Finite Group Databasebeta

← #16846537

Subgroups — #16846537

Order 3968.

360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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
6C42×Dic31C211yesmaximal, 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×Dic31—22no—
19C2×C4×Dic31C2211yescharacteristic
20C2×C4×Dic31C2211yescharacteristic
21C2×#92474C2211yescharacteristic
22C31×#104—22no—
23#11758425—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—28no—
57C4×Dic31—21no—
58C4×Dic31C2×C411yescharacteristic
59C4×Dic31C2×C411yescharacteristic
60C4×Dic31D412yes—
61C4×Dic31D412yescomplemented
62#92474—21no—
63#92474—21no—
64C2×C31⋊C8—21no—
65C23×C31—21no—
66C23×C31C2×D411yescharacteristic
67C22×D31—21no—
68Q8×C31—21no—
69Q8×C31—21no—
70D4×C31—21no—
71D4×C31—21no—
72D4×C31—41no—
73D4×C31—41no—
74C2×C4×C31—24no—
75C2×C4×C31—22no—
76C2×C4×C31—21no—
77C2×C4×C31—41no—
78C2×C4×C31—41no—
79C2×C4×C31C22×C411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31#4111yescharacteristic
84C2×C4×C31#4111yescharacteristic
85C22⋊D31—41no—
86C22⋊D31—41no—
87C22⋊D31—44no—
88C2×Dic31—24no—
89C2×Dic31—22no—
90C2×Dic31—24no—
91C2×Dic31—21no—
92C2×Dic31C22⋊C412yes—
93C2×Dic31C22⋊C412yes—
94D124—21no—
95D124—21no—
96C4×D31—41no—
97C4×D31—41no—
98Dic62—21no—
99Dic62—21no—
100C8×C31—41no—
101C31⋊C8—41no—
102#1962—311nomaximal, Sylow
103C22×C31—22no—
104C22×C31—41no—
105C22×C31—42no—
106C22×C31C2×C22⋊C411yescharacteristic
107C22×C31#12111yescharacteristic
108C22×C31#12111yescharacteristic
109C2×D31—41no—
110C2×D31—42no—
111C4×C31—24no—
112C4×C31—41no—
113C4×C31C4×D411yescharacteristic
114C4×C31C4×D411yescharacteristic
115C4×C31#12411yescharacteristic
116C4×C31#12711yescharacteristic
117Dic31—24no—
118Dic31—22no—
119Dic31—41no—
120Dic31#10414yescomplemented
121#532—311no—
122#423—311no—
123C2×#104—311no—
124C2×#104—311no—
125C2×#104—311no—
126C2×#104D3111yescharacteristic, complemented
127C43—311no—
128C2×C31—21no—
129C2×C31—21no—
130C2×C31—81no—
131C2×C31#39011yescharacteristic
132C2×C31C2×#10412yes—
133D31—81no—
134C2×#41—311no—
135C2×#41C2×D3111yescharacteristic
136C2×M16—311no—
137C2×M16C2×D3111yescharacteristic
138C4⋊Q8—311no—
139#127—311no—
140#124—311no—
141#124—311no—
142#121—622no—
143C4×D4—622no—
144C2×C42—311no—
145C2×C42—311no—
146C2×C42—622no—
147C2×C42C2×D3111yescharacteristic
148C4⋊C8—622no—
149#104—22no—
150#104—622no—
151#104—622no—
152#104—622no—
153C31#196211yescharacteristic, complemented, Sylow
154#41—21no—
155#41—21no—
156#41—21no—
157#41—21no—
158#41—621no—
159#41—621no—
160#41—621no—
161#41—621no—
162C2×Q8—311no—
163C2×Q8C4×D3111yescharacteristic
164C2×D4—21no—
165C2×D4—311no—
166C2×D4—622no—
167C2×D4—621no—
168C2×D4C4×D3111yescharacteristic
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—312no—
172C22×C4—621no—
173C22×C4—621no—
174C22×C4C22×D3111yescharacteristic
175M16—21no—
176M16—21no—
177M16—621no—
178M16—621no—
179C2×C8—21no—
180C2×C8—621no—
181C4⋊C4—622no—
182C22⋊C4—622no—
183C22⋊C4—622no—
184C42—21no—
185C42—311no—
186C42—311no—
187C42—312no—
188C42—312no—
189C42—628no—
190C42—621no—
191C42C22⋊D3112yescomplemented
192C23—21no—
193C23—621no—
194C23D4×D3111yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—621no—
198Q8—621no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—621no—
204D4—621no—
205D4—1244no—
206D4—1241no—
207D4—1241no—
208C2×C4—24no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—312no—
214C2×C4—312no—
215C2×C4—624no—
216C2×C4—624no—
217C2×C4—622no—
218C2×C4—621no—
219C2×C4—1241no—
220C2×C4—1241no—
221C2×C4C2×C4×D3111yescharacteristic
222C2×C4#9249511yescharacteristic
223C2×C4D4×D3111yescharacteristic
224C2×C4D4×D3111yescharacteristic
225C2×C4#9249711yescharacteristic
226C2×C4C2×C22⋊D3111yescharacteristic
227C8—41no—
228C8—1241no—
229C22—22no—
230C22—41no—
231C22—42no—
232C22—1241no—
233C22—1242no—
234C22C22⋊C4×D3111yescharacteristic
235C22#1175846111yescharacteristic
236C22#1175851611yescharacteristic
237C4—24no—
238C4—41no—
239C4—314no—
240C4—624no—
241C4—622no—
242C4—1241no—
243C4(C22⋊D31)⋊C411yescharacteristic
244C4#1175846211yescharacteristic
245C4C4×C22⋊D3111yescharacteristic
246C4#1175851711yescharacteristic
247C2—21no—
248C2—21no—
249C2—81no—
250C2—2481no—
251C2#1452094911yescharacteristic
252C2#104×D3112yes—
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#1962
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. C42×Dic31C2semidirect
7. C2×C31×#104C2semidirect
12. #11758524C4semidirect
13. #11758521C4semidirect
14. #11758517C4semidirect
16. #11758513C4semidirect
52. C42×C31D4semidirect
61. C4×Dic31D4semidirect
120. Dic31#104semidirect
126. C2×#104D31semidirect
153. C31#1962semidirect
191. 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
C42×Dic312
C2×C31×#1042
#196231