Finite Group Databasebeta

← #19145271

Subgroups — #19145271

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#14583522C211yesmaximal, characteristic, complemented
2#14583502C211yesmaximal, characteristic, complemented
3#14583307C211yesmaximal, characteristic, complemented
4#14583285C211yesmaximal, characteristic, complemented
5#14583255C211yesmaximal, characteristic, complemented
6#14583244C211yesmaximal, characteristic, complemented
7#14583152C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583130C211yesmaximal, characteristic, complemented
10#14583008C211yesmaximal, characteristic, complemented
11#14583002C211yesmaximal, characteristic, complemented
12SD16×Dic43C211yesmaximal, characteristic, complemented
13#14582981C211yesmaximal, characteristic, complemented
14#14582857C211yesmaximal, characteristic, complemented
15C43×#468C211yesmaximal, characteristic, complemented
16C2×#10621884C2211yescharacteristic
17C2×D344C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19C22×C43⋊C8C2211yescharacteristic
20#13063324C2211yescharacteristic
21#13063321C2211yescharacteristic
22#13063320—21no—
23#13063316C2211yescharacteristic
24#13063314C2211yescharacteristic
25#13063311—21no—
26#13063309—21no—
27#13063307—21no—
28#13063307—21no—
29#13063305—21no—
30#13063299C2211yescharacteristic
31#13063299C2211yescharacteristic
32#13063297—21no—
33#13063296—21no—
34Q8×Dic43C2211yescharacteristic
35D4×Dic43C2211yescharacteristic
36#13063287C2211yescharacteristic
37#13063287C2211yescharacteristic
38#13063284C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063246C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063235C2211yescharacteristic
49#13063235C2211yescharacteristic
50C8×Dic43C2211yescharacteristic
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⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68C2×D172C2311yescharacteristic
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43—21no—
72C2×Dic86—21no—
73SD16×C43—22no—
74M16×C43—22no—
75C2×C8×C43C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C4⋊C4×C43—21no—
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43D411yescharacteristic
84C22⋊Dic43D411yescharacteristic
85#10621884—22no—
86#10621882—22no—
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)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43D411yescharacteristic
96C4⋊Dic43D411yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101C4×Dic43—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8—22no—
105C2×C43⋊C8C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107D344—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112Q8×C43—21no—
113Q8×C43—21no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—81no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C22⋊D43—81no—
125C22⋊D43—81no—
126C22⋊D43—81no—
127C22⋊D43—81no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—21no—
136D172—21no—
137D172—21no—
138D172—21no—
139C4×D43—81no—
140C4×D43—81no—
141Dic86—81no—
142C8×C43—21no—
143C8×C43#4112yes—
144C43⋊C8—21no—
145C43⋊C8#4112yes—
146C22×C43—21no—
147C22×C43—21no—
148C22×C43—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—41no—
154C2×D43—41no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43—41no—
163C4×C43C2×#4111yescharacteristic
164C4×C43C2×#4111yescharacteristic
165Dic43—21no—
166Dic43—21no—
167Dic43—21no—
168Dic43—21no—
169Dic43—41no—
170Dic43—41no—
171#3179—431nomaximal, Sylow
172C2×C43—41no—
173C2×C43—81no—
174C2×C43#53211yescharacteristic
175C2×C43#57611yescharacteristic
176C2×C43#57711yescharacteristic
177D43—81no—
178D43—81no—
179#542—431no—
180#540—431no—
181#501—431no—
182#496—431no—
183#488—431no—
184#486—431no—
185#469—431no—
186#468D4311yescharacteristic, complemented
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×SD16C2×D4311yescharacteristic
197C2×D8—431no—
198C2×D8—431no—
199C2×M16C2×D4311yescharacteristic
200C22×C8—431no—
201C4⋊Q8—431no—
202#127—431no—
203#126—861no—
204#125—431no—
205#124—431no—
206#124—861no—
207#123—861no—
208#123—861no—
209#123—861no—
210C22⋊Q8—861no—
211C22⋊Q8C2×D4311yescharacteristic
212#121—431no—
213#121—431no—
214#121—861no—
215#121—861no—
216#121C2×D4311yescharacteristic
217C4×Q8—431no—
218C4×D4—431no—
219C4×D4—431no—
220C4×D4—431no—
221#117—431no—
222#107—431no—
223#107C2×D4311yescharacteristic
224#106—431no—
225#106—431no—
226#103—431no—
227#103C2×D4311yescharacteristic
228#102—431no—
229#102—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102C2×D4311yescharacteristic
234#97—431no—
235#97—431no—
236C4×C8—431no—
237C4×C8—431no—
238C2×Q8—861no—
239C2×Q8C22×D4311yescharacteristic
240C2×D4—21no—
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4—861no—
246C2×D4—861no—
247C2×D4C22×D4311yescharacteristic
248C22×C4—861no—
249C22×C4—861no—
250C22×C4—861no—
251C22×C4C22×D4311yescharacteristic
252SD16—22no—
253SD16—862no—
254D8—862no—
255D8—862no—
256M16—22no—
257C2×C8—431no—
258C2×C8—431no—
259C2×C8—862no—
260C2×C8C22×D4311yescharacteristic
261C2×C8C22×D4311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—431no—
264C4⋊C4—431no—
265C4⋊C4—431no—
266C4⋊C4—431no—
267C4⋊C4—861no—
268C4⋊C4—861no—
269C4⋊C4—861no—
270C4⋊C4—861no—
271C4⋊C4C22×D4311yescharacteristic
272C4⋊C4C22×D4311yescharacteristic
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—431no—
276C22⋊C4—431no—
277C22⋊C4—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C42—431no—
285C42—431no—
286C42—861no—
287C23—21no—
288C23—861no—
289C23—861no—
290C23D4×D4311yescharacteristic
291Q8—21no—
292Q8—21no—
293Q8—3441no—
294D4—21no—
295D4—21no—
296D4—81no—
297D4—861no—
298D4—861no—
299D4—861no—
300D4—861no—
301D4—3441no—
302D4—3441no—
303D4—3441no—
304D4—3441no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—431no—
311C2×C4—431no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—3441no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4D4×D4311yescharacteristic
320C2×C4C23×D4311yescharacteristic
321C8—21no—
322C8—432no—
323C8—861no—
324C8#1062190012yes—
325C22—21no—
326C22—21no—
327C22—21no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—1721no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22—1721no—
336C22—1721no—
337C22C2×D4×D4311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—861no—
343C4—861no—
344C4—861no—
345C4—861no—
346C4—1721no—
347C4—1721no—
348C4#41×D4311yescharacteristic
349C4C2×#1062190011yescharacteristic
350C2—41no—
351C2—81no—
352C2—3441no—
353C2—3441no—
354C2#1458344411yescharacteristic
355C2#1458370311yescharacteristic
356C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#468C2
socleC22×C43C22×D4
hypercenter#468D43
hypocenterC43#3179
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
1. #14583522C2semidirect
2. #14583502C2semidirect
3. #14583307C2semidirect
4. #14583285C2semidirect
5. #14583255C2semidirect
6. #14583244C2semidirect
7. #14583152C2semidirect
8. #14583133C2semidirect
9. #14583130C2semidirect
10. #14583008C2semidirect
11. #14583002C2semidirect
12. SD16×Dic43C2semidirect
13. #14582981C2semidirect
14. #14582857C2semidirect
15. C43×#468C2semidirect
186. #468D43semidirect
194. C43#3179semidirect