Finite Group Databasebeta

← #16844643

Subgroups — #16844643

Order 3968.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#14521648C211yesmaximal, characteristic, complemented
2#14521199C211yesmaximal, characteristic, complemented
3#14521185C211yesmaximal, characteristic
4#14520967C211yesmaximal, characteristic, complemented
5#14520782C211yesmaximal, characteristic, complemented
6#14520774C211yesmaximal, characteristic, complemented
7C31×#328C211yesmaximal, characteristic, complemented
8C22×D124C2211yescharacteristic
9C31×C22⋊Q8C2211yescharacteristic
10#11758523—21no—
11C2×#92481—21no—
12#11758507C2211yescharacteristic
13C2×(C2×D31)⋊C4—21no—
14C2×(C2×D31)⋊C4—21no—
15C2×Dic31⋊C4C2211yescharacteristic
16C2×D248—21no—
17#11758475—21no—
18#11758471—21no—
19#11758467—21no—
20#11758463—21no—
21(C22⋊D31)⋊C4—21no—
22C31×C22⋊C8C2211yescharacteristic
23C31×#95C2211yescharacteristic
24C22⋊(C31⋊C8)C2211yescharacteristic
25#11758409—21no—
26#11758397—21no—
27C23×D31—21no—
28C2×Q8×C31D411yescharacteristic
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C22×Dic31D411yescharacteristic
33C22×Dic31D411yescharacteristic
34C2×D124—21no—
35C2×D124—21no—
36C2×D124—42no—
37C2×D124D411yescharacteristic
38C2×C4×D31—21no—
39C2×C8×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31D411yescharacteristic
42C22⋊C4×C31—21no—
43#92481—42no—
44(C2×D31)⋊C4—21no—
45(C2×D31)⋊C4—21no—
46(C2×D31)⋊C4—21no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—42no—
49(C2×D31)⋊C4—42no—
50C4⋊Dic31—21no—
51C4⋊Dic31—21no—
52C4⋊Dic31D411yescharacteristic
53Dic31⋊C4—21no—
54Dic31⋊C4—21no—
55Dic31⋊C4—21no—
56C4×Dic31—21no—
57C2×C31⋊C8—21no—
58D248—42no—
59C23×C31C2×D411yescharacteristic
60C22×D31—22no—
61C22×D31—21no—
62C22×D31—41no—
63C22×D31—41no—
64C22×D31—41no—
65C22×D31—41no—
66C22×D31—41no—
67C22×D31—41no—
68Q8×C31—41no—
69C2×C4×C31—21no—
70C2×C4×C31—21no—
71C2×C4×C31—41no—
72C2×C4×C31—41no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31C2×D411yescharacteristic
76C2×C4×C31C2×D411yescharacteristic
77C22⋊D31—41no—
78C22⋊D31—41no—
79C2×Dic31—21no—
80C2×Dic31—21no—
81C2×Dic31—21no—
82C2×Dic31—21no—
83C2×Dic31—21no—
84C2×Dic31—41no—
85D124—22no—
86D124—22no—
87D124—41no—
88D124—41no—
89D124—41no—
90C4×D31—81no—
91C8×C31—41no—
92C31⋊C8—41no—
93#1597—311nomaximal, Sylow
94C22×C31—21no—
95C22×C31—21no—
96C22×C31#12011yescharacteristic
97C22×C31#13511yescharacteristic
98C22×C31AGL(1,ℤ/8)11yescharacteristic
99C2×D31—42no—
100C2×D31—42no—
101C2×D31—41no—
102C2×D31—41no—
103C2×D31—41no—
104C2×D31—42no—
105C2×D31—81no—
106C2×D31—81no—
107C2×D31—81no—
108C2×D31—81no—
109C4×C31—21no—
110C4×C31—21no—
111C4×C31—41no—
112C4×C31—41no—
113C4×C31—81no—
114Dic31—41no—
115Dic31—41no—
116Dic31—41no—
117#539—311no—
118#450—311no—
119#447—311no—
120#394—311no—
121#328D3111yescharacteristic, complemented
122#327—311no—
123#324—311no—
124C2×C31—21no—
125C2×C31—21no—
126C2×C31#44911yescharacteristic
127C2×C31#45411yescharacteristic
128C2×C31B(4,𝔽2)11yescharacteristic
129D31—81no—
130D31—82no—
131C22×D4—311no—
132C2×SD16—621no—
133C2×D8—621no—
134#126—621no—
135#125—621no—
136#123—621no—
137#123—621no—
138C22⋊Q8—621no—
139C22⋊Q8C2×D3111yescharacteristic
140#121—311no—
141C4×D4—621no—
142C2×C4⋊C4—311no—
143C2×C22⋊C4—621no—
144C2×C22⋊C4—621no—
145#102—621no—
146#102—621no—
147C22⋊C8—311no—
148C22⋊C8C2×D3111yescharacteristic
149#95C2×D3111yescharacteristic
150C31#159711yescharacteristic, complemented, Sylow
151C24—621no—
152C2×Q8D12411yescharacteristic
153C2×D4—311no—
154C2×D4—621no—
155C2×D4—621no—
156C2×D4—621no—
157C2×D4—1242no—
158C22×C4—21no—
159C22×C4—311no—
160C22×C4—311no—
161C22×C4—621no—
162C22×C4C22×D3111yescharacteristic
163SD16—1242no—
164D8—1242no—
165C2×C8—21no—
166C2×C8—621no—
167C4⋊C4—21no—
168C4⋊C4—311no—
169C4⋊C4—621no—
170C4⋊C4—621no—
171C4⋊C4—621no—
172C4⋊C4—621no—
173C4⋊C4—621no—
174C4⋊C4D12411yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—621no—
177C22⋊C4—621no—
178C22⋊C4—621no—
179C22⋊C4—621no—
180C22⋊C4—1242no—
181C22⋊C4—1242no—
182C42—621no—
183C23—622no—
184C23—621no—
185C23—1241no—
186C23—1241no—
187C23—1241no—
188C23—1241no—
189C23—1241no—
190C23—1241no—
191C23D4×D3111yescharacteristic
192Q8—41no—
193D4—622no—
194D4—622no—
195D4—1241no—
196D4—1241no—
197D4—1241no—
198D4—1241no—
199D4—1241no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—621no—
207C2×C4—621no—
208C2×C4—621no—
209C2×C4—621no—
210C2×C4—621no—
211C2×C4—1241no—
212C2×C4—2481no—
213C2×C4C2×D12411yescharacteristic
214C2×C4D4×D3111yescharacteristic
215C8—41no—
216C8—1241no—
217C22—21no—
218C22—21no—
219C22—1242no—
220C22—1242no—
221C22—1241no—
222C22—1241no—
223C22—1241no—
224C22—1242no—
225C22—2481no—
226C22—2481no—
227C22—2481no—
228C22—2481no—
229C22#1175845911yescharacteristic
230C22#1175849111yescharacteristic
231C22#1175849611yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—81no—
237C4—1241no—
238C4—1241no—
239C4—1241no—
240C2—21no—
241C2—21no—
242C2—2482no—
243C2—2481no—
244C2#1452119711yescharacteristic
245C2#1452122311yescharacteristic
246C2#1452123711yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#328C2
socleC22×C31#120
prime radical#14521185C2
hypercenter#328D31
hypocenterC31#1597
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #14521648C2semidirect
2. #14521199C2semidirect
4. #14520967C2semidirect
5. #14520782C2semidirect
6. #14520774C2semidirect
7. C31×#328C2semidirect
121. #328D31semidirect
150. C31#1597semidirect

Maximal subgroups

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

subgroupindex
#145216482
#145211992
#145211852
#145209672
#145207822
#145207742
C31×#3282
#159731