Finite Group Databasebeta

← #19146931

Subgroups — #19146931

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583604C211yesmaximal, characteristic, complemented
2#14583567C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583214C211yesmaximal, characteristic, complemented
5#14583193C211yesmaximal, characteristic, complemented
6#14583146C211yesmaximal, characteristic, complemented
7#14583143C211yesmaximal, characteristic, complemented
8#14583098C211yesmaximal, characteristic, complemented
9#14583063C211yesmaximal, characteristic, complemented
10#14583062C211yesmaximal, characteristic, complemented
11#14582993C211yesmaximal, characteristic, complemented
12#14582974C211yesmaximal, characteristic, complemented
13#14582898C211yesmaximal, characteristic, complemented
14#14582897C211yesmaximal, characteristic, complemented
15C43×#480C211yesmaximal, characteristic, complemented
16C2×#10621898C2211yescharacteristic
17C2×#10621900C2211yescharacteristic
18C2×Dic172C2211yescharacteristic
19C2×#10621873C2211yescharacteristic
20C2×#10621883C2211yescharacteristic
21C2×#10621877C2211yescharacteristic
22C2×#10621872C2211yescharacteristic
23#13063324C2211yescharacteristic
24#13063321—21no—
25#13063321C2211yescharacteristic
26#13063315—21no—
27#13063305C2211yescharacteristic
28#13063304—21no—
29#13063304C2211yescharacteristic
30#13063303—21no—
31#13063300C2211yescharacteristic
32#13063298—21no—
33#13063297—21no—
34#13063290C2211yescharacteristic
35#13063290C2211yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43C2211yescharacteristic
38(C22⋊D43)⋊C4—21no—
39C4⋊C4×D43C2211yescharacteristic
40#13063258C2211yescharacteristic
41Dic43⋊C8C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063248C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#121×C43C2211yescharacteristic
53C2×C4⋊C4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43C2311yescharacteristic
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67C2×C22⋊D43D411yescharacteristic
68C22×Dic43—21no—
69#10621900—22no—
70#10621900—41no—
71#10621898—22no—
72#10621898—41no—
73C2×D172—21no—
74C2×D172C2311yescharacteristic
75C2×C4×D43—21no—
76C2×C4×D43—21no—
77C2×C4×D43C2311yescharacteristic
78C2×Dic86—21no—
79C2×Dic86C2311yescharacteristic
80C2×Dic86C2311yescharacteristic
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43—21no—
84C4⋊C4×C43C2311yescharacteristic
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊C4×C43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621883—41no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4D411yescharacteristic
102C4×Dic43—21no—
103C4×Dic43—21no—
104C4×Dic43C2311yescharacteristic
105#10621877—41no—
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108Dic172—22no—
109#10621873—41no—
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—81no—
118C2×C4×C43—21no—
119C2×C4×C43—21no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—81no—
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2411yescharacteristic
126C22⋊D43—22no—
127C22⋊D43—42no—
128C22⋊D43—42no—
129C22⋊D43—42no—
130C22⋊D43—81no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43C2×D411yescharacteristic
136C2×Dic43C2×D411yescharacteristic
137C2×Dic43C2×D411yescharacteristic
138D172—21no—
139D172—21no—
140D172—81no—
141C4×D43—21no—
142C4×D43—21no—
143C4×D43—42no—
144C4×D43—81no—
145Dic86—21no—
146Dic86—21no—
147Dic86—21no—
148Dic86—81no—
149Dic86#4112yes—
150C8×C43—21no—
151C8×C43—21no—
152C43⋊C8—21no—
153C43⋊C8—21no—
154C22×C43—21no—
155C22×C43—21no—
156C22×C43—21no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43C22×D411yescharacteristic
161C2×D43—21no—
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—41no—
165C2×D43—41no—
166C2×D43—41no—
167C4×C43—21no—
168C4×C43—41no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—22no—
174Dic43—21no—
175Dic43—21no—
176Dic43—41no—
177Dic43—41no—
178Dic43#13712yes—
179#3333—431nomaximal, Sylow
180C2×C43—41no—
181C2×C43—81no—
182C2×C43#54611yescharacteristic
183C2×C43C2×#13711yescharacteristic
184C2×C43#57611yescharacteristic
185D43—41no—
186D43—81no—
187#554—431no—
188#550—431no—
189#486—431no—
190#480—431no—
191#480D4311yescharacteristic, complemented
192#477—431no—
193#468—431no—
194#468—431no—
195#460—431no—
196#452—431no—
197#452—431no—
198C4×Q16—431no—
199#436—431no—
200#417—431no—
201#417—431no—
202C43#333311yescharacteristic, complemented, Sylow
203C2×#41—431no—
204C2×#41—431no—
205C2×Q16—431no—
206C2×SD16—431no—
207C2×SD16—431no—
208C2×M16—431no—
209C2×M16—431no—
210C4⋊Q8—431no—
211#127—431no—
212#127—861no—
213#125—861no—
214C22⋊Q8—431no—
215C22⋊Q8—431no—
216C22⋊Q8—861no—
217C22⋊Q8—861no—
218#121—431no—
219#121—861no—
220#121—861no—
221#121C2×D4311yescharacteristic
222C4×Q8—431no—
223C4×Q8—431no—
224C4×D4—431no—
225C4×D4—861no—
226C4×D4—861no—
227C2×C4⋊C4—431no—
228C2×C4⋊C4C2×D4311yescharacteristic
229#107—431no—
230#107C2×D4311yescharacteristic
231#107C2×D4311yescharacteristic
232C4⋊C8—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242#102C2×D4311yescharacteristic
243C22⋊C8—431no—
244C22⋊C8C2×D4311yescharacteristic
245C4×C8—431no—
246#41—862no—
247#41—862no—
248#41—1721no—
249#41—1721no—
250C2×Q8—431no—
251C2×Q8—431no—
252C2×Q8—861no—
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—431no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4C22×D4311yescharacteristic
262C22×C4—21no—
263C22×C4—431no—
264C22×C4—861no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C22×D4311yescharacteristic
268Q16—862no—
269SD16—1721no—
270SD16—1721no—
271M16—1721no—
272M16—1721no—
273C2×C8—431no—
274C2×C8—431no—
275C2×C8C22×D4311yescharacteristic
276C2×C8C22×D4311yescharacteristic
277C4⋊C4—21no—
278C4⋊C4—431no—
279C4⋊C4—431no—
280C4⋊C4—861no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4C22×D4311yescharacteristic
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—21no—
290C22⋊C4—431no—
291C22⋊C4—431no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C42—431no—
296C42—861no—
297C42—861no—
298C23—21no—
299C23—431no—
300C23—861no—
301C23D4×D4311yescharacteristic
302Q8—432no—
303Q8—861no—
304Q8—861no—
305Q8—861no—
306Q8—3441no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—862no—
311D4—861no—
312D4—861no—
313D4—3441no—
314D4—3441no—
315D4—1722no—
316D4—1722no—
317D4—1722no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—81no—
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—3441no—
333C2×C4—1722no—
334C2×C4—1722no—
335C2×C4D4×D4311yescharacteristic
336C2×C4C23×D4311yescharacteristic
337C8—21no—
338C8—21no—
339C8—861no—
340C8—861no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—861no—
348C22—861no—
349C22—861no—
350C22—1721no—
351C22—1721no—
352C22—1721no—
353C22C2×D4×D4311yescharacteristic
354C4—21no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—432no—
359C4—861no—
360C4—861no—
361C4—862no—
362C4—1721no—
363C4—1721no—
364C4#41×D4311yescharacteristic
365C4#1306337111yescharacteristic
366C2—41no—
367C2—81no—
368C2—3441no—
369C2—1721no—
370C2#1458354111yescharacteristic
371C2#137×D4311yescharacteristic
372C2#1458370011yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#480C2
socleC22×C43C22×D4
hypercenter#480D43
hypocenterC43#3333
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #480

Complements

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

NH ≅ G/Ntype
1. #14583604C2semidirect
3. #14583244C2semidirect
4. #14583214C2semidirect
5. #14583193C2semidirect
6. #14583146C2semidirect
7. #14583143C2semidirect
8. #14583098C2semidirect
9. #14583063C2semidirect
10. #14583062C2semidirect
11. #14582993C2semidirect
12. #14582974C2semidirect
13. #14582898C2semidirect
14. #14582897C2semidirect
15. C43×#480C2semidirect
191. #480D43semidirect
202. C43#3333semidirect