Finite Group Databasebeta

← #352×D43 #19136229

Subgroups — #352×D43 #19136229

Order 5504.

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

normal subgroups only

This group has 278 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#123×D43C211yesmaximal, characteristic
2#100×D43C211yesmaximal, characteristic
3#99×D43C211yesmaximal, characteristic
4#14582690C211yesmaximal, characteristic, complemented
5#14582689C211yesmaximal, characteristic, complemented
6#14582688C211yesmaximal, characteristic, complemented
7C43×#352C211yesmaximal, characteristic, complemented
8C2×D4×D43C2211yescharacteristic
9C22×C4×D43C411yescharacteristic, complemented
10M16×D43—21no—
11#13063310—21no—
12#13063309C411yescharacteristic, complemented
13#13063308C411yescharacteristic, complemented
14#13063307—21no—
15#13063306C2211yescharacteristic
16C4⋊C4×D43—21no—
17C22⋊C4×D43—21no—
18C22⋊C4×D43—21no—
19C22⋊C4×D43C411yescharacteristic, complemented
20#13063242C2211yescharacteristic
21#13063241—21no—
22#13063240C2211yescharacteristic
23#13063239—21no—
24#123×C43C2211yescharacteristic
25#100×C43C2211yescharacteristic
26#99×C43C2211yescharacteristic
27C23×D43C2×C411yescharacteristic
28C23×D43D411yescharacteristic
29C2×D4×C43C2311yescharacteristic
30C22×C4×C43C2×C411yescharacteristic, complemented
31C2×C22⋊D43C2×C411yescharacteristic
32C2×C22⋊D43D411yescharacteristic
33C22×Dic43C2×C411yescharacteristic, complemented
34D4×D43—41no—
35D4×D43—41no—
36C2×D172D411yescharacteristic
37C2×C4×D43—21no—
38C2×C4×D43—21no—
39C2×C4×D43—21no—
40C2×C4×D43—41no—
41C2×C4×D43—41no—
42C2×C4×D43—41no—
43C2×C4×D43D411yescharacteristic
44M16×C43—21no—
45C4⋊C4×C43—21no—
46C22⋊C4×C43—21no—
47C22⋊C4×C43—21no—
48C22⋊C4×C43C2×C411yescharacteristic, complemented
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C22⋊Dic43C2×C411yescharacteristic, complemented
52(C2×D43)⋊C4—21no—
53(C2×D43)⋊C4—21no—
54(C2×D43)⋊C4—21no—
55(C2×D43)⋊C4—41no—
56C4⋊Dic43—21no—
57Dic43⋊C4—21no—
58Dic43⋊C4—21no—
59#10621877—21no—
60#10621872—41no—
61C8×D43—41no—
62C23×C43C22×C411yescharacteristic
63C23×C43C2×D411yescharacteristic
64C22×D43—21no—
65C22×D43—21no—
66C22×D43—21no—
67C22×D43—21no—
68C22×D43—42no—
69C22×D43—42no—
70C22×D43C22⋊C411yescharacteristic
71C22×D43C22⋊C411yescharacteristic
72C22×D43C22⋊C411yescharacteristic
73D4×C43—41no—
74C2×C4×C43—21no—
75C2×C4×C43—21no—
76C2×C4×C43—41no—
77C2×C4×C43—41no—
78C2×C4×C43C2×D411yescharacteristic
79C22⋊D43—41no—
80C22⋊D43—41no—
81C2×Dic43—21no—
82C2×Dic43—21no—
83C2×Dic43—41no—
84C2×Dic43—41no—
85C2×Dic43C22⋊C411yescharacteristic
86D172—41no—
87C4×D43—21no—
88C4×D43—21no—
89C4×D43—42no—
90C4×D43—42no—
91C4×D43—41no—
92C4×D43—41no—
93C4×D43—82no—
94C8×C43—41no—
95C43⋊C8—41no—
96C22×C43—21no—
97C22×C43—21no—
98C22×C43—41no—
99C22×C43—41no—
100C22×C43C2×C22⋊C411yescharacteristic
101C2×D43—22no—
102C2×D43—21no—
103C2×D43—21no—
104C2×D43—42no—
105C2×D43—42no—
106C2×D43—42no—
107C2×D43—41no—
108C2×D43—41no—
109C2×D43—81no—
110C2×D43#9911yescharacteristic
111C2×D43#9911yescharacteristic
112C4×C43—21no—
113C4×C43—41no—
114C4×C43—41no—
115C4×C43—81no—
116Dic43—21no—
117Dic43—41no—
118Dic43—41no—
119Dic43—81no—
120C2×#352—431nomaximal, Sylow
121C2×C43—21no—
122C2×C43—41no—
123C2×C43—41no—
124C2×C43C2×#9911yescharacteristic
125D43—21no—
126D43—41no—
127D43—41no—
128D43#35212yesdirect product factor
129C2×#123—431no—
130C2×#100—431no—
131C2×#99—431no—
132#352—431no—
133#352—431no—
134#352—431no—
135#352D4311yescharacteristic, direct product factor
136C43C2×#35211yescharacteristic, complemented, Sylow
137C22×D4—431no—
138C23×C4—431no—
139C2×M16—861no—
140#123—431no—
141#123—431no—
142#123—431no—
143#123—861no—
144#123—861no—
145#123C2×D4311yescharacteristic
146C2×C4⋊C4—861no—
147C2×C22⋊C4—431no—
148C2×C22⋊C4—861no—
149C2×C22⋊C4—861no—
150#100—431no—
151#100—861no—
152#100C2×D4311yescharacteristic
153#99—431no—
154#99—861no—
155#99C2×D4311yescharacteristic
156C24—431no—
157C24—431no—
158C2×D4—431no—
159C2×D4—431no—
160C2×D4—431no—
161C2×D4—1721no—
162C2×D4—1721no—
163C2×D4C22×D4311yescharacteristic
164C22×C4—431no—
165C22×C4—431no—
166C22×C4—861no—
167C22×C4—861no—
168C22×C4—861no—
169C22×C4—1721no—
170C22×C4—1721no—
171C22×C4—1721no—
172C22×C4C4×D4311yescharacteristic, complemented
173M16—21no—
174M16—861no—
175M16—1721no—
176C2×C8—1721no—
177C4⋊C4—21no—
178C4⋊C4—861no—
179C4⋊C4—861no—
180C4⋊C4—861no—
181C22⋊C4—21no—
182C22⋊C4—21no—
183C22⋊C4—431no—
184C22⋊C4—861no—
185C22⋊C4—861no—
186C22⋊C4—861no—
187C22⋊C4—861no—
188C22⋊C4—861no—
189C22⋊C4—1721no—
190C22⋊C4C4×D4311yescharacteristic, complemented
191C23—431no—
192C23—431no—
193C23—431no—
194C23—861no—
195C23—861no—
196C23—861no—
197C23—861no—
198C23—1722no—
199C23—1722no—
200C23C2×C4×D4311yescharacteristic
201C23D4×D4311yescharacteristic
202D4—41no—
203D4—1721no—
204D4—1721no—
205D4—1721no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—431no—
211C2×C4—861no—
212C2×C4—861no—
213C2×C4—861no—
214C2×C4—861no—
215C2×C4—3442no—
216C2×C4—1721no—
217C2×C4—1721no—
218C2×C4—1722no—
219C2×C4—1722no—
220C2×C4—1721no—
221C2×C4—1721no—
222C2×C4D4×D4311yescharacteristic
223C8—41no—
224C8—1721no—
225C22—21no—
226C22—21no—
227C22—41no—
228C22—41no—
229C22—431no—
230C22—431no—
231C22—862no—
232C22—861no—
233C22—861no—
234C22—3441no—
235C22—1721no—
236C22—1721no—
237C22—1722no—
238C22—1722no—
239C22—1722no—
240C22C22⋊C4×D4311yescharacteristic
241C4—21no—
242C4—41no—
243C4—41no—
244C4—81no—
245C4—861no—
246C4—3441no—
247C4—1721no—
248C4—1721no—
249C2—21no—
250C2—41no—
251C2—41no—
252C2—432no—
253C2—861no—
254C2—1721no—
255C2—1721no—
256C2#99×D4311yescharacteristic
subgroupG/H
centerC2#99×D43
commutatorC23×C43C22×C4
FrattiniC2×D4C22×D43
FittingC43×#352C2
socleC2×C43C2×#99
hypercenter#352D43
hypocenterC43C2×#352
LCSG ▷ C23×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #352

Complements

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

NH ≅ G/Ntype
4. #14582690C2semidirect
5. #14582689C2semidirect
6. #14582688C2semidirect
7. C43×#352C2semidirect
9. C22×C4×D43C4semidirect
12. #13063309C4semidirect
13. #13063308C4semidirect
19. C22⋊C4×D43C4semidirect
30. C22×C4×C43C2×C4semidirect
33. C22×Dic43C2×C4semidirect
48. C22⋊C4×C43C2×C4semidirect
51. C22⋊Dic43C2×C4semidirect
128. D43#352direct (N × H)
135. #352D43direct (N × H)
136. C43C2×#352semidirect
172. C22×C4C4×D43semidirect
190. C22⋊C4C4×D43semidirect