Finite Group Databasebeta

← #28391014

Subgroups — #28391014

Order 14464.

442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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×C42×D113C211yesmaximal, 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×D113—21no—
9C22×C4×D113C2211yescharacteristic
10C2×#14268631C2211yescharacteristic
11#16813603—21no—
12#16813598C412yescomplemented
13#16813593C412yescomplemented
14#16813590—21no—
15C4×C22⋊D113—22no—
16#16813581C2211yescharacteristic
17C2×C4×Dic113—21no—
18C2×C4×Dic113C2211yescharacteristic
19C42×D113—22no—
20C42×D113—22no—
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—24no—
32C2×C4×D113—28no—
33C2×C4×D113—21no—
34C2×C4×D113—21no—
35C2×C4×D113—21no—
36C2×C4×D113—21no—
37C2×C4×D113C2×C412yes—
38C2×C4×D113D412yes—
39#14268631—21no—
40#14268631—21no—
41C2×#11744751—21no—
42C4⋊Dic113C2×C412yescomplemented
43#14268626—22no—
44C22⋊Dic113—21no—
45C22⋊Dic113—22no—
46#14268624—22no—
47C4×Dic113—24no—
48C4×Dic113—21no—
49C4×Dic113—21no—
50C4×Dic113D412yescomplemented
51#41×C113—21no—
52#41×C113—21no—
53#41×C113—21no—
54#41×C113—21no—
55C2×Q8×C113C2×C411yescharacteristic, complemented
56C2×D4×C113—21no—
57C2×D4×C113C2×C411yescharacteristic, complemented
58C22×C4×C113—21no—
59C22×C4×C113—21no—
60C22×C4×C113C2311yescharacteristic
61M16×C113—21no—
62M16×C113—21no—
63C2×C8×C113—21no—
64C42×C113—21no—
65C42×C113D412yescomplemented
66C23×C113—21no—
67C23×C113C2×D411yescharacteristic
68C22×D113—21no—
69C22×D113—21no—
70C22×D113—24no—
71C22×D113C22⋊C412yes—
72Q8×C113—21no—
73Q8×C113—21no—
74D4×C113—21no—
75D4×C113—21no—
76D4×C113—41no—
77D4×C113—41no—
78C2×C4×C113—24no—
79C2×C4×C113—22no—
80C2×C4×C113—21no—
81C2×C4×C113—41no—
82C2×C4×C113—41no—
83C2×C4×C113C22×C411yescharacteristic
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113#4111yescharacteristic
88C2×C4×C113#4111yescharacteristic
89C22⋊D113—44no—
90C2×Dic113—24no—
91C2×Dic113—21no—
92C2×Dic113—22no—
93C2×Dic113—21no—
94C2×Dic113—22no—
95C2×Dic113C22⋊C412yes—
96C4×D113—216no—
97C4×D113—22no—
98C4×D113—22no—
99C4×D113—22no—
100C4×D113—22no—
101C8×C113—41no—
102#11744751—41no—
103C22×C113—22no—
104C22×C113—41no—
105C22×C113—42no—
106C22×C113C2×C22⋊C411yescharacteristic
107C22×C113#12011yescharacteristic
108C22×C113#12311yescharacteristic
109C2×D113—24no—
110C2×D113—24no—
111C2×D113—22no—
112C2×D113—22no—
113C2×D113#10414yescomplemented
114C4×C113—24no—
115C4×C113—41no—
116C4×C113C4×D411yescharacteristic
117C4×C113C4×D411yescharacteristic
118C4×C113#12111yescharacteristic
119C4×C113#12111yescharacteristic
120Dic113—24no—
121Dic113—22no—
122Dic113—42no—
123C2×C113—21no—
124C2×C113—21no—
125C2×C113—81no—
126C2×C113#38611yescharacteristic
127C2×C113C2×#10412yes—
128D113—24no—
129#1896—1131nomaximal, Sylow
130C113#189611yescharacteristic, complemented, Sylow
131#525—1131no—
132C22×C42—1131no—
133C2×#104—1131no—
134C2×#104D11311yescharacteristic, complemented
135#407—1131no—
136#339—1131no—
137#339—1131no—
138C2×#41C2×D11311yescharacteristic
139C23×C4—1131no—
140C23×C4—2261no—
141C2×M16—1131no—
142C2×M16C2×D11311yescharacteristic
143#123—2261no—
144C22⋊Q8—1132no—
145#121—1132no—
146#120—2261no—
147C4×D4—2262no—
148#117—1131no—
149C2×C42—1131no—
150C2×C42—2262no—
151C2×C42—2261no—
152C2×C42—2262no—
153C2×C42C2×D11311yescharacteristic
154#104—22no—
155#104—2262no—
156C22⋊C8—2262no—
157C24—1131no—
158#41—21no—
159#41—21no—
160#41—21no—
161#41—21no—
162C2×Q8C4×D11311yescharacteristic, complemented
163C2×D4—21no—
164C2×D4—2262no—
165C2×D4C4×D11311yescharacteristic, complemented
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—1131no—
169C22×C4—1132no—
170C22×C4—1132no—
171C22×C4—2264no—
172C22×C4—2268no—
173C22×C4—2261no—
174C22×C4—2261no—
175C22×C4—2261no—
176C22×C4—2261no—
177C22×C4—2261no—
178C22×C4C22×D11311yescharacteristic
179M16—21no—
180M16—21no—
181M16—2261no—
182M16—2261no—
183C2×C8—21no—
184C2×C8—2261no—
185C4⋊C4—1132no—
186C4⋊C4—2262no—
187C22⋊C4—2262no—
188C22⋊C4—2262no—
189C22⋊C4—2261no—
190C42—21no—
191C42—1132no—
192C42—2264no—
193C42—2261no—
194C42—2261no—
195C42C22⋊D11312yescomplemented
196C23—21no—
197C23—1132no—
198C23—2264no—
199C23—2261no—
200C23—2261no—
201C23D4×D11311yescharacteristic
202Q8—21no—
203Q8—21no—
204D4—21no—
205D4—21no—
206D4—41no—
207D4—41no—
208D4—4524no—
209C2×C4—24no—
210C2×C4—22no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—1132no—
215C2×C4—22616no—
216C2×C4—2262no—
217C2×C4—2264no—
218C2×C4—2262no—
219C2×C4—2261no—
220C2×C4—2261no—
221C2×C4—2262no—
222C2×C4—2262no—
223C2×C4—2262no—
224C2×C4—2262no—
225C2×C4C2×C4×D11311yescharacteristic
226C2×C4D4×D11311yescharacteristic
227C2×C4D4×D11311yescharacteristic
228C2×C4C2×C22⋊D11311yescharacteristic
229C2×C4#1426864611yescharacteristic
230C2×C4#1426864711yescharacteristic
231C8—41no—
232C8—4521no—
233C22—22no—
234C22—42no—
235C22—41no—
236C22—1134no—
237C22—2264no—
238C22—2264no—
239C22—2262no—
240C22—2262no—
241C22C22⋊C4×D11311yescharacteristic
242C22#1681359011yescharacteristic
243C22#1681360411yescharacteristic
244C4—24no—
245C4—41no—
246C4—4522no—
247C4—2264no—
248C4—2262no—
249C4#1681358211yescharacteristic
250C4C4×C22⋊D11311yescharacteristic
251C4#1681359311yescharacteristic
252C4#1681359511yescharacteristic
253C2—21no—
254C2—21no—
255C2—81no—
256C2—2264no—
257C2#2029847411yescharacteristic
258C2#104×D11312yes—
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#1896
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×C42×D113C2semidirect
3. C2×#16813549C2semidirect
4. #20298561C2semidirect
5. #20298359C2semidirect
6. #20298358C2semidirect
7. C2×#104×C113C2semidirect
12. #16813598C4semidirect
13. #16813593C4semidirect
42. C4⋊Dic113C2×C4semidirect
50. C4×Dic113D4semidirect
55. C2×Q8×C113C2×C4semidirect
57. C2×D4×C113C2×C4semidirect
65. C42×C113D4semidirect
113. C2×D113#104semidirect
130. C113#1896semidirect
134. C2×#104D113semidirect
162. C2×Q8C4×D113semidirect
165. C2×D4C4×D113semidirect
195. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
#202991052
C2×C42×D1132
C2×#168135492
#202985612
#202983592
#202983582
C2×#104×C1132
#1896113