Finite Group Databasebeta

← #16855833

Subgroups — #16855833

Order 3968.

424 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 133 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#14521599C211yesmaximal, characteristic
2#14521362C212yesmaximal, complemented
3#14521344C212yesmaximal, complemented
4#14521249C212yesmaximal, complemented
5#14521188C212yesmaximal, complemented
6#14521147C214yesmaximal, complemented
7#14521106C211yesmaximal, characteristic, complemented
8C2×C4×Q8×C31C211yesmaximal, characteristic, complemented
9C22×Q8×C31C2211yescharacteristic
10C2×#92495—21no—
11C4×Q8×C31—21no—
12C4×Q8×C31—21no—
13C4×Q8×C31C2212yes—
14C4×Q8×C31C2212yes—
15C2×C4⋊C4×C31—21no—
16C2×C4⋊C4×C31C2211yescharacteristic
17C2×C42×C31—21no—
18C2×C42×C31C2211yescharacteristic
19C2×#92481C2214yes—
20#11758507—21no—
21#11758507C2212yes—
22#11758452—21no—
23#11758451C2211yescharacteristic
24C4×D124—21no—
25C4×D124C2212yes—
26#11758446C2211yescharacteristic
27#11758423C2214yes—
28C22⋊(C31⋊C8)C2212yes—
29#11758397C2214yes—
30#11758395C2214yes—
31C4⋊(C31⋊C8)C2212yes—
32#11758391C2212yes—
33C2×Q8×C31—24no—
34C2×Q8×C31—21no—
35C2×Q8×C31C2312yes—
36C22×C4×C31—21no—
37C22×C4×C31—21no—
38C22×C4×C31D411yescharacteristic
39C22×C4×C31D411yescharacteristic
40C22×C4×C31C2311yescharacteristic
41C2×C22⋊D31—22no—
42#92495—44no—
43C2×D124—21no—
44C2×D124—21no—
45C2×D124C2312yes—
46C2×C4×D31—22no—
47C2×Dic62—21no—
48C4⋊C4×C31—22no—
49C4⋊C4×C31—22no—
50C4⋊C4×C31—21no—
51C4⋊C4×C31C2312yes—
52C42×C31—22no—
53C42×C31—22no—
54C42×C31D411yescharacteristic
55C42×C31D411yescharacteristic
56C42×C31C2311yescharacteristic
57C42×C31C2311yescharacteristic
58#92481—28no—
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—22no—
61C4⋊Dic31—21no—
62C4⋊Dic31C2312yes—
63C2×C31⋊C8C2314yes—
64C23×C31C2×D411yescharacteristic
65C22×D31—22no—
66Q8×C31—24no—
67Q8×C31—22no—
68Q8×C31#4114yescomplemented
69C2×C4×C31—24no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31—42no—
76C2×C4×C31C2×D411yescharacteristic
77C2×C4×C31C2×D411yescharacteristic
78C2×C4×C31C2×D411yescharacteristic
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2411yescharacteristic
82C22⋊D31—44no—
83C2×Dic31—22no—
84D124—24no—
85D124—42no—
86D124—42no—
87C4×D31—44no—
88Dic62—42no—
89C31⋊C8—24no—
90#3112—311nomaximal, Sylow
91C22×C31—21no—
92C22×C31—21no—
93C22×C31AGL(1,ℤ/8)12yes—
94C22×C31C22×D411yescharacteristic
95C2×D31—42no—
96C2×D31—42no—
97C2×D31—42no—
98C4×C31—24no—
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—21no—
102C4×C31—21no—
103C4×C31—42no—
104C4×C31#13712yes—
105C4×C31C2×#4112yes—
106Dic31—42no—
107#532—311no—
108C2×C4×Q8D3111yescharacteristic, complemented
109#480—312no—
110#477—312no—
111#460—312no—
112#448—312no—
113#440—314no—
114#432—311no—
115C2×C31—22no—
116C2×C31#52511yescharacteristic
117C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C31C2×#13711yescharacteristic
119D31—82no—
120C2×#41—621no—
121C22×Q8C2×D3111yescharacteristic
122C2×SD16—314no—
123C4⋊Q8—311no—
124#127—311no—
125#124—621no—
126#121—312no—
127#121—621no—
128C4×Q8—21no—
129C4×Q8—21no—
130C4×Q8C2×D3112yes—
131C4×Q8C2×D3112yes—
132C4×D4—312no—
133C4×D4—621no—
134C2×C4⋊C4—21no—
135C2×C4⋊C4C2×D3111yescharacteristic
136C2×C42—21no—
137C2×C42C2×D3111yescharacteristic
138#107—314no—
139C4⋊C8—312no—
140#103—314no—
141#102—314no—
142C22⋊C8—312no—
143#97—312no—
144C31#311211yescharacteristic, complemented, Sylow
145#41—1244no—
146C2×Q8—24no—
147C2×Q8—21no—
148C2×Q8—621no—
149C2×Q8C22×D3112yes—
150C2×D4—312no—
151C2×D4—622no—
152C2×D4—621no—
153C2×D4—621no—
154C22×C4—21no—
155C22×C4—21no—
156C22×C4—622no—
157C22×C4C22⋊D3111yescharacteristic
158C22×C4C22⋊D3111yescharacteristic
159C22×C4C22×D3111yescharacteristic
160SD16—628no—
161C2×C8—314no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—21no—
165C4⋊C4—312no—
166C4⋊C4—621no—
167C4⋊C4C22×D3112yes—
168C22⋊C4—622no—
169C22⋊C4—622no—
170C42—22no—
171C42—22no—
172C42C22⋊D3111yescharacteristic
173C42C22⋊D3111yescharacteristic
174C42C22×D3111yescharacteristic
175C42C22×D3111yescharacteristic
176C23—622no—
177C23C2×C22⋊D3111yescharacteristic
178Q8—24no—
179Q8—22no—
180Q8—1242no—
181Q8#9249514yescomplemented
182D4—624no—
183D4—1242no—
184D4—1244no—
185D4—1242no—
186C2×C4—24no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—622no—
194C2×C4—1244no—
195C2×C4C2×C22⋊D3111yescharacteristic
196C2×C4C2×C22⋊D3111yescharacteristic
197C2×C4C2×C22⋊D3111yescharacteristic
198C2×C4C2×C22⋊D3111yescharacteristic
199C2×C4C2×C22⋊D3111yescharacteristic
200C2×C4C23×D3111yescharacteristic
201C8—624no—
202C22—21no—
203C22—21no—
204C22—1242no—
205C22—1242no—
206C22—1242no—
207C22#1175852612yes—
208C22C22×C22⋊D3111yescharacteristic
209C4—24no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—21no—
214C4—42no—
215C4—1242no—
216C4#1175851912yes—
217C4C2×#9249512yes—
218C2—22no—
219C2—2482no—
220C2#1452156011yescharacteristic
221C2C2×#1175852611yescharacteristic
222C2C2×#1175851911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C4×Q8×C31C2
socleC22×C31C22×D4
prime radical#14521599C2
hypercenterC2×C4×Q8D31
hypocenterC31#3112
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #14521362C2semidirect
3. #14521344C2semidirect
4. #14521249C2semidirect
5. #14521188C2semidirect
6. #14521147C2semidirect
7. #14521106C2semidirect
8. C2×C4×Q8×C31C2semidirect
68. Q8×C31#41semidirect
108. C2×C4×Q8D31semidirect
144. C31#3112semidirect
181. Q8#92495semidirect

Maximal subgroups

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

subgroupindex
#145215992
#145213622
#145213442
#145212492
#145211882
#145211472
#145211062
C2×C4×Q8×C312
#311231