Finite Group Databasebeta

← #16846050

Subgroups — #16846050

Order 3968.

338 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C22×#92482C211yesmaximal, characteristic
2C2×Q8×Dic31C211yesmaximal, characteristic
3C2×#11758404C211yesmaximal, characteristic
4#14520954C211yesmaximal, characteristic
5#14520811C211yesmaximal, characteristic
6#14520803C211yesmaximal, characteristic
7C2×C31×#103C211yesmaximal, characteristic
8C22×Q8×C31C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C22×C8×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12Q8×Dic31—22no—
13Q8×Dic31—22no—
14C2×#92482—22no—
15C2×#92482—22no—
16C2×#92482C414yescomplemented
17C2×C4⋊Dic31—21no—
18C2×C4⋊Dic31C2211yescharacteristic
19C2×C4×Dic31—21no—
20C2×C4×Dic31C2211yescharacteristic
21C22×C31⋊C8C2211yescharacteristic
22C31×#103—22no—
23C31⋊#95—21no—
24C31⋊#95—21no—
25#11758404—22no—
26C2×Q8×C31—21no—
27C2×Q8×C31—21no—
28C2×Q8×C31—21no—
29C2×Q8×C31C2×C412yes—
30C2×Q8×C31D412yes—
31C2×Q8×C31D412yes—
32C22×C4×C31—21no—
33C22×C4×C31—21no—
34C22×C4×C31C2311yescharacteristic
35C22×Dic31—21no—
36C22×Dic31—21no—
37C22×Dic31D411yescharacteristic
38C22×Dic31D411yescharacteristic
39C2×Dic62—21no—
40C2×Dic62—21no—
41C2×Dic62—21no—
42C2×Dic62—21no—
43C2×Dic62—21no—
44C2×Dic62C2×C412yes—
45C2×C8×C31—21no—
46C2×C8×C31—21no—
47C2×C8×C31—21no—
48C4⋊C4×C31—21no—
49C4⋊C4×C31—21no—
50#92482—28no—
51C4⋊Dic31—24no—
52C4⋊Dic31—21no—
53C4⋊Dic31D412yes—
54C4×Dic31—24no—
55C4×Dic31—21no—
56C4×Dic31—21no—
57C2×C31⋊C8—21no—
58C2×C31⋊C8—21no—
59C2×C31⋊C8C2×C412yes—
60C23×C31C2×D411yescharacteristic
61Q8×C31—22no—
62Q8×C31—22no—
63Q8×C31—22no—
64Q8×C31C22⋊C414yes—
65C2×C4×C31—22no—
66C2×C4×C31—22no—
67C2×C4×C31—22no—
68C2×C4×C31—41no—
69C2×C4×C31—41no—
70C2×C4×C31—41no—
71C2×C4×C31C22×C411yescharacteristic
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2×D411yescharacteristic
75C2×C4×C31#4111yescharacteristic
76C2×C4×C31#4111yescharacteristic
77C2×Dic31—21no—
78C2×Dic31—21no—
79C2×Dic31—22no—
80C2×Dic31—21no—
81C2×Dic31—22no—
82C2×Dic31—21no—
83C2×Dic31—21no—
84C2×Dic31—41no—
85C2×Dic31—41no—
86C2×Dic31—41no—
87C2×Dic31—41no—
88C2×Dic31Q1612yescomplemented
89Dic62—22no—
90Dic62—22no—
91Dic62—41no—
92Dic62—41no—
93C8×C31—41no—
94C31⋊C8—22no—
95#1878—311nomaximal, Sylow
96C22×C31C4×D411yescharacteristic
97C22×C31#12011yescharacteristic
98C22×C31#12111yescharacteristic
99C22×C31C2×Q1611yescharacteristic
100C22×C31#13511yescharacteristic
101C22×C31#13711yescharacteristic
102C22×C31#13711yescharacteristic
103C4×C31—24no—
104C4×C31—81no—
105C4×C31C2×C22⋊C411yescharacteristic
106C4×C31C4×D411yescharacteristic
107C4×C31#12111yescharacteristic
108C4×C31#12311yescharacteristic
109Dic31—22no—
110Dic31—42no—
111Dic31—41no—
112Dic31—42no—
113C22×Q16—311no—
114C2×C4×Q8—311no—
115C2×#103—311no—
116C2×#103D3111yescharacteristic
117#391—311no—
118#340—311no—
119#336—311no—
120C2×C31#38611yescharacteristic
121C2×C31C4×Q1611yescharacteristic
122C2×C31#44111yescharacteristic
123C2×C31#45111yescharacteristic
124C2×C31#45211yescharacteristic
125C2×C31#46211yescharacteristic
126C2×C31#46411yescharacteristic
127C22×Q8—311no—
128C22×Q8C2×D3111yescharacteristic
129C2×Q16—314no—
130C2×Q16—622no—
131C2×Q16—622no—
132C22×C8—311no—
133C22×C8C2×D3111yescharacteristic
134C4×Q8—622no—
135C4×Q8—622no—
136C2×C4⋊C4—311no—
137C2×C4⋊C4—621no—
138C2×C4⋊C4C2×D3111yescharacteristic
139C2×C42—311no—
140C2×C42—621no—
141#103—22no—
142#103—622no—
143#95—621no—
144#95—621no—
145C31#187811yescharacteristic, complemented, Sylow
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—21no—
149C2×Q8—312no—
150C2×Q8—621no—
151C2×Q8—621no—
152C2×Q8—621no—
153C2×Q8—621no—
154C2×Q8—621no—
155C2×Q8C4×D3112yes—
156C2×Q8D12412yes—
157C2×Q8C22⋊D3112yes—
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—311no—
161C22×C4—311no—
162C22×C4—621no—
163C22×C4—621no—
164C22×C4C22×D3111yescharacteristic
165Q16—628no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—21no—
169C2×C8—312no—
170C2×C8—621no—
171C2×C8—621no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—312no—
175C4⋊C4—624no—
176C4⋊C4—621no—
177C42—624no—
178C42—621no—
179C42—621no—
180C23D4×D3111yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—22no—
184Q8—622no—
185Q8—622no—
186Q8—1241no—
187Q8—1241no—
188Q8(C2×D31)⋊C414yes—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—312no—
196C2×C4—621no—
197C2×C4—621no—
198C2×C4—622no—
199C2×C4—622no—
200C2×C4—621no—
201C2×C4—621no—
202C2×C4—621no—
203C2×C4—1241no—
204C2×C4—1241no—
205C2×C4—1241no—
206C2×C4—1241no—
207C2×C4C2×C4×D3111yescharacteristic
208C2×C4C2×D12411yescharacteristic
209C2×C4D4×D3111yescharacteristic
210C2×C4#9249711yescharacteristic
211C2×C4#9249711yescharacteristic
212C2×C4C2×C22⋊D3111yescharacteristic
213C8—41no—
214C8—622no—
215C22(C22⋊D31)⋊C411yescharacteristic
216C22#1175845911yescharacteristic
217C22#1175849211yescharacteristic
218C22#1175849311yescharacteristic
219C22Q16×D3111yescharacteristic
220C22#1175849511yescharacteristic
221C22#1175851611yescharacteristic
222C4—24no—
223C4—81no—
224C4—622no—
225C4—1242no—
226C4—1241no—
227C4—1242no—
228C4(C22⋊D31)⋊C411yescharacteristic
229C4#1175846311yescharacteristic
230C4C2×(C2×D31)⋊C411yescharacteristic
231C4#1175851611yescharacteristic
232C2#1452092611yescharacteristic
233C2#1452114111yescharacteristic
234C2#1452115311yescharacteristic
235C2#1452120611yescharacteristic
236C2#1452121411yescharacteristic
237C2#1452125711yescharacteristic
238C2#1452126911yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#103C2
socle, prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenterC2×#103D31
hypocenterC31#1878
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
16. C2×#92482C4semidirect
88. C2×Dic31Q16semidirect
145. C31#1878semidirect

Maximal subgroups

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

subgroupindex
C22×#924822
C2×Q8×Dic312
C2×#117584042
#145209542
#145208112
#145208032
C2×C31×#1032
#187831