Finite Group Databasebeta

← #355×D43 #19136271

Subgroups — #355×D43 #19136271

Order 5504.

260 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 57 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#124×D43C211yesmaximal, characteristic
2#101×D43C212yesmaximal, complemented
3#14582696C211yesmaximal, characteristic, complemented
4#14582695C212yesmaximal, complemented
5C43×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D43C2211yescharacteristic
7C2×D4×D43C411yescharacteristic
8M16×D43—22no—
9#13063314C2211yescharacteristic
10#13063313C411yescharacteristic
11#13063312C411yescharacteristic
12#13063311—22no—
13C22⋊C4×D43—22no—
14C42×D43C411yescharacteristic
15#13063244C2212yescomplemented
16#13063243—22no—
17#124×C43C2211yescharacteristic
18#101×C43C2212yescomplemented
19C23×D43—21no—
20C2×Q8×C43C2311yescharacteristic
21C2×D4×C43C2×C411yescharacteristic
22C2×C22⋊D43—21no—
23Q8×D43—41no—
24Q8×D43—41no—
25D4×D43—41no—
26D4×D43—41no—
27C2×D172C2×C411yescharacteristic
28C2×C4×D43—21no—
29C2×C4×D43C2×C411yescharacteristic
30C2×C4×D43D412yes—
31C2×Dic86C2×C411yescharacteristic
32C2×Dic86D412yes—
33M16×C43—22no—
34C22⋊C4×C43—22no—
35C42×C43C2×C411yescharacteristic
36C22⋊Dic43—22no—
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—22no—
39C4×Dic43—21no—
40C4×Dic43C2×C411yescharacteristic
41#10621877—22no—
42#10621872—42no—
43C8×D43—42no—
44C23×C43—21no—
45C22×D43—21no—
46C22×D43—44no—
47C22×D43—41no—
48C22×D43—41no—
49C22×D43C22⋊C411yescharacteristic
50Q8×C43—41no—
51D4×C43—41no—
52C2×C4×C43—21no—
53C2×C4×C43C22×C411yescharacteristic
54C2×C4×C43C2×D412yes—
55C22⋊D43—42no—
56C2×Dic43—21no—
57C2×Dic43C22⋊C411yescharacteristic
58C2×Dic43C22⋊C412yes—
59D172—41no—
60C4×D43—22no—
61C4×D43—22no—
62C4×D43—21no—
63C4×D43—21no—
64C4×D43—42no—
65Dic86—41no—
66Dic86—42no—
67C8×C43—42no—
68C43⋊C8—42no—
69C22×C43—42no—
70C22×C43—41no—
71C22×C43C2×C22⋊C411yescharacteristic
72C2×D43—22no—
73C2×D43—42no—
74C2×D43—41no—
75C2×D43—82no—
76C2×D43—82no—
77C2×D43#9911yescharacteristic
78C2×D43#9911yescharacteristic
79C4×C43—22no—
80C4×C43—21no—
81C4×C43—41no—
82Dic43—22no—
83Dic43—21no—
84Dic43—41no—
85C2×#355—431nomaximal, Sylow
86C2×C43—21no—
87C2×C43—81no—
88C2×C43C2×#9911yescharacteristic
89D43—21no—
90D43—81no—
91D43#35512yesdirect product factor
92C2×#124—431no—
93C2×#101—432no—
94#355—431no—
95#355—432no—
96#355D4311yescharacteristic, direct product factor
97C43C2×#35511yescharacteristic, complemented, Sylow
98C22×Q8—431no—
99C22×D4—431no—
100C2×M16—862no—
101#124—431no—
102#124—431no—
103#124—431no—
104#124—862no—
105#124C2×D4311yescharacteristic
106C2×C22⋊C4—862no—
107C2×C42—431no—
108#101—432no—
109#101—862no—
110#101C2×D4312yescomplemented
111C24—861no—
112C2×Q8—431no—
113C2×Q8—432no—
114C2×Q8—1721no—
115C2×Q8—1721no—
116C2×Q8C22×D4311yescharacteristic
117C2×D4—431no—
118C2×D4—861no—
119C2×D4—1721no—
120C2×D4—1721no—
121C2×D4C4×D4311yescharacteristic
122C22×C4—431no—
123C22×C4—432no—
124C22×C4—861no—
125M16—22no—
126M16—862no—
127M16—1722no—
128C2×C8—1722no—
129C22⋊C4—22no—
130C22⋊C4—862no—
131C22⋊C4—862no—
132C22⋊C4—862no—
133C42—431no—
134C42—861no—
135C42C4×D4311yescharacteristic
136C23—21no—
137C23—431no—
138C23—861no—
139C23—1721no—
140C23—1721no—
141C23—1724no—
142Q8—41no—
143Q8—1722no—
144Q8—1721no—
145D4—41no—
146D4—1721no—
147D4—1722no—
148C2×C4—21no—
149C2×C4—431no—
150C2×C4—432no—
151C2×C4—862no—
152C2×C4—862no—
153C2×C4—861no—
154C2×C4—861no—
155C2×C4—861no—
156C2×C4—1722no—
157C2×C4C2×C4×D4311yescharacteristic
158C2×C4D4×D4312yes—
159C8—42no—
160C8—1722no—
161C22—42no—
162C22—41no—
163C22—431no—
164C22—431no—
165C22—862no—
166C22—3442no—
167C22—3442no—
168C22—1722no—
169C22—1721no—
170C22C22⋊C4×D4311yescharacteristic
171C4—22no—
172C4—21no—
173C4—41no—
174C4—861no—
175C4—862no—
176C4—1721no—
177C2—21no—
178C2—81no—
179C2—432no—
180C2—861no—
181C2—3441no—
182C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×Q8C22×D43
FittingC43×#355C2
socleC2×C43C2×#99
hypercenter#355D43
hypocenterC43C2×#355
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D43C2semidirect
3. #14582696C2semidirect
4. #14582695C2semidirect
5. C43×#355C2semidirect
15. #13063244C22semidirect
18. #101×C43C22semidirect
91. D43#355direct (N × H)
96. #355D43direct (N × H)
97. C43C2×#355semidirect
110. #101C2×D43semidirect