Finite Group Databasebeta

← #28400704

Subgroups — #28400704

Order 14464.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#20299155C211yesmaximal, characteristic
2#20298928C212yesmaximal
3#20298883C212yesmaximal, complemented
4#20298808C212yesmaximal, complemented
5#20298754C212yesmaximal
6#20298703C214yesmaximal, complemented
7#20298655C211yesmaximal, characteristic
8C2×C4×Q8×C113C211yesmaximal, characteristic
9C2×#14268637C2214yes—
10#16813622C2211yescharacteristic
11#16813622C2211yescharacteristic
12#16813614—21no—
13#16813601—21no—
14#16813601C2212yes—
15C4×Dic226—21no—
16C4×Dic226C2212yes—
17#16813581—21no—
18#16813553C2214yes—
19C4⋊#11744751C2212yes—
20#16813546C2214yes—
21#16813545C2214yes—
22C22⋊#11744751C2212yes—
23#16813533C2212yes—
24C22×Q8×C113C2211yescharacteristic
25C4×Q8×C113—21no—
26C4×Q8×C113—21no—
27C4×Q8×C113C2212yes—
28C4×Q8×C113C2212yes—
29C2×C4⋊C4×C113—21no—
30C2×C4⋊C4×C113C2211yescharacteristic
31C2×C42×C113—21no—
32C2×C42×C113C2211yescharacteristic
33C2×Dic226—21no—
34C2×Dic226C2312yes—
35#14268637—28no—
36C2×#11744751C2314yes—
37C4⋊Dic113—21no—
38C4⋊Dic113—21no—
39C4⋊Dic113—21no—
40C4⋊Dic113C2312yes—
41#14268626—22no—
42#14268626—22no—
43C22⋊Dic113—22no—
44C4×Dic113—22no—
45C2×Q8×C113—24no—
46C2×Q8×C113—21no—
47C2×Q8×C113C2312yes—
48C22×C4×C113—21no—
49C22×C4×C113—21no—
50C22×C4×C113D411yescharacteristic
51C22×C4×C113D411yescharacteristic
52C22×C4×C113C2311yescharacteristic
53C4⋊C4×C113—22no—
54C4⋊C4×C113—22no—
55C4⋊C4×C113—21no—
56C4⋊C4×C113C2312yes—
57C42×C113—22no—
58C42×C113—22no—
59C42×C113D411yescharacteristic
60C42×C113D411yescharacteristic
61C42×C113C2311yescharacteristic
62C42×C113C2311yescharacteristic
63C23×C113C2×D411yescharacteristic
64Q8×C113—24no—
65Q8×C113—22no—
66Q8×C113#4114yes—
67C2×C4×C113—24no—
68C2×C4×C113—22no—
69C2×C4×C113—22no—
70C2×C4×C113—22no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—42no—
74C2×C4×C113C2×D411yescharacteristic
75C2×C4×C113C2×D411yescharacteristic
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2×D411yescharacteristic
79C2×C4×C113C2411yescharacteristic
80C2×Dic113—22no—
81C2×Dic113—22no—
82Dic226—24no—
83Dic226—42no—
84#11744751—24no—
85C22×C113—21no—
86C22×C113—21no—
87C22×C113#13712yes—
88C22×C113C22×D411yescharacteristic
89C4×C113—24no—
90C4×C113—21no—
91C4×C113—21no—
92C4×C113—21no—
93C4×C113—21no—
94C4×C113—42no—
95C4×C113#13712yes—
96C4×C113C2×#4112yes—
97Dic113—42no—
98Dic113—42no—
99C2×C113—22no—
100C2×C113#52511yescharacteristic
101C2×C113C2×#13711yescharacteristic
102C2×C113C2×#13711yescharacteristic
103#3113—1131nomaximal, Sylow
104C113#311311yescharacteristic, complemented, Sylow
105#533—1131no—
106C2×C4×Q8D11311yescharacteristic
107#483—1132no—
108#475—1132no—
109#462—1132no—
110#451—1132no—
111#441—1134no—
112#432—1131no—
113C22×Q8C2×D11311yescharacteristic
114C2×Q16—1134no—
115C4⋊Q8—1131no—
116C4⋊Q8—1131no—
117#125—2261no—
118C22⋊Q8—1132no—
119C22⋊Q8—2261no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—1132no—
123C4×Q8—2261no—
124C4×Q8C2×D11312yes—
125C4×Q8C2×D11312yes—
126#117—2261no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D11311yescharacteristic
129C2×C42—21no—
130C2×C42C2×D11311yescharacteristic
131#106—1134no—
132C4⋊C8—1132no—
133#103—1134no—
134#103—1134no—
135C22⋊C8—1132no—
136#97—1132no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—1132no—
140C2×Q8—2261no—
141C2×Q8C22×D11312yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D11311yescharacteristic
145C22×C4C22⋊D11311yescharacteristic
146C22×C4C22×D11311yescharacteristic
147Q16—2268no—
148C2×C8—1134no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—1132no—
153C4⋊C4—2261no—
154C4⋊C4—2261no—
155C4⋊C4—2262no—
156C4⋊C4—2262no—
157C4⋊C4—2261no—
158C4⋊C4C22×D11312yes—
159C22⋊C4—2262no—
160C42—22no—
161C42—22no—
162C42—2262no—
163C42C22⋊D11311yescharacteristic
164C42C22⋊D11311yescharacteristic
165C42C22×D11311yescharacteristic
166C42C22×D11311yescharacteristic
167C23C2×C22⋊D11311yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—4522no—
171Q8—2264no—
172Q8#1426864714yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—2262no—
181C2×C4—2262no—
182C2×C4C2×C22⋊D11311yescharacteristic
183C2×C4C2×C22⋊D11311yescharacteristic
184C2×C4C2×C22⋊D11311yescharacteristic
185C2×C4C2×C22⋊D11311yescharacteristic
186C2×C4C2×C22⋊D11311yescharacteristic
187C2×C4C23×D11311yescharacteristic
188C8—2264no—
189C22—21no—
190C22—21no—
191C22#1681365212yes—
192C22C22×C22⋊D11311yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—4522no—
200C4—4522no—
201C4#1681365312yes—
202C4C2×#1426864712yes—
203C2—22no—
204C2#2029910911yescharacteristic
205C2C2×#1681365211yescharacteristic
206C2C2×#1681365311yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×C4×Q8×C113C2
socleC22×C113C22×D4
prime radicalC23×C113C2×D4
hypercenterC2×C4×Q8D113
hypocenterC113#3113
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #20298883C2semidirect
4. #20298808C2semidirect
6. #20298703C2semidirect
104. C113#3113semidirect

Maximal subgroups

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

subgroupindex
#202991552
#202989282
#202988832
#202988082
#202987542
#202987032
#202986552
C2×C4×Q8×C1132
#3113113