Finite Group Databasebeta

← #16846625

Subgroups — #16846625

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#14521057C211yesmaximal, characteristic
4C2×#11758424C211yesmaximal, characteristic
5C2×#11758412C211yesmaximal, characteristic
6#14521005C211yesmaximal, characteristic
7C31×#419C211yesmaximal, characteristic
8C22×Q8×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12C2×#92482—21no—
13C2×#92482—21no—
14C2×#92482—22no—
15C2×#92482C414yescomplemented
16C2×#92474C2211yescharacteristic
17C2×#92474C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19C31×#103—22no—
20#11758424—22no—
21#11758412—22no—
22#11758410—22no—
23#11758398—22no—
24#11758391—21no—
25C4×C31⋊C8—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—
43C2×C8×C31—21no—
44C4⋊C4×C31D412yes—
45C22⋊C4×C31—21no—
46C42×C31—21no—
47#92482—24no—
48#92482—24no—
49#92474—21no—
50#92474—21no—
51#92474—21no—
52#92474D412yes—
53C2×C31⋊C8—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—22no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×D411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31#4111yescharacteristic
74C2×Dic31—22no—
75C2×Dic31—41no—
76C2×Dic31—41no—
77Dic62—22no—
78Dic62—22no—
79Dic62—41no—
80Dic62—41no—
81C8×C31—41no—
82C31⋊C8—22no—
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×C31—42no—
93C4×C31C2×C22⋊C411yescharacteristic
94C4×C31C4×D411yescharacteristic
95C4×C31#12111yescharacteristic
96C4×C31#12711yescharacteristic
97Dic31—42no—
98C22×Q16—311no—
99C2×#108—311no—
100#419—311no—
101#419D3111yescharacteristic
102C2×#101—311no—
103C2×#101—311no—
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×M16—311no—
117C2×M16C2×D3111yescharacteristic
118C22×C8—311no—
119#117C2×D3111yescharacteristic
120#108—622no—
121#103—22no—
122#103—622no—
123#101—622no—
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—312no—
148M16—621no—
149M16—621no—
150M16—621no—
151C2×C8—21no—
152C2×C8—312no—
153C2×C8—311no—
154C2×C8—311no—
155C2×C8—312no—
156C2×C8—621no—
157C2×C8—621no—
158C4⋊C4C22⋊D3112yes—
159C22⋊C4—21no—
160C42—21no—
161C23#9249711yescharacteristic
162Q8—22no—
163Q8—22no—
164Q8—41no—
165Q8—41no—
166Q8—622no—
167Q8—622no—
168Q8—1241no—
169Q8—1241no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—622no—
175C2×C4—1241no—
176C2×C4—1241no—
177C2×C4C2×C4×D3111yescharacteristic
178C2×C4#9249511yescharacteristic
179C2×C4D4×D3111yescharacteristic
180C2×C4D4×D3111yescharacteristic
181C2×C4D4×D3111yescharacteristic
182C2×C4C2×C22⋊D3111yescharacteristic
183C8—41no—
184C8—312no—
185C8—312no—
186C8—622no—
187C8—1241no—
188C22—22no—
189C22(C22⋊D31)⋊C411yescharacteristic
190C22#1175846211yescharacteristic
191C22#1175851611yescharacteristic
192C4—42no—
193C4—42no—
194C4—1242no—
195C4C22⋊C4×D3111yescharacteristic
196C4#1175846111yescharacteristic
197C4C4×C22⋊D3111yescharacteristic
198C4#1175851711yescharacteristic
199C2—21no—
200C2—21no—
201C2#1452094911yescharacteristic
202C2#1452132212yes—
subgroupG/H
centerC22#11758516
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#419C2
socleC22×C31#121
prime radicalC23×C31#41
cosocleC22×C4×C31C23
hypercenter#419D31
hypocenterC31#1979
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

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
#145210572
C2×#117584242
C2×#117584122
#145210052
C31×#4192
#197931