Finite Group Databasebeta

← #16847252

Subgroups — #16847252

Order 3968.

254 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 89 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×#11758405C211yesmaximal, characteristic
2C2×#11758396C211yesmaximal, characteristic
3C2×#11758423C211yesmaximal, characteristic
4#14520956C211yesmaximal, characteristic
5#14520918C211yesmaximal, characteristic
6#14520803C211yesmaximal, characteristic
7C2×C31×#103C211yesmaximal, characteristic
8C22×Q8×C31C2211yescharacteristic
9C22×C8×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊Dic31C2211yescharacteristic
12C2×C4⋊Dic31C2211yescharacteristic
13C2×Dic31⋊C4—22no—
14C2×C4×Dic31C2211yescharacteristic
15C22×C31⋊C8C2211yescharacteristic
16C31×#103—22no—
17#11758423—22no—
18C31⋊#95—22no—
19#11758405—22no—
20#11758396—22no—
21C2×Q8×C31—21no—
22C2×Q8×C31—21no—
23C2×Q8×C31—21no—
24C2×Q8×C31—21no—
25C2×Q8×C31—21no—
26C2×Q8×C31Q812yes—
27C22×C4×C31—21no—
28C22×C4×C31—21no—
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—21no—
31C22×Dic31—21no—
32C22×Dic31D412yes—
33C2×C8×C31—21no—
34C2×C8×C31—21no—
35C2×C8×C31D412yes—
36C4⋊C4×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊Dic31—21no—
39C4⋊Dic31—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
49Q8×C31—22no—
50Q8×C31—22no—
51Q8×C31—41no—
52Q8×C31—41no—
53C2×C4×C31—22no—
54C2×C4×C31—41no—
55C2×C4×C31—41no—
56C2×C4×C31—41no—
57C2×C4×C31—42no—
58C2×C4×C31C2×D411yescharacteristic
59C2×C4×C31C2×D411yescharacteristic
60C2×C4×C31C2×Q811yescharacteristic
61C2×C4×C31#4111yescharacteristic
62C2×C4×C31#4111yescharacteristic
63C2×C4×C31#4111yescharacteristic
64C2×Dic31—22no—
65C2×Dic31—22no—
66C2×Dic31—41no—
67C2×Dic31—41no—
68C2×Dic31—42no—
69C2×Dic31—42no—
70C2×Dic31SD1614yes—
71C8×C31—22no—
72C31⋊C8—22no—
73#2096—311nomaximal, Sylow
74C22×C31C22⋊Q811yescharacteristic
75C22×C31#12311yescharacteristic
76C22×C31#12711yescharacteristic
77C22×C31C2×SD1612yes—
78C22×C31#13712yes—
79C4×C31—42no—
80C4×C31—81no—
81C4×C31C22⋊Q811yescharacteristic
82C4×C31C22⋊Q811yescharacteristic
83C4×C31#12311yescharacteristic
84C4×C31#12311yescharacteristic
85Dic31—24no—
86Dic31—81no—
87Dic31—81no—
88C2×#106—311no—
89C2×#106—311no—
90C2×#103—311no—
91C2×#103D3111yescharacteristic
92#391—311no—
93#384—311no—
94#336—311no—
95C2×C31#39911yescharacteristic
96C2×C31#47512yes—
97C2×C31#48312yes—
98C2×C31#49211yescharacteristic
99C2×C31#49711yescharacteristic
100C22×Q8C2×D3111yescharacteristic
101C22×C8—311no—
102C22×C8C2×D3111yescharacteristic
103C2×C4⋊C4—311no—
104C2×C4⋊C4—311no—
105C2×C4⋊C4—622no—
106C2×C4⋊C4C2×D3111yescharacteristic
107C2×C42—311no—
108#106—622no—
109#106—622no—
110#103—22no—
111#103—622no—
112#95—622no—
113C31#209611yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—21no—
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—21no—
119C2×Q8Dic6212yes—
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—621no—
135C4⋊C4—621no—
136C4⋊C4—621no—
137C4⋊C4—621no—
138C4⋊C4—1244no—
139C42—621no—
140C42—621no—
141C23D4×D3111yescharacteristic
142Q8—22no—
143Q8—22no—
144Q8—41no—
145Q8—41no—
146C2×C4—22no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—42no—
150C2×C4—41no—
151C2×C4—314no—
152C2×C4—622no—
153C2×C4—622no—
154C2×C4—1242no—
155C2×C4—1242no—
156C2×C4—1241no—
157C2×C4—1241no—
158C2×C4C2×Dic6211yescharacteristic
159C2×C4#9249511yescharacteristic
160C2×C4D4×D3111yescharacteristic
161C2×C4#9249711yescharacteristic
162C2×C4#9249711yescharacteristic
163C2×C4C2×C22⋊D3111yescharacteristic
164C8—22no—
165C8—622no—
166C22#1175845511yescharacteristic
167C22#1175846011yescharacteristic
168C22SD16×D3112yes—
169C22#1175849512yes—
170C22#1175851711yescharacteristic
171C4—42no—
172C4—81no—
173C4—624no—
174C4—2481no—
175C4—2481no—
176C4#1175845511yescharacteristic
177C4#1175846011yescharacteristic
178C4#1175850111yescharacteristic
179C4#1175851211yescharacteristic
180C2#1452098511yescharacteristic
181C2#1452133212yes—
182C2#1452137812yes—
183C2#1452142011yescharacteristic
184C2#1452144211yescharacteristic
subgroupG/H
centerC23D4×D31
commutator, cosocleC22×C4×C31C23
FrattiniC22×C4C22×D31
FittingC2×C31×#103C2
socle, prime radicalC23×C31C2×D4
hypercenterC2×#103D31
hypocenterC31#2096
LCSG ▷ C22×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
113. C31#2096semidirect

Maximal subgroups

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

subgroupindex
C2×#117584052
C2×#117583962
C2×#117584232
#145209562
#145209182
#145208032
C2×C31×#1032
#209631