Finite Group Databasebeta

← #16846623

Subgroups — #16846623

Order 3968.

276 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 83 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
1C22×#92482C211yesmaximal, characteristic
2C2×#11758410C211yesmaximal, characteristic
3#14521059C211yesmaximal, characteristic
4#14521058C211yesmaximal, characteristic
5C2×#11758412C211yesmaximal, characteristic
6#14521007C211yesmaximal, characteristic
7C2×C31×#101C211yesmaximal, characteristic
8C22×Q8×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×#92482—21no—
13C2×#92482—21no—
14C2×#92482—22no—
15C2×#92482C414yescomplemented
16#11758503C2211yescharacteristic
17C2×#92474C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19C31×#101—22no—
20#11758423—22no—
21#11758412—22no—
22#11758410—22no—
23#11758404—22no—
24#11758403—21no—
25C8×Dic31—21no—
26C2×Q8×C31—21no—
27C2×Q8×C31—21no—
28C2×Q8×C31—21no—
29C2×Q8×C31—21no—
30C2×Q8×C31—21no—
31C2×Q8×C31C2×C412yes—
32C22×C4×C31—21no—
33C22×C4×C31C2311yescharacteristic
34C22×Dic31—21no—
35C2×Dic62—21no—
36C2×Dic62—21no—
37C2×Dic62—21no—
38C2×Dic62—21no—
39C2×Dic62—21no—
40C2×Dic62C2×C412yes—
41M16×C31—21no—
42M16×C31—21no—
43M16×C31—21no—
44M16×C31D412yes—
45C2×C8×C31—21no—
46C2×C8×C31—21no—
47C22⋊Dic31—21no—
48#92482—24no—
49#92482—24no—
50C4⋊Dic31D412yes—
51C4×Dic31—21no—
52#92474—21no—
53#92474—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8C2×C412yes—
56C2×C31⋊C8D411yescharacteristic
57C2×C31⋊C8D411yescharacteristic
58C2×C31⋊C8D412yes—
59C23×C31#4111yescharacteristic
60Q8×C31—22no—
61Q8×C31—22no—
62Q8×C31—41no—
63Q8×C31—41no—
64C2×C4×C31—22no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31C22×C411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31#4111yescharacteristic
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—41no—
76C2×Dic31—41no—
77Dic62—22no—
78Dic62—22no—
79Dic62—41no—
80Dic62—41no—
81C8×C31—22no—
82C8×C31—41no—
83C31⋊C8—41no—
84C31⋊C8C22⋊C412yes—
85C31⋊C8C22⋊C412yes—
86#1979—311nomaximal, Sylow
87C22×C31—22no—
88C22×C31C4×D411yescharacteristic
89C22×C31#12111yescharacteristic
90C22×C31#12411yescharacteristic
91C4×C31—42no—
92C4×C31C2×C22⋊C411yescharacteristic
93C4×C31C4×D411yescharacteristic
94C4×C31#12111yescharacteristic
95C4×C31#12711yescharacteristic
96Dic31—42no—
97Dic31—42no—
98C22×Q16—311no—
99C2×#108—311no—
100#419—311no—
101#419—311no—
102C2×#101—311no—
103C2×#101D3111yescharacteristic
104#405—311no—
105C2×C31—21no—
106C2×C31—21no—
107C2×C31#39011yescharacteristic
108C2×C31#47312yes—
109C22×Q8—311no—
110C22×Q8C2×D3111yescharacteristic
111C2×Q16—314no—
112C2×Q16—621no—
113C2×Q16—621no—
114C2×Q16—622no—
115C2×M16—311no—
116C2×M16C2×D3111yescharacteristic
117C2×M16C2×D3111yescharacteristic
118C22×C8—311no—
119#117—311no—
120#108—622no—
121#103—622no—
122#103—622no—
123#101—22no—
124#101—622no—
125#97—621no—
126C4×C8—621no—
127C31#197911yescharacteristic, complemented, Sylow
128C2×Q8—21no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—312no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C2×Q8—621no—
138C2×Q8—621no—
139C2×Q8C4×D3112yes—
140C22×C4—21no—
141C22×C4—621no—
142C22×C4C22×D3111yescharacteristic
143Q16—624no—
144Q16—624no—
145M16—21no—
146M16—21no—
147M16—21no—
148M16—621no—
149M16—621no—
150M16C22⋊D3112yes—
151C2×C8—21no—
152C2×C8—21no—
153C2×C8—312no—
154C2×C8—311no—
155C2×C8—311no—
156C2×C8—312no—
157C2×C8—621no—
158C4⋊C4—312no—
159C22⋊C4—621no—
160C42—621no—
161C23#9249511yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—622no—
167Q8—622no—
168Q8—1241no—
169Q8—1241no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4—1241no—
176C2×C4—1241no—
177C2×C4C2×C4×D3111yescharacteristic
178C2×C4D4×D3111yescharacteristic
179C2×C4D4×D3111yescharacteristic
180C2×C4D4×D3111yescharacteristic
181C2×C4#9249711yescharacteristic
182C2×C4C2×C22⋊D3111yescharacteristic
183C8—22no—
184C8—41no—
185C8—312no—
186C8—312no—
187C8—1241no—
188C22—22no—
189C22#1175846111yescharacteristic
190C22#1175846211yescharacteristic
191C22C4×C22⋊D3111yescharacteristic
192C4—42no—
193C4—1242no—
194C4—1242no—
195C4C22⋊C4×D3111yescharacteristic
196C4(C22⋊D31)⋊C411yescharacteristic
197C4#1175851611yescharacteristic
198C4#1175851711yescharacteristic
199C2—21no—
200C2—21no—
201C2#1452094911yescharacteristic
202C2#1452132312yes—
subgroupG/H
centerC22#11758461
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#101C2
socleC22×C31#121
prime radicalC23×C31#41
cosocleC22×C4×C31C23
hypercenterC2×#101D31
hypocenterC31#1979
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
15. C2×#92482C4semidirect
127. C31#1979semidirect

Maximal subgroups

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

subgroupindex
C22×#924822
C2×#117584102
#145210592
#145210582
C2×#117584122
#145210072
C2×C31×#1012
#197931