Finite Group Databasebeta

← #19147216

Subgroups — #19147216

Order 5504.

354 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583613C211yesmaximal, characteristic
2#14583607C211yesmaximal, characteristic, complemented
3#14583303C211yesmaximal, characteristic, complemented
4#14583238C211yesmaximal, characteristic, complemented
5#14583237C211yesmaximal, characteristic, complemented
6#14583211C211yesmaximal, characteristic, complemented
7#14583210C211yesmaximal, characteristic, complemented
8#14583192C211yesmaximal, characteristic, complemented
9#14583187C211yesmaximal, characteristic, complemented
10#14583142C211yesmaximal, characteristic, complemented
11SD16×Dic43C211yesmaximal, characteristic, complemented
12#14582975C211yesmaximal, characteristic, complemented
13#14582941C211yesmaximal, characteristic, complemented
14#14582940C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621872C2211yescharacteristic
17#13063324C2211yescharacteristic
18#13063324C2211yescharacteristic
19#13063315—21no—
20#13063312—21no—
21#13063311—21no—
22#13063305—21no—
23#13063302—21no—
24#13063301C2211yescharacteristic
25#13063297—21no—
26#13063296C2211yescharacteristic
27Q8×Dic43C2211yescharacteristic
28D4×Dic43C2211yescharacteristic
29C4×C22⋊D43C2211yescharacteristic
30(C22⋊D43)⋊C4—21no—
31#13063284C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063281—21no—
34C2×C4⋊Dic43C2211yescharacteristic
35C4⋊C4×D43C2211yescharacteristic
36#13063259C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063257C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063256C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063249C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54C22⋊Q8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43D411yescharacteristic
65C22×Dic43—21no—
66C22×Dic43—21no—
67C2×C4×D43—21no—
68C2×C4×D43C2311yescharacteristic
69C2×Dic86—21no—
70C2×Dic86—21no—
71SD16×C43—22no—
72M16×C43—22no—
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C22⋊C4×C43—21no—
79C22⋊C4×C43—21no—
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43D411yescharacteristic
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4D411yescharacteristic
87C4⋊Dic43—21no—
88C4⋊Dic43—21no—
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4D411yescharacteristic
98C4×Dic43—21no—
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104#10621872—22no—
105C23×C43—21no—
106C23×C43C2×D411yescharacteristic
107C22×D43C2×D411yescharacteristic
108Q8×C43—21no—
109Q8×C43—21no—
110D4×C43—21no—
111D4×C43—21no—
112D4×C43—81no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C22⋊D43—22no—
121C22⋊D43—81no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—42no—
127C2×Dic43—81no—
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130C2×Dic43C2×D411yescharacteristic
131C4×D43—21no—
132C4×D43—21no—
133C4×D43—81no—
134Dic86—81no—
135Dic86—81no—
136C8×C43—21no—
137C8×C43#4112yes—
138C43⋊C8—21no—
139C43⋊C8—21no—
140C22×C43—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43C22×D411yescharacteristic
147C2×D43—21no—
148C2×D43—21no—
149C2×D43—21no—
150C4×C43—21no—
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—
161Dic43—41no—
162Dic43#13712yes—
163#3357—431nomaximal, Sylow
164C2×C43—41no—
165C2×C43—81no—
166C2×C43#54711yescharacteristic
167C2×C43C2×#13711yescharacteristic
168C2×C43#57611yescharacteristic
169D43—41no—
170#555—431no—
171#554—431no—
172#500—431no—
173#485—431no—
174#485—431no—
175#480—431no—
176#480—431no—
177#477—431no—
178#476—431no—
179#468—431no—
180#468D4311yescharacteristic, complemented
181C4×SD16—431no—
182#436—431no—
183#428—431no—
184#428—431no—
185C43#335711yescharacteristic, complemented, Sylow
186C2×SD16C2×D4311yescharacteristic
187C2×M16—431no—
188C2×M16C2×D4311yescharacteristic
189C4⋊Q8—431no—
190C4⋊Q8—431no—
191#125—861no—
192#124—861no—
193#124—861no—
194C22⋊Q8—431no—
195C22⋊Q8—861no—
196C22⋊Q8—861no—
197C22⋊Q8C2×D4311yescharacteristic
198#121—431no—
199#121—861no—
200#121C2×D4311yescharacteristic
201C4×Q8—431no—
202C4×D4—431no—
203C4×D4—431no—
204C4×D4—861no—
205#117—431no—
206#117—431no—
207#117—861no—
208C2×C4⋊C4—431no—
209C2×C4⋊C4—431no—
210#107—431no—
211#107—431no—
212#107—431no—
213#107—431no—
214#107—431no—
215#107C2×D4311yescharacteristic
216#106—431no—
217#106—431no—
218#106—431no—
219C4⋊C8—431no—
220#103—431no—
221#103—431no—
222#103C2×D4311yescharacteristic
223#102—431no—
224#102—431no—
225#102C2×D4311yescharacteristic
226C22⋊C8—431no—
227C22⋊C8—431no—
228C4×C8—431no—
229C2×Q8—861no—
230C2×Q8—861no—
231C2×Q8C22×D4311yescharacteristic
232C2×D4—21no—
233C2×D4—431no—
234C2×D4—861no—
235C2×D4C22×D4311yescharacteristic
236C22×C4—431no—
237C22×C4—861no—
238C22×C4—861no—
239C22×C4—861no—
240C22×C4C22×D4311yescharacteristic
241SD16—22no—
242M16—22no—
243M16—862no—
244C2×C8—431no—
245C2×C8—431no—
246C2×C8C22×D4311yescharacteristic
247C2×C8C22×D4311yescharacteristic
248C4⋊C4—21no—
249C4⋊C4—431no—
250C4⋊C4—431no—
251C4⋊C4—431no—
252C4⋊C4—431no—
253C4⋊C4—431no—
254C4⋊C4—861no—
255C4⋊C4—861no—
256C4⋊C4—861no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4C22×D4311yescharacteristic
261C4⋊C4C22×D4311yescharacteristic
262C22⋊C4—21no—
263C22⋊C4—21no—
264C22⋊C4—431no—
265C22⋊C4—431no—
266C22⋊C4—861no—
267C22⋊C4—861no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C42—431no—
272C42—861no—
273C42—861no—
274C42—861no—
275C23—21no—
276C23—431no—
277C23D4×D4311yescharacteristic
278Q8—21no—
279Q8—21no—
280Q8—3441no—
281Q8—3441no—
282D4—21no—
283D4—21no—
284D4—81no—
285D4—862no—
286D4—3441no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—431no—
293C2×C4—431no—
294C2×C4—431no—
295C2×C4—861no—
296C2×C4—861no—
297C2×C4—861no—
298C2×C4—861no—
299C2×C4—861no—
300C2×C4—861no—
301C2×C4—3441no—
302C2×C4—3441no—
303C2×C4—1722no—
304C2×C4D4×D4311yescharacteristic
305C2×C4C23×D4311yescharacteristic
306C8—21no—
307C8—861no—
308C8—861no—
309C8#1062190012yes—
310C22—21no—
311C22—21no—
312C22—21no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—861no—
317C22—861no—
318C22—861no—
319C22C2×D4×D4311yescharacteristic
320C4—21no—
321C4—41no—
322C4—41no—
323C4—41no—
324C4—432no—
325C4—861no—
326C4—861no—
327C4—1721no—
328C4—1721no—
329C4—1721no—
330C4—1721no—
331C4C2×#1062190011yescharacteristic
332C4#1306337211yescharacteristic
333C2—41no—
334C2—81no—
335C2—1721no—
336C2#1458354911yescharacteristic
337C2#137×D4311yescharacteristic
338C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3357
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #468

Complements

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

NH ≅ G/Ntype
2. #14583607C2semidirect
3. #14583303C2semidirect
4. #14583238C2semidirect
5. #14583237C2semidirect
6. #14583211C2semidirect
7. #14583210C2semidirect
8. #14583192C2semidirect
9. #14583187C2semidirect
10. #14583142C2semidirect
11. SD16×Dic43C2semidirect
12. #14582975C2semidirect
13. #14582941C2semidirect
14. #14582940C2semidirect
15. C43×#468C2semidirect
180. #468D43semidirect
185. C43#3357semidirect