Finite Group Databasebeta

← #28389563

Subgroups — #28389563

Order 14464.

228 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 51 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#20299223C211yesmaximal, characteristic
2#20298928C211yesmaximal, characteristic, complemented
3#20298524C211yesmaximal, characteristic
4#20298336C211yesmaximal, characteristic, complemented
5#20298335C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic
7#483×C113C211yesmaximal, characteristic, complemented
8#16813602—21no—
9#16813601C2211yescharacteristic
10#16813600—21no—
11#16813600—21no—
12#16813599—21no—
13#16813598—21no—
14C2×#14268624—21no—
15C2×#14268624C2211yescharacteristic
16C22⋊C4×D113—21no—
17#16813553—21no—
18#16813545—21no—
19C22⋊#11744751C2211yescharacteristic
20#16813529—21no—
21#16813529C2211yescharacteristic
22C22⋊Q8×C113C2211yescharacteristic
23C2×C4⋊C4×C113C2211yescharacteristic
24#106×C113—21no—
25#103×C113—21no—
26C22⋊C8×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28C2×Dic226—21no—
29C2×Dic226D411yescharacteristic
30C22×Dic113—21no—
31C22×Dic113D411yescharacteristic
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×#11744751—21no—
35C4⋊Dic113—21no—
36C4⋊Dic113D411yescharacteristic
37#14268626—21no—
38#14268626—21no—
39#14268626—21no—
40C22⋊Dic113—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—42no—
46C2×Q8×C113D411yescharacteristic
47C22×C4×C113—21no—
48C22×C4×C113C2311yescharacteristic
49C2×C8×C113—21no—
50C4⋊C4×C113—21no—
51C4⋊C4×C113—21no—
52C4⋊C4×C113—21no—
53C4⋊C4×C113D411yescharacteristic
54C22⋊C4×C113—21no—
55C23×C113C2×D411yescharacteristic
56C22×D113—21no—
57C22×D113—21no—
58C22×D113—41no—
59C22×D113—41no—
60C22×D113SD1612yes—
61Q8×C113—41no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—41no—
65C2×C4×C113—41no—
66C2×C4×C113—41no—
67C2×C4×C113—41no—
68C2×C4×C113C2×D411yescharacteristic
69C2×C4×C113C2×D411yescharacteristic
70C2×Dic113—21no—
71C2×Dic113—21no—
72C2×Dic113—21no—
73C2×Dic113—41no—
74C2×Dic113—41no—
75C2×Dic113—41no—
76C2×Dic113—41no—
77C4×D113—81no—
78C4×D113—81no—
79Dic226—41no—
80Dic226—81no—
81C8×C113—41no—
82#11744751—41no—
83C22×C113—21no—
84C22×C113—21no—
85C22×C113#12011yescharacteristic
86C22×C113C2×SD1611yescharacteristic
87C22×C113#13711yescharacteristic
88C2×D113—22no—
89C2×D113—41no—
90C2×D113—41no—
91C2×D113—42no—
92C2×D113—81no—
93C4×C113—21no—
94C4×C113—21no—
95C4×C113—41no—
96C4×C113—41no—
97C4×C113—81no—
98Dic113—41no—
99Dic113—41no—
100Dic113—41no—
101Dic113—81no—
102C2×C113—21no—
103C2×C113—21no—
104C2×C113#44811yescharacteristic
105C2×C113#45511yescharacteristic
106C2×C113#45811yescharacteristic
107D113—42no—
108#1608—1131nomaximal, Sylow
109C113#160811yescharacteristic, complemented, Sylow
110#543—1131no—
111#483—1131no—
112#483D11311yescharacteristic, complemented
113#397—1131no—
114#328—1131no—
115#328—1131no—
116#323—1131no—
117C22⋊Q8—1131no—
118C22⋊Q8—2261no—
119C22⋊Q8—2261no—
120C22⋊Q8—2261no—
121C22⋊Q8—2261no—
122C22⋊Q8—2261no—
123C22⋊Q8C2×D11311yescharacteristic
124C2×C4⋊C4C2×D11311yescharacteristic
125C2×C22⋊C4—1131no—
126C2×C22⋊C4—2261no—
127C2×C22⋊C4—2261no—
128#106—21no—
129#106—2261no—
130#103—21no—
131#103—2261no—
132C22⋊C8—1131no—
133C22⋊C8C2×D11311yescharacteristic
134#95—1131no—
135#95—2261no—
136C24—1131no—
137C2×Q8—1131no—
138C2×Q8—2261no—
139C2×Q8C22⋊D11311yescharacteristic
140C22×C4—21no—
141C22×C4—1131no—
142C22×C4—2261no—
143C22×C4—2261no—
144C22×C4—2261no—
145C22×C4C22×D11311yescharacteristic
146C2×C8—21no—
147C2×C8—2261no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—21no—
151C4⋊C4—1131no—
152C4⋊C4—2261no—
153C4⋊C4—2261no—
154C4⋊C4—2261no—
155C4⋊C4—2261no—
156C4⋊C4C22⋊D11311yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—4522no—
159C22⋊C4—2261no—
160C22⋊C4—2261no—
161C22⋊C4—2261no—
162C22⋊C4—2261no—
163C22⋊C4—2261no—
164C23—1132no—
165C23—4521no—
166C23—4521no—
167C23—2261no—
168C23—2261no—
169C23D4×D11311yescharacteristic
170Q8—41no—
171Q8—9041no—
172Q8—4521no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—9041no—
180C2×C4—9041no—
181C2×C4—4521no—
182C2×C4—4521no—
183C2×C4—4521no—
184C2×C4—4521no—
185C2×C4—2261no—
186C2×C4—2261no—
187C2×C4—2261no—
188C2×C4D4×D11311yescharacteristic
189C2×C4C2×C22⋊D11311yescharacteristic
190C8—41no—
191C8—4521no—
192C22—21no—
193C22—21no—
194C22—9041no—
195C22—4522no—
196C22—4521no—
197C22—4521no—
198C22—2262no—
199C22#1681359011yescharacteristic
200C22SD16×D11311yescharacteristic
201C22#1681365111yescharacteristic
202C4—21no—
203C4—21no—
204C4—41no—
205C4—41no—
206C4—81no—
207C4—9041no—
208C4—4521no—
209C4—4521no—
210C4—4521no—
211C2—21no—
212C2—21no—
213C2—4522no—
214C2#2029873511yescharacteristic
215C2#2029877411yescharacteristic
216C2#2029878711yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#483×C113C2
socleC22×C113#120
prime radicalC23×D113D4
hypercenter#483D113
hypocenterC113#1608
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. #20298928C2semidirect
4. #20298336C2semidirect
5. #20298335C2semidirect
7. #483×C113C2semidirect
109. C113#1608semidirect
112. #483D113semidirect

Maximal subgroups

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

subgroupindex
#202992232
#202989282
#202985242
#202983362
#202983352
#202983212
#483×C1132
#1608113