Finite Group Databasebeta

← #16845730

Subgroups — #16845730

Order 3968.

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

normal subgroups only

This group has 312 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#14521517C211yesmaximal, characteristic
2#14521072C211yesmaximal, characteristic, complemented
3C2×#11758393C211yesmaximal, characteristic
4C2×#11758413C211yesmaximal, characteristic
5C4×Dic31⋊C4C211yesmaximal, characteristic, complemented
6#14520808C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C2×M16×C31C2211yescharacteristic
10C31×#117C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12C2×Dic31⋊C4—21no—
13C2×C4×Dic31C2211yescharacteristic
14C2×C4×Dic31C2211yescharacteristic
15C2×#92474C2211yescharacteristic
16#11758470C411yescharacteristic, complemented
17#11758470C411yescharacteristic, complemented
18#11758464C411yescharacteristic, complemented
19#11758464C411yescharacteristic, complemented
20(C22⋊D31)⋊C4—21no—
21(C22⋊D31)⋊C4—21no—
22#11758449—21no—
23C42×D31—21no—
24C31⋊#95—21no—
25#11758413—22no—
26Dic31⋊C8—21no—
27Dic31⋊C8—21no—
28#11758393—22no—
29C22×C4×C31—21no—
30C22×C4×C31C2311yescharacteristic
31C2×C22⋊D31—21no—
32C22×Dic31—21no—
33C22×Dic31D411yescharacteristic
34C22×Dic31D411yescharacteristic
35#92495—21no—
36#92495—21no—
37#92495D412yes—
38#92495Q812yes—
39C2×D124C2×C411yescharacteristic
40C2×C4×D31—21no—
41C2×C4×D31—21no—
42C2×C4×D31—21no—
43C2×Dic62C2×C411yescharacteristic
44M16×C31—21no—
45M16×C31—21no—
46C2×C8×C31—21no—
47C4⋊C4×C31C2×C411yescharacteristic
48C4⋊C4×C31C2×C411yescharacteristic
49C22⋊C4×C31—21no—
50C42×C31—21no—
51C42×C31—21no—
52C42×C31—21no—
53(C2×D31)⋊C4—21no—
54(C2×D31)⋊C4—21no—
55Dic31⋊C4—24no—
56Dic31⋊C4—21no—
57Dic31⋊C4—21no—
58C4×Dic31—21no—
59C4×Dic31—21no—
60C4×Dic31—21no—
61C4×Dic31—21no—
62C4×Dic31C2×C411yescharacteristic
63C4×Dic31C2×C411yescharacteristic
64C4×Dic31D411yescharacteristic
65C4×Dic31D411yescharacteristic
66#92474—21no—
67#92474—21no—
68C2×C31⋊C8—21no—
69C23×C31C2×D411yescharacteristic
70C22×D31—21no—
71C2×C4×C31—22no—
72C2×C4×C31—21no—
73C2×C4×C31—21no—
74C2×C4×C31—41no—
75C2×C4×C31—41no—
76C2×C4×C31C22×C411yescharacteristic
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×Q811yescharacteristic
80C2×C4×C31#4111yescharacteristic
81C2×C4×C31#4111yescharacteristic
82C22⋊D31—22no—
83C22⋊D31—22no—
84C2×Dic31—21no—
85C2×Dic31—22no—
86C2×Dic31—22no—
87C2×Dic31—41no—
88C2×Dic31—41no—
89C2×Dic31—41no—
90C2×Dic31C22⋊C411yescharacteristic
91C2×Dic31C22⋊C411yescharacteristic
92C2×Dic31C22⋊C411yescharacteristic
93C2×Dic31C22⋊C411yescharacteristic
94D124—21no—
95D124C4⋊C412yescomplemented
96C4×D31—22no—
97C4×D31—22no—
98C4×D31—42no—
99C4×D31—42no—
100Dic62—21no—
101Dic62C4⋊C412yescomplemented
102C8×C31—41no—
103C31⋊C8—41no—
104#1806—311nomaximal, Sylow
105C22×C31—21no—
106C22×C31—21no—
107C22×C31C2×C22⋊C411yescharacteristic
108C22×C31#12111yescharacteristic
109C22×C31C22⋊Q811yescharacteristic
110C2×D31—22no—
111C2×D31—41no—
112C2×D31—41no—
113C4×C31—42no—
114C4×C31—41no—
115C4×C31—41no—
116C4×C31C2×C4⋊C411yescharacteristic
117C4×C31#11711yescharacteristic
118C4×C31#12111yescharacteristic
119C4×C31C22⋊Q811yescharacteristic
120Dic31—22no—
121Dic31—21no—
122Dic31—21no—
123Dic31—21no—
124Dic31—42no—
125Dic31#10412yescomplemented
126C4×#41—311no—
127#423—311no—
128C2×#104—311no—
129C2×#104—311no—
130C4×C4⋊C4—311no—
131#339—311no—
132#339D3111yescharacteristic, complemented
133C2×C31—21no—
134C2×C31—21no—
135C2×C31#38011yescharacteristic
136C2×C31C2×#10411yescharacteristic
137C2×C31#42111yescharacteristic
138D31—42no—
139C2×#41—311no—
140C2×M16—311no—
141C2×M16C2×D3111yescharacteristic
142C4×Q8—311no—
143C4×Q8—311no—
144C4×D4—311no—
145C4×D4—311no—
146C4×D4—621no—
147C4×D4—621no—
148#117—621no—
149#117C2×D3111yescharacteristic
150C2×C4⋊C4—621no—
151C2×C42—311no—
152C2×C42—311no—
153C2×C42—621no—
154C2×C42C2×D3111yescharacteristic
155C4⋊C8—621no—
156C4⋊C8—621no—
157#104—622no—
158#104—622no—
159#95—621no—
160C31#180611yescharacteristic, complemented, Sylow
161#41—312no—
162#41—312no—
163#41—621no—
164#41—621no—
165C2×Q8—311no—
166C2×D4—311no—
167C2×D4—621no—
168C22×C4—21no—
169C22×C4—311no—
170C22×C4—311no—
171C22×C4—621no—
172C22×C4—621no—
173C22×C4—621no—
174C22×C4—621no—
175C22×C4C22×D3111yescharacteristic
176M16—21no—
177M16—21no—
178M16—621no—
179M16—621no—
180C2×C8—21no—
181C2×C8—621no—
182C4⋊C4—621no—
183C4⋊C4—621no—
184C4⋊C4—624no—
185C4⋊C4C4×D3111yescharacteristic
186C4⋊C4C4×D3111yescharacteristic
187C22⋊C4—21no—
188C22⋊C4—621no—
189C22⋊C4—621no—
190C42—21no—
191C42—21no—
192C42—21no—
193C42—311no—
194C42—311no—
195C42—311no—
196C42—311no—
197C42—621no—
198C42—621no—
199C42—621no—
200C42—621no—
201C23—621no—
202C23D4×D3111yescharacteristic
203Q8—312no—
204Q8—621no—
205D4—312no—
206D4—622no—
207D4—622no—
208D4—621no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—311no—
215C2×C4—311no—
216C2×C4—311no—
217C2×C4—311no—
218C2×C4—622no—
219C2×C4—621no—
220C2×C4—622no—
221C2×C4—622no—
222C2×C4—622no—
223C2×C4—1242no—
224C2×C4—1242no—
225C2×C4—1241no—
226C2×C4—1241no—
227C2×C4—1241no—
228C2×C4C2×C4×D3111yescharacteristic
229C2×C4#9249511yescharacteristic
230C2×C4#9249511yescharacteristic
231C2×C4D4×D3111yescharacteristic
232C2×C4D4×D3111yescharacteristic
233C2×C4Q8×D3111yescharacteristic
234C8—41no—
235C8—1241no—
236C22—21no—
237C22—21no—
238C22—622no—
239C22—1241no—
240C22—1241no—
241C22C22⋊C4×D3111yescharacteristic
242C22#1175846111yescharacteristic
243C22#1175847311yescharacteristic
244C4—42no—
245C4—41no—
246C4—41no—
247C4—312no—
248C4—622no—
249C4—621no—
250C4—621no—
251C4—621no—
252C4—1242no—
253C4#1175844911yescharacteristic
254C4#1175846111yescharacteristic
255C4C4⋊C4×D3111yescharacteristic
256C4#1175847311yescharacteristic
257C2—21no—
258C2—21no—
259C2—1242no—
260C2#1452090811yescharacteristic
261C2#104×D3111yescharacteristic
262C2#1452106411yescharacteristic
subgroupG/H
centerC2×C4D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31C2×C22⋊C4
prime radicalC2×#92495C22
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1806
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14521072C2semidirect
5. C4×Dic31⋊C4C2semidirect
6. #14520808C2semidirect
7. C31×#339C2semidirect
16. #11758470C4semidirect
17. #11758470C4semidirect
18. #11758464C4semidirect
19. #11758464C4semidirect
95. D124C4⋊C4semidirect
101. Dic62C4⋊C4semidirect
125. Dic31#104semidirect
132. #339D31semidirect
160. C31#1806semidirect

Maximal subgroups

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

subgroupindex
#145215172
#145210722
C2×#117583932
C2×#117584132
C4×Dic31⋊C42
#145208082
C31×#3392
#180631