Finite Group Databasebeta

← #49168920

Subgroups — #49168920

Order 37504.

450 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 450 conjugacy classes of subgroups — too many to draw. Only its 117 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
1#34036660C211yesmaximal, characteristic, complemented
2C2×#22627586C211yesmaximal, characteristic, complemented
3#34036459C211yesmaximal, characteristic, complemented
4#34036432C212yesmaximal, complemented
5#34036343C212yesmaximal, complemented
6#34036282C211yesmaximal, characteristic, complemented
7#34036262C211yesmaximal, characteristic
8#34036238C212yesmaximal, complemented
9#34036228C212yesmaximal, complemented
10#34036183C211yesmaximal, characteristic, complemented
11#480×C293C211yesmaximal, characteristic, complemented
12C22×D1172C2211yescharacteristic
13C22×C4×D293—21no—
14C2×#17989791C2212yes—
15C2×#17989787C2212yes—
16#22627617—21no—
17#22627615C2211yescharacteristic, complemented
18#22627611C2211yescharacteristic, complemented
19#22627605—21no—
20#22627603C2211yescharacteristic
21#22627589C2211yescharacteristic, complemented
22D4×Dic293—21no—
23D4×Dic293C2211yescharacteristic, complemented
24#22627586—21no—
25#22627586—21no—
26#22627586C2212yes—
27#22627586C2212yes—
28#22627580—21no—
29C2×#17989779—21no—
30C2×C4×Dic293C2211yescharacteristic
31#22627555C2212yescomplemented
32#22627553C2212yescomplemented
33#22627547C2212yescomplemented
34#22627546C2212yes—
35#22627544C2212yes—
36C22⋊#14556873C2211yescharacteristic
37#22627534C2212yescomplemented
38#121×C293C2211yescharacteristic
39C2×C4⋊C4×C293C2211yescharacteristic
40#107×C293C2212yescomplemented
41#102×C293C2212yescomplemented
42C22⋊C8×C293C2211yescharacteristic
43C23×D293—21no—
44C2×Dic586C2311yescharacteristic
45C2×D1172—24no—
46C2×D1172—21no—
47C2×D1172C2312yes—
48C22×Dic293—21no—
49C22×Dic293D411yescharacteristic
50C22×Dic293D411yescharacteristic
51C2×C4×D293—22no—
52C2×C4×D293—22no—
53C2×C4×D293—44no—
54#17989791—24no—
55#17989787—24no—
56C2×#14556873C2312yes—
57C4⋊Dic293—21no—
58C4⋊Dic293C2311yescharacteristic
59#17989781—21no—
60#17989781—21no—
61#17989781—21no—
62C22⋊Dic293—21no—
63C22⋊Dic293—21no—
64C22⋊Dic293—21no—
65C22⋊Dic293—21no—
66#17989779—22no—
67#17989779—22no—
68C4×Dic293—21no—
69C4×Dic293D411yescharacteristic
70C4×Dic293D411yescharacteristic
71C4×Dic293C2311yescharacteristic
72C4×Dic293C2311yescharacteristic
73C2×D4×C293—21no—
74C2×D4×C293C2311yescharacteristic
75C22×C4×C293—21no—
76C22×C4×C293C2311yescharacteristic
77C2×C8×C293C2312yes—
78C4⋊C4×C293—21no—
79C4⋊C4×C293C2312yes—
80C4⋊C4×C293C2311yescharacteristic
81C22⋊C4×C293—21no—
82C22×D293—24no—
83C22×D293—22no—
84C22×D293—42no—
85C22×D293—42no—
86Dic586—22no—
87D1172—24no—
88D1172—22no—
89D1172#4114yes—
90C2×Dic293—22no—
91C2×Dic293—21no—
92C2×Dic293—21no—
93C2×Dic293—41no—
94C2×Dic293—42no—
95C2×Dic293C2×D411yescharacteristic
96C2×Dic293C2×D411yescharacteristic
97C2×Dic293C2×D411yescharacteristic
98C2×Dic293C2×D411yescharacteristic
99C4×D293—44no—
100C4×D293—44no—
101#14556873—22no—
102C23×C293—21no—
103C23×C293C2×D411yescharacteristic
104D4×C293—22no—
105D4×C293—42no—
106C2×C4×C293—22no—
107C2×C4×C293—21no—
108C2×C4×C293—22no—
109C2×C4×C293—42no—
110C2×C4×C293C2×D411yescharacteristic
111C2×C4×C293C2411yescharacteristic
112C8×C293—22no—
113C22×C293—21no—
114C22×C293—21no—
115C22×C293—41no—
116C22×C293—41no—
117C22×C293—41no—
118C22×C293AGL(1,ℤ/8)12yes—
119C22×C293C22×D411yescharacteristic
120C2×D293—24no—
121C2×D293—48no—
122C2×D293—42no—
123C2×D293—42no—
124C4×C293—21no—
125C4×C293—42no—
126C4×C293—41no—
127C4×C293C2×#4112yes—
128Dic293—21no—
129Dic293—21no—
130Dic293—21no—
131Dic293—21no—
132Dic293—41no—
133Dic293—41no—
134C2×C293—22no—
135C2×C293—81no—
136C2×C293#52511yescharacteristic
137C2×C293C2×AGL(1,ℤ/8)11yescharacteristic
138C2×C293#57511yescharacteristic
139D293—44no—
140C293#311411yescharacteristic, complemented, Sylow
141#3114—2931nomaximal, Sylow
142#529—2931no—
143C2×C4×D4—2931no—
144#483—2931no—
145#480D29311yescharacteristic, complemented
146#478—2932no—
147#463—2932no—
148#450—2931no—
149#447—2931no—
150#442—2932no—
151#440—2932no—
152#432—2931no—
153C22×D4—2931no—
154C23×C4—5861no—
155C2×SD16—2932no—
156C2×D8—2932no—
157#126—5861no—
158#125—2931no—
159#124—2931no—
160#123—5861no—
161C22⋊Q8—2931no—
162#121C2×D29311yescharacteristic
163C4×Q8—2931no—
164C4×D4—2931no—
165C4×D4—2932no—
166C4×D4—2932no—
167C4×D4—5861no—
168C4×D4—5861no—
169C4×D4—5861no—
170#117—5861no—
171C2×C4⋊C4C2×D29311yescharacteristic
172C2×C22⋊C4—5861no—
173C2×C42—2931no—
174#107C2×D29312yescomplemented
175#106—2932no—
176C4⋊C8—2932no—
177#103—2932no—
178#102—2932no—
179#102—2932no—
180#102C2×D29312yescomplemented
181C22⋊C8—2931no—
182C22⋊C8C2×D29311yescharacteristic
183#97—2932no—
184C24—5861no—
185C2×Q8—2931no—
186C2×D4—21no—
187C2×D4—2932no—
188C2×D4—5864no—
189C2×D4—5861no—
190C2×D4C22×D29311yescharacteristic
191C22×C4—21no—
192C22×C4—2931no—
193C22×C4—2931no—
194C22×C4—5862no—
195C22×C4—5862no—
196C22×C4—5861no—
197C22×C4—11724no—
198C22×C4C22×D29311yescharacteristic
199SD16—5864no—
200D8—5864no—
201C2×C8—2932no—
202C2×C8C22×D29312yes—
203C4⋊C4—21no—
204C4⋊C4—2931no—
205C4⋊C4—5861no—
206C4⋊C4—5861no—
207C4⋊C4—5861no—
208C4⋊C4—5861no—
209C4⋊C4C22×D29311yescharacteristic
210C4⋊C4C22×D29312yes—
211C22⋊C4—21no—
212C22⋊C4—5862no—
213C22⋊C4—5862no—
214C22⋊C4—5861no—
215C22⋊C4—5861no—
216C22⋊C4—5861no—
217C22⋊C4—5861no—
218C42—2931no—
219C42—2931no—
220C42—2931no—
221C42—2931no—
222C42—5861no—
223C23—21no—
224C23—5864no—
225C23—5862no—
226C23—11722no—
227C23—11722no—
228C23D4×D29311yescharacteristic
229Q8—5862no—
230D4—22no—
231D4—42no—
232D4—2934no—
233D4—5864no—
234D4—5862no—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—42no—
239C2×C4—2931no—
240C2×C4—2931no—
241C2×C4—2931no—
242C2×C4—2931no—
243C2×C4—5862no—
244C2×C4—5861no—
245C2×C4—5861no—
246C2×C4—11724no—
247C2×C4—11724no—
248C2×C4—11721no—
249C2×C4—11722no—
250C2×C4D4×D29311yescharacteristic
251C2×C4C23×D29311yescharacteristic
252C8—22no—
253C8—5862no—
254C22—21no—
255C22—21no—
256C22—41no—
257C22—41no—
258C22—41no—
259C22—5864no—
260C22—11728no—
261C22—11722no—
262C22—11722no—
263C22#2262764812yes—
264C22C2×D4×D29311yescharacteristic
265C4—21no—
266C4—42no—
267C4—41no—
268C4—5861no—
269C4—5861no—
270C4—5861no—
271C4—5861no—
272C4—11721no—
273C4—11721no—
274C4#41×D29312yes—
275C2—22no—
276C2—81no—
277C2—11724no—
278C2#3403663711yescharacteristic
279C2C2×#2262764811yescharacteristic
280C2#3403692811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#480×C293C2
socleC22×C293C22×D4
prime radical#34036262C2
hypercenter#480D293
hypocenterC293#3114
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #34036660C2semidirect
2. C2×#22627586C2semidirect
3. #34036459C2semidirect
4. #34036432C2semidirect
5. #34036343C2semidirect
6. #34036282C2semidirect
8. #34036238C2semidirect
9. #34036228C2semidirect
10. #34036183C2semidirect
11. #480×C293C2semidirect
17. #22627615C22semidirect
18. #22627611C22semidirect
21. #22627589C22semidirect
23. D4×Dic293C22semidirect
31. #22627555C22semidirect
32. #22627553C22semidirect
33. #22627547C22semidirect
37. #22627534C22semidirect
40. #107×C293C22semidirect
41. #102×C293C22semidirect
140. C293#3114semidirect
145. #480D293semidirect
174. #107C2×D293semidirect
180. #102C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366602
C2×#226275862
#340364592
#340364322
#340363432
#340362822
#340362622
#340362382
#340362282
#340361832
#480×C2932
#3114293