Finite Group Databasebeta

← #354×D43 #19136254

Subgroups — #354×D43 #19136254

Order 5504.

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

normal subgroups only

This group has 284 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#99×D43C212yesmaximal
3#14582694C211yesmaximal, characteristic, complemented
4#14582693C212yesmaximal, complemented
5C43×#354C211yesmaximal, characteristic, complemented
6C2×Q8×D43C411yescharacteristic, complemented
7C2×D4×D43C2211yescharacteristic
8#13063314C411yescharacteristic, complemented
9#13063313C411yescharacteristic, complemented
10#13063312C2211yescharacteristic
11#13063311—22no—
12C22⋊C4×D43—22no—
13C22⋊C4×D43—22no—
14C42×D43C411yescharacteristic, complemented
15#13063240C2212yes—
16#13063239—22no—
17#124×C43C2211yescharacteristic
18#99×C43C2212yes—
19C23×D43D412yes—
20C2×Q8×C43C2×C411yescharacteristic, complemented
21C2×D4×C43C2311yescharacteristic
22C2×C22⋊D43D412yes—
23Q8×D43—41no—
24Q8×D43—41no—
25D4×D43—41no—
26D4×D43—41no—
27C2×D172C2×C411yescharacteristic
28C2×C4×D43—21no—
29C2×C4×D43—21no—
30C2×C4×D43—42no—
31C2×C4×D43C2×C411yescharacteristic
32C2×Dic86—21no—
33C2×Dic86C2×C411yescharacteristic, complemented
34C22⋊C4×C43—22no—
35C22⋊C4×C43—22no—
36C42×C43C2×C411yescharacteristic, complemented
37C22⋊Dic43—22no—
38C22⋊Dic43—22no—
39(C2×D43)⋊C4—22no—
40(C2×D43)⋊C4—22no—
41(C2×D43)⋊C4—42no—
42C4×Dic43—21no—
43C4×Dic43C2×C411yescharacteristic, complemented
44C23×C43C2×D412yes—
45C22×D43—22no—
46C22×D43—22no—
47C22×D43—44no—
48C22×D43C22⋊C411yescharacteristic
49C22×D43C22⋊C412yes—
50Q8×C43—41no—
51D4×C43—41no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—42no—
55C2×C4×C43C22×C411yescharacteristic
56C22⋊D43—42no—
57C2×Dic43—21no—
58C2×Dic43—21no—
59C2×Dic43—42no—
60C2×Dic43C22⋊C411yescharacteristic
61D172—41no—
62C4×D43—21no—
63C4×D43—21no—
64C4×D43—42no—
65C4×D43—41no—
66C4×D43—41no—
67C4×D43—84no—
68Dic86—42no—
69Dic86—41no—
70C22×C43—22no—
71C22×C43—42no—
72C22×C43C2×C22⋊C411yescharacteristic
73C2×D43—22no—
74C2×D43—22no—
75C2×D43—44no—
76C2×D43—42no—
77C2×D43—82no—
78C2×D43#9911yescharacteristic
79C2×D43#9911yescharacteristic
80C4×C43—21no—
81C4×C43—41no—
82C4×C43—41no—
83C4×C43—82no—
84Dic43—21no—
85Dic43—41no—
86Dic43—41no—
87Dic43—82no—
88C2×#354—431nomaximal, Sylow
89C2×C43—21no—
90C2×C43—42no—
91C2×C43C2×#9911yescharacteristic
92D43—21no—
93D43—42no—
94D43#35412yesdirect product factor
95C2×#124—431no—
96C2×#99—432no—
97#354—431no—
98#354—432no—
99#354D4311yescharacteristic, direct product factor
100C43C2×#35411yescharacteristic, complemented, Sylow
101C22×Q8—431no—
102C22×D4—431no—
103#124—431no—
104#124—431no—
105#124—431no—
106#124—862no—
107#124C2×D4311yescharacteristic
108C2×C22⋊C4—862no—
109C2×C22⋊C4—862no—
110C2×C42—431no—
111#99—432no—
112#99—862no—
113#99C2×D4312yes—
114C24—432no—
115C2×Q8—431no—
116C2×Q8—861no—
117C2×Q8—1721no—
118C2×Q8—1721no—
119C2×Q8C4×D4311yescharacteristic, complemented
120C2×D4—432no—
121C2×D4—431no—
122C2×D4—1721no—
123C2×D4—1721no—
124C2×D4C22×D4311yescharacteristic
125C22×C4—431no—
126C22×C4—861no—
127C22×C4—861no—
128C22×C4—1722no—
129C22⋊C4—22no—
130C22⋊C4—22no—
131C22⋊C4—862no—
132C22⋊C4—862no—
133C22⋊C4—862no—
134C22⋊C4—862no—
135C22⋊C4—1722no—
136C42—431no—
137C42—861no—
138C42C4×D4311yescharacteristic, complemented
139C23—431no—
140C23—432no—
141C23—862no—
142C23—862no—
143C23—1724no—
144C23D4×D4312yes—
145Q8—41no—
146Q8—1721no—
147Q8—1722no—
148D4—41no—
149D4—1721no—
150D4—1722no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—42no—
154C2×C4—431no—
155C2×C4—861no—
156C2×C4—861no—
157C2×C4—861no—
158C2×C4—861no—
159C2×C4—3444no—
160C2×C4—1721no—
161C2×C4—1721no—
162C2×C4—1722no—
163C2×C4—1722no—
164C2×C4C2×C4×D4311yescharacteristic
165C22—22no—
166C22—42no—
167C22—431no—
168C22—431no—
169C22—862no—
170C22—862no—
171C22—3442no—
172C22—1722no—
173C22—1724no—
174C22C22⋊C4×D4311yescharacteristic
175C4—21no—
176C4—41no—
177C4—41no—
178C4—82no—
179C4—861no—
180C4—3442no—
181C4—1721no—
182C4—1721no—
183C2—21no—
184C2—42no—
185C2—432no—
186C2—861no—
187C2—1722no—
188C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC2×C4×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#354C2
socleC2×C43C2×#99
hypercenter#354D43
hypocenterC43C2×#354
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
6. C2×Q8×D43C4semidirect
8. #13063314C4semidirect
9. #13063313C4semidirect
14. C42×D43C4semidirect
20. C2×Q8×C43C2×C4semidirect
33. C2×Dic86C2×C4semidirect
36. C42×C43C2×C4semidirect
43. C4×Dic43C2×C4semidirect
94. D43#354direct (N × H)
99. #354D43direct (N × H)
100. C43C2×#354semidirect
119. C2×Q8C4×D43semidirect
138. C42C4×D43semidirect