Finite Group Databasebeta

← #16847686

Subgroups — #16847686

Order 3968.

206 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 47 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#14521863C211yesmaximal, characteristic
2C2×#11758417C211yesmaximal, characteristic, complemented
3#14521321C211yesmaximal, characteristic, complemented
4#14520866C211yesmaximal, characteristic, complemented
5#14520856C211yesmaximal, characteristic, complemented
6#14520834C211yesmaximal, characteristic, complemented
7C31×#510C211yesmaximal, characteristic, complemented
8#11758567—21no—
9C31×#135C2211yescharacteristic
10C2×Q16×C31C2211yescharacteristic
11#11758528—21no—
12#11758519—21no—
13Q16×D31—21no—
14#11758492—22no—
15#11758489—21no—
16C2×Dic124C2211yescharacteristic
17#11758478C2211yescharacteristic
18C31×Q32—21no—
19C31×SD32—21no—
20C31×M32C2211yescharacteristic
21#11758424—21no—
22#11758417—22no—
23#11758407C2211yescharacteristic
24C2×C31⋊C16C2211yescharacteristic
25#41×C31—21no—
26C2×Q8×C31—21no—
27Q8×D31—22no—
28#92497—22no—
29#92497—42no—
30#92495—41no—
31#92495D411yescharacteristic
32C2×Dic62—21no—
33C2×Dic62—41no—
34Q16×C31—21no—
35Q16×C31—21no—
36Q16×C31D411yescharacteristic
37SD16×C31—21no—
38D8×C31D411yescharacteristic
39C2×C8×C31C2311yescharacteristic
40#92482—22no—
41#92482—41no—
42#92481—41no—
43#92480—22no—
44#92474—21no—
45#92474D411yescharacteristic
46Dic124—21no—
47Dic124D412yes—
48#92469—21no—
49C8×D31—21no—
50C16×C31—21no—
51C31⋊C16—21no—
52Q8×C31—21no—
53Q8×C31—41no—
54Q8×C31—41no—
55D4×C31—21no—
56D4×C31—41no—
57C2×C4×C31—41no—
58C2×C4×C31—41no—
59C2×C4×C31C2×D411yescharacteristic
60C22⋊D31—21no—
61C22⋊D31—42no—
62C2×Dic31—42no—
63C2×Dic31—41no—
64D124D811yescharacteristic
65C4×D31—21no—
66C4×D31—42no—
67Dic62—22no—
68Dic62—42no—
69Dic62—41no—
70Dic62D811yescharacteristic
71C8×C31C2×D411yescharacteristic
72C8×C31C2×D411yescharacteristic
73C31⋊C8—21no—
74C31⋊C8—41no—
75#2195—311nomaximal, Sylow
76C22×C31—41no—
77C22×C31AGL(1,ℤ/8)11yescharacteristic
78C2×D31—21no—
79C4×C31—41no—
80C4×C31—81no—
81C4×C31#12011yescharacteristic
82C4×C31C2×D811yescharacteristic
83Dic31—21no—
84Dic31—42no—
85#578—311no—
86#510D3111yescharacteristic, complemented
87C2×Q32—311no—
88#473—311no—
89#362—311no—
90#359—311no—
91#350—311no—
92C2×C31—21no—
93C2×C31—81no—
94C2×C31#44711yescharacteristic
95D31—41no—
962−1+4—621no—
97#137—621no—
98#137—622no—
99#137—621no—
100#135—621no—
101#135C2×D3111yescharacteristic
102C2×Q16—311no—
103C2×Q16—621no—
104C2×Q16C2×D3111yescharacteristic
105#131—311no—
106Q32—21no—
107Q32—622no—
108SD32—21no—
109M32C2×D3111yescharacteristic
110C2×C16—311no—
111#108—311no—
112#101—621no—
113C31#219511yescharacteristic, complemented, Sylow
114#41—21no—
115#41—311no—
116#41—622no—
117#41—1241no—
118#41—1242no—
119C2×Q8—21no—
120C2×Q8—622no—
121C2×Q8—621no—
122C2×Q8—1241no—
123Q16—21no—
124Q16—21no—
125Q16—312no—
126Q16—622no—
127Q16—621no—
128Q16—1241no—
129Q16C22⋊D3111yescharacteristic
130SD16—21no—
131SD16—622no—
132SD16—1241no—
133D8C22⋊D3111yescharacteristic
134M16—311no—
135M16—621no—
136M16—621no—
137C2×C8—621no—
138C2×C8C22×D3111yescharacteristic
139C16—21no—
140C16—621no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—311no—
145Q8—622no—
146Q8—1242no—
147Q8—1241no—
148D4—21no—
149D4—41no—
150D4—311no—
151D4—621no—
152D4—1242no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—621no—
156C2×C4—1242no—
157C2×C4—1242no—
158C2×C4—1241no—
159C2×C4D4×D3111yescharacteristic
160C8—621no—
161C8—1241no—
162C8D4×D3111yescharacteristic
163C8C2×C22⋊D3111yescharacteristic
164C22—41no—
165C22—621no—
166C22#1175848811yescharacteristic
167C4—41no—
168C4—81no—
169C4—621no—
170C4—1242no—
171C4D8×D3111yescharacteristic
172C4#1175851411yescharacteristic
173C2—21no—
174C2—81no—
175C2—1241no—
176C2#1452118111yescharacteristic
subgroupG/H
centerC2#14521181
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC31×#510C2
socleC2×C31#447
prime radical#14521863C2
hypercenter#510D31
hypocenterC31#2195
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. C2×#11758417C2semidirect
3. #14521321C2semidirect
4. #14520866C2semidirect
5. #14520856C2semidirect
6. #14520834C2semidirect
7. C31×#510C2semidirect
86. #510D31semidirect
113. C31#2195semidirect

Maximal subgroups

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

subgroupindex
#145218632
C2×#117584172
#145213212
#145208662
#145208562
#145208342
C31×#5102
#219531