Finite Group Databasebeta

← #49170554

Subgroups — #49170554

Order 37504.

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

normal subgroups only

This group has 464 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#34036938C212yesmaximal, complemented
2#34036932C212yesmaximal, complemented
3#34036519C211yesmaximal, characteristic, complemented
4#34036398C212yesmaximal, complemented
5#34036394C212yesmaximal, complemented
6#34036301C211yesmaximal, characteristic, complemented
7#34036298C212yesmaximal, complemented
8#34036248C212yesmaximal, complemented
9#455×C293C211yesmaximal, characteristic, complemented
10#22627672C2211yescharacteristic, complemented
11#22627670C2212yescomplemented
12#22627656—22no—
13#22627652C2212yescomplemented
14#22627651—22no—
15#22627650—22no—
16#22627650C2212yescomplemented
17#22627649—22no—
18#22627649C2212yes—
19#22627647—22no—
20#22627644—22no—
21#22627644C2212yes—
22C2×#17989789C2212yescomplemented
23SD16×D293—22no—
24C2×#17989787—22no—
25C2×#17989787C2212yescomplemented
26#22627632C2212yescomplemented
27#22627631C2212yescomplemented
28#22627621C2211yescharacteristic, complemented
29#22627559C2212yescomplemented
30#22627552C2212yescomplemented
31#22627543C2211yescharacteristic, complemented
32#22627540C2212yescomplemented
33#22627535C2211yescharacteristic, complemented
34H(5,𝔽2)×C293C2211yescharacteristic
35#137×C293C2212yescomplemented
36#124×C293C2211yescharacteristic, complemented
37#104×C293C2212yescomplemented
38#100×C293C2211yescharacteristic, complemented
39#17989803—22no—
40#17989803—22no—
41#17989802—22no—
42#17989802—41no—
43#17989802C2312yes—
44Q8×D293—22no—
45C2×D1172—22no—
46C2×D1172—41no—
47C2×D1172C2312yes—
48D4×D293—22no—
49D4×D293—42no—
50#17989792D412yescomplemented
51#17989791—22no—
52#17989790—22no—
53#17989790D412yescomplemented
54#17989789—22no—
55#17989789—22no—
56#17989789—22no—
57#17989789D412yescomplemented
58D2344—22no—
59#17989787—22no—
60#17989787—22no—
61#17989787—22no—
62#17989787—22no—
63#17989787D412yescomplemented
64#17989786—22no—
65#17989786C2312yes—
66#17989785—22no—
67C2×#14556873—22no—
68C2×#14556873C2312yes—
69C8×D293—22no—
70#41×C293—22no—
71#41×C293C2312yes—
72C2×Q8×C293C2311yescharacteristic
73C2×D4×C293—22no—
74C2×D4×C293—41no—
75C2×D4×C293C2311yescharacteristic
76Q16×C293—22no—
77SD16×C293—22no—
78M16×C293C2312yes—
79C22⋊C4×C293—41no—
80C42×C293C2311yescharacteristic
81C22×D293—22no—
82C22×D293—42no—
83Dic586—41no—
84Dic586C2×D412yes—
85D1172—22no—
86D1172—22no—
87D1172—42no—
88D1172—41no—
89D1172—82no—
90D1172C2×D412yes—
91C22⋊D293—22no—
92C22⋊D293—42no—
93C4×D293—22no—
94C4×D293—42no—
95C4×D293—42no—
96#14556873—22no—
97#14556873C2×D412yes—
98#14556873C2×D412yes—
99C23×C293—21no—
100C23×C293—41no—
101Q8×C293—22no—
102Q8×C293C2×D412yes—
103D4×C293—22no—
104D4×C293—22no—
105D4×C293—42no—
106D4×C293C2×D412yes—
107C2×C4×C293—22no—
108C2×C4×C293—21no—
109C2×C4×C293—21no—
110C2×C4×C293—41no—
111C2×C4×C293C2411yescharacteristic
112C8×C293—22no—
113C22×C293—22no—
114C22×C293—41no—
115C22×C293—81no—
116C22×C293—161no—
117C22×C293H(5,𝔽2)11yescharacteristic
118C2×D293—22no—
119C2×D293—42no—
120C2×D293—82no—
121C2×D293—162no—
122C4×C293—22no—
123C4×C293—41no—
124C4×C293—41no—
125C4×C293C22×D412yes—
126Dic293—22no—
127C2×C293—21no—
128C2×C293—42no—
129C2×C293—81no—
130C2×C293D4211yescharacteristic
131D293—42no—
132D293—82no—
133C293#328811yescharacteristic, complemented, Sylow
134#3288—2931nomaximal, Sylow
135#577—2932no—
136#576—2932no—
137#496—2931no—
138#472—2932no—
139#471—2932no—
140#455D29311yescharacteristic, complemented
141#454—2931no—
142#453—2932no—
143#444—2932no—
1442−1+4—2931no—
145H(5,𝔽2)—2932no—
146H(5,𝔽2)C2×D29311yescharacteristic
147#137—5862no—
148#137C2×D29312yescomplemented
149AGL(1,ℤ/8)—2932no—
150AGL(1,ℤ/8)—2932no—
151AGL(1,ℤ/8)—2932no—
152AGL(1,ℤ/8)—5862no—
153AGL(1,ℤ/8)—5862no—
154AGL(1,ℤ/8)—5862no—
155#135—2932no—
156#135—5862no—
157#135—5862no—
158C2×SD16—2932no—
159C2×SD16—5862no—
160C2×D8—2932no—
161C2×D8—5862no—
162#131—2932no—
163#131—2932no—
164#127—2931no—
165#124C2×D29311yescharacteristic, complemented
166#108—2932no—
167#104—2932no—
168#104C2×D29312yescomplemented
169#101—2931no—
170#100—2932no—
171#100C2×D29311yescharacteristic, complemented
172#97—2931no—
173#41—22no—
174#41—2932no—
175#41—5862no—
176#41—5862no—
177#41—5862no—
178#41—11721no—
179#41C22×D29312yes—
180C2×Q8—5862no—
181C2×Q8C22×D29311yescharacteristic
182C2×D4—22no—
183C2×D4—41no—
184C2×D4—2932no—
185C2×D4—5862no—
186C2×D4—5862no—
187C2×D4—11721no—
188C2×D4—11722no—
189C2×D4C22×D29311yescharacteristic
190Q16—22no—
191Q16—2932no—
192SD16—22no—
193SD16—2932no—
194SD16—2932no—
195SD16—5862no—
196SD16—5862no—
197SD16—5862no—
198SD16—5862no—
199SD16—5862no—
200D8—2932no—
201D8—5862no—
202D8—5862no—
203D8—5862no—
204D8—5862no—
205D8—5862no—
206M16—2932no—
207M16—5862no—
208M16—5862no—
209M16C22×D29312yes—
210C2×C8—2932no—
211C2×C8—5862no—
212C2×C8—5862no—
213C22⋊C4—41no—
214C42C22×D29311yescharacteristic
215C23—21no—
216C23—41no—
217C23—5862no—
218C23—11722no—
219Q8—22no—
220Q8—2932no—
221Q8—11721no—
222Q8D4×D29312yes—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—2932no—
227D4—23442no—
228D4—5862no—
229D4—5862no—
230D4—5862no—
231D4—11722no—
232D4—11721no—
233D4—11722no—
234D4D4×D29312yes—
235C2×C4—22no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—5862no—
240C2×C4—11722no—
241C2×C4—11722no—
242C2×C4C23×D29311yescharacteristic
243C8—22no—
244C8—2932no—
245C8—2932no—
246C8—5862no—
247C22—22no—
248C22—41no—
249C22—81no—
250C22—161no—
251C22—23442no—
252C22—5862no—
253C22—46882no—
254C22—11722no—
255C22#2262766911yescharacteristic
256C4—22no—
257C4—41no—
258C4—41no—
259C4—5862no—
260C4C2×D4×D29312yes—
261C2—21no—
262C2—42no—
263C2—81no—
264C2—23442no—
265C2—11722no—
266C2#3403676111yescharacteristic
subgroupG/H
centerC2#34036761
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#455×C293C2
socleC2×C293D42
hypercenter#455D293
hypocenterC293#3288
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #34036938C2semidirect
2. #34036932C2semidirect
3. #34036519C2semidirect
4. #34036398C2semidirect
5. #34036394C2semidirect
6. #34036301C2semidirect
7. #34036298C2semidirect
8. #34036248C2semidirect
9. #455×C293C2semidirect
10. #22627672C22semidirect
11. #22627670C22semidirect
13. #22627652C22semidirect
16. #22627650C22semidirect
22. C2×#17989789C22semidirect
25. C2×#17989787C22semidirect
26. #22627632C22semidirect
27. #22627631C22semidirect
28. #22627621C22semidirect
29. #22627559C22semidirect
30. #22627552C22semidirect
31. #22627543C22semidirect
32. #22627540C22semidirect
33. #22627535C22semidirect
35. #137×C293C22semidirect
36. #124×C293C22semidirect
37. #104×C293C22semidirect
38. #100×C293C22semidirect
50. #17989792D4semidirect
53. #17989790D4semidirect
57. #17989789D4semidirect
63. #17989787D4semidirect
133. C293#3288semidirect
140. #455D293semidirect
148. #137C2×D293semidirect
165. #124C2×D293semidirect
168. #104C2×D293semidirect
171. #100C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340369382
#340369322
#340365192
#340363982
#340363942
#340363012
#340362982
#340362482
#455×C2932
#3288293