Finite Group Databasebeta

← #16847378

Subgroups — #16847378

Order 3968.

286 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521616C211yesmaximal, characteristic
2C2×#11758422C211yesmaximal, characteristic, complemented
3#14520843C212yesmaximal, complemented
4#14520841C212yesmaximal, complemented
5C2×C31×#99C211yesmaximal, characteristic, complemented
6C22×D4×C31C2211yescharacteristic
7C2×#92495C411yescharacteristic, complemented
8C2×C22⋊C4×C31—21no—
9#11758530—21no—
10#11758530—21no—
11C2×C22⋊Dic31—21no—
12#11758517C411yescharacteristic, complemented
13#11758517C2211yescharacteristic
14#11758515—21no—
15#11758515—21no—
16#11758513C411yescharacteristic, complemented
17#11758513C2211yescharacteristic
18#11758503C411yescharacteristic, complemented
19C31×#99—21no—
20C31×#99C2212yes—
21#11758422—21no—
22#11758422C2212yes—
23C24×C31D411yescharacteristic
24C24×C31D411yescharacteristic
25C2×D4×C31—41no—
26C2×D4×C31—41no—
27C2×D4×C31C2×C411yescharacteristic
28C2×D4×C31D411yescharacteristic
29C2×D4×C31D411yescharacteristic
30C2×D4×C31C2311yescharacteristic
31C22×C4×C31—41no—
32C22×C4×C31C2×C411yescharacteristic
33C2×C22⋊D31—21no—
34C2×C22⋊D31—21no—
35C2×C22⋊D31—21no—
36C2×C22⋊D31—21no—
37C2×C22⋊D31—21no—
38C22×Dic31—41no—
39#92495—41no—
40#92495—41no—
41C2×D124C2×C411yescharacteristic, complemented
42C2×C4×D31—21no—
43C2×Dic62C2×C411yescharacteristic, complemented
44C22⋊C4×C31—22no—
45C22⋊C4×C31—41no—
46C22⋊Dic31—21no—
47C22⋊Dic31—21no—
48C22⋊Dic31—21no—
49C22⋊Dic31—21no—
50C22⋊Dic31—21no—
51C22⋊Dic31—22no—
52C22⋊Dic31—41no—
53C4⋊Dic31—21no—
54C4×Dic31C2×C411yescharacteristic, complemented
55C4×Dic31C2×C411yescharacteristic, complemented
56C23×C31—21no—
57C23×C31—21no—
58C23×C31—21no—
59C23×C31—21no—
60C23×C31—81no—
61C23×C31—81no—
62C23×C31C22⋊C411yescharacteristic
63C23×C31C22⋊C411yescharacteristic
64C23×C31C22⋊C411yescharacteristic
65C23×C31C2×D411yescharacteristic
66C23×C31C2×D411yescharacteristic
67C22×D31—21no—
68D4×C31—41no—
69D4×C31—41no—
70D4×C31—41no—
71D4×C31—41no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—42no—
75C2×C4×C31—82no—
76C2×C4×C31C22⋊C411yescharacteristic
77C2×C4×C31C22×C411yescharacteristic
78C22⋊D31—41no—
79C22⋊D31—41no—
80C22⋊D31—81no—
81C22⋊D31—81no—
82C22⋊D31—81no—
83C22⋊D31—81no—
84C2×Dic31—21no—
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—42no—
88C2×Dic31—82no—
89D124—41no—
90C4×D31—42no—
91Dic62—41no—
92#2127—311nomaximal, Sylow
93C22×C31—21no—
94C22×C31—21no—
95C22×C31—21no—
96C22×C31—21no—
97C22×C31—41no—
98C22×C31—41no—
99C22×C31—41no—
100C22×C31—41no—
101C22×C31—41no—
102C22×C31—42no—
103C22×C31—42no—
104C22×C31—81no—
105C22×C31—81no—
106C22×C31#9911yescharacteristic
107C22×C31#9911yescharacteristic
108C22×C31C2×C22⋊C411yescharacteristic
109C2×D31—41no—
110C2×D31—41no—
111C2×D31—41no—
112C4×C31—21no—
113C4×C31—21no—
114C4×C31—82no—
115Dic31—41no—
116Dic31—41no—
117Dic31—41no—
118Dic31—82no—
119#535—311no—
120C2×#99—311no—
121C2×#99D3111yescharacteristic, complemented
122#354—312no—
123#353—312no—
124C2×C31—21no—
125C2×C31—21no—
126C2×C31—21no—
127C2×C31—41no—
128C2×C31—41no—
129C2×C31—41no—
130C2×C31—41no—
131C2×C31C2×#9911yescharacteristic
132D31—81no—
133C2×#41—311no—
134C22×D4C2×D3111yescharacteristic
135#127—311no—
136#127—311no—
137#124—311no—
138#124—311no—
139#121—621no—
140#121—621no—
141#120—621no—
142#120—621no—
143#117—311no—
144C2×C22⋊C4—21no—
145C2×C22⋊C4—621no—
146#99—21no—
147#99—312no—
148#99—621no—
149#99C2×D3112yes—
150C31#212711yescharacteristic, complemented, Sylow
151C24D12411yescharacteristic
152C24C22⋊D3111yescharacteristic
153#41—1241no—
154#41—1241no—
155C2×Q8—311no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—311no—
159C2×D4—621no—
160C2×D4—621no—
161C2×D4—621no—
162C2×D4—621no—
163C2×D4—621no—
164C2×D4C4×D3111yescharacteristic
165C2×D4D12411yescharacteristic
166C2×D4C22⋊D3111yescharacteristic
167C2×D4C22×D3111yescharacteristic
168C22×C4—41no—
169C22×C4—621no—
170C22×C4—1241no—
171C22×C4C4×D3111yescharacteristic
172C4⋊C4—621no—
173C22⋊C4—22no—
174C22⋊C4—41no—
175C22⋊C4—621no—
176C22⋊C4—621no—
177C22⋊C4—621no—
178C22⋊C4—621no—
179C22⋊C4—621no—
180C22⋊C4—622no—
181C22⋊C4—1241no—
182C42—311no—
183C42—311no—
184C23—21no—
185C23—21no—
186C23—21no—
187C23—21no—
188C23—81no—
189C23—81no—
190C23—621no—
191C23(C2×D31)⋊C411yescharacteristic
192C23(C2×D31)⋊C411yescharacteristic
193C23(C2×D31)⋊C411yescharacteristic
194C23C2×D12411yescharacteristic
195C23C2×C22⋊D3111yescharacteristic
196Q8—1241no—
197D4—41no—
198D4—41no—
199D4—41no—
200D4—41no—
201D4—1241no—
202D4—1241no—
203D4—1241no—
204D4—2481no—
205D4—2481no—
206D4—2481no—
207D4—2481no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—621no—
213C2×C4—621no—
214C2×C4—621no—
215C2×C4—1242no—
216C2×C4—1242no—
217C2×C4—2482no—
218C2×C4(C2×D31)⋊C411yescharacteristic
219C2×C4C2×C4×D3111yescharacteristic
220C22—21no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—41no—
225C22—41no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—42no—
230C22—42no—
231C22—81no—
232C22—81no—
233C22—1241no—
234C22—1241no—
235C22—1241no—
236C22#1175839411yescharacteristic
237C22#1175839411yescharacteristic
238C22C2×(C2×D31)⋊C411yescharacteristic
239C4—21no—
240C4—21no—
241C4—82no—
242C4—1241no—
243C4—1241no—
244C4—1241no—
245C4—2482no—
246C2—21no—
247C2—21no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—41no—
252C2—41no—
253C2—2481no—
254C2C2×#1175839411yescharacteristic
subgroupG/H
centerC2C2×#11758394
commutatorC2×C4×C31C22×C4
FrattiniC2×D4C22×D31
FittingC2×C31×#99C2
socleC2×C31C2×#99
prime radical#14521616C2
cosocleC2×D4×C31C23
hypercenterC2×#99D31
hypocenterC31#2127
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C23 ◁ C22×D4 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#11758422C2semidirect
3. #14520843C2semidirect
4. #14520841C2semidirect
5. C2×C31×#99C2semidirect
7. C2×#92495C4semidirect
12. #11758517C4semidirect
16. #11758513C4semidirect
18. #11758503C4semidirect
41. C2×D124C2×C4semidirect
43. C2×Dic62C2×C4semidirect
54. C4×Dic31C2×C4semidirect
55. C4×Dic31C2×C4semidirect
121. C2×#99D31semidirect
150. C31#2127semidirect

Maximal subgroups

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

subgroupindex
#145216162
C2×#117584222
#145208432
#145208412
C2×C31×#992
#212731