Finite Group Databasebeta

← #19147154

Subgroups — #19147154

Order 5504.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583602C211yesmaximal, characteristic
2#14583587C211yesmaximal, characteristic, complemented
3#14583243C211yesmaximal, characteristic, complemented
4#14583231C211yesmaximal, characteristic, complemented
5#14583225C211yesmaximal, characteristic, complemented
6#14583219C211yesmaximal, characteristic, complemented
7#14583203C211yesmaximal, characteristic, complemented
8#14583196C211yesmaximal, characteristic, complemented
9#14583146C211yesmaximal, characteristic, complemented
10#14583146C211yesmaximal, characteristic, complemented
11C4×#10621873C211yesmaximal, characteristic, complemented
12#14582978C211yesmaximal, characteristic, complemented
13#14582940C211yesmaximal, characteristic, complemented
14#14582940C211yesmaximal, characteristic, complemented
15C43×#499C211yesmaximal, characteristic, complemented
16C2×#10621873C2211yescharacteristic
17C2×#10621872C2211yescharacteristic
18C2×#10621872C2211yescharacteristic
19#13063320—21no—
20#13063320—21no—
21#13063316—21no—
22#13063310—21no—
23#13063310—21no—
24#13063305C2211yescharacteristic
25#13063305C2211yescharacteristic
26#13063300—21no—
27#13063300C2211yescharacteristic
28#13063300C2211yescharacteristic
29C4×Dic86C2211yescharacteristic
30C4×D172C2211yescharacteristic
31C4×D172C2211yescharacteristic
32#13063287—21no—
33#13063283—21no—
34#13063283C2211yescharacteristic
35#13063283C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063256C2211yescharacteristic
43C4⋊(C43⋊C8)C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51(C2×D43)⋊C8C2211yescharacteristic
52#125×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58C4×C8×C43C2211yescharacteristic
59C2×D172—21no—
60C2×D172—21no—
61C2×D172D411yescharacteristic
62C2×D172C2311yescharacteristic
63C2×C4×D43—21no—
64C2×C4×D43—21no—
65C2×C4×D43—21no—
66C2×C4×D43C2311yescharacteristic
67C2×C4×D43C2311yescharacteristic
68C2×Dic86C2311yescharacteristic
69C2×C8×C43C2311yescharacteristic
70C2×C8×C43C2311yescharacteristic
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C42×C43C2311yescharacteristic
80(C2×D43)⋊C4—21no—
81(C2×D43)⋊C4—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4D411yescharacteristic
88(C2×D43)⋊C4D411yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43D411yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97C4×Dic43—21no—
98C4×Dic43—21no—
99C4×Dic43—21no—
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102#10621873—22no—
103#10621872—22no—
104#10621872—22no—
105C22×D43—21no—
106C22×D43C2×D411yescharacteristic
107C22×D43C2×D411yescharacteristic
108C2×C4×C43—21no—
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43C2×D411yescharacteristic
113C2×C4×C43C2×D411yescharacteristic
114C2×C4×C43C2411yescharacteristic
115C2×Dic43—21no—
116C2×Dic43—21no—
117C2×Dic43—21no—
118C2×Dic43C2×D411yescharacteristic
119C2×Dic43C2×D411yescharacteristic
120D172—21no—
121D172—21no—
122D172—41no—
123D172—42no—
124D172—81no—
125C4×D43—21no—
126C4×D43—21no—
127C4×D43—21no—
128C4×D43—21no—
129C4×D43—42no—
130C4×D43—81no—
131C4×D43—81no—
132Dic86—21no—
133Dic86—21no—
134C8×C43—21no—
135C8×C43#4112yes—
136C43⋊C8—21no—
137C43⋊C8—21no—
138C22×C43C22×D411yescharacteristic
139C2×D43—21no—
140C2×D43—21no—
141C2×D43—21no—
142C2×D43—21no—
143C2×D43—21no—
144C2×D43—21no—
145C2×D43—41no—
146C2×D43—41no—
147C2×D43—41no—
148C4×C43—21no—
149C4×C43—21no—
150C4×C43—41no—
151C4×C43—41no—
152C4×C43—41no—
153C4×C43—41no—
154C4×C43C2×#4111yescharacteristic
155C4×C432−1+411yescharacteristic
156Dic43—21no—
157Dic43—21no—
158Dic43—41no—
159Dic43—41no—
160Dic43—41no—
161#3351—431nomaximal, Sylow
162C2×C43#54711yescharacteristic
163C2×C43#57511yescharacteristic
164C2×C43#57711yescharacteristic
165D43—41no—
166D43—41no—
167D43—81no—
168#553—431no—
169#552—431no—
170#499D4311yescharacteristic, complemented
171#485—431no—
172#483—431no—
173#482—431no—
174#481—431no—
175#479—431no—
176#478—431no—
177#468—431no—
178#468—431no—
179C4×SD16—431no—
180#436—431no—
181#428—431no—
182#428—431no—
183C43#335111yescharacteristic, complemented, Sylow
184C2×SD16—431no—
185C2×M16—431no—
186C2×M16—431no—
187#126—861no—
188#126—861no—
189#125—861no—
190#125C2×D4311yescharacteristic
191#125C2×D4311yescharacteristic
192#123—861no—
193#123—861no—
194C22⋊Q8—431no—
195C22⋊Q8—431no—
196#121—431no—
197#121—431no—
198#121—861no—
199C4×Q8—431no—
200C4×D4—431no—
201C4×D4—431no—
202C4×D4—861no—
203#117—431no—
204#117—431no—
205#117—861no—
206C2×C4⋊C4—431no—
207C2×C4⋊C4—431no—
208#107—431no—
209#107—431no—
210#107C2×D4311yescharacteristic
211#107C2×D4311yescharacteristic
212#106—431no—
213#106—431no—
214#106—431no—
215#106C2×D4311yescharacteristic
216#106C2×D4311yescharacteristic
217C4⋊C8—431no—
218#103—431no—
219#103—431no—
220#103—431no—
221#102—431no—
222#102—431no—
223#102—431no—
224C22⋊C8—431no—
225C22⋊C8—431no—
226C4×C8C2×D4311yescharacteristic
227C2×Q8—431no—
228C2×D4—431no—
229C2×D4—431no—
230C2×D4—861no—
231C2×D4—861no—
232C22×C4—431no—
233C22×C4—431no—
234C22×C4—861no—
235C22×C4—861no—
236C22×C4—861no—
237SD16—862no—
238M16—862no—
239M16—862no—
240C2×C8—431no—
241C2×C8—431no—
242C2×C8C22×D4311yescharacteristic
243C2×C8C22×D4311yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—21no—
246C4⋊C4—21no—
247C4⋊C4—21no—
248C4⋊C4—431no—
249C4⋊C4—431no—
250C4⋊C4—431no—
251C4⋊C4—861no—
252C4⋊C4—861no—
253C4⋊C4—861no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4C22×D4311yescharacteristic
257C4⋊C4C22×D4311yescharacteristic
258C4⋊C4C22×D4311yescharacteristic
259C4⋊C4C22×D4311yescharacteristic
260C22⋊C4—431no—
261C22⋊C4—431no—
262C22⋊C4—861no—
263C22⋊C4—861no—
264C22⋊C4—861no—
265C22⋊C4—861no—
266C22⋊C4—861no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C42—861no—
270C42—861no—
271C42—861no—
272C42C22×D4311yescharacteristic
273C23—431no—
274C23—431no—
275C23—861no—
276Q8—861no—
277Q8—861no—
278D4—861no—
279D4—861no—
280D4—3441no—
281D4—1721no—
282D4—1722no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—431no—
288C2×C4—431no—
289C2×C4—861no—
290C2×C4—861no—
291C2×C4—861no—
292C2×C4—861no—
293C2×C4—861no—
294C2×C4—861no—
295C2×C4—861no—
296C2×C4—3441no—
297C2×C4—3441no—
298C2×C4—1722no—
299C2×C4D4×D4311yescharacteristic
300C2×C4D4×D4311yescharacteristic
301C2×C4C23×D4311yescharacteristic
302C8—21no—
303C8—861no—
304C8—861no—
305C8#1062190212yes—
306C22—861no—
307C22—861no—
308C22—861no—
309C22—861no—
310C22—861no—
311C22—861no—
312C22—1721no—
313C22—1721no—
314C22—1721no—
315C22C2×D4×D4311yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—41no—
322C4—861no—
323C4—861no—
324C4—1721no—
325C4—1721no—
326C4—1721no—
327C4C2×#1062190211yescharacteristic
328C4#1306337311yescharacteristic
329C2—3441no—
330C2—1721no—
331C2—1721no—
332C2#1458355211yescharacteristic
333C2#1458369611yescharacteristic
334C2#1458370611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#499C2
socleC22×C43C22×D4
hypercenter#499D43
hypocenterC43#3351
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. #14583587C2semidirect
3. #14583243C2semidirect
4. #14583231C2semidirect
5. #14583225C2semidirect
6. #14583219C2semidirect
7. #14583203C2semidirect
8. #14583196C2semidirect
9. #14583146C2semidirect
10. #14583146C2semidirect
11. C4×#10621873C2semidirect
12. #14582978C2semidirect
13. #14582940C2semidirect
14. #14582940C2semidirect
15. C43×#499C2semidirect
170. #499D43semidirect
183. C43#3351semidirect