Finite Group Databasebeta

← #22620304

Subgroups — #22620304

Order 9344.

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#17989143C211yesmaximal, characteristic, complemented
2#127×D73C211yesmaximal, characteristic
3#17988953C211yesmaximal, characteristic, complemented
4#17988952C211yesmaximal, characteristic, complemented
5#17988951C211yesmaximal, characteristic, complemented
6#17988932C214yesmaximal, complemented
7#17988590C214yesmaximal, complemented
8#17988539C211yesmaximal, characteristic, complemented
9#490×C73C211yesmaximal, characteristic, complemented
10C2×D4×D73—22no—
11C2×D4×D73C2212yes—
12C2×#11924011C2212yes—
13#14556590C2212yescomplemented
14#14556588C2211yescharacteristic
15#14556587—22no—
16#14556587C2212yes—
17#14556583C2211yescharacteristic, complemented
18#14556569—22no—
19#14556556—22no—
20#14556549C2212yes—
21C42×D73C2211yescharacteristic
22#14556513C2214yescomplemented
23#14556512C2214yescomplemented
24#14556511C2214yescomplemented
25#14556502C2211yescharacteristic, complemented
26C8×Dic73C2212yescomplemented
27#127×C73C2211yescharacteristic
28#125×C73C2211yescharacteristic, complemented
29#102×C73C2214yescomplemented
30#97×C73C2211yescharacteristic, complemented
31C23×D73—22no—
32C2×Dic146—22no—
33C2×D292—22no—
34C2×D292C2312yes—
35C2×C22⋊D73—22no—
36C2×C22⋊D73—24no—
37D4×D73—28no—
38D4×D73—48no—
39C2×C4×D73D412yes—
40C2×C4×D73C2311yescharacteristic
41#11924011—24no—
42C2×#10596831C2312yes—
43C4⋊Dic73C2312yes—
44#11924007—22no—
45#11924007—22no—
46#11924005—22no—
47C4×Dic73—22no—
48C4×Dic73D412yes—
49C4×Dic73C2311yescharacteristic
50C2×D4×C73—22no—
51C2×D4×C73C2312yes—
52C2×C8×C73C2312yes—
53C4⋊C4×C73—22no—
54C4⋊C4×C73C2312yes—
55C42×C73C2311yescharacteristic
56C23×C73—22no—
57C22×D73—22no—
58C22×D73—48no—
59C22×D73—44no—
60C22×D73C2×D411yescharacteristic
61D4×C73—24no—
62D4×C73—44no—
63C2×C4×C73—22no—
64C2×C4×C73C2×D412yes—
65C2×C4×C73C2411yescharacteristic
66C22⋊D73—44no—
67C22⋊D73—48no—
68C2×Dic73—22no—
69C2×Dic73C2×D411yescharacteristic
70C2×Dic73C2×D412yes—
71D292—24no—
72D292—44no—
73C4×D73—24no—
74C4×D73#4114yes—
75Dic146—44no—
76C8×C73—22no—
77#10596831—22no—
78C22×C73—42no—
79C22×C73—44no—
80C22×C73C22×D411yescharacteristic
81C2×D73—22no—
82C2×D73—42no—
83C2×D73—44no—
84C2×D73—88no—
85C2×D73#12412yes—
86C4×C73—22no—
87C4×C73—42no—
88C4×C73C2×#4112yes—
89Dic73—42no—
90Dic73#12412yes—
91Dic73AGL(1,ℤ/8)14yes—
92C2×C73—82no—
93C2×C73C2×#12411yescharacteristic
94C2×C73C2×AGL(1,ℤ/8)12yes—
95D73—22no—
96D73—82no—
97#3138—731nomaximal, Sylow
98C73#313811yescharacteristic, complemented, Sylow
99#533—731no—
100C2×#127—731no—
101#490—731no—
102#490—731no—
103#490—731no—
104#490D7311yescharacteristic, complemented
105#486—734no—
106#418—734no—
107C4×M16—731no—
108C22×D4—732no—
109C22×D4—1462no—
110C2×M16—732no—
111C4⋊Q8—732no—
112#127—732no—
113#127—731no—
114#127—1462no—
115#127C2×D7311yescharacteristic
116#125—731no—
117#125C2×D7311yescharacteristic, complemented
118C22⋊Q8—1462no—
119C4×Q8—1462no—
120#117—732no—
121C2×C42—731no—
122#102—734no—
123#102—734no—
124#102—734no—
125#102C2×D7314yescomplemented
126#97—731no—
127#97C2×D7311yescharacteristic, complemented
128C4×C8—732no—
129C24—1462no—
130C2×Q8—1462no—
131C2×D4—22no—
132C2×D4—2928no—
133C2×D4—732no—
134C2×D4—1468no—
135C2×D4—1464no—
136C2×D4—1462no—
137C2×D4—1462no—
138C2×D4C22×D7312yes—
139C22×C4—731no—
140C22×C4—732no—
141M16—1464no—
142C2×C8—732no—
143C2×C8C22×D7312yes—
144C4⋊C4—22no—
145C4⋊C4—732no—
146C4⋊C4—1462no—
147C4⋊C4—1462no—
148C4⋊C4C22×D7312yes—
149C22⋊C4—1462no—
150C42—732no—
151C42—731no—
152C42—1462no—
153C42C22×D7311yescharacteristic
154C23—22no—
155C23—2924no—
156C23—2928no—
157C23—731no—
158C23—1462no—
159Q8—2924no—
160D4—24no—
161D4—44no—
162D4—2924no—
163D4—2928no—
164D4—2924no—
165D4—1464no—
166C2×C4—22no—
167C2×C4—731no—
168C2×C4—732no—
169C2×C4—734no—
170C2×C4—1464no—
171C2×C4—1462no—
172C2×C4D4×D7312yes—
173C2×C4C23×D7311yescharacteristic
174C8—22no—
175C8—1462no—
176C22—42no—
177C22—44no—
178C22—2922no—
179C22—2924no—
180C22—5848no—
181C22—732no—
182C22—1462no—
183C22C2×D4×D7311yescharacteristic
184C4—22no—
185C4—42no—
186C4—2922no—
187C4—732no—
188C4—734no—
189C4#41×D7312yes—
190C2—82no—
191C2—5842no—
192C2—1462no—
193C2#124×D7311yescharacteristic
194C2AGL(1,ℤ/8)×D7312yes—
subgroupG/H
centerC22C2×D4×D73
commutatorC2×C4×C73C24
FrattiniC2×C4C23×D73
Fitting#490×C73C2
socleC22×C73C22×D4
hypercenter#490D73
hypocenterC73#3138
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #17989143C2semidirect
3. #17988953C2semidirect
4. #17988952C2semidirect
5. #17988951C2semidirect
6. #17988932C2semidirect
7. #17988590C2semidirect
8. #17988539C2semidirect
9. #490×C73C2semidirect
13. #14556590C22semidirect
17. #14556583C22semidirect
22. #14556513C22semidirect
23. #14556512C22semidirect
24. #14556511C22semidirect
25. #14556502C22semidirect
26. C8×Dic73C22semidirect
28. #125×C73C22semidirect
29. #102×C73C22semidirect
30. #97×C73C22semidirect
98. C73#3138semidirect
104. #490D73semidirect
117. #125C2×D73semidirect
125. #102C2×D73semidirect
127. #97C2×D73semidirect