Finite Group Databasebeta

← #16846615

Subgroups — #16846615

Order 3968.

296 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 83 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×#92481C211yesmaximal, characteristic
2C2×#11758410C211yesmaximal, characteristic, complemented
3#14521058C211yesmaximal, characteristic, complemented
4#14521055C211yesmaximal, characteristic
5C2×#11758411C211yesmaximal, characteristic
6#14521007C211yesmaximal, characteristic, complemented
7C2×C31×#101C211yesmaximal, characteristic, complemented
8C22×Q8×C31C2211yescharacteristic
9C22×D124C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C2×M16×C31C2211yescharacteristic
12C2×#92481—21no—
13C2×#92481—21no—
14C2×#92481—22no—
15C2×#92481C414yescomplemented
16#11758503C2211yescharacteristic
17C2×#92474C2211yescharacteristic
18C22×C31⋊C8C2211yescharacteristic
19C31×#101—22no—
20#11758423—22no—
21#11758411—22no—
22#11758410—22no—
23#11758409—22no—
24#11758403—21no—
25C8×Dic31—21no—
26C23×D31—21no—
27C2×Q8×C31—21no—
28C2×Q8×C31—21no—
29C2×Q8×C31—21no—
30C2×Q8×C31—21no—
31C2×Q8×C31—21no—
32C2×Q8×C31C2×C412yes—
33C22×C4×C31—21no—
34C22×C4×C31C2311yescharacteristic
35C2×D124—21no—
36C2×D124—21no—
37C2×D124—21no—
38C2×D124—21no—
39C2×D124—21no—
40C2×D124C2×C412yes—
41M16×C31—21no—
42M16×C31—21no—
43M16×C31—21no—
44M16×C31D412yes—
45C2×C8×C31—21no—
46C2×C8×C31—21no—
47C22⋊Dic31—21no—
48#92481—24no—
49#92481—24no—
50C4⋊Dic31D412yes—
51C4×Dic31—21no—
52#92474—21no—
53#92474—21no—
54C2×C31⋊C8—21no—
55C2×C31⋊C8C2×C412yes—
56C2×C31⋊C8D411yescharacteristic
57C2×C31⋊C8D411yescharacteristic
58C2×C31⋊C8D412yes—
59C23×C31#4111yescharacteristic
60C22×D31—22no—
61C22×D31—41no—
62C22×D31—41no—
63C22×D31—82no—
64Q8×C31—22no—
65Q8×C31—22no—
66Q8×C31—41no—
67Q8×C31—41no—
68C2×C4×C31—22no—
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×C31C2×D411yescharacteristic
76C2×C4×C31#4111yescharacteristic
77C2×Dic31—22no—
78D124—22no—
79D124—22no—
80D124—41no—
81D124—41no—
82C8×C31—22no—
83C8×C31—41no—
84C31⋊C8—41no—
85C31⋊C8C22⋊C412yes—
86C31⋊C8C22⋊C412yes—
87#1977—311nomaximal, Sylow
88C22×C31—22no—
89C22×C31C4×D411yescharacteristic
90C22×C31#12111yescharacteristic
91C22×C31#12411yescharacteristic
92C2×D31—42no—
93C2×D31—82no—
94C2×D31—82no—
95C2×D31—82no—
96C4×C31—42no—
97C4×C31C2×C22⋊C411yescharacteristic
98C4×C31C4×D411yescharacteristic
99C4×C31#12111yescharacteristic
100C4×C31#12711yescharacteristic
101Dic31—42no—
102C22×SD16—311no—
103C2×#108—311no—
104#419—311no—
105#418—311no—
106C2×#101D3111yescharacteristic, complemented
107C2×#100—311no—
108#405—311no—
109C2×C31—21no—
110C2×C31—21no—
111C2×C31#39011yescharacteristic
112C2×C31#47112yes—
113D31—82no—
114C22×Q8C2×D3111yescharacteristic
115C22×D4—311no—
116C2×SD16—314no—
117C2×SD16—621no—
118C2×SD16—621no—
119C2×SD16—622no—
120C2×M16—311no—
121C2×M16C2×D3111yescharacteristic
122C2×M16C2×D3111yescharacteristic
123C22×C8—311no—
124#117—311no—
125#108—622no—
126#103—622no—
127#102—622no—
128#101—22no—
129#100—622no—
130#97—621no—
131C4×C8—621no—
132C31#197711yescharacteristic, complemented, Sylow
133C24—621no—
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—21no—
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8C4×D3112yes—
140C2×D4—312no—
141C2×D4—621no—
142C2×D4—621no—
143C2×D4—621no—
144C2×D4—621no—
145C2×D4—621no—
146C22×C4—21no—
147C22×C4C22×D3111yescharacteristic
148SD16—624no—
149SD16—624no—
150M16—21no—
151M16—21no—
152M16—21no—
153M16—621no—
154M16—621no—
155M16C22⋊D3112yes—
156C2×C8—21no—
157C2×C8—21no—
158C2×C8—312no—
159C2×C8—311no—
160C2×C8—311no—
161C2×C8—312no—
162C2×C8—621no—
163C4⋊C4—312no—
164C22⋊C4—621no—
165C42—621no—
166C23—622no—
167C23—1241no—
168C23—1241no—
169C23—2482no—
170C23#9249511yescharacteristic
171Q8—22no—
172Q8—22no—
173Q8—41no—
174Q8—41no—
175D4—622no—
176D4—622no—
177D4—1241no—
178D4—1241no—
179C2×C4—22no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—622no—
183C2×C4C2×C4×D3111yescharacteristic
184C2×C4D4×D3111yescharacteristic
185C2×C4D4×D3111yescharacteristic
186C2×C4D4×D3111yescharacteristic
187C2×C4#9249711yescharacteristic
188C2×C4C2×C22⋊D3111yescharacteristic
189C8—22no—
190C8—41no—
191C8—312no—
192C8—312no—
193C8—1241no—
194C22—22no—
195C22—1242no—
196C22—2482no—
197C22—2482no—
198C22—2482no—
199C22#1175846111yescharacteristic
200C22#1175846211yescharacteristic
201C22C4×C22⋊D3111yescharacteristic
202C4—42no—
203C4—1242no—
204C4C22⋊C4×D3111yescharacteristic
205C4(C22⋊D31)⋊C411yescharacteristic
206C4#1175851611yescharacteristic
207C4#1175851711yescharacteristic
208C2—21no—
209C2—21no—
210C2—2482no—
211C2#1452094911yescharacteristic
212C2#1452131512yes—
subgroupG/H
centerC22#11758461
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#101C2
socleC22×C31#121
prime radicalC22×D124C22
cosocleC22×C4×C31C23
hypercenterC2×#101D31
hypocenterC31#1977
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. C2×#11758410C2semidirect
3. #14521058C2semidirect
6. #14521007C2semidirect
7. C2×C31×#101C2semidirect
15. C2×#92481C4semidirect
106. C2×#101D31semidirect
132. C31#1977semidirect

Maximal subgroups

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

subgroupindex
C22×#924812
C2×#117584102
#145210582
#145210552
C2×#117584112
#145210072
C2×C31×#1012
#197731