Finite Group Databasebeta

← #19136221

Subgroups — #19136221

Order 5504.

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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#131×D43C211yesmaximal, characteristic
2C2×#13063264C211yesmaximal, characteristic, complemented
3M32×D43C211yesmaximal, characteristic, complemented
4#14582684C211yesmaximal, characteristic, complemented
5#14582683C211yesmaximal, characteristic, complemented
6#14582682C211yesmaximal, characteristic, complemented
7C43×#350C211yesmaximal, characteristic, complemented
8#41×D43C411yescharacteristic
9#13063333—21no—
10#13063333C411yescharacteristic
11#13063332C411yescharacteristic
12#13063331—21no—
13#13063331C2211yescharacteristic
14M16×D43—21no—
15M16×D43C411yescharacteristic
16C2×C8×D43—21no—
17C2×C8×D43C2211yescharacteristic
18#13063265C2211yescharacteristic, complemented
19#13063264—21no—
20#13063264—21no—
21#13063264—21no—
22C2×C43⋊C16C2211yescharacteristic, complemented
23C16×D43—21no—
24#131×C43C2211yescharacteristic
25M32×C43C2211yescharacteristic, complemented
26C2×C16×C43C2211yescharacteristic, complemented
27#41×C43C2×C411yescharacteristic
28#10621902C811yescharacteristic
29Q8×D43C811yescharacteristic
30#10621900—21no—
31#10621900C811yescharacteristic
32D4×D43—21no—
33D4×D43C811yescharacteristic
34#10621898—21no—
35#10621898C2×C411yescharacteristic
36C2×C4×D43—21no—
37C2×C4×D43C2×C411yescharacteristic
38M16×C43—21no—
39M16×C43C2×C411yescharacteristic
40C2×C8×C43—21no—
41C2×C8×C43C2311yescharacteristic
42#10621877—21no—
43#10621877C2×C411yescharacteristic
44C2×C43⋊C8—21no—
45C2×C43⋊C8C2×C411yescharacteristic
46#10621872—21no—
47#10621872—21no—
48#10621872—21no—
49C8×D43—21no—
50C8×D43—21no—
51C8×D43—21no—
52C8×D43D411yescharacteristic
53C8×D43D411yescharacteristic
54C8×D43D411yescharacteristic
55C8×D43D411yescharacteristic
56C16×C43—21no—
57C16×C43—21no—
58C43⋊C16—21no—
59C43⋊C16—21no—
60C22×D43—21no—
61C22×D43M1611yescharacteristic
62Q8×C43C2×C811yescharacteristic
63D4×C43—21no—
64D4×C43C2×C811yescharacteristic
65C2×C4×C43—21no—
66C2×C4×C43C22×C411yescharacteristic
67C22⋊D43—21no—
68C22⋊D43—21no—
69C22⋊D43—21no—
70C2×Dic43—21no—
71C2×Dic43M1611yescharacteristic
72D172—21no—
73D172C2×C811yescharacteristic
74C4×D43—21no—
75C4×D43—21no—
76C4×D43—21no—
77C4×D43C22⋊C411yescharacteristic
78C4×D43C22⋊C411yescharacteristic
79C4×D43C2×C811yescharacteristic
80C4×D43C2×C811yescharacteristic
81Dic86—21no—
82Dic86C2×C811yescharacteristic
83C8×C43—21no—
84C8×C43C2×D411yescharacteristic
85C8×C43C2×D411yescharacteristic
86C43⋊C8—21no—
87C43⋊C8C22⋊C411yescharacteristic
88C43⋊C8C22⋊C411yescharacteristic
89C22×C43—21no—
90C22×C43C2×M1611yescharacteristic
91C2×D43—21no—
92C2×D43—41no—
93C2×D43—42no—
94C2×D43C22⋊C811yescharacteristic
95C2×D43C22⋊C811yescharacteristic
96C4×C43—21no—
97C4×C43C2×C22⋊C411yescharacteristic
98C4×C43C22×C811yescharacteristic
99Dic43—21no—
100Dic43C22⋊C811yescharacteristic
101Dic43C22⋊C811yescharacteristic
102#2117—431nomaximal, Sylow
103C2×C43—21no—
104C2×C43—41no—
105C2×C43C2×C22⋊C811yescharacteristic
106D43—21no—
107D43—21no—
108D43—41no—
109C2×#131—431no—
110C2×M32—431no—
111C2×M32—431no—
112#350—431no—
113#350—431no—
114#350—431no—
115#350D4311yescharacteristic, complemented
116C43#211711yescharacteristic, complemented, Sylow
117C2×#41—431no—
118#131—431no—
119#131—431no—
120#131—431no—
121#131—861no—
122#131—861no—
123#131C2×D4311yescharacteristic
124C2×M16—431no—
125C2×M16—861no—
126C22×C8—431no—
127C22×C8—861no—
128M32—431no—
129M32—861no—
130M32—861no—
131M32—861no—
132M32C2×D4311yescharacteristic, complemented
133C2×C16—431no—
134C2×C16—861no—
135C2×C16C2×D4311yescharacteristic, complemented
136#41—431no—
137#41—431no—
138#41—431no—
139#41—861no—
140#41—861no—
141#41C4×D4311yescharacteristic
142C2×Q8—431no—
143C2×D4—431no—
144C2×D4—861no—
145C22×C4—431no—
146C22×C4—861no—
147M16—21no—
148M16—431no—
149M16—861no—
150M16—861no—
151M16—861no—
152M16—861no—
153M16C4×D4311yescharacteristic
154C2×C8—21no—
155C2×C8—431no—
156C2×C8—431no—
157C2×C8—431no—
158C2×C8—431no—
159C2×C8—431no—
160C2×C8—861no—
161C2×C8—861no—
162C2×C8—861no—
163C2×C8—861no—
164C2×C8C22×D4311yescharacteristic
165C16—21no—
166C16—21no—
167C16—861no—
168C16—861no—
169C23—431no—
170C23—861no—
171Q8—431no—
172Q8—861no—
173Q8C8×D4311yescharacteristic
174D4—21no—
175D4—431no—
176D4—861no—
177D4—861no—
178D4—861no—
179D4—861no—
180D4C8×D4311yescharacteristic
181C2×C4—21no—
182C2×C4—431no—
183C2×C4—431no—
184C2×C4—431no—
185C2×C4—431no—
186C2×C4—431no—
187C2×C4—861no—
188C2×C4—861no—
189C2×C4—861no—
190C2×C4—861no—
191C2×C4C2×C4×D4311yescharacteristic
192C8—21no—
193C8—431no—
194C8—431no—
195C8—861no—
196C8D4×D4311yescharacteristic
197C8D4×D4311yescharacteristic
198C22—21no—
199C22—431no—
200C22—431no—
201C22—861no—
202C22—1721no—
203C22—1722no—
204C22M16×D4311yescharacteristic
205C4—21no—
206C4—431no—
207C4—431no—
208C4—861no—
209C4C22⋊C4×D4311yescharacteristic
210C4C2×C8×D4311yescharacteristic
211C2—21no—
212C2—41no—
213C2—861no—
214C2—861no—
215C2—1721no—
216C2C22⋊C8×D4311yescharacteristic
subgroupG/H
centerC8D4×D43
commutatorC4×C43C22×C8
FrattiniC2×C8C22×D43
FittingC43×#350C2
socleC2×C43C2×C22⋊C8
hypercenter#350D43
hypocenterC43#2117
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. C2×#13063264C2semidirect
3. M32×D43C2semidirect
4. #14582684C2semidirect
5. #14582683C2semidirect
6. #14582682C2semidirect
7. C43×#350C2semidirect
18. #13063265C22semidirect
22. C2×C43⋊C16C22semidirect
25. M32×C43C22semidirect
26. C2×C16×C43C22semidirect
115. #350D43semidirect
116. C43#2117semidirect
132. M32C2×D43semidirect
135. C2×C16C2×D43semidirect