Finite Group Databasebeta

← #16856003

Subgroups — #16856003

Order 3968.

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

normal subgroups only

This group has 382 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#14521654C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic, complemented
3#14521374C212yesmaximal, complemented
4#14521357C212yesmaximal, complemented
5#14521250C212yesmaximal, complemented
6#14521190C212yesmaximal, complemented
7#14521151C212yesmaximal, complemented
8C4×#92470C212yesmaximal, complemented
9C31×#433C211yesmaximal, characteristic, complemented
10C22×Dic62C2211yescharacteristic
11C31×#117C2211yescharacteristic
12#11758507C2212yes—
13#11758503C2211yescharacteristic
14C2×#92470C2212yes—
15C2×#92470C2212yes—
16#11758471—22no—
17#11758464—22no—
18#11758461—22no—
19#11758454—22no—
20#11758451C2211yescharacteristic
21C4×D124C2212yes—
22#11758447C2211yescharacteristic
23C4×Dic62C2212yes—
24C4×Dic62C2212yes—
25C31×C4⋊C8C2212yes—
26C31×C22⋊C8C2212yes—
27C31×#97C2211yescharacteristic
28C4×C8×C31C2211yescharacteristic
29#11758409C2212yes—
30#11758409C2212yes—
31#11758406C2212yes—
32#11758405C2212yes—
33#11758404C2212yes—
34#11758404C2212yes—
35C22×C4×C31C2311yescharacteristic
36C2×C22⋊D31—22no—
37C22×Dic31—21no—
38C2×D124—22no—
39C2×D124C2312yes—
40C2×C4×D31—22no—
41C2×Dic62—21no—
42C2×Dic62—24no—
43C2×Dic62C2312yes—
44C2×C8×C31C2312yes—
45C2×C8×C31C2312yes—
46C4⋊C4×C31D412yes—
47C22⋊C4×C31D412yes—
48C42×C31C2311yescharacteristic
49C42×C31C2311yescharacteristic
50C22⋊Dic31—21no—
51(C2×D31)⋊C4—22no—
52(C2×D31)⋊C4—22no—
53C4⋊Dic31C2312yes—
54C4⋊Dic31C2312yes—
55Dic31⋊C4—22no—
56Dic31⋊C4—22no—
57Dic31⋊C4—22no—
58C4×Dic31—22no—
59C4×Dic31—22no—
60C4×Dic31—21no—
61#92470—24no—
62#92470—24no—
63C23×C31C2×D411yescharacteristic
64C22×D31—22no—
65C2×C4×C31—22no—
66C2×C4×C31C2×D412yes—
67C2×C4×C31C2×D412yes—
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2411yescharacteristic
70C22⋊D31—82no—
71C2×Dic31—24no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75D124—22no—
76D124—22no—
77D124—82no—
78C4×D31—82no—
79Dic62—24no—
80Dic62—22no—
81Dic62#4114yes—
82C8×C31—22no—
83C8×C31—22no—
84#3126—311nomaximal, Sylow
85C22×C31—21no—
86C22×C31—22no—
87C22×C31C22×D411yescharacteristic
88C2×D31—42no—
89C2×D31—42no—
90C2×D31—42no—
91C4×C31—21no—
92C4×C31—22no—
93C4×C31—22no—
94C4×C31C2×#4112yes—
95Dic31—24no—
96Dic31—42no—
97Dic31—42no—
98#540—311no—
99#519—311no—
100#482—312no—
101#479—312no—
102#460—312no—
103#448—312no—
104#440—312no—
105C4×SD16—312no—
106#433D3111yescharacteristic, complemented
107C2×C31—41no—
108C2×C31#52511yescharacteristic
109C2×C31#57712yes—
110D31—82no—
111C22×Q8—311no—
112C2×SD16—312no—
113C2×SD16—312no—
114#127—311no—
115#125—311no—
116#123—622no—
117#121—312no—
118#121—622no—
119C4×Q8—312no—
120C4×Q8—312no—
121C4×Q8—622no—
122C4×D4—312no—
123#117—311no—
124#117—622no—
125#117C2×D3111yescharacteristic
126#107—312no—
127#106—312no—
128C4⋊C8C2×D3112yes—
129#103—312no—
130#103—312no—
131#102—312no—
132#102—312no—
133C22⋊C8C2×D3112yes—
134#97C2×D3111yescharacteristic
135C4×C8C2×D3111yescharacteristic
136C31#312611yescharacteristic, complemented, Sylow
137C2×Q8—312no—
138C2×Q8—624no—
139C2×Q8—621no—
140C2×D4—312no—
141C2×D4—622no—
142C2×D4—622no—
143C22×C4—621no—
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⋊C4D12412yes—
156C22⋊C4—621no—
157C22⋊C4—622no—
158C22⋊C4—622no—
159C22⋊C4D12412yes—
160C42—621no—
161C42—622no—
162C42—622no—
163C42C22×D3111yescharacteristic
164C42C22×D3111yescharacteristic
165C23—622no—
166C23C2×D12411yescharacteristic
167Q8—314no—
168Q8—624no—
169Q8—622no—
170D4—622no—
171D4—622no—
172D4—2482no—
173D4—2482no—
174C2×C4—22no—
175C2×C4—624no—
176C2×C4—622no—
177C2×C4—622no—
178C2×C4—622no—
179C2×C4—2482no—
180C2×C4C2×D12412yes—
181C2×C4C2×D12412yes—
182C2×C4C2×D12411yescharacteristic
183C2×C4C23×D3111yescharacteristic
184C8—22no—
185C8—22no—
186C22—22no—
187C22—21no—
188C22—1242no—
189C22—1242no—
190C22—1242no—
191C22C22×D12411yescharacteristic
192C4—22no—
193C4—22no—
194C4—21no—
195C4—624no—
196C4—1242no—
197C4—1242no—
198C4#41×D3112yes—
199C2—41no—
200C2—2482no—
201C2#1452156111yescharacteristic
202C2#1452186112yes—
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#433C2
socleC22×C31C22×D4
prime radical#14521654C2
hypercenter#433D31
hypocenterC31#3126
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
2. #14521526C2semidirect
3. #14521374C2semidirect
4. #14521357C2semidirect
5. #14521250C2semidirect
6. #14521190C2semidirect
7. #14521151C2semidirect
8. C4×#92470C2semidirect
9. C31×#433C2semidirect
106. #433D31semidirect
136. C31#3126semidirect

Maximal subgroups

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

subgroupindex
#145216542
#145215262
#145213742
#145213572
#145212502
#145211902
#145211512
C4×#924702
C31×#4332
#312631