Finite Group Databasebeta

← #16845911

Subgroups — #16845911

Order 3968.

316 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 99 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
1C2×#11758469C211yesmaximal, characteristic
2C2×#11758395C211yesmaximal, characteristic, complemented
3C2×#11758405C211yesmaximal, characteristic, complemented
4C2×(C2×D31)⋊C8C211yesmaximal, characteristic
5#14520906C211yesmaximal, characteristic
6#14520811C211yesmaximal, characteristic, complemented
7C31×#340C211yesmaximal, characteristic, complemented
8C22×C4×D31C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×(C2×D31)⋊C4—21no—
13C2×(C2×D31)⋊C4—21no—
14C2×C4⋊Dic31C2211yescharacteristic
15C2×C4⋊Dic31C2211yescharacteristic
16C2×C4×Dic31—21no—
17C22×C31⋊C8C2211yescharacteristic
18#11758469—22no—
19#11758469—22no—
20C31⋊#95—21no—
21(C2×D31)⋊C8C414yescomplemented
22#11758405—22no—
23#11758395—22no—
24C23×D31D411yescharacteristic
25C22×C4×C31—21no—
26C22×C4×C31—21no—
27C22×C4×C31C2311yescharacteristic
28C22×Dic31—21no—
29C22×Dic31—21no—
30C22×Dic31D411yescharacteristic
31C2×C4×D31—21no—
32C2×C4×D31—21no—
33C2×C4×D31—21no—
34C2×C4×D31—21no—
35C2×C4×D31C2×C412yes—
36C2×C4×D31Q812yes—
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C2×C8×C31C2×C412yes—
40C4⋊C4×C31—21no—
41C4⋊C4×C31—21no—
42C4⋊C4×C31—21no—
43C4⋊C4×C31D412yes—
44(C2×D31)⋊C4—24no—
45(C2×D31)⋊C4—42no—
46C4⋊Dic31—21no—
47C4⋊Dic31—21no—
48C4⋊Dic31—21no—
49C4⋊Dic31D412yes—
50C4×Dic31—24no—
51C2×C31⋊C8—21no—
52C2×C31⋊C8—21no—
53C2×C31⋊C8C2×C412yes—
54C23×C31C2×D411yescharacteristic
55C22×D31—21no—
56C22×D31—21no—
57C22×D31—21no—
58C22×D31—21no—
59C22×D31—21no—
60C22×D31—21no—
61C22×D31C4⋊C412yes—
62C2×C4×C31—22no—
63C2×C4×C31—41no—
64C2×C4×C31—41no—
65C2×C4×C31—41no—
66C2×C4×C31—41no—
67C2×C4×C31—41no—
68C2×C4×C31C22×C411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×D411yescharacteristic
71C2×C4×C31C2×Q811yescharacteristic
72C2×C4×C31#4111yescharacteristic
73C2×C4×C31#4111yescharacteristic
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—22no—
77C2×Dic31—41no—
78C2×Dic31—41no—
79C2×Dic31—41no—
80C2×Dic31—41no—
81C2×Dic31—41no—
82C2×Dic31C4⋊C412yes—
83C4×D31—22no—
84C4×D31—22no—
85C4×D31—22no—
86C4×D31—22no—
87C8×C31—22no—
88C31⋊C8—22no—
89#1854—311nomaximal, Sylow
90C22×C31C2×C4⋊C411yescharacteristic
91C22×C31#12011yescharacteristic
92C22×C31#12311yescharacteristic
93C22×C31#13511yescharacteristic
94C22×C31#13511yescharacteristic
95C22×C31AGL(1,ℤ/8)11yescharacteristic
96C22×C31#13711yescharacteristic
97C2×D31—22no—
98C2×D31—22no—
99C2×D31—22no—
100C2×D31—41no—
101C2×D31—41no—
102C2×D31—41no—
103C2×D31—41no—
104C4×C31—42no—
105C4×C31—81no—
106C4×C31C4×D411yescharacteristic
107C4×C31C4×D411yescharacteristic
108C4×C31C22⋊Q811yescharacteristic
109C4×C31C22⋊Q811yescharacteristic
110Dic31—22no—
111Dic31—42no—
112Dic31—81no—
113C2×#117—311no—
114C2×#107—311no—
115C2×#106—311no—
116C2×C22⋊C8—311no—
117#380—311no—
118#340—311no—
119#340D3111yescharacteristic, complemented
120C2×C31#38511yescharacteristic
121C2×C31#42711yescharacteristic
122C2×C31#42811yescharacteristic
123C2×C31#44911yescharacteristic
124C2×C31#45211yescharacteristic
125C2×C31#48211yescharacteristic
126C2×C31#48511yescharacteristic
127D31—42no—
128C23×C4—311no—
129C22×C8—311no—
130C22×C8C2×D3111yescharacteristic
131#117—622no—
132#117—622no—
133C2×C4⋊C4—311no—
134C2×C4⋊C4—311no—
135C2×C4⋊C4C2×D3111yescharacteristic
136C2×C4⋊C4C2×D3111yescharacteristic
137C2×C22⋊C4—621no—
138C2×C22⋊C4—621no—
139C2×C42—621no—
140#107—622no—
141#106—622no—
142C22⋊C8—314no—
143#95—621no—
144C31#185411yescharacteristic, complemented, Sylow
145C24—311no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—311no—
149C22×C4—312no—
150C22×C4—312no—
151C22×C4—621no—
152C22×C4—621no—
153C22×C4—621no—
154C22×C4—621no—
155C22×C4—621no—
156C22×C4—621no—
157C22×C4C22×D3111yescharacteristic
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—312no—
161C2×C8—621no—
162C2×C8—621no—
163C2×C8C4×D3112yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—312no—
168C4⋊C4—621no—
169C4⋊C4—621no—
170C4⋊C4—621no—
171C4⋊C4D12412yes—
172C22⋊C4—624no—
173C22⋊C4—1242no—
174C42—624no—
175C23—312no—
176C23—621no—
177C23—621no—
178C23—621no—
179C23—621no—
180C23—621no—
181C23—621no—
182C23D4×D3111yescharacteristic
183C2×C4—22no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—312no—
190C2×C4—621no—
191C2×C4—621no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4—622no—
197C2×C4—1241no—
198C2×C4—1241no—
199C2×C4—1241no—
200C2×C4—1241no—
201C2×C4—1241no—
202C2×C4C2×C4×D3111yescharacteristic
203C2×C4C2×D12411yescharacteristic
204C2×C4#9249511yescharacteristic
205C2×C4D4×D3111yescharacteristic
206C2×C4#9249711yescharacteristic
207C2×C4Q8×D3111yescharacteristic
208C8—22no—
209C8—622no—
210C22—622no—
211C22—622no—
212C22—622no—
213C22—1241no—
214C22—1241no—
215C22—1241no—
216C22—1241no—
217C22#1175845911yescharacteristic
218C22#1175846011yescharacteristic
219C22C4⋊C4×D3111yescharacteristic
220C22#1175848811yescharacteristic
221C22#1175849311yescharacteristic
222C22#1175849311yescharacteristic
223C22#1175849511yescharacteristic
224C4—42no—
225C4—81no—
226C4—622no—
227C4—1242no—
228C4—2481no—
229C4C4×D12411yescharacteristic
230C4(C22⋊D31)⋊C411yescharacteristic
231C4#1175847311yescharacteristic
232C4#1175847411yescharacteristic
233C2—1242no—
234C2#1452092311yescharacteristic
235C2#1452108411yescharacteristic
236C2#1452109011yescharacteristic
237C2#1452119511yescharacteristic
238C2#1452121411yescharacteristic
239C2#1452137211yescharacteristic
240C2#1452138811yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#340C2
socleC23×C31C2×D4
prime radicalC23×D31D4
cosocleC22×C4×C31C23
hypercenter#340D31
hypocenterC31#1854
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#11758395C2semidirect
3. C2×#11758405C2semidirect
6. #14520811C2semidirect
7. C31×#340C2semidirect
21. (C2×D31)⋊C8C4semidirect
119. #340D31semidirect
144. C31#1854semidirect

Maximal subgroups

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

subgroupindex
C2×#117584692
C2×#117583952
C2×#117584052
C2×(C2×D31)⋊C82
#145209062
#145208112
C31×#3402
#185431