Finite Group Databasebeta

← #28402882

Subgroups — #28402882

Order 14464.

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

normal subgroups only

This group has 420 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#20299253C211yesmaximal, characteristic, complemented
2#20299251C211yesmaximal, characteristic, complemented
3#20298948C211yesmaximal, characteristic, complemented
4#20298932C212yesmaximal, complemented
5#20298879C211yesmaximal, characteristic, complemented
6#20298841C212yesmaximal, complemented
7#20298742C212yesmaximal, complemented
8C4×#14268632C211yesmaximal, characteristic, complemented
9#20298675C211yesmaximal, characteristic, complemented
10#20298598C212yesmaximal, complemented
11#461×C113C211yesmaximal, characteristic, complemented
12C2×#14268648C2212yes—
13C2×#14268647—21no—
14C2×#14268632C2211yescharacteristic
15C2×#14268630C2212yes—
16#16813622C2211yescharacteristic
17#16813607—22no—
18#16813604—22no—
19#16813601—21no—
20#16813598C2212yes—
21#16813597—21no—
22#16813593C2212yes—
23C4×D452C2211yescharacteristic
24C4×D452C2211yescharacteristic
25C4⋊C4×D113—21no—
26C4⋊C4×D113C2212yes—
27#16813556C2212yes—
28#16813555C2211yescharacteristic
29#16813546C2212yes—
30#16813546C2212yes—
31#16813544C2212yes—
32#16813543C2211yescharacteristic
33#16813542C2211yescharacteristic
34#16813534C2212yes—
35C4×#11744751C2211yescharacteristic
36C2×SD16×C113C2212yes—
37C4⋊Q8×C113C2211yescharacteristic
38C4×D4×C113C2211yescharacteristic
39C4⋊C8×C113C2211yescharacteristic
40#103×C113C2212yes—
41#14268648—24no—
42#14268648—42no—
43#14268647—44no—
44C2×Dic226—21no—
45C2×D452—22no—
46C2×D452D411yescharacteristic
47C2×D452C2311yescharacteristic
48C2×C22⋊D113—22no—
49C2×C4×D113—22no—
50C2×C4×D113—21no—
51C2×C4×D113—22no—
52C2×C4×D113C2312yes—
53#14268632—22no—
54#14268630—42no—
55C2×#11744751C2311yescharacteristic
56C2×#11744751C2311yescharacteristic
57C4⋊Dic113—21no—
58C4⋊Dic113D411yescharacteristic
59C4⋊Dic113C2312yes—
60C4⋊Dic113C2311yescharacteristic
61#14268626—22no—
62#14268626—22no—
63C22⋊Dic113—22no—
64#14268624—22no—
65#14268624—21no—
66#14268624D412yes—
67C2×Q8×C113C2312yes—
68C2×D4×C113C2311yescharacteristic
69C22×C4×C113—21no—
70SD16×C113—42no—
71C2×C8×C113C2312yes—
72C4⋊C4×C113—21no—
73C4⋊C4×C113—21no—
74C4⋊C4×C113C2311yescharacteristic
75C22⋊C4×C113—21no—
76C42×C113C2311yescharacteristic
77C23×C113—21no—
78C22×D113—21no—
79C22×D113C2×D412yes—
80Q8×C113—22no—
81Q8×C113—22no—
82D4×C113—21no—
83D4×C113—21no—
84C2×C4×C113—21no—
85C2×C4×C113—22no—
86C2×C4×C113—42no—
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2411yescharacteristic
90C22⋊D113—44no—
91C2×Dic113—21no—
92C2×Dic113—22no—
93C2×Dic113C2×D412yes—
94D452—22no—
95D452—21no—
96D452—44no—
97D452#4112yescomplemented
98C4×D113—22no—
99C4×D113—22no—
100C4×D113—44no—
101C4×D113—44no—
102C4×D113—42no—
103Dic226—42no—
104C8×C113—22no—
105#11744751—21no—
106#11744751—21no—
107C22×C113—41no—
108C22×C113—41no—
109C22×C113—41no—
110C22×C113C22×D411yescharacteristic
111C2×D113—22no—
112C2×D113—22no—
113C2×D113—22no—
114C2×D113—22no—
115C2×D113—41no—
116C2×D113—41no—
117C4×C113—21no—
118C4×C113—42no—
119C4×C113—41no—
120C4×C113AGL(1,ℤ/8)12yes—
121C4×C113C2×#4111yescharacteristic
122C4×C113H(5,𝔽2)11yescharacteristic
123Dic113—22no—
124Dic113—42no—
125Dic113—41no—
126C2×C113—81no—
127C2×C113#54611yescharacteristic
128C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
129C2×C113#57811yescharacteristic
130D113—42no—
131D113—42no—
132#3330—1131nomaximal, Sylow
133C113#333011yescharacteristic, complemented, Sylow
134#547—1131no—
135#547—1131no—
136#487—1131no—
137#484—1132no—
138#474—1131no—
139#468—1132no—
140#461D11311yescharacteristic, complemented
141#449—1132no—
142C4×D8—1131no—
143#436—1131no—
144#417—1132no—
145C2×#41—1132no—
146C2×#41—2261no—
147C2×SD16C2×D11312yes—
148C2×D8—1131no—
149C2×M16—1132no—
150C4⋊Q8—1131no—
151C4⋊Q8C2×D11311yescharacteristic
152#123—2262no—
153#123—2262no—
154C22⋊Q8—1132no—
155C22⋊Q8—2261no—
156#121—1132no—
157#121—2261no—
158C4×D4—1131no—
159C4×D4—1131no—
160C4×D4C2×D11311yescharacteristic
161C2×C4⋊C4—1132no—
162C2×C4⋊C4—2261no—
163#107—1132no—
164#107—1131no—
165C4⋊C8C2×D11311yescharacteristic
166#103—1132no—
167#103—1132no—
168#103C2×D11312yes—
169#102—1131no—
170#102—1132no—
171#102—1131no—
172C22⋊C8—1132no—
173C4×C8—1131no—
174#41—4524no—
175#41—4522no—
176#41—2264no—
177C2×Q8—2261no—
178C2×Q8C22×D11312yes—
179C2×D4—1131no—
180C2×D4—1131no—
181C2×D4—2262no—
182C2×D4—2262no—
183C2×D4C22×D11311yescharacteristic
184C22×C4—21no—
185C22×C4—1132no—
186C22×C4—2262no—
187C22×C4—2262no—
188C22×C4—2261no—
189SD16—42no—
190D8—2262no—
191M16—4522no—
192C2×C8—1131no—
193C2×C8—1131no—
194C2×C8C22×D11312yes—
195C4⋊C4—21no—
196C4⋊C4—21no—
197C4⋊C4—1131no—
198C4⋊C4—1132no—
199C4⋊C4—1131no—
200C4⋊C4—2262no—
201C4⋊C4—2262no—
202C4⋊C4—2261no—
203C4⋊C4C22×D11311yescharacteristic
204C22⋊C4—21no—
205C22⋊C4—1132no—
206C22⋊C4—2262no—
207C22⋊C4—2262no—
208C22⋊C4—2261no—
209C42C22×D11311yescharacteristic
210C23—21no—
211C23—1132no—
212C23—2261no—
213Q8—22no—
214Q8—22no—
215Q8—4522no—
216D4—21no—
217D4—21no—
218D4—1132no—
219D4—4524no—
220D4—4524no—
221D4—2262no—
222D4—2261no—
223C2×C4—21no—
224C2×C4—22no—
225C2×C4—42no—
226C2×C4—1132no—
227C2×C4—4524no—
228C2×C4—4524no—
229C2×C4—4522no—
230C2×C4—2261no—
231C2×C4—2262no—
232C2×C4—2262no—
233C2×C4—2262no—
234C2×C4D4×D11311yescharacteristic
235C2×C4D4×D11311yescharacteristic
236C2×C4C23×D11311yescharacteristic
237C8—22no—
238C8—2261no—
239C8—2261no—
240C22—41no—
241C22—41no—
242C22—41no—
243C22—4521no—
244C22—4521no—
245C22—2262no—
246C22—2262no—
247C22—2262no—
248C22—2262no—
249C22C2×D4×D11311yescharacteristic
250C4—21no—
251C4—41no—
252C4—42no—
253C4—4522no—
254C4—4521no—
255C4—2262no—
256C4#1681364912yes—
257C4#41×D11311yescharacteristic
258C4#1681366711yescharacteristic
259C2—81no—
260C2—4522no—
261C2—4522no—
262C2#2029924511yescharacteristic
263C2C2×#1681364911yescharacteristic
264C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#461×C113C2
socleC22×C113C22×D4
hypercenter#461D113
hypocenterC113#3330
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #20299253C2semidirect
2. #20299251C2semidirect
3. #20298948C2semidirect
4. #20298932C2semidirect
5. #20298879C2semidirect
6. #20298841C2semidirect
7. #20298742C2semidirect
8. C4×#14268632C2semidirect
9. #20298675C2semidirect
10. #20298598C2semidirect
11. #461×C113C2semidirect
97. D452#41semidirect
133. C113#3330semidirect
140. #461D113semidirect

Maximal subgroups

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

subgroupindex
#202992532
#202992512
#202989482
#202989322
#202988792
#202988412
#202987422
C4×#142686322
#202986752
#202985982
#461×C1132
#3330113