Finite Group Databasebeta

← #28391588

Subgroups — #28391588

Order 14464.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#16813647C211yesmaximal, characteristic, complemented
2#20299162C211yesmaximal, characteristic, complemented
3C2×#16813619C211yesmaximal, characteristic, complemented
4#20298604C211yesmaximal, characteristic, complemented
5C2×#16813538C211yesmaximal, characteristic, complemented
6#20298358C211yesmaximal, characteristic, complemented
7C2×#104×C113C211yesmaximal, characteristic, complemented
8C22×D452—22no—
9C22×D452C2211yescharacteristic
10C22×D452C2211yescharacteristic
11#16813647—22no—
12#16813647—22no—
13C2×#14268634—21no—
14C2×#14268632—21no—
15C2×#14268631C2211yescharacteristic
16#16813619—22no—
17#16813619—22no—
18#16813618—21no—
19#16813611—21no—
20#16813596—22no—
21#16813590—22no—
22#16813581C2211yescharacteristic
23#16813544—22no—
24#16813538—22no—
25C2×#41×C113C2211yescharacteristic
26C2×M16×C113C2211yescharacteristic
27C2×C42×C113C2211yescharacteristic
28#104×C113—22no—
29C23×D113—21no—
30C23×D113D412yes—
31C2×D452—21no—
32C2×D452—21no—
33C2×D452—21no—
34C2×D452—21no—
35C2×D452—28no—
36C2×D452—21no—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452—21no—
40C2×D452—21no—
41C2×D452—21no—
42C2×D452—21no—
43C2×D452—48no—
44C2×D452D412yescomplemented
45C2×C22⋊D113—24no—
46#14268634—24no—
47#14268632—24no—
48#14268631—21no—
49#14268631D412yescomplemented
50C2×#11744751—21no—
51C4⋊Dic113D412yescomplemented
52C22⋊Dic113—21no—
53#14268624—24no—
54C4×Dic113—21no—
55#41×C113—21no—
56#41×C113—21no—
57#41×C113—21no—
58#41×C113—21no—
59C2×Q8×C113D411yescharacteristic, complemented
60C2×D4×C113—21no—
61C2×D4×C113D411yescharacteristic, complemented
62C22×C4×C113—21no—
63C22×C4×C113—21no—
64C22×C4×C113C2311yescharacteristic
65M16×C113—21no—
66M16×C113—21no—
67C2×C8×C113—21no—
68C42×C113—21no—
69C42×C113D412yescomplemented
70C23×C113—21no—
71C23×C113C2×D411yescharacteristic
72C22×D113—22no—
73C22×D113—22no—
74C22×D113—22no—
75C22×D113—22no—
76C22×D113—44no—
77C22×D113—44no—
78C22×D113—41no—
79C22×D113—41no—
80Q8×C113—21no—
81Q8×C113—21no—
82D4×C113—21no—
83D4×C113—21no—
84D4×C113—41no—
85D4×C113—41no—
86C2×C4×C113—24no—
87C2×C4×C113—22no—
88C2×C4×C113—21no—
89C2×C4×C113—41no—
90C2×C4×C113—41no—
91C2×C4×C113C2×D411yescharacteristic
92C2×C4×C113C2×D411yescharacteristic
93C2×C4×C113C2×D411yescharacteristic
94C2×C4×C113C2×D411yescharacteristic
95C2×C4×C113C2×D411yescharacteristic
96C2×C4×C113#4111yescharacteristic
97C22⋊D113—84no—
98C2×Dic113—22no—
99D452—22no—
100D452—22no—
101D452—416no—
102D452—41no—
103D452—41no—
104D452—41no—
105D452—41no—
106D452—41no—
107D452—41no—
108C8×C113—41no—
109#11744751—22no—
110C22×C113—22no—
111C22×C113—41no—
112C22×C113—42no—
113C22×C113#12011yescharacteristic
114C22×C113#12011yescharacteristic
115C22×C113#12111yescharacteristic
116C2×D113—44no—
117C2×D113—44no—
118C2×D113—42no—
119C2×D113—42no—
120C2×D113—44no—
121C2×D113—82no—
122C2×D113—82no—
123C2×D113—82no—
124C4×C113—24no—
125C4×C113—41no—
126C4×C113#12011yescharacteristic
127C4×C113#12111yescharacteristic
128C4×C113#12111yescharacteristic
129C4×C113#12711yescharacteristic
130Dic113—42no—
131C2×C113—21no—
132C2×C113—21no—
133C2×C113—81no—
134C2×C113#39211yescharacteristic
135C2×C113#45312yes—
136D113—82no—
137D113—82no—
138#2002—1131nomaximal, Sylow
139C113#200211yescharacteristic, complemented, Sylow
140C2×AGL(1,ℤ/8)—1131no—
141#535—1131no—
142C2×#127—1131no—
143C2×#104D11311yescharacteristic, complemented
144#418—1131no—
145C2×#100—1131no—
146#339—1131no—
147C2×#41C2×D11311yescharacteristic
148C22×D4—1131no—
149C22×D4—1131no—
150C22×D4—2262no—
151AGL(1,ℤ/8)—2262no—
152AGL(1,ℤ/8)—2262no—
153C2×SD16—2261no—
154C2×D8—2261no—
155C2×M16—1131no—
156C2×M16C2×D11311yescharacteristic
157#127—2262no—
158#127—2261no—
159#127—2262no—
160#124—2261no—
161#121—2262no—
162#120—2262no—
163#117—1131no—
164C2×C42C2×D11311yescharacteristic
165#104—22no—
166#102—2262no—
167#100—2262no—
168C24—1132no—
169C24—2261no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D45211yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—1132no—
177C2×D4—4528no—
178C2×D4—2268no—
179C2×D4—2264no—
180C2×D4—2261no—
181C2×D4—2261no—
182C2×D4—2261no—
183C2×D4—2261no—
184C2×D4—2261no—
185C2×D4—2261no—
186C2×D4—2261no—
187C2×D4—2261no—
188C2×D4—2261no—
189C2×D4—2261no—
190C2×D4—2261no—
191C2×D4D45211yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D11311yescharacteristic
195SD16—2264no—
196D8—2264no—
197M16—21no—
198M16—21no—
199M16—1132no—
200M16—2261no—
201C2×C8—21no—
202C2×C8—2261no—
203C4⋊C4—1132no—
204C22⋊C4—2264no—
205C22⋊C4—2261no—
206C42—21no—
207C42—2261no—
208C42C22⋊D11312yescomplemented
209C23—21no—
210C23—4524no—
211C23—4524no—
212C23—4521no—
213C23—4521no—
214C23—2262no—
215C23—2262no—
216C23—2262no—
217C23—2262no—
218C23D4×D11311yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—9044no—
226D4—45216no—
227D4—4521no—
228D4—4521no—
229D4—4521no—
230D4—4521no—
231D4—4521no—
232D4—4521no—
233D4—2262no—
234D4—2262no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—2262no—
241C2×C4D4×D11311yescharacteristic
242C2×C4D4×D11311yescharacteristic
243C2×C4D4×D11311yescharacteristic
244C2×C4C2×C22⋊D11311yescharacteristic
245C2×C4C2×D45211yescharacteristic
246C2×C4#1426864711yescharacteristic
247C8—41no—
248C8—2262no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—9042no—
253C22—9042no—
254C22—9042no—
255C22—4524no—
256C22—4524no—
257C22—4522no—
258C22—4522no—
259C22—4524no—
260C22#1681359011yescharacteristic
261C22#1681359211yescharacteristic
262C22#1681359511yescharacteristic
263C4—24no—
264C4—41no—
265C4—4522no—
266C4#1681359211yescharacteristic
267C4#1681359511yescharacteristic
268C4#1681359611yescharacteristic
269C4#1681361811yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—9042no—
274C2—9042no—
275C2#2029850711yescharacteristic
276C2#2029876712yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#104×C113C2
socleC22×C113#120
hypercenterC2×#104D113
hypocenterC113#2002
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. #20299162C2semidirect
3. C2×#16813619C2semidirect
4. #20298604C2semidirect
5. C2×#16813538C2semidirect
6. #20298358C2semidirect
7. C2×#104×C113C2semidirect
44. C2×D452D4semidirect
49. #14268631D4semidirect
51. C4⋊Dic113D4semidirect
59. C2×Q8×C113D4semidirect
61. C2×D4×C113D4semidirect
69. C42×C113D4semidirect
139. C113#2002semidirect
143. C2×#104D113semidirect
174. C2×Q8D452semidirect
191. C2×D4D452semidirect
208. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
#202991622
C2×#168136192
#202986042
C2×#168135382
#202983582
C2×#104×C1132
#2002113