Finite Group Databasebeta

← #49168699

Subgroups — #49168699

Order 37504.

420 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 121 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#34036642C211yesmaximal, characteristic
2C2×#22627582C211yesmaximal, characteristic, complemented
3#34036468C212yesmaximal, complemented
4#34036462C211yesmaximal, characteristic, complemented
5#34036455C212yesmaximal, complemented
6#34036448C211yesmaximal, characteristic, complemented
7#34036442C211yesmaximal, characteristic, complemented
8#34036164C212yesmaximal, complemented
9#34036124C212yesmaximal, complemented
10C22⋊C8×D293C211yesmaximal, characteristic, complemented
11#483×C293C211yesmaximal, characteristic, complemented
12C2×#17989803C2211yescharacteristic
13C22×C4×D293C2211yescharacteristic
14C2×C8×D293C2212yes—
15#22627609—21no—
16#22627600C2211yescharacteristic
17#22627599C2211yescharacteristic
18#22627598C2211yescharacteristic
19#22627594—21no—
20#22627586—21no—
21#22627584—21no—
22#22627582—21no—
23#22627582—21no—
24#22627582C2212yes—
25#22627582C2212yes—
26#22627582C2211yescharacteristic
27C2×C4⋊Dic293C2211yescharacteristic
28C2×#17989779—21no—
29C2×C4×Dic293—21no—
30#22627557C2212yescomplemented
31#22627557C2212yescomplemented
32#22627556C2212yescomplemented
33#22627548C2212yescomplemented
34#22627546C2212yescomplemented
35#22627544C2212yescomplemented
36C22⋊#14556873C2211yescharacteristic
37#22627536C2212yes—
38C22⋊Q8×C293C2211yescharacteristic
39C2×C4⋊C4×C293C2211yescharacteristic
40#106×C293C2212yescomplemented
41#103×C293C2212yescomplemented
42C22⋊C8×C293C2211yescharacteristic
43C23×D293D411yescharacteristic
44#17989803—24no—
45C2×D1172—21no—
46C2×D1172—21no—
47C2×D1172C2311yescharacteristic
48C2×C22⋊D293—21no—
49C22×Dic293—21no—
50C22×Dic293D411yescharacteristic
51C2×C4×D293—24no—
52C2×C4×D293—21no—
53C2×C4×D293D411yescharacteristic
54C2×C4×D293D411yescharacteristic
55C2×C4×D293C2311yescharacteristic
56C2×C4×D293C2311yescharacteristic
57C2×#14556873C2312yes—
58C8×D293—24no—
59C4⋊Dic293—21no—
60C4⋊Dic293C2311yescharacteristic
61C4⋊Dic293C2312yes—
62#17989781—21no—
63#17989779—21no—
64#17989779—21no—
65#17989779—22no—
66#17989779—22no—
67#17989779—21no—
68#17989779—21no—
69C4×Dic293—21no—
70C4×Dic293—22no—
71C4×Dic293—22no—
72C2×Q8×C293C2311yescharacteristic
73C22×C4×C293—21no—
74C22×C4×C293C2311yescharacteristic
75C2×C8×C293C2312yes—
76C4⋊C4×C293—21no—
77C4⋊C4×C293—21no—
78C4⋊C4×C293C2311yescharacteristic
79C4⋊C4×C293C2312yes—
80C22⋊C4×C293—21no—
81C22×D293—22no—
82C22×D293—22no—
83C22×D293—21no—
84C22×D293—41no—
85C22×D293C2×D411yescharacteristic
86C22×D293C2×D411yescharacteristic
87D1172—22no—
88D1172—42no—
89D1172—42no—
90C22⋊D293—42no—
91C2×Dic293—22no—
92C2×Dic293—22no—
93C2×Dic293—21no—
94C2×Dic293—42no—
95C2×Dic293C2×D411yescharacteristic
96C2×Dic293C2×D411yescharacteristic
97C4×D293—22no—
98C4×D293—22no—
99C4×D293—22no—
100C4×D293—42no—
101C4×D293#4114yes—
102#14556873—22no—
103C23×C293C2×D411yescharacteristic
104Q8×C293—22no—
105C2×C4×C293—22no—
106C2×C4×C293—21no—
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#13512yes—
116C22×C293C22×D411yescharacteristic
117C2×D293—21no—
118C2×D293—21no—
119C2×D293—21no—
120C2×D293—21no—
121C2×D293—21no—
122C2×D293—44no—
123C2×D293—41no—
124C2×D293—41no—
125C2×D293—41no—
126C2×D293#12312yes—
127C4×C293—21no—
128C4×C293—41no—
129C4×C293—42no—
130C4×C293—41no—
131C4×C293C2×#4112yes—
132Dic293—21no—
133Dic293—41no—
134Dic293—42no—
135Dic293#12312yes—
136C2×C293—22no—
137C2×C293C2×#12311yescharacteristic
138C2×C293C2×#13511yescharacteristic
139C2×C293#57511yescharacteristic
140D293—22no—
141D293—41no—
142D293—81no—
143C293#309111yescharacteristic, complemented, Sylow
144#3091—2931nomaximal, Sylow
145#525—2931no—
146C2×#117—2931no—
147#485—2932no—
148#484—2931no—
149#483D29311yescharacteristic, complemented
150#482—2932no—
151#481—2931no—
152#480—2931no—
153#427—2932no—
154#416—2932no—
155C2×C22⋊C8—2931no—
156C2×#41—2931no—
157C23×C4—2931no—
158C22×C8—2932no—
159#123—5861no—
160C22⋊Q8—2931no—
161C22⋊Q8C2×D29311yescharacteristic
162#121—2931no—
163#121—2931no—
164#120—5861no—
165C4×D4—5861no—
166C4×D4—5861no—
167#117—2932no—
168#117—2932no—
169#117—2931no—
170#117—5861no—
171#117—5861no—
172C2×C4⋊C4—2931no—
173C2×C4⋊C4C2×D29311yescharacteristic
174C2×C22⋊C4—5861no—
175C2×C42—5861no—
176#107—2932no—
177#107—2932no—
178#106—2932no—
179#106C2×D29312yescomplemented
180#103—2932no—
181#103C2×D29312yescomplemented
182#102—2932no—
183#102—2932no—
184C22⋊C8—2931no—
185C22⋊C8—2932no—
186C22⋊C8C2×D29311yescharacteristic
187C24—2931no—
188#41—5864no—
189C2×Q8C22×D29311yescharacteristic
190C2×D4—2931no—
191C2×D4—5861no—
192C2×D4—5861no—
193C2×D4—5861no—
194C22×C4—21no—
195C22×C4—2931no—
196C22×C4—2931no—
197C22×C4—2931no—
198C22×C4—2931no—
199C22×C4—2931no—
200C22×C4—5864no—
201C22×C4—5861no—
202C22×C4—5861no—
203C22×C4C22×D29311yescharacteristic
204C2×C8—2932no—
205C2×C8—5864no—
206C2×C8C22×D29312yes—
207C4⋊C4—21no—
208C4⋊C4—21no—
209C4⋊C4—2932no—
210C4⋊C4—2931no—
211C4⋊C4—5861no—
212C4⋊C4—5861no—
213C4⋊C4C22×D29312yes—
214C4⋊C4C22×D29311yescharacteristic
215C22⋊C4—21no—
216C22⋊C4—5861no—
217C22⋊C4—5862no—
218C22⋊C4—5862no—
219C22⋊C4—5861no—
220C22⋊C4—5861no—
221C22⋊C4—5861no—
222C42—5862no—
223C42—5862no—
224C42—5861no—
225C23—2931no—
226C23—2931no—
227C23—5862no—
228C23—5862no—
229C23—5861no—
230C23—11721no—
231C23D4×D29311yescharacteristic
232Q8—22no—
233D4—5862no—
234D4—11722no—
235D4—11722no—
236D4—11722no—
237C2×C4—22no—
238C2×C4—22no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—2931no—
243C2×C4—2934no—
244C2×C4—2931no—
245C2×C4—5862no—
246C2×C4—5862no—
247C2×C4—5862no—
248C2×C4—5862no—
249C2×C4—5862no—
250C2×C4—5861no—
251C2×C4—11722no—
252C2×C4—11722no—
253C2×C4D4×D29311yescharacteristic
254C2×C4C23×D29311yescharacteristic
255C8—22no—
256C8—5862no—
257C22—21no—
258C22—21no—
259C22—2932no—
260C22—5861no—
261C22—5861no—
262C22—5861no—
263C22—5861no—
264C22—5861no—
265C22—11724no—
266C22—11721no—
267C22—11721no—
268C22—11721no—
269C22#2262764512yes—
270C22C2×D4×D29311yescharacteristic
271C4—21no—
272C4—41no—
273C4—42no—
274C4—41no—
275C4—2932no—
276C4—5861no—
277C4—11721no—
278C4—11722no—
279C4#41×D29312yes—
280C2—22no—
281C2—23441no—
282C2—5862no—
283C2—11721no—
284C2#123×D29311yescharacteristic
285C2C2×#2262764511yescharacteristic
286C2#3403692811yescharacteristic
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#483×C293C2
socleC22×C293C22×D4
prime radical#34036642C2
hypercenter#483D293
hypocenterC293#3091
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
2. C2×#22627582C2semidirect
3. #34036468C2semidirect
4. #34036462C2semidirect
5. #34036455C2semidirect
6. #34036448C2semidirect
7. #34036442C2semidirect
8. #34036164C2semidirect
9. #34036124C2semidirect
10. C22⋊C8×D293C2semidirect
11. #483×C293C2semidirect
30. #22627557C22semidirect
31. #22627557C22semidirect
32. #22627556C22semidirect
33. #22627548C22semidirect
34. #22627546C22semidirect
35. #22627544C22semidirect
40. #106×C293C22semidirect
41. #103×C293C22semidirect
143. C293#3091semidirect
149. #483D293semidirect
179. #106C2×D293semidirect
181. #103C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366422
C2×#226275822
#340364682
#340364622
#340364552
#340364482
#340364422
#340361642
#340361242
C22⋊C8×D2932
#483×C2932
#3091293