Finite Group Databasebeta

← #19144797

Subgroups — #19144797

Order 5504.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583502C211yesmaximal, characteristic, complemented
2#14583380C211yesmaximal, characteristic, complemented
3#14583217C211yesmaximal, characteristic, complemented
4#14583205C211yesmaximal, characteristic, complemented
5#14583202C211yesmaximal, characteristic, complemented
6#14583098C211yesmaximal, characteristic, complemented
7#14583093C211yesmaximal, characteristic, complemented
8#14583046C211yesmaximal, characteristic, complemented
9#14583042C211yesmaximal, characteristic, complemented
10#14583008C211yesmaximal, characteristic, complemented
11#14582998C211yesmaximal, characteristic, complemented
12#14582990C211yesmaximal, characteristic, complemented
13#14582981C211yesmaximal, characteristic, complemented
14#14582957C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21#13063321C2211yescharacteristic
22#13063316C2211yescharacteristic
23#13063309—21no—
24#13063307—21no—
25#13063299C2211yescharacteristic
26#13063297—21no—
27#13063296—21no—
28#13063290C2211yescharacteristic
29#13063290C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31#13063287C2211yescharacteristic
32#13063287C2211yescharacteristic
33#13063287C2211yescharacteristic
34C4×C22⋊D43—21no—
35C4×C22⋊D43—21no—
36#13063284C2211yescharacteristic
37#13063283—21no—
38C4⋊C4×D43—21no—
39#13063256C2211yescharacteristic
40#13063256C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C22×Dic43—21no—
68#10621898—22no—
69#10621898—22no—
70C2×D172C2311yescharacteristic
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×Dic86C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C22⋊Dic43—21no—
85C22⋊Dic43D411yescharacteristic
86C22⋊Dic43D411yescharacteristic
87#10621883—22no—
88#10621882—22no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43D411yescharacteristic
95C4⋊Dic43D411yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100C4×Dic43—21no—
101C4×Dic43—21no—
102C4×Dic43C2311yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106D344—22no—
107#10621873—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—21no—
111C22×D43—21no—
112D4×C43—21no—
113D4×C43—21no—
114D4×C43—81no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—81no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2411yescharacteristic
123C22⋊D43—24no—
124C22⋊D43—81no—
125C22⋊D43—81no—
126C22⋊D43—81no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—81no—
130C2×Dic43C2×D411yescharacteristic
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134D172—21no—
135D172—21no—
136D172—21no—
137D172#4112yes—
138C4×D43—24no—
139C4×D43—81no—
140C4×D43—81no—
141C4×D43—81no—
142Dic86—21no—
143Dic86#4112yes—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—21no—
149C22×C43—21no—
150C22×C43—21no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—22no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—21no—
162C4×C43—41no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43C2×#4111yescharacteristic
166C4×C43C2×#4111yescharacteristic
167Dic43—22no—
168Dic43—21no—
169Dic43—21no—
170Dic43—21no—
171Dic43—21no—
172Dic43—41no—
173#3119—431nomaximal, Sylow
174C2×C43—41no—
175C2×C43—81no—
176C2×C43#52511yescharacteristic
177C2×C43#57611yescharacteristic
178C2×C43#57711yescharacteristic
179D43—42no—
180D43—81no—
181#540—431no—
182#520—431no—
183#481—431no—
184#480D4311yescharacteristic, complemented
185#479—431no—
186#478—431no—
187#460—431no—
188#459—431no—
189#449—431no—
190#449—431no—
191#442—431no—
192#440—431no—
193C4×SD16—431no—
194C4×D8—431no—
195#433—431no—
196C43#311911yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C2×SD16—431no—
199C2×SD16—431no—
200C2×D8—431no—
201C2×D8—431no—
202#127—431no—
203#125—431no—
204#123—861no—
205#123—861no—
206#121—431no—
207#121—861no—
208#121—861no—
209#121C2×D4311yescharacteristic
210C4×Q8—431no—
211C4×Q8—431no—
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—861no—
217C4×D4—861no—
218#117—431no—
219#117—861no—
220C2×C4⋊C4—861no—
221C2×C4⋊C4C2×D4311yescharacteristic
222#107C2×D4311yescharacteristic
223#107C2×D4311yescharacteristic
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228#103—431no—
229#103—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102C2×D4311yescharacteristic
235#102C2×D4311yescharacteristic
236C22⋊C8—431no—
237C22⋊C8C2×D4311yescharacteristic
238#97—431no—
239C4×C8—431no—
240#41—862no—
241#41—862no—
242C2×Q8—431no—
243C2×D4—21no—
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4C22×D4311yescharacteristic
251C22×C4—21no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4C22×D4311yescharacteristic
258SD16—862no—
259SD16—862no—
260D8—862no—
261D8—862no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8C22×D4311yescharacteristic
265C2×C8C22×D4311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4C22×D4311yescharacteristic
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—431no—
279C22⋊C4—431no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C42—431no—
286C42—431no—
287C42—861no—
288C42—861no—
289C23—21no—
290C23—861no—
291C23—861no—
292C23D4×D4311yescharacteristic
293Q8—432no—
294Q8—861no—
295D4—21no—
296D4—21no—
297D4—81no—
298D4—432no—
299D4—864no—
300D4—861no—
301D4—861no—
302D4—861no—
303D4—3441no—
304D4—3441no—
305D4—3441no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—431no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—864no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4—3441no—
323C2×C4D4×D4311yescharacteristic
324C2×C4C23×D4311yescharacteristic
325C8—21no—
326C8—21no—
327C8—861no—
328C8—861no—
329C22—21no—
330C22—21no—
331C22—21no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—862no—
336C22—1721no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22C2×D4×D4311yescharacteristic
342C4—21no—
343C4—41no—
344C4—41no—
345C4—41no—
346C4—862no—
347C4—861no—
348C4—861no—
349C4—861no—
350C4—861no—
351C4—1721no—
352C4#41×D4311yescharacteristic
353C4#41×D4311yescharacteristic
354C2—41no—
355C2—81no—
356C2—3441no—
357C2—1722no—
358C2#1458340711yescharacteristic
359C2#1458370011yescharacteristic
360C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3119
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583502C2semidirect
2. #14583380C2semidirect
3. #14583217C2semidirect
4. #14583205C2semidirect
5. #14583202C2semidirect
6. #14583098C2semidirect
7. #14583093C2semidirect
8. #14583046C2semidirect
9. #14583042C2semidirect
10. #14583008C2semidirect
11. #14582998C2semidirect
12. #14582990C2semidirect
13. #14582981C2semidirect
14. #14582957C2semidirect
15. C43×#480C2semidirect
184. #480D43semidirect
196. C43#3119semidirect