Finite Group Databasebeta

← #19136268

Subgroups — #19136268

Order 5504.

238 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 55 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#14583469C211yesmaximal, characteristic
2#14582871C212yesmaximal
3#14582694C211yesmaximal, characteristic, complemented
4#14582693C212yesmaximal, complemented
5C43×#354C211yesmaximal, characteristic, complemented
6C2×#10621900C2211yescharacteristic
7C2×Q8×D43C411yescharacteristic, complemented
8#13063325C411yescharacteristic, complemented
9#13063323C411yescharacteristic, complemented
10#13063312C2211yescharacteristic
11#13063307—22no—
12#13063302—22no—
13#13063282C411yescharacteristic, complemented
14#13063281—22no—
15#13063240C2212yes—
16#13063239—22no—
17#124×C43C2211yescharacteristic
18#99×C43C2212yes—
19C2×Q8×C43C2×C411yescharacteristic
20C2×D4×C43C2311yescharacteristic
21C2×C22⋊D43D412yes—
22C22×Dic43D412yes—
23Q8×D43—42no—
24#10621900—42no—
25C2×C4×D43—21no—
26C2×C4×D43C2×C411yescharacteristic
27C2×Dic86—21no—
28C2×Dic86C2×C411yescharacteristic
29C2×Dic86C2×C411yescharacteristic
30C22⋊C4×C43—22no—
31C22⋊C4×C43—22no—
32C42×C43C2×C411yescharacteristic
33C22⋊Dic43—22no—
34C22⋊Dic43—22no—
35(C2×D43)⋊C4—21no—
36C4⋊Dic43—22no—
37Dic43⋊C4—21no—
38Dic43⋊C4—22no—
39Dic43⋊C4—42no—
40C4×Dic43—42no—
41C4×Dic43C2×C411yescharacteristic
42C23×C43C2×D412yes—
43C22×D43C22⋊C411yescharacteristic
44Q8×C43—41no—
45D4×C43—41no—
46C2×C4×C43—21no—
47C2×C4×C43—21no—
48C2×C4×C43—42no—
49C2×C4×C43C22×C411yescharacteristic
50C22⋊D43—42no—
51C2×Dic43—22no—
52C2×Dic43—22no—
53C2×Dic43—21no—
54C2×Dic43—21no—
55C2×Dic43—42no—
56C2×Dic43C22⋊C412yes—
57C2×Dic43C22⋊C411yescharacteristic
58C4×D43—22no—
59C4×D43—42no—
60Dic86—41no—
61Dic86—42no—
62Dic86—41no—
63C22×C43—22no—
64C22×C43—42no—
65C22×C43C2×C22⋊C411yescharacteristic
66C2×D43—21no—
67C2×D43—41no—
68C4×C43—21no—
69C4×C43—41no—
70C4×C43—41no—
71C4×C43—82no—
72Dic43—22no—
73Dic43—41no—
74Dic43—41no—
75Dic43—82no—
76Dic43#9912yes—
77#2129—431nomaximal, Sylow
78C2×C43—21no—
79C2×C43—42no—
80C2×C43C2×#9911yescharacteristic
81D43—41no—
82#536—431no—
83#410—432no—
84#354—431no—
85#354—432no—
86#354D4311yescharacteristic, complemented
87C43#212911yescharacteristic, complemented, Sylow
88C2×#41—431no—
89C22×Q8—431no—
90C4⋊Q8—431no—
91C4⋊Q8—431no—
92#124—431no—
93#124C2×D4311yescharacteristic
94#123—862no—
95C22⋊Q8—862no—
96#117—431no—
97#117—862no—
98#99—432no—
99#99—862no—
100#99C2×D4312yes—
101#41—1722no—
102C2×Q8—431no—
103C2×Q8—431no—
104C2×Q8—861no—
105C2×Q8—1722no—
106C2×Q8C4×D4311yescharacteristic
107C2×D4—432no—
108C2×D4C22×D4311yescharacteristic
109C22×C4—432no—
110C22×C4—431no—
111C22×C4—861no—
112C4⋊C4—861no—
113C4⋊C4—862no—
114C4⋊C4—862no—
115C4⋊C4—1722no—
116C22⋊C4—22no—
117C22⋊C4—22no—
118C22⋊C4—861no—
119C22⋊C4—862no—
120C22⋊C4—862no—
121C42—431no—
122C42—1722no—
123C42C4×D4311yescharacteristic
124C23—431no—
125C23D4×D4312yes—
126Q8—41no—
127Q8—1721no—
128Q8—1721no—
129Q8—1722no—
130D4—41no—
131D4—1722no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—42no—
135C2×C4—431no—
136C2×C4—432no—
137C2×C4—862no—
138C2×C4—862no—
139C2×C4—862no—
140C2×C4—861no—
141C2×C4—861no—
142C2×C4—1722no—
143C2×C4—1722no—
144C2×C4C2×C4×D4311yescharacteristic
145C22—22no—
146C22—42no—
147C22—861no—
148C22—1721no—
149C22C22⋊C4×D4311yescharacteristic
150C4—21no—
151C4—41no—
152C4—41no—
153C4—82no—
154C4—432no—
155C4—862no—
156C4—3442no—
157C4—1721no—
158C4—1721no—
159C2—21no—
160C2—42no—
161C2—1721no—
162C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#354C2
socleC2×C43C2×#99
hypercenter#354D43
hypocenterC43#2129
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
3. #14582694C2semidirect
4. #14582693C2semidirect
5. C43×#354C2semidirect
7. C2×Q8×D43C4semidirect
8. #13063325C4semidirect
9. #13063323C4semidirect
13. #13063282C4semidirect
86. #354D43semidirect
87. C43#2129semidirect