Finite Group Databasebeta

← #16846856

Subgroups — #16846856

Order 3968.

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

normal subgroups only

This group has 294 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
1C2×#11758467C211yesmaximal, characteristic, complemented
2C2×#11758409C211yesmaximal, characteristic
3C2×#11758397C211yesmaximal, characteristic
4#14520950C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic, complemented
6#14520803C211yesmaximal, characteristic, complemented
7C31×#340C211yesmaximal, characteristic, complemented
8C22×D124C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×(C2×D31)⋊C4—21no—
13C2×(C2×D31)⋊C4—21no—
14C2×C4⋊Dic31—21no—
15C2×C4⋊Dic31C2211yescharacteristic
16C2×Dic31⋊C4—21no—
17C2×C4×Dic31C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19#11758467—22no—
20#11758467—22no—
21#11758409—22no—
22#11758397—22no—
23C23×D31—21no—
24C22×C4×C31—21no—
25C22×C4×C31—21no—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31—21no—
28C22×Dic31D411yescharacteristic
29C22×Dic31D411yescharacteristic
30C2×D124—21no—
31C2×D124—21no—
32C2×D124—21no—
33C2×D124—21no—
34C2×D124—21no—
35C2×D124Q812yes—
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C2×C8×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊C4×C31—21no—
41C4⋊C4×C31—21no—
42C4⋊C4×C31D412yes—
43(C2×D31)⋊C4—42no—
44(C2×D31)⋊C4—42no—
45C4⋊Dic31—24no—
46C4⋊Dic31—21no—
47C4⋊Dic31D412yes—
48Dic31⋊C4—24no—
49C4×Dic31—21no—
50C4×Dic31—21no—
51C2×C31⋊C8—21no—
52C2×C31⋊C8—21no—
53C2×C31⋊C8—21no—
54C23×C31C2×D411yescharacteristic
55C22×D31—22no—
56C22×D31—41no—
57C22×D31—41no—
58C22×D31—41no—
59C22×D31—41no—
60C22×D31—41no—
61C22×D31—41no—
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×C31C2×D411yescharacteristic
69C2×C4×C31C2×D411yescharacteristic
70C2×C4×C31C2×Q811yescharacteristic
71C2×C4×C31#4111yescharacteristic
72C2×C4×C31#4111yescharacteristic
73C2×C4×C31#4111yescharacteristic
74C2×Dic31—21no—
75C2×Dic31—21no—
76C2×Dic31—22no—
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—21no—
80C2×Dic31—21no—
81C2×Dic31—41no—
82C2×Dic31—41no—
83D124—22no—
84D124—22no—
85D124—41no—
86D124—41no—
87C8×C31—41no—
88C31⋊C8—41no—
89#2025—311nomaximal, Sylow
90C22×C31#12011yescharacteristic
91C22×C31C22⋊Q811yescharacteristic
92C22×C31#12411yescharacteristic
93C22×C31#13511yescharacteristic
94C22×C31#13511yescharacteristic
95C22×C31AGL(1,ℤ/8)11yescharacteristic
96C22×C31AGL(1,ℤ/8)11yescharacteristic
97C2×D31—42no—
98C2×D31—42no—
99C2×D31—42no—
100C2×D31—81no—
101C2×D31—81no—
102C2×D31—81no—
103C2×D31—81no—
104C4×C31—42no—
105C4×C31—81no—
106C4×C31C22⋊Q811yescharacteristic
107C4×C31C22⋊Q811yescharacteristic
108C4×C31#12411yescharacteristic
109C4×C31#12411yescharacteristic
110Dic31—41no—
111Dic31—41no—
112Dic31—42no—
113C2×#125—311no—
114C2×#102—311no—
115C2×#102—311no—
116#390—311no—
117#340—311no—
118#340D3111yescharacteristic, complemented
119#336—311no—
120C2×C31#39311yescharacteristic
121C2×C31#44911yescharacteristic
122C2×C31#44911yescharacteristic
123C2×C31#47811yescharacteristic
124C2×C31#47811yescharacteristic
125C2×C31#48811yescharacteristic
126C2×C31#49011yescharacteristic
127D31—82no—
128C22×D4—311no—
129C22×C8—311no—
130C22×C8C2×D3111yescharacteristic
131#125—622no—
132#125—622no—
133C2×C4⋊C4—311no—
134C2×C4⋊C4—621no—
135C2×C4⋊C4—621no—
136C2×C4⋊C4C2×D3111yescharacteristic
137C2×C4⋊C4C2×D3111yescharacteristic
138C2×C22⋊C4—621no—
139C2×C22⋊C4—621no—
140C2×C42—311no—
141#102—622no—
142#102—622no—
143C31#202511yescharacteristic, complemented, Sylow
144C24—621no—
145C2×D4—312no—
146C2×D4—621no—
147C2×D4—621no—
148C2×D4—621no—
149C2×D4—621no—
150C2×D4—621no—
151C22×C4—21no—
152C22×C4—21no—
153C22×C4—311no—
154C22×C4—311no—
155C22×C4—621no—
156C22×C4C22×D3111yescharacteristic
157C2×C8—21no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8—621no—
161C2×C8—621no—
162C2×C8—621no—
163C4⋊C4—21no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—312no—
167C4⋊C4—624no—
168C4⋊C4—624no—
169C4⋊C4—621no—
170C4⋊C4D12412yes—
171C22⋊C4—1242no—
172C22⋊C4—1242no—
173C42—621no—
174C42—621no—
175C23—622no—
176C23—1241no—
177C23—1241no—
178C23—1241no—
179C23—1241no—
180C23—1241no—
181C23—1241no—
182C23D4×D3111yescharacteristic
183D4—622no—
184D4—622no—
185D4—1241no—
186D4—1241no—
187C2×C4—22no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—621no—
194C2×C4—621no—
195C2×C4—622no—
196C2×C4—621no—
197C2×C4—621no—
198C2×C4—621no—
199C2×C4—621no—
200C2×C4—1241no—
201C2×C4—1241no—
202C2×C4C2×D12411yescharacteristic
203C2×C4#9249511yescharacteristic
204C2×C4#9249511yescharacteristic
205C2×C4D4×D3111yescharacteristic
206C2×C4#9249711yescharacteristic
207C2×C4Q8×D3111yescharacteristic
208C8—41no—
209C8—1241no—
210C22—1242no—
211C22—1242no—
212C22—1242no—
213C22—2481no—
214C22—2481no—
215C22—2481no—
216C22—2481no—
217C22#1175845911yescharacteristic
218C22#1175846211yescharacteristic
219C22#1175847311yescharacteristic
220C22#1175848811yescharacteristic
221C22#1175849111yescharacteristic
222C22#1175849311yescharacteristic
223C22#1175849611yescharacteristic
224C4—42no—
225C4—81no—
226C4—1241no—
227C4—1241no—
228C4—1242no—
229C4#1175845211yescharacteristic
230C4#1175846211yescharacteristic
231C4#1175847311yescharacteristic
232C4#1175847411yescharacteristic
233C2—2482no—
234C2#1452096211yescharacteristic
235C2#1452119511yescharacteristic
236C2#1452119711yescharacteristic
237C2#1452134811yescharacteristic
238C2#1452135211yescharacteristic
239C2#1452140511yescharacteristic
240C2#1452141211yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#340C2
socleC23×C31C2×D4
prime radicalC22×D124C22
hypercenter#340D31
hypocenterC31#2025
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
1. C2×#11758467C2semidirect
5. #14520811C2semidirect
6. #14520803C2semidirect
7. C31×#340C2semidirect
118. #340D31semidirect
143. C31#2025semidirect

Maximal subgroups

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

subgroupindex
C2×#117584672
C2×#117584092
C2×#117583972
#145209502
#145208112
#145208032
C31×#3402
#202531