Finite Group Databasebeta

← #19147655

Subgroups — #19147655

Order 5504.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583622C211yesmaximal, characteristic, complemented
2#14583294C211yesmaximal, characteristic, complemented
3#14583286C211yesmaximal, characteristic
4#14583281C211yesmaximal, characteristic, complemented
5#14583121C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583104C211yesmaximal, characteristic, complemented
10#14583096C211yesmaximal, characteristic, complemented
11#14583030C211yesmaximal, characteristic, complemented
12#14583009C211yesmaximal, characteristic, complemented
13#14583004C211yesmaximal, characteristic, complemented
14C4×#10621883C211yesmaximal, characteristic, complemented
15C43×#559C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621883C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063325C2211yescharacteristic
26#13063320—21no—
27#13063320—21no—
28#13063313C2211yescharacteristic
29#13063313C2211yescharacteristic
30#13063301—21no—
31C4×Dic86C2211yescharacteristic
32C4×Dic86C2211yescharacteristic
33C4×D172C2211yescharacteristic
34#13063283—21no—
35#13063256C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063248C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063246C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063236C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48#127×C43C2211yescharacteristic
49#124×C43—21no—
50#124×C43C2211yescharacteristic
51#124×C43C2211yescharacteristic
52#123×C43—21no—
53#123×C43—21no—
54C4×Q8×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4×D4×C43—21no—
57C4×D4×C43C2211yescharacteristic
58C4×D4×C43C2211yescharacteristic
59C2×Q8×C43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×D4×C43—21no—
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C2×D4×C43C2311yescharacteristic
65C22×C4×C43—21no—
66C22×C4×C43—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×Dic86C2311yescharacteristic
70C2×Dic86C2311yescharacteristic
71C4⋊C4×C43—21no—
72C4⋊C4×C43D411yescharacteristic
73C4⋊C4×C43D411yescharacteristic
74C4⋊C4×C43D411yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C22⋊C4×C43—21no—
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C42×C43—21no—
83C42×C43C2311yescharacteristic
84C42×C43C2311yescharacteristic
85C42×C43C2311yescharacteristic
86#10621885—22no—
87#10621885—41no—
88#10621884—41no—
89#10621883—22no—
90#10621883—41no—
91#10621883—41no—
92#10621883—41no—
93#10621882—22no—
94#10621882—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4—21no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100C4⋊Dic43—21no—
101C4⋊Dic43—21no—
102C4⋊Dic43C2311yescharacteristic
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C23×C43—21no—
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—41no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—42no—
122D4×C43—81no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—81no—
126C2×C4×C43—81no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137D172—21no—
138D172—21no—
139C4×D43—42no—
140Dic86—21no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144C43⋊C8—21no—
145C43⋊C8—21no—
146C43⋊C8—21no—
147C43⋊C8#4112yes—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C4×C43—21no—
159C4×C43—21no—
160C4×C43—21no—
161C4×C43—21no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43H(5,𝔽2)11yescharacteristic
168Dic43—41no—
169Dic43—41no—
170Dic43—41no—
171#3401—431nomaximal, Sylow
172C2×C43—81no—
173C2×C43—81no—
174C2×C43#55011yescharacteristic
175C2×C43#57511yescharacteristic
176C2×C43#57711yescharacteristic
177D43—81no—
178#559D4311yescharacteristic, complemented
179#556—431no—
180#497—431no—
181#496—431no—
182#495—431no—
183#464—431no—
184#464—431no—
185#463—431no—
186#463—431no—
187#461—431no—
188#460—431no—
189#446—431no—
190#442—431no—
191#441—431no—
192C4×SD16—431no—
193C43#340111yescharacteristic, complemented, Sylow
194C2×Q16—431no—
195C2×Q16—431no—
196C2×SD16—431no—
197C2×SD16—431no—
198C2×SD16—431no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
202C2×D8—431no—
203C4⋊Q8—431no—
204#127C2×D4311yescharacteristic
205#126—861no—
206#126—861no—
207#124—21no—
208#124—431no—
209#124—431no—
210#124C2×D4311yescharacteristic
211#124C2×D4311yescharacteristic
212#123—21no—
213#123—21no—
214C22⋊Q8—861no—
215C4×Q8—431no—
216C4×Q8—431no—
217C4×Q8C2×D4311yescharacteristic
218C4×Q8C2×D4311yescharacteristic
219C4×D4—21no—
220C4×D4—431no—
221C4×D4C2×D4311yescharacteristic
222C4×D4C2×D4311yescharacteristic
223#117—861no—
224#106—431no—
225C4⋊C8—431no—
226C4⋊C8—431no—
227C4⋊C8—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#97—431no—
235#97—431no—
236C4×C8—431no—
237C2×Q8—431no—
238C2×Q8—431no—
239C2×Q8C22⋊D4311yescharacteristic
240C2×Q8C22×D4311yescharacteristic
241C2×D4—21no—
242C2×D4—21no—
243C2×D4—431no—
244C2×D4C22×D4311yescharacteristic
245C2×D4C22×D4311yescharacteristic
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—861no—
249Q16—862no—
250Q16—1721no—
251SD16—862no—
252SD16—1721no—
253SD16—1721no—
254SD16—1721no—
255SD16—1721no—
256D8—862no—
257D8—1721no—
258C2×C8—431no—
259C2×C8—431no—
260C2×C8—431no—
261C2×C8—431no—
262C4⋊C4—21no—
263C4⋊C4—431no—
264C4⋊C4—861no—
265C4⋊C4—861no—
266C4⋊C4—861no—
267C4⋊C4—861no—
268C4⋊C4C22⋊D4311yescharacteristic
269C4⋊C4C22⋊D4311yescharacteristic
270C4⋊C4C22⋊D4311yescharacteristic
271C4⋊C4C22×D4311yescharacteristic
272C22⋊C4—21no—
273C22⋊C4—21no—
274C22⋊C4—21no—
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—21no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—21no—
284C42—861no—
285C42—861no—
286C42C22×D4311yescharacteristic
287C42C22×D4311yescharacteristic
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—21no—
291C23—861no—
292Q8—21no—
293Q8—21no—
294Q8—41no—
295Q8—861no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—42no—
304D4—81no—
305D4—861no—
306D4—861no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—81no—
310C2×C4—81no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—1722no—
315C2×C4C2×C22⋊D4311yescharacteristic
316C2×C4C2×C22⋊D4311yescharacteristic
317C2×C4C2×C22⋊D4311yescharacteristic
318C2×C4C2×C22⋊D4311yescharacteristic
319C2×C4C2×C22⋊D4311yescharacteristic
320C2×C4C2×C22⋊D4311yescharacteristic
321C2×C4C23×D4311yescharacteristic
322C8—432no—
323C8—861no—
324C8—861no—
325C8—861no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—1721no—
333C22—1721no—
334C22—1721no—
335C22C22×C22⋊D4311yescharacteristic
336C4—21no—
337C4—21no—
338C4—21no—
339C4—21no—
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—1721no—
345C4—1721no—
346C4—1721no—
347C4#41×D4311yescharacteristic
348C4#1306337111yescharacteristic
349C2—81no—
350C2—81no—
351C2—3441no—
352C2#1458356811yescharacteristic
353C2#1458369711yescharacteristic
354C2#1458371011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#559C2
socleC22×C43C22×D4
hypercenter#559D43
hypocenterC43#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #14583622C2semidirect
2. #14583294C2semidirect
4. #14583281C2semidirect
5. #14583121C2semidirect
6. #14583118C2semidirect
7. #14583114C2semidirect
8. #14583111C2semidirect
9. #14583104C2semidirect
10. #14583096C2semidirect
11. #14583030C2semidirect
12. #14583009C2semidirect
13. #14583004C2semidirect
14. C4×#10621883C2semidirect
15. C43×#559C2semidirect
178. #559D43semidirect
193. C43#3401semidirect