yescharacteristic
22C2×Dic43⋊C4C2212yes—
23C2×Dic43⋊C4C2212yes—
24C4⋊C4×D43—24no—
25C2×(C2×D43)⋊C4C2212yes—
26C2×(C2×D43)⋊C4C2212yes—
27C43⋊#95C2212yes—
28C43⋊#95C2211yescharacteristic
29C43⋊#95C2212yes—
30C43⋊#95C2212yes—
31C43⋊#95C2212yes—
32C2×C4⋊C4×C43C2211yescharacteristic
33C2×C4⋊C4×C43C2211yescharacteristic
34#95×C43C2211yescharacteristic
35#95×C43C2212yes—
36#95×C43C2212yes—
37C23×D43C2311yescharacteristic
38C22×C4×C43C2312yes—
39C22×C4×C43C2312yes—
40C22×C4×C43C2311yescharacteristic
41C22×C4×C43C2311yescharacteristic
42C22×C4×C43C2311yescharacteristic
43C22×Dic43C2312yes—
44C22×Dic43C2312yes—
45C22×Dic43C2311yescharacteristic
46C22×Dic43C2311yescharacteristic
47C22×Dic43C2311yescharacteristic
48C2×C4×D43—22no—
49C2×C4×D43—22no—
50C2×C4×D43—22no—
51C2×C4×D43—42no—
52C2×C4×D43—42no—
53C2×C4×D43D414yes—
54C2×C4×D43Q814yescomplemented
55C2×Dic86—22no—
56C2×Dic86—42no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—22no—
59(C2×D43)⋊C4—24no—
60(C2×D43)⋊C4—24no—
61C4⋊Dic43—22no—
62C4⋊Dic43—24no—
63C4⋊Dic43—42no—
64Dic43⋊C4—22no—
65Dic43⋊C4—22no—
66Dic43⋊C4—42no—
67Dic43⋊C4—42no—
68C23×C43C2411yescharacteristic
69C22×D43—22no—
70C22×D43—22no—
71C22×D43C2×D412yes—
72C22×D43C2×Q812yes—
73C22×D43#4112yes—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—22no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—24no—
83C2×C4×C43—22no—
84C2×C4×C43C2×D412yes—
85C2×C4×C43C2×Q812yes—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—21no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43C2×D412yes—
98C2×Dic43C2×Q812yes—
99C4×D43—28no—
100C4×D43—44no—
101C4×D43—44no—
102Dic86—44no—
103C22×C43C22×D411yescharacteristic
104C22×C43C22×Q811yescharacteristic
105C22×C43C2×#4111yescharacteristic
106C22×C43H(5,𝔽2)12yes—
107C22×C432−1+412yes—
108C2×D43—22no—
109C2×D43—22no—
110C2×D43—24no—
111C2×D43—24no—
112C2×D43C22⋊Q814yes—
113C4×C43—22no—
114C4×C43—22no—
115C4×C43—41no—
116C4×C43—42no—
117C4×C43—42no—
118Dic43—22no—
119Dic43—22no—
120Dic43—42no—
121Dic43—41no—
122Dic43—42no—
123#2627—431nomaximal, Sylow
124C2×C43C2×C22⋊Q811yescharacteristic
125C2×C43#53411yescharacteristic
126C2×C43#53611yescharacteristic
127C2×C43#53912yes—
128C2×C43#54412yes—
129D43—24no—
130C2×C22⋊Q8—431no—
131C22×C4⋊C4—431no—
132#400—431no—
133#400D4311yescharacteristic, complemented
134#398—432no—
135#398—432no—
136#395—431no—
137#395—431no—
138#385—432no—
139#381—432no—
140#380—431no—
141C43#262711yescharacteristic, complemented, Sylow
142C22×Q8—431no—
143C23×C4—431no—
144C23×C4—431no—
145C23×C4—431no—
146C22⋊Q8—864no—
147C2×C4⋊C4—431no—
148C2×C4⋊C4—431no—
149C2×C4⋊C4—431no—
150C2×C4⋊C4—432no—
151C2×C4⋊C4—432no—
152C2×C4⋊C4—432no—
153C2×C4⋊C4—432no—
154C2×C4⋊C4—864no—
155C2×C4⋊C4C2×D4311yescharacteristic
156C2×C4⋊C4C2×D4311yescharacteristic
157C2×C22⋊C4—432no—
158C2×C22⋊C4—432no—
159#95—431no—
160#95—432no—
161#95—432no—
162#95—432no—
163#95—432no—
164#95C2×D4311yescharacteristic
165#95C2×D4312yes—
166#95C2×D4312yes—
167C24—431no—
168C2×Q8—862no—
169C2×Q8—1722no—
170C22×C4—431no—
171C22×C4—431no—
172C22×C4—434no—
173C22×C4—434no—
174C22×C4—432no—
175C22×C4—432no—
176C22×C4—431no—
177C22×C4—862no—
178C22×C4—862no—
179C22×C4—862no—
180C22×C4—1722no—
181C22×C4—1722no—
182C22×C4C22×D4312yes—
183C22×C4C22×D4312yes—
184C22×C4C22×D4311yescharacteristic
185C22×C4C22×D4311yescharacteristic
186C22×C4C22×D4311yescharacteristic
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—862no—
190C4⋊C4—862no—
191C4⋊C4—864no—
192C4⋊C4—862no—
193C4⋊C4—1722no—
194C4⋊C4—1722no—
195C4⋊C4—1722no—
196C22⋊C4—864no—
197C22⋊C4—864no—
198C23—432no—
199C23—432no—
200C23—432no—
201C23—862no—
202C23—862no—
203C23C23×D4311yescharacteristic
204Q8—1724no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—24no—
214C2×C4—22no—
215C2×C4—432no—
216C2×C4—432no—
217C2×C4—868no—
218C2×C4—861no—
219C2×C4—861no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—861no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—862no—
227C2×C4—862no—
228C2×C4—862no—
229C2×C4—1724no—
230C2×C4—1724no—
231C2×C4D4×D4312yes—
232C2×C4Q8×D4312yes—
233C22—434no—
234C22—862no—
235C22—862no—
236C22—864no—
237C22—864no—
238C22C2×D4×D4311yescharacteristic
239C22C2×Q8×D4311yescharacteristic
240C22#41×D4311yescharacteristic
241C22#1306337112yes—
242C22#1306337212yes—
243C4—22no—
244C4—22no—
245C4—41no—
246C4—42no—
247C4—42no—
248C4—862no—
249C4—862no—
250C4—1721no—
251C4—1722no—
252C4—1722no—
253C2—864no—
254C2C22⋊Q8×D4311yescharacteristic
255C2#1458346011yescharacteristic
256C2#1458346911yescharacteristic
257C2#1458349012yes—
258C2#1458352912yes—
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#400C2
hypercenter#400D43
hypocenterC43#2627
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
3. #14582837C2semidirect
4. #14582833C2semidirect
5. #14582831C2semidirect
6. #14582820C2semidirect
7. #14582819C2semidirect
11. C43×#400C2semidirect
54. C2×C4×D43Q8semidirect
133. #400D43semidirect
141. C43#2627semidirect