Finite Group Databasebeta

← #16846541

Subgroups — #16846541

Order 3968.

320 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 83 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#14521595C211yesmaximal, characteristic
2#14521072C211yesmaximal, characteristic, complemented
3C2×#11758393C211yesmaximal, characteristic, complemented
4C2×#11758425C211yesmaximal, characteristic, complemented
5C2×#11758413C211yesmaximal, characteristic, complemented
6#14520895C211yesmaximal, characteristic, complemented
7C2×C31×#104C211yesmaximal, characteristic, complemented
8C2×#41×C31C2211yescharacteristic
9C2×#92495C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12#11758524C411yescharacteristic, complemented
13#11758521C411yescharacteristic, complemented
14#11758517C411yescharacteristic, complemented
15#11758516—22no—
16#11758513C411yescharacteristic, complemented
17C4×C22⋊D31—22no—
18C2×C4×Dic31C2211yescharacteristic
19C2×C4×Dic31C2211yescharacteristic
20C2×#92474C2211yescharacteristic
21C31×#104—22no—
22#11758425—22no—
23C31⋊#95—22no—
24#11758413—22no—
25Dic31⋊C8—22no—
26#11758393—22no—
27#41×C31—21no—
28#41×C31—21no—
29#41×C31—21no—
30#41×C31—21no—
31C2×Q8×C31C2×C411yescharacteristic
32C2×D4×C31—21no—
33C2×D4×C31C2×C411yescharacteristic
34C22×C4×C31—21no—
35C22×C4×C31—21no—
36C22×C4×C31C2311yescharacteristic
37C2×C22⋊D31—21no—
38C2×C22⋊D31—22no—
39C22×Dic31—21no—
40C22×Dic31D412yes—
41#92495—21no—
42#92495—21no—
43#92495—21no—
44#92495—21no—
45C2×D124C2×C411yescharacteristic
46C2×C4×D31—21no—
47C2×Dic62C2×C411yescharacteristic
48M16×C31—21no—
49M16×C31—21no—
50C2×C8×C31—21no—
51C42×C31—21no—
52C42×C31D412yescomplemented
53C22⋊Dic31—22no—
54(C2×D31)⋊C4—22no—
55Dic31⋊C4—22no—
56C4×Dic31—21no—
57C4×Dic31C2×C411yescharacteristic
58C4×Dic31C2×C411yescharacteristic
59C4×Dic31D412yes—
60C4×Dic31D412yescomplemented
61#92474—21no—
62#92474—21no—
63C2×C31⋊C8—21no—
64C23×C31—21no—
65C23×C31C2×D411yescharacteristic
66C22×D31—21no—
67Q8×C31—21no—
68Q8×C31—21no—
69D4×C31—21no—
70D4×C31—21no—
71D4×C31—41no—
72D4×C31—41no—
73C2×C4×C31—21no—
74C2×C4×C31—22no—
75C2×C4×C31—42no—
76C2×C4×C31—41no—
77C2×C4×C31—41no—
78C2×C4×C31C22×C411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31#4111yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C22⋊D31—44no—
85C22⋊D31—41no—
86C22⋊D31—41no—
87C2×Dic31—21no—
88C2×Dic31—22no—
89C2×Dic31—42no—
90C2×Dic31—42no—
91C2×Dic31C22⋊C412yes—
92C2×Dic31C22⋊C412yes—
93D124—21no—
94D124—21no—
95C4×D31—41no—
96C4×D31—41no—
97Dic62—21no—
98Dic62—21no—
99C8×C31—41no—
100C31⋊C8—41no—
101#1963—311nomaximal, Sylow
102C22×C31—22no—
103C22×C31—41no—
104C22×C31—42no—
105C22×C31C2×C22⋊C411yescharacteristic
106C22×C31#12111yescharacteristic
107C22×C31#12111yescharacteristic
108C2×D31—41no—
109C2×D31—42no—
110C4×C31—42no—
111C4×C31—41no—
112C4×C31C4×D411yescharacteristic
113C4×C31C4×D411yescharacteristic
114C4×C31#12411yescharacteristic
115C4×C31#12711yescharacteristic
116Dic31—22no—
117Dic31—22no—
118Dic31—42no—
119Dic31—41no—
120#532—311no—
121#423—311no—
122C2×#104—311no—
123C2×#104—311no—
124C2×#104—311no—
125C2×#104D3111yescharacteristic, complemented
126#376—311no—
127C2×C31—21no—
128C2×C31—21no—
129C2×C31—81no—
130C2×C31#39011yescharacteristic
131C2×C31#42112yes—
132D31—81no—
133C2×#41—311no—
134C2×#41C2×D3111yescharacteristic
135C2×M16—311no—
136C2×M16C2×D3111yescharacteristic
137C4⋊Q8—311no—
138#127—311no—
139#124—311no—
140#124—311no—
141#121—622no—
142C4×D4—622no—
143C2×C42—311no—
144C2×C42—311no—
145C2×C42C2×D3111yescharacteristic
146C4⋊C8—622no—
147#104—22no—
148#104—622no—
149#104—622no—
150#104—622no—
151#95—622no—
152C31#196311yescharacteristic, complemented, Sylow
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—621no—
158#41—621no—
159#41—621no—
160#41—621no—
161C2×Q8—311no—
162C2×Q8C4×D3111yescharacteristic
163C2×D4—21no—
164C2×D4—311no—
165C2×D4—622no—
166C2×D4—621no—
167C2×D4C4×D3111yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—312no—
171C22×C4—621no—
172C22×C4—621no—
173C22×C4C22×D3111yescharacteristic
174M16—21no—
175M16—21no—
176M16—621no—
177M16—621no—
178C2×C8—21no—
179C2×C8—621no—
180C4⋊C4—622no—
181C22⋊C4—622no—
182C22⋊C4—622no—
183C42—21no—
184C42—311no—
185C42—311no—
186C42—312no—
187C42—312no—
188C42—621no—
189C42C22⋊D3112yescomplemented
190C23—21no—
191C23—621no—
192C23D4×D3111yescharacteristic
193Q8—21no—
194Q8—21no—
195Q8—621no—
196Q8—621no—
197D4—21no—
198D4—21no—
199D4—41no—
200D4—41no—
201D4—621no—
202D4—621no—
203D4—1244no—
204D4—1241no—
205D4—1241no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—312no—
212C2×C4—312no—
213C2×C4—621no—
214C2×C4—622no—
215C2×C4—1242no—
216C2×C4—1242no—
217C2×C4—1241no—
218C2×C4—1241no—
219C2×C4C2×C4×D3111yescharacteristic
220C2×C4#9249511yescharacteristic
221C2×C4D4×D3111yescharacteristic
222C2×C4D4×D3111yescharacteristic
223C2×C4#9249711yescharacteristic
224C2×C4C2×C22⋊D3111yescharacteristic
225C8—41no—
226C8—1241no—
227C22—22no—
228C22—41no—
229C22—42no—
230C22—1241no—
231C22—1242no—
232C22C22⋊C4×D3111yescharacteristic
233C22#1175846111yescharacteristic
234C22#1175851611yescharacteristic
235C4—42no—
236C4—41no—
237C4—622no—
238C4—622no—
239C4—1242no—
240C4—1241no—
241C4(C22⋊D31)⋊C411yescharacteristic
242C4#1175846211yescharacteristic
243C4C4×C22⋊D3111yescharacteristic
244C4#1175851711yescharacteristic
245C2—21no—
246C2—21no—
247C2—81no—
248C2—2481no—
249C2#1452094911yescharacteristic
250C2#1452106412yes—
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#104C2
socleC22×C31C2×C22⋊C4
prime radical#14521595C2
cosocleC22×C4×C31C23
hypercenterC2×#104D31
hypocenterC31#1963
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #14521072C2semidirect
3. C2×#11758393C2semidirect
4. C2×#11758425C2semidirect
5. C2×#11758413C2semidirect
6. #14520895C2semidirect
7. C2×C31×#104C2semidirect
12. #11758524C4semidirect
13. #11758521C4semidirect
14. #11758517C4semidirect
16. #11758513C4semidirect
52. C42×C31D4semidirect
60. C4×Dic31D4semidirect
125. C2×#104D31semidirect
152. C31#1963semidirect
189. C42C22⋊D31semidirect

Maximal subgroups

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

subgroupindex
#145215952
#145210722
C2×#117583932
C2×#117584252
C2×#117584132
#145208952
C2×C31×#1042
#196331