Finite Group Databasebeta

← #19146870

Subgroups — #19146870

Order 5504.

380 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583590C211yesmaximal, characteristic, complemented
2#14583557C211yesmaximal, characteristic
3#14583253C211yesmaximal, characteristic, complemented
4#14583233C211yesmaximal, characteristic, complemented
5#14583222C211yesmaximal, characteristic, complemented
6#14583207C211yesmaximal, characteristic, complemented
7#14583154C211yesmaximal, characteristic, complemented
8#14583142C211yesmaximal, characteristic, complemented
9#14583058C211yesmaximal, characteristic, complemented
10#14583053C211yesmaximal, characteristic, complemented
11C4×#10621885C211yesmaximal, characteristic, complemented
12#14582976C211yesmaximal, characteristic, complemented
13#14582906C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#464C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C2×Q8×D43C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063319—21no—
22#13063317C2211yescharacteristic
23#13063315—21no—
24#13063311—21no—
25#13063310—21no—
26#13063302—21no—
27#13063301C2211yescharacteristic
28#13063301C2211yescharacteristic
29#13063301C2211yescharacteristic
30#13063298—21no—
31#13063296C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33C4×D172C2211yescharacteristic
34(C22⋊D43)⋊C4—21no—
35#13063283C2211yescharacteristic
36#13063282—21no—
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C4×C43⋊C8C2211yescharacteristic
52C2×Q16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54#124×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65Q8×D43—22no—
66Q8×D43—41no—
67#10621900—22no—
68#10621900—41no—
69C2×D172D411yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×C4×D43C2311yescharacteristic
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86C2311yescharacteristic
76Q16×C43—41no—
77SD16×C43—41no—
78C2×C8×C43C2311yescharacteristic
79C2×C8×C43C2311yescharacteristic
80C4⋊C4×C43—21no—
81C4⋊C4×C43C2311yescharacteristic
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C42×C43C2311yescharacteristic
86C22⋊Dic43—21no—
87#10621885—22no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4D411yescharacteristic
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43D411yescharacteristic
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109#10621872—41no—
110#10621872—41no—
111C23×C43—21no—
112C22×D43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—42no—
127C22⋊D43—42no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—42no—
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—41no—
136C4×D43—21no—
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—21no—
140C4×D43—42no—
141C4×D43—42no—
142Dic86—21no—
143Dic86—42no—
144Dic86#4112yes—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—21no—
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43C2×#4111yescharacteristic
165C4×C43H(5,𝔽2)11yescharacteristic
166Dic43—22no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171Dic43—41no—
172#3327—431nomaximal, Sylow
173C2×C43—81no—
174C2×C43#54611yescharacteristic
175C2×C43#57511yescharacteristic
176C2×C43#57811yescharacteristic
177D43—41no—
178D43—41no—
179#552—431no—
180#548—431no—
181#488—431no—
182#484—431no—
183#482—431no—
184#479—431no—
185#470—431no—
186#468—431no—
187#464D4311yescharacteristic, complemented
188#452—431no—
189#451—431no—
190C4×Q16—431no—
191#436—431no—
192#419—431no—
193#417—431no—
194C43#332711yescharacteristic, complemented, Sylow
195C2×#41—431no—
196C22×Q8—431no—
197C2×Q16—431no—
198C2×Q16C2×D4311yescharacteristic
199C2×SD16C2×D4311yescharacteristic
200C2×M16—431no—
201C2×M16—431no—
202#126—861no—
203#125—431no—
204#125—861no—
205#124—861no—
206#124C2×D4311yescharacteristic
207#123—861no—
208C22⋊Q8—431no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212#121—431no—
213#121—861no—
214C4×Q8—431no—
215C4×Q8C2×D4311yescharacteristic
216C4×D4—431no—
217C4×D4—861no—
218#117—431no—
219#117—861no—
220C2×C4⋊C4—431no—
221#107—431no—
222#107—431no—
223#106—431no—
224C4⋊C8C2×D4311yescharacteristic
225#103—431no—
226#103—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103C2×D4311yescharacteristic
232#102—431no—
233#102—431no—
234#102C2×D4311yescharacteristic
235C22⋊C8—431no—
236C22⋊C8—431no—
237C4×C8—431no—
238#41—862no—
239#41—1721no—
240C2×Q8—431no—
241C2×Q8—861no—
242C2×Q8—862no—
243C2×Q8—1721no—
244C2×Q8C22×D4311yescharacteristic
245C2×Q8C22×D4311yescharacteristic
246C2×D4—431no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C22×C4—431no—
251C22×C4—431no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255Q16—41no—
256Q16—862no—
257SD16—41no—
258M16—1721no—
259M16—1721no—
260C2×C8—431no—
261C2×C8—431no—
262C2×C8C22×D4311yescharacteristic
263C2×C8C22×D4311yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—431no—
280C22⋊C4—431no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—21no—
287C42—861no—
288C42—861no—
289C42C22×D4311yescharacteristic
290C23—21no—
291C23—431no—
292C23—431no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—21no—
297Q8—432no—
298Q8—861no—
299Q8—1722no—
300D4—21no—
301D4—21no—
302D4—1721no—
303D4—1722no—
304D4—1722no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—861no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—861no—
318C2×C4—1722no—
319C2×C4—1722no—
320C2×C4—1722no—
321C2×C4D4×D4311yescharacteristic
322C2×C4D4×D4311yescharacteristic
323C2×C4C23×D4311yescharacteristic
324C8—21no—
325C8—21no—
326C8—861no—
327C8—861no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—861no—
332C22—861no—
333C22—861no—
334C22—861no—
335C22—861no—
336C22—861no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—861no—
344C4—861no—
345C4—862no—
346C4—1721no—
347C4—1721no—
348C4—1721no—
349C4#41×D4311yescharacteristic
350C4#1306337011yescharacteristic
351C2—81no—
352C2—1721no—
353C2—1721no—
354C2#1458354611yescharacteristic
355C2#1458369611yescharacteristic
356C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#464C2
socleC22×C43C22×D4
hypercenter#464D43
hypocenterC43#3327
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #14583590C2semidirect
3. #14583253C2semidirect
4. #14583233C2semidirect
5. #14583222C2semidirect
6. #14583207C2semidirect
7. #14583154C2semidirect
8. #14583142C2semidirect
9. #14583058C2semidirect
10. #14583053C2semidirect
11. C4×#10621885C2semidirect
12. #14582976C2semidirect
13. #14582906C2semidirect
14. #14582897C2semidirect
15. C43×#464C2semidirect
187. #464D43semidirect
194. C43#3327semidirect