Finite Group Databasebeta

← #28391589

Subgroups — #28391589

Order 14464.

478 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 75 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×#16813648C211yesmaximal, characteristic, complemented
2#20299165C211yesmaximal, characteristic, complemented
3C2×#16813550C211yesmaximal, characteristic, complemented
4#20298603C211yesmaximal, characteristic, complemented
5C2×#16813539C211yesmaximal, characteristic, complemented
6#20298358C211yesmaximal, characteristic, complemented
7C2×#127×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9#16813648—22no—
10#16813648—22no—
11C2×#14268635—21no—
12C2×#14268632—21no—
13C2×#14268631C2211yescharacteristic
14C2×#14268631C2211yescharacteristic
15#16813618—21no—
16#16813609—21no—
17#16813593—22no—
18#16813591—22no—
19#16813581C2211yescharacteristic
20#16813550—22no—
21#16813543—22no—
22#16813539—22no—
23C22×D4×C113—22no—
24C22×D4×C113C2211yescharacteristic
25C22×D4×C113C2211yescharacteristic
26#127×C113—22no—
27#127×C113—22no—
28C2×C42×C113C2211yescharacteristic
29#14268647—21no—
30#14268647—21no—
31#14268647—21no—
32#14268647—21no—
33C2×Dic226D411yescharacteristic, complemented
34C2×D452D411yescharacteristic, complemented
35C2×C22⋊D113—21no—
36C2×C22⋊D113—24no—
37C2×C4×D113—21no—
38#14268635—24no—
39#14268632—24no—
40#14268631—21no—
41#14268631—21no—
42#14268631—21no—
43#14268631D412yescomplemented
44C2×#11744751—21no—
45C2×#11744751—21no—
46C4⋊Dic113D412yescomplemented
47C22⋊Dic113—24no—
48C22⋊Dic113—21no—
49C4×Dic113—21no—
50C24×C113—21no—
51C24×C113D412yes—
52C2×D4×C113—28no—
53C2×D4×C113—21no—
54C2×D4×C113—21no—
55C2×D4×C113—21no—
56C2×D4×C113—21no—
57C2×D4×C113—21no—
58C2×D4×C113—21no—
59C2×D4×C113—21no—
60C2×D4×C113—21no—
61C2×D4×C113—21no—
62C2×D4×C113—21no—
63C2×D4×C113—21no—
64C2×D4×C113—48no—
65C2×D4×C113D412yescomplemented
66C22×C4×C113—21no—
67C22×C4×C113C2311yescharacteristic
68C42×C113—21no—
69C42×C113D412yescomplemented
70C23×C113—22no—
71C23×C113—22no—
72C23×C113—22no—
73C23×C113—22no—
74C23×C113—44no—
75C23×C113—44no—
76C23×C113—41no—
77C23×C113—41no—
78C23×C113C2×D411yescharacteristic
79C22×D113—21no—
80D4×C113—22no—
81D4×C113—22no—
82D4×C113—416no—
83D4×C113—41no—
84D4×C113—41no—
85D4×C113—41no—
86D4×C113—41no—
87D4×C113—41no—
88D4×C113—41no—
89C2×C4×C113—24no—
90C2×C4×C113—22no—
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—41no—
98C22⋊D113—41no—
99C22⋊D113—84no—
100C2×Dic113—22no—
101C2×Dic113—21no—
102D452—21no—
103D452—21no—
104C4×D113—41no—
105C4×D113—41no—
106Dic226—21no—
107Dic226—21no—
108#11744751—22no—
109#11744751—41no—
110C22×C113—22no—
111C22×C113—44no—
112C22×C113—44no—
113C22×C113—42no—
114C22×C113—42no—
115C22×C113—44no—
116C22×C113—82no—
117C22×C113—82no—
118C22×C113—82no—
119C22×C113#12011yescharacteristic
120C22×C113#12011yescharacteristic
121C22×C113#12111yescharacteristic
122C2×D113—41no—
123C2×D113—42no—
124C4×C113—24no—
125C4×C113#12011yescharacteristic
126C4×C113#12111yescharacteristic
127C4×C113#12111yescharacteristic
128C4×C113#12711yescharacteristic
129Dic113—41no—
130Dic113—42no—
131C2×C113—21no—
132C2×C113—21no—
133C2×C113—82no—
134C2×C113—82no—
135C2×C113#39211yescharacteristic
136C2×C113#45312yes—
137D113—81no—
138#2002—1131nomaximal, Sylow
139C113#200211yescharacteristic, complemented, Sylow
140C2×AGL(1,ℤ/8)—1131no—
141#535—1131no—
142C2×#127D11311yescharacteristic, complemented
143C2×#104—1131no—
144#418—1131no—
145C2×#100—1131no—
146#339—1131no—
147C2×#41—1131no—
148C22×D4—22no—
149C22×D4C2×D11311yescharacteristic
150C22×D4C2×D11311yescharacteristic
151AGL(1,ℤ/8)—2262no—
152AGL(1,ℤ/8)—2262no—
153C2×SD16—2261no—
154C2×D8—2261no—
155C2×M16—1131no—
156C2×M16—1131no—
157#127—22no—
158#127—22no—
159#127—2261no—
160#124—2261no—
161#121—2262no—
162#120—2262no—
163#117—1131no—
164C2×C42C2×D11311yescharacteristic
165#104—2262no—
166#102—2262no—
167#100—2262no—
168C24—21no—
169C24C22⋊D11312yes—
170#41—2261no—
171#41—2261no—
172#41—2261no—
173#41—2261no—
174C2×Q8—1131no—
175C2×D4—28no—
176C2×D4—21no—
177C2×D4—21no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—21no—
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—21no—
184C2×D4—21no—
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—48no—
188C2×D4—1131no—
189C2×D4—2264no—
190C2×D4—2261no—
191C2×D4C22⋊D11312yescomplemented
192C22×C4—21no—
193C22×C4—2261no—
194C22×C4C22×D11311yescharacteristic
195SD16—2264no—
196D8—2264no—
197M16—1132no—
198M16—2261no—
199M16—2261no—
200M16—2261no—
201C2×C8—2261no—
202C2×C8—2261no—
203C4⋊C4—1132no—
204C22⋊C4—2264no—
205C22⋊C4—2261no—
206C42—21no—
207C42—2261no—
208C42C22⋊D11312yescomplemented
209C23—22no—
210C23—22no—
211C23—22no—
212C23—22no—
213C23—44no—
214C23—44no—
215C23—41no—
216C23—41no—
217C23—2261no—
218C23C2×C22⋊D11311yescharacteristic
219Q8—2261no—
220Q8—2261no—
221D4—22no—
222D4—22no—
223D4—416no—
224D4—41no—
225D4—41no—
226D4—41no—
227D4—41no—
228D4—41no—
229D4—41no—
230D4—9044no—
231D4—4521no—
232D4—4521no—
233D4—2261no—
234D4—2261no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—4521no—
238C2×C4—4521no—
239C2×C4—2262no—
240C2×C4—2261no—
241C2×C4D4×D11311yescharacteristic
242C2×C4D4×D11311yescharacteristic
243C2×C4D4×D11311yescharacteristic
244C2×C4C2×C22⋊D11311yescharacteristic
245C2×C4C2×C22⋊D11311yescharacteristic
246C2×C4#1426864611yescharacteristic
247C8—4521no—
248C8—2262no—
249C22—22no—
250C22—44no—
251C22—44no—
252C22—42no—
253C22—42no—
254C22—44no—
255C22—82no—
256C22—82no—
257C22—82no—
258C22—4521no—
259C22—4522no—
260C22#1681359011yescharacteristic
261C22#1681359111yescharacteristic
262C22#1681359411yescharacteristic
263C4—24no—
264C4—4521no—
265C4—4522no—
266C4#1681359011yescharacteristic
267C4#1681359311yescharacteristic
268C4#1681359411yescharacteristic
269C4#1681361811yescharacteristic
270C2—21no—
271C2—21no—
272C2—82no—
273C2—82no—
274C2—9041no—
275C2#2029850611yescharacteristic
276C2#2029876512yes—
subgroupG/H
centerC22#16813590
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#127×C113C2
socleC22×C113#120
hypercenterC2×#127D113
hypocenterC113#2002
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#127

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. #20299165C2semidirect
3. C2×#16813550C2semidirect
4. #20298603C2semidirect
5. C2×#16813539C2semidirect
6. #20298358C2semidirect
7. C2×#127×C113C2semidirect
33. C2×Dic226D4semidirect
34. C2×D452D4semidirect
43. #14268631D4semidirect
46. C4⋊Dic113D4semidirect
65. C2×D4×C113D4semidirect
69. C42×C113D4semidirect
139. C113#2002semidirect
142. C2×#127D113semidirect
191. C2×D4C22⋊D113semidirect
208. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
#202991652
C2×#168135502
#202986032
C2×#168135392
#202983582
C2×#127×C1132
#2002113