Finite Group Databasebeta

← #28389692

Subgroups — #28389692

Order 14464.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D452C211yesmaximal, characteristic
2#20298971C211yesmaximal, characteristic, complemented
3#20298889C211yesmaximal, characteristic, complemented
4#20298888C211yesmaximal, characteristic, complemented
5#20298341C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic, complemented
8C22×D452—21no—
9C2×D4×D113—21no—
10C2×#14268636—22no—
11#16813622C2211yescharacteristic, complemented
12#16813619C2211yescharacteristic
13#16813597—21no—
14#16813596—21no—
15#16813592—22no—
16C4×D452C2211yescharacteristic
17#16813554—21no—
18#16813553—21no—
19C4⋊#11744751C2211yescharacteristic, complemented
20#16813544—21no—
21#16813543—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic, complemented
24C4×C8×C113C2211yescharacteristic, complemented
25C23×D113—22no—
26C2×Dic226—21no—
27C2×D452—22no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452—42no—
31C2×D452—42no—
32C2×D452D411yescharacteristic
33C2×D452D412yes—
34C2×C22⋊D113—22no—
35D4×D113—42no—
36D4×D113—42no—
37C2×C4×D113—21no—
38#14268636—44no—
39C2×#11744751—21no—
40C4⋊Dic113—21no—
41C4⋊Dic113—21no—
42C4⋊Dic113D411yescharacteristic
43#14268624—22no—
44#14268624—21no—
45C2×D4×C113D411yescharacteristic
46C22×C4×C113—21no—
47C2×C8×C113—21no—
48C2×C8×C113—21no—
49C4⋊C4×C113D411yescharacteristic
50C22⋊C4×C113—21no—
51C42×C113C2311yescharacteristic
52C23×C113—21no—
53C22×D113—21no—
54C22×D113—22no—
55C22×D113—44no—
56C22×D113—44no—
57C22×D113—82no—
58D4×C113—21no—
59D4×C113SD1612yescomplemented
60C2×C4×C113—21no—
61C2×C4×C113—41no—
62C2×C4×C113—41no—
63C2×C4×C113C2×D411yescharacteristic
64C2×C4×C113C2×D411yescharacteristic
65C2×C4×C113C2×D411yescharacteristic
66C22⋊D113—44no—
67C2×Dic113—21no—
68C2×Dic113—41no—
69D452—21no—
70D452—42no—
71D452—44no—
72D452—41no—
73D452—41no—
74D452—41no—
75D452—41no—
76D452SD1612yescomplemented
77C4×D113—41no—
78C4×D113—41no—
79Dic226—42no—
80C8×C113—22no—
81C8×C113—41no—
82#11744751—41no—
83C22×C113—22no—
84C22×C113—41no—
85C22×C113—41no—
86C22×C113#12011yescharacteristic
87C2×D113—22no—
88C2×D113—41no—
89C2×D113—41no—
90C2×D113—42no—
91C2×D113—42no—
92C2×D113—42no—
93C2×D113—88no—
94C4×C113—21no—
95C4×C113—41no—
96C4×C113C2×SD1611yescharacteristic
97C4×C113C2×SD1611yescharacteristic
98C4×C113AGL(1,ℤ/8)11yescharacteristic
99C4×C113AGL(1,ℤ/8)11yescharacteristic
100Dic113—41no—
101Dic113—81no—
102C2×C113—42no—
103C2×C113#45011yescharacteristic
104C2×C113#45011yescharacteristic
105C2×C113#45311yescharacteristic
106D113—42no—
107D113—82no—
108#1629—1131nomaximal, Sylow
109C113#162911yescharacteristic, complemented, Sylow
110D42—1131no—
111#492—1131no—
112#476—1131no—
113#476—1131no—
114#331—1131no—
115D4⋊C8—1131no—
116D4⋊C8D11311yescharacteristic, complemented
117C22×D4—2261no—
118C22×D4—2261no—
119C2×SD16—2262no—
120C4⋊Q8—1131no—
121#127—1131no—
122#121—2261no—
123#121—2261no—
124#120—2262no—
125C4×D4—1131no—
126C4×D4C2×D11311yescharacteristic
127#106—2261no—
128#106—2261no—
129C4⋊C8—1131no—
130C4⋊C8C2×D11311yescharacteristic, complemented
131#102—2261no—
132#102—2261no—
133C4×C8C2×D11311yescharacteristic, complemented
134C24—2262no—
135C2×Q8—2261no—
136C2×D4—1131no—
137C2×D4—1132no—
138C2×D4—4522no—
139C2×D4—4522no—
140C2×D4—4522no—
141C2×D4—4522no—
142C2×D4—2262no—
143C2×D4—2262no—
144C2×D4—2261no—
145C2×D4—2261no—
146C2×D4D45211yescharacteristic
147C22×C4—21no—
148C22×C4—2261no—
149SD16—4524no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—2261no—
153C4⋊C4—1131no—
154C4⋊C4—2261no—
155C4⋊C4—2261no—
156C4⋊C4D45211yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—2262no—
159C22⋊C4—2261no—
160C42C22×D11311yescharacteristic
161C23—21no—
162C23—9042no—
163C23—4524no—
164C23—4524no—
165C23—2262no—
166C23—2261no—
167Q8—4522no—
168D4—21no—
169D4—1132no—
170D4—4522no—
171D4—4524no—
172D4—4524no—
173D4—4521no—
174D4—4521no—
175D4—4521no—
176D4—4521no—
177D4—2261no—
178D4#1426863612yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—4521no—
183C2×C4—4521no—
184C2×C4—4521no—
185C2×C4—2261no—
186C2×C4D4×D11311yescharacteristic
187C2×C4D4×D11311yescharacteristic
188C2×C4C2×D45211yescharacteristic
189C8—22no—
190C8—41no—
191C8—4521no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—9048no—
196C22—4522no—
197C22—4522no—
198C22—4522no—
199C22—4521no—
200C22—4521no—
201C22—2262no—
202C22#1681359211yescharacteristic
203C4—21no—
204C4—41no—
205C4—9041no—
206C4—4521no—
207C4SD16×D11311yescharacteristic
208C4C2×#1426863611yescharacteristic
209C4#1681364611yescharacteristic
210C4#1681365011yescharacteristic
211C2—42no—
212C2—9042no—
213C2—4522no—
214C2#2029875011yescharacteristic
215C2#2029875111yescharacteristic
216C2#2029876711yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radicalD4×D452C2
hypercenterD4⋊C8D113
hypocenterC113#1629
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
2. #20298971C2semidirect
3. #20298889C2semidirect
4. #20298888C2semidirect
5. #20298341C2semidirect
6. #20298327C2semidirect
7. D4⋊C8×C113C2semidirect
11. #16813622C22semidirect
19. C4⋊#11744751C22semidirect
23. C4⋊C8×C113C22semidirect
24. C4×C8×C113C22semidirect
59. D4×C113SD16semidirect
76. D452SD16semidirect
109. C113#1629semidirect
116. D4⋊C8D113semidirect
130. C4⋊C8C2×D113semidirect
133. C4×C8C2×D113semidirect
178. D4#14268636semidirect

Maximal subgroups

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

subgroupindex
D4×D4522
#202989712
#202988892
#202988882
#202983412
#202983272
D4⋊C8×C1132
#1629113