Finite Group Databasebeta

← #28389753

Subgroups — #28389753

Order 14464.

308 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 65 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#20298944C211yesmaximal, characteristic, complemented
2#20298878C211yesmaximal, characteristic, complemented
3#20298803C211yesmaximal, characteristic, complemented
4#20298342C211yesmaximal, characteristic, complemented
5D4⋊#11744751C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic, complemented
7D42×C113C211yesmaximal, characteristic
8C2×#14268635—21no—
9#16813622C2211yescharacteristic, complemented
10#16813555—21no—
11C4⋊#11744751C2211yescharacteristic, complemented
12C4⋊#11744751C2211yescharacteristic, complemented
13#16813545—21no—
14#16813543—21no—
15#16813543—22no—
16C4×#11744751C2211yescharacteristic, complemented
17C22×D4×C113—21no—
18C22×D4×C113—21no—
19#127×C113C2211yescharacteristic
20#121×C113—21no—
21#121×C113—21no—
22#120×C113—22no—
23C4×D4×C113C2211yescharacteristic
24C4×D4×C113C2211yescharacteristic
25C2×Dic226—21no—
26#14268635—42no—
27C2×#11744751—21no—
28C2×#11744751—21no—
29C2×#11744751—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32C24×C113—22no—
33C2×D4×C113—22no—
34C2×D4×C113—22no—
35C2×D4×C113—21no—
36C2×D4×C113—21no—
37C2×D4×C113—42no—
38C2×D4×C113—42no—
39C2×D4×C113—42no—
40C2×D4×C113—42no—
41C2×D4×C113D411yescharacteristic
42C2×D4×C113D411yescharacteristic
43C2×D4×C113D412yes—
44C22×C4×C113—21no—
45C22×C4×C113—21no—
46C4⋊C4×C113D411yescharacteristic
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—22no—
49C22⋊C4×C113—21no—
50C22⋊C4×C113—21no—
51C42×C113C2311yescharacteristic
52C23×C113—21no—
53C23×C113—21no—
54C23×C113—22no—
55C23×C113—44no—
56C23×C113—44no—
57C23×C113—82no—
58D4×C113—21no—
59D4×C113—21no—
60D4×C113—42no—
61D4×C113—44no—
62D4×C113—44no—
63D4×C113—41no—
64D4×C113—41no—
65D4×C113—41no—
66D4×C113—41no—
67D4×C113D812yes—
68D4×C113SD1612yescomplemented
69C2×C4×C113—21no—
70C2×C4×C113—21no—
71C2×C4×C113—41no—
72C2×C4×C113—41no—
73C2×C4×C113—41no—
74C2×C4×C113—41no—
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×Dic113—41no—
79Dic226—41no—
80Dic226—41no—
81#11744751—41no—
82#11744751—41no—
83#11744751—41no—
84C22×C113—22no—
85C22×C113—22no—
86C22×C113—41no—
87C22×C113—41no—
88C22×C113—41no—
89C22×C113—41no—
90C22×C113—42no—
91C22×C113—42no—
92C22×C113—42no—
93C22×C113—88no—
94C22×C113#12011yescharacteristic
95C4×C113—21no—
96C4×C113—41no—
97C4×C113—41no—
98C4×C113C2×D811yescharacteristic
99C4×C113C2×SD1611yescharacteristic
100C4×C113AGL(1,ℤ/8)11yescharacteristic
101C4×C113AGL(1,ℤ/8)11yescharacteristic
102Dic113—81no—
103C2×C113—42no—
104C2×C113—42no—
105C2×C113—82no—
106C2×C113#44711yescharacteristic
107C2×C113#45011yescharacteristic
108C2×C113#45511yescharacteristic
109#1639—1131nomaximal, Sylow
110C113#163911yescharacteristic, complemented, Sylow
111D42D11311yescharacteristic
112#486—1131no—
113#474—1131no—
114#461—1131no—
115#331—1131no—
116D4⋊C8—1131no—
117D4⋊C8—1131no—
118C22×D4—21no—
119C22×D4—21no—
120C2×SD16—2261no—
121C4⋊Q8—1131no—
122#127C2×D11311yescharacteristic
123#121—21no—
124#121—21no—
125#120—22no—
126C4×D4C2×D11311yescharacteristic
127C4×D4C2×D11311yescharacteristic
128#107—2261no—
129C4⋊C8—1131no—
130C4⋊C8—1131no—
131#103—2261no—
132#102—2261no—
133#102—2262no—
134C4×C8—1131no—
135C24—22no—
136C2×Q8—2261no—
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—21no—
140C2×D4—21no—
141C2×D4—42no—
142C2×D4—42no—
143C2×D4—42no—
144C2×D4—42no—
145C2×D4C22⋊D11311yescharacteristic
146C2×D4C22⋊D11311yescharacteristic
147C2×D4C22⋊D11312yes—
148C22×C4—21no—
149C22×C4—21no—
150SD16—4522no—
151C2×C8—2261no—
152C2×C8—2261no—
153C2×C8—2261no—
154C4⋊C4—2261no—
155C4⋊C4—2261no—
156C4⋊C4C22⋊D11311yescharacteristic
157C4⋊C4C22⋊D11311yescharacteristic
158C22⋊C4—22no—
159C22⋊C4—21no—
160C22⋊C4—21no—
161C42C22×D11311yescharacteristic
162C23—21no—
163C23—21no—
164C23—22no—
165C23—44no—
166C23—44no—
167C23—82no—
168Q8—4521no—
169Q8—4521no—
170D4—21no—
171D4—21no—
172D4—42no—
173D4—44no—
174D4—44no—
175D4—41no—
176D4—41no—
177D4—41no—
178D4—41no—
179D4#1426863212yes—
180D4#1426863512yescomplemented
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—4521no—
188C2×C4C2×C22⋊D11311yescharacteristic
189C2×C4C2×C22⋊D11311yescharacteristic
190C2×C4C2×C22⋊D11311yescharacteristic
191C8—4521no—
192C8—4521no—
193C8—4521no—
194C22—22no—
195C22—22no—
196C22—41no—
197C22—41no—
198C22—41no—
199C22—41no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—88no—
204C22#1681359111yescharacteristic
205C4—21no—
206C4—41no—
207C4—41no—
208C4—9041no—
209C4C2×#1426863211yescharacteristic
210C4C2×#1426863511yescharacteristic
211C4#1681364811yescharacteristic
212C4#1681364811yescharacteristic
213C2—42no—
214C2—42no—
215C2—82no—
216C2#2029873211yescharacteristic
217C2#2029874911yescharacteristic
218C2#2029877611yescharacteristic
subgroupG/H
centerC22#16813591
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting, prime radicalD42×C113C2
socleC22×C113#120
hypercenterD42D113
hypocenterC113#1639
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #20298944C2semidirect
2. #20298878C2semidirect
3. #20298803C2semidirect
4. #20298342C2semidirect
5. D4⋊#11744751C2semidirect
6. D4⋊#11744751C2semidirect
9. #16813622C22semidirect
11. C4⋊#11744751C22semidirect
12. C4⋊#11744751C22semidirect
16. C4×#11744751C22semidirect
68. D4×C113SD16semidirect
110. C113#1639semidirect
180. D4#14268635semidirect

Maximal subgroups

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

subgroupindex
#202989442
#202988782
#202988032
#202983422
D4⋊#117447512
D42×C1132
#1639113