Finite Group Databasebeta

← #28389702

Subgroups — #28389702

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#20299268C211yesmaximal, characteristic
2#20298970C211yesmaximal, characteristic, complemented
3#20298894C211yesmaximal, characteristic, complemented
4#20298889C211yesmaximal, characteristic, complemented
5#20298328C211yesmaximal, characteristic, complemented
6#20298325C211yesmaximal, characteristic, complemented
7#331×C113C211yesmaximal, characteristic, complemented
8C2×#14268646—21no—
9C2×#14268635—22no—
10#16813622C2211yescharacteristic
11#16813618—21no—
12#16813594—22no—
13#16813593—21no—
14C4×Dic226C2211yescharacteristic
15C4×D452C2211yescharacteristic
16D4×Dic113—21no—
17#16813556—21no—
18#16813554—21no—
19#16813547—21no—
20#16813544—21no—
21C4×#11744751C2211yescharacteristic
22#127×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25#14268646—42no—
26#14268646—42no—
27C2×Dic226—21no—
28C2×Dic226D411yescharacteristic
29C2×D452D411yescharacteristic
30C2×C22⋊D113—22no—
31C2×C22⋊D113—22no—
32C22×Dic113—22no—
33C2×C4×D113—21no—
34#14268635—44no—
35C2×#11744751—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113—21no—
38C4⋊Dic113D411yescharacteristic
39C4⋊Dic113D411yescharacteristic
40#14268626—21no—
41C22⋊Dic113—22no—
42#14268624—21no—
43C4×Dic113—21no—
44C2×D4×C113—21no—
45C2×D4×C113—21no—
46C2×D4×C113D412yes—
47C2×C8×C113—21no—
48C2×C8×C113—21no—
49C42×C113C2311yescharacteristic
50C23×C113—22no—
51C22×D113—21no—
52D4×C113—42no—
53D4×C113—41no—
54D4×C113—41no—
55D4×C113—41no—
56D4×C113—41no—
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C22⋊D113—44no—
61C22⋊D113—82no—
62C2×Dic113—21no—
63C2×Dic113—21no—
64C2×Dic113—21no—
65C2×Dic113—44no—
66C2×Dic113—41no—
67D452—21no—
68D452—21no—
69C4×D113—41no—
70C4×D113—41no—
71Dic226—21no—
72Dic226—42no—
73Dic226SD1612yescomplemented
74C8×C113—41no—
75C8×C113—41no—
76#11744751—22no—
77C22×C113—42no—
78C22×C113—42no—
79C22×C113—42no—
80C22×C113#12011yescharacteristic
81C2×D113—41no—
82C2×D113—41no—
83C2×D113—41no—
84C4×C113—21no—
85C4×C113C2×SD1611yescharacteristic
86C4×C113#13511yescharacteristic
87C4×C113AGL(1,ℤ/8)11yescharacteristic
88C4×C113#13711yescharacteristic
89Dic113—22no—
90Dic113—41no—
91Dic113—41no—
92Dic113—81no—
93C2×C113—82no—
94C2×C113#45011yescharacteristic
95C2×C113#45211yescharacteristic
96C2×C113#45311yescharacteristic
97D113—81no—
98#1631—1131nomaximal, Sylow
99C113#163111yescharacteristic, complemented, Sylow
100#550—1131no—
101#492—1131no—
102#477—1131no—
103#476—1131no—
104#331D11311yescharacteristic, complemented
105Q8⋊C8—1131no—
106D4⋊C8—1131no—
107C2×#41—2261no—
108C2×SD16—2262no—
109C4⋊Q8—1131no—
110#127—2261no—
111#127C2×D11311yescharacteristic
112#121—2261no—
113#121—2262no—
114C4×Q8—1131no—
115C4×D4—1131no—
116C4×D4—2261no—
117#107—2261no—
118#106—2261no—
119C4⋊C8C2×D11311yescharacteristic
120C4⋊C8C2×D11311yescharacteristic
121#103—2261no—
122#102—2261no—
123C4×C8—1131no—
124#41—4522no—
125#41—4522no—
126C2×Q8—1131no—
127C2×Q8—2261no—
128C2×D4—21no—
129C2×D4—21no—
130C2×D4—1131no—
131C2×D4—2262no—
132C2×D4—2262no—
133C2×D4D45212yes—
134C22×C4—2262no—
135C22×C4—2261no—
136SD16—4524no—
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—2261no—
140C4⋊C4—1131no—
141C4⋊C4—1131no—
142C4⋊C4—2261no—
143C4⋊C4—2261no—
144C4⋊C4—2261no—
145C22⋊C4—2262no—
146C22⋊C4—2261no—
147C42—2261no—
148C42C22×D11311yescharacteristic
149C23—22no—
150C23—2261no—
151Q8—1132no—
152Q8—4522no—
153Q8—2261no—
154D4—42no—
155D4—41no—
156D4—41no—
157D4—41no—
158D4—41no—
159D4—9042no—
160D4—4524no—
161D4—2261no—
162D4—2261no—
163C2×C4—4521no—
164C2×C4—4524no—
165C2×C4—4521no—
166C2×C4—4521no—
167C2×C4—2261no—
168C2×C4—2261no—
169C2×C4—2261no—
170C2×C4D4×D11311yescharacteristic
171C2×C4D4×D11311yescharacteristic
172C2×C4C2×D45211yescharacteristic
173C8—41no—
174C8—41no—
175C8—2262no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—4521no—
180C22—4521no—
181C22—4521no—
182C22#1681359211yescharacteristic
183C4—21no—
184C4—9041no—
185C4—4521no—
186C4—4521no—
187C4—2262no—
188C4SD16×D11311yescharacteristic
189C4#1681364111yescharacteristic
190C4#1681364611yescharacteristic
191C4#1681365111yescharacteristic
192C2—82no—
193C2—9041no—
194C2#2029875011yescharacteristic
195C2#2029876111yescharacteristic
196C2#2029876811yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#331×C113C2
socleC22×C113#120
prime radical#20299268C2
hypercenter#331D113
hypocenterC113#1631
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20298970C2semidirect
3. #20298894C2semidirect
4. #20298889C2semidirect
5. #20298328C2semidirect
6. #20298325C2semidirect
7. #331×C113C2semidirect
73. Dic226SD16semidirect
99. C113#1631semidirect
104. #331D113semidirect

Maximal subgroups

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

subgroupindex
#202992682
#202989702
#202988942
#202988892
#202983282
#202983252
#331×C1132
#1631113