Finite Group Databasebeta

← #19144288

Subgroups — #19144288

Order 5504.

472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#13063355C211yesmaximal, characteristic, complemented
2C2×#13063332C211yesmaximal, characteristic, complemented
3#14583470C211yesmaximal, characteristic, complemented
4#14583155C212yesmaximal, complemented
5#14583143C212yesmaximal, complemented
6#14583138C212yesmaximal, complemented
7#14583126C212yesmaximal, complemented
8#14582939C211yesmaximal, characteristic, complemented
9#14582895C211yesmaximal, characteristic, complemented
10C2×#13063248C211yesmaximal, characteristic, complemented
11C43×#537C211yesmaximal, characteristic
12C22×Dic86C2211yescharacteristic
13#13063355—24no—
14C2×#10621885C2212yes—
15C2×#10621883C2212yes—
16#13063332—24no—
17C2×#10621877C2212yes—
18C2×#10621877C2211yescharacteristic
19C22×C43⋊C8C2212yes—
20C22×C43⋊C8C2211yescharacteristic
21#13063323—21no—
22#13063312—21no—
23#13063306—22no—
24#13063304C2212yes—
25#13063304C2212yes—
26#13063284C2211yescharacteristic
27#13063258C2212yes—
28#13063256C2212yes—
29#13063249C2211yescharacteristic
30#13063249C2211yescharacteristic
31#13063248C2212yes—
32#13063248C2212yes—
33#13063246C2211yescharacteristic
34#13063246C2211yescharacteristic
35C2×#41×C43C2211yescharacteristic
36C2×#41×C43C2211yescharacteristic
37C22⋊Q8×C43—21no—
38C22⋊Q8×C43C2212yes—
39#121×C43—22no—
40#121×C43—21no—
41#121×C43C2212yes—
42C2×C4⋊C4×C43C2211yescharacteristic
43#41×C43—22no—
44#41×C43—22no—
45#41×C43—22no—
46#41×C43—22no—
47C2×Q8×C43D411yescharacteristic
48C2×Q8×C43C2311yescharacteristic
49C2×D4×C43—21no—
50C2×D4×C43—22no—
51C2×D4×C43D412yes—
52C2×D4×C43D411yescharacteristic
53C2×D4×C43C2311yescharacteristic
54C22×C4×C43—21no—
55C22×C4×C43—21no—
56C22×C4×C43C2312yes—
57C22×C4×C43C2311yescharacteristic
58C22×Dic43—21no—
59C2×Dic86—22no—
60C2×Dic86—22no—
61C2×Dic86—21no—
62C2×Dic86C2312yes—
63C4⋊C4×C43—21no—
64C4⋊C4×C43—22no—
65C4⋊C4×C43C2312yes—
66C22⋊C4×C43—22no—
67C22⋊C4×C43—22no—
68C22⋊Dic43—21no—
69C22⋊Dic43—22no—
70C22⋊Dic43—22no—
71#10621885—24no—
72#10621883—24no—
73C4⋊Dic43C2311yescharacteristic
74C4⋊Dic43C2311yescharacteristic
75Dic43⋊C4—22no—
76Dic43⋊C4—22no—
77C4×Dic43—21no—
78#10621877—24no—
79#10621877D414yescomplemented
80C2×C43⋊C8—22no—
81C2×C43⋊C8—24no—
82C2×C43⋊C8C2311yescharacteristic
83C2×C43⋊C8C2311yescharacteristic
84C2×C43⋊C8C2312yes—
85C23×C43—21no—
86C23×C43C2×D412yes—
87C23×C43C2×D411yescharacteristic
88Q8×C43—22no—
89Q8×C43—21no—
90Q8×C43—21no—
91D4×C43—24no—
92D4×C43—22no—
93D4×C43—21no—
94D4×C43—21no—
95D4×C43—42no—
96D4×C43—82no—
97C2×C4×C43—22no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—42no—
102C2×C4×C43—81no—
103C2×C4×C43C2×D412yes—
104C2×C4×C43C2×D412yes—
105C2×C4×C43C2×D411yescharacteristic
106C2×C4×C43#4112yes—
107C2×C4×C43C2411yescharacteristic
108C2×Dic43—21no—
109C2×Dic43—21no—
110C2×Dic43—22no—
111C2×Dic43—42no—
112Dic86—22no—
113Dic86—22no—
114Dic86—42no—
115C43⋊C8—21no—
116C43⋊C8—21no—
117C43⋊C8C2×D414yes—
118C22×C43—21no—
119C22×C43—21no—
120C22×C43—22no—
121C22×C43—22no—
122C22×C43—22no—
123C22×C43—41no—
124C22×C43—41no—
125C22×C43—41no—
126C22×C43#12112yes—
127C22×C43C22×D411yescharacteristic
128C4×C43—22no—
129C4×C43—41no—
130C4×C43—42no—
131C4×C43#12112yes—
132C4×C43C22×D411yescharacteristic
133C4×C43C2×#4111yescharacteristic
134Dic43—42no—
135Dic43—41no—
136Dic43—41no—
137#3063—431nomaximal, Sylow
138C2×C43—22no—
139C2×C43—42no—
140C2×C43—81no—
141C2×C43C2×#12111yescharacteristic
142C2×C43#57711yescharacteristic
143C2×C43#57811yescharacteristic
144C2×#137—431no—
145C2×#131—431no—
146#537D4311yescharacteristic
147#536—431no—
148#470—432no—
149#468—432no—
150#467—432no—
151#465—432no—
152#428—431no—
153#416—431no—
154C2×#103—431no—
155C43#306311yescharacteristic, complemented, Sylow
156C2×#41C2×D4311yescharacteristic
157C2×#41C2×D4311yescharacteristic
158C22×Q8—431no—
159#137—864no—
160C2×Q16—432no—
161C2×SD16—432no—
162#131—864no—
163C2×M16—431no—
164C2×M16—432no—
165C22×C8—431no—
166C22×C8—432no—
167C4⋊Q8—861no—
168#124—861no—
169#123—862no—
170C22⋊Q8—21no—
171C22⋊Q8—432no—
172C22⋊Q8—432no—
173C22⋊Q8C2×D4312yes—
174#121—21no—
175#121—22no—
176#121C2×D4312yes—
177#117—431no—
178C2×C4⋊C4C2×D4311yescharacteristic
179#107—432no—
180#106—432no—
181#103—431no—
182#103—431no—
183#103—432no—
184#103—432no—
185#102—431no—
186#102—431no—
187#41—22no—
188#41—22no—
189#41—22no—
190#41—22no—
191C2×Q8—432no—
192C2×Q8—861no—
193C2×Q8—862no—
194C2×Q8—862no—
195C2×Q8C22⋊D4311yescharacteristic
196C2×Q8C22×D4311yescharacteristic
197C2×D4—21no—
198C2×D4—22no—
199C2×D4C22⋊D4312yes—
200C2×D4C22⋊D4311yescharacteristic
201C2×D4C22×D4311yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—861no—
205C22×C4C22×D4312yes—
206C22×C4C22×D4311yescharacteristic
207Q16—864no—
208SD16—864no—
209M16—434no—
210M16—864no—
211C2×C8—432no—
212C2×C8—431no—
213C2×C8—431no—
214C2×C8—864no—
215C2×C8—862no—
216C4⋊C4—21no—
217C4⋊C4—22no—
218C4⋊C4—431no—
219C4⋊C4—431no—
220C4⋊C4—862no—
221C4⋊C4—862no—
222C4⋊C4C22×D4312yes—
223C22⋊C4—22no—
224C22⋊C4—22no—
225C22⋊C4—861no—
226C22⋊C4—862no—
227C22⋊C4—862no—
228C42—861no—
229C23—21no—
230C23C2×C22⋊D4312yes—
231C23C2×C22⋊D4311yescharacteristic
232Q8—22no—
233Q8—21no—
234Q8—21no—
235Q8—862no—
236Q8—862no—
237Q8—1722no—
238D4—24no—
239D4—22no—
240D4—21no—
241D4—21no—
242D4—42no—
243D4—82no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—22no—
247C2×C4—21no—
248C2×C4—42no—
249C2×C4—81no—
250C2×C4—861no—
251C2×C4—861no—
252C2×C4—862no—
253C2×C4—1722no—
254C2×C4D4×D4312yes—
255C2×C4#1062190012yes—
256C2×C4C2×C22⋊D4312yes—
257C2×C4C2×C22⋊D4311yescharacteristic
258C2×C4C23×D4311yescharacteristic
259C8—434no—
260C8—861no—
261C8—861no—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—22no—
266C22—22no—
267C22—41no—
268C22—41no—
269C22—41no—
270C22#1306329712yes—
271C22C22×C22⋊D4311yescharacteristic
272C4—22no—
273C4—41no—
274C4—42no—
275C4—1722no—
276C4—1721no—
277C4—1721no—
278C4#1306329712yes—
279C4C2×D4×D4311yescharacteristic
280C4C2×#1062190011yescharacteristic
281C2—22no—
282C2—42no—
283C2—81no—
284C2C2×#1306329711yescharacteristic
285C2#1458371011yescharacteristic
286C2#1458371411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#537C2
socleC22×C43C22×D4
hypercenter#537D43
hypocenterC43#3063
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#13063355C2semidirect
2. C2×#13063332C2semidirect
3. #14583470C2semidirect
4. #14583155C2semidirect
5. #14583143C2semidirect
6. #14583138C2semidirect
7. #14583126C2semidirect
8. #14582939C2semidirect
9. #14582895C2semidirect
10. C2×#13063248C2semidirect
79. #10621877D4semidirect
155. C43#3063semidirect