Finite Group Databasebeta

← #19146590

Subgroups — #19146590

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#14583560C211yesmaximal, characteristic, complemented
2#14583549C211yesmaximal, characteristic, complemented
3#14583260C211yesmaximal, characteristic, complemented
4#14583233C211yesmaximal, characteristic, complemented
5#14583213C211yesmaximal, characteristic, complemented
6#14583192C211yesmaximal, characteristic, complemented
7#14583142C211yesmaximal, characteristic, complemented
8#14583133C211yesmaximal, characteristic, complemented
9#14583116C211yesmaximal, characteristic, complemented
10#14583043C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12#14582967C211yesmaximal, characteristic, complemented
13#14582899C211yesmaximal, characteristic, complemented
14C2×#13063249C211yesmaximal, characteristic, complemented
15C43×#448C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621900—21no—
18C2×#10621882C2211yescharacteristic
19C2×#10621872C2211yescharacteristic
20C22×C43⋊C8C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063314—21no—
23#13063314C2211yescharacteristic
24#13063307—21no—
25#13063306—21no—
26#13063302—21no—
27#13063301—21no—
28#13063301C2211yescharacteristic
29#13063299—21no—
30#13063299C2211yescharacteristic
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#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C22×Q8×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54C2×SD16×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#103×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×Q8×C43—21no—
60C2×Q8×C43—22no—
61C2×Q8×C43—41no—
62C2×Q8×C43C2311yescharacteristic
63C2×Q8×C43C2311yescharacteristic
64C2×D4×C43—21no—
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—
73#10621902—22no—
74#10621902—41no—
75#10621900—44no—
76C2×D172—21no—
77C2×D172C2311yescharacteristic
78C2×C4×D43—21no—
79C2×C4×D43—21no—
80C2×C4×D43C2311yescharacteristic
81C2×Dic86—21no—
82SD16×C43—22no—
83SD16×C43—41no—
84C2×C8×C43C2311yescharacteristic
85C2×C8×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43D411yescharacteristic
91#10621882—41no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95(C2×D43)⋊C4—21no—
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
108C2×C43⋊C8—41no—
109C2×C43⋊C8C2311yescharacteristic
110C2×C43⋊C8C2311yescharacteristic
111#10621872—41no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43—21no—
115C22×D43C2×D411yescharacteristic
116Q8×C43—21no—
117Q8×C43—21no—
118Q8×C43—21no—
119Q8×C43—42no—
120Q8×C43#4112yescomplemented
121D4×C43—21no—
122D4×C43—21no—
123D4×C43—42no—
124C2×C4×C43—21no—
125C2×C4×C43—21no—
126C2×C4×C43—21no—
127C2×C4×C43—21no—
128C2×C4×C43—21no—
129C2×C4×C43—42no—
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2411yescharacteristic
132C22⋊D43—22no—
133C22⋊D43—42no—
134C22⋊D43—42no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43—21no—
138C2×Dic43—42no—
139C2×Dic43—42no—
140C2×Dic43C2×D411yescharacteristic
141C2×Dic43C2×D411yescharacteristic
142C2×Dic43C2×D411yescharacteristic
143D172—21no—
144D172—21no—
145D172—42no—
146C4×D43—21no—
147C4×D43—21no—
148C4×D43—42no—
149C4×D43—42no—
150Dic86—42no—
151C8×C43—21no—
152C8×C43—21no—
153C43⋊C8—21no—
154C43⋊C8—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43AGL(1,ℤ/8)12yes—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C2×D43—41no—
166C2×D43—41no—
167C2×D43—41no—
168C4×C43—22no—
169C4×C43—21no—
170C4×C43—41no—
171C4×C43—41no—
172C4×C43C2×#4111yescharacteristic
173C4×C43H(5,𝔽2)11yescharacteristic
174Dic43—21no—
175Dic43—21no—
176Dic43—21no—
177Dic43—41no—
178Dic43—41no—
179Dic43—41no—
180#3308—431nomaximal, Sylow
181C2×C43—22no—
182C2×C43—81no—
183C2×C43#54611yescharacteristic
184C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
185C2×C43#57811yescharacteristic
186D43—41no—
187D43—81no—
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#449—431no—
198#448D4311yescharacteristic, complemented
199#440—431no—
200#435—431no—
201#417—431no—
202C2×#103—431no—
203C43#330811yescharacteristic, complemented, Sylow
204C2×#41—431no—
205C2×#41—861no—
206C22×Q8C2×D4311yescharacteristic
207C2×SD16C2×D4311yescharacteristic
208C2×SD16C2×D4311yescharacteristic
209C2×D8—431no—
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#103C2×D4311yescharacteristic
239#103C2×D4311yescharacteristic
240#102—431no—
241#102—431no—
242#102—431no—
243#102—431no—
244C22⋊C8—431no—
245C22⋊C8C2×D4311yescharacteristic
246#97—431no—
247#41—862no—
248#41—1721no—
249#41—1724no—
250C2×Q8—21no—
251C2×Q8—22no—
252C2×Q8—41no—
253C2×Q8—861no—
254C2×Q8C22×D4311yescharacteristic
255C2×Q8C22×D4311yescharacteristic
256C2×D4—21no—
257C2×D4—431no—
258C2×D4—431no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
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—41no—
272D8—1721no—
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—431no—
302C23—861no—
303C23D4×D4311yescharacteristic
304Q8—21no—
305Q8—21no—
306Q8—21no—
307Q8—42no—
308Q8—1722no—
309Q8#1062190012yescomplemented
310D4—21no—
311D4—21no—
312D4—42no—
313D4—862no—
314D4—861no—
315D4—861no—
316D4—1722no—
317D4—1722no—
318D4—1722no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—21no—
324C2×C4—42no—
325C2×C4—431no—
326C2×C4—431no—
327C2×C4—431no—
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—41no—
346C22—41no—
347C22—41no—
348C22—861no—
349C22—861no—
350C22—861no—
351C22—1721no—
352C22—1721no—
353C22—1721no—
354C22#1306335212yes—
355C22C2×D4×D4311yescharacteristic
356C4—21no—
357C4—22no—
358C4—41no—
359C4—41no—
360C4—861no—
361C4—861no—
362C4—861no—
363C4—1721no—
364C4—1721no—
365C4—1721no—
366C4C2×#1062190011yescharacteristic
367C4#1306337011yescharacteristic
368C2—22no—
369C2—81no—
370C2—3441no—
371C2—1721no—
372C2#1458353611yescharacteristic
373C2C2×#1306335211yescharacteristic
374C2#1458371511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#448C2
socleC22×C43C22×D4
hypercenter#448D43
hypocenterC43#3308
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
1. #14583560C2semidirect
2. #14583549C2semidirect
3. #14583260C2semidirect
4. #14583233C2semidirect
5. #14583213C2semidirect
6. #14583192C2semidirect
7. #14583142C2semidirect
8. #14583133C2semidirect
9. #14583116C2semidirect
10. #14583043C2semidirect
11. #14583000C2semidirect
12. #14582967C2semidirect
13. #14582899C2semidirect
14. C2×#13063249C2semidirect
15. C43×#448C2semidirect
120. Q8×C43#41semidirect
198. #448D43semidirect
203. C43#3308semidirect
309. Q8#10621900semidirect