Finite Group Databasebeta

← #490×D109 #28373364

Subgroups — #490×D109 #28373364

Order 13952.

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×D109C211yesmaximal, characteristic
2#125×D109C211yesmaximal, characteristic, complemented
3#20295392C211yesmaximal, characteristic, complemented
4#20295391C211yesmaximal, characteristic, complemented
5#20295390C211yesmaximal, characteristic, complemented
6#20295389C214yesmaximal, complemented
7#102×D109C214yesmaximal, complemented
8#97×D109C211yesmaximal, characteristic, complemented
9#490×C109C211yesmaximal, characteristic, complemented
10C2×D4×D109—22no—
11C2×D4×D109C2212yes—
12C2×C8×D109C2212yes—
13#16812696C2211yescharacteristic
14#16812695—22no—
15#16812695C2212yes—
16#16812691C2211yescharacteristic, complemented
17#16812690C2212yescomplemented
18#16812689—22no—
19C4⋊C4×D109—22no—
20C4⋊C4×D109C2212yes—
21C42×D109C2211yescharacteristic
22#16812621C2214yescomplemented
23#16812620C2214yescomplemented
24#16812619C2214yescomplemented
25#16812610C2211yescharacteristic, complemented
26#16812609C2212yescomplemented
27#127×C109C2211yescharacteristic
28#125×C109C2211yescharacteristic, complemented
29#102×C109C2214yescomplemented
30#97×C109C2211yescharacteristic, complemented
31C23×D109—22no—
32C2×D436—22no—
33C2×D436C2312yes—
34C2×C22⋊D109—22no—
35C2×C22⋊D109—24no—
36D4×D109—28no—
37D4×D109—48no—
38C2×C4×D109—22no—
39C2×C4×D109D412yes—
40C2×C4×D109C2311yescharacteristic
41C2×#11724784C2312yes—
42C8×D109—24no—
43C4⋊Dic109—22no—
44C4⋊Dic109C2312yes—
45#13182008—22no—
46#13182008—22no—
47#13182008—22no—
48C4×Dic109D412yes—
49C4×Dic109C2311yescharacteristic
50C2×D4×C109—22no—
51C2×D4×C109C2312yes—
52C2×C8×C109C2312yes—
53C4⋊C4×C109—22no—
54C4⋊C4×C109C2312yes—
55C42×C109C2311yescharacteristic
56C23×C109—22no—
57C22×D109—22no—
58C22×D109—44no—
59C22×D109—48no—
60C22×D109C2×D411yescharacteristic
61D4×C109—24no—
62D4×C109—44no—
63C2×C4×C109—22no—
64C2×C4×C109C2×D412yes—
65C2×C4×C109C2411yescharacteristic
66C22⋊D109—48no—
67C22⋊D109—44no—
68C2×Dic109—22no—
69C2×Dic109C2×D412yes—
70C2×Dic109C2×D411yescharacteristic
71D436—24no—
72D436—44no—
73C4×D109—24no—
74C4×D109—44no—
75C4×D109#4114yes—
76C8×C109—22no—
77#11724784—22no—
78C22×C109—42no—
79C22×C109—44no—
80C22×C109C22×D411yescharacteristic
81C2×D109—42no—
82C2×D109—44no—
83C2×D109—88no—
84C2×D109#12412yes—
85C2×D109AGL(1,ℤ/8)14yes—
86C4×C109—22no—
87C4×C109—42no—
88C4×C109C2×#4112yes—
89Dic109—22no—
90Dic109—42no—
91Dic109#12412yes—
92C2×C109—82no—
93C2×C109C2×#12411yescharacteristic
94C2×C109C2×AGL(1,ℤ/8)12yes—
95D109—82no—
96D109#49014yesdirect product factor
97C2×#490—1091nomaximal, Sylow
98C109C2×#49011yescharacteristic, complemented, Sylow
99C2×#127—1091no—
100C2×#125—1091no—
101#490—1091no—
102#490—1091no—
103#490—1094no—
104#490—1091no—
105#490D10911yescharacteristic, direct product factor
106C2×#102—1094no—
107C2×#97—1091no—
108C22×D4—1092no—
109C22×D4—2182no—
110C22×C8—1092no—
111#127—1092no—
112#127—1091no—
113#127—2182no—
114#127C2×D10911yescharacteristic
115#125—1092no—
116#125—1091no—
117#125—2182no—
118#125C2×D10911yescharacteristic, complemented
119C2×C4⋊C4—1092no—
120C2×C4⋊C4—2182no—
121C2×C42—1091no—
122#102—1094no—
123#102—1094no—
124#102—1094no—
125#102C2×D10914yescomplemented
126#97—1092no—
127#97—1091no—
128#97C2×D10911yescharacteristic, complemented
129C24—2182no—
130C2×D4—22no—
131C2×D4—1092no—
132C2×D4—4368no—
133C2×D4—2188no—
134C2×D4—2184no—
135C2×D4—2182no—
136C2×D4—2182no—
137C2×D4C22×D10912yes—
138C22×C4—1091no—
139C22×C4—1092no—
140C22×C4—2182no—
141C2×C8—1092no—
142C2×C8—2184no—
143C2×C8C22×D10912yes—
144C4⋊C4—22no—
145C4⋊C4—1092no—
146C4⋊C4—2182no—
147C4⋊C4—2182no—
148C4⋊C4—2182no—
149C4⋊C4—2182no—
150C4⋊C4C22×D10912yes—
151C42—1092no—
152C42—1091no—
153C42C22×D10911yescharacteristic
154C23—22no—
155C23—1091no—
156C23—4368no—
157C23—4364no—
158C23—2182no—
159D4—24no—
160D4—44no—
161D4—4364no—
162D4—4364no—
163D4—4368no—
164D4—2184no—
165C2×C4—22no—
166C2×C4—1091no—
167C2×C4—1094no—
168C2×C4—1092no—
169C2×C4—4364no—
170C2×C4—2184no—
171C2×C4—2182no—
172C2×C4D4×D10912yes—
173C2×C4C23×D10911yescharacteristic
174C8—22no—
175C8—2182no—
176C22—42no—
177C22—44no—
178C22—8728no—
179C22—1092no—
180C22—1094no—
181C22—4362no—
182C22—4364no—
183C22C2×D4×D10911yescharacteristic
184C4—22no—
185C4—42no—
186C4—1092no—
187C4—4362no—
188C4—2182no—
189C4#41×D10912yes—
190C2—82no—
191C2—8722no—
192C2—1094no—
193C2#124×D10911yescharacteristic
194C2AGL(1,ℤ/8)×D10912yes—
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#490×C109C2
socleC22×C109C22×D4
prime radical#127×D109C2
hypercenter#490D109
hypocenterC109C2×#490
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
2. #125×D109C2semidirect
3. #20295392C2semidirect
4. #20295391C2semidirect
5. #20295390C2semidirect
6. #20295389C2semidirect
7. #102×D109C2semidirect
8. #97×D109C2semidirect
9. #490×C109C2semidirect
16. #16812691C22semidirect
17. #16812690C22semidirect
22. #16812621C22semidirect
23. #16812620C22semidirect
24. #16812619C22semidirect
25. #16812610C22semidirect
26. #16812609C22semidirect
28. #125×C109C22semidirect
29. #102×C109C22semidirect
30. #97×C109C22semidirect
96. D109#490direct (N × H)
98. C109C2×#490semidirect
105. #490D109direct (N × H)
118. #125C2×D109semidirect
125. #102C2×D109semidirect
128. #97C2×D109semidirect

Maximal subgroups

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

subgroupindex
#127×D1092
#125×D1092
#202953922
#202953912
#202953902
#202953892
#102×D1092
#97×D1092
#490×C1092
C2×#490109