Finite Group Databasebeta

← #49169158

Subgroups — #49169158

Order 37504.

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

normal subgroups only

This group has 484 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#34036685C211yesmaximal, characteristic, complemented
2#127×D293C211yesmaximal, characteristic
3#34036495C211yesmaximal, characteristic, complemented
4#34036494C211yesmaximal, characteristic, complemented
5#34036493C211yesmaximal, characteristic, complemented
6#34036474C214yesmaximal, complemented
7#34036132C214yesmaximal, complemented
8#34036081C211yesmaximal, characteristic, complemented
9#490×C293C211yesmaximal, characteristic, complemented
10C2×D4×D293—22no—
11C2×D4×D293C2212yes—
12C2×#17989785C2212yes—
13#22627623C2212yescomplemented
14#22627621C2211yescharacteristic
15#22627620—22no—
16#22627620C2212yes—
17#22627616C2211yescharacteristic, complemented
18#22627602—22no—
19#22627589—22no—
20#22627582C2212yes—
21C42×D293C2211yescharacteristic
22#22627546C2214yescomplemented
23#22627545C2214yescomplemented
24#22627544C2214yescomplemented
25#22627535C2211yescharacteristic, complemented
26C8×Dic293C2212yescomplemented
27#127×C293C2211yescharacteristic
28#125×C293C2211yescharacteristic, complemented
29#102×C293C2214yescomplemented
30#97×C293C2211yescharacteristic, complemented
31C23×D293—22no—
32C2×Dic586—22no—
33C2×D1172—22no—
34C2×D1172C2312yes—
35C2×C22⋊D293—22no—
36C2×C22⋊D293—24no—
37D4×D293—28no—
38D4×D293—48no—
39C2×C4×D293D412yes—
40C2×C4×D293C2311yescharacteristic
41#17989785—24no—
42C2×#14556873C2312yes—
43C4⋊Dic293C2312yes—
44#17989781—22no—
45#17989781—22no—
46#17989779—22no—
47C4×Dic293—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—48no—
58C22×D293—44no—
59C22×D293C2×D411yescharacteristic
60Dic586—44no—
61D1172—24no—
62D1172—44no—
63C22⋊D293—44no—
64C22⋊D293—48no—
65C2×Dic293—22no—
66C2×Dic293C2×D411yescharacteristic
67C2×Dic293C2×D412yes—
68C4×D293—24no—
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—22no—
82C2×D293—42no—
83C2×D293—44no—
84C2×D293—88no—
85C2×D293#12412yes—
86C4×C293—22no—
87C4×C293—42no—
88C4×C293C2×#4112yes—
89Dic293—42no—
90Dic293#12412yes—
91Dic293AGL(1,ℤ/8)14yes—
92C2×C293—82no—
93C2×C293C2×#12411yescharacteristic
94C2×C293C2×AGL(1,ℤ/8)12yes—
95D293—22no—
96D293—82no—
97C293#313811yescharacteristic, complemented, Sylow
98#3138—2931nomaximal, Sylow
99#533—2931no—
100C2×#127—2931no—
101#490—2931no—
102#490—2931no—
103#490—2931no—
104#490D29311yescharacteristic, complemented
105#486—2934no—
106#418—2934no—
107C4×M16—2931no—
108C22×D4—2932no—
109C22×D4—5862no—
110C2×M16—2932no—
111C4⋊Q8—2932no—
112#127—2932no—
113#127—2931no—
114#127—5862no—
115#127C2×D29311yescharacteristic
116#125—2931no—
117#125C2×D29311yescharacteristic, complemented
118C22⋊Q8—5862no—
119C4×Q8—5862no—
120#117—2932no—
121C2×C42—2931no—
122#102—2934no—
123#102—2934no—
124#102—2934no—
125#102C2×D29314yescomplemented
126#97—2931no—
127#97C2×D29311yescharacteristic, complemented
128C4×C8—2932no—
129C24—5862no—
130C2×Q8—5862no—
131C2×D4—22no—
132C2×D4—2932no—
133C2×D4—5868no—
134C2×D4—5864no—
135C2×D4—5862no—
136C2×D4—5862no—
137C2×D4—11728no—
138C2×D4C22×D29312yes—
139C22×C4—2931no—
140C22×C4—2932no—
141M16—5864no—
142C2×C8—2932no—
143C2×C8C22×D29312yes—
144C4⋊C4—22no—
145C4⋊C4—2932no—
146C4⋊C4—5862no—
147C4⋊C4—5862no—
148C4⋊C4C22×D29312yes—
149C22⋊C4—5862no—
150C42—2932no—
151C42—2931no—
152C42—5862no—
153C42C22×D29311yescharacteristic
154C23—22no—
155C23—2931no—
156C23—5862no—
157C23—11724no—
158C23—11728no—
159Q8—11724no—
160D4—24no—
161D4—44no—
162D4—5864no—
163D4—11724no—
164D4—11724no—
165D4—11728no—
166C2×C4—22no—
167C2×C4—2931no—
168C2×C4—2932no—
169C2×C4—2934no—
170C2×C4—5864no—
171C2×C4—5862no—
172C2×C4D4×D29312yes—
173C2×C4C23×D29311yescharacteristic
174C8—22no—
175C8—5862no—
176C22—42no—
177C22—44no—
178C22—2932no—
179C22—23448no—
180C22—5862no—
181C22—11722no—
182C22—11724no—
183C22C2×D4×D29311yescharacteristic
184C4—22no—
185C4—42no—
186C4—2932no—
187C4—2934no—
188C4—11722no—
189C4#41×D29312yes—
190C2—82no—
191C2—23442no—
192C2—5862no—
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
hypocenterC293#3138
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
1. #34036685C2semidirect
3. #34036495C2semidirect
4. #34036494C2semidirect
5. #34036493C2semidirect
6. #34036474C2semidirect
7. #34036132C2semidirect
8. #34036081C2semidirect
9. #490×C293C2semidirect
13. #22627623C22semidirect
17. #22627616C22semidirect
22. #22627546C22semidirect
23. #22627545C22semidirect
24. #22627544C22semidirect
25. #22627535C22semidirect
26. C8×Dic293C22semidirect
28. #125×C293C22semidirect
29. #102×C293C22semidirect
30. #97×C293C22semidirect
97. C293#3138semidirect
104. #490D293semidirect
117. #125C2×D293semidirect
125. #102C2×D293semidirect
127. #97C2×D293semidirect

Maximal subgroups

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

subgroupindex
#340366852
#127×D2932
#340364952
#340364942
#340364932
#340364742
#340361322
#340360812
#490×C2932
#3138293