Finite Group Databasebeta

← #28400748

Subgroups — #28400748

Order 14464.

386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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#20299134C211yesmaximal, characteristic
2C2×#16813587C211yesmaximal, characteristic, complemented
3#20298916C211yesmaximal, characteristic
4#20298904C212yesmaximal, complemented
5#20298823C212yesmaximal, complemented
6#20298753C211yesmaximal, characteristic, complemented
7#20298739C211yesmaximal, characteristic
8#20298702C212yesmaximal, complemented
9#20298697C212yesmaximal, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#484×C113C211yesmaximal, characteristic, complemented
12C22×Dic226C2211yescharacteristic
13C2×#14268637C2212yes—
14C2×#14268636C2212yes—
15#16813617—21no—
16#16813613C2211yescharacteristic
17#16813611C2211yescharacteristic
18#16813606—21no—
19#16813596C2211yescharacteristic
20Q8×Dic113C2211yescharacteristic
21#16813587—21no—
22#16813587—21no—
23#16813587C2212yes—
24#16813587C2212yes—
25#16813584C2211yescharacteristic
26#16813582—21no—
27#16813580—21no—
28C2×#14268626—21no—
29C2×C4×Dic113—21no—
30C2×C4×Dic113C2211yescharacteristic
31#16813553C2212yes—
32#16813551C2212yes—
33#16813547C2212yes—
34#16813545C2212yes—
35#16813542C2212yes—
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yes—
38C22⋊Q8×C113C2211yescharacteristic
39C2×C4⋊C4×C113C2211yescharacteristic
40#107×C113C2212yes—
41#103×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43C2×Dic226—21no—
44C2×Dic226—24no—
45C2×Dic226C2312yes—
46C2×D452C2311yescharacteristic
47C2×C22⋊D113—21no—
48C22×Dic113—21no—
49C22×Dic113D411yescharacteristic
50C22×Dic113D411yescharacteristic
51C2×C4×D113—21no—
52#14268637—24no—
53#14268636—24no—
54C2×#11744751C2312yes—
55C4⋊Dic113—21no—
56C4⋊Dic113—21no—
57C4⋊Dic113C2311yescharacteristic
58#14268626—22no—
59#14268626—22no—
60#14268626—21no—
61#14268624—21no—
62#14268624—21no—
63#14268624—21no—
64#14268624—21no—
65C4×Dic113—22no—
66C4×Dic113—22no—
67C4×Dic113—21no—
68C4×Dic113D411yescharacteristic
69C4×Dic113D411yescharacteristic
70C4×Dic113C2311yescharacteristic
71C4×Dic113C2311yescharacteristic
72C2×Q8×C113C2311yescharacteristic
73C22×C4×C113—21no—
74C22×C4×C113C2311yescharacteristic
75C2×C8×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113—21no—
78C4⋊C4×C113C2311yescharacteristic
79C4⋊C4×C113C2312yes—
80C22⋊C4×C113—21no—
81C23×C113C2×D411yescharacteristic
82C22×D113—21no—
83Q8×C113—22no—
84C2×C4×C113—22no—
85C2×C4×C113—21no—
86C2×C4×C113—21no—
87C2×C4×C113—22no—
88C2×C4×C113—42no—
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2411yescharacteristic
91C22⋊D113—42no—
92C2×Dic113—24no—
93C2×Dic113—22no—
94C2×Dic113—22no—
95C2×Dic113—21no—
96C2×Dic113—41no—
97C2×Dic113C2×D411yescharacteristic
98C2×Dic113C2×D411yescharacteristic
99C2×Dic113C2×D411yescharacteristic
100C2×Dic113C2×D411yescharacteristic
101D452—22no—
102C4×D113—42no—
103Dic226—24no—
104Dic226—22no—
105Dic226#4114yes—
106C8×C113—22no—
107#11744751—22no—
108C22×C113—21no—
109C22×C113—21no—
110C22×C113#13712yes—
111C22×C113C22×D411yescharacteristic
112C2×D113—41no—
113C2×D113—41no—
114C2×D113—41no—
115C4×C113—21no—
116C4×C113—41no—
117C4×C113—41no—
118C4×C113—42no—
119C4×C113C2×#4112yes—
120Dic113—24no—
121Dic113—21no—
122Dic113—21no—
123Dic113—21no—
124Dic113—21no—
125Dic113—41no—
126C2×C113—22no—
127C2×C113#52511yescharacteristic
128C2×C113C2×#13711yescharacteristic
129C2×C113#57511yescharacteristic
130D113—81no—
131#3117—1131nomaximal, Sylow
132C113#311711yescharacteristic, complemented, Sylow
133#529—1131no—
134C2×C4×Q8—1131no—
135#484D11311yescharacteristic, complemented
136#481—1131no—
137#479—1132no—
138#464—1132no—
139#451—1131no—
140#448—1131no—
141#441—1132no—
142#440—1132no—
143#432—1131no—
144C22×Q8—1131no—
145C2×Q16—1132no—
146C2×SD16—1132no—
147#126—2261no—
148#125—1131no—
149#124—1131no—
150#123—2261no—
151C22⋊Q8C2×D11311yescharacteristic
152#121—1131no—
153C4×Q8—1131no—
154C4×Q8—1132no—
155C4×Q8—1132no—
156C4×Q8—2261no—
157C4×Q8—2261no—
158C4×D4—1131no—
159C4×D4—2261no—
160#117—2261no—
161C2×C4⋊C4—2261no—
162C2×C4⋊C4C2×D11311yescharacteristic
163C2×C42—1131no—
164C2×C42—2261no—
165#107C2×D11312yes—
166#106—1132no—
167C4⋊C8—1132no—
168#103—1132no—
169#103—1132no—
170#103C2×D11312yes—
171#102—1132no—
172C22⋊C8—1131no—
173C22⋊C8C2×D11311yescharacteristic
174#97—1132no—
175C2×Q8—1132no—
176C2×Q8—2264no—
177C2×Q8—2261no—
178C2×Q8C22×D11311yescharacteristic
179C2×D4—1131no—
180C2×D4—2261no—
181C22×C4—21no—
182C22×C4—1131no—
183C22×C4—1131no—
184C22×C4—2261no—
185C22×C4—2261no—
186C22×C4C22×D11311yescharacteristic
187Q16—2264no—
188SD16—2264no—
189C2×C8—1132no—
190C2×C8C22×D11312yes—
191C4⋊C4—21no—
192C4⋊C4—21no—
193C4⋊C4—1131no—
194C4⋊C4—2262no—
195C4⋊C4—2262no—
196C4⋊C4—2261no—
197C4⋊C4—2261no—
198C4⋊C4—2261no—
199C4⋊C4C22×D11312yes—
200C4⋊C4C22×D11311yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—2261no—
203C22⋊C4—2261no—
204C22⋊C4—2261no—
205C22⋊C4—2261no—
206C42—1131no—
207C42—1131no—
208C42—1131no—
209C42—1131no—
210C42—2262no—
211C42—2262no—
212C42—2261no—
213C23—2261no—
214C23D4×D11311yescharacteristic
215Q8—22no—
216Q8—1134no—
217Q8—2264no—
218Q8—2262no—
219D4—4522no—
220D4—2262no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—42no—
226C2×C4—1131no—
227C2×C4—1131no—
228C2×C4—1131no—
229C2×C4—1131no—
230C2×C4—4522no—
231C2×C4—4521no—
232C2×C4—2261no—
233C2×C4—2264no—
234C2×C4—2262no—
235C2×C4—2262no—
236C2×C4D4×D11311yescharacteristic
237C2×C4C23×D11311yescharacteristic
238C8—22no—
239C8—2262no—
240C22—21no—
241C22—21no—
242C22—4521no—
243C22—4521no—
244C22—4521no—
245C22#1681365412yes—
246C22C2×D4×D11311yescharacteristic
247C4—21no—
248C4—41no—
249C4—42no—
250C4—41no—
251C4—4521no—
252C4—2264no—
253C4—2261no—
254C4—2261no—
255C4—2261no—
256C4—2261no—
257C4#41×D11312yes—
258C2—22no—
259C2—9041no—
260C2#2029910611yescharacteristic
261C2C2×#1681365411yescharacteristic
262C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#484×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#484D113
hypocenterC113#3117
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #484

Complements

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

NH ≅ G/Ntype
2. C2×#16813587C2semidirect
4. #20298904C2semidirect
5. #20298823C2semidirect
6. #20298753C2semidirect
8. #20298702C2semidirect
9. #20298697C2semidirect
10. #20298652C2semidirect
11. #484×C113C2semidirect
132. C113#3117semidirect
135. #484D113semidirect

Maximal subgroups

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

subgroupindex
#202991342
C2×#168135872
#202989162
#202989042
#202988232
#202987532
#202987392
#202987022
#202986972
#202986522
#484×C1132
#3117113