Finite Group Databasebeta

← #19136258

Subgroups — #19136258

Order 5504.

258 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#14583445C211yesmaximal, characteristic
2#14582873C211yesmaximal, characteristic, complemented
3#14582693C212yesmaximal, complemented
4#14582691C212yesmaximal, complemented
5C43×#410C211yesmaximal, characteristic, complemented
6C2×#10621898C411yescharacteristic, complemented
7#13063323C411yescharacteristic, complemented
8#13063321C2211yescharacteristic
9#13063314C411yescharacteristic, complemented
10#13063312C2211yescharacteristic
11#13063297—21no—
12#13063297—21no—
13C4×C22⋊D43—21no—
14C4×C22⋊D43—21no—
15#13063284—21no—
16C2×C4×Dic43C411yescharacteristic, complemented
17#13063240—21no—
18#13063240C2212yes—
19C2×#41×C43C2211yescharacteristic
20#117×C43—21no—
21#99×C43—21no—
22#99×C43C2212yes—
23#41×C43—41no—
24#41×C43—41no—
25C2×Q8×C43C2×C411yescharacteristic
26C2×D4×C43D411yescharacteristic
27C2×D4×C43D411yescharacteristic
28C2×D4×C43C2311yescharacteristic
29C22×C4×C43C2×C411yescharacteristic
30C22×C4×C43D411yescharacteristic
31C22×C4×C43D411yescharacteristic
32C2×C22⋊D43—21no—
33C2×C22⋊D43—21no—
34C2×C22⋊D43—21no—
35C22×Dic43—21no—
36#10621898—41no—
37#10621898—41no—
38C2×D172C2×C411yescharacteristic
39C2×C4×D43—21no—
40C2×Dic86C2×C411yescharacteristic
41C4⋊C4×C43—41no—
42C22⋊C4×C43—22no—
43C42×C43—41no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—22no—
47(C2×D43)⋊C4—21no—
48(C2×D43)⋊C4—21no—
49C4⋊Dic43—41no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53C4×Dic43—41no—
54C4×Dic43C2×C411yescharacteristic
55C4×Dic43C2×C411yescharacteristic
56C23×C43C22⋊C411yescharacteristic
57C23×C43C2×D411yescharacteristic
58C23×C43C2×D411yescharacteristic
59C22×D43—21no—
60Q8×C43—41no—
61D4×C43—41no—
62D4×C43—41no—
63D4×C43—41no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—42no—
71C2×C4×C43C22⋊C411yescharacteristic
72C2×C4×C43C22⋊C411yescharacteristic
73C2×C4×C43C22⋊C411yescharacteristic
74C2×C4×C43C22×C411yescharacteristic
75C22⋊D43—42no—
76C22⋊D43—42no—
77C22⋊D43—42no—
78C2×Dic43—21no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—42no—
82C2×Dic43—42no—
83D172—41no—
84C4×D43—41no—
85C4×D43—41no—
86Dic86—41no—
87C22×C43—21no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43—41no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43C2×C22⋊C411yescharacteristic
94C2×D43—41no—
95C2×D43—41no—
96C2×D43—41no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—82no—
101C4×C43#9911yescharacteristic
102C4×C43#9911yescharacteristic
103Dic43—22no—
104Dic43—41no—
105Dic43—41no—
106Dic43—82no—
107#2126—431nomaximal, Sylow
108C2×C43—21no—
109C2×C43—41no—
110C2×C43—41no—
111C2×C43—41no—
112C2×C43C2×#9911yescharacteristic
113D43—81no—
114#532—431no—
115#410—431no—
116#410D4311yescharacteristic, complemented
117#354—432no—
118#353—432no—
119C43#212611yescharacteristic, complemented, Sylow
120C2×#41—431no—
121C2×#41C2×D4311yescharacteristic
122C4⋊Q8—431no—
123#127—431no—
124#124—431no—
125#124—431no—
126#121—861no—
127#121—861no—
128C4×D4—861no—
129C4×D4—861no—
130#117—21no—
131#117—861no—
132C2×C42—431no—
133#99—21no—
134#99—432no—
135#99—861no—
136#99C2×D4312yes—
137#41—41no—
138#41—41no—
139#41—1721no—
140#41—1721no—
141C2×Q8—431no—
142C2×Q8C4×D4311yescharacteristic
143C2×D4—431no—
144C2×D4—861no—
145C2×D4—861no—
146C2×D4—861no—
147C2×D4D17211yescharacteristic
148C2×D4C22⋊D4311yescharacteristic
149C2×D4C22×D4311yescharacteristic
150C22×C4—861no—
151C22×C4—861no—
152C22×C4C4×D4311yescharacteristic
153C22×C4D17211yescharacteristic
154C22×C4C22⋊D4311yescharacteristic
155C4⋊C4—41no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—1721no—
159C22⋊C4—22no—
160C22⋊C4—861no—
161C22⋊C4—861no—
162C22⋊C4—861no—
163C22⋊C4—861no—
164C22⋊C4—862no—
165C42—41no—
166C42—431no—
167C42—431no—
168C42—861no—
169C42—1721no—
170C23—861no—
171C23(C2×D43)⋊C411yescharacteristic
172C23C2×D17211yescharacteristic
173C23C2×C22⋊D4311yescharacteristic
174Q8—41no—
175Q8—1721no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4—1721no—
180D4—1722no—
181D4—1722no—
182D4—1722no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—861no—
193C2×C4—1722no—
194C2×C4—1722no—
195C2×C4—1721no—
196C2×C4—1721no—
197C2×C4(C2×D43)⋊C411yescharacteristic
198C2×C4(C2×D43)⋊C411yescharacteristic
199C2×C4(C2×D43)⋊C411yescharacteristic
200C2×C4C2×C4×D4311yescharacteristic
201C22—21no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—1721no—
208C22—1721no—
209C22—1721no—
210C22C2×(C2×D43)⋊C411yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—82no—
215C4—862no—
216C4—3442no—
217C4—1721no—
218C4—1721no—
219C4#1306323911yescharacteristic
220C4#1306323911yescharacteristic
221C2—21no—
222C2—41no—
223C2—41no—
224C2—41no—
225C2—3441no—
226C2C2×#1306323911yescharacteristic
subgroupG/H
centerC4#13063239
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#410C2
socleC2×C43C2×#99
hypercenter#410D43
hypocenterC43#2126
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #14582873C2semidirect
3. #14582693C2semidirect
4. #14582691C2semidirect
5. C43×#410C2semidirect
6. C2×#10621898C4semidirect
7. #13063323C4semidirect
9. #13063314C4semidirect
16. C2×C4×Dic43C4semidirect
116. #410D43semidirect
119. C43#2126semidirect