Finite Group Databasebeta

← #19147661

Subgroups — #19147661

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#14583634C211yesmaximal, characteristic, complemented
2#14583291C211yesmaximal, characteristic, complemented
3#14583289C211yesmaximal, characteristic
4#14583281C211yesmaximal, characteristic, complemented
5#14583121C211yesmaximal, characteristic, complemented
6#14583118C211yesmaximal, characteristic, complemented
7#14583114C211yesmaximal, characteristic, complemented
8#14583111C211yesmaximal, characteristic, complemented
9#14583101C211yesmaximal, characteristic, complemented
10#14583099C211yesmaximal, characteristic, complemented
11#14583030C211yesmaximal, characteristic, complemented
12#14583009C211yesmaximal, characteristic, complemented
13#14583004C211yesmaximal, characteristic, complemented
14C4×#10621884C211yesmaximal, characteristic, complemented
15C43×#556C211yesmaximal, characteristic, complemented
16C2×#10621885C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621884C2211yescharacteristic
20C2×#10621884C2211yescharacteristic
21C2×#10621884C2211yescharacteristic
22C2×#10621884C2211yescharacteristic
23C2×#10621882C2211yescharacteristic
24C2×#10621882C2211yescharacteristic
25#13063322C2211yescharacteristic
26#13063314—21no—
27#13063313C2211yescharacteristic
28#13063313C2211yescharacteristic
29#13063310—21no—
30#13063310—21no—
31C4×Dic86C2211yescharacteristic
32C4×D172C2211yescharacteristic
33C4×D172C2211yescharacteristic
34#13063287—21no—
35#13063256C2211yescharacteristic
36C4⋊(C43⋊C8)C2211yescharacteristic
37C4⋊(C43⋊C8)C2211yescharacteristic
38C4⋊(C43⋊C8)C2211yescharacteristic
39#13063249C2211yescharacteristic
40#13063249C2211yescharacteristic
41#13063248C2211yescharacteristic
42#13063246C2211yescharacteristic
43#13063245C2211yescharacteristic
44#13063245C2211yescharacteristic
45#13063236C2211yescharacteristic
46#13063236C2211yescharacteristic
47C4×C43⋊C8C2211yescharacteristic
48C4⋊Q8×C43C2211yescharacteristic
49#126×C43—21no—
50#126×C43—21no—
51#124×C43C2211yescharacteristic
52#124×C43C2211yescharacteristic
53C22⋊Q8×C43—21no—
54C4×Q8×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4×Q8×C43C2211yescharacteristic
57C4×D4×C43C2211yescharacteristic
58#117×C43—21no—
59C2×Q8×C43D411yescharacteristic
60C2×Q8×C43C2311yescharacteristic
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43—21no—
64C2×D172—21no—
65C2×D172—21no—
66C2×D172C2311yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×Dic86C2311yescharacteristic
71C4⋊C4×C43—21no—
72C4⋊C4×C43—21no—
73C4⋊C4×C43—21no—
74C4⋊C4×C43—21no—
75C4⋊C4×C43D411yescharacteristic
76C4⋊C4×C43D411yescharacteristic
77C4⋊C4×C43D411yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C22⋊C4×C43—21no—
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C22⋊C4×C43—21no—
84C42×C43—21no—
85C42×C43—21no—
86C42×C43C2311yescharacteristic
87C42×C43C2311yescharacteristic
88C42×C43C2311yescharacteristic
89#10621885—22no—
90#10621885—41no—
91#10621884—22no—
92#10621884—41no—
93#10621884—41no—
94#10621884—41no—
95#10621883—41no—
96#10621882—22no—
97#10621882—41no—
98(C2×D43)⋊C4—21no—
99(C2×D43)⋊C4—21no—
100(C2×D43)⋊C4—21no—
101(C2×D43)⋊C4—21no—
102(C2×D43)⋊C4—21no—
103(C2×D43)⋊C4—21no—
104C4⋊Dic43C2311yescharacteristic
105Dic43⋊C4—21no—
106C4×Dic43—21no—
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C23×C43—21no—
112C22×D43—21no—
113C22×D43—21no—
114Q8×C43—21no—
115Q8×C43—21no—
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—41no—
119D4×C43—21no—
120D4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C2×Dic43—21no—
133C2×Dic43—21no—
134D172—21no—
135D172—21no—
136D172—21no—
137D172—21no—
138D172—42no—
139D172—81no—
140C4×D43—81no—
141C4×D43—81no—
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×C43C22×D411yescharacteristic
152C2×D43—41no—
153C2×D43—41no—
154C2×D43—41no—
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×C43—41no—
167C4×C43C2×#4111yescharacteristic
168C4×C43H(5,𝔽2)11yescharacteristic
169Dic43—41no—
170Dic43—41no—
171#3401—431nomaximal, Sylow
172C2×C43—81no—
173C2×C43#55011yescharacteristic
174C2×C43#57511yescharacteristic
175C2×C43#57711yescharacteristic
176D43—81no—
177D43—81no—
178#559—431no—
179#556D4311yescharacteristic, complemented
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⋊Q8C2×D4311yescharacteristic
204#127—431no—
205#126—21no—
206#126—21no—
207#124—431no—
208#124—431no—
209#124—861no—
210#124C2×D4311yescharacteristic
211#124C2×D4311yescharacteristic
212#123—861no—
213#123—861no—
214C22⋊Q8—21no—
215C4×Q8—431no—
216C4×Q8C2×D4311yescharacteristic
217C4×Q8C2×D4311yescharacteristic
218C4×Q8C2×D4311yescharacteristic
219C4×D4—431no—
220C4×D4—431no—
221C4×D4—861no—
222C4×D4C2×D4311yescharacteristic
223#117—21no—
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×Q8C22⋊D4311yescharacteristic
239C2×Q8C22×D4311yescharacteristic
240C2×Q8C22×D4311yescharacteristic
241C2×D4—431no—
242C2×D4—431no—
243C2×D4—861no—
244C2×D4—861no—
245C2×D4C22×D4311yescharacteristic
246C22×C4—21no—
247C22×C4—861no—
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—21no—
264C4⋊C4—21no—
265C4⋊C4—21no—
266C4⋊C4—431no—
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—861no—
278C22⋊C4—861no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C42—21no—
284C42—21no—
285C42—861no—
286C42C22×D4311yescharacteristic
287C42C22×D4311yescharacteristic
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—861no—
291C23—861no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—41no—
297Q8—861no—
298Q8—861no—
299D4—21no—
300D4—21no—
301D4—861no—
302D4—861no—
303D4—861no—
304D4—861no—
305D4—3441no—
306D4—1722no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—42no—
311C2×C4—861no—
312C2×C4—861no—
313C2×C4—3441no—
314C2×C4—3441no—
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—1721no—
330C22—1721no—
331C22—1721no—
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—41no—
345C4—1721no—
346C4—1721no—
347C4#41×D4311yescharacteristic
348C4#1306337111yescharacteristic
349C2—81no—
350C2—3441no—
351C2—3441no—
352C2#1458356811yescharacteristic
353C2#1458369711yescharacteristic
354C2#1458370711yescharacteristic
subgroupG/H
centerC22C22×C22⋊D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#556C2
socleC22×C43C22×D4
hypercenter#556D43
hypocenterC43#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #556

Complements

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

NH ≅ G/Ntype
1. #14583634C2semidirect
2. #14583291C2semidirect
4. #14583281C2semidirect
5. #14583121C2semidirect
6. #14583118C2semidirect
7. #14583114C2semidirect
8. #14583111C2semidirect
9. #14583101C2semidirect
10. #14583099C2semidirect
11. #14583030C2semidirect
12. #14583009C2semidirect
13. #14583004C2semidirect
14. C4×#10621884C2semidirect
15. C43×#556C2semidirect
179. #556D43semidirect
193. C43#3401semidirect