Finite Group Databasebeta

← #16848890

Subgroups — #16848890

Order 3968.

424 conjugacy classes of subgroups; only the 173 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 173 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
1C2×#11758521C211yesmaximal, characteristic
2#14520956C211yesmaximal, characteristic
3#14520953C212yesmaximal
4#14520936C212yesmaximal
5#14520933C212yesmaximal
6#14520931C212yesmaximal
7#14520930C212yesmaximal
8#14520916C212yesmaximal
9C31×#391C211yesmaximal, characteristic
10C22×Q8×C31C2211yescharacteristic
11C22×Dic62C2211yescharacteristic
12C2×C4⋊C4×C31C2211yescharacteristic
13C2×C42×C31C2211yescharacteristic
14#11758521C418yescomplemented
15C2×C4⋊Dic31C2211yescharacteristic
16C2×Dic31⋊C4C2212yes—
17C2×Dic31⋊C4C2212yes—
18C2×Dic31⋊C4C2212yes—
19C2×C4×Dic31C2212yes—
20C2×C4×Dic31C2211yescharacteristic
21C2×C4×Dic31C2211yescharacteristic
22C31×#95C2212yes—
23C31×#95C2212yes—
24C31⋊#95C2212yes—
25C31⋊#95C2212yes—
26C31⋊#95C2212yes—
27C31⋊#95C2212yes—
28C31⋊#95C2212yes—
29C31⋊#95C2212yes—
30C31⋊#95C2212yes—
31C31⋊#95C2212yes—
32C2×Q8×C31—41no—
33C2×Q8×C31—41no—
34C2×Q8×C31C2×C414yes—
35C22×C4×C31C2312yes—
36C22×C4×C31C2312yes—
37C22×C4×C31C2311yescharacteristic
38C22×C4×C31C2311yescharacteristic
39C22×C4×C31C2311yescharacteristic
40C22×Dic31C2312yes—
41C22×Dic31C2312yes—
42C22×Dic31C2312yes—
43C22×Dic31C2312yes—
44C2×Dic62—41no—
45C2×Dic62—41no—
46C2×Dic62C2×C414yes—
47C4⋊C4×C31—41no—
48C42×C31—41no—
49C4⋊Dic31—41no—
50Dic31⋊C4—42no—
51Dic31⋊C4C2×C418yes—
52Dic31⋊C4C2×C418yes—
53C4×Dic31—42no—
54C4×Dic31—41no—
55C4×Dic31C2×C414yes—
56C23×C31C2411yescharacteristic
57Q8×C31—44no—
58C2×C4×C31—21no—
59C2×C4×C31—21no—
60C2×C4×C31—21no—
61C2×C4×C31—21no—
62C2×C4×C31—21no—
63C2×C4×C31—21no—
64C2×C4×C31—22no—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—24no—
68C2×C4×C31—22no—
69C2×C4×C31C22×C412yes—
70C2×C4×C31C22×C412yes—
71C2×C4×C31C22×C412yes—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31—22no—
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31—22no—
78C2×Dic31—22no—
79C2×Dic31—24no—
80C2×Dic31—22no—
81C2×Dic31C22×C414yes—
82C2×Dic31C22×C414yes—
83Dic62—44no—
84#2381—311nomaximal, Sylow
85C22×C31C23×C411yescharacteristic
86C22×C31H(5,𝔽2)11yescharacteristic
87C22×C31H(5,𝔽2)11yescharacteristic
88C22×C312−1+412yes—
89C22×C312−1+412yes—
90C4×C31—22no—
91C4×C31—22no—
92C4×C31—22no—
93C4×C31—42no—
94C4×C31—42no—
95Dic31—24no—
96Dic31—24no—
97Dic31—42no—
98Dic31—42no—
99C2×C4⋊Q8—311no—
100#391—311no—
101#391—312no—
102#391D3111yescharacteristic
103#387—312no—
104#387—312no—
105#387—312no—
106#387—312no—
107#383—312no—
108C2×C31#51811yescharacteristic
109C2×C31#51912yes—
110C2×C31#56311yescharacteristic
111C2×C31#56311yescharacteristic
112C2×C31#56312yes—
113C22×Q8—311no—
114C22×Q8C2×D3111yescharacteristic
115C4⋊Q8—318no—
116C2×C4⋊C4—312no—
117C2×C4⋊C4—312no—
118C2×C4⋊C4—312no—
119C2×C4⋊C4—311no—
120C2×C4⋊C4C2×D3111yescharacteristic
121C2×C42—311no—
122C2×C42—312no—
123C2×C42—311no—
124C2×C42C2×D3111yescharacteristic
125#95—312no—
126#95—312no—
127#95—312no—
128#95—312no—
129#95—312no—
130#95—312no—
131#95—312no—
132#95—312no—
133#95C2×D3112yes—
134#95C2×D3112yes—
135C31#238111yescharacteristic, complemented, Sylow
136C2×Q8—41no—
137C2×Q8—41no—
138C2×Q8—314no—
139C2×Q8—1241no—
140C2×Q8—1241no—
141C2×Q8C4×D3114yes—
142C22×C4—312no—
143C22×C4—312no—
144C22×C4—312no—
145C22×C4—312no—
146C22×C4C22×D3112yes—
147C22×C4C22×D3112yes—
148C22×C4C22×D3111yescharacteristic
149C22×C4C22×D3111yescharacteristic
150C22×C4C22×D3111yescharacteristic
151C4⋊C4—41no—
152C4⋊C4—318no—
153C4⋊C4—318no—
154C4⋊C4—1242no—
155C4⋊C4—1241no—
156C42—41no—
157C42—314no—
158C42—1241no—
159C42—1242no—
160C23C23×D3111yescharacteristic
161Q8—44no—
162Q8—1244no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—22no—
172C2×C4—24no—
173C2×C4—22no—
174C2×C4—314no—
175C2×C4—314no—
176C2×C4—622no—
177C2×C4—622no—
178C2×C4—622no—
179C2×C4—622no—
180C2×C4—622no—
181C2×C4—622no—
182C2×C4—624no—
183C2×C4—622no—
184C2×C4—622no—
185C2×C4C2×C4×D3112yes—
186C2×C4C2×C4×D3112yes—
187C2×C4C2×C4×D3112yes—
188C22C22×C4×D3111yescharacteristic
189C22#1175856111yescharacteristic
190C22#1175856111yescharacteristic
191C22#1175856412yes—
192C22#1175856712yes—
193C4—22no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—42no—
198C4—624no—
199C4—624no—
200C4—1242no—
201C4—1242no—
202C2#1452152211yescharacteristic
203C2#1452152512yes—
204C2#1452179811yescharacteristic
205C2#1452179911yescharacteristic
206C2#1452180012yes—
subgroupG/H
center, FrattiniC23C23×D31
commutatorC22×C31C23×C4
FittingC31×#391C2
socle, prime radical, cosocleC23×C31C24
hypercenter#391D31
hypocenterC31#2381
LCSG ▷ C22×C31 ▷ C31
UCSC1 ◁ C23 ◁ #391

Complements

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

NH ≅ G/Ntype
14. #11758521C4semidirect
135. C31#2381semidirect

Maximal subgroups

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

subgroupindex
C2×#117585212
#145209562
#145209532
#145209362
#145209332
#145209312
#145209302
#145209162
C31×#3912
#238131