Finite Group Databasebeta

← #28389293

Subgroups — #28389293

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#20299146C211yesmaximal, characteristic
2#20298654C211yesmaximal, characteristic, complemented
3#20298620C211yesmaximal, characteristic, complemented
4#20298345C211yesmaximal, characteristic, complemented
5#20298343C211yesmaximal, characteristic, complemented
6#20298342C211yesmaximal, characteristic, complemented
7#331×C113C211yesmaximal, characteristic, complemented
8C2×#14268646—21no—
9C2×#14268630—21no—
10#16813622C2211yescharacteristic
11#16813609—21no—
12#16813593—21no—
13#16813593C412yes—
14D4×Dic113—21no—
15D4×Dic113C412yes—
16C42×D113C2211yescharacteristic
17C4⋊#11744751C2211yescharacteristic
18C4⋊#11744751C2211yescharacteristic
19#16813551—21no—
20#16813534—21no—
21#16813532—21no—
22#127×C113C2211yescharacteristic
23C4⋊C8×C113C2211yescharacteristic
24C4⋊C8×C113C2211yescharacteristic
25#14268646—42no—
26#14268646—42no—
27C2×Dic226—21no—
28C2×C22⋊D113—22no—
29C22×Dic113—22no—
30C2×C4×D113C2×C411yescharacteristic
31C2×C4×D113D411yescharacteristic
32C2×C4×D113D411yescharacteristic
33#14268630—42no—
34C2×#11744751—21no—
35C2×#11744751—21no—
36C4⋊Dic113—21no—
37C4⋊Dic113C2×C412yes—
38C22⋊Dic113—22no—
39C22⋊Dic113—22no—
40C4×Dic113C2×C411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113D411yescharacteristic
43C2×D4×C113—21no—
44C2×D4×C113—21no—
45C2×D4×C113C2×C412yes—
46C2×C8×C113—21no—
47C2×C8×C113—21no—
48C42×C113C2311yescharacteristic
49C23×C113—22no—
50C22×D113C22⋊C411yescharacteristic
51D4×C113—42no—
52D4×C113—41no—
53D4×C113—41no—
54D4×C113—41no—
55D4×C113—41no—
56C2×C4×C113C22×C411yescharacteristic
57C2×C4×C113C2×D411yescharacteristic
58C2×C4×C113C2×D411yescharacteristic
59C22⋊D113—44no—
60C2×Dic113—22no—
61C2×Dic113—44no—
62C2×Dic113C22⋊C411yescharacteristic
63C2×Dic113C22⋊C411yescharacteristic
64C2×Dic113C22⋊C411yescharacteristic
65C4×D113—21no—
66C4×D113—21no—
67C4×D113—21no—
68C4×D113—21no—
69C4×D113—41no—
70Dic226—41no—
71Dic226—41no—
72C8×C113—41no—
73C8×C113—41no—
74#11744751—41no—
75#11744751—41no—
76C22×C113—42no—
77C22×C113—42no—
78C22×C113—42no—
79C22×C113C2×C22⋊C411yescharacteristic
80C2×D113—21no—
81C2×D113—21no—
82C2×D113—21no—
83C4×C113—21no—
84C4×C113AGL(1,ℤ/8)11yescharacteristic
85C4×C113AGL(1,ℤ/8)11yescharacteristic
86C4×C113AGL(1,ℤ/8)11yescharacteristic
87C4×C113#13711yescharacteristic
88Dic113—21no—
89Dic113—21no—
90Dic113—21no—
91Dic113—42no—
92C2×C113—82no—
93C2×C113#41311yescharacteristic
94C2×C113#41711yescharacteristic
95C2×C113#41811yescharacteristic
96D113—41no—
97#1557—1131nomaximal, Sylow
98C113#155711yescharacteristic, complemented, Sylow
99#532—1131no—
100#432—1131no—
101#423—1131no—
102#332—1131no—
103#332—1131no—
104#331—1131no—
105#331D11311yescharacteristic, complemented
106C2×#41—2261no—
107C2×M16—2261no—
108C4⋊Q8—1131no—
109#127C2×D11311yescharacteristic
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—2261no—
126C2×D4—21no—
127C2×D4—21no—
128C2×D4—2262no—
129C2×D4C4×D11312yes—
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—1132no—
140C4⋊C4—2261no—
141C22⋊C4—2262no—
142C22⋊C4—2262no—
143C42—1131no—
144C42—1131no—
145C42—1131no—
146C42C22×D11311yescharacteristic
147C23—22no—
148C23—1131no—
149Q8—4521no—
150Q8—4521no—
151D4—42no—
152D4—41no—
153D4—41no—
154D4—41no—
155D4—41no—
156D4—4524no—
157C2×C4—1131no—
158C2×C4—1131no—
159C2×C4—1131no—
160C2×C4—4521no—
161C2×C4—4524no—
162C2×C4—2262no—
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—42no—
175C22—42no—
176C22—42no—
177C22—2261no—
178C22—2261no—
179C22—2261no—
180C22C22⋊C4×D11311yescharacteristic
181C4—21no—
182C4—4522no—
183C4—2261no—
184C4—2261no—
185C4—2261no—
186C4#1681364611yescharacteristic
187C4#1681364611yescharacteristic
188C4#1681364911yescharacteristic
189C4#1681365111yescharacteristic
190C2—82no—
191C2—4521no—
192C2#2029857911yescharacteristic
193C2#2029859611yescharacteristic
194C2#2029860111yescharacteristic
subgroupG/H
centerC22C22⋊C4×D113
commutatorC2×C4×C113C22×C4
FrattiniC42C22×D113
Fitting#331×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299146C2
cosocleC42×C113C23
hypercenter#331D113
hypocenterC113#1557
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #20298654C2semidirect
3. #20298620C2semidirect
4. #20298345C2semidirect
5. #20298343C2semidirect
6. #20298342C2semidirect
7. #331×C113C2semidirect
98. C113#1557semidirect
105. #331D113semidirect

Maximal subgroups

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

subgroupindex
#202991462
#202986542
#202986202
#202983452
#202983432
#202983422
#331×C1132
#1557113