Finite Group Databasebeta

← #19141103

Subgroups — #19141103

Order 5504.

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

normal subgroups only

This group has 568 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×#13063306C212yesmaximal, complemented
2#14582840C212yesmaximal, complemented
3#14582824C211yesmaximal, characteristic, complemented
4#14582822C212yesmaximal, complemented
5#14582779C212yesmaximal, complemented
6#14582779C212yesmaximal, complemented
7#14582771C211yesmaximal, characteristic, complemented
8#14582757C212yesmaximal, complemented
9C43×#392C211yesmaximal, characteristic
10C23×Dic43C2212yes—
11C23×Dic43C2211yescharacteristic
12#13063306—28no—
13C2×C4⋊Dic43C2211yescharacteristic
14C2×Dic43⋊C4C2212yes—
15C2×Dic43⋊C4C2212yes—
16C2×Dic43⋊C4C2212yes—
17C2×C22⋊Dic43C2212yes—
18C2×C22⋊Dic43C2212yes—
19C2×C22⋊Dic43C2212yes—
20C2×C22⋊Dic43C2212yes—
21C2×C22⋊Dic43C2211yescharacteristic
22C43⋊#95C2212yes—
23C43⋊#95C2212yes—
24C43⋊#95C2211yescharacteristic
25C43⋊#95C2212yes—
26C43⋊#95C2212yes—
27C22×D4×C43C2212yes—
28C22×D4×C43C2211yescharacteristic
29C2×C22⋊C4×C43C2212yes—
30C2×C22⋊C4×C43C2211yescharacteristic
31#95×C43C2211yescharacteristic
32C24×C43C2311yescharacteristic
33C24×C43C2312yes—
34C2×D4×C43—24no—
35C2×D4×C43—24no—
36C2×D4×C43—24no—
37C2×D4×C43—41no—
38C2×D4×C43—42no—
39C22×C4×C43C2311yescharacteristic
40C22×C4×C43C2312yes—
41C22×C4×C43C2311yescharacteristic
42C22×Dic43—24no—
43C22×Dic43—24no—
44C22×Dic43—41no—
45C22×Dic43—42no—
46C22×Dic43—42no—
47C22×Dic43C2312yes—
48C22×Dic43C2312yes—
49C22×Dic43C2312yes—
50C22×Dic43C2312yes—
51C22⋊C4×C43—42no—
52C22⋊C4×C43—41no—
53C22⋊Dic43—24no—
54C22⋊Dic43—24no—
55C22⋊Dic43—42no—
56C22⋊Dic43—42no—
57C22⋊Dic43D414yescomplemented
58C4⋊Dic43—41no—
59Dic43⋊C4—24no—
60Dic43⋊C4—24no—
61Dic43⋊C4—42no—
62C23×C43—22no—
63C23×C43—22no—
64C23×C43—22no—
65C23×C43—22no—
66C23×C43—22no—
67C23×C43—21no—
68C23×C43—22no—
69C23×C43—22no—
70C23×C43—21no—
71C23×C43—22no—
72C23×C43C2×D412yes—
73C23×C43#4114yes—
74C23×C43C2411yescharacteristic
75D4×C43—48no—
76D4×C43—44no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—21no—
84C2×Dic43—22no—
85C2×Dic43—22no—
86C2×Dic43—22no—
87C2×Dic43—22no—
88C2×Dic43—22no—
89C2×Dic43—22no—
90C2×Dic43—22no—
91C2×Dic43—22no—
92C2×Dic43—22no—
93C2×Dic43—22no—
94C2×Dic43—22no—
95C2×Dic43—48no—
96C2×Dic43—44no—
97C2×Dic43C2×D414yes—
98C22×C43—22no—
99C22×C43—24no—
100C22×C43—24no—
101C22×C43—24no—
102C22×C43—24no—
103C22×C43—42no—
104C22×C43—42no—
105C22×C43—42no—
106C22×C43—42no—
107C22×C43—41no—
108C22×C43—42no—
109C22×C43—41no—
110C22×C43C22×D411yescharacteristic
111C22×C43C2×#4112yes—
112C22×C43H(5,𝔽2)11yescharacteristic
113C22×C43H(5,𝔽2)12yes—
114C22×C432−1+411yescharacteristic
115C4×C43—42no—
116C4×C43—41no—
117C4×C43—41no—
118Dic43—24no—
119Dic43—42no—
120Dic43—42no—
121Dic43—42no—
122#2693—431nomaximal, Sylow
123C2×C43—42no—
124C2×C43—44no—
125C2×C43#53711yescharacteristic
126C2×C43#53912yes—
127C2×C43#54612yes—
128C2×C43#55111yescharacteristic
129C2×C43#56011yescharacteristic
130C2×#123—432no—
131#400—432no—
132#397—431no—
133#396—432no—
134#392D4311yescharacteristic
135#386—432no—
136#386—432no—
137#385—431no—
138#380—432no—
139C43#269311yescharacteristic, complemented, Sylow
140C22×D4C2×D4312yes—
141C22×D4C2×D4311yescharacteristic
142C23×C4—432no—
143C23×C4—431no—
144#123—868no—
145C2×C4⋊C4—432no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—431no—
149C2×C22⋊C4—431no—
150C2×C22⋊C4—432no—
151C2×C22⋊C4—432no—
152C2×C22⋊C4—432no—
153C2×C22⋊C4—432no—
154C2×C22⋊C4C2×D4312yes—
155C2×C22⋊C4C2×D4311yescharacteristic
156#95—431no—
157#95—432no—
158#95—432no—
159#95—432no—
160#95—432no—
161#95C2×D4311yescharacteristic
162C24C22×D4311yescharacteristic
163C24C22×D4312yes—
164C2×D4—24no—
165C2×D4—24no—
166C2×D4—24no—
167C2×D4—41no—
168C2×D4—42no—
169C22×C4—432no—
170C22×C4—432no—
171C22×C4—432no—
172C22×C4—432no—
173C22×C4—864no—
174C22×C4—864no—
175C22×C4—1722no—
176C22×C4—1721no—
177C22×C4—1722no—
178C22×C4C22×D4311yescharacteristic
179C22×C4C22×D4312yes—
180C22×C4C22×D4311yescharacteristic
181C4⋊C4—864no—
182C4⋊C4—864no—
183C4⋊C4—1722no—
184C4⋊C4—1721no—
185C22⋊C4—42no—
186C22⋊C4—41no—
187C22⋊C4—434no—
188C22⋊C4—864no—
189C22⋊C4—864no—
190C22⋊C4—1722no—
191C22⋊C4—1722no—
192C23—22no—
193C23—22no—
194C23—22no—
195C23—22no—
196C23—21no—
197C23—22no—
198C23—22no—
199C23—22no—
200C23—21no—
201C23—22no—
202C23D4×D4312yes—
203C23#1062190014yes—
204C23C23×D4311yescharacteristic
205D4—44no—
206D4—48no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—22no—
214C2×C4—434no—
215C2×C4—862no—
216C2×C4—862no—
217C2×C4—862no—
218C2×C4—862no—
219C2×C4—862no—
220C2×C4—862no—
221C2×C4—862no—
222C2×C4—862no—
223C2×C4—862no—
224C2×C4—862no—
225C2×C4—862no—
226C2×C4—1728no—
227C2×C4—1724no—
228C22—24no—
229C22—22no—
230C22—24no—
231C22—24no—
232C22—24no—
233C22—41no—
234C22—41no—
235C22—42no—
236C22—42no—
237C22—42no—
238C22—42no—
239C22—42no—
240C22C2×D4×D4311yescharacteristic
241C22C2×#1062190012yes—
242C22#1306337011yescharacteristic
243C22#1306337012yes—
244C22#1306337211yescharacteristic
245C4—41no—
246C4—41no—
247C4—42no—
248C4—864no—
249C4—1722no—
250C4—1722no—
251C4—1722no—
252C2—44no—
253C2—42no—
254C2#1458347611yescharacteristic
255C2#1458349412yes—
256C2#1458353612yes—
257C2#1458358011yescharacteristic
258C2#1458363611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2693
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063306C2semidirect
2. #14582840C2semidirect
3. #14582824C2semidirect
4. #14582822C2semidirect
5. #14582779C2semidirect
6. #14582779C2semidirect
7. #14582771C2semidirect
8. #14582757C2semidirect
57. C22⋊Dic43D4semidirect
139. C43#2693semidirect