Finite Group Databasebeta

← #16856002

Subgroups — #16856002

Order 3968.

382 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 125 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#14521654C211yesmaximal, characteristic
2#14521373C212yesmaximal, complemented
3#14521356C212yesmaximal, complemented
4#14521249C212yesmaximal, complemented
5#14521188C212yesmaximal, complemented
6#14521147C212yesmaximal, complemented
7C4×#92481C212yesmaximal, complemented
8#14521110C211yesmaximal, characteristic, complemented
9C31×#519C211yesmaximal, characteristic, complemented
10C22×Q8×C31C2211yescharacteristic
11C4×Q8×C31—22no—
12C4×Q8×C31C2212yes—
13C4×Q8×C31C2212yes—
14C31×#117—22no—
15C31×#117C2211yescharacteristic
16C31×#117C2211yescharacteristic
17C2×#92481C2212yes—
18C2×#92481C2212yes—
19#11758507C2212yes—
20#11758471—22no—
21#11758461—22no—
22#11758451C2211yescharacteristic
23C4×D124C2212yes—
24#11758447C2211yescharacteristic
25#11758423C2212yes—
26#11758423C2212yes—
27C22⋊(C31⋊C8)C2212yes—
28#11758397C2212yes—
29#11758397C2212yes—
30#11758396C2212yes—
31#11758395C2212yes—
32C4⋊(C31⋊C8)C2212yes—
33#11758391C2211yescharacteristic
34C4×C31⋊C8C2211yescharacteristic
35C2×Q8×C31—24no—
36C2×Q8×C31—21no—
37C2×Q8×C31C2312yes—
38C22×C4×C31—21no—
39C22×C4×C31C2311yescharacteristic
40C2×C22⋊D31—22no—
41C2×D124—22no—
42C2×D124C2312yes—
43C2×C4×D31—22no—
44C4⋊C4×C31—22no—
45C4⋊C4×C31—22no—
46C4⋊C4×C31D412yes—
47C4⋊C4×C31C2312yes—
48C22⋊C4×C31—21no—
49C22⋊C4×C31D412yes—
50C42×C31—22no—
51C42×C31—22no—
52C42×C31—21no—
53C42×C31C2311yescharacteristic
54C42×C31C2311yescharacteristic
55#92481—24no—
56#92481—24no—
57(C2×D31)⋊C4—22no—
58(C2×D31)⋊C4—22no—
59C4⋊Dic31C2312yes—
60Dic31⋊C4—22no—
61C2×C31⋊C8C2312yes—
62C2×C31⋊C8C2312yes—
63C23×C31C2×D411yescharacteristic
64C22×D31—22no—
65Q8×C31—24no—
66Q8×C31—22no—
67Q8×C31#4114yes—
68C2×C4×C31—24no—
69C2×C4×C31—22no—
70C2×C4×C31—22no—
71C2×C4×C31—22no—
72C2×C4×C31C2×D412yes—
73C2×C4×C31C2×D411yescharacteristic
74C2×C4×C31C2×D412yes—
75C2×C4×C31C2411yescharacteristic
76C22⋊D31—82no—
77C2×Dic31—22no—
78D124—22no—
79D124—22no—
80D124—82no—
81C4×D31—82no—
82C31⋊C8—22no—
83C31⋊C8—22no—
84#3126—311nomaximal, Sylow
85C22×C31—21no—
86C22×C31—22no—
87C22×C31C22×D411yescharacteristic
88C2×D31—42no—
89C2×D31—42no—
90C2×D31—42no—
91C4×C31—24no—
92C4×C31—21no—
93C4×C31—22no—
94C4×C31—22no—
95C4×C31—42no—
96C4×C31C2×#4112yes—
97Dic31—42no—
98#540—311no—
99#519D3111yescharacteristic, complemented
100#482—312no—
101#479—312no—
102#460—312no—
103#448—312no—
104#440—312no—
105C4×SD16—312no—
106#433—311no—
107C2×C31—41no—
108C2×C31#52511yescharacteristic
109C2×C31#57712yes—
110D31—82no—
111C22×Q8C2×D3111yescharacteristic
112C2×SD16—312no—
113C2×SD16—312no—
114#127—311no—
115#125—311no—
116#123—622no—
117#121—312no—
118#121—622no—
119C4×Q8—22no—
120C4×Q8C2×D3112yes—
121C4×Q8C2×D3112yes—
122C4×D4—312no—
123#117—22no—
124#117C2×D3111yescharacteristic
125#117C2×D3111yescharacteristic
126#107—312no—
127#106—312no—
128C4⋊C8—312no—
129#103—312no—
130#103—312no—
131#102—312no—
132#102—312no—
133C22⋊C8—312no—
134#97—311no—
135C4×C8—311no—
136C31#312611yescharacteristic, complemented, Sylow
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8C22×D3112yes—
140C2×D4—312no—
141C2×D4—622no—
142C2×D4—622no—
143C22×C4—21no—
144C22×C4—622no—
145C22×C4C22×D3111yescharacteristic
146SD16—624no—
147SD16—624no—
148C2×C8—312no—
149C2×C8—312no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—312no—
153C4⋊C4—622no—
154C4⋊C4C22⋊D3112yes—
155C4⋊C4C22×D3112yes—
156C22⋊C4—21no—
157C22⋊C4—622no—
158C22⋊C4—622no—
159C22⋊C4C22⋊D3112yes—
160C42—22no—
161C42—22no—
162C42—21no—
163C42C22×D3111yescharacteristic
164C42C22×D3111yescharacteristic
165C23—622no—
166C23C2×C22⋊D3111yescharacteristic
167Q8—24no—
168Q8—22no—
169Q8#9249514yes—
170D4—622no—
171D4—622no—
172D4—2482no—
173D4—2482no—
174C2×C4—24no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—622no—
179C2×C4—2482no—
180C2×C4C2×C22⋊D3112yes—
181C2×C4C2×C22⋊D3112yes—
182C2×C4C2×C22⋊D3111yescharacteristic
183C2×C4C23×D3111yescharacteristic
184C8—622no—
185C8—622no—
186C22—22no—
187C22—21no—
188C22—1242no—
189C22—1242no—
190C22—1242no—
191C22C22×C22⋊D3111yescharacteristic
192C4—22no—
193C4—22no—
194C4—24no—
195C4—21no—
196C4—42no—
197C4—1242no—
198C4C2×#9249512yes—
199C2—41no—
200C2—2482no—
201C2#1452156011yescharacteristic
202C2#1452185712yes—
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#519C2
socleC22×C31C22×D4
prime radical#14521654C2
hypercenter#519D31
hypocenterC31#3126
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ #117 ◁ #519

Complements

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

NH ≅ G/Ntype
2. #14521373C2semidirect
3. #14521356C2semidirect
4. #14521249C2semidirect
5. #14521188C2semidirect
6. #14521147C2semidirect
7. C4×#92481C2semidirect
8. #14521110C2semidirect
9. C31×#519C2semidirect
99. #519D31semidirect
136. C31#3126semidirect

Maximal subgroups

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

subgroupindex
#145216542
#145213732
#145213562
#145212492
#145211882
#145211472
C4×#924812
#145211102
C31×#5192
#312631