Finite Group Databasebeta

← D4×#14558725 #34056389

Subgroups — D4×#14558725 #34056389

Order 19072.

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×#14558725C212yesmaximal, complemented
2D4×Dic298C211yesmaximal, characteristic, complemented
3D4×D596C211yesmaximal, characteristic
4#23749998C211yesmaximal, characteristic, complemented
5#23749854C212yesmaximal, complemented
6#23749831C211yesmaximal, characteristic, complemented
7#23749826C211yesmaximal, characteristic, complemented
8#23749778C212yesmaximal, complemented
9#23749766C212yesmaximal, complemented
10C4×#14558725C211yesmaximal, characteristic, complemented
11C8×D4×C149C211yesmaximal, characteristic, complemented
12C22×Dic298C2212yescomplemented
13C22×D596C2212yes—
14C2×D4×D149—21no—
15C2×#14558725—28no—
16C2×#14558725C2212yes—
17C2×#14558725C2211yescharacteristic
18C2×#14558725C2212yescomplemented
19C2×#14558725C2212yescomplemented
20C2×#14558725C2212yescomplemented
21#18011911C2211yescharacteristic, complemented
22#18011910—21no—
23#18011908C2211yescharacteristic
24#18011890C2212yescomplemented
25#18011888—22no—
26#18011886—21no—
27#18011885C2212yes—
28#18011881—22no—
29C4×Dic298C2211yescharacteristic, complemented
30C4×D596C2211yescharacteristic
31D4×Dic149—21no—
32#18011843C2211yescharacteristic, complemented
33#18011836C2211yescharacteristic, complemented
34#18011836C2212yescomplemented
35#18011833C2211yescharacteristic
36#18011833C2212yescomplemented
37C22×C8×C149C2212yescomplemented
38C4×D4×C149C2211yescharacteristic
39C4⋊C8×C149C2211yescharacteristic, complemented
40C22⋊C8×C149C2212yescomplemented
41C4×C8×C149C2211yescharacteristic, complemented
42C23×D149—22no—
43C2×Dic298—24no—
44C2×Dic298—22no—
45C2×Dic298—42no—
46C2×Dic298C2312yes—
47C2×Dic298C2311yescharacteristic
48C2×D596—24no—
49C2×D596—21no—
50C2×D596—22no—
51C2×D596—21no—
52C2×D596—42no—
53C2×D596C2312yes—
54C2×D596C2311yescharacteristic
55C2×C22⋊D149—22no—
56D4×D149—44no—
57C22×Dic149—22no—
58C2×C4×D149—21no—
59#14558725—24no—
60#14558725—24no—
61#14558725—24no—
62#14558725—42no—
63#14558725D414yesdirect product factor
64C4⋊Dic149—21no—
65C4⋊Dic149—21no—
66C4⋊Dic149C2311yescharacteristic
67C4⋊Dic149C2311yescharacteristic
68#14558715—22no—
69#14558715—21no—
70C22⋊Dic149—22no—
71#14558713—21no—
72#14558713—22no—
73C4×Dic149—21no—
74C2×D4×C149D411yescharacteristic
75C22×C4×C149C2312yes—
76C2×C8×C149—24no—
77C2×C8×C149C2312yes—
78C2×C8×C149C2311yescharacteristic
79C2×C8×C149C2311yescharacteristic
80C4⋊C4×C149D411yescharacteristic
81C22⋊C4×C149D412yes—
82C42×C149C2311yescharacteristic
83C22×D149—21no—
84C22×D149—22no—
85C22×D149—44no—
86C22×D149—44no—
87C22×D149—82no—
88Dic298—21no—
89Dic298—22no—
90Dic298—22no—
91Dic298—44no—
92Dic298C2×D412yescomplemented
93D596—22no—
94D596—21no—
95D596—22no—
96D596—44no—
97D596—42no—
98D596—81no—
99D596C2×D412yes—
100C22⋊D149—44no—
101C2×Dic149—21no—
102C2×Dic149—21no—
103C2×Dic149—22no—
104C2×Dic149—21no—
105C2×Dic149—44no—
106C4×D149—42no—
107C23×C149C2×D412yes—
108D4×C149SD1614yescomplemented
109C2×C4×C149—22no—
110C2×C4×C149—22no—
111C2×C4×C149C2×D412yes—
112C2×C4×C149C2×D411yescharacteristic
113C2×C4×C149C2×D411yescharacteristic
114C2×C4×C149C2411yescharacteristic
115C8×C149—22no—
116C8×C149—21no—
117C8×C149C2×D412yescomplemented
118C22×C149—22no—
119C22×C149—22no—
120C22×C149C2×SD1614yescomplemented
121C22×C149C22×D411yescharacteristic
122C2×D149—22no—
123C2×D149—41no—
124C2×D149—41no—
125C2×D149—42no—
126C2×D149—42no—
127C2×D149—42no—
128C2×D149—88no—
129C4×C149—22no—
130C4×C149—21no—
131C4×C149C2×SD1612yescomplemented
132C4×C149C22×D411yescharacteristic
133C4×C149H(5,𝔽2)11yescharacteristic
134Dic149—22no—
135Dic149—42no—
136Dic149—41no—
137Dic149—41no—
138C2×C149—24no—
139C2×C149D4211yescharacteristic
140C2×C149C22×SD1611yescharacteristic
141C2×C149#57711yescharacteristic
142D149—42no—
143D149—82no—
144C149D4×SD1611yescharacteristic, complemented, Sylow
145D4×SD16—1491nomaximal, Sylow
146C22×SD16—1492no—
147D4×Q8—1491no—
148D42—1491no—
149#492—1491no—
150#465—1492no—
151#461—1491no—
152#460—1491no—
153#450—1492no—
154#448—1492no—
155C4×SD16—1491no—
156C8×D4D14911yescharacteristic, complemented
157C22×Q8—1492no—
158C22×D4—2981no—
159C22×D4—1492no—
160C2×SD16—2988no—
161C2×SD16—1492no—
162C2×SD16—1492no—
163C2×SD16—1492no—
164C2×SD16—1492no—
165C2×SD16—1491no—
166C22×C8C2×D14912yescomplemented
167C4⋊Q8—2981no—
168C4⋊Q8—1491no—
169#127—1491no—
170C22⋊Q8—2982no—
171C22⋊Q8—1492no—
172#121—2981no—
173#121—1492no—
174#120—2982no—
175C4×Q8—1491no—
176C4×D4—2981no—
177C4×D4—1491no—
178C4×D4C2×D14911yescharacteristic
179#106—1491no—
180C4⋊C8C2×D14911yescharacteristic, complemented
181#103—1491no—
182#103—1492no—
183#102—1491no—
184#102—1492no—
185C22⋊C8C2×D14912yescomplemented
186C4×C8C2×D14911yescharacteristic, complemented
187C24—2982no—
188C2×Q8—2984no—
189C2×Q8—2982no—
190C2×Q8—5962no—
191C2×Q8—1492no—
192C2×Q8—1491no—
193C2×D4—2984no—
194C2×D4—2982no—
195C2×D4—2982no—
196C2×D4—2981no—
197C2×D4—2981no—
198C2×D4—5962no—
199C2×D4—5964no—
200C2×D4—1492no—
201C2×D4—1491no—
202C2×D4D59611yescharacteristic
203C22×C4—2982no—
204C22×C4—2981no—
205C22×C4C22×D14912yes—
206SD16—2984no—
207SD16—2984no—
208SD16—2984no—
209SD16—5962no—
210SD16—1494no—
211C2×C8—24no—
212C2×C8C22×D14911yescharacteristic
213C2×C8C22×D14912yes—
214C2×C8C22×D14911yescharacteristic
215C4⋊C4—2981no—
216C4⋊C4—2981no—
217C4⋊C4—2981no—
218C4⋊C4—2982no—
219C4⋊C4—1491no—
220C4⋊C4—1491no—
221C4⋊C4D59611yescharacteristic
222C22⋊C4—2982no—
223C22⋊C4—2981no—
224C22⋊C4—2982no—
225C22⋊C4D59612yes—
226C42—2981no—
227C42C22×D14911yescharacteristic
228C23—2981no—
229C23—2982no—
230C23—5964no—
231C23—5964no—
232C23—11922no—
233C23C2×D59612yes—
234Q8—2981no—
235Q8—2982no—
236Q8—2982no—
237Q8—5964no—
238Q8—1492no—
239D4—2982no—
240D4—2981no—
241D4—2982no—
242D4—5964no—
243D4—5964no—
244D4—5962no—
245D4—1492no—
246D4—11921no—
247D4#1455872514yesdirect product factor
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—2981no—
251C2×C4—2981no—
252C2×C4—2981no—
253C2×C4—2982no—
254C2×C4—5964no—
255C2×C4—5962no—
256C2×C4C2×D59611yescharacteristic
257C2×C4C2×D59612yes—
258C2×C4C2×D59611yescharacteristic
259C2×C4C23×D14911yescharacteristic
260C8—22no—
261C8—21no—
262C8D4×D14912yescomplemented
263C22—22no—
264C22—22no—
265C22—2982no—
266C22—5961no—
267C22—5961no—
268C22—5962no—
269C22—5962no—
270C22—5962no—
271C22—11928no—
272C22C2×#1455872514yescomplemented
273C22C22×D59611yescharacteristic
274C4—21no—
275C4—22no—
276C4—2982no—
277C4—5961no—
278C4—5962no—
279C4—5961no—
280C4C2×#1455872512yescomplemented
281C4C2×D4×D14911yescharacteristic
282C4#1801195711yescharacteristic
283C2—24no—
284C2—5962no—
285C2—11922no—
286C2D4×D59611yescharacteristic
287C2C22×#1455872511yescharacteristic
288C2#2375043711yescharacteristic
subgroupG/H
centerC22C22×D596
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
FittingC8×D4×C149C2
socleC22×C149C22×D4
prime radicalD4×D596C2
hypercenterC8×D4D149
hypocenterC149D4×SD16
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C4×D4 ◁ C8×D4

Complements

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

NH ≅ G/Ntype
1. C22×#14558725C2semidirect
2. D4×Dic298C2semidirect
4. #23749998C2semidirect
5. #23749854C2semidirect
6. #23749831C2semidirect
7. #23749826C2semidirect
8. #23749778C2semidirect
9. #23749766C2semidirect
10. C4×#14558725C2semidirect
11. C8×D4×C149C2semidirect
12. C22×Dic298C22semidirect
18. C2×#14558725C22semidirect
19. C2×#14558725C22semidirect
20. C2×#14558725C22semidirect
21. #18011911C22semidirect
24. #18011890C22semidirect
29. C4×Dic298C22semidirect
32. #18011843C22semidirect
33. #18011836C22semidirect
34. #18011836C22semidirect
36. #18011833C22semidirect
37. C22×C8×C149C22semidirect
39. C4⋊C8×C149C22semidirect
40. C22⋊C8×C149C22semidirect
41. C4×C8×C149C22semidirect
63. #14558725D4direct (N × H)
92. Dic298C2×D4semidirect
108. D4×C149SD16semidirect
117. C8×C149C2×D4semidirect
120. C22×C149C2×SD16semidirect
131. C4×C149C2×SD16semidirect
144. C149D4×SD16semidirect
156. C8×D4D149semidirect
166. C22×C8C2×D149semidirect
180. C4⋊C8C2×D149semidirect
185. C22⋊C8C2×D149semidirect
186. C4×C8C2×D149semidirect
247. D4#14558725direct (N × H)
262. C8D4×D149semidirect
272. C22C2×#14558725semidirect
280. C4C2×#14558725semidirect

Maximal subgroups

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

subgroupindex
C22×#145587252
D4×Dic2982
D4×D5962
#237499982
#237498542
#237498312
#237498262
#237497782
#237497662
C4×#145587252
C8×D4×C1492
D4×SD16149