Finite Group Databasebeta

← #19144408

Subgroups — #19144408

Order 5504.

416 conjugacy classes of subgroups; only the 137 normal subgroups are shown.

normal subgroups only

This group has 416 conjugacy classes of subgroups — too many to draw. Only its 137 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
1C2×#13063324C211yesmaximal, characteristic, complemented
2#14583367C211yesmaximal, characteristic
3#14583193C212yesmaximal, complemented
4#14583188C212yesmaximal, complemented
5#14583183C212yesmaximal, complemented
6#14583178C212yesmaximal, complemented
7#14582942C211yesmaximal, characteristic, complemented
8#14582922C211yesmaximal, characteristic, complemented
9#14582901C211yesmaximal, characteristic
10#14582898C211yesmaximal, characteristic
11C43×#428C211yesmaximal, characteristic, complemented
12C2×#10621898C2211yescharacteristic
13C22×Dic86—21no—
14C2×#10621877C2211yescharacteristic
15#13063324—21no—
16#13063324—21no—
17#13063324C2212yes—
18#13063324C2212yes—
19#13063290C2211yescharacteristic
20#13063290C2211yescharacteristic
21#13063287C2211yescharacteristic
22#13063287C2211yescharacteristic
23(C22⋊D43)⋊C4—21no—
24(C22⋊D43)⋊C4—21no—
25#13063282—21no—
26C2×C4⋊Dic43C2211yescharacteristic
27C2×Dic43⋊C4—21no—
28C2×C4×Dic43C2211yescharacteristic
29C42×D43—21no—
30#13063258C2212yes—
31#13063256C2212yes—
32Dic43⋊C8C2212yes—
33Dic43⋊C8C2212yes—
34#13063250C2212yes—
35#13063248C2212yes—
36#13063247C2212yes—
37#13063245C2212yes—
38C2×M16×C43C2211yescharacteristic
39#117×C43C2211yescharacteristic
40C2×C4⋊C4×C43C2211yescharacteristic
41#107×C43C2212yes—
42#106×C43C2212yes—
43C22×C4×C43—21no—
44C22×C4×C43C2311yescharacteristic
45C2×C22⋊D43—21no—
46C22×Dic43—21no—
47C22×Dic43D411yescharacteristic
48C22×Dic43D411yescharacteristic
49#10621898—22no—
50#10621898Q814yescomplemented
51C2×D172C2311yescharacteristic
52C2×C4×D43—21no—
53C2×C4×D43—21no—
54C2×C4×D43—21no—
55C2×Dic86—22no—
56C2×Dic86—22no—
57C2×Dic86—44no—
58C2×Dic86C2311yescharacteristic
59M16×C43—22no—
60C2×C8×C43C2312yes—
61C4⋊C4×C43—21no—
62C4⋊C4×C43C2311yescharacteristic
63C4⋊C4×C43C2312yes—
64C4⋊C4×C43C2311yescharacteristic
65C22⋊C4×C43—21no—
66C42×C43—21no—
67(C2×D43)⋊C4—21no—
68(C2×D43)⋊C4—21no—
69C4⋊Dic43—21no—
70C4⋊Dic43C2312yes—
71Dic43⋊C4—22no—
72Dic43⋊C4—22no—
73Dic43⋊C4—21no—
74Dic43⋊C4—21no—
75C4×Dic43—21no—
76C4×Dic43—21no—
77C4×Dic43D411yescharacteristic
78C4×Dic43D411yescharacteristic
79C4×Dic43C2311yescharacteristic
80C4×Dic43C2311yescharacteristic
81#10621877—22no—
82C2×C43⋊C8C2312yes—
83C23×C43C2×D411yescharacteristic
84C22×D43—21no—
85C2×C4×C43—21no—
86C2×C4×C43—21no—
87C2×C4×C43—22no—
88C2×C4×C43—42no—
89C2×C4×C43C2×D411yescharacteristic
90C2×C4×C43C2×Q812yes—
91C2×C4×C43#4112yes—
92C2×C4×C43C2411yescharacteristic
93C22⋊D43—24no—
94C2×Dic43—21no—
95C2×Dic43—22no—
96C2×Dic43—22no—
97C2×Dic43—22no—
98C2×Dic43—42no—
99C2×Dic43C2×D411yescharacteristic
100C2×Dic43C2×D411yescharacteristic
101C2×Dic43C2×D411yescharacteristic
102C2×Dic43C2×D411yescharacteristic
103D172—21no—
104D172C2×Q812yescomplemented
105C4×D43—24no—
106C4×D43—42no—
107C4×D43—42no—
108Dic86—21no—
109Dic86—44no—
110Dic86—44no—
111Dic86C2×Q812yescomplemented
112C8×C43—22no—
113C43⋊C8—22no—
114C22×C43—21no—
115C22×C43—21no—
116C22×C43C22⋊Q812yes—
117C22×C43C22×D411yescharacteristic
118C2×D43—22no—
119C2×D43—41no—
120C2×D43—41no—
121C4×C43—42no—
122C4×C43—41no—
123C4×C43—41no—
124C4×C43C22⋊Q812yes—
125C4×C43C22×Q811yescharacteristic
126C4×C43C2×#4111yescharacteristic
127Dic43—22no—
128Dic43—21no—
129Dic43—21no—
130Dic43—42no—
131Dic43AGL(1,ℤ/8)12yes—
132Dic43#13712yes—
133#3079—431nomaximal, Sylow
134C2×C43—22no—
135C2×C43C2×C22⋊Q811yescharacteristic
136C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
137C2×C43C2×#13711yescharacteristic
138D43—42no—
139C2×C4⋊Q8—431no—
140C4×#41—431no—
141#477—432no—
142#476—432no—
143#475—432no—
144#474—432no—
145#428—431no—
146#428D4311yescharacteristic, complemented
147#423—431no—
148#417—431no—
149#417—431no—
150C43#307911yescharacteristic, complemented, Sylow
151C2×#41—431no—
152C22×Q8—861no—
153C2×M16—431no—
154C2×M16C2×D4311yescharacteristic
155C4⋊Q8—432no—
156C4⋊Q8—432no—
157C4⋊Q8—861no—
158C4⋊Q8—861no—
159C4×Q8—431no—
160C4×Q8—431no—
161C4×D4—431no—
162C4×D4—431no—
163C4×D4—861no—
164C4×D4—861no—
165#117—861no—
166#117C2×D4311yescharacteristic
167C2×C4⋊C4—431no—
168C2×C4⋊C4—861no—
169C2×C4⋊C4C2×D4311yescharacteristic
170C2×C42—431no—
171C2×C42—861no—
172#107—432no—
173#107C2×D4312yes—
174#106—432no—
175#106C2×D4312yes—
176C4⋊C8—432no—
177C4⋊C8—432no—
178#103—432no—
179#103—432no—
180#102—432no—
181#102—432no—
182#41—434no—
183#41—862no—
184C2×Q8—431no—
185C2×Q8—862no—
186C2×Q8—862no—
187C2×Q8—1724no—
188C2×D4—431no—
189C2×D4—861no—
190C22×C4—21no—
191C22×C4—431no—
192C22×C4—431no—
193C22×C4—861no—
194C22×C4—861no—
195C22×C4—861no—
196C22×C4—861no—
197C22×C4C22×D4311yescharacteristic
198M16—22no—
199M16—862no—
200C2×C8—432no—
201C2×C8C22×D4312yes—
202C4⋊C4—21no—
203C4⋊C4—432no—
204C4⋊C4—862no—
205C4⋊C4—862no—
206C4⋊C4—861no—
207C4⋊C4—861no—
208C4⋊C4—861no—
209C4⋊C4C22×D4312yes—
210C4⋊C4C22×D4311yescharacteristic
211C4⋊C4C22×D4311yescharacteristic
212C22⋊C4—21no—
213C22⋊C4—861no—
214C22⋊C4—861no—
215C42—21no—
216C42—431no—
217C42—431no—
218C42—431no—
219C42—431no—
220C42—861no—
221C42—861no—
222C23—861no—
223C23D4×D4311yescharacteristic
224Q8—432no—
225Q8—861no—
226Q8—1724no—
227Q8—1724no—
228D4—432no—
229D4—864no—
230D4—861no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—42no—
235C2×C4—431no—
236C2×C4—431no—
237C2×C4—431no—
238C2×C4—431no—
239C2×C4—862no—
240C2×C4—862no—
241C2×C4—861no—
242C2×C4—864no—
243C2×C4—862no—
244C2×C4—1722no—
245C2×C4—1722no—
246C2×C4—1722no—
247C2×C4#1062189812yes—
248C2×C4D4×D4311yescharacteristic
249C2×C4Q8×D4312yes—
250C2×C4C23×D4311yescharacteristic
251C8—22no—
252C8—862no—
253C22—21no—
254C22—21no—
255C22—862no—
256C22—1721no—
257C22—1721no—
258C22#1306330312yes—
259C22C2×D4×D4311yescharacteristic
260C4—42no—
261C4—41no—
262C4—41no—
263C4—432no—
264C4—432no—
265C4—862no—
266C4—861no—
267C4—861no—
268C4—1722no—
269C4#1306330312yes—
270C4C2×Q8×D4311yescharacteristic
271C4C2×#1062189811yescharacteristic
272C2—22no—
273C2—1722no—
274C2C2×#1306330311yescharacteristic
275C2AGL(1,ℤ/8)×D4311yescharacteristic
276C2#137×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3079
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. C2×#13063324C2semidirect
3. #14583193C2semidirect
4. #14583188C2semidirect
5. #14583183C2semidirect
6. #14583178C2semidirect
7. #14582942C2semidirect
8. #14582922C2semidirect
11. C43×#428C2semidirect
50. #10621898Q8semidirect
104. D172C2×Q8semidirect
111. Dic86C2×Q8semidirect
146. #428D43semidirect
150. C43#3079semidirect