Finite Group Databasebeta

← #16858797

Subgroups — #16858797

Order 3968.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#14521782C212yesmaximal, complemented
2#14521437C212yesmaximal, complemented
3#14521433C211yesmaximal, characteristic, complemented
4#14521270C212yesmaximal, complemented
5#14521264C212yesmaximal, complemented
6#14521243C212yesmaximal, complemented
7#14521179C211yesmaximal, characteristic, complemented
8#14521148C212yesmaximal, complemented
9C4×D8×C31C211yesmaximal, characteristic, complemented
10C2×D8×C31C2211yescharacteristic
11C4×D4×C31C2212yes—
12#11758517C2212yes—
13#11758513C2212yes—
14C2×#92480C2212yes—
15C2×#92479C2212yes—
16#11758506—22no—
17C4×C22⋊D31—22no—
18C2×Dic124C2211yescharacteristic
19C2×D248C2211yescharacteristic
20C2×#92470C2212yes—
21#11758470C2212yes—
22#11758464C2212yes—
23#11758462—22no—
24#11758460—22no—
25#11758452C2212yes—
26C4×Dic62C2211yescharacteristic
27C31×#107C2211yescharacteristic
28C31×#102C2212yes—
29C4×C8×C31C2211yescharacteristic
30#11758403C2212yes—
31Dic31⋊C8C2212yes—
32#11758398C2212yes—
33#11758397C2212yes—
34C4⋊(C31⋊C8)C2211yescharacteristic
35C2×D4×C31C2312yes—
36C22×C4×C31—22no—
37C2×C22⋊D31—22no—
38C2×C22⋊D31—22no—
39C2×D124C2312yes—
40C2×C4×D31—22no—
41C2×Dic62D411yescharacteristic
42C2×Dic62C2312yes—
43D8×C31—22no—
44C2×C8×C31C2311yescharacteristic
45C2×C8×C31C2311yescharacteristic
46C4⋊C4×C31C2312yes—
47C22⋊C4×C31—22no—
48C42×C31C2311yescharacteristic
49C22⋊Dic31—22no—
50C22⋊Dic31—22no—
51#92480—42no—
52#92479—42no—
53(C2×D31)⋊C4—22no—
54(C2×D31)⋊C4—22no—
55(C2×D31)⋊C4—22no—
56C4⋊Dic31D411yescharacteristic
57Dic31⋊C4—22no—
58Dic31⋊C4D412yes—
59C4×Dic31—22no—
60C4×Dic31C2312yes—
61C2×C31⋊C8C2312yes—
62Dic124—41no—
63D248—41no—
64#92470—24no—
65C23×C31—22no—
66C22×D31—22no—
67D4×C31—22no—
68D4×C31—22no—
69C2×C4×C31—22no—
70C2×C4×C31—82no—
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2411yescharacteristic
74C22⋊D31—44no—
75C22⋊D31—82no—
76C2×Dic31—22no—
77C2×Dic31C2×D412yes—
78C2×Dic31C2×D412yes—
79D124—22no—
80D124—22no—
81C4×D31—82no—
82Dic62—22no—
83Dic62—22no—
84Dic62—41no—
85C8×C31—21no—
86C8×C31#4112yes—
87C31⋊C8—22no—
88#3403—311nomaximal, Sylow
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31C22×D411yescharacteristic
93C2×D31—42no—
94C2×D31—42no—
95C2×D31—42no—
96C4×C31—21no—
97C4×C31—21no—
98C4×C31—42no—
99C4×C31C2×#4111yescharacteristic
100C4×C31H(5,𝔽2)11yescharacteristic
101Dic31—22no—
102Dic31—22no—
103Dic31—42no—
104#559—312no—
105#496—312no—
106#495—311no—
107#464—312no—
108#463—312no—
109#459—312no—
110#446—311no—
111#440—312no—
112C4×D8D3111yescharacteristic, complemented
113C2×C31—82no—
114C2×C31#55011yescharacteristic
115C2×C31#57511yescharacteristic
116C2×C31#57611yescharacteristic
117D31—82no—
118C2×Q16—311no—
119C2×SD16—312no—
120C2×SD16—312no—
121C2×D8—312no—
122C2×D8—311no—
123C2×D8C2×D3111yescharacteristic
124#127—312no—
125#124—312no—
126#124—312no—
127#124—622no—
128#123—622no—
129#123—622no—
130C4×Q8—311no—
131C4×Q8—312no—
132C4×D4—312no—
133C4×D4—622no—
134C4×D4C2×D3112yes—
135#107C2×D3111yescharacteristic
136C4⋊C8—312no—
137C4⋊C8—311no—
138#103—312no—
139#102—312no—
140#102C2×D3112yes—
141#97—312no—
142C4×C8C2×D3111yescharacteristic
143C31#340311yescharacteristic, complemented, Sylow
144C2×Q8—311no—
145C2×Q8—312no—
146C2×D4—312no—
147C2×D4—622no—
148C2×D4—622no—
149C2×D4C22×D3112yes—
150C22×C4—22no—
151C22×C4—622no—
152Q16—1241no—
153SD16—624no—
154SD16—1242no—
155D8—22no—
156D8—1241no—
157D8—1242no—
158C2×C8—312no—
159C2×C8C22×D3111yescharacteristic
160C2×C8C22×D3111yescharacteristic
161C4⋊C4—312no—
162C4⋊C4—311no—
163C4⋊C4—622no—
164C4⋊C4C22×D3112yes—
165C22⋊C4—22no—
166C22⋊C4—622no—
167C22⋊C4—622no—
168C22⋊C4—622no—
169C22⋊C4—622no—
170C22⋊C4—622no—
171C42—312no—
172C42—622no—
173C42C22×D3111yescharacteristic
174C23—22no—
175C23—622no—
176Q8—622no—
177Q8—622no—
178Q8—1241no—
179D4—22no—
180D4—22no—
181D4—622no—
182D4—622no—
183D4—1244no—
184D4—2482no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—312no—
188C2×C4—312no—
189C2×C4—622no—
190C2×C4—2482no—
191C2×C4D4×D3111yescharacteristic
192C2×C4D4×D3111yescharacteristic
193C2×C4C23×D3111yescharacteristic
194C8—21no—
195C8—622no—
196C8#9249512yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—1242no—
201C22—1242no—
202C22—1242no—
203C22C2×D4×D3111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—622no—
208C4—622no—
209C4—1242no—
210C4C2×#9249511yescharacteristic
211C4#1175856611yescharacteristic
212C2—82no—
213C2—2482no—
214C2#1452172011yescharacteristic
215C2#1452184611yescharacteristic
216C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC4×D8×C31C2
socleC22×C31C22×D4
hypercenterC4×D8D31
hypocenterC31#3403
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #14521782C2semidirect
2. #14521437C2semidirect
3. #14521433C2semidirect
4. #14521270C2semidirect
5. #14521264C2semidirect
6. #14521243C2semidirect
7. #14521179C2semidirect
8. #14521148C2semidirect
9. C4×D8×C31C2semidirect
112. C4×D8D31semidirect
143. C31#3403semidirect

Maximal subgroups

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

subgroupindex
#145217822
#145214372
#145214332
#145212702
#145212642
#145212432
#145211792
#145211482
C4×D8×C312
#340331