Finite Group Databasebeta

← #28401223

Subgroups — #28401223

Order 14464.

386 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 113 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#20299204C211yesmaximal, characteristic, complemented
2#20299202C211yesmaximal, characteristic, complemented
3#20298997C211yesmaximal, characteristic, complemented
4#20298974C211yesmaximal, characteristic, complemented
5#20298963C211yesmaximal, characteristic, complemented
6#20298850C212yesmaximal, complemented
7#20298833C212yesmaximal, complemented
8#20298707C212yesmaximal, complemented
9#20298678C212yesmaximal, complemented
10#20298555C211yesmaximal, characteristic, complemented
11#490×C113C211yesmaximal, characteristic, complemented
12C2×#14268632C2212yes—
13C2×#14268632C2212yes—
14C2×#14268630C2211yescharacteristic
15C2×C8×D113C2211yescharacteristic
16#16813619C2211yescharacteristic
17#16813614C2211yescharacteristic
18#16813607—22no—
19#16813603—22no—
20#16813597—22no—
21#16813597C2212yes—
22#16813594—22no—
23#16813593C2212yes—
24D4×Dic113C2212yes—
25#16813584C2212yes—
26#16813579C2211yescharacteristic
27#16813555C2212yes—
28#16813553C2212yes—
29#16813544C2212yes—
30#16813544C2212yes—
31#16813532C2211yescharacteristic
32C4×#11744751C2211yescharacteristic
33C8×Dic113C2211yescharacteristic
34#127×C113C2211yescharacteristic
35#125×C113C2211yescharacteristic
36#102×C113C2212yes—
37#102×C113C2212yes—
38#97×C113C2211yescharacteristic
39C2×D452—22no—
40C2×D452—22no—
41C2×D452C2312yes—
42C2×C22⋊D113—22no—
43C22×Dic113—22no—
44C2×C4×D113—22no—
45C2×C4×D113C2311yescharacteristic
46#14268632—24no—
47#14268632—24no—
48#14268630—22no—
49C2×#11744751C2311yescharacteristic
50C2×#11744751C2311yescharacteristic
51C8×D113—22no—
52C4⋊Dic113C2312yes—
53#14268626—22no—
54#14268626D412yes—
55C22⋊Dic113—22no—
56C22⋊Dic113—22no—
57#14268624—22no—
58#14268624—22no—
59#14268624D412yes—
60C4×Dic113C2311yescharacteristic
61C2×D4×C113—22no—
62C2×D4×C113C2312yes—
63C2×C8×C113C2311yescharacteristic
64C2×C8×C113C2311yescharacteristic
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C42×C113C2311yescharacteristic
68C23×C113—22no—
69C22×D113—22no—
70C22×D113C2×D411yescharacteristic
71D4×C113—22no—
72D4×C113—22no—
73D4×C113—82no—
74C2×C4×C113—22no—
75C2×C4×C113C2×D412yes—
76C2×C4×C113C2411yescharacteristic
77C22⋊D113—82no—
78C2×Dic113—22no—
79C2×Dic113—82no—
80C2×Dic113C2×D412yes—
81C2×Dic113C2×D411yescharacteristic
82D452—22no—
83D452—22no—
84D452—82no—
85D452—82no—
86C4×D113—21no—
87C4×D113—21no—
88C4×D113—82no—
89C8×C113—21no—
90C8×C113—21no—
91#11744751#4112yes—
92#11744751#4112yes—
93C22×C113—42no—
94C22×C113—42no—
95C22×C113—42no—
96C22×C113C22×D411yescharacteristic
97C2×D113—21no—
98C2×D113—22no—
99C2×D113—42no—
100C2×D113—42no—
101C2×D113—42no—
102C4×C113—22no—
103C4×C113—42no—
104C4×C113C2×#4111yescharacteristic
105C4×C113C2×#4111yescharacteristic
106Dic113—21no—
107Dic113—22no—
108Dic113—42no—
109C2×C113—82no—
110C2×C113#53211yescharacteristic
111C2×C113#57612yes—
112D113—41no—
113D113—82no—
114#3176—1131nomaximal, Sylow
115C113#317611yescharacteristic, complemented, Sylow
116#540—1131no—
117#540—1131no—
118#499—1131no—
119#493—1131no—
120#490—1131no—
121#490D11311yescharacteristic, complemented
122#469—1132no—
123#466—1132no—
124#442—1132no—
125C4×D8—1132no—
126#405—1131no—
127C2×D8—1132no—
128C2×D8—1132no—
129C2×M16—1131no—
130C22×C8—1131no—
131#127—1131no—
132#127C2×D11311yescharacteristic
133#125—1131no—
134#125C2×D11311yescharacteristic
135#123—2262no—
136#123—2262no—
137#121—1132no—
138#121—1132no—
139#121—2262no—
140#121—2262no—
141C4×D4—1132no—
142C4×D4—1132no—
143#117—1131no—
144#107—1132no—
145#106—1132no—
146#102—1132no—
147#102—1132no—
148#102C2×D11312yes—
149#102C2×D11312yes—
150#97—1131no—
151#97C2×D11311yescharacteristic
152C4×C8—1131no—
153C4×C8—1131no—
154C2×D4—22no—
155C2×D4—1132no—
156C2×D4—2262no—
157C2×D4—2262no—
158C2×D4—2262no—
159C2×D4C22×D11312yes—
160C22×C4—1131no—
161C22×C4—2262no—
162C22×C4—2262no—
163D8—2264no—
164D8—2264no—
165M16—2262no—
166C2×C8—1131no—
167C2×C8—1131no—
168C2×C8—2262no—
169C2×C8C22×D11311yescharacteristic
170C2×C8C22×D11311yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—1132no—
173C4⋊C4—1132no—
174C4⋊C4—2262no—
175C4⋊C4C22×D11312yes—
176C22⋊C4—1132no—
177C22⋊C4—2262no—
178C22⋊C4—2262no—
179C22⋊C4—2262no—
180C22⋊C4—2262no—
181C42—1131no—
182C42C22×D11311yescharacteristic
183C23—22no—
184C23—1131no—
185C23—2262no—
186D4—22no—
187D4—22no—
188D4—82no—
189D4—9042no—
190D4—9042no—
191D4—9042no—
192D4—2262no—
193D4—2262no—
194C2×C4—22no—
195C2×C4—1132no—
196C2×C4—1131no—
197C2×C4—9042no—
198C2×C4—9042no—
199C2×C4—2262no—
200C2×C4—2261no—
201C2×C4—2261no—
202C2×C4D4×D11312yes—
203C2×C4C23×D11311yescharacteristic
204C8—21no—
205C8—21no—
206C8—1132no—
207C8—1132no—
208C22—42no—
209C22—42no—
210C22—42no—
211C22—4522no—
212C22—4522no—
213C22—4522no—
214C22—2262no—
215C22—2261no—
216C22C2×D4×D11311yescharacteristic
217C4—22no—
218C4—42no—
219C4—4522no—
220C4—2262no—
221C4—2261no—
222C4#41×D11311yescharacteristic
223C4#41×D11311yescharacteristic
224C2—82no—
225C2—9042no—
226C2—4521no—
227C2#2029914711yescharacteristic
228C2#2029940212yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#490×C113C2
socleC22×C113C22×D4
hypercenter#490D113
hypocenterC113#3176
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20299204C2semidirect
2. #20299202C2semidirect
3. #20298997C2semidirect
4. #20298974C2semidirect
5. #20298963C2semidirect
6. #20298850C2semidirect
7. #20298833C2semidirect
8. #20298707C2semidirect
9. #20298678C2semidirect
10. #20298555C2semidirect
11. #490×C113C2semidirect
115. C113#3176semidirect
121. #490D113semidirect

Maximal subgroups

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

subgroupindex
#202992042
#202992022
#202989972
#202989742
#202989632
#202988502
#202988332
#202987072
#202986782
#202985552
#490×C1132
#3176113