Finite Group Databasebeta

← #19146707

Subgroups — #19146707

Order 5504.

388 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#14583604C211yesmaximal, characteristic, complemented
2#14583556C211yesmaximal, characteristic
3#14583257C211yesmaximal, characteristic, complemented
4#14583229C211yesmaximal, characteristic, complemented
5#14583216C211yesmaximal, characteristic, complemented
6#14583182C211yesmaximal, characteristic, complemented
7#14583157C211yesmaximal, characteristic, complemented
8#14583127C211yesmaximal, characteristic, complemented
9#14583120C211yesmaximal, characteristic, complemented
10#14583061C211yesmaximal, characteristic, complemented
11#14583056C211yesmaximal, characteristic, complemented
12#14583003C211yesmaximal, characteristic, complemented
13#14582968C211yesmaximal, characteristic, complemented
14#103×D43C211yesmaximal, characteristic, complemented
15C43×#417C211yesmaximal, characteristic, complemented
16C2×Q8×D43C2211yescharacteristic
17C2×Dic172C2211yescharacteristic
18C2×#10621885C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063315—21no—
23#13063312—21no—
24#13063312C2211yescharacteristic
25#13063305C2211yescharacteristic
26#13063304—21no—
27#13063304—21no—
28#13063304C2211yescharacteristic
29#13063304C2211yescharacteristic
30#13063303—21no—
31#13063296—21no—
32#13063296C2211yescharacteristic
33Q8×Dic43C2211yescharacteristic
34#13063290C2211yescharacteristic
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063249C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×#41×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54C2×C4⋊C4×C43C2211yescharacteristic
55#103×C43C2211yescharacteristic
56#103×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59#41×C43—22no—
60#41×C43—41no—
61C2×Q8×C43C2311yescharacteristic
62C2×D4×C43—21no—
63C2×D4×C43C2311yescharacteristic
64C22×C4×C43—21no—
65C22×C4×C43—21no—
66C22×C4×C43C2311yescharacteristic
67C2×C22⋊D43—21no—
68C2×C22⋊D43D411yescharacteristic
69Q8×D43—22no—
70Q8×D43—41no—
71C2×C4×D43—21no—
72C2×C4×D43—21no—
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86C2311yescharacteristic
77C2×Dic86C2311yescharacteristic
78M16×C43—41no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621885—22no—
91#10621883—41no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109Dic172—41no—
110C8×D43—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43C2×D411yescharacteristic
114Q8×C43—21no—
115Q8×C43#4112yes—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—42no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—42no—
125C2×C4×C43—81no—
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2411yescharacteristic
128C22⋊D43—22no—
129C22⋊D43—42no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43C2×D411yescharacteristic
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—42no—
140C4×D43—81no—
141Dic86—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—42no—
146Dic86—81no—
147C8×C43—21no—
148C8×C43—21no—
149C43⋊C8—21no—
150C43⋊C8—21no—
151C22×C43—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—41no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43C22×D411yescharacteristic
158C2×D43—21no—
159C2×D43—21no—
160C2×D43#13712yes—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—41no—
164C4×C43—41no—
165C4×C43C2×#4111yescharacteristic
166C4×C43H(5,𝔽2)11yescharacteristic
167Dic43—21no—
168Dic43—21no—
169Dic43—21no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3316—431nomaximal, Sylow
175C2×C43—41no—
176C2×C43—81no—
177C2×C43#54611yescharacteristic
178C2×C43C2×#13711yescharacteristic
179C2×C43#57711yescharacteristic
180D43—22no—
181#554—431no—
182#548—431no—
183#489—431no—
184#483—431no—
185#481—431no—
186#475—431no—
187#470—431no—
188#465—431no—
189#464—431no—
190#452—431no—
191#451—431no—
192#441—431no—
193#435—431no—
194#417D4311yescharacteristic, complemented
195C2×#103—431no—
196C43#331611yescharacteristic, complemented, Sylow
197C2×#41C2×D4311yescharacteristic
198C22×Q8—431no—
199C2×Q16—431no—
200C2×Q16—431no—
201C2×SD16—431no—
202C2×M16C2×D4311yescharacteristic
203C22×C8—431no—
204C4⋊Q8—431no—
205#125—861no—
206#124—431no—
207#124—861no—
208C22⋊Q8—431no—
209C22⋊Q8—431no—
210C22⋊Q8—431no—
211C22⋊Q8—861no—
212C22⋊Q8—861no—
213C22⋊Q8—861no—
214#121—431no—
215#121—861no—
216C4×Q8—431no—
217C4×Q8—431no—
218C4×D4—431no—
219C4×D4—861no—
220C4×D4—861no—
221C2×C4⋊C4—431no—
222C2×C4⋊C4C2×D4311yescharacteristic
223#106—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227#103—431no—
228#103—431no—
229#103—431no—
230#103—431no—
231#103—431no—
232#103C2×D4311yescharacteristic
233#103C2×D4311yescharacteristic
234#102—431no—
235#102C2×D4311yescharacteristic
236#102C2×D4311yescharacteristic
237C22⋊C8—431no—
238C22⋊C8—431no—
239#97—431no—
240#41—22no—
241#41—41no—
242C2×Q8—431no—
243C2×Q8—431no—
244C2×Q8—861no—
245C2×Q8—861no—
246C2×Q8—862no—
247C2×Q8—1721no—
248C2×Q8C22×D4311yescharacteristic
249C2×D4—21no—
250C2×D4—431no—
251C2×D4—861no—
252C2×D4C22×D4311yescharacteristic
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—431no—
256C22×C4—861no—
257C22×C4—861no—
258C22×C4C22×D4311yescharacteristic
259Q16—862no—
260Q16—1721no—
261SD16—1721no—
262M16—41no—
263C2×C8—431no—
264C2×C8—431no—
265C2×C8—1721no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—431no—
282C22⋊C4—431no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C42—431no—
290C42—861no—
291C42—861no—
292C23—21no—
293C23—431no—
294C23D4×D4311yescharacteristic
295Q8—21no—
296Q8—861no—
297Q8—861no—
298Q8—861no—
299Q8—861no—
300Q8—3441no—
301Q8—1722no—
302Q8#1062189812yes—
303D4—21no—
304D4—21no—
305D4—42no—
306D4—862no—
307D4—1722no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—42no—
314C2×C4—81no—
315C2×C4—431no—
316C2×C4—431no—
317C2×C4—431no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—3441no—
325C2×C4—1722no—
326C2×C4D4×D4311yescharacteristic
327C2×C4C23×D4311yescharacteristic
328C8—21no—
329C8—21no—
330C8—861no—
331C8—861no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—432no—
339C22—861no—
340C22—861no—
341C22C2×D4×D4311yescharacteristic
342C4—21no—
343C4—22no—
344C4—41no—
345C4—41no—
346C4—861no—
347C4—861no—
348C4—861no—
349C4—1721no—
350C4—1721no—
351C4—1721no—
352C4—1721no—
353C4C2×#1062189811yescharacteristic
354C4#1306337011yescharacteristic
355C2—41no—
356C2—81no—
357C2—862no—
358C2#1458353911yescharacteristic
359C2#137×D4311yescharacteristic
360C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#417C2
socleC22×C43C22×D4
hypercenter#417D43
hypocenterC43#3316
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
1. #14583604C2semidirect
3. #14583257C2semidirect
4. #14583229C2semidirect
5. #14583216C2semidirect
6. #14583182C2semidirect
7. #14583157C2semidirect
8. #14583127C2semidirect
9. #14583120C2semidirect
10. #14583061C2semidirect
11. #14583056C2semidirect
12. #14583003C2semidirect
13. #14582968C2semidirect
14. #103×D43C2semidirect
15. C43×#417C2semidirect
194. #417D43semidirect
196. C43#3316semidirect