Finite Group Databasebeta

← #19134567

Subgroups — #19134567

Order 5504.

536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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×#13063373C211yesmaximal, characteristic
2#14582917C211yesmaximal, characteristic, complemented
3#14582915C211yesmaximal, characteristic, complemented
4#14582908C211yesmaximal, characteristic, complemented
5#14582881C211yesmaximal, characteristic, complemented
6#14582872C211yesmaximal, characteristic, complemented
7C43×#419C211yesmaximal, characteristic, complemented
8#13063373—22no—
9#13063373—22no—
10#13063373—22no—
11#13063373—22no—
12C2×#10621902—21no—
13C2×#10621902C412yescomplemented
14C2×#10621898—22no—
15C2×#10621898C2211yescharacteristic
16C2×#10621898C2211yescharacteristic
17C2×Q8×D43—21no—
18C2×Q8×D43C412yescomplemented
19C2×#10621877C2211yescharacteristic
20#13063284C2211yescharacteristic
21#13063253—22no—
22#13063251—22no—
23#13063249—22no—
24#13063243—21no—
25#13063241—21no—
26#13063239—22no—
27C22×Q8×C43C2211yescharacteristic
28C2×M16×C43C2211yescharacteristic
29#117×C43C2211yescharacteristic
30#103×C43—22no—
31C2×Q8×C43—21no—
32C2×Q8×C43—21no—
33C2×Q8×C43—21no—
34C2×Q8×C43C2×C412yes—
35C2×Q8×C43D412yes—
36C2×Q8×C43D412yes—
37C22×C4×C43—21no—
38C22×C4×C43C2311yescharacteristic
39C2×C22⋊D43—21no—
40C2×C22⋊D43D412yes—
41#10621902—24no—
42#10621902—24no—
43#10621902—24no—
44#10621902—24no—
45Q8×D43—24no—
46Q8×D43—24no—
47Q8×D43—24no—
48Q8×D43—24no—
49#10621898—28no—
50#10621898—28no—
51#10621898—21no—
52#10621898—21no—
53#10621898—21no—
54#10621898—21no—
55#10621898—21no—
56#10621898—21no—
57#10621898D412yes—
58#10621898D412yes—
59C2×D172—22no—
60C2×D172C2×C411yescharacteristic
61C2×D172D411yescharacteristic
62C2×C4×D43—21no—
63C2×C4×D43—22no—
64C2×C4×D43—22no—
65C2×C4×D43C2×C412yes—
66C2×Dic86—22no—
67C2×Dic86C2×C411yescharacteristic
68C2×Dic86D411yescharacteristic
69M16×C43—21no—
70M16×C43—21no—
71C2×C8×C43—21no—
72C4⋊C4×C43—21no—
73C22⋊C4×C43—21no—
74C42×C43—21no—
75C22⋊Dic43—21no—
76C4⋊Dic43—21no—
77C4×Dic43—21no—
78#10621877—21no—
79#10621877—21no—
80C2×C43⋊C8—21no—
81C23×C43C2×D411yescharacteristic
82C22×D43—21no—
83C22×D43C22⋊C412yes—
84Q8×C43—22no—
85Q8×C43—22no—
86Q8×C43—22no—
87Q8×C43C22⋊C414yes—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—41no—
92C2×C4×C43C22×C411yescharacteristic
93C2×C4×C43C2×D411yescharacteristic
94C2×C4×C43C2×D411yescharacteristic
95C2×C4×C43C2×D411yescharacteristic
96C2×C4×C43C2×D411yescharacteristic
97C2×C4×C43C2×D411yescharacteristic
98C22⋊D43—22no—
99C22⋊D43—22no—
100C22⋊D43—22no—
101C22⋊D43—22no—
102C2×Dic43—21no—
103C2×Dic43—41no—
104C2×Dic43C22⋊C412yes—
105D172—28no—
106D172—21no—
107D172—21no—
108D172—21no—
109D172C22⋊C412yes—
110C4×D43—28no—
111C4×D43—28no—
112C4×D43—22no—
113C4×D43—22no—
114C4×D43—22no—
115C4×D43—22no—
116Dic86—28no—
117Dic86—21no—
118Dic86—21no—
119Dic86—21no—
120Dic86C22⋊C412yes—
121C8×C43—41no—
122C43⋊C8—41no—
123C22×C43—41no—
124C22×C43C2×C22⋊C411yescharacteristic
125C22×C43#12011yescharacteristic
126C22×C43#12011yescharacteristic
127C2×D43—22no—
128C2×D43—22no—
129C2×D43—42no—
130C2×D43—42no—
131C4×C43—24no—
132C4×C43—81no—
133C4×C43C2×C22⋊C411yescharacteristic
134C4×C43C2×C22⋊C411yescharacteristic
135C4×C43#12011yescharacteristic
136C4×C43#12011yescharacteristic
137Dic43—22no—
138Dic43—22no—
139Dic43—81no—
140#1796—431nomaximal, Sylow
141C2×C43—21no—
142C2×C43—21no—
143C2×C43—21no—
144C2×C43#37911yescharacteristic
145D43—42no—
146D43—42no—
147C2×2−1+4—431no—
148#421—431no—
149#421—431no—
150#419—431no—
151#419D4311yescharacteristic, complemented
152#413—431no—
153#410—431no—
154C43#179611yescharacteristic, complemented, Sylow
1552−1+4—862no—
1562−1+4—862no—
1572−1+4—862no—
1582−1+4—862no—
159C2×#41—431no—
160C2×#41—432no—
161C2×#41—431no—
162C2×#41—862no—
163C2×#41—861no—
164C22×Q8—432no—
165C22×Q8—861no—
166C22×Q8C2×D4311yescharacteristic
167C2×M16—431no—
168C2×M16C2×D4311yescharacteristic
169#117—431no—
170#117C2×D4311yescharacteristic
171#104—862no—
172#104—862no—
173#103—22no—
174#103—862no—
175#101—861no—
176#100—861no—
177#99—862no—
178#41—432no—
179#41—432no—
180#41—868no—
181#41—868no—
182#41—864no—
183#41—864no—
184#41—864no—
185#41—864no—
186#41—861no—
187#41—861no—
188#41—861no—
189#41—861no—
190#41—861no—
191#41—861no—
192C2×Q8—21no—
193C2×Q8—21no—
194C2×Q8—21no—
195C2×Q8—431no—
196C2×Q8—431no—
197C2×Q8—862no—
198C2×Q8—864no—
199C2×Q8—864no—
200C2×Q8—864no—
201C2×Q8—864no—
202C2×Q8C4×D4312yes—
203C2×Q8D17212yes—
204C2×Q8C22⋊D4312yes—
205C2×D4—432no—
206C2×D4—431no—
207C2×D4—431no—
208C2×D4—862no—
209C2×D4—861no—
210C22×C4—21no—
211C22×C4—432no—
212C22×C4—862no—
213C22×C4—862no—
214C22×C4—861no—
215C22×C4C22×D4311yescharacteristic
216M16—21no—
217M16—21no—
218M16—861no—
219M16—861no—
220C2×C8—21no—
221C2×C8—861no—
222C4⋊C4—21no—
223C4⋊C4—861no—
224C22⋊C4—21no—
225C22⋊C4—861no—
226C42—21no—
227C42—861no—
228C23—432no—
229C23—861no—
230C23D4×D4311yescharacteristic
231Q8—22no—
232Q8—22no—
233Q8—22no—
234Q8—432no—
235Q8—868no—
236Q8—861no—
237Q8—861no—
238Q8—861no—
239Q8(C2×D43)⋊C414yes—
240D4—432no—
241D4—868no—
242D4—862no—
243D4—862no—
244D4—862no—
245D4—862no—
246D4—861no—
247D4—861no—
248D4—861no—
249C2×C4—22no—
250C2×C4—22no—
251C2×C4—22no—
252C2×C4—41no—
253C2×C4—432no—
254C2×C4—868no—
255C2×C4—868no—
256C2×C4—861no—
257C2×C4—862no—
258C2×C4—862no—
259C2×C4—862no—
260C2×C4—862no—
261C2×C4—1721no—
262C2×C4C2×C4×D4311yescharacteristic
263C2×C4C2×D17211yescharacteristic
264C2×C4D4×D4311yescharacteristic
265C2×C4D4×D4311yescharacteristic
266C2×C4D4×D4311yescharacteristic
267C2×C4C2×C22⋊D4311yescharacteristic
268C8—41no—
269C8—1721no—
270C22—41no—
271C22—862no—
272C22—862no—
273C22—1722no—
274C22—1722no—
275C22C22⋊C4×D4311yescharacteristic
276C22#1306329311yescharacteristic
277C22#1306329511yescharacteristic
278C4—24no—
279C4—81no—
280C4—862no—
281C4—862no—
282C4—3441no—
283C4C22⋊C4×D4311yescharacteristic
284C4C2×(C2×D43)⋊C411yescharacteristic
285C4#1306329311yescharacteristic
286C4#1306329511yescharacteristic
287C2—21no—
288C2—21no—
289C2—21no—
290C2—1722no—
291C2—1722no—
292C2#1458275411yescharacteristic
subgroupG/H
centerC2#14582754
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#419C2
socleC2×C43#379
hypercenter#419D43
hypocenterC43#1796
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. #14582917C2semidirect
3. #14582915C2semidirect
4. #14582908C2semidirect
5. #14582881C2semidirect
6. #14582872C2semidirect
7. C43×#419C2semidirect
13. C2×#10621902C4semidirect
18. C2×Q8×D43C4semidirect
151. #419D43semidirect
154. C43#1796semidirect