Finite Group Databasebeta

← #19135524

Subgroups — #19135524

Order 5504.

344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 99 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×#13063314C211yesmaximal, characteristic
2C2×Dic43⋊C8C211yesmaximal, characteristic, complemented
3C2×#13063249C211yesmaximal, characteristic, complemented
4C2×#13063247C211yesmaximal, characteristic
5C2×#13063245C211yesmaximal, characteristic
6C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
7C2×#103×C43C211yesmaximal, characteristic, complemented
8C22×D172C2211yescharacteristic
9C22×C43⋊C8C2211yescharacteristic
10#13063314—22no—
11#13063314C414yescomplemented
12C2×C4⋊Dic43C2211yescharacteristic
13C2×(C2×D43)⋊C4—21no—
14C2×(C2×D43)⋊C4—21no—
15C2×C4×Dic43—21no—
16C2×C4×Dic43C2211yescharacteristic
17Dic43⋊C8—22no—
18#13063249—22no—
19#13063247—22no—
20#13063245—22no—
21C43⋊#95—21no—
22C22×Q8×C43C2211yescharacteristic
23C22×C8×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2211yescharacteristic
25#103×C43—22no—
26C23×D43—21no—
27C2×Q8×C43—21no—
28C2×Q8×C43—21no—
29C2×Q8×C43—21no—
30C2×Q8×C43—21no—
31C2×Q8×C43—21no—
32C2×Q8×C43C2×C412yes—
33C22×C4×C43—21no—
34C22×C4×C43—21no—
35C22×C4×C43C2311yescharacteristic
36C22×Dic43—21no—
37C22×Dic43D411yescharacteristic
38C22×Dic43D411yescharacteristic
39C2×D172—21no—
40C2×D172—21no—
41C2×D172—21no—
42C2×D172—21no—
43C2×D172—21no—
44C2×D172C2×C412yes—
45C2×C8×C43—21no—
46C2×C8×C43—21no—
47C2×C8×C43—21no—
48C4⋊C4×C43—21no—
49C4⋊C4×C43D412yes—
50(C2×D43)⋊C4—24no—
51(C2×D43)⋊C4—24no—
52C4⋊Dic43—21no—
53C4⋊Dic43D412yes—
54C4×Dic43—42no—
55C4×Dic43C2×C412yes—
56C4×Dic43D412yes—
57C2×C43⋊C8—21no—
58C2×C43⋊C8—21no—
59C2×C43⋊C8—21no—
60C23×C43C2×D411yescharacteristic
61C22×D43—22no—
62C22×D43—41no—
63C22×D43—41no—
64C22×D43—41no—
65C22×D43—41no—
66C22×D43—41no—
67C22×D43—41no—
68Q8×C43—22no—
69Q8×C43—22no—
70Q8×C43—41no—
71Q8×C43—41no—
72C2×C4×C43—22no—
73C2×C4×C43—22no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C22×C411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43#4111yescharacteristic
83C2×C4×C43#4111yescharacteristic
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—21no—
87C2×Dic43—21no—
88C2×Dic43—22no—
89C2×Dic43—41no—
90C2×Dic43—41no—
91C2×Dic43C22⋊C412yes—
92C2×Dic43C22⋊C412yes—
93D172—22no—
94D172—22no—
95D172—41no—
96D172—41no—
97C8×C43—41no—
98C43⋊C8—41no—
99C22×C43C2×C22⋊C411yescharacteristic
100C22×C43#12111yescharacteristic
101C22×C43#12111yescharacteristic
102C22×C43#13511yescharacteristic
103C22×C43#13511yescharacteristic
104C22×C43AGL(1,ℤ/8)11yescharacteristic
105C22×C43#13711yescharacteristic
106C2×D43—42no—
107C2×D43—42no—
108C2×D43—42no—
109C2×D43—81no—
110C2×D43—81no—
111C2×D43—81no—
112C2×D43—81no—
113C4×C43—42no—
114C4×C43—42no—
115C4×C43C4×D411yescharacteristic
116C4×C43C4×D411yescharacteristic
117C4×C43#12411yescharacteristic
118C4×C43#12711yescharacteristic
119Dic43—22no—
120Dic43—22no—
121Dic43—42no—
122#1983—431nomaximal, Sylow
123C2×C43#39011yescharacteristic
124C2×C43#41611yescharacteristic
125C2×C43#41711yescharacteristic
126C2×C43#46311yescharacteristic
127C2×C43#46311yescharacteristic
128C2×C43#46411yescharacteristic
129C2×C43#46411yescharacteristic
130D43—82no—
131C2×#124—431no—
132C2×C4⋊C8—431no—
133C2×#103—431no—
134C2×#103D4311yescharacteristic, complemented
135C2×#102—431no—
136C2×#102—431no—
137C4×C4⋊C4—431no—
138C43#198311yescharacteristic, complemented, Sylow
139C22×Q8C2×D4311yescharacteristic
140C22×D4—431no—
141C22×C8—431no—
142C22×C8C2×D4311yescharacteristic
143#124—434no—
144#124—862no—
145C2×C4⋊C4—431no—
146C2×C4⋊C4C2×D4311yescharacteristic
147C2×C22⋊C4—861no—
148C2×C22⋊C4—861no—
149C2×C42—431no—
150C2×C42—861no—
151C4⋊C8—862no—
152#103—22no—
153#103—862no—
154#102—862no—
155#102—862no—
156#95—861no—
157C24—861no—
158C2×Q8—21no—
159C2×Q8—21no—
160C2×Q8—21no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8C4×D4312yes—
164C2×D4—432no—
165C2×D4—861no—
166C2×D4—861no—
167C2×D4—861no—
168C2×D4—861no—
169C2×D4—861no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—431no—
173C22×C4—431no—
174C22×C4—861no—
175C22×C4C22×D4311yescharacteristic
176C2×C8—21no—
177C2×C8—21no—
178C2×C8—21no—
179C2×C8—861no—
180C2×C8—861no—
181C2×C8—861no—
182C4⋊C4—21no—
183C4⋊C4—432no—
184C4⋊C4—861no—
185C4⋊C4C22⋊D4312yes—
186C22⋊C4—864no—
187C22⋊C4—864no—
188C42—432no—
189C42—432no—
190C42—1722no—
191C23—862no—
192C23—1721no—
193C23—1721no—
194C23—1721no—
195C23—1721no—
196C23—1721no—
197C23—1721no—
198C23D4×D4311yescharacteristic
199Q8—22no—
200Q8—22no—
201Q8—41no—
202Q8—41no—
203D4—862no—
204D4—862no—
205D4—1721no—
206D4—1721no—
207C2×C4—22no—
208C2×C4—22no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—432no—
214C2×C4—432no—
215C2×C4—861no—
216C2×C4—861no—
217C2×C4—861no—
218C2×C4—861no—
219C2×C4—862no—
220C2×C4—1721no—
221C2×C4—1721no—
222C2×C4C2×C4×D4311yescharacteristic
223C2×C4#1062189811yescharacteristic
224C2×C4D4×D4311yescharacteristic
225C2×C4D4×D4311yescharacteristic
226C2×C4#1062190011yescharacteristic
227C2×C4C2×C22⋊D4311yescharacteristic
228C8—41no—
229C8—1721no—
230C22—3441no—
231C22—3441no—
232C22—3441no—
233C22—3441no—
234C22—1722no—
235C22—1722no—
236C22—1722no—
237C22C22⋊C4×D4311yescharacteristic
238C22#1306329711yescharacteristic
239C22#1306329811yescharacteristic
240C22#1306334611yescharacteristic
241C22#1306334811yescharacteristic
242C22#1306335211yescharacteristic
243C22#1306335711yescharacteristic
244C4—42no—
245C4—42no—
246C4—862no—
247C4—862no—
248C4—1722no—
249C4(C22⋊D43)⋊C411yescharacteristic
250C4C4×C22⋊D4311yescharacteristic
251C4#1306331111yescharacteristic
252C4#1306332111yescharacteristic
253C2—3442no—
254C2#1458279911yescharacteristic
255C2#1458289411yescharacteristic
256C2#1458289911yescharacteristic
257C2#1458311611yescharacteristic
258C2#1458311711yescharacteristic
259C2#1458312311yescharacteristic
260C2#1458312411yescharacteristic
subgroupG/H
centerC23D4×D43
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC2×#103×C43C2
socleC23×C43C2×D4
hypercenterC2×#103D43
hypocenterC43#1983
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
2. C2×Dic43⋊C8C2semidirect
3. C2×#13063249C2semidirect
6. C4⋊C4×Dic43C2semidirect
7. C2×#103×C43C2semidirect
11. #13063314C4semidirect
134. C2×#103D43semidirect
138. C43#1983semidirect