Finite Group Databasebeta

← #28391592

Subgroups — #28391592

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×#16813650C211yesmaximal, characteristic, complemented
2#20299167C211yesmaximal, characteristic, complemented
3C2×#16813619C211yesmaximal, characteristic, complemented
4C2×#16813550C211yesmaximal, characteristic, complemented
5#20298602C211yesmaximal, characteristic, complemented
6C2×#16813538C211yesmaximal, characteristic, complemented
7#339×C113C211yesmaximal, characteristic, complemented
8C2×#14268647C2211yescharacteristic
9C22×D452—22no—
10C22×D452C2211yescharacteristic
11C22×D452C2211yescharacteristic
12#16813650—22no—
13#16813650—22no—
14C2×#14268636—21no—
15C2×D904—21no—
16C2×#14268631C2211yescharacteristic
17#16813619—22no—
18#16813619—21no—
19#16813619—22no—
20#16813610—21no—
21#16813597—22no—
22#16813592—22no—
23#16813550—22no—
24#16813542—22no—
25#16813538—22no—
26C2×M16×C113C2211yescharacteristic
27#117×C113C2211yescharacteristic
28C2×C42×C113C2211yescharacteristic
29C23×D113—21no—
30C23×D113D412yes—
31#14268647—21no—
32#14268647—21no—
33#14268647—21no—
34#14268647—21no—
35C2×Dic226D411yescharacteristic, complemented
36C2×D452—21no—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452—21no—
40C2×D452—28no—
41C2×D452—21no—
42C2×D452—21no—
43C2×D452—21no—
44C2×D452—21no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—21no—
48C2×D452—24no—
49C2×D452—48no—
50C2×D452D411yescharacteristic, complemented
51C2×D452D412yescomplemented
52C2×C22⋊D113—21no—
53C2×C4×D113—21no—
54#14268636—24no—
55D904—24no—
56#14268631—21no—
57#14268631—21no—
58C2×#11744751—21no—
59#14268624—24no—
60C22×C4×C113—21no—
61C22×C4×C113C2311yescharacteristic
62M16×C113—21no—
63M16×C113D412yescomplemented
64C2×C8×C113—21no—
65C4⋊C4×C113D412yescomplemented
66C22⋊C4×C113—21no—
67C42×C113—21no—
68C42×C113—21no—
69C42×C113D412yescomplemented
70C23×C113C2×D411yescharacteristic
71C22×D113—22no—
72C22×D113—21no—
73C22×D113—22no—
74C22×D113—22no—
75C22×D113—22no—
76C22×D113—44no—
77C22×D113—44no—
78C22×D113—41no—
79C22×D113—41no—
80C2×C4×C113—24no—
81C2×C4×C113—22no—
82C2×C4×C113—22no—
83C2×C4×C113C2×D411yescharacteristic
84C2×C4×C113C2×D411yescharacteristic
85C2×C4×C113C2×D411yescharacteristic
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113#4111yescharacteristic
89C22⋊D113—41no—
90C22⋊D113—41no—
91C2×Dic113—21no—
92D452—21no—
93D452—22no—
94D452—22no—
95D452—21no—
96D452—416no—
97D452—41no—
98D452—41no—
99D452—41no—
100D452—41no—
101D452—41no—
102D452—41no—
103D452—84no—
104C4×D113—41no—
105C4×D113—41no—
106Dic226—21no—
107Dic226—21no—
108C8×C113—22no—
109#11744751—41no—
110C22×C113—22no—
111C22×C113#12011yescharacteristic
112C22×C113#12011yescharacteristic
113C22×C113#12111yescharacteristic
114C2×D113—44no—
115C2×D113—44no—
116C2×D113—41no—
117C2×D113—42no—
118C2×D113—42no—
119C2×D113—42no—
120C2×D113—44no—
121C2×D113—82no—
122C2×D113—82no—
123C2×D113—82no—
124C4×C113—24no—
125C4×C113—42no—
126C4×C113#12011yescharacteristic
127C4×C113#12111yescharacteristic
128C4×C113#12111yescharacteristic
129C4×C113#12711yescharacteristic
130Dic113—41no—
131C2×C113—21no—
132C2×C113—21no—
133C2×C113#39211yescharacteristic
134C2×C113#45312yes—
135D113—81no—
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×#104—1131no—
144#418—1131no—
145C2×#100—1131no—
146#339D11311yescharacteristic, complemented
147C2×#41—1131no—
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#117C2×D11311yescharacteristic
164C2×C42C2×D11311yescharacteristic
165#104—2262no—
166#102—2262no—
167#100—2262no—
168C24—1132no—
169C24—2261no—
170#41—2261no—
171#41—2261no—
172#41—2261no—
173#41—2261no—
174C2×Q8—1131no—
175C2×D4—1131no—
176C2×D4—1132no—
177C2×D4—4528no—
178C2×D4—2264no—
179C2×D4—2268no—
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×D4—2261no—
192C22×C4—21no—
193C22×C4—2261no—
194C22×C4C22×D11311yescharacteristic
195SD16—2264no—
196D8—2264no—
197M16—21no—
198M16—2261no—
199M16—2261no—
200M16D45212yescomplemented
201C2×C8—21no—
202C2×C8—2261no—
203C4⋊C4D45212yescomplemented
204C22⋊C4—21no—
205C22⋊C4—2264no—
206C42—21no—
207C42—21no—
208C42D45212yescomplemented
209C23—4524no—
210C23—4524no—
211C23—4521no—
212C23—4521no—
213C23—2262no—
214C23—2262no—
215C23—2262no—
216C23—2262no—
217C23—2261no—
218C23D4×D11311yescharacteristic
219Q8—2261no—
220Q8—2261no—
221D4—9044no—
222D4—45216no—
223D4—4521no—
224D4—4521no—
225D4—4521no—
226D4—4521no—
227D4—4521no—
228D4—4521no—
229D4—4521no—
230D4—4521no—
231D4—2261no—
232D4—2262no—
233D4—2262no—
234D4—2261no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—22no—
238C2×C4—4521no—
239C2×C4—4521no—
240C2×C4—2261no—
241C2×C4D4×D11311yescharacteristic
242C2×C4D4×D11311yescharacteristic
243C2×C4C2×D45211yescharacteristic
244C2×C4C2×D45211yescharacteristic
245C2×C4C2×D45211yescharacteristic
246C2×C4#1426864811yescharacteristic
247C8—22no—
248C8—4521no—
249C22—22no—
250C22—9042no—
251C22—9042no—
252C22—9042no—
253C22—4524no—
254C22—4524no—
255C22—4521no—
256C22—4522no—
257C22—4522no—
258C22—4522no—
259C22—4524no—
260C22#1681359211yescharacteristic
261C22#1681359211yescharacteristic
262C22#1681359711yescharacteristic
263C4—24no—
264C4—42no—
265C4—4521no—
266C4#1681359211yescharacteristic
267C4#1681359711yescharacteristic
268C4#1681359711yescharacteristic
269C4#1681361911yescharacteristic
270C2—21no—
271C2—21no—
272C2—9042no—
273C2—9042no—
274C2—9041no—
275C2#2029850811yescharacteristic
276C2#2029876712yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#339×C113C2
socleC22×C113#120
hypercenter#339D113
hypocenterC113#2002
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. C2×#16813650C2semidirect
2. #20299167C2semidirect
3. C2×#16813619C2semidirect
4. C2×#16813550C2semidirect
5. #20298602C2semidirect
6. C2×#16813538C2semidirect
7. #339×C113C2semidirect
35. C2×Dic226D4semidirect
50. C2×D452D4semidirect
51. C2×D452D4semidirect
63. M16×C113D4semidirect
65. C4⋊C4×C113D4semidirect
69. C42×C113D4semidirect
139. C113#2002semidirect
146. #339D113semidirect
200. M16D452semidirect
203. C4⋊C4D452semidirect
208. C42D452semidirect

Maximal subgroups

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

subgroupindex
C2×#168136502
#202991672
C2×#168136192
C2×#168135502
#202986022
C2×#168135382
#339×C1132
#2002113