Finite Group Databasebeta

← #16855949

Subgroups — #16855949

Order 3968.

418 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 121 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#14521523C211yesmaximal, characteristic, complemented
2#14521370C212yesmaximal, complemented
3#14521346C212yesmaximal, complemented
4#14521241C212yesmaximal, complemented
5#14521182C212yesmaximal, complemented
6#14521159C212yesmaximal, complemented
7C4×#92479C212yesmaximal, complemented
8#14521110C211yesmaximal, characteristic, complemented
9C31×#540C211yesmaximal, characteristic, complemented
10C22×D124C2211yescharacteristic
11C31×#127C2211yescharacteristic, complemented
12C31×#125C2211yescharacteristic, complemented
13C31×#123—22no—
14C31×#121—22no—
15C31×#121C2212yes—
16C4×D4×C31C2212yescomplemented
17C31×#117C2211yescharacteristic
18C2×#92479C2212yes—
19C2×#92479C2212yes—
20#11758503C2211yescharacteristic
21#11758470—22no—
22C22⋊C4×D31—22no—
23C4×D124C2212yes—
24C4×D124C2212yes—
25#11758420C2212yescomplemented
26#11758420C2212yescomplemented
27C22⋊(C31⋊C8)C2212yes—
28#11758397C2212yes—
29#11758397C2212yes—
30#11758396C2212yescomplemented
31#11758395C2212yescomplemented
32C4⋊(C31⋊C8)C2212yescomplemented
33#11758391C2211yescharacteristic, complemented
34C4×C31⋊C8C2211yescharacteristic, complemented
35C23×D31—21no—
36C2×D4×C31—22no—
37C2×D4×C31—22no—
38C2×D4×C31C2312yes—
39C22×C4×C31—22no—
40C22×C4×C31C2311yescharacteristic
41C2×D124—21no—
42C2×D124—24no—
43C2×D124C2312yes—
44C2×C4×D31—22no—
45C2×C4×D31—22no—
46C4⋊C4×C31—22no—
47C4⋊C4×C31D412yes—
48C4⋊C4×C31C2312yes—
49C22⋊C4×C31—22no—
50C22⋊C4×C31—22no—
51C22⋊C4×C31D412yes—
52C42×C31C2311yescharacteristic
53C42×C31C2311yescharacteristic
54C22⋊Dic31—21no—
55#92479—24no—
56#92479—24no—
57(C2×D31)⋊C4—22no—
58(C2×D31)⋊C4—22no—
59C4⋊Dic31C2312yes—
60C4×Dic31—21no—
61C2×C31⋊C8C2312yes—
62C2×C31⋊C8C2312yes—
63C23×C31—22no—
64C23×C31C2×D411yescharacteristic
65C22×D31—22no—
66C22×D31—24no—
67C22×D31—82no—
68D4×C31—22no—
69D4×C31—22no—
70D4×C31—82no—
71D4×C31—82no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—82no—
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×D412yes—
77C2×C4×C31C2×D412yes—
78C2×C4×C31C2411yescharacteristic
79C2×Dic31—22no—
80D124—24no—
81D124—22no—
82D124#4114yes—
83C4×D31—82no—
84C4×D31—82no—
85C31⋊C8—22no—
86C31⋊C8—22no—
87#3122—311nomaximal, Sylow
88C22×C31—21no—
89C22×C31—22no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31—42no—
93C22×C31C22×D411yescharacteristic
94C2×D31—24no—
95C2×D31—42no—
96C2×D31—42no—
97C2×D31—84no—
98C4×C31—21no—
99C4×C31—22no—
100C4×C31—22no—
101C4×C31—42no—
102C4×C31C2×#4112yes—
103Dic31—42no—
104#540D3111yescharacteristic, complemented
105#518—311no—
106#482—312no—
107#478—312no—
108#459—312no—
109#447—312no—
110#442—312no—
111C4×D8—312no—
112#433—311no—
113C2×C31—41no—
114C2×C31—82no—
115C2×C31#52511yescharacteristic
116C2×C31#57612yes—
117D31—44no—
118C22×D4—311no—
119C2×D8—312no—
120C2×D8—312no—
121#127C2×D3111yescharacteristic, complemented
122#125C2×D3111yescharacteristic, complemented
123#123—22no—
124#121—22no—
125#121C2×D3112yes—
126C4×D4—312no—
127C4×D4—312no—
128C4×D4—622no—
129C4×D4C2×D3112yescomplemented
130#117—311no—
131#117C2×D3111yescharacteristic
132C2×C22⋊C4—622no—
133#107—312no—
134#106—312no—
135C4⋊C8—312no—
136#102—312no—
137#102—312no—
138#102—312no—
139#102—312no—
140C22⋊C8—312no—
141#97—311no—
142C4×C8—311no—
143C31#312211yescharacteristic, complemented, Sylow
144C24—621no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—312no—
148C2×D4—624no—
149C2×D4—621no—
150C2×D4C22×D3112yes—
151C22×C4—22no—
152C22×C4—622no—
153C22×C4—622no—
154C22×C4C22×D3111yescharacteristic
155D8—624no—
156D8—624no—
157C2×C8—312no—
158C2×C8—312no—
159C4⋊C4—22no—
160C4⋊C4—312no—
161C4⋊C4C22⋊D3112yes—
162C4⋊C4C22×D3112yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—621no—
166C22⋊C4—622no—
167C22⋊C4—622no—
168C22⋊C4C22⋊D3112yes—
169C42—621no—
170C42C22×D3111yescharacteristic
171C42C22×D3111yescharacteristic
172C23—22no—
173C23—624no—
174C23—622no—
175C23—2482no—
176C23C2×C22⋊D3111yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—314no—
182D4—624no—
183D4—622no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—622no—
188C2×C4—2482no—
189C2×C4—2482no—
190C2×C4C2×C22⋊D3111yescharacteristic
191C2×C4C2×C22⋊D3112yes—
192C2×C4C2×C22⋊D3112yes—
193C2×C4C23×D3111yescharacteristic
194C8—622no—
195C8—622no—
196C22—21no—
197C22—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—624no—
202C22—1242no—
203C22—1242no—
204C22—2484no—
205C22C22×C22⋊D3111yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1242no—
211C4#41×D3112yes—
212C2—41no—
213C2—82no—
214C2—1244no—
215C2#1452155611yescharacteristic
216C2#1452185212yes—
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#540C2
socleC22×C31C22×D4
hypercenter#540D31
hypocenterC31#3122
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #14521523C2semidirect
2. #14521370C2semidirect
3. #14521346C2semidirect
4. #14521241C2semidirect
5. #14521182C2semidirect
6. #14521159C2semidirect
7. C4×#92479C2semidirect
8. #14521110C2semidirect
9. C31×#540C2semidirect
11. C31×#127C22semidirect
12. C31×#125C22semidirect
16. C4×D4×C31C22semidirect
25. #11758420C22semidirect
26. #11758420C22semidirect
30. #11758396C22semidirect
31. #11758395C22semidirect
32. C4⋊(C31⋊C8)C22semidirect
33. #11758391C22semidirect
34. C4×C31⋊C8C22semidirect
104. #540D31semidirect
121. #127C2×D31semidirect
122. #125C2×D31semidirect
129. C4×D4C2×D31semidirect
143. C31#3122semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#145215232
#145213702
#145213462
#145212412
#145211822
#145211592
C4×#924792
#145211102
C31×#5402
#312231