Finite Group Databasebeta

← #19133604

Subgroups — #19133604

Order 5504.

210 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 51 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#14583528C211yesmaximal, characteristic
2#14583230C211yesmaximal, characteristic
3#14583227C211yesmaximal, characteristic
4#14582831C211yesmaximal, characteristic
5#14582635C211yesmaximal, characteristic
6#14582624C211yesmaximal, characteristic
7C43×#328C211yesmaximal, characteristic
8#13063324—21no—
9#13063323—21no—
10#13063315—21no—
11#13063315—21no—
12#13063304C2211yescharacteristic
13#13063302—21no—
14#13063281—21no—
15C2×C4⋊Dic43—21no—
16C2×C4⋊Dic43C2211yescharacteristic
17C2×Dic43⋊C4C2211yescharacteristic
18#13063257—21no—
19#13063256—21no—
20#13063250—21no—
21#13063249—21no—
22C22⋊(C43⋊C8)C2211yescharacteristic
23C43⋊#95—21no—
24C22⋊Q8×C43C2211yescharacteristic
25C22⋊C8×C43C2211yescharacteristic
26#95×C43C2211yescharacteristic
27C2×Q8×C43D411yescharacteristic
28C22×C4×C43—21no—
29C22×C4×C43C2311yescharacteristic
30C22×Dic43—21no—
31C22×Dic43D411yescharacteristic
32C22×Dic43D411yescharacteristic
33C2×Dic86—21no—
34C2×Dic86D411yescharacteristic
35C2×C8×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C22⋊C4×C43—21no—
39C22⋊Dic43—21no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43—21no—
43C4⋊Dic43—42no—
44C4⋊Dic43D411yescharacteristic
45Dic43⋊C4—21no—
46Dic43⋊C4—21no—
47Dic43⋊C4—21no—
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51Dic43⋊C4—21no—
52C4×Dic43—21no—
53C4×Dic43—21no—
54C2×C43⋊C8—21no—
55C23×C43C2×D411yescharacteristic
56Q8×C43—41no—
57C2×C4×C43—22no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43—41no—
63C2×C4×C43C2×D411yescharacteristic
64C2×C4×C43C2×D411yescharacteristic
65C2×Dic43—21no—
66C2×Dic43—21no—
67C2×Dic43—21no—
68C2×Dic43—21no—
69C2×Dic43—21no—
70C2×Dic43—41no—
71C2×Dic43—41no—
72C2×Dic43—41no—
73C2×Dic43—41no—
74C2×Dic43SD1612yes—
75Dic86—41no—
76Dic86—81no—
77C8×C43—41no—
78C43⋊C8—41no—
79C22×C43—21no—
80C22×C43—21no—
81C22×C43#12011yescharacteristic
82C22×C43C2×SD1611yescharacteristic
83C22×C43#13711yescharacteristic
84C4×C43—21no—
85C4×C43—21no—
86C4×C43—42no—
87C4×C43—41no—
88C4×C43—41no—
89Dic43—22no—
90Dic43—41no—
91Dic43—41no—
92Dic43—41no—
93Dic43—81no—
94#1611—431nomaximal, Sylow
95C2×C43—21no—
96C2×C43—21no—
97C2×C43#44811yescharacteristic
98C2×C43#45611yescharacteristic
99C2×C43#45811yescharacteristic
100#544—431no—
101#483—431no—
102#483—431no—
103#398—431no—
104#328—431no—
105#328D4311yescharacteristic
106#324—431no—
107C43#161111yescharacteristic, complemented, Sylow
108C4⋊Q8—861no—
109C4⋊Q8—861no—
110#125—861no—
111#125—861no—
112C22⋊Q8—431no—
113C22⋊Q8—861no—
114C22⋊Q8C2×D4311yescharacteristic
115#117—861no—
116C2×C4⋊C4—431no—
117C2×C4⋊C4—431no—
118C2×C4⋊C4—861no—
119#106—861no—
120#106—861no—
121#103—861no—
122#103—861no—
123C22⋊C8—431no—
124C22⋊C8C2×D4311yescharacteristic
125#95—861no—
126#95C2×D4311yescharacteristic
127C2×Q8—431no—
128C2×Q8—861no—
129C2×Q8D17211yescharacteristic
130C22×C4—21no—
131C22×C4—431no—
132C22×C4—431no—
133C22×C4—861no—
134C22×C4C22×D4311yescharacteristic
135C2×C8—21no—
136C2×C8—861no—
137C4⋊C4—21no—
138C4⋊C4—431no—
139C4⋊C4—861no—
140C4⋊C4—861no—
141C4⋊C4—861no—
142C4⋊C4—861no—
143C4⋊C4—861no—
144C4⋊C4—861no—
145C4⋊C4—861no—
146C4⋊C4—861no—
147C4⋊C4—861no—
148C4⋊C4—861no—
149C4⋊C4—1722no—
150C4⋊C4D17211yescharacteristic
151C22⋊C4—21no—
152C22⋊C4—861no—
153C42—861no—
154C42—861no—
155C23D4×D4311yescharacteristic
156Q8—41no—
157Q8—3441no—
158Q8—1721no—
159C2×C4—22no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—432no—
166C2×C4—861no—
167C2×C4—861no—
168C2×C4—861no—
169C2×C4—861no—
170C2×C4—861no—
171C2×C4—1721no—
172C2×C4—1721no—
173C2×C4—1721no—
174C2×C4—1721no—
175C2×C4C2×D17211yescharacteristic
176C2×C4D4×D4311yescharacteristic
177C8—41no—
178C8—1721no—
179C22—21no—
180C22—21no—
181C22#1306329511yescharacteristic
182C22SD16×D4311yescharacteristic
183C22#1306335711yescharacteristic
184C4—21no—
185C4—21no—
186C4—42no—
187C4—41no—
188C4—41no—
189C4—862no—
190C4—3441no—
191C4—1721no—
192C4—1721no—
193C4—1721no—
194C2—21no—
195C2—21no—
196C2#1458303911yescharacteristic
197C2#1458308311yescharacteristic
198C2#1458309011yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#328C2
socleC22×C43#120
hypercenter#328D43
hypocenterC43#1611
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
107. C43#1611semidirect