Finite Group Databasebeta

← #28389742

Subgroups — #28389742

Order 14464.

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

normal subgroups only

This group has 228 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×Dic226C211yesmaximal, characteristic
2#20298949C211yesmaximal, characteristic, complemented
3#20298894C211yesmaximal, characteristic, complemented
4#20298888C211yesmaximal, characteristic
5#20298345C211yesmaximal, characteristic, complemented
6#20298330C211yesmaximal, characteristic, complemented
7D4⋊C8×C113C211yesmaximal, characteristic
8C22×Dic226—21no—
9#16813622C2211yescharacteristic
10#16813622C2211yescharacteristic
11#16813621—21no—
12#16813601—21no—
13#16813599—22no—
14C4×Dic226C2211yescharacteristic
15D4×Dic113—21no—
16#16813556—21no—
17#16813553—21no—
18C4⋊#11744751C2211yescharacteristic
19#16813547—21no—
20#16813547—22no—
21#16813543—21no—
22C4×D4×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4×C8×C113C2211yescharacteristic
25C2×Dic226—22no—
26C2×Dic226—21no—
27C2×Dic226—21no—
28C2×Dic226—42no—
29C2×Dic226—42no—
30C2×Dic226D411yescharacteristic
31C22×Dic113—22no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113D411yescharacteristic
37C4⋊Dic113D412yes—
38#14268626—22no—
39#14268626—21no—
40C22⋊Dic113—22no—
41C4×Dic113—21no—
42C2×D4×C113D411yescharacteristic
43C22×C4×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113D411yescharacteristic
47C22⋊C4×C113—21no—
48C42×C113C2311yescharacteristic
49C23×C113—21no—
50D4×C113—21no—
51D4×C113Q1612yes—
52C2×C4×C113—21no—
53C2×C4×C113—41no—
54C2×C4×C113—41no—
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113—22no—
61C2×Dic113—44no—
62C2×Dic113—41no—
63Dic226—21no—
64Dic226—44no—
65Dic226—41no—
66Dic226—41no—
67Dic226—42no—
68Dic226SD1612yes—
69C8×C113—41no—
70C8×C113—41no—
71#11744751—41no—
72C22×C113—22no—
73C22×C113—41no—
74C22×C113—41no—
75C22×C113#12011yescharacteristic
76C4×C113—21no—
77C4×C113—41no—
78C4×C113C2×SD1611yescharacteristic
79C4×C113C2×Q1611yescharacteristic
80C4×C113AGL(1,ℤ/8)11yescharacteristic
81C4×C113#13711yescharacteristic
82Dic113—22no—
83Dic113—42no—
84Dic113—41no—
85Dic113—81no—
86C2×C113—42no—
87C2×C113#45011yescharacteristic
88C2×C113#45111yescharacteristic
89C2×C113#45411yescharacteristic
90#1637—1131nomaximal, Sylow
91C113#163711yescharacteristic, complemented, Sylow
92D4×Q8—1131no—
93#487—1131no—
94#477—1131no—
95#476—1131no—
96#332—1131no—
97Q8⋊C8—1131no—
98D4⋊C8D11311yescharacteristic
99C22×Q8—2261no—
100C4⋊Q8—1131no—
101C4⋊Q8—1131no—
102C4⋊Q8—2261no—
103C22⋊Q8—2262no—
104C22⋊Q8—2261no—
105C4×Q8—1131no—
106C4×D4—2261no—
107C4×D4C2×D11311yescharacteristic
108#107—2261no—
109#106—2261no—
110C4⋊C8—1131no—
111C4⋊C8C2×D11311yescharacteristic
112#103—2262no—
113#103—2261no—
114#102—2261no—
115C4×C8C2×D11311yescharacteristic
116C2×Q8—1131no—
117C2×Q8—4522no—
118C2×Q8—4522no—
119C2×Q8—2262no—
120C2×Q8—2261no—
121C2×Q8—2261no—
122C2×D4D45211yescharacteristic
123C22×C4—21no—
124C22×C4—2262no—
125C2×C8—21no—
126C2×C8—21no—
127C2×C8—2261no—
128C4⋊C4—1132no—
129C4⋊C4—1131no—
130C4⋊C4—2262no—
131C4⋊C4—2261no—
132C4⋊C4—2261no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4D45211yescharacteristic
136C22⋊C4—21no—
137C22⋊C4—2262no—
138C42—2261no—
139C42C22×D11311yescharacteristic
140C23—21no—
141Q8—1132no—
142Q8—4522no—
143Q8—4524no—
144Q8—4521no—
145Q8—4521no—
146Q8—2261no—
147D4—21no—
148D4Dic45212yes—
149C2×C4—21no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—4521no—
153C2×C4—4524no—
154C2×C4—2261no—
155C2×C4—2262no—
156C2×C4—2261no—
157C2×C4D4×D11311yescharacteristic
158C2×C4D4×D11311yescharacteristic
159C2×C4C2×D45211yescharacteristic
160C8—41no—
161C8—41no—
162C8—4521no—
163C22—22no—
164C22—41no—
165C22—41no—
166C22#1681359211yescharacteristic
167C4—21no—
168C4—41no—
169C4—9041no—
170C4—4521no—
171C4—4522no—
172C4—2262no—
173C4SD16×D11311yescharacteristic
174C4C2×Dic45211yescharacteristic
175C4#1681364611yescharacteristic
176C4#1681365511yescharacteristic
177C2—42no—
178C2#2029875011yescharacteristic
179C2#2029875611yescharacteristic
180C2#2029877211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
FittingD4⋊C8×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenterD4⋊C8D113
hypocenterC113#1637
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. #20298949C2semidirect
3. #20298894C2semidirect
5. #20298345C2semidirect
6. #20298330C2semidirect
91. C113#1637semidirect

Maximal subgroups

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

subgroupindex
D4×Dic2262
#202989492
#202988942
#202988882
#202983452
#202983302
D4⋊C8×C1132
#1637113