Finite Group Databasebeta

← #16846884

Subgroups — #16846884

Order 3968.

244 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 63 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#14521606C211yesmaximal, characteristic, complemented
2#14521065C211yesmaximal, characteristic
3C2×#11758393C211yesmaximal, characteristic
4#14521022C211yesmaximal, characteristic
5#14520820C211yesmaximal, characteristic, complemented
6#14520805C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C2×#92495C2211yescharacteristic
9C2×M16×C31C2211yescharacteristic
10C31×#117C2211yescharacteristic
11C2×C42×C31C2211yescharacteristic
12#11758503C2211yescharacteristic
13#11758503C2211yescharacteristic
14#11758501—22no—
15C2×#92474C2211yescharacteristic
16#11758447—21no—
17#11758446—21no—
18C4×Dic62—22no—
19#11758413—22no—
20#11758394—22no—
21#11758393—21no—
22#11758393—21no—
23C22×C4×C31—21no—
24C22×C4×C31C2311yescharacteristic
25C2×C22⋊D31—21no—
26#92495—21no—
27#92495—21no—
28#92495—21no—
29#92495—21no—
30C2×D124Q811yescharacteristic, complemented
31C2×C4×D31—21no—
32C2×Dic62—22no—
33C2×Dic62Q811yescharacteristic, complemented
34M16×C31—21no—
35M16×C31—21no—
36C2×C8×C31—21no—
37C4⋊C4×C31—21no—
38C22⋊C4×C31—21no—
39C42×C31—21no—
40C42×C31—21no—
41C42×C31D411yescharacteristic
42C42×C31D411yescharacteristic
43C22⋊Dic31—21no—
44C22⋊Dic31D412yes—
45C4⋊Dic31—22no—
46C4⋊Dic31—21no—
47C4⋊Dic31—21no—
48Dic31⋊C4—24no—
49C4×Dic31—21no—
50C4×Dic31D412yes—
51#92474—21no—
52#92474—21no—
53C2×C31⋊C8—21no—
54C23×C31C2×D411yescharacteristic
55C22×D31—21no—
56C2×C4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—42no—
59C2×C4×C31—41no—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×Q811yescharacteristic
63C2×C4×C31#4111yescharacteristic
64C2×C4×C31#4111yescharacteristic
65C2×C4×C31#4111yescharacteristic
66C22⋊D31—41no—
67C22⋊D31—41no—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—21no—
71D124—21no—
72D124—21no—
73C4×D31—41no—
74C4×D31—41no—
75Dic62—21no—
76Dic62—21no—
77Dic62—44no—
78C8×C31—41no—
79C31⋊C8—41no—
80#2031—311nomaximal, Sylow
81C22×C31—41no—
82C22×C31#12011yescharacteristic
83C22×C31C22⋊Q811yescharacteristic
84C22×C31#12411yescharacteristic
85C2×D31—41no—
86C2×D31—81no—
87C4×C31—22no—
88C4×C31—41no—
89C4×C31—81no—
90C4×C31C22⋊Q811yescharacteristic
91C4×C31C22⋊Q811yescharacteristic
92C4×C31#12411yescharacteristic
93C4×C31#12411yescharacteristic
94Dic31—42no—
95Dic31—42no—
96Dic31—41no—
97#533—311no—
98#421—311no—
99C2×#104—311no—
100#410—311no—
101#344—311no—
102#339D3111yescharacteristic, complemented
103H(3,ℤ/4)—311no—
104C2×C31—21no—
105C2×C31—21no—
106C2×C31—21no—
107C2×C31#39311yescharacteristic
108D31—81no—
109C2×#41—311no—
110C2×M16—311no—
111C2×M16C2×D3111yescharacteristic
112C4⋊Q8—621no—
113#125—621no—
114C22⋊Q8—622no—
115C4×Q8—622no—
116#117—311no—
117#117—311no—
118#117C2×D3111yescharacteristic
119C2×C42C2×D3111yescharacteristic
120#104—622no—
121#104—621no—
122#104—621no—
123#99—622no—
124C31#203111yescharacteristic, complemented, Sylow
125#41—621no—
126#41—621no—
127#41—621no—
128#41—621no—
129C2×Q8—311no—
130C2×Q8—622no—
131C2×D4—311no—
132C2×D4—621no—
133C22×C4—21no—
134C22×C4—621no—
135C22×C4C22×D3111yescharacteristic
136M16—21no—
137M16—21no—
138M16—621no—
139M16—621no—
140C2×C8—21no—
141C2×C8—621no—
142C4⋊C4—21no—
143C4⋊C4—624no—
144C4⋊C4—622no—
145C4⋊C4—621no—
146C4⋊C4—621no—
147C22⋊C4—21no—
148C22⋊C4—312no—
149C22⋊C4—621no—
150C42—21no—
151C42—21no—
152C42—312no—
153C42—621no—
154C42D12411yescharacteristic
155C42D12411yescharacteristic
156C23—621no—
157C23D4×D3111yescharacteristic
158Q8—621no—
159Q8—621no—
160Q8—1244no—
161D4—621no—
162D4—621no—
163D4—1241no—
164D4—1241no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—42no—
168C2×C4—41no—
169C2×C4—622no—
170C2×C4—622no—
171C2×C4—621no—
172C2×C4—1241no—
173C2×C4—1241no—
174C2×C4C2×D12411yescharacteristic
175C2×C4#9249511yescharacteristic
176C2×C4#9249511yescharacteristic
177C2×C4D4×D3111yescharacteristic
178C2×C4#9249711yescharacteristic
179C2×C4Q8×D3111yescharacteristic
180C8—41no—
181C8—1241no—
182C22—41no—
183C22—1241no—
184C22—2481no—
185C22#1175845911yescharacteristic
186C22#1175846211yescharacteristic
187C22#1175847311yescharacteristic
188C4—22no—
189C4—41no—
190C4—81no—
191C4—1242no—
192C4—1242no—
193C4—1241no—
194C4#1175845211yescharacteristic
195C4#1175846211yescharacteristic
196C4#1175847311yescharacteristic
197C4#1175847411yescharacteristic
198C2—21no—
199C2—21no—
200C2—21no—
201C2—2481no—
202C2#1452096211yescharacteristic
subgroupG/H
centerC4#11758462
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC2×C31#393
prime radicalC2×#92495C22
hypercenter#339D31
hypocenterC31#2031
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #14521606C2semidirect
5. #14520820C2semidirect
6. #14520805C2semidirect
7. C31×#339C2semidirect
30. C2×D124Q8semidirect
33. C2×Dic62Q8semidirect
102. #339D31semidirect
124. C31#2031semidirect

Maximal subgroups

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

subgroupindex
#145216062
#145210652
C2×#117583932
#145210222
#145208202
#145208052
C31×#3392
#203131