Finite Group Databasebeta

← #28402194

Subgroups — #28402194

Order 14464.

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

normal subgroups only

This group has 556 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×#16813647C212yesmaximal, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20298974C211yesmaximal, characteristic, complemented
4#20298849C212yesmaximal, complemented
5#20298798C211yesmaximal, characteristic, complemented
6#20298790C211yesmaximal, characteristic, complemented
7#20298743C212yesmaximal, complemented
8#20298731C212yesmaximal, complemented
9C4×#14268634C211yesmaximal, characteristic, complemented
10#20298676C211yesmaximal, characteristic, complemented
11#550×C113C211yesmaximal, characteristic, complemented
12C22×D452C2212yes—
13C2×D4×D113—21no—
14#16813647—28no—
15C2×#14268634C2211yescharacteristic
16C2×#14268634C2212yescomplemented
17C2×#14268632C2212yes—
18C2×#14268632C2212yescomplemented
19C2×#14268632C2212yescomplemented
20C2×#14268631C2212yescomplemented
21#16813619C2211yescharacteristic
22#16813597—21no—
23#16813596C2212yes—
24#16813592—22no—
25C4×D452C2211yescharacteristic
26#16813553C2211yescharacteristic, complemented
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813546C2211yescharacteristic, complemented
29#16813543C2212yescomplemented
30#16813542C2211yescharacteristic
31#16813542C2212yescomplemented
32C22⋊#11744751C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34C2×#41×C113C2212yescomplemented
35#127×C113—21no—
36#127×C113C2211yescharacteristic, complemented
37#121×C113—22no—
38#121×C113C2212yescomplemented
39C4×Q8×C113C2211yescharacteristic, complemented
40C4×D4×C113—21no—
41C4×D4×C113C2211yescharacteristic
42C23×D113—22no—
43C2×D452—24no—
44C2×D452—22no—
45C2×D452—21no—
46C2×D452—21no—
47C2×D452—42no—
48C2×D452C2312yes—
49C2×D452C2311yescharacteristic
50C2×C22⋊D113—22no—
51D4×D113—44no—
52C2×C4×D113—21no—
53#14268634—24no—
54#14268634D414yescomplemented
55#14268632—24no—
56#14268632—24no—
57#14268632—42no—
58#14268631—24no—
59C2×#11744751C2312yes—
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C4⋊Dic113C2311yescharacteristic
63#14268624—21no—
64#14268624—22no—
65#41×C113—24no—
66#41×C113—42no—
67C2×Q8×C113C2311yescharacteristic
68C2×D4×C113—22no—
69C2×D4×C113—22no—
70C2×D4×C113—21no—
71C2×D4×C113—21no—
72C2×D4×C113D411yescharacteristic
73C2×D4×C113C2312yes—
74C22×C4×C113—22no—
75C22×C4×C113C2312yes—
76C4⋊C4×C113—21no—
77C4⋊C4×C113D411yescharacteristic
78C4⋊C4×C113C2311yescharacteristic
79C22⋊C4×C113—22no—
80C22⋊C4×C113D412yes—
81C42×C113—21no—
82C42×C113C2311yescharacteristic
83C23×C113—22no—
84C23×C113C2×D412yes—
85C22×D113—21no—
86C22×D113—22no—
87C22×D113—44no—
88C22×D113—44no—
89C22×D113—82no—
90Q8×C113—21no—
91Q8×C113C2×D412yescomplemented
92D4×C113—22no—
93D4×C113—22no—
94D4×C113—22no—
95D4×C113—44no—
96D4×C113—42no—
97D4×C113—81no—
98D4×C113—82no—
99C2×C4×C113—21no—
100C2×C4×C113—22no—
101C2×C4×C113—22no—
102C2×C4×C113—21no—
103C2×C4×C113—44no—
104C2×C4×C113C2×D411yescharacteristic
105C2×C4×C113C2×D412yes—
106C2×C4×C113C2×D411yescharacteristic
107C2×C4×C113C2411yescharacteristic
108C22⋊D113—44no—
109C2×Dic113—21no—
110D452—22no—
111D452—21no—
112D452—22no—
113D452—44no—
114D452—42no—
115D452—81no—
116D452C2×D412yes—
117C4×D113—42no—
118#11744751—22no—
119#11744751—21no—
120#11744751C2×D412yescomplemented
121C22×C113—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—42no—
125C22×C113—42no—
126C22×C113—42no—
127C22×C113C22×D411yescharacteristic
128C2×D113—22no—
129C2×D113—41no—
130C2×D113—41no—
131C2×D113—42no—
132C2×D113—42no—
133C2×D113—42no—
134C2×D113—88no—
135C4×C113—22no—
136C4×C113—22no—
137C4×C113—21no—
138C4×C113—41no—
139C4×C113AGL(1,ℤ/8)12yescomplemented
140C4×C113C22×D411yescharacteristic
141C4×C113H(5,𝔽2)11yescharacteristic
142Dic113—41no—
143C2×C113—42no—
144C2×C113—82no—
145C2×C113D4211yescharacteristic
146C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
147C2×C113#57611yescharacteristic
148D113—42no—
149D113—82no—
150#3274—1131nomaximal, Sylow
151C113#327411yescharacteristic, complemented, Sylow
152C2×AGL(1,ℤ/8)—1132no—
153#550D11311yescharacteristic, complemented
154D42—1131no—
155#493—1131no—
156#469—1132no—
157#460—1131no—
158#459—1131no—
159#449—1132no—
160#447—1132no—
161C4×SD16—1131no—
162#436—1131no—
163C2×#41C2×D11312yescomplemented
164C22×D4—1132no—
165C22×D4—2261no—
166AGL(1,ℤ/8)—2268no—
167C2×SD16—1131no—
168C2×SD16—1132no—
169C2×D8—1132no—
170C2×D8—1132no—
171C2×D8—1132no—
172C2×M16—1132no—
173#127—21no—
174#127—1131no—
175#127C2×D11311yescharacteristic, complemented
176#121—22no—
177#121—1132no—
178#121—2261no—
179#121C2×D11312yescomplemented
180#120—2262no—
181C4×Q8C2×D11311yescharacteristic, complemented
182C4×D4—21no—
183C4×D4—1131no—
184C4×D4C2×D11311yescharacteristic
185#106—1131no—
186C4⋊C8—1131no—
187#103—1131no—
188#102—1132no—
189#102—1131no—
190#102—1132no—
191C22⋊C8—1132no—
192C4×C8—1131no—
193C24—2262no—
194#41—24no—
195#41—42no—
196C2×Q8C22×D11311yescharacteristic
197C2×D4—22no—
198C2×D4—22no—
199C2×D4—21no—
200C2×D4—21no—
201C2×D4—1131no—
202C2×D4—1132no—
203C2×D4—4522no—
204C2×D4—4524no—
205C2×D4—2264no—
206C2×D4—2262no—
207C2×D4—2261no—
208C2×D4—2262no—
209C2×D4—2261no—
210C2×D4C22⋊D11311yescharacteristic
211C2×D4C22×D11312yes—
212C22×C4—22no—
213C22×C4—2261no—
214C22×C4C22×D11312yes—
215SD16—1134no—
216SD16—2264no—
217D8—4522no—
218D8—2264no—
219D8—2264no—
220M16—2264no—
221C2×C8—1131no—
222C2×C8—1131no—
223C2×C8—1132no—
224C4⋊C4—21no—
225C4⋊C4—1131no—
226C4⋊C4C22⋊D11311yescharacteristic
227C4⋊C4C22×D11311yescharacteristic
228C22⋊C4—22no—
229C22⋊C4—2261no—
230C22⋊C4—2262no—
231C22⋊C4C22⋊D11312yes—
232C42—21no—
233C42C22×D11311yescharacteristic
234C23—22no—
235C23—9042no—
236C23—4524no—
237C23—4524no—
238C23—2262no—
239C23—2261no—
240C23C2×C22⋊D11312yes—
241Q8—21no—
242Q8D4×D11312yescomplemented
243D4—22no—
244D4—22no—
245D4—22no—
246D4—44no—
247D4—42no—
248D4—81no—
249D4—82no—
250D4—1132no—
251D4—9041no—
252D4—4524no—
253D4—4524no—
254D4—4522no—
255D4—2262no—
256D4—2262no—
257D4—2261no—
258C2×C4—21no—
259C2×C4—22no—
260C2×C4—22no—
261C2×C4—21no—
262C2×C4—44no—
263C2×C4—4522no—
264C2×C4—2261no—
265C2×C4C2×C22⋊D11311yescharacteristic
266C2×C4C2×C22⋊D11312yes—
267C2×C4C2×C22⋊D11311yescharacteristic
268C2×C4C23×D11311yescharacteristic
269C8—1132no—
270C8—2262no—
271C8—2261no—
272C22—22no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—42no—
277C22—42no—
278C22—9048no—
279C22—4522no—
280C22—4522no—
281C22—4522no—
282C22—4521no—
283C22—4521no—
284C22—2262no—
285C22C22×C22⋊D11311yescharacteristic
286C4—21no—
287C4—22no—
288C4—22no—
289C4—41no—
290C4—4521no—
291C4#1681364712yescomplemented
292C4C2×D4×D11311yescharacteristic
293C4#1681366711yescharacteristic
294C2—42no—
295C2—82no—
296C2—9042no—
297C2—4522no—
298C2D4×C22⋊D11311yescharacteristic
299C2C2×#1681364711yescharacteristic
300C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#550×C113C2
socleC22×C113C22×D4
hypercenter#550D113
hypocenterC113#3274
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ #550

Complements

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

NH ≅ G/Ntype
1. C2×#16813647C2semidirect
2. D4×D452C2semidirect
3. #20298974C2semidirect
4. #20298849C2semidirect
5. #20298798C2semidirect
6. #20298790C2semidirect
7. #20298743C2semidirect
8. #20298731C2semidirect
9. C4×#14268634C2semidirect
10. #20298676C2semidirect
11. #550×C113C2semidirect
16. C2×#14268634C22semidirect
18. C2×#14268632C22semidirect
19. C2×#14268632C22semidirect
20. C2×#14268631C22semidirect
26. #16813553C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813546C22semidirect
29. #16813543C22semidirect
31. #16813542C22semidirect
32. C22⋊#11744751C22semidirect
33. C4×#11744751C22semidirect
34. C2×#41×C113C22semidirect
36. #127×C113C22semidirect
38. #121×C113C22semidirect
39. C4×Q8×C113C22semidirect
54. #14268634D4semidirect
91. Q8×C113C2×D4semidirect
120. #11744751C2×D4semidirect
139. C4×C113AGL(1,ℤ/8)semidirect
151. C113#3274semidirect
153. #550D113semidirect
163. C2×#41C2×D113semidirect
175. #127C2×D113semidirect
179. #121C2×D113semidirect
181. C4×Q8C2×D113semidirect
242. Q8D4×D113semidirect
291. C4#16813647semidirect

Maximal subgroups

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

subgroupindex
C2×#168136472
D4×D4522
#202989742
#202988492
#202987982
#202987902
#202987432
#202987312
C4×#142686342
#202986762
#550×C1132
#3274113