Finite Group Databasebeta

← D4×#14268632 #28402247

Subgroups — D4×#14268632 #28402247

Order 14464.

620 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14268632C212yesmaximal, complemented
2D4×D452C211yesmaximal, characteristic, complemented
3#20298974C211yesmaximal, characteristic, complemented
4#20298832C212yesmaximal, complemented
5#20298793C211yesmaximal, characteristic, complemented
6#20298790C211yesmaximal, characteristic, complemented
7#20298732C212yesmaximal, complemented
8#20298731C212yesmaximal, complemented
9C4×#14268632C211yesmaximal, characteristic, complemented
10D4×#11744751C211yesmaximal, characteristic, complemented
11D42×C113C211yesmaximal, characteristic, complemented
12C22×D452C2212yescomplemented
13C2×D4×D113—21no—
14C2×#14268632—28no—
15C2×#14268632C2211yescharacteristic
16C2×#14268632C2212yescomplemented
17C2×#14268632C2212yescomplemented
18C2×#14268632C2212yescomplemented
19C2×#14268632C2212yescomplemented
20C22×#11744751C2212yescomplemented
21#16813619C2211yescharacteristic, complemented
22#16813597—21no—
23#16813596C2212yescomplemented
24#16813592—22no—
25C4×D452C2211yescharacteristic, complemented
26#16813555C2211yescharacteristic, complemented
27C4⋊#11744751C2211yescharacteristic, complemented
28#16813543C2212yescomplemented
29#16813543C2211yescharacteristic, complemented
30#16813542C2212yescomplemented
31#16813542C2211yescharacteristic, complemented
32C22⋊#11744751C2212yescomplemented
33C4×#11744751C2211yescharacteristic, complemented
34C22×D4×C113—21no—
35C22×D4×C113C2212yescomplemented
36#127×C113C2211yescharacteristic, complemented
37#121×C113—21no—
38#121×C113C2212yescomplemented
39#120×C113—22no—
40C4×D4×C113C2211yescharacteristic
41C4×D4×C113C2211yescharacteristic, complemented
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#14268632—24no—
54#14268632—24no—
55#14268632—24no—
56#14268632—42no—
57#14268632D414yesdirect product factor
58C2×#11744751—24no—
59C2×#11744751C2312yes—
60C2×#11744751C2311yescharacteristic
61C2×#11744751C2311yescharacteristic
62C4⋊Dic113C2311yescharacteristic
63#14268624—21no—
64#14268624—22no—
65C24×C113—22no—
66C2×D4×C113—24no—
67C2×D4×C113—22no—
68C2×D4×C113—22no—
69C2×D4×C113—21no—
70C2×D4×C113—21no—
71C2×D4×C113—42no—
72C2×D4×C113—44no—
73C2×D4×C113D411yescharacteristic
74C2×D4×C113C2312yes—
75C2×D4×C113C2311yescharacteristic
76C22×C4×C113—21no—
77C22×C4×C113C2312yes—
78C4⋊C4×C113D411yescharacteristic
79C4⋊C4×C113C2311yescharacteristic
80C22⋊C4×C113—21no—
81C22⋊C4×C113—22no—
82C22⋊C4×C113D412yes—
83C42×C113C2311yescharacteristic
84C23×C113—21no—
85C23×C113—22no—
86C23×C113—44no—
87C23×C113—44no—
88C23×C113—82no—
89C23×C113C2×D412yes—
90C22×D113—21no—
91C22×D113—22no—
92C22×D113—44no—
93C22×D113—44no—
94C22×D113—82no—
95D4×C113—22no—
96D4×C113—21no—
97D4×C113—22no—
98D4×C113—44no—
99D4×C113—44no—
100D4×C113—42no—
101D4×C113—81no—
102D4×C113D814yescomplemented
103D4×C113C2×D412yescomplemented
104C2×C4×C113—22no—
105C2×C4×C113—22no—
106C2×C4×C113—21no—
107C2×C4×C113—42no—
108C2×C4×C113C2×D411yescharacteristic
109C2×C4×C113C2×D412yes—
110C2×C4×C113C2×D411yescharacteristic
111C2×C4×C113C2411yescharacteristic
112C22⋊D113—44no—
113C2×Dic113—21no—
114D452—22no—
115D452—21no—
116D452—22no—
117D452—44no—
118D452—42no—
119D452—81no—
120D452C2×D412yescomplemented
121C4×D113—42no—
122#11744751—22no—
123#11744751—21no—
124#11744751C2×D412yescomplemented
125C22×C113—22no—
126C22×C113—22no—
127C22×C113—22no—
128C22×C113—41no—
129C22×C113—41no—
130C22×C113—42no—
131C22×C113—42no—
132C22×C113—42no—
133C22×C113—88no—
134C22×C113C2×D814yescomplemented
135C22×C113C22×D411yescharacteristic
136C2×D113—22no—
137C2×D113—41no—
138C2×D113—41no—
139C2×D113—42no—
140C2×D113—42no—
141C2×D113—42no—
142C2×D113—88no—
143C4×C113—22no—
144C4×C113—21no—
145C4×C113—41no—
146C4×C113C2×D812yescomplemented
147C4×C113C22×D411yescharacteristic
148C4×C113H(5,𝔽2)11yescharacteristic
149Dic113—41no—
150C2×C113—24no—
151C2×C113—42no—
152C2×C113—82no—
153C2×C113D4211yescharacteristic
154C2×C113C22×D811yescharacteristic
155C2×C113#57611yescharacteristic
156D113—42no—
157D113—82no—
158D4×D8—1131nomaximal, Sylow
159C113D4×D811yescharacteristic, complemented, Sylow
160C22×D8—1132no—
161D42—1131no—
162D42D11311yescharacteristic, complemented
163#493—1131no—
164#466—1132no—
165#459—1131no—
166#459—1131no—
167#447—1132no—
168#447—1132no—
169C4×D8—1131no—
170C8×D4—1131no—
171C22×D4—21no—
172C22×D4—1132no—
173C22×D4—2261no—
174C22×D4C2×D11312yescomplemented
175C2×D8—1131no—
176C2×D8—1132no—
177C2×D8—1132no—
178C2×D8—1132no—
179C2×D8—1132no—
180C2×D8—2268no—
181C22×C8—1132no—
182#127—1131no—
183#127C2×D11311yescharacteristic, complemented
184#121—21no—
185#121—1132no—
186#121—2261no—
187#121C2×D11312yescomplemented
188#120—22no—
189#120—2262no—
190C4×D4—1131no—
191C4×D4C2×D11311yescharacteristic
192C4×D4C2×D11311yescharacteristic, complemented
193#107—1131no—
194C4⋊C8—1131no—
195#102—1131no—
196#102—1132no—
197#102—1131no—
198#102—1132no—
199C22⋊C8—1132no—
200C4×C8—1131no—
201C24—22no—
202C24—2262no—
203C2×D4—24no—
204C2×D4—22no—
205C2×D4—22no—
206C2×D4—21no—
207C2×D4—21no—
208C2×D4—42no—
209C2×D4—44no—
210C2×D4—1131no—
211C2×D4—1132no—
212C2×D4—4522no—
213C2×D4—4524no—
214C2×D4—2264no—
215C2×D4—2262no—
216C2×D4—2261no—
217C2×D4—2262no—
218C2×D4—2261no—
219C2×D4C22⋊D11311yescharacteristic
220C2×D4C22×D11312yes—
221C2×D4C22×D11311yescharacteristic
222C22×C4—21no—
223C22×C4—2261no—
224C22×C4C22×D11312yes—
225D8—1134no—
226D8—4522no—
227D8—2264no—
228D8—2264no—
229D8—2264no—
230C2×C8—1131no—
231C2×C8—1131no—
232C2×C8—1132no—
233C2×C8—2264no—
234C4⋊C4—1131no—
235C4⋊C4C22⋊D11311yescharacteristic
236C4⋊C4C22×D11311yescharacteristic
237C22⋊C4—21no—
238C22⋊C4—22no—
239C22⋊C4—2261no—
240C22⋊C4—2262no—
241C22⋊C4C22⋊D11312yes—
242C42C22×D11311yescharacteristic
243C23—21no—
244C23—22no—
245C23—44no—
246C23—44no—
247C23—82no—
248C23—9042no—
249C23—4524no—
250C23—4524no—
251C23—2262no—
252C23—2261no—
253C23C2×C22⋊D11312yes—
254D4—22no—
255D4—21no—
256D4—22no—
257D4—44no—
258D4—44no—
259D4—42no—
260D4—81no—
261D4—1132no—
262D4—9041no—
263D4—4524no—
264D4—4524no—
265D4—4522no—
266D4—2262no—
267D4—2262no—
268D4—2261no—
269D4#1426863214yesdirect product factor
270D4D4×D11312yescomplemented
271C2×C4—22no—
272C2×C4—22no—
273C2×C4—21no—
274C2×C4—42no—
275C2×C4—4522no—
276C2×C4—2261no—
277C2×C4C2×C22⋊D11311yescharacteristic
278C2×C4C2×C22⋊D11312yes—
279C2×C4C2×C22⋊D11311yescharacteristic
280C2×C4C23×D11311yescharacteristic
281C8—1132no—
282C8—2262no—
283C8—2261no—
284C22—22no—
285C22—22no—
286C22—22no—
287C22—41no—
288C22—41no—
289C22—42no—
290C22—42no—
291C22—42no—
292C22—88no—
293C22—9048no—
294C22—4522no—
295C22—4522no—
296C22—4522no—
297C22—4521no—
298C22—4521no—
299C22—2262no—
300C22C2×#1426863214yescomplemented
301C22C22×C22⋊D11311yescharacteristic
302C4—21no—
303C4—22no—
304C4—41no—
305C4—4521no—
306C4C2×#1426863212yescomplemented
307C4C2×D4×D11311yescharacteristic
308C4#1681366711yescharacteristic
309C2—24no—
310C2—42no—
311C2—82no—
312C2—9042no—
313C2—4522no—
314C2D4×C22⋊D11311yescharacteristic
315C2C22×#1426863211yescharacteristic
316C2#2029940111yescharacteristic
subgroupG/H
centerC22C22×C22⋊D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingD42×C113C2
socleC22×C113C22×D4
hypercenterD42D113
hypocenterC113D4×D8
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. C22×#14268632C2semidirect
2. D4×D452C2semidirect
3. #20298974C2semidirect
4. #20298832C2semidirect
5. #20298793C2semidirect
6. #20298790C2semidirect
7. #20298732C2semidirect
8. #20298731C2semidirect
9. C4×#14268632C2semidirect
10. D4×#11744751C2semidirect
11. D42×C113C2semidirect
12. C22×D452C22semidirect
16. C2×#14268632C22semidirect
17. C2×#14268632C22semidirect
18. C2×#14268632C22semidirect
19. C2×#14268632C22semidirect
20. C22×#11744751C22semidirect
21. #16813619C22semidirect
23. #16813596C22semidirect
25. C4×D452C22semidirect
26. #16813555C22semidirect
27. C4⋊#11744751C22semidirect
28. #16813543C22semidirect
29. #16813543C22semidirect
30. #16813542C22semidirect
31. #16813542C22semidirect
32. C22⋊#11744751C22semidirect
33. C4×#11744751C22semidirect
35. C22×D4×C113C22semidirect
36. #127×C113C22semidirect
38. #121×C113C22semidirect
41. C4×D4×C113C22semidirect
57. #14268632D4direct (N × H)
102. D4×C113D8semidirect
103. D4×C113C2×D4semidirect
120. D452C2×D4semidirect
124. #11744751C2×D4semidirect
134. C22×C113C2×D8semidirect
146. C4×C113C2×D8semidirect
159. C113D4×D8semidirect
162. D42D113semidirect
174. C22×D4C2×D113semidirect
183. #127C2×D113semidirect
187. #121C2×D113semidirect
192. C4×D4C2×D113semidirect
269. D4#14268632direct (N × H)
270. D4D4×D113semidirect
300. C22C2×#14268632semidirect
306. C4C2×#14268632semidirect

Maximal subgroups

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

subgroupindex
C22×#142686322
D4×D4522
#202989742
#202988322
#202987932
#202987902
#202987322
#202987312
C4×#142686322
D4×#117447512
D42×C1132
D4×D8113