Finite Group Databasebeta

← #28400118

Subgroups — #28400118

Order 14464.

504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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
2C2×#16813644C211yesmaximal, characteristic, complemented
3#20299165C211yesmaximal, characteristic, complemented
4#20299079C211yesmaximal, characteristic, complemented
5#20298819C212yesmaximal, complemented
6#20298812C212yesmaximal, complemented
7#20298797C212yesmaximal, complemented
8#20298792C212yesmaximal, complemented
9#20298624C211yesmaximal, characteristic, complemented
10#20298597C211yesmaximal, characteristic, complemented
11C2×#102×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13C2×#14268647C2211yescharacteristic
14#16813648—24no—
15#16813644—24no—
16C2×Dic452C2211yescharacteristic, complemented
17C2×#14268636C2211yescharacteristic, complemented
18C2×#14268636C2211yescharacteristic, complemented
19C2×#14268635C2212yes—
20C2×D904C2211yescharacteristic, complemented
21C2×#14268632C2212yes—
22C2×#14268631C2211yescharacteristic
23#16813618C2212yes—
24#16813609C2212yes—
25#16813593—21no—
26#16813593—21no—
27#16813591—22no—
28#16813587C2212yescomplemented
29#16813584C2212yescomplemented
30C4×C22⋊D113—22no—
31#16813581C2211yescharacteristic
32#16813580—21no—
33C4⋊C4×D113—21no—
34#16813551C2212yescomplemented
35#16813551C2212yescomplemented
36#16813545C2212yescomplemented
37#16813542C2212yescomplemented
38C22×D4×C113C2211yescharacteristic
39C22×C8×C113C2211yescharacteristic
40C2×C4⋊C4×C113C2211yescharacteristic
41#102×C113C2212yes—
42#102×C113C2212yes—
43#14268647—22no—
44#14268647—22no—
45#14268647—22no—
46#14268647D414yescomplemented
47C2×Dic226C2311yescharacteristic
48C2×Dic226C2311yescharacteristic
49C2×D452C2311yescharacteristic
50C2×D452C2311yescharacteristic
51C2×C22⋊D113—21no—
52C2×C22⋊D113—21no—
53C2×C22⋊D113—22no—
54C2×C22⋊D113—22no—
55C2×C4×D113—21no—
56C2×C4×D113—21no—
57C2×C4×D113—22no—
58Dic452—22no—
59#14268636—22no—
60#14268636—22no—
61#14268635—24no—
62D904—22no—
63#14268632—24no—
64#14268631—22no—
65C2×#11744751C2312yes—
66C4⋊Dic113D411yescharacteristic
67C4⋊Dic113D411yescharacteristic
68#14268626—22no—
69C22⋊Dic113—22no—
70C22⋊Dic113—22no—
71C22⋊Dic113D412yes—
72#14268624—22no—
73C4×Dic113—22no—
74C4×Dic113C2312yes—
75C24×C113—21no—
76C2×D4×C113—22no—
77C2×D4×C113—21no—
78C2×D4×C113—22no—
79C2×D4×C113C2312yes—
80C22×C4×C113—21no—
81C22×C4×C113C2311yescharacteristic
82C2×C8×C113—22no—
83C2×C8×C113C2311yescharacteristic
84C2×C8×C113C2311yescharacteristic
85C4⋊C4×C113—21no—
86C4⋊C4×C113C2312yes—
87C23×C113—22no—
88C23×C113—42no—
89C23×C113—81no—
90C23×C113—81no—
91C23×C113C2×D411yescharacteristic
92C22×D113—21no—
93C22×D113—21no—
94D4×C113—22no—
95D4×C113—22no—
96D4×C113—42no—
97C2×C4×C113—22no—
98C2×C4×C113—81no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D412yes—
101C2×C4×C113#4112yes—
102C2×C4×C113C2411yescharacteristic
103C22⋊D113—24no—
104C22⋊D113—42no—
105C22⋊D113—82no—
106C22⋊D113—82no—
107C2×Dic113—21no—
108C2×Dic113—21no—
109C2×Dic113C2×D412yes—
110C2×Dic113C2×D412yes—
111D452—21no—
112D452—21no—
113D452—21no—
114D452C2×D412yes—
115C4×D113—24no—
116C4×D113—42no—
117C4×D113—82no—
118Dic226—21no—
119Dic226—21no—
120Dic226—21no—
121Dic226C2×D412yes—
122C8×C113—21no—
123C8×C113—21no—
124#11744751—22no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—42no—
128C22×C113—42no—
129C22×C113—42no—
130C22×C113—84no—
131C22×C113#12112yes—
132C22×C113C22×D411yescharacteristic
133C2×D113—22no—
134C2×D113—41no—
135C2×D113—41no—
136C2×D113—41no—
137C2×D113—41no—
138C2×D113—41no—
139C4×C113—42no—
140C4×C113#12112yes—
141C4×C113C22×D411yescharacteristic
142C4×C113C2×#4111yescharacteristic
143Dic113—22no—
144Dic113—22no—
145Dic113—22no—
146Dic113—41no—
147C2×C113—22no—
148C2×C113—82no—
149C2×C113C2×#12111yescharacteristic
150C2×C113#57611yescharacteristic
151C2×C113#57711yescharacteristic
152D113—42no—
153D113—81no—
154#3045—1131nomaximal, Sylow
155C113#304511yescharacteristic, complemented, Sylow
156C2×AGL(1,ℤ/8)—1131no—
157C2×#135—1131no—
158#535—1131no—
159#520—1131no—
160#464—1132no—
161#463—1132no—
162#460—1132no—
163#459—1132no—
164#424—1131no—
165#417—1131no—
166C2×#102D11311yescharacteristic, complemented
167C2×#41—1131no—
168C2×#41—1131no—
169C22×D4C2×D11311yescharacteristic
170AGL(1,ℤ/8)—2264no—
171#135—2264no—
172C2×Q16—1131no—
173C2×SD16—1132no—
174C2×SD16—1131no—
175C2×SD16—1131no—
176C2×D8—1132no—
177C2×D8—1131no—
178C2×M16—1131no—
179C22×C8C2×D11311yescharacteristic
180#127—1132no—
181#124—1132no—
182#121—2261no—
183#121—2261no—
184#120—2262no—
185C4×Q8—1132no—
186C4×D4—1132no—
187C4×D4—2262no—
188#117—1131no—
189#117—2261no—
190C2×C4⋊C4—2261no—
191C2×C4⋊C4C2×D11311yescharacteristic
192C4⋊C8—1132no—
193C4⋊C8—1132no—
194#103—1132no—
195#102—1132no—
196#102C2×D11312yes—
197#102C2×D11312yes—
198C24—21no—
199#41—1134no—
200#41—2262no—
201#41—2262no—
202#41—2262no—
203C2×Q8—1131no—
204C2×Q8—1131no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—22no—
208C2×D4—1131no—
209C2×D4—1131no—
210C2×D4—2262no—
211C2×D4—2262no—
212C2×D4—2261no—
213C2×D4—2261no—
214C2×D4C22×D11312yes—
215C22×C4—21no—
216C22×C4—2262no—
217C22×C4—2261no—
218C22×C4—2261no—
219C22×C4C22×D11311yescharacteristic
220Q16—2262no—
221SD16—2262no—
222SD16—2262no—
223SD16—2264no—
224D8—2262no—
225D8—2264no—
226M16—2262no—
227C2×C8—22no—
228C2×C8—1132no—
229C2×C8C22×D11311yescharacteristic
230C2×C8C22×D11311yescharacteristic
231C4⋊C4—21no—
232C4⋊C4—1131no—
233C4⋊C4—1131no—
234C4⋊C4—2262no—
235C4⋊C4C22×D11312yes—
236C22⋊C4—1132no—
237C22⋊C4—2262no—
238C22⋊C4—2262no—
239C22⋊C4—2262no—
240C42—1132no—
241C42—2262no—
242C23—22no—
243C23—42no—
244C23—81no—
245C23—81no—
246C23—2261no—
247C23—2261no—
248C23D4×D11311yescharacteristic
249Q8—1132no—
250Q8—2261no—
251Q8—2261no—
252Q8—2261no—
253D4—22no—
254D4—22no—
255D4—42no—
256D4—1132no—
257D4—9042no—
258D4—9042no—
259D4—4522no—
260D4—2264no—
261D4—2261no—
262D4—2261no—
263D4—2261no—
264C2×C4—22no—
265C2×C4—81no—
266C2×C4—1132no—
267C2×C4—1132no—
268C2×C4—9042no—
269C2×C4—4522no—
270C2×C4—2261no—
271C2×C4—2261no—
272C2×C4—2264no—
273C2×C4D4×D11311yescharacteristic
274C2×C4D4×D11312yes—
275C2×C4#1426864712yes—
276C2×C4C23×D11311yescharacteristic
277C8—21no—
278C8—21no—
279C8—2262no—
280C22—21no—
281C22—21no—
282C22—42no—
283C22—42no—
284C22—42no—
285C22—84no—
286C22—4521no—
287C22—4521no—
288C22—4521no—
289C22—4521no—
290C22—4521no—
291C22—2262no—
292C22#1681359512yes—
293C22C2×D4×D11311yescharacteristic
294C4—42no—
295C4—4521no—
296C4—2262no—
297C4—2262no—
298C4—2262no—
299C4#1681359512yes—
300C4C2×D4×D11311yescharacteristic
301C4C2×#1426864711yescharacteristic
302C2—22no—
303C2—82no—
304C2—9041no—
305C2—4522no—
306C2C2×#1681359511yescharacteristic
307C2#2029939911yescharacteristic
308C2#2029940411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC2×#102×C113C2
socleC22×C113C22×D4
hypercenterC2×#102D113
hypocenterC113#3045
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C2×#16813644C2semidirect
3. #20299165C2semidirect
4. #20299079C2semidirect
5. #20298819C2semidirect
6. #20298812C2semidirect
7. #20298797C2semidirect
8. #20298792C2semidirect
9. #20298624C2semidirect
10. #20298597C2semidirect
11. C2×#102×C113C2semidirect
16. C2×Dic452C22semidirect
17. C2×#14268636C22semidirect
18. C2×#14268636C22semidirect
20. C2×D904C22semidirect
28. #16813587C22semidirect
29. #16813584C22semidirect
34. #16813551C22semidirect
35. #16813551C22semidirect
36. #16813545C22semidirect
37. #16813542C22semidirect
46. #14268647D4semidirect
155. C113#3045semidirect
166. C2×#102D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C2×#168136442
#202991652
#202990792
#202988192
#202988122
#202987972
#202987922
#202986242
#202985972
C2×#102×C1132
#3045113