Finite Group Databasebeta

← #483×D293 #49168659

Subgroups — #483×D293 #49168659

Order 37504.

460 conjugacy classes of subgroups; only the 135 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 135 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⋊Q8×D293C211yesmaximal, characteristic
2C2×C4⋊C4×D293C211yesmaximal, characteristic
3#34036461C212yesmaximal, complemented
4#34036460C211yesmaximal, characteristic, complemented
5#34036459C211yesmaximal, characteristic, complemented
6#34036458C212yesmaximal, complemented
7#34036457C211yesmaximal, characteristic, complemented
8#106×D293C212yesmaximal, complemented
9#103×D293C212yesmaximal, complemented
10C22⋊C8×D293C211yesmaximal, characteristic
11#483×C293C211yesmaximal, characteristic, complemented
12C2×Q8×D293C2211yescharacteristic
13C22×C4×D293—21no—
14C22×C4×D293C2211yescharacteristic
15C2×C8×D293C2212yes—
16#22627604C2211yescharacteristic
17#22627603C2211yescharacteristic
18#22627602—21no—
19#22627601—21no—
20#22627600C2211yescharacteristic
21C2×C4⋊Dic293C2211yescharacteristic
22C2×#17989781—21no—
23C4⋊C4×D293—21no—
24C4⋊C4×D293—21no—
25C4⋊C4×D293—21no—
26C4⋊C4×D293C2212yes—
27C4⋊C4×D293C2212yes—
28C4⋊C4×D293C2211yescharacteristic
29C22⋊C4×D293—21no—
30#22627556C2212yescomplemented
31#22627555C2212yescomplemented
32#22627555C2212yescomplemented
33#22627549C2212yescomplemented
34#22627548C2212yescomplemented
35#22627547C2212yescomplemented
36C22⋊#14556873C2211yescharacteristic
37#22627536C2212yes—
38C22⋊Q8×C293C2211yescharacteristic
39C2×C4⋊C4×C293C2211yescharacteristic
40#106×C293C2212yescomplemented
41#103×C293C2212yescomplemented
42C22⋊C8×C293C2211yescharacteristic
43C23×D293D411yescharacteristic
44C2×Dic586—21no—
45C2×Dic586C2311yescharacteristic
46Q8×D293—24no—
47C22×Dic293—21no—
48C22×Dic293D411yescharacteristic
49C2×C4×D293—24no—
50C2×C4×D293—22no—
51C2×C4×D293—22no—
52C2×C4×D293—21no—
53C2×C4×D293—21no—
54C2×C4×D293—44no—
55C2×C4×D293D411yescharacteristic
56C2×C4×D293D411yescharacteristic
57C2×C4×D293C2311yescharacteristic
58C2×C4×D293C2311yescharacteristic
59C2×#14556873C2312yes—
60C8×D293—24no—
61C4⋊Dic293—21no—
62C4⋊Dic293—21no—
63C4⋊Dic293C2311yescharacteristic
64C4⋊Dic293C2312yes—
65#17989781—21no—
66#17989781—21no—
67#17989781—22no—
68#17989781—22no—
69#17989781—21no—
70C22⋊Dic293—21no—
71#17989779—21no—
72#17989779—21no—
73C2×Q8×C293C2311yescharacteristic
74C22×C4×C293—21no—
75C22×C4×C293C2311yescharacteristic
76C2×C8×C293C2312yes—
77C4⋊C4×C293—21no—
78C4⋊C4×C293—21no—
79C4⋊C4×C293C2311yescharacteristic
80C4⋊C4×C293C2312yes—
81C22⋊C4×C293—21no—
82C22×D293—22no—
83C22×D293—22no—
84C22×D293SD1614yes—
85C22×D293C2×D411yescharacteristic
86C22×D293C2×D411yescharacteristic
87Dic586—22no—
88Dic586—42no—
89C2×Dic293—22no—
90C2×Dic293—21no—
91C2×Dic293—21no—
92C2×Dic293—22no—
93C2×Dic293—42no—
94C2×Dic293C2×D411yescharacteristic
95C2×Dic293C2×D411yescharacteristic
96C4×D293—22no—
97C4×D293—22no—
98C4×D293—22no—
99C4×D293—42no—
100C4×D293—44no—
101C4×D293—44no—
102C4×D293—42no—
103C4×D293#4114yes—
104#14556873—22no—
105C23×C293C2×D411yescharacteristic
106Q8×C293—22no—
107C2×C4×C293—22no—
108C2×C4×C293—21no—
109C2×C4×C293—21no—
110C2×C4×C293—22no—
111C2×C4×C293—42no—
112C2×C4×C293C2×D411yescharacteristic
113C2×C4×C293C2411yescharacteristic
114C8×C293—22no—
115C22×C293—21no—
116C22×C293—21no—
117C22×C293C2×SD1612yes—
118C22×C293C22×D411yescharacteristic
119C2×D293—21no—
120C2×D293—21no—
121C2×D293—28no—
122C2×D293#12312yes—
123C2×D293C2×SD1612yes—
124C2×D293C2×SD1612yes—
125C2×D293#13712yes—
126C4×C293—21no—
127C4×C293—41no—
128C4×C293—42no—
129C4×C293—41no—
130C4×C293C2×#4112yes—
131Dic293—21no—
132Dic293—41no—
133Dic293—42no—
134Dic293—41no—
135Dic293#12312yes—
136C2×C293—22no—
137C2×C293C2×#12311yescharacteristic
138C2×C293C22×SD1611yescharacteristic
139C2×C293C2×#13711yescharacteristic
140D293—22no—
141D293#48314yesdirect product factor
142C293C2×#48311yescharacteristic, complemented, Sylow
143C2×#483—2931nomaximal, Sylow
144C2×C22⋊Q8—2931no—
145C22×C4⋊C4—2931no—
146#483—2931no—
147#483—2931no—
148#483—2932no—
149#483—2932no—
150#483—2931no—
151#483D29311yescharacteristic, direct product factor
152C2×#106—2932no—
153C2×#103—2932no—
154C2×C22⋊C8—2931no—
155C22×Q8—2931no—
156C23×C4—2931no—
157C23×C4—5861no—
158C22×C8—2932no—
159C22⋊Q8—2931no—
160C22⋊Q8—2931no—
161C22⋊Q8—2931no—
162C22⋊Q8—5861no—
163C22⋊Q8—5861no—
164C22⋊Q8C2×D29311yescharacteristic
165C2×C4⋊C4—2931no—
166C2×C4⋊C4—2932no—
167C2×C4⋊C4—2932no—
168C2×C4⋊C4—2931no—
169C2×C4⋊C4—5861no—
170C2×C4⋊C4—5861no—
171C2×C4⋊C4—5861no—
172C2×C4⋊C4—5861no—
173C2×C4⋊C4C2×D29311yescharacteristic
174C2×C22⋊C4—5861no—
175#106—2932no—
176#106—2932no—
177#106—2932no—
178#106C2×D29312yescomplemented
179#103—2932no—
180#103—2932no—
181#103—2932no—
182#103C2×D29312yescomplemented
183C22⋊C8—2931no—
184C22⋊C8—2932no—
185C22⋊C8C2×D29311yescharacteristic
186C24—2931no—
187C2×Q8—2931no—
188C2×Q8—5861no—
189C2×Q8—5864no—
190C2×Q8C22×D29311yescharacteristic
191C22×C4—21no—
192C22×C4—2931no—
193C22×C4—2931no—
194C22×C4—2931no—
195C22×C4—2931no—
196C22×C4—2931no—
197C22×C4—5864no—
198C22×C4—5861no—
199C22×C4—5861no—
200C22×C4—5862no—
201C22×C4—5862no—
202C22×C4—5861no—
203C22×C4—11724no—
204C22×C4C22×D29311yescharacteristic
205C2×C8—2932no—
206C2×C8—5864no—
207C2×C8C22×D29312yes—
208C4⋊C4—21no—
209C4⋊C4—21no—
210C4⋊C4—2932no—
211C4⋊C4—2931no—
212C4⋊C4—5862no—
213C4⋊C4—5862no—
214C4⋊C4—5861no—
215C4⋊C4—5861no—
216C4⋊C4—5861no—
217C4⋊C4—5861no—
218C4⋊C4—5861no—
219C4⋊C4C22×D29312yes—
220C4⋊C4C22×D29311yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—5861no—
223C22⋊C4—5861no—
224C22⋊C4—5861no—
225C23—2931no—
226C23—2934no—
227C23—2931no—
228C23—5862no—
229C23—5862no—
230C23D4×D29311yescharacteristic
231Q8—22no—
232Q8—5862no—
233Q8—11722no—
234C2×C4—22no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—2931no—
240C2×C4—2934no—
241C2×C4—2931no—
242C2×C4—5862no—
243C2×C4—5862no—
244C2×C4—5862no—
245C2×C4—5862no—
246C2×C4—5861no—
247C2×C4—5861no—
248C2×C4—5862no—
249C2×C4—11724no—
250C2×C4—11724no—
251C2×C4—11722no—
252C2×C4—11722no—
253C2×C4—11722no—
254C2×C4D4×D29311yescharacteristic
255C2×C4C23×D29311yescharacteristic
256C8—22no—
257C8—5862no—
258C22—21no—
259C22—21no—
260C22—2932no—
261C22—2932no—
262C22—2932no—
263C22—2932no—
264C22—5868no—
265C22—5861no—
266C22—5861no—
267C22SD16×D29312yes—
268C22C2×D4×D29311yescharacteristic
269C4—21no—
270C4—41no—
271C4—42no—
272C4—41no—
273C4—2932no—
274C4—5861no—
275C4—11721no—
276C4—11722no—
277C4—11721no—
278C4#41×D29312yes—
279C2—22no—
280C2—2934no—
281C2—5862no—
282C2#123×D29311yescharacteristic
283C2C2×SD16×D29311yescharacteristic
284C2#137×D29311yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#483×C293C2
socleC22×C293C22×D4
prime radicalC23×D293D4
hypercenter#483D293
hypocenterC293C2×#483
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
3. #34036461C2semidirect
4. #34036460C2semidirect
5. #34036459C2semidirect
6. #34036458C2semidirect
7. #34036457C2semidirect
8. #106×D293C2semidirect
9. #103×D293C2semidirect
11. #483×C293C2semidirect
30. #22627556C22semidirect
31. #22627555C22semidirect
32. #22627555C22semidirect
33. #22627549C22semidirect
34. #22627548C22semidirect
35. #22627547C22semidirect
40. #106×C293C22semidirect
41. #103×C293C22semidirect
141. D293#483direct (N × H)
142. C293C2×#483semidirect
151. #483D293direct (N × H)
178. #106C2×D293semidirect
182. #103C2×D293semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D2932
C2×C4⋊C4×D2932
#340364612
#340364602
#340364592
#340364582
#340364572
#106×D2932
#103×D2932
C22⋊C8×D2932
#483×C2932
C2×#483293