Finite Group Databasebeta

← #28389665

Subgroups — #28389665

Order 14464.

256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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#20299252C211yesmaximal, characteristic, complemented
2#20298945C211yesmaximal, characteristic, complemented
3#20298794C211yesmaximal, characteristic, complemented
4#20298793C211yesmaximal, characteristic, complemented
5#20298343C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C2×#14268646—21no—
9C2×D904—21no—
10C2×#14268632—21no—
11#16813622C2211yescharacteristic
12#16813619C2211yescharacteristic
13#16813606—22no—
14#16813602—21no—
15#16813596—21no—
16C4×D452C2211yescharacteristic
17C2×C4⋊Dic113—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813544—21no—
20#16813544—22no—
21#16813542—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25#14268646—42no—
26#14268646—42no—
27C2×Dic226—21no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452—21no—
31C2×D452D411yescharacteristic
32C2×C22⋊D113—22no—
33C22×Dic113—22no—
34C2×C4×D113—21no—
35D904—42no—
36#14268632—42no—
37C2×#11744751—21no—
38C4⋊Dic113—22no—
39C4⋊Dic113—21no—
40C4⋊Dic113D411yescharacteristic
41C4⋊Dic113D412yes—
42#14268624—22no—
43#14268624—21no—
44C2×D4×C113D411yescharacteristic
45C22×C4×C113—21no—
46C2×C8×C113—21no—
47C2×C8×C113—21no—
48C4⋊C4×C113D411yescharacteristic
49C22⋊C4×C113—21no—
50C42×C113C2311yescharacteristic
51C23×C113—21no—
52C22×D113—21no—
53C22×D113—41no—
54D4×C113—21no—
55D4×C113D812yescomplemented
56C2×C4×C113—21no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C22⋊D113—44no—
63C2×Dic113—21no—
64C2×Dic113—22no—
65C2×Dic113—44no—
66D452—21no—
67D452—21no—
68D452—42no—
69D452—41no—
70D452—41no—
71D452—41no—
72D452—41no—
73C4×D113—41no—
74C4×D113—41no—
75Dic226—41no—
76Dic226—41no—
77C8×C113—41no—
78C8×C113—41no—
79#11744751—41no—
80C22×C113—22no—
81C22×C113—41no—
82C22×C113—41no—
83C22×C113#12011yescharacteristic
84C2×D113—41no—
85C2×D113—41no—
86C2×D113—41no—
87C2×D113—81no—
88C2×D113—81no—
89C2×D113—81no—
90C4×C113—21no—
91C4×C113—41no—
92C4×C113C2×D811yescharacteristic
93C4×C113#13511yescharacteristic
94C4×C113AGL(1,ℤ/8)11yescharacteristic
95C4×C113AGL(1,ℤ/8)11yescharacteristic
96Dic113—42no—
97Dic113—41no—
98C2×C113—42no—
99C2×C113#44711yescharacteristic
100C2×C113#44911yescharacteristic
101C2×C113#45411yescharacteristic
102D113—81no—
103D113—161no—
104#1625—1131nomaximal, Sylow
105C113#162511yescharacteristic, complemented, Sylow
106#547—1131no—
107#486—1131no—
108#459—1131no—
109#459—1131no—
110#332—1131no—
111D4⋊C8—1131no—
112D4⋊C8D11311yescharacteristic, complemented
113C2×#41—2261no—
114C2×D8—2261no—
115C2×D8—2261no—
116C4⋊Q8—1131no—
117#127—1131no—
118#123—2262no—
119C22⋊Q8—2261no—
120#121—2261no—
121C4×D4—1131no—
122C4×D4C2×D11311yescharacteristic
123C2×C4⋊C4—2261no—
124C4⋊C8—1131no—
125C4⋊C8C2×D11311yescharacteristic
126#102—2261no—
127#102—2262no—
128#102—2261no—
129C4×C8C2×D11311yescharacteristic
130#41—4522no—
131#41—4522no—
132C2×Q8—2261no—
133C2×D4—1131no—
134C2×D4—2262no—
135C2×D4—2261no—
136C2×D4—2261no—
137C2×D4—2261no—
138C2×D4D45211yescharacteristic
139C22×C4—21no—
140C22×C4—2262no—
141C22×C4—2261no—
142D8—4522no—
143D8—4522no—
144C2×C8—21no—
145C2×C8—21no—
146C2×C8—2261no—
147C4⋊C4—1131no—
148C4⋊C4—1132no—
149C4⋊C4—2262no—
150C4⋊C4—2261no—
151C4⋊C4D45211yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—2262no—
154C22⋊C4—2261no—
155C42C22×D11311yescharacteristic
156C23—21no—
157C23—4521no—
158C23—2261no—
159Q8—4521no—
160Q8—4521no—
161D4—21no—
162D4—4522no—
163D4—4524no—
164D4—4521no—
165D4—4521no—
166D4—4521no—
167D4—4521no—
168D4—2261no—
169D4—2261no—
170D4D90412yescomplemented
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—4524no—
175C2×C4—4521no—
176C2×C4—4521no—
177C2×C4—2261no—
178C2×C4—2262no—
179C2×C4D4×D11311yescharacteristic
180C2×C4D4×D11311yescharacteristic
181C2×C4C2×D45211yescharacteristic
182C8—41no—
183C8—41no—
184C8—4521no—
185C22—22no—
186C22—41no—
187C22—41no—
188C22—9041no—
189C22—9041no—
190C22—9041no—
191C22—4521no—
192C22—4521no—
193C22—4521no—
194C22#1681359211yescharacteristic
195C4—21no—
196C4—41no—
197C4—4521no—
198C4—4522no—
199C4C2×D90411yescharacteristic
200C4#1681364311yescharacteristic
201C4#1681364611yescharacteristic
202C4#1681365011yescharacteristic
203C2—42no—
204C2—18081no—
205C2—9041no—
206C2#2029873411yescharacteristic
207C2#2029874411yescharacteristic
208C2#2029877211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
hypercenterD4⋊C8D113
hypocenterC113#1625
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
1. #20299252C2semidirect
2. #20298945C2semidirect
3. #20298794C2semidirect
4. #20298793C2semidirect
5. #20298343C2semidirect
6. #20298327C2semidirect
7. D4⋊C8×C113C2semidirect
55. D4×C113D8semidirect
105. C113#1625semidirect
112. D4⋊C8D113semidirect
170. D4D904semidirect

Maximal subgroups

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

subgroupindex
#202992522
#202989452
#202987942
#202987932
#202983432
#202983272
D4⋊C8×C1132
#1625113