Finite Group Databasebeta

← #16855529

Subgroups — #16855529

Order 3968.

384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C4×#92495C211yesmaximal, characteristic
2#14521353C214yesmaximal, complemented
3#14521346C214yesmaximal, complemented
4#14521089C212yesmaximal, complemented
5#14521073C211yesmaximal, characteristic, complemented
6#14521048C212yesmaximal
7C2×C31×#125C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C31×#125—21no—
10C31×#125—21no—
11C31×#125C2214yes—
12C2×C4⋊C4×C31—22no—
13C2×C4⋊C4×C31C2212yes—
14C2×C42×C31C2211yescharacteristic
15C4×C22⋊D31—22no—
16#11758503C2211yescharacteristic
17C2×#92474C2212yes—
18C4×D124C2212yes—
19#11758449—21no—
20C42×D31—21no—
21C4×Dic62C2212yes—
22#11758398C2214yes—
23#11758397C2214yes—
24#11758396C2214yes—
25#11758395C2214yes—
26C4⋊(C31⋊C8)C2214yes—
27C22×C4×C31—22no—
28C22×C4×C31D412yes—
29C22×C4×C31C2311yescharacteristic
30C2×C22⋊D31—21no—
31#92495—22no—
32#92495Q814yes—
33C2×D124C2311yescharacteristic
34C2×C4×D31—21no—
35C2×C4×D31—22no—
36C2×Dic62C2311yescharacteristic
37C4⋊C4×C31—24no—
38C4⋊C4×C31—24no—
39C4⋊C4×C31—22no—
40C4⋊C4×C31C2314yes—
41C42×C31D411yescharacteristic
42C42×C31D411yescharacteristic
43C42×C31C2312yes—
44C22⋊Dic31—21no—
45(C2×D31)⋊C4—22no—
46C4⋊Dic31C2312yes—
47Dic31⋊C4—22no—
48C4×Dic31—22no—
49C4×Dic31—21no—
50#92474—24no—
51C2×C31⋊C8C2314yes—
52C23×C31C2×D411yescharacteristic
53C22×D31—21no—
54C2×C4×C31—24no—
55C2×C4×C31—42no—
56C2×C4×C31—44no—
57C2×C4×C31C2×D412yes—
58C2×C4×C31C2×D412yes—
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×Q812yes—
61C2×C4×C31#4112yes—
62C2×C4×C31C2411yescharacteristic
63C22⋊D31—24no—
64C2×Dic31—21no—
65C2×Dic31—22no—
66D124—21no—
67D124C2×Q812yes—
68C4×D31—24no—
69C4×D31—44no—
70Dic62—21no—
71Dic62C2×Q812yes—
72C31⋊C8—24no—
73#3080—311nomaximal, Sylow
74C22×C31—22no—
75C22×C31C22⋊Q812yes—
76C22×C31C22×D411yescharacteristic
77C2×D31—22no—
78C2×D31—42no—
79C4×C31—22no—
80C4×C31—22no—
81C4×C31—44no—
82C4×C31C22⋊Q812yes—
83C4×C31C22×Q811yescharacteristic
84C4×C31C2×#4111yescharacteristic
85Dic31—22no—
86Dic31—42no—
87C2×#125D3111yescharacteristic, complemented
88C4×#41—311no—
89#479—314no—
90#478—314no—
91#428—312no—
92#423—311no—
93#417—312no—
94C2×C31—22no—
95C2×C31C2×C22⋊Q811yescharacteristic
96C2×C31#57512yes—
97D31—42no—
98C2×#41—311no—
99C2×M16—312no—
100#125—21no—
101#125—21no—
102#125C2×D3114yes—
103C4×Q8—312no—
104C4×D4—312no—
105C4×D4—622no—
106#117—311no—
107#117—621no—
108C2×C4⋊C4—22no—
109C2×C4⋊C4C2×D3112yes—
110C2×C42—621no—
111C2×C42C2×D3111yescharacteristic
112#107—314no—
113#106—314no—
114C4⋊C8—314no—
115#103—314no—
116#102—314no—
117C31#308011yescharacteristic, complemented, Sylow
118#41—314no—
119#41—622no—
120C2×Q8—311no—
121C2×D4—311no—
122C2×D4—621no—
123C22×C4—22no—
124C22×C4—621no—
125C22×C4—622no—
126C22×C4C22⋊D3112yes—
127C22×C4C22×D3111yescharacteristic
128M16—624no—
129C2×C8—314no—
130C4⋊C4—24no—
131C4⋊C4—24no—
132C4⋊C4—22no—
133C4⋊C4—312no—
134C4⋊C4—622no—
135C4⋊C4C22×D3114yes—
136C22⋊C4—621no—
137C22⋊C4—622no—
138C42—621no—
139C42—622no—
140C42C22⋊D3111yescharacteristic
141C42C22⋊D3111yescharacteristic
142C42C22×D3112yes—
143C23—621no—
144C23C2×C22⋊D3111yescharacteristic
145Q8—312no—
146Q8—621no—
147D4—312no—
148D4—624no—
149D4—621no—
150C2×C4—24no—
151C2×C4—42no—
152C2×C4—44no—
153C2×C4—621no—
154C2×C4—624no—
155C2×C4—622no—
156C2×C4—1244no—
157C2×C4Q8×D3112yes—
158C2×C4#9249912yes—
159C2×C4C2×C22⋊D3112yes—
160C2×C4C2×C22⋊D3112yes—
161C2×C4C2×C22⋊D3111yescharacteristic
162C2×C4C23×D3111yescharacteristic
163C8—624no—
164C22—22no—
165C22—622no—
166C22—1242no—
167C22#1175852312yes—
168C22C22×C22⋊D3111yescharacteristic
169C4—22no—
170C4—22no—
171C4—44no—
172C4—622no—
173C4—1242no—
174C4#1175852312yes—
175C4C2×Q8×D3111yescharacteristic
176C4C2×#9249911yescharacteristic
177C2—22no—
178C2—1242no—
179C2C2×#1175852311yescharacteristic
180C2#1452184712yes—
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#125C2
socleC22×C31C22×D4
prime radicalC2×#92495C22
hypercenterC2×#125D31
hypocenterC31#3080
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
2. #14521353C2semidirect
3. #14521346C2semidirect
4. #14521089C2semidirect
5. #14521073C2semidirect
7. C2×C31×#125C2semidirect
87. C2×#125D31semidirect
117. C31#3080semidirect

Maximal subgroups

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

subgroupindex
C4×#924952
#145213532
#145213462
#145210892
#145210732
#145210482
C2×C31×#1252
#308031