Finite Group Databasebeta

← #19136586

Subgroups — #19136586

Order 5504.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#14583577C211yesmaximal, characteristic, complemented
2#14583088C211yesmaximal, characteristic, complemented
3#14583087C211yesmaximal, characteristic
4#14583079C211yesmaximal, characteristic, complemented
5#14582693C211yesmaximal, characteristic, complemented
6#14582687C211yesmaximal, characteristic, complemented
7C43×#352C211yesmaximal, characteristic, complemented
8#13063370C2211yescharacteristic
9#13063358—21no—
10#13063318—21no—
11#13063312C2211yescharacteristic
12#13063308—21no—
13#13063307—21no—
14#13063303—21no—
15#13063295—21no—
16#13063293C2211yescharacteristic
17C4×C22⋊D43—21no—
18#13063283—21no—
19C22⋊C4×D43—21no—
20#13063251—21no—
21#13063240C2211yescharacteristic
22#13063239—21no—
23#13063239—21no—
24#123×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C23×D43D411yescharacteristic
28C2×D4×C43C2311yescharacteristic
29C22×C4×C43D411yescharacteristic, complemented
30C2×C22⋊D43—21no—
31C2×C22⋊D43—21no—
32C2×C22⋊D43—21no—
33#10621900—41no—
34D4×D43—41no—
35#10621898—21no—
36C2×D172—41no—
37C2×C4×D43—21no—
38C2×C4×D43—21no—
39C2×Dic86D411yescharacteristic, complemented
40M16×C43—21no—
41C4⋊C4×C43—21no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43D411yescharacteristic, complemented
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43D411yescharacteristic
49(C2×D43)⋊C4—21no—
50(C2×D43)⋊C4—21no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—41no—
53(C2×D43)⋊C4—41no—
54C4⋊Dic43—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57Dic43⋊C4—41no—
58C4×Dic43—21no—
59C4×Dic43D411yescharacteristic, complemented
60Dic172—41no—
61#10621873—41no—
62C23×C43C2×D411yescharacteristic
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65C22×D43—21no—
66C22×D43—21no—
67C22×D43—42no—
68C22×D43—41no—
69D4×C43—41no—
70C2×C4×C43—21no—
71C2×C4×C43—21no—
72C2×C4×C43—41no—
73C2×C4×C43—41no—
74C2×C4×C43C2×D411yescharacteristic
75C22⋊D43—42no—
76C22⋊D43—41no—
77C22⋊D43—41no—
78C22⋊D43—41no—
79C2×Dic43—21no—
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—41no—
85D172—21no—
86D172—82no—
87C4×D43—41no—
88C4×D43—42no—
89C4×D43—81no—
90Dic86—21no—
91Dic86—41no—
92C8×C43—41no—
93C22×C43—21no—
94C22×C43—21no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43#12011yescharacteristic
98C2×D43—22no—
99C2×D43—41no—
100C2×D43—41no—
101C2×D43—42no—
102C2×D43—41no—
103C2×D43—81no—
104C2×D43—81no—
105C2×D43—81no—
106C4×C43—21no—
107C4×C43—41no—
108C4×C43—41no—
109C4×C43—81no—
110Dic43—41no—
111Dic43—41no—
112Dic43—41no—
113Dic43—41no—
114Dic43—81no—
115#2197—431nomaximal, Sylow
116C2×C43—21no—
117C2×C43—41no—
118C2×C43—41no—
119C2×C43B(4,𝔽2)11yescharacteristic
120D43—42no—
121D43—81no—
122#551—431no—
123#458—431no—
124B(4,𝔽2)—431no—
125#455—431no—
126#354—431no—
127#352D4311yescharacteristic, complemented
128AΣL(1,𝔽16)—431no—
129C43#219711yescharacteristic, complemented, Sylow
130H(5,𝔽2)—431no—
131#137—861no—
132#126—861no—
133#124—431no—
134#123—861no—
135#123—861no—
136#123C2×D4311yescharacteristic
137C22⋊Q8—861no—
138#120—431no—
139#120—861no—
140C4×D4—861no—
141#117—861no—
142C2×C22⋊C4—861no—
143#104—861no—
144#100C2×D4311yescharacteristic
145#99—431no—
146#99—861no—
147#99—861no—
148#99C2×D4311yescharacteristic
149C24—431no—
150#41—861no—
151#41—1721no—
152C2×Q8—431no—
153C2×D4—861no—
154C2×D4—861no—
155C2×D4—861no—
156C2×D4—1721no—
157C2×D4—1721no—
158C2×D4C22×D4311yescharacteristic
159C22×C4—861no—
160C22×C4—861no—
161C22×C4D17211yescharacteristic, complemented
162Q16—1721no—
163SD16—1721no—
164M16—21no—
165C4⋊C4—21no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C4⋊C4—1721no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—431no—
173C22⋊C4—861no—
174C22⋊C4—861no—
175C22⋊C4—861no—
176C22⋊C4—861no—
177C22⋊C4—861no—
178C22⋊C4—861no—
179C22⋊C4—1721no—
180C22⋊C4—1721no—
181C22⋊C4D17211yescharacteristic, complemented
182C42—431no—
183C42—861no—
184C23—861no—
185C23—861no—
186C23—861no—
187C23—1721no—
188C23—1722no—
189C23C2×D17211yescharacteristic
190C23D4×D4311yescharacteristic
191Q8—861no—
192Q8—1721no—
193D4—41no—
194D4—861no—
195D4—3442no—
196D4—1721no—
197D4—1721no—
198D4—1722no—
199D4—1721no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—861no—
207C2×C4—861no—
208C2×C4—861no—
209C2×C4—3441no—
210C2×C4—1721no—
211C2×C4—1722no—
212C2×C4—1721no—
213C2×C4D4×D4311yescharacteristic
214C8—41no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—862no—
220C22—3441no—
221C22—3441no—
222C22—3441no—
223C22—1721no—
224C22—1722no—
225C22—1721no—
226C22—1721no—
227C22#1306329511yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—81no—
232C4—3441no—
233C4—1721no—
234C4—1721no—
235C4—1721no—
236C4—1721no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—3441no—
241C2—1722no—
242C2#1458308711yescharacteristic
subgroupG/H
centerC2#14583087
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#352C2
socleC2×C43B(4,𝔽2)
hypercenter#352D43
hypocenterC43#2197
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
1. #14583577C2semidirect
2. #14583088C2semidirect
4. #14583079C2semidirect
5. #14582693C2semidirect
6. #14582687C2semidirect
7. C43×#352C2semidirect
29. C22×C4×C43D4semidirect
39. C2×Dic86D4semidirect
44. C22⋊C4×C43D4semidirect
59. C4×Dic43D4semidirect
127. #352D43semidirect
129. C43#2197semidirect
161. C22×C4D172semidirect
181. C22⋊C4D172semidirect