Finite Group Databasebeta

← #16847246

Subgroups — #16847246

Order 3968.

254 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 87 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×#11758395C211yesmaximal, characteristic
2C2×#11758404C211yesmaximal, characteristic
3C2×#11758398C211yesmaximal, characteristic
4#14520954C211yesmaximal, characteristic
5#14520918C211yesmaximal, characteristic
6#14520803C211yesmaximal, characteristic
7C2×C31×#107C211yesmaximal, characteristic
8C22×Dic62C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊C4×C31C2211yescharacteristic
12C2×C4⋊Dic31C2211yescharacteristic
13C2×Dic31⋊C4—22no—
14C2×C4×Dic31C2211yescharacteristic
15C22×C31⋊C8C2211yescharacteristic
16C31×#107—22no—
17C31⋊#95—22no—
18#11758404—22no—
19#11758398—22no—
20#11758395—22no—
21C22×C4×C31—21no—
22C22×C4×C31—21no—
23C22×C4×C31C2311yescharacteristic
24C22×Dic31—21no—
25C22×Dic31—21no—
26C22×Dic31D412yes—
27C2×Dic62—21no—
28C2×Dic62—21no—
29C2×Dic62—21no—
30C2×Dic62—21no—
31C2×Dic62—21no—
32C2×Dic62Q812yes—
33C2×C8×C31—21no—
34C2×C8×C31—21no—
35C2×C8×C31D412yes—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31—21no—
39C4⋊C4×C31—21no—
40C4⋊Dic31—21no—
41C4⋊Dic31—21no—
42Dic31⋊C4—44no—
43C4×Dic31—21no—
44C4×Dic31—21no—
45C2×C31⋊C8—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8D412yes—
48C23×C31C2×D411yescharacteristic
49C2×C4×C31—41no—
50C2×C4×C31—41no—
51C2×C4×C31—42no—
52C2×C4×C31—42no—
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×Q811yescharacteristic
56C2×C4×C31#4111yescharacteristic
57C2×C4×C31#4111yescharacteristic
58C2×C4×C31#4111yescharacteristic
59C2×Dic31—22no—
60C2×Dic31—22no—
61C2×Dic31—22no—
62C2×Dic31—41no—
63C2×Dic31—41no—
64C2×Dic31—41no—
65C2×Dic31—42no—
66C2×Dic31Q1614yes—
67Dic62—22no—
68Dic62—22no—
69Dic62—41no—
70Dic62—41no—
71C8×C31—22no—
72C31⋊C8—22no—
73#2095—311nomaximal, Sylow
74C22×C31C22⋊Q811yescharacteristic
75C22×C31#12311yescharacteristic
76C22×C31#12711yescharacteristic
77C22×C31C2×Q1612yes—
78C22×C31AGL(1,ℤ/8)12yes—
79C4×C31—81no—
80C4×C31—81no—
81C4×C31C22⋊Q811yescharacteristic
82C4×C31C22⋊Q811yescharacteristic
83C4×C31#12311yescharacteristic
84C4×C31#12311yescharacteristic
85Dic31—24no—
86Dic31—42no—
87Dic31—81no—
88C2×#107—311no—
89C2×#107D3111yescharacteristic
90C2×#103—311no—
91C2×#103—311no—
92#391—311no—
93#384—311no—
94#336—311no—
95C2×C31#39911yescharacteristic
96C2×C31#47712yes—
97C2×C31#48412yes—
98C2×C31#49411yescharacteristic
99C2×C31#49611yescharacteristic
100C22×Q8—311no—
101C22×C8—311no—
102C22×C8C2×D3111yescharacteristic
103C2×C4⋊C4—311no—
104C2×C4⋊C4—622no—
105C2×C4⋊C4C2×D3111yescharacteristic
106C2×C4⋊C4C2×D3111yescharacteristic
107C2×C42—311no—
108#107—22no—
109#107—622no—
110#103—622no—
111#103—622no—
112#95—622no—
113C31#209511yescharacteristic, complemented, Sylow
114C2×Q8—312no—
115C2×Q8—621no—
116C2×Q8—621no—
117C2×Q8—621no—
118C2×Q8—621no—
119C2×Q8—621no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—312no—
123C22×C4—621no—
124C22×C4—621no—
125C22×C4C22×D3111yescharacteristic
126C2×C8—21no—
127C2×C8—21no—
128C2×C8—312no—
129C2×C8—621no—
130C2×C8—621no—
131C2×C8C22⋊D3112yes—
132C4⋊C4—21no—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—621no—
137C4⋊C4—621no—
138C4⋊C4—1244no—
139C42—621no—
140C42—621no—
141C23D4×D3111yescharacteristic
142Q8—622no—
143Q8—622no—
144Q8—1241no—
145Q8—1241no—
146C2×C4—42no—
147C2×C4—42no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—314no—
151C2×C4—622no—
152C2×C4—622no—
153C2×C4—622no—
154C2×C4—1241no—
155C2×C4—1241no—
156C2×C4—1242no—
157C2×C4—1241no—
158C2×C4#9249511yescharacteristic
159C2×C4#9249511yescharacteristic
160C2×C4D4×D3111yescharacteristic
161C2×C4Q8×D3111yescharacteristic
162C2×C4#9249911yescharacteristic
163C2×C4C2×C22⋊D3111yescharacteristic
164C8—22no—
165C8—622no—
166C22#1175847111yescharacteristic
167C22#1175847311yescharacteristic
168C22#1175848812yes—
169C22Q16×D3112yes—
170C22#1175851711yescharacteristic
171C4—81no—
172C4—81no—
173C4—624no—
174C4—1242no—
175C4—2481no—
176C4#1175847111yescharacteristic
177C4#1175847311yescharacteristic
178C4#1175850611yescharacteristic
179C4#1175852311yescharacteristic
180C2#1452098411yescharacteristic
181C2#1452134312yes—
182C2#1452138612yes—
183C2#1452142711yescharacteristic
184C2#1452143711yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#107C2
socle, prime radicalC23×C31C2×D4
hypercenterC2×#107D31
hypocenterC31#2095
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
113. C31#2095semidirect

Maximal subgroups

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

subgroupindex
C2×#117583952
C2×#117584042
C2×#117583982
#145209542
#145209182
#145208032
C2×C31×#1072
#209531