Finite Group Databasebeta

← #19134557

Subgroups — #19134557

Order 5504.

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

normal subgroups only

This group has 548 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
1#14583735C211yesmaximal, characteristic
2#14582915C211yesmaximal, characteristic, complemented
3#14582895C211yesmaximal, characteristic, complemented
4#14582893C211yesmaximal, characteristic, complemented
5#14582872C211yesmaximal, characteristic, complemented
6#14582867C211yesmaximal, characteristic, complemented
7C43×#421C211yesmaximal, characteristic, complemented
8#13063373—21no—
9#13063372—21no—
10#13063372C412yescomplemented
11#13063371—21no—
12#13063371C412yescomplemented
13#13063370—21no—
14#13063370—22no—
15C2×#10621898—22no—
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic
18#41×D43—22no—
19#41×D43—22no—
20C22×C43⋊C8C2211yescharacteristic, complemented
21#13063284C2211yescharacteristic, complemented
22#13063251—22no—
23#13063249—21no—
24#13063248—21no—
25#13063246—21no—
26#13063245—21no—
27#13063239—22no—
28(C2×D43)⋊C8—22no—
29C2×#41×C43C2211yescharacteristic
30C2×M16×C43C2211yescharacteristic, complemented
31#117×C43C2211yescharacteristic, complemented
32#104×C43—22no—
33#41×C43—21no—
34#41×C43—21no—
35#41×C43C2×C412yes—
36#41×C43D412yes—
37C2×Q8×C43D411yescharacteristic
38C2×D4×C43—21no—
39C2×D4×C43D411yescharacteristic
40C22×C4×C43—21no—
41C22×C4×C43C2311yescharacteristic
42C2×C22⋊D43—24no—
43C2×C22⋊D43—21no—
44C2×C22⋊D43D412yes—
45#10621902—22no—
46#10621902—22no—
47Q8×D43—22no—
48Q8×D43—22no—
49#10621900—24no—
50#10621900—22no—
51#10621900—22no—
52#10621900—24no—
53D4×D43—22no—
54D4×D43—24no—
55D4×D43—22no—
56D4×D43—24no—
57#10621898—24no—
58#10621898—24no—
59#10621898—21no—
60#10621898—21no—
61#10621898—21no—
62#10621898—21no—
63#10621898—21no—
64#10621898—21no—
65#10621898—22no—
66#10621898—22no—
67#10621898C2×C412yes—
68#10621898D412yes—
69C2×D172—22no—
70C2×D172C2×C411yescharacteristic
71C2×D172D411yescharacteristic
72C2×C4×D43—24no—
73C2×C4×D43—21no—
74C2×C4×D43D412yes—
75C2×Dic86—22no—
76C2×Dic86C2×C411yescharacteristic
77C2×Dic86D411yescharacteristic
78M16×C43—21no—
79M16×C43—21no—
80C2×C8×C43—21no—
81C4⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C42×C43—21no—
84C22⋊Dic43—21no—
85C4⋊Dic43—21no—
86C4×Dic43—21no—
87C2×C43⋊C8—21no—
88C2×C43⋊C8—21no—
89C2×C43⋊C8—21no—
90C23×C43—21no—
91C23×C43C2×D411yescharacteristic
92C22×D43—24no—
93C22×D43—21no—
94C22×D43C22⋊C412yes—
95Q8×C43—21no—
96Q8×C43C22⋊C412yes—
97D4×C43—22no—
98D4×C43—22no—
99D4×C43—21no—
100D4×C43C22⋊C412yes—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—22no—
104C2×C4×C43—41no—
105C2×C4×C43C22×C411yescharacteristic
106C2×C4×C43C2×D411yescharacteristic
107C2×C4×C43C2×D411yescharacteristic
108C2×C4×C43C2×D411yescharacteristic
109C2×C4×C43C2×D411yescharacteristic
110C2×C4×C43C2×D411yescharacteristic
111C22⋊D43—24no—
112C22⋊D43—24no—
113C22⋊D43—22no—
114C22⋊D43—22no—
115C22⋊D43—22no—
116C22⋊D43—22no—
117C2×Dic43—24no—
118C2×Dic43—21no—
119C2×Dic43—41no—
120C2×Dic43C22⋊C412yes—
121D172—24no—
122D172—21no—
123D172—21no—
124D172—21no—
125D172C22⋊C412yes—
126C4×D43—24no—
127C4×D43—24no—
128C4×D43—22no—
129C4×D43—22no—
130C4×D43—22no—
131C4×D43—22no—
132Dic86—24no—
133Dic86—21no—
134Dic86—21no—
135Dic86—21no—
136Dic86C22⋊C412yes—
137C8×C43—41no—
138C43⋊C8—41no—
139C22×C43—22no—
140C22×C43—41no—
141C22×C43—81no—
142C22×C43C2×C22⋊C411yescharacteristic
143C22×C43#12011yescharacteristic
144C22×C43#12011yescharacteristic
145C2×D43—22no—
146C2×D43—22no—
147C2×D43—42no—
148C2×D43—81no—
149C2×D43—84no—
150C4×C43—22no—
151C4×C43—81no—
152C4×C43C2×C22⋊C411yescharacteristic
153C4×C43C2×C22⋊C411yescharacteristic
154C4×C43#12011yescharacteristic
155C4×C43#12011yescharacteristic
156Dic43—22no—
157Dic43—22no—
158Dic43—81no—
159#1794—431nomaximal, Sylow
160C2×C43—21no—
161C2×C43—21no—
162C2×C43—21no—
163C2×C43—42no—
164C2×C43#37911yescharacteristic
165D43—42no—
166D43—42no—
167#585—431no—
168#421—431no—
169#421D4311yescharacteristic, complemented
170#416—431no—
171#416—431no—
172#410—431no—
173#408—431no—
174C43#179411yescharacteristic, complemented, Sylow
1752−1+4—432no—
1762−1+4—861no—
1772−1+4—861no—
178H(5,𝔽2)—432no—
179H(5,𝔽2)—862no—
180H(5,𝔽2)—861no—
181H(5,𝔽2)—861no—
182C2×#41—431no—
183C2×#41—431no—
184C2×#41—862no—
185C2×#41—862no—
186C2×#41—862no—
187C2×#41C2×D4311yescharacteristic
188C2×M16C2×D4311yescharacteristic, complemented
189C22×C8—431no—
190#117—431no—
191#117C2×D4311yescharacteristic, complemented
192#104—22no—
193#104—862no—
194#103—861no—
195#103—861no—
196#102—861no—
197#102—861no—
198#99—862no—
199C22⋊C8—862no—
200#41—21no—
201#41—21no—
202#41—432no—
203#41—432no—
204#41—862no—
205#41—862no—
206#41—864no—
207#41—864no—
208#41—864no—
209#41—864no—
210#41—862no—
211#41—862no—
212#41—862no—
213#41—862no—
214#41—861no—
215#41—861no—
216#41—861no—
217#41—861no—
218#41—861no—
219#41—861no—
220#41C4×D4312yes—
221#41C22⋊D4312yes—
222C2×Q8—431no—
223C2×Q8—431no—
224C2×Q8—862no—
225C2×Q8—862no—
226C2×Q8—862no—
227C2×Q8D17211yescharacteristic
228C2×D4—21no—
229C2×D4—432no—
230C2×D4—431no—
231C2×D4—431no—
232C2×D4—862no—
233C2×D4—864no—
234C2×D4—864no—
235C2×D4—862no—
236C2×D4—864no—
237C2×D4—861no—
238C2×D4—862no—
239C2×D4D17211yescharacteristic
240C22×C4—21no—
241C22×C4—432no—
242C22×C4—864no—
243C22×C4—861no—
244C22×C4C22×D4311yescharacteristic
245M16—21no—
246M16—21no—
247C2×C8—21no—
248C2×C8—861no—
249C2×C8—861no—
250C2×C8—861no—
251C4⋊C4—21no—
252C4⋊C4—861no—
253C22⋊C4—21no—
254C22⋊C4—861no—
255C42—21no—
256C42—861no—
257C23—21no—
258C23—432no—
259C23—864no—
260C23—861no—
261C23D4×D4311yescharacteristic
262Q8—21no—
263Q8—432no—
264Q8—864no—
265Q8—861no—
266Q8—861no—
267Q8—861no—
268Q8(C2×D43)⋊C412yes—
269D4—22no—
270D4—22no—
271D4—21no—
272D4—432no—
273D4—864no—
274D4—864no—
275D4—864no—
276D4—862no—
277D4—862no—
278D4—862no—
279D4—862no—
280D4—861no—
281D4—861no—
282D4—861no—
283D4(C2×D43)⋊C412yes—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—22no—
287C2×C4—41no—
288C2×C4—432no—
289C2×C4—864no—
290C2×C4—864no—
291C2×C4—864no—
292C2×C4—861no—
293C2×C4—862no—
294C2×C4—862no—
295C2×C4—862no—
296C2×C4—862no—
297C2×C4—1721no—
298C2×C4C2×C4×D4311yescharacteristic
299C2×C4C2×D17211yescharacteristic
300C2×C4D4×D4311yescharacteristic
301C2×C4D4×D4311yescharacteristic
302C2×C4D4×D4311yescharacteristic
303C2×C4C2×C22⋊D4311yescharacteristic
304C8—41no—
305C8—1721no—
306C22—22no—
307C22—41no—
308C22—81no—
309C22—862no—
310C22—862no—
311C22—3441no—
312C22—3444no—
313C22—1722no—
314C22C22⋊C4×D4311yescharacteristic
315C22#1306329311yescharacteristic
316C22#1306329511yescharacteristic
317C4—22no—
318C4—81no—
319C4—862no—
320C4—862no—
321C4—3441no—
322C4C22⋊C4×D4311yescharacteristic
323C4C2×(C2×D43)⋊C411yescharacteristic
324C4#1306329311yescharacteristic
325C4#1306329511yescharacteristic
326C2—21no—
327C2—21no—
328C2—21no—
329C2—42no—
330C2—1722no—
331C2—1722no—
332C2#1458275411yescharacteristic
subgroupG/H
centerC4#13063293
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#421C2
socleC2×C43#379
hypercenter#421D43
hypocenterC43#1794
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #14582915C2semidirect
3. #14582895C2semidirect
4. #14582893C2semidirect
5. #14582872C2semidirect
6. #14582867C2semidirect
7. C43×#421C2semidirect
10. #13063372C4semidirect
12. #13063371C4semidirect
20. C22×C43⋊C8C22semidirect
21. #13063284C22semidirect
30. C2×M16×C43C22semidirect
31. #117×C43C22semidirect
169. #421D43semidirect
174. C43#1794semidirect
188. C2×M16C2×D43semidirect
191. #117C2×D43semidirect