Finite Group Databasebeta

← #28389700

Subgroups — #28389700

Order 14464.

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

normal subgroups only

This group has 256 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#20299269C211yesmaximal, characteristic
2#20298972C211yesmaximal, characteristic, complemented
3#20298890C211yesmaximal, characteristic, complemented
4#20298341C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6D4⋊#11744751C211yesmaximal, characteristic, complemented
7#476×C113C211yesmaximal, characteristic, complemented
8C2×#14268647—21no—
9C2×#14268634—22no—
10#16813619C2211yescharacteristic
11#16813618—21no—
12#16813596—21no—
13#16813595—22no—
14C4×Dic226C2211yescharacteristic
15#16813584—21no—
16#16813555—21no—
17C4⋊#11744751C2211yescharacteristic
18#16813545—21no—
19C4×#11744751C2211yescharacteristic
20C4⋊Q8×C113C2211yescharacteristic
21C4×D4×C113C2211yescharacteristic
22#106×C113—21no—
23C4⋊C8×C113C2211yescharacteristic
24#102×C113—21no—
25#14268647—42no—
26#14268647—42no—
27C2×Dic226D411yescharacteristic
28C2×D452—21no—
29C2×D452—21no—
30C2×D452D412yes—
31C2×C22⋊D113—22no—
32C2×C22⋊D113—22no—
33C2×C4×D113—22no—
34#14268634—44no—
35C2×#11744751—21no—
36C2×#11744751—21no—
37C4⋊Dic113D411yescharacteristic
38#14268626—21no—
39#14268624—22no—
40C4×Dic113—21no—
41C2×Q8×C113—21no—
42C2×D4×C113D411yescharacteristic
43C22×C4×C113—21no—
44C2×C8×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D411yescharacteristic
48C22⋊C4×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—21no—
51C22×D113—22no—
52Q8×C113—42no—
53D4×C113—21no—
54D4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113—41no—
57C2×C4×C113—41no—
58C2×C4×C113—41no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C22⋊D113—44no—
63C22⋊D113—82no—
64C2×Dic113—21no—
65C2×Dic113—21no—
66D452—42no—
67D452—41no—
68D452—41no—
69D452—41no—
70D452—41no—
71C4×D113—44no—
72Dic226—21no—
73Dic226SD1612yescomplemented
74C8×C113—41no—
75#11744751—22no—
76#11744751—41no—
77C22×C113—41no—
78C22×C113—41no—
79C22×C113—41no—
80C22×C113#12011yescharacteristic
81C2×D113—42no—
82C2×D113—42no—
83C2×D113—42no—
84C4×C113—21no—
85C4×C113—41no—
86C4×C113—81no—
87C4×C113C2×SD1611yescharacteristic
88C4×C113#13511yescharacteristic
89C4×C113AGL(1,ℤ/8)11yescharacteristic
90C4×C113#13711yescharacteristic
91Dic113—22no—
92Dic113—41no—
93C2×C113—81no—
94C2×C113#45011yescharacteristic
95C2×C113#45211yescharacteristic
96C2×C113#45311yescharacteristic
97D113—82no—
98#1631—1131nomaximal, Sylow
99C113#163111yescharacteristic, complemented, Sylow
100#550—1131no—
101#492—1131no—
102#477—1131no—
103#476D11311yescharacteristic, complemented
104#331—1131no—
105Q8⋊C8—1131no—
106D4⋊C8—1131no—
107C2×#41—2261no—
108C2×SD16—2262no—
109C4⋊Q8C2×D11311yescharacteristic
110#127—1131no—
111#127—2261no—
112#121—2262no—
113#121—2261no—
114C4×Q8—1131no—
115C4×D4—2261no—
116C4×D4C2×D11311yescharacteristic
117#107—2261no—
118#106—21no—
119C4⋊C8—1131no—
120C4⋊C8C2×D11311yescharacteristic
121#103—2261no—
122#102—21no—
123C4×C8—1131no—
124#41—4522no—
125#41—4522no—
126C2×Q8—21no—
127C2×Q8—1131no—
128C2×D4—1132no—
129C2×D4—2262no—
130C2×D4—2262no—
131C2×D4—2261no—
132C2×D4—2261no—
133C2×D4C22⋊D11311yescharacteristic
134C22×C4—21no—
135C22×C4—2262no—
136SD16—4524no—
137C2×C8—21no—
138C2×C8—2261no—
139C2×C8—2261no—
140C4⋊C4—21no—
141C4⋊C4—21no—
142C4⋊C4—1131no—
143C4⋊C4—2261no—
144C4⋊C4C22⋊D11311yescharacteristic
145C22⋊C4—21no—
146C22⋊C4—2262no—
147C42—2261no—
148C42C22×D11311yescharacteristic
149C23—21no—
150C23—2262no—
151Q8—42no—
152Q8—1132no—
153Q8—2261no—
154D4—21no—
155D4—21no—
156D4—9042no—
157D4—4522no—
158D4—4524no—
159D4—4521no—
160D4—4521no—
161D4—4521no—
162D4—4521no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—4524no—
168C2×C4—2261no—
169C2×C4—2261no—
170C2×C4D4×D11311yescharacteristic
171C2×C4D4×D11311yescharacteristic
172C2×C4C2×C22⋊D11311yescharacteristic
173C8—41no—
174C8—4521no—
175C8—2262no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—4522no—
180C22—4522no—
181C22—4522no—
182C22#1681359011yescharacteristic
183C4—21no—
184C4—41no—
185C4—81no—
186C4—4521no—
187C4—2262no—
188C4SD16×D11311yescharacteristic
189C4#1681364211yescharacteristic
190C4#1681364911yescharacteristic
191C4#1681365311yescharacteristic
192C2—81no—
193C2—9042no—
194C2#2029874711yescharacteristic
195C2#2029875811yescharacteristic
196C2#2029876411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#476×C113C2
socleC22×C113#120
prime radical#20299269C2
hypercenter#476D113
hypocenterC113#1631
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
2. #20298972C2semidirect
3. #20298890C2semidirect
4. #20298341C2semidirect
5. #20298328C2semidirect
6. D4⋊#11744751C2semidirect
7. #476×C113C2semidirect
73. Dic226SD16semidirect
99. C113#1631semidirect
103. #476D113semidirect

Maximal subgroups

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

subgroupindex
#202992692
#202989722
#202988902
#202983412
#202983282
D4⋊#117447512
#476×C1132
#1631113