Finite Group Databasebeta

← #16846172

Subgroups — #16846172

Order 3968.

390 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 93 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×#92474C211yesmaximal, characteristic, complemented
2C2×#11758507C211yesmaximal, characteristic
3C2×#11758411C212yesmaximal, complemented
4#14520817C212yesmaximal, complemented
5C31×#407C211yesmaximal, characteristic, complemented
6C23×C4×C31C2211yescharacteristic
7C22×C22⋊D31C412yes—
8C22×D124C2211yescharacteristic
9C2×M16×C31C2212yes—
10#11758507—21no—
11#11758507—21no—
12#11758507—21no—
13#11758507—21no—
14C2×(C2×D31)⋊C4C412yes—
15C2×C4⋊Dic31C2211yescharacteristic
16C2×#92474—21no—
17C2×#92474—24no—
18C2×#92474C2212yes—
19C22×C31⋊C8—21no—
20C31×C22⋊C8—21no—
21C31×C22⋊C8—21no—
22#11758411—24no—
23C24×C31C2×C411yescharacteristic
24C23×D31C2×C412yes—
25C22×C4×C31—22no—
26C22×C4×C31—22no—
27C22×C4×C31C2×C411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31D411yescharacteristic
30C22×C4×C31D411yescharacteristic
31C22×C4×C31D411yescharacteristic
32C22×C4×C31C2311yescharacteristic
33C2×C22⋊D31—22no—
34C2×C22⋊D31—22no—
35C2×C22⋊D31—44no—
36C22×Dic31C2×C412yes—
37C2×D124—22no—
38C2×D124—21no—
39C2×D124—21no—
40C2×D124—22no—
41M16×C31—22no—
42M16×C31—22no—
43C2×C8×C31—22no—
44(C2×D31)⋊C4—22no—
45(C2×D31)⋊C4—22no—
46C4⋊Dic31—21no—
47C4⋊Dic31—21no—
48#92474—24no—
49#92474—22no—
50#92474D414yescomplemented
51C2×C31⋊C8—24no—
52C2×C31⋊C8—22no—
53C23×C31—22no—
54C23×C31—22no—
55C23×C31—41no—
56C23×C31C22⋊C411yescharacteristic
57C23×C31C22⋊C411yescharacteristic
58C23×C31C22×C411yescharacteristic
59C22×D31—22no—
60C22×D31—24no—
61C22×D31—42no—
62C22×D31—42no—
63C2×C4×C31—22no—
64C2×C4×C31—21no—
65C2×C4×C31—21no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—21no—
69C2×C4×C31—21no—
70C2×C4×C31C22⋊C411yescharacteristic
71C2×C4×C31C22⋊C411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D412yes—
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31#4112yes—
76C22⋊D31—44no—
77C22⋊D31—44no—
78C2×Dic31—22no—
79C2×Dic31—42no—
80D124—41no—
81D124—42no—
82D124—41no—
83C8×C31—42no—
84C31⋊C8—24no—
85#1900—311nomaximal, Sylow
86C22×C31—21no—
87C22×C31—21no—
88C22×C31—21no—
89C22×C31—21no—
90C22×C31—21no—
91C22×C31—21no—
92C22×C31—21no—
93C22×C31—44no—
94C22×C31#10012yescomplemented
95C22×C31C2×C22⋊C411yescharacteristic
96C22×C31C4×D412yes—
97C2×D31—42no—
98C2×D31—42no—
99C2×D31—42no—
100C2×D31—84no—
101C4×C31—21no—
102C4×C31—21no—
103C4×C31#12011yescharacteristic
104C4×C31#12112yes—
105C4×C31#12311yescharacteristic
106Dic31—42no—
107C22×M16—311no—
108C2×#121—311no—
109C2×#100—312no—
110#407D3111yescharacteristic, complemented
111#343—312no—
112C2×C31—22no—
113C2×C31—22no—
114C2×C31—41no—
115C2×C31#38611yescharacteristic
116C2×C31C2×#10011yescharacteristic
117C2×C31#41311yescharacteristic
118D31—82no—
119C22×D4—312no—
120C22×D4—311no—
121C23×C4C2×D3111yescharacteristic
122C2×M16—312no—
123C2×M16—624no—
124C2×M16—621no—
125C2×M16C2×D3112yes—
126C22×C8—621no—
127#121—621no—
128#121—621no—
129#121—621no—
130#121—621no—
131C2×C4⋊C4—311no—
132C2×C22⋊C4—312no—
133#100—624no—
134C22⋊C8—21no—
135C22⋊C8—21no—
136C31#190011yescharacteristic, complemented, Sylow
137C24—312no—
138C24C4×D3111yescharacteristic
139C2×D4—622no—
140C2×D4—622no—
141C2×D4—621no—
142C2×D4—622no—
143C2×D4—622no—
144C2×D4—621no—
145C2×D4—1244no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—312no—
149C22×C4C4×D3111yescharacteristic
150C22×C4D12411yescharacteristic
151C22×C4D12411yescharacteristic
152C22×C4C22⋊D3111yescharacteristic
153C22×C4C22⋊D3111yescharacteristic
154C22×C4C22×D3111yescharacteristic
155M16—22no—
156M16—22no—
157M16—314no—
158M16—624no—
159M16—622no—
160C2×C8—22no—
161C2×C8—624no—
162C2×C8—622no—
163C4⋊C4—621no—
164C4⋊C4—621no—
165C22⋊C4—622no—
166C22⋊C4—622no—
167C23—22no—
168C23—22no—
169C23—41no—
170C23—622no—
171C23—624no—
172C23—1242no—
173C23—1242no—
174C23(C2×D31)⋊C411yescharacteristic
175C23(C2×D31)⋊C411yescharacteristic
176C23C2×C4×D3111yescharacteristic
177D4—1244no—
178D4—1244no—
179D4—1241no—
180D4—1241no—
181D4—1242no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—622no—
190C2×C4—1242no—
191C2×C4(C2×D31)⋊C411yescharacteristic
192C2×C4(C2×D31)⋊C411yescharacteristic
193C2×C4C2×D12411yescharacteristic
194C2×C4D4×D3112yes—
195C2×C4#9249712yes—
196C2×C4C2×C22⋊D3111yescharacteristic
197C8—42no—
198C8—624no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—44no—
207C22—1242no—
208C22—1242no—
209C22—1242no—
210C22—2484no—
211C22#1175841112yescomplemented
212C22(C22⋊D31)⋊C412yes—
213C22C2×(C2×D31)⋊C411yescharacteristic
214C4—21no—
215C4—21no—
216C4—1242no—
217C4#1175845911yescharacteristic
218C4#1175846311yescharacteristic
219C4#1175851612yes—
220C2—22no—
221C2—22no—
222C2—41no—
223C2—2482no—
224C2#1452092611yescharacteristic
225C2C2×#1175841111yescharacteristic
226C2#1452103111yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#407C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#11758507C2
cosocleC22×C4×C31C23
hypercenter#407D31
hypocenterC31#1900
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
1. C22×#92474C2semidirect
3. C2×#11758411C2semidirect
4. #14520817C2semidirect
5. C31×#407C2semidirect
50. #92474D4semidirect
94. C22×C31#100semidirect
110. #407D31semidirect
136. C31#1900semidirect
211. C22#11758411semidirect

Maximal subgroups

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

subgroupindex
C22×#924742
C2×#117585072
C2×#117584112
#145208172
C31×#4072
#190031