Finite Group Databasebeta

← #28391733

Subgroups — #28391733

Order 14464.

246 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 69 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#20299226C211yesmaximal, characteristic
2#20298607C211yesmaximal, characteristic
3#20298505C211yesmaximal, characteristic
4#20298366C211yesmaximal, characteristic
5#20298359C211yesmaximal, characteristic
6#20298357C211yesmaximal, characteristic
7#419×C113C211yesmaximal, characteristic
8C2×#14268631C2211yescharacteristic
9#16813622—21no—
10#16813621—21no—
11#16813614—21no—
12#16813613—21no—
13#16813599—22no—
14#16813581C2211yescharacteristic
15C2×C4⋊Dic113C2211yescharacteristic
16C2×C4×Dic113C2211yescharacteristic
17#16813546—21no—
18#16813546—21no—
19#16813529—22no—
20C22×Q8×C113C2211yescharacteristic
21C2×M16×C113C2211yescharacteristic
22#117×C113C2211yescharacteristic
23#103×C113—21no—
24#103×C113—21no—
25C2×Dic226—22no—
26C22×Dic113—21no—
27C22×Dic113D412yes—
28#14268631—21no—
29#14268631—21no—
30C2×#11744751—21no—
31C4⋊Dic113—22no—
32C4⋊Dic113—21no—
33C4⋊Dic113—21no—
34C4⋊Dic113D411yescharacteristic
35C4⋊Dic113D411yescharacteristic
36#14268626—22no—
37#14268626—22no—
38C22⋊Dic113—21no—
39C4×Dic113—21no—
40C4×Dic113—21no—
41C4×Dic113—21no—
42C2×Q8×C113—21no—
43C2×Q8×C113—21no—
44C2×Q8×C113—21no—
45C2×Q8×C113—21no—
46C2×Q8×C113—21no—
47C2×Q8×C113Q812yescomplemented
48C22×C4×C113—21no—
49C22×C4×C113C2311yescharacteristic
50M16×C113—21no—
51M16×C113—21no—
52C2×C8×C113—21no—
53C4⋊C4×C113D411yescharacteristic
54C4⋊C4×C113D411yescharacteristic
55C22⋊C4×C113—21no—
56C42×C113—21no—
57C23×C113C2×D411yescharacteristic
58Q8×C113—22no—
59Q8×C113—22no—
60Q8×C113—41no—
61Q8×C113—41no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—22no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113C2×D411yescharacteristic
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113C2×Q811yescharacteristic
70C2×C4×C113#4111yescharacteristic
71C2×C4×C113#4111yescharacteristic
72C2×C4×C113#4111yescharacteristic
73C2×Dic113—22no—
74C2×Dic113—21no—
75C2×Dic113—21no—
76C2×Dic113—22no—
77C2×Dic113—41no—
78C2×Dic113—41no—
79C2×Dic113—42no—
80Dic226—82no—
81C8×C113—41no—
82#11744751—41no—
83C22×C113—21no—
84C22×C113—21no—
85C22×C113#12011yescharacteristic
86C22×C113C22⋊Q811yescharacteristic
87C22×C113#12411yescharacteristic
88C4×C113—42no—
89C4×C113—41no—
90C4×C113—41no—
91C4×C113C22⋊Q811yescharacteristic
92C4×C113C22⋊Q811yescharacteristic
93C4×C113#12411yescharacteristic
94C4×C113#12411yescharacteristic
95Dic113—42no—
96Dic113—41no—
97Dic113—42no—
98Dic113—41no—
99C2×C113—21no—
100C2×C113—21no—
101C2×C113#39311yescharacteristic
102C2×C113#45511yescharacteristic
103C2×C113#45611yescharacteristic
104#2028—1131nomaximal, Sylow
105C113#202811yescharacteristic, complemented, Sylow
106#544—1131no—
107#419—1131no—
108#419D11311yescharacteristic
109#391—1131no—
110#343—1131no—
111#339—1131no—
112#339—1131no—
113C22×Q8C2×D11311yescharacteristic
114C2×M16—1131no—
115C2×M16C2×D11311yescharacteristic
116C4⋊Q8—2261no—
117C4⋊Q8—2261no—
118#125—2261no—
119#125—2261no—
120C22⋊Q8—2262no—
121#117—1131no—
122#117C2×D11311yescharacteristic
123C2×C4⋊C4—1131no—
124C2×C42—1131no—
125#103—21no—
126#103—21no—
127#103—2261no—
128#103—2261no—
129#95—2262no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—21no—
135C2×Q8—2262no—
136C2×Q8Dic22612yescomplemented
137C22×C4—21no—
138C22×C4—1132no—
139C22×C4—2261no—
140C22×C4C22×D11311yescharacteristic
141M16—21no—
142M16—21no—
143M16—2261no—
144M16—2261no—
145C2×C8—21no—
146C2×C8—2261no—
147C4⋊C4—1131no—
148C4⋊C4—1131no—
149C4⋊C4—2262no—
150C4⋊C4—2262no—
151C4⋊C4—2262no—
152C4⋊C4—2261no—
153C4⋊C4—2261no—
154C4⋊C4C22⋊D11311yescharacteristic
155C4⋊C4C22⋊D11311yescharacteristic
156C22⋊C4—21no—
157C22⋊C4—2261no—
158C42—21no—
159C42—2261no—
160C42—2261no—
161C42—2261no—
162C23D4×D11311yescharacteristic
163Q8—22no—
164Q8—22no—
165Q8—41no—
166Q8—41no—
167Q8—9042no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—22no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—4521no—
174C2×C4—4521no—
175C2×C4—4522no—
176C2×C4—2262no—
177C2×C4—2261no—
178C2×C4—2261no—
179C2×C4—2262no—
180C2×C4D4×D11311yescharacteristic
181C2×C4C2×C22⋊D11311yescharacteristic
182C2×C4C2×Dic22611yescharacteristic
183C2×C4#1426864611yescharacteristic
184C2×C4#1426864611yescharacteristic
185C2×C4#1426864711yescharacteristic
186C8—41no—
187C8—4521no—
188C22—21no—
189C22—21no—
190C22#1681359011yescharacteristic
191C22#1681359911yescharacteristic
192C22#1681360811yescharacteristic
193C4—42no—
194C4—41no—
195C4—41no—
196C4—4522no—
197C4—4522no—
198C4—4521no—
199C4—4521no—
200C4#1681359911yescharacteristic
201C4#1681360111yescharacteristic
202C4#1681360811yescharacteristic
203C4#1681360911yescharacteristic
204C2—21no—
205C2—21no—
206C2#2029851011yescharacteristic
207C2#2029877411yescharacteristic
208C2#2029877911yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#419×C113C2
socleC22×C113#120
prime radicalC23×C113C2×D4
hypercenter#419D113
hypocenterC113#2028
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
47. C2×Q8×C113Q8semidirect
105. C113#2028semidirect
136. C2×Q8Dic226semidirect

Maximal subgroups

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

subgroupindex
#202992262
#202986072
#202985052
#202983662
#202983592
#202983572
#419×C1132
#2028113