Finite Group Databasebeta

← #28392563

Subgroups — #28392563

Order 14464.

258 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 41 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#20299278C211yesmaximal, characteristic, complemented
2#20298788C211yesmaximal, characteristic, complemented
3#20298785C211yesmaximal, characteristic
4#20298393C211yesmaximal, characteristic, complemented
5#20298389C211yesmaximal, characteristic, complemented
6#20298386C211yesmaximal, characteristic, complemented
7#455×C113C211yesmaximal, characteristic, complemented
8#16813615—21no—
9#16813604—21no—
10#16813603—21no—
11#16813603C2211yescharacteristic
12#16813598—21no—
13#16813590—21no—
14#16813590C2211yescharacteristic
15#16813582—21no—
16#16813579—21no—
17C22⋊C4×D113—21no—
18#16813537—21no—
19#16813537—21no—
20#16813537C2211yescharacteristic
21#16813537C2211yescharacteristic
22H(5,𝔽2)×C113C2211yescharacteristic
23#137×C113—21no—
24#124×C113C2211yescharacteristic
25#104×C113—21no—
26#100×C113C2211yescharacteristic
27C23×D113D411yescharacteristic
28C2×C22⋊D113—21no—
29C2×C22⋊D113—41no—
30C22×Dic113D411yescharacteristic, complemented
31C2×C4×D113—21no—
32C2×C4×D113—21no—
33C4⋊Dic113—21no—
34#14268626—21no—
35#14268626—21no—
36#14268626—21no—
37#14268626—41no—
38C22⋊Dic113—21no—
39C22⋊Dic113—21no—
40C22⋊Dic113—21no—
41C22⋊Dic113—41no—
42C22⋊Dic113D411yescharacteristic
43C22⋊Dic113D411yescharacteristic, complemented
44#14268624—21no—
45#14268624—21no—
46#14268624—21no—
47#14268624—41no—
48C4×Dic113—21no—
49#41×C113—21no—
50#41×C113—41no—
51C2×Q8×C113D411yescharacteristic, complemented
52C2×D4×C113—21no—
53C2×D4×C113—21no—
54C2×D4×C113—41no—
55C2×D4×C113C2311yescharacteristic
56Q16×C113—41no—
57SD16×C113—41no—
58M16×C113—21no—
59C22⋊C4×C113—21no—
60C22⋊C4×C113—21no—
61C42×C113D411yescharacteristic, complemented
62C23×C113—21no—
63C23×C113—21no—
64C23×C113C2×D411yescharacteristic
65C23×C113C2×D411yescharacteristic
66C22×D113—21no—
67C22×D113—42no—
68C22×D113—41no—
69Q8×C113—21no—
70Q8×C113—41no—
71D4×C113—21no—
72D4×C113—41no—
73D4×C113—41no—
74D4×C113—41no—
75D4×C113—41no—
76C2×C4×C113—21no—
77C2×C4×C113—21no—
78C2×C4×C113—21no—
79C2×C4×C113—21no—
80C2×C4×C113—41no—
81C2×C4×C113C2×D411yescharacteristic
82C22⋊D113—42no—
83C22⋊D113—82no—
84C2×Dic113—21no—
85C2×Dic113—21no—
86C2×Dic113—21no—
87C2×Dic113—41no—
88C2×Dic113—41no—
89C2×Dic113—41no—
90C4×D113—42no—
91C4×D113—81no—
92C8×C113—41no—
93C22×C113—21no—
94C22×C113—21no—
95C22×C113—41no—
96C22×C113—41no—
97C22×C113—41no—
98C22×C113—81no—
99C22×C113—81no—
100C22×C113#12011yescharacteristic
101C2×D113—22no—
102C2×D113—41no—
103C2×D113—41no—
104C2×D113—42no—
105C2×D113—81no—
106C4×C113—21no—
107C4×C113—41no—
108C4×C113—41no—
109C4×C113—41no—
110Dic113—41no—
111Dic113—41no—
112Dic113—41no—
113Dic113—81no—
114Dic113—81no—
115C2×C113—21no—
116C2×C113—41no—
117C2×C113—41no—
118C2×C113—81no—
119C2×C113B(4,𝔽2)11yescharacteristic
120D113—42no—
121#2197—1131nomaximal, Sylow
122C113#219711yescharacteristic, complemented, Sylow
123#551—1131no—
124#458—1131no—
125B(4,𝔽2)—1131no—
126#455D11311yescharacteristic, complemented
127#354—1131no—
128#352—1131no—
129AΣL(1,𝔽16)—1131no—
130H(5,𝔽2)C2×D11311yescharacteristic
131#137—21no—
132#126—2261no—
133#124C2×D11311yescharacteristic
134#123—1131no—
135#123—2261no—
136#123—2261no—
137C22⋊Q8—2261no—
138#120—1131no—
139#120—2261no—
140C4×D4—2261no—
141#117—2261no—
142C2×C22⋊C4—2261no—
143#104—21no—
144#100C2×D11311yescharacteristic
145#99—1131no—
146#99—1131no—
147#99—2261no—
148#99—2261no—
149C24—1131no—
150#41—21no—
151#41—41no—
152C2×Q8C22⋊D11311yescharacteristic, complemented
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—41no—
156C2×D4—4521no—
157C2×D4—2261no—
158C2×D4C22×D11311yescharacteristic
159C22×C4—1131no—
160C22×C4—2261no—
161C22×C4—2261no—
162Q16—41no—
163SD16—41no—
164M16—21no—
165C4⋊C4—4521no—
166C4⋊C4—2261no—
167C4⋊C4—2261no—
168C4⋊C4—2261no—
169C4⋊C4—2261no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—1131no—
173C22⋊C4—1131no—
174C22⋊C4—4521no—
175C22⋊C4—4521no—
176C22⋊C4—2261no—
177C22⋊C4—2261no—
178C22⋊C4—2261no—
179C22⋊C4—2261no—
180C22⋊C4—2261no—
181C22⋊C4—2261no—
182C42—2261no—
183C42C22⋊D11311yescharacteristic, complemented
184C23—21no—
185C23—21no—
186C23—4521no—
187C23—4522no—
188C23—2261no—
189C23D4×D11311yescharacteristic
190C23D4×D11311yescharacteristic
191Q8—21no—
192Q8—41no—
193D4—21no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—41no—
198D4—9042no—
199D4—4522no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—41no—
205C2×C4—9041no—
206C2×C4—4522no—
207C2×C4—4521no—
208C2×C4—4521no—
209C2×C4—4521no—
210C2×C4—2261no—
211C2×C4—2261no—
212C2×C4—2261no—
213C2×C4C2×C22⋊D11311yescharacteristic
214C8—41no—
215C22—21no—
216C22—21no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—81no—
221C22—81no—
222C22—9041no—
223C22—4521no—
224C22—4522no—
225C22—4521no—
226C22—2262no—
227C22#1681359011yescharacteristic
228C4—21no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—9041no—
233C4—9041no—
234C4—4521no—
235C4—4521no—
236C4—4521no—
237C2—21no—
238C2—41no—
239C2—41no—
240C2—81no—
241C2—4522no—
242C2#2029878411yescharacteristic
subgroupG/H
centerC2#20298784
commutator, cosocleC2×D4×C113C23
FrattiniC2×D4C22×D113
Fitting#455×C113C2
socleC2×C113B(4,𝔽2)
prime radical#20298785C2
hypercenter#455D113
hypocenterC113#2197
LCSG ▷ C2×D4×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #20299278C2semidirect
2. #20298788C2semidirect
4. #20298393C2semidirect
5. #20298389C2semidirect
6. #20298386C2semidirect
7. #455×C113C2semidirect
30. C22×Dic113D4semidirect
43. C22⋊Dic113D4semidirect
51. C2×Q8×C113D4semidirect
61. C42×C113D4semidirect
122. C113#2197semidirect
126. #455D113semidirect
152. C2×Q8C22⋊D113semidirect
183. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202992782
#202987882
#202987852
#202983932
#202983892
#202983862
#455×C1132
#2197113