Finite Group Databasebeta

← #16855964

Subgroups — #16855964

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#14521661C211yesmaximal, characteristic, complemented
2#14521523C211yesmaximal, characteristic
3#14521391C212yesmaximal, complemented
4#14521350C212yesmaximal, complemented
5#14521255C212yesmaximal, complemented
6#14521202C212yesmaximal
7#14521151C212yesmaximal, complemented
8C4×#92470C212yesmaximal, complemented
9C31×#433C211yesmaximal, characteristic, complemented
10C22×D124C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758503C2211yescharacteristic
13#11758501C2212yes—
14C2×#92470C2212yes—
15C2×#92470C2212yes—
16#11758470—22no—
17#11758466—22no—
18C22⋊C4×D31—22no—
19#11758456—22no—
20C4×D124C2212yes—
21C4×D124C2212yes—
22#11758447C2211yescharacteristic, complemented
23#11758446C2211yescharacteristic, complemented
24C4×Dic62C2212yescomplemented
25C31×C4⋊C8C2212yescomplemented
26C31×C22⋊C8C2212yes—
27C31×#97C2211yescharacteristic, complemented
28C4×C8×C31C2211yescharacteristic, complemented
29#11758409C2212yes—
30#11758409C2212yes—
31#11758406C2212yescomplemented
32#11758405C2212yescomplemented
33#11758404C2212yescomplemented
34#11758404C2212yescomplemented
35C23×D31—21no—
36C22×C4×C31C2311yescharacteristic
37C2×D124—21no—
38C2×D124—24no—
39C2×D124C2312yes—
40C2×C4×D31—22no—
41C2×C4×D31—22no—
42C2×Dic62C2312yes—
43C2×C8×C31C2312yes—
44C2×C8×C31C2312yes—
45C4⋊C4×C31D412yes—
46C22⋊C4×C31D412yes—
47C42×C31C2311yescharacteristic
48C42×C31C2311yescharacteristic
49C22⋊Dic31—22no—
50C22⋊Dic31—21no—
51(C2×D31)⋊C4—22no—
52(C2×D31)⋊C4—22no—
53C4⋊Dic31—22no—
54C4⋊Dic31C2312yes—
55C4⋊Dic31C2312yes—
56Dic31⋊C4—22no—
57Dic31⋊C4—22no—
58Dic31⋊C4—22no—
59C4×Dic31—22no—
60C4×Dic31—21no—
61#92470—24no—
62#92470—24no—
63C23×C31C2×D411yescharacteristic
64C22×D31—22no—
65C22×D31—24no—
66C22×D31—82no—
67C2×C4×C31—22no—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D412yes—
70C2×C4×C31C2×D412yes—
71C2×C4×C31C2411yescharacteristic
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75D124—24no—
76D124—22no—
77D124#4114yes—
78C4×D31—82no—
79C4×D31—82no—
80Dic62—22no—
81Dic62—22no—
82C8×C31—22no—
83C8×C31—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×C31C2×#4112yes—
96Dic31—42no—
97Dic31—42no—
98Dic31—42no—
99#541—311no—
100#518—311no—
101#485—312no—
102#478—312no—
103#461—312no—
104#450—312no—
105#440—312no—
106C4×SD16—312no—
107#433D3111yescharacteristic, complemented
108C2×C31—41no—
109C2×C31#52511yescharacteristic
110C2×C31#57712yes—
111D31—44no—
112C22×D4—311no—
113C2×SD16—312no—
114C2×SD16—312no—
115C4⋊Q8—311no—
116#126—622no—
117#125—311no—
118#125—622no—
119C22⋊Q8—312no—
120C4×Q8—312no—
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⋊C8C2×D3112yescomplemented
130#103—312no—
131#103—312no—
132#102—312no—
133#102—312no—
134C22⋊C8C2×D3112yes—
135#97C2×D3111yescharacteristic, complemented
136C4×C8C2×D3111yescharacteristic, complemented
137C31#312311yescharacteristic, complemented, Sylow
138C24—621no—
139C2×Q8—312no—
140C2×D4—312no—
141C2×D4—624no—
142C2×D4—621no—
143C22×C4—622no—
144C22×C4—622no—
145C22×C4C22×D3111yescharacteristic
146SD16—624no—
147SD16—624no—
148C2×C8C22×D3112yes—
149C2×C8C22×D3112yes—
150C4⋊C4—312no—
151C4⋊C4—312no—
152C4⋊C4—622no—
153C4⋊C4—622no—
154C4⋊C4—622no—
155C4⋊C4—622no—
156C4⋊C4D12412yes—
157C22⋊C4—621no—
158C22⋊C4—622no—
159C22⋊C4—622no—
160C22⋊C4—622no—
161C22⋊C4D12412yes—
162C42—621no—
163C42—622no—
164C42C22×D3111yescharacteristic
165C42C22×D3111yescharacteristic
166C23—624no—
167C23—622no—
168C23—2482no—
169C23C2×D12411yescharacteristic
170Q8—622no—
171Q8—622no—
172D4—314no—
173D4—624no—
174D4—622no—
175C2×C4—22no—
176C2×C4—622no—
177C2×C4—622no—
178C2×C4—622no—
179C2×C4—2482no—
180C2×C4—2482no—
181C2×C4C2×D12412yes—
182C2×C4C2×D12411yescharacteristic
183C2×C4C2×D12412yes—
184C2×C4C23×D3111yescharacteristic
185C8—22no—
186C8—22no—
187C22—22no—
188C22—21no—
189C22—624no—
190C22—1242no—
191C22—1242no—
192C22—2484no—
193C22C22×D12411yescharacteristic
194C4—22no—
195C4—22no—
196C4—21no—
197C4—1242no—
198C4—1242no—
199C4—1242no—
200C4#41×D3112yes—
201C2—41no—
202C2—1244no—
203C2#1452156111yescharacteristic
204C2#1452186112yes—
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#433C2
socleC22×C31C22×D4
prime radicalC22×D124C22
hypercenter#433D31
hypocenterC31#3123
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #14521661C2semidirect
3. #14521391C2semidirect
4. #14521350C2semidirect
5. #14521255C2semidirect
7. #14521151C2semidirect
8. C4×#92470C2semidirect
9. C31×#433C2semidirect
22. #11758447C22semidirect
23. #11758446C22semidirect
24. C4×Dic62C22semidirect
25. C31×C4⋊C8C22semidirect
27. C31×#97C22semidirect
28. C4×C8×C31C22semidirect
31. #11758406C22semidirect
32. #11758405C22semidirect
33. #11758404C22semidirect
34. #11758404C22semidirect
107. #433D31semidirect
129. C4⋊C8C2×D31semidirect
135. #97C2×D31semidirect
136. C4×C8C2×D31semidirect
137. C31#3123semidirect

Maximal subgroups

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

subgroupindex
#145216612
#145215232
#145213912
#145213502
#145212552
#145212022
#145211512
C4×#924702
C31×#4332
#312331