Finite Group Databasebeta

← #28391019

Subgroups — #28391019

Order 14464.

358 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 83 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#20299105C211yesmaximal, characteristic
2C2×#16813579C211yesmaximal, characteristic, complemented
3C2×#16813549C211yesmaximal, characteristic, complemented
4#20298561C211yesmaximal, characteristic, complemented
5#20298359C211yesmaximal, characteristic, complemented
6#20298358C211yesmaximal, characteristic, complemented
7C2×#104×C113C211yesmaximal, characteristic, complemented
8C22×C4×D113C2211yescharacteristic
9C2×#14268631C2211yescharacteristic
10#16813603—21no—
11#16813598C412yescomplemented
12#16813593C412yescomplemented
13#16813590—21no—
14C4×C22⋊D113—22no—
15#16813581C2211yescharacteristic
16#16813579—22no—
17#16813579—22no—
18C2×#14268626—21no—
19C2×#14268624—21no—
20C2×C4×Dic113C2211yescharacteristic
21#16813549—22no—
22#16813534—22no—
23C2×#41×C113C2211yescharacteristic
24C2×M16×C113C2211yescharacteristic
25C2×C42×C113C2211yescharacteristic
26#104×C113—22no—
27C23×D113D411yescharacteristic
28C2×C22⋊D113—22no—
29C22×Dic113—21no—
30C22×Dic113D411yescharacteristic
31C2×C4×D113—21no—
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×C4×D113—21no—
35C2×C4×D113C2×C412yes—
36C2×C4×D113D412yes—
37#14268631—21no—
38#14268631—21no—
39C2×#11744751—21no—
40C4⋊Dic113C2×C412yes—
41#14268626—24no—
42#14268626—22no—
43C22⋊Dic113—21no—
44C22⋊Dic113—22no—
45#14268624—24no—
46#14268624—22no—
47C4×Dic113—21no—
48C4×Dic113—21no—
49C4×Dic113D412yescomplemented
50#41×C113—21no—
51#41×C113—21no—
52#41×C113—21no—
53#41×C113—21no—
54C2×Q8×C113C2×C411yescharacteristic
55C2×D4×C113—21no—
56C2×D4×C113C2×C411yescharacteristic
57C22×C4×C113—21no—
58C22×C4×C113—21no—
59C22×C4×C113C2311yescharacteristic
60M16×C113—21no—
61M16×C113—21no—
62C2×C8×C113—21no—
63C42×C113—21no—
64C42×C113D412yescomplemented
65C23×C113—21no—
66C23×C113C2×D411yescharacteristic
67C22×D113—21no—
68C22×D113—21no—
69C22×D113—42no—
70C22×D113C22⋊C412yes—
71Q8×C113—21no—
72Q8×C113—21no—
73D4×C113—21no—
74D4×C113—21no—
75D4×C113—41no—
76D4×C113—41no—
77C2×C4×C113—21no—
78C2×C4×C113—22no—
79C2×C4×C113—42no—
80C2×C4×C113—41no—
81C2×C4×C113—41no—
82C2×C4×C113C22×C411yescharacteristic
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113#4111yescharacteristic
87C2×C4×C113#4111yescharacteristic
88C22⋊D113—44no—
89C2×Dic113—21no—
90C2×Dic113—21no—
91C2×Dic113—22no—
92C2×Dic113—22no—
93C2×Dic113—42no—
94C2×Dic113C22⋊C412yes—
95C4×D113—22no—
96C4×D113—22no—
97C4×D113—22no—
98C4×D113—22no—
99C8×C113—41no—
100#11744751—41no—
101C22×C113—22no—
102C22×C113—41no—
103C22×C113—42no—
104C22×C113C2×C22⋊C411yescharacteristic
105C22×C113#12011yescharacteristic
106C22×C113#12311yescharacteristic
107C2×D113—22no—
108C2×D113—22no—
109C2×D113—22no—
110C2×D113—42no—
111C2×D113—42no—
112C4×C113—42no—
113C4×C113—41no—
114C4×C113C4×D411yescharacteristic
115C4×C113C4×D411yescharacteristic
116C4×C113#12111yescharacteristic
117C4×C113#12111yescharacteristic
118Dic113—22no—
119Dic113—42no—
120Dic113—42no—
121C2×C113—21no—
122C2×C113—21no—
123C2×C113—81no—
124C2×C113#38611yescharacteristic
125C2×C113#42112yes—
126D113—42no—
127#1897—1131nomaximal, Sylow
128C113#189711yescharacteristic, complemented, Sylow
129#525—1131no—
130C2×#117—1131no—
131C2×#104—1131no—
132C2×#104D11311yescharacteristic, complemented
133#407—1131no—
134#339—1131no—
135#339—1131no—
136C2×#41C2×D11311yescharacteristic
137C23×C4—1131no—
138C2×M16—1131no—
139C2×M16C2×D11311yescharacteristic
140#123—2261no—
141C22⋊Q8—1132no—
142#121—1132no—
143#120—2261no—
144C4×D4—2262no—
145#117—1131no—
146#117—2262no—
147#117—2262no—
148C2×C4⋊C4—2261no—
149C2×C22⋊C4—2261no—
150C2×C42—1131no—
151C2×C42C2×D11311yescharacteristic
152#104—22no—
153#104—2262no—
154C22⋊C8—2262no—
155C24—1131no—
156#41—21no—
157#41—21no—
158#41—21no—
159#41—21no—
160C2×Q8C4×D11311yescharacteristic
161C2×D4—21no—
162C2×D4—2262no—
163C2×D4C4×D11311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—1131no—
167C22×C4—1132no—
168C22×C4—1132no—
169C22×C4—2261no—
170C22×C4—2261no—
171C22×C4—2261no—
172C22×C4—2261no—
173C22×C4—2261no—
174C22×C4C22×D11311yescharacteristic
175M16—21no—
176M16—21no—
177M16—2261no—
178M16—2261no—
179C2×C8—21no—
180C2×C8—2261no—
181C4⋊C4—1132no—
182C4⋊C4—2262no—
183C4⋊C4—2264no—
184C22⋊C4—2262no—
185C22⋊C4—2264no—
186C22⋊C4—2262no—
187C22⋊C4—2261no—
188C42—21no—
189C42—1132no—
190C42—2261no—
191C42—2261no—
192C42C22⋊D11312yescomplemented
193C23—21no—
194C23—1132no—
195C23—4522no—
196C23—2261no—
197C23—2261no—
198C23D4×D11311yescharacteristic
199Q8—21no—
200Q8—21no—
201D4—21no—
202D4—21no—
203D4—41no—
204D4—41no—
205D4—4524no—
206C2×C4—21no—
207C2×C4—22no—
208C2×C4—42no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—1132no—
212C2×C4—4522no—
213C2×C4—2262no—
214C2×C4—2262no—
215C2×C4—2261no—
216C2×C4—2261no—
217C2×C4—2262no—
218C2×C4—2262no—
219C2×C4—2262no—
220C2×C4—2262no—
221C2×C4C2×C4×D11311yescharacteristic
222C2×C4D4×D11311yescharacteristic
223C2×C4D4×D11311yescharacteristic
224C2×C4C2×C22⋊D11311yescharacteristic
225C2×C4#1426864611yescharacteristic
226C2×C4#1426864711yescharacteristic
227C8—41no—
228C8—4521no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—4522no—
233C22—4522no—
234C22—2262no—
235C22—2262no—
236C22—2262no—
237C22C22⋊C4×D11311yescharacteristic
238C22#1681359011yescharacteristic
239C22#1681360411yescharacteristic
240C4—42no—
241C4—41no—
242C4—4522no—
243C4—4522no—
244C4—2262no—
245C4#1681358211yescharacteristic
246C4C4×C22⋊D11311yescharacteristic
247C4#1681359311yescharacteristic
248C4#1681359511yescharacteristic
249C2—21no—
250C2—21no—
251C2—81no—
252C2—4522no—
253C2#2029847411yescharacteristic
254C2#2029861312yes—
subgroupG/H
centerC2×C4D4×D113
commutatorC2×C4×C113C22×C4
FrattiniC22×C4C22×D113
FittingC2×#104×C113C2
socleC22×C113C2×C22⋊C4
prime radical#20299105C2
cosocleC22×C4×C113C23
hypercenterC2×#104D113
hypocenterC113#1897
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. C2×#16813579C2semidirect
3. C2×#16813549C2semidirect
4. #20298561C2semidirect
5. #20298359C2semidirect
6. #20298358C2semidirect
7. C2×#104×C113C2semidirect
11. #16813598C4semidirect
12. #16813593C4semidirect
49. C4×Dic113D4semidirect
64. C42×C113D4semidirect
128. C113#1897semidirect
132. C2×#104D113semidirect
192. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991052
C2×#168135792
C2×#168135492
#202985612
#202983592
#202983582
C2×#104×C1132
#1897113