Finite Group Databasebeta

← #16846697

Subgroups — #16846697

Order 3968.

324 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 101 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#14520909C211yesmaximal, characteristic
2C4×C22⋊Dic31C211yesmaximal, characteristic
3#14520816C214yesmaximal
4C2×C31×C22⋊Q8C211yesmaximal, characteristic
5C22×Q8×C31C411yescharacteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C31×C22⋊Q8—21no—
8C31×C22⋊Q8—21no—
9C31×C22⋊Q8—21no—
10C31×C22⋊Q8—21no—
11C2×C4⋊C4×C31C411yescharacteristic, complemented
12C2×C4⋊C4×C31C412yescomplemented
13C2×C22⋊C4×C31C2212yes—
14C2×C22⋊Dic31C2212yes—
15C2×C22⋊Dic31C2212yes—
16C2×C4⋊Dic31—21no—
17C2×C4×Dic31—21no—
18C31⋊#95—21no—
19C31⋊#95—21no—
20C24×C31C2311yescharacteristic
21C2×Q8×C31—21no—
22C2×Q8×C31—21no—
23C2×Q8×C31—42no—
24C22×C4×C31—42no—
25C22×C4×C31C2×C411yescharacteristic
26C22×C4×C31C2×C412yes—
27C22×C4×C31C2×C412yes—
28C22×C4×C31C2×C411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C22×C4×C31D411yescharacteristic
31C22×C4×C31D411yescharacteristic
32C22×C4×C31D411yescharacteristic
33C22×Dic31—22no—
34C22×Dic31—22no—
35C4⋊C4×C31—21no—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—22no—
38C4⋊C4×C31—22no—
39C22⋊C4×C31—22no—
40C22⋊C4×C31—22no—
41C22⋊Dic31—22no—
42C22⋊Dic31—24no—
43C22⋊Dic31Q814yescomplemented
44C4⋊Dic31—42no—
45C4×Dic31—42no—
46C23×C31—41no—
47C23×C31—41no—
48C23×C31C22×C411yescharacteristic
49C23×C31C2×D411yescharacteristic
50C23×C31C2×D411yescharacteristic
51C23×C31C2×Q812yes—
52C23×C31#4112yes—
53Q8×C31—42no—
54Q8×C31—42no—
55C2×C4×C31—22no—
56C2×C4×C31—22no—
57C2×C4×C31—22no—
58C2×C4×C31—22no—
59C2×C4×C31—22no—
60C2×C4×C31—41no—
61C2×C4×C31—41no—
62C2×C4×C31—41no—
63C2×C4×C31—42no—
64C2×C4×C31—42no—
65C2×C4×C31C22⋊C411yescharacteristic
66C2×C4×C31C22⋊C411yescharacteristic
67C2×C4×C31C22⋊C411yescharacteristic
68C2×C4×C31C22⋊C411yescharacteristic
69C2×Dic31—24no—
70C2×Dic31—42no—
71C2×Dic31—42no—
72C2×Dic31—42no—
73C2×Dic31—42no—
74C2×Dic31—42no—
75#1996—311nomaximal, Sylow
76C22×C31—21no—
77C22×C31—21no—
78C22×C31—21no—
79C22×C31—21no—
80C22×C31—21no—
81C22×C31—21no—
82C22×C31—42no—
83C22×C31—42no—
84C22×C31C2×C22⋊C411yescharacteristic
85C22×C31C4×Q812yes—
86C22×C31C22⋊Q812yes—
87C22×C31#12411yescharacteristic
88C22×C31C4⋊Q811yescharacteristic
89C4×C31—21no—
90C4×C31—21no—
91C4×C31—21no—
92C4×C31—42no—
93C4×C31—42no—
94C4×C31#9912yes—
95Dic31—44no—
96Dic31—82no—
97C2×C22⋊Q8D3111yescharacteristic
98#380—311no—
99C4×C22⋊C4—311no—
100#342—314no—
101C2×C31—22no—
102C2×C31—21no—
103C2×C31—22no—
104C2×C31—21no—
105C2×C31#39111yescharacteristic
106C2×C31C2×#9911yescharacteristic
107C2×C31#41011yescharacteristic
108C22×Q8Dic3111yescharacteristic, complemented
109C23×C4C2×D3111yescharacteristic
110C22⋊Q8—21no—
111C22⋊Q8—21no—
112C22⋊Q8—21no—
113C22⋊Q8—21no—
114C2×C4⋊C4—621no—
115C2×C4⋊C4Dic3111yescharacteristic, complemented
116C2×C4⋊C4Dic3112yescomplemented
117C2×C22⋊C4—312no—
118C2×C22⋊C4—312no—
119C2×C22⋊C4C2×D3112yes—
120C2×C42—621no—
121#95—621no—
122#95—621no—
123C31#199611yescharacteristic, complemented, Sylow
124C24C22×D3111yescharacteristic
125C2×Q8—21no—
126C2×Q8—21no—
127C2×Q8—42no—
128C22×C4—42no—
129C22×C4—622no—
130C22×C4—622no—
131C22×C4C2×Dic3111yescharacteristic
132C22×C4C2×Dic3112yes—
133C22×C4C2×Dic3112yes—
134C22×C4C2×Dic3111yescharacteristic
135C22×C4C22⋊D3111yescharacteristic
136C22×C4C22⋊D3111yescharacteristic
137C22×C4C22⋊D3111yescharacteristic
138C22×C4C22⋊D3111yescharacteristic
139C4⋊C4—21no—
140C4⋊C4—21no—
141C4⋊C4—22no—
142C4⋊C4—22no—
143C4⋊C4—1242no—
144C22⋊C4—22no—
145C22⋊C4—22no—
146C22⋊C4—314no—
147C22⋊C4—622no—
148C22⋊C4—624no—
149C42—1242no—
150C23—41no—
151C23—41no—
152C23Q8×D3112yes—
153C23#9249912yes—
154C23C22×Dic3111yescharacteristic
155C23C2×C22⋊D3111yescharacteristic
156C23C2×C22⋊D3111yescharacteristic
157Q8—42no—
158Q8—42no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—22no—
163C2×C4—22no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—624no—
170C2×C4—1242no—
171C2×C4—1242no—
172C2×C4—1242no—
173C2×C4—1242no—
174C2×C4—1242no—
175C2×C4C22⋊Dic3111yescharacteristic
176C2×C4C22⋊Dic3111yescharacteristic
177C2×C4C22⋊Dic3111yescharacteristic
178C2×C4C22⋊Dic3111yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22#1175852111yescharacteristic
188C22Q8×Dic3112yes—
189C22#1175852312yes—
190C22#1175852411yescharacteristic
191C22C2×C22⋊Dic3111yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—42no—
196C4—42no—
197C4—1244no—
198C4—2482no—
199C4#1175842212yes—
200C2—22no—
201C2—21no—
202C2—21no—
203C2—22no—
204C2#1452095611yescharacteristic
205C2C2×#1175842211yescharacteristic
206C2#1452102311yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic31
commutatorC23×C31C22×C4
FrattiniC24C22×D31
FittingC2×C31×C22⋊Q8C2
socleC22×C31C2×C22⋊C4
prime radical, cosocleC24×C31C23
hypercenterC2×C22⋊Q8D31
hypocenterC31#1996
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
5. C22×Q8×C31C4semidirect
11. C2×C4⋊C4×C31C4semidirect
12. C2×C4⋊C4×C31C4semidirect
43. C22⋊Dic31Q8semidirect
108. C22×Q8Dic31semidirect
115. C2×C4⋊C4Dic31semidirect
116. C2×C4⋊C4Dic31semidirect
123. C31#1996semidirect

Maximal subgroups

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

subgroupindex
#145209092
C4×C22⋊Dic312
#145208162
C2×C31×C22⋊Q82
#199631