Finite Group Databasebeta

← #28393911

Subgroups — #28393911

Order 14464.

864 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 864 conjugacy classes of subgroups — too many to draw. Only its 169 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
1C22×#14268647C211yesmaximal, characteristic
2C2×#16813606C212yesmaximal, complemented
3C22×#14268626C211yesmaximal, characteristic, complemented
4#20298519C212yesmaximal, complemented
5#20298516C212yesmaximal, complemented
6#20298475C212yesmaximal, complemented
7#20298472C214yesmaximal, complemented
8#381×C113C211yesmaximal, characteristic, complemented
9C2×#14268647—28no—
10C2×#14268647—24no—
11C22×Dic226C2211yescharacteristic
12C22×D452C2211yescharacteristic
13C22×C22⋊D113C2212yes—
14C23×Dic113C2211yescharacteristic
15C23×Dic113C2211yescharacteristic
16C22×C4×D113C2212yes—
17#16813606—28no—
18C2×C4⋊Dic113C2214yes—
19C2×#14268626—24no—
20C2×#14268626C2212yes—
21C2×#14268626C2212yes—
22C2×#14268624C2214yes—
23C2×#14268624C2214yes—
24#16813529C2214yes—
25C23×C4×C113C2211yescharacteristic
26C2×C22⋊C4×C113C2212yes—
27#95×C113C2212yes—
28#95×C113C2212yes—
29C23×D113C2312yes—
30#14268647—232no—
31C2×Dic226—22no—
32C2×Dic226—24no—
33C2×D452—24no—
34C2×D452—22no—
35C2×C22⋊D113—24no—
36C2×C22⋊D113—24no—
37C2×C22⋊D113D418yes—
38C22×Dic113—22no—
39C22×Dic113—24no—
40C22×Dic113—22no—
41C22×Dic113—24no—
42C22×Dic113C2312yes—
43C22×Dic113C2312yes—
44C22×Dic113C2312yes—
45C2×C4×D113—24no—
46C2×C4×D113—24no—
47C2×C4×D113—24no—
48C4⋊Dic113—28no—
49#14268626—24no—
50#14268626—24no—
51#14268624—28no—
52#14268624—28no—
53C24×C113C2311yescharacteristic
54C22×C4×C113—24no—
55C22×C4×C113D414yes—
56C22×C4×C113C2314yes—
57C22×C4×C113C2311yescharacteristic
58C22×C4×C113C2311yescharacteristic
59C22⋊C4×C113—24no—
60C23×C113—22no—
61C23×C113—22no—
62C23×C113C2×D414yes—
63C23×C113C2×D412yes—
64C23×C113C2411yescharacteristic
65C22×D113—22no—
66C22×D113—22no—
67C22×D113—24no—
68C22×D113—24no—
69C22×D113C2×D414yes—
70C2×C4×C113—28no—
71C2×C4×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—24no—
74C2×C4×C113—24no—
75C2×C4×C113—24no—
76C2×C4×C113C2×D412yes—
77C2×C4×C113C2×D412yes—
78C22⋊D113—216no—
79C2×Dic113—28no—
80C2×Dic113—22no—
81C2×Dic113—22no—
82C2×Dic113—22no—
83C2×Dic113—22no—
84C2×Dic113—24no—
85C2×Dic113—22no—
86C2×Dic113—44no—
87C2×Dic113C2×D414yes—
88C2×Dic113#4114yescomplemented
89D452—28no—
90C4×D113—216no—
91Dic226—28no—
92C22×C113—22no—
93C22×C113—22no—
94C22×C113—28no—
95C22×C113#12014yes—
96C22×C113C22×D412yes—
97C22×C113C22×D411yescharacteristic
98C22×C113C2×#4112yes—
99C22×C1132−1+412yes—
100C2×D113—24no—
101C2×D113—28no—
102C2×D113—42no—
103C2×D113—42no—
104C2×D113—44no—
105C4×C113—22no—
106C4×C113—22no—
107C4×C113—44no—
108Dic113—24no—
109Dic113—24no—
110Dic113—42no—
111C2×C113—24no—
112C2×C113C2×#12011yescharacteristic
113C2×C113#52511yescharacteristic
114C2×C113#53611yescharacteristic
115C2×C113#54714yes—
116D113—44no—
117#2406—1131nomaximal, Sylow
118C113#240611yescharacteristic, complemented, Sylow
119C22×#41—1131no—
120C2×#123—1132no—
121C22×C4⋊C4—1131no—
122#395—1132no—
123#394—1132no—
124#386—1132no—
125#385—1134no—
126#381D11311yescharacteristic, complemented
127C2×#41—2268no—
128C2×#41—2264no—
129C22×Q8—1131no—
130C22×D4—1132no—
131C22×D4—1131no—
132C23×C4—1131no—
133C23×C4—1131no—
134C23×C4—1132no—
135C23×C4C2×D11311yescharacteristic
136#123—2268no—
137C2×C4⋊C4—1132no—
138C2×C4⋊C4—1132no—
139C2×C4⋊C4—1134no—
140C2×C4⋊C4—2264no—
141C2×C22⋊C4—1134no—
142C2×C22⋊C4—1134no—
143C2×C22⋊C4C2×D11312yes—
144#95—1134no—
145#95C2×D11312yes—
146#95C2×D11312yes—
147C24—1132no—
148C24C22×D11311yescharacteristic
149#41—22632no—
150C2×Q8—2264no—
151C2×Q8—2262no—
152C2×D4—1138no—
153C2×D4—2264no—
154C2×D4—2264no—
155C2×D4—2264no—
156C2×D4—2262no—
157C22×C4—24no—
158C22×C4—1132no—
159C22×C4—1132no—
160C22×C4—1132no—
161C22×C4—2264no—
162C22×C4—2264no—
163C22×C4—2264no—
164C22×C4—2264no—
165C22×C4—2262no—
166C22×C4—2262no—
167C22×C4—2264no—
168C22×C4D45214yes—
169C22×C4C22×D11314yes—
170C22×C4C22×D11311yescharacteristic
171C22×C4C22×D11311yescharacteristic
172C4⋊C4—2268no—
173C4⋊C4—2264no—
174C4⋊C4—2264no—
175C22⋊C4—24no—
176C22⋊C4—2268no—
177C22⋊C4—2268no—
178C23—22no—
179C23—22no—
180C23—1134no—
181C23—2262no—
182C23—2262no—
183C23—2264no—
184C23—2264no—
185C23D4×D11314yes—
186C23C2×D45212yes—
187C23C23×D11311yescharacteristic
188Q8—2268no—
189D4—2268no—
190D4—22616no—
191C2×C4—28no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—24no—
195C2×C4—24no—
196C2×C4—24no—
197C2×C4—1134no—
198C2×C4—1134no—
199C2×C4—4524no—
200C2×C4—22616no—
201C2×C4—2264no—
202C2×C4—2262no—
203C2×C4—2268no—
204C2×C4—2262no—
205C2×C4—2262no—
206C2×C4—2262no—
207C2×C4—2262no—
208C2×C4C2×D45212yes—
209C2×C4C2×D45212yes—
210C22—22no—
211C22—22no—
212C22—28no—
213C22—4522no—
214C22—4522no—
215C22—4524no—
216C22—2264no—
217C22—2268no—
218C22#1681359214yes—
219C22C2×D4×D11312yes—
220C22C22×D45211yescharacteristic
221C22#41×D11312yes—
222C22#1681366912yes—
223C4—22no—
224C4—22no—
225C4—44no—
226C4—4522no—
227C4—2264no—
228C4—2264no—
229C2—24no—
230C2—4524no—
231C2C2×#1681359211yescharacteristic
232C2#2029911011yescharacteristic
233C2#2029917411yescharacteristic
234C2#2029924614yes—
subgroupG/H
center, FrattiniC23C23×D113
commutator, socle, cosocleC23×C113C24
Fitting#381×C113C2
prime radicalC22×#14268647C2
hypercenter#381D113
hypocenterC113#2406
LCSG ▷ C23×C113 ▷ C113
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#16813606C2semidirect
3. C22×#14268626C2semidirect
4. #20298519C2semidirect
5. #20298516C2semidirect
6. #20298475C2semidirect
7. #20298472C2semidirect
8. #381×C113C2semidirect
88. C2×Dic113#41semidirect
118. C113#2406semidirect
126. #381D113semidirect

Maximal subgroups

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

subgroupindex
C22×#142686472
C2×#168136062
C22×#142686262
#202985192
#202985162
#202984752
#202984722
#381×C1132
#2406113