Finite Group Databasebeta

← #28389736

Subgroups — #28389736

Order 14464.

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

normal subgroups only

This group has 228 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#20299263C211yesmaximal, characteristic
2#20298890C211yesmaximal, characteristic, complemented
3#20298885C211yesmaximal, characteristic
4#20298344C211yesmaximal, characteristic, complemented
5#20298330C211yesmaximal, characteristic, complemented
6#20298327C211yesmaximal, characteristic
7#487×C113C211yesmaximal, characteristic, complemented
8C2×Q8×D113—21no—
9#16813621—21no—
10#16813600—22no—
11#16813598—21no—
12C4×Dic226C2211yescharacteristic
13C4×D452C2211yescharacteristic
14#16813584—21no—
15#16813555—21no—
16#16813553—21no—
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813545—21no—
20#16813542—21no—
21C4⋊Q8×C113C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23#103×C113—22no—
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—22no—
26C2×Dic226D411yescharacteristic
27Q8×D113—42no—
28Q8×D113—42no—
29C2×D452D411yescharacteristic
30C2×C4×D113—22no—
31C2×C4×D113—21no—
32C2×#11744751—21no—
33C2×#11744751—21no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36#14268626—22no—
37#14268626—21no—
38#14268624—22no—
39#14268624—21no—
40C4×Dic113—21no—
41C2×Q8×C113—21no—
42C2×Q8×C113—21no—
43C2×C8×C113—21no—
44C4⋊C4×C113—21no—
45C4⋊C4×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113D412yes—
48C42×C113C2311yescharacteristic
49C22×D113—21no—
50Q8×C113—42no—
51Q8×C113—41no—
52Q8×C113—41no—
53C2×C4×C113—22no—
54C2×C4×C113—41no—
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113—21no—
61D452—21no—
62D452Q1612yes—
63C4×D113—44no—
64C4×D113—41no—
65C4×D113—41no—
66Dic226—21no—
67Dic226—44no—
68Dic226SD1612yes—
69C8×C113—41no—
70#11744751—41no—
71#11744751—41no—
72C22×C113#12011yescharacteristic
73C2×D113—22no—
74C2×D113—41no—
75C2×D113—41no—
76C4×C113—21no—
77C4×C113—42no—
78C4×C113—81no—
79C4×C113C2×SD1611yescharacteristic
80C4×C113C2×Q1611yescharacteristic
81C4×C113AGL(1,ℤ/8)11yescharacteristic
82C4×C113#13711yescharacteristic
83Dic113—22no—
84Dic113—41no—
85Dic113—41no—
86C2×C113#45011yescharacteristic
87C2×C113#45111yescharacteristic
88C2×C113#45411yescharacteristic
89D113—42no—
90#1637—1131nomaximal, Sylow
91C113#163711yescharacteristic, complemented, Sylow
92D4×Q8—1131no—
93#487D11311yescharacteristic, complemented
94#477—1131no—
95#476—1131no—
96#332—1131no—
97Q8⋊C8—1131no—
98D4⋊C8—1131no—
99C22×Q8—2261no—
100C4⋊Q8—2261no—
101C4⋊Q8C2×D11311yescharacteristic
102C4⋊Q8C2×D11311yescharacteristic
103C22⋊Q8—2261no—
104C22⋊Q8—2262no—
105C4×Q8—1131no—
106C4×D4—1131no—
107C4×D4—2261no—
108#107—2261no—
109#106—2261no—
110C4⋊C8—1131no—
111C4⋊C8—1131no—
112#103—22no—
113#103—2261no—
114#102—2261no—
115C4×C8C2×D11311yescharacteristic
116C2×Q8—21no—
117C2×Q8—21no—
118C2×Q8—1131no—
119C2×Q8—4522no—
120C2×Q8—4522no—
121C2×Q8—2262no—
122C2×D4—1131no—
123C22×C4—2262no—
124C22×C4—2261no—
125C2×C8—21no—
126C2×C8—2261no—
127C2×C8—2261no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—21no—
131C4⋊C4—1131no—
132C4⋊C4—1131no—
133C4⋊C4—2262no—
134C4⋊C4—2261no—
135C4⋊C4C22⋊D11312yes—
136C22⋊C4—2262no—
137C22⋊C4—2261no—
138C42—2261no—
139C42C22×D11311yescharacteristic
140C23—2261no—
141Q8—42no—
142Q8—41no—
143Q8—41no—
144Q8—1132no—
145Q8—4524no—
146Q8—2261no—
147D4—1132no—
148D4—2261no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—4524no—
152C2×C4—4521no—
153C2×C4—4521no—
154C2×C4—2261no—
155C2×C4—2261no—
156C2×C4—2261no—
157C2×C4D4×D11311yescharacteristic
158C2×C4D4×D11311yescharacteristic
159C2×C4C2×C22⋊D11311yescharacteristic
160C8—41no—
161C8—4521no—
162C8—4521no—
163C22—4521no—
164C22—4521no—
165C22—2262no—
166C22#1681359011yescharacteristic
167C4—21no—
168C4—42no—
169C4—81no—
170C4—4521no—
171C4—4521no—
172C4—2262no—
173C4SD16×D11311yescharacteristic
174C4Q16×D11311yescharacteristic
175C4#1681364911yescharacteristic
176C4#1681365411yescharacteristic
177C2—4522no—
178C2#2029874711yescharacteristic
179C2#2029875211yescharacteristic
180C2#2029877011yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#487×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#487D113
hypocenterC113#1637
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
2. #20298890C2semidirect
4. #20298344C2semidirect
5. #20298330C2semidirect
7. #487×C113C2semidirect
91. C113#1637semidirect
93. #487D113semidirect

Maximal subgroups

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

subgroupindex
#202992632
#202988902
#202988852
#202983442
#202983302
#202983272
#487×C1132
#1637113