Finite Group Databasebeta

← #19145283

Subgroups — #19145283

Order 5504.

374 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#14583523C211yesmaximal, characteristic, complemented
2#14583505C211yesmaximal, characteristic, complemented
3#14583288C211yesmaximal, characteristic, complemented
4#14583256C211yesmaximal, characteristic, complemented
5#14583247C211yesmaximal, characteristic, complemented
6#14583153C211yesmaximal, characteristic, complemented
7#14583146C211yesmaximal, characteristic, complemented
8#14583136C211yesmaximal, characteristic, complemented
9#14583129C211yesmaximal, characteristic, complemented
10#14583010C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582986C211yesmaximal, characteristic, complemented
13#14582981C211yesmaximal, characteristic, complemented
14#14582856C211yesmaximal, characteristic, complemented
15C43×#501C211yesmaximal, characteristic, complemented
16C2×#10621873C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×D344C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063322C2211yescharacteristic
23#13063320—21no—
24#13063314—21no—
25#13063313C2211yescharacteristic
26#13063310—21no—
27#13063310—21no—
28#13063310—21no—
29#13063305C2211yescharacteristic
30#13063301—21no—
31#13063300—21no—
32#13063300—21no—
33#13063300C2211yescharacteristic
34#13063300C2211yescharacteristic
35#13063300C2211yescharacteristic
36#13063290C2211yescharacteristic
37#13063287C2211yescharacteristic
38#13063287C2211yescharacteristic
39#13063287C2211yescharacteristic
40#13063282C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063248C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063235C2211yescharacteristic
50C4×C43⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic
53#125×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×D172—21no—
61C2×D172—21no—
62C2×D172—21no—
63C2×D172—21no—
64C2×D172—21no—
65C2×D172C2311yescharacteristic
66C2×D172C2311yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×Dic86C2311yescharacteristic
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43—21no—
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C42×C43C2311yescharacteristic
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
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⋊Dic43—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4D411yescharacteristic
97Dic43⋊C4D411yescharacteristic
98C4×Dic43—21no—
99C4×Dic43C2311yescharacteristic
100C2×C43⋊C8C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102D344—22no—
103D344—22no—
104#10621873—22no—
105#10621873—22no—
106#10621872—22no—
107C8×D43—22no—
108C22×D43—21no—
109C22×D43—21no—
110C22×D43—21no—
111C22×D43C2×D411yescharacteristic
112Q8×C43—81no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2×D411yescharacteristic
119C2×C4×C43C2411yescharacteristic
120C2×Dic43—21no—
121C2×Dic43C2×D411yescharacteristic
122C2×Dic43C2×D411yescharacteristic
123C2×Dic43C2×D411yescharacteristic
124D172—21no—
125D172—21no—
126D172—21no—
127D172—21no—
128D172—21no—
129D172—21no—
130D172—81no—
131D172—81no—
132D172—81no—
133D172—81no—
134D172—81no—
135C4×D43—21no—
136C4×D43—21no—
137C4×D43—81no—
138C4×D43—81no—
139C4×D43—81no—
140Dic86—21no—
141Dic86—21no—
142C8×C43#4112yes—
143C8×C43#4112yes—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C22×C43C22×D411yescharacteristic
147C2×D43—21no—
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43C2×#4111yescharacteristic
166C4×C43C2×#4111yescharacteristic
167Dic43—21no—
168Dic43—21no—
169Dic43—21no—
170Dic43—41no—
171#3179—431nomaximal, Sylow
172C2×C43#53211yescharacteristic
173C2×C43#57611yescharacteristic
174C2×C43#57711yescharacteristic
175D43—41no—
176D43—81no—
177D43—81no—
178D43—81no—
179#542—431no—
180#540—431no—
181#501D4311yescharacteristic, complemented
182#496—431no—
183#488—431no—
184#486—431no—
185#469—431no—
186#468—431no—
187#466—431no—
188#465—431no—
189#442—431no—
190#440—431no—
191C4×SD16—431no—
192C4×D8—431no—
193#405—431no—
194C43#317911yescharacteristic, complemented, Sylow
195C2×SD16—431no—
196C2×SD16—431no—
197C2×D8—431no—
198C2×D8—431no—
199C2×M16—431no—
200C22×C8—431no—
201C4⋊Q8C2×D4311yescharacteristic
202#127—431no—
203#126—861no—
204#125C2×D4311yescharacteristic
205#124—431no—
206#124—861no—
207#123—861no—
208#123—861no—
209#123—861no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212#121—431no—
213#121—431no—
214#121—431no—
215#121—861no—
216#121—861no—
217C4×Q8—431no—
218C4×D4—431no—
219C4×D4—431no—
220C4×D4—431no—
221#117—431no—
222#107C2×D4311yescharacteristic
223#107C2×D4311yescharacteristic
224#106C2×D4311yescharacteristic
225#106C2×D4311yescharacteristic
226#103—431no—
227#103—431no—
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#97—431no—
235#97C2×D4311yescharacteristic
236C4×C8—431no—
237C4×C8—431no—
238C2×Q8—21no—
239C2×Q8—431no—
240C2×D4—431no—
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C2×D4—861no—
247C2×D4—861no—
248C22×C4—431no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4—861no—
252SD16—862no—
253SD16—862no—
254D8—862no—
255D8—862no—
256M16—862no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—862no—
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—21no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4C22×D4311yescharacteristic
270C4⋊C4C22×D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C4⋊C4C22×D4311yescharacteristic
273C22⋊C4—431no—
274C22⋊C4—431no—
275C22⋊C4—861no—
276C22⋊C4—861no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C42—431no—
285C42—861no—
286C42C22×D4311yescharacteristic
287C23—431no—
288C23—861no—
289C23—861no—
290C23—861no—
291Q8—81no—
292Q8—861no—
293Q8—861no—
294D4—861no—
295D4—861no—
296D4—861no—
297D4—861no—
298D4—861no—
299D4—861no—
300D4—3441no—
301D4—3441no—
302D4—3441no—
303D4—3441no—
304D4—3441no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—431no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—3441no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4D4×D4311yescharacteristic
319C2×C4D4×D4311yescharacteristic
320C2×C4C23×D4311yescharacteristic
321C8—861no—
322C8—861no—
323C8#1062190212yes—
324C8#1062190212yes—
325C22—861no—
326C22—861no—
327C22—861no—
328C22—1721no—
329C22—1721no—
330C22—1721no—
331C22—1721no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—21no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—41no—
344C4—861no—
345C4—861no—
346C4—861no—
347C4—1721no—
348C4C2×#1062190211yescharacteristic
349C4C2×#1062190211yescharacteristic
350C2—3441no—
351C2—3441no—
352C2—3441no—
353C2—1721no—
354C2#1458345011yescharacteristic
355C2#1458370311yescharacteristic
356C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#501C2
socleC22×C43C22×D4
hypercenter#501D43
hypocenterC43#3179
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
1. #14583523C2semidirect
2. #14583505C2semidirect
3. #14583288C2semidirect
4. #14583256C2semidirect
5. #14583247C2semidirect
6. #14583153C2semidirect
7. #14583146C2semidirect
8. #14583136C2semidirect
9. #14583129C2semidirect
10. #14583010C2semidirect
11. #14582998C2semidirect
12. #14582986C2semidirect
13. #14582981C2semidirect
14. #14582856C2semidirect
15. C43×#501C2semidirect
181. #501D43semidirect
194. C43#3179semidirect