Finite Group Databasebeta

← #16846103

Subgroups — #16846103

Order 3968.

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

normal subgroups only

This group has 324 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×#11758446C211yesmaximal, characteristic
2#14521526C211yesmaximal, characteristic
3#14521059C211yesmaximal, characteristic
4#14521057C211yesmaximal, characteristic
5C2×#11758412C211yesmaximal, characteristic
6#14520809C211yesmaximal, characteristic
7C31×#339C211yesmaximal, characteristic
8C22×Dic62C2211yescharacteristic
9C22×Dic62C2211yescharacteristic
10C2×M16×C31C2211yescharacteristic
11C31×#117C2211yescharacteristic
12C2×C42×C31C2211yescharacteristic
13#11758503C2211yescharacteristic
14C2×C4⋊Dic31—22no—
15C2×#92474C2211yescharacteristic
16#11758464—22no—
17#11758454—22no—
18#11758446—22no—
19#11758446C414yescomplemented
20C4×Dic62—22no—
21#11758412—22no—
22#11758404—22no—
23#11758398—22no—
24C22×C4×C31—21no—
25C22×C4×C31C2311yescharacteristic
26C22×Dic31—21no—
27C22×Dic31D412yes—
28C2×Dic62—21no—
29C2×Dic62—21no—
30C2×Dic62—21no—
31C2×Dic62—21no—
32C2×Dic62—21no—
33C2×Dic62—21no—
34C2×Dic62—21no—
35C2×Dic62—21no—
36C2×Dic62—21no—
37C2×Dic62C2×C412yes—
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—
49C4⋊Dic31—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
58C2×C4×C31—24no—
59C2×C4×C31—22no—
60C2×C4×C31—22no—
61C2×C4×C31C22×C411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C2×C4×C31C2×D411yescharacteristic
64C2×C4×C31C2×D411yescharacteristic
65C2×C4×C31#4111yescharacteristic
66C2×C4×C31#4111yescharacteristic
67C2×Dic31—22no—
68C2×Dic31—22no—
69C2×Dic31—22no—
70C2×Dic31—22no—
71C2×Dic31—41no—
72C2×Dic31—41no—
73C2×Dic31C22⋊C414yes—
74Dic62—22no—
75Dic62—22no—
76Dic62—22no—
77Dic62—22no—
78Dic62—22no—
79Dic62—22no—
80Dic62—41no—
81Dic62—41no—
82C8×C31—41no—
83C31⋊C8—41no—
84#1886—311nomaximal, Sylow
85C22×C31—22no—
86C22×C31C2×C22⋊C411yescharacteristic
87C22×C31#12011yescharacteristic
88C22×C31#12311yescharacteristic
89C4×C31—24no—
90C4×C31—42no—
91C4×C31C4×D411yescharacteristic
92C4×C31C4×D411yescharacteristic
93C4×C31#12111yescharacteristic
94C4×C31#12111yescharacteristic
95Dic31—24no—
96Dic31—42no—
97Dic31—42no—
98C2×C4⋊Q8—311no—
99#519—311no—
100#419—311no—
101#419—311no—
102C2×#101—311no—
103#339—311no—
104#339D3111yescharacteristic
105C2×C31—21no—
106C2×C31—21no—
107C2×C31#38611yescharacteristic
108C2×C31#45612yes—
109C22×Q8—311no—
110C22×Q8—311no—
111C2×M16—311no—
112C2×M16C2×D3111yescharacteristic
113C4⋊Q8—314no—
114C4⋊Q8—622no—
115C4×Q8—622no—
116C4×Q8—622no—
117#117—311no—
118#117—622no—
119#117C2×D3111yescharacteristic
120C2×C4⋊C4—622no—
121C2×C42C2×D3111yescharacteristic
122#103—622no—
123#103—622no—
124#101—622no—
125C31#188611yescharacteristic, complemented, Sylow
126C2×Q8—312no—
127C2×Q8—312no—
128C2×Q8—312no—
129C2×Q8—621no—
130C2×Q8—621no—
131C2×Q8—621no—
132C2×Q8—621no—
133C2×Q8—621no—
134C2×Q8—621no—
135C2×Q8—621no—
136C2×Q8—621no—
137C2×Q8—621no—
138C22×C4—21no—
139C22×C4—312no—
140C22×C4—621no—
141C22×C4C22×D3111yescharacteristic
142M16—21no—
143M16—21no—
144M16—621no—
145M16—621no—
146C2×C8—21no—
147C2×C8—621no—
148C4⋊C4—312no—
149C4⋊C4—628no—
150C4⋊C4—624no—
151C4⋊C4D12412yes—
152C22⋊C4—21no—
153C22⋊C4—621no—
154C42—21no—
155C42—21no—
156C42—624no—
157C42—621no—
158C42C4×D3112yes—
159C23D4×D3111yescharacteristic
160Q8—622no—
161Q8—622no—
162Q8—622no—
163Q8—622no—
164Q8—622no—
165Q8—622no—
166Q8—1241no—
167Q8—1241no—
168C2×C4—24no—
169C2×C4—22no—
170C2×C4—22no—
171C2×C4—314no—
172C2×C4—622no—
173C2×C4—622no—
174C2×C4—622no—
175C2×C4—622no—
176C2×C4—1241no—
177C2×C4—1241no—
178C2×C4C2×C4×D3111yescharacteristic
179C2×C4C2×D12411yescharacteristic
180C2×C4#9249511yescharacteristic
181C2×C4D4×D3111yescharacteristic
182C2×C4D4×D3111yescharacteristic
183C2×C4#9249911yescharacteristic
184C8—41no—
185C8—1241no—
186C22—22no—
187C22C22⋊C4×D3111yescharacteristic
188C22#1175845911yescharacteristic
189C22#1175847111yescharacteristic
190C4—24no—
191C4—42no—
192C4—624no—
193C4—1242no—
194C4—1242no—
195C4C4×D12411yescharacteristic
196C4#1175846111yescharacteristic
197C4#1175847011yescharacteristic
198C4#1175847211yescharacteristic
199C2—21no—
200C2—21no—
201C2#1452092711yescharacteristic
202C2#1452123312yes—
subgroupG/H
centerC22#11758459
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#339C2
socleC22×C31#120
prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenter#339D31
hypocenterC31#1886
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
19. #11758446C4semidirect
125. C31#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#117584462
#145215262
#145210592
#145210572
C2×#117584122
#145208092
C31×#3392
#188631