Finite Group Databasebeta

← #28389494

Subgroups — #28389494

Order 14464.

368 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 53 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#20299160C211yesmaximal, characteristic, complemented
2#20298734C212yesmaximal, complemented
3#20298507C211yesmaximal, characteristic, complemented
4#20298333C212yesmaximal, complemented
5#323×C113C211yesmaximal, characteristic, complemented
6C22×D452C2211yescharacteristic, complemented
7C22×C22⋊D113—21no—
8C22×C22⋊D113—21no—
9C2×D904—22no—
10#16813606—22no—
11#16813596—21no—
12#16813596C2212yes—
13#16813592—22no—
14C2×#14268624—21no—
15#16813544—22no—
16#16813529C2211yescharacteristic, complemented
17C2×C22⋊C4×C113C2211yescharacteristic
18C22⋊C8×C113C2212yescomplemented
19C23×D113—21no—
20C23×D113—21no—
21C2×D452—22no—
22C2×D452—21no—
23C2×D452—42no—
24C2×D452D412yescomplemented
25C2×C22⋊D113—22no—
26C2×C22⋊D113—22no—
27C2×C22⋊D113—42no—
28C2×C22⋊D113—42no—
29C2×C22⋊D113—42no—
30C2×C22⋊D113—42no—
31C2×C22⋊D113—42no—
32C22×Dic113—21no—
33C22×Dic113—21no—
34D904—44no—
35C4⋊Dic113—21no—
36C4⋊Dic113D412yescomplemented
37#14268624—22no—
38#14268624—22no—
39#14268624—42no—
40C24×C113D411yescharacteristic
41C22×C4×C113D411yescharacteristic
42C22×C4×C113C2311yescharacteristic
43C2×C8×C113—22no—
44C22⋊C4×C113—22no—
45C23×C113—21no—
46C23×C113—21no—
47C23×C113—41no—
48C23×C113—41no—
49C23×C113D812yescomplemented
50C23×C113C2×D411yescharacteristic
51C22×D113—22no—
52C22×D113—22no—
53C22×D113—41no—
54C22×D113—41no—
55C22×D113—42no—
56C22×D113—41no—
57C22×D113—41no—
58C22×D113—41no—
59C22×D113—41no—
60C22×D113—81no—
61C22×D113—81no—
62C2×C4×C113—21no—
63C2×C4×C113—41no—
64C2×C4×C113—41no—
65C2×C4×C113C2×D412yes—
66C22⋊D113—44no—
67C22⋊D113—48no—
68C22⋊D113—42no—
69C22⋊D113—42no—
70C2×Dic113—22no—
71C2×Dic113—22no—
72C2×Dic113—41no—
73C2×Dic113—42no—
74C2×Dic113—41no—
75D452—24no—
76D452—42no—
77D452—42no—
78D452—81no—
79C8×C113—42no—
80C22×C113—21no—
81C22×C113—21no—
82C22×C113—22no—
83C22×C113—42no—
84C22×C113—41no—
85C22×C113—41no—
86C22×C113—81no—
87C22×C113#12011yescharacteristic
88C22×C113C2×D811yescharacteristic
89C22×C113AGL(1,ℤ/8)11yescharacteristic
90C2×D113—42no—
91C2×D113—42no—
92C2×D113—42no—
93C2×D113—42no—
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—81no—
97C2×D113—81no—
98C2×D113—84no—
99C2×D113—81no—
100C2×D113—81no—
101C4×C113—22no—
102C4×C113—41no—
103Dic113—42no—
104Dic113—42no—
105C2×C113—21no—
106C2×C113—21no—
107C2×C113—42no—
108C2×C113#44711yescharacteristic
109C2×C113#45311yescharacteristic
110C2×C113B(4,𝔽2)11yescharacteristic
111D113—82no—
112D113—82no—
113#1595—1131nomaximal, Sylow
114C113#159511yescharacteristic, complemented, Sylow
115#534—1131no—
116#447—1132no—
117#392—1131no—
118#327—1132no—
119#323D11311yescharacteristic, complemented
120C22×D4—1131no—
121C22×D4—2261no—
122C22×D4—2261no—
123C2×D8—2262no—
124#123—2262no—
125#121—1132no—
126#121—2261no—
127#120—2262no—
128C2×C22⋊C4—2261no—
129C2×C22⋊C4C2×D11311yescharacteristic
130#102—2262no—
131C22⋊C8C2×D11312yescomplemented
132#95—1131no—
133C24—2261no—
134C24—2261no—
135C24D45211yescharacteristic
136C2×D4—1132no—
137C2×D4—4522no—
138C2×D4—4522no—
139C2×D4—4522no—
140C2×D4—4522no—
141C2×D4—4522no—
142C2×D4—4522no—
143C2×D4—2261no—
144C2×D4—2262no—
145C2×D4—2262no—
146C2×D4—2262no—
147C22×C4—2261no—
148C22×C4—2261no—
149C22×C4D45211yescharacteristic
150C22×C4C22×D11311yescharacteristic
151D8—4524no—
152C2×C8—22no—
153C4⋊C4—1132no—
154C4⋊C4—2261no—
155C22⋊C4—22no—
156C22⋊C4—4522no—
157C22⋊C4—2262no—
158C22⋊C4—2262no—
159C23—21no—
160C23—21no—
161C23—41no—
162C23—41no—
163C23—9041no—
164C23—9041no—
165C23—4521no—
166C23—4521no—
167C23—4521no—
168C23—4522no—
169C23—4521no—
170C23—4521no—
171C23—4521no—
172C23—2262no—
173C23—2262no—
174C23D90412yescomplemented
175C23C2×D45211yescharacteristic
176D4—9041no—
177D4—4522no—
178D4—4522no—
179D4—4524no—
180D4—4528no—
181D4—4522no—
182D4—4522no—
183D4—2264no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—4521no—
188C2×C4—4522no—
189C2×C4—4521no—
190C2×C4—2262no—
191C2×C4—2262no—
192C2×C4D4×D11312yes—
193C8—42no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—81no—
201C22—9041no—
202C22—9041no—
203C22—9044no—
204C22—9041no—
205C22—9041no—
206C22—4522no—
207C22—4522no—
208C22—4522no—
209C22—4522no—
210C22—4522no—
211C22—4522no—
212C22#1681359211yescharacteristic
213C22C2×D90411yescharacteristic
214C22#1681365011yescharacteristic
215C4—22no—
216C4—41no—
217C4—4522no—
218C4—4522no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—9042no—
223C2—9042no—
224C2#2029873411yescharacteristic
225C2#2029876811yescharacteristic
226C2#2029878611yescharacteristic
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#323×C113C2
socleC22×C113#120
hypercenter#323D113
hypocenterC113#1595
LCSG ▷ C22×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
1. #20299160C2semidirect
2. #20298734C2semidirect
3. #20298507C2semidirect
4. #20298333C2semidirect
5. #323×C113C2semidirect
6. C22×D452C22semidirect
16. #16813529C22semidirect
18. C22⋊C8×C113C22semidirect
24. C2×D452D4semidirect
36. C4⋊Dic113D4semidirect
49. C23×C113D8semidirect
114. C113#1595semidirect
119. #323D113semidirect
131. C22⋊C8C2×D113semidirect
174. C23D904semidirect

Maximal subgroups

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

subgroupindex
#202991602
#202987342
#202985072
#202983332
#323×C1132
#1595113