Finite Group Databasebeta

← #28400109

Subgroups — #28400109

Order 14464.

504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16813642C211yesmaximal, characteristic, complemented
3#20299078C211yesmaximal, characteristic, complemented
4#20298817C212yesmaximal, complemented
5#20298810C212yesmaximal, complemented
6#20298795C212yesmaximal, complemented
7#20298790C212yesmaximal, complemented
8#20298625C211yesmaximal, characteristic, complemented
9#20298599C211yesmaximal, characteristic, complemented
10C2×#16813543C211yesmaximal, characteristic, complemented
11#535×C113C211yesmaximal, characteristic, complemented
12C2×#14268647C2211yescharacteristic
13#16813648—24no—
14#16813642—24no—
15C2×#14268637C2211yescharacteristic, complemented
16C2×#14268635C2212yes—
17C2×#14268635C2211yescharacteristic, complemented
18C2×#14268634C2211yescharacteristic, complemented
19C2×#14268632C2212yes—
20C2×#14268632C2211yescharacteristic, complemented
21C2×#14268631C2211yescharacteristic
22C22×#11744751C2211yescharacteristic
23C4×Dic226C2212yescomplemented
24C4×D452C2212yescomplemented
25#16813582—22no—
26#16813580—21no—
27C2×C4⋊Dic113C2211yescharacteristic
28C4⋊C4×D113—21no—
29C4⋊#11744751C2212yescomplemented
30C4⋊#11744751C2212yescomplemented
31#16813546C2212yescomplemented
32#16813543C2212yes—
33#16813543C2212yes—
34#16813543C2212yescomplemented
35C2×#41×C113C2211yescharacteristic
36C22×D4×C113C2211yescharacteristic
37#127×C113C2212yes—
38#124×C113C2212yes—
39#121×C113—21no—
40#121×C113—21no—
41#120×C113—22no—
42#117×C113C2211yescharacteristic
43#14268647—22no—
44#14268647D414yescomplemented
45C2×Dic226C2311yescharacteristic
46C2×D452C2311yescharacteristic
47C2×C22⋊D113—21no—
48C22×Dic113—21no—
49C2×C4×D113—21no—
50C2×C4×D113—22no—
51#14268637—22no—
52#14268635—24no—
53#14268635—22no—
54#14268634—22no—
55#14268632—24no—
56#14268632—22no—
57#14268631—22no—
58C2×#11744751—22no—
59C2×#11744751C2311yescharacteristic
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2312yes—
62C4⋊Dic113—21no—
63C4⋊Dic113C2312yes—
64#14268626—22no—
65#14268624—22no—
66C4×Dic113—22no—
67C24×C113—21no—
68#41×C113—22no—
69#41×C113—22no—
70C2×Q8×C113C2311yescharacteristic
71C2×D4×C113—21no—
72C2×D4×C113—22no—
73C2×D4×C113—21no—
74C2×D4×C113—22no—
75C2×D4×C113—22no—
76C2×D4×C113—22no—
77C2×D4×C113C2312yes—
78C2×D4×C113C2311yescharacteristic
79C22×C4×C113—21no—
80C22×C4×C113C2311yescharacteristic
81C4⋊C4×C113D411yescharacteristic
82C4⋊C4×C113D411yescharacteristic
83C22⋊C4×C113—22no—
84C22⋊C4×C113—22no—
85C22⋊C4×C113D412yes—
86C42×C113C2312yes—
87C23×C113—22no—
88C23×C113—21no—
89C23×C113—42no—
90C23×C113—81no—
91C23×C113—81no—
92C23×C113C2×D411yescharacteristic
93C22×D113—21no—
94Q8×C113—21no—
95Q8×C113—21no—
96D4×C113—22no—
97D4×C113—21no—
98D4×C113—22no—
99D4×C113—21no—
100D4×C113—42no—
101D4×C113—42no—
102D4×C113—82no—
103D4×C113—82no—
104C2×C4×C113—21no—
105C2×C4×C113—42no—
106C2×C4×C113C2×D412yes—
107C2×C4×C113C2×D412yes—
108C2×C4×C113C2×D412yes—
109C2×C4×C113C2×D411yescharacteristic
110C2×C4×C113#4112yes—
111C2×C4×C113C2411yescharacteristic
112C22⋊D113—24no—
113C2×Dic113—21no—
114C2×Dic113—22no—
115C2×Dic113—81no—
116D452—21no—
117D452C2×D412yes—
118C4×D113—24no—
119C4×D113—82no—
120Dic226—21no—
121Dic226C2×D412yes—
122#11744751—21no—
123#11744751—21no—
124#11744751—22no—
125C22×C113—21no—
126C22×C113—21no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113—41no—
130C22×C113—42no—
131C22×C113—41no—
132C22×C113—42no—
133C22×C113—84no—
134C22×C113#12112yes—
135C22×C113C22×D411yescharacteristic
136C2×D113—22no—
137C2×D113—41no—
138C2×D113—41no—
139C4×C113—22no—
140C4×C113—22no—
141C4×C113—41no—
142C4×C113#12112yes—
143C4×C113C22×D411yescharacteristic
144C4×C113C2×#4111yescharacteristic
145Dic113—22no—
146Dic113—42no—
147C2×C113—22no—
148C2×C113—81no—
149C2×C113—82no—
150C2×C113C2×#12111yescharacteristic
151C2×C113#57611yescharacteristic
152C2×C113#57711yescharacteristic
153D113—42no—
154#3045—1131nomaximal, Sylow
155C113#304511yescharacteristic, complemented, Sylow
156C2×AGL(1,ℤ/8)—1131no—
157C2×#135—1131no—
158#535D11311yescharacteristic, complemented
159#520—1131no—
160#464—1132no—
161#463—1132no—
162#460—1132no—
163#459—1132no—
164#424—1131no—
165#417—1131no—
166C2×#102—1131no—
167C2×#41—1131no—
168C2×#41C2×D11311yescharacteristic
169C22×D4C2×D11311yescharacteristic
170AGL(1,ℤ/8)—2264no—
171#135—2264no—
172C2×Q16—1131no—
173C2×SD16—1131no—
174C2×SD16—1131no—
175C2×SD16—1132no—
176C2×D8—1131no—
177C2×D8—1132no—
178C2×M16—1131no—
179C22×C8—1131no—
180#127C2×D11312yes—
181#124C2×D11312yes—
182#121—21no—
183#121—21no—
184#120—22no—
185C4×Q8—1132no—
186C4×D4—1132no—
187C4×D4—2262no—
188#117—2261no—
189#117C2×D11311yescharacteristic
190C2×C4⋊C4—1131no—
191C2×C4⋊C4—2261no—
192C4⋊C8—1132no—
193C4⋊C8—1132no—
194#103—1132no—
195#102—1132no—
196#102—1132no—
197#102—1132no—
198C24—21no—
199#41—22no—
200#41—22no—
201#41—1134no—
202#41—2262no—
203C2×Q8—1131no—
204C2×Q8C22×D11311yescharacteristic
205C2×D4—21no—
206C2×D4—22no—
207C2×D4—21no—
208C2×D4—22no—
209C2×D4—22no—
210C2×D4—22no—
211C2×D4—1131no—
212C2×D4—2261no—
213C2×D4C22×D11312yes—
214C2×D4C22×D11311yescharacteristic
215C22×C4—21no—
216C22×C4—2261no—
217C22×C4—2262no—
218C22×C4—2261no—
219C22×C4C22×D11311yescharacteristic
220Q16—2262no—
221SD16—2262no—
222SD16—2264no—
223SD16—2262no—
224D8—2262no—
225D8—2264no—
226M16—2262no—
227C2×C8—1131no—
228C2×C8—1131no—
229C2×C8—1132no—
230C2×C8—2262no—
231C4⋊C4—1132no—
232C4⋊C4—2261no—
233C4⋊C4—2262no—
234C4⋊C4C22⋊D11311yescharacteristic
235C4⋊C4C22⋊D11311yescharacteristic
236C22⋊C4—22no—
237C22⋊C4—22no—
238C22⋊C4—2262no—
239C22⋊C4C22⋊D11312yes—
240C42—2262no—
241C42C22×D11312yes—
242C23—22no—
243C23—21no—
244C23—42no—
245C23—81no—
246C23—81no—
247C23—2261no—
248C23C2×C22⋊D11311yescharacteristic
249Q8—21no—
250Q8—21no—
251Q8—1132no—
252Q8—2261no—
253D4—22no—
254D4—21no—
255D4—22no—
256D4—21no—
257D4—42no—
258D4—42no—
259D4—82no—
260D4—82no—
261D4—1132no—
262D4—2264no—
263D4—2261no—
264C2×C4—21no—
265C2×C4—42no—
266C2×C4—9042no—
267C2×C4—9041no—
268C2×C4—2262no—
269C2×C4—2261no—
270C2×C4—2264no—
271C2×C4D4×D11312yes—
272C2×C4C2×C22⋊D11312yes—
273C2×C4C2×C22⋊D11312yes—
274C2×C4C2×C22⋊D11311yescharacteristic
275C2×C4#1426864612yes—
276C2×C4C23×D11311yescharacteristic
277C8—2261no—
278C8—2261no—
279C8—2262no—
280C22—21no—
281C22—21no—
282C22—41no—
283C22—42no—
284C22—41no—
285C22—42no—
286C22—41no—
287C22—42no—
288C22—84no—
289C22—4521no—
290C22—4521no—
291C22—2262no—
292C22#1681359312yes—
293C22C22×C22⋊D11311yescharacteristic
294C4—22no—
295C4—22no—
296C4—41no—
297C4—4522no—
298C4—2262no—
299C4#1681359312yes—
300C4C2×D4×D11311yescharacteristic
301C4C2×#1426864611yescharacteristic
302C2—22no—
303C2—82no—
304C2—81no—
305C2—4522no—
306C2C2×#1681359311yescharacteristic
307C2#2029940111yescharacteristic
308C2#2029940911yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#535×C113C2
socleC22×C113C22×D4
hypercenter#535D113
hypocenterC113#3045
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ #117 ◁ #535

Complements

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

NH ≅ G/Ntype
1. C2×#16813648C2semidirect
2. C2×#16813642C2semidirect
3. #20299078C2semidirect
4. #20298817C2semidirect
5. #20298810C2semidirect
6. #20298795C2semidirect
7. #20298790C2semidirect
8. #20298625C2semidirect
9. #20298599C2semidirect
10. C2×#16813543C2semidirect
11. #535×C113C2semidirect
15. C2×#14268637C22semidirect
17. C2×#14268635C22semidirect
18. C2×#14268634C22semidirect
20. C2×#14268632C22semidirect
23. C4×Dic226C22semidirect
24. C4×D452C22semidirect
29. C4⋊#11744751C22semidirect
30. C4⋊#11744751C22semidirect
31. #16813546C22semidirect
34. #16813543C22semidirect
44. #14268647D4semidirect
155. C113#3045semidirect
158. #535D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136482
C2×#168136422
#202990782
#202988172
#202988102
#202987952
#202987902
#202986252
#202985992
C2×#168135432
#535×C1132
#3045113