Finite Group Databasebeta

← #489×D293 #49169111

Subgroups — #489×D293 #49169111

Order 37504.

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×D293C211yesmaximal, characteristic, complemented
2#124×D293C211yesmaximal, characteristic
3#34036491C211yesmaximal, characteristic, complemented
4#34036490C212yesmaximal, complemented
5#34036489C211yesmaximal, characteristic, complemented
6#34036488C211yesmaximal, characteristic, complemented
7#34036487C212yesmaximal, complemented
8#103×D293C212yesmaximal, complemented
9#102×D293C212yesmaximal
10#97×D293C211yesmaximal, characteristic, complemented
11#489×C293C211yesmaximal, characteristic, complemented
12C2×Q8×D293—21no—
13C2×Q8×D293C2211yescharacteristic
14C2×D4×D293C2211yescharacteristic
15C2×C8×D293C2212yes—
16#22627624C2211yescharacteristic, complemented
17#22627623—21no—
18#22627623C2212yescomplemented
19#22627622—21no—
20#22627613C2211yescharacteristic
21#22627612C2211yescharacteristic
22#22627611C2211yescharacteristic
23#22627610—21no—
24#22627610—21no—
25C4⋊C4×D293—21no—
26C4⋊C4×D293C2212yes—
27C22⋊C4×D293—21no—
28C22⋊C4×D293—21no—
29C42×D293C2211yescharacteristic
30#22627549C2212yescomplemented
31#22627548C2212yescomplemented
32#22627547C2212yescomplemented
33#22627546C2212yes—
34#22627545C2212yes—
35#22627544C2212yes—
36#22627535C2211yescharacteristic, complemented
37#22627534C2212yescomplemented
38C4⋊Q8×C293C2211yescharacteristic, complemented
39#124×C293C2211yescharacteristic
40#103×C293C2212yescomplemented
41#102×C293C2212yes—
42#97×C293C2211yescharacteristic, complemented
43C23×D293—21no—
44C2×Dic586—21no—
45C2×Dic586—22no—
46C2×Dic586—21no—
47C2×Dic586C2311yescharacteristic
48Q8×D293—24no—
49Q8×D293—44no—
50C2×D1172C2311yescharacteristic
51C2×C22⋊D293—21no—
52D4×D293—24no—
53C2×C4×D293—22no—
54C2×C4×D293—21no—
55C2×C4×D293D411yescharacteristic
56C2×C4×D293D411yescharacteristic
57C2×C4×D293C2311yescharacteristic
58C2×#14556873C2312yes—
59C8×D293—24no—
60C4⋊Dic293—21no—
61C4⋊Dic293C2312yes—
62#17989781—22no—
63#17989781—22no—
64C22⋊Dic293—21no—
65C22⋊Dic293—21no—
66#17989779—21no—
67#17989779—21no—
68#17989779—21no—
69#17989779—21no—
70C4×Dic293D411yescharacteristic
71C4×Dic293D411yescharacteristic
72C4×Dic293C2311yescharacteristic
73C2×Q8×C293—21no—
74C2×Q8×C293C2311yescharacteristic
75C2×D4×C293C2311yescharacteristic
76C2×C8×C293C2312yes—
77C4⋊C4×C293—21no—
78C4⋊C4×C293C2312yes—
79C22⋊C4×C293—21no—
80C22⋊C4×C293—21no—
81C42×C293C2311yescharacteristic
82C22×D293—21no—
83C22×D293—42no—
84C22×D293—42no—
85C22×D293—42no—
86C22×D293C2×D411yescharacteristic
87Dic586—22no—
88Dic586—44no—
89Dic586—42no—
90Dic586—42no—
91D1172—22no—
92C22⋊D293—42no—
93C2×Dic293—21no—
94C2×Dic293—22no—
95C2×Dic293C2×D411yescharacteristic
96C2×Dic293C2×D411yescharacteristic
97C2×Dic293C2×D411yescharacteristic
98C4×D293—22no—
99C4×D293—22no—
100C4×D293—42no—
101C4×D293—44no—
102C4×D293#4114yes—
103#14556873—22no—
104C23×C293—21no—
105Q8×C293—22no—
106Q8×C293—42no—
107D4×C293—22no—
108C2×C4×C293—21no—
109C2×C4×C293—22no—
110C2×C4×C293C2×D411yescharacteristic
111C2×C4×C293C2×D411yescharacteristic
112C2×C4×C293C2411yescharacteristic
113C8×C293—22no—
114C22×C293—41no—
115C22×C293—41no—
116C22×C293—41no—
117C22×C293C22×D411yescharacteristic
118C2×D293—41no—
119C2×D293—41no—
120C2×D293—41no—
121C2×D293—84no—
122C2×D293#12412yes—
123C2×D293AGL(1,ℤ/8)12yes—
124C2×D293#13712yes—
125C4×C293—21no—
126C4×C293—21no—
127C4×C293—41no—
128C4×C293—42no—
129C4×C293C2×#4112yes—
130Dic293—21no—
131Dic293—21no—
132Dic293—41no—
133Dic293—42no—
134Dic293#12412yes—
135C2×C293—81no—
136C2×C293C2×#12411yescharacteristic
137C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C293C2×#13711yescharacteristic
139D293—81no—
140D293#48914yesdirect product factor
141C293C2×#48911yescharacteristic, complemented, Sylow
142C2×#489—2931nomaximal, Sylow
143C2×C4⋊Q8—2931no—
144C2×#124—2931no—
145#489—2931no—
146#489—2931no—
147#489—2932no—
148#489—2932no—
149#489—2931no—
150#489D29311yescharacteristic, direct product factor
151C2×#103—2932no—
152C2×#102—2932no—
153C2×#97—2931no—
154C22×Q8—2931no—
155C22×Q8—5861no—
156C22×D4—2931no—
157C22×C8—2932no—
158C4⋊Q8—2932no—
159C4⋊Q8—2931no—
160C4⋊Q8—5861no—
161C4⋊Q8—5861no—
162C4⋊Q8C2×D29311yescharacteristic, complemented
163#124—2931no—
164#124—2931no—
165#124—2931no—
166#124—5861no—
167#124—5861no—
168#124C2×D29311yescharacteristic
169C2×C4⋊C4—2932no—
170C2×C4⋊C4—5861no—
171C2×C22⋊C4—5861no—
172C2×C22⋊C4—5861no—
173C2×C42—2931no—
174#103—2932no—
175#103—2932no—
176#103—2932no—
177#103C2×D29312yescomplemented
178#102—2932no—
179#102—2932no—
180#102—2932no—
181#102C2×D29312yes—
182#97—2932no—
183#97—2931no—
184#97C2×D29311yescharacteristic, complemented
185C24—5861no—
186C2×Q8—21no—
187C2×Q8—2931no—
188C2×Q8—5861no—
189C2×Q8—5862no—
190C2×Q8—5864no—
191C2×Q8—5861no—
192C2×Q8—11724no—
193C2×Q8C22×D29311yescharacteristic
194C2×D4—2931no—
195C2×D4—5864no—
196C2×D4—5861no—
197C2×D4C22×D29311yescharacteristic
198C22×C4—2931no—
199C22×C4—2931no—
200C22×C4—2931no—
201C22×C4—5861no—
202C22×C4—5862no—
203C2×C8—2932no—
204C2×C8—5864no—
205C2×C8C22×D29312yes—
206C4⋊C4—21no—
207C4⋊C4—2932no—
208C4⋊C4—5862no—
209C4⋊C4—5862no—
210C4⋊C4—5861no—
211C4⋊C4C22×D29312yes—
212C22⋊C4—21no—
213C22⋊C4—21no—
214C22⋊C4—5861no—
215C22⋊C4—5861no—
216C22⋊C4—5861no—
217C22⋊C4—5861no—
218C22⋊C4—5861no—
219C22⋊C4—5861no—
220C42—2931no—
221C42—2931no—
222C42—2931no—
223C42C22×D29311yescharacteristic
224C23—21no—
225C23—2931no—
226C23—5861no—
227C23—11722no—
228C23—11722no—
229C23—11722no—
230Q8—22no—
231Q8—42no—
232Q8—5862no—
233Q8—11722no—
234Q8—11722no—
235Q8—11724no—
236D4—22no—
237D4—5862no—
238D4—11722no—
239C2×C4—21no—
240C2×C4—22no—
241C2×C4—2931no—
242C2×C4—2934no—
243C2×C4—2931no—
244C2×C4—2931no—
245C2×C4—5862no—
246C2×C4—5862no—
247C2×C4—5861no—
248C2×C4—5862no—
249C2×C4—11722no—
250C2×C4—11724no—
251C2×C4D4×D29311yescharacteristic
252C2×C4D4×D29311yescharacteristic
253C2×C4C23×D29311yescharacteristic
254C8—22no—
255C8—5862no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—2932no—
260C22—2932no—
261C22—2932no—
262C22—23444no—
263C22—11721no—
264C22—11721no—
265C22—11721no—
266C22C2×D4×D29311yescharacteristic
267C4—21no—
268C4—21no—
269C4—41no—
270C4—42no—
271C4—2932no—
272C4—5861no—
273C4—5861no—
274C4—11721no—
275C4—11722no—
276C4#41×D29312yes—
277C2—81no—
278C2—2934no—
279C2—23441no—
280C2#124×D29311yescharacteristic
281C2AGL(1,ℤ/8)×D29311yescharacteristic
282C2#137×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#489×C293C2
socleC22×C293C22×D4
prime radicalC2×D4×D293C22
hypercenter#489D293
hypocenterC293C2×#489
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. C4⋊Q8×D293C2semidirect
3. #34036491C2semidirect
4. #34036490C2semidirect
5. #34036489C2semidirect
6. #34036488C2semidirect
7. #34036487C2semidirect
8. #103×D293C2semidirect
10. #97×D293C2semidirect
11. #489×C293C2semidirect
16. #22627624C22semidirect
18. #22627623C22semidirect
30. #22627549C22semidirect
31. #22627548C22semidirect
32. #22627547C22semidirect
36. #22627535C22semidirect
37. #22627534C22semidirect
38. C4⋊Q8×C293C22semidirect
40. #103×C293C22semidirect
42. #97×C293C22semidirect
140. D293#489direct (N × H)
141. C293C2×#489semidirect
150. #489D293direct (N × H)
162. C4⋊Q8C2×D293semidirect
177. #103C2×D293semidirect
184. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
C4⋊Q8×D2932
#124×D2932
#340364912
#340364902
#340364892
#340364882
#340364872
#103×D2932
#102×D2932
#97×D2932
#489×C2932
C2×#489293