Finite Group Databasebeta

← #353×D43 #19136251

Subgroups — #353×D43 #19136251

Order 5504.

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

normal subgroups only

This group has 368 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#127×D43C211yesmaximal, characteristic
2#99×D43C212yesmaximal, complemented
3#14582692C211yesmaximal, characteristic, complemented
4#14582691C212yesmaximal, complemented
5C43×#353C211yesmaximal, characteristic, complemented
6C2×D4×D43—22no—
7C2×D4×D43C411yescharacteristic, complemented
8C2×D4×D43C2211yescharacteristic
9#13063322C411yescharacteristic, complemented
10#13063321—22no—
11#13063321C411yescharacteristic, complemented
12#13063321C2211yescharacteristic
13C22⋊C4×D43—22no—
14C42×D43C411yescharacteristic, complemented
15#13063240C2212yescomplemented
16#13063239—22no—
17#127×C43C2211yescharacteristic
18#99×C43C2212yescomplemented
19C23×D43—21no—
20C23×D43D412yes—
21C2×D4×C43—22no—
22C2×D4×C43C2×C411yescharacteristic, complemented
23C2×D4×C43C2311yescharacteristic
24C2×C22⋊D43—21no—
25C2×C22⋊D43—22no—
26C2×C22⋊D43—22no—
27C2×C22⋊D43D412yes—
28D4×D43—41no—
29D4×D43—41no—
30D4×D43—48no—
31D4×D43—41no—
32D4×D43—41no—
33C2×D172—22no—
34C2×D172C2×C411yescharacteristic
35C2×D172C2×C411yescharacteristic, complemented
36C2×C4×D43—21no—
37C2×C4×D43—42no—
38C2×C4×D43C2×C411yescharacteristic
39C22⋊C4×C43—22no—
40C42×C43C2×C411yescharacteristic, complemented
41C22⋊Dic43—22no—
42(C2×D43)⋊C4—42no—
43C4×Dic43—21no—
44C4×Dic43C2×C411yescharacteristic, complemented
45C23×C43—21no—
46C23×C43C2×D412yes—
47C22×D43—22no—
48C22×D43—22no—
49C22×D43—21no—
50C22×D43—44no—
51C22×D43—44no—
52C22×D43—41no—
53C22×D43—41no—
54C22×D43C22⋊C411yescharacteristic
55C22×D43C22⋊C412yes—
56D4×C43—41no—
57D4×C43—41no—
58D4×C43—44no—
59C2×C4×C43—21no—
60C2×C4×C43—42no—
61C2×C4×C43C22×C411yescharacteristic
62C22⋊D43—42no—
63C22⋊D43—44no—
64C22⋊D43—44no—
65C22⋊D43—42no—
66C2×Dic43—21no—
67C2×Dic43—42no—
68C2×Dic43C22⋊C411yescharacteristic
69D172—41no—
70D172—41no—
71D172—44no—
72C4×D43—24no—
73C4×D43—21no—
74C4×D43—21no—
75C4×D43—84no—
76C22×C43—22no—
77C22×C43—42no—
78C22×C43—42no—
79C22×C43—41no—
80C22×C43C2×C22⋊C411yescharacteristic
81C2×D43—22no—
82C2×D43—22no—
83C2×D43—44no—
84C2×D43—42no—
85C2×D43—42no—
86C2×D43—41no—
87C2×D43—82no—
88C2×D43—82no—
89C2×D43—82no—
90C2×D43#9911yescharacteristic
91C2×D43#9911yescharacteristic
92C4×C43—22no—
93C4×C43—21no—
94C4×C43—82no—
95Dic43—22no—
96Dic43—21no—
97Dic43—82no—
98C2×#353—431nomaximal, Sylow
99C2×C43—21no—
100C2×C43—42no—
101C2×C43—81no—
102C2×C43C2×#9911yescharacteristic
103D43—21no—
104D43—42no—
105D43—81no—
106D43#35312yesdirect product factor
107C2×#127—431no—
108C2×#99—432no—
109#353—431no—
110#353—432no—
111#353D4311yescharacteristic, direct product factor
112C43C2×#35311yescharacteristic, complemented, Sylow
113C22×D4—431no—
114C22×D4—431no—
115C22×D4—862no—
116#127—431no—
117#127—431no—
118#127—431no—
119#127—862no—
120#127C2×D4311yescharacteristic
121C2×C22⋊C4—862no—
122C2×C42—431no—
123#99—432no—
124#99—862no—
125#99C2×D4312yescomplemented
126C24—432no—
127C24—861no—
128C2×D4—22no—
129C2×D4—432no—
130C2×D4—431no—
131C2×D4—431no—
132C2×D4—862no—
133C2×D4—861no—
134C2×D4—862no—
135C2×D4—862no—
136C2×D4—1721no—
137C2×D4—1721no—
138C2×D4—1721no—
139C2×D4—1721no—
140C2×D4—1728no—
141C2×D4C4×D4311yescharacteristic, complemented
142C2×D4C22×D4311yescharacteristic
143C22×C4—431no—
144C22×C4—861no—
145C22×C4—1722no—
146C22⋊C4—22no—
147C22⋊C4—862no—
148C22⋊C4—1722no—
149C42—431no—
150C42—861no—
151C42C4×D4311yescharacteristic, complemented
152C23—21no—
153C23—431no—
154C23—432no—
155C23—862no—
156C23—862no—
157C23—861no—
158C23—1721no—
159C23—1721no—
160C23—1724no—
161C23—1724no—
162C23D4×D4312yes—
163D4—41no—
164D4—41no—
165D4—44no—
166D4—1721no—
167D4—1721no—
168D4—1724no—
169D4—1722no—
170D4—1724no—
171D4—1724no—
172D4—1722no—
173C2×C4—21no—
174C2×C4—42no—
175C2×C4—431no—
176C2×C4—861no—
177C2×C4—861no—
178C2×C4—864no—
179C2×C4—861no—
180C2×C4—3444no—
181C2×C4—1722no—
182C2×C4C2×C4×D4311yescharacteristic
183C22—22no—
184C22—42no—
185C22—42no—
186C22—41no—
187C22—431no—
188C22—431no—
189C22—862no—
190C22—862no—
191C22—3442no—
192C22—3442no—
193C22—3442no—
194C22—1722no—
195C22—1722no—
196C22—1724no—
197C22—1721no—
198C22C22⋊C4×D4311yescharacteristic
199C4—22no—
200C4—21no—
201C4—82no—
202C4—862no—
203C4—861no—
204C4—3442no—
205C2—21no—
206C2—42no—
207C2—81no—
208C2—432no—
209C2—861no—
210C2—3441no—
211C2—1722no—
212C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#353C2
socleC2×C43C2×#99
hypercenter#353D43
hypocenterC43C2×#353
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #353

Complements

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

NH ≅ G/Ntype
2. #99×D43C2semidirect
3. #14582692C2semidirect
4. #14582691C2semidirect
5. C43×#353C2semidirect
7. C2×D4×D43C4semidirect
9. #13063322C4semidirect
11. #13063321C4semidirect
14. C42×D43C4semidirect
15. #13063240C22semidirect
18. #99×C43C22semidirect
22. C2×D4×C43C2×C4semidirect
35. C2×D172C2×C4semidirect
40. C42×C43C2×C4semidirect
44. C4×Dic43C2×C4semidirect
106. D43#353direct (N × H)
111. #353D43direct (N × H)
112. C43C2×#353semidirect
125. #99C2×D43semidirect
141. C2×D4C4×D43semidirect
151. C42C4×D43semidirect