Finite Group Databasebeta

← #16844779

Subgroups — #16844779

Order 3968.

278 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 55 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
1#14521720C211yesmaximal, characteristic, complemented
2#14521426C211yesmaximal, characteristic, complemented
3#14521250C211yesmaximal, characteristic, complemented
4#14521244C211yesmaximal, characteristic, complemented
5#14520792C211yesmaximal, characteristic, complemented
6#14520781C211yesmaximal, characteristic, complemented
7C31×D4⋊C8C211yesmaximal, characteristic, complemented
8C2×#92495—21no—
9C4×D4×C31C2211yescharacteristic
10#11758517—21no—
11C2×#92479—21no—
12#11758507—21no—
13C2×D248—22no—
14C2×#92470—21no—
15#11758470—21no—
16#11758461—22no—
17#11758451C2211yescharacteristic
18#11758451C2211yescharacteristic
19C4×Dic62C2211yescharacteristic
20C31×C4⋊C8C2211yescharacteristic
21C4×C8×C31C2211yescharacteristic
22#11758409—21no—
23#11758397—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×D4×C31D411yescharacteristic
26C22×C4×C31—21no—
27C2×C22⋊D31—22no—
28C2×C22⋊D31—22no—
29#92495—42no—
30#92495—42no—
31C2×D124—21no—
32C2×D124—21no—
33C2×D124—21no—
34C2×D124—21no—
35C2×D124—21no—
36C2×D124D412yes—
37C2×C4×D31—22no—
38C2×Dic62D411yescharacteristic
39C2×C8×C31—21no—
40C2×C8×C31—21no—
41C4⋊C4×C31D411yescharacteristic
42C22⋊C4×C31—21no—
43C42×C31C2311yescharacteristic
44#92479—42no—
45(C2×D31)⋊C4—22no—
46C4⋊Dic31D411yescharacteristic
47Dic31⋊C4—21no—
48C4×Dic31—21no—
49C2×C31⋊C8—21no—
50D248—44no—
51#92470—42no—
52C23×C31—21no—
53C22×D31—22no—
54C22×D31—41no—
55D4×C31—21no—
56D4×C31—21no—
57C2×C4×C31—21no—
58C2×C4×C31—41no—
59C2×C4×C31—41no—
60C2×C4×C31C2×D411yescharacteristic
61C2×C4×C31C2×D411yescharacteristic
62C2×C4×C31C2×D411yescharacteristic
63C22⋊D31—44no—
64C22⋊D31—82no—
65C2×Dic31—21no—
66C2×Dic31—21no—
67D124—42no—
68D124—42no—
69D124—41no—
70D124—41no—
71D124—41no—
72D124—41no—
73D124—41no—
74D124—41no—
75D124—41no—
76D124—41no—
77C4×D31—44no—
78Dic62—21no—
79Dic62D812yescomplemented
80C8×C31—22no—
81C8×C31—41no—
82C31⋊C8—41no—
83#1621—311nomaximal, Sylow
84C22×C31—41no—
85C22×C31—41no—
86C22×C31—41no—
87C22×C31#12011yescharacteristic
88C2×D31—42no—
89C2×D31—42no—
90C2×D31—42no—
91C2×D31—81no—
92C2×D31—81no—
93C2×D31—81no—
94C4×C31—21no—
95C4×C31—41no—
96C4×C31C2×D811yescharacteristic
97C4×C31#13511yescharacteristic
98C4×C31AGL(1,ℤ/8)11yescharacteristic
99C4×C31AGL(1,ℤ/8)11yescharacteristic
100Dic31—22no—
101Dic31—41no—
102#550—311no—
103#493—311no—
104#460—311no—
105#459—311no—
106#331—311no—
107Q8⋊C8—311no—
108D4⋊C8D3111yescharacteristic, complemented
109C2×C31—81no—
110C2×C31#44711yescharacteristic
111C2×C31#44911yescharacteristic
112C2×C31#45311yescharacteristic
113D31—82no—
114D31—161no—
115C2×#41—621no—
116C2×SD16—621no—
117C2×D8—622no—
118C2×D8—621no—
119#127—311no—
120#127—311no—
121#127—621no—
122#121—622no—
123#121—621no—
124C4×Q8—311no—
125C4×D4—621no—
126C4×D4C2×D3111yescharacteristic
127C4⋊C8—311no—
128C4⋊C8C2×D3111yescharacteristic
129#102—621no—
130#102—621no—
131C4×C8C2×D3111yescharacteristic
132C31#162111yescharacteristic, complemented, Sylow
133#41—1242no—
134#41—1242no—
135C2×Q8—311no—
136C2×D4—312no—
137C2×D4—622no—
138C2×D4—622no—
139C2×D4—621no—
140C2×D4—621no—
141C2×D4—621no—
142C2×D4—621no—
143C2×D4—621no—
144C2×D4D12411yescharacteristic
145C22×C4—21no—
146C22×C4—622no—
147SD16—1242no—
148D8—1244no—
149D8—1242no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—621no—
153C4⋊C4—311no—
154C4⋊C4—621no—
155C4⋊C4D12411yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—622no—
158C42—621no—
159C42C22×D3111yescharacteristic
160C23—21no—
161C23—622no—
162C23—1241no—
163Q8—312no—
164Q8—621no—
165D4—21no—
166D4—21no—
167D4—1242no—
168D4—1242no—
169D4—1244no—
170D4—1241no—
171D4—1241no—
172D4—1241no—
173D4—1241no—
174D4—1241no—
175D4—1241no—
176D4—1241no—
177D4—1241no—
178D4—2482no—
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—621no—
183C2×C4—621no—
184C2×C4—1244no—
185C2×C4C2×D12411yescharacteristic
186C2×C4D4×D3111yescharacteristic
187C2×C4D4×D3111yescharacteristic
188C8—22no—
189C8—41no—
190C8—1241no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—1242no—
195C22—1242no—
196C22—1242no—
197C22—2481no—
198C22—2481no—
199C22—2481no—
200C22#1175845911yescharacteristic
201C4—21no—
202C4—41no—
203C4—622no—
204C4—1241no—
205C4#1175848111yescharacteristic
206C4#1175848511yescharacteristic
207C4D8×D3111yescharacteristic
208C4#1175849111yescharacteristic
209C2—81no—
210C2—4961no—
211C2—2482no—
212C2#1452118411yescharacteristic
213C2#1452119611yescharacteristic
214C2#1452121811yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×D4⋊C8C2
socleC22×C31#120
hypercenterD4⋊C8D31
hypocenterC31#1621
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #14521720C2semidirect
2. #14521426C2semidirect
3. #14521250C2semidirect
4. #14521244C2semidirect
5. #14520792C2semidirect
6. #14520781C2semidirect
7. C31×D4⋊C8C2semidirect
79. Dic62D8semidirect
108. D4⋊C8D31semidirect
132. C31#1621semidirect

Maximal subgroups

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

subgroupindex
#145217202
#145214262
#145212502
#145212442
#145207922
#145207812
C31×D4⋊C82
#162131