Finite Group Databasebeta

← #19136589

Subgroups — #19136589

Order 5504.

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

normal subgroups only

This group has 246 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#14583633C211yesmaximal, characteristic, complemented
2#14583089C211yesmaximal, characteristic, complemented
3#14583067C211yesmaximal, characteristic
4#14582691C211yesmaximal, characteristic, complemented
5#14582689C211yesmaximal, characteristic, complemented
6#14582688C211yesmaximal, characteristic, complemented
7C43×#458C211yesmaximal, characteristic, complemented
8#13063350—21no—
9#13063321C2211yescharacteristic
10#13063311—21no—
11#13063311—21no—
12#13063310—21no—
13#13063306—21no—
14#13063306C2211yescharacteristic
15#13063290—21no—
16C4×C22⋊D43—21no—
17(C22⋊D43)⋊C4—21no—
18#13063252—21no—
19#13063242C2211yescharacteristic
20#13063240—21no—
21#13063240C2211yescharacteristic
22H(5,𝔽2)×C43C2211yescharacteristic
23#123×C43—21no—
24#123×C43C2211yescharacteristic
25#99×C43—21no—
26#99×C43C2211yescharacteristic
27#41×C43—21no—
28#41×C43—41no—
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43—41no—
32C2×D4×C43C2311yescharacteristic
33C22×C4×C43D411yescharacteristic
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C22×Dic43D411yescharacteristic
37C2×D172D411yescharacteristic
38C2×C4×D43—21no—
39C2×Dic86—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43—41no—
42C22⋊C4×C43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43—41no—
45C22⋊C4×C43D411yescharacteristic
46C22⋊Dic43—21no—
47C22⋊Dic43—21no—
48C22⋊Dic43—41no—
49C22⋊Dic43D411yescharacteristic
50#10621884—41no—
51#10621882—41no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57Dic43⋊C4—41no—
58C4×Dic43—21no—
59C4×Dic43—21no—
60C4×Dic43D411yescharacteristic
61#10621877—21no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43C2×D411yescharacteristic
65C23×C43C2×D411yescharacteristic
66C22×D43—21no—
67Q8×C43—21no—
68D4×C43—21no—
69D4×C43—41no—
70D4×C43—41no—
71D4×C43—41no—
72D4×C43—41no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—21no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43—41no—
80C2×C4×C43C2×D411yescharacteristic
81C22⋊D43—42no—
82C22⋊D43—42no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—21no—
86C2×Dic43—41no—
87C2×Dic43—41no—
88D172—41no—
89C4×D43—81no—
90Dic86—42no—
91C43⋊C8—41no—
92C22×C43—21no—
93C22×C43—21no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43—41no—
97C22×C43—81no—
98C22×C43—81no—
99C22×C43#12011yescharacteristic
100C2×D43—41no—
101C2×D43—41no—
102C2×D43—41no—
103C4×C43—21no—
104C4×C43—41no—
105C4×C43—41no—
106C4×C43—41no—
107C4×C43—81no—
108Dic43—22no—
109Dic43—41no—
110Dic43—41no—
111Dic43—81no—
112#2198—431nomaximal, Sylow
113C2×C43—21no—
114C2×C43—41no—
115C2×C43—41no—
116C2×C43—81no—
117C2×C43B(4,𝔽2)11yescharacteristic
118D43—81no—
119#559—431no—
120#458—431no—
121#458D4311yescharacteristic, complemented
122#453—431no—
123#353—431no—
124#352—431no—
125#352—431no—
126C43#219811yescharacteristic, complemented, Sylow
127H(5,𝔽2)C2×D4311yescharacteristic
128AGL(1,ℤ/8)—861no—
129#127—431no—
130#124—861no—
131#124—861no—
132#123—21no—
133#123—431no—
134#123—861no—
135#123—861no—
136#123C2×D4311yescharacteristic
137C4×Q8—861no—
138C4×D4—861no—
139C4×D4—861no—
140#104—861no—
141#100—431no—
142#99—21no—
143#99—431no—
144#99—861no—
145#99C2×D4311yescharacteristic
146#41—21no—
147#41—41no—
148C2×Q8—861no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—41no—
152C2×D4—431no—
153C2×D4—861no—
154C2×D4—861no—
155C2×D4C22×D4311yescharacteristic
156C22×C4—431no—
157C22×C4—861no—
158C22×C4C22⋊D4311yescharacteristic
159SD16—1721no—
160D8—1721no—
161M16—861no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C4⋊C4—1721no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—41no—
170C22⋊C4—431no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C22⋊C4—861no—
174C22⋊C4—861no—
175C22⋊C4—861no—
176C22⋊C4—1721no—
177C22⋊C4C22⋊D4311yescharacteristic
178C42—431no—
179C42—861no—
180C42—861no—
181C23—21no—
182C23—21no—
183C23—861no—
184C23D4×D4311yescharacteristic
185C23C2×C22⋊D4311yescharacteristic
186Q8—21no—
187Q8—1722no—
188D4—21no—
189D4—41no—
190D4—41no—
191D4—41no—
192D4—41no—
193D4—1721no—
194D4—1722no—
195D4—1722no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—861no—
204C2×C4—861no—
205C2×C4—861no—
206C2×C4—3441no—
207C2×C4—1721no—
208C2×C4—1721no—
209C2×C4D4×D4311yescharacteristic
210C8—1721no—
211C22—21no—
212C22—21no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—81no—
218C22—1721no—
219C22—1721no—
220C22—1721no—
221C22#1306329311yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—862no—
228C4—3441no—
229C4—1721no—
230C4—1721no—
231C2—21no—
232C2—41no—
233C2—41no—
234C2—81no—
235C2—3441no—
236C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#458C2
socleC2×C43B(4,𝔽2)
hypercenter#458D43
hypocenterC43#2198
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #458

Complements

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

NH ≅ G/Ntype
1. #14583633C2semidirect
2. #14583089C2semidirect
4. #14582691C2semidirect
5. #14582689C2semidirect
6. #14582688C2semidirect
7. C43×#458C2semidirect
121. #458D43semidirect
126. C43#2198semidirect