Finite Group Databasebeta

← #28389295

Subgroups — #28389295

Order 14464.

246 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 65 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#20299149C211yesmaximal, characteristic
2#20298654C211yesmaximal, characteristic, complemented
3#20298620C211yesmaximal, characteristic, complemented
4#20298344C211yesmaximal, characteristic, complemented
5#20298341C211yesmaximal, characteristic, complemented
6#20298341C211yesmaximal, characteristic, complemented
7#332×C113C211yesmaximal, characteristic, complemented
8C2×#14268648—21no—
9C2×#14268630—21no—
10#16813619C2211yescharacteristic
11#16813611—21no—
12#16813597—21no—
13#16813597C412yes—
14#16813584—21no—
15#16813584C412yes—
16C42×D113C2211yescharacteristic
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813551—21no—
20#16813534—21no—
21#16813532—21no—
22C4⋊Q8×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25#14268648—42no—
26#14268648—42no—
27C2×D452—22no—
28C2×D452—21no—
29C2×D452—21no—
30C2×D452C2×C412yes—
31C2×C4×D113—22no—
32C2×C4×D113C2×C411yescharacteristic
33C2×C4×D113D411yescharacteristic
34C2×C4×D113D411yescharacteristic
35#14268630—42no—
36C2×#11744751—21no—
37C2×#11744751—21no—
38#14268624—22no—
39#14268624—22no—
40C4×Dic113C2×C411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113D411yescharacteristic
43C2×Q8×C113—21no—
44C2×C8×C113—21no—
45C2×C8×C113—21no—
46C4⋊C4×C113—21no—
47C4⋊C4×C113C2×C412yes—
48C42×C113C2311yescharacteristic
49C22×D113—22no—
50C22×D113C22⋊C411yescharacteristic
51Q8×C113—41no—
52Q8×C113—41no—
53C2×C4×C113—22no—
54C2×C4×C113C22×C411yescharacteristic
55C2×C4×C113C2×D411yescharacteristic
56C2×C4×C113C2×D411yescharacteristic
57C2×Dic113C22⋊C411yescharacteristic
58C2×Dic113C22⋊C411yescharacteristic
59C2×Dic113C22⋊C411yescharacteristic
60D452—42no—
61D452—44no—
62D452—41no—
63D452—41no—
64D452—41no—
65D452—41no—
66C4×D113—21no—
67C4×D113—21no—
68C4×D113—21no—
69C4×D113—21no—
70C4×D113—41no—
71C4×D113—44no—
72C8×C113—41no—
73C8×C113—41no—
74#11744751—41no—
75#11744751—41no—
76C22×C113C2×C22⋊C411yescharacteristic
77C2×D113—21no—
78C2×D113—21no—
79C2×D113—21no—
80C2×D113—42no—
81C2×D113—42no—
82C2×D113—42no—
83C4×C113—21no—
84C4×C113—42no—
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87C4×C113AGL(1,ℤ/8)11yescharacteristic
88C4×C113#13711yescharacteristic
89Dic113—21no—
90Dic113—21no—
91Dic113—21no—
92C2×C113#41311yescharacteristic
93C2×C113#41711yescharacteristic
94C2×C113#41811yescharacteristic
95D113—41no—
96D113—82no—
97#1557—1131nomaximal, Sylow
98C113#155711yescharacteristic, complemented, Sylow
99#532—1131no—
100#432—1131no—
101#423—1131no—
102#332—1131no—
103#332D11311yescharacteristic, complemented
104#331—1131no—
105#331—1131no—
106C2×#41—2261no—
107C2×M16—2261no—
108C4⋊Q8C2×D11311yescharacteristic
109#127—1131no—
110#124—2261no—
111#121—1132no—
112#121—2261no—
113C4×D4—1132no—
114C4×D4—2261no—
115C2×C42—1131no—
116C4⋊C8—1131no—
117C4⋊C8—1131no—
118C4⋊C8—2261no—
119C4⋊C8C2×D11311yescharacteristic
120C4⋊C8C2×D11311yescharacteristic
121C22⋊C8—2261no—
122#97—2261no—
123#41—4522no—
124#41—4522no—
125C2×Q8—21no—
126C2×D4—1132no—
127C2×D4—2262no—
128C2×D4—2261no—
129C2×D4—2261no—
130C22×C4—1131no—
131C22×C4—1131no—
132C22×C4—1131no—
133C22×C4—2262no—
134M16—4522no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—2261no—
138C2×C8—2261no—
139C4⋊C4—21no—
140C4⋊C4C4×D11312yes—
141C22⋊C4—2262no—
142C22⋊C4—2262no—
143C42—1131no—
144C42—1131no—
145C42—1131no—
146C42C22×D11311yescharacteristic
147C23—1131no—
148C23—2262no—
149Q8—41no—
150Q8—41no—
151D4—4522no—
152D4—4524no—
153D4—4521no—
154D4—4521no—
155D4—4521no—
156D4—4521no—
157C2×C4—22no—
158C2×C4—1131no—
159C2×C4—1131no—
160C2×C4—1131no—
161C2×C4—4521no—
162C2×C4—4524no—
163C2×C4—2261no—
164C2×C4—2261no—
165C2×C4—2261no—
166C2×C4—2261no—
167C2×C4C2×C4×D11311yescharacteristic
168C2×C4D4×D11311yescharacteristic
169C2×C4D4×D11311yescharacteristic
170C8—41no—
171C8—41no—
172C8—4521no—
173C8—4521no—
174C22—4522no—
175C22—4522no—
176C22—4522no—
177C22—2261no—
178C22—2261no—
179C22—2261no—
180C22C22⋊C4×D11311yescharacteristic
181C4—21no—
182C4—42no—
183C4—2261no—
184C4—2261no—
185C4—2261no—
186C4#1681364611yescharacteristic
187C4#1681364911yescharacteristic
188C4#1681364911yescharacteristic
189C4#1681365411yescharacteristic
190C2—9042no—
191C2—4521no—
192C2#2029858111yescharacteristic
193C2#2029859811yescharacteristic
194C2#2029860111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#332×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299149C2
cosocleC42×C113C23
hypercenter#332D113
hypocenterC113#1557
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #20298654C2semidirect
3. #20298620C2semidirect
4. #20298344C2semidirect
5. #20298341C2semidirect
6. #20298341C2semidirect
7. #332×C113C2semidirect
98. C113#1557semidirect
103. #332D113semidirect

Maximal subgroups

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

subgroupindex
#202991492
#202986542
#202986202
#202983442
#202983412
#332×C1132
#1557113