Finite Group Databasebeta

← #28389911

Subgroups — #28389911

Order 14464.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#20299348C211yesmaximal, characteristic
2#20299007C211yesmaximal, characteristic, complemented
3#20298967C211yesmaximal, characteristic, complemented
4#20298957C211yesmaximal, characteristic
5#20298339C211yesmaximal, characteristic, complemented
6#20298339C211yesmaximal, characteristic, complemented
7#329×C113C211yesmaximal, characteristic
8#16813622C2211yescharacteristic
9#16813620—21no—
10#16813615—21no—
11#16813615—21no—
12#16813614C2211yescharacteristic
13#16813614C2211yescharacteristic
14#16813603—21no—
15#16813599—21no—
16#16813599—21no—
17#16813556—21no—
18#16813554—21no—
19#16813547—21no—
20#16813547—21no—
21#16813546—21no—
22#16813543—21no—
23#16813533C2211yescharacteristic
24#124×C113C2211yescharacteristic
25#97×C113C2211yescharacteristic
26#97×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226—21no—
29C22×Dic113—21no—
30C2×#11744751—21no—
31C4⋊Dic113—21no—
32C4⋊Dic113—21no—
33C4⋊Dic113D411yescharacteristic
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40#14268626—21no—
41#14268626—21no—
42#14268626—21no—
43C22⋊Dic113—21no—
44C22⋊Dic113—21no—
45C22⋊Dic113—21no—
46C4×Dic113—21no—
47C2×Q8×C113D411yescharacteristic
48C2×D4×C113D411yescharacteristic
49C2×C8×C113—21no—
50C2×C8×C113—21no—
51C22⋊C4×C113—21no—
52C22⋊C4×C113—21no—
53C42×C113C2311yescharacteristic
54C23×C113—21no—
55Q8×C113—41no—
56D4×C113—41no—
57C2×C4×C113—21no—
58C2×C4×C113C2×D411yescharacteristic
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×Dic113—21no—
62C2×Dic113—21no—
63C2×Dic113—21no—
64C2×Dic113—21no—
65C2×Dic113—41no—
66C2×Dic113—81no—
67Dic226—42no—
68Dic226—81no—
69C8×C113—22no—
70C8×C113—41no—
71#11744751—41no—
72C22×C113—41no—
73C22×C113—41no—
74C22×C113—41no—
75C22×C113#12011yescharacteristic
76C4×C113—21no—
77C4×C113—21no—
78C4×C113—21no—
79C4×C113—41no—
80Dic113—41no—
81Dic113—41no—
82Dic113—41no—
83Dic113—41no—
84Dic113—81no—
85C2×C113—81no—
86C2×C113#45411yescharacteristic
87C2×C113#45511yescharacteristic
88C2×C113#45611yescharacteristic
89#1664—1131nomaximal, Sylow
90C113#166411yescharacteristic, complemented, Sylow
91#563—1131no—
92#501—1131no—
93#491—1131no—
94#489—1131no—
95#330—1131no—
96#330—1131no—
97#329D11311yescharacteristic
98C4⋊Q8—1131no—
99C4⋊Q8—2261no—
100#126—2261no—
101#126—2261no—
102#125—1131no—
103#125—1131no—
104#124C2×D11311yescharacteristic
105#123—2261no—
106C22⋊Q8—2261no—
107C22⋊Q8—2261no—
108#107—2261no—
109#106—2261no—
110#103—2261no—
111#103—2261no—
112#103—2261no—
113#102—2261no—
114#97—1131no—
115#97C2×D11311yescharacteristic
116#97C2×D11311yescharacteristic
117C2×Q8—2261no—
118C2×Q8—2261no—
119C2×Q8D45211yescharacteristic
120C2×D4D45211yescharacteristic
121C22×C4—2261no—
122C2×C8—21no—
123C2×C8—21no—
124C2×C8—2261no—
125C4⋊C4—1131no—
126C4⋊C4—1131no—
127C4⋊C4—1131no—
128C4⋊C4—1131no—
129C4⋊C4—2261no—
130C4⋊C4—2261no—
131C4⋊C4—2261no—
132C4⋊C4—2261no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4—2261no—
136C4⋊C4—2261no—
137C22⋊C4—21no—
138C22⋊C4—21no—
139C22⋊C4—2261no—
140C22⋊C4—2261no—
141C22⋊C4—2261no—
142C42—2261no—
143C42C22×D11311yescharacteristic
144C23—21no—
145Q8—41no—
146Q8—9041no—
147Q8—4522no—
148D4—41no—
149C2×C4—21no—
150C2×C4—9041no—
151C2×C4—4521no—
152C2×C4—2261no—
153C2×C4—2261no—
154C2×C4—2261no—
155C2×C4—2261no—
156C2×C4D4×D11311yescharacteristic
157C2×C4D4×D11311yescharacteristic
158C2×C4C2×D45211yescharacteristic
159C8—22no—
160C8—41no—
161C8—4521no—
162C22—41no—
163C22—41no—
164C22—41no—
165C22#1681359211yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—9041no—
171C4—4521no—
172C4—4521no—
173C4—4521no—
174C4—4521no—
175C2—81no—
176C2#2029877211yescharacteristic
177C2#2029877811yescharacteristic
178C2#2029878211yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#329×C113C2
socleC22×C113#120
prime radicalC2×D4×C113D4
hypercenter#329D113
hypocenterC113#1664
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #20299007C2semidirect
3. #20298967C2semidirect
5. #20298339C2semidirect
6. #20298339C2semidirect
90. C113#1664semidirect

Maximal subgroups

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

subgroupindex
#202993482
#202990072
#202989672
#202989572
#202983392
#329×C1132
#1664113