Finite Group Databasebeta

← #28400746

Subgroups — #28400746

Order 14464.

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

normal subgroups only

This group has 386 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#20299134C211yesmaximal, characteristic
2C2×Q8×Dic113C211yesmaximal, characteristic, complemented
3#20298931C211yesmaximal, characteristic, complemented
4#20298917C211yesmaximal, characteristic
5#20298903C212yesmaximal, complemented
6#20298822C212yesmaximal, complemented
7#20298737C211yesmaximal, characteristic
8#20298705C212yesmaximal, complemented
9#20298701C212yesmaximal, complemented
10#20298652C211yesmaximal, characteristic, complemented
11#451×C113C211yesmaximal, characteristic, complemented
12C2×#14268634C2212yes—
13#16813617—21no—
14#16813613C2211yescharacteristic
15#16813611C2211yescharacteristic
16#16813606—21no—
17#16813596C2211yescharacteristic
18Q8×Dic113—21no—
19Q8×Dic113—21no—
20Q8×Dic113C2212yes—
21Q8×Dic113C2212yes—
22Q8×Dic113C2211yescharacteristic
23#16813584C2211yescharacteristic
24#16813582—21no—
25#16813580—21no—
26C2×C4⋊Dic113—21no—
27C2×C4⋊Dic113C2211yescharacteristic
28C2×C4×Dic113—21no—
29C2×C4×Dic113C2211yescharacteristic
30#16813555C2212yes—
31#16813554C2212yes—
32#16813551C2212yes—
33#16813546C2212yes—
34#16813546C2212yes—
35#16813544C2212yes—
36C22⋊#11744751C2211yescharacteristic
37#16813532C2212yes—
38C22×Q8×C113C2211yescharacteristic
39C2×Q16×C113C2212yes—
40C22⋊Q8×C113C2211yescharacteristic
41#103×C113C2212yes—
42C22⋊C8×C113C2211yescharacteristic
43C2×D452C2311yescharacteristic
44C2×C22⋊D113—21no—
45C22×Dic113—21no—
46C22×Dic113D411yescharacteristic
47C22×Dic113D411yescharacteristic
48C2×C4×D113—21no—
49#14268634—24no—
50C2×#11744751C2312yes—
51C4⋊Dic113—21no—
52C4⋊Dic113—22no—
53C4⋊Dic113—22no—
54C4⋊Dic113—21no—
55C4⋊Dic113—21no—
56C4⋊Dic113C2312yes—
57C4⋊Dic113C2311yescharacteristic
58#14268626—21no—
59#14268624—21no—
60#14268624—21no—
61#14268624—21no—
62#14268624—21no—
63C4×Dic113—22no—
64C4×Dic113—22no—
65C4×Dic113—21no—
66C4×Dic113D411yescharacteristic
67C4×Dic113D411yescharacteristic
68C4×Dic113C2311yescharacteristic
69C4×Dic113C2311yescharacteristic
70C2×Q8×C113—24no—
71C2×Q8×C113—21no—
72C2×Q8×C113C2311yescharacteristic
73C2×Q8×C113C2312yes—
74C22×C4×C113—21no—
75C22×C4×C113C2311yescharacteristic
76Q16×C113—24no—
77C2×C8×C113C2312yes—
78C4⋊C4×C113—21no—
79C4⋊C4×C113C2311yescharacteristic
80C22⋊C4×C113—21no—
81C23×C113C2×D411yescharacteristic
82C22×D113—21no—
83Q8×C113—24no—
84Q8×C113—22no—
85Q8×C113—22no—
86Q8×C113#4114yes—
87C2×C4×C113—24no—
88C2×C4×C113—22no—
89C2×C4×C113—22no—
90C2×C4×C113—21no—
91C2×C4×C113—21no—
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2411yescharacteristic
94C22⋊D113—42no—
95C2×Dic113—22no—
96C2×Dic113—22no—
97C2×Dic113—21no—
98C2×Dic113—41no—
99C2×Dic113—42no—
100C2×Dic113C2×D411yescharacteristic
101C2×Dic113C2×D411yescharacteristic
102C2×Dic113C2×D411yescharacteristic
103C2×Dic113C2×D411yescharacteristic
104D452—22no—
105C4×D113—42no—
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—24no—
116C4×C113—21no—
117C4×C113—41no—
118C4×C113—41no—
119C4×C113C2×#4112yes—
120Dic113—21no—
121Dic113—21no—
122Dic113—21no—
123Dic113—21no—
124Dic113—41no—
125Dic113—42no—
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#484—1131no—
136#481—1131no—
137#479—1132no—
138#464—1132no—
139#451D11311yescharacteristic, complemented
140#448—1131no—
141#441—1132no—
142#440—1132no—
143#432—1131no—
144C22×Q8C2×D11311yescharacteristic
145C2×Q16C2×D11312yes—
146C2×SD16—1132no—
147#126—2261no—
148#125—1131no—
149#124—1131no—
150#123—2261no—
151C22⋊Q8C2×D11311yescharacteristic
152#121—1131no—
153C4×Q8—1132no—
154C4×Q8—1132no—
155C4×Q8—1131no—
156C4×Q8—2261no—
157C4×Q8—2261no—
158C4×D4—1131no—
159C4×D4—2261no—
160#117—2261no—
161C2×C4⋊C4—1131no—
162C2×C4⋊C4—2261no—
163C2×C42—1131no—
164C2×C42—2261no—
165#107—1132no—
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—24no—
176C2×Q8—21no—
177C2×Q8C22×D11311yescharacteristic
178C2×Q8C22×D11312yes—
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—24no—
188SD16—2264no—
189C2×C8—1132no—
190C2×C8C22×D11312yes—
191C4⋊C4—21no—
192C4⋊C4—1132no—
193C4⋊C4—1131no—
194C4⋊C4—2262no—
195C4⋊C4—2262no—
196C4⋊C4—2261no—
197C4⋊C4—2261no—
198C4⋊C4—2261no—
199C4⋊C4—2261no—
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—24no—
216Q8—22no—
217Q8—22no—
218Q8#1426864614yes—
219D4—4522no—
220D4—2262no—
221C2×C4—24no—
222C2×C4—22no—
223C2×C4—22no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—1131no—
227C2×C4—1131no—
228C2×C4—1131no—
229C2×C4—1131no—
230C2×C4—4522no—
231C2×C4—4522no—
232C2×C4—4521no—
233C2×C4—2262no—
234C2×C4—2261no—
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—24no—
248C4—21no—
249C4—41no—
250C4—41no—
251C4—4521no—
252C4—4522no—
253C4—2261no—
254C4—2261no—
255C4—2261no—
256C4—2261no—
257C4C2×#1426864612yes—
258C2—22no—
259C2—9041no—
260C2#2029910411yescharacteristic
261C2C2×#1681365411yescharacteristic
262C2#2029939711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#451×C113C2
socleC22×C113C22×D4
prime radical#16813596C22
hypercenter#451D113
hypocenterC113#3117
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. C2×Q8×Dic113C2semidirect
3. #20298931C2semidirect
5. #20298903C2semidirect
6. #20298822C2semidirect
8. #20298705C2semidirect
9. #20298701C2semidirect
10. #20298652C2semidirect
11. #451×C113C2semidirect
132. C113#3117semidirect
139. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202991342
C2×Q8×Dic1132
#202989312
#202989172
#202989032
#202988222
#202987372
#202987052
#202987012
#202986522
#451×C1132
#3117113