Finite Group Databasebeta

← #16844690

Subgroups — #16844690

Order 3968.

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

normal subgroups only

This group has 260 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#14521639C211yesmaximal, characteristic
2#14521188C211yesmaximal, characteristic, complemented
3#14520960C211yesmaximal, characteristic, complemented
4#14520786C211yesmaximal, characteristic, complemented
5#14520784C211yesmaximal, characteristic, complemented
6#14520772C211yesmaximal, characteristic, complemented
7C31×#451C211yesmaximal, characteristic, complemented
8C22×Q8×C31C2211yescharacteristic
9C2×Q16×C31—21no—
10C31×C22⋊Q8C2211yescharacteristic
11#11758524—21no—
12C2×#92481—21no—
13#11758507C2211yescharacteristic
14C2×(C2×D31)⋊C4—21no—
15C2×(C2×D31)⋊C4C2211yescharacteristic
16#11758475—21no—
17#11758472—21no—
18#11758471—21no—
19#11758459—21no—
20(C22⋊D31)⋊C4—21no—
21C31×#103—21no—
22C31×C22⋊C8C2211yescharacteristic
23#11758423—21no—
24C31⋊#95—21no—
25C31⋊#95C2211yescharacteristic
26C22⋊(C31⋊C8)C2211yescharacteristic
27C23×D31D411yescharacteristic
28C2×Q8×C31—21no—
29C2×Q8×C31—21no—
30C2×Q8×C31—42no—
31C2×Q8×C31D411yescharacteristic
32C22×C4×C31—21no—
33C22×C4×C31C2311yescharacteristic
34C2×C22⋊D31—21no—
35C22×Dic31—21no—
36C22×Dic31D411yescharacteristic
37C2×D124—21no—
38C2×D124—21no—
39C2×D124D411yescharacteristic
40C2×C4×D31—21no—
41Q16×C31—42no—
42C2×C8×C31—21no—
43C4⋊C4×C31—21no—
44C4⋊C4×C31D411yescharacteristic
45C22⋊C4×C31—21no—
46#92481—42no—
47(C2×D31)⋊C4—21no—
48(C2×D31)⋊C4—21no—
49(C2×D31)⋊C4—21no—
50(C2×D31)⋊C4—21no—
51(C2×D31)⋊C4—21no—
52(C2×D31)⋊C4—21no—
53(C2×D31)⋊C4—42no—
54C4⋊Dic31D411yescharacteristic
55Dic31⋊C4—21no—
56C4×Dic31—21no—
57C2×C31⋊C8—21no—
58C23×C31C2×D411yescharacteristic
59C22×D31—21no—
60C22×D31—21no—
61C22×D31—21no—
62C22×D31—21no—
63C22×D31—41no—
64C22×D31—41no—
65Q8×C31—22no—
66Q8×C31—22no—
67Q8×C31—41no—
68Q8×C31—41no—
69Q8×C31—41no—
70C2×C4×C31—22no—
71C2×C4×C31—21no—
72C2×C4×C31—21no—
73C2×C4×C31—41no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31C2×D411yescharacteristic
77C2×C4×C31C2×D411yescharacteristic
78C22⋊D31—41no—
79C22⋊D31—41no—
80C2×Dic31—21no—
81C2×Dic31—21no—
82C2×Dic31—41no—
83C2×Dic31—41no—
84C2×Dic31—41no—
85C2×Dic31—41no—
86D124—41no—
87D124—81no—
88D124—81no—
89C4×D31—81no—
90C8×C31—41no—
91C31⋊C8—41no—
92#1606—311nomaximal, Sylow
93C22×C31—21no—
94C22×C31—21no—
95C22×C31#12011yescharacteristic
96C22×C31#13511yescharacteristic
97C22×C31#13711yescharacteristic
98C2×D31—42no—
99C2×D31—41no—
100C2×D31—41no—
101C2×D31—41no—
102C2×D31—41no—
103C2×D31—41no—
104C2×D31—41no—
105C2×D31—81no—
106C4×C31—21no—
107C4×C31—21no—
108C4×C31—41no—
109C4×C31—41no—
110C4×C31—42no—
111Dic31—41no—
112Dic31—41no—
113Dic31—81no—
114#538—311no—
115#451D3111yescharacteristic, complemented
116#448—311no—
117#393—311no—
118#328—311no—
119#327—311no—
120#323—311no—
121C2×C31—21no—
122C2×C31—21no—
123C2×C31#45211yescharacteristic
124C2×C31#45511yescharacteristic
125C2×C31B(4,𝔽2)11yescharacteristic
126D31—81no—
127D31—81no—
128C22×Q8C2×D3111yescharacteristic
129C2×Q16—21no—
130C2×SD16—621no—
131#126—621no—
132#124—621no—
133#123—621no—
134C22⋊Q8C2×D3111yescharacteristic
135#121—311no—
136#121—621no—
137#120—621no—
138C4×D4—621no—
139C2×C22⋊C4—311no—
140C2×C22⋊C4—621no—
141#103—21no—
142#103—621no—
143C22⋊C8—311no—
144C22⋊C8C2×D3111yescharacteristic
145#95—311no—
146#95—621no—
147C31#160611yescharacteristic, complemented, Sylow
148C24—311no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8C22⋊D3111yescharacteristic
153C2×D4—311no—
154C2×D4—621no—
155C2×D4—621no—
156C2×D4—621no—
157C22×C4—21no—
158C22×C4—311no—
159C22×C4—621no—
160C22×C4—621no—
161C22×C4C22×D3111yescharacteristic
162Q16—42no—
163SD16—1242no—
164C2×C8—21no—
165C2×C8—621no—
166C4⋊C4—21no—
167C4⋊C4—311no—
168C4⋊C4—621no—
169C4⋊C4C22⋊D3111yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—621no—
172C22⋊C4—621no—
173C22⋊C4—621no—
174C22⋊C4—621no—
175C22⋊C4—621no—
176C22⋊C4—621no—
177C22⋊C4—1242no—
178C42—621no—
179C23—621no—
180C23—621no—
181C23—621no—
182C23—621no—
183C23—1241no—
184C23—1241no—
185C23D4×D3111yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191D4—1241no—
192D4—1241no—
193D4—1241no—
194D4—2481no—
195D4—2481no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—621no—
203C2×C4—621no—
204C2×C4—1241no—
205C2×C4—1241no—
206C2×C4—1241no—
207C2×C4—1241no—
208C2×C4—2481no—
209C2×C4D4×D3111yescharacteristic
210C2×C4C2×C22⋊D3111yescharacteristic
211C8—41no—
212C8—1241no—
213C22—21no—
214C22—21no—
215C22—1242no—
216C22—1241no—
217C22—1241no—
218C22—1241no—
219C22—1241no—
220C22—1241no—
221C22—1241no—
222C22—2481no—
223C22#1175849511yescharacteristic
224C22#1175849611yescharacteristic
225C22#1175851411yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—41no—
231C4—1241no—
232C4—1241no—
233C4—2481no—
234C2—21no—
235C2—21no—
236C2—2481no—
237C2—2481no—
238C2#1452121011yescharacteristic
239C2#1452122511yescharacteristic
240C2#1452123511yescharacteristic
subgroupG/H
centerC22#11758514
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#451C2
socleC22×C31#120
prime radical#14521639C2
hypercenter#451D31
hypocenterC31#1606
LCSG ▷ C22×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #14521188C2semidirect
3. #14520960C2semidirect
4. #14520786C2semidirect
5. #14520784C2semidirect
6. #14520772C2semidirect
7. C31×#451C2semidirect
115. #451D31semidirect
147. C31#1606semidirect

Maximal subgroups

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

subgroupindex
#145216392
#145211882
#145209602
#145207862
#145207842
#145207722
C31×#4512
#160631