Finite Group Databasebeta

← #19136606

Subgroups — #19136606

Order 5504.

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

normal subgroups only

This group has 226 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#14583652C211yesmaximal, characteristic, complemented
2#14583089C211yesmaximal, characteristic
3#14583077C211yesmaximal, characteristic
4#14582693C211yesmaximal, characteristic, complemented
5#14582689C211yesmaximal, characteristic, complemented
6#14582688C211yesmaximal, characteristic, complemented
7C43×#458C211yesmaximal, characteristic
8#13063355—21no—
9#13063324—21no—
10#13063318—21no—
11#13063318—21no—
12#13063315—21no—
13#13063312C2211yescharacteristic
14#13063306—21no—
15#13063306C2211yescharacteristic
16#13063304—21no—
17#13063302—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
34C22×Dic43D411yescharacteristic
35C2×Dic86—21no—
36C2×Dic86D411yescharacteristic
37C4⋊C4×C43—21no—
38C4⋊C4×C43—41no—
39C22⋊C4×C43—21no—
40C22⋊C4×C43—21no—
41C22⋊C4×C43—41no—
42C22⋊C4×C43D411yescharacteristic
43C22⋊Dic43—21no—
44C22⋊Dic43—21no—
45C22⋊Dic43—21no—
46C22⋊Dic43—21no—
47C22⋊Dic43—41no—
48C22⋊Dic43D411yescharacteristic
49#10621885—41no—
50#10621883—41no—
51C4⋊Dic43—21no—
52C4⋊Dic43—21no—
53Dic43⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57Dic43⋊C4—21no—
58Dic43⋊C4—41no—
59C4×Dic43—21no—
60C4×Dic43D411yescharacteristic
61#10621877—21no—
62C23×C43—21no—
63C23×C43—21no—
64C23×C43C2×D411yescharacteristic
65C23×C43C2×D411yescharacteristic
66Q8×C43—21no—
67D4×C43—21no—
68D4×C43—41no—
69D4×C43—41no—
70D4×C43—41no—
71D4×C43—41no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43—41no—
79C2×C4×C43C2×D411yescharacteristic
80C2×Dic43—21no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—41no—
85C2×Dic43—41no—
86Dic86—41no—
87Dic86—81no—
88C43⋊C8—41no—
89C22×C43—21no—
90C22×C43—21no—
91C22×C43—41no—
92C22×C43—41no—
93C22×C43—41no—
94C22×C43—81no—
95C22×C43—81no—
96C22×C43#12011yescharacteristic
97C4×C43—21no—
98C4×C43—41no—
99C4×C43—41no—
100C4×C43—41no—
101C4×C43—81no—
102Dic43—41no—
103Dic43—41no—
104Dic43—41no—
105Dic43—41no—
106Dic43—81no—
107#2201—431nomaximal, Sylow
108C2×C43—21no—
109C2×C43—41no—
110C2×C43—41no—
111C2×C43—81no—
112C2×C43B(4,𝔽2)11yescharacteristic
113#563—431no—
114#458—431no—
115#458D4311yescharacteristic
116#455—431no—
117#354—431no—
118#352—431no—
119#352—431no—
120C43#220111yescharacteristic, complemented, Sylow
121H(5,𝔽2)C2×D4311yescharacteristic
122#137—861no—
123C4⋊Q8—861no—
124#126—861no—
125#126—861no—
126#125—861no—
127#124—431no—
128#123—21no—
129#123—431no—
130#123—861no—
131#123C2×D4311yescharacteristic
132C22⋊Q8—861no—
133C22⋊Q8—861no—
134#104—861no—
135#100—431no—
136#99—21no—
137#99—431no—
138#99—861no—
139#99C2×D4311yescharacteristic
140#41—21no—
141#41—41no—
142C2×Q8—431no—
143C2×Q8—861no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—41no—
147C2×D4C22×D4311yescharacteristic
148C22×C4—431no—
149C22×C4C22⋊D4311yescharacteristic
150Q16—1721no—
151SD16—1721no—
152M16—861no—
153C4⋊C4—21no—
154C4⋊C4—41no—
155C4⋊C4—861no—
156C4⋊C4—861no—
157C4⋊C4—861no—
158C4⋊C4—861no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4—1721no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—41no—
166C22⋊C4—431no—
167C22⋊C4—861no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C22⋊C4—861no—
171C22⋊C4—1721no—
172C22⋊C4C22⋊D4311yescharacteristic
173C42—431no—
174C42—861no—
175C23—21no—
176C23—21no—
177C23D4×D4311yescharacteristic
178C23C2×C22⋊D4311yescharacteristic
179Q8—21no—
180Q8—3441no—
181Q8—1721no—
182D4—21no—
183D4—41no—
184D4—41no—
185D4—41no—
186D4—41no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—861no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—1721no—
199C2×C4—1721no—
200C2×C4D4×D4311yescharacteristic
201C8—1721no—
202C22—21no—
203C22—21no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—81no—
208C22—81no—
209C22#1306329311yescharacteristic
210C4—21no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—81no—
215C4—3441no—
216C4—1721no—
217C4—1721no—
218C4—1721no—
219C4—1721no—
220C2—21no—
221C2—41no—
222C2—41no—
223C2—81no—
224C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#458C2
socleC2×C43B(4,𝔽2)
hypercenter#458D43
hypocenterC43#2201
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. #14583652C2semidirect
4. #14582693C2semidirect
5. #14582689C2semidirect
6. #14582688C2semidirect
120. C43#2201semidirect