Finite Group Databasebeta

← #16846113

Subgroups — #16846113

Order 3968.

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

normal subgroups only

This group has 344 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
1C2×#11758452C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic, complemented
3#14521055C211yesmaximal, characteristic
4#14521053C211yesmaximal, characteristic
5C2×#11758412C211yesmaximal, characteristic, complemented
6#14520809C211yesmaximal, characteristic, complemented
7C31×#339C211yesmaximal, characteristic, complemented
8C22×D124C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13C2×(C2×D31)⋊C4—22no—
14#11758503C2211yescharacteristic
15C2×#92474C2211yescharacteristic
16#11758464—22no—
17#11758454—22no—
18#11758452—22no—
19#11758452C414yescomplemented
20C4×Dic62—22no—
21#11758412—22no—
22#11758409—22no—
23#11758397—22no—
24C23×D31—21no—
25C22×C4×C31—21no—
26C22×C4×C31C2311yescharacteristic
27C22×Dic31D412yes—
28C2×D124—21no—
29C2×D124—21no—
30C2×D124—21no—
31C2×D124—21no—
32C2×D124—21no—
33C2×D124C2×C412yes—
34C2×Dic62—21no—
35C2×Dic62—21no—
36C2×Dic62—21no—
37C2×Dic62—21no—
38C2×Dic62C2×C412yes—
39C2×Dic62D412yes—
40M16×C31—21no—
41M16×C31—21no—
42C2×C8×C31—21no—
43C4⋊C4×C31D412yes—
44C22⋊C4×C31—21no—
45C42×C31—21no—
46C42×C31—21no—
47C42×C31C2×C412yes—
48C22⋊Dic31—21no—
49(C2×D31)⋊C4—28no—
50C4⋊Dic31D412yes—
51Dic31⋊C4—24no—
52C4×Dic31—24no—
53C4×Dic31—21no—
54#92474—21no—
55#92474—21no—
56C2×C31⋊C8—21no—
57C23×C31C2×D411yescharacteristic
58C22×D31—22no—
59C22×D31—44no—
60C22×D31—41no—
61C22×D31—41no—
62C2×C4×C31—22no—
63C2×C4×C31—22no—
64C2×C4×C31—42no—
65C2×C4×C31C22×C411yescharacteristic
66C2×C4×C31C2×D411yescharacteristic
67C2×C4×C31C2×D411yescharacteristic
68C2×C4×C31C2×D411yescharacteristic
69C2×C4×C31#4111yescharacteristic
70C2×C4×C31#4111yescharacteristic
71C2×Dic31—22no—
72C2×Dic31—22no—
73C2×Dic31—22no—
74C2×Dic31C22⋊C414yes—
75D124—22no—
76D124—22no—
77D124—41no—
78D124—41no—
79Dic62—22no—
80Dic62—22no—
81Dic62—22no—
82Dic62—22no—
83C8×C31—41no—
84C31⋊C8—41no—
85#1888—311nomaximal, Sylow
86C22×C31—22no—
87C22×C31C2×C22⋊C411yescharacteristic
88C22×C31#12011yescharacteristic
89C22×C31#12311yescharacteristic
90C2×D31—44no—
91C2×D31—42no—
92C2×D31—82no—
93C2×D31—82no—
94C4×C31—42no—
95C4×C31—42no—
96C4×C31C4×D411yescharacteristic
97C4×C31C4×D411yescharacteristic
98C4×C31#12111yescharacteristic
99C4×C31#12111yescharacteristic
100Dic31—24no—
101Dic31—42no—
102C2×#124—311no—
103#519—311no—
104#418—311no—
105#418—311no—
106C2×#101—311no—
107#339—311no—
108#339D3111yescharacteristic, complemented
109C2×C31—21no—
110C2×C31—21no—
111C2×C31#38611yescharacteristic
112C2×C31#45412yes—
113D31—82no—
114C22×Q8—311no—
115C22×D4—311no—
116C2×M16—311no—
117C2×M16C2×D3111yescharacteristic
118#124—314no—
119#124—622no—
120C4×Q8—622no—
121C4×Q8—622no—
122#117—311no—
123#117—622no—
124#117C2×D3111yescharacteristic
125C2×C22⋊C4—622no—
126C2×C42C2×D3111yescharacteristic
127#102—622no—
128#102—622no—
129#101—622no—
130C31#188811yescharacteristic, complemented, Sylow
131C24—621no—
132C2×Q8—312no—
133C2×Q8—312no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C2×Q8—621no—
138C2×D4—312no—
139C2×D4—621no—
140C2×D4—621no—
141C2×D4—621no—
142C2×D4—621no—
143C2×D4—621no—
144C22×C4—21no—
145C22×C4—312no—
146C22×C4C22×D3111yescharacteristic
147M16—21no—
148M16—21no—
149M16—621no—
150M16—621no—
151C2×C8—21no—
152C2×C8—621no—
153C4⋊C4—312no—
154C4⋊C4—624no—
155C4⋊C4D12412yes—
156C22⋊C4—21no—
157C22⋊C4—628no—
158C22⋊C4—621no—
159C42—21no—
160C42—21no—
161C42—624no—
162C42—621no—
163C42C4×D3112yes—
164C23—622no—
165C23—1244no—
166C23—1241no—
167C23—1241no—
168C23D4×D3111yescharacteristic
169Q8—622no—
170Q8—622no—
171Q8—622no—
172Q8—622no—
173D4—622no—
174D4—622no—
175D4—1241no—
176D4—1241no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—314no—
181C2×C4—622no—
182C2×C4—622no—
183C2×C4—622no—
184C2×C4C2×C4×D3111yescharacteristic
185C2×C4C2×D12411yescharacteristic
186C2×C4#9249511yescharacteristic
187C2×C4D4×D3111yescharacteristic
188C2×C4D4×D3111yescharacteristic
189C2×C4#9249911yescharacteristic
190C8—41no—
191C8—1241no—
192C22—22no—
193C22—1244no—
194C22—1242no—
195C22—2482no—
196C22—2482no—
197C22C22⋊C4×D3111yescharacteristic
198C22#1175845911yescharacteristic
199C22#1175847111yescharacteristic
200C4—42no—
201C4—42no—
202C4—624no—
203C4—1242no—
204C4C4×D12411yescharacteristic
205C4#1175846111yescharacteristic
206C4#1175847011yescharacteristic
207C4#1175847211yescharacteristic
208C2—21no—
209C2—21no—
210C2—2482no—
211C2#1452092711yescharacteristic
212C2#1452122312yes—
subgroupG/H
centerC22#11758459
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31#120
prime radicalC22×D124C22
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1888
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14521526C2semidirect
5. C2×#11758412C2semidirect
6. #14520809C2semidirect
7. C31×#339C2semidirect
19. #11758452C4semidirect
108. #339D31semidirect
130. C31#1888semidirect

Maximal subgroups

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

subgroupindex
C2×#117584522
#145215262
#145210552
#145210532
C2×#117584122
#145208092
C31×#3392
#188831