Finite Group Databasebeta

← #490×D293 #49169117

Subgroups — #490×D293 #49169117

Order 37504.

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

normal subgroups only

This group has 488 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#127×D293C211yesmaximal, characteristic
2#125×D293C211yesmaximal, characteristic, complemented
3#34036495C211yesmaximal, characteristic, complemented
4#34036494C211yesmaximal, characteristic, complemented
5#34036493C211yesmaximal, characteristic, complemented
6#34036492C214yesmaximal, complemented
7#102×D293C214yesmaximal, complemented
8#97×D293C211yesmaximal, characteristic, complemented
9#490×C293C211yesmaximal, characteristic, complemented
10C2×D4×D293—22no—
11C2×D4×D293C2212yes—
12C2×C8×D293C2212yes—
13#22627621C2211yescharacteristic
14#22627620—22no—
15#22627620C2212yes—
16#22627616C2211yescharacteristic, complemented
17#22627615C2212yescomplemented
18#22627614—22no—
19C4⋊C4×D293—22no—
20C4⋊C4×D293C2212yes—
21C42×D293C2211yescharacteristic
22#22627546C2214yescomplemented
23#22627545C2214yescomplemented
24#22627544C2214yescomplemented
25#22627535C2211yescharacteristic, complemented
26#22627534C2212yescomplemented
27#127×C293C2211yescharacteristic
28#125×C293C2211yescharacteristic, complemented
29#102×C293C2214yescomplemented
30#97×C293C2211yescharacteristic, complemented
31C23×D293—22no—
32C2×D1172—22no—
33C2×D1172C2312yes—
34C2×C22⋊D293—22no—
35C2×C22⋊D293—24no—
36D4×D293—28no—
37D4×D293—48no—
38C2×C4×D293—22no—
39C2×C4×D293D412yes—
40C2×C4×D293C2311yescharacteristic
41C2×#14556873C2312yes—
42C8×D293—24no—
43C4⋊Dic293—22no—
44C4⋊Dic293C2312yes—
45#17989781—22no—
46#17989781—22no—
47#17989781—22no—
48C4×Dic293D412yes—
49C4×Dic293C2311yescharacteristic
50C2×D4×C293—22no—
51C2×D4×C293C2312yes—
52C2×C8×C293C2312yes—
53C4⋊C4×C293—22no—
54C4⋊C4×C293C2312yes—
55C42×C293C2311yescharacteristic
56C22×D293—22no—
57C22×D293—44no—
58C22×D293—48no—
59C22×D293C2×D411yescharacteristic
60D1172—24no—
61D1172—44no—
62C22⋊D293—48no—
63C22⋊D293—44no—
64C2×Dic293—22no—
65C2×Dic293C2×D412yes—
66C2×Dic293C2×D411yescharacteristic
67C4×D293—24no—
68C4×D293—44no—
69C4×D293#4114yes—
70#14556873—22no—
71C23×C293—22no—
72D4×C293—24no—
73D4×C293—44no—
74C2×C4×C293—22no—
75C2×C4×C293C2×D412yes—
76C2×C4×C293C2411yescharacteristic
77C8×C293—22no—
78C22×C293—42no—
79C22×C293—44no—
80C22×C293C22×D411yescharacteristic
81C2×D293—42no—
82C2×D293—44no—
83C2×D293—88no—
84C2×D293#12412yes—
85C2×D293AGL(1,ℤ/8)14yes—
86C4×C293—22no—
87C4×C293—42no—
88C4×C293C2×#4112yes—
89Dic293—22no—
90Dic293—42no—
91Dic293#12412yes—
92C2×C293—82no—
93C2×C293C2×#12411yescharacteristic
94C2×C293C2×AGL(1,ℤ/8)12yes—
95D293—82no—
96D293#49014yesdirect product factor
97C293C2×#49011yescharacteristic, complemented, Sylow
98C2×#490—2931nomaximal, Sylow
99C2×#127—2931no—
100C2×#125—2931no—
101#490—2931no—
102#490—2931no—
103#490—2934no—
104#490—2931no—
105#490D29311yescharacteristic, direct product factor
106C2×#102—2934no—
107C2×#97—2931no—
108C22×D4—2932no—
109C22×D4—5862no—
110C22×C8—2932no—
111#127—2932no—
112#127—2931no—
113#127—5862no—
114#127C2×D29311yescharacteristic
115#125—2932no—
116#125—2931no—
117#125—5862no—
118#125C2×D29311yescharacteristic, complemented
119C2×C4⋊C4—2932no—
120C2×C4⋊C4—5862no—
121C2×C42—2931no—
122#102—2934no—
123#102—2934no—
124#102—2934no—
125#102C2×D29314yescomplemented
126#97—2932no—
127#97—2931no—
128#97C2×D29311yescharacteristic, complemented
129C24—5862no—
130C2×D4—22no—
131C2×D4—2932no—
132C2×D4—5868no—
133C2×D4—5864no—
134C2×D4—5862no—
135C2×D4—5862no—
136C2×D4—11728no—
137C2×D4C22×D29312yes—
138C22×C4—2931no—
139C22×C4—2932no—
140C22×C4—5862no—
141C2×C8—2932no—
142C2×C8—5864no—
143C2×C8C22×D29312yes—
144C4⋊C4—22no—
145C4⋊C4—2932no—
146C4⋊C4—5862no—
147C4⋊C4—5862no—
148C4⋊C4—5862no—
149C4⋊C4—5862no—
150C4⋊C4C22×D29312yes—
151C42—2932no—
152C42—2931no—
153C42C22×D29311yescharacteristic
154C23—22no—
155C23—2931no—
156C23—5862no—
157C23—11724no—
158C23—11728no—
159D4—24no—
160D4—44no—
161D4—5864no—
162D4—11724no—
163D4—11724no—
164D4—11728no—
165C2×C4—22no—
166C2×C4—2931no—
167C2×C4—2934no—
168C2×C4—2932no—
169C2×C4—5864no—
170C2×C4—5862no—
171C2×C4—11724no—
172C2×C4D4×D29312yes—
173C2×C4C23×D29311yescharacteristic
174C8—22no—
175C8—5862no—
176C22—42no—
177C22—44no—
178C22—2932no—
179C22—2934no—
180C22—23448no—
181C22—11722no—
182C22—11724no—
183C22C2×D4×D29311yescharacteristic
184C4—22no—
185C4—42no—
186C4—2932no—
187C4—5862no—
188C4—11722no—
189C4#41×D29312yes—
190C2—82no—
191C2—2934no—
192C2—23442no—
193C2#124×D29311yescharacteristic
194C2AGL(1,ℤ/8)×D29312yes—
subgroupG/H
centerC22C2×D4×D293
commutator, cosocleC2×C4×C293C24
FrattiniC2×C4C23×D293
Fitting#490×C293C2
socleC22×C293C22×D4
prime radical#127×D293C2
hypercenter#490D293
hypocenterC293C2×#490
LCSG ▷ C2×C4×C293 ▷ C2×C293 ▷ C293
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D293C2semidirect
3. #34036495C2semidirect
4. #34036494C2semidirect
5. #34036493C2semidirect
6. #34036492C2semidirect
7. #102×D293C2semidirect
8. #97×D293C2semidirect
9. #490×C293C2semidirect
16. #22627616C22semidirect
17. #22627615C22semidirect
22. #22627546C22semidirect
23. #22627545C22semidirect
24. #22627544C22semidirect
25. #22627535C22semidirect
26. #22627534C22semidirect
28. #125×C293C22semidirect
29. #102×C293C22semidirect
30. #97×C293C22semidirect
96. D293#490direct (N × H)
97. C293C2×#490semidirect
105. #490D293direct (N × H)
118. #125C2×D293semidirect
125. #102C2×D293semidirect
128. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#127×D2932
#125×D2932
#340364952
#340364942
#340364932
#340364922
#102×D2932
#97×D2932
#490×C2932
C2×#490293