Finite Group Databasebeta

← #19146929

Subgroups — #19146929

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#14583568C211yesmaximal, characteristic
3#14583244C211yesmaximal, characteristic, complemented
4#14583212C211yesmaximal, characteristic, complemented
5#14583211C211yesmaximal, characteristic, complemented
6#14583192C211yesmaximal, characteristic, complemented
7#14583145C211yesmaximal, characteristic, complemented
8#14583144C211yesmaximal, characteristic, complemented
9#14583098C211yesmaximal, characteristic, complemented
10#14583064C211yesmaximal, characteristic, complemented
11#14583061C211yesmaximal, characteristic, complemented
12#14582991C211yesmaximal, characteristic, complemented
13#14582975C211yesmaximal, characteristic, complemented
14#14582899C211yesmaximal, characteristic, complemented
15C43×#417C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621885C2211yescharacteristic
18C2×#10621873C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×#10621872C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063321—21no—
23#13063321C2211yescharacteristic
24#13063315—21no—
25#13063305C2211yescharacteristic
26#13063304—21no—
27#13063304C2211yescharacteristic
28#13063303—21no—
29#13063299—21no—
30#13063299C2211yescharacteristic
31#13063296—21no—
32#13063296C2211yescharacteristic
33Q8×Dic43C2211yescharacteristic
34#13063290C2211yescharacteristic
35C4×C22⋊D43—21no—
36C4×C22⋊D43—21no—
37C4×C22⋊D43C2211yescharacteristic
38C4⋊C4×D43C2211yescharacteristic
39#13063259C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063258C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063249C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
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⋊D43—21no—
69C2×C22⋊D43—21no—
70C2×C22⋊D43—21no—
71C2×C22⋊D43D411yescharacteristic
72#10621902—22no—
73#10621902—41no—
74C2×D172—21no—
75C2×D172C2311yescharacteristic
76C2×C4×D43—21no—
77C2×C4×D43—21no—
78C2×C4×D43C2311yescharacteristic
79C2×Dic86—21no—
80C2×Dic86C2311yescharacteristic
81M16×C43—41no—
82C2×C8×C43C2311yescharacteristic
83C2×C8×C43C2311yescharacteristic
84C4⋊C4×C43—21no—
85C4⋊C4×C43C2311yescharacteristic
86C4⋊C4×C43C2311yescharacteristic
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43D411yescharacteristic
90#10621885—22no—
91#10621883—41no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43—21no—
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
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
109#10621873—41no—
110#10621872—41no—
111C23×C43—21no—
112C23×C43C2×D411yescharacteristic
113C22×D43—21no—
114C22×D43C2×D411yescharacteristic
115Q8×C43—21no—
116Q8×C43#4112yes—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—42no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43—42no—
126C2×C4×C43—81no—
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—22no—
130C22⋊D43—42no—
131C22⋊D43—81no—
132C22⋊D43—81no—
133C22⋊D43—81no—
134C2×Dic43—21no—
135C2×Dic43—21no—
136C2×Dic43—21no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140D172—21no—
141D172—21no—
142D172—42no—
143C4×D43—21no—
144C4×D43—21no—
145C4×D43—42no—
146C4×D43—81no—
147Dic86—21no—
148Dic86—21no—
149Dic86—81no—
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—22no—
168C4×C43—21no—
169C4×C43—41no—
170C4×C43—41no—
171C4×C43C2×#4111yescharacteristic
172C4×C43H(5,𝔽2)11yescharacteristic
173Dic43—21no—
174Dic43—21no—
175Dic43—41no—
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#480—431no—
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#417D4311yescharacteristic, complemented
202C43#333311yescharacteristic, complemented, Sylow
203C2×#41—431no—
204C2×#41C2×D4311yescharacteristic
205C2×Q16—431no—
206C2×SD16—431no—
207C2×SD16—431no—
208C2×M16—431no—
209C2×M16C2×D4311yescharacteristic
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—431no—
220#121—861no—
221#121—861no—
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#107—431no—
231#107—431no—
232C4⋊C8—431no—
233#103—431no—
234#103—431no—
235#103C2×D4311yescharacteristic
236#103C2×D4311yescharacteristic
237#102—431no—
238#102—431no—
239#102—431no—
240#102—431no—
241#102C2×D4311yescharacteristic
242#102C2×D4311yescharacteristic
243C22⋊C8—431no—
244C22⋊C8—431no—
245C4×C8—431no—
246#41—22no—
247#41—41no—
248#41—862no—
249#41—1721no—
250C2×Q8—431no—
251C2×Q8—861no—
252C2×Q8C22×D4311yescharacteristic
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—21no—
264C22×C4—431no—
265C22×C4—861no—
266C22×C4—861no—
267C22×C4C22×D4311yescharacteristic
268Q16—862no—
269SD16—1721no—
270SD16—1721no—
271M16—41no—
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—431no—
281C4⋊C4—861no—
282C4⋊C4—861no—
283C4⋊C4—861no—
284C4⋊C4—861no—
285C4⋊C4—861no—
286C4⋊C4—861no—
287C4⋊C4C22×D4311yescharacteristic
288C4⋊C4C22×D4311yescharacteristic
289C22⋊C4—431no—
290C22⋊C4—431no—
291C22⋊C4—861no—
292C22⋊C4—861no—
293C22⋊C4—861no—
294C22⋊C4—861no—
295C42—431no—
296C42—861no—
297C42—861no—
298C23—21no—
299C23—431no—
300C23—861no—
301C23D4×D4311yescharacteristic
302Q8—21no—
303Q8—861no—
304Q8—861no—
305Q8—3441no—
306Q8#1062189812yes—
307D4—21no—
308D4—21no—
309D4—42no—
310D4—862no—
311D4—861no—
312D4—861no—
313D4—3441no—
314D4—3441no—
315D4—3441no—
316D4—1722no—
317D4—1722no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—21no—
322C2×C4—21no—
323C2×C4—42no—
324C2×C4—81no—
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—3441no—
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—22no—
356C4—41no—
357C4—41no—
358C4—432no—
359C4—861no—
360C4—861no—
361C4—1721no—
362C4—1721no—
363C4—1721no—
364C4C2×#1062189811yescharacteristic
365C4#1306337011yescharacteristic
366C2—41no—
367C2—81no—
368C2—3441no—
369C2—1721no—
370C2#1458353911yescharacteristic
371C2#137×D4311yescharacteristic
372C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#417C2
socleC22×C43C22×D4
hypercenter#417D43
hypocenterC43#3333
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. #14583244C2semidirect
4. #14583212C2semidirect
5. #14583211C2semidirect
6. #14583192C2semidirect
7. #14583145C2semidirect
8. #14583144C2semidirect
9. #14583098C2semidirect
10. #14583064C2semidirect
11. #14583061C2semidirect
12. #14582991C2semidirect
13. #14582975C2semidirect
14. #14582899C2semidirect
15. C43×#417C2semidirect
201. #417D43semidirect
202. C43#3333semidirect