Finite Group Databasebeta

← #19136619

Subgroups — #19136619

Order 5504.

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

normal subgroups only

This group has 236 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#14583611C211yesmaximal, characteristic, complemented
2#14583082C211yesmaximal, characteristic, complemented
3#14583072C211yesmaximal, characteristic, complemented
4#14582697C211yesmaximal, characteristic, complemented
5#14582696C211yesmaximal, characteristic, complemented
6#14582695C211yesmaximal, characteristic, complemented
7C43×#454C211yesmaximal, characteristic, complemented
8#13063355—21no—
9#13063350—21no—
10#13063323C2211yescharacteristic
11#13063314C2211yescharacteristic
12#13063311—21no—
13#13063298—21no—
14#13063297—21no—
15(C22⋊D43)⋊C4—21no—
16#13063282—21no—
17#13063281—21no—
18#13063252—21no—
19#13063252—21no—
20#13063244C2211yescharacteristic
21#13063244C2211yescharacteristic
222−1+4×C43C2211yescharacteristic
23AGL(1,ℤ/8)×C43—21no—
24#124×C43C2211yescharacteristic
25#104×C43—21no—
26#101×C43C2211yescharacteristic
27#41×C43—21no—
28#41×C43—21no—
29#41×C43—21no—
30#41×C43—41no—
31C2×Q8×C43—41no—
32C2×Q8×C43C2311yescharacteristic
33C2×D4×C43D411yescharacteristic
34C2×C22⋊D43—21no—
35C2×C22⋊D43—21no—
36C22×Dic43—21no—
37C2×D172D411yescharacteristic
38C2×C4×D43—21no—
39C2×Dic86D411yescharacteristic
40SD16×C43—41no—
41D8×C43—41no—
42M16×C43—21no—
43C22⋊C4×C43—21no—
44C22⋊C4×C43—21no—
45C42×C43D411yescharacteristic
46C22⋊Dic43—21no—
47#10621885—41no—
48#10621884—41no—
49#10621883—41no—
50#10621882—41no—
51(C2×D43)⋊C4—21no—
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54Dic43⋊C4—21no—
55Dic43⋊C4—21no—
56Dic43⋊C4—21no—
57C4×Dic43—21no—
58C4×Dic43D411yescharacteristic
59C4×Dic43D411yescharacteristic
60#10621877—21no—
61#10621877—21no—
62C23×C43—21no—
63C22×D43—21no—
64Q8×C43—21no—
65Q8×C43—21no—
66Q8×C43—21no—
67Q8×C43—41no—
68D4×C43—21no—
69D4×C43—21no—
70D4×C43—21no—
71D4×C43—41no—
72D4×C43—41no—
73C2×C4×C43—21no—
74C2×C4×C43—41no—
75C2×C4×C43—41no—
76C2×C4×C43—41no—
77C2×C4×C43C2×D411yescharacteristic
78C2×C4×C43C2×D411yescharacteristic
79C2×C4×C43C2×D411yescharacteristic
80C22⋊D43—42no—
81C22⋊D43—81no—
82C2×Dic43—21no—
83C2×Dic43—21no—
84C2×Dic43—21no—
85C2×Dic43—42no—
86D172—41no—
87C4×D43—42no—
88Dic86—41no—
89C8×C43—41no—
90C43⋊C8—41no—
91C43⋊C8—41no—
92C22×C43—41no—
93C22×C43—41no—
94C22×C43—41no—
95C22×C43—41no—
96C22×C43#12011yescharacteristic
97C2×D43—41no—
98C2×D43—41no—
99C2×D43—41no—
100C4×C43—21no—
101C4×C43—21no—
102C4×C43—21no—
103C4×C43—41no—
104C4×C43—41no—
105Dic43—22no—
106Dic43—41no—
107Dic43—41no—
108#2204—431nomaximal, Sylow
109C2×C43—21no—
110C2×C43—81no—
111C2×C43—81no—
112C2×C43B(4,𝔽2)11yescharacteristic
113D43—81no—
114#555—431no—
115#456—431no—
116#454—431no—
117#454D4311yescharacteristic, complemented
118#356—431no—
119#355—431no—
120#355—431no—
121C43#220411yescharacteristic, complemented, Sylow
1222−1+4C2×D4311yescharacteristic
123#137—861no—
124AGL(1,ℤ/8)—21no—
125AGL(1,ℤ/8)—861no—
126C4⋊Q8—431no—
127#124—431no—
128#124—861no—
129#124C2×D4311yescharacteristic
130#121—861no—
131#121—861no—
132C4×D4—861no—
133#117—861no—
134#117—861no—
135#104—21no—
136#104—861no—
137#104—861no—
138#101—431no—
139#101—431no—
140#101C2×D4311yescharacteristic
141#41—21no—
142#41—21no—
143#41—21no—
144#41—41no—
145C2×Q8—41no—
146C2×Q8—431no—
147C2×Q8C22×D4311yescharacteristic
148C2×D4—431no—
149C2×D4—861no—
150C2×D4—861no—
151C2×D4C22⋊D4311yescharacteristic
152C22×C4—861no—
153C22×C4—861no—
154Q16—1721no—
155SD16—41no—
156SD16—1721no—
157SD16—1721no—
158D8—41no—
159D8—1721no—
160M16—21no—
161M16—861no—
162M16—861no—
163C4⋊C4—861no—
164C4⋊C4—861no—
165C4⋊C4—861no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—861no—
169C22⋊C4—861no—
170C22⋊C4—861no—
171C22⋊C4—861no—
172C42—431no—
173C42—431no—
174C42—861no—
175C42C22⋊D4311yescharacteristic
176C23—21no—
177C23—861no—
178Q8—21no—
179Q8—21no—
180Q8—21no—
181Q8—41no—
182Q8—1721no—
183D4—21no—
184D4—21no—
185D4—21no—
186D4—41no—
187D4—41no—
188D4—3441no—
189D4—1721no—
190D4—1722no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—861no—
196C2×C4—861no—
197C2×C4—861no—
198C2×C4—1722no—
199C2×C4—1722no—
200C2×C4D4×D4311yescharacteristic
201C2×C4D4×D4311yescharacteristic
202C2×C4C2×C22⋊D4311yescharacteristic
203C8—41no—
204C8—1721no—
205C8—1721no—
206C22—41no—
207C22—41no—
208C22—41no—
209C22—41no—
210C22—1721no—
211C22—1721no—
212C22—1721no—
213C22#1306329311yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—41no—
218C4—41no—
219C4—862no—
220C4—1721no—
221C4—1721no—
222C2—21no—
223C2—81no—
224C2—81no—
225C2—3441no—
226C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#454C2
socleC2×C43B(4,𝔽2)
hypercenter#454D43
hypocenterC43#2204
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14583611C2semidirect
2. #14583082C2semidirect
3. #14583072C2semidirect
4. #14582697C2semidirect
5. #14582696C2semidirect
6. #14582695C2semidirect
7. C43×#454C2semidirect
117. #454D43semidirect
121. C43#2204semidirect