Finite Group Databasebeta

← D31×#487 #16856019

Subgroups — D31×#487 #16856019

Order 3968.

424 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C4⋊Q8×D31C211yesmaximal, characteristic
2C4⋊Q8×D31C211yesmaximal, characteristic
3#14521401C211yesmaximal, characteristic, complemented
4#14521400C211yesmaximal, characteristic, complemented
5#14521399C211yesmaximal, characteristic, complemented
6#14521398C214yesmaximal, complemented
7#103×D31C214yesmaximal
8C4×C8×D31C211yesmaximal, characteristic
9C31×#487C211yesmaximal, characteristic, complemented
10C2×Q8×D31—21no—
11C2×Q8×D31C2212yes—
12C31×C4⋊Q8C2211yescharacteristic
13C31×C4⋊Q8C2211yescharacteristic
14#11758521—21no—
15#11758521C2212yes—
16C2×C8×D31C2212yes—
17C4⋊C4×D31—21no—
18C4⋊C4×D31—21no—
19C4⋊C4×D31—21no—
20C4⋊C4×D31C2212yes—
21#11758465—21no—
22#11758465—21no—
23#11758465—21no—
24#11758465C2212yes—
25C42×D31C2211yescharacteristic
26#11758446C2211yescharacteristic
27#11758446C2211yescharacteristic
28C31×#103C2214yes—
29C4×C8×C31C2211yescharacteristic
30#11758423C2214yes—
31#11758404C2214yes—
32C8×Dic31C2212yes—
33#11758398C2214yes—
34C4×C31⋊C8C2211yescharacteristic
35C2×Q8×C31—21no—
36C2×Q8×C31C2312yes—
37Q8×D31—28no—
38Q8×D31—44no—
39C2×C4×D31—22no—
40C2×C4×D31—22no—
41C2×C4×D31D411yescharacteristic
42C2×C4×D31D411yescharacteristic
43C2×C4×D31C2311yescharacteristic
44C2×Dic62—21no—
45C2×Dic62—22no—
46C2×Dic62—22no—
47C2×Dic62C2312yes—
48C2×C8×C31C2312yes—
49C4⋊C4×C31—21no—
50C4⋊C4×C31—21no—
51C4⋊C4×C31—21no—
52C4⋊C4×C31C2312yes—
53C42×C31C2311yescharacteristic
54C4⋊Dic31—21no—
55C4⋊Dic31—21no—
56C4⋊Dic31—21no—
57C4⋊Dic31C2312yes—
58Dic31⋊C4—22no—
59Dic31⋊C4—22no—
60Dic31⋊C4—22no—
61Dic31⋊C4—22no—
62C4×Dic31D411yescharacteristic
63C4×Dic31D411yescharacteristic
64C4×Dic31C2311yescharacteristic
65C2×C31⋊C8C2312yes—
66C8×D31—24no—
67C22×D31C2×D411yescharacteristic
68Q8×C31—24no—
69Q8×C31—42no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2411yescharacteristic
75C2×Dic31—22no—
76C2×Dic31—22no—
77C2×Dic31C2×D411yescharacteristic
78C2×Dic31C2×D411yescharacteristic
79C2×Dic31C2×D411yescharacteristic
80C4×D31—44no—
81C4×D31—44no—
82C4×D31SD1614yes—
83C4×D31Q1614yes—
84C4×D31#4114yes—
85Dic62—24no—
86Dic62—42no—
87Dic62—44no—
88Dic62—44no—
89C8×C31—22no—
90C31⋊C8—22no—
91C2×#487—311nomaximal, Sylow
92C22×C31C22×D411yescharacteristic
93C2×D31#12412yes—
94C2×D31C2×SD1612yes—
95C2×D31C2×Q1612yes—
96C4×C31—42no—
97C4×C31—42no—
98C4×C31C2×SD1612yes—
99C4×C31C2×Q1612yes—
100C4×C31C2×#4112yes—
101Dic31—42no—
102Dic31—42no—
103Dic31#12412yes—
104Dic31C2×SD1612yes—
105Dic31C2×Q1612yes—
106C2×C4⋊Q8—311no—
107C2×C4⋊Q8—311no—
108#487—311no—
109#487—311no—
110#487—314no—
111#487—311no—
112#487D3111yescharacteristic, direct product factor
113C2×#103—314no—
114C2×C4×C8—311no—
115C2×C31C2×#12411yescharacteristic
116C2×C31C22×SD1611yescharacteristic
117C2×C31C22×Q1611yescharacteristic
118D31#48714yesdirect product factor
119C22×Q8—312no—
120C22×Q8—621no—
121C22×C8—312no—
122C4⋊Q8—312no—
123C4⋊Q8—312no—
124C4⋊Q8—311no—
125C4⋊Q8—311no—
126C4⋊Q8—621no—
127C4⋊Q8—621no—
128C4⋊Q8—621no—
129C4⋊Q8—621no—
130C4⋊Q8C2×D3111yescharacteristic
131C4⋊Q8C2×D3111yescharacteristic
132C2×C4⋊C4—312no—
133C2×C4⋊C4—621no—
134C2×C4⋊C4—621no—
135C2×C4⋊C4—621no—
136C2×C42—311no—
137#103—314no—
138#103—314no—
139#103—314no—
140#103C2×D3114yes—
141C4×C8—312no—
142C4×C8—311no—
143C4×C8C2×D3111yescharacteristic
144C31C2×#48711yescharacteristic, complemented, Sylow
145C2×Q8—21no—
146C2×Q8—312no—
147C2×Q8—622no—
148C2×Q8—622no—
149C2×Q8—628no—
150C2×Q8—621no—
151C2×Q8—1244no—
152C2×Q8C22×D3112yes—
153C22×C4—311no—
154C22×C4—311no—
155C22×C4—311no—
156C22×C4—622no—
157C22×C4—622no—
158C2×C8—312no—
159C2×C8—624no—
160C2×C8C22×D3112yes—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—21no—
164C4⋊C4—312no—
165C4⋊C4—622no—
166C4⋊C4—622no—
167C4⋊C4—622no—
168C4⋊C4—622no—
169C4⋊C4—621no—
170C4⋊C4—621no—
171C4⋊C4—621no—
172C4⋊C4C22×D3112yes—
173C42—311no—
174C42—311no—
175C42—311no—
176C42C22×D3111yescharacteristic
177C23—311no—
178Q8—24no—
179Q8—42no—
180Q8—624no—
181Q8—1244no—
182Q8—1244no—
183Q8—1242no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—311no—
187C2×C4—311no—
188C2×C4—311no—
189C2×C4—314no—
190C2×C4—314no—
191C2×C4—314no—
192C2×C4—622no—
193C2×C4—622no—
194C2×C4—1244no—
195C2×C4—1244no—
196C2×C4D4×D3111yescharacteristic
197C2×C4D4×D3111yescharacteristic
198C2×C4C23×D3111yescharacteristic
199C8—22no—
200C8—622no—
201C22—312no—
202C22—312no—
203C22—312no—
204C22C2×D4×D3111yescharacteristic
205C4—42no—
206C4—42no—
207C4—312no—
208C4—312no—
209C4—312no—
210C4—1242no—
211C4—1242no—
212C4SD16×D3112yes—
213C4Q16×D3112yes—
214C4#41×D3112yes—
215C2—314no—
216C2#124×D3111yescharacteristic
217C2C2×SD16×D3111yescharacteristic
218C2C2×Q16×D3111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#487C2
socleC22×C31C22×D4
prime radicalC22×D31C2×D4
hypercenter#487D31
hypocenterC31C2×#487
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
3. #14521401C2semidirect
4. #14521400C2semidirect
5. #14521399C2semidirect
6. #14521398C2semidirect
9. C31×#487C2semidirect
112. #487D31direct (N × H)
118. D31#487direct (N × H)
144. C31C2×#487semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D312
#145214012
#145214002
#145213992
#145213982
#103×D312
C4×C8×D312
C31×#4872
C2×#48731