Finite Group Databasebeta

← #28401192

Subgroups — #28401192

Order 14464.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#20299221C212yesmaximal, complemented
2#20298995C211yesmaximal, characteristic, complemented
3#20298983C211yesmaximal, characteristic, complemented
4#20298959C212yesmaximal, complemented
5#20298851C211yesmaximal, characteristic
6#20298829C212yesmaximal, complemented
7#20298709C211yesmaximal, characteristic, complemented
8#20298705C211yesmaximal, characteristic, complemented
9#20298683C212yesmaximal, complemented
10#20298556C211yesmaximal, characteristic, complemented
11#470×C113C211yesmaximal, characteristic, complemented
12C2×#14268634C2212yes—
13C2×D904C2211yescharacteristic
14C22×#11744751C2211yescharacteristic
15#16813621C2212yes—
16#16813617—22no—
17#16813611C2212yes—
18#16813608—22no—
19#16813604—22no—
20#16813602—22no—
21#16813596C2212yes—
22Q8×Dic113C2212yes—
23#16813584C2212yes—
24#16813581C2211yescharacteristic
25#16813554C2211yescharacteristic
26#16813553C2212yes—
27#16813546C2212yes—
28#16813544C2212yes—
29#16813542C2212yes—
30#16813532C2211yescharacteristic
31#16813532C2211yescharacteristic
32C8×Dic113C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34C2×Q16×C113C2211yescharacteristic
35C2×M16×C113C2211yescharacteristic
36C22⋊Q8×C113C2212yes—
37#106×C113C2211yescharacteristic
38#103×C113C2212yes—
39C2×Dic226—22no—
40C2×D452C2312yes—
41C2×C22⋊D113—22no—
42C2×C4×D113—22no—
43#14268634—24no—
44D904—22no—
45C2×#11744751—22no—
46C2×#11744751C2311yescharacteristic
47C2×#11744751C2311yescharacteristic
48C4⋊Dic113—22no—
49C4⋊Dic113D412yes—
50C4⋊Dic113C2312yes—
51#14268626—22no—
52C22⋊Dic113D412yes—
53#14268624—22no—
54#14268624—22no—
55#14268624—22no—
56#14268624—22no—
57C4×Dic113—22no—
58C4×Dic113C2311yescharacteristic
59C4×Dic113C2311yescharacteristic
60C2×Q8×C113C2312yes—
61C22×C4×C113C2311yescharacteristic
62Q16×C113—22no—
63M16×C113—22no—
64C2×C8×C113C2311yescharacteristic
65C2×C8×C113C2311yescharacteristic
66C4⋊C4×C113—22no—
67C4⋊C4×C113C2312yes—
68C22⋊C4×C113—22no—
69C23×C113C2×D411yescharacteristic
70C22×D113—22no—
71Q8×C113—22no—
72Q8×C113—22no—
73C2×C4×C113—21no—
74C2×C4×C113—21no—
75C2×C4×C113—22no—
76C2×C4×C113—22no—
77C2×C4×C113C2×D411yescharacteristic
78C2×C4×C113C2411yescharacteristic
79C22⋊D113—82no—
80C2×Dic113—22no—
81C2×Dic113C2×D412yes—
82C2×Dic113C2×D412yes—
83D452—22no—
84D452—22no—
85C4×D113—82no—
86Dic226—82no—
87C8×C113—21no—
88C8×C113#4112yes—
89#11744751—21no—
90#11744751#4112yes—
91C22×C113—21no—
92C22×C113—22no—
93C22×C113C22×D411yescharacteristic
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—42no—
97C4×C113—21no—
98C4×C113—42no—
99C4×C113—42no—
100C4×C113C2×#4111yescharacteristic
101C4×C113C2×#4111yescharacteristic
102Dic113—22no—
103Dic113—22no—
104Dic113—42no—
105C2×C113—41no—
106C2×C113#53211yescharacteristic
107C2×C113#57712yes—
108D113—82no—
109#3173—1131nomaximal, Sylow
110C113#317311yescharacteristic, complemented, Sylow
111#542—1132no—
112#498—1131no—
113#495—1131no—
114#489—1132no—
115#470D11311yescharacteristic, complemented
116#469—1131no—
117#465—1132no—
118#442—1131no—
119#441—1131no—
120C4×SD16—1132no—
121#405—1131no—
122C2×Q16C2×D11311yescharacteristic
123C2×SD16—1132no—
124C2×D8—1131no—
125C2×M16C2×D11311yescharacteristic
126C22×C8—1131no—
127C4⋊Q8—1132no—
128#126—2262no—
129#124—1132no—
130#124—2262no—
131#123—2262no—
132C22⋊Q8—2262no—
133C22⋊Q8C2×D11312yes—
134#121—1132no—
135C4×Q8—1132no—
136C4×D4—1132no—
137#117—1131no—
138#106—1131no—
139#106—1132no—
140#106C2×D11311yescharacteristic
141#103—1132no—
142#103C2×D11312yes—
143#102—1132no—
144#102—1132no—
145#97—1131no—
146#97—1131no—
147C4×C8—1131no—
148C4×C8—1131no—
149C2×Q8—2262no—
150C2×Q8C22×D11312yes—
151C2×D4—1132no—
152C2×D4—2262no—
153C22×C4—2262no—
154C22×C4C22×D11311yescharacteristic
155Q16—22no—
156SD16—2264no—
157D8—2262no—
158M16—22no—
159C2×C8—1131no—
160C2×C8—1131no—
161C2×C8—2262no—
162C2×C8C22×D11311yescharacteristic
163C2×C8C22×D11311yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—1132no—
166C4⋊C4—1132no—
167C4⋊C4—2262no—
168C4⋊C4—2262no—
169C4⋊C4C22×D11312yes—
170C22⋊C4—22no—
171C22⋊C4—1132no—
172C22⋊C4—2262no—
173C22⋊C4—2262no—
174C22⋊C4—2262no—
175C22⋊C4—2262no—
176C42—1131no—
177C42—1131no—
178C42—2262no—
179C23—2262no—
180C23D4×D11311yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—9042no—
184D4—9042no—
185D4—2262no—
186D4—2262no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—1132no—
192C2×C4—1132no—
193C2×C4—9042no—
194C2×C4—2262no—
195C2×C4D4×D11311yescharacteristic
196C2×C4C23×D11311yescharacteristic
197C8—21no—
198C8—1132no—
199C8—2261no—
200C8#1426864612yes—
201C22—21no—
202C22—22no—
203C22—4522no—
204C22—4522no—
205C22—4522no—
206C22C2×D4×D11311yescharacteristic
207C4—21no—
208C4—42no—
209C4—42no—
210C4—4522no—
211C4—2262no—
212C4—2262no—
213C4#41×D11311yescharacteristic
214C4C2×#1426864611yescharacteristic
215C2—41no—
216C2—9042no—
217C2#2029914311yescharacteristic
218C2#2029940712yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#470×C113C2
socleC22×C113C22×D4
prime radical#20298851C2
hypercenter#470D113
hypocenterC113#3173
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #20299221C2semidirect
2. #20298995C2semidirect
3. #20298983C2semidirect
4. #20298959C2semidirect
6. #20298829C2semidirect
7. #20298709C2semidirect
8. #20298705C2semidirect
9. #20298683C2semidirect
10. #20298556C2semidirect
11. #470×C113C2semidirect
110. C113#3173semidirect
115. #470D113semidirect

Maximal subgroups

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

subgroupindex
#202992212
#202989952
#202989832
#202989592
#202988512
#202988292
#202987092
#202987052
#202986832
#202985562
#470×C1132
#3173113