Finite Group Databasebeta

← #16847723

Subgroups — #16847723

Order 3968.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#14521799C211yesmaximal, characteristic, complemented
2#14521239C212yesmaximal
3#14520844C211yesmaximal, characteristic, complemented
4#14520840C212yesmaximal, complemented
5C31×#455C211yesmaximal, characteristic
6C31×H(5,𝔽2)C2211yescharacteristic
7C31×#137—21no—
8C31×#124C2211yescharacteristic
9#11758521—21no—
10#11758512—22no—
11#11758512C2212yes—
12#11758456—22no—
13#11758455—22no—
14#11758447—21no—
15C31×#104—21no—
16C31×#100C2211yescharacteristic
17#11758422—22no—
18#11758422C2212yes—
19#41×C31—21no—
20#41×C31—41no—
21C2×Q8×C31D411yescharacteristic
22C2×D4×C31—22no—
23C2×D4×C31—41no—
24C2×D4×C31C2311yescharacteristic
25C22×Dic31D412yes—
26C2×Dic62—21no—
27Q16×C31—41no—
28SD16×C31—41no—
29M16×C31—21no—
30C22⋊C4×C31—22no—
31C42×C31D411yescharacteristic
32C22⋊Dic31—22no—
33C22⋊Dic31—22no—
34C22⋊Dic31—42no—
35C22⋊Dic31D412yes—
36C4⋊Dic31—21no—
37C4⋊Dic31—21no—
38Dic31⋊C4—22no—
39Dic31⋊C4—22no—
40Dic31⋊C4—22no—
41Dic31⋊C4—42no—
42C4×Dic31—21no—
43C23×C31—22no—
44C23×C31C2×D412yes—
45Q8×C31—21no—
46Q8×C31—41no—
47D4×C31—21no—
48D4×C31—41no—
49D4×C31—42no—
50D4×C31—41no—
51C2×C4×C31—22no—
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31—41no—
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31—22no—
57C2×Dic31—22no—
58C2×Dic31—42no—
59C2×Dic31—42no—
60Dic62—81no—
61C8×C31—41no—
62#2201—311nomaximal, Sylow
63C22×C31—22no—
64C22×C31—42no—
65C22×C31—41no—
66C22×C31—82no—
67C22×C31#12011yescharacteristic
68C4×C31—21no—
69C4×C31—41no—
70C4×C31—41no—
71C4×C31—41no—
72Dic31—42no—
73Dic31—42no—
74Dic31—82no—
75#563—311no—
76#458—312no—
77#455D3111yescharacteristic
78#354—311no—
79#352—312no—
80C2×C31—21no—
81C2×C31—42no—
82C2×C31—81no—
83C2×C31B(4,𝔽2)11yescharacteristic
84H(5,𝔽2)C2×D3111yescharacteristic
85#137—21no—
86C4⋊Q8—621no—
87#126—622no—
88#125—621no—
89#124C2×D3111yescharacteristic
90#123—312no—
91#123—622no—
92C22⋊Q8—622no—
93#104—21no—
94#100C2×D3111yescharacteristic
95#99—312no—
96#99—622no—
97C31#220111yescharacteristic, complemented, Sylow
98#41—21no—
99#41—41no—
100C2×Q8—621no—
101C2×Q8C22⋊D3111yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D3111yescharacteristic
105C22×C4—312no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—622no—
110C4⋊C4—622no—
111C4⋊C4—621no—
112C4⋊C4—621no—
113C4⋊C4—622no—
114C4⋊C4—1242no—
115C22⋊C4—22no—
116C22⋊C4—312no—
117C22⋊C4—622no—
118C22⋊C4—622no—
119C22⋊C4—1242no—
120C42—621no—
121C42C22⋊D3111yescharacteristic
122C23—22no—
123C23D4×D3112yes—
124Q8—21no—
125Q8—41no—
126Q8—2481no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—622no—
136C2×C4—622no—
137C2×C4—1242no—
138C2×C4—1242no—
139C2×C4C2×C22⋊D3111yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1175851411yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—1242no—
151C4—1242no—
152C4—2482no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#1452123511yescharacteristic
subgroupG/H
centerC2#14521235
commutator, cosocleC2×D4×C31C23
FrattiniC2×D4C22×D31
FittingC31×#455C2
socleC2×C31B(4,𝔽2)
prime radicalC31×H(5,𝔽2)C22
hypercenter#455D31
hypocenterC31#2201
LCSG ▷ C2×D4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14521799C2semidirect
3. #14520844C2semidirect
4. #14520840C2semidirect
97. C31#2201semidirect

Maximal subgroups

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

subgroupindex
#145217992
#145212392
#145208442
#145208402
C31×#4552
#220131