Finite Group Databasebeta

← D4×#14578943 #34111834

Subgroups — D4×#14578943 #34111834

Order 20096.

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

normal subgroups only

This group has 546 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×#14578943C212yesmaximal, complemented
2D4×Dic314C211yesmaximal, characteristic, complemented
3D4×D628C211yesmaximal, characteristic
4#23757646C211yesmaximal, characteristic, complemented
5#23757502C212yesmaximal, complemented
6#23757479C211yesmaximal, characteristic, complemented
7#23757474C211yesmaximal, characteristic, complemented
8#23757426C212yesmaximal, complemented
9#23757414C212yesmaximal, complemented
10C4×#14578943C211yesmaximal, characteristic, complemented
11C8×D4×C157C211yesmaximal, characteristic, complemented
12C22×Dic314C2212yescomplemented
13C22×D628C2212yes—
14C2×D4×D157—21no—
15C2×#14578943—28no—
16C2×#14578943C2212yes—
17C2×#14578943C2211yescharacteristic
18C2×#14578943C2212yescomplemented
19C2×#14578943C2212yescomplemented
20C2×#14578943C2212yescomplemented
21#19097771C2211yescharacteristic, complemented
22#19097770—21no—
23#19097768C2211yescharacteristic
24#19097750C2212yescomplemented
25#19097748—22no—
26#19097746—21no—
27#19097745C2212yes—
28#19097741—22no—
29C4×Dic314C2211yescharacteristic, complemented
30C4×D628C2211yescharacteristic
31D4×Dic157—21no—
32#19097703C2211yescharacteristic, complemented
33#19097696C2211yescharacteristic, complemented
34#19097696C2212yescomplemented
35#19097693C2211yescharacteristic
36#19097693C2212yescomplemented
37C22×C8×C157C2212yescomplemented
38C4×D4×C157C2211yescharacteristic
39C4⋊C8×C157C2211yescharacteristic, complemented
40C22⋊C8×C157C2212yescomplemented
41C4×C8×C157C2211yescharacteristic, complemented
42C23×D157—22no—
43C2×Dic314—24no—
44C2×Dic314—22no—
45C2×Dic314—42no—
46C2×Dic314C2312yes—
47C2×Dic314C2311yescharacteristic
48C2×D628—24no—
49C2×D628—22no—
50C2×D628—21no—
51C2×D628—21no—
52C2×D628—42no—
53C2×D628C2312yes—
54C2×D628C2311yescharacteristic
55C2×C22⋊D157—22no—
56D4×D157—44no—
57C22×Dic157—22no—
58C2×C4×D157—21no—
59#14578943—24no—
60#14578943—24no—
61#14578943—24no—
62#14578943—42no—
63#14578943D414yesdirect product factor
64C4⋊Dic157—21no—
65C4⋊Dic157—21no—
66C4⋊Dic157C2311yescharacteristic
67C4⋊Dic157C2311yescharacteristic
68#14578933—21no—
69#14578933—22no—
70C22⋊Dic157—22no—
71#14578931—21no—
72#14578931—22no—
73C4×Dic157—21no—
74C2×D4×C157D411yescharacteristic
75C22×C4×C157C2312yes—
76C2×C8×C157—24no—
77C2×C8×C157C2311yescharacteristic
78C2×C8×C157C2312yes—
79C2×C8×C157C2311yescharacteristic
80C4⋊C4×C157D411yescharacteristic
81C22⋊C4×C157D412yes—
82C42×C157C2311yescharacteristic
83C22×D157—21no—
84C22×D157—22no—
85C22×D157—44no—
86C22×D157—44no—
87C22×D157—82no—
88Dic314—21no—
89Dic314—22no—
90Dic314—22no—
91Dic314—44no—
92Dic314C2×D412yescomplemented
93D628—22no—
94D628—21no—
95D628—22no—
96D628—44no—
97D628—42no—
98D628—81no—
99D628C2×D412yes—
100C22⋊D157—44no—
101C2×Dic157—21no—
102C2×Dic157—21no—
103C2×Dic157—22no—
104C2×Dic157—21no—
105C2×Dic157—44no—
106C4×D157—42no—
107C23×C157C2×D412yes—
108D4×C157SD1614yescomplemented
109C2×C4×C157—22no—
110C2×C4×C157—22no—
111C2×C4×C157C2×D412yes—
112C2×C4×C157C2×D411yescharacteristic
113C2×C4×C157C2×D411yescharacteristic
114C2×C4×C157C2411yescharacteristic
115C8×C157—22no—
116C8×C157—21no—
117C8×C157C2×D412yescomplemented
118C22×C157—22no—
119C22×C157—22no—
120C22×C157C2×SD1614yescomplemented
121C22×C157C22×D411yescharacteristic
122C2×D157—22no—
123C2×D157—41no—
124C2×D157—41no—
125C2×D157—42no—
126C2×D157—42no—
127C2×D157—42no—
128C2×D157—88no—
129C4×C157—22no—
130C4×C157—21no—
131C4×C157C2×SD1612yescomplemented
132C4×C157C22×D411yescharacteristic
133C4×C157H(5,𝔽2)11yescharacteristic
134Dic157—22no—
135Dic157—42no—
136Dic157—41no—
137Dic157—41no—
138C2×C157—24no—
139C2×C157D4211yescharacteristic
140C2×C157C22×SD1611yescharacteristic
141C2×C157#57711yescharacteristic
142D157—42no—
143D157—82no—
144C157D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1571nomaximal, Sylow
146C22×SD16—1572no—
147D4×Q8—1571no—
148D42—1571no—
149#492—1571no—
150#465—1572no—
151#461—1571no—
152#460—1571no—
153#450—1572no—
154#448—1572no—
155C4×SD16—1571no—
156C8×D4D15711yescharacteristic, complemented
157C22×Q8—1572no—
158C22×D4—3141no—
159C22×D4—1572no—
160C2×SD16—3148no—
161C2×SD16—1572no—
162C2×SD16—1572no—
163C2×SD16—1572no—
164C2×SD16—1572no—
165C2×SD16—1571no—
166C22×C8C2×D15712yescomplemented
167C4⋊Q8—3141no—
168C4⋊Q8—1571no—
169#127—1571no—
170C22⋊Q8—3142no—
171C22⋊Q8—1572no—
172#121—3141no—
173#121—1572no—
174#120—3142no—
175C4×Q8—1571no—
176C4×D4—3141no—
177C4×D4—1571no—
178C4×D4C2×D15711yescharacteristic
179#106—1571no—
180C4⋊C8C2×D15711yescharacteristic, complemented
181#103—1571no—
182#103—1572no—
183#102—1571no—
184#102—1572no—
185C22⋊C8C2×D15712yescomplemented
186C4×C8C2×D15711yescharacteristic, complemented
187C24—3142no—
188C2×Q8—3144no—
189C2×Q8—3142no—
190C2×Q8—6282no—
191C2×Q8—1572no—
192C2×Q8—1571no—
193C2×D4—3144no—
194C2×D4—3142no—
195C2×D4—3142no—
196C2×D4—3141no—
197C2×D4—3141no—
198C2×D4—6282no—
199C2×D4—6284no—
200C2×D4—1572no—
201C2×D4—1571no—
202C2×D4D62811yescharacteristic
203C22×C4—3142no—
204C22×C4—3141no—
205C22×C4C22×D15712yes—
206SD16—3144no—
207SD16—3144no—
208SD16—3144no—
209SD16—6282no—
210SD16—1574no—
211C2×C8—24no—
212C2×C8C22×D15711yescharacteristic
213C2×C8C22×D15712yes—
214C2×C8C22×D15711yescharacteristic
215C4⋊C4—3141no—
216C4⋊C4—3141no—
217C4⋊C4—3141no—
218C4⋊C4—3142no—
219C4⋊C4—1571no—
220C4⋊C4—1571no—
221C4⋊C4D62811yescharacteristic
222C22⋊C4—3142no—
223C22⋊C4—3141no—
224C22⋊C4—3142no—
225C22⋊C4D62812yes—
226C42—3141no—
227C42C22×D15711yescharacteristic
228C23—3141no—
229C23—3142no—
230C23—6284no—
231C23—6284no—
232C23—12562no—
233C23C2×D62812yes—
234Q8—3141no—
235Q8—3142no—
236Q8—3142no—
237Q8—6284no—
238Q8—1572no—
239D4—3142no—
240D4—3141no—
241D4—3142no—
242D4—6284no—
243D4—6284no—
244D4—6282no—
245D4—1572no—
246D4—12561no—
247D4#1457894314yesdirect product factor
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—3141no—
251C2×C4—3141no—
252C2×C4—3141no—
253C2×C4—3142no—
254C2×C4—6284no—
255C2×C4—6282no—
256C2×C4C2×D62811yescharacteristic
257C2×C4C2×D62812yes—
258C2×C4C2×D62811yescharacteristic
259C2×C4C23×D15711yescharacteristic
260C8—22no—
261C8—21no—
262C8D4×D15712yescomplemented
263C22—22no—
264C22—22no—
265C22—3142no—
266C22—6281no—
267C22—6281no—
268C22—6282no—
269C22—6282no—
270C22—6282no—
271C22—12568no—
272C22C2×#1457894314yescomplemented
273C22C22×D62811yescharacteristic
274C4—21no—
275C4—22no—
276C4—3142no—
277C4—6281no—
278C4—6282no—
279C4—6281no—
280C4C2×#1457894312yescomplemented
281C4C2×D4×D15711yescharacteristic
282C4#1909781711yescharacteristic
283C2—24no—
284C2—6282no—
285C2—12562no—
286C2D4×D62811yescharacteristic
287C2C22×#1457894311yescharacteristic
288C2#2375808511yescharacteristic
subgroupG/H
centerC22C22×D628
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC8×D4×C157C2
socleC22×C157C22×D4
prime radicalD4×D628C2
hypercenterC8×D4D157
hypocenterC157D4×SD16
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14578943C2semidirect
2. D4×Dic314C2semidirect
4. #23757646C2semidirect
5. #23757502C2semidirect
6. #23757479C2semidirect
7. #23757474C2semidirect
8. #23757426C2semidirect
9. #23757414C2semidirect
10. C4×#14578943C2semidirect
11. C8×D4×C157C2semidirect
12. C22×Dic314C22semidirect
18. C2×#14578943C22semidirect
19. C2×#14578943C22semidirect
20. C2×#14578943C22semidirect
21. #19097771C22semidirect
24. #19097750C22semidirect
29. C4×Dic314C22semidirect
32. #19097703C22semidirect
33. #19097696C22semidirect
34. #19097696C22semidirect
36. #19097693C22semidirect
37. C22×C8×C157C22semidirect
39. C4⋊C8×C157C22semidirect
40. C22⋊C8×C157C22semidirect
41. C4×C8×C157C22semidirect
63. #14578943D4direct (N × H)
92. Dic314C2×D4semidirect
108. D4×C157SD16semidirect
117. C8×C157C2×D4semidirect
120. C22×C157C2×SD16semidirect
131. C4×C157C2×SD16semidirect
144. C157D4×SD16semidirect
156. C8×D4D157semidirect
166. C22×C8C2×D157semidirect
180. C4⋊C8C2×D157semidirect
185. C22⋊C8C2×D157semidirect
186. C4×C8C2×D157semidirect
247. D4#14578943direct (N × H)
262. C8D4×D157semidirect
272. C22C2×#14578943semidirect
280. C4C2×#14578943semidirect

Maximal subgroups

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

subgroupindex
C22×#145789432
D4×Dic3142
D4×D6282
#237576462
#237575022
#237574792
#237574742
#237574262
#237574142
C4×#145789432
C8×D4×C1572
D4×SD16157