Finite Group Databasebeta

← #19145309

Subgroups — #19145309

Order 5504.

402 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 129 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#14583456C211yesmaximal, characteristic, complemented
2#14583302C211yesmaximal, characteristic, complemented
3#14583271C211yesmaximal, characteristic, complemented
4#14583251C211yesmaximal, characteristic, complemented
5#14583245C211yesmaximal, characteristic, complemented
6#14583143C214yesmaximal, complemented
7#14582999C214yesmaximal, complemented
8C4×#10621877C211yesmaximal, characteristic, complemented
9C43×#532C211yesmaximal, characteristic
10C2×#10621883C2214yes—
11C2×#10621877C2212yes—
12#13063325C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063317—21no—
15#13063304—21no—
16#13063304C2212yes—
17C4×Dic86—21no—
18C4×Dic86C2212yes—
19#13063284—21no—
20#13063258C2214yes—
21#13063248C2214yes—
22#13063246C2214yes—
23#13063236C2212yes—
24C4×C43⋊C8C2211yescharacteristic
25C4×C43⋊C8C2211yescharacteristic
26C2×#41×C43—21no—
27C4⋊Q8×C43C2211yescharacteristic
28#127×C43C2211yescharacteristic
29#124×C43—21no—
30#121×C43—21no—
31#121×C43C2212yes—
32C4×D4×C43—21no—
33C4×D4×C43C2212yes—
34C2×C42×C43C2211yescharacteristic
35#41×C43—44no—
36C2×Q8×C43—21no—
37C2×D4×C43—21no—
38C2×D4×C43—21no—
39C2×D4×C43—22no—
40C2×D4×C43C2312yes—
41C22×C4×C43—22no—
42C22×C4×C43D411yescharacteristic
43C22×C4×C43D411yescharacteristic
44C22×C4×C43C2311yescharacteristic
45C2×Dic86—21no—
46C2×Dic86C2312yes—
47C4⋊C4×C43—21no—
48C4⋊C4×C43C2312yes—
49C22⋊C4×C43—22no—
50C22⋊C4×C43—22no—
51C42×C43D411yescharacteristic
52C42×C43D411yescharacteristic
53C42×C43C2311yescharacteristic
54C42×C43C2311yescharacteristic
55C22⋊Dic43—22no—
56#10621883—28no—
57C4⋊Dic43—21no—
58C4⋊Dic43—21no—
59C4⋊Dic43—21no—
60C4⋊Dic43C2312yes—
61Dic43⋊C4—22no—
62Dic43⋊C4—22no—
63C4×Dic43—22no—
64#10621877—24no—
65C2×C43⋊C8C2312yes—
66C2×C43⋊C8C2312yes—
67C23×C43—22no—
68C23×C43C2×D411yescharacteristic
69Q8×C43—42no—
70D4×C43—24no—
71D4×C43—44no—
72D4×C43—42no—
73D4×C43—42no—
74C2×C4×C43—22no—
75C2×C4×C43—22no—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—44no—
79C2×C4×C43C2×D411yescharacteristic
80C2×C4×C43C2×D411yescharacteristic
81C2×C4×C43C2×D411yescharacteristic
82C2×C4×C43C2×D411yescharacteristic
83C2×C4×C43C2×D411yescharacteristic
84C2×C4×C43C2411yescharacteristic
85C2×Dic43—22no—
86C2×Dic43—22no—
87Dic86—24no—
88Dic86—42no—
89C43⋊C8—22no—
90C43⋊C8#4114yescomplemented
91C22×C43—21no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—42no—
95C22×C43—42no—
96C22×C43—42no—
97C22×C43C22×D411yescharacteristic
98C4×C43—21no—
99C4×C43—21no—
100C4×C43—21no—
101C4×C43—42no—
102C4×C43AGL(1,ℤ/8)12yes—
103C4×C43#13712yes—
104C4×C43C2×#4112yes—
105Dic43—42no—
106Dic43—42no—
107#3182—431nomaximal, Sylow
108C2×C43—41no—
109C2×C43—82no—
110C2×C43#53211yescharacteristic
111C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
112C2×C43C2×#13711yescharacteristic
113#533—431no—
114#532D4311yescharacteristic
115#500—431no—
116#492—431no—
117#487—431no—
118#486—431no—
119#468—434no—
120#440—434no—
121C4×M16—431no—
122C43#318211yescharacteristic, complemented, Sylow
123C2×#41—21no—
124C2×SD16—434no—
125C2×M16—432no—
126C4⋊Q8—431no—
127C4⋊Q8—431no—
128C4⋊Q8C2×D4311yescharacteristic
129#127C2×D4311yescharacteristic
130#125—861no—
131#124—21no—
132C22⋊Q8—432no—
133C22⋊Q8—861no—
134#121—21no—
135#121C2×D4312yes—
136C4×Q8—432no—
137C4×Q8—861no—
138C4×D4—21no—
139C4×D4C2×D4312yes—
140#117—861no—
141C2×C42C2×D4311yescharacteristic
142#107—434no—
143#103—434no—
144#102—434no—
145#97—432no—
146C4×C8—431no—
147C4×C8—431no—
148#41—44no—
149C2×Q8—21no—
150C2×Q8—432no—
151C2×Q8—861no—
152C2×D4—22no—
153C2×D4—21no—
154C2×D4—21no—
155C2×D4C22×D4312yes—
156C22×C4—22no—
157C22×C4C22⋊D4311yescharacteristic
158C22×C4C22⋊D4311yescharacteristic
159C22×C4C22×D4311yescharacteristic
160SD16—868no—
161M16—864no—
162C2×C8—432no—
163C2×C8—432no—
164C4⋊C4—21no—
165C4⋊C4—432no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—862no—
169C4⋊C4—862no—
170C4⋊C4—861no—
171C4⋊C4C22×D4312yes—
172C22⋊C4—22no—
173C22⋊C4—22no—
174C22⋊C4—862no—
175C42—862no—
176C42C22⋊D4311yescharacteristic
177C42C22⋊D4311yescharacteristic
178C42C22×D4311yescharacteristic
179C42C22×D4311yescharacteristic
180C23—22no—
181C23C2×C22⋊D4311yescharacteristic
182Q8—42no—
183Q8—864no—
184Q8—1722no—
185D4—24no—
186D4—44no—
187D4—42no—
188D4—42no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—44no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4C2×C22⋊D4311yescharacteristic
197C2×C4C2×C22⋊D4311yescharacteristic
198C2×C4C2×C22⋊D4311yescharacteristic
199C2×C4C2×C22⋊D4311yescharacteristic
200C2×C4C2×C22⋊D4311yescharacteristic
201C2×C4C23×D4311yescharacteristic
202C8—434no—
203C8—862no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—42no—
208C22—42no—
209C22—42no—
210C22C22×C22⋊D4311yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—1722no—
216C4—1722no—
217C4#1306335112yes—
218C4#1306335512yes—
219C4#41×D4312yes—
220C2—41no—
221C2—82no—
222C2#1458344511yescharacteristic
223C2C2×#1306335111yescharacteristic
224C2C2×#1306335511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#532C2
socleC22×C43C22×D4
hypercenter#532D43
hypocenterC43#3182
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14583456C2semidirect
2. #14583302C2semidirect
3. #14583271C2semidirect
4. #14583251C2semidirect
5. #14583245C2semidirect
6. #14583143C2semidirect
7. #14582999C2semidirect
8. C4×#10621877C2semidirect
90. C43⋊C8#41semidirect
122. C43#3182semidirect