Finite Group Databasebeta

← #489×D149 #34055017

Subgroups — #489×D149 #34055017

Order 19072.

436 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C4⋊Q8×D149C211yesmaximal, characteristic, complemented
2#124×D149C211yesmaximal, characteristic
3#23749987C211yesmaximal, characteristic, complemented
4#23749986C212yesmaximal, complemented
5#23749985C211yesmaximal, characteristic, complemented
6#23749984C211yesmaximal, characteristic, complemented
7#23749983C212yesmaximal, complemented
8#103×D149C212yesmaximal, complemented
9#102×D149C212yesmaximal
10#97×D149C211yesmaximal, characteristic, complemented
11#489×C149C211yesmaximal, characteristic, complemented
12C2×Q8×D149—21no—
13C2×Q8×D149C2211yescharacteristic
14C2×D4×D149C2211yescharacteristic
15C2×C8×D149C2212yes—
16#18011911C2211yescharacteristic, complemented
17#18011910—21no—
18#18011910C2212yescomplemented
19#18011909—21no—
20#18011900C2211yescharacteristic
21#18011899C2211yescharacteristic
22#18011898C2211yescharacteristic
23#18011897—21no—
24#18011897—21no—
25C4⋊C4×D149—21no—
26C4⋊C4×D149C2212yes—
27C22⋊C4×D149—21no—
28C22⋊C4×D149—21no—
29C42×D149C2211yescharacteristic
30#18011836C2212yescomplemented
31#18011835C2212yescomplemented
32#18011834C2212yescomplemented
33#18011833C2212yes—
34#18011832C2212yes—
35#18011831C2212yes—
36#18011822C2211yescharacteristic, complemented
37#18011821C2212yescomplemented
38C4⋊Q8×C149C2211yescharacteristic, complemented
39#124×C149C2211yescharacteristic
40#103×C149C2212yescomplemented
41#102×C149C2212yes—
42#97×C149C2211yescharacteristic, complemented
43C23×D149—21no—
44C2×Dic298—22no—
45C2×Dic298—21no—
46C2×Dic298—21no—
47C2×Dic298C2311yescharacteristic
48Q8×D149—24no—
49Q8×D149—44no—
50C2×D596C2311yescharacteristic
51C2×C22⋊D149—21no—
52D4×D149—24no—
53C2×C4×D149—22no—
54C2×C4×D149—21no—
55C2×C4×D149D411yescharacteristic
56C2×C4×D149D411yescharacteristic
57C2×C4×D149C2311yescharacteristic
58C2×#11924746C2312yes—
59C8×D149—24no—
60C4⋊Dic149—21no—
61C4⋊Dic149C2312yes—
62#14558715—22no—
63#14558715—22no—
64C22⋊Dic149—21no—
65C22⋊Dic149—21no—
66#14558713—21no—
67#14558713—21no—
68#14558713—21no—
69#14558713—21no—
70C4×Dic149D411yescharacteristic
71C4×Dic149D411yescharacteristic
72C4×Dic149C2311yescharacteristic
73C2×Q8×C149—21no—
74C2×Q8×C149C2311yescharacteristic
75C2×D4×C149C2311yescharacteristic
76C2×C8×C149C2312yes—
77C4⋊C4×C149—21no—
78C4⋊C4×C149C2312yes—
79C22⋊C4×C149—21no—
80C22⋊C4×C149—21no—
81C42×C149C2311yescharacteristic
82C22×D149—21no—
83C22×D149—42no—
84C22×D149—42no—
85C22×D149—42no—
86C22×D149C2×D411yescharacteristic
87Dic298—22no—
88Dic298—44no—
89Dic298—42no—
90Dic298—42no—
91D596—22no—
92C22⋊D149—42no—
93C2×Dic149—22no—
94C2×Dic149—21no—
95C2×Dic149C2×D411yescharacteristic
96C2×Dic149C2×D411yescharacteristic
97C2×Dic149C2×D411yescharacteristic
98C4×D149—22no—
99C4×D149—22no—
100C4×D149—42no—
101C4×D149—44no—
102C4×D149#4114yes—
103#11924746—22no—
104C23×C149—21no—
105Q8×C149—22no—
106Q8×C149—42no—
107D4×C149—22no—
108C2×C4×C149—21no—
109C2×C4×C149—22no—
110C2×C4×C149C2×D411yescharacteristic
111C2×C4×C149C2×D411yescharacteristic
112C2×C4×C149C2411yescharacteristic
113C8×C149—22no—
114C22×C149—41no—
115C22×C149—41no—
116C22×C149—41no—
117C22×C149C22×D411yescharacteristic
118C2×D149—41no—
119C2×D149—41no—
120C2×D149—41no—
121C2×D149—84no—
122C2×D149#12412yes—
123C2×D149AGL(1,ℤ/8)12yes—
124C2×D149#13712yes—
125C4×C149—21no—
126C4×C149—21no—
127C4×C149—41no—
128C4×C149—42no—
129C4×C149C2×#4112yes—
130Dic149—21no—
131Dic149—21no—
132Dic149—41no—
133Dic149—42no—
134Dic149#12412yes—
135C2×C149—81no—
136C2×C149C2×#12411yescharacteristic
137C2×C149C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C149C2×#13711yescharacteristic
139D149—81no—
140D149#48914yesdirect product factor
141C149C2×#48911yescharacteristic, complemented, Sylow
142C2×#489—1491nomaximal, Sylow
143C2×C4⋊Q8—1491no—
144C2×#124—1491no—
145#489—1491no—
146#489—1491no—
147#489—1492no—
148#489—1492no—
149#489—1491no—
150#489D14911yescharacteristic, direct product factor
151C2×#103—1492no—
152C2×#102—1492no—
153C2×#97—1491no—
154C22×Q8—2981no—
155C22×Q8—1491no—
156C22×D4—1491no—
157C22×C8—1492no—
158C4⋊Q8—2981no—
159C4⋊Q8—2981no—
160C4⋊Q8—1492no—
161C4⋊Q8—1491no—
162C4⋊Q8C2×D14911yescharacteristic, complemented
163#124—2981no—
164#124—2981no—
165#124—1491no—
166#124—1491no—
167#124—1491no—
168#124C2×D14911yescharacteristic
169C2×C4⋊C4—2981no—
170C2×C4⋊C4—1492no—
171C2×C22⋊C4—2981no—
172C2×C22⋊C4—2981no—
173C2×C42—1491no—
174#103—1492no—
175#103—1492no—
176#103—1492no—
177#103C2×D14912yescomplemented
178#102—1492no—
179#102—1492no—
180#102—1492no—
181#102C2×D14912yes—
182#97—1492no—
183#97—1491no—
184#97C2×D14911yescharacteristic, complemented
185C24—2981no—
186C2×Q8—21no—
187C2×Q8—2981no—
188C2×Q8—2982no—
189C2×Q8—2981no—
190C2×Q8—2984no—
191C2×Q8—5964no—
192C2×Q8—1491no—
193C2×Q8C22×D14911yescharacteristic
194C2×D4—2984no—
195C2×D4—2981no—
196C2×D4—1491no—
197C2×D4C22×D14911yescharacteristic
198C22×C4—2981no—
199C22×C4—2982no—
200C22×C4—1491no—
201C22×C4—1491no—
202C22×C4—1491no—
203C2×C8—2984no—
204C2×C8—1492no—
205C2×C8C22×D14912yes—
206C4⋊C4—21no—
207C4⋊C4—2982no—
208C4⋊C4—2982no—
209C4⋊C4—2981no—
210C4⋊C4—1492no—
211C4⋊C4C22×D14912yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—2981no—
215C22⋊C4—2981no—
216C22⋊C4—2981no—
217C22⋊C4—2981no—
218C22⋊C4—2981no—
219C22⋊C4—2981no—
220C42—1491no—
221C42—1491no—
222C42—1491no—
223C42C22×D14911yescharacteristic
224C23—21no—
225C23—2981no—
226C23—5962no—
227C23—5962no—
228C23—5962no—
229C23—1491no—
230Q8—22no—
231Q8—42no—
232Q8—2982no—
233Q8—5962no—
234Q8—5964no—
235Q8—5962no—
236D4—22no—
237D4—2982no—
238D4—5962no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—2982no—
242C2×C4—2982no—
243C2×C4—2981no—
244C2×C4—2982no—
245C2×C4—5962no—
246C2×C4—5964no—
247C2×C4—1491no—
248C2×C4—1491no—
249C2×C4—1491no—
250C2×C4—1494no—
251C2×C4D4×D14911yescharacteristic
252C2×C4D4×D14911yescharacteristic
253C2×C4C23×D14911yescharacteristic
254C8—22no—
255C8—2982no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—5961no—
260C22—5961no—
261C22—5961no—
262C22—1492no—
263C22—1492no—
264C22—1492no—
265C22—11924no—
266C22C2×D4×D14911yescharacteristic
267C4—21no—
268C4—21no—
269C4—42no—
270C4—41no—
271C4—2981no—
272C4—2981no—
273C4—5962no—
274C4—5961no—
275C4—1492no—
276C4#41×D14912yes—
277C2—81no—
278C2—1494no—
279C2—11921no—
280C2#124×D14911yescharacteristic
281C2AGL(1,ℤ/8)×D14911yescharacteristic
282C2#137×D14911yescharacteristic
subgroupG/H
centerC22C2×D4×D149
commutator, cosocleC2×C4×C149C24
FrattiniC2×C4C23×D149
Fitting#489×C149C2
socleC22×C149C22×D4
prime radicalC2×D4×D149C22
hypercenter#489D149
hypocenterC149C2×#489
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D149C2semidirect
3. #23749987C2semidirect
4. #23749986C2semidirect
5. #23749985C2semidirect
6. #23749984C2semidirect
7. #23749983C2semidirect
8. #103×D149C2semidirect
10. #97×D149C2semidirect
11. #489×C149C2semidirect
16. #18011911C22semidirect
18. #18011910C22semidirect
30. #18011836C22semidirect
31. #18011835C22semidirect
32. #18011834C22semidirect
36. #18011822C22semidirect
37. #18011821C22semidirect
38. C4⋊Q8×C149C22semidirect
40. #103×C149C22semidirect
42. #97×C149C22semidirect
140. D149#489direct (N × H)
141. C149C2×#489semidirect
150. #489D149direct (N × H)
162. C4⋊Q8C2×D149semidirect
177. #103C2×D149semidirect
184. #97C2×D149semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D1492
#124×D1492
#237499872
#237499862
#237499852
#237499842
#237499832
#103×D1492
#102×D1492
#97×D1492
#489×C1492
C2×#489149