Finite Group Databasebeta

← #28400895

Subgroups — #28400895

Order 14464.

400 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 121 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#20299154C211yesmaximal, characteristic, complemented
2#20299147C211yesmaximal, characteristic
3#20298955C211yesmaximal, characteristic, complemented
4#20298953C211yesmaximal, characteristic, complemented
5#20298952C211yesmaximal, characteristic, complemented
6#20298947C212yesmaximal, complemented
7#20298943C212yesmaximal, complemented
8#20298593C212yesmaximal, complemented
9#20298591C212yesmaximal, complemented
10C4×C8×D113C211yesmaximal, characteristic, complemented
11#488×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2211yescharacteristic
13C2×#14268646C2211yescharacteristic
14C2×C8×D113C2212yes—
15#16813621C2212yes—
16#16813620C2211yescharacteristic
17#16813618C2211yescharacteristic
18#16813614C2211yescharacteristic
19#16813610C2211yescharacteristic
20#16813600—22no—
21#16813595—22no—
22#16813587—22no—
23#16813582—22no—
24#16813580C2212yes—
25C42×D113C2211yescharacteristic
26#16813547C2212yes—
27#16813546C2212yes—
28#16813545C2212yes—
29#16813544C2212yes—
30#16813543C2212yes—
31#16813542C2212yes—
32C4×#11744751C2211yescharacteristic
33C8×Dic113C2212yes—
34#125×C113C2211yescharacteristic
35#124×C113C2211yescharacteristic
36#103×C113C2212yes—
37#102×C113C2212yes—
38C4×C8×C113C2211yescharacteristic
39#14268648—24no—
40#14268646—24no—
41C2×Dic226—22no—
42C2×Dic226C2311yescharacteristic
43C2×D452—21no—
44C2×D452C2311yescharacteristic
45C2×C22⋊D113—21no—
46C2×C22⋊D113—22no—
47C22×Dic113—21no—
48C2×C4×D113—21no—
49C2×C4×D113D412yes—
50C2×C4×D113C2311yescharacteristic
51C2×#11744751C2312yes—
52C8×D113—24no—
53C4⋊Dic113C2312yes—
54#14268626—22no—
55#14268626—22no—
56#14268626—22no—
57#14268624—22no—
58#14268624—22no—
59C4×Dic113—22no—
60C4×Dic113D412yes—
61C4×Dic113C2311yescharacteristic
62C2×Q8×C113C2311yescharacteristic
63C2×D4×C113C2311yescharacteristic
64C2×C8×C113C2312yes—
65C4⋊C4×C113—22no—
66C4⋊C4×C113C2312yes—
67C22⋊C4×C113—22no—
68C42×C113C2311yescharacteristic
69C23×C113—21no—
70C22×D113—21no—
71C22×D113C2×D411yescharacteristic
72Q8×C113—22no—
73D4×C113—22no—
74C2×C4×C113—21no—
75C2×C4×C113—22no—
76C2×C4×C113C2×D412yes—
77C2×C4×C113C2411yescharacteristic
78C22⋊D113—42no—
79C22⋊D113—44no—
80C2×Dic113—22no—
81C2×Dic113—21no—
82C2×Dic113—42no—
83C2×Dic113C2×D411yescharacteristic
84C2×Dic113C2×D412yes—
85D452—22no—
86D452—42no—
87C4×D113—24no—
88C4×D113—42no—
89C4×D113#4114yes—
90Dic226—22no—
91Dic226—44no—
92C8×C113—22no—
93#11744751—22no—
94C22×C113—41no—
95C22×C113—42no—
96C22×C113C22×D411yescharacteristic
97C2×D113—22no—
98C2×D113—41no—
99C2×D113—42no—
100C2×D113#12412yes—
101C4×C113—22no—
102C4×C113—41no—
103C4×C113—42no—
104C4×C113C2×#4112yes—
105Dic113—41no—
106Dic113—42no—
107Dic113#12412yes—
108Dic113#13514yes—
109C2×C113—81no—
110C2×C113C2×#12411yescharacteristic
111C2×C113C2×#13512yes—
112D113—22no—
113D113—81no—
114#3131—1131nomaximal, Sylow
115C113#313111yescharacteristic, complemented, Sylow
116#533—1131no—
117#532—1131no—
118#488—1131no—
119#488—1131no—
120#488—1131no—
121#488D11311yescharacteristic, complemented
122#487—1132no—
123#486—1132no—
124#416—1132no—
125#416—1132no—
126C2×C4×C8—1131no—
127C2×#41—1131no—
128C2×#41—1131no—
129C22×C8—1132no—
130C4⋊Q8—1132no—
131C4⋊Q8—1131no—
132#127—1131no—
133#125—1131no—
134#125C2×D11311yescharacteristic
135#124—1131no—
136#124C2×D11311yescharacteristic
137C22⋊Q8—2262no—
138#121—2262no—
139C4×Q8—2262no—
140C4×D4—2262no—
141#117—1132no—
142C2×C42—1131no—
143#103—1132no—
144#103—1132no—
145#103—1132no—
146#103C2×D11312yes—
147#102—1132no—
148#102—1132no—
149#102—1132no—
150#102C2×D11312yes—
151C4×C8—1132no—
152C4×C8—1131no—
153C4×C8C2×D11311yescharacteristic
154#41—2264no—
155#41—2264no—
156C2×Q8—1131no—
157C2×Q8—2262no—
158C2×Q8C22×D11311yescharacteristic
159C2×D4—1131no—
160C2×D4—2261no—
161C2×D4—2262no—
162C2×D4—2261no—
163C2×D4C22×D11311yescharacteristic
164C22×C4—1131no—
165C22×C4—1132no—
166C22×C4—2261no—
167C22×C4—2261no—
168C2×C8—1132no—
169C2×C8—2264no—
170C2×C8C22×D11312yes—
171C4⋊C4—22no—
172C4⋊C4—1132no—
173C4⋊C4—2262no—
174C4⋊C4—2262no—
175C4⋊C4—2262no—
176C4⋊C4C22×D11312yes—
177C22⋊C4—22no—
178C22⋊C4—2262no—
179C22⋊C4—2262no—
180C42—1132no—
181C42—1131no—
182C42—2262no—
183C42C22×D11311yescharacteristic
184C23—21no—
185C23—1131no—
186C23—2261no—
187Q8—22no—
188Q8—4524no—
189Q8—2262no—
190D4—22no—
191D4—4522no—
192D4—4524no—
193D4—4522no—
194D4—2262no—
195C2×C4—22no—
196C2×C4—21no—
197C2×C4—1131no—
198C2×C4—1132no—
199C2×C4—1134no—
200C2×C4—4522no—
201C2×C4—4522no—
202C2×C4—2264no—
203C2×C4—2262no—
204C2×C4—2261no—
205C2×C4D4×D11312yes—
206C2×C4C23×D11311yescharacteristic
207C8—22no—
208C8—2262no—
209C22—41no—
210C22—42no—
211C22—1132no—
212C22—4521no—
213C22—4522no—
214C22—2262no—
215C22C2×D4×D11311yescharacteristic
216C4—22no—
217C4—41no—
218C4—42no—
219C4—1132no—
220C4—1134no—
221C4—4521no—
222C4—4522no—
223C4#41×D11312yes—
224C2—81no—
225C2—9041no—
226C2—2262no—
227C2#124×D11311yescharacteristic
228C2#135×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#488×C113C2
socleC22×C113C22×D4
prime radical#20299147C2
hypercenter#488D113
hypocenterC113#3131
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #488

Complements

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

NH ≅ G/Ntype
1. #20299154C2semidirect
3. #20298955C2semidirect
4. #20298953C2semidirect
5. #20298952C2semidirect
6. #20298947C2semidirect
7. #20298943C2semidirect
8. #20298593C2semidirect
9. #20298591C2semidirect
10. C4×C8×D113C2semidirect
11. #488×C113C2semidirect
115. C113#3131semidirect
121. #488D113semidirect

Maximal subgroups

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

subgroupindex
#202991542
#202991472
#202989552
#202989532
#202989522
#202989472
#202989432
#202985932
#202985912
C4×C8×D1132
#488×C1132
#3131113