Finite Group Databasebeta

← #19146579

Subgroups — #19146579

Order 5504.

420 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583556C211yesmaximal, characteristic, complemented
2#14583549C211yesmaximal, characteristic, complemented
3#14583257C211yesmaximal, characteristic, complemented
4#14583235C211yesmaximal, characteristic, complemented
5#14583211C211yesmaximal, characteristic, complemented
6#14583192C211yesmaximal, characteristic, complemented
7#14583143C211yesmaximal, characteristic, complemented
8#14583132C211yesmaximal, characteristic, complemented
9#14583112C211yesmaximal, characteristic, complemented
10#14583036C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12#14582973C211yesmaximal, characteristic, complemented
13#14582900C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#449C211yesmaximal, characteristic, complemented
16C2×#10621900—21no—
17C2×Q8×D43C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621877C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063312—21no—
23#13063312C2211yescharacteristic
24#13063307—21no—
25#13063306—21no—
26#13063304—21no—
27#13063304C2211yescharacteristic
28#13063302—21no—
29#13063296—21no—
30#13063296C2211yescharacteristic
31#13063296C2211yescharacteristic
32Q8×Dic43C2211yescharacteristic
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43—21no—
35C4×C22⋊D43C2211yescharacteristic
36C2×C4⋊Dic43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×D8×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43—21no—
64C2×D4×C43C2311yescharacteristic
65C2×D4×C43C2311yescharacteristic
66C22×C4×C43—21no—
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43D411yescharacteristic
71C22×Dic43—21no—
72C22×Dic43—21no—
73Q8×D43—22no—
74Q8×D43—41no—
75#10621900—44no—
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—21no—
80C2×Dic86—21no—
81C2×Dic86C2311yescharacteristic
82SD16×C43—22no—
83D8×C43—41no—
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43—21no—
93C22⋊Dic43—21no—
94C22⋊Dic43D411yescharacteristic
95#10621883—41no—
96(C2×D43)⋊C4D411yescharacteristic
97C4⋊Dic43—21no—
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101C4⋊Dic43C2311yescharacteristic
102Dic43⋊C4—21no—
103Dic43⋊C4—21no—
104Dic43⋊C4—21no—
105Dic43⋊C4D411yescharacteristic
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108#10621877—41no—
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111C8×D43—41no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43C2×D411yescharacteristic
115C22×D43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43#4112yescomplemented
118D4×C43—21no—
119D4×C43—21no—
120D4×C43—21no—
121D4×C43—21no—
122D4×C43—42no—
123D4×C43—42no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—42no—
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2411yescharacteristic
131C22⋊D43—22no—
132C22⋊D43—42no—
133C22⋊D43—42no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—42no—
146C4×D43—42no—
147Dic86—21no—
148Dic86—21no—
149Dic86—42no—
150Dic86—42no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—21no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43—41no—
162C22×C43—41no—
163C22×C43—41no—
164C22×C43C22×D411yescharacteristic
165C2×D43—21no—
166C2×D43—21no—
167C2×D43AGL(1,ℤ/8)12yes—
168C4×C43—22no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3308—431nomaximal, Sylow
181C2×C43—41no—
182C2×C43—81no—
183C2×C43—81no—
184C2×C43#54611yescharacteristic
185C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
186C2×C43#57811yescharacteristic
187D43—22no—
188#548—431no—
189#547—431no—
190#489—431no—
191#484—431no—
192#480—431no—
193#477—431no—
194#468—431no—
195#466—431no—
196#463—431no—
197#449D4311yescharacteristic, complemented
198#448—431no—
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#103—431no—
203C43#330811yescharacteristic, complemented, Sylow
204C2×#41—861no—
205C2×#41C2×D4311yescharacteristic
206C22×Q8—431no—
207C2×SD16—431no—
208C2×SD16C2×D4311yescharacteristic
209C2×D8C2×D4311yescharacteristic
210C2×M16—431no—
211C22×C8—431no—
212C4⋊Q8—431no—
213#124—431no—
214#124—861no—
215#123—861no—
216#123—861no—
217C22⋊Q8—431no—
218C22⋊Q8—861no—
219C22⋊Q8—861no—
220#121—431no—
221#121—431no—
222#121—861no—
223#121C2×D4311yescharacteristic
224C4×Q8—431no—
225C4×D4—431no—
226C4×D4—431no—
227C4×D4—861no—
228C2×C4⋊C4—431no—
229C2×C4⋊C4—431no—
230#107—431no—
231#107—431no—
232#107—431no—
233C4⋊C8—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#103—431no—
238#103—431no—
239#103C2×D4311yescharacteristic
240#102—431no—
241#102—431no—
242#102—431no—
243#102C2×D4311yescharacteristic
244C22⋊C8—431no—
245C22⋊C8C2×D4311yescharacteristic
246#97—431no—
247#41—22no—
248#41—41no—
249#41—1724no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8—861no—
253C2×Q8—862no—
254C2×Q8—1721no—
255C2×Q8C22×D4311yescharacteristic
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4C22×D4311yescharacteristic
262C2×D4C22×D4311yescharacteristic
263C22×C4—21no—
264C22×C4—431no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4—861no—
268C22×C4—861no—
269C22×C4C22×D4311yescharacteristic
270SD16—22no—
271SD16—1721no—
272D8—41no—
273M16—1721no—
274C2×C8—431no—
275C2×C8—431no—
276C2×C8—1721no—
277C2×C8C22×D4311yescharacteristic
278C2×C8C22×D4311yescharacteristic
279C4⋊C4—431no—
280C4⋊C4—431no—
281C4⋊C4—431no—
282C4⋊C4—431no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4—861no—
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C22⋊C4—861no—
296C22⋊C4—861no—
297C22⋊C4—861no—
298C42—431no—
299C42—861no—
300C23—21no—
301C23—21no—
302C23—431no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—861no—
306Q8—861no—
307Q8—1722no—
308Q8—1722no—
309Q8#1062190012yescomplemented
310D4—21no—
311D4—21no—
312D4—21no—
313D4—21no—
314D4—42no—
315D4—42no—
316D4—862no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—431no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—861no—
328C2×C4—861no—
329C2×C4—861no—
330C2×C4—861no—
331C2×C4—861no—
332C2×C4—861no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4—1722no—
336C2×C4—1722no—
337C2×C4D4×D4311yescharacteristic
338C2×C4C23×D4311yescharacteristic
339C8—21no—
340C8—21no—
341C8—861no—
342C8—861no—
343C22—21no—
344C22—21no—
345C22—21no—
346C22—41no—
347C22—41no—
348C22—41no—
349C22—41no—
350C22—41no—
351C22—41no—
352C22—432no—
353C22—861no—
354C22—861no—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—861no—
360C4—861no—
361C4—861no—
362C4—1721no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4C2×#1062190011yescharacteristic
367C4#1306337011yescharacteristic
368C2—41no—
369C2—81no—
370C2—81no—
371C2—862no—
372C2#1458353611yescharacteristic
373C2AGL(1,ℤ/8)×D4311yescharacteristic
374C2#1458371311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#449C2
socleC22×C43C22×D4
hypercenter#449D43
hypocenterC43#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #449

Complements

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

NH ≅ G/Ntype
1. #14583556C2semidirect
2. #14583549C2semidirect
3. #14583257C2semidirect
4. #14583235C2semidirect
5. #14583211C2semidirect
6. #14583192C2semidirect
7. #14583143C2semidirect
8. #14583132C2semidirect
9. #14583112C2semidirect
10. #14583036C2semidirect
11. #14583000C2semidirect
12. #14582973C2semidirect
13. #14582900C2semidirect
14. #103×D43C2semidirect
15. C43×#449C2semidirect
117. Q8×C43#41semidirect
197. #449D43semidirect
203. C43#3308semidirect
309. Q8#10621900semidirect