Finite Group Databasebeta

← #28389553

Subgroups — #28389553

Order 14464.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 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#20299188C211yesmaximal, characteristic
2#20298737C211yesmaximal, characteristic, complemented
3#20298509C211yesmaximal, characteristic, complemented
4#20298335C211yesmaximal, characteristic, complemented
5#20298333C211yesmaximal, characteristic, complemented
6#20298321C211yesmaximal, characteristic, complemented
7#451×C113C211yesmaximal, characteristic, complemented
8C2×#14268634—21no—
9#16813617—21no—
10#16813611—21no—
11#16813607—21no—
12#16813597—21no—
13#16813596C2211yescharacteristic
14#16813592—21no—
15#16813582—21no—
16C2×#14268624—21no—
17C2×#14268624C2211yescharacteristic
18#16813546—21no—
19C22⋊#11744751C2211yescharacteristic
20#16813529—21no—
21#16813529C2211yescharacteristic
22C22×Q8×C113C2211yescharacteristic
23C2×Q16×C113—21no—
24C22⋊Q8×C113C2211yescharacteristic
25#103×C113—21no—
26C22⋊C8×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28C2×D452—21no—
29C2×D452—21no—
30C2×D452D411yescharacteristic
31C2×C22⋊D113—21no—
32C22×Dic113—21no—
33C22×Dic113D411yescharacteristic
34C2×C4×D113—21no—
35#14268634—42no—
36C2×#11744751—21no—
37C4⋊Dic113D411yescharacteristic
38#14268626—21no—
39#14268624—21no—
40#14268624—21no—
41#14268624—21no—
42#14268624—21no—
43#14268624—21no—
44#14268624—21no—
45#14268624—42no—
46C4×Dic113—21no—
47C2×Q8×C113—21no—
48C2×Q8×C113—21no—
49C2×Q8×C113—42no—
50C2×Q8×C113D411yescharacteristic
51C22×C4×C113—21no—
52C22×C4×C113C2311yescharacteristic
53Q16×C113—42no—
54C2×C8×C113—21no—
55C4⋊C4×C113—21no—
56C4⋊C4×C113D411yescharacteristic
57C22⋊C4×C113—21no—
58C23×C113C2×D411yescharacteristic
59C22×D113—21no—
60C22×D113—21no—
61C22×D113—21no—
62C22×D113—21no—
63C22×D113—41no—
64C22×D113—41no—
65Q8×C113—22no—
66Q8×C113—22no—
67Q8×C113—41no—
68Q8×C113—41no—
69Q8×C113—41no—
70C2×C4×C113—22no—
71C2×C4×C113—21no—
72C2×C4×C113—21no—
73C2×C4×C113—41no—
74C2×C4×C113—41no—
75C2×C4×C113—41no—
76C2×C4×C113C2×D411yescharacteristic
77C2×C4×C113C2×D411yescharacteristic
78C22⋊D113—41no—
79C22⋊D113—41no—
80C2×Dic113—21no—
81C2×Dic113—21no—
82C2×Dic113—41no—
83C2×Dic113—41no—
84C2×Dic113—41no—
85C2×Dic113—41no—
86D452—41no—
87D452—81no—
88D452—81no—
89C4×D113—81no—
90C8×C113—41no—
91#11744751—41no—
92C22×C113—21no—
93C22×C113—21no—
94C22×C113#12011yescharacteristic
95C22×C113#13511yescharacteristic
96C22×C113#13711yescharacteristic
97C2×D113—42no—
98C2×D113—41no—
99C2×D113—41no—
100C2×D113—41no—
101C2×D113—41no—
102C2×D113—41no—
103C2×D113—41no—
104C2×D113—81no—
105C4×C113—21no—
106C4×C113—21no—
107C4×C113—41no—
108C4×C113—41no—
109C4×C113—42no—
110Dic113—41no—
111Dic113—41no—
112Dic113—81no—
113C2×C113—21no—
114C2×C113—21no—
115C2×C113#45211yescharacteristic
116C2×C113#45511yescharacteristic
117C2×C113B(4,𝔽2)11yescharacteristic
118D113—81no—
119D113—81no—
120#1606—1131nomaximal, Sylow
121C113#160611yescharacteristic, complemented, Sylow
122#538—1131no—
123#451D11311yescharacteristic, complemented
124#448—1131no—
125#393—1131no—
126#328—1131no—
127#327—1131no—
128#323—1131no—
129C22×Q8C2×D11311yescharacteristic
130C2×Q16—21no—
131C2×SD16—2261no—
132#126—2261no—
133#124—2261no—
134#123—2261no—
135C22⋊Q8C2×D11311yescharacteristic
136#121—1131no—
137#121—2261no—
138#120—2261no—
139C4×D4—2261no—
140C2×C22⋊C4—1131no—
141C2×C22⋊C4—2261no—
142#103—21no—
143#103—2261no—
144C22⋊C8—1131no—
145C22⋊C8C2×D11311yescharacteristic
146#95—1131no—
147#95—2261no—
148C24—1131no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—42no—
152C2×Q8C22⋊D11311yescharacteristic
153C2×D4—1131no—
154C2×D4—2261no—
155C2×D4—2261no—
156C2×D4—2261no—
157C22×C4—21no—
158C22×C4—1131no—
159C22×C4—2261no—
160C22×C4—2261no—
161C22×C4C22×D11311yescharacteristic
162Q16—42no—
163SD16—4522no—
164C2×C8—21no—
165C2×C8—2261no—
166C4⋊C4—21no—
167C4⋊C4—1131no—
168C4⋊C4—2261no—
169C4⋊C4C22⋊D11311yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—4522no—
172C22⋊C4—2261no—
173C22⋊C4—2261no—
174C22⋊C4—2261no—
175C22⋊C4—2261no—
176C22⋊C4—2261no—
177C22⋊C4—2261no—
178C42—2261no—
179C23—4521no—
180C23—4521no—
181C23—2261no—
182C23—2261no—
183C23—2261no—
184C23—2261no—
185C23D4×D11311yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—41no—
191D4—9041no—
192D4—9041no—
193D4—4521no—
194D4—4521no—
195D4—4521no—
196C2×C4—22no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—9041no—
203C2×C4—4521no—
204C2×C4—4521no—
205C2×C4—4521no—
206C2×C4—4521no—
207C2×C4—2261no—
208C2×C4—2261no—
209C2×C4D4×D11311yescharacteristic
210C2×C4C2×C22⋊D11311yescharacteristic
211C8—41no—
212C8—4521no—
213C22—21no—
214C22—21no—
215C22—9041no—
216C22—4522no—
217C22—4521no—
218C22—4521no—
219C22—4521no—
220C22—4521no—
221C22—4521no—
222C22—4521no—
223C22#1681359011yescharacteristic
224C22#1681364511yescharacteristic
225C22#1681365411yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—42no—
230C4—41no—
231C4—9041no—
232C4—4521no—
233C4—4521no—
234C2—21no—
235C2—21no—
236C2—9041no—
237C2—9041no—
238C2#2029875911yescharacteristic
239C2#2029877411yescharacteristic
240C2#2029878411yescharacteristic
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#451×C113C2
socleC22×C113#120
prime radical#20299188C2
hypercenter#451D113
hypocenterC113#1606
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
2. #20298737C2semidirect
3. #20298509C2semidirect
4. #20298335C2semidirect
5. #20298333C2semidirect
6. #20298321C2semidirect
7. #451×C113C2semidirect
121. C113#1606semidirect
123. #451D113semidirect

Maximal subgroups

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

subgroupindex
#202991882
#202987372
#202985092
#202983352
#202983332
#202983212
#451×C1132
#1606113