Finite Group Databasebeta

← #16858802

Subgroups — #16858802

Order 3968.

380 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 113 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#14521781C212yesmaximal, complemented
2#14521435C212yesmaximal, complemented
3#14521273C212yesmaximal, complemented
4#14521261C212yesmaximal, complemented
5#14521242C212yesmaximal, complemented
6#14521179C211yesmaximal, characteristic, complemented
7#14521150C212yesmaximal, complemented
8C4×D248C211yesmaximal, characteristic, complemented
9C31×#495C211yesmaximal, characteristic, complemented
10C2×Q16×C31C2211yescharacteristic
11C2×SD16×C31C2212yes—
12C2×D8×C31C2211yescharacteristic
13C31×#124C2212yes—
14#11758524C2212yes—
15Q8×Dic31C2212yes—
16C2×#92481C2212yes—
17#11758517C2212yes—
18D4×Dic31C2212yes—
19C2×#92479C2212yes—
20C2×D248C2211yescharacteristic
21#11758463—22no—
22#11758462—22no—
23#11758460—22no—
24(C22⋊D31)⋊C4—22no—
25C4×D124C2212yes—
26C4×Dic62C2211yescharacteristic
27C4×C8×C31C2211yescharacteristic
28#11758423C2212yes—
29#11758420C2212yes—
30#11758409C2212yes—
31#11758406C2211yescharacteristic
32#11758403C2212yes—
33Dic31⋊C8C2212yes—
34C4⋊(C31⋊C8)C2211yescharacteristic
35C2×Q8×C31C2312yes—
36C2×D4×C31C2312yes—
37C2×C22⋊D31—22no—
38C2×C22⋊D31—22no—
39C22×Dic31—22no—
40C2×D124C2312yes—
41C2×C4×D31—22no—
42C2×Dic62D411yescharacteristic
43Q16×C31—41no—
44SD16×C31—24no—
45D8×C31—41no—
46C2×C8×C31C2311yescharacteristic
47C2×C8×C31C2311yescharacteristic
48C22⋊C4×C31—22no—
49C22⋊C4×C31—22no—
50C42×C31C2311yescharacteristic
51C22⋊Dic31—22no—
52#92481—42no—
53#92479—42no—
54(C2×D31)⋊C4—22no—
55(C2×D31)⋊C4—22no—
56(C2×D31)⋊C4—22no—
57C4⋊Dic31—22no—
58C4⋊Dic31D411yescharacteristic
59C4⋊Dic31C2312yes—
60Dic31⋊C4D412yes—
61C4×Dic31—22no—
62C4×Dic31C2312yes—
63C2×C31⋊C8C2312yes—
64D248—22no—
65C23×C31—22no—
66C22×D31—22no—
67Q8×C31—22no—
68Q8×C31—22no—
69D4×C31—22no—
70D4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31C2×D411yescharacteristic
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2411yescharacteristic
75C22⋊D31—44no—
76C22⋊D31—82no—
77C2×Dic31—22no—
78C2×Dic31—82no—
79C2×Dic31C2×D412yes—
80C2×Dic31C2×D412yes—
81D124—22no—
82D124—22no—
83C4×D31—82no—
84Dic62—41no—
85C8×C31—21no—
86C8×C31#4112yes—
87C31⋊C8—22no—
88#3403—311nomaximal, Sylow
89C22×C31—42no—
90C22×C31—42no—
91C22×C31—42no—
92C22×C31C22×D411yescharacteristic
93C2×D31—42no—
94C2×D31—42no—
95C2×D31—42no—
96C4×C31—21no—
97C4×C31—21no—
98C4×C31—42no—
99C4×C31C2×#4111yescharacteristic
100C4×C31H(5,𝔽2)11yescharacteristic
101Dic31—22no—
102Dic31—22no—
103Dic31—42no—
104#559—312no—
105#496—312no—
106#495D3111yescharacteristic, complemented
107#464—312no—
108#463—312no—
109#459—312no—
110#446—311no—
111#440—312no—
112C4×D8—311no—
113C2×C31—82no—
114C2×C31#55011yescharacteristic
115C2×C31#57511yescharacteristic
116C2×C31#57611yescharacteristic
117D31—82no—
118C2×Q16C2×D3111yescharacteristic
119C2×SD16—312no—
120C2×SD16C2×D3112yes—
121C2×D8—312no—
122C2×D8—311no—
123C2×D8C2×D3111yescharacteristic
124#127—312no—
125#124—312no—
126#124—622no—
127#124C2×D3112yes—
128#123—622no—
129#123—622no—
130C4×Q8—311no—
131C4×Q8—312no—
132C4×D4—312no—
133C4×D4—312no—
134C4×D4—622no—
135#107—311no—
136C4⋊C8—312no—
137C4⋊C8—311no—
138#103—312no—
139#102—312no—
140#102—312no—
141#97—312no—
142C4×C8C2×D3111yescharacteristic
143C31#340311yescharacteristic, complemented, Sylow
144C2×Q8—311no—
145C2×Q8C22×D3112yes—
146C2×D4—312no—
147C2×D4—622no—
148C2×D4—622no—
149C2×D4C22×D3112yes—
150C22×C4—622no—
151C22×C4—622no—
152Q16—41no—
153SD16—24no—
154SD16—1242no—
155D8—41no—
156D8—622no—
157D8—1242no—
158C2×C8—312no—
159C2×C8C22×D3111yescharacteristic
160C2×C8C22×D3111yescharacteristic
161C4⋊C4—312no—
162C4⋊C4—311no—
163C4⋊C4—312no—
164C4⋊C4—622no—
165C22⋊C4—22no—
166C22⋊C4—22no—
167C22⋊C4—622no—
168C22⋊C4—622no—
169C22⋊C4—622no—
170C22⋊C4—622no—
171C42—312no—
172C42—622no—
173C42C22×D3111yescharacteristic
174C23—22no—
175C23—622no—
176Q8—22no—
177Q8—22no—
178Q8—1241no—
179D4—22no—
180D4—22no—
181D4—622no—
182D4—622no—
183D4—1244no—
184D4—2482no—
185C2×C4—22no—
186C2×C4—312no—
187C2×C4—312no—
188C2×C4—622no—
189C2×C4—2482no—
190C2×C4—2482no—
191C2×C4D4×D3111yescharacteristic
192C2×C4D4×D3111yescharacteristic
193C2×C4C23×D3111yescharacteristic
194C8—21no—
195C8—622no—
196C8#9249712yes—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—1242no—
201C22—1242no—
202C22—1242no—
203C22C2×D4×D3111yescharacteristic
204C4—21no—
205C4—21no—
206C4—42no—
207C4—622no—
208C4—622no—
209C4—1242no—
210C4C2×#9249711yescharacteristic
211C4#1175856111yescharacteristic
212C2—82no—
213C2—2482no—
214C2#1452171911yescharacteristic
215C2#1452184611yescharacteristic
216C2#1452185111yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#495C2
socleC22×C31C22×D4
hypercenter#495D31
hypocenterC31#3403
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14521781C2semidirect
2. #14521435C2semidirect
3. #14521273C2semidirect
4. #14521261C2semidirect
5. #14521242C2semidirect
6. #14521179C2semidirect
7. #14521150C2semidirect
8. C4×D248C2semidirect
9. C31×#495C2semidirect
106. #495D31semidirect
143. C31#3403semidirect

Maximal subgroups

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

subgroupindex
#145217812
#145214352
#145212732
#145212612
#145212422
#145211792
#145211502
C4×D2482
C31×#4952
#340331