Finite Group Databasebeta

← #49170579

Subgroups — #49170579

Order 37504.

460 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 460 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
1#34036941C212yesmaximal, complemented
2#34036936C212yesmaximal, complemented
3#34036502C211yesmaximal, characteristic, complemented
4#34036393C212yesmaximal, complemented
5#34036392C212yesmaximal, complemented
6#34036313C212yesmaximal, complemented
7#34036298C212yesmaximal, complemented
8#34036247C211yesmaximal, characteristic, complemented
9#443×C293C211yesmaximal, characteristic, complemented
10#22627671C2212yes—
11#22627670C2212yescomplemented
12#22627657—22no—
13#22627657C2212yescomplemented
14#22627656—22no—
15#22627654C2212yescomplemented
16#22627652—22no—
17#22627652C2212yes—
18#22627649C2212yes—
19#22627648—22no—
20#22627646—22no—
21#22627646C2211yescharacteristic
22#22627645—22no—
23C2×#17989791—22no—
24C2×#17989791C2212yescomplemented
25C2×#17989791C2212yescomplemented
26SD16×D293—22no—
27#22627630C2212yescomplemented
28#22627624C2211yescharacteristic, complemented
29#22627621C2211yescharacteristic
30#22627560C2211yescharacteristic, complemented
31#22627552C2212yescomplemented
32#22627542C2212yescomplemented
33#22627540C2212yescomplemented
34#135×C293C2211yescharacteristic
35#131×C293C2212yescomplemented
36#108×C293C2211yescharacteristic, complemented
37#104×C293C2212yescomplemented
38C4×C8×C293C2211yescharacteristic, complemented
39#17989803—22no—
40#17989802—22no—
41#17989802—22no—
42#17989802C2312yes—
43#17989801—22no—
44#17989801—42no—
45C2×Dic586—22no—
46C2×Dic586C2312yes—
47Q8×D293—22no—
48C2×D1172—22no—
49C2×D1172—41no—
50C2×D1172C2312yes—
51D4×D293—22no—
52D4×D293—42no—
53Dic1172—22no—
54Dic1172D411yescharacteristic, complemented
55#17989792—22no—
56#17989791—22no—
57#17989791—22no—
58#17989791—22no—
59#17989791—22no—
60#17989791—22no—
61#17989791—22no—
62#17989791D412yescomplemented
63#17989790—22no—
64#17989789—22no—
65D2344—22no—
66D2344D411yescharacteristic, complemented
67#17989787—22no—
68#17989786C2312yes—
69#17989785—22no—
70C8×D293—22no—
71C4⋊Dic293—41no—
72#41×C293C2312yes—
73Q16×C293D411yescharacteristic, complemented
74SD16×C293D412yescomplemented
75D8×C293D411yescharacteristic, complemented
76M16×C293—22no—
77M16×C293C2312yes—
78C2×C8×C293—22no—
79C2×C8×C293C2311yescharacteristic
80C2×C8×C293C2311yescharacteristic
81C42×C293C2311yescharacteristic
82C22×D293—22no—
83C22×D293—42no—
84Dic586—22no—
85Dic586—22no—
86Dic586—42no—
87Dic586C2×D412yes—
88D1172—22no—
89D1172—22no—
90D1172—42no—
91D1172—82no—
92D1172C2×D412yes—
93C22⋊D293—22no—
94C22⋊D293—42no—
95C22⋊D293—42no—
96C2×Dic293—22no—
97C2×Dic293—42no—
98C4×D293—22no—
99C4×D293—42no—
100C4×D293—42no—
101#14556873—22no—
102Q8×C293C2×D412yes—
103D4×C293—22no—
104D4×C293C2×D412yes—
105C2×C4×C293—21no—
106C2×C4×C293—22no—
107C2×C4×C293C2411yescharacteristic
108C8×C293—22no—
109C8×C293C2×D411yescharacteristic
110C8×C293C2×D411yescharacteristic
111C8×C293C2×D411yescharacteristic
112C8×C293C2×D411yescharacteristic
113C22×C293—22no—
114C22×C293H(5,𝔽2)11yescharacteristic
115C2×D293—22no—
116C2×D293—42no—
117C2×D293—82no—
118C2×D293—162no—
119C4×C293—22no—
120C4×C293—22no—
121C4×C293C22×D411yescharacteristic
122C4×C293C22×D411yescharacteristic
123Dic293—22no—
124Dic293—42no—
125C2×C293—21no—
126C2×C293—42no—
127C2×C293D4211yescharacteristic
128D293—42no—
129D293—82no—
130C293#329111yescharacteristic, complemented, Sylow
131#3291—2931nomaximal, Sylow
132#577—2932no—
133#577—2932no—
134#492—2931no—
135#471—2932no—
136#471—2932no—
137#456—2932no—
138#453—2932no—
139#443—2931no—
140#443D29311yescharacteristic, complemented
1412−1+4—2932no—
142H(5,𝔽2)—2932no—
143#137—2932no—
144#137—2932no—
145#137—5862no—
146#137—5862no—
147AGL(1,ℤ/8)—2932no—
148AGL(1,ℤ/8)—2932no—
149AGL(1,ℤ/8)—5862no—
150AGL(1,ℤ/8)—5862no—
151#135—2931no—
152#135—5862no—
153#135—5862no—
154#135C2×D29311yescharacteristic
155C2×SD16—2932no—
156C2×SD16—2932no—
157C2×SD16—5862no—
158C2×SD16—5862no—
159#131—2932no—
160#131C2×D29312yescomplemented
161C4⋊Q8—2931no—
162#127—2931no—
163#108—2931no—
164#108C2×D29311yescharacteristic, complemented
165#104—2932no—
166#104C2×D29312yescomplemented
167#101—2932no—
168#100—2932no—
169C4×C8C2×D29311yescharacteristic, complemented
170#41—2932no—
171#41—5862no—
172#41—5862no—
173#41—5862no—
174#41—5862no—
175#41—11722no—
176#41C22×D29312yes—
177C2×Q8—2932no—
178C2×Q8—5862no—
179C2×Q8—5862no—
180C2×D4—2932no—
181C2×D4—5862no—
182C2×D4—5862no—
183C2×D4—11721no—
184C2×D4—11722no—
185Q16—2931no—
186Q16—5862no—
187Q16—5862no—
188Q16D117211yescharacteristic, complemented
189SD16—2932no—
190SD16—5862no—
191SD16—5862no—
192SD16—5862no—
193SD16—5862no—
194SD16—5862no—
195SD16—5862no—
196SD16—5862no—
197SD16—5862no—
198SD16D117212yescomplemented
199D8—2931no—
200D8—5862no—
201D8—5862no—
202D8D117211yescharacteristic, complemented
203M16—22no—
204M16—2932no—
205M16—5862no—
206M16C22×D29312yes—
207C2×C8—22no—
208C2×C8—5862no—
209C2×C8C22×D29311yescharacteristic
210C2×C8C22×D29311yescharacteristic
211C4⋊C4—11721no—
212C42C22×D29311yescharacteristic
213C23—5862no—
214C23—11722no—
215Q8—2932no—
216Q8—5862no—
217Q8—5862no—
218Q8—11722no—
219Q8C2×D117212yes—
220D4—22no—
221D4—2932no—
222D4—23442no—
223D4—5862no—
224D4—5862no—
225D4—5862no—
226D4—11722no—
227D4—11722no—
228D4—11722no—
229D4C2×D117212yes—
230C2×C4—21no—
231C2×C4—22no—
232C2×C4—5862no—
233C2×C4—5862no—
234C2×C4—11722no—
235C2×C4—11722no—
236C2×C4—11722no—
237C2×C4C23×D29311yescharacteristic
238C8—22no—
239C8—5862no—
240C8D4×D29311yescharacteristic
241C8D4×D29311yescharacteristic
242C8C2×D117211yescharacteristic
243C8C2×D117211yescharacteristic
244C22—22no—
245C22—23442no—
246C22—5862no—
247C22—46882no—
248C22—11722no—
249C22#2262767011yescharacteristic
250C4—22no—
251C4—22no—
252C4—5862no—
253C4—11722no—
254C4C2×D4×D29311yescharacteristic
255C4C22×D117211yescharacteristic
256C2—21no—
257C2—42no—
258C2—23442no—
259C2—11722no—
260C2D4×D117211yescharacteristic
subgroupG/H
centerC2D4×D1172
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#443×C293C2
socleC2×C293D42
hypercenter#443D293
hypocenterC293#3291
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C2 ◁ C2×C4 ◁ #443

Complements

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

NH ≅ G/Ntype
1. #34036941C2semidirect
2. #34036936C2semidirect
3. #34036502C2semidirect
4. #34036393C2semidirect
5. #34036392C2semidirect
6. #34036313C2semidirect
7. #34036298C2semidirect
8. #34036247C2semidirect
9. #443×C293C2semidirect
11. #22627670C22semidirect
13. #22627657C22semidirect
15. #22627654C22semidirect
24. C2×#17989791C22semidirect
25. C2×#17989791C22semidirect
27. #22627630C22semidirect
28. #22627624C22semidirect
30. #22627560C22semidirect
31. #22627552C22semidirect
32. #22627542C22semidirect
33. #22627540C22semidirect
35. #131×C293C22semidirect
36. #108×C293C22semidirect
37. #104×C293C22semidirect
38. C4×C8×C293C22semidirect
54. Dic1172D4semidirect
62. #17989791D4semidirect
66. D2344D4semidirect
73. Q16×C293D4semidirect
74. SD16×C293D4semidirect
75. D8×C293D4semidirect
130. C293#3291semidirect
140. #443D293semidirect
160. #131C2×D293semidirect
164. #108C2×D293semidirect
166. #104C2×D293semidirect
169. C4×C8C2×D293semidirect
188. Q16D1172semidirect
198. SD16D1172semidirect
202. D8D1172semidirect

Maximal subgroups

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

subgroupindex
#340369412
#340369362
#340365022
#340363932
#340363922
#340363132
#340362982
#340362472
#443×C2932
#3291293