Finite Group Databasebeta

← #28399803

Subgroups — #28399803

Order 14464.

994 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 994 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C22×D4×D113C211yesmaximal, characteristic, complemented
2C2×#16813650C211yesmaximal, characteristic, complemented
3C2×#16813648C211yesmaximal, characteristic, complemented
4#20299110C211yesmaximal, characteristic, complemented
5#20298750C214yesmaximal, complemented
6#20298733C214yesmaximal, complemented
7#20298602C211yesmaximal, characteristic, complemented
8#20298561C211yesmaximal, characteristic, complemented
9#418×C113C211yesmaximal, characteristic, complemented
10C24×D113—21no—
11C2×#14268647C2211yescharacteristic, complemented
12C22×D452C2211yescharacteristic
13C22×C22⋊D113—21no—
14C2×D4×D113—24no—
15C2×D4×D113—22no—
16C2×D4×D113—24no—
17C2×D4×D113C2214yes—
18C22×C4×D113C2211yescharacteristic
19#16813650—24no—
20#16813648—24no—
21C2×#14268636C2212yescomplemented
22C2×#14268635C2212yescomplemented
23C2×D904C2212yescomplemented
24C2×#14268632C2212yescomplemented
25C2×#14268631C2211yescharacteristic, complemented
26#16813606—21no—
27#16813602C2212yescomplemented
28#16813597C2212yescomplemented
29#16813592—21no—
30C4×D452—22no—
31#16813542C2214yescomplemented
32#16813534C2214yescomplemented
33C22×D4×C113C2211yescharacteristic
34C2×M16×C113C2211yescharacteristic, complemented
35#117×C113C2211yescharacteristic, complemented
36#102×C113C2214yescomplemented
37C23×D113—28no—
38C23×D113—21no—
39C23×D113—24no—
40C23×D113—48no—
41C23×D113D411yescharacteristic
42#14268647—22no—
43#14268647—22no—
44C2×Dic226C2311yescharacteristic, complemented
45C2×D452—21no—
46C2×D452—22no—
47C2×D452—22no—
48C2×D452D414yescomplemented
49C2×D452C2312yes—
50C2×D452C2311yescharacteristic, complemented
51C2×C22⋊D113—28no—
52C2×C22⋊D113—21no—
53C2×C22⋊D113—24no—
54D4×D113—216no—
55D4×D113—28no—
56D4×D113—28no—
57C22×Dic113D411yescharacteristic
58C2×C4×D113—22no—
59C2×C4×D113—22no—
60C2×C4×D113—21no—
61C2×C4×D113D412yes—
62C2×C4×D113C2312yes—
63#14268636—24no—
64#14268635—24no—
65D904—24no—
66#14268632—24no—
67#14268631—22no—
68C2×#11744751C2312yescomplemented
69C4⋊Dic113—22no—
70#14268624—22no—
71#14268624—22no—
72C24×C113—21no—
73C2×D4×C113—21no—
74C2×D4×C113—22no—
75C2×D4×C113D414yescomplemented
76C2×D4×C113C2312yes—
77C22×C4×C113C2311yescharacteristic
78M16×C113—22no—
79C2×C8×C113C2312yescomplemented
80C4⋊C4×C113C2312yescomplemented
81C22⋊C4×C113—21no—
82C42×C113—21no—
83C23×C113—24no—
84C23×C113—22no—
85C23×C113—44no—
86C23×C113C2×D411yescharacteristic
87C22×D113—22no—
88C22×D113—24no—
89C22×D113—216no—
90C22×D113—24no—
91C22×D113—22no—
92C22×D113—21no—
93C22×D113—432no—
94C22×D113—48no—
95C22×D113—44no—
96C22×D113—48no—
97C22×D113C2×D412yes—
98D4×C113—24no—
99D4×C113—22no—
100D4×C113C2×D414yes—
101C2×C4×C113—22no—
102C2×C4×C113C2×D411yescharacteristic
103C2×C4×C113C2×D412yes—
104C2×C4×C113C2×D412yes—
105C2×C4×C113C2411yescharacteristic
106C22⋊D113—216no—
107C22⋊D113—42no—
108C2×Dic113—22no—
109C2×Dic113—21no—
110C2×Dic113C2×D412yes—
111D452—24no—
112D452—22no—
113D452—21no—
114D452—21no—
115D452—44no—
116D452C2×D414yes—
117C4×D113—24no—
118C4×D113—22no—
119C4×D113—22no—
120C4×D113—42no—
121Dic226—21no—
122Dic226—21no—
123C8×C113—22no—
124#11744751—22no—
125C22×C113—22no—
126C22×C113—24no—
127C22×C113—48no—
128C22×C113—44no—
129C22×C113#12012yes—
130C22×C113C22×D411yescharacteristic
131C2×D113—28no—
132C2×D113—22no—
133C2×D113—22no—
134C2×D113—24no—
135C2×D113—432no—
136C2×D113—48no—
137C2×D113—44no—
138C2×D113—41no—
139C2×D113—42no—
140C2×D113AGL(1,ℤ/8)14yescomplemented
141C4×C113—42no—
142C4×C113#12012yes—
143C4×C113C22×D411yescharacteristic
144C4×C113C22×D411yescharacteristic
145Dic113—22no—
146Dic113—41no—
147C2×C113—22no—
148C2×C113—44no—
149C2×C113C2×#12011yescharacteristic
150C2×C113C2×AGL(1,ℤ/8)12yes—
151D113—24no—
152D113—44no—
153D113—81no—
154#3003—1131nomaximal, Sylow
155C113#300311yescharacteristic, complemented, Sylow
156C23×D4—1131no—
157C2×AGL(1,ℤ/8)—1131no—
158C2×AGL(1,ℤ/8)—1131no—
159#525—1131no—
160#450—1134no—
161#447—1134no—
162#418—1131no—
163#418D11311yescharacteristic, complemented
164#407—1131no—
165C25—2261no—
166C2×#41—1131no—
167C22×D4—1134no—
168C22×D4—1131no—
169C22×D4—2262no—
170C22×D4—2261no—
171C22×D4—2264no—
172C22×D4—2264no—
173C22×D4C2×D11311yescharacteristic
174C23×C4—1131no—
175AGL(1,ℤ/8)—2264no—
176AGL(1,ℤ/8)—2264no—
177C2×SD16—1132no—
178C2×SD16—1132no—
179C2×D8—1132no—
180C2×D8—1132no—
181C2×M16—1131no—
182C2×M16C2×D11311yescharacteristic, complemented
183#123—2261no—
184C22⋊Q8—1132no—
185#121—1132no—
186#120—2261no—
187C4×D4—2262no—
188#117C2×D11311yescharacteristic, complemented
189#102—1134no—
190#102C2×D11314yescomplemented
191C22⋊C8—1134no—
192C24—21no—
193C24—1131no—
194C24—4528no—
195C24—2264no—
196C24—2268no—
197C24—2261no—
198#41—2262no—
199#41—2262no—
200C2×Q8—1131no—
201C2×D4—21no—
202C2×D4—22no—
203C2×D4—1134no—
204C2×D4—1132no—
205C2×D4—1131no—
206C2×D4—2262no—
207C2×D4—2264no—
208C2×D4—2268no—
209C2×D4—22616no—
210C2×D4—2261no—
211C2×D4—2268no—
212C2×D4—2268no—
213C2×D4—2261no—
214C2×D4—2262no—
215C2×D4D45214yescomplemented
216C2×D4C22×D11312yes—
217C22×C4—1131no—
218C22×C4—1132no—
219C22×C4—1132no—
220C22×C4—2261no—
221C22×C4—2262no—
222C22×C4—2262no—
223C22×C4C22×D11311yescharacteristic
224SD16—2264no—
225SD16—2264no—
226D8—2264no—
227D8—2264no—
228M16—22no—
229M16—2262no—
230C2×C8—1132no—
231C2×C8C22×D11312yescomplemented
232C4⋊C4—2262no—
233C4⋊C4C22×D11312yescomplemented
234C22⋊C4—21no—
235C22⋊C4—2262no—
236C22⋊C4—2262no—
237C42—21no—
238C23—24no—
239C23—22no—
240C23—44no—
241C23—1132no—
242C23—4524no—
243C23—4528no—
244C23—45232no—
245C23—4528no—
246C23—2264no—
247C23—22616no—
248C23—2261no—
249C23—2264no—
250C23—2262no—
251C23—2262no—
252C23D4×D11311yescharacteristic
253Q8—2261no—
254Q8—2261no—
255D4—24no—
256D4—22no—
257D4—1134no—
258D4—4524no—
259D4—4522no—
260D4—22616no—
261D4—2264no—
262D4—2261no—
263D4—2261no—
264D4—2262no—
265D4C2×D45214yes—
266C2×C4—22no—
267C2×C4—1132no—
268C2×C4—4522no—
269C2×C4—2261no—
270C2×C4—2262no—
271C2×C4—2264no—
272C2×C4—2262no—
273C2×C4—2262no—
274C2×C4D4×D11311yescharacteristic
275C2×C4D4×D11312yes—
276C2×C4C2×D45212yes—
277C2×C4C23×D11311yescharacteristic
278C8—22no—
279C8—2262no—
280C22—22no—
281C22—24no—
282C22—48no—
283C22—44no—
284C22—1134no—
285C22—4528no—
286C22—45232no—
287C22—4521no—
288C22—4522no—
289C22—4524no—
290C22—2268no—
291C22—2264no—
292C22—2262no—
293C22—2262no—
294C22#1681359212yes—
295C22C2×D4×D11311yescharacteristic
296C4—42no—
297C4—4521no—
298C4—2262no—
299C4#1681359212yes—
300C4C2×D4×D11311yescharacteristic
301C4C22×D45211yescharacteristic
302C2—22no—
303C2—44no—
304C2—9041no—
305C2—4524no—
306C2—2264no—
307C2C2×#1681359211yescharacteristic
308C2AGL(1,ℤ/8)×D11312yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#418×C113C2
socleC22×C113C22×D4
hypercenter#418D113
hypocenterC113#3003
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. C22×D4×D113C2semidirect
2. C2×#16813650C2semidirect
3. C2×#16813648C2semidirect
4. #20299110C2semidirect
5. #20298750C2semidirect
6. #20298733C2semidirect
7. #20298602C2semidirect
8. #20298561C2semidirect
9. #418×C113C2semidirect
11. C2×#14268647C22semidirect
21. C2×#14268636C22semidirect
22. C2×#14268635C22semidirect
23. C2×D904C22semidirect
24. C2×#14268632C22semidirect
25. C2×#14268631C22semidirect
27. #16813602C22semidirect
28. #16813597C22semidirect
31. #16813542C22semidirect
32. #16813534C22semidirect
34. C2×M16×C113C22semidirect
35. #117×C113C22semidirect
36. #102×C113C22semidirect
44. C2×Dic226C23semidirect
48. C2×D452D4semidirect
50. C2×D452C23semidirect
68. C2×#11744751C23semidirect
75. C2×D4×C113D4semidirect
79. C2×C8×C113C23semidirect
80. C4⋊C4×C113C23semidirect
140. C2×D113AGL(1,ℤ/8)semidirect
155. C113#3003semidirect
163. #418D113semidirect
182. C2×M16C2×D113semidirect
188. #117C2×D113semidirect
190. #102C2×D113semidirect
215. C2×D4D452semidirect
231. C2×C8C22×D113semidirect
233. C4⋊C4C22×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C2×#168136502
C2×#168136482
#202991102
#202987502
#202987332
#202986022
#202985612
#418×C1132
#3003113