Finite Group Databasebeta

← #16855958

Subgroups — #16855958

Order 3968.

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

normal subgroups only

This group has 394 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
2#14521387C212yesmaximal, complemented
3#14521346C212yesmaximal, complemented
4#14521251C212yesmaximal, complemented
5#14521199C212yesmaximal
6#14521147C212yesmaximal, complemented
7C4×#92481C212yesmaximal, complemented
8#14521110C211yesmaximal, characteristic, complemented
9C31×#541C211yesmaximal, characteristic, complemented
10C22×D124C2211yescharacteristic
11C31×C4⋊Q8C2211yescharacteristic, complemented
12C31×#126—22no—
13C31×#125—22no—
14C31×#125C2211yescharacteristic, complemented
15C31×C22⋊Q8C2212yes—
16C4×Q8×C31C2212yescomplemented
17C31×#117C2211yescharacteristic
18C2×#92481C2212yes—
19C2×#92481C2212yes—
20#11758503C2211yescharacteristic
21#11758470—22no—
22C22⋊C4×D31—22no—
23C4×D124C2212yes—
24C4×D124C2212yes—
25#11758423C2212yescomplemented
26#11758423C2212yescomplemented
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×Q8×C31C2312yes—
37C22×C4×C31C2311yescharacteristic
38C2×D124—21no—
39C2×D124—24no—
40C2×D124C2312yes—
41C2×C4×D31—22no—
42C2×C4×D31—22no—
43C4⋊C4×C31—22no—
44C4⋊C4×C31—22no—
45C4⋊C4×C31—22no—
46C4⋊C4×C31—22no—
47C4⋊C4×C31D412yes—
48C4⋊C4×C31C2312yes—
49C22⋊C4×C31—22no—
50C22⋊C4×C31D412yes—
51C42×C31—22no—
52C42×C31C2311yescharacteristic
53C42×C31C2311yescharacteristic
54C22⋊Dic31—21no—
55#92481—24no—
56#92481—24no—
57(C2×D31)⋊C4—22no—
58(C2×D31)⋊C4—22no—
59C4⋊Dic31C2312yes—
60C4×Dic31—21no—
61C2×C31⋊C8C2312yes—
62C2×C31⋊C8C2312yes—
63C23×C31C2×D411yescharacteristic
64C22×D31—22no—
65C22×D31—24no—
66C22×D31—82no—
67Q8×C31—22no—
68Q8×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D412yes—
74C2×C4×C31C2×D412yes—
75C2×C4×C31C2411yescharacteristic
76C2×Dic31—22no—
77D124—24no—
78D124—22no—
79D124#4114yes—
80C4×D31—82no—
81C4×D31—82no—
82C31⋊C8—22no—
83C31⋊C8—22no—
84#3123—311nomaximal, Sylow
85C22×C31—21no—
86C22×C31—22no—
87C22×C31C22×D411yescharacteristic
88C2×D31—24no—
89C2×D31—42no—
90C2×D31—42no—
91C2×D31—84no—
92C4×C31—21no—
93C4×C31—22no—
94C4×C31—22no—
95C4×C31—42no—
96C4×C31—42no—
97C4×C31C2×#4112yes—
98Dic31—42no—
99#541D3111yescharacteristic, complemented
100#518—311no—
101#485—312no—
102#478—312no—
103#461—312no—
104#450—312no—
105#440—312no—
106C4×SD16—312no—
107#433—311no—
108C2×C31—41no—
109C2×C31#52511yescharacteristic
110C2×C31#57712yes—
111D31—44no—
112C22×D4—311no—
113C2×SD16—312no—
114C2×SD16—312no—
115C4⋊Q8C2×D3111yescharacteristic, complemented
116#126—22no—
117#125—22no—
118#125C2×D3111yescharacteristic, complemented
119C22⋊Q8C2×D3112yes—
120C4×Q8C2×D3112yescomplemented
121C4×D4—312no—
122C4×D4—312no—
123C4×D4—622no—
124#117—311no—
125#117C2×D3111yescharacteristic
126C2×C22⋊C4—622no—
127#107—312no—
128#106—312no—
129C4⋊C8—312no—
130#103—312no—
131#103—312no—
132#102—312no—
133#102—312no—
134C22⋊C8—312no—
135#97—311no—
136C4×C8—311no—
137C31#312311yescharacteristic, complemented, Sylow
138C24—621no—
139C2×Q8C22×D3112yes—
140C2×D4—312no—
141C2×D4—624no—
142C2×D4—621no—
143C22×C4—622no—
144C22×C4—622no—
145C22×C4C22×D3111yescharacteristic
146SD16—624no—
147SD16—624no—
148C2×C8—312no—
149C2×C8—312no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—312no—
155C4⋊C4C22⋊D3112yes—
156C4⋊C4C22×D3112yes—
157C22⋊C4—22no—
158C22⋊C4—621no—
159C22⋊C4—622no—
160C22⋊C4—622no—
161C22⋊C4C22⋊D3112yes—
162C42—22no—
163C42—621no—
164C42C22×D3111yescharacteristic
165C42C22×D3111yescharacteristic
166C23—624no—
167C23—622no—
168C23—2482no—
169C23C2×C22⋊D3111yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—314no—
173D4—624no—
174D4—622no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—622no—
179C2×C4—2482no—
180C2×C4—2482no—
181C2×C4C2×C22⋊D3112yes—
182C2×C4C2×C22⋊D3111yescharacteristic
183C2×C4C2×C22⋊D3112yes—
184C2×C4C23×D3111yescharacteristic
185C8—622no—
186C8—622no—
187C22—22no—
188C22—21no—
189C22—624no—
190C22—1242no—
191C22—1242no—
192C22—2484no—
193C22C22×C22⋊D3111yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—42no—
198C4—42no—
199C4—1242no—
200C4#41×D3112yes—
201C2—41no—
202C2—1244no—
203C2#1452155611yescharacteristic
204C2#1452185712yes—
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#541C2
socleC22×C31C22×D4
prime radicalC22×D124C22
hypercenter#541D31
hypocenterC31#3123
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #14521387C2semidirect
3. #14521346C2semidirect
4. #14521251C2semidirect
6. #14521147C2semidirect
7. C4×#92481C2semidirect
8. #14521110C2semidirect
9. C31×#541C2semidirect
11. C31×C4⋊Q8C22semidirect
14. C31×#125C22semidirect
16. C4×Q8×C31C22semidirect
25. #11758423C22semidirect
26. #11758423C22semidirect
30. #11758396C22semidirect
31. #11758395C22semidirect
32. C4⋊(C31⋊C8)C22semidirect
33. #11758391C22semidirect
34. C4×C31⋊C8C22semidirect
99. #541D31semidirect
115. C4⋊Q8C2×D31semidirect
118. #125C2×D31semidirect
120. C4×Q8C2×D31semidirect
137. C31#3123semidirect

Maximal subgroups

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

subgroupindex
#145215232
#145213872
#145213462
#145212512
#145211992
#145211472
C4×#924812
#145211102
C31×#5412
#312331