Finite Group Databasebeta

← #28389905

Subgroups — #28389905

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#20299352C211yesmaximal, characteristic
2#20299004C211yesmaximal, characteristic, complemented
3#20298960C211yesmaximal, characteristic
4#20298340C211yesmaximal, characteristic, complemented
5#20298339C211yesmaximal, characteristic, complemented
6#20298337C211yesmaximal, characteristic
7#491×C113C211yesmaximal, characteristic, complemented
8#16813621—21no—
9#16813617—21no—
10#16813617—21no—
11#16813614C2211yescharacteristic
12#16813610C2211yescharacteristic
13#16813607—21no—
14#16813602—21no—
15#16813600—21no—
16#16813555—21no—
17#16813553—21no—
18#16813545—21no—
19#16813542—21no—
20#16813533C2211yescharacteristic
21#16813533C2211yescharacteristic
22C4⋊Q8×C113C2211yescharacteristic
23#125×C113C2211yescharacteristic
24#103×C113—21no—
25#103×C113—21no—
26#97×C113C2211yescharacteristic
27C2×Dic226—21no—
28C2×Dic226D411yescharacteristic
29C2×D452D411yescharacteristic
30C2×C4×D113—21no—
31C2×#11744751—21no—
32C2×#11744751—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36#14268626—21no—
37#14268626—21no—
38#14268626—21no—
39#14268624—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44C4×Dic113—21no—
45C2×Q8×C113—21no—
46C2×C8×C113—21no—
47C4⋊C4×C113—21no—
48C4⋊C4×C113—21no—
49C4⋊C4×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113D411yescharacteristic
52C4⋊C4×C113D411yescharacteristic
53C42×C113C2311yescharacteristic
54C22×D113—21no—
55Q8×C113—42no—
56C2×C4×C113—21no—
57C2×C4×C113—21no—
58C2×C4×C113—41no—
59C2×C4×C113C2×D411yescharacteristic
60C2×C4×C113C2×D411yescharacteristic
61C2×C4×C113C2×D411yescharacteristic
62C2×Dic113—21no—
63C2×Dic113—21no—
64C2×Dic113—21no—
65D452—41no—
66C4×D113—81no—
67Dic226—41no—
68Dic226—81no—
69C8×C113—41no—
70#11744751—22no—
71#11744751—41no—
72C22×C113#12011yescharacteristic
73C2×D113—41no—
74C2×D113—41no—
75C2×D113—41no—
76C4×C113—21no—
77C4×C113—21no—
78C4×C113—21no—
79C4×C113—41no—
80C4×C113—41no—
81C4×C113—81no—
82Dic113—41no—
83Dic113—41no—
84Dic113—41no—
85C2×C113#45411yescharacteristic
86C2×C113#45511yescharacteristic
87C2×C113#45611yescharacteristic
88D113—81no—
89#1664—1131nomaximal, Sylow
90C113#166411yescharacteristic, complemented, Sylow
91#563—1131no—
92#501—1131no—
93#491D11311yescharacteristic, complemented
94#489—1131no—
95#330—1131no—
96#330—1131no—
97#329—1131no—
98C4⋊Q8—2261no—
99C4⋊Q8C2×D11311yescharacteristic
100#126—2261no—
101#126—2261no—
102#125—1131no—
103#125C2×D11311yescharacteristic
104#124—1131no—
105#123—2261no—
106C22⋊Q8—2261no—
107C22⋊Q8—2261no—
108#107—2261no—
109#106—2261no—
110#103—21no—
111#103—21no—
112#103—2261no—
113#102—2261no—
114#97—1131no—
115#97—1131no—
116#97C2×D11311yescharacteristic
117C2×Q8—21no—
118C2×Q8—1131no—
119C2×Q8—2261no—
120C2×D4—1131no—
121C22×C4—2261no—
122C2×C8—21no—
123C2×C8—2261no—
124C2×C8—2261no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—1131no—
130C4⋊C4—1131no—
131C4⋊C4—2261no—
132C4⋊C4—2261no—
133C4⋊C4—2261no—
134C4⋊C4—2261no—
135C4⋊C4C22⋊D11311yescharacteristic
136C4⋊C4C22⋊D11311yescharacteristic
137C22⋊C4—2261no—
138C22⋊C4—2261no—
139C22⋊C4—2261no—
140C22⋊C4—2261no—
141C22⋊C4—2261no—
142C42—2261no—
143C42C22×D11311yescharacteristic
144C23—2261no—
145Q8—42no—
146Q8—9041no—
147Q8—4521no—
148D4—4521no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—9041no—
153C2×C4—2261no—
154C2×C4—2261no—
155C2×C4—2261no—
156C2×C4D4×D11311yescharacteristic
157C2×C4D4×D11311yescharacteristic
158C2×C4C2×C22⋊D11311yescharacteristic
159C8—41no—
160C8—4521no—
161C8—2262no—
162C22—4521no—
163C22—4521no—
164C22—4521no—
165C22#1681359011yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—4521no—
173C4—4521no—
174C4—4521no—
175C2—9041no—
176C2#2029877011yescharacteristic
177C2#2029877411yescharacteristic
178C2#2029877911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC42×C113C23
FrattiniC42C22×D113
Fitting#491×C113C2
socleC22×C113#120
prime radicalC2×D452D4
hypercenter#491D113
hypocenterC113#1664
LCSG ▷ C42×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #20299004C2semidirect
4. #20298340C2semidirect
5. #20298339C2semidirect
7. #491×C113C2semidirect
90. C113#1664semidirect
93. #491D113semidirect

Maximal subgroups

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

subgroupindex
#202993522
#202990042
#202989602
#202983402
#202983392
#202983372
#491×C1132
#1664113