Finite Group Databasebeta

← #16846466

Subgroups — #16846466

Order 3968.

256 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 107 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×Dic31⋊C8C211yesmaximal, characteristic
3#14520918C211yesmaximal, characteristic
4C4⋊C4×Dic31C211yesmaximal, characteristic
5#14520812C211yesmaximal, characteristic
6#14520811C211yesmaximal, characteristic
7C2×C31×#107C211yesmaximal, characteristic
8C22×C8×C31C2211yescharacteristic
9C2×C4⋊C4×C31C2211yescharacteristic
10C2×C4⋊C4×C31C2211yescharacteristic
11C2×C4⋊Dic31C2211yescharacteristic
12C2×C4⋊Dic31C2211yescharacteristic
13C2×Dic31⋊C4—21no—
14C2×Dic31⋊C4—21no—
15C2×C4×Dic31—21no—
16C2×C4×Dic31C2211yescharacteristic
17C22×C31⋊C8C2211yescharacteristic
18C31×#107—22no—
19C31⋊#95—21no—
20Dic31⋊C8C414yescomplemented
21#11758395—22no—
22C22×C4×C31—21no—
23C22×C4×C31—21no—
24C22×C4×C31C2311yescharacteristic
25C22×Dic31—21no—
26C22×Dic31—21no—
27C22×Dic31D411yescharacteristic
28C22×Dic31D411yescharacteristic
29C2×C8×C31—21no—
30C2×C8×C31—21no—
31C2×C8×C31C2×C412yes—
32C4⋊C4×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31—21no—
35C4⋊C4×C31D412yes—
36C4⋊Dic31—21no—
37C4⋊Dic31—21no—
38C4⋊Dic31—21no—
39C4⋊Dic31Q812yes—
40Dic31⋊C4—42no—
41Dic31⋊C4—42no—
42C4×Dic31—42no—
43C4×Dic31C2×C412yes—
44C4×Dic31Q812yes—
45C2×C31⋊C8—21no—
46C2×C31⋊C8—21no—
47C2×C31⋊C8C2×C412yes—
48C23×C31C2×D411yescharacteristic
49C2×C4×C31—22no—
50C2×C4×C31—41no—
51C2×C4×C31—41no—
52C2×C4×C31—41no—
53C2×C4×C31—41no—
54C2×C4×C31—41no—
55C2×C4×C31C22×C411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×Q811yescharacteristic
58C2×C4×C31C2×Q811yescharacteristic
59C2×C4×C31#4111yescharacteristic
60C2×C4×C31#4111yescharacteristic
61C2×Dic31—21no—
62C2×Dic31—21no—
63C2×Dic31—22no—
64C2×Dic31—41no—
65C2×Dic31—41no—
66C2×Dic31—41no—
67C2×Dic31—41no—
68C2×Dic31—41no—
69C2×Dic31C4⋊C412yes—
70C2×Dic31C4⋊C412yes—
71C2×Dic31D812yes—
72C2×Dic31Q1612yes—
73C8×C31—22no—
74C31⋊C8—22no—
75#1947—311nomaximal, Sylow
76C22×C31C2×C4⋊C411yescharacteristic
77C22×C31#12111yescharacteristic
78C22×C31C22⋊Q811yescharacteristic
79C22×C31C2×D811yescharacteristic
80C22×C31C2×Q1611yescharacteristic
81C22×C31AGL(1,ℤ/8)11yescharacteristic
82C22×C31#13711yescharacteristic
83C4×C31—42no—
84C4×C31—81no—
85C4×C31C4×D411yescharacteristic
86C4×C31C4×Q811yescharacteristic
87C4×C31#12511yescharacteristic
88C4×C31C4⋊Q811yescharacteristic
89Dic31—22no—
90Dic31—42no—
91Dic31—81no—
92Dic31#10714yescomplemented
93C2×#107—311no—
94C2×#107D3111yescharacteristic
95C2×C4⋊C8—311no—
96#384—311no—
97C4×C4⋊C4—311no—
98#340—311no—
99#340—311no—
100C2×C31#38911yescharacteristic
101C2×C31C2×#10711yescharacteristic
102C2×C31#42811yescharacteristic
103C2×C31#45911yescharacteristic
104C2×C31#46211yescharacteristic
105C2×C31#47411yescharacteristic
106C2×C31#47711yescharacteristic
107C22×C8—311no—
108C22×C8C2×D3111yescharacteristic
109C2×C4⋊C4—311no—
110C2×C4⋊C4—311no—
111C2×C4⋊C4—621no—
112C2×C4⋊C4—621no—
113C2×C4⋊C4C2×D3111yescharacteristic
114C2×C4⋊C4C2×D3111yescharacteristic
115C2×C42—311no—
116C2×C42—621no—
117#107—22no—
118#107—622no—
119C4⋊C8—314no—
120#95—621no—
121C31#194711yescharacteristic, complemented, Sylow
122C22×C4—21no—
123C22×C4—21no—
124C22×C4—311no—
125C22×C4—311no—
126C22×C4—621no—
127C22×C4—621no—
128C22×C4C22×D3111yescharacteristic
129C2×C8—21no—
130C2×C8—21no—
131C2×C8—312no—
132C2×C8—621no—
133C2×C8—621no—
134C2×C8C4×D3112yes—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—312no—
139C4⋊C4—621no—
140C4⋊C4—621no—
141C4⋊C4—621no—
142C4⋊C4—1242no—
143C4⋊C4—1242no—
144C4⋊C4C22⋊D3112yes—
145C42—312no—
146C42—312no—
147C42—1242no—
148C23D4×D3111yescharacteristic
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—41no—
155C2×C4—312no—
156C2×C4—312no—
157C2×C4—312no—
158C2×C4—312no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—622no—
162C2×C4—1241no—
163C2×C4—1241no—
164C2×C4—1241no—
165C2×C4—1241no—
166C2×C4—1241no—
167C2×C4C2×C4×D3111yescharacteristic
168C2×C4#9249511yescharacteristic
169C2×C4#9249711yescharacteristic
170C2×C4Q8×D3111yescharacteristic
171C2×C4Q8×D3111yescharacteristic
172C2×C4C2×C22⋊D3111yescharacteristic
173C8—22no—
174C8—622no—
175C22C4⋊C4×D3111yescharacteristic
176C22#1175847311yescharacteristic
177C22D8×D3111yescharacteristic
178C22#1175848811yescharacteristic
179C22Q16×D3111yescharacteristic
180C22#1175849511yescharacteristic
181C22#1175851611yescharacteristic
182C4—42no—
183C4—81no—
184C4—314no—
185C4—622no—
186C4—1242no—
187C4—2481no—
188C4#1175846411yescharacteristic
189C4#1175846611yescharacteristic
190C4C4×C22⋊D3111yescharacteristic
191C4#1175852111yescharacteristic
192C2#1452094411yescharacteristic
193C2#107×D3111yescharacteristic
194C2#1452109011yescharacteristic
195C2#1452124211yescharacteristic
196C2#1452125711yescharacteristic
197C2#1452132811yescharacteristic
198C2#1452134311yescharacteristic
subgroupG/H
centerC23D4×D31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC2×C31×#107C2
socle, prime radicalC23×C31C2×D4
cosocleC22×C4×C31C23
hypercenterC2×#107D31
hypocenterC31#1947
LCSG ▷ C2×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
20. Dic31⋊C8C4semidirect
92. Dic31#107semidirect
121. C31#1947semidirect

Maximal subgroups

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

subgroupindex
C2×#117583952
C2×Dic31⋊C82
#145209182
C4⋊C4×Dic312
#145208122
#145208112
C2×C31×#1072
#194731